单价的函数的一个特殊类Hele-Shaw流问题</gydF4y2Batitle> <link rel="preload stylesheet" as="style" type="text/css" href="https://cdn.bibblio.org/rcm/4.28.0/bib-related-content.min.css"> <link rel="preload" href="https://static.hindawi.com/new/next_assets/2023-08-03-0017a694320dbe69a559e8120be98c/_next/static/css/b2661f2cd4bd618b.css" as="style"> <link rel="stylesheet" href="https://static.hindawi.com/new/next_assets/2023-08-03-0017a694320dbe69a559e8120be98c/_next/static/css/b2661f2cd4bd618b.css" data-n-g=""> <style id="__jsx-903e4b2e5d3241e4">div#__next{display:-webkit-box;display:-webkit-flex;display:-moz-box;display:-ms-flexbox;display:flex;min-height:100vh;-webkit-box-orient:vertical;-webkit-box-direction:normal;-webkit-flex-direction:column;-moz-box-orient:vertical;-moz-box-direction:normal;-ms-flex-direction:column;flex-direction:column}</style> </head> <body> <div id="__next"> <section class="ant-layout"> <div> <header class="ant-layout-header"> <div class="header__width-wrapper"> <div class="ant-anchor-wrapper ant-anchor-logo" style="max-height:100vh"> <div class="ant-anchor ant-anchor-fixed"> <div class="ant-anchor-ink"> <span class="ant-anchor-ink-ball"></span> </div> <div class="ant-anchor-link ant-link-logo"> <a class="ant-anchor-link-title" href="//www.newsama.com/" title=""> <div class="ant-image"> <img alt="标志gydF4y2Ba" class="ant-image-img ant-image-logo" src="https://static.hindawi.com/new/next_assets/2023-08-03-0017a694320dbe69a559e8120be98c/public/logo.svg"> </div></a> </div> </div> </div> <div class="TopNavigation_topNavigationWrapper__QzFKB"> <div class="TopNavigation_rightSideMenuItems__0bKf1"> <ul class="ant-menu-overflow ant-menu ant-menu-root ant-menu-horizontal ant-menu-light header-ant-menu-horizontal" role="menu" tabindex="0" data-menu-list="true" data-testid="desktop-menu"> <li class="ant-menu-overflow-item ant-menu-item ant-menu-item-only-child" style="opacity:1;order:0" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/journals/" aria-label="Journals">期刊</一个></span></li> <li class="ant-menu-overflow-item ant-menu-item ant-menu-item-only-child" style="opacity:1;order:1" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/publish-research/" aria-label="Publish with us">雷电竞下载苹果</a></span></li> <li class="ant-menu-overflow-item ant-menu-item ant-menu-item-only-child" style="opacity:1;order:2" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/publishing-partnerships/" aria-label="Publishing partnerships">raybet推荐吗</a></span></li> <li class="ant-menu-overflow-item ant-menu-item ant-menu-item-only-child" style="opacity:1;order:3" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/about/" aria-label="About us">关于我们</一个></span></li> <li class="ant-menu-overflow-item ant-menu-item ant-menu-item-only-child" style="opacity:1;order:4" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/blog/" aria-label="Blog">博客</一个></span></li> <li class="ant-menu-overflow-item ant-menu-overflow-item-rest ant-menu-submenu ant-menu-submenu-horizontal" style="opacity:0;height:0;overflow-y:hidden;order:9007199254740991;pointer-events:none;position:absolute" aria-hidden="true" role="none"> <div role="menuitem" class="ant-menu-submenu-title" tabindex="-1" aria-expanded="false" aria-haspopup="true"> <span role="img" aria-label="ellipsis" class="anticon anticon-ellipsis"> <svg viewbox="64 64 896 896" focusable="false" data-icon="ellipsis" width="1em" height="1em" fill="currentColor" aria-hidden="true"> <path d="M176 511a56 56 0 10112 0 56 56 0 10-112 0zm280 0a56 56 0 10112 0 56 56 0 10-112 0zm280 0a56 56 0 10112 0 56 56 0 10-112 0z"></path> </svg></span> <i class="ant-menu-submenu-arrow"></i> </div></li> </ul> <div style="display:none" aria-hidden="true"></div> <button data-testid="search-button-icon" aria-label="Search" type="button" class="ant-btn ant-btn-default SearchToggleButton_btn__kmpSM"><span role="img" class="anticon SearchToggleButton_icon__nurvY"> <svg width="1em" height="1em" viewbox="0 0 26 26" fill="none"> <path fill-rule="evenodd" clip-rule="evenodd" d="M22.1,23.813l-5.478-5.479a10.282,10.282,0,1,1,1.709-1.709L23.813,22.1a1.209,1.209,0,0,1-1.71,1.71ZM2.416,10.27A7.851,7.851,0,0,0,15.78,15.864l.041-.043.043-.041A7.853,7.853,0,1,0,2.416,10.27Z" fill="currentColor"></path> </svg></span></button> <div></div> <button data-testid="menu-button-icon" aria-label="Menu" type="button" class="ant-btn ant-btn-default MenuToggleButton_btn__Go00X"><span role="img" class="anticon MenuToggleButton_icon__5uVd5"> <svg width="1em" height="1em" viewbox="0 -2 28 28" fill="none"> <path fill-rule="evenodd" clip-rule="evenodd" d="M1.833,25.667a1.834,1.834,0,0,1,0-3.668H25.667a1.834,1.834,0,0,1,0,3.668Zm0-11a1.833,1.833,0,0,1,0-3.666H25.667a1.833,1.833,0,0,1,0,3.666Zm0-11A1.833,1.833,0,1,1,1.833,0H25.667a1.833,1.833,0,0,1,0,3.666Z" fill="currentColor"></path> </svg></span></button> <div></div> </div> </div> </div> </header> </div> <main class="ant-layout-content ArticleLayout_articleLayoutWrapper__oukM3"> <div> <div id="journal-header" class=" JournalNavigation_journalHeader__vGN2X" data-istranslated="false"> <a href="//www.newsama.com/journals/aaa" class="JournalNavigation_journalHeader__titleLink__sZyGb"><h1 id="journal-header-title" data-testid="journal-header-title" class="JournalNavigation_small__sXDLc JournalNavigation_journalHeader__title__fsEHD">抽象和应用分析</h1></一个><div class="JournalNavigation_navigationBarHorizontal__YojZL"> <div id="navigation-bar-horizontal" class="navigation-bar-horizontal"> <button id="Journal overview" type="button" class="ant-btn ant-btn-default ant-dropdown-trigger bordered"><span role="img" class="anticon"> <svg width="1em" height="1em" viewbox="0 0 32 32" fill="none"> <path fill-rule="evenodd" clip-rule="evenodd" d="M17.773 23.453l11.2-11.265a1.918 1.918 0 000-2.641 1.75 1.75 0 00-2.542 0l-9.929 10.101-9.933-10.1a1.75 1.75 0 00-2.542 0 1.919 1.919 0 000 2.64L15.23 23.453c.352.365.811.547 1.271.547.46 0 .92-.182 1.271-.547z" fill="currentColor"></path> </svg></span><span>日报》概述</gydF4y2Baspan></button> <a class="bordered" href="//www.newsama.com/journals/aaa/guidelines">对于作者</一个><一个cl作为s="bordered" href="//www.newsama.com/publish-research/reviewers">对于审查员</一个><一个cl作为s="bordered" href="//www.newsama.com/publish-research/editors">的编辑器</一个><一个cl作为s="bordered" href="//www.newsama.com/journals/aaa/contents/">表的内容</一个><button id="Special Issues" type="button" class="ant-btn ant-btn-default ant-dropdown-trigger"><span role="img" class="anticon"> <svg width="1em" height="1em" viewbox="0 0 32 32" fill="none"> <path fill-rule="evenodd" clip-rule="evenodd" d="M17.773 23.453l11.2-11.265a1.918 1.918 0 000-2.641 1.75 1.75 0 00-2.542 0l-9.929 10.101-9.933-10.1a1.75 1.75 0 00-2.542 0 1.919 1.919 0 000 2.64L15.23 23.453c.352.365.811.547 1.271.547.46 0 .92-.182 1.271-.547z" fill="currentColor"></path> </svg></span><span>特殊的问题</gydF4y2Baspan></button> </div> </div> </div> </div> <nav class="ant-breadcrumb ArticleLayout_breadcrumbs__hsc4o"> <ol> <li><span class="ant-breadcrumb-link"><a href="//www.newsama.com/journals/aaa/" aria-label="Abstract and Applied Analysis">抽象和应用分析</一个></span><span class="ant-breadcrumb-separator">/</gydF4y2Baspan></li> <li><span class="ant-breadcrumb-link"><a href="//www.newsama.com/journals/aaa/contents/year/2011/" aria-label="2011">2011年</一个></span><span class="ant-breadcrumb-separator">/</gydF4y2Baspan></li> <li><span class="ant-breadcrumb-link">文章</gydF4y2Baspan><span class="ant-breadcrumb-separator">/</gydF4y2Baspan></li> </ol> </nav> <div class="ant-row ThreeColumnLayout_wrapper__gPK_l"> <div class="ant-col ThreeColumnLayout_leftColumn__yqNgV"> <div> <div> <div id="article-table-of-contents" data-ismobile="false"> <div class="TableOfContents_tableOfContents__0jAuv"> <div class="TableOfContents_tableOfContents__title__CH9Lz"> 在这一页上</gydF4y2Badiv> <a class="TableOfContents_tableOfContents__item__JJil1" href="#abstract">文摘</一个><一个cl作为s="TableOfContents_tableOfContents__item__JJil1" href="#introduction">介绍</一个><一个cl作为s="TableOfContents_tableOfContents__item__JJil1" href="#acknowledgments">确认</一个><一个cl作为s="TableOfContents_tableOfContents__item__JJil1" href="#references">引用</一个><一个cl作为s="TableOfContents_tableOfContents__item__JJil1" href="#copyright">版权</一个><一个cl作为s="TableOfContents_tableOfContents__item__JJil1" href="#related-articles">相关文章</一个></div> </div> </div> </div> </div> <div class="ant-col ThreeColumnLayout_middleColumn__sbd41"> <div class="ArticleMiddleSection_articleMiddleSection__gAv9z"> <div class="articleHeader"> <strong>研究文章|<gydF4y2Ba!-- -->开放获取</gydF4y2Bastrong> <div class="articleHeader__meta"> <span>体积<gydF4y2Ba!-- -->2011年<gydF4y2Ba!-- -->|</gydF4y2Baspan> <span>文章的ID<gydF4y2Ba!-- -->948236年<gydF4y2Ba!-- -->|</gydF4y2Baspan> <span class="articleHeader__meta_doiLink"><a href="https://doi.org/10.1155/2011/948236" aria-label="Doi-link" target="_blank" rel="noreferrer">https://doi.org/10.1155/2011/948236</一个></span> </div> <div class="simpleShowMore"> <button class="simpleShowMore__button">显示引用</gydF4y2Babutton> </div> <h1 class="articleHeader__title">单价的函数的一个特殊类Hele-Shaw流问题</h1><gydF4y2Badiv class="articleHeader__authors"> <span class="articleHeader__authors_author"><strong>Paula Curt</gydF4y2Bastrong><a href="//www.newsama.com/cdn-cgi/l/email-protection" aria-label="Mail Option"><span role="img" class="anticon"> <svg version="1.0" xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="0 0 1401 1101"> <path fill="#6ba439" d="M132.5 2.1C101.4 6 71.1 20.5 48.3 42.4c-22.7 21.7-37.5 48.3-44.6 80l-2.2 10.1v837l2.2 10.1c6.7 30 19.3 53.9 39.8 75.3 23.3 24.3 56.4 40.9 90 45 12.8 1.6 1122.2 1.6 1135 0 38.9-4.8 75.9-25.6 100-56.4 15-19.3 24.2-39 29.8-63.9l2.2-10.1v-837l-2.2-10.1c-7.1-31.8-21.9-58.3-44.6-80.1-20.2-19.2-43.9-31.7-73.6-38.5l-9.6-2.3L705 1.4c-321.9-.1-568.5.2-572.5.7zm1123.4 99.5c1.7.4 3.1 1 3.1 1.4 0 .5-125.6 87.7-279 194L700.9 490.2 422 297C268.5 190.7 143 103.4 143 103c0-.5 1-1.1 2.3-1.3 3.5-.7 1107.1-.8 1110.6-.1zM401 404c164.4 113.8 299.4 207 300 207 .6 0 135.6-93.2 300.1-207 164.5-113.9 299.3-207 299.5-207 .2 0 .4 170.9.4 379.7 0 417.9.5 386-6.1 398.3-6.2 11.6-19 21.4-31.9 24.4-5.8 1.4-67.4 1.6-562 1.6s-556.2-.2-562-1.6c-12.9-3-25.7-12.8-31.9-24.4-6.6-12.3-6.1 19.6-6.1-398.3 0-208.8.2-379.7.5-379.7S236.6 290.1 401 404z"></path> </svg></span></a><sup>1</gydF4y2Basup></span> <span class="articleHeader__authors_author">和<gydF4y2Ba!-- -->Denisa Fericean<gydF4y2Basup>2</gydF4y2Basup></span> </div> <div class="simpleShowMore"> <button class="simpleShowMore__button">显示更多</gydF4y2Babutton> </div> <div class="articleHeader__academicEditor"> <strong>学术编辑器:</gydF4y2Bastrong> <span>Yoshikazu gb</gydF4y2Baspan> </div> <div class="articleHeader__timeline"> <div class="articleHeader__timeline_item "> <strong>收到了</gydF4y2Bastrong> <span>2010年12月07</gydF4y2Baspan> </div> <div class="articleHeader__timeline_item "> <strong>接受</gydF4y2Bastrong> <span>2011年2月23日</gydF4y2Baspan> </div> <div class="articleHeader__timeline_item articleHeader__timeline_item_sticky"> <strong>发表</gydF4y2Bastrong> <span>2011年4月26日</gydF4y2Baspan> </div> </div> </div> <div class="articleBody"> <div class="xml-content"> <h4 class="header" id="abstract">文摘</h4><gydF4y2Bap>我们学习的时间演化自由边界平面流动的粘性流体在Hele-Shaw细胞注入。理论的应用方法单价的函数,我们证明时间的不变性<gydF4y2Basvg height="10.475" id="M1" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>样式属性(几何属性包括starlikeness和spiral-likeness)两个基本例:内部问题和外部问题。我们研究两个零,零表面张力模型。某些特定的情况下。</gydF4y2Bap> <span class="end-abs"></span> <h4 id="introduction">1。介绍</h4><gydF4y2Bap>自由边界的时间演化的粘性流体平面流在Hele-Shaw细胞注入被许多作者研究。通过使用单价的方法函数理论,他们证明了某些几何性质(如starlikeness和定向凸性)保存在时间<一个href="#B5">1</一个>- - - - - -<一个href="#B15">6</一个>]。在本文中,我们继续研究证明另一个几何性质的时间不变性:<gydF4y2Basvg height="10.475" id="M2" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>相似。</gydF4y2Bap> <p>在论文的第一部分,我们需要审查的主要结果。我们首先给出基本概念的关于有界的情况。</gydF4y2Bap> <p>在这种情况下,我们研究粘性流体的流动在一个平面Hele-Shaw细胞注入通过(持续的力量源泉<gydF4y2Basvg height="12.925" id="M3" style="vertical-align:-1.90608pt;width:12.325px;" version="1.1" viewbox="0 0 12.325 12.925" width="12.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.0625" id="M4" style="vertical-align:-1.90608pt;width:39.537498px;" version="1.1" viewbox="0 0 39.537498 13.0625" width="39.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0625)"> <g transform="translate(72,-61.55)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.228174" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.268562" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>在注射),坐落在原点。假设在初始时刻的域<gydF4y2Basvg height="13.45" id="M5" style="vertical-align:-2.21957pt;width:29.975px;" version="1.1" viewbox="0 0 29.975 13.45" width="29.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.717232" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>被液体是单连通的,有限的分析和光滑的曲线<gydF4y2Basvg height="13.45" id="M6" style="vertical-align:-2.21957pt;width:84.75px;" version="1.1" viewbox="0 0 84.75 13.45" width="84.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.3392611" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.50276" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.754259" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.421478" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.810513" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.112743" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.276241" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.527744" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。通过使用众所周知的黎曼映射定理,域<gydF4y2Basvg height="13.45" id="M7" style="vertical-align:-2.21957pt;width:27.049999px;" version="1.1" viewbox="0 0 27.049999 13.45" width="27.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.379169" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>(被液体<gydF4y2Basvg height="9.125" id="M8" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>)可以被描述为一个单叶函数<gydF4y2Basvg height="13.6125" id="M9" style="vertical-align:-2.34499pt;width:38.974998px;" version="1.1" viewbox="0 0 38.974998 13.6125" width="38.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>单位圆的<gydF4y2Basvg height="13.6125" id="M10" style="vertical-align:-2.29482pt;width:112.3875px;" version="1.1" viewbox="0 0 112.3875 13.6125" width="112.3875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.277946" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.318335" y="0"> {</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.319775" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.484715" y="0"> ∶</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.349583" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.850182" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.539288" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.50322" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="77.54361" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="83.795105" y="0"> }</gydF4y2Batspan> </text> </g> </g> </svg>到<gydF4y2Basvg height="13.45" id="M11" style="vertical-align:-2.21957pt;width:27.049999px;" version="1.1" viewbox="0 0 27.049999 13.45" width="27.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.379169" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>归一化的<gydF4y2Basvg height="13.6125" id="M12" style="vertical-align:-2.34499pt;width:65.625px;" version="1.1" viewbox="0 0 65.625 13.6125" width="65.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.354164" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.555412" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.468851" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.108185" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.148575" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.6375" id="M13" style="vertical-align:-2.34499pt;width:70.150002px;" version="1.1" viewbox="0 0 70.150002 13.6375" width="70.150002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6375)"> <g transform="translate(72,-61.09)"> <text transform="matrix(1,0,0,-1,-71.95,63.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.552532" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.716031" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.967531" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.168779" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.082218" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.72155" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.76194" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。我们表示<gydF4y2Basvg height="13.45" id="M14" style="vertical-align:-2.21957pt;width:78.900002px;" version="1.1" viewbox="0 0 78.900002 13.45" width="78.900002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.3392611" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.50276" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.416199" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.04303" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.08342" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.47245" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.774685" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.938183" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.85162" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。这个函数<gydF4y2Basvg height="14.75" id="M15" style="vertical-align:-3.25793pt;width:94.824997px;" version="1.1" viewbox="0 0 94.824997 14.75" width="94.824997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.244516" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.88385" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.92424" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.08,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-11.21,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>产生一个参数化的<gydF4y2Basvg height="17.75" id="M16" style="vertical-align:-3.25793pt;width:173.02499px;" version="1.1" viewbox="0 0 173.02499 17.75" width="173.02499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.75)"> <g transform="translate(72,-57.8)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.61,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.26,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> {</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.029325" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-31.29,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-26.41,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.68,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-8.88,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.540749" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.555653" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.596043" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.759541" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.01104" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="51.224792" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.476292" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.078117" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="69.241615" y="0"> }</gydF4y2Batspan> </text> </g> </g> </svg>和移动边界的参数化<gydF4y2Basvg height="16.612499" id="M17" style="vertical-align:-2.34499pt;width:187.53751px;" version="1.1" viewbox="0 0 187.53751 16.612499" width="187.53751" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6125)"> <g transform="translate(72,-58.71)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.3392611" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.50276" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.416199" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.04303" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.08342" y="0"> {</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.084858" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.024021" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.187523" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-14.19,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-6.39,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.1271896" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.290689" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.667938" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.682842" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.723232" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.88673" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.138229" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="60.351982" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.603477" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="74.205307" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="78.368805" y="0"> }</gydF4y2Batspan> </text> </g> </g> </svg>。</gydF4y2Bap> <p>满足方程的自由边界首次导出了Galin [<一个href="#B2">7</一个>]和Polubarinova-Kochina [<一个href="#B8">8</一个>,<gydF4y2Ba一个href="#B9">9</一个>]:<gydF4y2Baspan class="equation" id="EEq1.1"> <svg height="31.5875" id="M18" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 31.5875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,31.5875)"> <g transform="translate(72,-46.73)"> <text transform="matrix(1,0,0,-1,107.29,55.7)"> <tspan style="font-size: 12.50px; " x="18.059999" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.889999" y="-2.72"> ̇</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.799999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.315022" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.478523" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.167625" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.381378" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.294819" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 167.83,68.6 44.83,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,167.83,55.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.689105" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,182.96,60.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,188.52,55.7)"> <tspan style="font-size: 12.50px; " x="24.139999" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.189999" y="-7.9099998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.349998" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.377888" y="0"> −</gydF4y2Batspan> </text> <g> <path d="m 243.67,58.82 13.85,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,243.67,46.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.05" y="-8.7600002"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.216139" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.381077" y="-8.7600002"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.408962" y="-8.7600002"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,301.66,60.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,464.75,56.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.540749" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>(在前面的平等我们使用符号:<gydF4y2Basvg height="15.5625" id="M19" style="vertical-align:-2.34499pt;width:71.762497px;" version="1.1" viewbox="0 0 71.762497 15.5625" width="71.762497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.5625)"> <g transform="translate(72,-59.55)"> <text transform="matrix(1,0,0,-1,-71.95,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-63.51,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.56,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.41692" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.356085" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.831919" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.220951" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="16.174999" id="M20" style="vertical-align:-2.34499pt;width:63.950001px;" version="1.1" viewbox="0 0 63.950001 16.174999" width="63.950001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.175)"> <g transform="translate(72,-59.06)"> <text transform="matrix(1,0,0,-1,-64.85,64.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̇</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-7.0999999" y="2.72"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.802856" y="2.72"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.843245" y="2.72"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.232279" y="2.72"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.171444" y="2.72"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.647278" y="2.72"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.036308" y="2.72"> </gydF4y2Batspan> </text> </g> </g> </svg>)。</gydF4y2Bap> <p>经典解决方案的区间<gydF4y2Basvg height="13.45" id="M21" style="vertical-align:-2.21957pt;width:33.450001px;" version="1.1" viewbox="0 0 33.450001 13.45" width="33.450001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.492897" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是一个函数<gydF4y2Basvg height="13.6125" id="M22" style="vertical-align:-2.34499pt;width:38.974998px;" version="1.1" viewbox="0 0 38.974998 13.6125" width="38.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.45" id="M23" style="vertical-align:-2.21957pt;width:57.737499px;" version="1.1" viewbox="0 0 57.737499 13.45" width="57.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.922558" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,这是单价的<gydF4y2Basvg height="15.6875" id="M24" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 15.6875" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.6875)"> <g transform="translate(72,-59.45)"> <g> <path d="m -71.95,70.71 10.19,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="13.9625" id="M25" style="vertical-align:-0.15048pt;width:17.950001px;" version="1.1" viewbox="0 0 17.950001 13.9625" width="17.950001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9625)"> <g transform="translate(72,-60.83)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.56,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>关于<gydF4y2Basvg height="9.125" id="M26" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>在<gydF4y2Basvg height="13.45" id="M27" style="vertical-align:-2.21957pt;width:33.450001px;" version="1.1" viewbox="0 0 33.450001 13.45" width="33.450001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.492897" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。众所周知,,从一个分析和光滑的边界<gydF4y2Basvg height="13.45" id="M28" style="vertical-align:-2.21957pt;width:27.525px;" version="1.1" viewbox="0 0 27.525 13.45" width="27.525" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.3392611" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.50276" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.754259" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>经典解决方案并在本地是独一无二的存在于时间(见[<一个href="#B16">10</一个>];看到如(<一个href="#B4">11</一个>,第1章)。请注意,<gydF4y2Basvg height="10.325" id="M29" style="vertical-align:-0.0pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 10.325" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>被称为<我>充气时间</我>。</gydF4y2Bap> <p>在注入的问题<gydF4y2Basvg height="13.45" id="M30" style="vertical-align:-2.21957pt;width:49.9375px;" version="1.1" viewbox="0 0 49.9375 13.45" width="49.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.391672" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.432062" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.683563" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>的液体变成一个有界单连通和较小的表面张力<gydF4y2Basvg height="13.6125" id="M31" style="vertical-align:-2.34499pt;width:35.262501px;" version="1.1" viewbox="0 0 35.262501 13.6125" width="35.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.8148546" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.855244" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,Polubarinova-Galin方程(<一个href="#B15">6</一个>)的形式:<gydF4y2Baspan class="equation" id="EEq1.2"> <svg height="31.5875" id="M32" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 31.5875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,31.5875)"> <g transform="translate(72,-46.73)"> <text transform="matrix(1,0,0,-1,45.3,55.7)"> <tspan style="font-size: 12.50px; " x="18.059999" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.9" y="-2.72"> ̇</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.799999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.315022" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.478523" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.167625" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.381378" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.294819" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 105.85,68.6 44.82,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,105.85,55.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.6766019" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,120.98,60.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,126.53,55.7)"> <tspan style="font-size: 12.50px; " x="24.139999" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.200001" y="-7.9099998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.066355" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.979794" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.360001" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.387886" y="0"> −</gydF4y2Batspan> </text> <g> <path d="m 181.68,58.82 13.86,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,181.68,46.94)"> <tspan style="font-size: 12.50px; " x="49.650002" y="-3.8399999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.389999" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.83" y="-8.7600002"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.170221" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.521744" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="60.470001" y="-16.01"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.859032" y="-16.01"> </gydF4y2Batspan> </text> <g> <path d="m 242.15,58.82 13.17,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,242.27,46.94)"> <tspan style="font-size: 12.50px; " x="16.33" y="-6.2399998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.18" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,270.01,60.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,277.82,55.7)"> <tspan style="font-size: 12.50px; " x="9.1199999" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.97" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.799999" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.963499" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.502567" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.754066" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.920208" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.085144" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="77.125534" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,360.52,60.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,368.32,55.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="96.43" y="-0.54000002"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="100.5935" y="-0.54000002"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="106.845" y="-0.54000002"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="109.97075" y="-0.54000002"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="116.22225" y="-0.54000002"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<gydF4y2Basvg height="16.612499" id="M33" style="vertical-align:-2.34499pt;width:349.21249px;" version="1.1" viewbox="0 0 349.21249 16.612499" width="349.21249" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6125)"> <g transform="translate(72,-58.71)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7766261" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.940125" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-55.45,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-47.64,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.754021" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.794409" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.957909" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.209408" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.685242" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.185841" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,5.99,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,9.46,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,19.19,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,27,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.278186" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.030287" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.369787" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.996616" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.160114" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="51.187283" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.540005" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.703506" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,99.27,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,107.08,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,115.52,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,121.97,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,131.69,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,139.5,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.278186" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.754021" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,164.7,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,168.17,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,177.9,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,185.71,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.278186" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.45" id="M34" style="vertical-align:-2.21957pt;width:69.75px;" version="1.1" viewbox="0 0 69.75 13.45" width="69.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.014903" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.055292" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.21879" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.470291" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.684044" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.935543" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="51.537365" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>和希尔伯特变换(<一个href="#EEq1.2">1.2</一个>)是由<gydF4y2Basvg height="22" id="M35" style="vertical-align:-4.59964pt;width:308.29999px;" version="1.1" viewbox="0 0 308.29999 22" width="308.29999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22)"> <g transform="translate(72,-54.4)"> <text transform="matrix(1,0,0,-1,-71.95,59.04)"> <tspan style="font-size: 12.50px; " x="54.16" y="0.029999999"> ∫</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.480154" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.643654" y="0"> P</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.495056" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.620808" y="0"> V</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.397675" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.523422" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-12.09,66.03)"> <tspan style="font-size: 8.75px; " x="-1" y="11.46"> 0</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,0.19,59.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,19.46,64.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,26.77,67.54)"> <tspan style="font-size: 6.25px; " x="0" y="0"> ′</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,29.57,59.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.170219" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,67.31,64.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.6362882" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.213584" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="16.208704" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,88.11,67.54)"> <tspan style="font-size: 6.25px; " x="0" y="0"> ′</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,90.42,64.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,93.83,59.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.552772" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,111.95,64.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,118.89,59.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.955507" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.119007" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.658794" y="0"> ]</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.822296" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.985794" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="51.537365" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。</gydF4y2Bap> <p>我们提到以下技术成果:<gydF4y2Basvg height="19.725" id="M36" style="vertical-align:-4.77652pt;width:294.60001px;" version="1.1" viewbox="0 0 294.60001 19.725" width="294.60001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.725)"> <g transform="translate(72,-56.22)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.540029" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.316654" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.792488" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.181522" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.733093" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.896591" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.060093" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-24.31,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.51,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.754021" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.794409" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.446964" y="0"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.610462" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.501297" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="61.664795" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,50.72,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="7.0978718" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,62.91,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,71.03,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,77.44,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,87.17,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,94.97,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.278186" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.917519" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.418119" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,126.84,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,130.31,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,140.04,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,147.85,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.278186" y="0"> |</gydF4y2Batspan> </text> </g> </g> </svg>在哪里<gydF4y2Basvg height="16.512501" id="M37" style="vertical-align:-4.77652pt;width:18.2875px;" version="1.1" viewbox="0 0 18.2875 16.512501" width="18.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5125)"> <g transform="translate(72,-58.79)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-63.82,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>Schwarzian导数由吗<gydF4y2Basvg height="21.887501" id="M38" style="vertical-align:-4.77652pt;width:332.125px;" version="1.1" viewbox="0 0 332.125 21.887501" width="332.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,21.8875)"> <g transform="translate(72,-54.49)"> <text transform="matrix(1,0,0,-1,-71.95,59.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-63.82,56.18)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-57.42,59.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.479433" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.519823" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.683323" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-14.29,64.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-7.84,59.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.130791" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.606625" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,28.22,64.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,31.69,59.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.130791" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,59.99,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,66.25,59.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.491217" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.218552" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.470051" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.633549" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.79705" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,114.5,64.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,120.95,59.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.130791" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.606625" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,157,64.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,160.48,59.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.130791" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,188.78,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Baspan class="equation" id="EEq1.3"> <svg height="48.1875" id="M39" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.1875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.1875)"> <g transform="translate(72,-33.45)"> <text transform="matrix(1,0,0,-1,48.81,56.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 45.54,52.73 12.94,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,45.54,40.85)"> <tspan style="font-size: 12.50px; " x="16.219999" y="-3.8299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.959999" y="-8.75"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.040001" y="-16"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.429031" y="-16"> </gydF4y2Batspan> </text> <g> <path d="m 72.58,52.73 13.17,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,72.69,40.85)"> <tspan style="font-size: 12.50px; " x="16.34" y="-6.2399998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.190001" y="-8.75"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,100.44,54.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,108.25,49.6)"> <tspan style="font-size: 12.50px; " x="9.1199999" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.97" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.220001" y="-7.25"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.799999" y="-0.0099999998"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.963499" y="-0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.502567" y="-0.0099999998"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.141899" y="-0.0099999998"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.182289" y="-0.0099999998"> −</gydF4y2Batspan> </text> <g> <path d="m 171.19,52.73 12.95,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,171.19,40.85)"> <tspan style="font-size: 12.50px; " x="16.23" y="0.98000002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.720001" y="-17.01"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.57" y="-19.530001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.690001" y="-19.530001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.653931" y="-19.530001"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.817429" y="-19.530001"> 米</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,232.32,65.38)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="7.0978718" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,244.5,60.38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,252.63,57.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,261.12,57.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,272.54,65.38)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,280.34,57.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 196.88,52.73 95.16,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,222.42,40.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="3.1800001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="2.5" y="1.6"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,233.36,44.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,238.92,36.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,250.34,42.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,258.14,36.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8600001" y="-4.1100001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8600001" y="-0.93000001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.099998" y="-3.3599999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73" y="-13.05"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="90.019997" y="-13.05"> ]</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.84" y="-13.09"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.867886" y="-13.09"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="77.160004" y="-13.09"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="81.048431" y="-13.09"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="96.260002" y="-13.1"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="100.4235" y="-13.1"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="106.97507" y="-13.1"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="111.13857" y="-13.1"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="206.61" y="-13.09"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="210.7735" y="-13.09"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="217.02499" y="-13.09"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="220.15074" y="-13.09"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="226.40225" y="-13.09"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<gydF4y2Baspan class="equation" id="eq1"> <svg height="94.050003" id="M40" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 94.050003" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,94.05)"> <g transform="translate(72,3.24)"> <text transform="matrix(1,0,0,-1,13.4,51.78)"> <tspan style="font-size: 12.50px; " x="41.580002" y="7.3200002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.029999" y="-7.25"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.203648" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.892754" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.532085" y="0"> =</gydF4y2Batspan> </text> <g> <path d="m 65.55,54.91 34.02,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,65.55,43.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="3.1700001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="2.5" y="1.59"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,76.49,47.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,82.05,41.99)"> <tspan style="font-size: 12.50px; " x="15.02" y="-1.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.02" y="1.59"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.580002" y="-2.47"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.709999" y="-2.47"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.162748" y="-2.47"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.52" y="-9.79"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.859501" y="-9.79"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.959999" y="-9.79"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="70.211502" y="-9.79"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,158.95,56.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,163.83,51.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,171.95,48.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,180.44,51.79)"> <tspan style="font-size: 12.50px; " x="54.84" y="-8.3400002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.791769" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.13199" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.91" y="7.3299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.261524" y="7.3299999"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,243.72,65.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,252.25,60.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 235.28,54.91 31.99,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,236.77,42.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,245.2,47.08)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,250.76,42.01)"> <tspan style="font-size: 12.50px; " x="17.700001" y="-2.45"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,277.84,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,284.09,51.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.54" y="-8.3500004"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,305.07,65.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,313.6,60.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 296.63,54.91 31.99,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,298.12,42.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,306.56,47.08)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,312.12,42.01)"> <tspan style="font-size: 12.50px; " x="17.700001" y="-2.45"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.27" y="-18.120001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,348.83,65.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,357.36,60.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 340.39,54.91 31.99,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,341.88,42.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,350.32,47.08)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,355.87,42.01)"> <tspan style="font-size: 12.50px; " x="17.700001" y="-2.45"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,382.95,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,386.42,44.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-273.92999" y="35.400002"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-263.28995" y="35.400002"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-259.12643" y="35.400002"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-246.12" y="27.049999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-239.43089" y="27.049999"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,155.43,22.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,163.97,17.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 140.3,12.18 38.68,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,145.14,-0.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,153.58,4.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,159.13,-0.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.129999" y="-9.7700005"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.293499" y="-9.7700005"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.096333" y="-9.7700005"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,204.93,14.13)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,209.8,9.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,217.93,5.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,226.42,9.06)"> <tspan style="font-size: 12.50px; " x="17.1" y="7.3299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.530001" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="238.33" y="-22.190001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="242.4935" y="-22.190001"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="248.745" y="-22.190001"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="251.87074" y="-22.190001"> 4</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="258.12225" y="-22.190001"> )</gydF4y2Batspan> </text> </g> </g> </svg></span></p> <p>无限域与有界的情况下补充可以看作是动态以来Hele-Shaw细胞收缩泡沫流体占据了一个附近的无穷和注入(持续的力量<gydF4y2Basvg height="13.0625" id="M41" style="vertical-align:-1.90608pt;width:39.537498px;" version="1.1" viewbox="0 0 39.537498 13.0625" width="39.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0625)"> <g transform="translate(72,-61.55)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.228174" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.268562" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>)是应该发生在无穷。再一次,我们表示<gydF4y2Basvg height="13.45" id="M42" style="vertical-align:-2.21957pt;width:27.049999px;" version="1.1" viewbox="0 0 27.049999 13.45" width="27.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.379169" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>域的流体<gydF4y2Basvg height="9.125" id="M43" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.45" id="M44" style="vertical-align:-2.21957pt;width:78.900002px;" version="1.1" viewbox="0 0 78.900002 13.45" width="78.900002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.3392611" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.50276" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.416199" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.04303" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.08342" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.47245" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.774685" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.938183" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.85162" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。通过使用黎曼映射定理,域<gydF4y2Basvg height="13.45" id="M45" style="vertical-align:-2.21957pt;width:27.049999px;" version="1.1" viewbox="0 0 27.049999 13.45" width="27.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.379169" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>可以被描述为单叶函数<gydF4y2Basvg height="13.55" id="M46" style="vertical-align:-2.29482pt;width:39.962502px;" version="1.1" viewbox="0 0 39.962502 13.55" width="39.962502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.780706" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.694145" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>从单位的外部磁盘<gydF4y2Basvg height="13.8625" id="M47" style="vertical-align:-2.37006pt;width:118.3875px;" version="1.1" viewbox="0 0 118.3875 13.8625" width="118.3875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.8625)"> <g transform="translate(72,-60.91)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,68.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-51.79,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> {</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.029325" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.194265" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.995895" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.496498" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.1856" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.149532" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.189922" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.441422" y="0"> }</gydF4y2Batspan> </text> </g> </g> </svg>到<gydF4y2Basvg height="13.45" id="M48" style="vertical-align:-2.21957pt;width:27.049999px;" version="1.1" viewbox="0 0 27.049999 13.45" width="27.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.379169" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="14.75" id="M49" style="vertical-align:-3.25793pt;width:186.175px;" version="1.1" viewbox="0 0 186.175 14.75" width="186.175" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.780706" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.694145" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.333477" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.373867" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.650372" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.115143" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="74.455368" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,8.79,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,16.44,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,34.06,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,38.94,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.940605" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.280827" y="0"> ⋯</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="11.0625" id="M50" style="vertical-align:-0.30096pt;width:35.174999px;" version="1.1" viewbox="0 0 35.174999 11.0625" width="35.174999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.7398367" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.780226" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。</gydF4y2Bap> <p>满足方程的自由边界(<一个href="#B13">4</一个>,<gydF4y2Ba一个href="#B15">6</一个>]<ggydF4y2BaydF4y2Baspan class="equation" id="EEq1.4"> <svg height="31.5875" id="M51" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 31.5875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,31.5875)"> <g transform="translate(72,-46.73)"> <text transform="matrix(1,0,0,-1,110.47,55.7)"> <tspan style="font-size: 12.50px; " x="18.059999" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.450001" y="-2.53"> ̇</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.799999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.415287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.578785" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.267891" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="51.481644" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.395081" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 172.12,68.41 45.92,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,172.12,55.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.6766019" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,188.35,60.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,193.9,55.7)"> <tspan style="font-size: 12.50px; " x="24.139999" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.349998" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.630001" y="-7.9099998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 240.49,58.82 13.85,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,240.49,46.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.05" y="-8.7600002"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.216139" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.381077" y="-8.7600002"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.408962" y="-8.7600002"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,298.47,60.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,464.75,56.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.540749" y="0"> 5</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>为零和表面张力模型<gydF4y2Baspan class="equation" id="EEq1.5"> <svg height="31.5875" id="M52" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 31.5875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,31.5875)"> <g transform="translate(72,-46.73)"> <text transform="matrix(1,0,0,-1,50.05,55.7)"> <tspan style="font-size: 12.50px; " x="18.059999" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.440001" y="-2.53"> ̇</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.799999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.415287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.578785" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.267891" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="51.481644" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.395081" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 111.69,68.41 45.93,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,111.69,55.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.689105" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,127.92,60.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,133.48,55.7)"> <tspan style="font-size: 12.50px; " x="24.139999" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.349998" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.630001" y="-7.9099998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 180.06,58.82 13.86,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,180.06,46.94)"> <tspan style="font-size: 12.50px; " x="49.650002" y="-3.8399999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.389999" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.83" y="-8.7600002"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.170221" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.521744" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="60.470001" y="-16.01"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.859032" y="-16.01"> </gydF4y2Batspan> </text> <g> <path d="m 240.53,58.82 13.17,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,241.97,46.94)"> <tspan style="font-size: 12.50px; " x="15.01" y="-6.2399998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.860001" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,268.39,60.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,276.2,55.7)"> <tspan style="font-size: 12.50px; " x="9.1199999" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.98" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.799999" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.963499" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.502567" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.754066" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.920208" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.085144" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="77.125534" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,358.9,60.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,464.75,56.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.540749" y="0"> 6</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>小的表面张力模型。</gydF4y2Bap> <h4 id="the-inner-problem-(bounded-domains)">2。内部问题(有限域)</h4><gydF4y2Bap>在本节中,我们获得时间的不变性<gydF4y2Basvg height="10.475" id="M53" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>样式属性的内在问题。从最初的有限域<gydF4y2Basvg height="13.45" id="M54" style="vertical-align:-2.21957pt;width:29.975px;" version="1.1" viewbox="0 0 29.975 13.45" width="29.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.717232" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>这是<gydF4y2Basvg height="10.475" id="M55" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如,我们证明在每个时刻<gydF4y2Basvg height="13.45" id="M56" style="vertical-align:-2.21957pt;width:57.737499px;" version="1.1" viewbox="0 0 57.737499 13.45" width="57.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.922558" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>域<gydF4y2Basvg height="13.45" id="M57" style="vertical-align:-2.21957pt;width:27.049999px;" version="1.1" viewbox="0 0 27.049999 13.45" width="27.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.379169" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="10.475" id="M58" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>——(表面张力为零,零模型)。</gydF4y2Bap> <p><span class="statement" id="deff2.1"><span class="statement-title"><i class="statement-title">定义2.1。</我></span>让<gydF4y2Basvg height="13.4875" id="M59" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是一个全纯函数<gydF4y2Basvg height="10.5375" id="M60" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>这样<gydF4y2Basvg height="13.6125" id="M61" style="vertical-align:-2.34499pt;width:54.224998px;" version="1.1" viewbox="0 0 54.224998 13.6125" width="54.224998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.354164" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.980993" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.021381" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="13.6375" id="M62" style="vertical-align:-2.34499pt;width:55.262501px;" version="1.1" viewbox="0 0 55.262501 13.6375" width="55.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6375)"> <g transform="translate(72,-61.09)"> <text transform="matrix(1,0,0,-1,-71.95,63.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.552532" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.716031" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.967531" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.206528" y="0"> ≠</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.859085" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。让<gydF4y2Basvg height="10.475" id="M63" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>是一个全纯函数<gydF4y2Basvg height="13.6125" id="M64" style="vertical-align:-2.34499pt;width:30.225px;" version="1.1" viewbox="0 0 30.225 13.6125" width="30.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.917278" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>这样<gydF4y2Basvg height="13.45" id="M65" style="vertical-align:-2.21957pt;width:57.474998px;" version="1.1" viewbox="0 0 57.474998 13.45" width="57.474998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.954788" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.581617" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.622005" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="13.4875" id="M66" style="vertical-align:-2.21957pt;width:84.5625px;" version="1.1" viewbox="0 0 84.5625 13.4875" width="84.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.054333" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.594122" y="0"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.207487" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.370987" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.622486" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.261822" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="61.289707" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。我们说<gydF4y2Basvg height="13.4875" id="M67" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="10.475" id="M68" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如在<gydF4y2Basvg height="10.5375" id="M69" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>(或<gydF4y2Basvg height="10.475" id="M70" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>——如果<gydF4y2Baspan class="equation" id="EEq2.1"> <svg height="38.575001" id="M71" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.575001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,38.575)"> <g transform="translate(72,-41.14)"> <text transform="matrix(1,0,0,-1,111.88,53.45)"> <tspan style="font-size: 12.50px; " x="18.059999" y="7.3299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.4" y="-8.3500004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.638996" y="-8.3500004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.578163" y="-8.3500004"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.267029" y="-8.3500004"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.430527" y="-8.3500004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="60.669521" y="-8.3500004"> )</gydF4y2Batspan> </text> <g> <path d="m 137.48,56.57 45.04,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,137.48,44.69)"> <tspan style="font-size: 12.50px; " x="46.240002" y="-1.4299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.306313" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.46981" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.708809" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.872307" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.060001" y="-8.7600002"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.100388" y="-8.7600002"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="74.351891" y="-8.7600002"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="89.518028" y="-8.7600002"> f</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="93.293938" y="-8.7600002"> o</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="99.545433" y="-8.7600002"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="106.82218" y="-8.7600002"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="112.37351" y="-8.7600002"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="117.92484" y="-8.7600002"> c</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="123.28863" y="-8.7600002"> h</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="133.69113" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="143.40596" y="-8.7600002"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="155.44635" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="164.26096" y="-8.7600002"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="327.26999" y="-8.7600002"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="331.4335" y="-8.7600002"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="337.685" y="-8.7600002"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="340.81076" y="-8.7600002"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="347.06226" y="-8.7600002"> )</gydF4y2Batspan> </text> </g> </g> </svg></span></span></p> <p>我们的话,<gydF4y2Basvg height="10.475" id="M72" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>——函数是单价的。事实上,任何单价的函数<gydF4y2Basvg height="10.475" id="M73" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如对于一些<gydF4y2Basvg height="10.475" id="M74" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>。</gydF4y2Bap> <p><span class="statement" id="rem2.2"><span class="statement-title"><i class="statement-title">2.2的话。</我></span>(一)的概念<gydF4y2Basvg height="10.475" id="M75" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>肖像Brickman于1973年被引入和研究[<一个href="#B1">12</一个>)和概括的概念starlikeness spiral-likeness。这一概念的应用研究的单价可能会发现在<一个href="#B3">13</一个>]。<gydF4y2Babr>(b)如果<gydF4y2Basvg height="13.45" id="M76" style="vertical-align:-2.21957pt;width:66.074997px;" version="1.1" viewbox="0 0 66.074997 13.45" width="66.074997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.393112" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.019943" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.060333" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>在上面的定义中,<gydF4y2Basvg height="13.4875" id="M77" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是星形的。<gydF4y2Babr>(c)如果<gydF4y2Basvg height="13.45" id="M78" style="vertical-align:-2.21957pt;width:74.525002px;" version="1.1" viewbox="0 0 74.525002 13.45" width="74.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.393112" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.019943" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.060333" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.824455" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="11.0625" id="M79" style="vertical-align:-0.30096pt;width:55.75px;" version="1.1" viewbox="0 0 55.75 11.0625" width="55.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.206287" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.246677" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,然后<gydF4y2Basvg height="13.4875" id="M80" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是spiral-like类型的<gydF4y2Basvg height="13.975" id="M81" style="vertical-align:-2.73372pt;width:44.450001px;" version="1.1" viewbox="0 0 44.450001 13.975" width="44.450001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.975)"> <g transform="translate(72,-60.82)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.640053" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.354883" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.694386" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。</gydF4y2Baspan></p> <p>我们重申,一个全纯函数<gydF4y2Basvg height="13.4875" id="M82" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>在<gydF4y2Basvg height="10.5375" id="M83" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>这样<gydF4y2Basvg height="13.6125" id="M84" style="vertical-align:-2.34499pt;width:54.224998px;" version="1.1" viewbox="0 0 54.224998 13.6125" width="54.224998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.354164" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.980993" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.021381" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="13.6375" id="M85" style="vertical-align:-2.34499pt;width:55.262501px;" version="1.1" viewbox="0 0 55.262501 13.6375" width="55.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6375)"> <g transform="translate(72,-61.09)"> <text transform="matrix(1,0,0,-1,-71.95,63.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.552532" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.716031" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.967531" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.206528" y="0"> ≠</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.859085" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>据说spiral-like类型的吗<gydF4y2Basvg height="13.45" id="M86" style="vertical-align:-2.21957pt;width:99.275002px;" version="1.1" viewbox="0 0 99.275002 13.45" width="99.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.515023" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.555412" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.71891" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.283466" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.885288" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.361122" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.612625" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.826374" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.4282" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.90403" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.155533" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>如果<gydF4y2Basvg height="16.0375" id="M87" style="vertical-align:-2.34499pt;width:145.27499px;" version="1.1" viewbox="0 0 145.27499 16.0375" width="145.27499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.0375)"> <g transform="translate(72,-59.17)"> <text transform="matrix(1,0,0,-1,-71.95,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.129829" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-46.25,66.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-38.09,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.238997" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.178162" y="0"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.791529" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.955029" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.194025" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.357525" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.833359" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.772522" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.936024" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.175018" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.338516" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.965347" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="76.005737" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="10.75" id="M88" style="vertical-align:-0.33858pt;width:40.049999px;" version="1.1" viewbox="0 0 40.049999 10.75" width="40.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.75)"> <g transform="translate(72,-63.4)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>(<一个href="#B3">13</一个>,<gydF4y2Ba一个href="#B10">14</一个>]。</gydF4y2Bap> <p>下面的结果是一个概括的<一个href="#B5">1</一个>定理1)的情况下<gydF4y2Basvg height="10.475" id="M89" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>——功能。提到定理可能获得通过<gydF4y2Basvg height="13.45" id="M90" style="vertical-align:-2.21957pt;width:66.074997px;" version="1.1" viewbox="0 0 66.074997 13.45" width="66.074997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.393112" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.019943" y="0"> ≡</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.060333" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>在定理<一个href="#thm2.3">2。3</一个>在下面。</gydF4y2Bap> <p><span class="statement" id="thm2.3"><span class="statement-title">定理2.3。</gydF4y2Baspan><i>让<gydF4y2Basvg height="13.0625" id="M91" style="vertical-align:-1.90608pt;width:39.537498px;" version="1.1" viewbox="0 0 39.537498 13.0625" width="39.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0625)"> <g transform="translate(72,-61.55)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.228174" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.268562" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="14.625" id="M92" style="vertical-align:-3.25793pt;width:14.8875px;" version="1.1" viewbox="0 0 14.8875 14.625" width="14.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>是一个函数<gydF4y2Basvg height="10.475" id="M93" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如在<gydF4y2Basvg height="10.5375" id="M94" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和单价的<gydF4y2Basvg height="15.6875" id="M95" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 15.6875" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.6875)"> <g transform="translate(72,-59.45)"> <g> <path d="m -71.95,70.71 10.19,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。让<gydF4y2Basvg height="13.6125" id="M96" style="vertical-align:-2.34499pt;width:38.974998px;" version="1.1" viewbox="0 0 38.974998 13.6125" width="38.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>的经典解决方案Polubarinova-Galin方程(<一个href="#EEq1.1">1.1</一个>与初始条件)<gydF4y2Basvg height="14.75" id="M97" style="vertical-align:-3.25793pt;width:94.824997px;" version="1.1" viewbox="0 0 94.824997 14.75" width="94.824997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.244516" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.88385" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.92424" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.08,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-11.21,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。也让<gydF4y2Basvg height="17.924999" id="M98" style="vertical-align:-4.67863pt;width:217.60001px;" version="1.1" viewbox="0 0 217.60001 17.924999" width="217.60001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.925)"> <g transform="translate(72,-57.66)"> <text transform="matrix(1,0,0,-1,-71.95,62.37)"> <tspan style="font-size: 12.50px; " x="24.809999" y="0.02"> ⋃</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.765563" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-35.58,58.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="13.110496" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="19.105616" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-7.68,62.37)"> <tspan style="font-size: 12.50px; " x="37.049999" y="0.02"> ⋃</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.379169" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,40.92,58.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="13.110496" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="19.105616" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,68.83,62.