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no-repeat 6px;background-position:center;margin-top:10px;min-width:55px;display:none;} @media (min-width:768px){.pzSfk .floats-partial-section .floats-partial-footer .floats-partial-caption .expand_btn{display:none;}} .pzSfk .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{-webkit-flex:9;-ms-flex:9;flex:9;text-align:left;padding:21px 37px 10px 0px;font-size:16px;font-weight:700;} @media (min-width:768px){.pzSfk .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 18px 10px 18px;}} @media (min-width:992px){.pzSfk .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 21px 10px 21px;}} .pzSfk .floats-partial-section .floats-partial-footer .floats-partial-caption 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no-repeat 6px;background-position:center;padding:16px 0 16px 0;min-width:62px;max-width:62px;} @media (min-width:768px){.pzSfk .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{padding:16px 0 17px 0;min-width:52px;max-width:52px;}} @media (min-width:992px){.pzSfk .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{padding:15px 0 17px 0;min-width:60px;max-width:60px;}} .pzSfk .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url:hover{-webkit-text-decoration:none;text-decoration:none;} .pzSfk .floats-partial-section .floats-partial-footer .floats-partial-caption-text{font-size:14px;padding:0px 18px 17px 22px;} @media (min-width:768px){.pzSfk .floats-partial-section .floats-partial-footer .floats-partial-caption-text{padding:0px 15px 15px 18px;}} @media (min-width:992px){.pzSfk .floats-partial-section .floats-partial-footer .floats-partial-caption-text{padding:0px 18px 19px 21px;}} .pzSfk .floats-partial-section .floats-partial-footer .floats-partial-caption-text figcaption{margin:0;padding:0;} .pzSfk .floats-partial-section .floats-partial-footer .floats-partial-caption-text svg{max-width:100%;} .pzSfk ol{font-size:16px;padding-left:32px;font-family:STIXGeneral-Regular;line-height:24px;margin:15px 0;} .pzSfk ol li{margin:10px 0;padding-left:10px;word-break:normal;} .pzSfk ol li a{word-break:break-all;} .pzSfk ol li .reflinks{display:block;} .pzSfk ol li .reflinks a{color:#4D8A17;-webkit-text-decoration:none;text-decoration:none;cursor:pointer;} .pzSfk ol li .reflinks a:hover{-webkit-text-decoration:underline;text-decoration:underline;} .pzSfk ol li .reflinks .sep{color:#000000;} .pzSfk .table-wrapper{width:auto;overflow-x:auto;} .pzSfk .table-wrapper::-webkit-scrollbar{-webkit-appearance:none;width:5px;height:5px;} .pzSfk .table-wrapper::-webkit-scrollbar-thumb{border-radius:5px;background-color:rgba(0,0,0,.5);-webkit-box-shadow:0 0 1px rgba(255,255,255,.5);} @media (min-width:768px){.pzSfk .table-wrapper{overflow-x:auto;width:auto;-webkit-break-word:word-break;break-word:word-break;margin:0 auto;}} @media (min-width:992px){.pzSfk .table-wrapper{width:auto;}} @media (min-width:1324px){.pzSfk .table-wrapper{width:auto;}} @media (min-width:320px){.pzSfk{margin-bottom:33px;padding:0;}} @media (min-width:992px){.pzSfk{padding:0;margin-bottom:100px;}} @media (min-width:1325px){.pzSfk{margin-bottom:100px;}} .pzSfk .owl-stage{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;} .pzSfk .floats-partial-middle--thumbs{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;} .pzSfk .floats-partial-middle--thumbs .partial-carousel-dot svg{fill:#4D8A17;} .pzSfk .floats-partial-middle--thumbs .partial-carousel-dot strong{color:#4D8A17;font-weight:500;} .pzSfk .floats-partial-middle--thumbs .partial-carousel-dot.active strong{color:#007B8B;} .pzSfk .floats-partial-middle--thumbs 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height="24"><span class="text">提交</年代pan></span><span class="sc-htoDjs kNoiZu sc-dqBHgY cQgXqt fileArrow icon-colored undefined icon-themeable" title="" font-size="16"></span></a> <div class="sc-krDsej ewCAZX hide__submenu journalSubmenuCheck" id="journalnav__submenu"> <button class="sc-itybZL kdvWPs journalSubmenuCheck"><span class="sc-htoDjs gvAGTV sc-fzsDOv hAFFGk journalSubmenuCheck icon-colored _1CwL9R82TPl2HxDleeYGDR icon-themeable" title="" font-size="9"></span></button> </div> <div class="sc-dTdPqK lkWWFY hide__submenu journal__nav__desktop" id="journalnav__submenudesktop"> <div order="0" class="sc-kUaPvJ ehYbwJ"> <div class="sc-gPWkxV legory"></div> <div class="sc-gPWkxV legory"></div> </div> <div class="sc-jVODtj epgILe"></div> <span class="sc-fONwsr kCfRMJ"></span> </div> </nav> </div> <div class="sc-nrwXf byflLi breadcrumb__wrapper journal_article__BreadCrumbStyle-sc-12fk6zy-2 bjwAQR article"> <a class="sc-htpNat bUhGXt link sc-eitiEO jXeALb breadCrumb" href="//www.newsama.com/journals/jps/" aria-label="Journal of Probability and Statistics">概率与统计杂志</一个>/<一个cl一个年代年代＝＂年代c-htpNat bUhGXt link sc-eitiEO jXeALb breadCrumb" href="//www.newsama.com/journals/jps/contents/year/2011/" aria-label="2011">2011</一个>/<年代pan class="sc-bhlBdH UVThf">文章</年代pan> </div> <div class="threeColumn__ThreeColumnWrapper-sc-1bf4078-0 dDyxFF threeColumnWrapper"> <div class="threeColumn__LeftWrapper-sc-1bf4078-1 fkVFlF leftWrapper"> <button type="button" class="sc-eKZiaR dzZrgS section__button " id="sectionButton"><span class="sc-htoDjs diutvq icon__dots dots__detector icon-colored _3n-7Ho7DlfjMlZbrRr9Q4a icon-themeable" title="" font-size="22"></span>文章部分</button> <div class="sc-bEjcJn jLUVhb static_contents__section_links links__hidden "> <div id="leftSectionMenu" class="sc-cbkKFq prcY sc-bGbJRg dVCLgr left_section_menu"> <p>在这一页上</p> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#abstract" aria-label="">摘要</一个></年代pan> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#introduction" aria-label="">介绍</一个></年代pan> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#references" aria-label="">参考文献</一个></年代pan> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#copyright" aria-label="">版权</一个></年代pan> </div> </div> </div> <div class="threeColumn__ContentWrapper-sc-1bf4078-3 bbzREB contentWrapper"> <div class="threeColumn__Content-sc-1bf4078-4 jknsZc content"> <div class="articleContent__ArticleContentsWrapper-sc-2yl9jy-0 eSvjPB article_contents"> <div class="articleContent__ArticleContentsSectionsWrapper-sc-2yl9jy-1 jntdRu article_contents__sections_wrapper"> <div class="articleContent__ArticleWrapper-sc-2yl9jy-2 hAzjHP"> <div class="sc-chbbiW mBGSe article_header_class"> <p class="sc-kZmsYB bkiEfx article_type">研究文章|开放获取</p> <div class="sc-RcBXQ ztvYg article_citation"> 体积 2011 <span class="sc-fZwumE cUsFHx">|</年代pan>文章的ID 689427 <span class="sc-fZwumE cUsFHx">|</年代pan> <a class="sc-htpNat bUhGXt link sc-fQejPQ duuwge" href="https://doi.org/10.1155/2011/689427" aria-label="Doi-link">https://doi.org/10.1155/2011/689427</一个></div> <div class="sc-LKuAh lcOiDF article_full_citation"> <div class="sc-hzNEM gsmOCv isHide"> <p>马里奥Lefebvre， ＂<年代pan class="adjust-article-svg-size">概率偏微分方程的相似解</年代pan>"，<i>概率与统计杂志</我>， 卷。2011， 文章的ID689427， 13   页面， 2011． https://doi.org/10.1155/2011/689427</p> </div> <button class="sc-hSdWYo etauus sc-iBEsjs kPshFw" color="">显示引用</button> </div> <h1 class="sc-iRbamj jZOxOO sc-iSDuPN gaKwvw article_title adjust-article-svg-size heading-title">概率偏微分方程的相似解</h1> </div> <div class="sc-jrIrqw eHMFfo article_authors"> <hr class="sc-cEvuZC XkrFe hr__author"> <span class=""><b>马里奥Lefebvre</b><a class="sc-htpNat bUhGXt link" href="mailto:" aria-label="Mail Option"><span class="sc-htoDjs kNoiZu sc-hjRWVT irNWJI icon-colored _2zt-1j0LmaF8UjTQAM413G icon-themeable" title="" font-size="16"></span></a><sup>1</年代up></span> <div class="sc-fHxwqH dMuGGA isHide"> <p><sup>1</年代up><span>Département de Mathématiques et de Génie Industriel， École Polytechnique de Montréal, C.P. 6079, Succursale Centre-Ville, Montréal, QC，加拿大</年代pan></p> </div> <button class="sc-hSdWYo etauus sc-iQtOjA kfDwZY" color="">显示更多</button> </div> <div class="articleContent__EditorWrapper-sc-2yl9jy-3 evMkvU"> <div class="articleContent__TextWrapper-sc-2yl9jy-8 fYrLtk"> <b>学术编辑器:</b>Shein-chung周润发</div> <div class="articleContent__PublicationTimeLineWrapper-sc-2yl9jy-4 fjviok"> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">收到了</年代pan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2011年5月02</年代pan> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">接受</年代pan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">06年6月2011年</年代pan> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC isPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">发表</年代pan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">09年2011年8月</年代pan> </div> </div> </div> <article class="sc-jtRlXQ pzSfk article_body "> <div> <div class="xml-content"> <h4 class="header" id="abstract">摘要</h4> <p>考虑了同心圆间和角扇区内的二维扩散过程。本文的目的是计算过程将首先到达停止区域边界的给定部分的概率。采用相似解法和分离变量法，对适当的偏微分方程进行了显式求解。一些解用广义傅里叶级数表示。</p> <span class="end-abs"></span> <h4 id="introduction">1.介绍</h4> <p>让<年代vg height="14.6" id="M1" style="vertical-align:-3.13504pt;width:84.525002px;" version="1.1" viewbox="0 0 84.525002 14.6" width="84.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.91,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.03,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-25.71,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-20.83,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ）</t年代pan> </text> </g> </g> </svg>为随机微分方程定义的二维扩散过程<年代pan class="equation" id="EEq1"> <svg height="22.637501" id="M2" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 22.637501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.6375)"> <g transform="translate(72,-53.89)"> <text transform="matrix(1,0,0,-1,87.8,58.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,104.33,55.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,109.63,58.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="15.716271" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="27.744158" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,144.33,55.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,149.63,55.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="4.79" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,164.3,55.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,169.6,58.51)"> <tspan style="font-size: 12.50px; " x="12.24" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="43.799999" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="50.990002" y="0.0099999998"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="19.110001" y="0.0099999998"> </t年代pan> <tspan style="font-size: 12.50px; " x="25.761597" y="0.0099999998"> </t年代pan> <tspan style="font-size: 12.50px; " x="32.450703" y="0.0099999998"> +</t年代pan> </text> <text transform="matrix(1,0,0,-1,226.92,55.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,232.22,55.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="4.79" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,246.89,55.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,252.19,58.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.24" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.028648" y="2.52"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,276.41,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="6.8090558" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,288.09,58.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,306.2,55.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,311.5,58.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="14.315935" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="153.25" y="-1.3099999"> （</t年代pan> <tspan style="font-size: 12.50px; " x="157.4135" y="-1.3099999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="163.66499" y="-1.3099999"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="166.79076" y="-1.3099999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="173.04225" y="-1.3099999"> ）</t年代pan> </text> </g> </g> </svg></span>为<年代vg height="12.8875" id="M3" style="vertical-align:-1.76814pt;width:46.512501px;" version="1.1" viewbox="0 0 46.512501 12.8875" width="46.512501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.8875)"> <g transform="translate(72,-61.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.3517642" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="19.392153" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="25.643654" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="30.857405" y="0"> 2</t年代pan> </text> </g> </g> </svg>,在那里<年代vg height="14.7125" id="M4" style="vertical-align:-3.2316pt;width:26.9375px;" version="1.1" viewbox="0 0 26.9375 14.7125" width="26.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.62,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.4,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</t年代pan> <tspan style="font-size: 12.50px; " x="7.739357" y="0"> ）</t年代pan> </text> </g> </g> </svg>是负的,<年代vg height="14.6" id="M5" style="vertical-align:-3.13504pt;width:35.837502px;" version="1.1" viewbox="0 0 35.837502 14.6" width="35.837502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.5,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-55.62,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.6" id="M6" style="vertical-align:-3.13504pt;width:35.837502px;" version="1.1" viewbox="0 0 35.837502 14.6" width="35.837502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.5,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-55.62,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> </text> </g> </g> </svg>是独立的标准布朗运动。在这篇笔记中，计算的概率问题的过程<年代vg height="14.6" id="M7" style="vertical-align:-3.13504pt;width:84.525002px;" version="1.1" viewbox="0 0 84.525002 14.6" width="84.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.91,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.03,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-25.71,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-20.83,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ）</t年代pan> </text> </g> </g> </svg>，从两个同心圆之间开始，对于最重要的特殊情况，会先击中较大的圆。这个过程也考虑在以原点为圆心的圆内，这一次，概率<年代vg height="14.6" id="M8" style="vertical-align:-3.13504pt;width:84.525002px;" version="1.1" viewbox="0 0 84.525002 14.6" width="84.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.91,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.03,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-25.71,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-20.83,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ）</t年代pan> </text> </g> </g> </svg>将在两个半径中的任何一个被处理之前击中圆的边界。再次，分析了最重要的特殊情况。</p> <p>假设我们只考虑过程<年代vg height="14.6" id="M9" style="vertical-align:-3.13504pt;width:33.862499px;" version="1.1" viewbox="0 0 33.862499 14.6" width="33.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.2,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> </text> </g> </g> </svg>在这一期间<年代vg height="13" id="M10" style="vertical-align:-1.95624pt;width:32.237499px;" version="1.1" viewbox="0 0 32.237499 13" width="32.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13)"> <g transform="translate(72,-61.6)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ［</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.440005" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="15.641253" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="21.517662" y="0"> ］</t年代pan> </text> </g> </g> </svg>．让<年代pan class="equation" id="eq1"> <svg height="19.35" id="M11" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.35" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.35)"> <g transform="translate(72,-56.52)"> <text transform="matrix(1,0,0,-1,55.2,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="64.900002" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.4899998" y="-0.0099999998"> （</t年代pan> <tspan style="font-size: 12.50px; " x="12.653499" y="-0.0099999998"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.530149" y="-0.0099999998"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="27.156979" y="-0.0099999998"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="33.546013" y="-0.0099999998"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="45.586403" y="-0.0099999998"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="49.062237" y="-0.0099999998"> n</t年代pan> <tspan style="font-size: 12.50px; " x="55.313736" y="-0.0099999998"> f</t年代pan> <tspan style="font-size: 12.50px; " x="72.089996" y="7.1054274e-015"> </t年代pan> <tspan style="font-size: 12.50px; " x="79.466766" y="7.1054274e-015"> ≥</t年代pan> <tspan style="font-size: 12.50px; " x="91.507156" y="7.1054274e-015"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="101.23449" y="7.1054274e-015"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="111.09936" y="7.1054274e-015"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,176.18,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,183.14,61.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="15.703768" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="27.744158" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="38.184162" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="44.435661" y="0"> r</t年代pan> <tspan style="font-size: 12.50px; " x="52.762661" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="62.114902" y="0"> ∣</t年代pan> <tspan style="font-size: 12.50px; " x="68.916534" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,261.94,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,268.9,61.14)"> <tspan style="font-size: 12.50px; " x="54.560001" y="0.039999999"> ［</t年代pan> <tspan style="font-size: 12.50px; " x="76.089996" y="0.039999999"> ］</t年代pan> <tspan style="font-size: 12.50px; " x="80.25" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="18.041828" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="30.082218" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="40.434704" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="58.720001" y="0.0099999998"> </t年代pan> <tspan style="font-size: 12.50px; " x="64.996506" y="0.0099999998"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="70.197754" y="0.0099999998"> </t年代pan> <tspan style="font-size: 12.50px; " x="89.519997" y="0.0099999998"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="195.85001" y="0.0099999998"> （</t年代pan> <tspan style="font-size: 12.50px; " x="200.0135" y="0.0099999998"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="206.265" y="0.0099999998"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="209.39075" y="0.0099999998"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="215.64224" y="0.0099999998"> ）</t年代pan> </text> </g> </g> </svg></span></p> <p>那么，这是众所周知的(参见Cox和Miller [<一个href="#B3">1</一个>例如，p. 230])的矩源函数(它是一个拉普拉斯变换)<年代pan class="equation" id="eq2"> <svg height="19.475" id="M12" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.475" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.475)"> <g transform="translate(72,-56.42)"> <text transform="matrix(1,0,0,-1,152.64,61.03)"> <tspan style="font-size: 12.50px; " x="70.860001" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="75.650002" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.927622" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="15.091121" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="21.967772" y="0"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="27.531607" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="33.032925" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="40.67226" y="0"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="47.061291" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="59.089176" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,233.85,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.8459997" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="14.327024" y="0"> （</t年代pan> <tspan style="font-size: 8.75px; " x="17.24144" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="22.05504" y="0"> ）</t年代pan> </text> <text transform="matrix(1,0,0,-1,259.32,58.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="205.42999" y="-2.5599999"> （</t年代pan> <tspan style="font-size: 12.50px; " x="209.59351" y="-2.5599999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="215.845" y="-2.5599999"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="218.97075" y="-2.5599999"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="225.22224" y="-2.5599999"> ）</t年代pan> </text> </g> </g> </svg></span>第一次通过的时间<年代vg height="13.45" id="M13" style="vertical-align:-2.21957pt;width:27.137501px;" version="1.1" viewbox="0 0 27.137501 13.45" width="27.137501" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="10.552532" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.429182" y="0"> ）</t年代pan> </text> </g> </g> </svg>,在那里<年代vg height="7.1875" id="M14" style="vertical-align:-0.13794pt;width:7px;" version="1.1" viewbox="0 0 7 7.1875" width="7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1875)"> <g transform="translate(72,-66.25)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>是一个非负参数，满足Kolmogorov倒向方程<年代pan class="equation" id="eq3"> <svg height="33.0625" id="M15" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 33.0625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,33.0625)"> <g transform="translate(72,-45.55)"> <text transform="matrix(1,0,0,-1,97.6,63.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,103.93,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,110.89,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> ）</t年代pan> </text> <g> <path d="m 97.6,57.48 28.49,0" 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,-1,108.72,45.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="18.57" y="-8.75"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,136.14,59.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,144.67,54.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="16.59148" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="22.0928" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="29.04447" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="40.384689" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,192,51.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,198.96,54.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="17.279146" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,225.1,59.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,230.66,54.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="16.59148" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="22.0928" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="29.732134" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="41.760021" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="47.261341" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="58.201466" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="62.364964" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="69.241615" y="0"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="74.80545" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="80.30677" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="86.545769" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="234.09" y="-1.29"> （</t年代pan> <tspan style="font-size: 12.50px; " x="238.25349" y="-1.29"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="244.505" y="-1.29"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="247.63075" y="-1.29"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="253.88225" y="-1.29"> ）</t年代pan> </text> </g> </g> </svg></span>它受边界条件的约束<年代pan class="equation" id="eq4"> <svg height="16.5375" id="M16" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 16.5375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5375)"> <g transform="translate(72,-58.77)"> <text transform="matrix(1,0,0,-1,151.78,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.927622" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="15.091121" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="21.367626" y="0"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="26.918959" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="32.42028" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="40.059612" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="52.100002" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="63.040127" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="67.203629" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="73.080032" y="0"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="78.631371" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="84.13269" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="91.772018" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="103.81241" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="110.06391" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="312.97" y="0.63"> （</t年代pan> <tspan style="font-size: 12.50px; " x="317.13348" y="0.63"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="323.38501" y="0.63"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="326.51074" y="0.63"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="332.76224" y="0.63"> ）</t年代pan> </text> </g> </g> </svg></span></p> <p>接下来,我们<年代pan class="equation" id="eq5"> <svg height="19.35" id="M17" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.35" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.35)"> <g transform="translate(72,-56.52)"> <text transform="matrix(1,0,0,-1,105.28,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="56.689999" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="61.48" y="7.1054274e-015"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.1999998" y="-0.0099999998"> （</t年代pan> <tspan style="font-size: 12.50px; " x="12.363499" y="-0.0099999998"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.240149" y="-0.0099999998"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="26.86698" y="-0.0099999998"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="33.256012" y="-0.0099999998"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="45.296402" y="-0.0099999998"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,176.64,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,183.59,61.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.640533" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="16.804031" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="23.680681" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="27.844181" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="35.483513" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="47.523903" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="57.276241" y="0"> ∣</t年代pan> <tspan style="font-size: 12.50px; " x="64.077873" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,257.55,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,264.5,61.14)"> <tspan style="font-size: 12.50px; " x="36.970001" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="18.054333" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="30.082218" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="43.84" y="0.0099999998"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="200.25" y="0.0099999998"> （</t年代pan> <tspan style="font-size: 12.50px; " x="204.4135" y="0.0099999998"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="210.66499" y="0.0099999998"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="213.79076" y="0.0099999998"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="220.04225" y="0.0099999998"> ）</t年代pan> </text> </g> </g> </svg></span>这个函数<年代vg height="13.55" id="M18" style="vertical-align:-2.29482pt;width:26.775px;" version="1.1" viewbox="0 0 26.775 13.55" width="26.775" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.1139669" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="10.277466" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.154116" y="0"> ）</t年代pan> </text> </g> </g> </svg>满足常微分方程(见Cox and Miller [<一个href="#B3">1</一个>，第231页)<年代pan class="equation" id="eq6"> <svg height="33.0625" id="M19" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 33.0625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,33.0625)"> <g transform="translate(72,-45.55)"> <text transform="matrix(1,0,0,-1,130.67,63.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,137,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,143.96,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> ）</t年代pan> </text> <g> <path d="m 130.67,57.48 28.49,0" 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,-1,141.79,45.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="18.559999" y="-8.75"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,166.47,59.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,175,54.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="17.979315" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="29.319534" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,211.27,51.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,218.22,54.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="17.291649" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,241.63,59.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,247.18,54.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="18.679482" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="30.707369" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="36.958866" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="217.57001" y="-1.29"> （</t年代pan> <tspan style="font-size: 12.50px; " x="221.73351" y="-1.29"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="227.985" y="-1.29"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="231.11075" y="-1.29"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="237.36224" y="-1.29"> ）</t年代pan> </text> </g> </g> </svg></span>与<年代pan class="equation" id="eq7"> <svg height="16.5375" id="M20" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 16.5375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5375)"> <g transform="translate(72,-58.77)"> <text transform="matrix(1,0,0,-1,149.88,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.1894646" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="12.352964" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.629471" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="26.268803" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="38.309193" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="44.560692" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="69.691719" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="77.893692" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="82.05719" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="87.933601" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="95.572929" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="107.60081" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="113.85232" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="314.87" y="0.63"> （</t年代pan> <tspan style="font-size: 12.50px; " x="319.03351" y="0.63"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="325.285" y="0.63"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="328.41074" y="0.63"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="334.66226" y="0.63"> ）</t年代pan> </text> </g> </g> </svg></span>因此，明确地计算概率是一件简单的事情<年代vg height="13.55" id="M21" style="vertical-align:-2.29482pt;width:26.775px;" version="1.1" viewbox="0 0 26.775 13.55" width="26.775" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.1139669" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="10.277466" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.154116" y="0"> ）</t年代pan> </text> </g> </g> </svg>击中要害<年代vg height="7.1750002" id="M22" style="vertical-align:-0.1254pt;width:7.9749999px;" version="1.1" viewbox="0 0 7.9749999 7.1750002" width="7.9749999" 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"> </t年代pan> </text> </g> </g> </svg>之前<年代vg height="10.7375" id="M23" style="vertical-align:-0.13794pt;width:7.4749999px;" version="1.1" viewbox="0 0 7.4749999 10.7375" width="7.4749999" 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"> </t年代pan> </text> </g> </g> </svg>,从<年代vg height="13" id="M24" style="vertical-align:-1.95624pt;width:60.224998px;" version="1.1" viewbox="0 0 60.224998 13" width="60.224998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13)"> <g transform="translate(72,-61.6)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.339981" y="0"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="22.380369" y="0"> ［</t年代pan> <tspan style="font-size: 12.50px; " x="26.543869" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="32.820374" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="38.034126" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="43.910538" y="0"> ］</t年代pan> </text> </g> </g> </svg>．特别是，当<年代vg height="14.6" id="M25" style="vertical-align:-3.13504pt;width:33.862499px;" version="1.1" viewbox="0 0 33.862499 14.6" width="33.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.2,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> </text> </g> </g> </svg>是标准布朗运动，所以呢<年代vg height="14.6" id="M26" style="vertical-align:-3.13504pt;width:61.099998px;" version="1.1" viewbox="0 0 61.099998 14.6" width="61.099998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.01,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.14,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="18.679482" y="0"> ≡</t年代pan> <tspan style="font-size: 12.50px; " x="30.707369" y="0"> 0</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.6" id="M27" style="vertical-align:-3.13504pt;width:60.337502px;" version="1.1" viewbox="0 0 60.337502 14.6" width="60.337502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.62,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.75,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="18.666979" y="0"> ≡</t年代pan> <tspan style="font-size: 12.50px; " x="30.707369" y="0"> 1</t年代pan> </text> </g> </g> </svg>，我们立刻发现<年代pan class="equation" id="eq8"> <svg height="30.737499" id="M28" 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,-1,133.54,56.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.1894646" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="12.352964" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.229614" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="26.868946" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="40.110001" y="-7.25"> </t年代pan> <tspan style="font-size: 12.50px; " x="48.762077" y="-7.25"> −</t年代pan> <tspan style="font-size: 12.50px; " x="60.102299" y="-7.25"> </t年代pan> </text> <g> <path d="m 173.65,59.47 26.88,0" 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,-1,173.95,47.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.6520758" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="19.992296" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="37.73" y="-8.7600002"> f</t年代pan> <tspan style="font-size: 12.50px; " x="41.505905" y="-8.7600002"> o</t年代pan> <tspan style="font-size: 12.50px; " x="47.757404" y="-8.7600002"> r</t年代pan> <tspan style="font-size: 12.50px; " x="56.071899" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="65.824242" y="-8.7600002"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="77.864632" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="88.217117" y="-8.7600002"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="100.245" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="106.12141" y="-8.7600002"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="290.79999" y="-8.9899998"> （</t年代pan> <tspan style="font-size: 12.50px; " x="294.9635" y="-8.9899998"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="301.215" y="-8.9899998"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="304.34076" y="-8.9899998"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="310.59225" y="-8.9899998"> ）</t年代pan> </text> </g> </g> </svg></span></p> <p>许多论文致力于研究一维或多维扩散过程的首次通过时间问题;特别是Doob的经典论文[<一个href="#B4">2</一个>］和斯皮策[<一个href="#B9">3.</一个>］， Wendel [<一个href="#B10">4</一个>］.然而，相当少的论文是在第一次攻击时写的<我>的地方</我>问题;例如，尹和吴的论文[<一个href="#B12">5</一个>和Yin等人[<一个href="#B11">6</一个>］.吉堡和列斐伏尔(见[<一个href="#B6">7</一个>，<一个href="#B8">8</一个>］）已考虑与本照会处理的问题有关的问题;然而，在这些问题中，过程被考虑在矩形内。</p> <p>现在,定义<年代pan class="equation" id="EEq2"> <svg height="19.35" id="M29" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.35" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.35)"> <g transform="translate(72,-56.52)"> <text transform="matrix(1,0,0,-1,51.89,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.96" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="16.809999" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,75.58,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,80.45,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,92.54,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,97.41,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="40.68" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="86.879997" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="92.730003" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3299999" y="-2.51"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="21.357885" y="-2.51"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="24.833719" y="-2.51"> n</t年代pan> <tspan style="font-size: 12.50px; " x="31.08522" y="-2.51"> f</t年代pan> <tspan style="font-size: 12.50px; " x="47.860001" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="55.249271" y="-2.51"> ≥</t年代pan> <tspan style="font-size: 12.50px; " x="67.277161" y="-2.51"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="77.004494" y="-2.51"> ∶</t年代pan> </text> <text transform="matrix(1,0,0,-1,200.01,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,206.97,61.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="14.315935" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="19.529686" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,236.38,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,243.34,61.14)"> <tspan style="font-size: 12.50px; " x="12.24" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="21.57" y="0.0099999998"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="33.597885" y="0.0099999998"> </t年代pan> <tspan style="font-size: 12.50px; " x="46.951092" y="0.0099999998"> ∣</t年代pan> <tspan style="font-size: 12.50px; " x="53.752724" y="0.0099999998"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,306.97,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,312.28,61.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="18.041828" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="30.082218" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,349.24,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,352.46,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.2799997" y="-2.51"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="106.03" y="-2.51"> （</t年代pan> <tspan style="font-size: 12.50px; " x="110.1935" y="-2.51"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="116.445" y="-2.51"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="119.57075" y="-2.51"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="125.82225" y="-2.51"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="132.07375" y="-2.51"> ）</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="10.325" id="M30" style="vertical-align:-0.0pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" 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"> </t年代pan> </text> </g> </g> </svg>是<年代vg height="13.775" id="M31" style="vertical-align:-0.0pt;width:17.887501px;" version="1.1" viewbox="0 0 17.887501 13.775" width="17.