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no-repeat 6px;background-position:center;margin-top:10px;min-width:55px;display:none;} @media (min-width:768px){.bfymXb .floats-partial-section .floats-partial-footer .floats-partial-caption .expand_btn{display:none;}} .bfymXb .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){.bfymXb .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 18px 10px 18px;}} @media (min-width:992px){.bfymXb .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 21px 10px 21px;}} .bfymXb .floats-partial-section .floats-partial-footer .floats-partial-caption 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height="24"><span class="text">提交</年代p一个n></年代p一个n><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/cmmm/" aria-label="Computational and Mathematical Methods in Medicine">医学中的计算和数学方法</一个>/<一个class="sc-htpNat bUhGXt link sc-eitiEO jXeALb breadCrumb" href="//www.newsama.com/journals/cmmm/contents/year/2011/" aria-label="2011">2011</一个>/<年代p一个nclass="sc-bhlBdH UVThf">文章</年代p一个n></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><年代p一个nclass="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p一个n><年代pan 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p一个n><年代pan class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#conclusion" aria-label="">结论</一个></年代p一个n><年代pan 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p一个n><年代pan 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p一个n></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p一个n>文章的ID 674318 <span class="sc-fZwumE cUsFHx">|</年代p一个n><一个class="sc-htpNat bUhGXt link sc-fQejPQ duuwge" href="https://doi.org/10.1155/2011/674318" aria-label="Doi-link">https://doi.org/10.1155/2011/674318</一个></div> <div class="sc-LKuAh lcOiDF article_full_citation"> <div class="sc-hzNEM gsmOCv isHide"> <p>H. Zarei，A. V. Kamyad，M. H. Farahi， ＂<年代p一个nclass="adjust-article-svg-size">基于嵌入方法的HIV动态优化控制</年代p一个n>＂，<i>医学中的计算和数学方法</我>， 卷。2011， 文章的ID674318， 9   页面， 2011． https://doi.org/10.1155/2011/674318</p></div> <button class="sc-hSdWYo etauus sc-iBEsjs kPshFw" color="">显示引用</button> </div> <h1 class="sc-iRbamj jZOxOO sc-iSDuPN gbcGIy article_title adjust-article-svg-size heading-title">基于嵌入方法的HIV动态优化控制</h1></div> <div class="sc-jrIrqw eHMFfo article_authors"> <hr class="sc-cEvuZC XkrFe hr__author"> <span class=""><b>h . Zarei</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>，<年代up>1</年代up></年代p一个n><年代pan class="">答:诉Kamyad，<年代up>1</年代up>和</年代p一个n><年代p一个nclass="">m·h·Farahi<一个class="sc-htpNat bUhGXt link" href="http://orcid.org/0000-0002-9711-6936" aria-label="Redirect to Doi" target="_blank"><img alt="" class="sc-EHOje iiusBg sc-iybRtq iQSObO" title="" role="presentation" src="data:image/svg+xml;base64,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" height="16"></a><sup>1</年代up></年代p一个n><div class="sc-fHxwqH dMuGGA isHide"> <p><sup>1</年代up><年代p一个n>马什哈德费尔多西大学应用数学系，马什哈德91775，伊朗</年代p一个n></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>海地楚</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p一个n><年代p一个nclass="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2010年12月30日</年代p一个n></div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">接受</年代p一个n><年代p一个nclass="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2011年2月22日</年代p一个n></div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC isPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">发表</年代p一个n><年代p一个nclass="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2011年4月18日</年代p一个n></div> </div> </div> <article class="sc-jtRlXQ bfymXb article_body "> <div> <div class="xml-content"> <h4 class="header" id="abstract">摘要</h4><p>本研究提出一个最优控制问题，最终目标是采用描述免疫系统与人类免疫缺陷病毒(HIV)相互作用的常微分方程组，实现最佳治疗方案，使患者的生存时间最大化，药物成本最小化。最优控制问题通过嵌入方法在测度空间中转化为一个修正问题，其中最优解的存在性由测度空间的紧性保证。然后用线性规划(LP)问题逼近该问题，并通过求解该问题得到次最优的分段常数控制函数，从临床的角度更具有实用性。介绍了治疗和未治疗患者免疫系统动力学的比较。最后，健康细胞和病毒之间的关系被展示出来。</p><年代p一个nclass="end-abs"></span> <h4 id="introduction">1.介绍</h4><p>人的免疫缺陷病毒感染CD4 + T细胞，这是人免疫系统和其他靶细胞的重要组成部分。感染的细胞产生大量病毒。在过去的二十年里，艾滋病毒的医疗治疗极大地改善了。高活性的抗逆转录病毒治疗（HAART）允许有效地抑制艾滋病毒感染的个体，并延长了多年甚至数十年的获得性免疫缺陷综合征（艾滋病）发作前的时间，并将预期寿命和质量提高给患者。但由于长期受感染的细胞和身体内的部位，抗逆转录病毒治疗不能从受感染的患者免于艾滋病毒，其中药物可能无法达到有效水平[<一个href="#B1">1</一个>- - - - - -<一个href="#B3">3.</一个>］．HAART含有两种主要类型的抗HIV药物：逆转录酶抑制剂（RTI）和蛋白酶抑制剂（PI）。逆转录酶抑制剂通过阻止HIV病毒代码的整合到宿主细胞基因组中，以防止蛋白酶抑制剂免受感染感染病毒颗粒的复制的感染细胞来阻止感染细胞的HIV，并且可以减少并保持低于许多患者的检测极限的病毒载荷．此外，用一种类型的药物治疗也可以增加艾滋病毒靶细胞的CD4 + T细胞计数。</p><p>艾滋病毒感染和艾滋病进展期间的许多宿主病原体相互作用机制仍然未知。艾滋病毒感染的数学建模对医学界感到兴趣，因为没有足够的动物模型来测试药物制度的疗效。这些模型可以测试不同的假设，并以临床或实验研究难以回答的问题提供新的洞察力。已经制定了许多数学模型以描述HIV与健康细胞相互作用的各个方面。其中一些模型在[<一个href="#B4">4</一个>］．HIV感染的基本模型由Wodarz和Nowak提出[<一个href="#B5">5</一个>，包含三个状态变量:健康的CD4+ t细胞、感染的CD4+ t细胞和游离病毒浓度。他们的模型已经被修改，为基于治疗策略的病毒免疫控制提供重要的理论见解，同时保持一个简单的结构[<一个href="#B6">6</一个>］．此外，正如几个临床研究定性描述的那样，这一修正模型已被开发用于猜测HIV感染的自然进化[<一个href="#B7">7</一个>］．</p><p>一些作者将HIV感染的数学模型与控制理论结合起来，以达到适当的目标。例如，这些目标可能包括最大化健康CD4+ t细胞水平和最小化治疗成本[<一个href="#B8">8</一个>- - - - - -<一个href="#B11">11</一个>］，最大限度地提高健康CD4+ t细胞的水平，同时尽量减少治疗成本和病毒载量[<一个href="#B12">12</一个>］，在最大限度地提高免疫反应的同时，尽量减少艾滋病毒感染人数和身体的系统成本[<一个href="#B13">13</一个>，<一个href="#B14">14</一个>］，并最大限度地提高健康CD4+ t细胞数量和免疫反应，同时最大限度地降低治疗成本[<一个href="#B15">15</一个>］，最大化健康的CD4 + T细胞计数，最大限度地减少副作用和耐药性[<一个href="#B16">16</一个>］．</p><p>论文(<一个href="#B17">17</一个>- - - - - -<一个href="#B21">21</一个>］只考虑RTI药物，而论文[<一个href="#B22">22</一个>，<一个href="#B23">23</一个>只考虑法律公正派。在[<一个href="#B24">24</一个>- - - - - -<一个href="#B27">27</一个>， HAART药物的所有效果都合并到模型中的一个控制变量中。在[<一个href="#B28">28</一个>- - - - - -<一个href="#B32">32</一个>］，设计了基于RTIs和pi的动态多药治疗。</p><p>本文考虑了包含抗逆转录病毒治疗效果的HIV动态数学模型，并针对适当的目标进行了最优控制分析。</p><p>论文组织如下:第一部分<一个href="#sec2">2</一个>，描述了HIV的基本数学模型。我们制定的控制问题，试图延长患者的生存时间尽可能长，描述在部分<一个href="#sec3">3.</一个>．用LP问题逼近得到的最优控制问题是本节的主题<一个href="#sec4">4</一个>．从求解LP问题的数值结果介绍<一个href="#sec5">5</一个>．最后,部分<一个href="#sec6">6</一个>用于结束语。</p><h4我d="presentation-of-a-working-model">2.工作模型的呈现</h4><p>本文考虑HIV的病理行为，用常微分方程组(ode)的简化版本建模，如[<一个href="#B17">17</一个>］．该模型与临床数据一致，给出如下:<年代p一个nclass="equation" id="EEq1"> <svg height="173.6125" id="M1" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 173.6125" width="700.9375" xmlns="http://www.w3.org/2000/svg"> 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style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,149.96,16.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.37773" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.541229" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.454668" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.393833" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.746555" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,194.11,13.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,201.12,16.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.37773" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.541229" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.454668" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.393833" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.734055" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,244.06,13.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,251.06,16.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3645067" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.528006" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.441444" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.680443" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.158195" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.321693" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.235134" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.486633" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.864365" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="64.027863" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="67.941299" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="74.192802" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="223.06" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="227.2235" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="233.47501" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-111.26" y="26.33"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-104.60841" y="26.33"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-96.25" y="26.32"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-92.086502" y="26.32"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-88.173065" y="26.32"> ）</t年代p一个n></text> <g> <path d="m 139.8,-14.53 27.25,0" 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,-1,148.14,-26.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.58" y="-8.75"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.607887" y="-8.75"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.972393" y="-8.75"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.135891" y="-8.75"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.049332" y="-8.75"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.300831" y="-8.75"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.464329" y="-8.75"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.891113" y="-8.75"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="79.218353" y="-8.75"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="90.558571" y="-8.75"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="96.910095" y="-8.75"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="108.38785" y="-8.75"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="112.55135" y="-8.75"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="116.46479" y="-8.75"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="120.62829" y="-8.75"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="126.87978" y="-8.75"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="325.98001" y="-8.75"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="330.14349" y="-8.75"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="336.39499" y="-8.75"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-64.809998" y="19.959999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-58.158405" y="19.959999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-46.693153" y="19.959999"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-42.529655" y="19.959999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-38.616215" y="19.959999"> ）</t年代p一个n></text> <g> <path d="m 83.33,-51.46 30.37,0" 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,-1,93.23,-63.34)"> <tspan style="font-size: 12.50px; " x="59.860001" y="-6.2399998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.129999" y="-8.75"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.170387" y="-8.75"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.522392" y="-8.75"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.68589" y="-8.75"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.599331" y="-8.75"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.709999" y="-8.75"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.761452" y="-8.75"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,170.99,-57.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,180.84,-54.59)"> <tspan style="font-size: 12.50px; " x="42.110001" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.049999" y="7.3299999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.391912" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.857164" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.033165" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.946606" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.619999" y="-8.2200003"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.997726" y="-8.2200003"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="76.161232" y="-8.2200003"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="80.074669" y="-8.2200003"> ）</t年代p一个n></text> <g> <path d="m 241.46,-51.46 23.63,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,247.12,-63.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,254.55,-66.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,266.28,-61.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,275.66,-39.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,282.96,-54.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,300.71,-57.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,307.78,-54.59)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.465251" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.62875" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.542189" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.79369" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="166.34" y="-0.28"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="170.50349" y="-0.28"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="176.755" y="-0.28"> ）</t年代p一个n></text> </g> </g> </svg></span>这个模型中的大多数术语都有直接的解释。<年代vg height="18.25" id="M5" style="vertical-align:-2.21957pt;width:26.625px;" version="1.1" viewbox="0 0 26.625 18.25" width="26.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.25)"> <g transform="translate(72,-57.4)"> <g> <path d="m -71.95,70.71 9.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.2897291" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.453228" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.029085" y="0"> ）</t年代p一个n></text> </g> </g> </svg>和<年代vg height="13.45" id="M6" style="vertical-align:-2.21957pt;width:24.2875px;" version="1.1" viewbox="0 0 24.2875 13.45" width="24.2875" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="7.4267821" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.590281" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.166139" y="0"> ）</t年代p一个n></text> </g> </g> </svg>分别表示未成熟CD4+ t细胞和成熟CD4+ t细胞的数量。这个词<年代vg height="13.45" id="M7" style="vertical-align:-2.21957pt;width:22.85px;" version="1.1" viewbox="0 0 22.85 13.45" width="22.85" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2765059" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.440005" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.015863" y="0"> ）</t年代p一个n></text> </g> </g> </svg>表明是HIV粒子<年代vg height="13.45" id="M8" style="vertical-align:-2.21957pt;width:25.487499px;" version="1.1" viewbox="0 0 25.487499 13.45" width="25.487499" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="8.389513" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.553012" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.12887" y="0"> ）</t年代p一个n></text> </g> </g> </svg>指定了HIV特异性的细胞毒t细胞(ctl)作为时间的函数。在这里,<年代vg height="15.4625" id="M9" style="vertical-align:-4.1142pt;width:16.387501px;" version="1.1" viewbox="0 0 16.387501 15.4625" width="16.387501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.4625)"> <g transform="translate(72,-59.63)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m -65.95,67.42 7.01,0" 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,-65.95,59.68)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>这是恒定速率吗<年代vg height="15.4875" id="M10" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 15.4875" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.4875)"> <g transform="translate(72,-59.61)"> <g> <path d="m -71.95,70.71 9.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>细胞产生,<年代vg height="17.875" id="M11" style="vertical-align:-4.74141pt;width:14.1px;" version="1.1" viewbox="0 0 14.1 17.875" width="14.1" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.875)"> <g transform="translate(72,-57.7)"> <g> <path d="m -71.95,70.71 6.4,0" 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,-71.95,62.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.55,59.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>成熟的速度是<年代vg height="15.4875" id="M12" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 15.4875" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.4875)"> <g transform="translate(72,-59.61)"> <g> <path d="m -71.95,70.71 9.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>细胞<年代vg height="10.325" id="M13" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.325" width="11.75" 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p一个n></text> </g> </g> </svg>细胞,<年代vg height="12.725" id="M14" style="vertical-align:-4.74141pt;width:14.1px;" version="1.1" viewbox="0 0 14.1 12.725" width="14.1" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.725)"> <g transform="translate(72,-61.82)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.55,63.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>自然死亡率是多少<年代vg height="10.325" id="M15" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.325" width="11.75" 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p一个n></text> </g> </g> </svg>细胞。此外,<年代vg height="13.425" id="M16" style="vertical-align:-2.29482pt;width:8.8500004px;" version="1.1" viewbox="0 0 8.8500004 13.425" width="8.8500004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>放大系数的线性反馈效应是<年代vg height="10.325" id="M17" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.325" width="11.75" 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p一个n></text> </g> </g> </svg>细胞在流入时减少<年代vg height="15.4875" id="M18" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 15.4875" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.4875)"> <g transform="translate(72,-59.61)"> <g> <path d="m -71.95,70.71 9.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>细胞在时间<年代vg height="9.125" id="M19" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>．免费的病毒颗粒<年代vg height="13.45" id="M20" style="vertical-align:-2.21957pt;width:23.275px;" version="1.1" viewbox="0 0 23.275 13.45" width="23.275" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2765059" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.440005" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.353444" y="0"> ）</t年代p一个n></text> </g> </g> </svg>消除<年代vg height="18.25" id="M21" style="vertical-align:-2.21957pt;width:26.625px;" version="1.1" viewbox="0 0 26.625 18.25" width="26.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.25)"> <g transform="translate(72,-57.4)"> <g> <path d="m -71.95,70.71 9.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.2897291" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.453228" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.029085" y="0"> ）</t年代p一个n></text> </g> </g> </svg>细胞的速率与<年代vg height="19.4" id="M22" style="vertical-align:-3.13504pt;width:92.012497px;" version="1.1" viewbox="0 0 92.012497 19.4" width="92.012497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.4)"> <g transform="translate(72,-56.48)"> <g> <path d="m -71.95,68.06 5.81,0" 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,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.14,56.53)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.13,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2765059" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.440005" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.353444" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.516943" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.906456" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.069956" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.983395" y="0"> ）</t年代p一个n></text> <g> <path d="m -19.98,70.71 9.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-19.98,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3022318" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.465731" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.379169" y="0"> ）</t年代p一个n></text> </g> </g> </svg>在时间<年代vg height="9.125" id="M23" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>．同样的,<年代vg height="14.6" id="M24" style="vertical-align:-3.13504pt;width:88.887497px;" version="1.1" viewbox="0 0 88.887497 14.6" width="88.887497" 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p一个n></text> <text transform="matrix(1,0,0,-1,-66.76,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.75,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2765059" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.440005" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.353444" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.516943" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.906456" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.069956" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.983395" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.146893" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.573673" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.737175" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.650612" y="0"> ）</t年代p一个n></text> </g> </g> </svg>是消除速度<年代vg height="10.325" id="M25" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.325" width="11.75" 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p一个n></text> </g> </g> </svg>细胞。这个词<年代vg height="10.7375" id="M26" 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p一个n></text> </g> </g> </svg>描述了艾滋病毒颗粒的增长速度<年代vg height="9.9375" id="M27" style="vertical-align:-2.34499pt;width:8.0625px;" version="1.1" viewbox="0 0 8.0625 9.9375" width="8.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.9375)"> <g transform="translate(72,-64.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>HIV产物的失活率是由细胞毒素介导的吗<年代vg height="10.6125" id="M28" 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p一个n></text> </g> </g> </svg>细胞。<年代vg height="14.375" id="M29" style="vertical-align:-3.24037pt;width:16.4625px;" version="1.1" viewbox="0 0 16.4625 14.375" width="16.4625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.95,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是大量涌入<年代vg height="10.6125" id="M30" 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p一个n></text> </g> </g> </svg>细胞前体,<年代vg height="7.1875" id="M31" style="vertical-align:-0.13794pt;width:7.6875px;" version="1.1" viewbox="0 0 7.6875 7.1875" width="7.6875" 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p一个n></text> </g> </g> </svg>是他们的成熟率，<年代vg height="7.1750002" id="M32" 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p一个n></text> </g> </g> </svg>增殖率是多少<年代vg height="10.6125" id="M33" 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p一个n></text> </g> </g> </svg>通过HIV产品的抗原刺激下的细胞，和<年代vg height="10.85" id="M34" style="vertical-align:-3.24037pt;width:16.9625px;" version="1.1" viewbox="0 0 16.9625 10.85" width="16.9625" 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,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.55,63.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是自然死亡率辅助t细胞对细胞成熟和增殖的影响<年代vg height="10.6125" id="M35" 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p一个n></text> </g> </g> </svg>细胞用比率表示<年代vg height="14.75" id="M36" style="vertical-align:-3.25793pt;width:44.424999px;" version="1.1" viewbox="0 0 44.424999 14.75" width="44.424999" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="7.4267821" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.590281" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.50372" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.667219" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.143053" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-41.38,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> </g> </g> </svg>,<年代vg height="7.2375002" id="M37" style="vertical-align:-0.11285pt;width:7.9749999px;" version="1.1" viewbox="0 0 7.9749999 7.2375002" width="7.9749999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.2375)"> <g transform="translate(72,-66.21)"> <text transform="matrix(1,0,0,-1,-71.95,66.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>介绍了表征这种辅助效果的强度。通过降低价值来模拟化学治疗剂<年代vg height="7.0124998" id="M38" style="vertical-align:-0.0pt;width:9.4125004px;" version="1.1" viewbox="0 0 9.4125004 7.0124998" width="9.4125004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.0125)"> <g transform="translate(72,-66.39)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>，即艾滋病毒的增殖率。较低的值<年代vg height="7.0124998" id="M39" style="vertical-align:-0.0pt;width:9.4125004px;" version="1.1" viewbox="0 0 9.4125004 7.0124998" width="9.4125004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.0125)"> <g transform="translate(72,-66.39)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>对应较高的rti药物剂量。</p><h4我d="optimal-control-formulation">3.最优控制配方</h4><p>在本节中，我们制定了识别抑制参数的最佳控制问题<年代vg height="7.0124998" id="M40" style="vertical-align:-0.0pt;width:9.4125004px;" version="1.1" viewbox="0 0 9.4125004 7.0124998" width="9.4125004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.0125)"> <g transform="translate(72,-66.39)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>在（<一个href="#EEq1">3.</一个>），具有控制变量的函数。特别是，我们将更换参数<年代vg height="7.0124998" id="M41" style="vertical-align:-0.0pt;width:9.4125004px;" version="1.1" viewbox="0 0 9.4125004 7.0124998" width="9.4125004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.0125)"> <g transform="translate(72,-66.39)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>与函数<年代vg height="13.45" id="M42" style="vertical-align:-2.21957pt;width:48.299999px;" version="1.1" viewbox="0 0 48.299999 13.45" width="48.299999" 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"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0271664" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.367388" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.29381" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.457308" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.370747" y="0"> ）</t年代p一个n></text> </g> </g> </svg>．然后，该选择标识控制变量<年代vg height="13.45" id="M43" style="vertical-align:-2.21957pt;width:22.8375px;" version="1.1" viewbox="0 0 22.8375 13.45" width="22.8375" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="5.9264221" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.089921" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.00336" y="0"> ）</t年代p一个n></text> </g> </g> </svg>以抑制病毒繁殖的速率为模型，其模型为药物剂量的简单函数。</p><p>在临床实践中，通常使用以下指南。<年代p一个nclass="list"><span class="list-item"><span class="list-label">(我)</年代p一个n><年代p一个nclass="list-content">抗逆转录病毒疗法始于<年代vg height="13.05" id="M44" style="vertical-align:-3.25793pt;width:11.1125px;" version="1.1" viewbox="0 0 11.1125 13.05" width="11.1125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> </g> </g> </svg>也就是CD4+ t细胞数量降到350个/以下的时间<我>μ.。</我>l</年代p一个n></年代p一个n><span class="list-item"><span class="list-label">(2)</年代p一个n><年代p一个nclass="list-content">CD4+ t细胞计数低于200个/细胞，标志着从HIV到AIDS的转变<我>μ.。</我>l</年代p一个n></年代p一个n><span class="list-item"><span class="list-label">(3)</年代p一个n><年代p一个nclass="list-content">当一个人的CD4+ t细胞计数低于正常值时，他/她就被认为患有全面的艾滋病<年代vg height="18.262501" id="M45" style="vertical-align:-4.56824pt;width:45.0625px;" version="1.1" viewbox="0 0 45.0625 18.262501" width="45.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.2625)"> <g transform="translate(72,-57.39)"> <text transform="matrix(1,0,0,-1,-71.95,61.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> C</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3395014" y="0"> D</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.366667" y="0"> 4</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-48.33,67.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> +</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-48.33,57.53)"> <tspan style="font-size: 8.75px; " x="0" y="0"> c</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.8858881" y="0"> r</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.95784" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3908958" y="0"> t</t年代p一个n></text> </g> </g> </svg>，通常为50个细胞/<我>μ.。</我>l</年代p一个n></年代p一个n></span></p> <p>这篇论文的目的是提出一种药物治疗方案，在尽量减少药物成本的同时，尽可能推迟艾滋病的全面发作，延长生存时间。可以这样建模。</p><p>假设艾滋病的全面爆发发生在时间之后<年代vg height="14.9375" id="M46" style="vertical-align:-4.77652pt;width:13.025px;" version="1.1" viewbox="0 0 13.025 14.9375" width="13.025" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.9375)"> <g transform="translate(72,-60.05)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>．因此，我们应该这样做<年代p一个nclass="equation" id="EEq5"> <svg height="19.6" id="M47" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.6" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.6)"> <g transform="translate(72,-56.32)"> <text transform="matrix(1,0,0,-1,77.94,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.38" y="-0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.543499" y="-0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.456938" y="-0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.096272" y="-0.0099999998"> ≥</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.124157" y="-0.0099999998"> C</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.463657" y="-0.0099999998"> D</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.490826" y="-0.0099999998"> 4</t年代p一个n></text> <text transform="matrix(1,0,0,-1,140.69,66.3)"> <tspan style="font-size: 8.75px; " x="0" y="0"> +</t年代p一个n></text> <text transform="matrix(1,0,0,-1,140.69,56.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> c</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.8858881" y="0"> r</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.9665918" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="0"> t</t年代p一个n></text> <text transform="matrix(1,0,0,-1,153.03,61.13)"> <tspan style="font-size: 12.50px; " x="36.68" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.459999" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.166139" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.54291" y="0"> ∈</t年代p一个n></text> <text transform="matrix(1,0,0,-1,198.41,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,203.28,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,212.41,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,218.81,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.389999" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.25" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.8699999" y="-2.51"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.00103" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,271.97,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,278.38,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3199997" y="-2.51"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.347885" y="-2.51"> C</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.687387" y="-2.51"> D</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.714554" y="-2.51"> 4</t年代p一个n></text> <text transform="matrix(1,0,0,-1,323.36,66.3)"> <tspan style="font-size: 8.75px; " x="0" y="0"> +</t年代p一个n></text> <text transform="matrix(1,0,0,-1,323.36,56.67)"> <tspan style="font-size: 8.75px; " x="0" y="0"> c</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.8858881" y="0"> r</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.95784" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3908958" y="0"> t</t年代p一个n></text> <text transform="matrix(1,0,0,-1,335.69,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="138.42999" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="142.59351" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="148.845" y="0"> ）</t年代p一个n></text> </g> </g> </svg></span>使用大多数化学疗法产生的问题是多种且有时有害的副作用，以及由于病毒对突变的能力进行了一定时间后治疗的无效性，并且对治疗进行抗性。通过施加有限的治疗间隔来考虑这些现象的全球效果[<一个href="#B22">22</一个>，即持续一段时间的治疗<年代vg height="13.05" id="M48" style="vertical-align:-3.25793pt;width:11.1125px;" version="1.1" viewbox="0 0 11.1125 13.05" width="11.1125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> </g> </g> </svg>来<年代vg height="13.05" id="M49" style="vertical-align:-3.25793pt;width:36.575001px;" version="1.1" viewbox="0 0 36.575001 13.05" width="36.575001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.38,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.327718" y="0"> </t年代p一个n></text> </g> </g> </svg>．因此，支持控制功能<年代vg height="13.45" id="M50" style="vertical-align:-2.21957pt;width:22.4125px;" version="1.1" viewbox="0 0 22.4125 13.45" width="22.4125" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="5.9264221" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.089921" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.665779" y="0"> ）</t年代p一个n></text> </g> </g> </svg>必须在治疗期间吗<年代p一个nclass="equation" id="EEq6"> <svg height="19.35" id="M51" 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,-1,154.79,61.13)"> <tspan style="font-size: 12.50px; " x="49.220001" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.009998" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.863667" y="0"> u</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.115167" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.366667" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.693665" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.095921" y="0"> ⊆</t年代p一个n></text> <text transform="matrix(1,0,0,-1,212.72,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,217.59,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,226.71,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,234.37,61.13)"> <tspan style="font-size: 12.50px; " x="17.59" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.327718" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.459999" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="239.75" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="243.9135" y="0"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="250.16499" y="0"> ）</t年代p一个n></text> </g> </g> </svg></span>这里，我们遵循[<一个href="#B8">8</一个>，<一个href="#B22">22</一个>］假设治疗的成本与之成比例<年代vg height="16.5375" id="M52" style="vertical-align:-2.21957pt;width:28.924999px;" version="1.1" viewbox="0 0 28.924999 16.5375" width="28.924999" 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,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.02,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61.15,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代p一个n></text> </g> </g> </svg>在时间<年代vg height="9.125" id="M53" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>．因此，总的治疗费用是<年代vg height="23.700001" id="M54" style="vertical-align:-6.05542pt;width:61.8125px;" version="1.1" viewbox="0 0 61.8125 23.700001" width="61.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,23.7)"> <g transform="translate(72,-53.04)"> <text transform="matrix(1,0,0,-1,-71.95,59.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∫</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.25,66.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.51,64.8)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.5,55.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.76,53.18)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.21,59.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-50.28,64.13)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-45.41,59.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.240437" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.892033" y="0"> </t年代p一个n></text> </g> </g> </svg>．所以，应该最大限度地发挥以下功能:<年代p一个nclass="equation" id="EEq7"> <svg height="41.075001" id="M55" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 41.075001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,41.075)"> <g transform="translate(72,-39.14)"> <text transform="matrix(1,0,0,-1,133.71,52.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.4300003" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.28" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,152.9,49.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,159.31,52.96)"> <tspan style="font-size: 12.50px; " x="11.13" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.459999" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.487885" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,195.72,49.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,204.9,52.96)"> <tspan style="font-size: 12.50px; " x="20.200001" y="7.6999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,232.1,66.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,234.84,64.8)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,230.85,41.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,233.59,39.27)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,242.14,52.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,248.06,57.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,255.02,52.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0734386" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.324939" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.976536" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.889975" y="0.0099999998"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="219.10001" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="223.2635" y="0.0099999998"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="229.515" y="0.0099999998"> ）</t年代p一个n></text> </g> </g> </svg></span>参数<年代vg height="10.8125" id="M56" 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p一个n></text> </g> </g> </svg>是用来设置最大生存时间之间的相对重要性<年代vg height="14.9375" id="M57" style="vertical-align:-4.77652pt;width:13.025px;" version="1.1" viewbox="0 0 13.025 14.9375" width="13.025" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.9375)"> <g transform="translate(72,-60.05)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>并将身体的系统成本降至最低。设置<年代vg height="19.4" id="M58" style="vertical-align:-3.13504pt;width:45.825001px;" version="1.1" viewbox="0 0 45.825001 19.4" width="45.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.4)"> <g transform="translate(72,-56.48)"> <g> <path d="m -71.95,70.71 9.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.765563" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.805952" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-40.26,56.53)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>，<年代vg height="14.2375" id="M59" style="vertical-align:-3.13504pt;width:43.487499px;" version="1.1" viewbox="0 0 43.487499 14.2375" width="43.487499" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="10.890113" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.930502" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-42.14,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>，<年代vg height="11.075" id="M60" style="vertical-align:-3.25793pt;width:42.049999px;" version="1.1" viewbox="0 0 42.049999 11.075" width="42.049999" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="9.7398367" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.780226" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-43.29,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</t年代p一个n></text> </g> </g> </svg>,<年代vg height="14.3375" id="M61" style="vertical-align:-3.13504pt;width:44.6875px;" version="1.1" viewbox="0 0 44.6875 14.3375" width="44.6875" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="11.852844" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.893232" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-41.17,60.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</t年代p一个n></text> </g> </g> </svg>，微分方程组(<一个href="#EEq1">1</一个>）- (<一个href="#EEq1">4</一个>）可以概括地表示为<年代p一个nclass="equation" id="EEq8"> <svg height="147.47501" id="M62" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 147.47501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,147.475)"> <g transform="translate(72,45.98)"> <text transform="matrix(1,0,0,-1,61.98,63.2)"> <tspan style="font-size: 12.50px; " x="18" y="64.050003"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.030001" y="27.780001"> ⎛</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.030001" y="39.049999"> ⎜</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.030001" y="50.330002"> ⎜</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.030001" y="61.599998"> ⎜</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.030001" y="72.879997"> ⎜</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.030001" y="84.150002"> ⎜</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.030001" y="95.43"> ⎜</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.030001" y="106.64"> ⎝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.66" y="23.639999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ̇</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-6.6766019" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="2.2755461" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.439045" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.352484" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.991817" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.032206" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.7593" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.922798" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.836239" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.049988" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.014641" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.178139" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.091576" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="75.330574" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="80.544327" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="88.558746" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="92.722244" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="96.635689" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="100.79919" y="0"> ）</t年代p一个n></text> <text transform="matrix(1,0,0,-1,103.64,36.