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.917278" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.118526" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.031965" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="10.325" id="M99" style="vertical-align:-0.0pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 10.325" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>充气时间。如果<gydF4y2Basvg height="10.475" id="M100" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>全纯在<gydF4y2Basvg height="15.85" id="M101" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 15.85" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.85)"> <g transform="translate(72,-59.32)"> <g> <path d="m -71.95,70.71 9.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> </text> </g> </g> </svg>和满足条件</我><span class="equation" id="EEq2.2"> <svg height="20.5375" id="M102" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 20.5375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.5375)"> <g transform="translate(72,-55.57)"> <text transform="matrix(1,0,0,-1,141.94,59.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.054333" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.594122" y="0"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.282986" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.446484" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.136311" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.775642" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.816032" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73.067535" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="88.233673" y="0"> ∀</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="95.235352" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="108.40101" y="0"> ∈</gydF4y2Batspan> </text> <g> <path d="m 262.39,70.71 9.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,262.39,59.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="202.36" y="-1.29"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="206.5235" y="-1.29"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="212.77499" y="-1.29"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="215.90074" y="-1.29"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="222.15225" y="-1.29"> )</gydF4y2Batspan> </text> </g> </g> </svg></span><i>然后<gydF4y2Basvg height="13.6125" id="M103" style="vertical-align:-2.34499pt;width:38.974998px;" version="1.1" viewbox="0 0 38.974998 13.6125" width="38.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="10.475" id="M104" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>像<gydF4y2Basvg height="13.45" id="M105" style="vertical-align:-2.21957pt;width:57.737499px;" version="1.1" viewbox="0 0 57.737499 13.45" width="57.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.922558" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。</我></span></p> <p><span class="statement" id="proof1"><span class="statement-title"><i class="statement-title">证明。</我></span>考虑到所有的功能<gydF4y2Basvg height="13.6125" id="M106" style="vertical-align:-2.34499pt;width:38.974998px;" version="1.1" viewbox="0 0 38.974998 13.6125" width="38.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>分析单价的扩展吗<gydF4y2Basvg height="15.6875" id="M107" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 15.6875" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.6875)"> <g transform="translate(72,-59.45)"> <g> <path d="m -71.95,70.71 10.19,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>为每一个<gydF4y2Basvg height="13.45" id="M108" style="vertical-align:-2.21957pt;width:57.737499px;" version="1.1" viewbox="0 0 57.737499 13.45" width="57.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.922558" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>结果他们的衍生品<gydF4y2Basvg height="13.6375" id="M109" style="vertical-align:-2.34499pt;width:43.487499px;" version="1.1" viewbox="0 0 43.487499 13.6375" width="43.487499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6375)"> <g transform="translate(72,-61.09)"> <text transform="matrix(1,0,0,-1,-71.95,63.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.552532" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.716031" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.392633" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.606384" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.519823" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是连续的,不消失<gydF4y2Basvg height="15.6875" id="M110" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 15.6875" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.6875)"> <g transform="translate(72,-59.45)"> <g> <path d="m -71.95,70.71 10.19,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,我们可以替换为“≥”定义的不平等(<一个href="#EEq2.1">2。1</一个>)<ggydF4y2BaydF4y2Basvg height="10.475" id="M111" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>式函数。的平等只能获得<gydF4y2Basvg height="13.55" id="M112" style="vertical-align:-2.29482pt;width:41.9375px;" version="1.1" viewbox="0 0 41.9375 13.55" width="41.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.1772022" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.153636" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.194025" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>。<gydF4y2Babr>我们假设相反,定理的结论<一个href="#thm2.3">2。3</一个>是不正确的。然后存在<gydF4y2Basvg height="14.75" id="M113" style="vertical-align:-3.25793pt;width:38.3125px;" version="1.1" viewbox="0 0 38.3125 14.75" width="38.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-59.69,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≥</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="17.75" id="M114" style="vertical-align:-3.25793pt;width:55.212502px;" version="1.1" viewbox="0 0 55.212502 17.75" width="55.212502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.75)"> <g transform="translate(72,-57.8)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.26,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.91,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-39.31,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-32,63.92)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>这样<gydF4y2Basvg height="16.700001" id="M115" style="vertical-align:-3.25793pt;width:299.32501px;" version="1.1" viewbox="0 0 299.32501 16.700001" width="299.32501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.7)"> <g transform="translate(72,-58.64)"> <text transform="matrix(1,0,0,-1,-71.95,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.129829" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.293329" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-40.96,58.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-36.09,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-27.65,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-24.18,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-13.32,58.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-8.45,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,0.67,58.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,5.55,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.179123" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.342621" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.281786" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.445286" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,44.68,58.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,49.56,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,58.68,58.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,63.55,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3269978" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.994217" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.596043" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.071877" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.662876" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.826374" y="0"> o</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="64.077873" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="71.017036" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="82.369766" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="89.971588" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="93.447418" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="99.698921" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,相当于<gydF4y2Baspan class="equation" id="EEq2.3"> <svg height="45.787498" id="M116" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 45.787498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,45.7875)"> <g transform="translate(72,-35.37)"> <text transform="matrix(1,0,0,-1,84.39,50.56)"> <tspan style="font-size: 12.50px; " x="22" y="-10.57"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,113.08,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,117.95,61.13)"> <tspan style="font-size: 12.50px; " x="12.64" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.49" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> ′</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,143.13,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,148,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,157.13,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,162,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 101.56,53.68 71.12,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,101.56,39.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.63" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.48" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.849998" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,142.1,36.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,146.98,39.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,156.1,36.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,160.97,37.47)"> <tspan style="font-size: 12.50px; " x="81.790001" y="-23.66"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.379999" y="-13.09"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.407887" y="-13.09"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.659386" y="-13.09"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.790417" y="-13.09"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.953915" y="-13.09"> 米</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,249.45,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,254.33,61.13)"> <tspan style="font-size: 12.50px; " x="12.63" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.49" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> ′</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,279.51,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,284.38,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,293.5,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,298.38,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 237.94,53.68 71.11,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,237.94,39.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.62" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.469999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.849998" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,278.48,36.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,283.35,39.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,292.48,36.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,297.35,37.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.98" y="-13.09"> ≠</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.620052" y="-13.09"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.871553" y="-13.09"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="167.39999" y="-13.09"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="171.56349" y="-13.09"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="177.815" y="-13.09"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="180.94075" y="-13.09"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="187.19225" y="-13.09"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>对于每个<gydF4y2Basvg height="11.0625" id="M117" style="vertical-align:-0.30096pt;width:34.887501px;" version="1.1" viewbox="0 0 34.887501 11.0625" width="34.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5147829" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.555172" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,有<gydF4y2Basvg height="13.05" id="M118" style="vertical-align:-3.25793pt;width:35.387501px;" version="1.1" viewbox="0 0 35.387501 13.05" width="35.387501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-48.61,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="14.75" id="M119" style="vertical-align:-3.25793pt;width:123.625px;" version="1.1" viewbox="0 0 123.625 14.75" width="123.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.014903" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.055292" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.21879" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-39.17,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-31.52,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.391672" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.59292" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-2.36,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,5.29,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.391672" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>这样<gydF4y2Baspan class="equation" id="EEq2.4"> <svg height="45.837502" id="M120" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 45.837502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,45.8375)"> <g transform="translate(72,-35.33)"> <text transform="matrix(1,0,0,-1,110.25,50.52)"> <tspan style="font-size: 12.50px; " x="22.49" y="-10.58"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> g</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,138.3,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,146.11,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,154.55,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,160.1,58.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,171.52,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,179.32,61.1)"> <tspan style="font-size: 12.50px; " x="9.1300001" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 129.49,53.65 68.05,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,129.49,39.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.63" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.48" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.849998" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,168.91,43.39)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,176.71,39.95)"> <tspan style="font-size: 12.50px; " x="25.5" y="-10.57"> ≥</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.73" y="-17.83"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.1300001" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.981404" y="2.52"> </gydF4y2Batspan> </text> <g> <path d="m 215.44,53.65 7.6,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,216.12,41.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.17" y="-3.8299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.769997" y="-16.01"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.530001" y="-8.75"> o</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.781502" y="-8.75"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.408329" y="-8.75"> ≤</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.224384" y="-8.75"> −</gydF4y2Batspan> </text> <g> <path d="m 284.89,53.65 7.61,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,285.57,41.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.1199999" y="-3.8299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.809999" y="-8.75"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="179.17999" y="-8.7700005"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="183.34351" y="-8.7700005"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="189.595" y="-8.7700005"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="192.72075" y="-8.7700005"> 4</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="198.97224" y="-8.7700005"> )</gydF4y2Batspan> </text> </g> </g> </svg></span><br>让<gydF4y2Basvg height="13.05" id="M121" style="vertical-align:-3.25793pt;width:11.1125px;" version="1.1" viewbox="0 0 11.1125 13.05" width="11.1125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>是第一个这样的点,<gydF4y2Basvg height="14.75" id="M122" style="vertical-align:-3.25793pt;width:63.825001px;" version="1.1" viewbox="0 0 63.825001 14.75" width="63.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-59.69,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.442884" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.656635" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.533287" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。不失一般性,我们假设<gydF4y2Baspan class="equation" id="EEq2.5"> <svg height="45.787498" id="M123" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 45.787498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,45.7875)"> <g transform="translate(72,-35.37)"> <text transform="matrix(1,0,0,-1,151.19,50.56)"> <tspan style="font-size: 12.50px; " x="21.32" y="-10.57"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 米</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,179.2,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,184.07,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,192.51,66.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,198.07,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,210.61,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,215.48,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,224.61,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,229.48,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 168.36,53.68 71.12,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,168.36,39.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.63" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.48" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.849998" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,208.9,36.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,213.78,39.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,222.9,36.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,227.77,37.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.370001" y="-13.09"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.410389" y="-13.09"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.661888" y="-13.09"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="236.98" y="-13.09"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="241.14349" y="-13.09"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="247.395" y="-13.09"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="250.52075" y="-13.09"> 5</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="256.77225" y="-13.09"> )</gydF4y2Batspan> </text> </g> </g> </svg></span><br>事实上,<gydF4y2Basvg height="14.75" id="M124" style="vertical-align:-3.25793pt;width:39.137501px;" version="1.1" viewbox="0 0 39.137501 14.75" width="39.137501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-49.77,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-44.9,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是一个函数的最大值点<gydF4y2Basvg height="17.75" id="M125" style="vertical-align:-3.25793pt;width:269.58749px;" version="1.1" viewbox="0 0 269.58749 17.75" width="269.58749" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.75)"> <g transform="translate(72,-57.8)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.1514759" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.314975" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.416199" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.617447" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.16902" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.808353" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.84874" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.400074" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.563572" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.978569" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="71.142067" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="76.243294" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,9.86,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,17.67,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,26.11,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,29.58,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.2647228" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,44.41,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,52.22,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,61.34,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,66.22,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.179123" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.342621" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.281786" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.445286" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.546509" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,109.33,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,117.13,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,126.26,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,131.13,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3269978" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="13.125" id="M126" style="vertical-align:-1.95624pt;width:58.4375px;" version="1.1" viewbox="0 0 58.4375 13.125" width="58.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.125)"> <g transform="translate(72,-61.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.5645552" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.604944" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.768442" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.019943" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.233692" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.485195" y="0"> ]</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.125" id="M127" style="vertical-align:-1.95624pt;width:69.75px;" version="1.1" viewbox="0 0 69.75 13.125" width="69.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.125)"> <g transform="translate(72,-61.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.014903" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.055292" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.21879" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.470291" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.684044" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.935543" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="51.537365" y="0"> ]</gydF4y2Batspan> </text> </g> </g> </svg>。因此,<gydF4y2Basvg height="14.75" id="M128" style="vertical-align:-3.25793pt;width:112.95px;" version="1.1" viewbox="0 0 112.95 14.75" width="112.95" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.540029" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.015863" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.404896" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.956469" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.119967" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.271442" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.43494" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.686443" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.900192" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-12.49,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-7.62,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="14.75" id="M129" style="vertical-align:-3.25793pt;width:111.1375px;" version="1.1" viewbox="0 0 111.1375 14.75" width="111.1375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.540029" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.015863" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.404896" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.506121" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.669619" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.821095" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.984592" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.236095" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="51.449844" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-13.94,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-9.07,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> ≥</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>(平稳性条件在一个区间的端点),结果我们获得<gydF4y2Baspan class="equation" id="EEq2.6"> <svg height="107.45" id="M130" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 107.45" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,107.45)"> <g transform="translate(72,13.96)"> <text transform="matrix(1,0,0,-1,55.56,49.6)"> <tspan style="font-size: 12.50px; " x="18.049999" y="9.7299995"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.73" y="-10.58"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.16" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.174664" y="0"> +</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,111.97,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,116.85,60.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,125.29,65.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,133.82,57.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,146.36,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,151.24,60.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,160.36,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,165.23,57.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 105.29,52.73 65.8,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,112.55,39.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,120.99,44.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,126.55,36.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,139.09,35.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,143.97,39.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,153.09,35.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,157.96,36.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.1" y="-13.09"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.639999" y="-23.67"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,197.14,65.18)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,202.7,57.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.370001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.219999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,231.61,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,236.49,60.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,245.61,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,250.48,57.67)"> <tspan style="font-size: 12.50px; " x="13.79" y="-2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,270.96,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,275.83,60.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,284.27,65.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,289.83,57.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,302.37,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,307.24,60.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,316.37,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,321.24,57.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 187.6,52.73 139.49,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,221.79,39.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.62" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.469999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.849998" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,262.33,35.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,267.2,39.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,276.33,35.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,281.2,36.51)"> <tspan style="font-size: 12.50px; " x="47.09" y="-3.3599999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-207.59" y="44.060001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-175.91" y="23.75"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="60.66" y="-13.09"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.700386" y="-13.09"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="78.951889" y="-13.09"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="183.55" y="-13.09"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="187.7135" y="-13.09"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="193.965" y="-13.09"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="197.09074" y="-13.09"> 6</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="203.34225" y="-13.09"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-225.64" y="34.32"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-221.4765" y="34.32"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-197.48" y="34.32"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-188.46533" y="34.32"> +</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,111.97,9.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,116.85,12.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,125.29,17.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,133.82,10.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,146.36,9.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,151.24,12.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,160.36,9.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,165.23,10.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 105.29,5.31 65.8,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,112.55,-8.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,120.99,-3.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,126.55,-10.9)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,139.09,-11.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,143.97,-8.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,153.09,-11.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,157.96,-10.9)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.1" y="-13.09"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.639999" y="-23.66"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,197.14,17.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,202.7,10.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.370001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.219999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,231.61,9.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,236.49,12.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,245.61,9.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,250.48,10.25)"> <tspan style="font-size: 12.50px; " x="13.79" y="-2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,270.96,9.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,275.83,12.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,284.27,17.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,289.83,10.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,302.37,9.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,307.24,12.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,316.37,9.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,321.24,10.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 187.6,5.31 139.49,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,221.79,-8.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.62" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.469999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.849998" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,262.33,-11.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,267.2,-8.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,276.33,-11.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,281.2,-10.9)"> <tspan style="font-size: 12.50px; " x="47.09" y="-3.3499999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="60.66" y="-13.09"> ≥</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.700386" y="-13.09"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="78.951889" y="-13.09"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="183.55" y="-13.09"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="187.7135" y="-13.09"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="193.965" y="-13.09"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="197.09074" y="-13.09"> 7</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="203.34225" y="-13.09"> )</gydF4y2Batspan> </text> </g> </g> </svg></span><br>通过简单的计算,我们得到的<gydF4y2Baspan class="equation" id="EEq2.8"> <svg height="38.575001" id="M132" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.575001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,38.575)"> <g transform="translate(72,-41.14)"> <text transform="matrix(1,0,0,-1,32.37,60.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 30.41,56.57 10.31,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,30.41,44.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.59" y="-8.7600002"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.141333" y="-8.7600002"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.304831" y="-8.7600002"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.73" y="-17.110001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.406601" y="-17.110001"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,83.26,66.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,88.82,61.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 63.24,56.57 54.62,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,63.24,44.69)"> <tspan style="font-size: 12.50px; " x="89.379997" y="-1.4299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.306313" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.46981" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.158916" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.372665" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.286106" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.449604" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.279999" y="-8.7600002"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="71.320389" y="-8.7600002"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.483887" y="-8.7600002"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="99.949997" y="-17.110001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="104.1135" y="-17.110001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="110.50253" y="-17.110001"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="113.97836" y="-17.110001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="120.3674" y="-17.110001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="124.28084" y="-17.110001"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="130.51984" y="-17.110001"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,202.21,66.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,207.77,61.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 163.19,56.57 68.72,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,178.48,43.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,186.92,48.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,192.48,43.67)"> <tspan style="font-size: 12.50px; " x="43.400002" y="-9.7799997"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.939999" y="-18.129999"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,257.96,66.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,263.52,61.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.678522" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.842022" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.531126" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.744877" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.658318" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.821815" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.060814" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.224312" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.613342" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.089176" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.47821" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="69.391647" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.64315" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="86.170677" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="90.334175" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="97.023277" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="102.22453" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="106.13797" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 248.42,56.57 125.41,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,283.82,44.69)"> <tspan style="font-size: 12.50px; " x="91.209999" y="-1.4299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.306313" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.46981" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.158916" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.372665" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.286106" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.449604" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="100.59" y="-8.7600002"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="180.92999" y="-8.7600002"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="185.09351" y="-8.7600002"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="191.345" y="-8.7600002"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="194.47075" y="-8.7600002"> 8</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="200.72224" y="-8.7600002"> )</gydF4y2Batspan> </text> </g> </g> </svg></span><br>通过区分Polubarinova-Galin方程对<gydF4y2Basvg height="10.7375" id="M133" style="vertical-align:-0.13794pt;width:8.3125px;" version="1.1" viewbox="0 0 8.3125 10.7375" width="8.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,我们获得<gydF4y2Basvg height="21.9375" id="M134" style="vertical-align:-2.34499pt;width:486.96249px;" version="1.1" viewbox="0 0 486.96249 21.9375" width="486.96249" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,21.9375)"> <g transform="translate(72,-54.45)"> <text transform="matrix(1,0,0,-1,-71.95,56.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.054333" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.217831" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.38133" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.770363" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.246197" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.635231" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.548668" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.71217" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-12.79,61.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-9.32,56.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 14.82,69.74 36.05,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,14.82,56.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,23.26,61.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,26.73,56.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.918959" y="0"> −</gydF4y2Batspan> </text> <g> <path d="m 64.99,69.74 42.75,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,64.99,56.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.689105" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,80.12,61.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,83.6,56.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.130791" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.294289" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.683323" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.159157" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.548187" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.461628" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.625126" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.564293" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.727791" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="70.416893" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.630646" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="79.544083" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="86.483253" y="0"> −</gydF4y2Batspan> </text> <g> <path d="m 181.43,70.71 50.59,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,181.43,56.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,188.12,61.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,192.99,56.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,201.43,61.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,207.88,56.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.130791" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.294289" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.683323" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.159157" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.548187" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.461628" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.625126" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.564293" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.727791" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="70.416893" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.630646" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="79.544083" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="83.707588" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="91.346916" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="103.38731" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>为<gydF4y2Basvg height="16.549999" id="M135" style="vertical-align:-2.29482pt;width:44.587502px;" version="1.1" viewbox="0 0 44.587502 16.549999" width="44.587502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.55)"> <g transform="translate(72,-58.76)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.152436" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.192825" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-44.19,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。前面的平等收益率以下关系:<gydF4y2Baspan class="equation" id="eq2"> <svg height="98.1875" id="M136" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 98.1875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,98.1875)"> <g transform="translate(72,6.55)"> <text transform="matrix(1,0,0,-1,13.43,55.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="2.51" y="1.58"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,24.37,58.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,29.93,53.45)"> <tspan style="font-size: 12.50px; " x="24.139999" y="-1.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.139999" y="1.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,56.57,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,63.53,53.45)"> <tspan style="font-size: 12.50px; " x="18.059999" y="7.3299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.629999" y="-8.3500004"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.793499" y="-8.3500004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.182533" y="-8.3500004"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.658367" y="-8.3500004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.047398" y="-8.3500004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.960838" y="-8.3500004"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.199837" y="-8.3500004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.139" y="-8.3500004"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="71.84037" y="-8.3500004"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="76.003868" y="-8.3500004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="82.69297" y="-8.3500004"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="87.906723" y="-8.3500004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="91.82016" y="-8.3500004"> )</gydF4y2Batspan> </text> <g> <path d="m 92.16,56.57 67.36,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,107.45,44.69)"> <tspan style="font-size: 12.50px; " x="56.040001" y="-8.7600002"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.580002" y="-17.110001"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.62803" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.791529" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.480635" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.694386" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.607822" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,185.57,66.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,191.13,61.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.678522" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.842022" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.531126" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.744877" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.658318" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.821815" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.760979" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.112503" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.276005" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.665035" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.140869" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.5299" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="76.443344" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="82.694839" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="93.209862" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="97.373367" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="104.06247" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="109.27622" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="113.18966" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 176.03,56.57 132.46,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,214.95,44.69)"> <tspan style="font-size: 12.50px; " x="94.739998" y="-1.4299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-148.02" y="40.009998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.306313" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.46981" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.158916" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.372665" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.286106" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.449604" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-178.12" y="35.09"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-166.09212" y="35.09"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-161.91611" y="35.09"> 米</gydF4y2Batspan> </text> <g> <path d="m 74.29,22.5 44.83,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,74.29,9.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.689105" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,89.42,14.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,94.98,9.6)"> <tspan style="font-size: 12.50px; " x="31.23" y="-2.72"> ̇</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.799999" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.489998" y="9.7399998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.139999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.655022" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.818523" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.507626" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.721378" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.634815" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="78.589996" y="1.7763568e-015"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="87.617165" y="1.7763568e-015"> +</gydF4y2Batspan> </text> <g> <path d="m 193.94,30.99 66.87,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,193.94,2.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.58" y="-15.68"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.256601" y="-15.68"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,219.65,23.02)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,226.09,17.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.066355" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.979794" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 204.52,12.72 45.71,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,209.35,-0.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,217.79,4.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,221.26,-0.18)"> <tspan style="font-size: 12.50px; " x="30.17" y="-2.45"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.330002" y="-9.7799997"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.860001" y="-18.129999"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,285.66,22.95)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,291.22,17.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.678522" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.842022" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.531126" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.744877" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.658318" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.821815" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.760979" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.112503" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.801609" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.740776" y="0"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="71.442139" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.605644" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="82.294746" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="87.508499" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="91.421936" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 276.12,12.72 110.69,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,304.16,0.84)"> <tspan style="font-size: 12.50px; " x="83.839996" y="0.98000002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="96.029999" y="-8.7600002"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.306313" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.46981" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.158916" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.360165" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.273602" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.437103" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="160.59" y="-28.76"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="164.75349" y="-28.76"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="171.005" y="-28.76"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="174.13075" y="-28.76"> 9</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="180.38225" y="-28.76"> )</gydF4y2Batspan> </text> </g> </g> </svg></span><br>如果我们用(<一个href="#EEq2.6">2。6</一个>),(<gydF4y2Ba一个href="#EEq2.6">2。7</一个>),(<gydF4y2Ba一个href="#EEq2.8">2。8</一个>)和(<一个href="#EEq1.1">1.1</一个>)在上面的表达式和替换<gydF4y2Basvg height="10.7375" id="M137" style="vertical-align:-0.13794pt;width:8.3125px;" version="1.1" viewbox="0 0 8.3125 10.7375" width="8.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>通过<gydF4y2Basvg height="14.625" id="M138" style="vertical-align:-3.25793pt;width:14.4125px;" version="1.1" viewbox="0 0 14.4125 14.625" width="14.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.4,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="9.125" id="M139" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>通过<gydF4y2Basvg height="13.05" id="M140" style="vertical-align:-3.25793pt;width:11.1125px;" version="1.1" viewbox="0 0 11.1125 13.05" width="11.1125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,我们获得<gydF4y2Baspan class="equation" id="eq3"> <svg height="108.7875" id="M141" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 108.7875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,108.7875)"> <g transform="translate(72,15.03)"> <text transform="matrix(1,0,0,-1,-52.42,56.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m -54.37,52.73 10.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-54.37,40.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.58" y="-8.75"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.131332" y="-8.75"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.29483" y="-8.75"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.720001" y="-17.1"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.396603" y="-17.1"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-1.52,63.02)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,4.04,57.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m -21.54,52.73 54.61,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-21.54,40.85)"> <tspan style="font-size: 12.50px; " x="55.799999" y="-21"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.799999" y="-10.34"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.799999" y="0.33000001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.799999" y="3.49"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.29381" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.457308" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.146412" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.360165" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.273602" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.437103" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,36.77,34.71)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.6735678" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.668688" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,52.13,32.52)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,55.75,34.71)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.9273758" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.922496" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,69.41,32.52)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,77.01,49.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.110001" y="-7.9200001"> </gydF4y2Batspan> </text> <g> <path d="m 90.24,52.73 69.53,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,90.24,37.16)"> <tspan style="font-size: 12.50px; " x="13.85" y="-1.59"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.85" y="1.5700001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.35" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,115.03,42.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,118.51,37.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,129.36,34.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,134.23,37.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,143.36,34.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,148.23,37.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1599998" y="-1.59"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1599998" y="1.5700001"> |</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,154.9,43.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,163.05,39.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.32" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.619999" y="-20.309999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.2600002" y="-9.7299995"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.423499" y="-9.7299995"> 米</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,207.36,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,212.23,60.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,220.67,65.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,229.21,57.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,241.75,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,246.62,60.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,255.74,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,260.62,57.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 200.67,52.73 65.8,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,207.94,39.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,216.38,44.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,221.94,36.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,234.48,35.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,239.35,39.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,248.47,35.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,253.35,36.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.26" y="-13.09"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.799999" y="-23.67"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,296.69,65.18)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,302.25,57.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.370001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.219999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,331.16,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,336.04,60.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,345.16,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,350.04,57.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,364.66,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,369.53,60.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,377.97,65.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,383.53,57.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.02" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,400.24,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,405.11,60.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,414.24,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,419.11,57.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 287.15,52.73 143.66,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,323.43,39.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.62" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.469999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.99" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.849998" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,363.96,35.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,368.84,39.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,377.96,35.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,382.84,36.51)"> <tspan style="font-size: 12.50px; " x="49.169998" y="-3.3599999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-226.33" y="35.389999"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-217.76544" y="35.389999"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-209.43845" y="35.389999"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-201.09895" y="35.389999"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-193.45961" y="35.389999"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,198.93,6.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,204.49,-1.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.370001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.219999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,233.4,-2.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,238.28,1.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,247.4,-2.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,252.27,-1.39)"> <tspan style="font-size: 12.50px; " x="35.099998" y="-13.09"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.79" y="-2.51"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.953499" y="-2.51"> 米</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,294.06,8.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,298.94,11.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,307.38,16.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,312.94,9.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,325.48,8.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,330.35,11.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,339.47,8.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,344.35,9.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 283.23,4.24 71.11,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,283.23,-9.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.62" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.48" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.849998" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,323.77,-12.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,328.64,-9.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,337.77,-12.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,342.64,-11.97)"> <tspan style="font-size: 12.50px; " x="12.9" y="-3.3499999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.639999" y="-13.09"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.667885" y="-13.09"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.919388" y="-13.09"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="115.85" y="-37.330002"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="120.0135" y="-37.330002"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="126.265" y="-37.330002"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="129.39075" y="-37.330002"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="135.64224" y="-37.330002"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="141.89375" y="-37.330002"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>由于(<一个href="#EEq2.2">2。2</一个>),(<gydF4y2Ba一个href="#EEq2.3">2。3</一个>)和(<一个href="#EEq2.5">2。5</一个>)。最后,我们得到<gydF4y2Basvg height="19.4" id="M142" style="vertical-align:-5.41734pt;width:266.5625px;" version="1.1" viewbox="0 0 266.5625 19.4" width="266.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.4)"> <g transform="translate(72,-56.48)"> <text transform="matrix(1,0,0,-1,-71.95,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.540029" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.015863" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.404896" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.318335" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.569836" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.121166" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.284664" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.624168" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.787666" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.476772" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-4.03,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-0.56,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.066355" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.979794" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.143293" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.619127" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.158916" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.322414" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.261581" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.425079" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.114185" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="64.31543" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.228874" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.392372" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="76.55587" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="80.719368" y="0"> |</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,82.67,58.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.6735678" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.668688" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,98.03,56.62)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,101.65,58.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.9273758" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.922496" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,115.32,56.62)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,122.91,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。因此,<gydF4y2Basvg height="17.0875" id="M143" style="vertical-align:-2.73372pt;width:220.7625px;" version="1.1" viewbox="0 0 220.7625 17.0875" width="220.7625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.0875)"> <g transform="translate(72,-58.33)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.129829" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.293329" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-42.09,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-34.28,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-25.84,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-22.37,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-12.64,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-4.84,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.1271896" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.290689" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.766523" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.306313" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.46981" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.408978" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.572475" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,42.3,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,50.1,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.278186" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.081018" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.121407" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.723232" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.199066" y="0"> 2</gydF4y2Batspan> </text> </g> </g> </svg>,因为<gydF4y2Basvg height="13.05" id="M144" style="vertical-align:-3.25793pt;width:35.387501px;" version="1.1" viewbox="0 0 35.387501 13.05" width="35.387501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-48.61,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>(接近<gydF4y2Basvg height="13.05" id="M145" style="vertical-align:-3.25793pt;width:11.1125px;" version="1.1" viewbox="0 0 11.1125 13.05" width="11.1125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>在某些地段)<gydF4y2Basvg height="14.625" id="M146" style="vertical-align:-3.25793pt;width:14.4125px;" version="1.1" viewbox="0 0 14.4125 14.625" width="14.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.4,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。这与假设(<一个href="#EEq2.4">2。4</一个>),完成了证明。</gydF4y2Baspan></p> <p>如果在前面的定理,我们<gydF4y2Basvg height="15.8875" id="M147" style="vertical-align:-2.21957pt;width:90.712502px;" version="1.1" viewbox="0 0 90.712502 15.8875" width="90.712502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.8875)"> <g transform="translate(72,-59.29)"> <text transform="matrix(1,0,0,-1,-71.95,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.393112" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.019943" y="0"> ≡</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.060333" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-23.32,66.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="8.7169924" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-9.17,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.45" id="M148" style="vertical-align:-2.21957pt;width:99.275002px;" version="1.1" viewbox="0 0 99.275002 13.45" width="99.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.515023" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.555412" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.71891" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.283466" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.885288" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.361122" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.612625" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.826374" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.4282" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.90403" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.155533" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>;然后我们得到下面的推论。</gydF4y2Bap> <p><span class="statement" id="coro2.4"><span class="statement-title">推论2.4。</gydF4y2Baspan><i>让<gydF4y2Basvg height="13.0625" id="M149" style="vertical-align:-1.90608pt;width:39.537498px;" version="1.1" viewbox="0 0 39.537498 13.0625" width="39.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0625)"> <g transform="translate(72,-61.55)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.228174" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.268562" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,让<gydF4y2Basvg height="14.625" id="M150" style="vertical-align:-3.25793pt;width:14.8875px;" version="1.1" viewbox="0 0 14.8875 14.625" width="14.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>是一个函数的spiral-like类型<gydF4y2Basvg height="13.45" id="M151" style="vertical-align:-2.21957pt;width:99.275002px;" version="1.1" viewbox="0 0 99.275002 13.45" width="99.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.515023" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.555412" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.71891" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.283466" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.885288" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.361122" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.612625" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.826374" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.4282" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.90403" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.155533" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>在<gydF4y2Basvg height="10.5375" id="M152" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和单价的<gydF4y2Basvg height="15.6875" id="M153" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 15.6875" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.6875)"> <g transform="translate(72,-59.45)"> <g> <path d="m -71.95,70.71 10.19,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。然后Polubarinova-Galin方程的经典解决方案(<一个href="#EEq1.1">1.1</一个>与初始条件)<gydF4y2Basvg height="14.75" id="M154" style="vertical-align:-3.25793pt;width:94.824997px;" version="1.1" viewbox="0 0 94.824997 14.75" width="94.824997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.244516" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.88385" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.92424" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.08,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-11.21,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是spiral-like类型的<gydF4y2Basvg height="7.1750002" id="M155" style="vertical-align:-0.1254pt;width:8.9375px;" version="1.1" viewbox="0 0 8.9375 7.1750002" width="8.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.175)"> <g transform="translate(72,-66.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>为<gydF4y2Basvg height="13.45" id="M156" style="vertical-align:-2.21957pt;width:57.737499px;" version="1.1" viewbox="0 0 57.737499 13.45" width="57.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.922558" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="10.325" id="M157" style="vertical-align:-0.0pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 10.325" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>充气时间。</我></span></p> <p>下面的结果是一个概括的<一个href="#B15">6</一个>定理1)的情况下<gydF4y2Basvg height="10.475" id="M158" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>——功能。提到定理可能获得通过<gydF4y2Basvg height="13.45" id="M159" style="vertical-align:-2.21957pt;width:66.074997px;" version="1.1" viewbox="0 0 66.074997 13.45" width="66.074997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.393112" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.019943" y="0"> ≡</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.060333" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>在定理<一个href="#thm2.5">2。5</一个>在下面。</gydF4y2Bap> <p><span class="statement" id="thm2.5"><span class="statement-title">定理2.5。</gydF4y2Baspan><i>让<gydF4y2Basvg height="13.0625" id="M160" style="vertical-align:-1.90608pt;width:39.537498px;" version="1.1" viewbox="0 0 39.537498 13.0625" width="39.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0625)"> <g transform="translate(72,-61.55)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.228174" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.268562" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和表面张力<gydF4y2Basvg height="9.9375" id="M161" style="vertical-align:-2.34499pt;width:8.0625px;" version="1.1" viewbox="0 0 8.0625 9.9375" width="8.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.9375)"> <g transform="translate(72,-64.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是足够小。如果<gydF4y2Basvg height="14.625" id="M162" style="vertical-align:-3.25793pt;width:14.8875px;" version="1.1" viewbox="0 0 14.8875 14.625" width="14.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>是一个函数<gydF4y2Basvg height="10.475" id="M163" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如在<gydF4y2Basvg height="10.5375" id="M164" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和单价的<gydF4y2Basvg height="15.6875" id="M165" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 15.6875" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.6875)"> <g transform="translate(72,-59.45)"> <g> <path d="m -71.95,70.71 10.19,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,然后存在<gydF4y2Basvg height="13.6125" id="M166" style="vertical-align:-2.34499pt;width:53.849998px;" version="1.1" viewbox="0 0 53.849998 13.6125" width="53.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="3.913439" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.415959" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.055292" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.09568" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>这样经典的解决方案<gydF4y2Basvg height="13.6125" id="M167" style="vertical-align:-2.34499pt;width:38.974998px;" version="1.1" viewbox="0 0 38.974998 13.6125" width="38.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>(<一个href="#EEq1.2">1.2</一个>与初始条件)<gydF4y2Basvg height="14.75" id="M168" style="vertical-align:-3.25793pt;width:94.824997px;" version="1.1" viewbox="0 0 94.824997 14.75" width="94.824997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.244516" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.88385" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.92424" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.08,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-11.21,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="10.475" id="M169" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>式为<gydF4y2Basvg height="13.6125" id="M170" style="vertical-align:-2.34499pt;width:72.375px;" version="1.1" viewbox="0 0 72.375 13.6125" width="72.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.959347" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.122849" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.474373" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.637871" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="10.325" id="M171" style="vertical-align:-0.0pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 10.325" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>充气时间,<gydF4y2Basvg height="18.85" id="M172" style="vertical-align:-5.41599pt;width:234.60001px;" version="1.1" viewbox="0 0 234.60001 18.85" width="234.60001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.85)"> <g transform="translate(72,-56.92)"> <text transform="matrix(1,0,0,-1,-71.95,62.37)"> <tspan style="font-size: 12.50px; " x="24.809999" y="0.02"> ⋃</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.765563" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-35.58,58.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="13.110496" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="19.105616" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="21.844992" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="24.759409" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="29.196672" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-0.88,62.37)"> <tspan style="font-size: 12.50px; " x="37.049999" y="0.02"> ⋃</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.379169" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,47.72,58.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="13.110496" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="19.105616" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="21.844992" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="24.759409" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="29.205423" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,82.43,62.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.917278" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.118526" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.031965" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="10.475" id="M173" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>是一个全纯函数<gydF4y2Basvg height="15.85" id="M174" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 15.85" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.85)"> <g transform="translate(72,-59.32)"> <g> <path d="m -71.95,70.71 9.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> </text> </g> </g> </svg>满足条件(<一个href="#EEq2.2">2。2</一个>)。</我></span></p> <p><span class="statement" id="proof2"><span class="statement-title"><i class="statement-title">证明。</我></span>如果我们考虑<gydF4y2Basvg height="13.4875" id="M175" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>的关闭<gydF4y2Basvg height="10.5375" id="M176" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,然后的不等号(<一个href="#EEq2.1">2。1</一个>)可以取代“≥”可以获得平等的地方<gydF4y2Basvg height="13.55" id="M177" style="vertical-align:-2.29482pt;width:41.9375px;" version="1.1" viewbox="0 0 41.9375 13.55" width="41.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.1772022" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.153636" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.194025" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>。