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.775)"> <g transform="translate(72,-60.98)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℝ</t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.61,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>随机变量<年代vg height="14.6" id="M32" style="vertical-align:-3.13504pt;width:55.012501px;" version="1.1" viewbox="0 0 55.012501 14.6" width="55.012501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.8766499" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-54.03,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-49.16,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-37.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.2,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> </text> </g> </g> </svg>是定义良好的。的矩母函数<年代vg height="14.6" id="M33" style="vertical-align:-3.13504pt;width:55.012501px;" version="1.1" viewbox="0 0 55.012501 14.6" width="55.012501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.8766499" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-54.03,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-49.16,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-37.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.2,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> </text> </g> </g> </svg>,即<年代pan class="equation" id="eq9"> <svg height="19.475" id="M34" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.475" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.475)"> <g transform="translate(72,-56.42)"> <text transform="matrix(1,0,0,-1,130.32,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.78" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="21.629999" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,158.83,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,163.7,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,175.79,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,180.66,61.03)"> <tspan style="font-size: 12.50px; " x="11.06" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="50.580002" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="55.360001" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="20.389999" y="0"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="26.779034" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="38.806919" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,241.59,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.8459997" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="14.6596" y="0"> （</t年代pan> <tspan style="font-size: 8.75px; " x="17.574017" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,263.98,63.85)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,267.6,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 8.75px; " x="2.188" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,274.6,63.85)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,278.23,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ）</t年代pan> </text> <text transform="matrix(1,0,0,-1,281.64,58.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="176.85001" y="-2.5599999"> （</t年代pan> <tspan style="font-size: 12.50px; " x="181.0135" y="-2.5599999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="187.265" y="-2.5599999"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="190.39075" y="-2.5599999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="196.64224" y="-2.5599999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="202.89375" y="-2.5599999"> ）</t年代pan> </text> </g> </g> </svg></span>满足Kolmogorov倒向方程<年代pan class="equation" id="EEq3"> <svg height="50.924999" id="M35" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.924999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.925)"> <g transform="translate(72,-31.26)"> <text transform="matrix(1,0,0,-1,106.36,63.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,100.47,41.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,102,33.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> ＝</t年代pan> <tspan style="font-size: 8.75px; " x="8.7169924" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,118.71,37.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="14.65" y="-20.309999"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,139.68,55.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,144.99,55.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,157.71,55.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,160.93,55.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 133.36,50.74 33.43,0" 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,-1,146.95,38.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="21.030001" y="-8.7600002"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,180.55,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,185.36,42.3)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,187.8,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,192.62,42.3)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,198.34,47.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,216.62,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,221.92,45.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,234.65,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,237.87,45.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9400001" y="-2.52"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,258.37,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,263.18,42.3)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,266.13,37.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="16.92" y="-9.7399998"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="28.947886" y="-9.7399998"> </t年代pan> <tspan style="font-size: 12.50px; " x="34.449207" y="-9.7399998"> </t年代pan> <tspan style="font-size: 12.50px; " x="47.014721" y="-9.7399998"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="192.36" y="-10.63"> （</t年代pan> <tspan style="font-size: 12.50px; " x="196.5235" y="-10.63"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="202.77499" y="-10.63"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="205.90074" y="-10.63"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="212.15225" y="-10.63"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="218.40375" y="-10.63"> ）</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="17.4125" id="M36" style="vertical-align:-5.39853pt;width:101.55px;" version="1.1" viewbox="0 0 101.55 17.4125" width="101.55" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.4125)"> <g transform="translate(72,-58.07)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-59.38,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-54.57,58.18)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-48.16,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="18.41692" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="24.805952" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="37.371468" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="40.847301" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="47.236336" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,5.97,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>和<年代vg height="20.5875" id="M37" style="vertical-align:-5.39853pt;width:118.775px;" version="1.1" viewbox="0 0 118.775 20.5875" width="118.775" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.5875)"> <g transform="translate(72,-55.53)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-59.38,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-54.57,55.65)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-52.13,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-47.31,55.65)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-40.9,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="18.41692" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-16.09,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-11.21,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.565515" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="16.041349" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="22.417879" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,18.1,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="8.6999998"> </t年代pan> </text> </g> </g> </svg>．该偏微分方程在延拓区域是有效的<年代vg height="11.4" id="M38" style="vertical-align:-0.16302pt;width:56.275002px;" version="1.1" viewbox="0 0 56.275002 11.4" width="56.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.4)"> <g transform="translate(72,-62.88)"> <text transform="matrix(1,0,0,-1,-71.95,63.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.852844" y="0"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="18.241877" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="30.282267" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-31.6,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>并且服从边界条件<年代pan class="equation" id="eq10"> <svg height="19.35" id="M39" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.35" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.35)"> <g transform="translate(72,-56.52)"> <text transform="matrix(1,0,0,-1,114.28,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.78" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="21.629999" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,142.79,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,147.66,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,159.75,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,164.62,61.13)"> <tspan style="font-size: 12.50px; " x="11.06" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="62.529999" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="68.379997" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="20.389999" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="32.417885" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="48.634277" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="52.110111" y="0"> f</t年代pan> </text> <text transform="matrix(1,0,0,-1,239.88,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,244.75,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,256.84,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,261.71,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3299999" y="-2.51"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="21.357885" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.74692" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="37.62429" y="-2.51"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="196.78" y="-2.51"> （</t年代pan> <tspan style="font-size: 12.50px; " x="200.9435" y="-2.51"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="207.19499" y="-2.51"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="210.32076" y="-2.51"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="216.57225" y="-2.51"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="222.82375" y="-2.51"> ）</t年代pan> </text> </g> </g> </svg></span></p> <p>节<一个href="#sec2">2</一个>，一组<年代vg height="10.6125" id="M40" style="vertical-align:-0.15048pt;width:11.8625px;" version="1.1" viewbox="0 0 11.8625 10.6125" width="11.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6125)"> <g transform="translate(72,-63.51)"> <text transform="matrix(1,0,0,-1,-71.95,63.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>将由<年代pan class="equation" id="EEq4"> <svg height="19.5625" id="M41" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.5625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.5625)"> <g transform="translate(72,-56.35)"> <text transform="matrix(1,0,0,-1,92.66,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,101.05,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,109.4,60.96)"> <tspan style="font-size: 12.50px; " x="31.469999" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="18.43" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="25.619225" y="2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,147.75,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,152.62,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,164.71,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,169.58,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3199997" y="-2.51"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="21.36039" y="-2.51"> ℝ</t年代pan> </text> <text transform="matrix(1,0,0,-1,200.28,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,208.63,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="9.8523636" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,225.89,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.21"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,234.24,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,253.15,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,260.81,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,279.03,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,287.37,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,306.81,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.21"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,311.69,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.2700005" y="-2.51"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="146.8" y="-2.5999999"> （</t年代pan> <tspan style="font-size: 12.50px; " x="150.9635" y="-2.5999999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="157.215" y="-2.5999999"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="160.34074" y="-2.5999999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="166.59225" y="-2.5999999"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="172.84375" y="-2.5999999"> ）</t年代pan> </text> </g> </g> </svg></span>和功能<年代pan class="equation" id="EEq5"> <svg height="19.5625" id="M42" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.5625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.5625)"> <g transform="translate(72,-56.35)"> <text transform="matrix(1,0,0,-1,54.8,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.6800003" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.53" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,77.21,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,82.09,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,94.17,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,99.05,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="39.130001" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="43.919998" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3199997" y="-2.51"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="15.709033" y="-2.51"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="27.736919" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,153.6,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.2200003"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,160.56,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,173.29,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,180.24,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8600001" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,192.97,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,197.85,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,209.93,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,214.81,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="14.48" y="-2.51"> +</t年代pan> <tspan style="font-size: 12.50px; " x="25.820221" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,251.26,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.2200003"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,258.22,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,270.95,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,277.9,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,290.63,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,295.51,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,307.59,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,312.47,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.17" y="-2.51"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="27.197886" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,347.08,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.21"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,351.96,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.8699999" y="-2.51"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="106.53" y="-2.5999999"> （</t年代pan> <tspan style="font-size: 12.50px; " x="110.6935" y="-2.5999999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="116.945" y="-2.5999999"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="120.07075" y="-2.5999999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="126.32225" y="-2.5999999"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="132.57375" y="-2.5999999"> ）</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="14.2375" id="M43" style="vertical-align:-3.13504pt;width:14.8125px;" version="1.1" viewbox="0 0 14.8125 14.2375" width="14.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>为中定义的随机变量<一个href="#EEq2">1．10</一个>），<年代vg height="16.5875" id="M44" style="vertical-align:-4.32487pt;width:87.137497px;" version="1.1" viewbox="0 0 87.137497 16.5875" width="87.137497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5875)"> <g transform="translate(72,-58.73)"> <text transform="matrix(1,0,0,-1,-71.95,63.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="25.38109" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-36.68,59.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-28.34,63.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-6.91,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="-1" y="9.3100004"> 1</t年代pan> </text> </g> </g> </svg>，将在重要的特殊情况下计算，例如when<年代vg height="14.6" id="M45" style="vertical-align:-3.13504pt;width:84.525002px;" version="1.1" viewbox="0 0 84.525002 14.6" width="84.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.91,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.03,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-25.71,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-20.83,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ）</t年代pan> </text> </g> </g> </svg>是一个二维维纳过程。</p> <p>节<一个href="#sec3">3.</一个>，我们将选择<年代pan class="equation" id="EEq6"> <svg height="38.575001" id="M46" 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,-1,21.9,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,30.29,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,38.63,53.45)"> <tspan style="font-size: 12.50px; " x="18.43" y="7.3299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="29.76" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.610001" y="-7.1054274e-015"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> ＝</t年代pan> </text> <text transform="matrix(1,0,0,-1,81.12,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,85.99,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,98.08,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,102.95,50.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3299999" y="-2.52"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="21.357885" y="-2.52"> ℝ</t年代pan> </text> <text transform="matrix(1,0,0,-1,133.65,58.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,142,53.45)"> <tspan style="font-size: 12.50px; " x="31.629999" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="37.48" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="9.8523636" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="19.579699" y="0"> <</t年代pan> </text> <text transform="matrix(1,0,0,-1,186.35,58.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,194.01,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,212.23,58.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,217.1,50.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,222.95,61.08)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="6.8090558" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,238.11,53.45)"> <tspan style="font-size: 12.50px; " x="80.370003" y="7.3299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="90.949997" y="-9.1400003"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.679482" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="23.893232" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="33.620567" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="45.648453" y="0"> 一个</t年代pan> <tspan style="font-size: 12.50px; " x="51.199783" y="0"> r</t年代pan> <tspan style="font-size: 12.50px; " x="55.363285" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="60.914616" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="64.39045" y="0"> 一个</t年代pan> <tspan style="font-size: 12.50px; " x="69.94178" y="0"> n</t年代pan> </text> <text transform="matrix(1,0,0,-1,335.93,59.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <g> <path d="m 329.06,56.57 11.75,0" 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,-1,329.06,44.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,335.93,41.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,342,46.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.85" y="-7.3299999"> <</t年代pan> <tspan style="font-size: 12.50px; " x="24.877886" y="-7.3299999"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,373.44,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,378.32,46.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.41" y="-7.3299999"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="80.169998" y="-7.3299999"> （</t年代pan> <tspan style="font-size: 12.50px; " x="84.333496" y="-7.3299999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="90.584999" y="-7.3299999"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="93.710747" y="-7.3299999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="99.96225" y="-7.3299999"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="106.21375" y="-7.3299999"> ）</t年代pan> </text> </g> </g> </svg></span>我们将计算重要二维扩散过程的概率<年代pan class="equation" id="EEq7"> <svg height="19.5625" id="M47" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.5625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.5625)"> <g transform="translate(72,-56.35)"> <text transform="matrix(1,0,0,-1,55.46,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.3599997" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="14.21" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,76.55,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,81.42,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,93.51,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,98.38,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="39.139999" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="43.93" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3299999" y="-2.51"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="15.719033" y="-2.51"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="27.74692" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,152.94,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.2200003"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,159.9,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,172.62,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,179.58,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,192.31,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,197.18,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,209.27,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,214.14,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="14.49" y="-2.51"> +</t年代pan> <tspan style="font-size: 12.50px; " x="25.817719" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,250.6,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.2200003"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,257.55,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8600001" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,270.28,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,277.24,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,289.97,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,294.84,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,306.93,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,311.8,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.18" y="-2.51"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="27.207886" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,346.42,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,351.29,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.8800001" y="-2.51"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="107.2" y="-2.5999999"> （</t年代pan> <tspan style="font-size: 12.50px; " x="111.3635" y="-2.5999999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="117.615" y="-2.5999999"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="120.74075" y="-2.5999999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="126.99225" y="-2.5999999"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="133.24374" y="-2.5999999"> ）</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="14.2375" id="M48" style="vertical-align:-3.13504pt;width:14.8125px;" version="1.1" viewbox="0 0 14.8125 14.2375" width="14.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>花费的时间是多少<年代vg height="14.6" id="M49" style="vertical-align:-3.13504pt;width:84.525002px;" version="1.1" viewbox="0 0 84.525002 14.6" width="84.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.91,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.03,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-25.71,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-20.83,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ）</t年代pan> </text> </g> </g> </svg>离开片场<年代vg height="14.3375" id="M50" style="vertical-align:-3.13504pt;width:16.700001px;" version="1.1" viewbox="0 0 16.700001 14.3375" width="16.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.56,60.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>,从<年代vg height="14.7125" id="M51" style="vertical-align:-3.2316pt;width:66.724998px;" version="1.1" viewbox="0 0 66.724998 14.7125" width="66.724998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.85,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="18.041828" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="30.082218" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-21.89,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>为<年代vg height="12.8875" id="M52" style="vertical-align:-1.76814pt;width:46.512501px;" version="1.1" viewbox="0 0 46.512501 12.8875" width="46.512501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.8875)"> <g transform="translate(72,-61.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.3517642" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="19.392153" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="25.643654" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="30.857405" y="0"> 2</t年代pan> </text> </g> </g> </svg>．</p> <p>最后，将在本节中作一些说明<一个href="#sec4">4</一个>结论。</p> <h4 id="first-hitting-place-probabilities-when-starting-between-two-circles">2.当从两个圆之间开始时，第一次击中地点的概率</h4> <p>由Kolmogorov倒向方程(<一个href="#EEq3">1．12</一个>），我们推导出该函数<年代vg height="14.6" id="M53" style="vertical-align:-3.13504pt;width:55.924999px;" version="1.1" viewbox="0 0 55.924999 14.6" width="55.924999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.5893211" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="11.75282" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.31,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-48.43,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-36.35,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-31.47,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> </text> </g> </g> </svg>中定义的(<一个href="#EEq5">1.15</一个>）满足偏微分方程<年代pan class="equation" id="EEq8"> <svg height="50.924999" id="M54" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.924999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.925)"> <g transform="translate(72,-31.26)"> <text transform="matrix(1,0,0,-1,118.79,63.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,112.9,41.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,114.43,33.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> ＝</t年代pan> <tspan style="font-size: 8.75px; " x="8.7169924" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,131.14,37.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="14.65" y="-20.309999"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,152.12,55.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,157.42,55.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,170.15,55.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,173.37,55.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 145.79,50.74 33.43,0" 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,-1,159.38,38.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="21.040001" y="-8.7600002"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,188.02,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,192.83,42.3)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,195.27,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,200.09,42.3)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,205.81,47.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,224.09,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,229.39,45.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,242.12,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,245.34,45.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9400001" y="-2.52"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,260.88,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,265.69,42.3)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,268.63,37.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="16.93" y="-9.7399998"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="28.957886" y="-9.7399998"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="196.12" y="-10.63"> （</t年代pan> <tspan style="font-size: 12.50px; " x="200.28349" y="-10.63"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="206.535" y="-10.63"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="209.66075" y="-10.63"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="215.91225" y="-10.63"> ）</t年代pan> </text> </g> </g> </svg></span>在一组<年代vg height="14.3375" id="M55" style="vertical-align:-3.13504pt;width:16.700001px;" version="1.1" viewbox="0 0 16.700001 14.3375" width="16.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.56,60.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>中定义的(<一个href="#EEq4">1．14</一个>），并受边界条件的约束<年代pan class="equation" id="EEq9"> <svg height="53.887501" id="M56" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 53.887501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,53.8875)"> <g transform="translate(72,-28.89)"> <text transform="matrix(1,0,0,-1,121.42,47.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.6899996" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.54" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,143.84,44.19)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,148.71,47.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,160.8,44.19)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,165.67,44.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3299999" y="-2.51"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="21.360001" y="-14.57"> ⎧</t年代pan> <tspan style="font-size: 12.50px; " x="21.360001" y="-9.4499998"> ⎪</t年代pan> <tspan style="font-size: 12.50px; " x="21.360001" y="0.68000001"> ⎨</t年代pan> <tspan style="font-size: 12.50px; " x="21.360001" y="10.81"> ⎪</t年代pan> <tspan style="font-size: 12.50px; " x="21.360001" y="15.87"> ⎩</t年代pan> <tspan style="font-size: 12.50px; " x="29.370001" y="-16.110001"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="48.111996" y="-16.110001"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="51.58783" y="-16.110001"> f</t年代pan> <tspan style="font-size: 12.50px; " x="59.914829" y="-16.110001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,232.47,65.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.21"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,240.13,60.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,258.35,65.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.21"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,266.69,60.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,286.13,65.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.21"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,291.01,60.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="-95.970001" y="27.440001"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="-77.228004" y="27.440001"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="-73.752167" y="27.440001"> f</t年代pan> <tspan style="font-size: 12.50px; " x="-65.425171" y="27.440001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,232.47,38.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,240.13,33.48)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,258.35,38.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,266.69,33.48)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,286.13,38.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.2200003"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,291.01,33.48)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="173.74001" y="-13.84"> （</t年代pan> <tspan style="font-size: 12.50px; " x="177.9035" y="-13.84"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="184.155" y="-13.84"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="187.28075" y="-13.84"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="193.53224" y="-13.84"> ）</t年代pan> </text> </g> </g> </svg></span>因为二维过程<年代vg height="14.6" id="M57" style="vertical-align:-3.13504pt;width:84.525002px;" version="1.1" viewbox="0 0 84.525002 14.6" width="84.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.91,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.03,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-25.71,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-20.83,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ）</t年代pan> </text> </g> </g> </svg>是考虑在两个同心圆之间，似乎很自然地试图找到一个解的形式<年代pan class="equation" id="eq11"> <svg height="19.35" id="M58" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.35" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.35)"> <g transform="translate(72,-56.52)"> <text transform="matrix(1,0,0,-1,161.55,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.6800003" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.53" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,183.96,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,188.83,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,200.92,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,205.79,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3299999" y="-2.51"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="21.357885" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="29.68" y="-2.52"> （</t年代pan> <tspan style="font-size: 12.50px; " x="33.843498" y="-2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="40.044987" y="-2.52"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="46.283985" y="-2.52"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="258.95999" y="-2.51"> （</t年代pan> <tspan style="font-size: 12.50px; " x="263.1235" y="-2.51"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="269.375" y="-2.51"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="272.50076" y="-2.51"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="278.75226" y="-2.51"> ）</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="19.0375" id="M59" style="vertical-align:-4.22832pt;width:82.275002px;" version="1.1" viewbox="0 0 82.275002 19.0375" width="82.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.0375)"> <g transform="translate(72,-56.77)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.6648188" y="0"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="16.053852" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="28.09424" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-36.97,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.21"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-29.32,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-11.1,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.21"> 2</t年代pan> </text> </g> </g> </svg>．实际上，这只在少数非常重要的特殊情况下有效，下面将介绍其中一些情况。偏微分方程(<一个href="#EEq8">2.1</一个>）成为<年代pan class="equation" id="EEq10"> <svg height="50.924999" id="M60" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.924999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.925)"> <g transform="translate(72,-31.26)"> <text transform="matrix(1,0,0,-1,69.09,63.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,63.2,41.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,64.73,33.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> ＝</t年代pan> <tspan style="font-size: 8.75px; " x="8.7169924" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,81.44,45.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.1900001" y="-2.52"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="13.4415" y="-2.52"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,101.21,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,106.51,45.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,119.24,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,122.46,45.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.52"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,137.27,52.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="8.6899996"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,142.15,47.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,148.37,52.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,156.91,47.62)"> <tspan style="font-size: 12.50px; " x="28.65" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="33.43" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.364987" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="17.291649" y="0"> +</t年代pan> </text> <text transform="matrix(1,0,0,-1,196.67,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,201.97,45.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8600001" y="-2.52"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,214.7,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,217.92,45.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.6300001" y="-2.52"> +</t年代pan> <tspan style="font-size: 12.50px; " x="19.970221" y="-2.52"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="26.221722" y="-2.52"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,251.02,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,254.24,47.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,261.18,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,266.49,45.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,279.22,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,282.44,45.1)"> <tspan style="font-size: 12.50px; " x="12.72" y="-2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8514042" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,301.39,52.