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,113.43,39.56)"> <tspan style="font-size: 12.50px; " x="20.4" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.25" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,146.56,44.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.3400002"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,154.21,39.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,172.43,36.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,177.31,37.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.6300001" y="-2.51"> −</t年代p一个n></text> <g> <path d="m 197.28,47.8 6.4,0" 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,-1,197.28,39.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,203.68,36.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,210.69,39.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,217.57,36.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,225.22,39.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n></text> <g> <path d="m 236.56,47.96 5.82,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,236.56,39.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,242.38,36.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,249.39,39.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,256.26,36.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,261.14,39.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,268.02,36.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</t年代p一个n></text> <text transform="matrix(1,0,0,-1,272.89,39.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,279.77,36.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <g> <path d="m 128.13,29.59 6.4,0" 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,-1,128.13,21.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,134.53,18.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,141.54,21.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,148.42,18.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,156.07,21.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,173.82,18.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,180.83,21.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,187.7,18.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,195.36,21.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.327718" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,211.89,18.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,218.9,21.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,225.77,18.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,230.65,21.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,237.52,18.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</t年代p一个n></text> <text transform="matrix(1,0,0,-1,242.4,21.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,249.28,18.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,140.63,1.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,147.5,-1.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,154.46,-0.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.52"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.013499" y="-2.52"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.040665" y="-2.52"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.380886" y="-2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.307308" y="-2.52"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.558807" y="-2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.886047" y="-2.52"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="63.226269" y="-2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.577789" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,230.93,-1.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</t年代p一个n></text> <text transform="matrix(1,0,0,-1,235.8,-0.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-122.56" y="31.639999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-116.71" y="29.129999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-110.65855" y="29.129999"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,131.14,-32.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,140.99,-29.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.391912" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,166.26,-32.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</t年代p一个n></text> <text transform="matrix(1,0,0,-1,171.14,-32.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9299998" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,185.95,-32.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,190.83,-39.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.29" y="-18.870001"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,209,-23.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <g> <path d="m 202.12,-26.71 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,-1,202.12,-40.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,209,-35.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.3400002"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,215.07,-39.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,225.17,-10.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,232.47,-29.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,250.22,-32.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,257.29,-29.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,264.17,-32.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</t年代p一个n></text> <text transform="matrix(1,0,0,-1,284.64,35.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⎞</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="11.27"> ⎟</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="22.549999"> ⎟</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="33.82"> ⎟</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="45.099998"> ⎟</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="56.369999"> ⎟</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="67.650002"> ⎟</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="78.860001"> ⎠</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.71" y="36.27"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.876139" y="36.27"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.84079" y="36.27"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.004288" y="36.27"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.255791" y="36.27"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.895123" y="36.27"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.923008" y="36.27"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,353.45,-3.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,358.32,-0.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="115.8" y="-10.73"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="119.9635" y="-10.73"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="126.215" y="-10.73"> ）</t年代p一个n></text> </g> </g> </svg></span>假设<年代vg height="10.325" id="M63" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" 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p一个n></text> </g> </g> </svg>表示所有可测量控制功能的集合<年代vg height="13.45" id="M64" style="vertical-align:-2.21957pt;width:79.5625px;" version="1.1" viewbox="0 0 79.5625 13.45" width="79.5625" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="5.9264221" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.089921" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.665779" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.292608" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.332996" y="0"> ［</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.496498" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.747997" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.125248" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.376747" y="0"> ］</t年代p一个n></text> </g> </g> </svg>，在哪里<年代vg height="13.45" id="M65" style="vertical-align:-2.21957pt;width:22.4125px;" version="1.1" viewbox="0 0 22.4125 13.45" width="22.4125" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="5.9264221" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.089921" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.665779" y="0"> ）</t年代p一个n></text> </g> </g> </svg>满足(<一个href="#EEq6">6</一个>），以及(的相应解<一个href="#EEq8">8</一个>在最后时刻<年代vg height="14.9375" id="M66" style="vertical-align:-4.77652pt;width:13.025px;" version="1.1" viewbox="0 0 13.025 14.9375" width="13.025" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.9375)"> <g transform="translate(72,-60.05)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>满足(<一个href="#EEq5">5</一个>）．因此，我们正在寻找<年代vg height="14.3" id="M67" style="vertical-align:-2.21957pt;width:61.299999px;" version="1.1" viewbox="0 0 61.299999 14.3" width="61.299999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3)"> <g transform="translate(72,-60.56)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.02,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.739357" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.366187" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.406576" y="0"> </t年代p一个n></text> </g> </g> </svg>这样<年代p一个nclass="equation" id="EEq9"> <svg height="28.9625" id="M68" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 28.9625" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,28.9625)"> <g transform="translate(72,-48.83)"> <text transform="matrix(1,0,0,-1,124.7,57.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.4200001" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.27" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,143.88,54.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,150.29,57.29)"> <tspan style="font-size: 12.50px; " x="11.14" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.919998" y="4.9200001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.290001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.459999" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.487885" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,203.49,62.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.1499996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,209.89,57.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,221.03,62.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,226.11,52.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.6800003" y="-4.9200001"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.84614" y="-4.9200001"> ∀</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.847818" y="-4.9200001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.250076" y="-4.9200001"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.290462" y="-4.9200001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.817749" y="-4.9200001"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="248.00999" y="-4.9200001"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="252.17349" y="-4.9200001"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="258.42499" y="-4.9200001"> ）</t年代p一个n></text> </g> </g> </svg></span>设置<年代vg height="17.8375" id="M69" style="vertical-align:-3.25793pt;width:171.9375px;" version="1.1" viewbox="0 0 171.9375 17.8375" width="171.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8375)"> <g transform="translate(72,-57.73)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.01,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.14,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0769377" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.278186" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.154837" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.318335" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.231773" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.395271" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.609024" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.535446" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.698944" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.612385" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.775883" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="63.415215" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="75.455605" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="84.482773" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="95.82299" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="102.58711" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,48.38,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,53.26,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代p一个n></text> </g> </g> </svg>，则最优用药方案问题，而忽略<年代vg height="13.05" id="M70" style="vertical-align:-3.25793pt;width:11.1125px;" version="1.1" viewbox="0 0 11.1125 13.05" width="11.1125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.05)"> <g transform="translate(72,-61.56)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> </g> </g> </svg>，可以表示为:<年代p一个nclass="equation" id="EEq10"> <svg height="41.075001" id="M71" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 41.075001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,41.075)"> <g transform="translate(72,-39.14)"> <text transform="matrix(1,0,0,-1,138.55,52.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.727334" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.278666" y="0"> x</t年代p一个n></text> <text transform="matrix(1,0,0,-1,133.13,45.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,135.87,43.06)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,140.59,45.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.6408319" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.703696" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="19.621984" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,169.67,45.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,176.67,66.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,179.41,64.8)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,175.42,41.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,178.16,39.27)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,186.71,52.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,193.65,49.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,200.61,52.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0734386" y="0.0099999998"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.274687" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.239338" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.402838" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.316277" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.567776" y="0.0099999998"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.769024" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.783447" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.946945" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.860386" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.023884" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="68.275383" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="74.926979" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="267.26001" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="271.42349" y="0.0099999998"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="277.67499" y="0.0099999998"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="283.92651" y="0.0099999998"> ）</t年代p一个n></text> </g> </g> </svg></span>受<年代p一个nclass="equation" id="EEq11"> <svg height="78.699997" id="M72" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 78.699997" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,78.7)"> <g transform="translate(72,-9.04)"> <text transform="matrix(1,0,0,-1,164.83,63.2)"> <tspan style="font-size: 12.50px; " x="-43.59" y="24.16"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-34.630001" y="26.67"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-28.780001" y="24.16"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ̇</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-6.6640992" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.663379" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.703768" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.443365" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.606865" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.520302" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.72155" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.686203" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.849701" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.763142" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.014641" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.215889" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="74.230309" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="78.393806" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="82.307251" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="86.470749" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="92.722244" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="303.04001" y="0.63"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="307.20349" y="0.63"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="313.45499" y="0.63"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="319.70651" y="0.63"> ）</t年代p一个n></text> <text transform="matrix(1,0,0,-1,139.96,35.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,144.84,36.53)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3199997" y="-2.51"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.347885" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,173.08,35.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,175.81,33.73)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,179.94,39.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.131029" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,211.95,35.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,218.91,36.53)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,228.67,35.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,235.08,36.53)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3199997" y="-2.51"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.347885" y="-2.51"> C</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.687387" y="-2.51"> D</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.714554" y="-2.51"> 4</t年代p一个n></text> <text transform="matrix(1,0,0,-1,280.06,44.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> +</t年代p一个n></text> <text transform="matrix(1,0,0,-1,280.06,34.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> c</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.8858881" y="0"> r</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.95784" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3908958" y="0"> t</t年代p一个n></text> <text transform="matrix(1,0,0,-1,292.39,39.04)"> <tspan style="font-size: 12.50px; " x="-158.59" y="25.18"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="175.48" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="179.64349" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="185.895" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="192.1465" y="0"> ）</t年代p一个n></text> <text transform="matrix(1,0,0,-1,140.68,10.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,147.63,13.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.716271" y="0"> ≥</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.744158" y="0"> C</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.083656" y="0"> D</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.110825" y="0"> 4</t年代p一个n></text> <text transform="matrix(1,0,0,-1,199,19.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> +</t年代p一个n></text> <text transform="matrix(1,0,0,-1,199,9.39)"> <tspan style="font-size: 8.75px; " x="0" y="0"> c</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.8858881" y="0"> r</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.9665918" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="0"> t</t年代p一个n></text> <text transform="matrix(1,0,0,-1,211.34,13.86)"> <tspan style="font-size: 12.50px; " x="36.68" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.459999" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.166139" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.54291" y="0"> ∈</t年代p一个n></text> <text transform="matrix(1,0,0,-1,256.72,10.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,261.59,13.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,270.72,10.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,277.12,11.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.79" y="-2.4200001"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="190.75" y="-2.4200001"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="194.9135" y="-2.4200001"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="201.16499" y="-2.4200001"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="207.4165" y="-2.4200001"> ）</t年代p一个n></text> </g> </g> </svg></span></p> <p>这种最优控制问题称为OCP。在解决OCP的过程中，可能会出现一些问题。一组<年代vg height="10.325" id="M75" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" 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p一个n></text> </g> </g> </svg>可能是空的。如果<年代vg height="10.325" id="M76" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" 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p一个n></text> </g> </g> </svg>是不是空的，功能测量系统的性能可能达不到其设定的最大值<年代vg height="10.325" id="M77" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" 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p一个n></text> </g> </g> </svg>．为了克服这些困难，在下一节中，我们将OCP转换为度量空间中的一个修改过的问题。</p><h4我d="approximation-of-ocp-by-linear-programming-problem">4.OCP的线性规划逼近</h4><p>基于Young思想的度量理论求解最优控制问题[<一个href="#B33">33</一个>），由威尔逊和卢比奥首次申请[<一个href="#B34">34</一个>，在理论上是由鲁比奥在[<一个href="#B35">35</一个>］．然后，将该方法推广为用LP模型逼近时间最优问题[<一个href="#B36">36</一个>］．这里使用的是这种方法。</p><h5我d="sec4.1">4.1。功能空间</h5><p>我们假设状态变量<年代vg height="13.45" id="M78" style="vertical-align:-2.21957pt;width:23.6px;" version="1.1" viewbox="0 0 23.6 13.45" width="23.6" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="6.8766499" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.616007" y="0"> ）</t年代p一个n></text> </g> </g> </svg>以及控制输入<年代vg height="13.45" id="M79" style="vertical-align:-2.21957pt;width:22.4125px;" version="1.1" viewbox="0 0 22.4125 13.45" width="22.4125" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="5.9264221" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.089921" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.665779" y="0"> ）</t年代p一个n></text> </g> </g> </svg>，分别得到它们在紧集中的值<年代vg height="18.475" id="M80" style="vertical-align:-3.25793pt;width:189.89999px;" version="1.1" viewbox="0 0 189.89999 18.475" width="189.89999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.475)"> <g transform="translate(72,-57.22)"> <text transform="matrix(1,0,0,-1,-71.95,60.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.427982" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.46837" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-38.51,57.39)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-30.86,60.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.777586" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-11.11,57.39)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-3.46,60.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.777586" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,16.29,57.39)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,23.94,60.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.777586" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,43.68,57.39)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</t年代p一个n></text> <text transform="matrix(1,0,0,-1,52.03,60.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊂</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> ℜ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,75,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</t年代p一个n></text> </g> </g> </svg>和<年代vg height="11.5125" id="M81" style="vertical-align:-0.3135pt;width:44.1875px;" version="1.1" viewbox="0 0 44.1875 11.5125" width="44.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.5125)"> <g transform="translate(72,-62.79)"> <text transform="matrix(1,0,0,-1,-71.95,63.15)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.277946" y="0"> ⊂</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.318335" y="0"> ℜ</t年代p一个n></text> </g> </g> </svg>．放<年代vg height="16.424999" id="M82" style="vertical-align:-4.77652pt;width:68.762497px;" version="1.1" viewbox="0 0 68.762497 16.424999" width="68.762497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.425)"> <g transform="translate(72,-58.86)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.214951" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.255341" y="0"> ［</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.418839" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-41.61,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-36.74,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-27.61,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-21.21,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ］</t年代p一个n></text> </g> </g> </svg>．在这里，我们将推导(<一个href="#EEq11">11</一个>）- (<一个href="#EEq11">13</一个>）．</p><p><年代p一个nclass="statement" id="deff1"><span class="statement-title"><i class="statement-title">定义1。</我></年代p一个n>一个三<年代vg height="16.424999" id="M83" style="vertical-align:-4.77652pt;width:79.487503px;" version="1.1" viewbox="0 0 79.487503 16.424999" width="79.487503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.425)"> <g transform="translate(72,-58.86)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.5772982" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.617687" y="0"> ［</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.781185" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-42.25,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.84,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.077898" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.291649" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.218071" y="0"> ］</t年代p一个n></text> </g> </g> </svg>如果满足下列条件，则称为可接受的。<年代p一个nclass="list"><span class="list-item"><span class="list-label">(我)</年代p一个n><年代p一个nclass="list-content">向量函数<年代vg height="13.45" id="M84" style="vertical-align:-2.21957pt;width:23.6px;" version="1.1" viewbox="0 0 23.6 13.45" width="23.6" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="6.8766499" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.616007" y="0"> ）</t年代p一个n></text> </g> </g> </svg>是绝对连续的和属于<年代vg height="10.55" id="M85" style="vertical-align:-0.0pt;width:11.325px;" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.55)"> <g transform="translate(72,-63.56)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>对所有<年代vg height="10.75" id="M86" style="vertical-align:-0.33858pt;width:34.724998px;" version="1.1" viewbox="0 0 34.724998 10.75" width="34.724998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.75)"> <g transform="translate(72,-63.4)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.37677" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.417158" y="0"> </t年代p一个n></text> </g> </g> </svg>．</年代p一个n></年代p一个n><span class="list-item"><span class="list-label">(2)</年代p一个n><年代p一个nclass="list-content">这个函数<年代vg height="13.45" id="M87" style="vertical-align:-2.21957pt;width:22.4125px;" version="1.1" viewbox="0 0 22.4125 13.45" width="22.4125" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="5.9264221" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.089921" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.665779" y="0"> ）</t年代p一个n></text> </g> </g> </svg>在集合中取得其值<年代vg height="10.5375" id="M88" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>勒贝格是可测量的<年代vg height="10.5125" id="M89" style="vertical-align:-0.15048pt;width:10.4375px;" version="1.1" viewbox="0 0 10.4375 10.5125" width="10.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5125)"> <g transform="translate(72,-63.59)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>．</年代p一个n></年代p一个n><span class="list-item"><span class="list-label">(3)</年代p一个n><年代p一个nclass="list-content"> <svg height="9.875" id="M90" style="vertical-align:-2.29482pt;width:7.7624998px;" version="1.1" viewbox="0 0 7.7624998 9.875" width="7.7624998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.875)"> <g transform="translate(72,-64.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>满足(<一个href="#EEq11">11</一个>）- (<一个href="#EEq11">13</一个>），在<年代vg height="13.9625" id="M91" style="vertical-align:-0.15048pt;width:16.5375px;" version="1.1" viewbox="0 0 16.5375 13.9625" width="16.5375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9625)"> <g transform="translate(72,-60.83)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.7,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> </g> </g> </svg>的内部集合<年代vg height="10.5125" id="M92" style="vertical-align:-0.15048pt;width:10.4375px;" version="1.1" viewbox="0 0 10.4375 10.5125" width="10.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5125)"> <g transform="translate(72,-63.59)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>．</年代p一个n></年代p一个n></span>假设所有可允许的三元组的集合是非空的，并表示它<年代vg height="10.575" id="M93" style="vertical-align:-0.20064pt;width:17.9625px;" version="1.1" viewbox="0 0 17.9625 10.575" width="17.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.575)"> <g transform="translate(72,-63.54)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>．让<年代vg height="9.875" id="M94" style="vertical-align:-2.29482pt;width:7.7624998px;" version="1.1" viewbox="0 0 7.7624998 9.875" width="7.7624998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.875)"> <g transform="translate(72,-64.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是一个可容许的三元组，<年代vg height="10.325" id="M95" style="vertical-align:-0.0pt;width:11.625px;" version="1.1" viewbox="0 0 11.625 10.325" width="11.625" 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p一个n></text> </g> </g> </svg>是一个开放的球<年代vg height="14.9" id="M96" style="vertical-align:-0.27588pt;width:19.875px;" version="1.1" viewbox="0 0 19.875 14.9" width="19.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.9)"> <g transform="translate(72,-60.08)"> <text transform="matrix(1,0,0,-1,-71.95,60.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℜ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61.02,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5</t年代p一个n></text> </g> </g> </svg>包含<年代vg height="10.9375" id="M97" style="vertical-align:-0.3135pt;width:36.712502px;" version="1.1" viewbox="0 0 36.712502 10.9375" width="36.712502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9375)"> <g transform="translate(72,-63.25)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.5272856" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.304873" y="0"> </t年代p一个n></text> </g> </g> </svg>,让<年代vg height="15.325" id="M98" style="vertical-align:-2.21957pt;width:37.487499px;" version="1.1" viewbox="0 0 37.487499 15.325" width="37.487499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.325)"> <g transform="translate(72,-59.74)"> <text transform="matrix(1,0,0,-1,-71.95,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.56,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.09,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.865587" y="0"> ）</t年代p一个n></text> </g> </g> </svg>是所有实值连续可微函数的空间。让<年代vg height="15.4125" id="M99" style="vertical-align:-2.29482pt;width:67.287498px;" version="1.1" viewbox="0 0 67.287498 15.4125" width="67.287498" 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"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.790329" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.830717" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-38.72,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.25,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.865587" y="0"> ）</t年代p一个n></text> </g> </g> </svg>以及定义<年代vg height="14.0625" id="M100" style="vertical-align:-2.29482pt;width:16.975px;" version="1.1" viewbox="0 0 16.975 14.0625" width="16.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.0625)"> <g transform="translate(72,-60.75)"> <text transform="matrix(1,0,0,-1,-71.95,63.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.62,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>如下:<年代p一个nclass="equation" id="EEq14"> <svg height="15.8875" id="M101" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 15.8875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.8875)"> <g transform="translate(72,-59.29)"> <text transform="matrix(1,0,0,-1,57.31,63.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,65.64,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,72.88,63.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0734386" y="0.0099999998"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.274687" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.239338" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.402838" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.316277" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.555271" y="0.0099999998"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.769024" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.783447" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.946945" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.860386" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.023884" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.663216" y="0.0099999998"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="81.691101" y="0.0099999998"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,162.91,59.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,170.3,63.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1700001" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0834389" y="0.0099999998"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.284687" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.249338" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.412836" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.326277" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.489777" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.42894" y="0.0099999998"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.780464" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.520061" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.683559" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="64.597" y="0.0099999998"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.798248" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="78.762901" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="82.926399" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="86.839836" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="93.091339" y="0.0099999998"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="98.292587" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="106.30701" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="110.4705" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="114.38394" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="118.54745" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="125.48661" y="0.0099999998"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="136.83934" y="0.0099999998"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,315.47,59.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,320.79,63.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0734386" y="0.0099999998"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.274687" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.239338" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.402838" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.316277" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.479774" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="147.08" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="151.2435" y="0.0099999998"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="157.495" y="0.0099999998"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="163.74651" y="0.0099999998"> ）</t年代p一个n></text> </g> </g> </svg></span>为每一个<年代vg height="13.45" id="M102" style="vertical-align:-2.21957pt;width:106.075px;" version="1.1" viewbox="0 0 106.075 13.45" width="106.075" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0769377" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.278186" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.154837" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.318335" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.231773" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.395271" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.609024" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.535446" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.698944" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.612385" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.775883" y="0"> ］</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="63.415215" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="75.4431" y="0"> ω.</t年代p一个n></text> </g> </g> </svg>，在哪里<年代vg height="11.075" id="M103" style="vertical-align:-0.3135pt;width:97.425003px;" version="1.1" viewbox="0 0 97.425003 11.075" width="97.425003" 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,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ω.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.765563" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.805952" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.333237" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.110825" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.863644" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="67.641228" y="0"> </t年代p一个n></text> </g> </g> </svg>．这个函数<年代vg height="14.0625" id="M104" style="vertical-align:-2.29482pt;width:16.975px;" version="1.1" viewbox="0 0 16.975 14.0625" width="16.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.0625)"> <g transform="translate(72,-60.75)"> <text transform="matrix(1,0,0,-1,-71.95,63.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.62,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>在空间中<年代vg height="13.45" id="M105" style="vertical-align:-2.21957pt;width:32.650002px;" version="1.1" viewbox="0 0 32.650002 13.45" width="32.650002" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="8.389513" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.553012" y="0"> ω.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.855244" y="0"> ）</t年代p一个n></text> </g> </g> </svg>，紧集上所有连续函数的集合<年代vg height="10.6875" id="M106" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ω.</t年代p一个n></text> </g> </g> </svg>．自<年代vg height="16.424999" id="M107" style="vertical-align:-4.77652pt;width:79.487503px;" version="1.1" viewbox="0 0 79.487503 16.424999" width="79.487503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.425)"> <g transform="translate(72,-58.86)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.5772982" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.617687" y="0"> ［</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.781185" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-42.25,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.84,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.077898" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.291649" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.218071" y="0"> ］</t年代p一个n></text> </g> </g> </svg>这是可以接受的三倍体吗<年代p一个nclass="equation" id="EEq15"> <svg height="71.762497" id="M108" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 71.762497" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,71.7625)"> <g transform="translate(72,-14.59)"> <text transform="matrix(1,0,0,-1,53.16,45.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,60.17,66.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,62.9,64.8)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,58.92,41.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,61.65,39.27)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,70.2,52.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,78.53,57.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,85.77,52.