<gydF4y2Babr>相反,假设定理的结论<一个href="#thm2.5">2。5</一个>是不正确的。然后存在<gydF4y2Basvg height="14.75" id="M178" style="vertical-align:-3.25793pt;width:38.3125px;" version="1.1" viewbox="0 0 38.3125 14.75" width="38.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-59.69,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≥</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="17.75" id="M179" style="vertical-align:-3.25793pt;width:55.212502px;" version="1.1" viewbox="0 0 55.212502 17.75" width="55.212502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.75)"> <g transform="translate(72,-57.8)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.26,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.91,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-39.31,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-32,63.92)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>这样,(<一个href="#EEq2.3">2。3</一个>),(<gydF4y2Ba一个href="#EEq2.4">2。4</一个>),(<gydF4y2Ba一个href="#EEq2.5">2。5</一个>),(<gydF4y2Ba一个href="#EEq2.6">2。6</一个>)和(<一个href="#EEq2.6">2。7</一个>)是正确的。与此同时,平等(<一个href="#EEq2.8">2。8</一个>)是实现。通过区分Polubarinova-Galin方程(<一个href="#EEq1.2">1.2</一个>)对<gydF4y2Basvg height="10.7375" id="M180" style="vertical-align:-0.13794pt;width:8.3125px;" version="1.1" viewbox="0 0 8.3125 10.7375" width="8.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,我们获得<gydF4y2Baspan class="equation" id="eq4"> <svg height="30.737499" id="M181" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 30.737499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,30.7375)"> <g transform="translate(72,-47.41)"> <text transform="matrix(1,0,0,-1,-3.56,56.35)"> <tspan style="font-size: 12.50px; " x="18.059999" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.57" y="-7.25"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 米</gydF4y2Batspan> </text> <g> <path d="m 23.06,59.47 10.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,23.06,47.59)"> <tspan style="font-size: 12.50px; " x="11.5" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,43,61.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,48.55,56.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 74.78,69.25 38.13,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,74.78,56.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,83.22,61.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,88.77,56.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.918959" y="0"> −</gydF4y2Batspan> </text> <g> <path d="m 127.03,69.25 44.83,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,127.03,56.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.689105" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,142.16,61.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,147.72,56.35)"> <tspan style="font-size: 12.50px; " x="27.290001" y="-7.25"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 173.06,59.47 10.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,173.06,47.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.49" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.017527" y="-8.7600002"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.181025" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.870129" y="-8.7600002"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.071377" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.984818" y="-8.7600002"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.923981" y="-8.7600002"> −</gydF4y2Batspan> </text> <g> <path d="m 233.34,70.22 52.67,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,233.34,56.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,240.03,61.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,244.9,56.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,253.34,61.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,261.88,56.35)"> <tspan style="font-size: 12.50px; " x="27.290001" y="-7.25"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 287.21,59.47 10.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,287.21,47.59)"> <tspan style="font-size: 12.50px; " x="46.16" y="-3.8399999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="89.75" y="-8.7200003"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="106.77" y="-8.7200003"> ]</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.5" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.015022" y="-8.7600002"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.178522" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.867626" y="-8.7600002"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.081379" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.994816" y="-8.7600002"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.240002" y="-8.7600002"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="69.267883" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.619408" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="93.910004" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="97.798431" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="113.01" y="-8.7600002"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="117.1735" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="123.72507" y="-8.7600002"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="129.96407" y="-8.7600002"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="171.28" y="-8.9899998"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="175.4435" y="-8.9899998"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="181.69499" y="-8.9899998"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="184.82076" y="-8.9899998"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="191.07225" y="-8.9899998"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="197.32375" y="-8.9899998"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>为<gydF4y2Basvg height="16.549999" id="M182" style="vertical-align:-2.29482pt;width:44.587502px;" version="1.1" viewbox="0 0 44.587502 16.549999" width="44.587502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.55)"> <g transform="translate(72,-58.76)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.152436" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.192825" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-44.19,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。前面的平等相当于以下:<gydF4y2Baspan class="equation" id="eq5"> <svg height="155.66251" id="M183" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 155.66251" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,155.6625)"> <g transform="translate(72,52.53)"> <text transform="matrix(1,0,0,-1,-55.24,52.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="2.5" y="1.59"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-44.3,56.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-38.74,51.25)"> <tspan style="font-size: 12.50px; " x="24.139999" y="-1.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.139999" y="1.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-12.1,58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-3.95,51.24)"> <tspan style="font-size: 12.50px; " x="18.059999" y="7.3200002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.629999" y="-8.3599997"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.793499" y="-8.3599997"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.182533" y="-8.3599997"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.658367" y="-8.3599997"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.047398" y="-8.3599997"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.960838" y="-8.3599997"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.199837" y="-8.3599997"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,63.7,64.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,67.17,59.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 24.68,54.37 66.63,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,39.97,41.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,48.41,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,51.88,41.47)"> <tspan style="font-size: 12.50px; " x="43.41" y="-9.7700005"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.066355" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.979794" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.950001" y="-18.129999"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="67.565285" y="-18.129999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="71.728783" y="-18.129999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="82.25631" y="-18.129999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="86.419807" y="-18.129999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="93.108917" y="-18.129999"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="98.310165" y="-18.129999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="102.2236" y="-18.129999"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="106.3871" y="-18.129999"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="112.6386" y="-18.129999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="116.8021" y="-18.129999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="123.19113" y="-18.129999"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="126.66697" y="-18.129999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="133.056" y="-18.129999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="136.96944" y="-18.129999"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="143.22095" y="-18.129999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="150.16011" y="-18.129999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="154.32361" y="-18.129999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="161.01271" y="-18.129999"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="166.21396" y="-18.129999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="170.1274" y="-18.129999"> )</gydF4y2Batspan> </text> <g> <path d="m 107.83,54.37 118.35,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,142.53,42.49)"> <tspan style="font-size: 12.50px; " x="84.849998" y="-1.4299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="94.220001" y="-21.01"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="94.220001" y="-10.34"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="94.220001" y="0.31999999"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="94.220001" y="3.49"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.642452" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.805952" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.495056" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.696304" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.609745" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.773243" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,239.25,36.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.6823201" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.67744" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,254.61,34.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,258.24,36.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,268.13,39.4)"> <tspan style="font-size: 6.25px; " x="5.2199998" y="1.97"> 0</gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="1.9443721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,277.47,36.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.9273758" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.922496" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,291.13,34.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-41.81,6.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.04" y="7.3299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.66" y="-7.9099998"> </gydF4y2Batspan> </text> <g> <path d="m -19.19,9.73 13.85,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-19.19,-2.15)"> <tspan style="font-size: 12.50px; " x="49.639999" y="-3.8399999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.009998" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.82" y="-8.7600002"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.160221" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.511745" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.09" y="-16.01"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.479034" y="-16.01"> </gydF4y2Batspan> </text> <g> <path d="m 42.9,9.73 13.17,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,43.01,-2.15)"> <tspan style="font-size: 12.50px; " x="16.34" y="-6.2399998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.190001" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,70.76,11.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,78.57,6.61)"> <tspan style="font-size: 12.50px; " x="9.1199999" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.97" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.57" y="7.3299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-111.11" y="41.93"> ×</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-99.129997" y="49.25"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-74.720001" y="49.25"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-92.779999" y="41.93"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-88.616501" y="41.93"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-64.150002" y="33.580002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-57.460896" y="33.580002"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,29.55,-21.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 14.42,-32.19 21.58,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,19.25,-45.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,27.69,-40.02)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,39.97,-35.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.54" y="-8.3500004"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,62.05,-21.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,67.61,-26.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.603024" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 52.51,-32.19 31.87,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,54.25,-44.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.218311" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.32" y="-8.75"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.009106" y="-8.75"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,100.7,-30.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,104.18,-42.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.15" y="-7.3200002"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.490221" y="-7.3200002"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.817219" y="-7.3200002"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.156719" y="-7.3200002"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.796055" y="-7.3200002"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,161.52,-30.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,167.08,-35.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.603024" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.842022" y="0"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.00552" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.919998" y="-8.3400002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.596603" y="-8.3400002"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,223.13,-21.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 203.1,-32.19 28.39,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,203.1,-44.07)"> <tspan style="font-size: 12.50px; " x="29.59" y="-1.4299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.939999" y="-21.01"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.939999" y="-10.34"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.939999" y="0.31999999"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.939999" y="3.49"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.218311" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,241.54,-50.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.6823201" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.67744" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,256.9,-52.4)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,260.52,-50.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.9273758" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.922496" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,274.19,-52.4)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,277.81,-50.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="6.7740479" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="12.769168" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,295.17,-52.4)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,302.07,-35.32)"> <tspan style="font-size: 12.50px; " x="31.82" y="0.029999999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.830002" y="0.029999999"> ]</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.679241" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.98" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.868435" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.080002" y="-0.0099999998"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.2435" y="-0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.795074" y="-0.0099999998"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.034065" y="-0.0099999998"> ∣</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,380.91,-38.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.6823201" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.67744" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,396.27,-40.63)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,399.9,-38.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.9273758" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.922496" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,413.56,-40.63)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,417.18,-38.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="6.7740479" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="12.769168" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,434.54,-40.63)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,438.66,-35.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.83" y="-41.93"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.9935" y="-41.93"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.244999" y="-41.93"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.37075" y="-41.93"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.62225" y="-41.93"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.873749" y="-41.93"> )</gydF4y2Batspan> </text> </g> </g> </svg></span> <svg height="0.125" id="M184" style="vertical-align:-0.0pt;width:10.55px;" version="1.1" viewbox="0 0 10.55 0.125" width="10.55" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,0.125)"> <g transform="translate(72,-71.9)"></g> </g> </svg><br>这个等式的右边是严格-小<gydF4y2Basvg height="9.9375" id="M185" style="vertical-align:-2.34499pt;width:8.0625px;" version="1.1" viewbox="0 0 8.0625 9.9375" width="8.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.9375)"> <g transform="translate(72,-64.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>因为(<一个href="#EEq2.5">2。5</一个>),(<gydF4y2Ba一个href="#EEq2.6">2。7</一个>),这一事实<gydF4y2Basvg height="15.475" id="M186" style="vertical-align:-2.34499pt;width:82.650002px;" version="1.1" viewbox="0 0 82.650002 15.475" width="82.650002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.475)"> <g transform="translate(72,-59.62)"> <text transform="matrix(1,0,0,-1,-71.95,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-46.44,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-42.96,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.729494" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.769882" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。<gydF4y2Babr>通过使用(<一个href="#EEq2.8">2。8</一个>),我们获得<gydF4y2Basvg height="17.0875" id="M187" style="vertical-align:-2.73372pt;width:220.7625px;" version="1.1" viewbox="0 0 220.7625 17.0875" width="220.7625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.0875)"> <g transform="translate(72,-58.33)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.129829" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.293329" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-42.09,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-34.28,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-25.84,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-22.37,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-12.64,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-4.84,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.1271896" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.290689" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.766523" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.306313" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.46981" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.408978" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.572475" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,42.3,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,50.1,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.278186" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.081018" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.121407" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.723232" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.199066" y="0"> 2</gydF4y2Batspan> </text> </g> </g> </svg>为<gydF4y2Basvg height="13.05" id="M188" style="vertical-align:-3.25793pt;width:35.387501px;" version="1.1" viewbox="0 0 35.387501 13.05" width="35.387501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-48.61,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>(接近<gydF4y2Basvg height="13.05" id="M189" style="vertical-align:-3.25793pt;width:11.1125px;" version="1.1" viewbox="0 0 11.1125 13.05" width="11.1125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>)在附近<gydF4y2Basvg height="14.625" id="M190" style="vertical-align:-3.25793pt;width:14.4125px;" version="1.1" viewbox="0 0 14.4125 14.625" width="14.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.4,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。这是在矛盾与我们的假设和证明。</gydF4y2Baspan></p> <p><span class="statement" id="rem2.6"><span class="statement-title"><i class="statement-title">2.6的话。</我></span>让<gydF4y2Basvg height="13.0625" id="M191" style="vertical-align:-1.90608pt;width:39.537498px;" version="1.1" viewbox="0 0 39.537498 13.0625" width="39.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0625)"> <g transform="translate(72,-61.55)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.228174" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.268562" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,让<gydF4y2Basvg height="14.625" id="M192" style="vertical-align:-3.25793pt;width:14.8875px;" version="1.1" viewbox="0 0 14.8875 14.625" width="14.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>是一个函数<gydF4y2Basvg height="10.475" id="M193" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如在<gydF4y2Basvg height="10.5375" id="M194" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和单价的<gydF4y2Basvg height="15.6875" id="M195" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 15.6875" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.6875)"> <g transform="translate(72,-59.45)"> <g> <path d="m -71.95,70.71 10.19,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。如果<gydF4y2Basvg height="14.625" id="M196" style="vertical-align:-3.25793pt;width:14.8875px;" version="1.1" viewbox="0 0 14.8875 14.625" width="14.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>满足条件(<一个href="#EEq2.1">2。1</一个>)为每一个<gydF4y2Basvg height="18.35" id="M197" style="vertical-align:-2.29482pt;width:40.612499px;" version="1.1" viewbox="0 0 40.612499 18.35" width="40.612499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.35)"> <g transform="translate(72,-57.32)"> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.152436" y="0"> ∈</gydF4y2Batspan> </text> <g> <path d="m -49.75,70.71 10.19,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-49.75,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,然后存在表面张力<gydF4y2Basvg height="9.9375" id="M198" style="vertical-align:-2.34499pt;width:8.0625px;" version="1.1" viewbox="0 0 8.0625 9.9375" width="8.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.9375)"> <g transform="translate(72,-64.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>(这取决于<gydF4y2Basvg height="14.625" id="M199" style="vertical-align:-3.25793pt;width:14.8875px;" version="1.1" viewbox="0 0 14.8875 14.625" width="14.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>)足够小,<gydF4y2Basvg height="13.6125" id="M200" style="vertical-align:-2.34499pt;width:53.849998px;" version="1.1" viewbox="0 0 53.849998 13.6125" width="53.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="3.913439" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.415959" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.055292" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.09568" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>这样经典的解决方案<gydF4y2Basvg height="13.6125" id="M201" style="vertical-align:-2.34499pt;width:38.974998px;" version="1.1" viewbox="0 0 38.974998 13.6125" width="38.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>(<一个href="#EEq1.2">1.2</一个>与初始条件)<gydF4y2Basvg height="14.75" id="M202" style="vertical-align:-3.25793pt;width:94.824997px;" version="1.1" viewbox="0 0 94.824997 14.75" width="94.824997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.244516" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.88385" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.92424" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.08,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-11.21,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="10.475" id="M203" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>式为<gydF4y2Basvg height="13.6125" id="M204" style="vertical-align:-2.34499pt;width:72.375px;" version="1.1" viewbox="0 0 72.375 13.6125" width="72.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.959347" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.122849" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.474373" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.637871" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="10.325" id="M205" style="vertical-align:-0.0pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 10.325" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>充气时间。</gydF4y2Baspan></p> <p><span class="statement" id="proof3"><span class="statement-title"><i class="statement-title">证明。</我></span>结论是直接从古典解的光滑性(<一个href="#EEq1.1">1.1</一个>)。</gydF4y2Baspan></p> <p>如果<gydF4y2Basvg height="15.8875" id="M206" style="vertical-align:-2.21957pt;width:90.712502px;" version="1.1" viewbox="0 0 90.712502 15.8875" width="90.712502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.8875)"> <g transform="translate(72,-59.29)"> <text transform="matrix(1,0,0,-1,-71.95,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.393112" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.019943" y="0"> ≡</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.060333" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-23.32,66.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="8.7169924" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-9.17,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>在定理<一个href="#thm2.5">2。5</一个>,在那里<gydF4y2Basvg height="13.45" id="M207" style="vertical-align:-2.21957pt;width:99.275002px;" version="1.1" viewbox="0 0 99.275002 13.45" width="99.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.515023" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.555412" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.71891" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.283466" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.885288" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.361122" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.612625" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.826374" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.4282" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.90403" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.155533" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,我们获得以下推论:</gydF4y2Bap> <p><span class="statement" id="coro2.7"><span class="statement-title">推论2.7。</gydF4y2Baspan><i>让<gydF4y2Basvg height="13.0625" id="M208" style="vertical-align:-1.90608pt;width:39.537498px;" version="1.1" viewbox="0 0 39.537498 13.0625" width="39.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0625)"> <g transform="translate(72,-61.55)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.228174" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.268562" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和表面张力<gydF4y2Basvg height="9.9375" id="M209" style="vertical-align:-2.34499pt;width:8.0625px;" version="1.1" viewbox="0 0 8.0625 9.9375" width="8.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.9375)"> <g transform="translate(72,-64.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是足够小。如果<gydF4y2Basvg height="14.625" id="M210" style="vertical-align:-3.25793pt;width:14.8875px;" version="1.1" viewbox="0 0 14.8875 14.625" width="14.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>是一个函数的spiral-like类型<gydF4y2Basvg height="13.45" id="M211" style="vertical-align:-2.21957pt;width:99.275002px;" version="1.1" viewbox="0 0 99.275002 13.45" width="99.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.515023" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.555412" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.71891" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.283466" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.885288" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.361122" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.612625" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.826374" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.4282" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.90403" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.155533" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>在<gydF4y2Basvg height="10.5375" id="M212" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和单价的<gydF4y2Basvg height="15.6875" id="M213" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 15.6875" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.6875)"> <g transform="translate(72,-59.45)"> <g> <path d="m -71.95,70.71 10.19,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,然后存在<gydF4y2Basvg height="13.6125" id="M214" style="vertical-align:-2.34499pt;width:53.849998px;" version="1.1" viewbox="0 0 53.849998 13.6125" width="53.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="3.913439" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.415959" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.055292" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.09568" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>这样经典的解决方案<gydF4y2Basvg height="13.6125" id="M215" style="vertical-align:-2.34499pt;width:38.974998px;" version="1.1" viewbox="0 0 38.974998 13.6125" width="38.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>(<一个href="#EEq1.2">1.2</一个>与初始条件)<gydF4y2Basvg height="14.75" id="M216" style="vertical-align:-3.25793pt;width:94.824997px;" version="1.1" viewbox="0 0 94.824997 14.75" width="94.824997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.244516" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.88385" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.92424" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.08,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-11.21,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是spiral-like类型的<gydF4y2Basvg height="7.1750002" id="M217" style="vertical-align:-0.1254pt;width:8.9375px;" version="1.1" viewbox="0 0 8.9375 7.1750002" width="8.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.175)"> <g transform="translate(72,-66.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>为<gydF4y2Basvg height="13.6125" id="M218" style="vertical-align:-2.34499pt;width:72.375px;" version="1.1" viewbox="0 0 72.375 13.6125" width="72.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.959347" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.122849" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.474373" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.637871" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="10.325" id="M219" style="vertical-align:-0.0pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 10.325" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>充气时间。</我></span></p> <h4 id="the-outer-problem-(unbounded-domain-with-bounded-complement)">3所示。外部问题(无限域界补充)</h4><gydF4y2Bap>在本节中,我们获得的不变性时间相同的几何属性(用<gydF4y2Basvg height="15.1625" id="M220" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>)外的问题。</gydF4y2Bap> <p><span class="statement" id="deff3.1"><span class="statement-title"><i class="statement-title">定义3.1。</我></span>让<gydF4y2Basvg height="10.325" id="M221" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.325" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是一个全纯函数<gydF4y2Basvg height="13.8625" id="M222" style="vertical-align:-2.37006pt;width:118.3875px;" version="1.1" viewbox="0 0 118.3875 13.8625" width="118.3875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.8625)"> <g transform="translate(72,-60.91)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,68.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-51.79,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> {</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.029325" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.194265" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.995895" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.496498" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.1856" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.149532" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.189922" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.441422" y="0"> }</gydF4y2Batspan> </text> </g> </g> </svg>这样<gydF4y2Basvg height="14.75" id="M223" style="vertical-align:-3.25793pt;width:182.2625px;" version="1.1" viewbox="0 0 182.2625 14.75" width="182.2625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.206287" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.246677" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.523182" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.987953" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.328178" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-0.33,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,7.32,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,24.94,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,35.81,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.940605" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.280827" y="0"> ⋯</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="13.125" id="M224" style="vertical-align:-1.95624pt;width:31.700001px;" version="1.1" viewbox="0 0 31.700001 13.125" width="31.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.125)"> <g transform="translate(72,-61.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3520041" y="0"> ≠</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.00456" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。让<gydF4y2Basvg height="15.1625" id="M225" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>是一个全纯函数<gydF4y2Basvg height="13.45" id="M226" style="vertical-align:-2.21957pt;width:41.049999px;" version="1.1" viewbox="0 0 41.049999 13.45" width="41.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-49.87,68.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-43.38,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>这样<gydF4y2Basvg height="21.075001" id="M227" style="vertical-align:-4.74141pt;width:123.725px;" version="1.1" viewbox="0 0 123.725 21.075001" width="123.725" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,21.075)"> <g transform="translate(72,-55.14)"> <text transform="matrix(1,0,0,-1,-71.95,59.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> l</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9516678" y="0"> 米</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-51.1,56.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="6.1351519" y="0"> →</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="15.692336" y="0"> ∞</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-23.44,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.2697887" y="2.6500001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.433288" y="2.6500001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.10989" y="2.6500001"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.749224" y="2.6500001"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.789612" y="2.6500001"> ∞</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="23.15" id="M228" style="vertical-align:-4.74141pt;width:121.4125px;" version="1.1" viewbox="0 0 121.4125 23.15" width="121.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,23.15)"> <g transform="translate(72,-53.48)"> <text transform="matrix(1,0,0,-1,-71.95,58.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> l</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9516678" y="0"> 米</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-51.1,55.13)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="6.1351519" y="0"> →</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="15.692336" y="0"> ∞</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-23.44,60.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-15.17,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-11.7,58.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.479433" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.519823" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。我们说<gydF4y2Basvg height="10.325" id="M229" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.325" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="15.1625" id="M230" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如在<gydF4y2Basvg height="10.5375" id="M231" style="vertical-align:-0.16302pt;width:20.975px;" version="1.1" viewbox="0 0 20.975 10.5375" width="20.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,68.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>如果<gydF4y2Baspan class="equation" id="EEq3.1"> <svg height="48.1875" id="M232" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.1875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.1875)"> <g transform="translate(72,-33.45)"> <text transform="matrix(1,0,0,-1,127.12,49.6)"> <tspan style="font-size: 12.50px; " x="18.059999" y="9.7299995"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.41" y="-8.3000002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.099106" y="-8.3000002"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,175.76,62.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,181.32,57.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 154.64,52.73 46.59,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,155.91,40.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.509998" y="0.58999997"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.345287" y="2.6500001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.508786" y="2.6500001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.136576" y="2.6500001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.300076" y="2.6500001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.989182" y="2.6500001"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.152679" y="2.6500001"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.25" y="-9.1400003"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="70.277885" y="-9.1400003"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="76.529388" y="-9.1400003"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="91.708031" y="-9.1400003"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="101.87297" y="-9.1400003"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="113.90086" y="-9.1400003"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,280.01,54.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,286.51,49.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="178.24001" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="182.4035" y="0"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="188.655" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="191.78075" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="198.03224" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg></span></span></p> <p><span class="statement" id="rem3.2"><span class="statement-title"><i class="statement-title">3.2的话。</我></span>(一)如果<gydF4y2Basvg height="10.325" id="M233" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.325" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是一个<gydF4y2Basvg height="15.1625" id="M234" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>——功能<gydF4y2Basvg height="10.5375" id="M235" style="vertical-align:-0.16302pt;width:20.975px;" version="1.1" viewbox="0 0 20.975 10.5375" width="20.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,68.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>,那么这个函数<gydF4y2Basvg height="13.85" id="M236" style="vertical-align:-2.34499pt;width:77.849998px;" version="1.1" viewbox="0 0 77.849998 13.85" width="77.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.85)"> <g transform="translate(72,-60.92)"> <text transform="matrix(1,0,0,-1,-71.95,63.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> ∶</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.267363" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.00864" y="0"> →</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.150253" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>给出的<gydF4y2Basvg height="13.6125" id="M237" style="vertical-align:-2.34499pt;width:98.574997px;" version="1.1" viewbox="0 0 98.574997 13.6125" width="98.574997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.341661" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.968491" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.008881" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.26038" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.736214" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.463066" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.626568" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="64.878067" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.353905" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="74.592896" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.125" id="M238" style="vertical-align:-1.95624pt;width:31.65px;" version="1.1" viewbox="0 0 31.65 13.125" width="31.65" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.125)"> <g transform="translate(72,-61.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3144951" y="0"> ≠</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.967051" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.6125" id="M239" style="vertical-align:-2.34499pt;width:54.224998px;" version="1.1" viewbox="0 0 54.224998 13.6125" width="54.224998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.354164" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.980993" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.021381" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,是<gydF4y2Basvg height="10.475" id="M240" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如在<gydF4y2Basvg height="10.5375" id="M241" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="13.85" id="M242" style="vertical-align:-2.34499pt;width:98.462502px;" version="1.1" viewbox="0 0 98.462502 13.85" width="98.462502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.85)"> <g transform="translate(72,-60.92)"> <text transform="matrix(1,0,0,-1,-71.95,63.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.00312" y="0"> ∶</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.867987" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.807152" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.97065" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.785267" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.500095" y="0"> →</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="69.641708" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="17.924999" id="M243" style="vertical-align:-2.21957pt;width:118.775px;" version="1.1" viewbox="0 0 118.775 17.924999" width="118.775" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.925)"> <g transform="translate(72,-57.66)"> <text transform="matrix(1,0,0,-1,-71.95,59.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.393112" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.019943" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.060333" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-19.19,64.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-13.05,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.2697887" y="2.6500001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.433288" y="2.6500001"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.684788" y="2.6500001"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.160622" y="2.6500001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.850447" y="2.6500001"> )</gydF4y2Batspan> </text> </g> </g> </svg>,尽管<gydF4y2Basvg height="14.6875" id="M244" style="vertical-align:-2.78387pt;width:104.875px;" version="1.1" viewbox="0 0 104.875 14.6875" width="104.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6875)"> <g transform="translate(72,-60.25)"> <text transform="matrix(1,0,0,-1,-67.78,63.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.153156" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.193544" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.13271" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.296207" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.110825" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.049988" y="0"> ⧵</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="61.364723" y="0"> {</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="67.366165" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73.617661" y="0"> }</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="13.45" id="M245" style="vertical-align:-2.21957pt;width:57.474998px;" version="1.1" viewbox="0 0 57.474998 13.45" width="57.474998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.954788" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.581617" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.622005" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。<gydF4y2Babr>(b)如果<gydF4y2Basvg height="13.4875" id="M246" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是一个<gydF4y2Basvg height="10.475" id="M247" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>——功能<gydF4y2Basvg height="10.5375" id="M248" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,那么这个函数<gydF4y2Basvg height="11.225" id="M249" style="vertical-align:-0.23827pt;width:86.949997px;" version="1.1" viewbox="0 0 86.949997 11.225" width="86.949997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.225)"> <g transform="translate(72,-63.02)"> <text transform="matrix(1,0,0,-1,-71.95,63.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.190185" y="0"> ∶</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.055052" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-40.7,68.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-28.65,63.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> →</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.12911" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.6125" id="M250" style="vertical-align:-2.34499pt;width:99.699997px;" version="1.1" viewbox="0 0 99.699997 13.6125" width="99.699997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.206287" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.246677" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.498177" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.97401" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.913177" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.076675" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.328178" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.804008" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.493111" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="15.1625" id="M251" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如在<gydF4y2Basvg height="10.5375" id="M252" style="vertical-align:-0.16302pt;width:20.975px;" version="1.1" viewbox="0 0 20.975 10.5375" width="20.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,68.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="17.924999" id="M253" style="vertical-align:-2.21957pt;width:109.2875px;" version="1.1" viewbox="0 0 109.2875 17.924999" width="109.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.925)"> <g transform="translate(72,-57.66)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.73312" y="2.6500001"> ∶</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.597986" y="2.6500001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.324841" y="2.6500001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.488338" y="2.6500001"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-26.99,64.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-20.5,59.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> →</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.843941" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="17.924999" id="M254" style="vertical-align:-2.21957pt;width:114.3625px;" version="1.1" viewbox="0 0 114.3625 17.924999" width="114.3625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.925)"> <g transform="translate(72,-57.66)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.2697887" y="2.6500001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.433288" y="2.6500001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.94783" y="2.6500001"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.574661" y="2.6500001"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.615051" y="2.6500001"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-21.54,64.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.67,59.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.954788" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.430622" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.945166" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,尽管<gydF4y2Basvg height="13.45" id="M255" style="vertical-align:-2.21957pt;width:71.074997px;" version="1.1" viewbox="0 0 71.074997 13.45" width="71.074997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.977874" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.018263" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.745117" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.908615" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-25.84,68.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-19.35,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。<gydF4y2Babr>(c)任何<gydF4y2Basvg height="15.1625" id="M256" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>——全纯函数<gydF4y2Basvg height="10.325" id="M257" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.325" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>在<gydF4y2Basvg height="10.5375" id="M258" style="vertical-align:-0.16302pt;width:20.975px;" version="1.1" viewbox="0 0 20.975 10.5375" width="20.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,68.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>是单价的<gydF4y2Basvg height="10.5375" id="M259" style="vertical-align:-0.16302pt;width:20.975px;" version="1.1" viewbox="0 0 20.975 10.5375" width="20.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,68.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>。</gydF4y2Baspan></p> <p><span class="statement" id="proof4"><span class="statement-title"><i class="statement-title">证明。</我></span>这句话可以通过简单的计算和证明,因此,留给了读者。</gydF4y2Baspan></p> <p>下面的结果是一个概括的<一个href="#B14">5</一个>定理3)。提到定理可能获得通过<gydF4y2Basvg height="17.924999" id="M260" style="vertical-align:-2.21957pt;width:66.074997px;" version="1.1" viewbox="0 0 66.074997 17.924999" width="66.074997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.925)"> <g transform="translate(72,-57.66)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.2697887" y="2.6500001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.433288" y="2.6500001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.123114" y="2.6500001"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.749943" y="2.6500001"> ≡</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.790333" y="2.6500001"> </gydF4y2Batspan> </text> </g> </g> </svg>在定理<一个href="#thm3.3">3.3</一个>在下面。</gydF4y2Bap> <p><span class="statement" id="thm3.3"><span class="statement-title">定理3.3。</gydF4y2Baspan><i>让<gydF4y2Basvg height="14.3875" id="M261" style="vertical-align:-3.25793pt;width:15.875px;" version="1.1" viewbox="0 0 15.875 14.3875" width="15.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.22,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>是一个函数<gydF4y2Basvg height="15.1625" id="M262" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如在<gydF4y2Basvg height="10.5375" id="M263" style="vertical-align:-0.16302pt;width:20.975px;" version="1.1" viewbox="0 0 20.975 10.5375" width="20.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,68.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>和单价的<gydF4y2Basvg height="15.6875" id="M264" style="vertical-align:-0.16302pt;width:20.975px;" version="1.1" viewbox="0 0 20.975 15.6875" width="20.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.6875)"> <g transform="translate(72,-59.45)"> <g> <path d="m -71.95,70.71 16.68,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,64.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>。那么解决方案<gydF4y2Basvg height="13.55" id="M265" style="vertical-align:-2.29482pt;width:39.962502px;" version="1.1" viewbox="0 0 39.962502 13.55" width="39.962502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.780706" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.694145" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>Polubarinova-Galin方程(<一个href="#EEq1.4">1.5</一个>与初始条件)<gydF4y2Basvg height="14.75" id="M266" style="vertical-align:-3.25793pt;width:96.787498px;" version="1.1" viewbox="0 0 96.787498 14.75" width="96.787498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.780706" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.032206" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.671539" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.711929" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-14.51,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-9.63,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="15.1625" id="M267" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>式为<gydF4y2Basvg height="13.45" id="M268" style="vertical-align:-2.21957pt;width:57.737499px;" version="1.1" viewbox="0 0 57.737499 13.45" width="57.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.922558" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="10.325" id="M269" style="vertical-align:-0.0pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 10.325" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>充气时间,<gydF4y2Basvg height="17.924999" id="M270" style="vertical-align:-4.67863pt;width:228.425px;" version="1.1" viewbox="0 0 228.425 17.924999" width="228.425" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.925)"> <g transform="translate(72,-57.66)"> <text transform="matrix(1,0,0,-1,-71.95,62.37)"> <tspan style="font-size: 12.50px; " x="24.809999" y="0.02"> ⋃</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.765563" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-35.58,58.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="13.110496" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="19.105616" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-7.68,62.37)"> <tspan style="font-size: 12.50px; " x="37.049999" y="0.02"> ⋃</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.379169" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,40.92,58.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="13.110496" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="19.105616" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,68.83,62.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,90.91,67.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,97.4,62.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="15.1625" id="M271" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>是一个全纯函数<gydF4y2Basvg height="15.85" id="M272" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 15.85" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.85)"> <g transform="translate(72,-59.32)"> <g> <path d="m -71.95,70.71 9.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> </text> </g> </g> </svg>满足下列条件:</我><span class="equation" id="EEq3.2"> <svg height="36.549999" id="M273" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 36.549999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,36.55)"> <g transform="translate(72,-42.76)"> <text transform="matrix(1,0,0,-1,77.88,51.7)"> <tspan style="font-size: 12.50px; " x="18.440001" y="-10.87"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.17" y="-8.2200003"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.785288" y="-8.2200003"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.948788" y="-8.2200003"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.463329" y="-8.2200003"> )</gydF4y2Batspan> </text> <g> <path d="m 95.05,54.83 28.47,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,105.03,42.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73.860001" y="-11.4"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.589996" y="-8.75"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.16" y="-8.75"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.187885" y="-8.75"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.439384" y="-8.75"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.618027" y="-8.75"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="64.957527" y="-8.75"> e</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,187.16,60.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,192.72,51.71)"> <tspan style="font-size: 12.50px; " x="59.130001" y="-10.86"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.678042" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.304873" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.345261" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.684761" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.024261" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.860001" y="-8.21"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="69.475288" y="-8.21"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73.638786" y="-8.21"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="82.153328" y="-8.21"> )</gydF4y2Batspan> </text> <g> <path d="m 250.58,54.83 28.47,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,260.56,42.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.68" y="-8.75"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.846138" y="-8.75"> ∀</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.84782" y="-8.75"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.838196" y="-8.75"> ∈</gydF4y2Batspan> </text> <g> <path d="m 326.44,63.04 9.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,326.44,51.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="138.31" y="-2.5599999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="142.4735" y="-2.5599999"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="148.72501" y="-2.5599999"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="151.85075" y="-2.5599999"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="158.10225" y="-2.5599999"> )</gydF4y2Batspan> </text> </g> </g> </svg></span><i></i></span></p> <p><span class="statement" id="proof5"><span class="statement-title"><i class="statement-title">证明。</我></span>通过考虑函数<gydF4y2Basvg height="13.6125" id="M274" style="vertical-align:-2.34499pt;width:122.5125px;" version="1.1" viewbox="0 0 122.5125 13.6125" width="122.5125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.545788" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.586178" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.837677" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.313511" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="64.040367" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.203865" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="74.455368" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="77.931198" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="84.6203" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="89.821548" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="93.734993" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>Polubarinova-Galin方程(<一个href="#EEq1.4">1.5</一个>)可以改写的<gydF4y2Basvg height="13.4875" id="M275" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>如下:<gydF4y2Baspan class="equation" id="EEq3.3"> <svg height="39.362499" id="M276" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 39.362499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,39.3625)"> <g transform="translate(72,-40.51)"> <text transform="matrix(1,0,0,-1,94.38,49.47)"> <tspan style="font-size: 12.50px; " x="23.07" y="-2.73"> ̇</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.98" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.495024" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.658522" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.347626" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.561378" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.474815" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 147.11,62.38 42.74,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,147.11,49.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.6766019" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,162.23,54.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,165.71,49.47)"> <tspan style="font-size: 12.50px; " x="49.41" y="-9.8100004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.169998" y="-11.39"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.169998" y="-8.2299995"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="96.339996" y="-11.39"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="96.339996" y="-8.2299995"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.606625" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.647015" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="61.669998" y="-9.8100004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.18502" y="-9.8100004"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="76.348518" y="-9.8100004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="83.037628" y="-9.8100004"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="88.251381" y="-9.8100004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="92.164818" y="-9.8100004"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,264.55,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</gydF4y2Batspan> </text> <g> <path d="m 215.12,52.6 54.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,235.34,40.72)"> <tspan style="font-size: 12.50px; " x="35.279999" y="-8.75"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.450001" y="-10.34"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.450001" y="-7.1799998"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.950001" y="-8.75"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.639999" y="-10.34"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.639999" y="-7.1799998"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.610001" y="-8.75"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="77.637886" y="-8.75"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="83.889389" y="-8.75"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="229.41" y="-12.41"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="233.5735" y="-12.41"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="239.825" y="-12.41"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="242.95074" y="-12.41"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="249.20226" y="-12.41"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>由于前面的话,函数<gydF4y2Basvg height="13.55" id="M277" style="vertical-align:-2.29482pt;width:39.962502px;" version="1.1" viewbox="0 0 39.962502 13.55" width="39.962502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.780706" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.694145" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.425" id="M278" style="vertical-align:-2.29482pt;width:48.724998px;" version="1.1" viewbox="0 0 48.724998 13.425" width="48.724998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.152436" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.192825" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-39.56,68.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>,是<gydF4y2Basvg height="15.1625" id="M279" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如当且仅当<gydF4y2Basvg height="13.6125" id="M280" style="vertical-align:-2.34499pt;width:38.974998px;" version="1.1" viewbox="0 0 38.974998 13.6125" width="38.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.425" id="M281" style="vertical-align:-2.29482pt;width:40.612499px;" version="1.1" viewbox="0 0 40.612499 13.425" width="40.612499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.152436" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.192825" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,是<gydF4y2Basvg height="10.475" id="M282" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如,之间的关系<gydF4y2Basvg height="15.1625" id="M283" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="10.475" id="M284" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="17.924999" id="M285" style="vertical-align:-2.21957pt;width:114.3625px;" version="1.1" viewbox="0 0 114.3625 17.924999" width="114.3625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.925)"> <g transform="translate(72,-57.66)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.2697887" y="2.6500001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.433288" y="2.6500001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.94783" y="2.6500001"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.574661" y="2.6500001"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.615051" y="2.6500001"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-21.54,64.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.67,59.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.954788" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.430622" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.945166" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,尽管<gydF4y2Basvg height="17.924999" id="M286" style="vertical-align:-2.21957pt;width:218.3625px;" version="1.1" viewbox="0 0 218.3625 17.924999" width="218.3625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.925)"> <g transform="translate(72,-57.66)"> <text transform="matrix(1,0,0,-1,-71.95,59.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.977874" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.018263" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.745117" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.908615" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-25.84,64.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-19.35,59.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3269978" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.490497" y="0"> o</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.741997" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.068995" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.608784" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.772282" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.462109" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.10144" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="70.14183" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,60.48,64.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,66.63,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.2697887" y="2.6500001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.433288" y="2.6500001"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.684788" y="2.6500001"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.160622" y="2.6500001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.850447" y="2.6500001"> )</gydF4y2Batspan> </text> </g> </g> </svg>,尽管<gydF4y2Basvg height="13.6125" id="M287" style="vertical-align:-2.34499pt;width:66.925003px;" version="1.1" viewbox="0 0 66.925003 13.6125" width="66.925003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.153156" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.193544" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.13271" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.296207" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.110825" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.274323" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。因此,它可以证明的功能<gydF4y2Basvg height="13.6125" id="M288" style="vertical-align:-2.34499pt;width:38.974998px;" version="1.1" viewbox="0 0 38.974998 13.6125" width="38.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="10.475" id="M289" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>式为<gydF4y2Basvg height="13.45" id="M290" style="vertical-align:-2.21957pt;width:57.737499px;" version="1.1" viewbox="0 0 57.737499 13.45" width="57.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.922558" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。<gydF4y2Babr>假设相反,前面的表述是不正确的。然后存在<gydF4y2Basvg height="14.75" id="M291" style="vertical-align:-3.25793pt;width:38.3125px;" version="1.1" viewbox="0 0 38.3125 14.75" width="38.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-59.69,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≥</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="17.75" id="M292" style="vertical-align:-3.25793pt;width:55.212502px;" version="1.1" viewbox="0 0 55.212502 17.75" width="55.212502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.75)"> <g transform="translate(72,-57.8)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.26,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.91,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-39.31,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-32,63.92)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>这样,(<一个href="#EEq2.3">2。3</一个>),(<gydF4y2Ba一个href="#EEq2.4">2。4</一个>),(<gydF4y2Ba一个href="#EEq2.5">2。5</一个>),(<gydF4y2Ba一个href="#EEq2.6">2。6</一个>)和(<一个href="#EEq2.6">2。7</一个>)是正确的。与此同时,平等(<一个href="#EEq2.8">2。8</一个>)是实现。我们必须确定函数的符号<gydF4y2Basvg height="16.049999" id="M293" style="vertical-align:-2.73372pt;width:195.4875px;" version="1.1" viewbox="0 0 195.4875 16.049999" width="195.4875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.05)"> <g transform="translate(72,-59.16)"> <text transform="matrix(1,0,0,-1,-71.95,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.540029" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.015863" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.404896" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.318335" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.569836" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.121166" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.284664" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.787666" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.951164" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.64027" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,0.14,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,3.61,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.130791" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.606625" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.146412" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.309914" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.249077" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.412575" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.101681" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="64.31543" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.228874" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.392372" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="76.55587" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>在点<gydF4y2Basvg height="14.75" id="M294" style="vertical-align:-3.25793pt;width:42.487499px;" version="1.1" viewbox="0 0 42.487499 14.75" width="42.487499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.1,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.22,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-47.1,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-42.23,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。<gydF4y2Babr>通过区分(<一个href="#EEq3.3">3.3</一个>)和使用(<一个href="#EEq2.6">2。6</一个>),(<gydF4y2Ba一个href="#EEq2.8">2。8</一个>)和(<一个href="#EEq3.3">3.3</一个>),我们得到<gydF4y2Baspan class="equation" id="eq6"> <svg height="119.3375" id="M295" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 119.3375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,119.3375)"> <g transform="translate(72,23.47)"> <text transform="matrix(1,0,0,-1,-33.65,58.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m -35.61,54.37 10.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-35.61,42.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.58" y="-8.75"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.131332" y="-8.75"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.29483" y="-8.75"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.610001" y="-17.110001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.299107" y="-17.110001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.23827" y="-17.110001"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.851639" y="-17.110001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.015137" y="-17.110001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="64.704239" y="-17.110001"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="69.905487" y="-17.110001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73.818932" y="-17.110001"> )</gydF4y2Batspan> </text> <g> <path d="m -2.78,54.37 48.94,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-2.78,42.49)"> <tspan style="font-size: 12.50px; " x="50.139999" y="-21.01"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.139999" y="-10.34"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.139999" y="0.31999999"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.139999" y="3.49"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.642452" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.805952" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.482553" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.696304" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.609745" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.773243" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,49.86,36.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.6735678" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.668688" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,65.22,34.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,68.84,36.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.9273758" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.922496" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,82.51,34.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-14.6,-0.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.209999" y="-9.8100004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.969999" y="-11.39"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.969999" y="-8.2299995"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.469999" y="-9.8100004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.91" y="-11.39"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.91" y="-8.2299995"> |</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,26.81,15.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</gydF4y2Batspan> </text> <g> <path d="m -0.17,2.2 35.64,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-0.17,-13.36)"> <tspan style="font-size: 12.50px; " x="13.85" y="-1.59"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.85" y="1.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.35" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,24.62,-8.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,28.09,-11.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="3.1700001"> |</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,30.59,-6.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,38.75,-0.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.059999" y="7.3200002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.411524" y="7.3200002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.98" y="-8.3599997"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.669106" y="-8.3599997"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,88.86,12.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 73.73,2.2 21.58,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,78.56,-10.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,87,-5.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,99.28,-0.