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,306.94,47.62)"> <tspan style="font-size: 12.50px; " x="14.53" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.364987" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="25.190001" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="37.230389" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="43.481888" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="157.81" y="-0.88999999"> （</t年代pan> <tspan style="font-size: 12.50px; " x="161.9735" y="-0.88999999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="168.22501" y="-0.88999999"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="171.35075" y="-0.88999999"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="177.60225" y="-0.88999999"> ）</t年代pan> </text> </g> </g> </svg></span></p> <p><span class="statement" id="rem1"><span class="statement-title"><i class="statement-title">2.1的话。</我></年代pan>因为该地区<年代vg height="14.3375" id="M61" style="vertical-align:-3.13504pt;width:16.700001px;" version="1.1" viewbox="0 0 16.700001 14.3375" width="16.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.56,60.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>是有界的，问题的解(<一个href="#EEq8">2.1</一个>），（<一个href="#EEq9">2.2</一个>）是独一无二的。因此，如果我们能找到解的形式<年代vg height="14.6" id="M62" style="vertical-align:-3.13504pt;width:100.6375px;" version="1.1" viewbox="0 0 100.6375 14.6" width="100.6375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.5893211" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="11.75282" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.31,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-48.43,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-36.35,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-31.47,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="25.393593" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="29.557093" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.758579" y="0"> ）</t年代pan> </text> </g> </g> </svg>，那么我们就可以说，这确实是我们一直在寻找的解决方案。</年代pan></p> <h5 id="sec2.1">2．1.二维维纳过程</h5> <p>首先,我们需要<年代vg height="14.7125" id="M63" style="vertical-align:-3.2316pt;width:63.0625px;" version="1.1" viewbox="0 0 63.0625 14.7125" width="63.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.01,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-61.79,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-50.75,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-47.53,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> ≡</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> 0</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.75" id="M64" style="vertical-align:-3.25793pt;width:95.675003px;" version="1.1" viewbox="0 0 95.675003 14.75" width="95.675003" 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"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.62,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.4,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-51.36,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-48.14,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> ≡</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-22.14,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-13.8,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 0</t年代pan> </text> </g> </g> </svg>．然后<年代vg height="14.6" id="M65" style="vertical-align:-3.13504pt;width:84.525002px;" version="1.1" viewbox="0 0 84.525002 14.6" width="84.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.91,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.03,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-25.71,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-20.83,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ）</t年代pan> </text> </g> </g> </svg>一个无限小均值和无限小方差都为零的二维维纳过程是否等于<年代vg height="11.3375" id="M66" style="vertical-align:-3.25793pt;width:14.125px;" version="1.1" viewbox="0 0 14.125 11.3375" width="14.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3375)"> <g transform="translate(72,-62.93)"> <text transform="matrix(1,0,0,-1,-71.95,66.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.62,63.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>．方程(<一个href="#EEq10">2.4</一个>）可以重写为<年代pan class="equation" id="eq12"> <svg height="17.2875" id="M67" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 17.2875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.2875)"> <g transform="translate(72,-58.17)"> <text transform="matrix(1,0,0,-1,157.97,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.201488" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,170.4,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,178.93,62.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.364987" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="17.304152" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="28.644373" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,213.81,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,219.37,62.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.364987" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="17.991817" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="30.032206" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="36.283707" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="245.38" y="0.029999999"> （</t年代pan> <tspan style="font-size: 12.50px; " x="249.5435" y="0.029999999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="255.795" y="0.029999999"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="258.92075" y="0.029999999"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="265.17224" y="0.029999999"> ）</t年代pan> </text> </g> </g> </svg></span>注意这是一个一阶线性常微分方程<年代vg height="15.4125" id="M68" style="vertical-align:-2.29482pt;width:84.962502px;" version="1.1" viewbox="0 0 84.962502 15.4125" width="84.962502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.4125)"> <g transform="translate(72,-59.67)"> <text transform="matrix(1,0,0,-1,-71.95,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代pan> <tspan style="font-size: 12.50px; " x="7.214231" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="11.37773" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.579218" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="25.206047" y="0"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="31.595081" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="43.635471" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-22.08,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-18.61,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.364987" y="0"> ）</t年代pan> </text> </g> </g> </svg>．这是很容易发现的<年代pan class="equation" id="eq13"> <svg height="16.5375" id="M69" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 16.5375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5375)"> <g transform="translate(72,-58.77)"> <text transform="matrix(1,0,0,-1,155.26,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.3019924" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="12.465491" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.666979" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="26.306313" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="38.346703" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,198.8,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,205.76,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> l</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="18.054333" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="24.255819" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="31.194984" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="42.535206" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,253.49,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,258.37,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="206.38" y="0.63"> （</t年代pan> <tspan style="font-size: 12.50px; " x="210.5435" y="0.63"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="216.795" y="0.63"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="219.92075" y="0.63"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="226.17226" y="0.63"> ）</t年代pan> </text> </g> </g> </svg></span></p> <p>在哪里<年代vg height="10.925" id="M70" style="vertical-align:-3.13504pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.925" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-66.76,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>和<年代vg height="11.075" id="M71" style="vertical-align:-3.25793pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 11.075" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-66.76,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>是常数。因此,<年代pan class="equation" id="eq14"> <svg height="19.475" id="M72" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.475" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.475)"> <g transform="translate(72,-56.42)"> <text transform="matrix(1,0,0,-1,124.23,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.6899996" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.54" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,146.64,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,151.52,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,163.61,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,168.48,58.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3199997" y="-2.51"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="21.36039" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,195.03,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,201.99,61.03)"> <tspan style="font-size: 12.50px; " x="13.89" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.75" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> l</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> n</t年代pan> </text> <text transform="matrix(1,0,0,-1,228.61,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.21"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,236.26,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,254.48,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.21"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,259.36,58.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.6300001" y="-2.51"> +</t年代pan> <tspan style="font-size: 12.50px; " x="19.970221" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,284.52,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,289.39,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="175.36" y="-0.050000001"> （</t年代pan> <tspan style="font-size: 12.50px; " x="179.5235" y="-0.050000001"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="185.77499" y="-0.050000001"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="188.90074" y="-0.050000001"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="195.15225" y="-0.050000001"> ）</t年代pan> </text> </g> </g> </svg></span>边界条件(<一个href="#EEq9">2.2</一个>）的收益率<年代pan class="equation" id="eq15"> <svg height="46.224998" id="M73" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 46.224998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,46.225)"> <g transform="translate(72,-35.02)"> <text transform="matrix(1,0,0,-1,65.68,50.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.6800003" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.54" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,88.09,47.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,92.97,50.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,105.05,47.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,109.93,47.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3199997" y="-2.52"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="48.150002" y="-13.09"> </t年代pan> <tspan style="font-size: 12.50px; " x="22.559999" y="-13.09"> l</t年代pan> <tspan style="font-size: 12.50px; " x="26.035833" y="-13.09"> n</t年代pan> <tspan style="font-size: 12.50px; " x="36.450001" y="-10.58"> </t年代pan> <tspan style="font-size: 12.50px; " x="42.301403" y="-10.58"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,164.96,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,172.61,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,190.83,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,195.71,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.51"> /</t年代pan> <tspan style="font-size: 12.50px; " x="11.405834" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,214.52,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.21"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,219.39,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 132.49,53.51 92.76,0" 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,-1,152.05,39.64)"> <tspan style="font-size: 12.50px; " x="13.9" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.75" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> l</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> n</t年代pan> </text> <text transform="matrix(1,0,0,-1,179.2,44.71)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.2200003"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,184.07,39.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,194.95,44.71)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.2200003"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,199.83,37.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="36.57" y="-13.27"> f</t年代pan> <tspan style="font-size: 12.50px; " x="40.345905" y="-13.27"> o</t年代pan> <tspan style="font-size: 12.50px; " x="46.597404" y="-13.27"> r</t年代pan> <tspan style="font-size: 12.50px; " x="54.9119" y="-13.27"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,262.15,55.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.2200003"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,270.5,50.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,289.41,55.39)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,297.07,50.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,315.29,55.39)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,323.63,50.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,343.07,55.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.2200003"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,347.95,50.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="116.8" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="120.9635" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="127.215" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="130.34074" y="0"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="136.59225" y="0"> ）</t年代pan> </text> </g> </g> </svg></span></p> <p><span class="statement" id="rem2"><span class="statement-title"><i class="statement-title">2.2的话。</我></年代pan>如果我们选择<年代vg height="14.75" id="M74" style="vertical-align:-3.25793pt;width:93.737503px;" version="1.1" viewbox="0 0 93.737503 14.75" width="93.737503" 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"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.01,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-61.79,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-50.75,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-47.53,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> ≡</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-20.92,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-13.96,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≠</t年代pan> <tspan style="font-size: 12.50px; " x="10.640053" y="0"> 0</t年代pan> </text> </g> </g> </svg>或者,如果<年代vg height="14.75" id="M75" style="vertical-align:-3.25793pt;width:99.087502px;" version="1.1" viewbox="0 0 99.087502 14.75" width="99.087502" 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"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.62,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.4,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-51.36,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-48.14,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> ≡</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-22.14,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-11.07,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代pan> </text> </g> </g> </svg>为<年代vg height="12.8875" id="M76" style="vertical-align:-1.76814pt;width:46.512501px;" version="1.1" viewbox="0 0 46.512501 12.8875" width="46.512501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.8875)"> <g transform="translate(72,-61.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.3517642" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="19.392153" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="25.643654" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="30.857405" y="0"> 2</t年代pan> </text> </g> </g> </svg>,<年代vg height="14.5375" id="M77" style="vertical-align:-3.25793pt;width:54.987499px;" version="1.1" viewbox="0 0 54.987499 14.5375" width="54.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5375)"> <g transform="translate(72,-60.37)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.62,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-54.29,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≠</t年代pan> <tspan style="font-size: 12.50px; " x="10.640053" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-37.31,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 2</t年代pan> </text> </g> </g> </svg>，则上述相似解方法的特殊情况失效。还要注意，解决方案并不依赖于参数<年代vg height="11.3375" id="M78" style="vertical-align:-3.25793pt;width:14.125px;" version="1.1" viewbox="0 0 14.125 11.3375" width="14.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3375)"> <g transform="translate(72,-62.93)"> <text transform="matrix(1,0,0,-1,-71.95,66.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.62,63.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>．</年代pan></p> <h5 id="sec2.2">2．2．二维奥恩斯坦-乌伦贝克过程</h5> <p>接下来,我们选择<年代vg height="14.7125" id="M79" style="vertical-align:-3.2316pt;width:87.387497px;" version="1.1" viewbox="0 0 87.387497 14.7125" width="87.387497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.01,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-61.79,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-50.75,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-47.53,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="28.231773" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.283466" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-5.36,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>和<年代vg height="14.75" id="M80" style="vertical-align:-3.25793pt;width:68.474998px;" version="1.1" viewbox="0 0 68.474998 14.75" width="68.474998" 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"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.62,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.4,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-51.36,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-48.14,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> ≡</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-22.14,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>为<年代vg height="12.8875" id="M81" style="vertical-align:-1.76814pt;width:46.512501px;" version="1.1" viewbox="0 0 46.512501 12.8875" width="46.512501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.8875)"> <g transform="translate(72,-61.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.3517642" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="19.392153" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="25.643654" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="30.857405" y="0"> 2</t年代pan> </text> </g> </g> </svg>,在那里<年代vg height="7.1750002" id="M82" 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"> </t年代pan> </text> </g> </g> </svg>是正参数，所以呢<年代vg height="14.6" id="M83" style="vertical-align:-3.13504pt;width:84.525002px;" version="1.1" viewbox="0 0 84.525002 14.6" width="84.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.91,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.03,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-25.71,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-20.83,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ）</t年代pan> </text> </g> </g> </svg>是具有相同无穷小参数的二维Ornstein-Uhlenbeck过程。这一次,(<一个href="#EEq10">2.4</一个>）成为<年代pan class="equation" id="eq16"> <svg height="19.35" id="M84" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.35" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.35)"> <g transform="translate(72,-56.52)"> <text transform="matrix(1,0,0,-1,126.19,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,132.51,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,137.39,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.201488" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,149.82,66.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,158.35,61.14)"> <tspan style="font-size: 12.50px; " x="28.65" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="34.5" y="0.0099999998"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.364987" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="17.304152" y="0"> +</t年代pan> </text> <text transform="matrix(1,0,0,-1,199.18,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,206.83,61.13)"> <tspan style="font-size: 12.50px; " x="24.6" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="32.529999" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.391912" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,245.59,66.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,251.15,61.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.364987" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="17.991817" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="30.032206" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="36.283707" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="213.60001" y="0.0099999998"> （</t年代pan> <tspan style="font-size: 12.50px; " x="217.7635" y="0.0099999998"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="224.015" y="0.0099999998"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="227.14075" y="0.0099999998"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="233.39224" y="0.0099999998"> ）</t年代pan> </text> </g> </g> </svg></span>其通解可表示为<年代pan class="equation" id="eq17"> <svg height="38.575001" id="M85" 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,-1,146.72,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.3019924" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="12.465491" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.666979" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="26.306313" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="38.334198" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,190.25,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,195.13,53.45)"> <tspan style="font-size: 12.50px; " x="13.2" y="7.3299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> E</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="23.77" y="-8.3000002"> </t年代pan> <tspan style="font-size: 12.50px; " x="30.809189" y="-8.3000002"> </t年代pan> </text> <g> <path d="m 218.9,56.57 13.25,0" 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,-1,219.93,44.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,226.25,41.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,233.35,46.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.15" y="-7.3299999"> +</t年代pan> <tspan style="font-size: 12.50px; " x="23.490221" y="-7.3299999"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,262.04,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,266.91,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="191.58" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="195.7435" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="201.995" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="205.12074" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="211.37225" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="217.62375" y="0"> ）</t年代pan> </text> </g> </g> </svg></span>在Ei<年代vg height="13.45" id="M86" style="vertical-align:-2.21957pt;width:15px;" version="1.1" viewbox="0 0 15 13.45" width="15" 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"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</t年代pan> <tspan style="font-size: 12.50px; " x="7.739357" y="0"> ）</t年代pan> </text> </g> </g> </svg>指数积分函数是由<年代pan class="equation" id="eq18"> <svg height="36.887501" id="M87" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 36.887501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,36.8875)"> <g transform="translate(72,-42.49)"> <text transform="matrix(1,0,0,-1,128.47,54.16)"> <tspan style="font-size: 12.50px; " x="53.93" y="7.6999998"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> E</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="17.354164" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="23.593161" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="31.232494" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="43.272884" y="0"> −</t年代pan> </text> <text transform="matrix(1,0,0,-1,189.4,68.19)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代pan> <tspan style="font-size: 8.75px; " x="-1.25" y="25.530001"> −</t年代pan> <tspan style="font-size: 8.75px; " x="4.74512" y="25.530001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,202.29,61.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,207.85,66.41)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <g> <path d="m 202.29,57.28 14.79,0" 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,-1,207.73,45.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.55" y="-8.75"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.201595" y="-8.75"> </t年代pan> <tspan style="font-size: 12.50px; " x="31.067423" y="-8.75"> f</t年代pan> <tspan style="font-size: 12.50px; " x="34.84333" y="-8.75"> o</t年代pan> <tspan style="font-size: 12.50px; " x="41.09483" y="-8.75"> r</t年代pan> <tspan style="font-size: 12.50px; " x="49.421825" y="-8.75"> </t年代pan> <tspan style="font-size: 12.50px; " x="59.124153" y="-8.75"> ></t年代pan> <tspan style="font-size: 12.50px; " x="71.164543" y="-8.75"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="77.416046" y="-8.75"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="250.75999" y="-8.71"> （</t年代pan> <tspan style="font-size: 12.50px; " x="254.92349" y="-8.71"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="261.17499" y="-8.71"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="264.30075" y="-8.71"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="270.55225" y="-8.71"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="276.80374" y="-8.71"> ）</t年代pan> </text> </g> </g> </svg></span>取积分的主值。由此可见,<年代pan class="equation" id="eq19"> <svg height="46.224998" id="M88" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 46.224998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,46.225)"> <g transform="translate(72,-35.02)"> <text transform="matrix(1,0,0,-1,25.48,50.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.6899996" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.54" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,47.9,47.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,52.77,50.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,64.86,47.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,69.73,47.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3299999" y="-2.52"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="35.759998" y="-10.58"> </t年代pan> <tspan style="font-size: 12.50px; " x="41.610001" y="-13.09"> </t年代pan> <tspan style="font-size: 12.50px; " x="50.75" y="-10.58"> </t年代pan> <tspan style="font-size: 12.50px; " x="56.599998" y="-13.09"> </t年代pan> <tspan style="font-size: 12.50px; " x="22.559999" y="-13.09"> E</t年代pan> <tspan style="font-size: 12.50px; " x="30.199333" y="-13.09"> 我</t年代pan> </text> <text transform="matrix(1,0,0,-1,133.2,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,140.86,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,159.08,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,163.95,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9400001" y="-2.51"> /</t年代pan> <tspan style="font-size: 12.50px; " x="11.415834" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,181.69,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,186.56,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="33.169998" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.6300001" y="-2.51"> −</t年代pan> <tspan style="font-size: 12.50px; " x="19.970221" y="-2.51"> E</t年代pan> <tspan style="font-size: 12.50px; " x="27.609554" y="-2.51"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="39.029999" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="46.069187" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,240.04,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.21"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,244.91,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,254.72,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,259.59,58.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 92.29,53.51 173.15,0" 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,-1,112.9,39.64)"> <tspan style="font-size: 12.50px; " x="13.2" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> E</t年代pan> <tspan style="font-size: 12.50px; " x="7.6393328" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="19.049999" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="26.08919" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,146.4,44.71)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.2200003"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,151.28,39.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,161.08,36.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,165.95,37.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="33.18" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.6300001" y="-2.52"> −</t年代pan> <tspan style="font-size: 12.50px; " x="19.970221" y="-2.52"> E</t年代pan> <tspan style="font-size: 12.50px; " x="27.609554" y="-2.52"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="39.029999" y="-2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="46.069187" y="-2.52"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,219.43,44.71)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.2200003"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,224.3,39.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,234.11,36.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,238.98,37.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="37.619999" y="-13.27"> f</t年代pan> <tspan style="font-size: 12.50px; " x="41.383404" y="-13.27"> o</t年代pan> <tspan style="font-size: 12.50px; " x="47.634903" y="-13.27"> r</t年代pan> <tspan style="font-size: 12.50px; " x="55.961903" y="-13.27"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,302.35,55.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,310.7,50.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,329.61,55.39)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,337.26,50.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,355.48,55.39)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,363.83,50.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,383.27,55.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.2200003"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,388.14,50.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="70.349998" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="74.513496" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="80.764999" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="83.890747" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="90.14225" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="96.393745" y="0"> ）</t年代pan> </text> </g> </g> </svg></span></p> <h5 id="sec2.3">2．3.二维贝塞尔过程</h5> <p>我们考虑的最后一个特殊情况是<年代vg height="14.7125" id="M89" style="vertical-align:-3.2316pt;width:124.7125px;" version="1.1" viewbox="0 0 124.7125 14.7125" width="124.7125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.01,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-61.79,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-50.75,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-47.53,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="23.830717" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="33.658077" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="44.998299" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="51.249798" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="55.413296" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="58.88913" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="65.140633" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,24.5,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>和<年代vg height="14.7125" id="M90" style="vertical-align:-3.2316pt;width:62.287498px;" version="1.1" viewbox="0 0 62.287498 14.7125" width="62.287498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.62,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.4,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-51.36,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-48.14,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> ≡</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> 1</t年代pan> </text> </g> </g> </svg>为<年代vg height="12.8875" id="M91" style="vertical-align:-1.76814pt;width:46.512501px;" version="1.1" viewbox="0 0 46.512501 12.8875" width="46.512501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.8875)"> <g transform="translate(72,-61.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.3517642" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="19.392153" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="25.643654" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="30.857405" y="0"> 2</t年代pan> </text> </g> </g> </svg>．再一次,<年代vg height="7.1750002" id="M92" 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"> </t年代pan> </text> </g> </g> </svg>是正参数，所以呢<年代vg height="14.6" id="M93" style="vertical-align:-3.13504pt;width:84.525002px;" version="1.1" viewbox="0 0 84.525002 14.6" width="84.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.91,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.03,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-25.71,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-20.83,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ）</t年代pan> </text> </g> </g> </svg>是一个二维贝塞尔过程。我们假设<年代vg height="11.0625" id="M94" style="vertical-align:-0.30096pt;width:63.349998px;" version="1.1" viewbox="0 0 63.349998 11.0625" width="63.349998" 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"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="32.282745" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="44.323135" y="0"> 2</t年代pan> </text> </g> </g> </svg>(和<年代vg height="13.125" id="M95" style="vertical-align:-1.95624pt;width:32.674999px;" version="1.1" viewbox="0 0 32.674999 13.125" width="32.674999" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.1271896" y="0"> ≠</t年代pan> <tspan style="font-size: 12.50px; " x="19.779745" y="0"> 1</t年代pan> </text> </g> </g> </svg>）;那么，原点是规则边界<年代vg height="14.6" id="M96" style="vertical-align:-3.13504pt;width:33.862499px;" version="1.1" viewbox="0 0 33.862499 14.6" width="33.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.2,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.6" id="M97" style="vertical-align:-3.13504pt;width:33.862499px;" version="1.1" viewbox="0 0 33.862499 14.6" width="33.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.2,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> </text> </g> </g> </svg>(参见卡琳和泰勒[<一个href="#B7">9</一个>，23.8- 239页)。</p> <p>方程(<一个href="#EEq10">2.4</一个>）以形式<年代pan class="equation" id="eq20"> <svg height="17.2875" id="M98" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 17.2875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.2875)"> <g transform="translate(72,-58.17)"> <text transform="matrix(1,0,0,-1,154.44,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.201488" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,166.87,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,175.4,62.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.364987" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="17.304152" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="28.644373" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.696064" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,217.33,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,222.89,62.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.364987" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="17.991817" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="30.032206" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="36.283707" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="235.60001" y="0.029999999"> （</t年代pan> <tspan style="font-size: 12.50px; " x="239.7635" y="0.029999999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="246.015" y="0.029999999"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="249.14075" y="0.029999999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="255.39224" y="0.029999999"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="261.64374" y="0.029999999"> ）</t年代pan> </text> </g> </g> </svg></span>我们发现<年代vg height="13.125" id="M99" style="vertical-align:-1.95624pt;width:32.674999px;" version="1.1" viewbox="0 0 32.674999 13.125" width="32.674999" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.1271896" y="0"> ≠</t年代pan> <tspan style="font-size: 12.50px; " x="19.779745" y="0"> 1</t年代pan> </text> </g> </g> </svg>,函数<年代vg height="13.55" id="M100" style="vertical-align:-2.29482pt;width:25.4375px;" version="1.1" viewbox="0 0 25.4375 13.55" width="25.4375" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.7263741" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="9.8898726" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="16.09136" y="0"> ）</t年代pan> </text> </g> </g> </svg>是<年代pan class="equation" id="EEq11"> <svg height="18.4625" id="M101" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.4625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.4625)"> <g transform="translate(72,-57.23)"> <text transform="matrix(1,0,0,-1,159.51,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.3019924" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="12.465491" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.666979" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="26.306313" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="38.346703" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,203.05,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,207.92,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,214.12,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,232.71,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,249.24,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,254.12,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="204.37" y="-0.46000001"> （</t年代pan> <tspan style="font-size: 12.50px; " x="208.53349" y="-0.46000001"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="214.785" y="-0.46000001"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="217.91075" y="-0.46000001"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="224.16225" y="-0.46000001"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="230.41374" y="-0.46000001"> ）</t年代pan> </text> </g> </g> </svg></span>最后，满足边界条件的解(<一个href="#EEq9">2.2</一个>）是<年代pan class="equation" id="eq21"> <svg height="51.037498" id="M102" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 51.037498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,51.0375)"> <g transform="translate(72,-31.17)"> <text transform="matrix(1,0,0,-1,55.73,47.