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="93.519997" y="7.71"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0734386" y="0.0099999998"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.274687" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.401636" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.565136" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.478575" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.730076" y="0.0099999998"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.931324" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.945747" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.109245" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.022682" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.186184" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="67.437683" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="74.089279" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="81.478554" y="0.0099999998"> ＝</t年代p一个n></text> <text transform="matrix(1,0,0,-1,186.29,66.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,189.03,64.8)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,185.04,41.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,187.78,39.27)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,196.33,52.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,204.66,49.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,212.05,52.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0734386" y="0.0099999998"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.28719" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.239338" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.402838" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.316277" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.479774" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.418941" y="0.0099999998"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.459568" y="0.0099999998"> ̇</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.795471" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.735115" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.898613" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="64.81205" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.763718" y="0.0099999998"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="83.103943" y="0.0099999998"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,303.49,49.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,308.81,52.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-119.11" y="36.080002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-113.26" y="33.560001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0734386" y="0.0099999998"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.274687" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.239338" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.402838" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.316277" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.479774" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.731274" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.38287" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-141.56" y="33.560001"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-129.53212" y="33.560001"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,199.46,16.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,205.87,19.41)"> <tspan style="font-size: 12.50px; " x="14.17" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.02" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,229.8,16.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,236.21,16.89)"> <tspan style="font-size: 12.50px; " x="36.240002" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.09" y="-2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8514042" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.48" y="-2.52"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.820221" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,282.21,16.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,287.08,19.41)"> <tspan style="font-size: 12.50px; " x="14.17" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.030001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,311.02,16.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,315.89,16.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8514042" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.18" y="-2.52"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.207886" y="-2.52"> δ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.23505" y="-2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.56205" y="-2.52"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="151.98" y="-23.280001"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="156.14349" y="-23.280001"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="162.395" y="-23.280001"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="168.6465" y="-23.280001"> ）</t年代p一个n></text> </g> </g> </svg></span>对所有<年代vg height="13.575" id="M109" style="vertical-align:-2.29482pt;width:66.212502px;" version="1.1" viewbox="0 0 66.212502 13.575" width="66.212502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.575)"> <g transform="translate(72,-61.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.790329" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.830717" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.22023" y="0"> ”</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.833599" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.997097" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.699184" y="0"> ）</t年代p一个n></text> </g> </g> </svg>．让<年代vg height="16.5375" id="M110" style="vertical-align:-2.21957pt;width:39.287498px;" version="1.1" viewbox="0 0 39.287498 16.5375" width="39.287498" 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,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8773699" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.040869" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-49.66,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-44.78,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代p一个n></text> </g> </g> </svg>是所有具有紧支撑的无穷可微实值函数的空间<年代vg height="13.9625" id="M111" style="vertical-align:-0.15048pt;width:16.5375px;" version="1.1" viewbox="0 0 16.5375 13.9625" width="16.5375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9625)"> <g transform="translate(72,-60.83)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.7,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> </g> </g> </svg>．定义<年代p一个nclass="equation" id="EEq16"> <svg height="47.799999" id="M112" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 47.799999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,47.8)"> <g transform="translate(72,-33.76)"> <text transform="matrix(1,0,0,-1,68.04,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,80.35,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,87.28,62.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0769377" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.278186" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.242838" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.406336" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.319775" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.558773" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.772522" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.786945" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.950443" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.863884" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.027382" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.654213" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="81.694603" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,175.86,58.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,182.79,62.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.315935" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,206.51,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,212.06,62.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.016103" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.356323" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,244.58,58.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,251.51,62.01)"> <tspan style="font-size: 12.50px; " x="67.160004" y="26.15"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="73.019997" y="23.639999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0769377" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.278186" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.242838" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.406336" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.319775" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.558773" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.772522" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.786945" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.950443" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.863884" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.027382" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="68.26638" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="79.744133" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="83.907631" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="87.821075" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="94.072571" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-48.619999" y="23.639999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-38.942677" y="23.639999"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-26.902288" y="23.639999"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-20.650789" y="23.639999"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-15.449541" y="23.639999"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-9.198041" y="23.639999"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-3.9842899" y="23.639999"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="2.26721" y="23.639999"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.4809608" y="23.639999"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.732461" y="23.639999"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.109711" y="23.639999"> ∀</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.111391" y="23.639999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.964474" y="23.639999"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.004864" y="23.639999"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,332.78,43.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,337.65,35.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9400001" y="-2.51"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="130.22" y="-13.89"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="134.3835" y="-13.89"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="140.63499" y="-13.89"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="146.88651" y="-13.89"> ）</t年代p一个n></text> </g> </g> </svg></span>假设<年代vg height="16.424999" id="M113" style="vertical-align:-4.77652pt;width:79.487503px;" version="1.1" viewbox="0 0 79.487503 16.424999" width="79.487503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.425)"> <g transform="translate(72,-58.86)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.5772982" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.617687" y="0"> ［</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.781185" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-42.25,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.84,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.077898" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.291649" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.218071" y="0"> ］</t年代p一个n></text> </g> </g> </svg>是一个可接受的三倍。因为这个函数<年代vg height="13.55" id="M114" style="vertical-align:-2.29482pt;width:26.737499px;" version="1.1" viewbox="0 0 26.737499 13.55" width="26.737499" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3772497" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.540749" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.116608" y="0"> ）</t年代p一个n></text> </g> </g> </svg>有紧密的支持<年代vg height="13.9625" id="M115" style="vertical-align:-0.15048pt;width:16.5375px;" version="1.1" viewbox="0 0 16.5375 13.9625" width="16.5375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9625)"> <g transform="translate(72,-60.83)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.7,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> </g> </g> </svg>，<年代vg height="16.637501" id="M116" style="vertical-align:-4.77652pt;width:114.8875px;" version="1.1" viewbox="0 0 114.8875 16.637501" width="114.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3772497" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.540749" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.48,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-49.61,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6268301" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.667219" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.056973" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.22047" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-12.47,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-6.06,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6268301" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.667219" y="0"> 0</t年代p一个n></text> </g> </g> </svg>．因此,对于<年代vg height="12.8875" id="M117" style="vertical-align:-1.76814pt;width:78.074997px;" version="1.1" viewbox="0 0 78.074997 12.8875" width="78.074997" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="9.6773224" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.71771" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.969212" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.182961" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.434464" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.635712" y="0"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.887211" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.10096" y="0"> 4</t年代p一个n></text> </g> </g> </svg>，以及所有人<年代vg height="16.637501" id="M118" style="vertical-align:-2.29482pt;width:70.412498px;" version="1.1" viewbox="0 0 70.412498 16.637501" width="70.412498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.853084" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.893473" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.770844" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.934341" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-24.76,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-19.88,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代p一个n></text> </g> </g> </svg>，从（<一个href="#EEq16">16</一个>），用分部积分法，我们得到<年代p一个nclass="equation" id="EEq17"> <svg height="120.075" id="M119" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 120.075" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,120.075)"> <g transform="translate(72,24.06)"> <text transform="matrix(1,0,0,-1,72.85,45.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,79.85,66.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,82.59,64.8)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,78.6,41.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,81.34,39.27)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,89.89,52.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,99.28,57.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,106.21,52.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="94.349998" y="7.71"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0734386" y="0.0099999998"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.274687" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.239338" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.402838" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.316277" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.567776" y="0.0099999998"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.769024" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.783447" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.946945" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.860386" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.023884" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="68.275383" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="74.926979" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="82.303749" y="0.0099999998"> ＝</t年代p一个n></text> <text transform="matrix(1,0,0,-1,207.57,66.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,210.31,64.8)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,209.23,41.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,211.97,39.27)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,218.18,52.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,225.06,49.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,231.99,52.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0734386" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.312436" y="0.0099999998"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,255.7,57.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,261.26,52.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-63.470001" y="41.740002"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-52.119999" y="49.439999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0734386" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.312436" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.964031" y="0.0099999998"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,216.14,25.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,218.88,23.07)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,214.89,-0.27)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,217.63,-2.45)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,226.18,11.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,232.33,8.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,239.26,11.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1700001" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0834389" y="0.0099999998"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.284687" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.236835" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.400333" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.313772" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.565273" y="0.0099999998"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.779022" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.780945" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.944443" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.857883" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.033882" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="68.272881" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="79.750633" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="83.914131" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="87.827576" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="94.079071" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="100.73067" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-50.73" y="31.5"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-38.702114" y="31.5"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-32.450615" y="31.5"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="228.61" y="-9.6000004"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="232.7735" y="-9.6000004"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="239.02499" y="-9.6000004"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="245.2765" y="-9.6000004"> ）</t年代p一个n></text> </g> </g> </svg></span>同样，通过选择只依赖于时间的函数，我们有<年代p一个nclass="equation" id="EEq18"> <svg height="41.075001" id="M120" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 41.075001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,41.075)"> <g transform="translate(72,-39.14)"> <text transform="matrix(1,0,0,-1,100.46,45.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,107.46,66.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,110.2,64.8)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,106.21,41.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,108.95,39.27)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,117.5,52.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0021601" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.165659" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.079098" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.292849" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.2575" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.420998" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.334438" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.573437" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.787186" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.801609" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.965107" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.878548" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.042046" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="77.281044" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="83.93264" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="91.321915" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="103.3623" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,227.14,49.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,232.49,52.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.166139" y="0"> ∀</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.167818" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.570316" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.610703" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,286.49,57.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,293.45,52.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> ω.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.462232" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.713732" y="0.0099999998"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="174.42" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="178.5835" y="0.0099999998"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="184.83499" y="0.0099999998"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="191.0865" y="0.0099999998"> ）</t年代p一个n></text> </g> </g> </svg></span>在哪里<年代vg height="16.5375" id="M121" style="vertical-align:-2.21957pt;width:39.987499px;" version="1.1" viewbox="0 0 39.987499 16.5375" width="39.987499" 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,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.56,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.69,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ω.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.465731" y="0"> ）</t年代p一个n></text> </g> </g> </svg>所有函数的空间都在吗<年代vg height="13.45" id="M122" style="vertical-align:-2.21957pt;width:32.650002px;" version="1.1" viewbox="0 0 32.650002 13.45" width="32.650002" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="8.389513" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.553012" y="0"> ω.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.855244" y="0"> ）</t年代p一个n></text> </g> </g> </svg>这只取决于时间和<年代vg height="11.0375" id="M123" style="vertical-align:-3.22282pt;width:14.65px;" version="1.1" viewbox="0 0 14.65 11.0375" width="14.65" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0375)"> <g transform="translate(72,-63.17)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></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p一个n></text> </g> </g> </svg>是<年代vg height="13.4875" id="M124" style="vertical-align:-2.21957pt;width:23.6625px;" version="1.1" viewbox="0 0 23.6625 13.4875" width="23.6625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.926662" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.090161" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.666019" y="0"> ）</t年代p一个n></text> </g> </g> </svg>在<年代vg height="10.5125" id="M125" style="vertical-align:-0.15048pt;width:10.4375px;" version="1.1" viewbox="0 0 10.4375 10.5125" width="10.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5125)"> <g transform="translate(72,-63.59)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>．<br>方程(<一个href="#EEq15">15</一个>）， (<一个href="#EEq17">17</一个>）和(<一个href="#EEq18">18</一个>）是(<一个href="#EEq11">11</一个>）- (<一个href="#EEq11">13</一个>）．注意约束(<一个href="#EEq11">12</一个>）被认为在(的右边<一个href="#EEq15">15</一个>）通过选择合适的功能<年代vg height="15.4125" id="M126" style="vertical-align:-2.29482pt;width:67.287498px;" version="1.1" viewbox="0 0 67.287498 15.4125" width="67.287498" 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"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.790329" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.830717" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-38.72,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.25,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.865587" y="0"> ）</t年代p一个n></text> </g> </g> </svg>哪些是单项式<年代vg height="10.925" id="M127" style="vertical-align:-3.13504pt;width:14.8125px;" version="1.1" viewbox="0 0 14.8125 10.925" width="14.8125" 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p一个n></text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>．此外，约束(<一个href="#EEq11">13</一个>通过选择合适的集合来考虑）。<年代vg height="10.55" id="M128" style="vertical-align:-0.0pt;width:11.325px;" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.55)"> <g transform="translate(72,-63.56)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>．现在，我们考虑下面的正线性泛函<年代vg height="13.45" id="M129" style="vertical-align:-2.21957pt;width:32.650002px;" version="1.1" viewbox="0 0 32.650002 13.45" width="32.650002" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="8.389513" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.553012" y="0"> ω.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.855244" y="0"> ）</t年代p一个n></text> </g> </g> </svg>：<年代p一个nclass="equation" id="EEq19"> <svg height="36.262501" id="M130" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 36.262501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,36.2625)"> <g transform="translate(72,-42.99)"> <text transform="matrix(1,0,0,-1,85.28,54.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> γ.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,92.62,51.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,100.87,54.64)"> <tspan style="font-size: 12.50px; " x="46.299999" y="7.6999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ∶</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8523636" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.055052" y="0"> ⟶</t年代p一个n></text> <text transform="matrix(1,0,0,-1,152.92,43.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,161.28,54.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.615287" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.778786" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.692225" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.905975" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.858124" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.021622" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.935062" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.186562" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.400314" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.402233" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.565735" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.479172" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="73.64267" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="79.894173" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="86.545769" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="90.459206" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="105.63785" y="0"> ∀</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="112.63953" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="123.82971" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="135.8701" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="147.34785" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="151.51135" y="0"> ω.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="160.81358" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="167.05258" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="306.59" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="310.75351" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="317.005" y="0"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="323.2565" y="0"> ）</t年代p一个n></text> </g> </g> </svg></span></span></p> <p><span class="statement" id="prop1"><span class="statement-title">命题1。</年代p一个n><我>转换<年代vg height="16.375" id="M131" style="vertical-align:-4.74141pt;width:51.275002px;" version="1.1" viewbox="0 0 51.275002 16.375" width="51.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.375)"> <g transform="translate(72,-58.9)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.665299" y="0"> →</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.794409" y="0"> γ.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.81,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>可接受的三元组<年代vg height="10.575" id="M132" style="vertical-align:-0.20064pt;width:17.9625px;" version="1.1" viewbox="0 0 17.9625 10.575" width="17.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.575)"> <g transform="translate(72,-63.54)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>转化成线性映射<年代vg height="16.375" id="M133" style="vertical-align:-4.74141pt;width:15.275px;" version="1.1" viewbox="0 0 15.275 16.375" width="15.275" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.375)"> <g transform="translate(72,-58.9)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> γ.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.61,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>中定义的(<一个href="#EEq19">19</一个>）是注射。</我></年代p一个n></p> <p><span class="statement" id="proof1"><span class="statement-title"><i class="statement-title">证明。</我></年代p一个n>我们必须证明如果<年代vg height="14.375" id="M134" style="vertical-align:-3.13504pt;width:43.512501px;" version="1.1" viewbox="0 0 43.512501 14.375" width="43.512501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-58.88,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≠</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.640053" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-42.12,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>,然后<年代vg height="17.112499" id="M135" style="vertical-align:-5.32956pt;width:55.387501px;" version="1.1" viewbox="0 0 55.387501 17.112499" width="55.387501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.1125)"> <g transform="translate(72,-58.31)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> γ.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.61,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.33,58.36)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.13,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≠</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.652556" y="0"> γ.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-36.14,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-31.86,58.36)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>．让<年代vg height="18.575001" id="M136" style="vertical-align:-6.50204pt;width:108.0375px;" version="1.1" viewbox="0 0 108.0375 18.575001" width="108.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.575)"> <g transform="translate(72,-57.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.94,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> ［</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.203888" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-37.82,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-32.96,58.36)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-29.16,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-17.07,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-12.65,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-1.51,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,2.92,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ］</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ，</t年代p一个n></text> </g> </g> </svg> <svg height="13.6125" id="M137" style="vertical-align:-2.34499pt;width:52.9375px;" version="1.1" viewbox="0 0 52.9375 13.6125" width="52.9375" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3269978" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.367388" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.618887" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.996136" y="0"> 2</t年代p一个n></text> </g> </g> </svg>是不同的可容许三元组。如果<年代vg height="15.625" id="M138" style="vertical-align:-5.32956pt;width:51.75px;" version="1.1" viewbox="0 0 51.75 15.625" width="51.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.625)"> <g transform="translate(72,-59.5)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.18,59.55)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.58,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-39.63,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-34.78,59.55)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>，则有一个子区间<年代vg height="17.112499" id="M139" style="vertical-align:-5.32956pt;width:44.150002px;" version="1.1" viewbox="0 0 44.150002 17.112499" width="44.150002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.1125)"> <g transform="translate(72,-58.31)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ［</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.87,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-49.88,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-45.02,58.36)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-40.9,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ］</t年代p一个n></text> </g> </g> </svg>，说<年代vg height="14.2375" id="M140" style="vertical-align:-3.13504pt;width:14.6625px;" version="1.1" viewbox="0 0 14.6625 14.2375" width="14.6625" 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p一个n></text> <text transform="matrix(1,0,0,-1,-65.2,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>，在哪里<年代vg height="14.6" id="M141" style="vertical-align:-3.13504pt;width:76.012497px;" version="1.1" viewbox="0 0 76.012497 14.6" width="76.012497" 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p一个n></text> <text transform="matrix(1,0,0,-1,-65.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.2,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.315935" y="0"> ≠</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.968491" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-28.35,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-23.48,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代p一个n></text> </g> </g> </svg>为每一个<年代vg height="14.2375" id="M142" style="vertical-align:-3.13504pt;width:38.9375px;" version="1.1" viewbox="0 0 38.9375 14.2375" width="38.9375" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="7.37677" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.417158" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-45.77,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg><i>．</我>一个连续函数<年代vg height="10.325" id="M143" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.325" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>可以建立在<年代vg height="10.6875" id="M144" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ω.</t年代p一个n></text> </g> </g> </svg>所以(<一个href="#EEq19">19</一个>）对应<年代vg height="10.925" id="M145" style="vertical-align:-3.13504pt;width:13.8625px;" version="1.1" viewbox="0 0 13.8625 10.925" width="13.8625" 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p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>和<年代vg height="10.925" id="M146" style="vertical-align:-3.13504pt;width:13.8625px;" version="1.1" viewbox="0 0 13.8625 10.925" width="13.8625" 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p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>是不平等的。例如，一个人可以<年代vg height="10.325" id="M147" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.325" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>独立的<年代vg height="7.1624999" id="M148" style="vertical-align:-0.11285pt;width:7.5374999px;" version="1.1" viewbox="0 0 7.5374999 7.1624999" width="7.5374999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>，等于零<年代vg height="9.125" id="M149" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>外部<年代vg height="14.2375" id="M150" style="vertical-align:-3.13504pt;width:14.6625px;" version="1.1" viewbox="0 0 14.6625 14.2375" width="14.6625" 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p一个n></text> <text transform="matrix(1,0,0,-1,-65.2,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>，使它在适当的部分上是正的<年代vg height="14.6" id="M151" style="vertical-align:-3.13504pt;width:29.6875px;" version="1.1" viewbox="0 0 29.6875 14.6" width="29.6875" 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p一个n></text> <text transform="matrix(1,0,0,-1,-65.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.2,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.739357" y="0"> ）</t年代p一个n></text> </g> </g> </svg>，上为零<年代vg height="14.6" id="M152" style="vertical-align:-3.13504pt;width:29.6875px;" version="1.1" viewbox="0 0 29.6875 14.6" width="29.6875" 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p一个n></text> <text transform="matrix(1,0,0,-1,-65.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.2,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.739357" y="0"> ）</t年代p一个n></text> </g> </g> </svg>，然后线性功能不等于。换句话说，如果<年代vg height="17.112499" id="M153" style="vertical-align:-5.32956pt;width:48.275002px;" version="1.1" viewbox="0 0 48.275002 17.112499" width="48.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.1125)"> <g transform="translate(72,-58.31)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.18,58.36)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.97,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≠</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.640053" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-42.41,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-37.55,58.36)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>,然后<年代vg height="17.112499" id="M154" style="vertical-align:-5.32956pt;width:19.799999px;" version="1.1" viewbox="0 0 19.799999 17.112499" width="19.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.1125)"> <g transform="translate(72,-58.31)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> γ.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.61,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.33,58.36)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>和<年代vg height="17.112499" id="M155" style="vertical-align:-5.32956pt;width:19.799999px;" version="1.1" viewbox="0 0 19.799999 17.112499" width="19.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.1125)"> <g transform="translate(72,-58.31)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> γ.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.61,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.33,58.36)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>有不同的域，不等于。</年代p一个n></p><p>因此,从(<一个href="#EEq15">15</一个>）， (<一个href="#EEq17">17</一个>）和(<一个href="#EEq18">18</一个>）可以得出结论，最大化功能（<一个href="#EEq10">10</一个>）在容许空间上<年代vg height="10.575" id="M156" style="vertical-align:-0.20064pt;width:17.9625px;" version="1.1" viewbox="0 0 17.9625 10.575" width="17.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.575)"> <g transform="translate(72,-63.54)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>，转变为以下功能空间的优化问题:<年代p一个nclass="equation" id="EEq20"> <svg height="28.387501" id="M157" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 28.387501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,28.3875)"> <g transform="translate(72,-49.29)"> <text transform="matrix(1,0,0,-1,174.58,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.727334" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.278666" y="0"> x</t年代p一个n></text> <text transform="matrix(1,0,0,-1,176.26,53.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.2797279" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.274848" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,200.28,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> γ.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,207.62,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,214.48,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,227.27,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,232.15,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="235.72" y="-2.51"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="239.8835" y="-2.51"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="246.13499" y="-2.51"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="252.38651" y="-2.51"> ）</t年代p一个n></text> </g> </g> </svg></span>受<年代p一个nclass="equation" id="EEq21"> <svg height="80" id="M158" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 80" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,80)"> <g transform="translate(72,-8)"> <text transform="matrix(1,0,0,-1,136.63,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> γ.