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.54" y="-8.3599997"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,121.36,12.43)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,126.92,7.43)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.590521" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.842022" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.531126" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,160.9,12.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 111.82,2.2 52.55,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,123.9,-9.68)"> <tspan style="font-size: 12.50px; " x="41.669998" y="-1.4299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.218311" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.82" y="-8.75"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.160217" y="-8.75"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73.499725" y="-8.75"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="77.663223" y="-8.75"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="95.57" y="-17.110001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="102.2466" y="-17.110001"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,234.6,12.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 214.57,2.2 28.39,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,214.57,-9.68)"> <tspan style="font-size: 12.50px; " x="31.67" y="-1.4299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.218311" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.049999" y="-8.75"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.3895" y="-8.75"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.016331" y="-8.75"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,281.14,4.08)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,286.69,-0.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.603024" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.542189" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.88241" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.221912" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.561413" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.400002" y="-8.3500004"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.015289" y="-8.3500004"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.178787" y="-8.3500004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="80.618309" y="-8.3500004"> )</gydF4y2Batspan> </text> <g> <path d="m 343.09,2.2 28.39,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,353.06,-9.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.34" y="-26.34"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.34" y="-15.67"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.34" y="-5.0100002"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.34" y="5.6599998"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.34" y="8.8199997"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.610001" y="-1.4299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.987249" y="-1.4299999"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,390.9,-21.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.6823201" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.67744" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,406.26,-23.34)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,409.89,-21.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.9273758" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.922496" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,423.55,-23.34)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,427.67,-0.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.080002" y="-22.07"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.2435" y="-22.07"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.494999" y="-22.07"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.62075" y="-22.07"> 4</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.87225" y="-22.07"> )</gydF4y2Batspan> </text> </g> </g> </svg></span><br>右边的平等是严格负的(<一个href="#EEq2.5">2。5</一个>),(<gydF4y2Ba一个href="#EEq2.6">2。7</一个>),<ggydF4y2BaydF4y2Basvg height="15.475" id="M296" style="vertical-align:-2.34499pt;width:85.25px;" version="1.1" viewbox="0 0 85.25 15.475" width="85.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.475)"> <g transform="translate(72,-59.62)"> <text transform="matrix(1,0,0,-1,-71.95,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.054333" y="0"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-44.35,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-40.88,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.729494" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.769882" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.6125" id="M297" style="vertical-align:-2.34499pt;width:101.7375px;" version="1.1" viewbox="0 0 101.7375 13.6125" width="101.7375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.129829" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.669619" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.833118" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.772282" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.935783" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.411617" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.35078" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.990112" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.030502" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>(前面的简单的后果是不平等<一个href="#EEq3.2">3.2</一个>))。因此,<gydF4y2Basvg height="17.0875" id="M298" style="vertical-align:-2.73372pt;width:220.7625px;" version="1.1" viewbox="0 0 220.7625 17.0875" width="220.7625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.0875)"> <g transform="translate(72,-58.33)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.129829" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.293329" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-42.09,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-34.28,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-25.84,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-22.37,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-12.64,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-4.84,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.1271896" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.290689" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.766523" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.306313" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.46981" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.408978" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.572475" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,42.3,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,50.1,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.278186" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.081018" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.121407" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.723232" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.199066" y="0"> 2</gydF4y2Batspan> </text> </g> </g> </svg>,因为<gydF4y2Basvg height="13.05" id="M299" style="vertical-align:-3.25793pt;width:35.387501px;" version="1.1" viewbox="0 0 35.387501 13.05" width="35.387501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-48.61,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>(接近<gydF4y2Basvg height="13.05" id="M300" style="vertical-align:-3.25793pt;width:11.1125px;" version="1.1" viewbox="0 0 11.1125 13.05" width="11.1125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>在某些地段)<gydF4y2Basvg height="14.625" id="M301" style="vertical-align:-3.25793pt;width:14.4125px;" version="1.1" viewbox="0 0 14.4125 14.625" width="14.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.4,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。这一矛盾就完成了证明。</gydF4y2Baspan></p> <p>下面的结果是一个概括的<一个href="#B15">6</一个>定理3.1)。提到定理可能获得通过<gydF4y2Basvg height="17.924999" id="M302" style="vertical-align:-2.21957pt;width:66.074997px;" version="1.1" viewbox="0 0 66.074997 17.924999" width="66.074997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.925)"> <g transform="translate(72,-57.66)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.2697887" y="2.6500001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.433288" y="2.6500001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.123114" y="2.6500001"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.749943" y="2.6500001"> ≡</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.790333" y="2.6500001"> </gydF4y2Batspan> </text> </g> </g> </svg>在定理<一个href="#thm3.4">3.4</一个>在下面。</gydF4y2Bap> <p><span class="statement" id="thm3.4"><span class="statement-title">定理3.4。</gydF4y2Baspan><i>让<gydF4y2Basvg height="13.0625" id="M303" style="vertical-align:-1.90608pt;width:39.537498px;" version="1.1" viewbox="0 0 39.537498 13.0625" width="39.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0625)"> <g transform="translate(72,-61.55)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.228174" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.268562" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,让表面张力<gydF4y2Basvg height="9.9375" id="M304" style="vertical-align:-2.34499pt;width:8.0625px;" version="1.1" viewbox="0 0 8.0625 9.9375" width="8.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.9375)"> <g transform="translate(72,-64.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是足够小。如果<gydF4y2Basvg height="14.3875" id="M305" style="vertical-align:-3.25793pt;width:15.875px;" version="1.1" viewbox="0 0 15.875 14.3875" width="15.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.22,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>是一个函数<gydF4y2Basvg height="15.1625" id="M306" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如在<gydF4y2Basvg height="10.5375" id="M307" style="vertical-align:-0.16302pt;width:20.975px;" version="1.1" viewbox="0 0 20.975 10.5375" width="20.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,68.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>和单价的<gydF4y2Basvg height="15.6875" id="M308" style="vertical-align:-0.16302pt;width:20.975px;" version="1.1" viewbox="0 0 20.975 15.6875" width="20.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.6875)"> <g transform="translate(72,-59.45)"> <g> <path d="m -71.95,70.71 16.68,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,64.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>,然后存在<gydF4y2Basvg height="13.6125" id="M309" style="vertical-align:-2.34499pt;width:53.849998px;" version="1.1" viewbox="0 0 53.849998 13.6125" width="53.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="3.913439" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.415959" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.055292" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.09568" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>这样的解决方案<gydF4y2Basvg height="13.55" id="M310" style="vertical-align:-2.29482pt;width:39.962502px;" version="1.1" viewbox="0 0 39.962502 13.55" width="39.962502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.780706" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.694145" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>(<一个href="#EEq1.5">1.6</一个>与初始条件)<gydF4y2Basvg height="14.75" id="M311" style="vertical-align:-3.25793pt;width:96.787498px;" version="1.1" viewbox="0 0 96.787498 14.75" width="96.787498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.780706" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.032206" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.671539" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.711929" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-14.51,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-9.63,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="15.1625" id="M312" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>式为<gydF4y2Basvg height="13.6125" id="M313" style="vertical-align:-2.34499pt;width:72.375px;" version="1.1" viewbox="0 0 72.375 13.6125" width="72.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.959347" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.122849" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.474373" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.637871" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="10.325" id="M314" style="vertical-align:-0.0pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 10.325" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>充气时间,<gydF4y2Basvg height="18.85" id="M315" style="vertical-align:-5.41599pt;width:245.425px;" version="1.1" viewbox="0 0 245.425 18.85" width="245.425" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.85)"> <g transform="translate(72,-56.92)"> <text transform="matrix(1,0,0,-1,-71.95,62.37)"> <tspan style="font-size: 12.50px; " x="24.809999" y="0.02"> ⋃</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.765563" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-35.58,58.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="13.110496" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="19.105616" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="21.844992" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="24.759409" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="29.196672" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-0.88,62.37)"> <tspan style="font-size: 12.50px; " x="37.049999" y="0.02"> ⋃</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.379169" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,47.72,58.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="13.110496" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="19.105616" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="21.844992" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="24.759409" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="29.205423" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,82.43,62.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,104.51,67.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,111,62.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="15.1625" id="M316" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>是一个全纯函数<gydF4y2Basvg height="15.85" id="M317" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 15.85" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.85)"> <g transform="translate(72,-59.32)"> <g> <path d="m -71.95,70.71 9.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> </text> </g> </g> </svg>满足的条件(<一个href="#EEq3.2">3.2</一个>)。</我></span></p> <p><span class="statement" id="proof6"><span class="statement-title"><i class="statement-title">证明。</我></span>我们引入了(如定理的证明<一个href="#thm3.3">3.3</一个>)函数<gydF4y2Basvg height="13.6125" id="M318" style="vertical-align:-2.34499pt;width:174.72501px;" version="1.1" viewbox="0 0 174.72501 13.6125" width="174.72501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.545788" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.586178" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.837677" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.313511" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="64.040367" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.203865" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="74.455368" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="77.931198" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="84.6203" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="89.821548" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="93.734993" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="97.898491" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="107.27574" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="117.44068" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="129.48106" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,这是<gydF4y2Basvg height="10.475" id="M319" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如<gydF4y2Basvg height="17.924999" id="M320" style="vertical-align:-2.21957pt;width:129.175px;" version="1.1" viewbox="0 0 129.175 17.924999" width="129.175" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.925)"> <g transform="translate(72,-57.66)"> <text transform="matrix(1,0,0,-1,-71.95,59.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.866787" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.556612" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.183441" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.223831" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-15.03,64.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-8.89,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.26" y="2.6500001"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.279789" y="2.6500001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.443288" y="2.6500001"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.694788" y="2.6500001"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.170622" y="2.6500001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.860447" y="2.6500001"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.023945" y="2.6500001"> )</gydF4y2Batspan> </text> </g> </g> </svg>当且仅当<gydF4y2Basvg height="13.55" id="M321" style="vertical-align:-2.29482pt;width:39.962502px;" version="1.1" viewbox="0 0 39.962502 13.55" width="39.962502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.780706" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.694145" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="15.1625" id="M322" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>的地方。<gydF4y2Babr>Polubarinova-Galin方程可以写成的<gydF4y2Basvg height="13.4875" id="M323" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>作为<gydF4y2Baspan class="equation" id="EEq3.4"> <svg height="38.575001" id="M324" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.575001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,38.575)"> <g transform="translate(72,-41.14)"> <text transform="matrix(1,0,0,-1,46.73,53.45)"> <tspan style="font-size: 12.50px; " x="23.07" y="-2.72"> ̇</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.97" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.485023" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.648521" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.337627" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.551376" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.464817" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 99.45,66.35 44.82,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,99.45,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.6766019" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,114.58,58.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,120.13,53.45)"> <tspan style="font-size: 12.50px; " x="48.220001" y="-1.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.220001" y="1.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.720001" y="7.1054274e-015"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.16" y="-1.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.16" y="1.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.606625" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.647015" y="0"> −</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,181.79,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,188.75,46.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.61" y="-15.24"> </gydF4y2Batspan> </text> <g> <path d="m 199.32,56.57 13.85,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,199.32,44.69)"> <tspan style="font-size: 12.50px; " x="49.650002" y="-3.8399999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.380001" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.83" y="-8.7600002"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.157719" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.509243" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="60.470001" y="-16.01"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.846527" y="-16.01"> </gydF4y2Batspan> </text> <g> <path d="m 259.79,56.57 13.16,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,259.9,44.69)"> <tspan style="font-size: 12.50px; " x="14.25" y="-3.8399999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.950001" y="-1.4299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.41" y="-8.7600002"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73.550003" y="-10.34"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73.550003" y="-7.1799998"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="76.050003" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="82.739998" y="-10.34"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="82.739998" y="-7.1799998"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.07" y="-8.7600002"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.2335" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.785072" y="-8.7600002"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="88.709999" y="-8.7600002"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="100.73788" y="-8.7600002"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="106.98939" y="-8.7600002"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="204.85001" y="-8.7600002"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="209.0135" y="-8.7600002"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="215.265" y="-8.7600002"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="218.39075" y="-8.7600002"> 5</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="224.64224" y="-8.7600002"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>相反,假设定理的结论<一个href="#thm3.4">3.4</一个>是不正确的。然后存在<gydF4y2Basvg height="14.75" id="M325" style="vertical-align:-3.25793pt;width:38.3125px;" version="1.1" viewbox="0 0 38.3125 14.75" width="38.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-59.69,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≥</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="17.75" id="M326" style="vertical-align:-3.25793pt;width:55.212502px;" version="1.1" viewbox="0 0 55.212502 17.75" width="55.212502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.75)"> <g transform="translate(72,-57.8)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.26,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.91,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-39.31,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-32,63.92)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>这样,(<一个href="#EEq2.3">2。3</一个>),(<gydF4y2Ba一个href="#EEq2.4">2。4</一个>),(<gydF4y2Ba一个href="#EEq2.5">2。5</一个>),(<gydF4y2Ba一个href="#EEq2.6">2。6</一个>)和(<一个href="#EEq2.6">2。7</一个>)是正确的。与此同时,平等(<一个href="#EEq2.8">2。8</一个>)是实现。我们区分(<一个href="#EEq3.4">3.5</一个>)对<gydF4y2Basvg height="10.7375" id="M327" style="vertical-align:-0.13794pt;width:8.3125px;" version="1.1" viewbox="0 0 8.3125 10.7375" width="8.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。因为左边是可微的对<gydF4y2Basvg height="10.7375" id="M328" style="vertical-align:-0.13794pt;width:8.3125px;" version="1.1" viewbox="0 0 8.3125 10.7375" width="8.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>的解决方案(<一个href="#EEq3.4">3.5</一个>)存在,而且是独一无二的,那么右边是可微的,它的导数是有界的<gydF4y2Basvg height="13.125" id="M329" style="vertical-align:-1.95624pt;width:42.174999px;" version="1.1" viewbox="0 0 42.174999 13.125" width="42.174999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.125)"> <g transform="translate(72,-61.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.867746" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.46957" y="0"> ]</gydF4y2Batspan> </text> </g> </g> </svg>。<gydF4y2Babr>如果我们表示<gydF4y2Basvg height="13.45" id="M330" style="vertical-align:-2.21957pt;width:184.125px;" version="1.1" viewbox="0 0 184.125 13.45" width="184.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.9646511" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.12815" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.88097" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.794409" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.433743" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.474133" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.63763" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.026665" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.502499" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.891533" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.4431" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="79.606598" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="90.521721" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="94.685219" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="98.573654" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="104.96268" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="111.73931" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="115.21514" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="121.60418" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="128.15575" y="0"> ]</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="132.31924" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="136.48274" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="143.03432" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>;然后通过使用(<一个href="#EEq2.6">2。6</一个>),(<gydF4y2Ba一个href="#EEq2.8">2。8</一个>)和(<一个href="#EEq3.4">3.5</一个>),我们得到<gydF4y2Baspan class="equation" id="eq7"> <svg height="237.47501" id="M331" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 237.47501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,237.475)"> <g transform="translate(72,117.98)"> <text transform="matrix(1,0,0,-1,-4.06,58.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m -6.02,54.37 10.31,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-6.02,42.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.59" y="-8.75"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.141333" y="-8.75"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.304831" y="-8.75"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.93" y="-17.110001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.619106" y="-17.110001"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,45.04,64.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,48.52,59.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 26.81,54.37 48.95,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,26.81,42.49)"> <tspan style="font-size: 12.50px; " x="50.139999" y="-21.01"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.139999" y="-10.34"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.139999" y="0.31999999"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.139999" y="3.49"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.642452" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.805952" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.495056" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.696304" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.609745" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.773243" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,79.45,36.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.6823201" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.67744" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,94.81,34.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,98.44,36.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,108.33,39.4)"> <tspan style="font-size: 6.25px; " x="5.2199998" y="1.97"> 0</gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="1.9443721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,117.67,36.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.9273758" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.922496" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,131.33,34.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,14.99,2.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.97" y="-11.39"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.97" y="-8.2200003"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.469999" y="-9.8000002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.91" y="-11.39"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.91" y="-8.2200003"> |</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,43.4,19.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</gydF4y2Batspan> </text> <g> <path d="m 28.23,5.76 21.78,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,28.23,-8.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="3.1700001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="2.5" y="1.59"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,39.17,-4.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,42.64,-8.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="3.1700001"> |</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,45.14,-3.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,53.29,-4.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.62" y="-15.24"> </gydF4y2Batspan> </text> <g> <path d="m 63.87,5.76 13.85,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,63.87,-6.12)"> <tspan style="font-size: 12.50px; " x="49.639999" y="-3.8399999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.009998" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.82" y="-8.7600002"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.160221" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.511745" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.09" y="-16.01"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.479034" y="-16.01"> </gydF4y2Batspan> </text> <g> <path d="m 125.96,5.76 13.17,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,126.07,-6.12)"> <tspan style="font-size: 12.50px; " x="14.25" y="-3.8399999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.82" y="-1.4299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-101.81" y="37.139999"> ×</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-89.830002" y="44.470001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-65.419998" y="44.470001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.940001" y="-8.7600002"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.103498" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.642567" y="-8.7600002"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-83.480003" y="37.139999"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-79.316498" y="37.139999"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-54.849998" y="28.790001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-48.173397" y="28.790001"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,86.35,-29.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 71.22,-40.14 21.58,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,76.05,-53.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,84.49,-47.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,96.77,-43.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.54" y="-8.3500004"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,118.85,-29.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,124.41,-34.9)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.590521" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.842022" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.531126" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,158.39,-29.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 109.31,-40.14 52.55,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,121.39,-52.01)"> <tspan style="font-size: 12.50px; " x="41.669998" y="-1.42"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.218311" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.82" y="-8.75"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.160217" y="-8.75"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="69.323723" y="-8.75"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="87.230003" y="-17.1"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="93.906601" y="-17.1"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,223.75,-29.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 203.73,-40.14 28.39,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,203.73,-52.01)"> <tspan style="font-size: 12.50px; " x="31.67" y="-1.42"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.218311" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.040001" y="-8.75"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.366997" y="-8.75"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.706497" y="-8.75"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.345833" y="-8.75"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,278.62,-38.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,284.18,-43.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.603024" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.542189" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.88241" y="0"> 4</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.221912" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.561413" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.389999" y="-8.3500004"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.017792" y="-8.3500004"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.18129" y="-8.3500004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="80.620811" y="-8.3500004"> )</gydF4y2Batspan> </text> <g> <path d="m 340.57,-40.14 28.39,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,350.55,-52.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.34" y="-21"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.34" y="-10.34"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.34" y="0.33000001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.34" y="3.49"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.610001" y="-1.42"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.987249" y="-1.42"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,388.39,-58.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.6735678" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.668688" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,403.75,-60.34)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,407.37,-58.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.9273758" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.922496" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,421.04,-60.34)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,24.26,-95.43)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.47" y="-11.39"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.47" y="-8.2200003"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.969999" y="-9.8000002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.41" y="-11.39"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.41" y="-8.2200003"> |</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,53.17,-78.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</gydF4y2Batspan> </text> <g> <path d="m 37.99,-92.31 21.79,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,37.99,-106.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="2.5" y="1.59"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,48.93,-102.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,52.41,-106.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,54.91,-101.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,63.76,-95.43)"> <tspan style="font-size: 12.50px; " x="47.75" y="-17.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.75" y="-6.9200001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.75" y="3.75"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.75" y="14.41"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.75" y="17.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3390212" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.690545" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.743196" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.906696" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.458267" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.67202" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.585457" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,114.01,-115.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.6823201" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.67744" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,129.37,-117.84)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,133,-115.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.9273758" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.922496" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,146.66,-117.84)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,150.78,-95.43)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="313.97" y="-69.309998"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="318.13348" y="-69.309998"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="324.38501" y="-69.309998"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="327.51074" y="-69.309998"> 6</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="333.76224" y="-69.309998"> )</gydF4y2Batspan> </text> </g> </g> </svg></span><br>右边的平等是严格-小<gydF4y2Basvg height="9.9375" id="M332" style="vertical-align:-2.34499pt;width:8.0625px;" version="1.1" viewbox="0 0 8.0625 9.9375" width="8.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.9375)"> <g transform="translate(72,-64.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>因为(<一个href="#EEq2.5">2。5</一个>),(<gydF4y2Ba一个href="#EEq2.6">2。7</一个>),<ggydF4y2BaydF4y2Basvg height="15.475" id="M333" style="vertical-align:-2.34499pt;width:82.650002px;" version="1.1" viewbox="0 0 82.650002 15.475" width="82.650002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.475)"> <g transform="translate(72,-59.62)"> <text transform="matrix(1,0,0,-1,-71.95,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-46.44,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-42.96,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.729494" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.769882" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.6125" id="M334" style="vertical-align:-2.34499pt;width:101.7375px;" version="1.1" viewbox="0 0 101.7375 13.6125" width="101.7375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.129829" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.669619" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.833118" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.772282" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.935783" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.411617" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.35078" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.990112" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.030502" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。因此,<gydF4y2Basvg height="17.0875" id="M335" style="vertical-align:-2.73372pt;width:223.3625px;" version="1.1" viewbox="0 0 223.3625 17.0875" width="223.3625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.0875)"> <g transform="translate(72,-58.33)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.205328" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.368828" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-40,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-32.2,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-23.76,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-20.29,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-10.56,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-2.75,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.278186" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.754021" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.29381" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.457308" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.396473" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.559971" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,44.38,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,52.19,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.278186" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.081018" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.121407" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.723232" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.199066" y="0"> 2</gydF4y2Batspan> </text> </g> </g> </svg>,因为<gydF4y2Basvg height="13.05" id="M336" style="vertical-align:-3.25793pt;width:35.387501px;" version="1.1" viewbox="0 0 35.387501 13.05" width="35.387501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-48.61,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>(接近<gydF4y2Basvg height="13.05" id="M337" style="vertical-align:-3.25793pt;width:11.1125px;" version="1.1" viewbox="0 0 11.1125 13.05" width="11.1125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>在某些地段)<gydF4y2Basvg height="14.625" id="M338" style="vertical-align:-3.25793pt;width:14.4125px;" version="1.1" viewbox="0 0 14.4125 14.625" width="14.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.4,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。这一矛盾就完成了证明。</gydF4y2Baspan></p> <p><span class="statement" id="rem3.5"><span class="statement-title"><i class="statement-title">3.5的话。</我></span>让<gydF4y2Basvg height="13.0625" id="M339" style="vertical-align:-1.90608pt;width:39.537498px;" version="1.1" viewbox="0 0 39.537498 13.0625" width="39.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0625)"> <g transform="translate(72,-61.55)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.228174" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.268562" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,让<gydF4y2Basvg height="14.3875" id="M340" style="vertical-align:-3.25793pt;width:15.875px;" version="1.1" viewbox="0 0 15.875 14.3875" width="15.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.22,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>是一个函数<gydF4y2Basvg height="15.1625" id="M341" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如在<gydF4y2Basvg height="10.5375" id="M342" style="vertical-align:-0.16302pt;width:20.975px;" version="1.1" viewbox="0 0 20.975 10.5375" width="20.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,68.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>和单价的<gydF4y2Basvg height="15.6875" id="M343" style="vertical-align:-0.16302pt;width:20.975px;" version="1.1" viewbox="0 0 20.975 15.6875" width="20.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.6875)"> <g transform="translate(72,-59.45)"> <g> <path d="m -71.95,70.71 16.68,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,64.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>。如果<gydF4y2Basvg height="14.3875" id="M344" style="vertical-align:-3.25793pt;width:15.875px;" version="1.1" viewbox="0 0 15.875 14.3875" width="15.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.22,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>满足条件(<一个href="#EEq3.1">3.1</一个>)为每一个<gydF4y2Basvg height="18.35" id="M345" style="vertical-align:-2.29482pt;width:48.724998px;" version="1.1" viewbox="0 0 48.724998 18.35" width="48.724998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.35)"> <g transform="translate(72,-57.32)"> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.152436" y="0"> ∈</gydF4y2Batspan> </text> <g> <path d="m -49.75,70.71 16.68,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-49.75,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-39.56,64.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>,然后存在表面张力<gydF4y2Basvg height="9.9375" id="M346" style="vertical-align:-2.34499pt;width:8.0625px;" version="1.1" viewbox="0 0 8.0625 9.9375" width="8.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.9375)"> <g transform="translate(72,-64.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>(这取决于<gydF4y2Basvg height="14.3875" id="M347" style="vertical-align:-3.25793pt;width:15.875px;" version="1.1" viewbox="0 0 15.875 14.3875" width="15.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.22,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>)足够小,<gydF4y2Basvg height="13.6125" id="M348" style="vertical-align:-2.34499pt;width:53.849998px;" version="1.1" viewbox="0 0 53.849998 13.6125" width="53.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="3.913439" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.415959" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.055292" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.09568" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>这样经典的解决方案<gydF4y2Basvg height="13.55" id="M349" style="vertical-align:-2.29482pt;width:39.962502px;" version="1.1" viewbox="0 0 39.962502 13.55" width="39.962502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.780706" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.694145" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>(<一个href="#EEq1.5">1.6</一个>与初始条件)<gydF4y2Basvg height="14.75" id="M350" style="vertical-align:-3.25793pt;width:107.2125px;" version="1.1" viewbox="0 0 107.2125 14.75" width="107.2125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.780706" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.032206" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.835037" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.038925" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-6.17,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-1.3,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="15.1625" id="M351" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>式为<gydF4y2Basvg height="13.6125" id="M352" style="vertical-align:-2.34499pt;width:72.375px;" version="1.1" viewbox="0 0 72.375 13.6125" width="72.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.959347" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.122849" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.474373" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.637871" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<我>T</gydF4y2Ba我>充气时间。</gydF4y2Baspan></p> <p><span class="statement" id="proof7"><span class="statement-title"><i class="statement-title">证明。</我></span>结论是直接从古典解的光滑性(<一个href="#EEq1.5">1.6</一个>)</ggydF4y2BaydF4y2Baspan></p> <h4 id="acknowledgments">确认</h4><gydF4y2Bap>作者感谢加芙Kohr暗示这个话题和有价值的讨论在本文的准备。Denisa Fericean支持合同编号。POSDRU / 88/1.5 / S / 60185——“知识型社会”创新的博士研究。作者感谢裁判有用的建议,改善纸张的方面。</gydF4y2Bap> </div> </div> <div class="ArticleReferences_xmlContent__p_40j"> <h4 class="ArticleReferences_references__GH2t_" id="references">引用</h4><olcl作为s="ArticleReferences_orderedReferences__mJr9M"> <li class="ArticleReferences_articleReference__ouEuh" id="B5"> <div class="referenceContent"> <p class="referenceText">y . e . Hohlov d . v .普罗霍罗夫,a . j .主席Vasil“自由边界的几何性质Hele-Shaw流移动边界问题,“<我>Lobachevskii数学杂志</我>,卷1,3 - 12,1998页。</gydF4y2Bap>视图:<gydF4y2Ba!-- --> <a href="https://scholar.google.com/scholar_lookup?title=On%20geometrical%20properties%20of%20free%20boundaries%20in%20the%20Hele-Shaw%20flows%20moving%20boundary%20problem&author=Y.%20E.%20Hohlov&author=D.%20V.%20Prokhorov&author=A.%20J.%20Vasil%E2%80%99ev&publication_year=1998" target="_blank" rel="noreferrer">谷歌学术搜索</一个></div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B7"> <div class="referenceContent"> <p class="referenceText">k . Kornev和a .主席Vasil几何Hele-Shaw类型方程的解的性质,“<我>美国数学学会学报》上</我>,卷128,不。9日,第2685 - 2683页,2000年。</gydF4y2Bap>视图:<gydF4y2Ba!-- --> <a href="https://doi.org/10.1090/S0002-9939-00-05348-X" target="_blank" rel="noreferrer">出版商的网站</一个><span class="sep">|</gydF4y2Baspan> <a href="https://scholar.google.com/scholar_lookup?title=Geometric%20properties%20of%20the%20solutions%20of%20a%20Hele-Shaw%20type%20equation&author=K.%20Kornev&author=A.%20Vasil%E2%80%99ev&publication_year=2000" target="_blank" rel="noreferrer">谷歌学术搜索</一个><span class="sep">|</gydF4y2Baspan> <a href="https://www.zentralblatt-math.org/zmath/en/advanced/?q=an:0956.35110" target="_blank" rel="noreferrer">Zentralblatt数学</一个></div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B11"> <div class="referenceContent"> <p class="referenceText">d·普罗霍罗夫和a .主席Vasil凸Hele-Shaw细胞动力学”,<我>国际数学和数学科学杂志》上</我>没有,卷。31日。11日,第650 - 639页,2002年。</gydF4y2Bap>视图:<gydF4y2Ba!-- --> <a href="https://doi.org/10.1155/S0161171202203142" target="_blank" rel="noreferrer">出版商的网站</一个><span class="sep">|</gydF4y2Baspan> <a href="https://scholar.google.com/scholar_lookup?title=Convex%20dynamics%20in%20Hele-Shaw%20cells&author=D.%20Prokhorov&author=A.%20Vasil'ev&publication_year=2002" target="_blank" rel="noreferrer">谷歌学术搜索</一个><span class="sep">|</gydF4y2Baspan> <a href="https://www.zentralblatt-math.org/zmath/en/advanced/?q=an:1023.30018" target="_blank" rel="noreferrer">Zentralblatt数学</一个></div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B13"> <div class="referenceContent"> <p class="referenceText">a . Vasil主席”,在粘性流动的动力学,单价的功能”<我>理论计算方法和功能</我>,1卷,不。2、311 - 337年,2001页。</gydF4y2Bap>视图:<gydF4y2Ba!-- --> <a href="https://scholar.google.com/scholar_lookup?title=Univalent%20functions%20in%20the%20dynamics%20of%20viscous%20flows&author=A.%20Vasil%E2%80%99ev&publication_year=2001" target="_blank" rel="noreferrer">谷歌学术搜索</一个></div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B14"> <div class="referenceContent"> <p class="referenceText">a . Vasil主席,“在二维自由边界问题,单价的功能”<我>Acta Applicandae Mathematicae</gydF4y2Ba我>,卷79,不。3、249 - 280年,2003页。</gydF4y2Bap>视图:<gydF4y2Ba!-- --> <a href="https://doi.org/10.1023/B:ACAP.0000003674.35389.bb" target="_blank" rel="noreferrer">出版商的网站</一个><span class="sep">|</gydF4y2Baspan> <a href="https://scholar.google.com/scholar_lookup?title=Univalent%20functions%20in%20two-dimensional%20free%20boundary%20problems&author=A.%20Vasil%E2%80%99ev&publication_year=2003" target="_blank" rel="noreferrer">谷歌学术搜索</一个></div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B15"> <div class="referenceContent"> <p class="referenceText">a . Vasil主席和i Markina Hele-Shaw流动的几何形状和表面张力小,”<我>接口和自由边界</我>,5卷,不。2、183 - 192年,2003页。</gydF4y2Bap>视图:<gydF4y2Ba!-- --> <a href="https://doi.org/10.4171/IFB/77" target="_blank" rel="noreferrer">出版商的网站</一个><span class="sep">|</gydF4y2Baspan> <a href="https://scholar.google.com/scholar_lookup?title=On%20the%20geometry%20of%20Hele-Shaw%20flows%20with%20small%20surface%20tension&author=A.%20Vasil%E2%80%99ev&author=I.%20Markina&publication_year=2003" target="_blank" rel="noreferrer">谷歌学术搜索</一个></div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B2"> <div class="referenceContent"> <p class="referenceText">洛杉矶Galin,“不稳定与自由表面过滤,”<我>研究Doklady Akademii苏联</我>47卷,第249 - 246页,1945年。</gydF4y2Bap>视图:<gydF4y2Ba!-- --> <a href="https://scholar.google.com/scholar_lookup?title=Unsteady%20filtration%20with%20a%20free%20surface&author=L.%20A.%20Galin&publication_year=1945" target="_blank" rel="noreferrer">谷歌学术搜索</一个><span class="sep">|</gydF4y2Baspan> <a href="https://www.zentralblatt-math.org/zmath/en/advanced/?q=an:0061.46202" target="_blank" rel="noreferrer">Zentralblatt数学</一个></div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B8"> <div class="referenceContent"> <p class="referenceText">p . y . Polubarinova-Kochina”问题的运动轮廓的石油壳,”<我>研究Doklady Akademii苏联</我>47卷,第257 - 254页,1945年(俄罗斯)。</gydF4y2Bap>视图:<gydF4y2Ba!-- --> <a href="https://scholar.google.com/scholar_lookup?title=On%20a%20problem%20of%20the%20motion%20of%20the%20contour%20of%20a%20petroleum%20shell&author=P.%20Y.%20Polubarinova-Kochina&publication_year=1945" target="_blank" rel="noreferrer">谷歌学术搜索</一个></div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B9"> <div class="referenceContent"> <p class="referenceText">p . j . Poloubarinova-Kochina“过滤理论关于不稳定运动”,9卷,没有。1,第90 - 79页,1945年(俄罗斯)。</gydF4y2Bap>视图:<gydF4y2Ba!-- --> <a href="https://scholar.google.com/scholar_lookup?title=Concerning%20unsteady%20motions%20in%20the%20theory%20of%20filtration&author=P.%20J.%20Poloubarinova-Kochina&publication_year=1945" target="_blank" rel="noreferrer">谷歌学术搜索</一个></div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B16"> <div class="referenceContent"> <p class="referenceText">y . p . Vinogradov和p . p . Kufarev过滤的问题。”<我>研究Akademii苏联</我>》12卷,第198 - 181页,1948年(俄罗斯)。</gydF4y2Bap>视图:<gydF4y2Ba!-- --> <a href="https://scholar.google.com/scholar_lookup?title=On%20a%20problem%20of%20filtration&author=Y.%20P.%20Vinogradov&author=P.%20P.%20Kufarev&publication_year=1948" target="_blank" rel="noreferrer">谷歌学术搜索</一个></div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B4"> <div class="referenceContent"> <p class="referenceText">b . Gustafsson和a .主席Vasil<我>正形和潜力分析Hele-Shaw细胞</我>数学流体力学的发展,Birkhauser, 2006年在瑞士巴塞尔。</gydF4y2Bap> </div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B1"> <div class="referenceContent"> <p class="referenceText">l . Brickman。”<米一个th id="M353" xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mover accent="true"> <mi mathvariant="normal"> Φ</米我><米o>˜</gydF4y2Ba米o></米over> </mrow> </math>——解析函数”,<我>《美国数学学会</我>卷,79年,第558 - 555页,1973年。</gydF4y2Bap>视图:<gydF4y2Ba!-- --> <a href="https://doi.org/10.1090/S0002-9904-1973-13200-8" target="_blank" rel="noreferrer">出版商的网站</一个><span class="sep">|</gydF4y2Baspan> <a href="https://scholar.google.com/scholar_lookup?title=%CE%A6%CB%9C-like%20analytic%20functions%E2%80%94I&author=L.%20Brickman&publication_year=1973" target="_blank" rel="noreferrer">谷歌学术搜索</一个><span class="sep">|</gydF4y2Baspan> <a href="https://www.zentralblatt-math.org/zmath/en/advanced/?q=an:0273.30010" target="_blank" rel="noreferrer">Zentralblatt数学</一个></div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B3"> <div class="referenceContent"> <p class="referenceText">格雷厄姆和g . Kohr,<我>几何函数理论和更高的维度</我>卷,255<我>专著和教科书纯粹与应用数学</我>,马塞尔·德克,纽约,纽约,美国,2003年。</gydF4y2Bap> </div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B10"> <div class="referenceContent"> <p class="referenceText">c . Pommerenke<我>单价的功能</我>德国哥廷根,Vandenhoeck &鲁普雷希特,1975年。</gydF4y2Bap> </div></li> </ol> </div> <h4 class="copyright-title" id="copyright">版权</h4><gydF4y2Badiv class="copyright-body"> 版权©2011 Paula Curt Denisa Fericean。这是一个开放的分布式下文章<一个rel="license" href="http://creativecommons.org/licenses/by/3.0/">知识共享归属许可</一个>,它允许无限制的使用、分配和复制在任何媒介,提供最初的工作是正确引用。</gydF4y2Badiv> <div id="related-articles"></div> </div> </div> <div class="ant-col ThreeColumnLayout_rightColumn__b_MuL"> <div> <div> <div class="ArticleRightSection_articleRightSection__rG8Zh"> <div class="ArticleToolbar_articleToolbar__8fsAH"> <a href="https://downloads.hindawi.com/journals/aaa/2011/948236.pdf" class="ButtonGroup_buttonGroupWrapper__Rqhy0" role="button" type="primary" aria-label="PDF" tabindex="0" unselectable="on" target="_blank" data-testid="download-pdf"><span class="ButtonGroup_leftGroup__FJAmS"><span role="img" class="anticon ButtonGroup_buttonGroupWrapperIcon__CFikg"> <svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="0 0 19 24"> <path d="M16.772,24H2.227A2.163,2.163,0,0,1,0,21.746V2.255A2.159,2.159,0,0,1,2.227,0H12.415L12.9.494h.03V.523L19,6.669V21.746A2.161,2.161,0,0,1,16.772,24ZM2.334,1A1.276,1.276,0,0,0,1,2.358V21.642A1.283,1.283,0,0,0,2.334,23H16.665A1.276,1.276,0,0,0,18,21.642V7.087l-.032-.033H14.215A2.131,2.131,0,0,1,12.02,4.832V1.005L12.015,1ZM13,2V4.745A1.192,1.192,0,0,0,14.261,6H17ZM4.012,20A1.032,1.032,0,0,1,3,18.923a2.505,2.505,0,0,1,.967-1.539,8.15,8.15,0,0,1,2.377-1.418c.344-.779.65-1.6.92-2.327l.008-.022.017-.046.009-.024c.2-.539.453-1.209.71-1.827a4.545,4.545,0,0,1-.372-3.862c.267-.569.6-.858.976-.858.556,0,.964.621,1.015,1.546a7.125,7.125,0,0,1-.681,3.143c.158.305.343.624.55.949a7.127,7.127,0,0,0,1.806,1.9,8.681,8.681,0,0,1,2.023-.279,4.23,4.23,0,0,1,1.468.238c.118.047,1.156.478,1.2,1.143a.688.688,0,0,1-.412.67,2.509,2.509,0,0,1-1.164.242,4.757,4.757,0,0,1-.671-.052,6.631,6.631,0,0,1-2.608-1.025c-.163.042-.323.086-.514.138l-.1.026-.15.041c-.235.067-.464.13-.679.185l-.292.076-.025.006-.019,0c-.794.205-1.615.418-2.4.705A14.033,14.033,0,0,1,6,18.437C5.832,18.7,4.941,20,4.012,20ZM6,17a6.865,6.865,0,0,0-1.287.871A1.927,1.927,0,0,0,4,18.831a.12.12,0,0,0,.041.1A.165.165,0,0,0,4.17,19c.327,0,.965-.631,1.356-1.219C5.671,17.564,5.83,17.3,6,17Zm7.044-2A4.632,4.632,0,0,0,12,15.131a4.76,4.76,0,0,0,1.675.792A2.906,2.906,0,0,0,14.32,16a1.629,1.629,0,0,0,.68-.13,2.672,2.672,0,0,0-.584-.528A2.752,2.752,0,0,0,13.045,15ZM8.166,13c-.177.449-.343.884-.481,1.25l-.01.025-.009.024-.007.02-.035.092-.032.085c-.156.409-.37.97-.59,1.5.6-.181,1.229-.341,1.733-.469l.031-.008.055-.014.028-.007.028-.007.307-.078c.191-.048.4-.105.674-.179l.03-.008.005,0,.036-.01.036-.01.01,0,.01,0,.016,0a8.291,8.291,0,0,1-1.566-1.767C8.341,13.285,8.264,13.16,8.166,13Zm.516-5a1.64,1.64,0,0,0-.34.365A2.425,2.425,0,0,0,8.437,11a4.012,4.012,0,0,0,.553-2.22A1.309,1.309,0,0,0,8.681,8Z" fill="currentColor"></path> </svg></span><span>PDF</gydF4y2Baspan></span><span role="img" class="anticon ButtonGroup_buttonGroupWrapperIcon__CFikg"> <svg width="1em" height="1em" viewbox="0 0 20 22"> <defs> <clippath> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </clippath> </defs> <g> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </g> </svg></span></a> <a href="//www.newsama.com/journals/aaa/2011/948236.ris" class="ButtonGroup_buttonGroupWrapper__Rqhy0" role="button" type="ghost" aria-label="Download Citation" tabindex="0" unselectable="on" data-testid="download-citation"><span class="ButtonGroup_leftGroup__FJAmS"><span role="img" class="anticon ButtonGroup_buttonGroupWrapperIcon__CFikg"> <svg width="1em" height="1em" viewbox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"> <path d="M16 12H8C7.44772 12 7 12.4477 7 13C7 13.5523 7.44772 14 8 14H16C16.5523 14 17 13.5523 17 13C17 12.4477 16.5523 12 16 12Z" fill="currentColor"></path> <path d="M16 16H8C7.44772 16 7 16.4477 7 17C7 17.5523 7.44772 18 8 18H16C16.5523 18 17 17.5523 17 17C17 16.4477 16.5523 16 16 16Z" fill="currentColor"></path> <path d="M10 8H8C7.44772 8 7 8.44772 7 9C7 9.55228 7.44772 10 8 10H10C10.5523 10 11 9.55228 11 9C11 8.44772 10.5523 8 10 8Z" fill="currentColor"></path> <path d="M15 2C15 1.44772 14.5523 1 14 1C13.4477 1 13 1.44772 13 2V8C13 8.55228 13.4477 9 14 9H20C20.5523 9 21 8.55228 21 8C21 7.44772 20.5523 7 20 7H15V2Z" fill="currentColor"></path> <path fill-rule="evenodd" clip-rule="evenodd" d="M14.7071 1.29289C14.5196 1.10536 14.2652 1 14 1H6C4.34315 1 3 2.34315 3 4V20C3 21.6569 4.34315 23 6 23H18C19.6569 23 21 21.6569 21 20V8C21 7.73478 20.8946 7.48043 20.7071 7.29289L14.7071 1.29289ZM6 3H13.5858L19 8.41421V20C19 20.5523 18.5523 21 18 21H6C5.44772 21 5 20.5523 5 20V4C5 3.44772 5.44772 3 6 3Z" fill="currentColor"></path> </svg></span><span>下载引用</gydF4y2Baspan></span><span role="img" class="anticon ButtonGroup_buttonGroupWrapperIcon__CFikg"> <svg width="1em" height="1em" viewbox="0 0 20 22"> <defs> <clippath> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </clippath> </defs> <g> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </g> </svg></span></a> <div class="ant-collapse ant-collapse-icon-position-end articleToolbarOtherFormats_otherFormatsCollapse__VHaOL"> <div class="ant-collapse-item"> <div class="ant-collapse-header" aria-expanded="false" aria-disabled="false" role="button" tabindex="0"> <div class="ant-collapse-expand-icon"> <span role="img" class="anticon ant-collapse-arrow"> <svg width="1em" height="1em" viewbox="0 0 32 32" fill="none"> <path fill-rule="evenodd" clip-rule="evenodd" d="M17.773 23.453l11.2-11.265a1.918 1.918 0 000-2.641 1.75 1.75 0 00-2.542 0l-9.929 10.101-9.933-10.1a1.75 1.75 0 00-2.542 0 1.919 1.919 0 000 2.64L15.23 23.453c.352.365.811.547 1.271.547.46 0 .92-.182 1.271-.547z" fill="currentColor"></path> </svg></span> </div> <span class="ant-collapse-header-text"><span><span role="img" class="anticon articleToolbarOtherFormats_atofDownloadIcon__YRM5T"> <svg width="1em" height="1em" viewbox="0 0 20 22"> <defs> <clippath> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </clippath> </defs> <g> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </g> </svg></span><span>下载其他格式</gydF4y2Baspan></span></span> </div> </div> </div> <a href="//www.newsama.com/reprints/948236/confirm" class="ButtonGroup_buttonGroupWrapper__Rqhy0" role="button" type="ghost" aria-label="Order printed copies" tabindex="0" unselectable="on" target="_blank"><span class="ButtonGroup_leftGroup__FJAmS"><span role="img" class="anticon ButtonGroup_buttonGroupWrapperIcon__CFikg"> <svg width="1em" height="1em" viewbox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"> <path fill-rule="evenodd" clip-rule="evenodd" d="M7.41667 1H18.6667C19.1269 1 19.5 1.44772 19.5 2V22C19.5 22.5523 19.1269 23 18.6667 23H7.41667C5.80584 23 4.5 21.433 4.5 19.5V4.5C4.5 2.567 5.80584 1 7.41667 1ZM6.16667 16.3368V4.5C6.16667 3.67157 6.72631 3 7.41667 3H17.8333V16H7.41667C6.96933 16 6.54552 16.1208 6.16667 16.3368ZM17.8333 18H7.41667C6.72631 18 6.16667 18.6716 6.16667 19.5C6.16667 20.3284 6.72631 21 7.41667 21H17.8333V18Z" fill="currentColor"></path> </svg></span><span>订单打印副本</gydF4y2Baspan></span><span role="img" class="anticon ButtonGroup_buttonGroupWrapperIcon__CFikg"> <svg width="1em" height="1em" viewbox="0 0 18 14"> <defs> <clippath id="a"> <path d="M10.293,13.707a1,1,0,0,1,0-1.414L14.586,8H1A1,1,0,0,1,1,6H14.586L10.293,1.707A1,1,0,0,1,11.707.293l6,6a1,1,0,0,1,.172.231h0l.01.019,0,.005.007.014.006.012,0,.008.008.018v0a1,1,0,0,1-.009.817l0,0L17.9,7.44l0,.009-.005.011-.007.013,0,.008-.008.015,0,.005-.01.016,0,0-.011.017,0,0-.012.018,0,0-.012.017,0,0L17.8,7.6l0,0-.011.014,0,.006-.01.012-.009.011-.006.007-.015.017h0l-.04.042-6,6a1,1,0,0,1-1.414,0Z" transform="translate(3 5)"></path> </clippath> </defs> <g transform="translate(-3 -5)"> <path d="M10.293,13.707a1,1,0,0,1,0-1.414L14.586,8H1A1,1,0,0,1,1,6H14.586L10.293,1.707A1,1,0,0,1,11.707.293l6,6a1,1,0,0,1,.172.231h0l.01.019,0,.005.007.014.006.012,0,.008.008.018v0a1,1,0,0,1-.009.817l0,0L17.9,7.44l0,.009-.005.011-.007.013,0,.008-.008.015,0,.005-.01.016,0,0-.011.017,0,0-.012.018,0,0-.012.017,0,0L17.8,7.6l0,0-.011.014,0,.006-.01.012-.009.011-.006.007-.015.017h0l-.04.042-6,6a1,1,0,0,1-1.414,0Z" transform="translate(3 5)" fill="currentColor"></path> </g> </svg></span></a> <div class="articleToolbarStatistics_articleToolbarStatistics__8_woN"> <div class="articleToolbarStatistics_column__R2GqD"> <div> <div> <span>的观点</gydF4y2Baspan> <div class="articleToolbarStatistics_amount__vJIDp"> 1002年</gydF4y2Badiv> </div> <div> <span>下载</gydF4y2Baspan> <div class="articleToolbarStatistics_amount__vJIDp"> 1044年</gydF4y2Badiv> </div> </div> </div> <div class="articleToolbarStatistics_column__R2GqD articleToolbarStatistics_dimensions__pe7pO"> <div> 引用</gydF4y2Badiv> <span class="__dimensions_badge_embed__ articleToolbarStatistics_circle__p2dSc" data-doi="10.1155/2011/948236" data-style="small_circle"></span> </div> </div> <ul class="articleToolbarSocials_articleToolbarSocials__g02HH"> <li><a href="https://twitter.com/share?url=https://doi.org/10.1155/2011/948236&via=Hindawi" unselectable="on" title="" rel="noopener noreferrer" target="_blank"><span role="img" class="anticon"> <svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="126.444 2.281 589 589"> <circle cx="420.944" cy="296.781" r="294.5" fill="#2daae1"></circle> <path d="M609.773 179.634c-13.891 6.164-28.811 10.331-44.498 12.204 16.01-9.587 28.275-24.779 34.066-42.86a154.78 154.78 0 0 1-49.209 18.801c-14.125-15.056-34.267-24.456-56.551-24.456-42.773 0-77.462 34.675-77.462 77.473 0 6.064.683 11.98 1.996 17.66-64.389-3.236-121.474-34.079-159.684-80.945-6.672 11.446-10.491 24.754-10.491 38.953 0 26.875 13.679 50.587 34.464 64.477a77.122 77.122 0 0 1-35.097-9.686v.979c0 37.54 26.701 68.842 62.145 75.961-6.511 1.784-13.344 2.716-20.413 2.716-4.998 0-9.847-.473-14.584-1.364 9.859 30.769 38.471 53.166 72.363 53.799-26.515 20.785-59.925 33.175-96.212 33.175-6.25 0-12.427-.373-18.491-1.104 34.291 21.988 75.006 34.824 118.759 34.824 142.496 0 220.428-118.052 220.428-220.428 0-3.361-.074-6.697-.236-10.021a157.855 157.855 0 0 0 38.707-40.158z" fill="#fff"></path> </svg></span></a></li> <li><a href="https://www.linkedin.com/shareArticle/?url=https://doi.org/10.1155/2011/948236" unselectable="on" title="" rel="noopener noreferrer" target="_blank"><span role="img" class="anticon"> <svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="0 0 256 256" xml:space="preserve"> <g transform="translate(-373.642 -318.344)"> <path fill="#1D8CB5" d="M583.659 328.849H419.625c-19.599 0-35.487 15.888-35.487 35.487v164.015c0 19.599 15.888 35.486 35.487 35.486h164.033c19.599 0 35.487-15.888 35.487-35.486V364.337c.001-19.599-15.888-35.488-35.486-35.488z"></path> <lineargradient id="a" gradientunits="userSpaceOnUse" x1="-808.873" y1="199.892" x2="-860.569" y2="49.203" gradienttransform="rotate(180 -17.27 206.273) scale(.5915)"> <stop offset="0" style="stop-color:#fff"></stop> <stop offset="1" style="stop-color:#fff;stop-opacity:0"></stop> </lineargradient> <path opacity=".781" fill="url(#a)" d="M557.056 338.895H446.227c-29.337 0-52.955 23.81-52.955 53.385v108.127c.95 23.087 4.603 8.491 11.555-17.075 8.081-29.713 34.396-55.682 66.445-75.145 24.461-14.855 51.84-24.341 101.679-25.244 28.265-.511 25.77-36.683-15.895-44.048z"></path> </g> <g fill="#FFF"> <path d="M81.604 207.76V101.49h-35.32v106.27h35.32zM63.951 86.98c12.308 0 19.981-8.161 19.981-18.36-.228-10.426-7.673-18.36-19.75-18.36-12.087 0-19.984 7.934-19.984 18.36 0 10.199 7.662 18.36 19.52 18.36h.233zM101.151 207.76h35.326v-59.345c0-3.178.23-6.352 1.165-8.621 2.547-6.35 8.363-12.92 18.118-12.92 12.784 0 17.893 9.748 17.893 24.032v56.855h35.319v-60.936c0-32.643-17.422-47.83-40.665-47.83-19.053 0-27.421 10.647-32.068 17.902h.238V101.49h-35.326c.469 9.97 0 106.27 0 106.27z"></path> </g> </svg></span></a></li> <li><a href="https://www.facebook.com/sharer/sharer.php?u=https://doi.org/10.1155/2011/948236" unselectable="on" title="" rel="noopener noreferrer" target="_blank"><span role="img" class="anticon"> <svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="0 0 14222 14222"> <circle cx="7111" cy="7112" r="7111" fill="#1977f3"></circle> <path d="M9879 9168l315-2056H8222V5778c0-562 275-1111 1159-1111h897V2917s-814-139-1592-139c-1624 0-2686 984-2686 2767v1567H4194v2056h1806v4969c362 57 733 86 1111 86s749-30 1111-86V9168z" fill="#fff"></path> </svg></span></a></li> <li><a href="//www.newsama.com/cdn-cgi/l/email-protection" unselectable="on" title="" rel="noopener noreferrer" target="_blank"><span role="img" class="anticon"> <svg version="1.0" xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="0 0 1401 1101"> <path fill="#6ba439" d="M132.5 2.1C101.4 6 71.1 20.5 48.3 42.4c-22.7 21.7-37.5 48.3-44.6 80l-2.2 10.1v837l2.2 10.1c6.7 30 19.3 53.9 39.8 75.3 23.3 24.3 56.4 40.9 90 45 12.8 1.6 1122.2 1.6 1135 0 38.9-4.8 75.9-25.6 100-56.4 15-19.3 24.2-39 29.8-63.9l2.2-10.1v-837l-2.2-10.1c-7.1-31.8-21.9-58.3-44.6-80.1-20.2-19.2-43.9-31.7-73.6-38.5l-9.6-2.3L705 1.4c-321.9-.1-568.5.2-572.5.7zm1123.4 99.5c1.7.4 3.1 1 3.1 1.4 0 .5-125.6 87.7-279 194L700.9 490.2 422 297C268.5 190.7 143 103.4 143 103c0-.5 1-1.1 2.3-1.3 3.5-.7 1107.1-.8 1110.6-.1zM401 404c164.4 113.8 299.4 207 300 207 .6 0 135.6-93.2 300.1-207 164.5-113.9 299.3-207 299.5-207 .2 0 .4 170.9.4 379.7 0 417.9.5 386-6.1 398.3-6.2 11.6-19 21.4-31.9 24.4-5.8 1.4-67.4 1.6-562 1.6s-556.2-.2-562-1.6c-12.9-3-25.7-12.8-31.9-24.4-6.6-12.3-6.1 19.6-6.1-398.3 0-208.8.2-379.7.5-379.7S236.6 290.1 401 404z"></path> </svg></span></a></li> </ul> </div> </div> </div> </div> </div> </div> </main> <div> <footer class="ant-layout-footer"> <div class="footer-main-nav-section"> <div class="footer-main-nav"> <div class="ant-col footer-main-nav__column"> <ul class="ant-menu ant-menu-root ant-menu-vertical ant-menu-light footer-main-nav__menu" role="menu" tabindex="0" data-menu-list="true"> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/about/" aria-label="About Us">关于我们</一个></span></li> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/about/contact/" aria-label="Contact us">联系我们</一个></span></li> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/publishing-partnerships/" aria-label="Partnerships">合作伙伴关系</一个></span></li> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/blog/" aria-label="Blog">博客</一个></span></li> </ul> <div style="display:none" aria-hidden="true"></div> </div> <div class="ant-col footer-main-nav__column"> <ul class="ant-menu ant-menu-root ant-menu-vertical ant-menu-light footer-main-nav__menu" role="menu" tabindex="0" data-menu-list="true"> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/journals/" aria-label="Journals">期刊</一个></span></li> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/publish-research/authors/article-processing-charges/" aria-label="Article Processing Charges">文章处理费用</一个></span></li> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/print-editions/" aria-label="Print editions">印刷版</一个></span></li> </ul> <div style="display:none" aria-hidden="true"></div> </div> <div class="ant-col footer-main-nav__column"> <ul class="ant-menu ant-menu-root ant-menu-vertical ant-menu-light footer-main-nav__menu" role="menu" tabindex="0" data-menu-list="true"> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/publish-research/authors/" aria-label="Authors">作者</一个></span></li> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/publish-research/editors/" aria-label="Editors">编辑器</一个></span></li> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/publish-research/reviewers/" aria-label="Reviewers">评论家</一个></span></li> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/publishing-partnerships/" aria-label="Partnerships">合作伙伴关系</一个></span></li> </ul> <div style="display:none" aria-hidden="true"></div> </div> <div class="ant-col footer-main-nav__column"> <ul class="ant-menu ant-menu-root ant-menu-vertical ant-menu-light footer-main-nav__menu" role="menu" tabindex="0" data-menu-list="true"> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/hindawi-xml-corpus/" aria-label="Hindawi XML Corpus">雷电竞APP</a></span></li> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/open-archives-initiative/" aria-label="Open Archives Initiative">开放档案计划</一个></span></li> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/preventing-and-protecting-against-fraud/" aria-label="Fraud prevention">欺诈防范</一个></span></li> </ul> <div style="display:none" aria-hidden="true"></div> </div> </div> <div class="social-links"> 遵循我们:<gydF4y2Badiv class="social-links__icons"> <a aria-label="Twitter" rel="noopener noreferrer" href="https://twitter.com/hindawi" target="_blank" class="social-links__icon"><span role="img" class="anticon"> <svg xmlns="http://www.w3.org/2000/svg" width="40" height="40" viewbox="0 0 40 40" fill="none"> <path fill-rule="evenodd" clip-rule="evenodd" d="M0 20C0 8.95599 8.95599 0 20 0C31.044 0 40 8.95599 40 20C40 31.044 31.044 40 20 40C8.95599 40 0 31.044 0 20ZM29.1449 16.1871C29.1449 15.9885 29.1406 15.7907 29.1318 15.5939C30.0281 14.946 30.8072 14.1373 31.4215 13.2166C30.5991 13.5822 29.7141 13.8284 28.7854 13.9395C29.7333 13.371 30.4608 12.4719 30.8041 11.4005C29.917 11.9263 28.9349 12.3083 27.8891 12.5146C27.0514 11.6223 25.8588 11.0641 24.5383 11.0641C22.0032 11.0641 19.9472 13.1201 19.9472 15.6543C19.9472 16.0144 19.9878 16.3647 20.0665 16.701C16.2512 16.5091 12.868 14.6823 10.6042 11.9046C10.21 12.583 9.9826 13.371 9.9826 14.212C9.9826 15.8047 10.7928 17.2107 12.0255 18.0331C11.2723 18.0099 10.5649 17.803 9.94629 17.4591C9.94568 17.4783 9.94568 17.4969 9.94568 17.5177C9.94568 19.7406 11.528 21.597 13.6285 22.0175C13.2428 22.1228 12.8369 22.1793 12.4179 22.1793C12.1228 22.1793 11.835 22.15 11.5552 22.0963C12.1399 23.9203 13.8342 25.2475 15.8438 25.2847C14.2725 26.5161 12.2931 27.2498 10.1422 27.2498C9.77203 27.2498 9.40643 27.2287 9.04724 27.1863C11.0788 28.4885 13.4912 29.2484 16.0837 29.2484C24.5276 29.248 29.1449 22.2531 29.1449 16.1871Z" fill="#F2F2F2"></path> </svg></span></a> <a aria-label="Linkedin" rel="noopener noreferrer" href="https://www.linkedin.com/company/hindawilimited/" target="_blank" class="social-links__icon"><span role="img" class="anticon"> <svg width="40" height="40" viewbox="0 0 40 40" fill="none" xmlns="http://www.w3.org/2000/svg"> <path fill-rule="evenodd" clip-rule="evenodd" d="M0 20C0 8.95599 8.95599 0 20 0C31.044 0 40 8.95599 40 20C40 31.044 31.044 40 20 40C8.95599 40 0 31.044 0 20ZM9.31732 30.2344H14.1882V15.5801H9.31732V30.2344ZM11.7529 13.5791H11.7212C10.0867 13.5791 9.02954 12.4539 9.02954 11.0477C9.02954 9.60968 10.119 8.51562 11.7853 8.51562C13.4515 8.51562 14.4769 9.60968 14.5087 11.0477C14.5087 12.4539 13.4515 13.5791 11.7529 13.5791ZM26.8814 30.2344H31.7517V21.8317C31.7517 17.3306 29.3488 15.2362 26.1441 15.2362C23.5599 15.2362 22.4017 16.6565 21.7545 17.655V15.5801H16.8839C16.9476 16.955 16.8839 30.2344 16.8839 30.2344H21.7545V22.0508C21.7545 21.6129 21.7859 21.1752 21.9147 20.8621C22.2668 19.9872 23.0682 19.0808 24.4138 19.0808C26.1761 19.0808 26.8814 20.4245 26.8814 22.3947V30.2344Z" fill="#F2F2F2"></path> </svg></span></a> <a aria-label="Youtube" rel="noopener noreferrer" href="https://www.youtube.com/channel/UCDIK_O7FATPEkhad_sQVaSg" target="_blank" class="social-links__icon"><span role="img" class="anticon"> <svg width="40" height="40" viewbox="0 0 40 40" fill="none" xmlns="http://www.w3.org/2000/svg"> <path d="M17.2973 23.7838L23.7838 20L17.2973 16.2162V23.7838Z" fill="#F2F2F2"></path> <path fill-rule="evenodd" clip-rule="evenodd" d="M0 20C0 8.95599 8.95599 0 20 0C31.044 0 40 8.95599 40 20C40 31.044 31.044 40 20 40C8.95599 40 0 31.044 0 20ZM31.9824 26.0324C32.4969 24.0765 32.4969 20.0204 32.4969 20.0204C32.4969 20.0204 32.5177 15.9442 31.9824 13.9883C31.694 12.9178 30.8499 12.0734 29.7794 11.7853C27.8235 11.25 20 11.25 20 11.25C20 11.25 12.1765 11.25 10.2206 11.7648C9.17053 12.0529 8.30566 12.9178 8.01758 13.9883C7.50275 15.9442 7.50275 20 7.50275 20C7.50275 20 7.50275 24.0765 8.01758 26.0117C8.30597 27.0822 9.15009 27.9266 10.2206 28.2147C12.197 28.75 20 28.75 20 28.75C20 28.75 27.8235 28.75 29.7794 28.2352C30.8499 27.9471 31.694 27.103 31.9824 26.0324Z" fill="#F2F2F2"></path> </svg></span></a> <a aria-label="Facebook" rel="noopener noreferrer" href="https://www.facebook.com/HindawiLimited/" target="_blank" class="social-links__icon"><span role="img" class="anticon"> <svg width="40" height="39" viewbox="0 0 40 39" fill="none" xmlns="http://www.w3.org/2000/svg"> <path d="M40 19.4595C40 8.71394 31.044 0 20 0C8.95599 0 0 8.71394 0 19.4595C0 30.205 8.95599 38.9189 20 38.9189C20.1175 38.9189 20.2344 38.9165 20.3516 38.9145V23.7661H16.0547V18.8938H20.3516V15.3084C20.3516 11.1502 22.9605 8.88705 26.7728 8.88705C28.5983 8.88705 30.1675 9.01948 30.625 9.07857V13.4244H27.9962C25.9222 13.4244 25.5206 14.3835 25.5206 15.7906V18.8938H30.4797L29.8334 23.7661H25.5206V38.1671C33.8803 35.8353 40 28.3418 40 19.4595Z" fill="#F2F2F2"></path> </svg></span></a> </div> </div> </div> <div class="footer-minor-nav"> <span><a href="//www.newsama.com/privacy/" class="footer-minor-nav__link" aria-label="Privacy Policy">隐私政策</一个><div class="ant-divider ant-divider-vertical" role="separator"></div></span> <span><a href="//www.newsama.com/terms/" class="footer-minor-nav__link" aria-label="Terms of Service">服务条款</一个><div class="ant-divider ant-divider-vertical" role="separator"></div></span> <span><a href="//www.newsama.com/responsible-disclosure-policy/" class="footer-minor-nav__link" aria-label="Responsible Disclosure Policy">负责信息披露政策</一个><div class="ant-divider ant-divider-vertical" role="separator"></div></span> <span><a href="//www.newsama.com/cookie-policy/" class="footer-minor-nav__link" aria-label="Cookie Policy">饼干的政策</一个><div class="ant-divider ant-divider-vertical" role="separator"></div></span> <span><a href="//www.newsama.com/copyright/" class="footer-minor-nav__link" aria-label="Copyright">版权</一个><div class="ant-divider ant-divider-vertical" role="separator"></div></span> <span><a href="//www.newsama.com/modern-slavery-statement/" class="footer-minor-nav__link" aria-label="Modern slavery statement">现代奴隶制的声明</一个><div class="ant-divider ant-divider-vertical" role="separator"></div></span> <span><a class="footer-minor-nav__link" aria-label="Cookie Preferences">饼干的偏好</一个></span> </div> </footer> </div> </section> <noscript> <iframe src="https://www.newsama.com/ns.html?id=GTM-MQ4MGW" height="0" width="0" style="display:none;visibility:hidden"></iframe> </noscript> </div> </body> </html>