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.6800003" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.53" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,78.14,44.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,83.01,47.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,95.1,44.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,99.97,45.15)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3299999" y="-2.52"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="22.559999" y="-10.73"> </t年代pan> <tspan style="font-size: 12.50px; " x="28.41" y="-13.25"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,135.26,63.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,142.91,58.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,161.13,63.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,166.01,55.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,171.86,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,190.44,58.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,209.19,64.45)"> <tspan style="font-size: 8.75px; " x="-0.75" y="10.77"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> （</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="11.666416" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="17.661535" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="22.588911" y="0"> ）</t年代pan> </text> <g> <path d="m 122.53,50.79 112.67,0" 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,-1,138.39,35.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,145.79,41.99)"> <tspan style="font-size: 8.75px; " x="-0.75" y="10.77"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> （</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="11.666416" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="17.661535" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="22.597664" y="0"> ）</t年代pan> </text> <text transform="matrix(1,0,0,-1,174.58,35.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,193.33,41.99)"> <tspan style="font-size: 8.75px; " x="-0.75" y="10.77"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> （</t年代pan> <tspan style="font-size: 8.75px; " x="7.2904158" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="11.666416" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="17.661535" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="22.588911" y="0"> ）</t年代pan> </text> <text transform="matrix(1,0,0,-1,246.36,47.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> f</t年代pan> <tspan style="font-size: 12.50px; " x="3.7634029" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="10.014903" y="0"> r</t年代pan> <tspan style="font-size: 12.50px; " x="18.341902" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,272.1,52.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.2200003"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,280.45,47.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,299.37,52.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,307.02,47.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,325.24,52.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,333.59,47.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,353.03,52.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.75" y="9.2200003"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,357.9,47.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="100.59" y="-0.79000002"> （</t年代pan> <tspan style="font-size: 12.50px; " x="104.7535" y="-0.79000002"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="111.005" y="-0.79000002"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="114.13075" y="-0.79000002"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="120.38225" y="-0.79000002"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="126.63375" y="-0.79000002"> ）</t年代pan> </text> </g> </g> </svg></span></p> <p><span class="statement" id="rems1"><span class="statement-title"><i class="statement-title">2.3讲话。</我></年代pan>(1)当<年代vg height="10.85" id="M103" style="vertical-align:-0.1254pt;width:36.137501px;" version="1.1" viewbox="0 0 36.137501 10.85" width="36.137501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.85)"> <g transform="translate(72,-63.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.515023" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="22.555412" y="0"> 1</t年代pan> </text> </g> </g> </svg>，常微分方程(<一个href="#EEq11">2．14</一个>）简化为本节所述的<一个href="#sec2.1">2.1</一个>二维维纳过程，如果<年代vg height="14.75" id="M104" style="vertical-align:-3.25793pt;width:41.325001px;" version="1.1" viewbox="0 0 41.325001 14.75" width="41.325001" 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"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.62,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.28,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 1</t年代pan> </text> </g> </g> </svg>．<br>(2)如果参数<年代vg height="7.1750002" id="M105" 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"> </t年代pan> </text> </g> </g> </svg>是否大于或等于2，原点是不可达边界<年代vg height="14.6" id="M106" style="vertical-align:-3.13504pt;width:33.862499px;" version="1.1" viewbox="0 0 33.862499 14.6" width="33.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.2,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.6" id="M107" style="vertical-align:-3.13504pt;width:33.862499px;" version="1.1" viewbox="0 0 33.862499 14.6" width="33.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.2,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> </text> </g> </g> </svg>；也就是说，它不能在有限的时间内到达。因此，在这种情况下，连续区域可以是两个同心圆之间的区域，但在第一象限内(例如)。</年代pan></p> <p>在下一节中，显式计算函数的问题<年代vg height="14.6" id="M108" style="vertical-align:-3.13504pt;width:54.262501px;" version="1.1" viewbox="0 0 54.262501 14.6" width="54.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.2640028" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="10.427502" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-54.63,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-49.76,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-37.67,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.8,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> </text> </g> </g> </svg>中定义的(<一个href="#EEq7">1．17</一个>）的重要二维扩散过程的角扇区将被处理。这一次，我们将在极坐标下工作，并利用分离变量的方法，这可以看作是相似解方法的一个特殊情况。解将表示为广义傅里叶级数，因此将比本节中获得的简单解更复杂。</p> <h4 id="first-hitting-place-probabilities-when-starting-in-angular-sectors">3.从角扇区开始时的第一次命中位置概率</h4> 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style="font-size: 12.50px; " x="55.838398" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="62.389969" y="0"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="67.953804" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="73.455124" y="0"> ）</t年代pan> </text> </g> </g> </svg>满足Kolmogorov倒向方程(见<一个href="#EEq3">1．12</一个>））<年代pan class="equation" id="eq22"> <svg height="148.375" id="M111" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 148.375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,148.375)"> <g transform="translate(72,46.7)"> <text transform="matrix(1,0,0,-1,19.3,49.6)"> <tspan style="font-size: 12.50px; " x="33.540001" y="-7.25"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.5013199" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.604704" y="0"> ＝</t年代pan> </text> <g> <path d="m 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transform="matrix(1,0,0,-1,193.23,-6.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,198.33,-3.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</t年代pan> </text> <text transform="matrix(1,0,0,-1,211.17,2.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,221.81,-0.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.570816" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,233.24,2.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="12.54" y="-10.23"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,252.66,17.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 1</t年代pan> </text> <g> <path d="m 245.78,5.31 11.75,0" 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,-1,246.67,-6.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,251.77,-3.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</t年代pan> </text> <text transform="matrix(1,0,0,-1,258.73,2.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,269.37,-0.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.5772958" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,281.82,2.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="12.53" y="-10.23"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,301.23,17.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 1</t年代pan> </text> <g> <path d="m 294.35,5.31 11.75,0" 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,-1,295.24,-6.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,300.34,-3.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</t年代pan> </text> <text transform="matrix(1,0,0,-1,307.3,2.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,317.94,-0.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,324.79,2.19)"> <tspan style="font-size: 12.50px; " x="18.790001" y="-9.1400003"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,350.45,8.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,355.33,11.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,362.21,8.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <g> <path d="m 343.58,5.31 23.5,0" 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,-1,350.34,-6.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,355.44,-3.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</t年代pan> </text> <text transform="matrix(1,0,0,-1,368.28,2.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,378.92,-0.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,384,-7.55)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="-323.78" y="29.99"> +</t年代pan> <tspan style="font-size: 12.50px; " x="-312.43979" y="29.99"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,78.5,-40.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,85.46,-40.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,98.19,-40.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,103.06,-40.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9400001" y="2.4100001"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.1" y="-11.65"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,128.03,-31.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <g> <path d="m 121.16,-34.41 11.75,0" 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,-1,124.48,-46.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.6199999" y="-8.75"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,144.74,-40.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,151.59,-37.54)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="12.54" y="-9.1400003"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,171.01,-31.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <g> <path d="m 164.13,-34.41 11.75,0" 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,-1,165.02,-46.65)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,170.12,-43.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,177.08,-37.54)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,187.72,-40.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,192.8,-42.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.74" y="-4.9200001"> +</t年代pan> <tspan style="font-size: 12.50px; " x="23.080221" y="-4.9200001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,222.83,-40.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,229.78,-40.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8600001" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,242.51,-40.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,247.39,-40.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9299998" y="2.4100001"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.09" y="-11.65"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,272.36,-31.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <g> <path d="m 265.48,-34.41 11.75,0" 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,-1,268.81,-46.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.6199999" y="-8.75"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,289.07,-40.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,295.92,-37.54)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="12.53" y="-9.1400003"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,315.33,-31.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <g> <path d="m 308.45,-34.41 11.76,0" 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,-1,309.34,-46.65)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,314.44,-43.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,321.4,-37.54)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,332.04,-40.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,337.13,-42.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.04" y="-4.9200001"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="127.62" y="-51.98"> （</t年代pan> <tspan style="font-size: 12.50px; " x="131.78349" y="-51.98"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="138.035" y="-51.98"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="141.16075" y="-51.98"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="147.41225" y="-51.98"> ）</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="22.3375" id="M112" style="vertical-align:-4.22832pt;width:105.9125px;" version="1.1" viewbox="0 0 105.9125 22.3375" width="105.9125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.3375)"> <g transform="translate(72,-54.13)"> <text transform="matrix(1,0,0,-1,-71.95,58.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.5645552" y="0"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="14.953588" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="26.993977" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="31.157476" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-33.91,63.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-26.26,58.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-8.04,63.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-3.16,58.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> </text> <text transform="matrix(1,0,0,-1,1,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="6.8090558" y="0"> 2</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.6" id="M113" style="vertical-align:-3.13504pt;width:123.2125px;" version="1.1" viewbox="0 0 123.2125 14.6" width="123.2125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.014903" y="0"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="16.403936" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="28.444324" y="0"> 一个</t年代pan> <tspan style="font-size: 12.50px; " x="33.995659" y="0"> r</t年代pan> <tspan style="font-size: 12.50px; " x="38.159157" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="43.710487" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="47.186321" y="0"> 一个</t年代pan> <tspan style="font-size: 12.50px; " x="52.737656" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="63.152653" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="67.316154" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,2.25,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,7.13,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,17.48,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,22.36,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> </text> </g> </g> </svg>．让<年代pan class="equation" id="eq23"> <svg height="19.35" id="M114" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.35" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.35)"> <g transform="translate(72,-56.52)"> <text transform="matrix(1,0,0,-1,9.74,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.96" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="16.809999" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,33.43,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,38.31,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,50.39,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,55.27,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="47.060001" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3199997" y="-2.51"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="15.709033" y="-2.51"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="27.736919" y="-2.51"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="31.212753" y="-2.51"> n</t年代pan> <tspan style="font-size: 12.50px; " x="37.464252" y="-2.51"> f</t年代pan> <tspan style="font-size: 12.50px; " x="54.25" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="61.62677" y="-2.51"> ≥</t年代pan> <tspan style="font-size: 12.50px; " x="73.66716" y="-2.51"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="83.381989" y="-2.51"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="93.246857" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="101.82391" y="-2.51"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="113.8643" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="125.42958" y="-2.51"> o</t年代pan> <tspan style="font-size: 12.50px; " x="131.68108" y="-2.51"> r</t年代pan> <tspan style="font-size: 12.50px; " x="140.00807" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="150.03548" y="-2.51"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="162.07587" y="-2.51"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="172.49088" y="-2.51"> o</t年代pan> <tspan style="font-size: 12.50px; " x="178.74237" y="-2.51"> r</t年代pan> <tspan style="font-size: 12.50px; " x="187.08188" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,248.91,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,260.03,61.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="16.203888" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="22.455387" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="30.082218" y="0"> ∣</t年代pan> <tspan style="font-size: 12.50px; " x="36.88385" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,306.8,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,312.1,61.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="18.041828" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="30.082218" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,349.07,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,352.29,61.13)"> <tspan style="font-size: 12.50px; " x="42.32" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.565515" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="24.605904" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="30.857405" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="36.058651" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="51.59" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="112.46" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="116.6235" y="0"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="122.875" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="126.00075" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="132.25224" y="0"> ）</t年代pan> </text> </g> </g> </svg></span>也就是说,<年代pan class="equation" id="eq24"> <svg height="19.35" id="M115" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.35" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.35)"> <g transform="translate(72,-56.52)"> <text transform="matrix(1,0,0,-1,47.4,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.96" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="16.82" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,71.09,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,75.97,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,88.05,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,92.93,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="40.669998" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="86.870003" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="92.720001" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3199997" y="-2.51"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="21.347885" y="-2.51"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="24.823721" y="-2.51"> n</t年代pan> <tspan style="font-size: 12.50px; " x="31.07522" y="-2.51"> f</t年代pan> <tspan style="font-size: 12.50px; " x="47.860001" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="55.236771" y="-2.51"> ≥</t年代pan> <tspan style="font-size: 12.50px; " x="67.277161" y="-2.51"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="77.004494" y="-2.51"> ∶</t年代pan> </text> <text transform="matrix(1,0,0,-1,192.53,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,197.4,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,209.49,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,214.36,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3299999" y="-2.51"> ∉</t年代pan> <tspan style="font-size: 12.50px; " x="21.357885" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,244.11,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,252.46,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∣</t年代pan> <tspan style="font-size: 12.50px; " x="6.7891288" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,269.14,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,274.44,61.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="18.041828" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="30.082218" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,311.41,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,314.63,61.13)"> <tspan style="font-size: 12.50px; " x="42.32" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.565515" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="24.605904" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="30.857405" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="36.058651" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="51.59" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="150.12" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="154.28349" y="0"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="160.535" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="163.66075" y="0"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="169.91225" y="0"> ）</t年代pan> </text> </g> </g> </svg></span>与<年代vg height="14.3375" id="M116" style="vertical-align:-3.13504pt;width:16.700001px;" version="1.1" viewbox="0 0 16.700001 14.3375" width="16.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.56,60.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>中定义的(<一个href="#EEq6">1．16</一个>）。的概率<年代vg height="14.6" id="M117" style="vertical-align:-3.13504pt;width:54.262501px;" version="1.1" viewbox="0 0 54.262501 14.6" width="54.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.2640028" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="10.427502" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-54.63,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-49.76,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-37.67,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.8,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> </text> </g> </g> </svg>中定义的(<一个href="#EEq7">1．17</一个>）满足相同的偏微分方程<年代vg height="14.6" id="M118" style="vertical-align:-3.13504pt;width:81.162498px;" version="1.1" viewbox="0 0 81.162498 14.6" width="81.162498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.565515" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="16.729013" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-48.34,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-43.47,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-31.38,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-26.51,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.052652" y="0"> ）</t年代pan> </text> </g> </g> </svg>在极坐标下<年代vg height="10.9125" id="M119" style="vertical-align:-0.17555pt;width:34.200001px;" version="1.1" viewbox="0 0 34.200001 10.9125" width="34.200001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.9646511" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="21.005039" y="0"> 0</t年代pan> </text> </g> </g> </svg>．此外,<年代vg height="14.6" id="M120" style="vertical-align:-3.13504pt;width:112.9875px;" version="1.1" viewbox="0 0 112.9875 14.6" width="112.9875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.2640028" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="10.427502" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-54.63,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-49.76,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-37.67,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.8,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="25.943726" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="30.107224" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.208447" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="40.422199" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="46.97377" y="0"> ）</t年代pan> </text> </g> </g> </svg>是这样的,<年代pan class="equation" id="eq25"> <svg height="49.775002" id="M121" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 49.775002" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,49.775)"> <g transform="translate(72,-32.18)"> <text transform="matrix(1,0,0,-1,141.59,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="97.980003" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.3599997" y="-0.0099999998"> （</t年代pan> <tspan style="font-size: 12.50px; " x="12.523499" y="-0.0099999998"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.175095" y="-0.0099999998"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="24.388845" y="-0.0099999998"> </t年代pan> <tspan style="font-size: 12.50px; " x="30.940418" y="-0.0099999998"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="38.567249" y="-0.0099999998"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="50.607635" y="-0.0099999998"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="66.824028" y="-0.0099999998"> ∀</t年代pan> <tspan style="font-size: 12.50px; " x="73.825706" y="-0.0099999998"> </t年代pan> <tspan style="font-size: 12.50px; " x="83.853111" y="-0.0099999998"> ∈</t年代pan> <tspan style="font-size: 12.50px; " x="102.77" y="7.1054274e-015"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="109.0215" y="7.1054274e-015"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="114.22275" y="7.1054274e-015"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,262.37,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,267.24,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.8800001" y="-2.51"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="-82.940002" y="24.34"> </t年代pan> <tspan style="font-size: 12.50px; " x="-140.06" y="21.83"> </t年代pan> <tspan style="font-size: 12.50px; " x="-131.70799" y="21.83"> （</t年代pan> <tspan style="font-size: 12.50px; " x="-127.54449" y="21.83"> </t年代pan> <tspan style="font-size: 12.50px; " x="-122.44328" y="21.83"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="-117.22952" y="21.83"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="-110.97802" y="21.83"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="-103.35119" y="21.83"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="-91.310806" y="21.83"> </t年代pan> <tspan style="font-size: 12.50px; " x="-77.089996" y="21.83"> </t年代pan> <tspan style="font-size: 12.50px; " x="-71.988777" y="21.83"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="-66.787529" y="21.83"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,207.01,33.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,211.89,34.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3199997" y="-2.51"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="21.347885" y="-2.51"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="37.564278" y="-2.51"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="41.040112" y="-2.51"> f</t年代pan> <tspan style="font-size: 12.50px; " x="49.367107" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="57.944168" y="-2.51"> <</t年代pan> <tspan style="font-size: 12.50px; " x="69.984558" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="76.636154" y="-2.51"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="252.86" y="-14.68"> （</t年代pan> <tspan style="font-size: 12.50px; " x="257.0235" y="-14.68"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="263.27499" y="-14.68"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="266.40076" y="-14.68"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="272.65225" y="-14.68"> ）</t年代pan> </text> </g> </g> </svg></span></p> <p>正如在前一节中所述，对于最重要的特定情况，我们将获得第一个击球位置问题的明确(和确切)解决方案。</p> <h5 id="sec3.1">３．１．二维维纳过程</h5> <p>当<年代vg height="14.6" id="M122" style="vertical-align:-3.13504pt;width:84.525002px;" version="1.1" viewbox="0 0 84.525002 14.6" width="84.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.91,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.03,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-25.71,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-20.83,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ）</t年代pan> </text> </g> </g> </svg>是一个二维维纳过程，具有独立分量和无限小参数0和<年代vg height="11.3375" id="M123" style="vertical-align:-3.25793pt;width:14.125px;" version="1.1" viewbox="0 0 14.125 11.3375" width="14.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3375)"> <g transform="translate(72,-62.93)"> <text transform="matrix(1,0,0,-1,-71.95,66.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.62,63.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>，我们必须解的偏微分方程简化为<年代pan class="equation" id="eq26"> <svg height="31.15" id="M124" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 31.15" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,31.15)"> <g transform="translate(72,-47.08)"> <text transform="matrix(1,0,0,-1,151.2,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,157.48,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.570816" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,167.9,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="12.53" y="-7.25"> 1</t年代pan> </text> <g> <path d="m 180.43,59.37 6.26,0" 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,-1,181.01,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.8699999" y="-8.7600002"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,194.16,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,201.01,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="14.4" y="-7.25"> 1</t年代pan> </text> <g> <path d="m 213.54,59.37 9.98,0" 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,-1,213.54,47.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,218.65,50.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,224.72,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,230.99,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.5860481" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,244.14,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="220.61" y="-0.16"> （</t年代pan> <tspan style="font-size: 12.50px; " x="224.7735" y="-0.16"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="231.02499" y="-0.16"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="234.15074" y="-0.16"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="240.40225" y="-0.16"> ）</t年代pan> </text> </g> </g> </svg></span>寻找该形式的解<年代vg height="13.55" id="M125" style="vertical-align:-2.29482pt;width:115.3625px;" version="1.1" viewbox="0 0 115.3625 13.55" width="115.3625" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.2765059" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="10.440005" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.541229" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="20.742477" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.294048" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="34.93338" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="46.97377" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="54.700626" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="58.864124" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="63.965347" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="68.128845" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="77.306046" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="81.469551" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="88.021118" y="0"> ）</t年代pan> </text> </g> </g> </svg>，我们发现<年代pan class="equation" id="eq27"> <svg height="31.15" id="M126" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 31.15" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,31.15)"> <g transform="translate(72,-47.08)"> <text transform="matrix(1,0,0,-1,82.83,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,92.37,61.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,100.9,56.25)"> <tspan style="font-size: 12.50px; " x="57.220001" y="-7.25"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.2647228" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="15.50372" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.018984" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="31.182482" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="37.734055" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="44.673218" y="0"> +</t年代pan> </text> <g> <path d="m 158.12,59.37 6.25,0" 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,-1,158.7,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.8699999" y="-8.7600002"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,175.11,61.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,180.67,56.25)"> <tspan style="font-size: 12.50px; " x="59.080002" y="-7.25"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.2647228" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="15.50372" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.018984" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="31.182482" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="37.734055" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="44.673218" y="0"> +</t年代pan> </text> <g> <path d="m 237.89,59.37 9.97,0" 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,-1,237.89,47.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,242.99,50.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,249.06,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="20.880011" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="27.13151" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,285.62,61.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,294.15,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.715071" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="18.354404" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="30.38229" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="36.633789" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="170.60001" y="-0.16"> （</t年代pan> <tspan style="font-size: 12.50px; " x="174.7635" y="-0.16"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="181.015" y="-0.16"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="184.14075" y="-0.16"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="190.39224" y="-0.16"> ）</t年代pan> </text> </g> </g> </svg></span>这样我们就得到了常微分方程<年代pan class="equation" id="EEq12"> <svg height="46.875" id="M127" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 46.875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,46.875)"> <g transform="translate(72,-34.5)"> <text transform="matrix(1,0,0,-1,163.98,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,173.4,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,181.94,61.94)"> <tspan style="font-size: 12.50px; " x="-52.549999" y="23.639999"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.702568" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="18.341902" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="30.38229" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="37.146412" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="48.661674" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="52.825176" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="59.376747" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="65.615746" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="282.81" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="286.97351" y="0"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="293.22501" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="296.35074" y="0"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="302.60223" y="0"> ）</t年代pan> </text> <text transform="matrix(1,0,0,-1,134.49,43.3)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,139.37,38.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,148.91,43.3)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,157.44,38.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.2647228" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="16.203888" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="27.544109" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="32.645332" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,199.63,43.3)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,205.19,38.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.2647228" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="16.203888" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="27.544109" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="34.308231" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="45.936024" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="50.099522" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="55.200745" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="62.827576" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="74.867966" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="81.119461" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="259.56" y="-0.44999999"> （</t年代pan> <tspan style="font-size: 12.50px; " x="263.72351" y="-0.44999999"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="269.97501" y="-0.44999999"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="273.10074" y="-0.44999999"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="279.35223" y="-0.44999999"> ）</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="10.8125" id="M129" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>为分离常数。常微分方程(<一个href="#EEq12">３．