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,143.97,58.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,150.83,62.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,163.32,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,168.48,62.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6268301" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.667219" y="0"> δ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.694386" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.021381" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.187523" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="63.990353" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="76.030746" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,253.91,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,259.46,62.01)"> <tspan style="font-size: 12.50px; " x="-157.35001" y="24.620001"> γ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.365707" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.617207" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="208.41" y="0.51999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="212.5735" y="0.51999998"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="218.825" y="0.51999998"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="225.07649" y="0.51999998"> ）</t年代p一个n></text> <text transform="matrix(1,0,0,-1,109.45,34.27)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,116.31,37.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,129.87,42.39)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,134.72,37.4)"> <tspan style="font-size: 12.50px; " x="149.88" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="155.73" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6268301" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.667219" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.918718" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.084858" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.774685" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.815071" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.066574" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="74.267822" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="80.519318" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="85.73307" y="0"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="91.984573" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="97.198318" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="103.44982" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="112.82707" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="125.68015" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="137.72055" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,298.7,42.39)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,303.58,34.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-160.86" y="22.1"> γ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9299998" y="-2.51"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="164.28999" y="-2.51"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="168.45351" y="-2.51"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="174.705" y="-2.51"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="180.9565" y="-2.51"> ）</t年代p一个n></text> <text transform="matrix(1,0,0,-1,150.06,9.65)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,156.93,12.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.090161" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.716991" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.75738" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,193.97,9.65)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,199.31,12.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.166139" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.568636" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.609024" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,246.31,17.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,253.27,12.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ω.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.465731" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.704727" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="214.60001" y="0.039999999"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="218.7635" y="0.039999999"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="225.015" y="0.039999999"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="231.26649" y="0.039999999"> ）</t年代p一个n></text> </g> </g> </svg></span></p> <h5 id="sec4.2">4．2．测度空间</h5><p>让<年代vg height="15.125" id="M161" style="vertical-align:-2.21957pt;width:47.387501px;" version="1.1" viewbox="0 0 47.387501 15.125" width="47.387501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.125)"> <g transform="translate(72,-59.9)"> <text transform="matrix(1,0,0,-1,-71.95,62.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-58.26,67.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> +</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-51.77,62.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ω.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.465731" y="0"> ）</t年代p一个n></text> </g> </g> </svg>表示氡所有正测度的空间<年代vg height="10.6875" id="M162" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ω.</t年代p一个n></text> </g> </g> </svg>．由Riesz表示定理[<一个href="#B35">35</一个>，存在一个独特的正氡测量值<年代vg height="9.6750002" id="M163" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>在<年代vg height="10.6875" id="M164" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ω.</t年代p一个n></text> </g> </g> </svg>这样<年代p一个nclass="equation" id="EEq24"> <svg height="83.487503" id="M165" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 83.487503" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,83.4875)"> <g transform="translate(72,-5.21)"> <text transform="matrix(1,0,0,-1,86.5,54.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> γ.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,93.84,51.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,100.71,54.65)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.369999" y="7.71"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.687286" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.326618" y="0.0099999998"> ＝</t年代p一个n></text> <text transform="matrix(1,0,0,-1,139.83,43.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,148.19,54.64)"> <tspan style="font-size: 12.50px; " x="-26.139999" y="37.880001"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-14.11" y="45.57"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.615287" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.778786" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.692225" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.905975" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.870628" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.034126" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.947563" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.186562" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.400314" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.414738" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.578232" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.491676" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="73.655174" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="79.894173" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="86.545769" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,139.83,5.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ω.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,148.93,16.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.615287" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.778786" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.692225" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.905975" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.782625" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.983875" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.910297" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.161797" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.813393" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.903549" y="0"> ≡</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="78.943939" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="88.633766" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="92.797264" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="102.33705" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="108.58855" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="123.75469" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="134.95738" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="146.99777" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="158.47552" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="162.63902" y="0"> ω.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="171.94125" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="178.18025" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="318.94" y="-18.719999"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="323.10349" y="-18.719999"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="329.35501" y="-18.719999"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="335.60651" y="-18.719999"> ）</t年代p一个n></text> </g> </g> </svg></span>因此，我们可能会改变优化问题的功能空间以测量空间。换句话说，优化问题（<一个href="#EEq20">20.</一个>）- (<一个href="#EEq21">23</一个>）可以转化为测度空间中的以下优化问题:<年代p一个nclass="equation" id="EEq25"> <svg height="29.725" id="M166" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 29.725" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,29.725)"> <g transform="translate(72,-48.22)"> <text transform="matrix(1,0,0,-1,165.38,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.115167" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.666498" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.917999" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.393833" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.121166" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.597" y="0"> z</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.148335" y="0"> e</t年代p一个n></text> <text transform="matrix(1,0,0,-1,171.71,52.34)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.329968" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="11.325088" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,192.62,55.71)"> <tspan style="font-size: 6.25px; " x="0" y="0"> +</t年代p一个n></text> <text transform="matrix(1,0,0,-1,197.4,52.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.9144161" y="0"> ω.</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.4259043" y="0"> ）</t年代p一个n></text> <text transform="matrix(1,0,0,-1,218.16,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.6999998" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.55" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,240.65,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,245.52,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="222.35001" y="-2.51"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="226.5135" y="-2.51"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="232.765" y="-2.51"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="239.01649" y="-2.51"> ）</t年代p一个n></text> </g> </g> </svg></span>受<年代p一个nclass="equation" id="EEq26"> <svg height="77.387497" id="M167" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 77.387497" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,77.3875)"> <g transform="translate(72,-10.09)"> <text transform="matrix(1,0,0,-1,138.88,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.6999998" y="-0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.863499" y="-0.0099999998"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,161.07,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,166.23,62.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6268301" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.667219" y="0"> δ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.694386" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.021381" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.187523" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="63.990353" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="76.030746" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,251.66,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,257.21,62.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.365707" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.604704" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="210.66" y="0.029999999"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="214.8235" y="0.029999999"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="221.075" y="0.029999999"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="227.32649" y="0.029999999"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-152.85001" y="23.67"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-143.16017" y="23.67"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-138.99667" y="23.67"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,127.62,43.34)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,132.46,38.35)"> <tspan style="font-size: 12.50px; " x="149.89" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="155.74001" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.667219" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.918718" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.097363" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.787186" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.815071" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.066574" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="74.280319" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="80.531822" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="85.745575" y="0"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="91.99707" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="97.198318" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="103.44982" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="112.82707" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="125.69266" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="137.73305" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,296.45,43.34)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,301.33,35.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9299998" y="-2.51"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="166.53999" y="-2.51"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="170.70351" y="-2.51"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="176.955" y="-2.51"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="183.2065" y="-2.51"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-156.35001" y="21.940001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-146.66017" y="21.940001"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-142.49667" y="21.940001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-135.57001" y="21.940001"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-127.93068" y="21.940001"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-115.90279" y="21.940001"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,191.72,10.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,197.06,13.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.166139" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.568636" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.609024" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,244.06,18.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,251.02,13.9)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ω.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.465731" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.704727" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="216.85001" y="-0.44999999"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="221.0135" y="-0.44999999"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="227.265" y="-0.44999999"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="233.51649" y="-0.44999999"> ）</t年代p一个n></text> </g> </g> </svg></span></p> <p>我们会考虑将(<一个href="#EEq25">25</一个>）在电视机上<年代vg height="12.925" id="M170" style="vertical-align:-1.90608pt;width:12.325px;" version="1.1" viewbox="0 0 12.325 12.925" width="12.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>所有氡阳性测量<年代vg height="10.6875" id="M171" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ω.</t年代p一个n></text> </g> </g> </svg>令人满意的(<一个href="#EEq26">26</一个>）- (<一个href="#EEq26">28</一个>）．考虑这一测度理论形式问题的主要优点是集中存在最优测度<年代vg height="12.925" id="M172" style="vertical-align:-1.90608pt;width:12.325px;" version="1.1" viewbox="0 0 12.325 12.925" width="12.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>这一点可以用一种直接的方式来研究，而不必强加一些条件，比如可能是人为的凸性。</p><p>定义函数<年代vg height="12.925" id="M173" style="vertical-align:-1.90608pt;width:76.4375px;" version="1.1" viewbox="0 0 76.4375 12.925" width="76.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.4647713" y="0"> ∶</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.329638" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.645813" y="0"> →</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.787426" y="0"> </t年代p一个n></text> </g> </g> </svg>作为<年代vg height="14.75" id="M174" style="vertical-align:-3.25793pt;width:81.637497px;" version="1.1" viewbox="0 0 81.637497 14.75" width="81.637497" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="6.00144" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.164939" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.766764" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.406096" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.446484" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.060814" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.224312" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-15.78,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-10.91,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代p一个n></text> </g> </g> </svg>．下面的定理保证了最优解的存在性。</p><p><年代p一个nclass="statement" id="thm1"><span class="statement-title">定理1。</年代p一个n><我>最大化的度量理论问题(<一个href="#EEq25">25</一个>）的约束条件(<一个href="#EEq26">26</一个>）- (<一个href="#EEq26">28</一个>）有一个最佳解决方案，例如<年代vg height="14.3875" id="M175" style="vertical-align:-2.29482pt;width:15.9875px;" version="1.1" viewbox="0 0 15.9875 14.3875" width="15.9875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.34,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> </g> </g> </svg>，在哪里<年代vg height="14.3875" id="M176" style="vertical-align:-2.29482pt;width:47.587502px;" version="1.1" viewbox="0 0 47.587502 14.3875" width="47.587502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.34,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.79,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> </t年代p一个n></text> </g> </g> </svg>．</我></年代p一个n></p> <p><span class="statement" id="proof2"><span class="statement-title"><i class="statement-title">证明。</我></年代p一个n>所谓的约束(<一个href="#EEq26">27</一个>）和(<一个href="#EEq26">28</一个>）是(的特殊情况<一个href="#EEq26">26</一个>）［<一个href="#B35">35</一个>］．因此,一组<我>问</我>可以写成<年代p一个nclass="equation" id="eq1"> <svg height="39.974998" id="M177" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 39.974998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,39.975)"> <g transform="translate(72,-40.02)"> <text transform="matrix(1,0,0,-1,96.14,59.69)"> <tspan style="font-size: 12.50px; " x="32.639999" y="6.6199999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.228174" y="0"> ＝</t年代p一个n></text> <text transform="matrix(1,0,0,-1,121.42,44.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.8288321" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="11.823952" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,139.81,47.57)"> <tspan style="font-size: 6.25px; " x="0" y="0"> ”</t年代p一个n></text> <text transform="matrix(1,0,0,-1,142.12,44.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.0058079" y="0"> ）</t年代p一个n></text> <text transform="matrix(1,0,0,-1,156.12,57.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1900001" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.280161" y="-2.51"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.308046" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,200.13,64.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> +</t年代p一个n></text> <text transform="matrix(1,0,0,-1,208.71,59.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ω.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.465731" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.092562" y="0"> ∶</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.120926" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.823254" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.986755" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,266.03,64.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,271.18,59.7)"> <tspan style="font-size: 12.50px; " x="37.029999" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6268301" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.667219" y="0"> δ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.694386" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.299999" y="0.0099999998"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="196.69" y="0.0099999998"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="200.8535" y="0.0099999998"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="207.105" y="0.0099999998"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="213.35651" y="0.0099999998"> ）</t年代p一个n></text> </g> </g> </svg></span>假设<年代vg height="16.424999" id="M178" style="vertical-align:-4.77652pt;width:79.487503px;" version="1.1" viewbox="0 0 79.487503 16.424999" width="79.487503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.425)"> <g transform="translate(72,-58.86)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.5772982" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.617687" y="0"> ［</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.781185" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-42.25,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.84,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.077898" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.291649" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.218071" y="0"> ］</t年代p一个n></text> </g> </g> </svg>是一个可容许的三重。众所周知，这一套<年代vg height="18.3125" id="M179" style="vertical-align:-4.77652pt;width:196.6375px;" version="1.1" viewbox="0 0 196.6375 18.3125" width="196.6375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.3125)"> <g transform="translate(72,-57.35)"> <text transform="matrix(1,0,0,-1,-71.95,62.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ｛</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.00144" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.079098" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.119488" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-29.13,67.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> +</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-22.64,62.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ω.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.465731" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.092562" y="0"> ∶</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.957428" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.571754" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.735252" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.986755" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.626087" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="68.666473" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,49.94,59.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,59.13,62.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.327718" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,74.38,59.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,79.26,62.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ｝</t年代p一个n></text> </g> </g> </svg>在弱*拓扑中是紧致的。此外,一组<年代vg height="12.925" id="M180" style="vertical-align:-1.90608pt;width:12.325px;" version="1.1" viewbox="0 0 12.325 12.925" width="12.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>为封闭单例集逆像的交点<年代vg height="13.6125" id="M181" style="vertical-align:-2.29482pt;width:36.825001px;" version="1.1" viewbox="0 0 36.825001 13.6125" width="36.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ｛</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.00144" y="0"> δ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.028606" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.355604" y="0"> ｝</t年代p一个n></text> </g> </g> </svg>在连续函数下<年代vg height="14.0625" id="M182" style="vertical-align:-2.29482pt;width:74.787498px;" version="1.1" viewbox="0 0 74.787498 14.0625" width="74.787498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.0625)"> <g transform="translate(72,-60.75)"> <text transform="matrix(1,0,0,-1,-71.95,63.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.165659" y="0"> →</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.294769" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.909096" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.072594" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-21.54,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-16.38,63.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代p一个n></text> </g> </g> </svg>也关闭。因此,<年代vg height="12.925" id="M183" style="vertical-align:-1.90608pt;width:12.325px;" version="1.1" viewbox="0 0 12.325 12.925" width="12.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是紧集的闭子集。证明了集合的紧性<年代vg height="12.925" id="M184" style="vertical-align:-1.90608pt;width:12.325px;" version="1.1" viewbox="0 0 12.325 12.925" width="12.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>．由于功能<年代vg height="10.325" id="M185" style="vertical-align:-0.0pt;width:9.0375004px;" version="1.1" viewbox="0 0 9.0375004 10.325" width="9.0375004" 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p一个n></text> </g> </g> </svg>，映射紧集<年代vg height="12.925" id="M186" style="vertical-align:-1.90608pt;width:12.325px;" version="1.1" viewbox="0 0 12.325 12.925" width="12.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>在实线上，是连续的，因此在紧集上取最大值<年代vg height="12.925" id="M187" style="vertical-align:-1.90608pt;width:12.325px;" version="1.1" viewbox="0 0 12.325 12.925" width="12.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>．</年代p一个n></p><p>接下来，根据[<一个href="#B35">35</一个>］，问题(<一个href="#EEq25">25</一个>）- (<一个href="#EEq26">28</一个>）的近似值是一个LP问题和一个三重问题<年代vg height="14.3875" id="M188" style="vertical-align:-2.29482pt;width:14.1125px;" version="1.1" viewbox="0 0 14.1125 14.3875" width="14.1125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> </g> </g> </svg>哪个近似于<年代vg height="14.3875" id="M189" style="vertical-align:-2.29482pt;width:47.587502px;" version="1.1" viewbox="0 0 47.587502 14.3875" width="47.587502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.34,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.79,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> </t年代p一个n></text> </g> </g> </svg>是实现。</p><h5我d="sec4.3">4．3．近似</h5><p>问题(<一个href="#EEq25">25</一个>）- (<一个href="#EEq26">28</一个>）是一个无限维线性规划问题，我们主要感兴趣的是逼近它。第一，最大化<年代vg height="10.325" id="M190" style="vertical-align:-0.0pt;width:9.0375004px;" version="1.1" viewbox="0 0 9.0375004 10.325" width="9.0375004" 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p一个n></text> </g> </g> </svg>是不是认为过不了台<年代vg height="12.925" id="M191" style="vertical-align:-1.90608pt;width:12.325px;" version="1.1" viewbox="0 0 12.325 12.925" width="12.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg><i>，</我>但是，它在它的子集上表示，只需只需要一个有限数量的约束（<一个href="#EEq26">26</一个>）- (<一个href="#EEq26">28</一个>）感到满意。让<年代vg height="14.775" id="M192" style="vertical-align:-3.2316pt;width:117.3625px;" version="1.1" viewbox="0 0 117.3625 14.775" width="117.3625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.775)"> <g transform="translate(72,-60.18)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ｛</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.00144" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.62,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-50.93,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∶</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8523636" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.216631" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.257021" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.508518" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.722271" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.97377" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.175018" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.766022" y="0"> ｝</t年代p一个n></text> </g> </g> </svg>，<年代vg height="16.700001" id="M193" style="vertical-align:-4.77652pt;width:126.6375px;" version="1.1" viewbox="0 0 126.6375 16.700001" width="126.6375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.7)"> <g transform="translate(72,-58.64)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ｛</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.00144" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.56,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-48.66,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∶</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8523636" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.191866" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.232254" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.483753" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.861004" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.112503" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.326256" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.904755" y="0"> ｝</t年代p一个n></text> </g> </g> </svg>,<年代vg height="14.775" id="M194" style="vertical-align:-3.2316pt;width:119.05px;" version="1.1" viewbox="0 0 119.05 14.775" width="119.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.775)"> <g transform="translate(72,-60.18)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ｛</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.00144" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.02,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-51.2,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∶</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8523636" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.829517" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.869907" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.121407" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.335159" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.586658" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.787907" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="68.378906" y="0"> ｝</t年代p一个n></text> </g> </g> </svg>分别为中全部函数的集合<年代vg height="13.4875" id="M195" style="vertical-align:-2.21957pt;width:36.412498px;" version="1.1" viewbox="0 0 36.412498 13.4875" width="36.412498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.389513" y="0"> ”</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.00288" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.16638" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.868467" y="0"> ）</t年代p一个n></text> </g> </g> </svg>，<年代vg height="16.5375" id="M196" style="vertical-align:-2.21957pt;width:39.287498px;" version="1.1" viewbox="0 0 39.287498 16.5375" width="39.287498" 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,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8773699" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.040869" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-49.66,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-44.78,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代p一个n></text> </g> </g> </svg>,<年代vg height="16.5375" id="M197" style="vertical-align:-2.21957pt;width:39.987499px;" version="1.1" viewbox="0 0 39.987499 16.5375" width="39.987499" 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,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.56,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.69,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ω.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.465731" y="0"> ）</t年代p一个n></text> </g> </g> </svg>．通过选择有限数目的函数来完成第一次逼近<年代vg height="11.05" id="M198" style="vertical-align:-3.2316pt;width:14.5625px;" version="1.1" viewbox="0 0 14.5625 11.05" width="14.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.62,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>年代,<年代vg height="12.975" id="M199" style="vertical-align:-4.77652pt;width:17.4px;" version="1.1" viewbox="0 0 17.4 12.975" width="17.4" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.975)"> <g transform="translate(72,-61.62)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.56,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>年代,<年代vg height="14.75" id="M200" style="vertical-align:-3.2316pt;width:14.225px;" version="1.1" viewbox="0 0 14.225 14.75" width="14.225" 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,-71.95,63.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.02,60.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>s。现在我们有以下命题。</p><p><年代p一个nclass="statement" id="prop2"><span class="statement-title">命题2。</年代p一个n><我>考虑由函数最大化组成的线性规划问题<年代vg height="10.325" id="M201" style="vertical-align:-0.0pt;width:9.0375004px;" version="1.1" viewbox="0 0 9.0375004 10.325" width="9.0375004" 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p一个n></text> </g> </g> </svg>在一组<年代vg height="14.4625" id="M202" style="vertical-align:-3.13504pt;width:24.9375px;" version="1.1" viewbox="0 0 24.9375 14.4625" width="24.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4625)"> <g transform="translate(72,-60.43)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.19,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>的措施<年代vg height="15.125" id="M203" style="vertical-align:-2.21957pt;width:47.387501px;" version="1.1" viewbox="0 0 47.387501 15.125" width="47.387501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.125)"> <g transform="translate(72,-59.9)"> <text transform="matrix(1,0,0,-1,-71.95,62.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-58.26,67.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> +</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-51.77,62.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ω.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.465731" y="0"> ）</t年代p一个n></text> </g> </g> </svg>让人满意的原因:</我><年代p一个nclass="equation" id="eq2"> <svg height="19.35" id="M204" 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,-1,132.13,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.6999998" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.55" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,156.01,67.27)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="10.33"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,161.16,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3299999" y="-2.51"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.357885" y="-2.51"> δ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.385052" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,199.88,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,203.1,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.166139" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.530407" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.558292" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.809792" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.023544" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.614544" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.815788" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="78.38131" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="264.76999" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="268.9335" y="0"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="275.185" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="281.43649" y="0"> ）</t年代p一个n></text> </g> </g> </svg></span><i>然后,<年代vg height="16.975" id="M205" style="vertical-align:-5.32956pt;width:102.5375px;" version="1.1" viewbox="0 0 102.5375 16.975" width="102.5375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.975)"> <g transform="translate(72,-58.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.2,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-51.64,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≡</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.75522" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.306553" y="0"> x</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-13.91,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-7.07,58.47)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,2.85,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>倾向于<年代vg height="15.9" id="M206" style="vertical-align:-4.46928pt;width:80.75px;" version="1.1" viewbox="0 0 80.75 15.9" width="80.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.9)"> <g transform="translate(72,-59.28)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.214951" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.255341" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.982674" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.534004" y="0"> x</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-23.99,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-14.57,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>作为<年代vg height="10.325" id="M207" style="vertical-align:-0.0pt;width:60.075001px;" version="1.1" viewbox="0 0 60.075001 10.325" width="60.075001" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="19.242117" y="0"> →</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.371227" y="0"> ∞</t年代p一个n></text> </g> </g> </svg>．</我></年代p一个n></p> <p><span class="statement" id="proof3"><span class="statement-title"><i class="statement-title">证明。</我></年代p一个n>我们有<年代vg height="14.4625" id="M208" style="vertical-align:-3.13504pt;width:210.03751px;" version="1.1" viewbox="0 0 210.03751 14.4625" width="210.03751" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4625)"> <g transform="translate(72,-60.43)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.19,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-53.84,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊇</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-32.04,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-23.69,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊇</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.115887" y="0"> ⋯</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.2575" y="0"> ⊇</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.285385" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,29.37,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,42.93,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊇</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.115887" y="0"> ⋯</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.244997" y="0"> ⊇</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.285385" y="0"> </t年代p一个n></text> </g> </g> </svg>因此,<年代vg height="14.2375" id="M209" style="vertical-align:-3.13504pt;width:196.85001px;" version="1.1" viewbox="0 0 196.85001 14.2375" width="196.85001" 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p一个n></text> <text transform="matrix(1,0,0,-1,-65.2,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.85,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≥</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-38.06,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-29.71,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≥</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.115887" y="0"> ⋯</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.244997" y="0"> ≥</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.285385" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,20.33,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,33.89,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≥</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.115887" y="0"> ⋯</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.244997" y="0"> ≥</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.285385" y="0"> </t年代p一个n></text> </g> </g> </svg>．序列<年代vg height="19.9" id="M210" style="vertical-align:-6.8569pt;width:46.950001px;" version="1.1" viewbox="0 0 46.950001 19.9" width="46.950001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.9)"> <g transform="translate(72,-56.08)"> <text transform="matrix(1,0,0,-1,-71.95,62.