Φ-likeness property (a geometric property which includes starlikeness and spiral-likeness) for two basic cases: the inner problem and the outer problem. We study both zero and nonzero surface tension models. Certain particular cases are also presented."> 单价的函数的一个特殊类Hele-Shaw流问题</gydF4y2Batitle> <link rel="preload stylesheet" as="style" type="text/css" href="https://cdn.bibblio.org/rcm/4.28.0/bib-related-content.min.css"> <link rel="preload" href="https://static.hindawi.com/new/next_assets/2023-08-03-0017a694320dbe69a559e8120be98c/_next/static/css/b2661f2cd4bd618b.css" as="style"> <link rel="stylesheet" href="https://static.hindawi.com/new/next_assets/2023-08-03-0017a694320dbe69a559e8120be98c/_next/static/css/b2661f2cd4bd618b.css" data-n-g=""> <style id="__jsx-903e4b2e5d3241e4">div#__next{display:-webkit-box;display:-webkit-flex;display:-moz-box;display:-ms-flexbox;display:flex;min-height:100vh;-webkit-box-orient:vertical;-webkit-box-direction:normal;-webkit-flex-direction:column;-moz-box-orient:vertical;-moz-box-direction:normal;-ms-flex-direction:column;flex-direction:column}</style> </head> <body> <div id="__next"> <section class="ant-layout"> <div> <header class="ant-layout-header"> <div class="header__width-wrapper"> <div class="ant-anchor-wrapper ant-anchor-logo" style="max-height:100vh"> <div class="ant-anchor ant-anchor-fixed"> <div class="ant-anchor-ink"> <span class="ant-anchor-ink-ball"></span> </div> <div class="ant-anchor-link ant-link-logo"> <a class="ant-anchor-link-title" href="//www.newsama.com/" title=""> <div class="ant-image"> <img alt="标志gydF4y2Ba" class="ant-image-img ant-image-logo" src="https://static.hindawi.com/new/next_assets/2023-08-03-0017a694320dbe69a559e8120be98c/public/logo.svg"> </div></a> </div> </div> </div> <div class="TopNavigation_topNavigationWrapper__QzFKB"> <div class="TopNavigation_rightSideMenuItems__0bKf1"> <ul class="ant-menu-overflow ant-menu ant-menu-root ant-menu-horizontal ant-menu-light header-ant-menu-horizontal" role="menu" tabindex="0" data-menu-list="true" data-testid="desktop-menu"> <li class="ant-menu-overflow-item ant-menu-item ant-menu-item-only-child" style="opacity:1;order:0" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/journals/" aria-label="Journals">期刊</一个></span></li> <li class="ant-menu-overflow-item ant-menu-item ant-menu-item-only-child" style="opacity:1;order:1" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/publish-research/" aria-label="Publish with us">雷电竞下载苹果</a></span></li> <li class="ant-menu-overflow-item ant-menu-item ant-menu-item-only-child" style="opacity:1;order:2" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/publishing-partnerships/" aria-label="Publishing partnerships">raybet推荐吗</a></span></li> <li class="ant-menu-overflow-item ant-menu-item ant-menu-item-only-child" style="opacity:1;order:3" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/about/" aria-label="About us">关于我们</一个></span></li> <li class="ant-menu-overflow-item ant-menu-item ant-menu-item-only-child" style="opacity:1;order:4" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/blog/" aria-label="Blog">博客</一个></span></li> <li class="ant-menu-overflow-item ant-menu-overflow-item-rest ant-menu-submenu ant-menu-submenu-horizontal" style="opacity:0;height:0;overflow-y:hidden;order:9007199254740991;pointer-events:none;position:absolute" aria-hidden="true" role="none"> <div role="menuitem" class="ant-menu-submenu-title" tabindex="-1" aria-expanded="false" aria-haspopup="true"> <span role="img" aria-label="ellipsis" class="anticon anticon-ellipsis"> <svg viewbox="64 64 896 896" focusable="false" data-icon="ellipsis" width="1em" height="1em" fill="currentColor" aria-hidden="true"> <path d="M176 511a56 56 0 10112 0 56 56 0 10-112 0zm280 0a56 56 0 10112 0 56 56 0 10-112 0zm280 0a56 56 0 10112 0 56 56 0 10-112 0z"></path> </svg></span> <i class="ant-menu-submenu-arrow"></i> </div></li> </ul> <div style="display:none" aria-hidden="true"></div> <button data-testid="search-button-icon" aria-label="Search" type="button" class="ant-btn ant-btn-default SearchToggleButton_btn__kmpSM"><span role="img" class="anticon SearchToggleButton_icon__nurvY"> <svg width="1em" height="1em" viewbox="0 0 26 26" fill="none"> <path fill-rule="evenodd" clip-rule="evenodd" d="M22.1,23.813l-5.478-5.479a10.282,10.282,0,1,1,1.709-1.709L23.813,22.1a1.209,1.209,0,0,1-1.71,1.71ZM2.416,10.27A7.851,7.851,0,0,0,15.78,15.864l.041-.043.043-.041A7.853,7.853,0,1,0,2.416,10.27Z" fill="currentColor"></path> </svg></span></button> <div></div> <button data-testid="menu-button-icon" aria-label="Menu" type="button" class="ant-btn ant-btn-default MenuToggleButton_btn__Go00X"><span role="img" class="anticon MenuToggleButton_icon__5uVd5"> <svg width="1em" height="1em" viewbox="0 -2 28 28" fill="none"> <path fill-rule="evenodd" clip-rule="evenodd" d="M1.833,25.667a1.834,1.834,0,0,1,0-3.668H25.667a1.834,1.834,0,0,1,0,3.668Zm0-11a1.833,1.833,0,0,1,0-3.666H25.667a1.833,1.833,0,0,1,0,3.666Zm0-11A1.833,1.833,0,1,1,1.833,0H25.667a1.833,1.833,0,0,1,0,3.666Z" fill="currentColor"></path> </svg></span></button> <div></div> </div> </div> </div> </header> </div> <main class="ant-layout-content ArticleLayout_articleLayoutWrapper__oukM3"> <div> <div id="journal-header" class=" JournalNavigation_journalHeader__vGN2X" data-istranslated="false"> <a href="//www.newsama.com/journals/aaa" class="JournalNavigation_journalHeader__titleLink__sZyGb"><h1 id="journal-header-title" data-testid="journal-header-title" class="JournalNavigation_small__sXDLc JournalNavigation_journalHeader__title__fsEHD">抽象和应用分析</h1></一个><div class="JournalNavigation_navigationBarHorizontal__YojZL"> <div id="navigation-bar-horizontal" class="navigation-bar-horizontal"> <button id="Journal overview" type="button" class="ant-btn ant-btn-default ant-dropdown-trigger bordered"><span role="img" class="anticon"> <svg width="1em" height="1em" viewbox="0 0 32 32" fill="none"> <path fill-rule="evenodd" clip-rule="evenodd" d="M17.773 23.453l11.2-11.265a1.918 1.918 0 000-2.641 1.75 1.75 0 00-2.542 0l-9.929 10.101-9.933-10.1a1.75 1.75 0 00-2.542 0 1.919 1.919 0 000 2.64L15.23 23.453c.352.365.811.547 1.271.547.46 0 .92-.182 1.271-.547z" fill="currentColor"></path> </svg></span><span>日报》概述</gydF4y2Baspan></button> <a class="bordered" href="//www.newsama.com/journals/aaa/guidelines">对于作者</一个><一个cl作为s="bordered" href="//www.newsama.com/publish-research/reviewers">对于审查员</一个><一个cl作为s="bordered" href="//www.newsama.com/publish-research/editors">的编辑器</一个><一个cl作为s="bordered" href="//www.newsama.com/journals/aaa/contents/">表的内容</一个><button id="Special Issues" type="button" class="ant-btn ant-btn-default ant-dropdown-trigger"><span role="img" class="anticon"> <svg width="1em" height="1em" viewbox="0 0 32 32" fill="none"> <path fill-rule="evenodd" clip-rule="evenodd" d="M17.773 23.453l11.2-11.265a1.918 1.918 0 000-2.641 1.75 1.75 0 00-2.542 0l-9.929 10.101-9.933-10.1a1.75 1.75 0 00-2.542 0 1.919 1.919 0 000 2.64L15.23 23.453c.352.365.811.547 1.271.547.46 0 .92-.182 1.271-.547z" fill="currentColor"></path> </svg></span><span>特殊的问题</gydF4y2Baspan></button> </div> </div> </div> </div> <nav class="ant-breadcrumb ArticleLayout_breadcrumbs__hsc4o"> <ol> <li><span class="ant-breadcrumb-link"><a href="//www.newsama.com/journals/aaa/" aria-label="Abstract and Applied Analysis">抽象和应用分析</一个></span><span class="ant-breadcrumb-separator">/</gydF4y2Baspan></li> <li><span class="ant-breadcrumb-link"><a href="//www.newsama.com/journals/aaa/contents/year/2011/" aria-label="2011">2011年</一个></span><span class="ant-breadcrumb-separator">/</gydF4y2Baspan></li> <li><span class="ant-breadcrumb-link">文章</gydF4y2Baspan><span class="ant-breadcrumb-separator">/</gydF4y2Baspan></li> </ol> </nav> <div class="ant-row ThreeColumnLayout_wrapper__gPK_l"> <div class="ant-col ThreeColumnLayout_leftColumn__yqNgV"> <div> <div> <div id="article-table-of-contents" data-ismobile="false"> <div class="TableOfContents_tableOfContents__0jAuv"> <div class="TableOfContents_tableOfContents__title__CH9Lz"> 在这一页上</gydF4y2Badiv> <a class="TableOfContents_tableOfContents__item__JJil1" href="#abstract">文摘</一个><一个cl作为s="TableOfContents_tableOfContents__item__JJil1" href="#introduction">介绍</一个><一个cl作为s="TableOfContents_tableOfContents__item__JJil1" href="#acknowledgments">确认</一个><一个cl作为s="TableOfContents_tableOfContents__item__JJil1" href="#references">引用</一个><一个cl作为s="TableOfContents_tableOfContents__item__JJil1" href="#copyright">版权</一个><一个cl作为s="TableOfContents_tableOfContents__item__JJil1" href="#related-articles">相关文章</一个></div> </div> </div> </div> </div> <div class="ant-col ThreeColumnLayout_middleColumn__sbd41"> <div class="ArticleMiddleSection_articleMiddleSection__gAv9z"> <div class="articleHeader"> <strong>研究文章|<gydF4y2Ba!-- -->开放获取</gydF4y2Bastrong> <div class="articleHeader__meta"> <span>体积<gydF4y2Ba!-- -->2011年<gydF4y2Ba!-- -->|</gydF4y2Baspan> <span>文章的ID<gydF4y2Ba!-- -->948236年<gydF4y2Ba!-- -->|</gydF4y2Baspan> <span class="articleHeader__meta_doiLink"><a href="https://doi.org/10.1155/2011/948236" aria-label="Doi-link" target="_blank" rel="noreferrer">https://doi.org/10.1155/2011/948236</一个></span> </div> <div class="simpleShowMore"> <button class="simpleShowMore__button">显示引用</gydF4y2Babutton> </div> <h1 class="articleHeader__title">单价的函数的一个特殊类Hele-Shaw流问题</h1><gydF4y2Badiv class="articleHeader__authors"> <span class="articleHeader__authors_author"><strong>Paula Curt</gydF4y2Bastrong><a href="//www.newsama.com/cdn-cgi/l/email-protection" aria-label="Mail Option"><span role="img" class="anticon"> <svg version="1.0" xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="0 0 1401 1101"> <path fill="#6ba439" d="M132.5 2.1C101.4 6 71.1 20.5 48.3 42.4c-22.7 21.7-37.5 48.3-44.6 80l-2.2 10.1v837l2.2 10.1c6.7 30 19.3 53.9 39.8 75.3 23.3 24.3 56.4 40.9 90 45 12.8 1.6 1122.2 1.6 1135 0 38.9-4.8 75.9-25.6 100-56.4 15-19.3 24.2-39 29.8-63.9l2.2-10.1v-837l-2.2-10.1c-7.1-31.8-21.9-58.3-44.6-80.1-20.2-19.2-43.9-31.7-73.6-38.5l-9.6-2.3L705 1.4c-321.9-.1-568.5.2-572.5.7zm1123.4 99.5c1.7.4 3.1 1 3.1 1.4 0 .5-125.6 87.7-279 194L700.9 490.2 422 297C268.5 190.7 143 103.4 143 103c0-.5 1-1.1 2.3-1.3 3.5-.7 1107.1-.8 1110.6-.1zM401 404c164.4 113.8 299.4 207 300 207 .6 0 135.6-93.2 300.1-207 164.5-113.9 299.3-207 299.5-207 .2 0 .4 170.9.4 379.7 0 417.9.5 386-6.1 398.3-6.2 11.6-19 21.4-31.9 24.4-5.8 1.4-67.4 1.6-562 1.6s-556.2-.2-562-1.6c-12.9-3-25.7-12.8-31.9-24.4-6.6-12.3-6.1 19.6-6.1-398.3 0-208.8.2-379.7.5-379.7S236.6 290.1 401 404z"></path> </svg></span></a><sup>1</gydF4y2Basup></span> <span class="articleHeader__authors_author">和<gydF4y2Ba!-- -->Denisa Fericean<gydF4y2Basup>2</gydF4y2Basup></span> </div> <div class="simpleShowMore"> <button class="simpleShowMore__button">显示更多</gydF4y2Babutton> </div> <div class="articleHeader__academicEditor"> <strong>学术编辑器:</gydF4y2Bastrong> <span>Yoshikazu gb</gydF4y2Baspan> </div> <div class="articleHeader__timeline"> <div class="articleHeader__timeline_item "> <strong>收到了</gydF4y2Bastrong> <span>2010年12月07</gydF4y2Baspan> </div> <div class="articleHeader__timeline_item "> <strong>接受</gydF4y2Bastrong> <span>2011年2月23日</gydF4y2Baspan> </div> <div class="articleHeader__timeline_item articleHeader__timeline_item_sticky"> <strong>发表</gydF4y2Bastrong> <span>2011年4月26日</gydF4y2Baspan> </div> </div> </div> <div class="articleBody"> <div class="xml-content"> <h4 class="header" id="abstract">文摘</h4><gydF4y2Bap>我们学习的时间演化自由边界平面流动的粘性流体在Hele-Shaw细胞注入。理论的应用方法单价的函数,我们证明时间的不变性<gydF4y2Basvg height="10.475" id="M1" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>样式属性(几何属性包括starlikeness和spiral-likeness)两个基本例:内部问题和外部问题。我们研究两个零,零表面张力模型。某些特定的情况下。</gydF4y2Bap> <span class="end-abs"></span> <h4 id="introduction">1。介绍</h4><gydF4y2Bap>自由边界的时间演化的粘性流体平面流在Hele-Shaw细胞注入被许多作者研究。通过使用单价的方法函数理论,他们证明了某些几何性质(如starlikeness和定向凸性)保存在时间<一个href="#B5">1</一个>- - - - - -<一个href="#B15">6</一个>]。在本文中,我们继续研究证明另一个几何性质的时间不变性:<gydF4y2Basvg height="10.475" id="M2" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>相似。</gydF4y2Bap> <p>在论文的第一部分,我们需要审查的主要结果。我们首先给出基本概念的关于有界的情况。</gydF4y2Bap> <p>在这种情况下,我们研究粘性流体的流动在一个平面Hele-Shaw细胞注入通过(持续的力量源泉<gydF4y2Basvg height="12.925" id="M3" style="vertical-align:-1.90608pt;width:12.325px;" version="1.1" viewbox="0 0 12.325 12.925" width="12.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.0625" id="M4" style="vertical-align:-1.90608pt;width:39.537498px;" version="1.1" viewbox="0 0 39.537498 13.0625" width="39.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0625)"> <g transform="translate(72,-61.55)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.228174" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.268562" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>在注射),坐落在原点。假设在初始时刻的域<gydF4y2Basvg height="13.45" id="M5" style="vertical-align:-2.21957pt;width:29.975px;" version="1.1" viewbox="0 0 29.975 13.45" width="29.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.717232" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>被液体是单连通的,有限的分析和光滑的曲线<gydF4y2Basvg height="13.45" id="M6" style="vertical-align:-2.21957pt;width:84.75px;" version="1.1" viewbox="0 0 84.75 13.45" width="84.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.3392611" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.50276" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.754259" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.421478" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.810513" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.112743" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.276241" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.527744" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。通过使用众所周知的黎曼映射定理,域<gydF4y2Basvg height="13.45" id="M7" style="vertical-align:-2.21957pt;width:27.049999px;" version="1.1" viewbox="0 0 27.049999 13.45" width="27.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.379169" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>(被液体<gydF4y2Basvg height="9.125" id="M8" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>)可以被描述为一个单叶函数<gydF4y2Basvg height="13.6125" id="M9" style="vertical-align:-2.34499pt;width:38.974998px;" version="1.1" viewbox="0 0 38.974998 13.6125" width="38.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>单位圆的<gydF4y2Basvg height="13.6125" id="M10" style="vertical-align:-2.29482pt;width:112.3875px;" version="1.1" viewbox="0 0 112.3875 13.6125" width="112.3875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.277946" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.318335" y="0"> {</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.319775" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.484715" y="0"> ∶</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.349583" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.850182" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.539288" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.50322" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="77.54361" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="83.795105" y="0"> }</gydF4y2Batspan> </text> </g> </g> </svg>到<gydF4y2Basvg height="13.45" id="M11" style="vertical-align:-2.21957pt;width:27.049999px;" version="1.1" viewbox="0 0 27.049999 13.45" width="27.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.379169" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>归一化的<gydF4y2Basvg height="13.6125" id="M12" style="vertical-align:-2.34499pt;width:65.625px;" version="1.1" viewbox="0 0 65.625 13.6125" width="65.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.354164" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.555412" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.468851" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.108185" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.148575" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.6375" id="M13" style="vertical-align:-2.34499pt;width:70.150002px;" version="1.1" viewbox="0 0 70.150002 13.6375" width="70.150002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6375)"> <g transform="translate(72,-61.09)"> <text transform="matrix(1,0,0,-1,-71.95,63.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.552532" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.716031" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.967531" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.168779" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.082218" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.72155" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.76194" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。我们表示<gydF4y2Basvg height="13.45" id="M14" style="vertical-align:-2.21957pt;width:78.900002px;" version="1.1" viewbox="0 0 78.900002 13.45" width="78.900002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.3392611" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.50276" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.416199" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.04303" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.08342" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.47245" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.774685" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.938183" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.85162" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。这个函数<gydF4y2Basvg height="14.75" id="M15" style="vertical-align:-3.25793pt;width:94.824997px;" version="1.1" viewbox="0 0 94.824997 14.75" width="94.824997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.244516" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.88385" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.92424" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.08,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-11.21,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>产生一个参数化的<gydF4y2Basvg height="17.75" id="M16" style="vertical-align:-3.25793pt;width:173.02499px;" version="1.1" viewbox="0 0 173.02499 17.75" width="173.02499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.75)"> <g transform="translate(72,-57.8)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.61,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.26,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> {</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.029325" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-31.29,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-26.41,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.68,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-8.88,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.540749" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.555653" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.596043" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.759541" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.01104" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="51.224792" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.476292" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.078117" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="69.241615" y="0"> }</gydF4y2Batspan> </text> </g> </g> </svg>和移动边界的参数化<gydF4y2Basvg height="16.612499" id="M17" style="vertical-align:-2.34499pt;width:187.53751px;" version="1.1" viewbox="0 0 187.53751 16.612499" width="187.53751" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6125)"> <g transform="translate(72,-58.71)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.3392611" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.50276" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.416199" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.04303" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.08342" y="0"> {</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.084858" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.024021" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.187523" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-14.19,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-6.39,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.1271896" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.290689" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.667938" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.682842" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.723232" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.88673" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.138229" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="60.351982" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.603477" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="74.205307" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="78.368805" y="0"> }</gydF4y2Batspan> </text> </g> </g> </svg>。</gydF4y2Bap> <p>满足方程的自由边界首次导出了Galin [<一个href="#B2">7</一个>]和Polubarinova-Kochina [<一个href="#B8">8</一个>,<gydF4y2Ba一个href="#B9">9</一个>]:<gydF4y2Baspan class="equation" id="EEq1.1"> <svg height="31.5875" id="M18" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 31.5875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,31.5875)"> <g transform="translate(72,-46.73)"> <text transform="matrix(1,0,0,-1,107.29,55.7)"> <tspan style="font-size: 12.50px; " x="18.059999" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.889999" y="-2.72"> ̇</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.799999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.315022" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.478523" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.167625" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.381378" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.294819" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 167.83,68.6 44.83,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,167.83,55.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.689105" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,182.96,60.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,188.52,55.7)"> <tspan style="font-size: 12.50px; " x="24.139999" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.189999" y="-7.9099998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.349998" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.377888" y="0"> −</gydF4y2Batspan> </text> <g> <path d="m 243.67,58.82 13.85,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,243.67,46.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.05" y="-8.7600002"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.216139" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.381077" y="-8.7600002"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.408962" y="-8.7600002"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,301.66,60.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,464.75,56.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.540749" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>(在前面的平等我们使用符号:<gydF4y2Basvg height="15.5625" id="M19" style="vertical-align:-2.34499pt;width:71.762497px;" version="1.1" viewbox="0 0 71.762497 15.5625" width="71.762497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.5625)"> <g transform="translate(72,-59.55)"> <text transform="matrix(1,0,0,-1,-71.95,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-63.51,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.56,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.41692" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.356085" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.831919" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.220951" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="16.174999" id="M20" style="vertical-align:-2.34499pt;width:63.950001px;" version="1.1" viewbox="0 0 63.950001 16.174999" width="63.950001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.175)"> <g transform="translate(72,-59.06)"> <text transform="matrix(1,0,0,-1,-64.85,64.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̇</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-7.0999999" y="2.72"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.802856" y="2.72"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.843245" y="2.72"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.232279" y="2.72"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.171444" y="2.72"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.647278" y="2.72"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.036308" y="2.72"> </gydF4y2Batspan> </text> </g> </g> </svg>)。</gydF4y2Bap> <p>经典解决方案的区间<gydF4y2Basvg height="13.45" id="M21" style="vertical-align:-2.21957pt;width:33.450001px;" version="1.1" viewbox="0 0 33.450001 13.45" width="33.450001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.492897" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是一个函数<gydF4y2Basvg height="13.6125" id="M22" style="vertical-align:-2.34499pt;width:38.974998px;" version="1.1" viewbox="0 0 38.974998 13.6125" width="38.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.45" id="M23" style="vertical-align:-2.21957pt;width:57.737499px;" version="1.1" viewbox="0 0 57.737499 13.45" width="57.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.922558" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,这是单价的<gydF4y2Basvg height="15.6875" id="M24" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 15.6875" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.6875)"> <g transform="translate(72,-59.45)"> <g> <path d="m -71.95,70.71 10.19,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="13.9625" id="M25" style="vertical-align:-0.15048pt;width:17.950001px;" version="1.1" viewbox="0 0 17.950001 13.9625" width="17.950001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9625)"> <g transform="translate(72,-60.83)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-62.56,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>关于<gydF4y2Basvg height="9.125" id="M26" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>在<gydF4y2Basvg height="13.45" id="M27" style="vertical-align:-2.21957pt;width:33.450001px;" version="1.1" viewbox="0 0 33.450001 13.45" width="33.450001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.492897" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。众所周知,,从一个分析和光滑的边界<gydF4y2Basvg height="13.45" id="M28" style="vertical-align:-2.21957pt;width:27.525px;" version="1.1" viewbox="0 0 27.525 13.45" width="27.525" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.3392611" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.50276" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.754259" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>经典解决方案并在本地是独一无二的存在于时间(见[<一个href="#B16">10</一个>];看到如(<一个href="#B4">11</一个>,第1章)。请注意,<gydF4y2Basvg height="10.325" id="M29" style="vertical-align:-0.0pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 10.325" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>被称为<我>充气时间</我>。</gydF4y2Bap> <p>在注入的问题<gydF4y2Basvg height="13.45" id="M30" style="vertical-align:-2.21957pt;width:49.9375px;" version="1.1" viewbox="0 0 49.9375 13.45" width="49.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.391672" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.432062" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.683563" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>的液体变成一个有界单连通和较小的表面张力<gydF4y2Basvg height="13.6125" id="M31" style="vertical-align:-2.34499pt;width:35.262501px;" version="1.1" viewbox="0 0 35.262501 13.6125" width="35.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.8148546" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.855244" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,Polubarinova-Galin方程(<一个href="#B15">6</一个>)的形式:<gydF4y2Baspan class="equation" id="EEq1.2"> <svg height="31.5875" id="M32" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 31.5875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,31.5875)"> <g transform="translate(72,-46.73)"> <text transform="matrix(1,0,0,-1,45.3,55.7)"> <tspan style="font-size: 12.50px; " x="18.059999" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.9" y="-2.72"> ̇</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.799999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.315022" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.478523" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.167625" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.381378" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.294819" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 105.85,68.6 44.82,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,105.85,55.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.6766019" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,120.98,60.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,126.53,55.7)"> <tspan style="font-size: 12.50px; " x="24.139999" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.200001" y="-7.9099998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.066355" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.979794" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.360001" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.387886" y="0"> −</gydF4y2Batspan> </text> <g> <path d="m 181.68,58.82 13.86,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,181.68,46.94)"> <tspan style="font-size: 12.50px; " x="49.650002" y="-3.8399999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.389999" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.83" y="-8.7600002"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.170221" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.521744" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="60.470001" y="-16.01"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.859032" y="-16.01"> </gydF4y2Batspan> </text> <g> <path d="m 242.15,58.82 13.17,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,242.27,46.94)"> <tspan style="font-size: 12.50px; " x="16.33" y="-6.2399998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.18" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,270.01,60.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,277.82,55.7)"> <tspan style="font-size: 12.50px; " x="9.1199999" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.97" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.799999" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.963499" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.502567" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.754066" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.920208" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.085144" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="77.125534" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,360.52,60.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,368.32,55.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="96.43" y="-0.54000002"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="100.5935" y="-0.54000002"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="106.845" y="-0.54000002"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="109.97075" y="-0.54000002"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="116.22225" y="-0.54000002"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<gydF4y2Basvg height="16.612499" id="M33" style="vertical-align:-2.34499pt;width:349.21249px;" version="1.1" viewbox="0 0 349.21249 16.612499" width="349.21249" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6125)"> <g transform="translate(72,-58.71)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.7766261" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.940125" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-55.45,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-47.64,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.754021" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.794409" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.957909" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.209408" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.685242" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.185841" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,5.99,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,9.46,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,19.19,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,27,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.278186" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.030287" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.369787" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.996616" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.160114" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="51.187283" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.540005" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.703506" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,99.27,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,107.08,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,115.52,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,121.97,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,131.69,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,139.5,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.278186" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.754021" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,164.7,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,168.17,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,177.9,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,185.71,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.278186" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.45" id="M34" style="vertical-align:-2.21957pt;width:69.75px;" version="1.1" viewbox="0 0 69.75 13.45" width="69.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.014903" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.055292" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.21879" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.470291" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.684044" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.935543" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="51.537365" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>和希尔伯特变换(<一个href="#EEq1.2">1.2</一个>)是由<gydF4y2Basvg height="22" id="M35" style="vertical-align:-4.59964pt;width:308.29999px;" version="1.1" viewbox="0 0 308.29999 22" width="308.29999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22)"> <g transform="translate(72,-54.4)"> <text transform="matrix(1,0,0,-1,-71.95,59.04)"> <tspan style="font-size: 12.50px; " x="54.16" y="0.029999999"> ∫</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.480154" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.643654" y="0"> P</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.495056" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.620808" y="0"> V</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.397675" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.523422" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-12.09,66.03)"> <tspan style="font-size: 8.75px; " x="-1" y="11.46"> 0</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,0.19,59.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,19.46,64.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,26.77,67.54)"> <tspan style="font-size: 6.25px; " x="0" y="0"> ′</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,29.57,59.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.829998" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.170219" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,67.31,64.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.6362882" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.213584" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="16.208704" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,88.11,67.54)"> <tspan style="font-size: 6.25px; " x="0" y="0"> ′</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,90.42,64.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,93.83,59.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.552772" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,111.95,64.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,118.89,59.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.955507" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.119007" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.658794" y="0"> ]</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.822296" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.985794" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="51.537365" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。</gydF4y2Bap> <p>我们提到以下技术成果:<gydF4y2Basvg height="19.725" id="M36" style="vertical-align:-4.77652pt;width:294.60001px;" version="1.1" viewbox="0 0 294.60001 19.725" width="294.60001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.725)"> <g transform="translate(72,-56.22)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.540029" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.316654" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.792488" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.181522" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.733093" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.896591" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.060093" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-24.31,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.51,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.754021" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.794409" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.446964" y="0"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.610462" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.501297" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="61.664795" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,50.72,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="7.0978718" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,62.91,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,71.03,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,77.44,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,87.17,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,94.97,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.278186" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.917519" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.418119" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,126.84,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,130.31,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,140.04,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,147.85,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.278186" y="0"> |</gydF4y2Batspan> </text> </g> </g> </svg>在哪里<gydF4y2Basvg height="16.512501" id="M37" style="vertical-align:-4.77652pt;width:18.2875px;" version="1.1" viewbox="0 0 18.2875 16.512501" width="18.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5125)"> <g transform="translate(72,-58.79)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-63.82,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>Schwarzian导数由吗<gydF4y2Basvg height="21.887501" id="M38" style="vertical-align:-4.77652pt;width:332.125px;" version="1.1" viewbox="0 0 332.125 21.887501" width="332.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,21.8875)"> <g transform="translate(72,-54.49)"> <text transform="matrix(1,0,0,-1,-71.95,59.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-63.82,56.18)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-57.42,59.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.479433" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.519823" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.683323" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-14.29,64.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-7.84,59.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.130791" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.606625" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,28.22,64.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,31.69,59.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.130791" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,59.99,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,66.25,59.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.491217" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.218552" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.470051" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.633549" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.79705" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,114.5,64.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,120.95,59.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.130791" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.606625" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,157,64.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,160.48,59.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.130791" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,188.78,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Baspan class="equation" id="EEq1.3"> <svg height="48.1875" id="M39" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.1875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.1875)"> <g transform="translate(72,-33.45)"> <text transform="matrix(1,0,0,-1,48.81,56.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 45.54,52.73 12.94,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,45.54,40.85)"> <tspan style="font-size: 12.50px; " x="16.219999" y="-3.8299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.959999" y="-8.75"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.040001" y="-16"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.429031" y="-16"> </gydF4y2Batspan> </text> <g> <path d="m 72.58,52.73 13.17,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,72.69,40.85)"> <tspan style="font-size: 12.50px; " x="16.34" y="-6.2399998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.190001" y="-8.75"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,100.44,54.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,108.25,49.6)"> <tspan style="font-size: 12.50px; " x="9.1199999" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.97" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.220001" y="-7.25"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.799999" y="-0.0099999998"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.963499" y="-0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.502567" y="-0.0099999998"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.141899" y="-0.0099999998"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.182289" y="-0.0099999998"> −</gydF4y2Batspan> </text> <g> <path d="m 171.19,52.73 12.95,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,171.19,40.85)"> <tspan style="font-size: 12.50px; " x="16.23" y="0.98000002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.720001" y="-17.01"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.57" y="-19.530001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.690001" y="-19.530001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.653931" y="-19.530001"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.817429" y="-19.530001"> 米</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,232.32,65.38)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="7.0978718" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,244.5,60.38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,252.63,57.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,261.12,57.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,272.54,65.38)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,280.34,57.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 196.88,52.73 95.16,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,222.42,40.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="3.1800001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="2.5" y="1.6"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,233.36,44.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,238.92,36.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,250.34,42.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,258.14,36.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8600001" y="-4.1100001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8600001" y="-0.93000001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.099998" y="-3.3599999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73" y="-13.05"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="90.019997" y="-13.05"> ]</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.84" y="-13.09"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.867886" y="-13.09"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="77.160004" y="-13.09"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="81.048431" y="-13.09"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="96.260002" y="-13.1"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="100.4235" y="-13.1"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="106.97507" y="-13.1"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="111.13857" y="-13.1"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="206.61" y="-13.09"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="210.7735" y="-13.09"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="217.02499" y="-13.09"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="220.15074" y="-13.09"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="226.40225" y="-13.09"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>在哪里<gydF4y2Baspan class="equation" id="eq1"> <svg height="94.050003" id="M40" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 94.050003" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,94.05)"> <g transform="translate(72,3.24)"> <text transform="matrix(1,0,0,-1,13.4,51.78)"> <tspan style="font-size: 12.50px; " x="41.580002" y="7.3200002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.029999" y="-7.25"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.203648" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.892754" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.532085" y="0"> =</gydF4y2Batspan> </text> <g> <path d="m 65.55,54.91 34.02,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,65.55,43.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="3.1700001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="2.5" y="1.59"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,76.49,47.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,82.05,41.99)"> <tspan style="font-size: 12.50px; " x="15.02" y="-1.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.02" y="1.59"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.580002" y="-2.47"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.709999" y="-2.47"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.162748" y="-2.47"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.52" y="-9.79"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.859501" y="-9.79"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.959999" y="-9.79"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="70.211502" y="-9.79"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,158.95,56.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,163.83,51.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,171.95,48.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,180.44,51.79)"> <tspan style="font-size: 12.50px; " x="54.84" y="-8.3400002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.791769" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.13199" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.91" y="7.3299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.261524" y="7.3299999"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,243.72,65.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,252.25,60.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 235.28,54.91 31.99,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,236.77,42.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,245.2,47.08)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,250.76,42.01)"> <tspan style="font-size: 12.50px; " x="17.700001" y="-2.45"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,277.84,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,284.09,51.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.54" y="-8.3500004"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,305.07,65.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,313.6,60.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 296.63,54.91 31.99,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,298.12,42.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,306.56,47.08)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,312.12,42.01)"> <tspan style="font-size: 12.50px; " x="17.700001" y="-2.45"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.27" y="-18.120001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,348.83,65.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,357.36,60.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 340.39,54.91 31.99,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,341.88,42.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,350.32,47.08)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,355.87,42.01)"> <tspan style="font-size: 12.50px; " x="17.700001" y="-2.45"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,382.95,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,386.42,44.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3515239" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-273.92999" y="35.400002"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-263.28995" y="35.400002"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-259.12643" y="35.400002"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-246.12" y="27.049999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-239.43089" y="27.049999"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,155.43,22.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,163.97,17.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 140.3,12.18 38.68,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,145.14,-0.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,153.58,4.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,159.13,-0.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.129999" y="-9.7700005"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.293499" y="-9.7700005"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.096333" y="-9.7700005"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,204.93,14.13)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,209.8,9.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,217.93,5.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,226.42,9.06)"> <tspan style="font-size: 12.50px; " x="17.1" y="7.3299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.530001" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="238.33" y="-22.190001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="242.4935" y="-22.190001"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="248.745" y="-22.190001"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="251.87074" y="-22.190001"> 4</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="258.12225" y="-22.190001"> )</gydF4y2Batspan> </text> </g> </g> </svg></span></p> <p>无限域与有界的情况下补充可以看作是动态以来Hele-Shaw细胞收缩泡沫流体占据了一个附近的无穷和注入(持续的力量<gydF4y2Basvg height="13.0625" id="M41" style="vertical-align:-1.90608pt;width:39.537498px;" version="1.1" viewbox="0 0 39.537498 13.0625" width="39.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0625)"> <g transform="translate(72,-61.55)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.228174" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.268562" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>)是应该发生在无穷。再一次,我们表示<gydF4y2Basvg height="13.45" id="M42" style="vertical-align:-2.21957pt;width:27.049999px;" version="1.1" viewbox="0 0 27.049999 13.45" width="27.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.379169" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>域的流体<gydF4y2Basvg height="9.125" id="M43" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.45" id="M44" style="vertical-align:-2.21957pt;width:78.900002px;" version="1.1" viewbox="0 0 78.900002 13.45" width="78.900002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.3392611" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.50276" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.416199" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.04303" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.08342" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.47245" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.774685" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.938183" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.85162" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。通过使用黎曼映射定理,域<gydF4y2Basvg height="13.45" id="M45" style="vertical-align:-2.21957pt;width:27.049999px;" version="1.1" viewbox="0 0 27.049999 13.45" width="27.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.379169" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>可以被描述为单叶函数<gydF4y2Basvg height="13.55" id="M46" style="vertical-align:-2.29482pt;width:39.962502px;" version="1.1" viewbox="0 0 39.962502 13.55" width="39.962502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.780706" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.694145" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>从单位的外部磁盘<gydF4y2Basvg height="13.8625" id="M47" style="vertical-align:-2.37006pt;width:118.3875px;" version="1.1" viewbox="0 0 118.3875 13.8625" width="118.3875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.8625)"> <g transform="translate(72,-60.91)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,68.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-51.79,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> {</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.029325" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.194265" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.995895" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.496498" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.1856" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.149532" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.189922" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.441422" y="0"> }</gydF4y2Batspan> </text> </g> </g> </svg>到<gydF4y2Basvg height="13.45" id="M48" style="vertical-align:-2.21957pt;width:27.049999px;" version="1.1" viewbox="0 0 27.049999 13.45" width="27.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.379169" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="14.75" id="M49" style="vertical-align:-3.25793pt;width:186.175px;" version="1.1" viewbox="0 0 186.175 14.75" width="186.175" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.780706" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.694145" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.333477" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.373867" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.650372" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.115143" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="74.455368" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,8.79,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,16.44,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,34.06,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,38.94,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.940605" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.280827" y="0"> ⋯</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="11.0625" id="M50" style="vertical-align:-0.30096pt;width:35.174999px;" version="1.1" viewbox="0 0 35.174999 11.0625" width="35.174999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.7398367" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.780226" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。</gydF4y2Bap> <p>满足方程的自由边界(<一个href="#B13">4</一个>,<gydF4y2Ba一个href="#B15">6</一个>]<ggydF4y2BaydF4y2Baspan class="equation" id="EEq1.4"> <svg height="31.5875" id="M51" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 31.5875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,31.5875)"> <g transform="translate(72,-46.73)"> <text transform="matrix(1,0,0,-1,110.47,55.7)"> <tspan style="font-size: 12.50px; " x="18.059999" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.450001" y="-2.53"> ̇</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.799999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.415287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.578785" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.267891" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="51.481644" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.395081" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 172.12,68.41 45.92,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,172.12,55.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.6766019" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,188.35,60.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,193.9,55.7)"> <tspan style="font-size: 12.50px; " x="24.139999" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.349998" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.630001" y="-7.9099998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 240.49,58.82 13.85,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,240.49,46.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.05" y="-8.7600002"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.216139" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.381077" y="-8.7600002"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.408962" y="-8.7600002"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,298.47,60.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,464.75,56.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.540749" y="0"> 5</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>为零和表面张力模型<gydF4y2Baspan class="equation" id="EEq1.5"> <svg height="31.5875" id="M52" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 31.5875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,31.5875)"> <g transform="translate(72,-46.73)"> <text transform="matrix(1,0,0,-1,50.05,55.7)"> <tspan style="font-size: 12.50px; " x="18.059999" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.440001" y="-2.53"> ̇</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.799999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.415287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.578785" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.267891" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="51.481644" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.395081" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 111.69,68.41 45.93,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,111.69,55.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.689105" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,127.92,60.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,133.48,55.7)"> <tspan style="font-size: 12.50px; " x="24.139999" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.349998" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.630001" y="-7.9099998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 180.06,58.82 13.86,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,180.06,46.94)"> <tspan style="font-size: 12.50px; " x="49.650002" y="-3.8399999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.389999" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.83" y="-8.7600002"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.170221" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.521744" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="60.470001" y="-16.01"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.859032" y="-16.01"> </gydF4y2Batspan> </text> <g> <path d="m 240.53,58.82 13.17,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,241.97,46.94)"> <tspan style="font-size: 12.50px; " x="15.01" y="-6.2399998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.860001" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,268.39,60.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,276.2,55.7)"> <tspan style="font-size: 12.50px; " x="9.1199999" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.98" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.799999" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.963499" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.502567" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.754066" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.920208" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.085144" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="77.125534" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,358.9,60.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,464.75,56.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.540749" y="0"> 6</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>小的表面张力模型。</gydF4y2Bap> <h4 id="the-inner-problem-(bounded-domains)">2。内部问题(有限域)</h4><gydF4y2Bap>在本节中,我们获得时间的不变性<gydF4y2Basvg height="10.475" id="M53" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>样式属性的内在问题。从最初的有限域<gydF4y2Basvg height="13.45" id="M54" style="vertical-align:-2.21957pt;width:29.975px;" version="1.1" viewbox="0 0 29.975 13.45" width="29.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.717232" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>这是<gydF4y2Basvg height="10.475" id="M55" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如,我们证明在每个时刻<gydF4y2Basvg height="13.45" id="M56" style="vertical-align:-2.21957pt;width:57.737499px;" version="1.1" viewbox="0 0 57.737499 13.45" width="57.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.922558" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>域<gydF4y2Basvg height="13.45" id="M57" style="vertical-align:-2.21957pt;width:27.049999px;" version="1.1" viewbox="0 0 27.049999 13.45" width="27.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.379169" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="10.475" id="M58" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>——(表面张力为零,零模型)。</gydF4y2Bap> <p><span class="statement" id="deff2.1"><span class="statement-title"><i class="statement-title">定义2.1。</我></span>让<gydF4y2Basvg height="13.4875" id="M59" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是一个全纯函数<gydF4y2Basvg height="10.5375" id="M60" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>这样<gydF4y2Basvg height="13.6125" id="M61" style="vertical-align:-2.34499pt;width:54.224998px;" version="1.1" viewbox="0 0 54.224998 13.6125" width="54.224998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.354164" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.980993" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.021381" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="13.6375" id="M62" style="vertical-align:-2.34499pt;width:55.262501px;" version="1.1" viewbox="0 0 55.262501 13.6375" width="55.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6375)"> <g transform="translate(72,-61.09)"> <text transform="matrix(1,0,0,-1,-71.95,63.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.552532" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.716031" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.967531" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.206528" y="0"> ≠</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.859085" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。让<gydF4y2Basvg height="10.475" id="M63" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>是一个全纯函数<gydF4y2Basvg height="13.6125" id="M64" style="vertical-align:-2.34499pt;width:30.225px;" version="1.1" viewbox="0 0 30.225 13.6125" width="30.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.917278" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>这样<gydF4y2Basvg height="13.45" id="M65" style="vertical-align:-2.21957pt;width:57.474998px;" version="1.1" viewbox="0 0 57.474998 13.45" width="57.474998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.954788" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.581617" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.622005" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="13.4875" id="M66" style="vertical-align:-2.21957pt;width:84.5625px;" version="1.1" viewbox="0 0 84.5625 13.4875" width="84.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.054333" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.594122" y="0"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.207487" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.370987" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.622486" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.261822" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="61.289707" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。我们说<gydF4y2Basvg height="13.4875" id="M67" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="10.475" id="M68" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如在<gydF4y2Basvg height="10.5375" id="M69" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>(或<gydF4y2Basvg height="10.475" id="M70" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>——如果<gydF4y2Baspan class="equation" id="EEq2.1"> <svg height="38.575001" id="M71" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.575001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,38.575)"> <g transform="translate(72,-41.14)"> <text transform="matrix(1,0,0,-1,111.88,53.45)"> <tspan style="font-size: 12.50px; " x="18.059999" y="7.3299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.4" y="-8.3500004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.638996" y="-8.3500004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.578163" y="-8.3500004"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.267029" y="-8.3500004"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.430527" y="-8.3500004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="60.669521" y="-8.3500004"> )</gydF4y2Batspan> </text> <g> <path d="m 137.48,56.57 45.04,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,137.48,44.69)"> <tspan style="font-size: 12.50px; " x="46.240002" y="-1.4299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.306313" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.46981" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.708809" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.872307" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.060001" y="-8.7600002"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.100388" y="-8.7600002"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="74.351891" y="-8.7600002"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="89.518028" y="-8.7600002"> f</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="93.293938" y="-8.7600002"> o</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="99.545433" y="-8.7600002"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="106.82218" y="-8.7600002"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="112.37351" y="-8.7600002"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="117.92484" y="-8.7600002"> c</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="123.28863" y="-8.7600002"> h</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="133.69113" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="143.40596" y="-8.7600002"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="155.44635" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="164.26096" y="-8.7600002"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="327.26999" y="-8.7600002"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="331.4335" y="-8.7600002"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="337.685" y="-8.7600002"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="340.81076" y="-8.7600002"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="347.06226" y="-8.7600002"> )</gydF4y2Batspan> </text> </g> </g> </svg></span></span></p> <p>我们的话,<gydF4y2Basvg height="10.475" id="M72" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>——函数是单价的。事实上,任何单价的函数<gydF4y2Basvg height="10.475" id="M73" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如对于一些<gydF4y2Basvg height="10.475" id="M74" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>。</gydF4y2Bap> <p><span class="statement" id="rem2.2"><span class="statement-title"><i class="statement-title">2.2的话。</我></span>(一)的概念<gydF4y2Basvg height="10.475" id="M75" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>肖像Brickman于1973年被引入和研究[<一个href="#B1">12</一个>)和概括的概念starlikeness spiral-likeness。这一概念的应用研究的单价可能会发现在<一个href="#B3">13</一个>]。<gydF4y2Babr>(b)如果<gydF4y2Basvg height="13.45" id="M76" style="vertical-align:-2.21957pt;width:66.074997px;" version="1.1" viewbox="0 0 66.074997 13.45" width="66.074997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.393112" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.019943" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.060333" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>在上面的定义中,<gydF4y2Basvg height="13.4875" id="M77" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是星形的。<gydF4y2Babr>(c)如果<gydF4y2Basvg height="13.45" id="M78" style="vertical-align:-2.21957pt;width:74.525002px;" version="1.1" viewbox="0 0 74.525002 13.45" width="74.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.393112" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.019943" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.060333" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.824455" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="11.0625" id="M79" style="vertical-align:-0.30096pt;width:55.75px;" version="1.1" viewbox="0 0 55.75 11.0625" width="55.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.206287" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.246677" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,然后<gydF4y2Basvg height="13.4875" id="M80" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是spiral-like类型的<gydF4y2Basvg height="13.975" id="M81" style="vertical-align:-2.73372pt;width:44.450001px;" version="1.1" viewbox="0 0 44.450001 13.975" width="44.450001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.975)"> <g transform="translate(72,-60.82)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.640053" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.354883" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.694386" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。</gydF4y2Baspan></p> <p>我们重申,一个全纯函数<gydF4y2Basvg height="13.4875" id="M82" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>在<gydF4y2Basvg height="10.5375" id="M83" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>这样<gydF4y2Basvg height="13.6125" id="M84" style="vertical-align:-2.34499pt;width:54.224998px;" version="1.1" viewbox="0 0 54.224998 13.6125" width="54.224998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.354164" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.980993" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.021381" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="13.6375" id="M85" style="vertical-align:-2.34499pt;width:55.262501px;" version="1.1" viewbox="0 0 55.262501 13.6375" width="55.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6375)"> <g transform="translate(72,-61.09)"> <text transform="matrix(1,0,0,-1,-71.95,63.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.552532" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.716031" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.967531" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.206528" y="0"> ≠</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.859085" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>据说spiral-like类型的吗<gydF4y2Basvg height="13.45" id="M86" style="vertical-align:-2.21957pt;width:99.275002px;" version="1.1" viewbox="0 0 99.275002 13.45" width="99.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.515023" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.555412" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.71891" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.283466" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.885288" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.361122" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.612625" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.826374" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.4282" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.90403" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.155533" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>如果<gydF4y2Basvg height="16.0375" id="M87" style="vertical-align:-2.34499pt;width:145.27499px;" version="1.1" viewbox="0 0 145.27499 16.0375" width="145.27499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.0375)"> <g transform="translate(72,-59.17)"> <text transform="matrix(1,0,0,-1,-71.95,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.129829" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-46.25,66.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-38.09,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.238997" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.178162" y="0"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.791529" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.955029" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.194025" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.357525" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.833359" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.772522" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.936024" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.175018" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.338516" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.965347" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="76.005737" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="10.75" id="M88" style="vertical-align:-0.33858pt;width:40.049999px;" version="1.1" viewbox="0 0 40.049999 10.75" width="40.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.75)"> <g transform="translate(72,-63.4)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.742718" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>(<一个href="#B3">13</一个>,<gydF4y2Ba一个href="#B10">14</一个>]。</gydF4y2Bap> <p>下面的结果是一个概括的<一个href="#B5">1</一个>定理1)的情况下<gydF4y2Basvg height="10.475" id="M89" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>——功能。提到定理可能获得通过<gydF4y2Basvg height="13.45" id="M90" style="vertical-align:-2.21957pt;width:66.074997px;" version="1.1" viewbox="0 0 66.074997 13.45" width="66.074997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.393112" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.019943" y="0"> ≡</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.060333" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>在定理<一个href="#thm2.3">2。3</一个>在下面。</gydF4y2Bap> <p><span class="statement" id="thm2.3"><span class="statement-title">定理2.3。</gydF4y2Baspan><i>让<gydF4y2Basvg height="13.0625" id="M91" style="vertical-align:-1.90608pt;width:39.537498px;" version="1.1" viewbox="0 0 39.537498 13.0625" width="39.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0625)"> <g transform="translate(72,-61.55)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.228174" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.268562" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="14.625" id="M92" style="vertical-align:-3.25793pt;width:14.8875px;" version="1.1" viewbox="0 0 14.8875 14.625" width="14.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>是一个函数<gydF4y2Basvg height="10.475" id="M93" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如在<gydF4y2Basvg height="10.5375" id="M94" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和单价的<gydF4y2Basvg height="15.6875" id="M95" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 15.6875" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.6875)"> <g transform="translate(72,-59.45)"> <g> <path d="m -71.95,70.71 10.19,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。让<gydF4y2Basvg height="13.6125" id="M96" style="vertical-align:-2.34499pt;width:38.974998px;" version="1.1" viewbox="0 0 38.974998 13.6125" width="38.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>的经典解决方案Polubarinova-Galin方程(<一个href="#EEq1.1">1.1</一个>与初始条件)<gydF4y2Basvg height="14.75" id="M97" style="vertical-align:-3.25793pt;width:94.824997px;" version="1.1" viewbox="0 0 94.824997 14.75" width="94.824997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.244516" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.88385" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.92424" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.08,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-11.21,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。也让<gydF4y2Basvg height="17.924999" id="M98" style="vertical-align:-4.67863pt;width:217.60001px;" version="1.1" viewbox="0 0 217.60001 17.924999" width="217.60001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.925)"> <g transform="translate(72,-57.66)"> <text transform="matrix(1,0,0,-1,-71.95,62.37)"> <tspan style="font-size: 12.50px; " x="24.809999" y="0.02"> ⋃</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.765563" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-35.58,58.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="13.110496" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="19.105616" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-7.68,62.37)"> <tspan style="font-size: 12.50px; " x="37.049999" y="0.02"> ⋃</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.379169" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,40.92,58.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="13.110496" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="19.105616" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,68.83,62.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.917278" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.118526" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.031965" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="10.325" id="M99" style="vertical-align:-0.0pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 10.325" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>充气时间。如果<gydF4y2Basvg height="10.475" id="M100" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>全纯在<gydF4y2Basvg height="15.85" id="M101" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 15.85" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.85)"> <g transform="translate(72,-59.32)"> <g> <path d="m -71.95,70.71 9.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> </text> </g> </g> </svg>和满足条件</我><span class="equation" id="EEq2.2"> <svg height="20.5375" id="M102" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 20.5375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.5375)"> <g transform="translate(72,-55.57)"> <text transform="matrix(1,0,0,-1,141.94,59.