７</一个>）受边界条件的约束<年代pan class="equation" id="EEq14"> <svg height="19.35" id="M130" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.35" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.35)"> <g transform="translate(72,-56.52)"> <text transform="matrix(1,0,0,-1,157.81,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="53.110001" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="58.959999" y="7.1054274e-015"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.51" y="-0.0099999998"> （</t年代pan> <tspan style="font-size: 12.50px; " x="15.673499" y="-0.0099999998"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="21.924999" y="-0.0099999998"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="29.551828" y="-0.0099999998"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="41.592216" y="-0.0099999998"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,223.33,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,228.2,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.3199997" y="-2.51"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="21.36039" y="-2.51"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="27.611889" y="-2.51"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="236.55" y="-2.51"> （</t年代pan> <tspan style="font-size: 12.50px; " x="240.7135" y="-2.51"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="246.965" y="-2.51"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="250.09074" y="-2.51"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="256.34225" y="-2.51"> ）</t年代pan> </text> </g> </g> </svg></span>而<年代pan class="equation" id="eq28"> <svg height="16.5375" id="M131" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 16.5375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5375)"> <g transform="translate(72,-58.77)"> <text transform="matrix(1,0,0,-1,182.83,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="22.030287" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="29.669619" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="41.710007" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="47.96151" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="275.66" y="0.63"> （</t年代pan> <tspan style="font-size: 12.50px; " x="279.82349" y="0.63"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="286.07501" y="0.63"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="289.20074" y="0.63"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="295.45224" y="0.63"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="301.70374" y="0.63"> ）</t年代pan> </text> </g> </g> </svg></span>众所周知，函数<年代vg height="13.45" id="M132" style="vertical-align:-2.21957pt;width:30.200001px;" version="1.1" viewbox="0 0 30.200001 13.45" width="30.200001" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.1772022" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.87977" y="0"> ）</t年代pan> </text> </g> </g> </svg>必须是那种形式的吗<年代pan class="equation" id="eq29"> <svg height="38.575001" id="M133" 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,-1,102.55,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,111.73,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,118.66,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.715071" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="18.354404" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="30.38229" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,154.24,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,161.17,53.45)"> <tspan style="font-size: 12.50px; " x="18.76" y="7.3299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="29.33" y="-7.25"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.543991" y="-7.25"> </t年代pan> <tspan style="font-size: 12.50px; " x="43.145817" y="-7.25"> </t年代pan> </text> <g> <path d="m 190.5,56.57 20.37,0" 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,-1,194.98,44.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,201.53,41.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,212.07,46.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="21.42" y="-7.3299999"> f</t年代pan> <tspan style="font-size: 12.50px; " x="25.195906" y="-7.3299999"> o</t年代pan> <tspan style="font-size: 12.50px; " x="31.447407" y="-7.3299999"> r</t年代pan> <tspan style="font-size: 12.50px; " x="39.761902" y="-7.3299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="49.451725" y="-7.3299999"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="61.492115" y="-7.3299999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="67.743614" y="-7.3299999"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="72.944862" y="-7.3299999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="79.196365" y="-7.3299999"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="84.41011" y="-7.3299999"> ．．．</t年代pan> <tspan style="font-size: 12.50px; " x="99.001114" y="-7.3299999"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="246.42" y="-7.3299999"> （</t年代pan> <tspan style="font-size: 12.50px; " x="250.5835" y="-7.3299999"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="256.83499" y="-7.3299999"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="259.96075" y="-7.3299999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="266.21225" y="-7.3299999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="272.46375" y="-7.3299999"> ）</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="11.0125" id="M134" style="vertical-align:-3.20526pt;width:12.675px;" version="1.1" viewbox="0 0 12.675 11.0125" width="12.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0125)"> <g transform="translate(72,-63.19)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-66.76,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>是一个常数;因此，分离常数必须为<年代pan class="equation" id="eq30"> <svg height="43.037498" id="M135" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 43.037498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,43.0375)"> <g transform="translate(72,-37.57)"> <text transform="matrix(1,0,0,-1,120.92,52.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.227454" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="22.267843" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,149.96,49.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,158.28,52.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="21.799999" y="-8.2200003"> （</t年代pan> <tspan style="font-size: 12.50px; " x="25.963499" y="-8.2200003"> </t年代pan> <tspan style="font-size: 12.50px; " x="32.17749" y="-8.2200003"> </t年代pan> <tspan style="font-size: 12.50px; " x="39.766811" y="-8.2200003"> ）</t年代pan> </text> <text transform="matrix(1,0,0,-1,202.22,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <g> <path d="m 180.08,55.76 27.01,0" 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,-1,187.87,41.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,194.42,46.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.2200003"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,218.25,52.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> f</t年代pan> <tspan style="font-size: 12.50px; " x="3.7759061" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="10.027406" y="0"> r</t年代pan> <tspan style="font-size: 12.50px; " x="18.341902" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="28.031727" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="40.072117" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="46.323616" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="51.524864" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="57.776363" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="62.990112" y="0"> ．．．</t年代pan> <tspan style="font-size: 12.50px; " x="240.24001" y="0.98000002"> （</t年代pan> <tspan style="font-size: 12.50px; " x="244.4035" y="0.98000002"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="250.655" y="0.98000002"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="253.78075" y="0.98000002"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="260.03226" y="0.98000002"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="266.28375" y="0.98000002"> ）</t年代pan> </text> </g> </g> </svg></span></p> <p>接下来，解决(<一个href="#EEq12">3．8</一个>）（这是一个欧拉-柯西方程)<年代vg height="19.325001" id="M136" style="vertical-align:-4.28235pt;width:91.074997px;" version="1.1" viewbox="0 0 91.074997 19.325001" width="91.074997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.325)"> <g transform="translate(72,-56.54)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.227454" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="22.267843" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="30.832397" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="34.995895" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="42.597721" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="48.81171" y="0"> ）</t年代pan> </text> <text transform="matrix(1,0,0,-1,-18.97,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-14.09,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-4.07,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.21"> 0</t年代pan> </text> </g> </g> </svg>就是这样<年代vg height="13.45" id="M137" style="vertical-align:-2.21957pt;width:28.012501px;" version="1.1" viewbox="0 0 28.012501 13.45" width="28.012501" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="18.141853" y="0"> ）</t年代pan> </text> </g> </g> </svg>= 0<年代pan class="equation" id="eq31"> <svg height="18.4625" id="M138" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.4625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.4625)"> <g transform="translate(72,-57.23)"> <text transform="matrix(1,0,0,-1,155.26,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,162.99,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,169.92,61.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.2647228" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="16.891554" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="28.931942" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="34.483273" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="40.734776" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="46.986275" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="51.762421" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="55.238255" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="62.527504" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,237.55,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.6622076" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="12.095264" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,254.24,63.85)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,258.36,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="200.13" y="-0.46000001"> （</t年代pan> <tspan style="font-size: 12.50px; " x="204.2935" y="-0.46000001"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="210.545" y="-0.46000001"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="213.67075" y="-0.46000001"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="219.92226" y="-0.46000001"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="226.17375" y="-0.46000001"> ）</t年代pan> </text> </g> </g> </svg></span>然后我们考虑无穷级数<年代pan class="equation" id="eq32"> <svg height="48.200001" id="M139" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.200001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.2)"> <g transform="translate(72,-33.44)"> <text transform="matrix(1,0,0,-1,123.47,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.3520041" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="12.515503" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.616728" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="22.830479" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="29.38205" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="37.008881" y="0"> ＝</t年代pan> </text> <text transform="matrix(1,0,0,-1,176.55,65.71)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代pan> </text> <text transform="matrix(1,0,0,-1,172.53,43.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,173.24,36.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> ＝</t年代pan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,188.68,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,194.96,46.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,201.89,49.77)"> <tspan style="font-size: 12.50px; " x="18.76" y="7.3299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="29.33" y="-7.25"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.543991" y="-7.25"> </t年代pan> <tspan style="font-size: 12.50px; " x="43.145817" y="-7.25"> </t年代pan> </text> <g> <path d="m 231.22,52.9 20.37,0" 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,-1,235.69,41.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,242.24,37.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,252.78,42.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.47" y="-7.3299999"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,269.35,54.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.6622076" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="12.095264" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,286.04,52.58)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,290.16,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="168.33" y="0.17"> （</t年代pan> <tspan style="font-size: 12.50px; " x="172.4935" y="0.17"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="178.745" y="0.17"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="181.87074" y="0.17"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="188.12225" y="0.17"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="194.37375" y="0.17"> ）</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="11.0125" id="M140" style="vertical-align:-3.20526pt;width:14.025px;" version="1.1" viewbox="0 0 14.025 11.0125" width="14.025" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0125)"> <g transform="translate(72,-63.19)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>是一个常数。这个级数，作为<年代vg height="10.7375" id="M141" 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"> </t年代pan> </text> </g> </g> </svg>，是一个傅里叶级数。<年代vg height="0.125" id="M142" style="vertical-align:-0.0pt;width:5.3375001px;" version="1.1" viewbox="0 0 5.3375001 0.125" width="5.3375001" 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>的条件<年代vg height="13.55" id="M143" style="vertical-align:-2.29482pt;width:68.599998px;" version="1.1" viewbox="0 0 68.599998 13.55" width="68.599998" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.2765059" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="10.440005" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.0916" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="22.292849" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="28.844421" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="36.483753" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="48.524143" y="0"> 1</t年代pan> </text> </g> </g> </svg>意味着<年代pan class="equation" id="eq33"> <svg height="40.287498" id="M144" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 40.287498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,40.2875)"> <g transform="translate(72,-39.77)"> <text transform="matrix(1,0,0,-1,62.17,52.08)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,68.45,48.95)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,76.77,52.08)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="15.82" y="-7.25"> 2</t年代pan> </text> <g> <path d="m 90,55.2 11.43,0" 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,-1,90,43.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,96.55,40.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,104.71,44.38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,111.71,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,116.3,63.92)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,110.46,40.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,122.5,52.08)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,129.9,57.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="15.66608" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="18.099136" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,152.59,54.96)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,158.8,52.08)"> <tspan style="font-size: 12.50px; " x="18.75" y="7.3299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="29.33" y="-7.25"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.543991" y="-7.25"> </t年代pan> <tspan style="font-size: 12.50px; " x="43.133312" y="-7.25"> </t年代pan> </text> <g> <path d="m 188.13,55.2 20.36,0" 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,-1,192.6,43.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,199.15,40.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,209.69,44.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.46" y="-7.3299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.111595" y="-7.3299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="28.126499" y="-7.3299999"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="40.166889" y="-7.3299999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="46.418388" y="-7.3299999"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,263.52,57.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="15.657328" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="18.090384" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,286.2,54.96)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,291.52,60.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="12.728054" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.979553" y="0"> ）</t年代pan> </text> <text transform="matrix(1,0,0,-1,314.67,65.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</t年代pan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,332.66,60.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> 1</t年代pan> </text> <g> <path d="m 291.52,55.2 58.74,0" 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,-1,313.98,43.32)"> <tspan style="font-size: 12.50px; " x="37.470001" y="-8.7600002"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.2139912" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="144.50999" y="-9.4399996"> （</t年代pan> <tspan style="font-size: 12.50px; " x="148.67349" y="-9.4399996"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="154.925" y="-9.4399996"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="158.05075" y="-9.4399996"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="164.30225" y="-9.4399996"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="170.55374" y="-9.4399996"> ）</t年代pan> </text> </g> </g> </svg></span>因此，解决方案是<年代pan class="equation" id="eq34"> <svg height="48.200001" id="M145" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.200001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.2)"> <g transform="translate(72,-33.44)"> <text transform="matrix(1,0,0,-1,85.51,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.3520041" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="12.515503" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.616728" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="22.830479" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="29.38205" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="37.021381" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="49.049271" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,144.85,65.71)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代pan> </text> <text transform="matrix(1,0,0,-1,140.82,43.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,141.54,36.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> ＝</t年代pan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,156.98,44.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.71" y="-12.17"> </t年代pan> </text> <g> <path d="m 165.54,52.9 7.4,0" 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,-1,165.54,41.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.5900002" y="-3.8299999"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,181.74,61.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="9.6622076" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="12.095264" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,198.43,58.96)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,203.74,57.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="20.367388" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="33.09544" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="39.346943" y="0"> ）</t年代pan> </text> <text transform="matrix(1,0,0,-1,247.26,63.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</t年代pan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</t年代pan> </text> <g> <path d="m 203.74,52.9 58.74,0" 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,-1,226.2,41.02)"> <tspan style="font-size: 12.50px; " x="58.32" y="-1.42"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.2139912" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="39.560001" y="-8.75"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="44.423668" y="-8.75"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="47.899502" y="-8.75"> n</t年代pan> <tspan style="font-size: 12.50px; " x="68.889999" y="-16"> </t年代pan> <tspan style="font-size: 12.50px; " x="75.103989" y="-16"> </t年代pan> <tspan style="font-size: 12.50px; " x="82.705818" y="-16"> </t年代pan> </text> <g> <path d="m 295.09,52.9 20.37,0" 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,-1,299.56,41.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,306.11,37.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,316.65,42.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.46" y="-7.3299999"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="141.84" y="-7.1599998"> （</t年代pan> <tspan style="font-size: 12.50px; " x="146.00349" y="-7.1599998"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="152.255" y="-7.1599998"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="155.38075" y="-7.1599998"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="161.63225" y="-7.1599998"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="167.88374" y="-7.1599998"> ）</t年代pan> </text> </g> </g> </svg></span>为<年代vg height="14.75" id="M146" style="vertical-align:-3.25793pt;width:69.1875px;" version="1.1" viewbox="0 0 69.1875 14.75" width="69.1875" 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"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="31.782625" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="43.823013" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-21.57,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>和<年代vg height="12.3" id="M147" style="vertical-align:-1.29163pt;width:62.349998px;" version="1.1" viewbox="0 0 62.349998 12.3" width="62.349998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.3)"> <g transform="translate(72,-62.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="30.332277" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="42.372665" y="0"> </t年代pan> </text> </g> </g> </svg>．</p> <p><span class="statement" id="rem3"><span class="statement-title"><i class="statement-title">3.1的话。</我></年代pan>的无穷小均值<年代vg height="14.7125" id="M148" style="vertical-align:-3.2316pt;width:31.799999px;" version="1.1" viewbox="0 0 31.799999 14.7125" width="31.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.85,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> </text> </g> </g> </svg>不等于0时，我们不能分离偏微分方程中的变量<年代vg height="13.55" id="M149" style="vertical-align:-2.29482pt;width:39.462502px;" version="1.1" viewbox="0 0 39.462502 13.55" width="39.462502" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.2765059" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="10.440005" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.541229" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="20.742477" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.294048" y="0"> ）</t年代pan> </text> </g> </g> </svg>．在Section中<一个href="#sec2">2</一个>在美国，我们所使用的技术能够发挥作用的情况实际上是相当少的。幸运的是,这<我>做</我>在应用程序的最重要的情况下工作。</年代pan></p> <h5 id="sec3.2">３.２．二维奥恩斯坦-乌伦贝克过程</h5> <p>当<年代vg height="14.6" id="M150" style="vertical-align:-3.13504pt;width:33.862499px;" version="1.1" viewbox="0 0 33.862499 14.6" width="33.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.2,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.6" id="M151" style="vertical-align:-3.13504pt;width:33.862499px;" version="1.1" viewbox="0 0 33.862499 14.6" width="33.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.2,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> </text> </g> </g> </svg>具有无限小参数的独立奥恩斯坦-乌伦贝克过程<年代vg height="14.7125" id="M152" style="vertical-align:-3.2316pt;width:51.3125px;" version="1.1" viewbox="0 0 51.3125 14.7125" width="51.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="8.5645552" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.603744" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-46.46,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-43.24,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> </text> </g> </g> </svg>和<年代vg height="11.3375" id="M153" style="vertical-align:-3.25793pt;width:14.125px;" version="1.1" viewbox="0 0 14.125 11.3375" width="14.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.3375)"> <g transform="translate(72,-62.93)"> <text transform="matrix(1,0,0,-1,-71.95,66.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.62,63.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>为<年代vg height="12.8875" id="M154" style="vertical-align:-1.76814pt;width:46.512501px;" version="1.1" viewbox="0 0 46.512501 12.8875" width="46.512501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.8875)"> <g transform="translate(72,-61.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.3517642" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="19.392153" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="25.643654" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="30.857405" y="0"> 2</t年代pan> </text> </g> </g> </svg>，我们必须解偏微分方程<年代pan class="equation" id="eq35"> <svg height="31.15" id="M155" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 31.15" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,31.15)"> <g transform="translate(72,-47.08)"> <text transform="matrix(1,0,0,-1,114.16,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代pan> </text> <g> <path d="m 114.16,59.37 6.25,0" 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,-1,114.16,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="7.4499998" y="-8.7600002"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,127.93,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,134.89,51.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.96" y="-4.9200001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,150.13,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.570816" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,160.55,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="12.54" y="-7.25"> 1</t年代pan> </text> <g> <path d="m 173.09,59.37 6.25,0" 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,-1,173.66,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.8800001" y="-8.7600002"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,186.81,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,193.66,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="14.4" y="-7.25"> 1</t年代pan> </text> <g> <path d="m 206.2,59.37 9.97,0" 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,-1,206.2,47.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,211.3,50.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,217.37,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,223.65,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.5772958" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,233.32,51.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.74" y="-4.9200001"> −</t年代pan> <tspan style="font-size: 12.50px; " x="23.080221" y="-4.9200001"> </t年代pan> <tspan style="font-size: 12.50px; " x="30.131912" y="-4.9200001"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.233135" y="-4.9200001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,274.83,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,282.37,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="18.291889" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="176.12" y="-0.16"> （</t年代pan> <tspan style="font-size: 12.50px; " x="180.28349" y="-0.16"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="186.535" y="-0.16"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="189.66075" y="-0.16"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="195.91225" y="-0.16"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="202.16374" y="-0.16"> ）</t年代pan> </text> </g> </g> </svg></span>写作<年代vg height="13.55" id="M156" style="vertical-align:-2.29482pt;width:115.3625px;" version="1.1" viewbox="0 0 115.3625 13.55" width="115.3625" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.2765059" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="10.440005" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.541229" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="20.742477" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.294048" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="34.93338" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="46.97377" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="54.700626" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="58.864124" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="63.965347" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="68.128845" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="77.306046" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="81.469551" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="88.021118" y="0"> ）</t年代pan> </text> </g> </g> </svg>，我们得到常微分方程<年代pan class="equation" id="eq36"> <svg height="59.5" id="M157" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 59.5" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,59.5)"> <g transform="translate(72,-24.4)"> <text transform="matrix(1,0,0,-1,166.06,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,175.49,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,184.02,61.94)"> <tspan style="font-size: 12.50px; " x="-90.860001" y="25.49"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.715071" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="18.341902" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="30.38229" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="37.146412" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="48.661674" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="52.825176" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="59.376747" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="65.62825" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="274.47" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="278.63348" y="0"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="284.88501" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="288.01074" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="294.26224" y="0"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="300.51376" y="0"> ）</t年代pan> </text> <text transform="matrix(1,0,0,-1,98.26,41.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,103.13,36.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,112.67,41.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,121.21,36.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.2647228" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="16.203888" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="27.544109" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="32.645332" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,163.4,41.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,168.96,36.46)"> <tspan style="font-size: 12.50px; " x="37.07" y="-7.2399998"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.2647228" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="27.544109" y="0"> 2</t年代pan> </text> <g> <path d="m 203.95,39.58 11.2,0" 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,-1,203.95,27.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,210.28,24.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,216.35,36.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,221.45,41.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</t年代pan> </text> <text transform="matrix(1,0,0,-1,226.32,36.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,235.86,41.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,241.42,36.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.2647228" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="16.203888" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="27.544109" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="34.308231" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="45.936024" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="50.099522" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="55.200745" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="62.840076" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="74.867966" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="81.119461" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="217.07001" y="2.75"> （</t年代pan> <tspan style="font-size: 12.50px; " x="221.23351" y="2.75"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="227.485" y="2.75"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="230.61075" y="2.75"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="236.86224" y="2.75"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="243.11375" y="2.75"> ）</t年代pan> </text> </g> </g> </svg></span>边界条件与本节相同<一个href="#sec3.1">3．1</一个>．因此，我们发现我们仍然拥有<年代vg height="19.325001" id="M159" style="vertical-align:-4.28235pt;width:124.975px;" version="1.1" viewbox="0 0 124.975 19.325001" width="124.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.325)"> <g transform="translate(72,-56.54)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.227454" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="22.267843" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-42.91,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-34.59,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="20.592442" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="24.755939" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="32.357765" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="38.571754" y="0"> ）</t年代pan> </text> <text transform="matrix(1,0,0,-1,8.16,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,13.03,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,23.06,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="9.21"> 0</t年代pan> </text> </g> </g> </svg>和<年代pan class="equation" id="eq37"> <svg height="38.575001" id="M160" 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,-1,104.1,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,113.28,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,120.21,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.702568" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="18.341902" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="30.38229" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,155.79,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,162.72,53.45)"> <tspan style="font-size: 12.50px; " x="18.76" y="7.3299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="29.33" y="-7.25"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.543991" y="-7.25"> </t年代pan> <tspan style="font-size: 12.50px; " x="43.133312" y="-7.25"> </t年代pan> </text> <g> <path d="m 192.05,56.57 20.37,0" 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,-1,196.52,44.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,203.07,41.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,213.61,46.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="21.43" y="-7.3299999"> f</t年代pan> <tspan style="font-size: 12.50px; " x="25.193403" y="-7.3299999"> o</t年代pan> <tspan style="font-size: 12.50px; " x="31.444902" y="-7.3299999"> r</t年代pan> <tspan style="font-size: 12.50px; " x="39.759399" y="-7.3299999"> n</t年代pan> <tspan style="font-size: 12.50px; " x="49.486732" y="-7.3299999"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="61.527122" y="-7.3299999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="67.778618" y="-7.3299999"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="72.992371" y="-7.3299999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="79.243874" y="-7.3299999"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="84.445122" y="-7.3299999"> ．．．</t年代pan> <tspan style="font-size: 12.50px; " x="244.88" y="-7.3299999"> （</t年代pan> <tspan style="font-size: 12.50px; " x="249.0435" y="-7.3299999"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="255.295" y="-7.3299999"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="258.42075" y="-7.3299999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="264.67224" y="-7.3299999"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="270.92374" y="-7.3299999"> ）</t年代pan> </text> </g> </g> </svg></span></p> <p>(的通解<一个href="#eq36">3.19</一个>）可以写成<年代pan class="equation" id="eq38"> <svg height="57.974998" id="M161" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 57.974998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,57.975)"> <g transform="translate(72,-25.62)"> <text transform="matrix(1,0,0,-1,-50.78,55.9)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="20.880011" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="28.519342" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="43.060333" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-2.52,52.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,2.35,55.9)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,7.45,60.9)"> <tspan style="font-size: 8.75px; " x="10.37" y="-0.37"> √</t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 2</t年代pan> </text> <g> <path d="m 25.95,69.5 10.73,0" style="fill:none;stroke:#000000;stroke-width:0.57800001;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,25.95,60.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,37.17,55.9)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.78" y="4.9200001"> </t年代pan> <tspan style="font-size: 12.50px; " x="23.139999" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="32.900002" y="-7.25"> 1</t年代pan> </text> <g> <path d="m 70.07,59.02 6.25,0" 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,-1,70.07,47.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="7.4499998" y="-9.29"> √</t年代pan> </text> <g> <path d="m 89.12,68.19 15.33,0" 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,-1,89.12,55.9)"> <tspan style="font-size: 12.50px; " x="40.91" y="-0.52999997"> √</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="8.5645552" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.328678" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="20.529926" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="29.569595" y="0"> −</t年代pan> </text> <g> <path d="m 141.64,68.19 15.33,0" 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,-1,141.64,55.9)"> <tspan style="font-size: 12.50px; " x="30.299999" y="-7.25"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="8.5645552" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.328678" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="20.529926" y="0"> −</t年代pan> </text> <g> <path d="m 171.94,59.02 6.25,0" 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,-1,171.94,47.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="7.4400001" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="14.216626" y="-8.7600002"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,191.26,60.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,196.14,50.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.6800003" y="-4.9200001"> +</t年代pan> <tspan style="font-size: 12.50px; " x="21.23" y="-5.27"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,222.56,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,227.44,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,232.54,61.