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ｛</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.00144" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.2,59.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.77,62.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ｝</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-48.77,68.19)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="10.42"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="10.42"> ＝</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="10.42"> 1</t年代p一个n></text> </g> </g> </svg>是不是非递增且有界，所以它收敛于一个数<年代vg height="13.425" id="M211" style="vertical-align:-2.29482pt;width:8.4875002px;" version="1.1" viewbox="0 0 8.4875002 13.425" width="8.4875002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>这样<年代vg height="13.425" id="M212" style="vertical-align:-2.29482pt;width:38.1875px;" version="1.1" viewbox="0 0 38.1875 13.425" width="38.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.152436" y="0"> ≥</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.192825" y="0"> </t年代p一个n></text> </g> </g> </svg>．我们表明,<年代vg height="13.425" id="M213" style="vertical-align:-2.29482pt;width:38.1875px;" version="1.1" viewbox="0 0 38.1875 13.425" width="38.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.152436" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.192825" y="0"> </t年代p一个n></text> </g> </g> </svg>．放<年代vg height="17.4" id="M214" style="vertical-align:-3.7745pt;width:97.512497px;" version="1.1" viewbox="0 0 97.512497 17.4" width="97.512497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.4)"> <g transform="translate(72,-58.08)"> <text transform="matrix(1,0,0,-1,-71.95,61.89)"> <tspan style="font-size: 12.50px; " x="24.76" y="0.15000001"> ⋂</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.715551" y="0"> ≡</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-33.55,68.19)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="10.06"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7957602" y="10.06"> ＝</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="14.79088" y="10.06"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-13.89,61.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-4.12,58.77)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>．然后,<年代vg height="12.925" id="M215" style="vertical-align:-1.90608pt;width:43.287498px;" version="1.1" viewbox="0 0 43.287498 12.925" width="43.287498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.715551" y="0"> ⊇</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.755939" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="14.475" id="M216" style="vertical-align:-3.13504pt;width:72.412498px;" version="1.1" viewbox="0 0 72.412498 14.475" width="72.412498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.152436" y="0"> ≡</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.192825" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.920158" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.471493" y="0"> x</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-28.22,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-21.25,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>．它足以显示<年代vg height="12.925" id="M217" style="vertical-align:-1.90608pt;width:43.287498px;" version="1.1" viewbox="0 0 43.287498 12.925" width="43.287498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.715551" y="0"> ⊆</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.755939" y="0"> </t年代p一个n></text> </g> </g> </svg>．假设<年代vg height="13.1875" id="M218" style="vertical-align:-2.29482pt;width:40.599998px;" version="1.1" viewbox="0 0 40.599998 13.1875" width="40.599998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.1875)"> <g transform="translate(72,-61.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.077658" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.118048" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="15.4125" id="M219" style="vertical-align:-2.29482pt;width:67.287498px;" version="1.1" viewbox="0 0 67.287498 15.4125" width="67.287498" 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"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.790329" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.830717" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-38.72,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.25,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.865587" y="0"> ）</t年代p一个n></text> </g> </g> </svg>．因为函数的线性组合<年代vg height="16.700001" id="M220" style="vertical-align:-4.77652pt;width:115.15px;" version="1.1" viewbox="0 0 115.15 16.700001" width="115.15" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.7)"> <g transform="translate(72,-58.64)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ｛</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.00144" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.62,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-53.19,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.364747" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.704248" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.744637" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.996136" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.197384" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.448887" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.662636" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="67.253639" y="0"> ｝</t年代p一个n></text> </g> </g> </svg>均匀密集的<年代vg height="15.325" id="M221" style="vertical-align:-2.21957pt;width:37.487499px;" version="1.1" viewbox="0 0 37.487499 15.325" width="37.487499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.325)"> <g transform="translate(72,-59.74)"> <text transform="matrix(1,0,0,-1,-71.95,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.56,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.09,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.865587" y="0"> ）</t年代p一个n></text> </g> </g> </svg>，有一个序列<年代vg height="17.799999" id="M222" style="vertical-align:-4.77652pt;width:200.3625px;" version="1.1" viewbox="0 0 200.3625 17.799999" width="200.3625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8)"> <g transform="translate(72,-57.76)"> <text transform="matrix(1,0,0,-1,-71.95,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ｛</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.00144" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.62,59.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-52.38,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ｝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.4647713" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.593161" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.456827" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.708328" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.259659" y="0"> n</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.762661" y="0"> ｛</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.764099" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,14.71,59.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,19.14,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.540749" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.581139" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.832638" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.046391" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.29789" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.499138" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="63.090137" y="0"> ｝</t年代p一个n></text> </g> </g> </svg>,这样<年代vg height="15.875" id="M223" style="vertical-align:-3.2316pt;width:17.0875px;" version="1.1" viewbox="0 0 17.0875 15.875" width="17.0875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.875)"> <g transform="translate(72,-59.3)"> <text transform="matrix(1,0,0,-1,-71.29,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-0.65015602" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.62,59.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>倾向于<年代vg height="9.875" id="M224" style="vertical-align:-2.29482pt;width:10.5375px;" version="1.1" viewbox="0 0 10.5375 9.875" width="10.5375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.875)"> <g transform="translate(72,-64.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>统一原样<年代vg height="10.7375" id="M225" style="vertical-align:-0.13794pt;width:51.4375px;" version="1.1" viewbox="0 0 51.4375 10.7375" width="51.4375" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="12.327958" y="0"> →</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.457067" y="0"> ∞</t年代p一个n></text> </g> </g> </svg>．因此,<年代vg height="14.475" id="M226" style="vertical-align:-3.13504pt;width:16.375px;" version="1.1" viewbox="0 0 16.375 14.475" width="16.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.82,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>，<年代vg height="14.475" id="M227" style="vertical-align:-3.13504pt;width:16.375px;" version="1.1" viewbox="0 0 16.375 14.475" width="16.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.82,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>,<年代vg height="14.625" id="M228" style="vertical-align:-3.25793pt;width:16.375px;" version="1.1" viewbox="0 0 16.375 14.625" width="16.375" 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p一个n></text> <text transform="matrix(1,0,0,-1,-63.82,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</t年代p一个n></text> </g> </g> </svg>趋于零<年代vg height="10.7375" id="M229" style="vertical-align:-0.13794pt;width:51.4375px;" version="1.1" viewbox="0 0 51.4375 10.7375" width="51.4375" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="12.327958" y="0"> →</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.457067" y="0"> ∞</t年代p一个n></text> </g> </g> </svg>在哪里<年代vg height="18.5625" id="M230" style="vertical-align:-5.38599pt;width:125.5125px;" version="1.1" viewbox="0 0 125.5125 18.5625" width="125.5125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.5625)"> <g transform="translate(72,-57.15)"> <text transform="matrix(1,0,0,-1,-71.95,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.82,59.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.48,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.904057" y="0"> u</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.155556" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.570557" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.071156" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-11.08,59.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-2.99,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.00288" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.352724" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,16.68,59.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,21.43,57.26)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,25.86,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n></text> </g> </g> </svg>，<年代vg height="18.5625" id="M231" style="vertical-align:-5.38599pt;width:121.075px;" version="1.1" viewbox="0 0 121.075 18.5625" width="121.075" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.5625)"> <g transform="translate(72,-57.15)"> <text transform="matrix(1,0,0,-1,-71.95,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.82,59.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.48,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.904057" y="0"> u</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.155556" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.570557" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.071156" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-11.08,59.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-5.06,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.00288" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.352724" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,14.61,59.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,19.35,57.26)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,22.31,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n></text> </g> </g> </svg>,<年代vg height="15.9125" id="M232" style="vertical-align:-3.25793pt;width:113.95px;" version="1.1" viewbox="0 0 113.95 15.9125" width="113.95" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.9125)"> <g transform="translate(72,-59.27)"> <text transform="matrix(1,0,0,-1,-71.95,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.82,59.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.48,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.904057" y="0"> u</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.155556" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.570557" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.071156" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.17382" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.176701" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.526543" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,11.37,59.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,16.61,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n></text> </g> </g> </svg>．自<年代vg height="13.1875" id="M233" style="vertical-align:-2.29482pt;width:40.599998px;" version="1.1" viewbox="0 0 40.599998 13.1875" width="40.599998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.1875)"> <g transform="translate(72,-61.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.077658" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.118048" y="0"> </t年代p一个n></text> </g> </g> </svg>和功能<年代vg height="13.6125" id="M234" style="vertical-align:-2.34499pt;width:67.637497px;" version="1.1" viewbox="0 0 67.637497 13.6125" width="67.637497" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="13.990857" y="0"> →</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.119967" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.734295" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.897793" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.83696" y="0"> ）</t年代p一个n></text> </g> </g> </svg>是线性的,<年代vg height="16.6" id="M235" style="vertical-align:-3.2316pt;width:91.087502px;" version="1.1" viewbox="0 0 91.087502 16.6" width="91.087502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6018238" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.427982" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.777826" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-51.85,58.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.25" y="-9.2200003"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-41.45,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6268301" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.667219" y="0"> δ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.357044" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.706888" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-4.42,58.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代p一个nclass="equation" id="eq3"> <svg height="205.375" id="M236" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 205.375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,205.375)"> <g transform="translate(72,92.3)"> <text transform="matrix(1,0,0,-1,66.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="3.1700001"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="2.5" y="1.59"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.189825" y="1.59"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.353325" y="1.59"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,91.63,66.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,96.79,61.92)"> <tspan style="font-size: 12.50px; " x="35.639999" y="-1.58"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.639999" y="1.59"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-8.5299997" y="23.58"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.51" y="21.98"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.51" y="25.16"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.9391651" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> δ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.306553" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.0100002" y="23.58"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.699825" y="23.58"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.863323" y="23.58"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,124.99,43.34)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,130.14,38.35)"> <tspan style="font-size: 12.50px; " x="59.459999" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.9391651" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> δ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.306553" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.409218" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.76194" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.970001" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.319847" y="0.0099999998"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,203.78,35.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.2399998" y="-9.2299995"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,214.18,35.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.6300001" y="-2.51"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.957718" y="-2.51"> δ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.647543" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.997387" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,251.5,35.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,256.74,39.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="3.1800001"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-168.48" y="35.84"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-156.44" y="23.58"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-156.44" y="34.25"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-156.44" y="44.91"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-156.44" y="48.080002"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-153.94" y="43.529999"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,108.55,-7.39)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ω.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,117.64,1.59)"> <tspan style="font-size: 12.50px; " x="11.98" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1892252" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,137.95,0.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,145.34,4.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0769377" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.278186" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.154837" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.106504" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.109383" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.459229" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,192.12,0.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,196.86,-1.21)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,203.38,4.11)"> <tspan style="font-size: 12.50px; " x="24.33" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.200001" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-74.269997" y="44.130001"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-63.619999" y="46.639999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-58.830002" y="44.130001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0769377" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.278186" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.154837" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.939999" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.1035" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.016937" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.218185" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.094837" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.308586" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.235008" y="0"> ）</t年代p一个n></text> <text transform="matrix(1,0,0,-1,152.88,-43.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,158.2,-40.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0734386" y="0.0099999998"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.274687" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.151337" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.103004" y="0.0099999998"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.105885" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.45573" y="0.0099999998"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,204.97,-43.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,209.72,-45.33)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,214.75,-40.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.779999" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1700001" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0834389" y="0.0099999998"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.284687" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.161337" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.33" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.118649" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.389999" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.041595" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.431587" y="0.0099999998"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="72.629997" y="0.0099999998"> δ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="81.657166" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="92.759827" y="0.0099999998"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="104.10005" y="0.0099999998"> δ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="113.78988" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="113.13972" y="0.0099999998"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,336.21,-43.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,341.45,-42.53)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9400001" y="-14.76"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9400001" y="-4.0999999"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9400001" y="6.5700002"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9400001" y="9.7299995"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-253.19" y="38.220001"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-241.16211" y="38.220001"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,108.42,-83.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,115.38,-88.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,121.13,-92.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ω.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,130.23,-79.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="3.1700001"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.700001" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.700001" y="3.1700001"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="2.5" y="1.59"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.227094" y="1.59"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.390593" y="1.59"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.304031" y="1.59"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.517782" y="1.59"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.394432" y="1.59"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.59568" y="1.59"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.522102" y="1.59"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.279999" y="1.59"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.931595" y="1.59"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="68.321587" y="1.59"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="79.661812" y="1.59"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,218.03,-83.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,224.98,-88.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,230.74,-92.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ω.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,239.83,-80.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.04159" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.381809" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.633308" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,282.6,-83.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,287.47,-80.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="180.39999" y="-67.480003"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="184.56349" y="-67.480003"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="190.815" y="-67.480003"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="197.0665" y="-67.480003"> ）</t年代p一个n></text> </g> </g> </svg></span>上面不等式的右边趋近于零为<年代vg height="10.7375" id="M237" style="vertical-align:-0.13794pt;width:51.4375px;" version="1.1" viewbox="0 0 51.4375 10.7375" width="51.4375" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="12.327958" y="0"> →</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.457067" y="0"> ∞</t年代p一个n></text> </g> </g> </svg>，左边是独立的<年代vg height="10.7375" id="M238" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" 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p一个n></text> </g> </g> </svg>；因此<年代vg height="14.0625" id="M239" style="vertical-align:-2.29482pt;width:77.987503px;" version="1.1" viewbox="0 0 77.987503 14.0625" width="77.987503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.0625)"> <g transform="translate(72,-60.75)"> <text transform="matrix(1,0,0,-1,-71.95,63.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6018238" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.765323" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-51.85,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-46.69,63.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6268301" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.667219" y="0"> δ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.694386" y="0"> </t年代p一个n></text> </g> </g> </svg>．因此,<年代vg height="12.925" id="M240" style="vertical-align:-1.90608pt;width:43.287498px;" version="1.1" viewbox="0 0 43.287498 12.925" width="43.287498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.715551" y="0"> ⊆</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.755939" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="13.425" id="M241" style="vertical-align:-2.29482pt;width:38.1875px;" version="1.1" viewbox="0 0 38.1875 13.425" width="38.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.152436" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.192825" y="0"> </t年代p一个n></text> </g> </g> </svg>,这意味着<年代vg height="13.425" id="M242" style="vertical-align:-2.29482pt;width:38.1875px;" version="1.1" viewbox="0 0 38.1875 13.425" width="38.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.152436" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.192825" y="0"> </t年代p一个n></text> </g> </g> </svg>．</年代p一个n></p><p><span class="statement" id="prop3"><span class="statement-title">命题3。</年代p一个n><我>的措施<年代vg height="14.3875" id="M243" style="vertical-align:-2.29482pt;width:15.9875px;" version="1.1" viewbox="0 0 15.9875 14.3875" width="15.9875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.34,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> </g> </g> </svg>在一组<年代vg height="14.4625" id="M244" style="vertical-align:-3.13504pt;width:24.9375px;" version="1.1" viewbox="0 0 24.9375 14.4625" width="24.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4625)"> <g transform="translate(72,-60.43)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.19,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>功能性的<年代vg height="10.325" id="M245" style="vertical-align:-0.0pt;width:9.0375004px;" version="1.1" viewbox="0 0 9.0375004 10.325" width="9.0375004" 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p一个n></text> </g> </g> </svg>达到其最大的具有形式</我><年代p一个nclass="equation" id="EEq29"> <svg height="28.424999" id="M246" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 28.424999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,28.425)"> <g transform="translate(72,-49.26)"> <text transform="matrix(1,0,0,-1,152.48,57.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,160.1,62.33)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,168.65,57.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.03" y="6.5599999"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,196.84,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="15.29"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="15.29"> ＝</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="15.29"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,211.11,57.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,218.16,62.33)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.0799999" y="8.1300001"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,227.67,57.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3699999" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.22" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,248.13,62.33)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="8.6899996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,253.21,54.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9299998" y="-2.52"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="214.66" y="-2.52"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="218.8235" y="-2.52"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="225.075" y="-2.52"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="231.32649" y="-2.52"> ）</t年代p一个n></text> </g> </g> </svg></span><i>在哪里<年代vg height="18.1875" id="M247" style="vertical-align:-5.34312pt;width:42.487499px;" version="1.1" viewbox="0 0 42.487499 18.1875" width="42.487499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.1875)"> <g transform="translate(72,-57.45)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.9,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="8.6899996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.35,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≥</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n></text> </g> </g> </svg>，<年代vg height="18.1875" id="M248" style="vertical-align:-5.34312pt;width:45.287498px;" version="1.1" viewbox="0 0 45.287498 18.1875" width="45.287498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.1875)"> <g transform="translate(72,-57.45)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.71,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="8.6899996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.16,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> ω.</t年代p一个n></text> </g> </g> </svg>,<年代vg height="13.45" id="M249" style="vertical-align:-2.21957pt;width:26.1875px;" version="1.1" viewbox="0 0 26.1875 13.45" width="26.1875" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2765059" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.440005" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.679003" y="0"> ）</t年代p一个n></text> </g> </g> </svg>支持单例集的单原子度量是吗<年代vg height="18.1875" id="M250" style="vertical-align:-5.34312pt;width:29.275px;" version="1.1" viewbox="0 0 29.275 18.1875" width="29.275" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.1875)"> <g transform="translate(72,-57.45)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ｛</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.00144" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.71,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="8.6899996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.63,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ｝</t年代p一个n></text> </g> </g> </svg>,其特点是<年代vg height="13.45" id="M251" style="vertical-align:-2.21957pt;width:93.512497px;" version="1.1" viewbox="0 0 93.512497 13.45" width="93.512497" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2765059" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.440005" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.679003" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.842501" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.006001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.732853" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.372189" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.412575" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.139431" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="64.302933" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="70.541924" y="0"> ）</t年代p一个n></text> </g> </g> </svg>，<年代vg height="11.1125" id="M252" style="vertical-align:-0.33858pt;width:38.9375px;" version="1.1" viewbox="0 0 38.9375 11.1125" width="38.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1125)"> <g transform="translate(72,-63.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.7023277" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.742718" y="0"> ω.</t年代p一个n></text> </g> </g> </svg>．</我></年代p一个n></p> <p><span class="statement" id="proof4"><span class="statement-title"><i class="statement-title">证明。</我></年代p一个n>看 [<一个href="#B35">35</一个>］．</年代p一个n></p><p>因此，我们的注意力局限于以(<一个href="#EEq29">32</一个>），使功能最大化<年代vg height="10.325" id="M253" style="vertical-align:-0.0pt;width:9.0375004px;" version="1.1" viewbox="0 0 9.0375004 10.325" width="9.0375004" 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p一个n></text> </g> </g> </svg>和满足<年代vg height="10.325" id="M254" style="vertical-align:-0.0pt;width:17.237499px;" version="1.1" viewbox="0 0 17.237499 10.325" width="17.237499" 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p一个n></text> </g> </g> </svg>约束条件数目(<一个href="#EEq26">26</一个>）- (<一个href="#EEq26">28</一个>）．因此，通过选择功能<年代vg height="11.05" id="M255" style="vertical-align:-3.2316pt;width:14.5625px;" version="1.1" viewbox="0 0 14.5625 11.05" width="14.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.62,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>，<年代vg height="14.6" id="M256" style="vertical-align:-3.13504pt;width:99.574997px;" version="1.1" viewbox="0 0 99.574997 14.6" width="99.574997" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="7.3517642" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.392153" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.643654" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.857405" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.108906" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.31015" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.901154" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.114902" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,2.73,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>，<年代vg height="11.05" id="M257" style="vertical-align:-3.2316pt;width:18.4125px;" version="1.1" viewbox="0 0 18.4125 11.05" width="18.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.56,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>，<年代vg height="14.6" id="M258" style="vertical-align:-3.13504pt;width:94.0625px;" version="1.1" viewbox="0 0 94.0625 14.6" width="94.0625" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="10.239957" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.280346" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.531845" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.745598" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.324097" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.701344" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-1.67,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>,<年代vg height="14.75" id="M259" style="vertical-align:-3.2316pt;width:14.225px;" version="1.1" viewbox="0 0 14.225 14.75" width="14.225" 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,-71.95,63.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.02,60.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>，<年代vg height="12.8875" id="M260" style="vertical-align:-1.76814pt;width:76.712502px;" version="1.1" viewbox="0 0 76.712502 12.8875" width="76.712502" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="8.9646511" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.005039" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.25654" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.470291" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.04879" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.262539" y="0"> </t年代p一个n></text> </g> </g> </svg>，无限维度问题(<一个href="#EEq25">25</一个>）- (<一个href="#EEq26">28</一个>）近似为有限维非线性规划(NLP)问题:<年代p一个nclass="equation" id="EEq30"> <svg height="35.587502" id="M261" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 35.587502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,35.5875)"> <g transform="translate(72,-43.53)"> <text transform="matrix(1,0,0,-1,143.94,57.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.115167" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.666498" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.917999" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.393833" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.121166" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.597" y="0"> z</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.148335" y="0"> e</t年代p一个n></text> <text transform="matrix(1,0,0,-1,148.07,49.41)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,153.01,47.22)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,156.31,49.41)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ≥</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.37112" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="14.011952" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,174.7,47.22)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,178,49.41)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> ω.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,194.64,50.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,210.79,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="15.29"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="15.29"> ＝</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="15.29"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,225.07,57.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,232.12,54.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,236.55,57.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,243.49,54.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,250.44,54.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,262.53,54.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,266.96,54.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="200.91" y="0.17"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="205.0735" y="0.17"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="211.325" y="0.17"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="217.57649" y="0.17"> ）</t年代p一个n></text> </g> </g> </svg></span>受<年代p一个nclass="equation" id="EEq31"> <svg height="107.425" id="M262" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 107.425" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,107.425)"> <g transform="translate(72,13.94)"> <text transform="matrix(1,0,0,-1,108.26,50.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,124.41,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="15.29"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="15.29"> ＝</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="15.29"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,138.68,57.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,145.74,54.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,150.16,57.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,158.49,63.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="10.32"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,165.73,54.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,177.82,54.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,182.25,54.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3199997" y="-2.52"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.347885" y="-2.52"> δ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.375051" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,220.96,54.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,224.18,57.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.166139" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.530407" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.570793" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.822296" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.036045" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.614544" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.828293" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,302.58,54.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,307.45,57.