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.054333" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.594122" y="0"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.282986" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.446484" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.136311" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.775642" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.816032" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73.067535" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="88.233673" y="0"> ∀</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="95.235352" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="108.40101" y="0"> ∈</gydF4y2Batspan> </text> <g> <path d="m 262.39,70.71 9.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,262.39,59.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="202.36" y="-1.29"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="206.5235" y="-1.29"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="212.77499" y="-1.29"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="215.90074" y="-1.29"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="222.15225" y="-1.29"> )</gydF4y2Batspan> </text> </g> </g> </svg></span><i>然后<gydF4y2Basvg height="13.6125" id="M103" style="vertical-align:-2.34499pt;width:38.974998px;" version="1.1" viewbox="0 0 38.974998 13.6125" width="38.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="10.475" id="M104" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>像<gydF4y2Basvg height="13.45" id="M105" style="vertical-align:-2.21957pt;width:57.737499px;" version="1.1" viewbox="0 0 57.737499 13.45" width="57.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.922558" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。</我></span></p> <p><span class="statement" id="proof1"><span class="statement-title"><i class="statement-title">证明。</我></span>考虑到所有的功能<gydF4y2Basvg height="13.6125" id="M106" style="vertical-align:-2.34499pt;width:38.974998px;" version="1.1" viewbox="0 0 38.974998 13.6125" width="38.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>分析单价的扩展吗<gydF4y2Basvg height="15.6875" id="M107" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 15.6875" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.6875)"> <g transform="translate(72,-59.45)"> <g> <path d="m -71.95,70.71 10.19,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>为每一个<gydF4y2Basvg height="13.45" id="M108" style="vertical-align:-2.21957pt;width:57.737499px;" version="1.1" viewbox="0 0 57.737499 13.45" width="57.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.922558" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>结果他们的衍生品<gydF4y2Basvg height="13.6375" id="M109" style="vertical-align:-2.34499pt;width:43.487499px;" version="1.1" viewbox="0 0 43.487499 13.6375" width="43.487499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6375)"> <g transform="translate(72,-61.09)"> <text transform="matrix(1,0,0,-1,-71.95,63.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.552532" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.716031" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.392633" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.606384" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.519823" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是连续的,不消失<gydF4y2Basvg height="15.6875" id="M110" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 15.6875" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.6875)"> <g transform="translate(72,-59.45)"> <g> <path d="m -71.95,70.71 10.19,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,我们可以替换为“≥”定义的不平等(<一个href="#EEq2.1">2。1</一个>)<ggydF4y2BaydF4y2Basvg height="10.475" id="M111" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>式函数。的平等只能获得<gydF4y2Basvg height="13.55" id="M112" style="vertical-align:-2.29482pt;width:41.9375px;" version="1.1" viewbox="0 0 41.9375 13.55" width="41.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.1772022" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.153636" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.194025" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>。<gydF4y2Babr>我们假设相反,定理的结论<一个href="#thm2.3">2。3</一个>是不正确的。然后存在<gydF4y2Basvg height="14.75" id="M113" style="vertical-align:-3.25793pt;width:38.3125px;" version="1.1" viewbox="0 0 38.3125 14.75" width="38.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-59.69,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≥</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="17.75" id="M114" style="vertical-align:-3.25793pt;width:55.212502px;" version="1.1" viewbox="0 0 55.212502 17.75" width="55.212502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.75)"> <g transform="translate(72,-57.8)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.26,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.91,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-39.31,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-32,63.92)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>这样<gydF4y2Basvg height="16.700001" id="M115" style="vertical-align:-3.25793pt;width:299.32501px;" version="1.1" viewbox="0 0 299.32501 16.700001" width="299.32501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.7)"> <g transform="translate(72,-58.64)"> <text transform="matrix(1,0,0,-1,-71.95,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.129829" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.293329" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-40.96,58.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-36.09,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-27.65,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-24.18,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-13.32,58.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-8.45,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,0.67,58.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,5.55,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.179123" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.342621" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.281786" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.445286" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,44.68,58.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,49.56,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,58.68,58.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,63.55,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3269978" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.994217" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.596043" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.071877" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.662876" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.826374" y="0"> o</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="64.077873" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="71.017036" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="82.369766" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="89.971588" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="93.447418" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="99.698921" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,相当于<gydF4y2Baspan class="equation" id="EEq2.3"> <svg height="45.787498" id="M116" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 45.787498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,45.7875)"> <g transform="translate(72,-35.37)"> <text transform="matrix(1,0,0,-1,84.39,50.56)"> <tspan style="font-size: 12.50px; " x="22" y="-10.57"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,113.08,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,117.95,61.13)"> <tspan style="font-size: 12.50px; " x="12.64" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.49" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> ′</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,143.13,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,148,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,157.13,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,162,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 101.56,53.68 71.12,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,101.56,39.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.63" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.48" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.849998" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,142.1,36.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,146.98,39.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,156.1,36.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,160.97,37.47)"> <tspan style="font-size: 12.50px; " x="81.790001" y="-23.66"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.379999" y="-13.09"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.407887" y="-13.09"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.659386" y="-13.09"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.790417" y="-13.09"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.953915" y="-13.09"> 米</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,249.45,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,254.33,61.13)"> <tspan style="font-size: 12.50px; " x="12.63" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.49" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> ′</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,279.51,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,284.38,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,293.5,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,298.38,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 237.94,53.68 71.11,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,237.94,39.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.62" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.469999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.849998" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,278.48,36.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,283.35,39.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,292.48,36.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,297.35,37.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.98" y="-13.09"> ≠</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.620052" y="-13.09"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.871553" y="-13.09"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="167.39999" y="-13.09"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="171.56349" y="-13.09"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="177.815" y="-13.09"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="180.94075" y="-13.09"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="187.19225" y="-13.09"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>对于每个<gydF4y2Basvg height="11.0625" id="M117" style="vertical-align:-0.30096pt;width:34.887501px;" version="1.1" viewbox="0 0 34.887501 11.0625" width="34.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5147829" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.555172" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,有<gydF4y2Basvg height="13.05" id="M118" style="vertical-align:-3.25793pt;width:35.387501px;" version="1.1" viewbox="0 0 35.387501 13.05" width="35.387501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-48.61,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="14.75" id="M119" style="vertical-align:-3.25793pt;width:123.625px;" version="1.1" viewbox="0 0 123.625 14.75" width="123.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.014903" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.055292" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.21879" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-39.17,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-31.52,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.391672" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.59292" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-2.36,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,5.29,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.391672" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>这样<gydF4y2Baspan class="equation" id="EEq2.4"> <svg height="45.837502" id="M120" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 45.837502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,45.8375)"> <g transform="translate(72,-35.33)"> <text transform="matrix(1,0,0,-1,110.25,50.52)"> <tspan style="font-size: 12.50px; " x="22.49" y="-10.58"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> g</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,138.3,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,146.11,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,154.55,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,160.1,58.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,171.52,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,179.32,61.1)"> <tspan style="font-size: 12.50px; " x="9.1300001" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 129.49,53.65 68.05,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,129.49,39.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.63" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.48" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.849998" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,168.91,43.39)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,176.71,39.95)"> <tspan style="font-size: 12.50px; " x="25.5" y="-10.57"> ≥</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.73" y="-17.83"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.1300001" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.981404" y="2.52"> </gydF4y2Batspan> </text> <g> <path d="m 215.44,53.65 7.6,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,216.12,41.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.17" y="-3.8299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.769997" y="-16.01"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.530001" y="-8.75"> o</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.781502" y="-8.75"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.408329" y="-8.75"> ≤</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.224384" y="-8.75"> −</gydF4y2Batspan> </text> <g> <path d="m 284.89,53.65 7.61,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,285.57,41.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.1199999" y="-3.8299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.809999" y="-8.75"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="179.17999" y="-8.7700005"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="183.34351" y="-8.7700005"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="189.595" y="-8.7700005"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="192.72075" y="-8.7700005"> 4</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="198.97224" y="-8.7700005"> )</gydF4y2Batspan> </text> </g> </g> </svg></span><br>让<gydF4y2Basvg height="13.05" id="M121" style="vertical-align:-3.25793pt;width:11.1125px;" version="1.1" viewbox="0 0 11.1125 13.05" width="11.1125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>是第一个这样的点,<gydF4y2Basvg height="14.75" id="M122" style="vertical-align:-3.25793pt;width:63.825001px;" version="1.1" viewbox="0 0 63.825001 14.75" width="63.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-59.69,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.442884" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.656635" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.533287" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。不失一般性,我们假设<gydF4y2Baspan class="equation" id="EEq2.5"> <svg height="45.787498" id="M123" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 45.787498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,45.7875)"> <g transform="translate(72,-35.37)"> <text transform="matrix(1,0,0,-1,151.19,50.56)"> <tspan style="font-size: 12.50px; " x="21.32" y="-10.57"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 米</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,179.2,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,184.07,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,192.51,66.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,198.07,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,210.61,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,215.48,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,224.61,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,229.48,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 168.36,53.68 71.12,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,168.36,39.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.63" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.48" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.849998" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,208.9,36.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,213.78,39.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,222.9,36.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,227.77,37.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.370001" y="-13.09"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.410389" y="-13.09"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.661888" y="-13.09"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="236.98" y="-13.09"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="241.14349" y="-13.09"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="247.395" y="-13.09"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="250.52075" y="-13.09"> 5</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="256.77225" y="-13.09"> )</gydF4y2Batspan> </text> </g> </g> </svg></span><br>事实上,<gydF4y2Basvg height="14.75" id="M124" style="vertical-align:-3.25793pt;width:39.137501px;" version="1.1" viewbox="0 0 39.137501 14.75" width="39.137501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-49.77,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-44.9,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是一个函数的最大值点<gydF4y2Basvg height="17.75" id="M125" style="vertical-align:-3.25793pt;width:269.58749px;" version="1.1" viewbox="0 0 269.58749 17.75" width="269.58749" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.75)"> <g transform="translate(72,-57.8)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.1514759" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.314975" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.416199" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.617447" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.16902" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.808353" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.84874" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.400074" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.563572" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.978569" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="71.142067" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="76.243294" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,9.86,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,17.67,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,26.11,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,29.58,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.2647228" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,44.41,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,52.22,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,61.34,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,66.22,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.179123" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.342621" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.281786" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.445286" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.546509" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,109.33,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,117.13,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,126.26,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,131.13,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3269978" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="13.125" id="M126" style="vertical-align:-1.95624pt;width:58.4375px;" version="1.1" viewbox="0 0 58.4375 13.125" width="58.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.125)"> <g transform="translate(72,-61.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.5645552" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.604944" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.768442" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.019943" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.233692" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.485195" y="0"> ]</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.125" id="M127" style="vertical-align:-1.95624pt;width:69.75px;" version="1.1" viewbox="0 0 69.75 13.125" width="69.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.125)"> <g transform="translate(72,-61.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.014903" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.055292" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.21879" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.470291" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.684044" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.935543" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="51.537365" y="0"> ]</gydF4y2Batspan> </text> </g> </g> </svg>。因此,<gydF4y2Basvg height="14.75" id="M128" style="vertical-align:-3.25793pt;width:112.95px;" version="1.1" viewbox="0 0 112.95 14.75" width="112.95" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.540029" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.015863" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.404896" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.956469" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.119967" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.271442" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.43494" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.686443" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.900192" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-12.49,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-7.62,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="14.75" id="M129" style="vertical-align:-3.25793pt;width:111.1375px;" version="1.1" viewbox="0 0 111.1375 14.75" width="111.1375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.540029" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.015863" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.404896" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.506121" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.669619" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.821095" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.984592" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.236095" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="51.449844" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-13.94,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-9.07,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> ≥</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>(平稳性条件在一个区间的端点),结果我们获得<gydF4y2Baspan class="equation" id="EEq2.6"> <svg height="107.45" id="M130" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 107.45" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,107.45)"> <g transform="translate(72,13.96)"> <text transform="matrix(1,0,0,-1,55.56,49.6)"> <tspan style="font-size: 12.50px; " x="18.049999" y="9.7299995"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.73" y="-10.58"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.16" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.174664" y="0"> +</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,111.97,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,116.85,60.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,125.29,65.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,133.82,57.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,146.36,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,151.24,60.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,160.36,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,165.23,57.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 105.29,52.73 65.8,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,112.55,39.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,120.99,44.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,126.55,36.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,139.09,35.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,143.97,39.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,153.09,35.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,157.96,36.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.1" y="-13.09"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.639999" y="-23.67"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,197.14,65.18)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,202.7,57.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.370001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.219999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,231.61,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,236.49,60.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,245.61,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,250.48,57.67)"> <tspan style="font-size: 12.50px; " x="13.79" y="-2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,270.96,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,275.83,60.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,284.27,65.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,289.83,57.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,302.37,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,307.24,60.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,316.37,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,321.24,57.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 187.6,52.73 139.49,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,221.79,39.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.62" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.469999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.849998" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,262.33,35.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,267.2,39.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,276.33,35.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,281.2,36.51)"> <tspan style="font-size: 12.50px; " x="47.09" y="-3.3599999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-207.59" y="44.060001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-175.91" y="23.75"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="60.66" y="-13.09"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.700386" y="-13.09"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="78.951889" y="-13.09"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="183.55" y="-13.09"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="187.7135" y="-13.09"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="193.965" y="-13.09"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="197.09074" y="-13.09"> 6</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="203.34225" y="-13.09"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-225.64" y="34.32"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-221.4765" y="34.32"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-197.48" y="34.32"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-188.46533" y="34.32"> +</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,111.97,9.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,116.85,12.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,125.29,17.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,133.82,10.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,146.36,9.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,151.24,12.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,160.36,9.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,165.23,10.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 105.29,5.31 65.8,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,112.55,-8.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,120.99,-3.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,126.55,-10.9)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,139.09,-11.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,143.97,-8.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,153.09,-11.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,157.96,-10.9)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.1" y="-13.09"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.639999" y="-23.66"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,197.14,17.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,202.7,10.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.370001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.219999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,231.61,9.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,236.49,12.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,245.61,9.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,250.48,10.25)"> <tspan style="font-size: 12.50px; " x="13.79" y="-2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,270.96,9.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,275.83,12.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,284.27,17.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,289.83,10.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,302.37,9.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,307.24,12.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,316.37,9.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,321.24,10.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 187.6,5.31 139.49,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,221.79,-8.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.62" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.469999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.849998" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,262.33,-11.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,267.2,-8.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,276.33,-11.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,281.2,-10.9)"> <tspan style="font-size: 12.50px; " x="47.09" y="-3.3499999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="60.66" y="-13.09"> ≥</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.700386" y="-13.09"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="78.951889" y="-13.09"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="183.55" y="-13.09"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="187.7135" y="-13.09"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="193.965" y="-13.09"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="197.09074" y="-13.09"> 7</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="203.34225" y="-13.09"> )</gydF4y2Batspan> </text> </g> </g> </svg></span><br>通过简单的计算,我们得到的<gydF4y2Baspan class="equation" id="EEq2.8"> <svg height="38.575001" id="M132" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.575001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,38.575)"> <g transform="translate(72,-41.14)"> <text transform="matrix(1,0,0,-1,32.37,60.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 30.41,56.57 10.31,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,30.41,44.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.59" y="-8.7600002"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.141333" y="-8.7600002"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.304831" y="-8.7600002"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.73" y="-17.110001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.406601" y="-17.110001"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,83.26,66.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,88.82,61.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 63.24,56.57 54.62,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,63.24,44.69)"> <tspan style="font-size: 12.50px; " x="89.379997" y="-1.4299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.306313" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.46981" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.158916" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.372665" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.286106" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.449604" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.279999" y="-8.7600002"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="71.320389" y="-8.7600002"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.483887" y="-8.7600002"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="99.949997" y="-17.110001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="104.1135" y="-17.110001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="110.50253" y="-17.110001"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="113.97836" y="-17.110001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="120.3674" y="-17.110001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="124.28084" y="-17.110001"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="130.51984" y="-17.110001"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,202.21,66.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,207.77,61.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 163.19,56.57 68.72,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,178.48,43.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,186.92,48.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,192.48,43.67)"> <tspan style="font-size: 12.50px; " x="43.400002" y="-9.7799997"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.939999" y="-18.129999"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,257.96,66.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,263.52,61.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.678522" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.842022" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.531126" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.744877" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.658318" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.821815" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.060814" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.224312" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.613342" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.089176" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.47821" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="69.391647" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.64315" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="86.170677" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="90.334175" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="97.023277" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="102.22453" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="106.13797" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 248.42,56.57 125.41,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,283.82,44.69)"> <tspan style="font-size: 12.50px; " x="91.209999" y="-1.4299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.306313" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.46981" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.158916" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.372665" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.286106" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.449604" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="100.59" y="-8.7600002"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="180.92999" y="-8.7600002"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="185.09351" y="-8.7600002"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="191.345" y="-8.7600002"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="194.47075" y="-8.7600002"> 8</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="200.72224" y="-8.7600002"> )</gydF4y2Batspan> </text> </g> </g> </svg></span><br>通过区分Polubarinova-Galin方程对<gydF4y2Basvg height="10.7375" id="M133" style="vertical-align:-0.13794pt;width:8.3125px;" version="1.1" viewbox="0 0 8.3125 10.7375" width="8.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,我们获得<gydF4y2Basvg height="21.9375" id="M134" style="vertical-align:-2.34499pt;width:486.96249px;" version="1.1" viewbox="0 0 486.96249 21.9375" width="486.96249" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,21.9375)"> <g transform="translate(72,-54.45)"> <text transform="matrix(1,0,0,-1,-71.95,56.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.054333" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.217831" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.38133" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.770363" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.246197" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.635231" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.548668" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.71217" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-12.79,61.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-9.32,56.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 14.82,69.74 36.05,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,14.82,56.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,23.26,61.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,26.73,56.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.918959" y="0"> −</gydF4y2Batspan> </text> <g> <path d="m 64.99,69.74 42.75,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,64.99,56.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.689105" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,80.12,61.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,83.6,56.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.130791" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.294289" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.683323" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.159157" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.548187" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.461628" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.625126" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.564293" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.727791" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="70.416893" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.630646" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="79.544083" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="86.483253" y="0"> −</gydF4y2Batspan> </text> <g> <path d="m 181.43,70.71 50.59,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,181.43,56.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,188.12,61.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,192.99,56.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,201.43,61.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,207.88,56.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.130791" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.294289" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.683323" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.159157" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.548187" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.461628" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.625126" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.564293" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.727791" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="70.416893" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.630646" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="79.544083" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="83.707588" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="91.346916" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="103.38731" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>为<gydF4y2Basvg height="16.549999" id="M135" style="vertical-align:-2.29482pt;width:44.587502px;" version="1.1" viewbox="0 0 44.587502 16.549999" width="44.587502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.55)"> <g transform="translate(72,-58.76)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.152436" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.192825" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-44.19,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。前面的平等收益率以下关系:<gydF4y2Baspan class="equation" id="eq2"> <svg height="98.1875" id="M136" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 98.1875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,98.1875)"> <g transform="translate(72,6.55)"> <text transform="matrix(1,0,0,-1,13.43,55.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="2.51" y="1.58"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,24.37,58.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,29.93,53.45)"> <tspan style="font-size: 12.50px; " x="24.139999" y="-1.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.139999" y="1.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,56.57,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,63.53,53.45)"> <tspan style="font-size: 12.50px; " x="18.059999" y="7.3299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.629999" y="-8.3500004"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.793499" y="-8.3500004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.182533" y="-8.3500004"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.658367" y="-8.3500004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.047398" y="-8.3500004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.960838" y="-8.3500004"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.199837" y="-8.3500004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.139" y="-8.3500004"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="71.84037" y="-8.3500004"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="76.003868" y="-8.3500004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="82.69297" y="-8.3500004"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="87.906723" y="-8.3500004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="91.82016" y="-8.3500004"> )</gydF4y2Batspan> </text> <g> <path d="m 92.16,56.57 67.36,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,107.45,44.69)"> <tspan style="font-size: 12.50px; " x="56.040001" y="-8.7600002"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.580002" y="-17.110001"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.62803" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.791529" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.480635" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.694386" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.607822" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,185.57,66.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,191.13,61.8)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.678522" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.842022" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.531126" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.744877" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.658318" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.821815" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.760979" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.112503" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.276005" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.665035" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.140869" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.5299" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="76.443344" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="82.694839" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="93.209862" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="97.373367" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="104.06247" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="109.27622" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="113.18966" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 176.03,56.57 132.46,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,214.95,44.69)"> <tspan style="font-size: 12.50px; " x="94.739998" y="-1.4299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-148.02" y="40.009998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.306313" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.46981" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.158916" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.372665" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.286106" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.449604" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-178.12" y="35.09"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-166.09212" y="35.09"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-161.91611" y="35.09"> 米</gydF4y2Batspan> </text> <g> <path d="m 74.29,22.5 44.83,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,74.29,9.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.689105" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,89.42,14.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,94.98,9.6)"> <tspan style="font-size: 12.50px; " x="31.23" y="-2.72"> ̇</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.799999" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.489998" y="9.7399998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.139999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.655022" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.818523" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.507626" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.721378" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.634815" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="78.589996" y="1.7763568e-015"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="87.617165" y="1.7763568e-015"> +</gydF4y2Batspan> </text> <g> <path d="m 193.94,30.99 66.87,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,193.94,2.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.58" y="-15.68"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.256601" y="-15.68"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,219.65,23.02)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,226.09,17.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.066355" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.979794" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 204.52,12.72 45.71,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,209.35,-0.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,217.79,4.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,221.26,-0.18)"> <tspan style="font-size: 12.50px; " x="30.17" y="-2.45"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.330002" y="-9.7799997"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.860001" y="-18.129999"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,285.66,22.95)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,291.22,17.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.678522" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.842022" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.531126" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.744877" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.658318" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.821815" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.760979" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.112503" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.801609" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.740776" y="0"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="71.442139" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.605644" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="82.294746" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="87.508499" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="91.421936" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 276.12,12.72 110.69,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,304.16,0.84)"> <tspan style="font-size: 12.50px; " x="83.839996" y="0.98000002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="96.029999" y="-8.7600002"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.306313" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.46981" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.158916" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.360165" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.273602" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.437103" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="160.59" y="-28.76"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="164.75349" y="-28.76"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="171.005" y="-28.76"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="174.13075" y="-28.76"> 9</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="180.38225" y="-28.76"> )</gydF4y2Batspan> </text> </g> </g> </svg></span><br>如果我们用(<一个href="#EEq2.6">2。6</一个>),(<gydF4y2Ba一个href="#EEq2.6">2。7</一个>),(<gydF4y2Ba一个href="#EEq2.8">2。8</一个>)和(<一个href="#EEq1.1">1.1</一个>)在上面的表达式和替换<gydF4y2Basvg height="10.7375" id="M137" style="vertical-align:-0.13794pt;width:8.3125px;" version="1.1" viewbox="0 0 8.3125 10.7375" width="8.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>通过<gydF4y2Basvg height="14.625" id="M138" style="vertical-align:-3.25793pt;width:14.4125px;" version="1.1" viewbox="0 0 14.4125 14.625" width="14.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.4,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="9.125" id="M139" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>通过<gydF4y2Basvg height="13.05" id="M140" style="vertical-align:-3.25793pt;width:11.1125px;" version="1.1" viewbox="0 0 11.1125 13.05" width="11.1125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,我们获得<gydF4y2Baspan class="equation" id="eq3"> <svg height="108.7875" id="M141" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 108.7875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,108.7875)"> <g transform="translate(72,15.03)"> <text transform="matrix(1,0,0,-1,-52.42,56.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m -54.37,52.73 10.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-54.37,40.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.58" y="-8.75"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.131332" y="-8.75"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.29483" y="-8.75"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.720001" y="-17.1"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.396603" y="-17.1"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-1.52,63.02)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,4.04,57.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m -21.54,52.73 54.61,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-21.54,40.85)"> <tspan style="font-size: 12.50px; " x="55.799999" y="-21"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.799999" y="-10.34"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.799999" y="0.33000001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.799999" y="3.49"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.29381" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.457308" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.146412" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.360165" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.273602" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.437103" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,36.77,34.71)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.6735678" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.668688" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,52.13,32.52)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,55.75,34.71)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.9273758" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.922496" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,69.41,32.52)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,77.01,49.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.110001" y="-7.9200001"> </gydF4y2Batspan> </text> <g> <path d="m 90.24,52.73 69.53,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,90.24,37.16)"> <tspan style="font-size: 12.50px; " x="13.85" y="-1.59"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.85" y="1.5700001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.35" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,115.03,42.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,118.51,37.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,129.36,34.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,134.23,37.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,143.36,34.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,148.23,37.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1599998" y="-1.59"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1599998" y="1.5700001"> |</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,154.9,43.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,163.05,39.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.32" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.619999" y="-20.309999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.2600002" y="-9.7299995"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.423499" y="-9.7299995"> 米</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,207.36,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,212.23,60.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,220.67,65.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,229.21,57.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,241.75,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,246.62,60.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,255.74,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,260.62,57.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 200.67,52.73 65.8,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,207.94,39.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,216.38,44.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,221.94,36.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,234.48,35.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,239.35,39.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,248.47,35.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,253.35,36.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.26" y="-13.09"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.799999" y="-23.67"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,296.69,65.18)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,302.25,57.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.370001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.219999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,331.16,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,336.04,60.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,345.16,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,350.04,57.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,364.66,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,369.53,60.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,377.97,65.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,383.53,57.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.02" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,400.24,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,405.11,60.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,414.24,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,419.11,57.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 287.15,52.73 143.66,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,323.43,39.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.62" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.469999" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.99" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.849998" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,363.96,35.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,368.84,39.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,377.96,35.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,382.84,36.51)"> <tspan style="font-size: 12.50px; " x="49.169998" y="-3.3599999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-226.33" y="35.389999"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-217.76544" y="35.389999"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-209.43845" y="35.389999"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-201.09895" y="35.389999"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-193.45961" y="35.389999"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,198.93,6.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,204.49,-1.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.370001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.219999" y="-2.51"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,233.4,-2.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,238.28,1.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,247.4,-2.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,252.27,-1.39)"> <tspan style="font-size: 12.50px; " x="35.099998" y="-13.09"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.79" y="-2.51"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.953499" y="-2.51"> 米</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,294.06,8.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,298.94,11.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,307.38,16.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,312.94,9.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,325.48,8.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,330.35,11.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,339.47,8.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,344.35,9.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 283.23,4.24 71.11,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,283.23,-9.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.62" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.48" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28" y="2.51"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.849998" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,323.77,-12.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,328.64,-9.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,337.77,-12.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,342.64,-11.97)"> <tspan style="font-size: 12.50px; " x="12.9" y="-3.3499999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.639999" y="-13.09"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.667885" y="-13.09"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.919388" y="-13.09"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="115.85" y="-37.330002"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="120.0135" y="-37.330002"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="126.265" y="-37.330002"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="129.39075" y="-37.330002"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="135.64224" y="-37.330002"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="141.89375" y="-37.330002"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>由于(<一个href="#EEq2.2">2。2</一个>),(<gydF4y2Ba一个href="#EEq2.3">2。3</一个>)和(<一个href="#EEq2.5">2。5</一个>)。最后,我们得到<gydF4y2Basvg height="19.4" id="M142" style="vertical-align:-5.41734pt;width:266.5625px;" version="1.1" viewbox="0 0 266.5625 19.4" width="266.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.4)"> <g transform="translate(72,-56.48)"> <text transform="matrix(1,0,0,-1,-71.95,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.540029" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.015863" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.404896" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.318335" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.569836" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.121166" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.284664" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.624168" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.787666" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.476772" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-4.03,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-0.56,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.066355" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.979794" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.143293" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.619127" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.158916" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.322414" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.261581" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.425079" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.114185" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="64.31543" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.228874" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.392372" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="76.55587" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="80.719368" y="0"> |</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,82.67,58.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.6735678" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.668688" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,98.03,56.62)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,101.65,58.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.9273758" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.922496" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,115.32,56.62)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,122.91,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。因此,<gydF4y2Basvg height="17.0875" id="M143" style="vertical-align:-2.73372pt;width:220.7625px;" version="1.1" viewbox="0 0 220.7625 17.0875" width="220.7625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.0875)"> <g transform="translate(72,-58.33)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.129829" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.293329" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-42.09,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-34.28,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-25.84,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-22.37,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-12.64,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-4.84,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.1271896" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.290689" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.766523" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.306313" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.46981" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.408978" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.572475" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,42.3,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,50.1,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.278186" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.081018" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.121407" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.723232" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.199066" y="0"> 2</gydF4y2Batspan> </text> </g> </g> </svg>,因为<gydF4y2Basvg height="13.05" id="M144" style="vertical-align:-3.25793pt;width:35.387501px;" version="1.1" viewbox="0 0 35.387501 13.05" width="35.387501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-48.61,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>(接近<gydF4y2Basvg height="13.05" id="M145" style="vertical-align:-3.25793pt;width:11.1125px;" version="1.1" viewbox="0 0 11.1125 13.05" width="11.1125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>在某些地段)<gydF4y2Basvg height="14.625" id="M146" style="vertical-align:-3.25793pt;width:14.4125px;" version="1.1" viewbox="0 0 14.4125 14.625" width="14.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.4,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。这与假设(<一个href="#EEq2.4">2。4</一个>),完成了证明。</gydF4y2Baspan></p> <p>如果在前面的定理,我们<gydF4y2Basvg height="15.8875" id="M147" style="vertical-align:-2.21957pt;width:90.712502px;" version="1.1" viewbox="0 0 90.712502 15.8875" width="90.712502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.8875)"> <g transform="translate(72,-59.29)"> <text transform="matrix(1,0,0,-1,-71.95,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.393112" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.019943" y="0"> ≡</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.060333" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-23.32,66.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="8.7169924" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-9.17,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.45" id="M148" style="vertical-align:-2.21957pt;width:99.275002px;" version="1.1" viewbox="0 0 99.275002 13.45" width="99.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.515023" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.555412" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.71891" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.283466" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.885288" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.361122" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.612625" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.826374" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.4282" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.90403" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.155533" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>;然后我们得到下面的推论。</gydF4y2Bap> <p><span class="statement" id="coro2.4"><span class="statement-title">推论2.4。</gydF4y2Baspan><i>让<gydF4y2Basvg height="13.0625" id="M149" style="vertical-align:-1.90608pt;width:39.537498px;" version="1.1" viewbox="0 0 39.537498 13.0625" width="39.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0625)"> <g transform="translate(72,-61.55)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.228174" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.268562" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,让<gydF4y2Basvg height="14.625" id="M150" style="vertical-align:-3.25793pt;width:14.8875px;" version="1.1" viewbox="0 0 14.8875 14.625" width="14.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>是一个函数的spiral-like类型<gydF4y2Basvg height="13.45" id="M151" style="vertical-align:-2.21957pt;width:99.275002px;" version="1.1" viewbox="0 0 99.275002 13.45" width="99.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.515023" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.555412" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.71891" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.283466" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.885288" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.361122" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.612625" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.826374" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.4282" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.90403" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.155533" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>在<gydF4y2Basvg height="10.5375" id="M152" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和单价的<gydF4y2Basvg height="15.6875" id="M153" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 15.6875" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.6875)"> <g transform="translate(72,-59.45)"> <g> <path d="m -71.95,70.71 10.19,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。然后Polubarinova-Galin方程的经典解决方案(<一个href="#EEq1.1">1.1</一个>与初始条件)<gydF4y2Basvg height="14.75" id="M154" style="vertical-align:-3.25793pt;width:94.824997px;" version="1.1" viewbox="0 0 94.824997 14.75" width="94.824997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.244516" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.88385" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.92424" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.08,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-11.21,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是spiral-like类型的<gydF4y2Basvg height="7.1750002" id="M155" style="vertical-align:-0.1254pt;width:8.9375px;" version="1.1" viewbox="0 0 8.9375 7.1750002" width="8.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.175)"> <g transform="translate(72,-66.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>为<gydF4y2Basvg height="13.45" id="M156" style="vertical-align:-2.21957pt;width:57.737499px;" version="1.1" viewbox="0 0 57.737499 13.45" width="57.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.922558" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="10.325" id="M157" style="vertical-align:-0.0pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 10.325" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>充气时间。</我></span></p> <p>下面的结果是一个概括的<一个href="#B15">6</一个>定理1)的情况下<gydF4y2Basvg height="10.475" id="M158" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>——功能。提到定理可能获得通过<gydF4y2Basvg height="13.45" id="M159" style="vertical-align:-2.21957pt;width:66.074997px;" version="1.1" viewbox="0 0 66.074997 13.45" width="66.074997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.393112" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.019943" y="0"> ≡</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.060333" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>在定理<一个href="#thm2.5">2。5</一个>在下面。</gydF4y2Bap> <p><span class="statement" id="thm2.5"><span class="statement-title">定理2.5。</gydF4y2Baspan><i>让<gydF4y2Basvg height="13.0625" id="M160" style="vertical-align:-1.90608pt;width:39.537498px;" version="1.1" viewbox="0 0 39.537498 13.0625" width="39.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0625)"> <g transform="translate(72,-61.55)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.228174" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.268562" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和表面张力<gydF4y2Basvg height="9.9375" id="M161" style="vertical-align:-2.34499pt;width:8.0625px;" version="1.1" viewbox="0 0 8.0625 9.9375" width="8.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.9375)"> <g transform="translate(72,-64.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是足够小。如果<gydF4y2Basvg height="14.625" id="M162" style="vertical-align:-3.25793pt;width:14.8875px;" version="1.1" viewbox="0 0 14.8875 14.625" width="14.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>是一个函数<gydF4y2Basvg height="10.475" id="M163" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如在<gydF4y2Basvg height="10.5375" id="M164" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和单价的<gydF4y2Basvg height="15.6875" id="M165" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 15.6875" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.6875)"> <g transform="translate(72,-59.45)"> <g> <path d="m -71.95,70.71 10.19,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,然后存在<gydF4y2Basvg height="13.6125" id="M166" style="vertical-align:-2.34499pt;width:53.849998px;" version="1.1" viewbox="0 0 53.849998 13.6125" width="53.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="3.913439" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.415959" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.055292" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.09568" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>这样经典的解决方案<gydF4y2Basvg height="13.6125" id="M167" style="vertical-align:-2.34499pt;width:38.974998px;" version="1.1" viewbox="0 0 38.974998 13.6125" width="38.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>(<一个href="#EEq1.2">1.2</一个>与初始条件)<gydF4y2Basvg height="14.75" id="M168" style="vertical-align:-3.25793pt;width:94.824997px;" version="1.1" viewbox="0 0 94.824997 14.75" width="94.824997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.244516" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.88385" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.92424" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.08,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-11.21,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="10.475" id="M169" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>式为<gydF4y2Basvg height="13.6125" id="M170" style="vertical-align:-2.34499pt;width:72.375px;" version="1.1" viewbox="0 0 72.375 13.6125" width="72.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.959347" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.122849" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.474373" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.637871" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="10.325" id="M171" style="vertical-align:-0.0pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 10.325" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>充气时间,<gydF4y2Basvg height="18.85" id="M172" style="vertical-align:-5.41599pt;width:234.60001px;" version="1.1" viewbox="0 0 234.60001 18.85" width="234.60001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.85)"> <g transform="translate(72,-56.92)"> <text transform="matrix(1,0,0,-1,-71.95,62.37)"> <tspan style="font-size: 12.50px; " x="24.809999" y="0.02"> ⋃</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.765563" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-35.58,58.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="13.110496" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="19.105616" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="21.844992" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="24.759409" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="29.196672" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-0.88,62.37)"> <tspan style="font-size: 12.50px; " x="37.049999" y="0.02"> ⋃</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.379169" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,47.72,58.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="13.110496" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="19.105616" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="21.844992" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="24.759409" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="29.205423" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,82.43,62.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.917278" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.118526" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.031965" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="10.475" id="M173" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>是一个全纯函数<gydF4y2Basvg height="15.85" id="M174" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 15.85" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.85)"> <g transform="translate(72,-59.32)"> <g> <path d="m -71.95,70.71 9.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> </text> </g> </g> </svg>满足条件(<一个href="#EEq2.2">2。2</一个>)。</我></span></p> <p><span class="statement" id="proof2"><span class="statement-title"><i class="statement-title">证明。</我></span>如果我们考虑<gydF4y2Basvg height="13.4875" id="M175" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>的关闭<gydF4y2Basvg height="10.5375" id="M176" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,然后的不等号(<一个href="#EEq2.1">2。1</一个>)可以取代“≥”可以获得平等的地方<gydF4y2Basvg height="13.55" id="M177" style="vertical-align:-2.29482pt;width:41.9375px;" version="1.1" viewbox="0 0 41.9375 13.55" width="41.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.1772022" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.153636" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.194025" y="0"> 1</gydF4y2Batspan> </text> </g> </g> </svg>。<gydF4y2Babr>相反,假设定理的结论<一个href="#thm2.5">2。5</一个>是不正确的。然后存在<gydF4y2Basvg height="14.75" id="M178" style="vertical-align:-3.25793pt;width:38.3125px;" version="1.1" viewbox="0 0 38.3125 14.75" width="38.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-59.69,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≥</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="17.75" id="M179" style="vertical-align:-3.25793pt;width:55.212502px;" version="1.1" viewbox="0 0 55.212502 17.75" width="55.212502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.75)"> <g transform="translate(72,-57.8)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.26,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.91,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-39.31,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-32,63.92)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>这样,(<一个href="#EEq2.3">2。3</一个>),(<gydF4y2Ba一个href="#EEq2.4">2。4</一个>),(<gydF4y2Ba一个href="#EEq2.5">2。5</一个>),(<gydF4y2Ba一个href="#EEq2.6">2。6</一个>)和(<一个href="#EEq2.6">2。7</一个>)是正确的。与此同时,平等(<一个href="#EEq2.8">2。8</一个>)是实现。