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="4.3699999" y="-0.37"> √</t年代pan> </text> <g> <path d="m 245.04,69.85 10.73,0" style="fill:none;stroke:#000000;stroke-width:0.57800001;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,245.04,61.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,256.27,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.77" y="4.9200001"> </t年代pan> <tspan style="font-size: 12.50px; " x="24.33" y="-7.25"> 1</t年代pan> </text> <g> <path d="m 280.6,59.37 6.25,0" 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,-1,280.6,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="7.4499998" y="-9.9399996"> √</t年代pan> </text> <g> <path d="m 299.65,69.19 15.33,0" 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,-1,299.65,56.25)"> <tspan style="font-size: 12.50px; " x="40.91" y="-1.1799999"> √</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="8.5645552" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.328678" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="20.529926" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="29.557093" y="0"> +</t年代pan> </text> <g> <path d="m 352.16,69.19 15.33,0" 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,-1,352.16,56.25)"> <tspan style="font-size: 12.50px; " x="30.299999" y="-7.25"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="8.5645552" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.328678" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="20.529926" y="0"> −</t年代pan> </text> <g> <path d="m 382.46,59.37 6.25,0" 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,-1,382.46,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="7.4499998" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="14.226626" y="-8.7600002"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,401.79,61.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,406.66,51.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.6899996" y="-4.9200001"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="51.830002" y="5.6399999"> （</t年代pan> <tspan style="font-size: 12.50px; " x="55.9935" y="5.6399999"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="62.244999" y="5.6399999"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="65.37075" y="5.6399999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="71.622246" y="5.6399999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="77.873749" y="5.6399999"> ）</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="14.75" id="M162" style="vertical-align:-3.25793pt;width:81.650002px;" version="1.1" viewbox="0 0 81.650002 14.75" width="81.650002" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.239957" y="0"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="16.62899" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="28.669378" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="37.233932" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="43.485435" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="50.537125" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="54.012959" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-11.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>和<年代vg height="13.45" id="M163" style="vertical-align:-2.21957pt;width:52.674999px;" version="1.1" viewbox="0 0 52.674999 13.45" width="52.674999" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.565515" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="16.729013" y="0"> ⋅</t年代pan> <tspan style="font-size: 12.50px; " x="20.304873" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="25.506121" y="0"> ⋅</t年代pan> <tspan style="font-size: 12.50px; " x="29.081978" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="34.295731" y="0"> ⋅</t年代pan> <tspan style="font-size: 12.50px; " x="37.871586" y="0"> ）</t年代pan> </text> </g> </g> </svg>是一个合流的超几何函数(见阿布拉莫维茨和斯特贡[<一个href="#B1">10</一个>，p . 504])。我们立刻发现，我们必须做出选择<年代vg height="10.925" id="M164" style="vertical-align:-3.13504pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.925" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-66.76,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>等于零。然后我们考虑无穷级数<年代pan class="equation" id="eq39"> <svg height="48.200001" id="M165" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.200001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.2)"> <g transform="translate(72,-33.44)"> <text transform="matrix(1,0,0,-1,52.46,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.3520041" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="12.515503" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.616728" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="22.830479" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="29.38205" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="37.008881" y="0"> ＝</t年代pan> </text> <text transform="matrix(1,0,0,-1,105.54,65.71)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代pan> </text> <text transform="matrix(1,0,0,-1,101.52,43.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,102.24,36.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> ＝</t年代pan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,117.67,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,123.95,46.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,130.88,49.77)"> <tspan style="font-size: 12.50px; " x="18.76" y="7.3299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="29.33" y="-7.25"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.543991" y="-7.25"> </t年代pan> <tspan style="font-size: 12.50px; " x="43.145817" y="-7.25"> </t年代pan> </text> <g> <path d="m 160.21,52.9 20.37,0" 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,-1,164.68,41.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,171.24,37.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,181.78,42.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.46" y="-7.3299999"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,198.34,54.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="8.7257442" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="14.038208" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="16.471264" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,219.4,52.58)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,223.53,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.77" y="7.3299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="28.280001" y="-7.25"> </t年代pan> <tspan style="font-size: 12.50px; " x="34.493992" y="-7.25"> </t年代pan> </text> <g> <path d="m 249.87,52.9 17.68,0" 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,-1,249.87,41.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,262.68,37.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,268.75,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="14.228414" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="26.780001" y="-7.25"> </t年代pan> <tspan style="font-size: 12.50px; " x="32.993992" y="-7.25"> </t年代pan> </text> <g> <path d="m 295.53,52.9 13.81,0" 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,-1,296.72,41.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,303.27,37.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,310.54,49.77)"> <tspan style="font-size: 12.50px; " x="14.97" y="-7.25"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> −</t年代pan> </text> <g> <path d="m 325.51,52.9 6.25,0" 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,-1,325.51,41.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="7.4400001" y="-8.75"> </t年代pan> <tspan style="font-size: 12.50px; " x="14.216626" y="-8.75"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,344.83,54.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,349.71,42.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.46" y="-7.3299999"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="108.78" y="-7.1599998"> （</t年代pan> <tspan style="font-size: 12.50px; " x="112.9435" y="-7.1599998"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="119.195" y="-7.1599998"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="122.32075" y="-7.1599998"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="128.57225" y="-7.1599998"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="134.82375" y="-7.1599998"> ）</t年代pan> </text> </g> </g> </svg></span>利用边界条件<年代vg height="13.55" id="M166" style="vertical-align:-2.29482pt;width:41.400002px;" version="1.1" viewbox="0 0 41.400002 13.55" width="41.400002" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.2765059" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="10.440005" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.0916" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="22.292849" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="28.844421" y="0"> ）</t年代pan> </text> </g> </g> </svg>= 1，我们发现<年代pan class="equation" id="eq40"> <svg height="48.200001" id="M167" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.200001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.2)"> <g transform="translate(72,-33.44)"> <text transform="matrix(1,0,0,-1,-3.77,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.3520041" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="12.515503" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.616728" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="22.830479" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="29.38205" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="37.021381" y="0"> ＝</t年代pan> </text> <text transform="matrix(1,0,0,-1,49.31,65.71)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代pan> </text> <text transform="matrix(1,0,0,-1,45.29,43.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,46.01,36.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> ＝</t年代pan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,62.64,57.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="20.367388" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="33.09544" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="39.346943" y="0"> ）</t年代pan> </text> <text transform="matrix(1,0,0,-1,106.16,63.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> +</t年代pan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</t年代pan> </text> <g> <path d="m 62.64,52.9 58.73,0" 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,-1,85.1,41.02)"> <tspan style="font-size: 12.50px; " x="58.310001" y="-1.42"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.2139912" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="39.549999" y="-8.75"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="44.413666" y="-8.75"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="47.8895" y="-8.75"> n</t年代pan> <tspan style="font-size: 12.50px; " x="68.889999" y="-16"> </t年代pan> <tspan style="font-size: 12.50px; " x="75.103989" y="-16"> </t年代pan> <tspan style="font-size: 12.50px; " x="82.693314" y="-16"> </t年代pan> </text> <g> <path d="m 153.99,52.9 20.36,0" 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,-1,158.46,41.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,165.01,37.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,175.55,42.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.46" y="-2.4100001"> </t年代pan> <tspan style="font-size: 12.50px; " x="21.17" y="-14.58"> </t年代pan> </text> <g> <path d="m 195.57,52.9 7.4,0" 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,-1,195.57,41.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.6000004" y="-3.8299999"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,211.77,61.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="8.7257442" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="14.038208" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="16.471264" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,232.84,58.96)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,239.3,60.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.78" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="21.629999" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.84399" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.433311" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="38.909145" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="45.160645" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,291.02,57.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,295.9,60.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="14.228414" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="25.581139" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="31.79513" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="39.396954" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="42.872787" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,345.33,57.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,350.2,60.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="15.853804" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="20.017303" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="26.268803" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="29.744637" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="35.996136" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="42.235134" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="49.011761" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,404.33,65.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,409.2,57.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 238.15,52.9 178.05,0" 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,-1,238.15,39.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.78" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="21.629999" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.84399" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.433311" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="38.909145" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="45.160645" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,289.87,35.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,294.75,39.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="14.228414" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="25.581139" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="31.79513" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="39.396954" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="42.872787" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,344.17,35.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,349.05,39.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="15.853804" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="20.017303" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="26.268803" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="29.744637" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="35.996136" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="42.235134" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="49.011761" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,405.48,44.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,410.35,36.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.0500002" y="-13.26"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="48.139999" y="-13.09"> （</t年代pan> <tspan style="font-size: 12.50px; " x="52.303497" y="-13.09"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="58.555" y="-13.09"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="61.680748" y="-13.09"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="67.932251" y="-13.09"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="74.183746" y="-13.09"> ）</t年代pan> </text> </g> </g> </svg></span>为<年代vg height="14.75" id="M168" style="vertical-align:-3.25793pt;width:69.1875px;" version="1.1" viewbox="0 0 69.1875 14.75" width="69.1875" 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"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="31.782625" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="43.823013" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-21.57,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>和<年代vg height="12.3" id="M169" style="vertical-align:-1.29163pt;width:62.349998px;" version="1.1" viewbox="0 0 62.349998 12.3" width="62.349998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.3)"> <g transform="translate(72,-62.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="30.332277" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="42.372665" y="0"> </t年代pan> </text> </g> </g> </svg>．</p> <h5 id="sec3.3">３．３．二维贝塞尔过程</h5> <p>最后,与<年代vg height="14.7125" id="M170" style="vertical-align:-3.2316pt;width:129.925px;" version="1.1" viewbox="0 0 129.925 14.7125" width="129.925" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.01,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-61.79,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-50.75,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-47.53,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="23.830717" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="33.658077" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="44.998299" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="51.249798" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="55.413296" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="58.88913" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="65.140633" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,24.5,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg> <svg height="13.45" id="M171" style="vertical-align:-2.21957pt;width:112.8125px;" version="1.1" viewbox="0 0 112.8125 13.45" width="112.8125" 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"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="13.87833" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="25.918718" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="36.446243" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="48.486633" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="54.738132" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="59.939381" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="69.079079" y="0"> ≠</t年代pan> <tspan style="font-size: 12.50px; " x="79.731628" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="85.983131" y="0"> ）</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.7125" id="M172" style="vertical-align:-3.2316pt;width:62.287498px;" version="1.1" viewbox="0 0 62.287498 14.7125" width="62.287498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.62,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.4,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-51.36,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-48.14,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> ≡</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> 1</t年代pan> </text> </g> </g> </svg>为<年代vg height="12.8875" id="M173" style="vertical-align:-1.76814pt;width:46.512501px;" version="1.1" viewbox="0 0 46.512501 12.8875" width="46.512501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.8875)"> <g transform="translate(72,-61.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.3517642" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="19.392153" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="25.643654" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="30.857405" y="0"> 2</t年代pan> </text> </g> </g> </svg>，得到偏微分方程<年代pan class="equation" id="eq41"> <svg height="31.262501" id="M174" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 31.262501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,31.2625)"> <g transform="translate(72,-46.99)"> <text transform="matrix(1,0,0,-1,33.35,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代pan> </text> <g> <path d="m 33.35,59.28 6.26,0" 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,-1,33.35,47.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="9.5299997" y="-3.8299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.5" y="-8.75"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,58.13,53.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.570816" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,68.54,56.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="12.54" y="-7.25"> 1</t年代pan> </text> <g> <path d="m 81.08,59.28 6.25,0" 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,-1,81.66,47.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.8699999" y="-8.75"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,94.81,53.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,101.65,56.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="14.4" y="-7.25"> 1</t年代pan> </text> <g> <path d="m 114.19,59.28 9.98,0" 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,-1,114.19,47.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,119.29,50.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,125.36,56.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,131.64,53.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.5860481" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,141.31,51.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.74" y="-4.9200001"> +</t年代pan> <tspan style="font-size: 12.50px; " x="24.280001" y="-12.17"> </t年代pan> <tspan style="font-size: 12.50px; " x="34.107357" y="-12.17"> −</t年代pan> <tspan style="font-size: 12.50px; " x="45.447578" y="-12.17"> 1</t年代pan> </text> <g> <path d="m 165.59,59.28 27.43,0" 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,-1,176.18,47.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="20.120001" y="-3.8299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="30.280001" y="-16"> 2</t年代pan> </text> <g> <path d="m 206.46,59.28 6.25,0" 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,-1,207.03,47.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.8699999" y="-8.75"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,220.18,53.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,227.03,56.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="14.4" y="-7.25"> 1</t年代pan> </text> <g> <path d="m 239.57,59.28 9.97,0" 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,-1,239.57,47.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,244.67,50.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,252.82,51.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.5600004" y="-12.17"> c</t年代pan> <tspan style="font-size: 12.50px; " x="14.111332" y="-12.17"> o</t年代pan> <tspan style="font-size: 12.50px; " x="20.362831" y="-12.17"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="27.301996" y="-12.17"> </t年代pan> </text> <g> <path d="m 261.38,59.28 25.3,0" 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,-1,262.42,47.41)"> <tspan style="font-size: 12.50px; " x="28.24" y="-8.75"> −</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="41.810001" y="-16"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="46.673668" y="-16"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="50.149502" y="-16"> n</t年代pan> <tspan style="font-size: 12.50px; " x="58.476498" y="-16"> </t年代pan> </text> <g> <path d="m 303.2,59.28 25.3,0" 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,-1,303.2,47.41)"> <tspan style="font-size: 12.50px; " x="26.49" y="-3.8299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="36.18" y="-8.75"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="18.741997" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,345.66,53.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,350.74,51.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.44" y="-4.9200001"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="24.467886" y="-4.9200001"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="30.719385" y="-4.9200001"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="107.75" y="-5.1300001"> （</t年代pan> <tspan style="font-size: 12.50px; " x="111.9135" y="-5.1300001"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="118.165" y="-5.1300001"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="121.29075" y="-5.1300001"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="127.54225" y="-5.1300001"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="133.79375" y="-5.1300001"> ）</t年代pan> </text> </g> </g> </svg></span>因此，我们必须解常微分方程<年代pan class="equation" id="EEq16"> <svg height="30.975" id="M175" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 30.975" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,30.975)"> <g transform="translate(72,-47.22)"> <text transform="matrix(1,0,0,-1,71.68,56.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,81.11,61.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,89.65,56.16)"> <tspan style="font-size: 12.50px; " x="66.830002" y="4.9200001"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.702568" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="17.641733" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="28.994457" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="33.157955" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="42.985313" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="54.325535" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="60.577034" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="75.389999" y="-7.25"> c</t年代pan> <tspan style="font-size: 12.50px; " x="80.94133" y="-7.25"> o</t年代pan> <tspan style="font-size: 12.50px; " x="87.192833" y="-7.25"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="94.131996" y="-7.25"> </t年代pan> </text> <g> <path d="m 165.04,59.28 25.3,0" 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,-1,166.08,47.41)"> <tspan style="font-size: 12.50px; " x="28.24" y="-8.75"> −</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="4.863667" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="41.810001" y="-16"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="46.673668" y="-16"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="50.149502" y="-16"> n</t年代pan> <tspan style="font-size: 12.50px; " x="58.476498" y="-16"> </t年代pan> </text> <g> <path d="m 206.86,59.28 25.3,0" 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,-1,206.86,47.41)"> <tspan style="font-size: 12.50px; " x="26.49" y="-3.8299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="36.18" y="-8.75"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="18.741997" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,252.47,61.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,258.02,56.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.715071" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="17.654236" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="28.994457" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.758579" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="47.273842" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="51.437344" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="57.988914" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="65.62825" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="77.668633" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="83.920135" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="200.47" y="-0.31999999"> （</t年代pan> <tspan style="font-size: 12.50px; " x="204.6335" y="-0.31999999"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="210.88499" y="-0.31999999"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="214.01074" y="-0.31999999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="220.26225" y="-0.31999999"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="226.51375" y="-0.31999999"> ）</t年代pan> </text> </g> </g> </svg></span>我们假设<年代vg height="14.625" id="M176" 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"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.4,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>在区间内<年代vg height="13.45" id="M177" style="vertical-align:-2.21957pt;width:46.525002px;" version="1.1" viewbox="0 0 46.525002 13.45" width="46.525002" 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"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="15.616247" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="23.218071" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="26.693905" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="32.945404" y="0"> ）</t年代pan> </text> </g> </g> </svg>．写作<年代vg height="13.45" id="M178" style="vertical-align:-2.21957pt;width:81.4375px;" version="1.1" viewbox="0 0 81.4375 13.45" width="81.4375" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.1772022" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.87977" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="27.519102" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="39.55949" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="50.474609" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="54.638111" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="60.877106" y="0"> ）</t年代pan> </text> </g> </g> </svg>,在那里<年代vg height="11.0125" id="M179" style="vertical-align:-0.17555pt;width:64.337502px;" version="1.1" viewbox="0 0 64.337502 11.0125" width="64.337502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0125)"> <g transform="translate(72,-63.19)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="16.09136" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="28.13175" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="32.995419" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="36.471252" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="44.810753" y="0"> </t年代pan> </text> </g> </g> </svg>，我们发现将这个常微分方程转化为<年代pan class="equation" id="EEq17"> <svg height="34" id="M180" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 34" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,34)"> <g transform="translate(72,-44.8)"> <text transform="matrix(1,0,0,-1,42.55,51.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="14.877166" y="-2.51"> −</t年代pan> <tspan style="font-size: 12.50px; " x="26.217386" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,75.01,58.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,79.89,51.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,99.86,58.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,108.4,53.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="17.329159" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="28.681883" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="34.920879" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,155.36,58.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,160.92,53.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="17.341661" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="28.681883" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="32.845383" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="42.672737" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="54.012959" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="60.264462" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="67.720001" y="-7.2399998"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="76.747169" y="-7.2399998"> −</t年代pan> <tspan style="font-size: 12.50px; " x="88.087387" y="-7.2399998"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="94.33889" y="-7.2399998"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,261.5,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <g> <path d="m 228.64,56.91 37.74,0" 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,-1,244.39,45.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="23.18" y="-8.75"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,279.61,58.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,285.17,53.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="17.341661" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="28.681883" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.446007" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="49.574394" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="53.737892" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="59.976891" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="67.616226" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="79.644112" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="85.895607" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="173.32001" y="-1.49"> （</t年代pan> <tspan style="font-size: 12.50px; " x="177.48351" y="-1.49"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="183.735" y="-1.49"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="186.86075" y="-1.49"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="193.11224" y="-1.49"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="199.36375" y="-1.49"> ）</t年代pan> </text> </g> </g> </svg></span>(的通解<一个href="#EEq17">3.26</一个>）可以用该表格填写<年代pan class="equation" id="eq42"> <svg height="111.9" id="M181" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 111.9" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,111.9)"> <g transform="translate(72,17.52)"> <text transform="matrix(1,0,0,-1,42.19,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="14.115887" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="24.518383" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="32.157715" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="44.885769" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,93.33,52.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,109.13,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,114.32,44.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,119.19,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.63" y="9.7299995"> </t年代pan> <tspan style="font-size: 12.50px; " x="22.93" y="-7.25"> 1</t年代pan> </text> <g> <path d="m 142.12,50.95 6.25,0" 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,-1,142.12,39.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="10.22" y="-8.75"> −</t年代pan> <tspan style="font-size: 12.50px; " x="22.76" y="-16.809999"> </t年代pan> <tspan style="font-size: 12.50px; " x="28.610001" y="-19.33"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,177.08,63.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,184.74,58.4)"> <tspan style="font-size: 12.50px; " x="18.1" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,208.7,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="6.8090558" y="0"> 2</t年代pan> </text> <g> <path d="m 164.88,50.95 55.5,0" 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,-1,189.5,39.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="32.07" y="-8.75"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="38.48" y="-16"> 1</t年代pan> </text> <g> <path d="m 227.98,50.95 6.25,0" 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,-1,227.98,39.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="10.22" y="-8.75"> +</t年代pan> <tspan style="font-size: 12.50px; " x="22.76" y="-16.809999"> </t年代pan> <tspan style="font-size: 12.50px; " x="28.610001" y="-19.33"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,262.95,63.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,270.6,58.4)"> <tspan style="font-size: 12.50px; " x="18.110001" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,294.56,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="6.8090558" y="0"> 2</t年代pan> </text> <g> <path d="m 250.74,50.95 55.5,0" 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,-1,275.37,39.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="32.07" y="-8.75"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="38.82" y="-16"> 3.</t年代pan> </text> <g> <path d="m 314.19,50.95 6.25,0" 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,-1,314.19,39.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="10.23" y="-8.75"> −</t年代pan> <tspan style="font-size: 12.50px; " x="22.77" y="-17.1"> </t年代pan> </text> <g> <path d="m 336.96,50.95 6.35,0" 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,-1,337.01,39.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="7.4899998" y="-8.75"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="13.041332" y="-8.75"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,356.3,52.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,361.18,38.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="-265.51999" y="39.459999"> +</t年代pan> <tspan style="font-size: 12.50px; " x="-254.17978" y="39.459999"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,112.19,-4.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,117.07,-1.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.62" y="9.7399998"> </t年代pan> <tspan style="font-size: 12.50px; " x="22.92" y="-8.3500004"> </t年代pan> </text> <g> <path d="m 139.99,1.75 6.35,0" 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,-1,140.04,-10.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="10.27" y="-8.7600002"> −</t年代pan> <tspan style="font-size: 12.50px; " x="22.809999" y="-16.82"> </t年代pan> <tspan style="font-size: 12.50px; " x="28.66" y="-19.33"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,175.06,14.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,182.71,9.2)"> <tspan style="font-size: 12.50px; " x="18.110001" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,206.67,16.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="6.8090558" y="0"> 2</t年代pan> </text> <g> <path d="m 162.85,1.75 55.5,0" 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,-1,187.48,-10.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="32.07" y="-8.7600002"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="38.470001" y="-17.110001"> </t年代pan> </text> <g> <path d="m 225.95,1.75 6.35,0" 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,-1,226,-10.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="10.28" y="-8.7600002"> +</t年代pan> <tspan style="font-size: 12.50px; " x="22.82" y="-16.82"> </t年代pan> <tspan style="font-size: 12.50px; " x="28.67" y="-19.33"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,261.02,14.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,268.67,9.2)"> <tspan style="font-size: 12.50px; " x="18.110001" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,292.63,16.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="6.8090558" y="0"> 2</t年代pan> </text> <g> <path d="m 248.82,1.75 55.49,0" 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,-1,273.44,-10.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="32.07" y="-8.7600002"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="38.82" y="-16.01"> 1</t年代pan> </text> <g> <path d="m 312.26,1.75 6.26,0" 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,-1,312.26,-10.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="10.23" y="-8.7600002"> +</t年代pan> <tspan style="font-size: 12.50px; " x="22.77" y="-17.110001"> </t年代pan> </text> <g> <path d="m 335.03,1.75 6.35,0" 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,-1,335.08,-10.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="7.4899998" y="-8.7600002"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="13.053835" y="-8.7600002"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,354.37,3.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,359.25,-11.