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-232.22" y="38.16"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="160.42" y="-0.18000001"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="164.5835" y="-0.18000001"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="170.83499" y="-0.18000001"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="177.0865" y="-0.18000001"> ）</t年代p一个n></text> <text transform="matrix(1,0,0,-1,91.38,34.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="15.28"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="15.28"> ＝</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="15.28"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,105.65,25.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,112.71,22.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,117.13,25.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,129.44,30.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="-2.9200001" y="9.21"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,136.37,23.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,148.46,22.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,152.89,23.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3299999" y="-2.51"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.357885" y="-2.51"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.609386" y="-2.51"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.775524" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.027985" y="-2.51"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.068375" y="-2.51"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.319878" y="-2.51"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="76.533623" y="-2.51"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="91.112122" y="-2.51"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="96.325874" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,261.79,22.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,266.66,25.72)"> <tspan style="font-size: 12.50px; " x="-150.60001" y="38.150002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3772497" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.054571" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.094961" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.346462" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.560211" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.81171" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.025463" y="0"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.276962" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.47821" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.729713" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="201.21001" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="205.3735" y="0"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="211.625" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="217.8765" y="0"> ）</t年代p一个n></text> <text transform="matrix(1,0,0,-1,132.21,3.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="15.29"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="15.29"> ＝</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="15.29"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,146.49,-5.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,153.54,-9.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,157.97,-5.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,164.89,-9.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,171.33,-8.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,183.42,-9.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,187.85,-8.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3199997" y="-2.51"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.347885" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,215.48,-9.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,220.33,-11.19)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,224.08,-5.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.166139" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.143293" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.183681" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.435181" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.636429" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.227432" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="67.441185" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="75.56813" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="243.78999" y="-0.18000001"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="247.95351" y="-0.18000001"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="254.205" y="-0.18000001"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="260.45651" y="-0.18000001"> ）</t年代p一个n></text> </g> </g> </svg></span>在哪里<年代vg height="14.6" id="M265" style="vertical-align:-3.13504pt;width:133.1875px;" version="1.1" viewbox="0 0 133.1875 14.6" width="133.1875" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="16.028847" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.069235" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-31.31,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-23.66,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.591721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,6.5,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,14.16,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> </g> </g> </svg>．显然,(<一个href="#EEq30">33</一个>）- (<一个href="#EEq31">36</一个>）是一个NLP问题2<年代vg height="10.325" id="M266" style="vertical-align:-0.0pt;width:17.237499px;" version="1.1" viewbox="0 0 17.237499 10.325" width="17.237499" 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p一个n></text> </g> </g> </svg>未知数：<年代vg height="12.975" id="M267" style="vertical-align:-4.77652pt;width:14.475px;" version="1.1" viewbox="0 0 14.475 12.975" width="14.475" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.975)"> <g transform="translate(72,-61.62)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.9,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="13.1125" id="M268" style="vertical-align:-4.77652pt;width:13.4625px;" version="1.1" viewbox="0 0 13.4625 13.1125" width="13.4625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.1125)"> <g transform="translate(72,-61.51)"> <text transform="matrix(1,0,0,-1,-71.95,66.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.71,63.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>，<年代vg height="13.6125" id="M269" style="vertical-align:-2.34499pt;width:81.775002px;" version="1.1" viewbox="0 0 81.775002 13.6125" width="81.775002" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3269978" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.367388" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.618887" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.832638" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.411137" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.624886" y="0"> </t年代p一个n></text> </g> </g> </svg>．一个对LP问题感兴趣。下面的命题使我们能够近似地解决NLP问题(<一个href="#EEq30">33</一个>）- (<一个href="#EEq31">36</一个>）的有限维LP问题。</p><p><年代p一个nclass="statement" id="prop4"><span class="statement-title">命题4。</年代p一个n><我>让<年代vg height="14.6625" id="M270" style="vertical-align:-3.13504pt;width:141.1875px;" version="1.1" viewbox="0 0 141.1875 14.6625" width="141.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6625)"> <g transform="translate(72,-60.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ω.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.65,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-50.44,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> ｛</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.029325" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-26.2,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-21.33,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-9.91,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-5.04,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.79225" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.993498" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,26.17,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,34.9,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ｝</t年代p一个n></text> </g> </g> </svg>是可数稠密的子集<年代vg height="10.6875" id="M271" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ω.</t年代p一个n></text> </g> </g> </svg>．鉴于<年代vg height="11.0625" id="M272" style="vertical-align:-0.30096pt;width:34.887501px;" version="1.1" viewbox="0 0 34.887501 11.0625" width="34.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.5147829" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.555172" y="0"> 0</t年代p一个n></text> </g> </g> </svg>衡量<年代vg height="15.125" id="M273" style="vertical-align:-2.21957pt;width:74.6875px;" version="1.1" viewbox="0 0 74.6875 15.125" width="74.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.125)"> <g transform="translate(72,-59.9)"> <text transform="matrix(1,0,0,-1,-71.95,62.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.7898493" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.830238" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-36.42,67.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> +</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-29.93,62.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ω.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.465731" y="0"> ）</t年代p一个n></text> </g> </g> </svg>可以这样找到:</我><年代p一个nclass="equation" id="eq4"> <svg height="110.6375" id="M274" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 110.6375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,110.6375)"> <g transform="translate(72,16.51)"> <text transform="matrix(1,0,0,-1,152.4,62.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="3.1800001"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="2.5" y="1.6"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.91" y="4.1100001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.77" y="1.6"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,176.11,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,180.98,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.6300001" y="-2.51"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.970221" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,208.57,66.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,215.73,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,228.52,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,233.39,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-4.1100001"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-0.93000001"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-124.29" y="20.23"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-124.29" y="23.42"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-121.79" y="21.83"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-113.38" y="24.34"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-107.53" y="21.83"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.83" y="-2.51"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.857885" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.909338" y="-2.51"> ，</t年代p一个n></text> <text transform="matrix(1,0,0,-1,134.19,42.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="10.33"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,139.35,34.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.6300001" y="-2.51"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.957718" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,166.93,41.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,174.09,34.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,188.27,42.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="10.33"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,193.42,34.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8600001" y="-4.1100001"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8600001" y="-0.92000002"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.83" y="-2.51"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.857885" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.909338" y="-2.51"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.087978" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.452248" y="-2.51"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="64.480133" y="-2.51"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="70.731636" y="-2.51"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="75.945381" y="-2.51"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="90.536385" y="-2.51"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="95.737633" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,301.73,33.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,306.61,36.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-235.97" y="22.75"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-235.97" y="25.93"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-233.47" y="24.35"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-225.06" y="26.860001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-219.21001" y="24.35"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,96.79,17.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.2200003"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,102.03,9.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.6300001" y="-2.51"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.970221" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,129.62,17.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,136.78,9.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,152.02,17.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.2200003"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,157.26,9.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-4.1100001"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-0.93000001"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.83" y="-2.51"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.857885" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.909338" y="-2.51"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.087978" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.327938" y="-2.51"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="67.368324" y="-2.51"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="73.619827" y="-2.51"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="78.83358" y="-2.51"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="93.412071" y="-2.51"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="98.625824" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,268.46,9.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,273.33,12.44)"> <tspan style="font-size: 12.50px; " x="-158.17" y="22.74"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-158.17" y="25.93"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-155.67" y="24.34"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-147.25999" y="26.85"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-141.41" y="24.34"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3772497" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.067076" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.094961" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.346462" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.560211" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.81171" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.025463" y="0"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.276962" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.47821" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.729713" y="0"> ，</t年代p一个n></text> <text transform="matrix(1,0,0,-1,138.85,-15.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,143.2,-14.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.6300001" y="-2.51"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.957718" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,170.78,-6.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,177.94,-14.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,190.72,-15.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,195.07,-14.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-4.1100001"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-0.92000002"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.82" y="-2.51"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.86039" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.91184" y="-2.51"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.07798" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.055134" y="-2.51"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.09552" y="-2.51"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="72.347023" y="-2.51"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="77.548271" y="-2.51"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="92.139275" y="-2.51"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="97.35302" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="105.47997" y="-2.51"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="272.79999" y="-39.029999"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="276.9635" y="-39.029999"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="283.215" y="-39.029999"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="289.46649" y="-39.029999"> ）</t年代p一个n></text> </g> </g> </svg></span><i>在测量<年代vg height="7.4250002" id="M275" style="vertical-align:-0.11285pt;width:8.0375004px;" version="1.1" viewbox="0 0 8.0375004 7.4250002" width="8.0375004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.425)"> <g transform="translate(72,-66.06)"> <text transform="matrix(1,0,0,-1,-71.95,66.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>有表格</我><年代p一个nclass="equation" id="EEq34"> <svg height="28.424999" id="M276" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 28.424999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,28.425)"> <g transform="translate(72,-49.26)"> <text transform="matrix(1,0,0,-1,158.22,57.33)"> <tspan style="font-size: 12.50px; " x="21.84" y="6.5599999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.7898493" y="0"> ＝</t年代p一个n></text> <text transform="matrix(1,0,0,-1,196.21,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="15.29"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="15.29"> ＝</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="15.29"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,210.49,57.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,217.54,62.33)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="8.6899996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,222.61,57.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3800001" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.23" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,243.04,54.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,247.47,54.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9299998" y="-2.52"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="220.39999" y="-2.52"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="224.56349" y="-2.52"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="230.815" y="-2.52"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="237.0665" y="-2.52"> ）</t年代p一个n></text> </g> </g> </svg></span><i>和系数<年代vg height="18.1875" id="M277" style="vertical-align:-5.34312pt;width:15.2875px;" version="1.1" viewbox="0 0 15.2875 18.1875" width="15.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.1875)"> <g transform="translate(72,-57.45)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.9,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="8.6899996"> </t年代p一个n></text> </g> </g> </svg>，<年代vg height="13.6125" id="M278" style="vertical-align:-2.34499pt;width:81.775002px;" version="1.1" viewbox="0 0 81.775002 13.6125" width="81.775002" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3269978" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.367388" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.618887" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.832638" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.411137" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.624886" y="0"> </t年代p一个n></text> </g> </g> </svg>，与最佳测量相同(<一个href="#EEq29">32</一个>)，<年代vg height="16.637501" id="M279" style="vertical-align:-4.77652pt;width:58.987499px;" version="1.1" viewbox="0 0 58.987499 16.637501" width="58.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.75,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.85,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> ω.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-33.59,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>，<年代vg height="13.6125" id="M280" style="vertical-align:-2.34499pt;width:81.775002px;" version="1.1" viewbox="0 0 81.775002 13.6125" width="81.775002" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3269978" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.367388" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.618887" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.832638" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.411137" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.624886" y="0"> </t年代p一个n></text> </g> </g> </svg>．</我></年代p一个n></p> <p><span class="statement" id="proof5"><span class="statement-title"><i class="statement-title">证明。</我></年代p一个n>我们重命名函数<年代vg height="14.625" id="M281" style="vertical-align:-3.25793pt;width:14.8875px;" version="1.1" viewbox="0 0 14.8875 14.625" width="14.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> </g> </g> </svg>，<年代vg height="17.975" id="M282" style="vertical-align:-4.2998pt;width:20.625px;" version="1.1" viewbox="0 0 20.625 17.975" width="20.625" 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,-71.95,61.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.71,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="10.33"> </t年代p一个n></text> </g> </g> </svg>那，<年代vg height="16.5875" id="M283" style="vertical-align:-4.32487pt;width:18.4125px;" version="1.1" viewbox="0 0 18.4125 16.5875" width="18.4125" 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p一个n></text> <text transform="matrix(1,0,0,-1,-62.56,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.2200003"> </t年代p一个n></text> </g> </g> </svg>的年代,<年代vg height="14.75" id="M284" style="vertical-align:-3.2316pt;width:14.225px;" version="1.1" viewbox="0 0 14.225 14.75" width="14.225" 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,-71.95,63.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.02,60.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>的顺序是<年代vg height="16.75" id="M285" style="vertical-align:-4.77652pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 16.75" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.75)"> <g transform="translate(72,-58.6)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.74,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>，<年代vg height="13.6125" id="M286" style="vertical-align:-2.34499pt;width:120.1625px;" version="1.1" viewbox="0 0 120.1625 13.6125" width="120.1625" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3269978" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.367388" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.618887" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.832638" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.084137" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.285385" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.876389" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="63.090137" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="78.43132" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="89.771538" y="0"> 1</t年代p一个n></text> </g> </g> </svg>．然后,对于<年代vg height="13.6125" id="M287" style="vertical-align:-2.34499pt;width:105.8375px;" version="1.1" viewbox="0 0 105.8375 13.6125" width="105.8375" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3269978" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.367388" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.618887" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.832638" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.411137" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.624886" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.966064" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="78.30629" y="0"> 1</t年代p一个n></text> </g> </g> </svg>，<年代p一个nclass="equation" id="eq5"> <svg height="74.949997" id="M288" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 74.949997" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,74.95)"> <g transform="translate(72,-12.04)"> <text transform="matrix(1,0,0,-1,73.35,58.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="3.54"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="2.5" y="4.29"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3599997" y="1.77"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,89.32,61.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,97.17,56.58)"> <tspan style="font-size: 12.50px; " x="21.84" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.780001" y="0"> ℎ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,134.16,53.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,138.59,58.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="3.54"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.9699998" y="1.77"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.01" y="-5.1500001"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.01" y="5.52"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.01" y="8.6800003"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.51" y="8.3199997"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,175.25,65.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="15.29"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="15.29"> ＝</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="15.29"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,188.85,56.58)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,195.9,61.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="8.6899996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,203.06,54.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.79" y="-2.52"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,215.06,53.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,221.57,54.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,233.66,61.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="8.6899996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,238.74,54.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.6300001" y="-2.52"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.970221" y="-2.52"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,265.92,53.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,272.44,54.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,284.49,53.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,287.71,54.06)"> <tspan style="font-size: 12.50px; " x="10.64" y="-9.4399996"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.64" y="1.23"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.64" y="4.3899999"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-143.14999" y="30.23"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-129.03" y="35.150002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-121.66" y="36.779999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8514042" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,182.2,32.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="15.29"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="15.29"> ＝</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="15.29"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,195.79,23.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,202.85,28.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="8.6899996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,207.92,18.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.6899996" y="-4.9200001"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.417334" y="-4.9200001"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.968666" y="-4.9200001"> x</t年代p一个n></text> <text transform="matrix(1,0,0,-1,224.99,16.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.9098721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,243.3,25.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="3.54"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="2.5" y="1.78"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,253.02,20.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,259.53,21.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,271.62,28.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="8.6899996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,276.7,21.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.6300001" y="-2.51"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.13372" y="-2.51"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,308.05,20.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,314.56,21.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8600001" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,326.62,20.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,329.84,21.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-4.29"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-0.75"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.43" y="-2.51"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="138.03" y="-17.57"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="142.1935" y="-17.57"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="148.44499" y="-17.57"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="154.6965" y="-17.57"> ）</t年代p一个n></text> </g> </g> </svg></span> <svg height="16.75" id="M289" style="vertical-align:-4.77652pt;width:14.675px;" version="1.1" viewbox="0 0 14.675 16.75" width="14.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.75)"> <g transform="translate(72,-58.6)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.74,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>s是连续的。因此,<年代vg height="13.2625" id="M290" style="vertical-align:-4.77652pt;width:46.525002px;" version="1.1" viewbox="0 0 46.525002 13.2625" width="46.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.2625)"> <g transform="translate(72,-61.39)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.727334" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.278666" y="0"> x</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-46.25,63.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.9098721" y="0"> </t年代p一个n></text> </g> </g> </svg>能做不到吗<年代vg height="21.737499" id="M291" style="vertical-align:-5.35329pt;width:59.325001px;" version="1.1" viewbox="0 0 59.325001 21.737499" width="59.325001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,21.7375)"> <g transform="translate(72,-54.61)"> <text transform="matrix(1,0,0,-1,-71.95,60)"> <tspan style="font-size: 12.50px; " x="9.5299997" y="0.02"> ∑</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.0514522" y="0"> /</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-50.99,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.9399996"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="9.9399996"> ＝</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="9.9399996"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-36.72,60)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-29.67,65)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="8.6899996"> </t年代p一个n></text> </g> </g> </svg>通过选择<年代vg height="11.025" id="M292" style="vertical-align:-3.2316pt;width:11.9px;" version="1.1" viewbox="0 0 11.9 11.025" width="11.9" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.025)"> <g transform="translate(72,-63.18)"> <text transform="matrix(1,0,0,-1,-71.95,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.75,63.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>，<年代vg height="12.8875" id="M293" style="vertical-align:-1.76814pt;width:94.887497px;" version="1.1" viewbox="0 0 94.887497 12.8875" width="94.887497" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="7.3517642" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.392153" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.643654" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.857405" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.108906" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.31015" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.901154" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.114902" y="0"> </t年代p一个n></text> </g> </g> </svg>足够接近<年代vg height="16.262501" id="M294" style="vertical-align:-3.7982pt;width:14.2625px;" version="1.1" viewbox="0 0 14.2625 16.262501" width="14.2625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2625)"> <g transform="translate(72,-58.99)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.71,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="8.6899996"> </t年代p一个n></text> </g> </g> </svg>．</年代p一个n></p><p>构造一个合适的集合<年代vg height="14.6" id="M295" style="vertical-align:-3.13504pt;width:22.674999px;" version="1.1" viewbox="0 0 22.674999 14.6" width="22.674999" 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"> ω.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.65,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>，它保存了关系(<一个href="#EEq6">6</一个>），<年代vg height="10.5125" id="M296" style="vertical-align:-0.15048pt;width:10.4375px;" version="1.1" viewbox="0 0 10.4375 10.5125" width="10.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5125)"> <g transform="translate(72,-63.59)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>分为<年代vg height="10.725" id="M297" style="vertical-align:-0.1254pt;width:11.375px;" version="1.1" viewbox="0 0 11.375 10.725" width="11.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.725)"> <g transform="translate(72,-63.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>个子区间如下:<年代p一个nclass="equation" id="EEq35"> <svg height="69.25" id="M298" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 69.25" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,69.25)"> <g transform="translate(72,-16.6)"> <text transform="matrix(1,0,0,-1,114.31,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,121.06,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,128.88,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.04" y="7.3299999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.389999" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,151.19,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,158.84,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.54" y="-8.2200003"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.703499" y="-8.2200003"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.967981" y="-8.2200003"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.320705" y="-8.2200003"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.572205" y="-8.2200003"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.811203" y="-8.2200003"> δ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.838367" y="-8.2200003"> </t年代p一个n></text> <g> <path d="m 171.38,56.57 54.19,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,184.22,44.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.902616" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.242838" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.540001" y="-8.7600002"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.741249" y="-8.7600002"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,235.88,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,243.54,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.08" y="-7.25"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.58132" y="-7.25"> δ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.608486" y="-7.25"> </t年代p一个n></text> <g> <path d="m 256.08,56.57 28.5,0" 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,-1,256.08,44.69)"> <tspan style="font-size: 12.50px; " x="29.690001" y="-1.4299999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.150002" y="-8.7600002"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.890113" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.242838" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-130.94" y="23.280001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-121.96284" y="23.280001"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-109.93496" y="23.280001"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-103.68346" y="23.280001"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-98.469711" y="23.280001"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-92.218208" y="23.280001"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-87.004456" y="23.280001"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-72.425957" y="23.280001"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-67.212212" y="23.280001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-56.309593" y="23.280001"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-44.956867" y="23.280001"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-38.705368" y="23.280001"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-23.53923" y="23.280001"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,239.3,18.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,249.57,21.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.04" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.83" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,270.31,18.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,273.77,21.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,282.89,18.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,289.3,18.9)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9299998" y="-2.51"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="178.57001" y="-22.27"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="182.73351" y="-22.27"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="188.985" y="-22.27"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="195.2365" y="-22.27"> ）</t年代p一个n></text> </g> </g> </svg></span>在哪里<年代vg height="13" id="M299" style="vertical-align:-3.22282pt;width:9.3374996px;" version="1.1" viewbox="0 0 9.3374996 13" width="9.3374996" 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,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是最佳时间的下限<年代vg height="14.9375" id="M300" style="vertical-align:-4.77652pt;width:13.025px;" version="1.1" viewbox="0 0 13.025 14.9375" width="13.025" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.9375)"> <g transform="translate(72,-60.05)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>，可以通过使用基于Golden Section的搜索算法来获得[<一个href="#B36">36</一个>］或<我>Fibonnaci</我>搜索方法(<一个href="#B37">37</一个>］．让<年代vg height="15.875" id="M301" style="vertical-align:-0.1254pt;width:11.375px;" version="1.1" viewbox="0 0 11.375 15.875" width="11.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.875)"> <g transform="translate(72,-59.3)"> <g> <path d="m -71.95,70.71 9,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是这样一个最大的数<年代vg height="15.875" id="M302" style="vertical-align:-4.33365pt;width:100.8125px;" version="1.1" viewbox="0 0 100.8125 15.875" width="100.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.875)"> <g transform="translate(72,-59.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m -65.2,67.31 6.8,0" 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,-65.2,59.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.93,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊆</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> ［</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.203888" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-34.81,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-29.94,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-20.81,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-13.16,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.591721" y="0"> ］</t年代p一个n></text> </g> </g> </svg>．放<年代vg height="23.737499" id="M303" style="vertical-align:-3.87106pt;width:85.237503px;" version="1.1" viewbox="0 0 85.237503 23.737499" width="85.237503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,23.7375)"> <g transform="translate(72,-53.01)"> <text transform="matrix(1,0,0,-1,-71.95,56.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.7,61.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.35,56.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.04" y="0.02"> ⋃</t年代p一个n></text> <g> <path d="m -31.76,71.08 6.8,0" 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,-31.76,63.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="10.06"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.8508799" y="10.06"> ＝</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.8459997" y="10.06"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-14.96,56.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-8.2,53.