通过区分Polubarinova-Galin方程(<一个href="#EEq1.2">1.2</一个>)对<gydF4y2Basvg height="10.7375" id="M180" style="vertical-align:-0.13794pt;width:8.3125px;" version="1.1" viewbox="0 0 8.3125 10.7375" width="8.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,我们获得<gydF4y2Baspan class="equation" id="eq4"> <svg height="30.737499" id="M181" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 30.737499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,30.7375)"> <g transform="translate(72,-47.41)"> <text transform="matrix(1,0,0,-1,-3.56,56.35)"> <tspan style="font-size: 12.50px; " x="18.059999" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.57" y="-7.25"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 米</gydF4y2Batspan> </text> <g> <path d="m 23.06,59.47 10.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,23.06,47.59)"> <tspan style="font-size: 12.50px; " x="11.5" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,43,61.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,48.55,56.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 74.78,69.25 38.13,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,74.78,56.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,83.22,61.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,88.77,56.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.918959" y="0"> −</gydF4y2Batspan> </text> <g> <path d="m 127.03,69.25 44.83,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,127.03,56.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.689105" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,142.16,61.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,147.72,56.35)"> <tspan style="font-size: 12.50px; " x="27.290001" y="-7.25"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 173.06,59.47 10.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,173.06,47.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.49" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.017527" y="-8.7600002"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.181025" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.870129" y="-8.7600002"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.071377" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.984818" y="-8.7600002"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.923981" y="-8.7600002"> −</gydF4y2Batspan> </text> <g> <path d="m 233.34,70.22 52.67,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,233.34,56.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,240.03,61.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,244.9,56.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,253.34,61.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,261.88,56.35)"> <tspan style="font-size: 12.50px; " x="27.290001" y="-7.25"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 287.21,59.47 10.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,287.21,47.59)"> <tspan style="font-size: 12.50px; " x="46.16" y="-3.8399999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="89.75" y="-8.7200003"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="106.77" y="-8.7200003"> ]</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.5" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.015022" y="-8.7600002"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.178522" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.867626" y="-8.7600002"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.081379" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.994816" y="-8.7600002"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.240002" y="-8.7600002"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="69.267883" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.619408" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="93.910004" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="97.798431" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="113.01" y="-8.7600002"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="117.1735" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="123.72507" y="-8.7600002"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="129.96407" y="-8.7600002"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="171.28" y="-8.9899998"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="175.4435" y="-8.9899998"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="181.69499" y="-8.9899998"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="184.82076" y="-8.9899998"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="191.07225" y="-8.9899998"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="197.32375" y="-8.9899998"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>为<gydF4y2Basvg height="16.549999" id="M182" style="vertical-align:-2.29482pt;width:44.587502px;" version="1.1" viewbox="0 0 44.587502 16.549999" width="44.587502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.55)"> <g transform="translate(72,-58.76)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.152436" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.192825" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-44.19,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。前面的平等相当于以下:<gydF4y2Baspan class="equation" id="eq5"> <svg height="155.66251" id="M183" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 155.66251" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,155.6625)"> <g transform="translate(72,52.53)"> <text transform="matrix(1,0,0,-1,-55.24,52.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="2.5" y="1.59"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-44.3,56.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-38.74,51.25)"> <tspan style="font-size: 12.50px; " x="24.139999" y="-1.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.139999" y="1.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-12.1,58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-3.95,51.24)"> <tspan style="font-size: 12.50px; " x="18.059999" y="7.3200002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.629999" y="-8.3599997"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.793499" y="-8.3599997"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.182533" y="-8.3599997"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.658367" y="-8.3599997"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.047398" y="-8.3599997"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.960838" y="-8.3599997"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.199837" y="-8.3599997"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,63.7,64.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,67.17,59.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 24.68,54.37 66.63,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,39.97,41.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,48.41,46.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,51.88,41.47)"> <tspan style="font-size: 12.50px; " x="43.41" y="-9.7700005"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.066355" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.979794" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.950001" y="-18.129999"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="67.565285" y="-18.129999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="71.728783" y="-18.129999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="82.25631" y="-18.129999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="86.419807" y="-18.129999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="93.108917" y="-18.129999"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="98.310165" y="-18.129999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="102.2236" y="-18.129999"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="106.3871" y="-18.129999"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="112.6386" y="-18.129999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="116.8021" y="-18.129999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="123.19113" y="-18.129999"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="126.66697" y="-18.129999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="133.056" y="-18.129999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="136.96944" y="-18.129999"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="143.22095" y="-18.129999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="150.16011" y="-18.129999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="154.32361" y="-18.129999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="161.01271" y="-18.129999"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="166.21396" y="-18.129999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="170.1274" y="-18.129999"> )</gydF4y2Batspan> </text> <g> <path d="m 107.83,54.37 118.35,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,142.53,42.49)"> <tspan style="font-size: 12.50px; " x="84.849998" y="-1.4299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="94.220001" y="-21.01"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="94.220001" y="-10.34"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="94.220001" y="0.31999999"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="94.220001" y="3.49"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.642452" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.805952" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.495056" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.696304" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.609745" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.773243" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,239.25,36.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.6823201" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.67744" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,254.61,34.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,258.24,36.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,268.13,39.4)"> <tspan style="font-size: 6.25px; " x="5.2199998" y="1.97"> 0</gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="1.9443721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,277.47,36.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.9273758" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.922496" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,291.13,34.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-41.81,6.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.04" y="7.3299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.66" y="-7.9099998"> </gydF4y2Batspan> </text> <g> <path d="m -19.19,9.73 13.85,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-19.19,-2.15)"> <tspan style="font-size: 12.50px; " x="49.639999" y="-3.8399999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.009998" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.82" y="-8.7600002"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.160221" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.511745" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.09" y="-16.01"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.479034" y="-16.01"> </gydF4y2Batspan> </text> <g> <path d="m 42.9,9.73 13.17,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,43.01,-2.15)"> <tspan style="font-size: 12.50px; " x="16.34" y="-6.2399998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.190001" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,70.76,11.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,78.57,6.61)"> <tspan style="font-size: 12.50px; " x="9.1199999" y="2.52"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.97" y="4.9200001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.57" y="7.3299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-111.11" y="41.93"> ×</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-99.129997" y="49.25"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-74.720001" y="49.25"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-92.779999" y="41.93"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-88.616501" y="41.93"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-64.150002" y="33.580002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-57.460896" y="33.580002"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,29.55,-21.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 14.42,-32.19 21.58,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,19.25,-45.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,27.69,-40.02)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,39.97,-35.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.54" y="-8.3500004"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,62.05,-21.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,67.61,-26.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.603024" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 52.51,-32.19 31.87,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,54.25,-44.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.218311" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.32" y="-8.75"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.009106" y="-8.75"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,100.7,-30.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,104.18,-42.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.15" y="-7.3200002"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.490221" y="-7.3200002"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.817219" y="-7.3200002"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.156719" y="-7.3200002"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.796055" y="-7.3200002"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,161.52,-30.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,167.08,-35.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.603024" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.842022" y="0"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.00552" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.919998" y="-8.3400002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.596603" y="-8.3400002"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,223.13,-21.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 203.1,-32.19 28.39,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,203.1,-44.07)"> <tspan style="font-size: 12.50px; " x="29.59" y="-1.4299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.939999" y="-21.01"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.939999" y="-10.34"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.939999" y="0.31999999"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.939999" y="3.49"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.218311" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,241.54,-50.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.6823201" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.67744" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,256.9,-52.4)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,260.52,-50.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.9273758" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.922496" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,274.19,-52.4)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,277.81,-50.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="6.7740479" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="12.769168" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,295.17,-52.4)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,302.07,-35.32)"> <tspan style="font-size: 12.50px; " x="31.82" y="0.029999999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.830002" y="0.029999999"> ]</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.679241" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.98" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.868435" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.080002" y="-0.0099999998"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.2435" y="-0.0099999998"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.795074" y="-0.0099999998"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.034065" y="-0.0099999998"> ∣</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,380.91,-38.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.6823201" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.67744" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,396.27,-40.63)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,399.9,-38.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.9273758" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.922496" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,413.56,-40.63)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,417.18,-38.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="6.7740479" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="12.769168" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,434.54,-40.63)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,438.66,-35.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.83" y="-41.93"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.9935" y="-41.93"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.244999" y="-41.93"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.37075" y="-41.93"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.62225" y="-41.93"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.873749" y="-41.93"> )</gydF4y2Batspan> </text> </g> </g> </svg></span> <svg height="0.125" id="M184" style="vertical-align:-0.0pt;width:10.55px;" version="1.1" viewbox="0 0 10.55 0.125" width="10.55" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,0.125)"> <g transform="translate(72,-71.9)"></g> </g> </svg><br>这个等式的右边是严格-小<gydF4y2Basvg height="9.9375" id="M185" style="vertical-align:-2.34499pt;width:8.0625px;" version="1.1" viewbox="0 0 8.0625 9.9375" width="8.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.9375)"> <g transform="translate(72,-64.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>因为(<一个href="#EEq2.5">2。5</一个>),(<gydF4y2Ba一个href="#EEq2.6">2。7</一个>),这一事实<gydF4y2Basvg height="15.475" id="M186" style="vertical-align:-2.34499pt;width:82.650002px;" version="1.1" viewbox="0 0 82.650002 15.475" width="82.650002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.475)"> <g transform="translate(72,-59.62)"> <text transform="matrix(1,0,0,-1,-71.95,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-46.44,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-42.96,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.729494" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.769882" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。<gydF4y2Babr>通过使用(<一个href="#EEq2.8">2。8</一个>),我们获得<gydF4y2Basvg height="17.0875" id="M187" style="vertical-align:-2.73372pt;width:220.7625px;" version="1.1" viewbox="0 0 220.7625 17.0875" width="220.7625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.0875)"> <g transform="translate(72,-58.33)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.129829" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.293329" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-42.09,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-34.28,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-25.84,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-22.37,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-12.64,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-4.84,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.1271896" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.290689" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.766523" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.306313" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.46981" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.408978" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.572475" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,42.3,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,50.1,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.278186" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.081018" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.121407" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.723232" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.199066" y="0"> 2</gydF4y2Batspan> </text> </g> </g> </svg>为<gydF4y2Basvg height="13.05" id="M188" style="vertical-align:-3.25793pt;width:35.387501px;" version="1.1" viewbox="0 0 35.387501 13.05" width="35.387501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-48.61,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>(接近<gydF4y2Basvg height="13.05" id="M189" style="vertical-align:-3.25793pt;width:11.1125px;" version="1.1" viewbox="0 0 11.1125 13.05" width="11.1125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>)在附近<gydF4y2Basvg height="14.625" id="M190" style="vertical-align:-3.25793pt;width:14.4125px;" version="1.1" viewbox="0 0 14.4125 14.625" width="14.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.4,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。这是在矛盾与我们的假设和证明。</gydF4y2Baspan></p> <p><span class="statement" id="rem2.6"><span class="statement-title"><i class="statement-title">2.6的话。</我></span>让<gydF4y2Basvg height="13.0625" id="M191" style="vertical-align:-1.90608pt;width:39.537498px;" version="1.1" viewbox="0 0 39.537498 13.0625" width="39.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0625)"> <g transform="translate(72,-61.55)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.228174" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.268562" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,让<gydF4y2Basvg height="14.625" id="M192" style="vertical-align:-3.25793pt;width:14.8875px;" version="1.1" viewbox="0 0 14.8875 14.625" width="14.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>是一个函数<gydF4y2Basvg height="10.475" id="M193" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如在<gydF4y2Basvg height="10.5375" id="M194" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和单价的<gydF4y2Basvg height="15.6875" id="M195" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 15.6875" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.6875)"> <g transform="translate(72,-59.45)"> <g> <path d="m -71.95,70.71 10.19,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。如果<gydF4y2Basvg height="14.625" id="M196" style="vertical-align:-3.25793pt;width:14.8875px;" version="1.1" viewbox="0 0 14.8875 14.625" width="14.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>满足条件(<一个href="#EEq2.1">2。1</一个>)为每一个<gydF4y2Basvg height="18.35" id="M197" style="vertical-align:-2.29482pt;width:40.612499px;" version="1.1" viewbox="0 0 40.612499 18.35" width="40.612499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.35)"> <g transform="translate(72,-57.32)"> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.152436" y="0"> ∈</gydF4y2Batspan> </text> <g> <path d="m -49.75,70.71 10.19,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-49.75,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,然后存在表面张力<gydF4y2Basvg height="9.9375" id="M198" style="vertical-align:-2.34499pt;width:8.0625px;" version="1.1" viewbox="0 0 8.0625 9.9375" width="8.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.9375)"> <g transform="translate(72,-64.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>(这取决于<gydF4y2Basvg height="14.625" id="M199" style="vertical-align:-3.25793pt;width:14.8875px;" version="1.1" viewbox="0 0 14.8875 14.625" width="14.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>)足够小,<gydF4y2Basvg height="13.6125" id="M200" style="vertical-align:-2.34499pt;width:53.849998px;" version="1.1" viewbox="0 0 53.849998 13.6125" width="53.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="3.913439" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.415959" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.055292" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.09568" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>这样经典的解决方案<gydF4y2Basvg height="13.6125" id="M201" style="vertical-align:-2.34499pt;width:38.974998px;" version="1.1" viewbox="0 0 38.974998 13.6125" width="38.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>(<一个href="#EEq1.2">1.2</一个>与初始条件)<gydF4y2Basvg height="14.75" id="M202" style="vertical-align:-3.25793pt;width:94.824997px;" version="1.1" viewbox="0 0 94.824997 14.75" width="94.824997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.244516" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.88385" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.92424" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.08,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-11.21,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="10.475" id="M203" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>式为<gydF4y2Basvg height="13.6125" id="M204" style="vertical-align:-2.34499pt;width:72.375px;" version="1.1" viewbox="0 0 72.375 13.6125" width="72.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.959347" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.122849" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.474373" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.637871" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="10.325" id="M205" style="vertical-align:-0.0pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 10.325" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>充气时间。</gydF4y2Baspan></p> <p><span class="statement" id="proof3"><span class="statement-title"><i class="statement-title">证明。</我></span>结论是直接从古典解的光滑性(<一个href="#EEq1.1">1.1</一个>)。</gydF4y2Baspan></p> <p>如果<gydF4y2Basvg height="15.8875" id="M206" style="vertical-align:-2.21957pt;width:90.712502px;" version="1.1" viewbox="0 0 90.712502 15.8875" width="90.712502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.8875)"> <g transform="translate(72,-59.29)"> <text transform="matrix(1,0,0,-1,-71.95,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.393112" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.019943" y="0"> ≡</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.060333" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-23.32,66.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="8.7169924" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-9.17,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>在定理<一个href="#thm2.5">2。5</一个>,在那里<gydF4y2Basvg height="13.45" id="M207" style="vertical-align:-2.21957pt;width:99.275002px;" version="1.1" viewbox="0 0 99.275002 13.45" width="99.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.515023" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.555412" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.71891" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.283466" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.885288" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.361122" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.612625" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.826374" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.4282" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.90403" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.155533" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,我们获得以下推论:</gydF4y2Bap> <p><span class="statement" id="coro2.7"><span class="statement-title">推论2.7。</gydF4y2Baspan><i>让<gydF4y2Basvg height="13.0625" id="M208" style="vertical-align:-1.90608pt;width:39.537498px;" version="1.1" viewbox="0 0 39.537498 13.0625" width="39.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0625)"> <g transform="translate(72,-61.55)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.228174" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.268562" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和表面张力<gydF4y2Basvg height="9.9375" id="M209" style="vertical-align:-2.34499pt;width:8.0625px;" version="1.1" viewbox="0 0 8.0625 9.9375" width="8.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.9375)"> <g transform="translate(72,-64.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是足够小。如果<gydF4y2Basvg height="14.625" id="M210" style="vertical-align:-3.25793pt;width:14.8875px;" version="1.1" viewbox="0 0 14.8875 14.625" width="14.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>是一个函数的spiral-like类型<gydF4y2Basvg height="13.45" id="M211" style="vertical-align:-2.21957pt;width:99.275002px;" version="1.1" viewbox="0 0 99.275002 13.45" width="99.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.515023" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.555412" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.71891" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.283466" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.885288" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.361122" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.612625" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.826374" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.4282" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.90403" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.155533" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>在<gydF4y2Basvg height="10.5375" id="M212" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>和单价的<gydF4y2Basvg height="15.6875" id="M213" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 15.6875" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.6875)"> <g transform="translate(72,-59.45)"> <g> <path d="m -71.95,70.71 10.19,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,然后存在<gydF4y2Basvg height="13.6125" id="M214" style="vertical-align:-2.34499pt;width:53.849998px;" version="1.1" viewbox="0 0 53.849998 13.6125" width="53.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="3.913439" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.415959" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.055292" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.09568" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>这样经典的解决方案<gydF4y2Basvg height="13.6125" id="M215" style="vertical-align:-2.34499pt;width:38.974998px;" version="1.1" viewbox="0 0 38.974998 13.6125" width="38.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>(<一个href="#EEq1.2">1.2</一个>与初始条件)<gydF4y2Basvg height="14.75" id="M216" style="vertical-align:-3.25793pt;width:94.824997px;" version="1.1" viewbox="0 0 94.824997 14.75" width="94.824997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.244516" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.88385" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.92424" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.08,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-11.21,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是spiral-like类型的<gydF4y2Basvg height="7.1750002" id="M217" style="vertical-align:-0.1254pt;width:8.9375px;" version="1.1" viewbox="0 0 8.9375 7.1750002" width="8.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.175)"> <g transform="translate(72,-66.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>为<gydF4y2Basvg height="13.6125" id="M218" style="vertical-align:-2.34499pt;width:72.375px;" version="1.1" viewbox="0 0 72.375 13.6125" width="72.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.959347" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.122849" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.474373" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.637871" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="10.325" id="M219" style="vertical-align:-0.0pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 10.325" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>充气时间。</我></span></p> <h4 id="the-outer-problem-(unbounded-domain-with-bounded-complement)">3所示。外部问题(无限域界补充)</h4><gydF4y2Bap>在本节中,我们获得的不变性时间相同的几何属性(用<gydF4y2Basvg height="15.1625" id="M220" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>)外的问题。</gydF4y2Bap> <p><span class="statement" id="deff3.1"><span class="statement-title"><i class="statement-title">定义3.1。</我></span>让<gydF4y2Basvg height="10.325" id="M221" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.325" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是一个全纯函数<gydF4y2Basvg height="13.8625" id="M222" style="vertical-align:-2.37006pt;width:118.3875px;" version="1.1" viewbox="0 0 118.3875 13.8625" width="118.3875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.8625)"> <g transform="translate(72,-60.91)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,68.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-51.79,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> {</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.029325" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.194265" y="0"> ∣</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.995895" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.496498" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.1856" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.149532" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.189922" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.441422" y="0"> }</gydF4y2Batspan> </text> </g> </g> </svg>这样<gydF4y2Basvg height="14.75" id="M223" style="vertical-align:-3.25793pt;width:182.2625px;" version="1.1" viewbox="0 0 182.2625 14.75" width="182.2625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.206287" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.246677" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.523182" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.987953" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.328178" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-0.33,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,7.32,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,24.94,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,35.81,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.940605" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.280827" y="0"> ⋯</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="13.125" id="M224" style="vertical-align:-1.95624pt;width:31.700001px;" version="1.1" viewbox="0 0 31.700001 13.125" width="31.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.125)"> <g transform="translate(72,-61.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3520041" y="0"> ≠</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.00456" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。让<gydF4y2Basvg height="15.1625" id="M225" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>是一个全纯函数<gydF4y2Basvg height="13.45" id="M226" style="vertical-align:-2.21957pt;width:41.049999px;" version="1.1" viewbox="0 0 41.049999 13.45" width="41.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-49.87,68.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-43.38,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>这样<gydF4y2Basvg height="21.075001" id="M227" style="vertical-align:-4.74141pt;width:123.725px;" version="1.1" viewbox="0 0 123.725 21.075001" width="123.725" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,21.075)"> <g transform="translate(72,-55.14)"> <text transform="matrix(1,0,0,-1,-71.95,59.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> l</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9516678" y="0"> 米</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-51.1,56.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="6.1351519" y="0"> →</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="15.692336" y="0"> ∞</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-23.44,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.2697887" y="2.6500001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.433288" y="2.6500001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.10989" y="2.6500001"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.749224" y="2.6500001"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.789612" y="2.6500001"> ∞</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="23.15" id="M228" style="vertical-align:-4.74141pt;width:121.4125px;" version="1.1" viewbox="0 0 121.4125 23.15" width="121.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,23.15)"> <g transform="translate(72,-53.48)"> <text transform="matrix(1,0,0,-1,-71.95,58.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> l</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9516678" y="0"> 米</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-51.1,55.13)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="6.1351519" y="0"> →</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="15.692336" y="0"> ∞</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-23.44,60.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-15.17,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-11.7,58.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.479433" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.519823" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。我们说<gydF4y2Basvg height="10.325" id="M229" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.325" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="15.1625" id="M230" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如在<gydF4y2Basvg height="10.5375" id="M231" style="vertical-align:-0.16302pt;width:20.975px;" version="1.1" viewbox="0 0 20.975 10.5375" width="20.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,68.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>如果<gydF4y2Baspan class="equation" id="EEq3.1"> <svg height="48.1875" id="M232" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.1875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.1875)"> <g transform="translate(72,-33.45)"> <text transform="matrix(1,0,0,-1,127.12,49.6)"> <tspan style="font-size: 12.50px; " x="18.059999" y="9.7299995"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.41" y="-8.3000002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.099106" y="-8.3000002"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,175.76,62.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,181.32,57.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 154.64,52.73 46.59,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,155.91,40.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.509998" y="0.58999997"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.345287" y="2.6500001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.508786" y="2.6500001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.136576" y="2.6500001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.300076" y="2.6500001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.989182" y="2.6500001"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.152679" y="2.6500001"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.25" y="-9.1400003"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="70.277885" y="-9.1400003"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="76.529388" y="-9.1400003"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="91.708031" y="-9.1400003"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="101.87297" y="-9.1400003"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="113.90086" y="-9.1400003"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,280.01,54.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,286.51,49.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="178.24001" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="182.4035" y="0"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="188.655" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="191.78075" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="198.03224" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg></span></span></p> <p><span class="statement" id="rem3.2"><span class="statement-title"><i class="statement-title">3.2的话。</我></span>(一)如果<gydF4y2Basvg height="10.325" id="M233" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.325" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是一个<gydF4y2Basvg height="15.1625" id="M234" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>——功能<gydF4y2Basvg height="10.5375" id="M235" style="vertical-align:-0.16302pt;width:20.975px;" version="1.1" viewbox="0 0 20.975 10.5375" width="20.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,68.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>,那么这个函数<gydF4y2Basvg height="13.85" id="M236" style="vertical-align:-2.34499pt;width:77.849998px;" version="1.1" viewbox="0 0 77.849998 13.85" width="77.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.85)"> <g transform="translate(72,-60.92)"> <text transform="matrix(1,0,0,-1,-71.95,63.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> ∶</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.267363" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.00864" y="0"> →</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.150253" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>给出的<gydF4y2Basvg height="13.6125" id="M237" style="vertical-align:-2.34499pt;width:98.574997px;" version="1.1" viewbox="0 0 98.574997 13.6125" width="98.574997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.341661" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.968491" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.008881" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.26038" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.736214" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.463066" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.626568" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="64.878067" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.353905" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="74.592896" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.125" id="M238" style="vertical-align:-1.95624pt;width:31.65px;" version="1.1" viewbox="0 0 31.65 13.125" width="31.65" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.125)"> <g transform="translate(72,-61.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3144951" y="0"> ≠</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.967051" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.6125" id="M239" style="vertical-align:-2.34499pt;width:54.224998px;" version="1.1" viewbox="0 0 54.224998 13.6125" width="54.224998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.354164" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.980993" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.021381" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,是<gydF4y2Basvg height="10.475" id="M240" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如在<gydF4y2Basvg height="10.5375" id="M241" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="13.85" id="M242" style="vertical-align:-2.34499pt;width:98.462502px;" version="1.1" viewbox="0 0 98.462502 13.85" width="98.462502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.85)"> <g transform="translate(72,-60.92)"> <text transform="matrix(1,0,0,-1,-71.95,63.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.00312" y="0"> ∶</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.867987" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.807152" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.97065" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.785267" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.500095" y="0"> →</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="69.641708" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="17.924999" id="M243" style="vertical-align:-2.21957pt;width:118.775px;" version="1.1" viewbox="0 0 118.775 17.924999" width="118.775" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.925)"> <g transform="translate(72,-57.66)"> <text transform="matrix(1,0,0,-1,-71.95,59.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.393112" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.019943" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.060333" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-19.19,64.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-13.05,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.2697887" y="2.6500001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.433288" y="2.6500001"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.684788" y="2.6500001"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.160622" y="2.6500001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.850447" y="2.6500001"> )</gydF4y2Batspan> </text> </g> </g> </svg>,尽管<gydF4y2Basvg height="14.6875" id="M244" style="vertical-align:-2.78387pt;width:104.875px;" version="1.1" viewbox="0 0 104.875 14.6875" width="104.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6875)"> <g transform="translate(72,-60.25)"> <text transform="matrix(1,0,0,-1,-67.78,63.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.153156" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.193544" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.13271" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.296207" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.110825" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.049988" y="0"> ⧵</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="61.364723" y="0"> {</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="67.366165" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73.617661" y="0"> }</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="13.45" id="M245" style="vertical-align:-2.21957pt;width:57.474998px;" version="1.1" viewbox="0 0 57.474998 13.45" width="57.474998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.954788" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.581617" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.622005" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。<gydF4y2Babr>(b)如果<gydF4y2Basvg height="13.4875" id="M246" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是一个<gydF4y2Basvg height="10.475" id="M247" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>——功能<gydF4y2Basvg height="10.5375" id="M248" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,那么这个函数<gydF4y2Basvg height="11.225" id="M249" style="vertical-align:-0.23827pt;width:86.949997px;" version="1.1" viewbox="0 0 86.949997 11.225" width="86.949997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.225)"> <g transform="translate(72,-63.02)"> <text transform="matrix(1,0,0,-1,-71.95,63.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.190185" y="0"> ∶</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.055052" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-40.7,68.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-28.65,63.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> →</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.12911" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.6125" id="M250" style="vertical-align:-2.34499pt;width:99.699997px;" version="1.1" viewbox="0 0 99.699997 13.6125" width="99.699997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.206287" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.246677" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.498177" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.97401" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="54.913177" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.076675" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.328178" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.804008" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.493111" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="15.1625" id="M251" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如在<gydF4y2Basvg height="10.5375" id="M252" style="vertical-align:-0.16302pt;width:20.975px;" version="1.1" viewbox="0 0 20.975 10.5375" width="20.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,68.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="17.924999" id="M253" style="vertical-align:-2.21957pt;width:109.2875px;" version="1.1" viewbox="0 0 109.2875 17.924999" width="109.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.925)"> <g transform="translate(72,-57.66)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.73312" y="2.6500001"> ∶</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.597986" y="2.6500001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.324841" y="2.6500001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.488338" y="2.6500001"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-26.99,64.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-20.5,59.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> →</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.843941" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="17.924999" id="M254" style="vertical-align:-2.21957pt;width:114.3625px;" version="1.1" viewbox="0 0 114.3625 17.924999" width="114.3625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.925)"> <g transform="translate(72,-57.66)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.2697887" y="2.6500001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.433288" y="2.6500001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.94783" y="2.6500001"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.574661" y="2.6500001"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.615051" y="2.6500001"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-21.54,64.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.67,59.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.954788" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.430622" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.945166" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,尽管<gydF4y2Basvg height="13.45" id="M255" style="vertical-align:-2.21957pt;width:71.074997px;" version="1.1" viewbox="0 0 71.074997 13.45" width="71.074997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.977874" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.018263" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.745117" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.908615" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-25.84,68.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-19.35,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。<gydF4y2Babr>(c)任何<gydF4y2Basvg height="15.1625" id="M256" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>——全纯函数<gydF4y2Basvg height="10.325" id="M257" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.325" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>在<gydF4y2Basvg height="10.5375" id="M258" style="vertical-align:-0.16302pt;width:20.975px;" version="1.1" viewbox="0 0 20.975 10.5375" width="20.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,68.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>是单价的<gydF4y2Basvg height="10.5375" id="M259" style="vertical-align:-0.16302pt;width:20.975px;" version="1.1" viewbox="0 0 20.975 10.5375" width="20.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,68.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>。</gydF4y2Baspan></p> <p><span class="statement" id="proof4"><span class="statement-title"><i class="statement-title">证明。</我></span>这句话可以通过简单的计算和证明,因此,留给了读者。</gydF4y2Baspan></p> <p>下面的结果是一个概括的<一个href="#B14">5</一个>定理3)。提到定理可能获得通过<gydF4y2Basvg height="17.924999" id="M260" style="vertical-align:-2.21957pt;width:66.074997px;" version="1.1" viewbox="0 0 66.074997 17.924999" width="66.074997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.925)"> <g transform="translate(72,-57.66)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.2697887" y="2.6500001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.433288" y="2.6500001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.123114" y="2.6500001"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.749943" y="2.6500001"> ≡</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.790333" y="2.6500001"> </gydF4y2Batspan> </text> </g> </g> </svg>在定理<一个href="#thm3.3">3.3</一个>在下面。</gydF4y2Bap> <p><span class="statement" id="thm3.3"><span class="statement-title">定理3.3。</gydF4y2Baspan><i>让<gydF4y2Basvg height="14.3875" id="M261" style="vertical-align:-3.25793pt;width:15.875px;" version="1.1" viewbox="0 0 15.875 14.3875" width="15.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.22,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>是一个函数<gydF4y2Basvg height="15.1625" id="M262" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如在<gydF4y2Basvg height="10.5375" id="M263" style="vertical-align:-0.16302pt;width:20.975px;" version="1.1" viewbox="0 0 20.975 10.5375" width="20.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,68.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>和单价的<gydF4y2Basvg height="15.6875" id="M264" style="vertical-align:-0.16302pt;width:20.975px;" version="1.1" viewbox="0 0 20.975 15.6875" width="20.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.6875)"> <g transform="translate(72,-59.45)"> <g> <path d="m -71.95,70.71 16.68,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,64.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>。那么解决方案<gydF4y2Basvg height="13.55" id="M265" style="vertical-align:-2.29482pt;width:39.962502px;" version="1.1" viewbox="0 0 39.962502 13.55" width="39.962502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.780706" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.694145" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>Polubarinova-Galin方程(<一个href="#EEq1.4">1.5</一个>与初始条件)<gydF4y2Basvg height="14.75" id="M266" style="vertical-align:-3.25793pt;width:96.787498px;" version="1.1" viewbox="0 0 96.787498 14.75" width="96.787498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.780706" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.032206" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.671539" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.711929" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-14.51,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-9.63,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="15.1625" id="M267" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>式为<gydF4y2Basvg height="13.45" id="M268" style="vertical-align:-2.21957pt;width:57.737499px;" version="1.1" viewbox="0 0 57.737499 13.45" width="57.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.922558" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="10.325" id="M269" style="vertical-align:-0.0pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 10.325" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>充气时间,<gydF4y2Basvg height="17.924999" id="M270" style="vertical-align:-4.67863pt;width:228.425px;" version="1.1" viewbox="0 0 228.425 17.924999" width="228.425" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.925)"> <g transform="translate(72,-57.66)"> <text transform="matrix(1,0,0,-1,-71.95,62.37)"> <tspan style="font-size: 12.50px; " x="24.809999" y="0.02"> ⋃</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.765563" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-35.58,58.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="13.110496" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="19.105616" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-7.68,62.37)"> <tspan style="font-size: 12.50px; " x="37.049999" y="0.02"> ⋃</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.379169" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,40.92,58.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="13.110496" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="19.105616" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,68.83,62.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,90.91,67.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,97.4,62.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="15.1625" id="M271" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>是一个全纯函数<gydF4y2Basvg height="15.85" id="M272" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 15.85" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.85)"> <g transform="translate(72,-59.32)"> <g> <path d="m -71.95,70.71 9.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> </text> </g> </g> </svg>满足下列条件:</我><span class="equation" id="EEq3.2"> <svg height="36.549999" id="M273" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 36.549999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,36.55)"> <g transform="translate(72,-42.76)"> <text transform="matrix(1,0,0,-1,77.88,51.7)"> <tspan style="font-size: 12.50px; " x="18.440001" y="-10.87"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.17" y="-8.2200003"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.785288" y="-8.2200003"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.948788" y="-8.2200003"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.463329" y="-8.2200003"> )</gydF4y2Batspan> </text> <g> <path d="m 95.05,54.83 28.47,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,105.03,42.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73.860001" y="-11.4"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.589996" y="-8.75"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.16" y="-8.75"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.187885" y="-8.75"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.439384" y="-8.75"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.618027" y="-8.75"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="64.957527" y="-8.75"> e</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,187.16,60.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,192.72,51.71)"> <tspan style="font-size: 12.50px; " x="59.130001" y="-10.86"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.678042" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.304873" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.345261" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.684761" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.024261" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.860001" y="-8.21"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="69.475288" y="-8.21"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73.638786" y="-8.21"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="82.153328" y="-8.21"> )</gydF4y2Batspan> </text> <g> <path d="m 250.58,54.83 28.47,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,260.56,42.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.68" y="-8.75"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.846138" y="-8.75"> ∀</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.84782" y="-8.75"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.838196" y="-8.75"> ∈</gydF4y2Batspan> </text> <g> <path d="m 326.44,63.04 9.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,326.44,51.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="138.31" y="-2.5599999"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="142.4735" y="-2.5599999"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="148.72501" y="-2.5599999"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="151.85075" y="-2.5599999"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="158.10225" y="-2.5599999"> )</gydF4y2Batspan> </text> </g> </g> </svg></span><i></i></span></p> <p><span class="statement" id="proof5"><span class="statement-title"><i class="statement-title">证明。</我></span>通过考虑函数<gydF4y2Basvg height="13.6125" id="M274" style="vertical-align:-2.34499pt;width:122.5125px;" version="1.1" viewbox="0 0 122.5125 13.6125" width="122.5125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.545788" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.586178" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.837677" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.313511" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="64.040367" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.203865" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="74.455368" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="77.931198" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="84.6203" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="89.821548" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="93.734993" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>Polubarinova-Galin方程(<一个href="#EEq1.4">1.5</一个>)可以改写的<gydF4y2Basvg height="13.4875" id="M275" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>如下:<gydF4y2Baspan class="equation" id="EEq3.3"> <svg height="39.362499" id="M276" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 39.362499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,39.3625)"> <g transform="translate(72,-40.51)"> <text transform="matrix(1,0,0,-1,94.38,49.47)"> <tspan style="font-size: 12.50px; " x="23.07" y="-2.73"> ̇</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.98" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.495024" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.658522" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.347626" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.561378" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.474815" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 147.11,62.38 42.74,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,147.11,49.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.6766019" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,162.23,54.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,165.71,49.47)"> <tspan style="font-size: 12.50px; " x="49.41" y="-9.8100004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.169998" y="-11.39"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.169998" y="-8.2299995"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="96.339996" y="-11.39"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="96.339996" y="-8.2299995"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.606625" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.647015" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="61.669998" y="-9.8100004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.18502" y="-9.8100004"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="76.348518" y="-9.8100004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="83.037628" y="-9.8100004"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="88.251381" y="-9.8100004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="92.164818" y="-9.8100004"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,264.55,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</gydF4y2Batspan> </text> <g> <path d="m 215.12,52.6 54.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,235.34,40.72)"> <tspan style="font-size: 12.50px; " x="35.279999" y="-8.75"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.450001" y="-10.34"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.450001" y="-7.1799998"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.950001" y="-8.75"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.639999" y="-10.34"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.639999" y="-7.1799998"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.610001" y="-8.75"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="77.637886" y="-8.75"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="83.889389" y="-8.75"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="229.41" y="-12.41"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="233.5735" y="-12.41"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="239.825" y="-12.41"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="242.95074" y="-12.41"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="249.20226" y="-12.41"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>由于前面的话,函数<gydF4y2Basvg height="13.55" id="M277" style="vertical-align:-2.29482pt;width:39.962502px;" version="1.1" viewbox="0 0 39.962502 13.55" width="39.962502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.780706" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.694145" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.425" id="M278" style="vertical-align:-2.29482pt;width:48.724998px;" version="1.1" viewbox="0 0 48.724998 13.425" width="48.724998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.152436" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.192825" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-39.56,68.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>,是<gydF4y2Basvg height="15.1625" id="M279" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如当且仅当<gydF4y2Basvg height="13.6125" id="M280" style="vertical-align:-2.34499pt;width:38.974998px;" version="1.1" viewbox="0 0 38.974998 13.6125" width="38.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.425" id="M281" style="vertical-align:-2.29482pt;width:40.612499px;" version="1.1" viewbox="0 0 40.612499 13.425" width="40.612499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.152436" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.192825" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,是<gydF4y2Basvg height="10.475" id="M282" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如,之间的关系<gydF4y2Basvg height="15.1625" id="M283" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="10.475" id="M284" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="17.924999" id="M285" style="vertical-align:-2.21957pt;width:114.3625px;" version="1.1" viewbox="0 0 114.3625 17.924999" width="114.3625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.925)"> <g transform="translate(72,-57.66)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.2697887" y="2.6500001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.433288" y="2.6500001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.94783" y="2.6500001"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.574661" y="2.6500001"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.615051" y="2.6500001"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-21.54,64.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-16.67,59.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.954788" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.430622" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.945166" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,尽管<gydF4y2Basvg height="17.924999" id="M286" style="vertical-align:-2.21957pt;width:218.3625px;" version="1.1" viewbox="0 0 218.3625 17.924999" width="218.3625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.925)"> <g transform="translate(72,-57.66)"> <text transform="matrix(1,0,0,-1,-71.95,59.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.977874" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.018263" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.745117" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.908615" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-25.84,64.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-19.35,59.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3269978" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.490497" y="0"> o</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.741997" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.068995" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.608784" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.772282" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.462109" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.10144" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="70.14183" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,60.48,64.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,66.63,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.2697887" y="2.6500001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.433288" y="2.6500001"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.684788" y="2.6500001"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.160622" y="2.6500001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.850447" y="2.6500001"> )</gydF4y2Batspan> </text> </g> </g> </svg>,尽管<gydF4y2Basvg height="13.6125" id="M287" style="vertical-align:-2.34499pt;width:66.925003px;" version="1.1" viewbox="0 0 66.925003 13.6125" width="66.925003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.153156" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.193544" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.13271" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.296207" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="45.110825" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.274323" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。因此,它可以证明的功能<gydF4y2Basvg height="13.6125" id="M288" style="vertical-align:-2.34499pt;width:38.974998px;" version="1.1" viewbox="0 0 38.974998 13.6125" width="38.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="10.475" id="M289" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>式为<gydF4y2Basvg height="13.45" id="M290" style="vertical-align:-2.21957pt;width:57.737499px;" version="1.1" viewbox="0 0 57.737499 13.45" width="57.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.922558" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。<gydF4y2Babr>假设相反,前面的表述是不正确的。然后存在<gydF4y2Basvg height="14.75" id="M291" style="vertical-align:-3.25793pt;width:38.3125px;" version="1.1" viewbox="0 0 38.3125 14.75" width="38.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-59.69,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≥</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="17.75" id="M292" style="vertical-align:-3.25793pt;width:55.212502px;" version="1.1" viewbox="0 0 55.212502 17.75" width="55.212502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.75)"> <g transform="translate(72,-57.8)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.26,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.91,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-39.31,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-32,63.92)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>这样,(<一个href="#EEq2.3">2。3</一个>),(<gydF4y2Ba一个href="#EEq2.4">2。4</一个>),(<gydF4y2Ba一个href="#EEq2.5">2。5</一个>),(<gydF4y2Ba一个href="#EEq2.6">2。6</一个>)和(<一个href="#EEq2.6">2。7</一个>)是正确的。与此同时,平等(<一个href="#EEq2.8">2。8</一个>)是实现。我们必须确定函数的符号<gydF4y2Basvg height="16.049999" id="M293" style="vertical-align:-2.73372pt;width:195.4875px;" version="1.1" viewbox="0 0 195.4875 16.049999" width="195.4875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.05)"> <g transform="translate(72,-59.16)"> <text transform="matrix(1,0,0,-1,-71.95,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.540029" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.015863" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.404896" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.318335" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.569836" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.121166" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.284664" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.787666" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.951164" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="63.64027" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,0.14,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,3.61,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.130791" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.606625" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.146412" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.309914" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.249077" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.412575" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.101681" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="64.31543" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.228874" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.392372" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="76.55587" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>在点<gydF4y2Basvg height="14.75" id="M294" style="vertical-align:-3.25793pt;width:42.487499px;" version="1.1" viewbox="0 0 42.487499 14.75" width="42.487499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.1,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.22,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-47.1,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-42.23,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>。<gydF4y2Babr>通过区分(<一个href="#EEq3.3">3.3</一个>)和使用(<一个href="#EEq2.6">2。6</一个>),(<gydF4y2Ba一个href="#EEq2.8">2。8</一个>)和(<一个href="#EEq3.3">3.3</一个>),我们得到<gydF4y2Baspan class="equation" id="eq6"> <svg height="119.3375" id="M295" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 119.3375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,119.3375)"> <g transform="translate(72,23.47)"> <text transform="matrix(1,0,0,-1,-33.65,58.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m -35.61,54.37 10.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-35.61,42.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.58" y="-8.75"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.131332" y="-8.75"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.29483" y="-8.75"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.610001" y="-17.110001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.299107" y="-17.110001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.23827" y="-17.110001"> ′</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.851639" y="-17.110001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.015137" y="-17.110001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="64.704239" y="-17.110001"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="69.905487" y="-17.110001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73.818932" y="-17.110001"> )</gydF4y2Batspan> </text> <g> <path d="m -2.78,54.37 48.94,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-2.78,42.49)"> <tspan style="font-size: 12.50px; " x="50.139999" y="-21.01"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.139999" y="-10.34"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.139999" y="0.31999999"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.139999" y="3.49"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.642452" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.805952" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.482553" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.696304" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.609745" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.773243" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,49.86,36.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.6735678" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.668688" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,65.22,34.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,68.84,36.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.9273758" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.922496" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,82.51,34.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-14.6,-0.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.209999" y="-9.8100004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.969999" y="-11.39"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.969999" y="-8.2299995"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.469999" y="-9.8100004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.91" y="-11.39"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.91" y="-8.2299995"> |</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,26.81,15.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</gydF4y2Batspan> </text> <g> <path d="m -0.17,2.2 35.64,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-0.17,-13.36)"> <tspan style="font-size: 12.50px; " x="13.85" y="-1.59"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.85" y="1.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.35" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,24.62,-8.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,28.09,-11.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="3.1700001"> |</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,30.59,-6.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,38.75,-0.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.059999" y="7.3200002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.411524" y="7.3200002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.98" y="-8.3599997"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.669106" y="-8.3599997"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,88.86,12.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 73.73,2.2 21.58,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,78.56,-10.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,87,-5.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,99.28,-0.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.54" y="-8.3599997"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,121.36,12.43)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,126.92,7.43)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.590521" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.842022" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.531126" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,160.9,12.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 111.82,2.2 52.55,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,123.9,-9.68)"> <tspan style="font-size: 12.50px; " x="41.669998" y="-1.4299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.218311" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.82" y="-8.75"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.160217" y="-8.75"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73.499725" y="-8.75"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="77.663223" y="-8.75"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="95.57" y="-17.110001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="102.2466" y="-17.110001"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,234.6,12.