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.18" y="-9.7399998"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="99.239998" y="-35.220001"> （</t年代pan> <tspan style="font-size: 12.50px; " x="103.4035" y="-35.220001"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="109.655" y="-35.220001"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="112.78075" y="-35.220001"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="119.03225" y="-35.220001"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="125.28375" y="-35.220001"> ）</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="13.6125" id="M182" style="vertical-align:-2.34499pt;width:69.724998px;" version="1.1" viewbox="0 0 69.724998 13.6125" width="69.724998" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.8148546" y="0"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="16.203888" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="28.244276" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="38.071636" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="49.411858" y="0"> 1</t年代pan> </text> </g> </g> </svg>和<年代vg height="13.45" id="M183" style="vertical-align:-2.21957pt;width:70.074997px;" version="1.1" viewbox="0 0 70.074997 13.45" width="70.074997" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.166859" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="23.368107" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="29.244516" y="0"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="34.808353" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="39.997097" y="0"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="45.548428" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="51.787426" y="0"> ）</t年代pan> </text> </g> </g> </svg>是一个超几何函数(见阿布拉莫维茨和斯特贡[<一个href="#B1">10</一个>，p . 556])。因此,我们有<年代pan class="equation" id="eq43"> <svg height="96.800003" id="M184" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 96.800003" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,96.8)"> <g transform="translate(72,5.44)"> <text transform="matrix(1,0,0,-1,73.61,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.50276" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="15.666259" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="22.217831" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="29.857164" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="45.648453" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="49.811951" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="54.675617" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="58.151451" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="66.490952" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="73.042526" y="0"> ）</t年代pan> </text> <text transform="matrix(1,0,0,-1,150.82,61.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,166.63,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,171.82,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,176.69,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.63" y="4.9200001"> </t年代pan> <tspan style="font-size: 12.50px; " x="20.190001" y="-7.25"> 1</t年代pan> </text> <g> <path d="m 196.88,59.37 6.25,0" 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,-1,196.88,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="34.259998" y="-16.01"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="10.22" y="-8.7600002"> −</t年代pan> <tspan style="font-size: 12.50px; " x="21.560221" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.84923" y="-8.7600002"> ，</t年代pan> </text> <g> <path d="m 231.14,59.37 6.25,0" 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,-1,231.14,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="54.990002" y="-16.01"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.22" y="-8.7600002"> +</t年代pan> <tspan style="font-size: 12.50px; " x="21.560221" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.84923" y="-8.7600002"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="33.413067" y="-8.7600002"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="42.440231" y="-8.7600002"> −</t年代pan> </text> <g> <path d="m 286.13,59.37 7.05,0" 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,-1,286.53,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="7.8400002" y="-8.7600002"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="13.391332" y="-8.7600002"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="18.254999" y="-8.7600002"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="21.730833" y="-8.7600002"> n</t年代pan> </text> <text transform="matrix(1,0,0,-1,316.61,61.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,323.57,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.5500002" y="4.9200001"> </t年代pan> <tspan style="font-size: 12.50px; " x="-195.60001" y="31.41"> +</t年代pan> <tspan style="font-size: 12.50px; " x="-182.87195" y="31.41"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,145.89,21.71)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,150.77,24.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.62" y="4.9200001"> </t年代pan> <tspan style="font-size: 12.50px; " x="20.18" y="-7.25"> </t年代pan> <tspan style="font-size: 12.50px; " x="30.007359" y="-7.25"> −</t年代pan> <tspan style="font-size: 12.50px; " x="41.34758" y="-7.25"> 1</t年代pan> </text> <g> <path d="m 170.95,27.96 27.43,0" 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,-1,181.54,16.08)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="20.809999" y="-8.7600002"> −</t年代pan> <tspan style="font-size: 12.50px; " x="32.150223" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="38.439232" y="-8.7600002"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="44.849998" y="-16.01"> </t年代pan> <tspan style="font-size: 12.50px; " x="54.677357" y="-16.01"> −</t年代pan> <tspan style="font-size: 12.50px; " x="66.017578" y="-16.01"> 1</t年代pan> </text> <g> <path d="m 226.39,27.96 27.42,0" 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,-1,236.98,16.08)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="45.189999" y="-16.01"> </t年代pan> <tspan style="font-size: 12.50px; " x="20.809999" y="-8.7600002"> +</t年代pan> <tspan style="font-size: 12.50px; " x="32.150223" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="38.439232" y="-8.7600002"> ；</t年代pan> </text> <g> <path d="m 282.17,27.96 7.06,0" 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,-1,282.57,16.08)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="7.8499999" y="-8.7600002"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="13.401332" y="-8.7600002"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="18.264999" y="-8.7600002"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="21.740833" y="-8.7600002"> n</t年代pan> </text> <text transform="matrix(1,0,0,-1,312.66,30.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,319.61,24.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.5599999" y="4.9200001"> </t年代pan> <tspan style="font-size: 12.50px; " x="16.24" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="138.88" y="-5.3200002"> （</t年代pan> <tspan style="font-size: 12.50px; " x="143.0435" y="-5.3200002"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="149.295" y="-5.3200002"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="152.42075" y="-5.3200002"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="158.67226" y="-5.3200002"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="164.92375" y="-5.3200002"> ）</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="19.987499" id="M185" style="vertical-align:-2.34499pt;width:130.89999px;" version="1.1" viewbox="0 0 130.89999 19.987499" width="130.89999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.9875)"> <g transform="translate(72,-56.01)"> <text transform="matrix(1,0,0,-1,-71.95,58.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.7523403" y="0"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="16.141373" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="28.181763" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="32.345261" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="38.59676" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="42.072594" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="48.324097" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="52.487595" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="56.651093" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-8.94,63.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-1.29,58.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.104343" y="0"> ）</t年代pan> </text> <text transform="matrix(1,0,0,-1,20.98,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="6.8090558" y="0"> 2</t年代pan> </text> </g> </g> </svg>．</p> <p>的条件<年代vg height="13.45" id="M186" style="vertical-align:-2.21957pt;width:57.025002px;" version="1.1" viewbox="0 0 57.025002 13.45" width="57.025002" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.1772022" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="19.592201" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="27.21903" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="39.259418" y="0"> 0</t年代pan> </text> </g> </g> </svg>意味着我们必须<年代vg height="10.925" id="M187" style="vertical-align:-3.13504pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.925" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-66.76,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>等于零。接下来，我们必须找到分离常数的值<年代vg height="10.8125" id="M188" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8125)"> <g transform="translate(72,-63.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>的<年代vg height="14.75" id="M189" style="vertical-align:-3.25793pt;width:36.287498px;" version="1.1" viewbox="0 0 36.287498 14.75" width="36.287498" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.1772022" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-52.06,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-47.18,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> </text> </g> </g> </svg>= 0;也就是说,<年代pan class="equation" id="eq44"> <svg height="30.700001" id="M190" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 30.700001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,30.7)"> <g transform="translate(72,-47.44)"> <text transform="matrix(1,0,0,-1,85.18,53.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.52"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="10.713667" y="-2.52"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="14.189501" y="-2.52"> n</t年代pan> <tspan style="font-size: 12.50px; " x="22.516499" y="-2.52"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,114.25,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,119.13,53.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,124.98,63.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,140.79,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.62" y="4.9200001"> </t年代pan> <tspan style="font-size: 12.50px; " x="20.18" y="-7.25"> 1</t年代pan> </text> <g> <path d="m 160.97,59.37 6.25,0" 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,-1,160.97,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="34.259998" y="-16.01"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="10.23" y="-8.7600002"> −</t年代pan> <tspan style="font-size: 12.50px; " x="21.557718" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.846727" y="-8.7600002"> ，</t年代pan> </text> <g> <path d="m 195.23,59.37 6.25,0" 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,-1,195.23,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="54.990002" y="-16.01"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.23" y="-8.7600002"> +</t年代pan> <tspan style="font-size: 12.50px; " x="21.570221" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.85923" y="-8.7600002"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="33.410561" y="-8.7600002"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="42.437729" y="-8.7600002"> −</t年代pan> </text> <g> <path d="m 250.22,59.37 7.05,0" 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,-1,250.62,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="7.8499999" y="-8.7600002"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="13.401332" y="-8.7600002"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="18.264999" y="-8.7600002"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="21.740833" y="-8.7600002"> n</t年代pan> </text> <text transform="matrix(1,0,0,-1,280.7,61.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,287.66,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,294.21,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,299.08,51.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.08" y="-4.9200001"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="23.107885" y="-4.9200001"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="29.359386" y="-4.9200001"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="159.41" y="-5.27"> （</t年代pan> <tspan style="font-size: 12.50px; " x="163.5735" y="-5.27"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="169.825" y="-5.27"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="172.95074" y="-5.27"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="179.20226" y="-5.27"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="185.45375" y="-5.27"> ）</t年代pan> </text> </g> </g> </svg></span></p> <p>现在，注意(<一个href="#EEq16">3.25</一个>）可以用该表格填写<年代pan class="equation" id="eq45"> <svg height="30.762501" id="M191" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 30.762501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,30.7625)"> <g transform="translate(72,-47.39)"> <text transform="matrix(1,0,0,-1,78.22,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 75.32,59.47 13.2,0" 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,-1,75.32,47.59)"> <tspan style="font-size: 12.50px; " x="16.48" y="-3.8399999"> </t年代pan> <tspan style="font-size: 12.50px; " x="54.66" y="-16.01"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="22.219999" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="33.597729" y="-8.7600002"> （</t年代pan> <tspan style="font-size: 12.50px; " x="37.76123" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="44.312801" y="-8.7600002"> ）</t年代pan> </text> <g> <path d="m 127.08,59.47 13.2,0" 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,-1,127.08,47.59)"> <tspan style="font-size: 12.50px; " x="40.790001" y="-3.8399999"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="14.4" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="25.90276" y="-8.7600002"> （</t年代pan> <tspan style="font-size: 12.50px; " x="30.066259" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="36.617832" y="-8.7600002"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="49.310001" y="-8.7600002"> −</t年代pan> <tspan style="font-size: 12.50px; " x="60.650223" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="71.727882" y="-8.7600002"> （</t年代pan> <tspan style="font-size: 12.50px; " x="75.89138" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="82.442947" y="-8.7600002"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="88.69445" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="100.20972" y="-8.7600002"> （</t年代pan> <tspan style="font-size: 12.50px; " x="104.37321" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="110.92478" y="-8.7600002"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="117.86395" y="-8.7600002"> +</t年代pan> <tspan style="font-size: 12.50px; " x="129.20416" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="135.96829" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="147.30852" y="-8.7600002"> （</t年代pan> <tspan style="font-size: 12.50px; " x="151.47202" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="158.02359" y="-8.7600002"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="164.26259" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="175.77785" y="-8.7600002"> （</t年代pan> <tspan style="font-size: 12.50px; " x="179.94135" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="186.49292" y="-8.7600002"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="194.13225" y="-8.7600002"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="206.17264" y="-8.7600002"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="212.42413" y="-8.7600002"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="331.41" y="-8.9799995"> （</t年代pan> <tspan style="font-size: 12.50px; " x="335.57349" y="-8.9799995"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="341.82501" y="-8.9799995"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="344.95074" y="-8.9799995"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="351.20224" y="-8.9799995"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="357.45374" y="-8.9799995"> ）</t年代pan> </text> </g> </g> </svg></span>与<年代vg height="16.862499" id="M192" style="vertical-align:-2.21957pt;width:143.4375px;" version="1.1" viewbox="0 0 143.4375 16.862499" width="143.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.8625)"> <g transform="translate(72,-58.51)"> <text transform="matrix(1,0,0,-1,-71.95,60.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.4267821" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="11.590281" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.129351" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="25.768682" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="37.809071" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="41.972572" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="46.836239" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="50.312073" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="58.651573" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="67.278641" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="72.829971" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="79.081474" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="88.121147" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="94.672714" y="0"> ）</t年代pan> </text> <text transform="matrix(1,0,0,-1,26.89,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.9273758" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="10.922496" y="0"> 1</t年代pan> </text> </g> </g> </svg>，<年代vg height="13.45" id="M193" style="vertical-align:-2.21957pt;width:56.087502px;" version="1.1" viewbox="0 0 56.087502 13.45" width="56.087502" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.1269503" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="12.290449" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.829517" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="26.468851" y="0"> ≡</t年代pan> <tspan style="font-size: 12.50px; " x="38.509239" y="0"> 0</t年代pan> </text> </g> </g> </svg>和<年代vg height="13.45" id="M194" style="vertical-align:-2.21957pt;width:77.5625px;" version="1.1" viewbox="0 0 77.5625 13.45" width="77.5625" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.2522202" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="13.415719" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.954788" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="27.594122" y="0"> ≡</t年代pan> <tspan style="font-size: 12.50px; " x="39.63451" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="47.061291" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="51.224792" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="57.776363" y="0"> ）</t年代pan> </text> </g> </g> </svg>．如果我们假设<年代vg height="14.75" id="M195" style="vertical-align:-3.25793pt;width:149.375px;" version="1.1" viewbox="0 0 149.375 14.75" width="149.375" 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"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-43.64,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-30.91,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="22.055292" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="34.09568" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,9.74,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,18.09,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.629709" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="23.105543" y="0"> 2</t年代pan> </text> </g> </g> </svg>在<年代vg height="14.3375" id="M196" style="vertical-align:-3.13504pt;width:16.700001px;" version="1.1" viewbox="0 0 16.700001 14.3375" width="16.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.56,60.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>，那么解决的问题(<一个href="#EEq16">3.25</一个>）以及边界条件<年代vg height="14.75" id="M197" style="vertical-align:-3.25793pt;width:97.3125px;" version="1.1" viewbox="0 0 97.3125 14.75" width="97.3125" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.1772022" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-52.06,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-42.81,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="28.844421" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="33.007919" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-3.24,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,1.63,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> </text> </g> </g> </svg>= 0是a<我>常规的</我>Sturm-Liouville问题。因此，我们可以这样说(参见小爱德华兹和彭尼[<一个href="#B5">11</一个>（例如，p. 519])，即存在无限个特征值<年代vg height="14.5625" id="M198" style="vertical-align:-3.20526pt;width:14.6375px;" version="1.1" viewbox="0 0 14.6375 14.5625" width="14.6375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5625)"> <g transform="translate(72,-60.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>这些条件<年代vg height="14.75" id="M199" style="vertical-align:-3.25793pt;width:41.762501px;" version="1.1" viewbox="0 0 41.762501 14.75" width="41.762501" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.1772022" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-52.06,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-42.81,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> </text> </g> </g> </svg>= 0和<年代vg height="14.75" id="M200" style="vertical-align:-3.25793pt;width:36.287498px;" version="1.1" viewbox="0 0 36.287498 14.75" width="36.287498" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.1772022" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-52.06,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-47.18,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> </text> </g> </g> </svg>= 0表示满足。这些特征值构成一个递增序列<年代vg height="14.5625" id="M201" style="vertical-align:-3.20526pt;width:155.45px;" version="1.1" viewbox="0 0 155.45 14.5625" width="155.45" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5625)"> <g transform="translate(72,-60.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.84,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-38.04,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-29.69,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> ⋯</t年代pan> <tspan style="font-size: 12.50px; " x="29.169498" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="41.209888" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,18.28,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,26.61,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> ⋯</t年代pan> </text> </g> </g> </svg>实数的<年代vg height="14.8" id="M202" style="vertical-align:-3.20526pt;width:104.525px;" version="1.1" viewbox="0 0 104.525 14.8" width="104.525" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8)"> <g transform="translate(72,-60.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> l</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="6.9516678" y="0"> 米</t年代pan> </text> <text transform="matrix(1,0,0,-1,-51.1,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="5.8025761" y="0"> →</t年代pan> <tspan style="font-size: 8.75px; " x="15.35976" y="0"> ∞</t年代pan> </text> <text transform="matrix(1,0,0,-1,-27.13,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-20.36,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-12.04,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> ∞</t年代pan> </text> </g> </g> </svg>．此外，我们还可以声明(参见Butkov [<一个href="#B2">12</一个>（p. 337-340)，本征函数<年代vg height="14.6875" id="M203" style="vertical-align:-3.20526pt;width:36.25px;" version="1.1" viewbox="0 0 36.25 14.6875" width="36.25" 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,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.77,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.92,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.702568" y="0"> ）</t年代pan> </text> </g> </g> </svg>对应于特征值<年代vg height="14.5625" id="M204" style="vertical-align:-3.20526pt;width:14.6375px;" version="1.1" viewbox="0 0 14.6375 14.5625" width="14.6375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5625)"> <g transform="translate(72,-60.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>它们是相对于权函数正交的吗<年代vg height="13.45" id="M205" style="vertical-align:-2.21957pt;width:30.2875px;" version="1.1" viewbox="0 0 30.2875 13.45" width="30.2875" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.2522202" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="13.415719" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.954788" y="0"> ）</t年代pan> </text> </g> </g> </svg>．然而，明确地计算这些特征值是另一个问题。</p> <p>这里，我们考虑这样一种情况<年代vg height="14.75" id="M206" style="vertical-align:-3.25793pt;width:47.075001px;" version="1.1" viewbox="0 0 47.075001 14.75" width="47.075001" 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"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.4,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-52.68,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 0</t年代pan> </text> </g> </g> </svg>，这样我们就不会经常遇到Sturm-Liouville问题。然而，人们可以用计算机软件来图形化地检查，是否存在无数个正常数<年代vg height="14.5625" id="M207" style="vertical-align:-3.20526pt;width:14.6375px;" version="1.1" viewbox="0 0 14.6375 14.5625" width="14.6375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5625)"> <g transform="translate(72,-60.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>的<年代pan class="equation" id="eq46"> <svg height="30.700001" id="M208" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 30.700001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,30.7)"> <g transform="translate(72,-47.44)"> <text transform="matrix(1,0,0,-1,108.13,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.63" y="4.9200001"> </t年代pan> <tspan style="font-size: 12.50px; " x="20.190001" y="-7.25"> 1</t年代pan> </text> <g> <path d="m 128.32,59.37 6.25,0" 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,-1,128.32,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="10.22" y="-8.7600002"> −</t年代pan> <tspan style="font-size: 12.50px; " x="21.560221" y="-8.7600002"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,156.17,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,161.02,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="6.4099998" y="-7.25"> 1</t年代pan> </text> <g> <path d="m 167.43,59.37 6.25,0" 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,-1,167.43,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="10.22" y="-8.7600002"> +</t年代pan> <tspan style="font-size: 12.50px; " x="21.560221" y="-8.7600002"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,195.29,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,200.13,56.25)"> <tspan style="font-size: 12.50px; " x="27.129999" y="-7.25"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="14.591001" y="0"> −</t年代pan> </text> <g> <path d="m 227.26,59.37 7.05,0" 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,-1,227.66,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="7.8499999" y="-8.7600002"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="13.401332" y="-8.7600002"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="18.264999" y="-8.7600002"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="21.740833" y="-8.7600002"> n</t年代pan> </text> <text transform="matrix(1,0,0,-1,257.74,61.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,264.7,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,271.25,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,276.13,51.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.07" y="-4.9200001"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="23.097885" y="-4.9200001"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="29.349386" y="-4.9200001"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="182.36" y="-5.27"> （</t年代pan> <tspan style="font-size: 12.50px; " x="186.5235" y="-5.27"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="192.77499" y="-5.27"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="195.90074" y="-5.27"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="202.15225" y="-5.27"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="208.40375" y="-5.27"> ）</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="17.975" id="M209" style="vertical-align:-3.20526pt;width:179.7625px;" version="1.1" viewbox="0 0 179.7625 17.975" width="179.7625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.975)"> <g transform="translate(72,-57.62)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.66,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.34,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="18.41692" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="22.580418" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="28.831919" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="32.307751" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="38.559254" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="42.722752" y="0"> ［</t年代pan> <tspan style="font-size: 12.50px; " x="46.88625" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="51.049747" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="60.88961" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="72.229828" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="78.481331" y="0"> ）</t年代pan> </text> <text transform="matrix(1,0,0,-1,25.31,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,32.96,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,51.07,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,55.92,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ］</t年代pan> </text> <text transform="matrix(1,0,0,-1,60.08,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="6.8090558" y="0"> 2</t年代pan> </text> </g> </g> </svg>为<年代vg height="12.8875" id="M210" style="vertical-align:-1.76814pt;width:74.162498px;" version="1.1" viewbox="0 0 74.162498 12.8875" width="74.162498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.8875)"> <g transform="translate(72,-61.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.6773224" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="21.71771" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="27.969212" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="33.182961" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="39.434464" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="44.635712" y="0"> ．．．</t年代pan> </text> </g> </g> </svg>因此，除了一个任意常数，<年代pan class="equation" id="eq47"> <svg height="30.700001" id="M211" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 30.700001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,30.7)"> <g transform="translate(72,-47.44)"> <text transform="matrix(1,0,0,-1,72.89,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,82.07,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,89,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.715071" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="18.341902" y="0"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="24.730934" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="36.771324" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="40.934822" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="45.798489" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="49.274323" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="57.613823" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="64.165398" y="0"> ）</t年代pan> </text> <text transform="matrix(1,0,0,-1,157.33,61.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,173.14,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.62" y="4.9200001"> </t年代pan> <tspan style="font-size: 12.50px; " x="20.18" y="-7.25"> 1</t年代pan> </text> <g> <path d="m 193.32,59.37 6.25,0" 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,-1,193.32,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="10.23" y="-8.7600002"> −</t年代pan> <tspan style="font-size: 12.50px; " x="21.570221" y="-8.7600002"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,221.18,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,226.03,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="6.4000001" y="-7.25"> 1</t年代pan> </text> <g> <path d="m 232.43,59.37 6.25,0" 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,-1,232.43,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="10.23" y="-8.7600002"> +</t年代pan> <tspan style="font-size: 12.50px; " x="21.570221" y="-8.7600002"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,260.29,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,265.14,56.25)"> <tspan style="font-size: 12.50px; " x="27.129999" y="-7.25"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="14.578498" y="0"> −</t年代pan> </text> <g> <path d="m 292.27,59.37 7.05,0" 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,-1,292.67,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="7.8400002" y="-8.7600002"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="13.391332" y="-8.7600002"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="18.254999" y="-8.7600002"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="21.730833" y="-8.7600002"> n</t年代pan> </text> <text transform="matrix(1,0,0,-1,322.75,61.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,329.71,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.5500002" y="4.9200001"> </t年代pan> <tspan style="font-size: 12.50px; " x="128.78" y="-0.34999999"> （</t年代pan> <tspan style="font-size: 12.50px; " x="132.9435" y="-0.34999999"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="139.19499" y="-0.34999999"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="142.32076" y="-0.34999999"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="148.57225" y="-0.34999999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="154.82375" y="-0.34999999"> ）</t年代pan> </text> </g> </g> </svg></span>为<年代vg height="14.75" id="M212" style="vertical-align:-3.25793pt;width:69.1875px;" version="1.1" viewbox="0 0 69.1875 14.75" width="69.1875" 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"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="31.782625" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="43.823013" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-21.57,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>．</p> <p>最后，求解常微分方程<年代pan class="equation" id="eq48"> <svg height="18.4625" id="M213" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.4625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.4625)"> <g transform="translate(72,-57.23)"> <text transform="matrix(1,0,0,-1,113.03,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,118.13,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,123,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,132.54,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,141.08,61.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.2647228" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="27.544109" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="31.707607" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="37.959106" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="47.786465" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="59.126686" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="65.378189" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="71.629684" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="76.730911" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,227.35,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,232.91,61.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.2647228" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="16.891554" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="28.931942" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,268.62,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,273.46,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="20.880011" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="27.13151" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="185.03" y="-0.46000001"> （</t年代pan> <tspan style="font-size: 12.50px; " x="189.1935" y="-0.46000001"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="195.44499" y="-0.46000001"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="198.57076" y="-0.46000001"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="204.82225" y="-0.46000001"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="211.07375" y="-0.46000001"> ）</t年代pan> </text> </g> </g> </svg></span>受<年代vg height="13.45" id="M214" style="vertical-align:-2.21957pt;width:28.012501px;" version="1.1" viewbox="0 0 28.012501 13.45" width="28.012501" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="18.141853" y="0"> ）</t年代pan> </text> </g> </g> </svg>= 0。这是一个欧拉-柯西微分方程;对于所有正的特征值<年代vg height="14.5625" id="M215" style="vertical-align:-3.20526pt;width:14.6375px;" version="1.1" viewbox="0 0 14.6375 14.5625" width="14.6375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5625)"> <g transform="translate(72,-60.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>，我们可以这样写<年代pan class="equation" id="eq49"> <svg height="18.375" id="M216" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.375)"> <g transform="translate(72,-57.3)"> <text transform="matrix(1,0,0,-1,161.25,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,168.97,57.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,175.9,61.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.2647228" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="16.904057" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="28.931942" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="34.483273" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="40.734776" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="46.986275" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="51.762421" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="55.238255" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="62.527504" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,243.53,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,248.28,63.92)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,252.38,61.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="206.11" y="-0.41999999"> （</t年代pan> <tspan style="font-size: 12.50px; " x="210.2735" y="-0.41999999"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="216.52499" y="-0.41999999"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="219.65074" y="-0.41999999"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="225.90225" y="-0.41999999"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="232.15375" y="-0.41999999"> ）</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="17.975" id="M217" style="vertical-align:-3.20526pt;width:212.33749px;" version="1.1" viewbox="0 0 212.33749 17.975" width="212.33749" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.975)"> <g transform="translate(72,-57.62)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.17,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-56.85,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="18.41692" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="22.580418" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="31.607584" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="42.960308" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="50.012001" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="56.951164" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="68.291389" y="0"> ［</t年代pan> <tspan style="font-size: 12.50px; " x="72.454887" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="76.618385" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="86.44574" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="97.785965" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="104.03746" y="0"> ）</t年代pan> </text> <text transform="matrix(1,0,0,-1,51.36,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,59.02,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,77.12,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,81.97,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ］</t年代pan> </text> <text transform="matrix(1,0,0,-1,86.13,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="6.8090558" y="0"> 2</t年代pan> </text> </g> </g> </svg>．