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>，<年代vg height="23.0375" id="M304" style="vertical-align:-6.20459pt;width:100.6125px;" version="1.1" viewbox="0 0 100.6125 23.0375" width="100.6125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,23.0375)"> <g transform="translate(72,-53.57)"> <text transform="matrix(1,0,0,-1,-71.95,59.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.7,64.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.35,59.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.04" y="0.029999999"> ⋃</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-31.76,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="12.12"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.8508799" y="12.12"> ＝</t年代p一个n></text> <g> <path d="m -21.91,61.85 6.3,0" 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,-21.91,53.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.2926879" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="12.287808" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-2.66,59.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,4.09,56.68)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>，<年代vg height="14.375" id="M305" style="vertical-align:-0.3135pt;width:111.4875px;" version="1.1" viewbox="0 0 111.4875 14.375" width="111.4875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ω.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.65,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.3,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-34.01,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-26.36,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.777586" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.517902" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.29549" y="0"> </t年代p一个n></text> </g> </g> </svg>,<年代vg height="16.8125" id="M306" style="vertical-align:-2.26974pt;width:121.5625px;" version="1.1" viewbox="0 0 121.5625 16.8125" width="121.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.8125)"> <g transform="translate(72,-58.55)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ω.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.65,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.3,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-34.01,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-26.36,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.777586" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.517902" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.29549" y="0"> ｛</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.296928" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.548428" y="0"> ｝</t年代p一个n></text> </g> </g> </svg>．此外,间隔<年代vg height="14.575" id="M307" style="vertical-align:-3.2316pt;width:15.35px;" version="1.1" viewbox="0 0 15.35 14.575" width="15.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.575)"> <g transform="translate(72,-60.34)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.99,60.48)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>（<年代vg height="12.8875" id="M308" style="vertical-align:-1.76814pt;width:75.162498px;" version="1.1" viewbox="0 0 75.162498 12.8875" width="75.162498" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="7.3517642" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.392153" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.643654" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.857405" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.108906" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.31015" y="0"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.561653" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.775402" y="0"> 4</t年代p一个n></text> </g> </g> </svg>）和<年代vg height="10.5375" id="M309" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>分别分为<年代vg height="11.05" id="M310" style="vertical-align:-3.2316pt;width:11.9125px;" version="1.1" viewbox="0 0 11.9125 11.05" width="11.9125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.74,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="7.1374998" id="M311" style="vertical-align:-0.10033pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 7.1374998" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>小区间。因此,集<年代vg height="13.325" id="M312" style="vertical-align:-0.0pt;width:15.775px;" version="1.1" viewbox="0 0 15.775 13.325" width="15.775" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.325)"> <g transform="translate(72,-61.34)"> <text transform="matrix(1,0,0,-1,-71.95,61.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ω.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.65,66.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>，<年代vg height="12.8875" id="M313" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="7.3517642" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.392153" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.643654" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.857405" y="0"> 2</t年代p一个n></text> </g> </g> </svg>，被分割成<年代vg height="19.7875" id="M314" style="vertical-align:-3.25793pt;width:121.9px;" version="1.1" viewbox="0 0 121.9 19.7875" width="121.9" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.7875)"> <g transform="translate(72,-56.17)"> <text transform="matrix(1,0,0,-1,-71.95,59.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61.31,56.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-52.96,59.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n></text> <g> <path d="m -40.93,70.71 9.01,0" 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,-40.93,59.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0021601" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-25.71,56.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-20.83,59.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-14.62,56.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-9.75,59.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-3.53,56.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,1.34,59.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,7.56,56.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</t年代p一个n></text> <text transform="matrix(1,0,0,-1,12.43,59.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="19.7875" id="M315" style="vertical-align:-3.25793pt;width:143.825px;" version="1.1" viewbox="0 0 143.825 19.7875" width="143.825" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.7875)"> <g transform="translate(72,-56.17)"> <text transform="matrix(1,0,0,-1,-71.95,59.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61.31,56.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-52.96,59.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.191385" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.094002" y="0"> −</t年代p一个n></text> <g> <path d="m -14.51,70.71 9,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-14.51,59.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.9896574" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.153156" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,4.87,56.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,9.74,59.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,15.96,56.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,20.83,59.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,27.04,56.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,31.92,59.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,38.13,56.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</t年代p一个n></text> </g> </g> </svg>细胞,分别。从每个单元格中选择一个点。用这种方法，我们将得到一个由点组成的网格，这些点按顺序编号为<年代vg height="18.7875" id="M316" style="vertical-align:-6.50204pt;width:148.5px;" version="1.1" viewbox="0 0 148.5 18.7875" width="148.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.7875)"> <g transform="translate(72,-56.97)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.75,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.85,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.191385" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-37.73,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-33.31,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-21.22,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-16.84,58.18)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-13.04,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.79225" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.006001" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,18.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</t年代p一个n></text> <text transform="matrix(1,0,0,-1,23.22,58.18)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,27.02,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,38.16,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,42.59,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代p一个n></text> </g> </g> </svg>，<年代vg height="13.6125" id="M317" style="vertical-align:-2.34499pt;width:79.375px;" version="1.1" viewbox="0 0 79.375 13.6125" width="79.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3269978" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.367388" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.618887" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.832638" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.411137" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.624886" y="0"> </t年代p一个n></text> </g> </g> </svg>，在哪里<年代vg height="14.2375" id="M318" style="vertical-align:-3.13504pt;width:89.25px;" version="1.1" viewbox="0 0 89.25 14.2375" width="89.25" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="14.103384" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.143772" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.16,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-27.51,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-5.52,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>．</p><p>因此，根据(<一个href="#EEq34">38</一个>）、NLP问题(<一个href="#EEq30">33</一个>）- (<一个href="#EEq31">36</一个>）转换为以下LP问题:<年代p一个nclass="equation" id="EEq36"> <svg height="35.587502" id="M319" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 35.587502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,35.5875)"> <g transform="translate(72,-43.53)"> <text transform="matrix(1,0,0,-1,143.96,57.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.115167" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.666498" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.917999" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.393833" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.121166" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.597" y="0"> z</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.148335" y="0"> e</t年代p一个n></text> <text transform="matrix(1,0,0,-1,160,49.41)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,164.94,47.22)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,168.24,49.41)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ≥</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,194.66,50.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,210.81,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="15.29"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="15.29"> ＝</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="15.29"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,225.09,57.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,232.14,54.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,236.56,57.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,243.5,54.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,250.46,54.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,262.52,54.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,266.94,54.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="200.92999" y="0.17"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="205.09351" y="0.17"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="211.345" y="0.17"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="217.5965" y="0.17"> ）</t年代p一个n></text> </g> </g> </svg></span>受<年代p一个nclass="equation" id="EEq37"> <svg height="107.425" id="M320" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 107.425" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,107.425)"> <g transform="translate(72,13.94)"> <text transform="matrix(1,0,0,-1,108.28,50.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,124.43,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="15.29"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="15.29"> ＝</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="15.29"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,138.7,57.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,145.75,54.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,150.18,57.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,158.51,63.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="10.32"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,165.75,54.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,177.8,54.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,182.23,54.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3199997" y="-2.52"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.36039" y="-2.52"> δ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.387554" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,220.95,54.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,224.17,57.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.166139" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.517902" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.558292" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.809792" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.023544" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.602039" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.815788" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,302.56,54.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,307.43,57.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-238.44" y="38.16"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="160.44" y="-0.18000001"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="164.6035" y="-0.18000001"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="170.855" y="-0.18000001"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="177.10651" y="-0.18000001"> ）</t年代p一个n></text> <text transform="matrix(1,0,0,-1,85.15,34.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="15.28"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="15.28"> ＝</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="15.28"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,99.42,25.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,106.47,22.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,110.9,25.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,123.21,30.72)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="-2.9200001" y="9.21"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,130.14,23.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,142.19,22.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,146.62,23.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3299999" y="-2.51"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.357885" y="-2.51"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.609386" y="-2.51"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.775524" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.027985" y="-2.51"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.068375" y="-2.51"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.319878" y="-2.51"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="76.533623" y="-2.51"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="91.112122" y="-2.51"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="96.325874" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,255.52,22.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,260.39,25.72)"> <tspan style="font-size: 12.50px; " x="-144.31" y="38.150002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3772497" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.054571" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.094961" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.346462" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.723709" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.975212" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.352463" y="0"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="72.779961" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="77.981209" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="84.232712" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="207.48" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="211.64349" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="217.895" y="0"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="224.1465" y="0"> ）</t年代p一个n></text> <text transform="matrix(1,0,0,-1,132.23,3.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="15.29"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="15.29"> ＝</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="15.29"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,146.51,-5.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,153.56,-9.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,157.99,-5.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,164.91,-9.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,171.35,-8.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,183.4,-9.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,187.83,-8.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3199997" y="-2.51"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.347885" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,215.47,-9.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,220.31,-11.19)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,224.06,-5.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.166139" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.143293" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.183681" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.435181" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.636429" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.227432" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="67.441185" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="75.56813" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="243.81" y="-0.18000001"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="247.9735" y="-0.18000001"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="254.22501" y="-0.18000001"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="260.4765" y="-0.18000001"> ）</t年代p一个n></text> </g> </g> </svg></span></p> <p>在这里，我们讨论合适的总函数<年代vg height="11.05" id="M323" style="vertical-align:-3.2316pt;width:14.5625px;" version="1.1" viewbox="0 0 14.5625 11.05" width="14.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.62,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>年代,<年代vg height="11.05" id="M324" style="vertical-align:-3.2316pt;width:18.4125px;" version="1.1" viewbox="0 0 18.4125 11.05" width="18.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.56,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>年代,<年代vg height="14.75" id="M325" style="vertical-align:-3.2316pt;width:14.225px;" version="1.1" viewbox="0 0 14.225 14.75" width="14.225" 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,-71.95,63.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.02,60.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>年代。功能<年代vg height="11.05" id="M326" style="vertical-align:-3.2316pt;width:14.5625px;" version="1.1" viewbox="0 0 14.5625 11.05" width="14.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.62,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>S可以被看成是的单项式<年代vg height="9.125" id="M327" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>以及向量的分量<年代vg height="7.1624999" id="M328" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>如下:<年代p一个nclass="equation" id="eq6"> <svg height="20.424999" id="M329" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 20.424999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.425)"> <g transform="translate(72,-55.66)"> <text transform="matrix(1,0,0,-1,63.84,60.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,67.76,65.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,70.98,60.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,77.85,66.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="10.86"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,82.73,60.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.364747" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,98.98,66.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="10.86"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,103.86,60.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,110.73,65.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.3699999"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,116.28,60.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.166139" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.530407" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.646294" y="0"> ｛</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.647732" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.899235" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.112984" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.364483" y="0"> ｝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="68.453926" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="77.831177" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="86.158173" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="100.28656" y="0"> ｛</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="106.288" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="112.53951" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="117.74075" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="123.99225" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="133.36951" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="147.96049" y="0"> ｝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="156.04994" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="165.4272" y="0"> ℎ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="176.11726" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="190.23314" y="0"> ｛</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="196.23459" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="202.48608" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="207.69983" y="0"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="213.95134" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="219.15259" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="225.40408" y="0"> ｝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="233.49353" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="351.59" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="355.75351" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="362.005" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="368.2565" y="0"> ）</t年代p一个n></text> </g> </g> </svg></span>另外，我们选择了一些支持紧凑的函数，形式如下[<一个href="#B36">36</一个>，<一个href="#B37">37</一个>］：<年代p一个nclass="equation" id="eq7"> <svg height="144.96249" id="M330" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 144.96249" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,144.9625)"> <g transform="translate(72,43.97)"> <text transform="matrix(1,0,0,-1,93.1,42.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,102.49,38.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="7.946816" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="13.941936" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,123.39,42.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.75" y="-14.78"> ⎧</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.75" y="-7.5100002"> ⎪</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.75" y="3.2"> ⎨</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.75" y="13.91"> ⎪</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.75" y="21.120001"> ⎩</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.509998" y="2.24"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="86.849998" y="-15.56"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0734386" y="0.0099999998"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.712772" y="0.0099999998"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.75" y="-7.4899998"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.613667" y="-7.4899998"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.0895" y="-7.4899998"> n</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.809998" y="-18.07"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="72.061501" y="-18.07"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="79.650818" y="-18.07"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="92.699997" y="-18.07"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="99.389107" y="-18.07"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="110.72932" y="-18.07"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,238.04,57.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,242.91,57.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m 189.2,52.73 59.56,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,210.03,40.85)"> <tspan style="font-size: 12.50px; " x="39.93" y="0.98000002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> δ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.529999" y="-8.75"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.919273" y="-8.75"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="81.947159" y="-8.75"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,295.9,46.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,159.14,23)"> <tspan style="font-size: 12.50px; " x="-73.120003" y="43.32"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="113.42" y="0"> o</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="119.58398" y="0"> t</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="123.14733" y="0"> h</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="129.39883" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="134.95016" y="0"> r</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="139.35123" y="0"> w</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="148.37839" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="151.85422" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="156.7179" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="162.26923" y="0"> ，</t年代p一个n></text> <text transform="matrix(1,0,0,-1,95.41,-23.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,105.94,-20.31)"> <tspan style="font-size: 12.50px; " x="27.75" y="-14.79"> ⎧</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.75" y="-7.52"> ⎪</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.75" y="3.2"> ⎨</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.75" y="13.91"> ⎪</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.75" y="21.120001"> ⎩</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="76.959999" y="2.24"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="109.29" y="-15.56"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.703768" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.75" y="-7.4899998"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.777164" y="-7.4899998"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.117386" y="-7.4899998"> c</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.66872" y="-7.4899998"> o</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="67.920219" y="-7.4899998"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="88.260002" y="-18.07"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="94.511497" y="-18.07"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="102.10082" y="-18.07"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="115.15" y="-18.07"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="121.8266" y="-18.07"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="133.17932" y="-18.07"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,243.03,-5.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,247.91,-4.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m 194.2,-9.69 59.56,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,215.03,-21.57)"> <tspan style="font-size: 12.50px; " x="39.93" y="0.98000002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> δ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.529999" y="-8.75"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.906769" y="-8.75"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="81.947159" y="-8.75"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,300.9,-15.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,141.69,-39.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="137.96001" y="0"> o</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="144.11148" y="0"> t</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="147.67484" y="0"> h</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="153.92633" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="159.47766" y="0"> r</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="163.87872" y="0"> w</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="172.90588" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="176.38171" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="181.24539" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="186.79672" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="326.17999" y="-50.310001"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="330.34351" y="-50.310001"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="336.595" y="-50.310001"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="342.8465" y="-50.310001"> ）</t年代p一个n></text> </g> </g> </svg></span>在哪里<年代vg height="12.8875" id="M331" style="vertical-align:-1.76814pt;width:72.775002px;" version="1.1" viewbox="0 0 72.775002 12.8875" width="72.775002" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="8.5645552" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.604944" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.856443" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.070194" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.321693" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.522942" y="0"> .．.</t年代p一个n></text> </g> </g> </svg>和<年代vg height="14.725" id="M332" style="vertical-align:-3.25793pt;width:77.237503px;" version="1.1" viewbox="0 0 77.237503 14.725" width="77.237503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.725)"> <g transform="translate(72,-60.22)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> δ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.367147" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.407536" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-36.62,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-30.39,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-15.13,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> </g> </g> </svg>．最后，下面的函数被认为是依赖的<年代vg height="9.125" id="M333" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>只有:<年代p一个nclass="equation" id="eq8"> <svg height="48.1875" id="M334" 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,-1,145.13,49.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,152.06,46.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,158.49,49.61)"> <tspan style="font-size: 12.50px; " x="27.75" y="9.7399998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0769377" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.703768" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.200001" y="-10.11"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.954498" y="-10.11"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="67.343773" y="-10.11"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="79.371658" y="-10.11"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,244.63,56.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,199.69,39.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.754499" y="0"> o</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.91848" y="0"> t</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.481834" y="0"> h</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.733334" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.284664" y="0"> r</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.685722" y="0"> w</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.712887" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.188721" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.052387" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="67.603722" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="268.17999" y="-9.8699999"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="272.34351" y="-9.8699999"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="278.595" y="-9.8699999"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="284.8465" y="-9.8699999"> ）</t年代p一个n></text> </g> </g> </svg></span>在哪里<年代vg height="14.3625" id="M335" style="vertical-align:-3.2316pt;width:14px;" version="1.1" viewbox="0 0 14 14.3625" width="14" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3625)"> <g transform="translate(72,-60.51)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.2,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>，<年代vg height="12.8875" id="M336" style="vertical-align:-1.76814pt;width:76.712502px;" version="1.1" viewbox="0 0 76.712502 12.8875" width="76.712502" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="8.9646511" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.005039" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.25654" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.470291" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.04879" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.262539" y="0"> </t年代p一个n></text> </g> </g> </svg>，由(<一个href="#EEq35">40</一个>）．这些函数用于构造近似分段常数控制[<一个href="#B35">35</一个>- - - - - -<一个href="#B37">37</一个>］．由以上定义<年代vg height="14.75" id="M337" style="vertical-align:-3.2316pt;width:14.225px;" version="1.1" viewbox="0 0 14.225 14.75" width="14.225" 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,-71.95,63.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.02,60.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,我们认为<年代vg height="14.9375" id="M338" style="vertical-align:-4.77652pt;width:13.025px;" version="1.1" viewbox="0 0 13.025 14.9375" width="13.025" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.9375)"> <g transform="translate(72,-60.05)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>作为约束条件中的未知变量(<一个href="#EEq37">44</一个>）可以写成<年代p一个nclass="equation" id="eq9"> <svg height="139.4375" id="M339" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 139.4375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,139.4375)"> <g transform="translate(72,39.55)"> <text transform="matrix(1,0,0,-1,167.35,49.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,183.5,65.18)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℓ</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="15.29"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="15.29"> ＝</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="15.29"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,197.77,56.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,204.83,53.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,212.73,56.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.530001" y="-7.25"> δ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.557165" y="-7.25"> </t年代p一个n></text> <g> <path d="m 225.96,59.4 28.5,0" 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,-1,225.96,47.52)"> <tspan style="font-size: 12.50px; " x="-21.469999" y="17.84"> ⋮</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-77.169998" y="52.790001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.902616" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.242838" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,164.94,10.19)"> <tspan style="font-size: 8.75px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.6032162" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="14.598336" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="18.974337" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="21.888752" y="0"> ℓ</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="15.29"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="15.29"> ＝</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="15.29"> （</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="12.314064" y="15.29"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="18.002865" y="15.29"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="23.997984" y="15.29"> 2</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="28.373983" y="15.29"> ）</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="31.288401" y="15.29"> ℓ</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="36.355808" y="15.29"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="42.350929" y="15.29"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,212.17,1.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,219.22,-1.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,227.12,1.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.530001" y="-7.25"> δ.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.557165" y="-7.25"> </t年代p一个n></text> <g> <path d="m 240.35,4.4 28.5,0" 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,-1,240.35,-7.47)"> <tspan style="font-size: 12.50px; " x="-93.589996" y="30.57"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.902616" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.242838" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,162.92,-22.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.6887999" y="0"> ℓ</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="15.28"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="15.28"> ＝</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="15.28"> （</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="12.314064" y="15.28"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="18.002865" y="15.28"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="23.997984" y="15.28"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="28.373983" y="15.28"> ）</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="31.288401" y="15.28"> ℓ</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="36.355808" y="15.28"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="42.350929" y="15.28"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,210.14,-31.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,217.2,-34.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,225.1,-31.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,241.05,-34.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,250.23,-31.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,265.49,-34.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,268.95,-31.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="198.92" y="-44.59"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="203.0835" y="-44.59"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="209.33499" y="-44.59"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="215.5865" y="-44.59"> ）</t年代p一个n></text> </g> </g> </svg></span>在哪里<年代vg height="11.075" id="M340" style="vertical-align:-0.17555pt;width:57.462502px;" version="1.1" viewbox="0 0 57.462502 11.075" width="57.462502" 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,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℓ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.702568" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.742956" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.383011" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.858845" y="0"> </t年代p一个n></text> </g> </g> </svg>．当然，我们只需要构造控制函数<年代vg height="13.45" id="M341" style="vertical-align:-2.21957pt;width:22.4125px;" version="1.1" viewbox="0 0 22.4125 13.45" width="22.4125" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="5.9264221" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.089921" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.665779" y="0"> ）</t年代p一个n></text> </g> </g> </svg>,因为<年代vg height="13.45" id="M342" style="vertical-align:-2.21957pt;width:23.6px;" version="1.1" viewbox="0 0 23.6 13.45" width="23.6" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="6.8766499" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.616007" y="0"> ）</t年代p一个n></text> </g> </g> </svg>可以通过求解ode (<一个href="#EEq8">8</一个>）．