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 214.57,2.2 28.39,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,214.57,-9.68)"> <tspan style="font-size: 12.50px; " x="31.67" y="-1.4299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.218311" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.049999" y="-8.75"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.3895" y="-8.75"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.016331" y="-8.75"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,281.14,4.08)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,286.69,-0.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.603024" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.542189" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.88241" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.221912" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.561413" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.400002" y="-8.3500004"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.015289" y="-8.3500004"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.178787" y="-8.3500004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="80.618309" y="-8.3500004"> )</gydF4y2Batspan> </text> <g> <path d="m 343.09,2.2 28.39,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,353.06,-9.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.34" y="-26.34"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.34" y="-15.67"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.34" y="-5.0100002"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.34" y="5.6599998"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.34" y="8.8199997"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.610001" y="-1.4299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.987249" y="-1.4299999"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,390.9,-21.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.6823201" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.67744" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,406.26,-23.34)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,409.89,-21.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.9273758" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.922496" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,423.55,-23.34)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,427.67,-0.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.080002" y="-22.07"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.2435" y="-22.07"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.494999" y="-22.07"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.62075" y="-22.07"> 4</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.87225" y="-22.07"> )</gydF4y2Batspan> </text> </g> </g> </svg></span><br>右边的平等是严格负的(<一个href="#EEq2.5">2。5</一个>),(<gydF4y2Ba一个href="#EEq2.6">2。7</一个>),<ggydF4y2BaydF4y2Basvg height="15.475" id="M296" style="vertical-align:-2.34499pt;width:85.25px;" version="1.1" viewbox="0 0 85.25 15.475" width="85.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.475)"> <g transform="translate(72,-59.62)"> <text transform="matrix(1,0,0,-1,-71.95,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.054333" y="0"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-44.35,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-40.88,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.729494" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.769882" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.6125" id="M297" style="vertical-align:-2.34499pt;width:101.7375px;" version="1.1" viewbox="0 0 101.7375 13.6125" width="101.7375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.129829" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.669619" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.833118" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.772282" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.935783" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.411617" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.35078" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.990112" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.030502" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>(前面的简单的后果是不平等<一个href="#EEq3.2">3.2</一个>))。因此,<gydF4y2Basvg height="17.0875" id="M298" style="vertical-align:-2.73372pt;width:220.7625px;" version="1.1" viewbox="0 0 220.7625 17.0875" width="220.7625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.0875)"> <g transform="translate(72,-58.33)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.129829" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.293329" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-42.09,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-34.28,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-25.84,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-22.37,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-12.64,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-4.84,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.1271896" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.290689" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.766523" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.306313" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.46981" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.408978" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.572475" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,42.3,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,50.1,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.278186" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.081018" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.121407" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.723232" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.199066" y="0"> 2</gydF4y2Batspan> </text> </g> </g> </svg>,因为<gydF4y2Basvg height="13.05" id="M299" style="vertical-align:-3.25793pt;width:35.387501px;" version="1.1" viewbox="0 0 35.387501 13.05" width="35.387501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-48.61,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>(接近<gydF4y2Basvg height="13.05" id="M300" style="vertical-align:-3.25793pt;width:11.1125px;" version="1.1" viewbox="0 0 11.1125 13.05" width="11.1125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>在某些地段)<gydF4y2Basvg height="14.625" id="M301" style="vertical-align:-3.25793pt;width:14.4125px;" version="1.1" viewbox="0 0 14.4125 14.625" width="14.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.4,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。这一矛盾就完成了证明。</gydF4y2Baspan></p> <p>下面的结果是一个概括的<一个href="#B15">6</一个>定理3.1)。提到定理可能获得通过<gydF4y2Basvg height="17.924999" id="M302" style="vertical-align:-2.21957pt;width:66.074997px;" version="1.1" viewbox="0 0 66.074997 17.924999" width="66.074997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.925)"> <g transform="translate(72,-57.66)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.2697887" y="2.6500001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.433288" y="2.6500001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.123114" y="2.6500001"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.749943" y="2.6500001"> ≡</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.790333" y="2.6500001"> </gydF4y2Batspan> </text> </g> </g> </svg>在定理<一个href="#thm3.4">3.4</一个>在下面。</gydF4y2Bap> <p><span class="statement" id="thm3.4"><span class="statement-title">定理3.4。</gydF4y2Baspan><i>让<gydF4y2Basvg height="13.0625" id="M303" style="vertical-align:-1.90608pt;width:39.537498px;" version="1.1" viewbox="0 0 39.537498 13.0625" width="39.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0625)"> <g transform="translate(72,-61.55)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.228174" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.268562" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,让表面张力<gydF4y2Basvg height="9.9375" id="M304" style="vertical-align:-2.34499pt;width:8.0625px;" version="1.1" viewbox="0 0 8.0625 9.9375" width="8.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.9375)"> <g transform="translate(72,-64.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>是足够小。如果<gydF4y2Basvg height="14.3875" id="M305" style="vertical-align:-3.25793pt;width:15.875px;" version="1.1" viewbox="0 0 15.875 14.3875" width="15.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.22,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>是一个函数<gydF4y2Basvg height="15.1625" id="M306" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如在<gydF4y2Basvg height="10.5375" id="M307" style="vertical-align:-0.16302pt;width:20.975px;" version="1.1" viewbox="0 0 20.975 10.5375" width="20.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,68.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>和单价的<gydF4y2Basvg height="15.6875" id="M308" style="vertical-align:-0.16302pt;width:20.975px;" version="1.1" viewbox="0 0 20.975 15.6875" width="20.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.6875)"> <g transform="translate(72,-59.45)"> <g> <path d="m -71.95,70.71 16.68,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,64.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>,然后存在<gydF4y2Basvg height="13.6125" id="M309" style="vertical-align:-2.34499pt;width:53.849998px;" version="1.1" viewbox="0 0 53.849998 13.6125" width="53.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="3.913439" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.415959" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.055292" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.09568" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>这样的解决方案<gydF4y2Basvg height="13.55" id="M310" style="vertical-align:-2.29482pt;width:39.962502px;" version="1.1" viewbox="0 0 39.962502 13.55" width="39.962502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.780706" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.694145" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>(<一个href="#EEq1.5">1.6</一个>与初始条件)<gydF4y2Basvg height="14.75" id="M311" style="vertical-align:-3.25793pt;width:96.787498px;" version="1.1" viewbox="0 0 96.787498 14.75" width="96.787498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.780706" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.032206" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.671539" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.711929" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-14.51,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-9.63,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="15.1625" id="M312" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>式为<gydF4y2Basvg height="13.6125" id="M313" style="vertical-align:-2.34499pt;width:72.375px;" version="1.1" viewbox="0 0 72.375 13.6125" width="72.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.959347" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.122849" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.474373" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.637871" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<gydF4y2Basvg height="10.325" id="M314" style="vertical-align:-0.0pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 10.325" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>充气时间,<gydF4y2Basvg height="18.85" id="M315" style="vertical-align:-5.41599pt;width:245.425px;" version="1.1" viewbox="0 0 245.425 18.85" width="245.425" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.85)"> <g transform="translate(72,-56.92)"> <text transform="matrix(1,0,0,-1,-71.95,62.37)"> <tspan style="font-size: 12.50px; " x="24.809999" y="0.02"> ⋃</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.765563" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-35.58,58.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="13.110496" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="19.105616" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="21.844992" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="24.759409" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="29.196672" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-0.88,62.37)"> <tspan style="font-size: 12.50px; " x="37.049999" y="0.02"> ⋃</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.3022318" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.465731" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.379169" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.006001" y="0"> =</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,47.72,58.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="13.110496" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="19.105616" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="21.844992" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="24.759409" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="29.205423" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,82.43,62.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,104.51,67.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,111,62.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="15.1625" id="M316" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>是一个全纯函数<gydF4y2Basvg height="15.85" id="M317" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 15.85" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.85)"> <g transform="translate(72,-59.32)"> <g> <path d="m -71.95,70.71 9.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</gydF4y2Batspan> </text> </g> </g> </svg>满足的条件(<一个href="#EEq3.2">3.2</一个>)。</我></span></p> <p><span class="statement" id="proof6"><span class="statement-title"><i class="statement-title">证明。</我></span>我们引入了(如定理的证明<一个href="#thm3.3">3.3</一个>)函数<gydF4y2Basvg height="13.6125" id="M318" style="vertical-align:-2.34499pt;width:174.72501px;" version="1.1" viewbox="0 0 174.72501 13.6125" width="174.72501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.779266" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.993017" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.906456" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.545788" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.586178" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.837677" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.313511" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="64.040367" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.203865" y="0"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="74.455368" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="77.931198" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="84.6203" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="89.821548" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="93.734993" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="97.898491" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="107.27574" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="117.44068" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="129.48106" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>,这是<gydF4y2Basvg height="10.475" id="M319" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如<gydF4y2Basvg height="17.924999" id="M320" style="vertical-align:-2.21957pt;width:129.175px;" version="1.1" viewbox="0 0 129.175 17.924999" width="129.175" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.925)"> <g transform="translate(72,-57.66)"> <text transform="matrix(1,0,0,-1,-71.95,59.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.866787" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.556612" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.183441" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.223831" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-15.03,64.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-8.89,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.26" y="2.6500001"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.279789" y="2.6500001"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.443288" y="2.6500001"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.694788" y="2.6500001"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.170622" y="2.6500001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.860447" y="2.6500001"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.023945" y="2.6500001"> )</gydF4y2Batspan> </text> </g> </g> </svg>当且仅当<gydF4y2Basvg height="13.55" id="M321" style="vertical-align:-2.29482pt;width:39.962502px;" version="1.1" viewbox="0 0 39.962502 13.55" width="39.962502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.780706" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.694145" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="15.1625" id="M322" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>的地方。<gydF4y2Babr>Polubarinova-Galin方程可以写成的<gydF4y2Basvg height="13.4875" id="M323" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>作为<gydF4y2Baspan class="equation" id="EEq3.4"> <svg height="38.575001" id="M324" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.575001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,38.575)"> <g transform="translate(72,-41.14)"> <text transform="matrix(1,0,0,-1,46.73,53.45)"> <tspan style="font-size: 12.50px; " x="23.07" y="-2.72"> ̇</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.97" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.485023" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.648521" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.337627" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.551376" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="46.464817" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 99.45,66.35 44.82,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,99.45,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.6766019" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,114.58,58.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,120.13,53.45)"> <tspan style="font-size: 12.50px; " x="48.220001" y="-1.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.220001" y="1.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.720001" y="7.1054274e-015"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.16" y="-1.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.16" y="1.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.606625" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.647015" y="0"> −</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,181.79,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,188.75,46.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.61" y="-15.24"> </gydF4y2Batspan> </text> <g> <path d="m 199.32,56.57 13.85,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,199.32,44.69)"> <tspan style="font-size: 12.50px; " x="49.650002" y="-3.8399999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.380001" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.83" y="-8.7600002"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.157719" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.509243" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="60.470001" y="-16.01"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="66.846527" y="-16.01"> </gydF4y2Batspan> </text> <g> <path d="m 259.79,56.57 13.16,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,259.9,44.69)"> <tspan style="font-size: 12.50px; " x="14.25" y="-3.8399999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.950001" y="-1.4299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.41" y="-8.7600002"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73.550003" y="-10.34"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="73.550003" y="-7.1799998"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="76.050003" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="82.739998" y="-10.34"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="82.739998" y="-7.1799998"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.07" y="-8.7600002"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.2335" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="32.785072" y="-8.7600002"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="88.709999" y="-8.7600002"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="100.73788" y="-8.7600002"> 1</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="106.98939" y="-8.7600002"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="204.85001" y="-8.7600002"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="209.0135" y="-8.7600002"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="215.265" y="-8.7600002"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="218.39075" y="-8.7600002"> 5</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="224.64224" y="-8.7600002"> )</gydF4y2Batspan> </text> </g> </g> </svg></span>相反,假设定理的结论<一个href="#thm3.4">3.4</一个>是不正确的。然后存在<gydF4y2Basvg height="14.75" id="M325" style="vertical-align:-3.25793pt;width:38.3125px;" version="1.1" viewbox="0 0 38.3125 14.75" width="38.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-59.69,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≥</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>和<gydF4y2Basvg height="17.75" id="M326" style="vertical-align:-3.25793pt;width:55.212502px;" version="1.1" viewbox="0 0 55.212502 17.75" width="55.212502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.75)"> <g transform="translate(72,-57.8)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.26,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-56.91,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-39.31,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-32,63.92)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>这样,(<一个href="#EEq2.3">2。3</一个>),(<gydF4y2Ba一个href="#EEq2.4">2。4</一个>),(<gydF4y2Ba一个href="#EEq2.5">2。5</一个>),(<gydF4y2Ba一个href="#EEq2.6">2。6</一个>)和(<一个href="#EEq2.6">2。7</一个>)是正确的。与此同时,平等(<一个href="#EEq2.8">2。8</一个>)是实现。我们区分(<一个href="#EEq3.4">3.5</一个>)对<gydF4y2Basvg height="10.7375" id="M327" style="vertical-align:-0.13794pt;width:8.3125px;" version="1.1" viewbox="0 0 8.3125 10.7375" width="8.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>。因为左边是可微的对<gydF4y2Basvg height="10.7375" id="M328" style="vertical-align:-0.13794pt;width:8.3125px;" version="1.1" viewbox="0 0 8.3125 10.7375" width="8.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>的解决方案(<一个href="#EEq3.4">3.5</一个>)存在,而且是独一无二的,那么右边是可微的,它的导数是有界的<gydF4y2Basvg height="13.125" id="M329" style="vertical-align:-1.95624pt;width:42.174999px;" version="1.1" viewbox="0 0 42.174999 13.125" width="42.174999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.125)"> <g transform="translate(72,-61.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="21.867746" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.46957" y="0"> ]</gydF4y2Batspan> </text> </g> </g> </svg>。<gydF4y2Babr>如果我们表示<gydF4y2Basvg height="13.45" id="M330" style="vertical-align:-2.21957pt;width:184.125px;" version="1.1" viewbox="0 0 184.125 13.45" width="184.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.9646511" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.12815" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.88097" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.794409" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.433743" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.474133" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="52.63763" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="59.026665" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.502499" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.891533" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.4431" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="79.606598" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="90.521721" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="94.685219" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="98.573654" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="104.96268" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="111.73931" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="115.21514" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="121.60418" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="128.15575" y="0"> ]</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="132.31924" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="136.48274" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="143.03432" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>;然后通过使用(<一个href="#EEq2.6">2。6</一个>),(<gydF4y2Ba一个href="#EEq2.8">2。8</一个>)和(<一个href="#EEq3.4">3.5</一个>),我们得到<gydF4y2Baspan class="equation" id="eq7"> <svg height="237.47501" id="M331" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 237.47501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,237.475)"> <g transform="translate(72,117.98)"> <text transform="matrix(1,0,0,-1,-4.06,58.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m -6.02,54.37 10.31,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-6.02,42.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.59" y="-8.75"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.141333" y="-8.75"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.304831" y="-8.75"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.93" y="-17.110001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="42.619106" y="-17.110001"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,45.04,64.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,48.52,59.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.840101" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.967291" y="0"> )</gydF4y2Batspan> </text> <g> <path d="m 26.81,54.37 48.95,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,26.81,42.49)"> <tspan style="font-size: 12.50px; " x="50.139999" y="-21.01"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.139999" y="-10.34"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.139999" y="0.31999999"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="50.139999" y="3.49"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.5397892" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.703288" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.642452" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.805952" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="31.495056" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="36.696304" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.609745" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.773243" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,79.45,36.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.6823201" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.67744" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,94.81,34.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,98.44,36.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,108.33,39.4)"> <tspan style="font-size: 6.25px; " x="5.2199998" y="1.97"> 0</gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 6.25px; " x="1.9443721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,117.67,36.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.9273758" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.922496" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,131.33,34.17)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,14.99,2.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.97" y="-11.39"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.97" y="-8.2200003"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.469999" y="-9.8000002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.91" y="-11.39"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.91" y="-8.2200003"> |</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,43.4,19.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</gydF4y2Batspan> </text> <g> <path d="m 28.23,5.76 21.78,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,28.23,-8.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="3.1700001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="2.5" y="1.59"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,39.17,-4.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,42.64,-8.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="3.1700001"> |</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,45.14,-3.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,53.29,-4.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.62" y="-15.24"> </gydF4y2Batspan> </text> <g> <path d="m 63.87,5.76 13.85,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,63.87,-6.12)"> <tspan style="font-size: 12.50px; " x="49.639999" y="-3.8399999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.009998" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.82" y="-8.7600002"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.160221" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.511745" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.09" y="-16.01"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.479034" y="-16.01"> </gydF4y2Batspan> </text> <g> <path d="m 125.96,5.76 13.17,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,126.07,-6.12)"> <tspan style="font-size: 12.50px; " x="14.25" y="-3.8399999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.82" y="-1.4299999"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-101.81" y="37.139999"> ×</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-89.830002" y="44.470001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-65.419998" y="44.470001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.940001" y="-8.7600002"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.103498" y="-8.7600002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.642567" y="-8.7600002"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-83.480003" y="37.139999"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-79.316498" y="37.139999"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-54.849998" y="28.790001"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-48.173397" y="28.790001"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,86.35,-29.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 71.22,-40.14 21.58,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,76.05,-53.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,84.49,-47.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,96.77,-43.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.54" y="-8.3500004"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,118.85,-29.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,124.41,-34.9)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.590521" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.842022" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.531126" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,158.39,-29.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 109.31,-40.14 52.55,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,121.39,-52.01)"> <tspan style="font-size: 12.50px; " x="41.669998" y="-1.42"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.218311" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.82" y="-8.75"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.160217" y="-8.75"> 我</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="69.323723" y="-8.75"> 米</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="87.230003" y="-17.1"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="93.906601" y="-17.1"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,223.75,-29.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <g> <path d="m 203.73,-40.14 28.39,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,203.73,-52.01)"> <tspan style="font-size: 12.50px; " x="31.67" y="-1.42"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="24.218311" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.040001" y="-8.75"> 2</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.366997" y="-8.75"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="57.706497" y="-8.75"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="65.345833" y="-8.75"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,278.62,-38.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,284.18,-43.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.603024" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.542189" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.88241" y="0"> 4</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.221912" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.561413" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="56.389999" y="-8.3500004"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="68.017792" y="-8.3500004"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="72.18129" y="-8.3500004"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="80.620811" y="-8.3500004"> )</gydF4y2Batspan> </text> <g> <path d="m 340.57,-40.14 28.39,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,350.55,-52.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.34" y="-21"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.34" y="-10.34"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.34" y="0.33000001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.34" y="3.49"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.610001" y="-1.42"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="28.987249" y="-1.42"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,388.39,-58.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.6735678" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.668688" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,403.75,-60.34)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,407.37,-58.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.9273758" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.922496" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,421.04,-60.34)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,24.26,-95.43)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.47" y="-11.39"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.47" y="-8.2200003"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.969999" y="-9.8000002"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.41" y="-11.39"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.41" y="-8.2200003"> |</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,53.17,-78.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</gydF4y2Batspan> </text> <g> <path d="m 37.99,-92.31 21.79,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,37.99,-106.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="2.5" y="1.59"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,48.93,-102.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,52.41,-106.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,54.91,-101.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,63.76,-95.43)"> <tspan style="font-size: 12.50px; " x="47.75" y="-17.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.75" y="-6.9200001"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.75" y="3.75"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.75" y="14.41"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="47.75" y="17.58"> |</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋅</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="6.3390212" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="12.690545" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.743196" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.906696" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.458267" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="39.67202" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.585457" y="0"> )</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,114.01,-115.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.6823201" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.67744" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,129.37,-117.84)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,133,-115.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="4.9273758" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="10.922496" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,146.66,-117.84)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,150.78,-95.43)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="313.97" y="-69.309998"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="318.13348" y="-69.309998"> 3</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="324.38501" y="-69.309998"> 。</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="327.51074" y="-69.309998"> 6</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="333.76224" y="-69.309998"> )</gydF4y2Batspan> </text> </g> </g> </svg></span><br>右边的平等是严格-小<gydF4y2Basvg height="9.9375" id="M332" style="vertical-align:-2.34499pt;width:8.0625px;" version="1.1" viewbox="0 0 8.0625 9.9375" width="8.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.9375)"> <g transform="translate(72,-64.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>因为(<一个href="#EEq2.5">2。5</一个>),(<gydF4y2Ba一个href="#EEq2.6">2。7</一个>),<ggydF4y2BaydF4y2Basvg height="15.475" id="M333" style="vertical-align:-2.34499pt;width:82.650002px;" version="1.1" viewbox="0 0 82.650002 15.475" width="82.650002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.475)"> <g transform="translate(72,-59.62)"> <text transform="matrix(1,0,0,-1,-71.95,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> Φ</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-46.44,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-42.96,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.729494" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.769882" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,<gydF4y2Basvg height="13.6125" id="M334" style="vertical-align:-2.34499pt;width:101.7375px;" version="1.1" viewbox="0 0 101.7375 13.6125" width="101.7375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="15.966331" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="20.129829" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.669619" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="33.833118" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="40.772282" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.935783" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.411617" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="55.35078" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="62.990112" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="75.030502" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。因此,<gydF4y2Basvg height="17.0875" id="M335" style="vertical-align:-2.73372pt;width:223.3625px;" version="1.1" viewbox="0 0 223.3625 17.0875" width="223.3625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.0875)"> <g transform="translate(72,-58.33)"> <text transform="matrix(1,0,0,-1,-71.95,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一个</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> r</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> g</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.205328" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.368828" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-40,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-32.2,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-23.76,66.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-20.29,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-10.56,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-2.75,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.278186" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="16.754021" y="0"> Φ</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="26.29381" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.457308" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.396473" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.559971" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,44.38,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,52.19,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="9.114687" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.278186" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.081018" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="37.121407" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="44.723232" y="0"> /</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="48.199066" y="0"> 2</gydF4y2Batspan> </text> </g> </g> </svg>,因为<gydF4y2Basvg height="13.05" id="M336" style="vertical-align:-3.25793pt;width:35.387501px;" version="1.1" viewbox="0 0 35.387501 13.05" width="35.387501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ></gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-48.61,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>(接近<gydF4y2Basvg height="13.05" id="M337" style="vertical-align:-3.25793pt;width:11.1125px;" version="1.1" viewbox="0 0 11.1125 13.05" width="11.1125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>在某些地段)<gydF4y2Basvg height="14.625" id="M338" style="vertical-align:-3.25793pt;width:14.4125px;" version="1.1" viewbox="0 0 14.4125 14.625" width="14.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-65.4,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>。这一矛盾就完成了证明。</gydF4y2Baspan></p> <p><span class="statement" id="rem3.5"><span class="statement-title"><i class="statement-title">3.5的话。</我></span>让<gydF4y2Basvg height="13.0625" id="M339" style="vertical-align:-1.90608pt;width:39.537498px;" version="1.1" viewbox="0 0 39.537498 13.0625" width="39.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0625)"> <g transform="translate(72,-61.55)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="13.228174" y="0"> <</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="25.268562" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>,让<gydF4y2Basvg height="14.3875" id="M340" style="vertical-align:-3.25793pt;width:15.875px;" version="1.1" viewbox="0 0 15.875 14.3875" width="15.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.22,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>是一个函数<gydF4y2Basvg height="15.1625" id="M341" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>例如在<gydF4y2Basvg height="10.5375" id="M342" style="vertical-align:-0.16302pt;width:20.975px;" version="1.1" viewbox="0 0 20.975 10.5375" width="20.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,68.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>和单价的<gydF4y2Basvg height="15.6875" id="M343" style="vertical-align:-0.16302pt;width:20.975px;" version="1.1" viewbox="0 0 20.975 15.6875" width="20.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.6875)"> <g transform="translate(72,-59.45)"> <g> <path d="m -71.95,70.71 16.68,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-61.76,64.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>。如果<gydF4y2Basvg height="14.3875" id="M344" style="vertical-align:-3.25793pt;width:15.875px;" version="1.1" viewbox="0 0 15.875 14.3875" width="15.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.22,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>满足条件(<一个href="#EEq3.1">3.1</一个>)为每一个<gydF4y2Basvg height="18.35" id="M345" style="vertical-align:-2.29482pt;width:48.724998px;" version="1.1" viewbox="0 0 48.724998 18.35" width="48.724998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.35)"> <g transform="translate(72,-57.32)"> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.152436" y="0"> ∈</gydF4y2Batspan> </text> <g> <path d="m -49.75,70.71 16.68,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-49.75,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-39.56,64.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</gydF4y2Batspan> </text> </g> </g> </svg>,然后存在表面张力<gydF4y2Basvg height="9.9375" id="M346" style="vertical-align:-2.34499pt;width:8.0625px;" version="1.1" viewbox="0 0 8.0625 9.9375" width="8.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.9375)"> <g transform="translate(72,-64.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>(这取决于<gydF4y2Basvg height="14.3875" id="M347" style="vertical-align:-3.25793pt;width:15.875px;" version="1.1" viewbox="0 0 15.875 14.3875" width="15.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-64.22,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> </g> </g> </svg>)足够小,<gydF4y2Basvg height="13.6125" id="M348" style="vertical-align:-2.34499pt;width:53.849998px;" version="1.1" viewbox="0 0 53.849998 13.6125" width="53.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="3.913439" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="14.415959" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="22.055292" y="0"> ≤</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="34.09568" y="0"> </gydF4y2Batspan> </text> </g> </g> </svg>这样经典的解决方案<gydF4y2Basvg height="13.55" id="M349" style="vertical-align:-2.29482pt;width:39.962502px;" version="1.1" viewbox="0 0 39.962502 13.55" width="39.962502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.780706" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="27.694145" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>(<一个href="#EEq1.5">1.6</一个>与初始条件)<gydF4y2Basvg height="14.75" id="M350" style="vertical-align:-3.25793pt;width:107.2125px;" version="1.1" viewbox="0 0 107.2125 14.75" width="107.2125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="18.566956" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.780706" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="30.032206" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="41.835037" y="0"> =</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="58.038925" y="0"> </gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-6.17,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</gydF4y2Batspan> </text> <text transform="matrix(1,0,0,-1,-1.3,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="10.852604" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>是<gydF4y2Basvg height="15.1625" id="M351" style="vertical-align:-0.17555pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 15.1625" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1625)"> <g transform="translate(72,-59.87)"> <text transform="matrix(1,0,0,-1,-70.68,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="-1.27" y="2.6500001"> Φ</gydF4y2Batspan> </text> </g> </g> </svg>式为<gydF4y2Basvg height="13.6125" id="M352" style="vertical-align:-2.34499pt;width:72.375px;" version="1.1" viewbox="0 0 72.375 13.6125" width="72.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="7.37677" y="0"> ∈</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="19.417158" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="23.580658" y="0"> 0</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="29.832157" y="0"> ,</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="35.04591" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="38.959347" y="0"> (</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="43.122849" y="0"> </gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="49.474373" y="0"> )</gydF4y2Batspan> <tspan style="font-size: 12.50px; " x="53.637871" y="0"> )</gydF4y2Batspan> </text> </g> </g> </svg>,在那里<我>T</gydF4y2Ba我>充气时间。</gydF4y2Baspan></p> <p><span class="statement" id="proof7"><span class="statement-title"><i class="statement-title">证明。</我></span>结论是直接从古典解的光滑性(<一个href="#EEq1.5">1.6</一个>)</ggydF4y2BaydF4y2Baspan></p> <h4 id="acknowledgments">确认</h4><gydF4y2Bap>作者感谢加芙Kohr暗示这个话题和有价值的讨论在本文的准备。Denisa Fericean支持合同编号。POSDRU / 88/1.5 / S / 60185——“知识型社会”创新的博士研究。作者感谢裁判有用的建议,改善纸张的方面。</gydF4y2Bap> </div> </div> <div class="ArticleReferences_xmlContent__p_40j"> <h4 class="ArticleReferences_references__GH2t_" id="references">引用</h4><olcl作为s="ArticleReferences_orderedReferences__mJr9M"> <li class="ArticleReferences_articleReference__ouEuh" id="B5"> <div class="referenceContent"> <p class="referenceText">y . e . Hohlov d . v .普罗霍罗夫,a . j .主席Vasil“自由边界的几何性质Hele-Shaw流移动边界问题,“<我>Lobachevskii数学杂志</我>,卷1,3 - 12,1998页。</gydF4y2Bap>视图:<gydF4y2Ba!-- --> <a href="https://scholar.google.com/scholar_lookup?title=On%20geometrical%20properties%20of%20free%20boundaries%20in%20the%20Hele-Shaw%20flows%20moving%20boundary%20problem&author=Y.%20E.%20Hohlov&author=D.%20V.%20Prokhorov&author=A.%20J.%20Vasil%E2%80%99ev&publication_year=1998" target="_blank" rel="noreferrer">谷歌学术搜索</一个></div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B7"> <div class="referenceContent"> <p class="referenceText">k . Kornev和a .主席Vasil几何Hele-Shaw类型方程的解的性质,“<我>美国数学学会学报》上</我>,卷128,不。9日,第2685 - 2683页,2000年。</gydF4y2Bap>视图:<gydF4y2Ba!-- --> <a href="https://doi.org/10.1090/S0002-9939-00-05348-X" target="_blank" rel="noreferrer">出版商的网站</一个><span class="sep">|</gydF4y2Baspan> <a href="https://scholar.google.com/scholar_lookup?title=Geometric%20properties%20of%20the%20solutions%20of%20a%20Hele-Shaw%20type%20equation&author=K.%20Kornev&author=A.%20Vasil%E2%80%99ev&publication_year=2000" target="_blank" rel="noreferrer">谷歌学术搜索</一个><span class="sep">|</gydF4y2Baspan> <a href="https://www.zentralblatt-math.org/zmath/en/advanced/?q=an:0956.35110" target="_blank" rel="noreferrer">Zentralblatt数学</一个></div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B11"> <div class="referenceContent"> <p class="referenceText">d·普罗霍罗夫和a .主席Vasil凸Hele-Shaw细胞动力学”,<我>国际数学和数学科学杂志》上</我>没有,卷。31日。11日,第650 - 639页,2002年。</gydF4y2Bap>视图:<gydF4y2Ba!-- --> <a href="https://doi.org/10.1155/S0161171202203142" target="_blank" rel="noreferrer">出版商的网站</一个><span class="sep">|</gydF4y2Baspan> <a href="https://scholar.google.com/scholar_lookup?title=Convex%20dynamics%20in%20Hele-Shaw%20cells&author=D.%20Prokhorov&author=A.%20Vasil'ev&publication_year=2002" target="_blank" rel="noreferrer">谷歌学术搜索</一个><span class="sep">|</gydF4y2Baspan> <a href="https://www.zentralblatt-math.org/zmath/en/advanced/?q=an:1023.30018" target="_blank" rel="noreferrer">Zentralblatt数学</一个></div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B13"> <div class="referenceContent"> <p class="referenceText">a . Vasil主席”,在粘性流动的动力学,单价的功能”<我>理论计算方法和功能</我>,1卷,不。2、311 - 337年,2001页。</gydF4y2Bap>视图:<gydF4y2Ba!-- --> <a href="https://scholar.google.com/scholar_lookup?title=Univalent%20functions%20in%20the%20dynamics%20of%20viscous%20flows&author=A.%20Vasil%E2%80%99ev&publication_year=2001" target="_blank" rel="noreferrer">谷歌学术搜索</一个></div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B14"> <div class="referenceContent"> <p class="referenceText">a . Vasil主席,“在二维自由边界问题,单价的功能”<我>Acta Applicandae Mathematicae</gydF4y2Ba我>,卷79,不。3、249 - 280年,2003页。</gydF4y2Bap>视图:<gydF4y2Ba!-- --> <a href="https://doi.org/10.1023/B:ACAP.0000003674.35389.bb" target="_blank" rel="noreferrer">出版商的网站</一个><span class="sep">|</gydF4y2Baspan> <a href="https://scholar.google.com/scholar_lookup?title=Univalent%20functions%20in%20two-dimensional%20free%20boundary%20problems&author=A.%20Vasil%E2%80%99ev&publication_year=2003" target="_blank" rel="noreferrer">谷歌学术搜索</一个></div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B15"> <div class="referenceContent"> <p class="referenceText">a . Vasil主席和i Markina Hele-Shaw流动的几何形状和表面张力小,”<我>接口和自由边界</我>,5卷,不。2、183 - 192年,2003页。</gydF4y2Bap>视图:<gydF4y2Ba!-- --> <a href="https://doi.org/10.4171/IFB/77" target="_blank" rel="noreferrer">出版商的网站</一个><span class="sep">|</gydF4y2Baspan> <a href="https://scholar.google.com/scholar_lookup?title=On%20the%20geometry%20of%20Hele-Shaw%20flows%20with%20small%20surface%20tension&author=A.%20Vasil%E2%80%99ev&author=I.%20Markina&publication_year=2003" target="_blank" rel="noreferrer">谷歌学术搜索</一个></div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B2"> <div class="referenceContent"> <p class="referenceText">洛杉矶Galin,“不稳定与自由表面过滤,”<我>研究Doklady Akademii苏联</我>47卷,第249 - 246页,1945年。</gydF4y2Bap>视图:<gydF4y2Ba!-- --> <a href="https://scholar.google.com/scholar_lookup?title=Unsteady%20filtration%20with%20a%20free%20surface&author=L.%20A.%20Galin&publication_year=1945" target="_blank" rel="noreferrer">谷歌学术搜索</一个><span class="sep">|</gydF4y2Baspan> <a href="https://www.zentralblatt-math.org/zmath/en/advanced/?q=an:0061.46202" target="_blank" rel="noreferrer">Zentralblatt数学</一个></div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B8"> <div class="referenceContent"> <p class="referenceText">p . y . Polubarinova-Kochina”问题的运动轮廓的石油壳,”<我>研究Doklady Akademii苏联</我>47卷,第257 - 254页,1945年(俄罗斯)。</gydF4y2Bap>视图:<gydF4y2Ba!-- --> <a href="https://scholar.google.com/scholar_lookup?title=On%20a%20problem%20of%20the%20motion%20of%20the%20contour%20of%20a%20petroleum%20shell&author=P.%20Y.%20Polubarinova-Kochina&publication_year=1945" target="_blank" rel="noreferrer">谷歌学术搜索</一个></div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B9"> <div class="referenceContent"> <p class="referenceText">p . j . Poloubarinova-Kochina“过滤理论关于不稳定运动”,9卷,没有。1,第90 - 79页,1945年(俄罗斯)。</gydF4y2Bap>视图:<gydF4y2Ba!-- --> <a href="https://scholar.google.com/scholar_lookup?title=Concerning%20unsteady%20motions%20in%20the%20theory%20of%20filtration&author=P.%20J.%20Poloubarinova-Kochina&publication_year=1945" target="_blank" rel="noreferrer">谷歌学术搜索</一个></div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B16"> <div class="referenceContent"> <p class="referenceText">y . p . Vinogradov和p . p . Kufarev过滤的问题。”<我>研究Akademii苏联</我>》12卷,第198 - 181页,1948年(俄罗斯)。</gydF4y2Bap>视图:<gydF4y2Ba!-- --> <a href="https://scholar.google.com/scholar_lookup?title=On%20a%20problem%20of%20filtration&author=Y.%20P.%20Vinogradov&author=P.%20P.%20Kufarev&publication_year=1948" target="_blank" rel="noreferrer">谷歌学术搜索</一个></div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B4"> <div class="referenceContent"> <p class="referenceText">b . Gustafsson和a .主席Vasil<我>正形和潜力分析Hele-Shaw细胞</我>数学流体力学的发展,Birkhauser, 2006年在瑞士巴塞尔。</gydF4y2Bap> </div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B1"> <div class="referenceContent"> <p class="referenceText">l . Brickman。”<米一个th id="M353" xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mover accent="true"> <mi mathvariant="normal"> Φ</米我><米o>˜</gydF4y2Ba米o></米over> </mrow> </math>——解析函数”,<我>《美国数学学会</我>卷,79年,第558 - 555页,1973年。</gydF4y2Bap>视图:<gydF4y2Ba!-- --> <a href="https://doi.org/10.1090/S0002-9904-1973-13200-8" target="_blank" rel="noreferrer">出版商的网站</一个><span class="sep">|</gydF4y2Baspan> <a href="https://scholar.google.com/scholar_lookup?title=%CE%A6%CB%9C-like%20analytic%20functions%E2%80%94I&author=L.%20Brickman&publication_year=1973" target="_blank" rel="noreferrer">谷歌学术搜索</一个><span class="sep">|</gydF4y2Baspan> <a href="https://www.zentralblatt-math.org/zmath/en/advanced/?q=an:0273.30010" target="_blank" rel="noreferrer">Zentralblatt数学</一个></div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B3"> <div class="referenceContent"> <p class="referenceText">格雷厄姆和g . Kohr,<我>几何函数理论和更高的维度</我>卷,255<我>专著和教科书纯粹与应用数学</我>,马塞尔·德克,纽约,纽约,美国,2003年。</gydF4y2Bap> </div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B10"> <div class="referenceContent"> <p class="referenceText">c . Pommerenke<我>单价的功能</我>德国哥廷根,Vandenhoeck &鲁普雷希特,1975年。</gydF4y2Bap> </div></li> </ol> </div> <h4 class="copyright-title" id="copyright">版权</h4><gydF4y2Badiv class="copyright-body"> 版权©2011 Paula Curt Denisa Fericean。这是一个开放的分布式下文章<一个rel="license" href="http://creativecommons.org/licenses/by/3.0/">知识共享归属许可</一个>,它允许无限制的使用、分配和复制在任何媒介,提供最初的工作是正确引用。</gydF4y2Badiv> <div id="related-articles"></div> </div> </div> <div class="ant-col ThreeColumnLayout_rightColumn__b_MuL"> <div> <div> <div class="ArticleRightSection_articleRightSection__rG8Zh"> <div class="ArticleToolbar_articleToolbar__8fsAH"> <a href="https://downloads.hindawi.com/journals/aaa/2011/948236.pdf" class="ButtonGroup_buttonGroupWrapper__Rqhy0" role="button" type="primary" aria-label="PDF" tabindex="0" unselectable="on" target="_blank" data-testid="download-pdf"><span class="ButtonGroup_leftGroup__FJAmS"><span role="img" class="anticon ButtonGroup_buttonGroupWrapperIcon__CFikg"> <svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="0 0 19 24"> <path d="M16.772,24H2.227A2.163,2.163,0,0,1,0,21.746V2.255A2.159,2.159,0,0,1,2.227,0H12.415L12.9.494h.03V.523L19,6.669V21.746A2.161,2.161,0,0,1,16.772,24ZM2.334,1A1.276,1.276,0,0,0,1,2.358V21.642A1.283,1.283,0,0,0,2.334,23H16.665A1.276,1.276,0,0,0,18,21.642V7.087l-.032-.033H14.215A2.131,2.131,0,0,1,12.02,4.832V1.005L12.015,1ZM13,2V4.745A1.192,1.192,0,0,0,14.261,6H17ZM4.012,20A1.032,1.032,0,0,1,3,18.923a2.505,2.505,0,0,1,.967-1.539,8.15,8.15,0,0,1,2.377-1.418c.344-.779.65-1.6.92-2.327l.008-.022.017-.046.009-.024c.2-.539.453-1.209.71-1.827a4.545,4.545,0,0,1-.372-3.862c.267-.569.6-.858.976-.858.556,0,.964.621,1.015,1.546a7.125,7.125,0,0,1-.681,3.143c.158.305.343.624.55.949a7.127,7.127,0,0,0,1.806,1.9,8.681,8.681,0,0,1,2.023-.279,4.23,4.23,0,0,1,1.468.238c.118.047,1.156.478,1.2,1.143a.688.688,0,0,1-.412.67,2.509,2.509,0,0,1-1.164.242,4.757,4.757,0,0,1-.671-.052,6.631,6.631,0,0,1-2.608-1.025c-.163.042-.323.086-.514.138l-.1.026-.15.041c-.235.067-.464.13-.679.185l-.292.076-.025.006-.019,0c-.794.205-1.615.418-2.4.705A14.033,14.033,0,0,1,6,18.437C5.832,18.7,4.941,20,4.012,20ZM6,17a6.865,6.865,0,0,0-1.287.871A1.927,1.927,0,0,0,4,18.831a.12.12,0,0,0,.041.1A.165.165,0,0,0,4.17,19c.327,0,.965-.631,1.356-1.219C5.671,17.564,5.83,17.3,6,17Zm7.044-2A4.632,4.632,0,0,0,12,15.131a4.76,4.76,0,0,0,1.675.792A2.906,2.906,0,0,0,14.32,16a1.629,1.629,0,0,0,.68-.13,2.672,2.672,0,0,0-.584-.528A2.752,2.752,0,0,0,13.045,15ZM8.166,13c-.177.449-.343.884-.481,1.25l-.01.025-.009.024-.007.02-.035.092-.032.085c-.156.409-.37.97-.59,1.5.6-.181,1.229-.341,1.733-.469l.031-.008.055-.014.028-.007.028-.007.307-.078c.191-.048.4-.105.674-.179l.03-.008.005,0,.036-.01.036-.01.01,0,.01,0,.016,0a8.291,8.291,0,0,1-1.566-1.767C8.341,13.285,8.264,13.16,8.166,13Zm.516-5a1.64,1.64,0,0,0-.34.365A2.425,2.425,0,0,0,8.437,11a4.012,4.012,0,0,0,.553-2.22A1.309,1.309,0,0,0,8.681,8Z" fill="currentColor"></path> </svg></span><span>PDF</gydF4y2Baspan></span><span role="img" class="anticon ButtonGroup_buttonGroupWrapperIcon__CFikg"> <svg width="1em" height="1em" viewbox="0 0 20 22"> <defs> <clippath> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </clippath> </defs> <g> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </g> </svg></span></a> <a href="//www.newsama.com/journals/aaa/2011/948236.ris" class="ButtonGroup_buttonGroupWrapper__Rqhy0" role="button" type="ghost" aria-label="Download Citation" tabindex="0" unselectable="on" data-testid="download-citation"><span class="ButtonGroup_leftGroup__FJAmS"><span role="img" class="anticon ButtonGroup_buttonGroupWrapperIcon__CFikg"> <svg width="1em" height="1em" viewbox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"> <path d="M16 12H8C7.44772 12 7 12.4477 7 13C7 13.5523 7.44772 14 8 14H16C16.5523 14 17 13.5523 17 13C17 12.4477 16.5523 12 16 12Z" fill="currentColor"></path> <path d="M16 16H8C7.44772 16 7 16.4477 7 17C7 17.5523 7.44772 18 8 18H16C16.5523 18 17 17.5523 17 17C17 16.4477 16.5523 16 16 16Z" fill="currentColor"></path> <path d="M10 8H8C7.44772 8 7 8.44772 7 9C7 9.55228 7.44772 10 8 10H10C10.5523 10 11 9.55228 11 9C11 8.44772 10.5523 8 10 8Z" fill="currentColor"></path> <path d="M15 2C15 1.44772 14.5523 1 14 1C13.4477 1 13 1.44772 13 2V8C13 8.55228 13.4477 9 14 9H20C20.5523 9 21 8.55228 21 8C21 7.44772 20.5523 7 20 7H15V2Z" fill="currentColor"></path> <path fill-rule="evenodd" clip-rule="evenodd" d="M14.7071 1.29289C14.5196 1.10536 14.2652 1 14 1H6C4.34315 1 3 2.34315 3 4V20C3 21.6569 4.34315 23 6 23H18C19.6569 23 21 21.6569 21 20V8C21 7.73478 20.8946 7.48043 20.7071 7.29289L14.7071 1.29289ZM6 3H13.5858L19 8.41421V20C19 20.5523 18.5523 21 18 21H6C5.44772 21 5 20.5523 5 20V4C5 3.44772 5.44772 3 6 3Z" fill="currentColor"></path> </svg></span><span>下载引用</gydF4y2Baspan></span><span role="img" class="anticon ButtonGroup_buttonGroupWrapperIcon__CFikg"> <svg width="1em" height="1em" viewbox="0 0 20 22"> <defs> <clippath> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </clippath> </defs> <g> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </g> </svg></span></a> <div class="ant-collapse ant-collapse-icon-position-end articleToolbarOtherFormats_otherFormatsCollapse__VHaOL"> <div class="ant-collapse-item"> <div class="ant-collapse-header" aria-expanded="false" aria-disabled="false" role="button" tabindex="0"> <div class="ant-collapse-expand-icon"> <span role="img" class="anticon ant-collapse-arrow"> <svg width="1em" height="1em" viewbox="0 0 32 32" fill="none"> <path fill-rule="evenodd" clip-rule="evenodd" d="M17.773 23.453l11.2-11.265a1.918 1.918 0 000-2.641 1.75 1.75 0 00-2.542 0l-9.929 10.101-9.933-10.1a1.75 1.75 0 00-2.542 0 1.919 1.919 0 000 2.64L15.23 23.453c.352.365.811.547 1.271.547.46 0 .92-.182 1.271-.547z" fill="currentColor"></path> </svg></span> </div> <span class="ant-collapse-header-text"><span><span role="img" class="anticon articleToolbarOtherFormats_atofDownloadIcon__YRM5T"> <svg width="1em" height="1em" viewbox="0 0 20 22"> <defs> <clippath> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </clippath> </defs> <g> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </g> </svg></span><span>下载其他格式</gydF4y2Baspan></span></span> </div> </div> </div> <a href="//www.newsama.com/reprints/948236/confirm" class="ButtonGroup_buttonGroupWrapper__Rqhy0" role="button" type="ghost" aria-label="Order printed copies" tabindex="0" unselectable="on" target="_blank"><span class="ButtonGroup_leftGroup__FJAmS"><span role="img" class="anticon ButtonGroup_buttonGroupWrapperIcon__CFikg"> <svg width="1em" height="1em" viewbox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"> <path fill-rule="evenodd" clip-rule="evenodd" d="M7.41667 1H18.6667C19.1269 1 19.5 1.44772 19.5 2V22C19.5 22.5523 19.1269 23 18.6667 23H7.41667C5.80584 23 4.5 21.433 4.5 19.5V4.5C4.5 2.567 5.80584 1 7.41667 1ZM6.16667 16.3368V4.5C6.16667 3.67157 6.72631 3 7.41667 3H17.8333V16H7.41667C6.96933 16 6.54552 16.1208 6.16667 16.3368ZM17.8333 18H7.41667C6.72631 18 6.16667 18.6716 6.16667 19.5C6.16667 20.3284 6.72631 21 7.41667 21H17.8333V18Z" fill="currentColor"></path> </svg></span><span>订单打印副本</gydF4y2Baspan></span><span role="img" class="anticon ButtonGroup_buttonGroupWrapperIcon__CFikg"> <svg width="1em" height="1em" viewbox="0 0 18 14"> <defs> <clippath id="a"> <path d="M10.293,13.707a1,1,0,0,1,0-1.414L14.586,8H1A1,1,0,0,1,1,6H14.586L10.293,1.707A1,1,0,0,1,11.707.293l6,6a1,1,0,0,1,.172.231h0l.01.019,0,.005.007.014.006.012,0,.008.008.018v0a1,1,0,0,1-.009.817l0,0L17.9,7.44l0,.009-.005.011-.007.013,0,.008-.008.015,0,.005-.01.016,0,0-.011.017,0,0-.012.018,0,0-.012.017,0,0L17.8,7.6l0,0-.011.014,0,.006-.01.012-.009.011-.006.007-.015.017h0l-.04.042-6,6a1,1,0,0,1-1.414,0Z" transform="translate(3 5)"></path> </clippath> </defs> <g transform="translate(-3 -5)"> <path d="M10.293,13.707a1,1,0,0,1,0-1.414L14.586,8H1A1,1,0,0,1,1,6H14.586L10.293,1.707A1,1,0,0,1,11.707.293l6,6a1,1,0,0,1,.172.231h0l.01.019,0,.005.007.014.006.012,0,.008.008.018v0a1,1,0,0,1-.009.817l0,0L17.9,7.44l0,.009-.005.011-.007.013,0,.008-.008.015,0,.005-.01.016,0,0-.011.017,0,0-.012.018,0,0-.012.017,0,0L17.8,7.6l0,0-.011.014,0,.006-.01.012-.009.011-.006.007-.015.017h0l-.04.042-6,6a1,1,0,0,1-1.414,0Z" transform="translate(3 5)" fill="currentColor"></path> </g> </svg></span></a> <div class="articleToolbarStatistics_articleToolbarStatistics__8_woN"> <div class="articleToolbarStatistics_column__R2GqD"> <div> <div> <span>的观点</gydF4y2Baspan> <div class="articleToolbarStatistics_amount__vJIDp"> 1002年</gydF4y2Badiv> </div> <div> <span>下载</gydF4y2Baspan> <div class="articleToolbarStatistics_amount__vJIDp"> 1044年</gydF4y2Badiv> </div> </div> </div> <div class="articleToolbarStatistics_column__R2GqD articleToolbarStatistics_dimensions__pe7pO"> <div> 引用</gydF4y2Badiv> <span class="__dimensions_badge_embed__ articleToolbarStatistics_circle__p2dSc" data-doi="10.1155/2011/948236" data-style="small_circle"></span> </div> </div> <ul class="articleToolbarSocials_articleToolbarSocials__g02HH"> <li><a href="https://twitter.com/share?url=https://doi.org/10.1155/2011/948236&via=Hindawi" unselectable="on" title="" rel="noopener noreferrer" target="_blank"><span role="img" class="anticon"> <svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="126.444 2.281 589 589"> <circle cx="420.944" cy="296.781" r="294.5" fill="#2daae1"></circle> <path d="M609.773 179.634c-13.891 6.164-28.811 10.331-44.498 12.204 16.01-9.587 28.275-24.779 34.066-42.86a154.78 154.78 0 0 1-49.209 18.801c-14.125-15.056-34.267-24.456-56.551-24.456-42.773 0-77.462 34.675-77.462 77.473 0 6.064.683 11.98 1.996 17.66-64.389-3.236-121.474-34.079-159.684-80.945-6.672 11.446-10.491 24.754-10.491 38.953 0 26.875 13.679 50.587 34.464 64.477a77.122 77.122 0 0 1-35.097-9.686v.979c0 37.54 26.701 68.842 62.145 75.961-6.511 1.784-13.344 2.716-20.413 2.716-4.998 0-9.847-.473-14.584-1.364 9.859 30.769 38.471 53.166 72.363 53.799-26.515 20.785-59.925 33.175-96.212 33.175-6.25 0-12.427-.373-18.491-1.104 34.291 21.988 75.006 34.824 118.759 34.824 142.496 0 220.428-118.052 220.428-220.428 0-3.361-.074-6.697-.236-10.021a157.855 157.855 0 0 0 38.707-40.158z" fill="#fff"></path> </svg></span></a></li> <li><a href="https://www.linkedin.com/shareArticle/?url=https://doi.org/10.1155/2011/948236" unselectable="on" title="" rel="noopener noreferrer" target="_blank"><span role="img" class="anticon"> <svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="0 0 256 256" xml:space="preserve"> <g transform="translate(-373.642 -318.344)"> <path fill="#1D8CB5" d="M583.659 328.849H419.625c-19.599 0-35.487 15.888-35.487 35.487v164.015c0 19.599 15.888 35.486 35.487 35.486h164.033c19.599 0 35.487-15.888 35.487-35.486V364.337c.001-19.599-15.888-35.488-35.486-35.488z"></path> <lineargradient id="a" gradientunits="userSpaceOnUse" x1="-808.873" y1="199.892" x2="-860.569" y2="49.203" gradienttransform="rotate(180 -17.27 206.273) scale(.5915)"> <stop offset="0" style="stop-color:#fff"></stop> <stop offset="1" style="stop-color:#fff;stop-opacity:0"></stop> </lineargradient> <path opacity=".781" fill="url(#a)" d="M557.056 338.895H446.227c-29.337 0-52.955 23.81-52.955 53.385v108.127c.95 23.087 4.603 8.491 11.555-17.075 8.081-29.713 34.396-55.682 66.445-75.145 24.461-14.855 51.84-24.341 101.679-25.244 28.265-.511 25.77-36.683-15.895-44.048z"></path> </g> <g fill="#FFF"> <path d="M81.604 207.76V101.49h-35.32v106.27h35.32zM63.951 86.98c12.308 0 19.981-8.161 19.981-18.36-.228-10.426-7.673-18.36-19.75-18.36-12.087 0-19.984 7.934-19.984 18.36 0 10.199 7.662 18.36 19.52 18.36h.233zM101.151 207.76h35.326v-59.345c0-3.178.23-6.352 1.165-8.621 2.547-6.35 8.363-12.92 18.118-12.92 12.784 0 17.893 9.748 17.893 24.032v56.855h35.319v-60.936c0-32.643-17.422-47.83-40.665-47.83-19.053 0-27.421 10.647-32.068 17.902h.238V101.49h-35.326c.469 9.97 0 106.27 0 106.27z"></path> </g> </svg></span></a></li> <li><a href="https://www.facebook.com/sharer/sharer.php?u=https://doi.org/10.1155/2011/948236" unselectable="on" title="" rel="noopener noreferrer" target="_blank"><span role="img" class="anticon"> <svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="0 0 14222 14222"> <circle cx="7111" cy="7112" r="7111" fill="#1977f3"></circle> <path d="M9879 9168l315-2056H8222V5778c0-562 275-1111 1159-1111h897V2917s-814-139-1592-139c-1624 0-2686 984-2686 2767v1567H4194v2056h1806v4969c362 57 733 86 1111 86s749-30 1111-86V9168z" fill="#fff"></path> </svg></span></a></li> <li><a href="//www.newsama.com/cdn-cgi/l/email-protection" unselectable="on" title="" rel="noopener noreferrer" target="_blank"><span role="img" class="anticon"> <svg version="1.0" xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="0 0 1401 1101"> <path fill="#6ba439" d="M132.5 2.1C101.4 6 71.1 20.5 48.3 42.4c-22.7 21.7-37.5 48.3-44.6 80l-2.2 10.1v837l2.2 10.1c6.7 30 19.3 53.9 39.8 75.3 23.3 24.3 56.4 40.9 90 45 12.8 1.6 1122.2 1.6 1135 0 38.9-4.8 75.9-25.6 100-56.4 15-19.3 24.2-39 29.8-63.9l2.2-10.1v-837l-2.2-10.1c-7.1-31.8-21.9-58.3-44.6-80.1-20.2-19.2-43.9-31.7-73.6-38.5l-9.6-2.3L705 1.4c-321.9-.1-568.5.2-572.5.7zm1123.4 99.5c1.7.4 3.1 1 3.1 1.4 0 .5-125.6 87.7-279 194L700.9 490.2 422 297C268.5 190.7 143 103.4 143 103c0-.5 1-1.1 2.3-1.3 3.5-.7 1107.1-.8 1110.6-.1zM401 404c164.4 113.8 299.4 207 300 207 .6 0 135.6-93.2 300.1-207 164.5-113.9 299.3-207 299.5-207 .2 0 .4 170.9.4 379.7 0 417.9.5 386-6.1 398.3-6.2 11.6-19 21.4-31.9 24.4-5.8 1.4-67.4 1.6-562 1.6s-556.2-.2-562-1.6c-12.9-3-25.7-12.8-31.9-24.4-6.6-12.3-6.1 19.6-6.1-398.3 0-208.8.2-379.7.5-379.7S236.6 290.1 401 404z"></path> </svg></span></a></li> </ul> </div> </div> </div> </div> </div> </div> </main> <div> <footer class="ant-layout-footer"> <div class="footer-main-nav-section"> <div class="footer-main-nav"> <div class="ant-col footer-main-nav__column"> <ul class="ant-menu ant-menu-root ant-menu-vertical ant-menu-light footer-main-nav__menu" role="menu" tabindex="0" data-menu-list="true"> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/about/" aria-label="About Us">关于我们</一个></span></li> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/about/contact/" aria-label="Contact us">联系我们</一个></span></li> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/publishing-partnerships/" aria-label="Partnerships">合作伙伴关系</一个></span></li> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/blog/" aria-label="Blog">博客</一个></span></li> </ul> <div style="display:none" aria-hidden="true"></div> </div> <div class="ant-col footer-main-nav__column"> <ul class="ant-menu ant-menu-root ant-menu-vertical ant-menu-light footer-main-nav__menu" role="menu" tabindex="0" data-menu-list="true"> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/journals/" aria-label="Journals">期刊</一个></span></li> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/publish-research/authors/article-processing-charges/" aria-label="Article Processing Charges">文章处理费用</一个></span></li> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/print-editions/" aria-label="Print editions">印刷版</一个></span></li> </ul> <div style="display:none" aria-hidden="true"></div> </div> <div class="ant-col footer-main-nav__column"> <ul class="ant-menu ant-menu-root ant-menu-vertical ant-menu-light footer-main-nav__menu" role="menu" tabindex="0" data-menu-list="true"> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/publish-research/authors/" aria-label="Authors">作者</一个></span></li> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/publish-research/editors/" aria-label="Editors">编辑器</一个></span></li> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/publish-research/reviewers/" aria-label="Reviewers">评论家</一个></span></li> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/publishing-partnerships/" aria-label="Partnerships">合作伙伴关系</一个></span></li> </ul> <div style="display:none" aria-hidden="true"></div> </div> <div class="ant-col footer-main-nav__column"> <ul class="ant-menu ant-menu-root ant-menu-vertical ant-menu-light footer-main-nav__menu" role="menu" tabindex="0" data-menu-list="true"> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/hindawi-xml-corpus/" aria-label="Hindawi XML Corpus">雷电竞APP</a></span></li> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/open-archives-initiative/" aria-label="Open Archives Initiative">开放档案计划</一个></span></li> <li class="ant-menu-item ant-menu-item-only-child footer-main-nav__item" role="menuitem" tabindex="-1"><span class="ant-menu-title-content"><a href="//www.newsama.com/preventing-and-protecting-against-fraud/" aria-label="Fraud prevention">欺诈防范</一个></span></li> </ul> <div style="display:none" aria-hidden="true"></div> </div> </div> <div class="social-links"> 遵循我们:<gydF4y2Badiv class="social-links__icons"> <a aria-label="Twitter" rel="noopener noreferrer" href="https://twitter.com/hindawi" target="_blank" class="social-links__icon"><span role="img" class="anticon"> <svg xmlns="http://www.w3.org/2000/svg" width="40" height="40" viewbox="0 0 40 40" fill="none"> <path fill-rule="evenodd" clip-rule="evenodd" d="M0 20C0 8.95599 8.95599 0 20 0C31.044 0 40 8.95599 40 20C40 31.044 31.044 40 20 40C8.95599 40 0 31.044 0 20ZM29.1449 16.1871C29.1449 15.9885 29.1406 15.7907 29.1318 15.5939C30.0281 14.946 30.8072 14.1373 31.4215 13.2166C30.5991 13.5822 29.7141 13.8284 28.7854 13.9395C29.7333 13.371 30.4608 12.4719 30.8041 11.4005C29.917 11.9263 28.9349 12.3083 27.8891 12.5146C27.0514 11.6223 25.8588 11.0641 24.5383 11.0641C22.0032 11.0641 19.9472 13.1201 19.9472 15.6543C19.9472 16.0144 19.9878 16.3647 20.0665 16.701C16.2512 16.5091 12.868 14.6823 10.6042 11.9046C10.21 12.583 9.9826 13.371 9.9826 14.212C9.9826 15.8047 10.7928 17.2107 12.0255 18.0331C11.2723 18.0099 10.5649 17.803 9.94629 17.4591C9.94568 17.4783 9.94568 17.4969 9.94568 17.5177C9.94568 19.7406 11.528 21.597 13.6285 22.0175C13.2428 22.1228 12.8369 22.1793 12.4179 22.1793C12.1228 22.1793 11.835 22.15 11.5552 22.0963C12.1399 23.9203 13.8342 25.2475 15.8438 25.2847C14.2725 26.5161 12.2931 27.2498 10.1422 27.2498C9.77203 27.2498 9.40643 27.2287 9.04724 27.1863C11.0788 28.4885 13.4912 29.2484 16.0837 29.2484C24.5276 29.248 29.1449 22.2531 29.1449 16.1871Z" fill="#F2F2F2"></path> </svg></span></a> <a aria-label="Linkedin" rel="noopener noreferrer" href="https://www.linkedin.com/company/hindawilimited/" target="_blank" class="social-links__icon"><span role="img" class="anticon"> <svg width="40" height="40" viewbox="0 0 40 40" fill="none" xmlns="http://www.w3.org/2000/svg"> <path fill-rule="evenodd" clip-rule="evenodd" d="M0 20C0 8.95599 8.95599 0 20 0C31.044 0 40 8.95599 40 20C40 31.044 31.044 40 20 40C8.95599 40 0 31.044 0 20ZM9.31732 30.2344H14.1882V15.5801H9.31732V30.2344ZM11.7529 13.5791H11.7212C10.0867 13.5791 9.02954 12.4539 9.02954 11.0477C9.02954 9.60968 10.119 8.51562 11.7853 8.51562C13.4515 8.51562 14.4769 9.60968 14.5087 11.0477C14.5087 12.4539 13.4515 13.5791 11.7529 13.5791ZM26.8814 30.2344H31.7517V21.8317C31.7517 17.3306 29.3488 15.2362 26.1441 15.2362C23.5599 15.2362 22.4017 16.6565 21.7545 17.655V15.5801H16.8839C16.9476 16.955 16.8839 30.2344 16.8839 30.2344H21.7545V22.0508C21.7545 21.6129 21.7859 21.1752 21.9147 20.8621C22.2668 19.9872 23.0682 19.0808 24.4138 19.0808C26.1761 19.0808 26.8814 20.4245 26.8814 22.3947V30.2344Z" fill="#F2F2F2"></path> </svg></span></a> <a aria-label="Youtube" rel="noopener noreferrer" href="https://www.youtube.com/channel/UCDIK_O7FATPEkhad_sQVaSg" target="_blank" class="social-links__icon"><span role="img" class="anticon"> <svg width="40" height="40" viewbox="0 0 40 40" fill="none" xmlns="http://www.w3.org/2000/svg"> <path d="M17.2973 23.7838L23.7838 20L17.2973 16.2162V23.7838Z" fill="#F2F2F2"></path> <path fill-rule="evenodd" clip-rule="evenodd" d="M0 20C0 8.95599 8.95599 0 20 0C31.044 0 40 8.95599 40 20C40 31.044 31.044 40 20 40C8.95599 40 0 31.044 0 20ZM31.9824 26.0324C32.4969 24.0765 32.4969 20.0204 32.4969 20.0204C32.4969 20.0204 32.5177 15.9442 31.9824 13.9883C31.694 12.9178 30.8499 12.0734 29.7794 11.7853C27.8235 11.25 20 11.25 20 11.25C20 11.25 12.1765 11.25 10.2206 11.7648C9.17053 12.0529 8.30566 12.9178 8.01758 13.9883C7.50275 15.9442 7.50275 20 7.50275 20C7.50275 20 7.50275 24.0765 8.01758 26.0117C8.30597 27.0822 9.15009 27.9266 10.2206 28.2147C12.197 28.75 20 28.75 20 28.75C20 28.75 27.8235 28.75 29.7794 28.2352C30.8499 27.9471 31.694 27.103 31.9824 26.0324Z" fill="#F2F2F2"></path> </svg></span></a> <a aria-label="Facebook" rel="noopener noreferrer" href="https://www.facebook.com/HindawiLimited/" target="_blank" class="social-links__icon"><span role="img" class="anticon"> <svg width="40" height="39" viewbox="0 0 40 39" fill="none" xmlns="http://www.w3.org/2000/svg"> <path d="M40 19.4595C40 8.71394 31.044 0 20 0C8.95599 0 0 8.71394 0 19.4595C0 30.205 8.95599 38.9189 20 38.9189C20.1175 38.9189 20.2344 38.9165 20.3516 38.9145V23.7661H16.0547V18.8938H20.3516V15.3084C20.3516 11.1502 22.9605 8.88705 26.7728 8.88705C28.5983 8.88705 30.1675 9.01948 30.625 9.07857V13.4244H27.9962C25.9222 13.4244 25.5206 14.3835 25.5206 15.7906V18.8938H30.4797L29.8334 23.7661H25.5206V38.1671C33.8803 35.8353 40 28.3418 40 19.4595Z" fill="#F2F2F2"></path> </svg></span></a> </div> </div> </div> <div class="footer-minor-nav"> <span><a href="//www.newsama.com/privacy/" class="footer-minor-nav__link" aria-label="Privacy Policy">隐私政策</一个><div class="ant-divider ant-divider-vertical" role="separator"></div></span> <span><a href="//www.newsama.com/terms/" class="footer-minor-nav__link" aria-label="Terms of Service">服务条款</一个><div class="ant-divider ant-divider-vertical" role="separator"></div></span> <span><a href="//www.newsama.com/responsible-disclosure-policy/" class="footer-minor-nav__link" aria-label="Responsible Disclosure Policy">负责信息披露政策</一个><div class="ant-divider ant-divider-vertical" role="separator"></div></span> <span><a href="//www.newsama.com/cookie-policy/" class="footer-minor-nav__link" aria-label="Cookie Policy">饼干的政策</一个><div class="ant-divider ant-divider-vertical" role="separator"></div></span> <span><a href="//www.newsama.com/copyright/" class="footer-minor-nav__link" aria-label="Copyright">版权</一个><div class="ant-divider ant-divider-vertical" role="separator"></div></span> <span><a href="//www.newsama.com/modern-slavery-statement/" class="footer-minor-nav__link" aria-label="Modern slavery statement">现代奴隶制的声明</一个><div class="ant-divider ant-divider-vertical" role="separator"></div></span> <span><a class="footer-minor-nav__link" aria-label="Cookie Preferences">饼干的偏好</一个></span> </div> </footer> </div> </section> <noscript> <iframe src="https://www.newsama.com/ns.html?id=GTM-MQ4MGW" height="0" width="0" style="display:none;visibility:hidden"></iframe> </noscript> </div> </body> </html>