由于有无穷多个这样的特征值，我们可以考虑无穷级数(广义傅立叶级数)<年代pan class="equation" id="eq50"> <svg height="48.200001" id="M218" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.200001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.2)"> <g transform="translate(72,-33.44)"> <text transform="matrix(1,0,0,-1,145.13,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.3520041" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="12.515503" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.616728" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="22.830479" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="29.38205" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="37.021381" y="0"> ＝</t年代pan> </text> <text transform="matrix(1,0,0,-1,198.22,65.71)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代pan> </text> <text transform="matrix(1,0,0,-1,194.19,43.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,194.91,36.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.3497438" y="0"> ＝</t年代pan> <tspan style="font-size: 8.75px; " x="10.344864" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,210.35,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,216.62,46.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,221.47,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,226.57,54.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,231.32,52.58)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,235.42,49.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,244.6,46.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,251.53,49.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.711572" y="0.0099999998"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="16.950569" y="0.0099999998"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="206.96001" y="0.18000001"> （</t年代pan> <tspan style="font-size: 12.50px; " x="211.1235" y="0.18000001"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="217.375" y="0.18000001"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="220.50075" y="0.18000001"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="226.75224" y="0.18000001"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="233.00375" y="0.18000001"> ）</t年代pan> </text> </g> </g> </svg></span>利用边界条件<年代vg height="13.55" id="M219" style="vertical-align:-2.29482pt;width:68.599998px;" version="1.1" viewbox="0 0 68.599998 13.55" width="68.599998" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.2765059" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="10.440005" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.0916" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="22.292849" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="28.844421" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="36.483753" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="48.524143" y="0"> 1</t年代pan> </text> </g> </g> </svg>，我们可以把它写成常数<年代vg height="11.0125" id="M220" style="vertical-align:-3.20526pt;width:14.025px;" version="1.1" viewbox="0 0 14.025 11.0125" width="14.025" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0125)"> <g transform="translate(72,-63.19)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>是由(见Butkov [<一个href="#B2">12</一个>，第339页)<年代pan class="equation" id="eq51"> <svg height="51" id="M221" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 51" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,51)"> <g transform="translate(72,-31.2)"> <text transform="matrix(1,0,0,-1,134.6,48.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,140.88,45.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,149.2,48.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="13.23" y="-10.64"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,169.83,64.18)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,180.57,61.99)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,186.76,59.08)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∫</t年代pan> </text> <text transform="matrix(1,0,0,-1,192.46,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,197.05,63.92)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,190.21,54.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,203.25,59.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="15.50372" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="22.055292" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="28.294289" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,240.73,55.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,247.66,59.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.715071" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="16.954067" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="23.605663" y="0"> </t年代pan> </text> <g> <path d="m 162.43,51.6 115.4,0" 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,-1,172.37,35.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∫</t年代pan> </text> <text transform="matrix(1,0,0,-1,178.08,42.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,182.66,40.68)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,175.83,31.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,188.87,35.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="15.491217" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="22.042789" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="28.294289" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,226.59,40.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="-0.25" y="8.1999998"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,233.55,35.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.715071" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="21.13007" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.781666" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="45.470001" y="-12.59"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="224.94" y="-12.59"> （</t年代pan> <tspan style="font-size: 12.50px; " x="229.1035" y="-12.59"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="235.355" y="-12.59"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="238.48074" y="-12.59"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="244.73225" y="-12.59"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="250.98375" y="-12.59"> ）</t年代pan> </text> </g> </g> </svg></span></p> <p><span class="statement" id="rem4"><span class="statement-title"><i class="statement-title">3.2的话。</我></年代pan>至少有另一种特殊情况，我们可以获得显式表达式(当<年代vg height="14.75" id="M222" style="vertical-align:-3.25793pt;width:149.375px;" version="1.1" viewbox="0 0 149.375 14.75" width="149.375" 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"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-43.64,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-30.91,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="22.055292" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="34.09568" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,9.74,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,18.09,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.629709" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="23.105543" y="0"> 2</t年代pan> </text> </g> </g> </svg>)。的确，如果我们愿意的话<年代vg height="14.6" id="M223" style="vertical-align:-3.13504pt;width:104.75px;" version="1.1" viewbox="0 0 104.75 14.6" width="104.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.01,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.14,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-49.1,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-44.22,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="28.231773" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="34.483273" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="37.959106" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="44.210609" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,6.87,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> </g> </g> </svg>(例如,<年代vg height="10.9125" id="M224" style="vertical-align:-0.17555pt;width:36.137501px;" version="1.1" viewbox="0 0 36.137501 10.9125" width="36.137501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.515023" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="22.555412" y="0"> 0</t年代pan> </text> </g> </g> </svg>),<年代vg height="14.6" id="M225" style="vertical-align:-3.13504pt;width:94.037498px;" version="1.1" viewbox="0 0 94.037498 14.6" width="94.037498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.01,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-60.14,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-49.1,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-44.22,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="25.918718" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="29.394552" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="35.646053" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-1.69,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg>(对应于<年代vg height="10.85" id="M226" style="vertical-align:-0.1254pt;width:36.137501px;" version="1.1" viewbox="0 0 36.137501 10.85" width="36.137501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.85)"> <g transform="translate(72,-63.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.515023" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="22.555412" y="0"> 2</t年代pan> </text> </g> </g> </svg>),<年代vg height="14.7125" id="M227" style="vertical-align:-3.2316pt;width:62.287498px;" version="1.1" viewbox="0 0 62.287498 14.7125" width="62.287498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.62,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.4,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-51.36,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-48.14,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> ≡</t年代pan> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> 2</t年代pan> </text> </g> </g> </svg>，我们发现我们必须解的偏微分方程为<年代pan class="equation" id="eq52"> <svg height="31.15" id="M228" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 31.15" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,31.15)"> <g transform="translate(72,-47.08)"> <text transform="matrix(1,0,0,-1,83.08,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="8.3299999" y="4.9200001"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.299999" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,106.65,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="3.570816" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,117.07,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="12.54" y="-7.25"> 1</t年代pan> </text> <g> <path d="m 129.61,59.37 6.25,0" 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,-1,130.18,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.8800001" y="-8.7600002"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,143.33,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,150.18,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="14.4" y="-7.25"> 1</t年代pan> </text> <g> <path d="m 162.72,59.37 9.97,0" 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,-1,162.72,47.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,167.82,50.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,173.89,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,180.17,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="4.5772958" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,189.84,51.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.74" y="-4.9200001"> +</t年代pan> <tspan style="font-size: 12.50px; " x="26.139999" y="-12.17"> 1</t年代pan> </text> <g> <path d="m 214.12,59.37 9.97,0" 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,-1,214.12,47.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,219.22,50.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,227.37,51.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="30.74" y="-12.17"> 1</t年代pan> </text> <g> <path d="m 235.93,59.37 50.62,0" 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,-1,235.93,47.49)"> <tspan style="font-size: 12.50px; " x="51.810001" y="-3.8399999"> </t年代pan> <tspan style="font-size: 12.50px; " x="61.5" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="5.551332" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="11.802832" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="18.741997" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.381571" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="32.245235" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="35.721069" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="44.060574" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,303.7,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,312.26,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="146.23" y="-0.16"> （</t年代pan> <tspan style="font-size: 12.50px; " x="150.39349" y="-0.16"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="156.645" y="-0.16"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="159.77075" y="-0.16"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="166.02225" y="-0.16"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="172.27374" y="-0.16"> ）</t年代pan> </text> </g> </g> </svg></span>这个方程是可分离的;由变量分离得到的两个常微分方程是<年代pan class="equation" id="EEq18"> <svg height="60.412498" id="M229" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 60.412498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,60.4125)"> <g transform="translate(72,-23.67)"> <text transform="matrix(1,0,0,-1,95.73,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,105.16,61.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,113.69,56.25)"> <tspan style="font-size: 12.50px; " x="29" y="4.9200001"> </t年代pan> <tspan style="font-size: 12.50px; " x="63.91" y="-7.25"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.702568" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="17.654236" y="0"> +</t年代pan> </text> <g> <path d="m 151.25,59.37 58.95,0" 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,-1,151.25,47.49)"> <tspan style="font-size: 12.50px; " x="60.139999" y="-3.8399999"> </t年代pan> <tspan style="font-size: 12.50px; " x="69.830002" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="8.3269978" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="13.87833" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="20.129829" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="27.081497" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.708569" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="40.572235" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="44.048069" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="52.387569" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,230.51,61.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,236.06,56.25)"> <tspan style="font-size: 12.50px; " x="-95.790001" y="28.780001"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.715071" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="17.654236" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="28.994457" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.758579" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="47.273842" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="51.437344" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="57.988914" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="65.62825" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="77.656136" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="83.907631" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="222.42999" y="-0.28"> （</t年代pan> <tspan style="font-size: 12.50px; " x="226.59351" y="-0.28"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="232.845" y="-0.28"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="235.97075" y="-0.28"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="242.22224" y="-0.28"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="248.47375" y="-0.28"> ）</t年代pan> </text> <text transform="matrix(1,0,0,-1,145.37,32.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,150.25,27.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,159.79,32.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,168.32,27.48)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.2647228" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="16.203888" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="27.544109" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="32.645332" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="44.273125" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="48.436623" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="53.537846" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="61.177177" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="73.205063" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="79.969185" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="91.596977" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="95.760475" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="100.8617" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="107.1132" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="290.17001" y="-0.44999999"> （</t年代pan> <tspan style="font-size: 12.50px; " x="294.3335" y="-0.44999999"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="300.58499" y="-0.44999999"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="303.71075" y="-0.44999999"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="309.96225" y="-0.44999999"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="316.21375" y="-0.44999999"> ）</t年代pan> </text> </g> </g> </svg></span><br>写作<年代vg height="13.45" id="M231" style="vertical-align:-2.21957pt;width:81.4375px;" version="1.1" viewbox="0 0 81.4375 13.45" width="81.4375" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.1772022" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="13.340701" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.87977" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="27.519102" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="39.55949" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="50.474609" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="54.638111" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="60.877106" y="0"> ）</t年代pan> </text> </g> </g> </svg>与<年代vg height="11.0125" id="M232" style="vertical-align:-0.17555pt;width:64.337502px;" version="1.1" viewbox="0 0 64.337502 11.0125" width="64.337502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0125)"> <g transform="translate(72,-63.19)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.7023277" y="0"> ∶</t年代pan> <tspan style="font-size: 12.50px; " x="16.09136" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="28.13175" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="32.995419" y="0"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="36.471252" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="44.810753" y="0"> </t年代pan> </text> </g> </g> </svg>，（<一个href="#EEq18">3．38</一个>）成为<年代pan class="equation" id="eq53"> <svg height="30.9125" id="M233" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 30.9125" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,30.9125)"> <g transform="translate(72,-47.27)"> <text transform="matrix(1,0,0,-1,74.09,53.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.52"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="14.877166" y="-2.52"> −</t年代pan> <tspan style="font-size: 12.50px; " x="26.217386" y="-2.52"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,106.55,61.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,111.43,53.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.52"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,131.4,61.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="2.9756801" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,139.94,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="17.341661" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="28.681883" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="34.920879" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,186.9,61.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,192.46,56.25)"> <tspan style="font-size: 12.50px; " x="33.009998" y="-7.25"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="17.341661" y="0"> +</t年代pan> </text> <g> <path d="m 222.35,59.37 12.49,0" 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,-1,222.35,47.49)"> <tspan style="font-size: 12.50px; " x="13.68" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,248.07,61.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,253.63,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.402496" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="17.341661" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="28.681883" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="35.446007" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="49.574394" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="53.737892" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="59.976891" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="67.603722" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="79.644112" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="85.895607" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="204.86" y="-0.25999999"> （</t年代pan> <tspan style="font-size: 12.50px; " x="209.0235" y="-0.25999999"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="215.27499" y="-0.25999999"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="218.40074" y="-0.25999999"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="224.65225" y="-0.25999999"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="230.90375" y="-0.25999999"> ）</t年代pan> </text> </g> </g> </svg></span>我们能求出什么<年代pan class="equation" id="eq54"> <svg height="48.1875" id="M234" 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,-1,21.11,49.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="14.115887" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="24.518383" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="32.157715" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="44.198105" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,71.55,54.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="6.8090558" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,83.23,49.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,88.42,46.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,93.3,49.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.62" y="9.7299995"> </t年代pan> <tspan style="font-size: 12.50px; " x="22.92" y="-7.25"> 1</t年代pan> </text> <g> <path d="m 116.22,52.73 6.25,0" 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,-1,116.22,40.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="10.22" y="-8.75"> −</t年代pan> <tspan style="font-size: 12.50px; " x="22.76" y="-18"> √</t年代pan> </text> <g> <path d="m 150.58,70.61 6.77,0" 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,-1,150.58,58.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 138.98,52.73 18.37,0" 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,-1,145.04,40.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="13.5" y="-8.75"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="19.91" y="-16"> 1</t年代pan> </text> <g> <path d="m 164.95,52.73 6.25,0" 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,-1,164.95,40.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="10.22" y="-8.75"> +</t年代pan> <tspan style="font-size: 12.50px; " x="22.76" y="-18"> √</t年代pan> </text> <g> <path d="m 199.32,70.61 6.76,0" 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,-1,199.32,58.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 187.71,52.73 18.37,0" 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,-1,193.77,40.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="13.51" y="-8.75"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="20.26" y="-16"> 5</t年代pan> </text> <g> <path d="m 214.03,52.73 6.25,0" 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,-1,214.03,40.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="7.4499998" y="-8.75"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="13.001332" y="-8.75"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,233.28,54.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,238.15,39.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.88" y="-9.7299995"> +</t年代pan> <tspan style="font-size: 12.50px; " x="24.220221" y="-9.7299995"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,267.56,46.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,272.44,49.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.62" y="9.7299995"> </t年代pan> <tspan style="font-size: 12.50px; " x="21.719999" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="31.48" y="-9.25"> √</t年代pan> </text> <g> <path d="m 315.53,70.61 6.76,0" 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,-1,315.53,58.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 303.92,52.73 18.37,0" 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,-1,309.98,40.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="13.51" y="-8.75"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="19.91" y="-18"> √</t年代pan> </text> <g> <path d="m 341.5,70.61 6.76,0" 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,-1,341.5,58.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 329.89,52.73 18.37,0" 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,-1,335.95,40.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="13.51" y="-8.75"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="20.26" y="-16"> 3.</t年代pan> </text> <g> <path d="m 356.21,52.73 6.25,0" 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,-1,356.21,40.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="7.4499998" y="-8.75"> ；</t年代pan> <tspan style="font-size: 12.50px; " x="13.001332" y="-8.75"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,375.46,54.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,380.33,39.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.19" y="-9.7299995"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="78.160004" y="-9.7299995"> （</t年代pan> <tspan style="font-size: 12.50px; " x="82.323502" y="-9.7299995"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="88.574997" y="-9.7299995"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="91.700752" y="-9.7299995"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="97.952248" y="-9.7299995"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="104.20375" y="-9.7299995"> ）</t年代pan> </text> </g> </g> </svg></span>此外,(<一个href="#EEq18">3.39</一个>）也是欧拉-柯西方程;满足边界条件的解<年代vg height="13.45" id="M235" style="vertical-align:-2.21957pt;width:28.012501px;" version="1.1" viewbox="0 0 28.012501 13.45" width="28.012501" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.7268538" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="11.890353" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="18.141853" y="0"> ）</t年代pan> </text> </g> </g> </svg>= 0是(对于正的特征值<年代vg height="14.5625" id="M236" style="vertical-align:-3.20526pt;width:14.6375px;" version="1.1" viewbox="0 0 14.6375 14.5625" width="14.6375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5625)"> <g transform="translate(72,-60.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.19,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>）<年代pan class="equation" id="eq55"> <svg height="21.5875" id="M237" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 21.5875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,21.5875)"> <g transform="translate(72,-54.73)"> <text transform="matrix(1,0,0,-1,158.71,58.53)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.615287" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="15.778786" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="20.880011" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="28.519342" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="40.54723" y="0"> c</t年代pan> <tspan style="font-size: 12.50px; " x="46.09856" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="52.35006" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="58.601563" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="63.377708" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="66.853539" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="74.142792" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,237.96,62.86)"> <tspan style="font-size: 8.75px; " x="0" y="0"> √</t年代pan> </text> <g> <path d="m 246.08,71.08 8.34,0" style="fill:none;stroke:#000000;stroke-width:0.57800001;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,246.08,63.53)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,250.82,61.34)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,254.92,58.53)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="203.57001" y="-1.71"> （</t年代pan> <tspan style="font-size: 12.50px; " x="207.73351" y="-1.71"> 3.</t年代pan> <tspan style="font-size: 12.50px; " x="213.985" y="-1.71"> ．</t年代pan> <tspan style="font-size: 12.50px; " x="217.11075" y="-1.71"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="223.36224" y="-1.71"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="229.61375" y="-1.71"> ）</t年代pan> </text> </g> </g> </svg></span>因此，按照上面的步骤，我们可以得到这个函数<年代vg height="13.55" id="M238" style="vertical-align:-2.29482pt;width:39.462502px;" version="1.1" viewbox="0 0 39.462502 13.55" width="39.462502" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.2765059" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="10.440005" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.541229" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="20.742477" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.294048" y="0"> ）</t年代pan> </text> </g> </g> </svg>，表示为一个广义傅里叶级数，在这种情况下也是。</年代pan></p> <h4 id="concluding-remarks">4.结束语</h4> <p>在本文中，我们考虑了从两个同心圆之间或在一个角扇形中开始的重要二维扩散过程的首次碰撞概率的计算问题。我们已经在章节中获得了对一些问题的明确(和精确)的解决方案<一个href="#sec2">2</一个>和<一个href="#sec3">3.</一个>．此外，我们在Section中任意选择<一个href="#sec2">2</一个>来计算概率<年代vg height="14.6" id="M239" style="vertical-align:-3.13504pt;width:55.924999px;" version="1.1" viewbox="0 0 55.924999 14.6" width="55.924999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.5893211" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="11.75282" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.31,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-48.43,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-36.35,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-31.47,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> </text> </g> </g> </svg>先击中大圆。这将是一个简单的事情，以获得先击中较小的圆的概率。实际上，因为延拓区域是有界的，所以先到达小圆的概率应该是<年代vg height="14.6" id="M240" style="vertical-align:-3.13504pt;width:81.387497px;" version="1.1" viewbox="0 0 81.387497 14.6" width="81.387497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="20.367388" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.969212" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="32.13271" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.93,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-28.06,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-15.97,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-11.1,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代pan> </text> </g> </g> </svg>至少在这里治疗的病例中是这样。同样,在节<一个href="#sec3">3.</一个>我们可以计算这个过程的概率<年代vg height="14.6" id="M241" style="vertical-align:-3.13504pt;width:84.525002px;" version="1.1" viewbox="0 0 84.525002 14.6" width="84.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.91,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.03,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-25.71,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-20.83,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ）</t年代pan> </text> </g> </g> </svg>会通过半径离开延续区域吗<年代vg height="10.7375" id="M242" 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"> </t年代pan> </text> </g> </g> </svg>= 0，或通过<年代vg height="14.625" id="M243" style="vertical-align:-3.25793pt;width:41.987499px;" version="1.1" viewbox="0 0 41.987499 14.625" width="41.987499" 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"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.014903" y="0"> ＝</t年代pan> <tspan style="font-size: 12.50px; " x="22.055292" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-43.34,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> </text> </g> </g> </svg>．</p> <p>现在，还有其他重要的二维扩散过程，本文中使用的技术是行不通的。特别是具有非零无穷小均值的二维维纳过程和几何布朗运动。此外，除了上面的最后一句，我们一直假设这两个扩散过程，<年代vg height="14.6" id="M244" style="vertical-align:-3.13504pt;width:33.862499px;" version="1.1" viewbox="0 0 33.862499 14.6" width="33.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.2,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> </text> </g> </g> </svg>和<年代vg height="14.6" id="M245" style="vertical-align:-3.13504pt;width:33.862499px;" version="1.1" viewbox="0 0 33.862499 14.6" width="33.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.2,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> </text> </g> </g> </svg>，具有相同的无穷小参数;在一般情况下，尝试找到第一次撞击地点问题的解决方案是很有趣的。</p> <p>接下来，我们还可以尝试在三个或更多的维度中找到明确的第一次击球问题的解决方案。至少可以解决一些特殊的问题。</p> <p>最后，我们计算了该过程的概率<年代vg height="14.6" id="M246" style="vertical-align:-3.13504pt;width:84.525002px;" version="1.1" viewbox="0 0 84.525002 14.6" width="84.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.91,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.03,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-25.71,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-20.83,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="12.240437" y="0"> ）</t年代pan> </text> </g> </g> </svg>将首先击中停止区域边界的给定部分。另一个问题是试图获得分布<年代vg height="14.6" id="M247" style="vertical-align:-3.13504pt;width:91.9375px;" version="1.1" viewbox="0 0 91.9375 14.6" width="91.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.91,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-53.03,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="15.203648" y="0"> ，</t年代pan> <tspan style="font-size: 12.50px; " x="20.404896" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-22.74,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-17.87,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> ）</t年代pan> <tspan style="font-size: 12.50px; " x="15.203648" y="0"> ）</t年代pan> </text> </g> </g> </svg>．</p> </div> <div class="xml-content"> <h4 class="references" id="references">参考文献</h4> <ol> <li id="B3">考克斯和米勒，<我>随机过程理论</我>1965年，英国伦敦，麦修恩。<年代pan class="reflinks">视图:<一个href="https://www.zentralblatt-math.org/zmath/en/advanced/?q=an%3A0178.53501">Zentralblatt数学</一个></年代pan></li> <li id="B4">J. L. Doob，《热方程的概率方法》<我>美国数学学会学报</我>，第80卷，第216-280页，1955年。<年代pan class="reflinks">视图:<一个href="https://doi.org/10.1090/S0002-9947-1955-0079376-0">出版商的网站</一个><年代pan class="sep">|</年代pan><a href="https://scholar.google.com/scholar_lookup?title=A%20probability%20approach%20to%20the%20heat%20equation&author=J. L. Doob&publication_year=1955" target="_blank">谷歌学者</一个><年代pan class="sep">|</年代pan><a href="https://www.zentralblatt-math.org/zmath/en/advanced/?q=an%3A0068.32705">Zentralblatt数学</一个></年代pan></li> <li id="B9">F.斯皮策，《关于二维布朗运动的一些定理》<我>美国数学学会学报</我>1958年第87卷第187-197页。<年代pan class="reflinks">视图:<一个href="https://scholar.google.com/scholar_lookup?title=Some%20theorems%20concerning%202-dimensional%20Brownian%20motion&author=F. Spitzer&publication_year=1958" target="_blank">谷歌学者</一个><年代pan class="sep">|</年代pan><a href="https://www.zentralblatt-math.org/zmath/en/advanced/?q=an%3A0089.13601">Zentralblatt数学</一个></年代pan></li> <li id="B10">J. 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Butkov<我>数学物理</我>， Addison-Wesley，美国马萨诸塞州雷丁，1968年。<年代pan class="reflinks">视图:<一个href="https://www.zentralblatt-math.org/zmath/en/advanced/?q=an%3A0189.33501">Zentralblatt数学</一个></年代pan></li> </ol> </div> <div class="xml-content"> <h4 class="copyright" id="copyright">版权</h4> <p>版权所有©2011 Mario Lefebvre。这是一篇发布在<一个rel="license" href="http://creativecommons.org/licenses/by/3.0/">知识共享署名许可协议</一个>，允许在任何媒介上不受限制地使用、传播和复制，但必须正确引用原作。</p> </div> </div> </article> </div> </div> </div> <div class="biblio__Wrapper-sc-1nou1lz-0 eyHfWh journal_article__BiblioIntegratorWidget-sc-12fk6zy-5 dbAANp article_widget biblioWrapper hide"> <hr> <h4 class="biblio__H4-sc-1nou1lz-2 kgAKHb hrTitleRef">更多相关文章</h4> <div id="biblio_widget" class="biblio__BiblioWrapper-sc-1nou1lz-1 jgHHJS"></div> </div> </div> </div> <div class="threeColumn__RightWrapper-sc-1bf4078-2 jzTMLK rightWrapper" id="rightSectionMenu"> <div> <div class="journal_article__ArticleStickyTopToolbar-sc-12fk6zy-0 gbrQxi article_sticky_top_toolbar"> 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height="24"><span class="sc-dRFtgE jrsDZP">下载其他格式</年代pan><span class="sc-gkFcWv gWTCXQ">更多的</年代pan></span> <span class="sc-htoDjs bMdQcY sc-gbOuXE jGPvPL icon-colored _1CwL9R82TPl2HxDleeYGDR icon-themeable" title="" font-size="11"></span> </div> <div class="sc-fnwBNb etzuBr"> <a class="sc-htpNat bUhGXt link sc-iNhVCk gWgCNb open_panel" href="//www.newsama.com/downloads/journals/jps/2011/689427.epub" aria-label="ePub" property="background-color" color="#D8D8D8"> <div class="sc-eAKXzc WHkfb"> ePub</div><img alt="" class="sc-EHOje jOLhQl sc-bfYoXt cGuwDn" title="" role="presentation" 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height="24"><span class="sc-dRFtgE jrsDZP">订单打印副本</年代pan><span class="sc-gkFcWv gWTCXQ">订单</年代pan></span><span class="sc-htoDjs kNoiZu sc-gbOuXE jGPvPL right__icon icon-colored _32KP5uexH-Bgs7Kj8Gk1Tz icon-themeable" title="" font-size="16"></span></a> <div class="sc-hBbWxd kdRRST"> <div class="sc-dyGzUR cHatnS"> <div> 的观点<年代pan>1606</年代pan> </div> <div> 下载<年代pan>603</年代pan> </div> </div> <div> <div class="sc-drKuOJ kxdGAZ"> <span class="__dimensions_badge_embed__" data-doi="10.1155/2011/689427" data-style="small_circle"></span>引用</div> </div> </div> <nav class="sc-bRBYWo fXBKFa sc-hUfwpO jHPgUP" id="toolbar__iconNav"> <h3 class="sc-Rmtcm hNPrIr">分享文章</h3> <ul class="sc-hzDkRC bnbfTS"> <li class="iconBorder"><a class="sc-htpNat bUhGXt link" href="https://twitter.com/share?url=https://doi.org/10.1155/2011/689427&via=Hindawi" aria-label="Sharing on Twitter" rel="noopener noreferrer" target="_blank"><img alt="" class="sc-EHOje jOLhQl socialTwitter" title="" role="presentation" 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