用单纯形法求出非零最优解<年代vg height="18.9625" id="M343" style="vertical-align:-5.96513pt;width:90.337502px;" version="1.1" viewbox="0 0 90.337502 18.9625" width="90.337502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.9625)"> <g transform="translate(72,-56.83)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.9,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="8.6899996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.18,56.95)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-58.05,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-45.79,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="8.6899996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-43.07,56.95)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-38.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.79225" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.006001" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-6.89,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="8.6899996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-4.17,56.95)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>，<年代vg height="13.775" id="M344" style="vertical-align:-3.2316pt;width:108.6875px;" version="1.1" viewbox="0 0 108.6875 13.775" width="108.6875" 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,-71.95,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.06,61.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.71,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-43.79,61.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.44,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> ⋯</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.169498" y="0"> <</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.197384" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,9.66,61.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>LP问题(<一个href="#EEq36">41</一个>）- (<一个href="#EEq37">44</一个>）可以在哪里找到<年代vg height="10.7375" id="M345" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" 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p一个n></text> </g> </g> </svg>不能超过约束的数量，即<年代vg height="14.475" id="M346" style="vertical-align:-3.13504pt;width:123.35px;" version="1.1" viewbox="0 0 123.35 14.475" width="123.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-67.78,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.239957" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.280346" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-32.93,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-25.28,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-1.37,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,6.28,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> </g> </g> </svg>．设置<年代vg height="18.987499" id="M347" style="vertical-align:-5.98395pt;width:47.862499px;" version="1.1" viewbox="0 0 47.862499 18.987499" width="47.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.9875)"> <g transform="translate(72,-56.81)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.9,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="8.6899996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.18,56.95)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.58,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-38.63,59.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> </g> </g> </svg>，一个分段控制函数<年代vg height="13.45" id="M348" style="vertical-align:-2.21957pt;width:22.4125px;" version="1.1" viewbox="0 0 22.4125 13.45" width="22.4125" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="5.9264221" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.089921" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.665779" y="0"> ）</t年代p一个n></text> </g> </g> </svg>基于这些非零系数构造最优控制逼近方法如下[<一个href="#B35">35</一个>，<一个href="#B36">36</一个>］：<年代p一个nclass="equation" id="eq10"> <svg height="69.787498" id="M349" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 69.787498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,69.7875)"> <g transform="translate(72,-16.17)"> <text transform="matrix(1,0,0,-1,75.22,40.96)"> <tspan style="font-size: 12.50px; " x="35.759998" y="-15.93"> ⎧</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.759998" y="-7.77"> ⎪</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.759998" y="3.1900001"> ⎨</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.759998" y="14.14"> ⎪</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.759998" y="22.25"> ⎩</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.759998" y="-6.6599998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0019197" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.165419" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.078857" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.718191" y="0"> ＝</t年代p一个n></text> <text transform="matrix(1,0,0,-1,124.91,44.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,127.63,42.3)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,143.94,47.62)"> <tspan style="font-size: 12.50px; " x="21.51" y="9.7399998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.37677" y="0"> ∈</t年代p一个n></text> <text transform="matrix(1,0,0,-1,174.9,63.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,173.71,41.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,174.08,33.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.0499039" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="11.045024" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,189.86,47.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,196.92,52.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="8.6899996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,199.64,41.74)"> <tspan style="font-size: 6.25px; " x="0" y="0"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,204.24,47.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n></text> <text transform="matrix(1,0,0,-1,215.56,63.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,209.45,41.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,209.82,33.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.0499039" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="11.045024" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,225.6,47.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,232.66,52.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="8.6899996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,235.38,41.74)"> <tspan style="font-size: 6.25px; " x="0" y="0"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,239.98,37.88)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-121" y="17.16"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-96.044014" y="17.16"> o</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-89.880035" y="17.16"> t</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-86.316681" y="17.16"> h</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-80.065178" y="17.16"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-74.513847" y="17.16"> r</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-70.112793" y="17.16"> w</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-61.085625" y="17.16"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-57.609791" y="17.16"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-52.746124" y="17.16"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.38" y="-3.0799999"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.546139" y="-3.0799999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.885639" y="-3.0799999"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.926029" y="-3.0799999"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.177528" y="-3.0799999"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.391281" y="-3.0799999"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.642776" y="-3.0799999"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.844025" y="-3.0799999"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="86.435028" y="-3.0799999"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="91.648781" y="-3.0799999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="98.425407" y="-3.0799999"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="227.89" y="-3.0799999"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="232.0535" y="-3.0799999"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="238.30499" y="-3.0799999"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="244.5565" y="-3.0799999"> ）</t年代p一个n></text> </g> </g> </svg></span>在哪里<年代vg height="15.125" id="M350" style="vertical-align:-6.50204pt;width:15.6875px;" version="1.1" viewbox="0 0 15.6875 15.125" width="15.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.125)"> <g transform="translate(72,-59.9)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.02,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.3,61.12)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是第六个组成部分吗<年代vg height="15.1" id="M351" style="vertical-align:-6.50204pt;width:16.0375px;" version="1.1" viewbox="0 0 16.0375 15.1" width="16.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1)"> <g transform="translate(72,-59.92)"> <text transform="matrix(1,0,0,-1,-71.95,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.75,63.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.03,61.13)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>．</p><p>要开始提出的方法，需要有<年代vg height="13" id="M352" style="vertical-align:-3.22282pt;width:9.3374996px;" version="1.1" viewbox="0 0 9.3374996 13" width="9.3374996" 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,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>．本文提出了一种求解期望下界的二分法<年代vg height="13" id="M353" style="vertical-align:-3.22282pt;width:9.3374996px;" version="1.1" viewbox="0 0 9.3374996 13" width="9.3374996" 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,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>的最佳时间<年代vg height="18.762501" id="M354" style="vertical-align:-5.79958pt;width:13.025px;" version="1.1" viewbox="0 0 13.025 18.762501" width="13.025" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.7625)"> <g transform="translate(72,-56.99)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.1499996"> </t年代p一个n></text> </g> </g> </svg>．该算法结构简单，从给定的上界开始<年代vg height="12.9875" id="M355" style="vertical-align:-3.21404pt;width:10.825px;" version="1.1" viewbox="0 0 10.825 12.9875" width="10.825" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.9875)"> <g transform="translate(72,-61.61)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>，这里假设下界从<年代vg height="14.7125" id="M356" style="vertical-align:-3.22282pt;width:36.537498px;" version="1.1" viewbox="0 0 36.537498 14.7125" width="36.537498" 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p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61.11,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n></text> </g> </g> </svg>．假设<年代vg height="18.762501" id="M357" style="vertical-align:-5.79958pt;width:32.650002px;" version="1.1" viewbox="0 0 32.650002 18.762501" width="32.650002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.7625)"> <g transform="translate(72,-56.99)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.1499996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61.63,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-53.55,59.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-50.1,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代p一个n></text> </g> </g> </svg>表示LP问题的解(<一个href="#EEq36">41</一个>）- (<一个href="#EEq37">44</一个>）对应于给定的下界<年代vg height="13" id="M358" style="vertical-align:-3.22282pt;width:9.3374996px;" version="1.1" viewbox="0 0 9.3374996 13" width="9.3374996" 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,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>，平分法概述如下。</p><p><年代p一个nclass="statement" id="algg1"><span class="statement-title"><i class="statement-title">算法1(估计下界<年代vg height="13" id="M359" style="vertical-align:-3.22282pt;width:9.3374996px;" version="1.1" viewbox="0 0 9.3374996 13" width="9.3374996" 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,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>)．</我></年代p一个n>首先,让<年代vg height="14.4875" id="M360" style="vertical-align:-3.22282pt;width:64.349998px;" version="1.1" viewbox="0 0 64.349998 14.4875" width="64.349998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4875)"> <g transform="translate(72,-60.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8648672" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.905256" y="0"> ［</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.068754" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-41.96,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-38.5,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-29.38,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-24.73,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ］</t年代p一个n></text> </g> </g> </svg>，在哪里<年代vg height="14.7125" id="M361" style="vertical-align:-3.22282pt;width:36.537498px;" version="1.1" viewbox="0 0 36.537498 14.7125" width="36.537498" 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p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61.11,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n></text> </g> </g> </svg>和<年代vg height="12.9875" id="M362" style="vertical-align:-3.21404pt;width:10.825px;" version="1.1" viewbox="0 0 10.825 12.9875" width="10.825" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.9875)"> <g transform="translate(72,-61.61)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>的上界是<年代vg height="18.762501" id="M363" style="vertical-align:-5.79958pt;width:13.025px;" version="1.1" viewbox="0 0 13.025 18.762501" width="13.025" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.7625)"> <g transform="translate(72,-56.99)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.1499996"> </t年代p一个n></text> </g> </g> </svg>．<br><span class="statement" id="step1"><span class="statement-title"><i class="statement-title">步骤1。</我></年代p一个n>让<年代vg height="14.7125" id="M364" style="vertical-align:-3.22282pt;width:87.487503px;" version="1.1" viewbox="0 0 87.487503 14.7125" width="87.487503" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="9.7398367" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.780226" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.943726" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-42.09,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.85,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-20.59,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-15.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> 2</t年代p一个n></text> </g> </g> </svg>并解决相应的LP问题找到<年代vg height="18.762501" id="M365" style="vertical-align:-5.79958pt;width:31.275px;" version="1.1" viewbox="0 0 31.275 18.762501" width="31.275" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.7625)"> <g transform="translate(72,-56.99)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.1499996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61.63,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.440005" y="0"> ）</t年代p一个n></text> </g> </g> </svg>．如果对相应的LP问题没有找到可行的解决方案或<年代vg height="18.762501" id="M366" style="vertical-align:-5.79958pt;width:58.512501px;" version="1.1" viewbox="0 0 58.512501 18.762501" width="58.512501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.7625)"> <g transform="translate(72,-56.99)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.1499996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61.63,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.440005" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.066835" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.107224" y="0"> </t年代p一个n></text> </g> </g> </svg>,设置<年代vg height="12.9875" id="M367" style="vertical-align:-3.21404pt;width:38.0625px;" version="1.1" viewbox="0 0 38.0625 12.9875" width="38.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.9875)"> <g transform="translate(72,-61.61)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.92,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> </t年代p一个n></text> </g> </g> </svg>；其他设置<年代vg height="13" id="M368" style="vertical-align:-3.22282pt;width:36.575001px;" version="1.1" viewbox="0 0 36.575001 13" width="36.575001" 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,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61.11,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> </g> </g> </svg>．</年代p一个n><br><span class="statement" id="step2"><span class="statement-title"><i class="statement-title">步骤2。</我></年代p一个n>如果是间隔的长度<年代vg height="14.4875" id="M369" style="vertical-align:-3.22282pt;width:64.349998px;" version="1.1" viewbox="0 0 64.349998 14.4875" width="64.349998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4875)"> <g transform="translate(72,-60.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8648672" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.905256" y="0"> ［</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.068754" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-41.96,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-38.5,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-29.38,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-24.73,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ］</t年代p一个n></text> </g> </g> </svg>够小，那就选<年代vg height="13" id="M370" style="vertical-align:-3.22282pt;width:9.3374996px;" version="1.1" viewbox="0 0 9.3374996 13" width="9.3374996" 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,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>作为下界的一个很好的估计<年代vg height="18.762501" id="M371" style="vertical-align:-5.79958pt;width:13.025px;" version="1.1" viewbox="0 0 13.025 18.762501" width="13.025" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.7625)"> <g transform="translate(72,-56.99)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.1499996"> </t年代p一个n></text> </g> </g> </svg>否则，执行步骤步骤<一个href="#step1">1</一个>．</年代p一个n></年代p一个n></p> <h4 id="numerical-results">5.数值结果</h4><p>在这个实现中，我们设置<年代vg height="14.6" id="M372" style="vertical-align:-3.13504pt;width:56.9375px;" version="1.1" viewbox="0 0 56.9375 14.6" width="56.9375" 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p一个n></text> <text transform="matrix(1,0,0,-1,-59.38,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-51.04,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代p一个n></text> </g> </g> </svg>并选择功能<年代vg height="11.05" id="M373" style="vertical-align:-3.2316pt;width:14.5625px;" version="1.1" viewbox="0 0 14.5625 11.05" width="14.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.62,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>，<年代vg height="14.6" id="M374" style="vertical-align:-3.13504pt;width:99.574997px;" version="1.1" viewbox="0 0 99.574997 14.6" width="99.574997" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="7.3517642" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.392153" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.643654" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.857405" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.108906" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.31015" y="0"> .．.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.901154" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.114902" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,2.73,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>,从<年代vg height="15.325" id="M375" style="vertical-align:-2.21957pt;width:37.487499px;" version="1.1" viewbox="0 0 37.487499 15.325" width="37.487499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.325)"> <g transform="translate(72,-59.74)"> <text transform="matrix(1,0,0,-1,-71.95,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.56,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.09,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.865587" y="0"> ）</t年代p一个n></text> </g> </g> </svg>如下:<年代p一个nclass="equation" id="eq11"> <svg height="19.200001" id="M376" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.200001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.2)"> <g transform="translate(72,-56.64)"> <text transform="matrix(1,0,0,-1,105.03,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,111.91,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,116.78,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,128.87,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,133.74,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,145.83,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,150.7,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,162.79,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</t年代p一个n></text> <text transform="matrix(1,0,0,-1,167.66,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,179.75,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.21"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,184.62,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,196.71,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.3400002"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,201.59,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,213.67,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,218.55,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,225.42,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,230.3,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,242.38,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,247.26,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,254.13,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,259.01,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,271.09,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</t年代p一个n></text> <text transform="matrix(1,0,0,-1,275.97,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,282.85,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,287.72,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.114687" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,303.72,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,308.59,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="159.28" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="163.4435" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="169.69499" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="175.9465" y="0"> ）</t年代p一个n></text> </g> </g> </svg></span>此外,我们组<年代vg height="10.9125" id="M377" style="vertical-align:-0.17555pt;width:45.299999px;" version="1.1" viewbox="0 0 45.299999 10.9125" width="45.299999" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="11.590281" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.630671" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.88217" y="0"> 3.</t年代p一个n></text> </g> </g> </svg>和<年代vg height="14.725" id="M378" style="vertical-align:-3.13504pt;width:49.125px;" version="1.1" viewbox="0 0 49.125 14.725" width="49.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.725)"> <g transform="translate(72,-60.22)"> <text transform="matrix(1,0,0,-1,-71.95,63.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.38,60.27)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-51.04,63.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 6</t年代p一个n></text> </g> </g> </svg>．设置<年代vg height="10.9125" id="M379" style="vertical-align:-0.17555pt;width:34.737499px;" version="1.1" viewbox="0 0 34.737499 10.9125" width="34.737499" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3897533" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.430141" y="0"> 0</t年代p一个n></text> </g> </g> </svg>在（<一个href="#EEq8">8</一个>），我们发现在<年代vg height="14.875" id="M380" style="vertical-align:-3.25793pt;width:61.75px;" version="1.1" viewbox="0 0 61.75 14.875" width="61.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.875)"> <g transform="translate(72,-60.1)"> <text transform="matrix(1,0,0,-1,-71.95,63.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,60.27)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.69,63.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.530886" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.782387" y="0"> 2</t年代p一个n></text> </g> </g> </svg>，<年代vg height="14.9375" id="M381" style="vertical-align:-3.25793pt;width:177.125px;" version="1.1" viewbox="0 0 177.125 14.9375" width="177.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.9375)"> <g transform="translate(72,-60.05)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.8766499" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57,60.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-52.12,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6268301" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.667219" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.830717" y="0"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.082218" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.20797" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.459469" y="0"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.710968" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.924721" y="0"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.17622" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="63.427719" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="68.628967" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="74.88047" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="78.006218" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="84.257713" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="90.509216" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="95.722969" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="101.97446" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="105.10022" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="111.35172" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="117.60322" y="0"> ）</t年代p一个n></text> </g> </g> </svg>．模型参数的选择如下[<一个href="#B17">17</一个>］：<年代p一个nclass="equation" id="eq12"> <svg height="72.974998" id="M382" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 72.974998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,72.975)"> <g transform="translate(72,-13.62)"> <text transform="matrix(1,0,0,-1,68.5,62.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m 74.5,65.95 7.01,0" 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,-1,74.5,58.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,84.99,62.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.405136" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.656635" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.835278" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.275284" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.315674" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.567169" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="74.692924" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="80.94442" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="87.195923" y="0"> ，</t年代p一个n></text> <g> <path d="m 187.37,70.55 6.4,0" 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,-1,187.37,62.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,193.77,59.18)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,202.02,62.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.405136" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.656635" y="0"> ，</t年代p一个n></text> <g> <path d="m 244.86,70.71 5.81,0" 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,-1,244.86,62.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,250.67,59.18)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,258.92,62.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.458027" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,298.79,59.18)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,307.04,62.31)"> <tspan style="font-size: 12.50px; " x="-236.19" y="22.450001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.405136" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.656635" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.908134" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.159637" y="0"> ，</t年代p一个n></text> <text transform="matrix(1,0,0,-1,76.04,36.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,84.29,39.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.530886" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.70953" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.72443" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.76482" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="68.016319" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.142067" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="77.39357" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="83.645073" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="98.823715" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="108.65107" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="120.67896" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="126.93046" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="130.05621" y="0"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="136.30771" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="151.48634" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="161.01364" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="173.04152" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="179.29301" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="182.41878" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="188.67027" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="194.92177" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="201.17326" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="216.35191" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,306.65,36.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,317.19,39.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.291889" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.417639" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.66914" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-150.06" y="22.440001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-139.54498" y="22.440001"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-127.50459" y="22.440001"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-121.25309" y="22.440001"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-118.12733" y="22.440001"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-111.87584" y="22.440001"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-96.709702" y="22.440001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-86.907349" y="22.440001"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-74.866959" y="22.440001"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-68.615456" y="22.440001"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="150.67999" y="0.18000001"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="154.84351" y="0.18000001"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="161.095" y="0.18000001"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="167.3465" y="0.18000001"> ）</t年代p一个n></text> </g> </g> </svg></span>并采用以下初始条件:<年代p一个nclass="equation" id="eq13"> <svg height="15.75" id="M383" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 15.75" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.75)"> <g transform="translate(72,-59.4)"> <text transform="matrix(1,0,0,-1,141.45,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.9521484" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.115647" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.367147" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.006479" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.034367" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.210369" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.461868" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.663116" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.914616" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="67.166115" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="73.417618" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="78.631371" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="84.882866" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="88.008614" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="94.260117" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="100.51162" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="106.76311" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="113.01462" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="118.22837" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="124.47987" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="130.71887" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="326.42001" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="330.5835" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="336.83499" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="343.08649" y="0"> ）</t年代p一个n></text> </g> </g> </svg></span>除此之外,<年代vg height="10.8125" id="M384" 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p一个n></text> </g> </g> </svg>被设置为<年代vg height="10.9375" id="M385" style="vertical-align:-0.20064pt;width:43.599998px;" version="1.1" viewbox="0 0 43.599998 10.9375" width="43.599998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9375)"> <g transform="translate(72,-63.25)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.227454" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.267843" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.519342" y="0"> 0</t年代p一个n></text> </g> </g> </svg>，治疗时间设置为<年代vg height="13.7375" id="M386" style="vertical-align:-2.29482pt;width:50.775002px;" version="1.1" viewbox="0 0 50.775002 13.7375" width="50.775002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.7375)"> <g transform="translate(72,-61.01)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.7148314" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.75522" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.00672" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.258221" y="0"> 0</t年代p一个n></text> </g> </g> </svg>(天)。利用动态控制系统的可控性，可以假设<年代vg height="14.6" id="M387" style="vertical-align:-3.13504pt;width:77.175003px;" version="1.1" viewbox="0 0 77.175003 14.6" width="77.175003" 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p一个n></text> <text transform="matrix(1,0,0,-1,-62.99,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.64,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> ［</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.191385" y="0"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.442884" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.656635" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.908134" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.159637" y="0"> ］</t年代p一个n></text> </g> </g> </svg>，<年代vg height="14.7875" id="M388" style="vertical-align:-3.13504pt;width:77.175003px;" version="1.1" viewbox="0 0 77.175003 14.7875" width="77.175003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7875)"> <g transform="translate(72,-60.17)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.99,60.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.64,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> ［</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.191385" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.442884" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.656635" y="0"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.908134" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.159637" y="0"> ］</t年代p一个n></text> </g> </g> </svg>，<年代vg height="14.9375" id="M389" style="vertical-align:-3.25793pt;width:69.362503px;" version="1.1" viewbox="0 0 69.362503 14.9375" width="69.362503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.9375)"> <g transform="translate(72,-60.05)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.99,60.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.64,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> ［</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.191385" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.442884" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.656635" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.908134" y="0"> ］</t年代p一个n></text> </g> </g> </svg>，<年代vg height="14.6" id="M390" style="vertical-align:-3.13504pt;width:81.087502px;" version="1.1" viewbox="0 0 81.087502 14.6" width="81.087502" 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p一个n></text> <text transform="matrix(1,0,0,-1,-62.99,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.64,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> ［</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.191385" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.442884" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.656635" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.908134" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.033886" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.285385" y="0"> ］</t年代p一个n></text> </g> </g> </svg>,<年代vg height="13.125" id="M391" style="vertical-align:-1.95624pt;width:63.075001px;" version="1.1" viewbox="0 0 63.075001 13.125" width="63.075001" 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p一个n><t年代p一个n style="font-size: 12.50px; " x="12.277946" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.318335" y="0"> ［</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.481834" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.733334" y="0"> ，</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.947086" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.198586" y="0"> ］</t年代p一个n></text> </g> </g> </svg>．此外，在构造集合的分区数<年代vg height="14.6" id="M392" style="vertical-align:-3.13504pt;width:22.674999px;" version="1.1" viewbox="0 0 22.674999 14.6" width="22.674999" 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"> ω.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.65,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是<年代vg height="14.6" id="M393" style="vertical-align:-3.13504pt;width:41.1875px;" version="1.1" viewbox="0 0 41.1875 14.6" width="41.1875" 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p一个n></text> <text transform="matrix(1,0,0,-1,-65.74,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.39,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 4</t年代p一个n></text> </g> </g> </svg>，<年代vg height="14.6" id="M394" style="vertical-align:-3.13504pt;width:49px;" version="1.1" viewbox="0 0 49 14.6" width="49" 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p一个n></text> <text transform="matrix(1,0,0,-1,-65.74,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.39,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代p一个n></text> </g> </g> </svg>，<年代vg height="14.75" id="M395" style="vertical-align:-3.25793pt;width:41.1875px;" version="1.1" viewbox="0 0 41.1875 14.75" width="41.1875" 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"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.74,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3.</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.39,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 4</t年代p一个n></text> </g> </g> </svg>，<年代vg height="14.6" id="M396" style="vertical-align:-3.13504pt;width:41.1875px;" version="1.1" viewbox="0 0 41.1875 14.6" width="41.1875" 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p一个n></text> <text transform="matrix(1,0,0,-1,-65.74,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.39,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 4</t年代p一个n></text> </g> </g> </svg>,<年代vg height="14.6" id="M397" style="vertical-align:-3.13504pt;width:44.512501px;" version="1.1" viewbox="0 0 44.512501 14.6" width="44.512501" 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p一个n></text> <text transform="matrix(1,0,0,-1,-63.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.73,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> 4</t年代p一个n></text> </g> </g> </svg>．最优时间的上界<年代vg height="18.762501" id="M398" style="vertical-align:-5.79958pt;width:13.025px;" version="1.1" viewbox="0 0 13.025 18.762501" width="13.025" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.7625)"> <g transform="translate(72,-56.99)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.1499996"> </t年代p一个n></text> </g> </g> </svg>被设置为<年代vg height="14.8875" id="M399" style="vertical-align:-3.21404pt;width:81.012497px;" version="1.1" viewbox="0 0 81.012497 14.8875" width="81.012497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8875)"> <g transform="translate(72,-60.09)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,60.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.92,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.291889" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.543388" y="0"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.794889" y="0"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.046391" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.172138" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.423637" y="0"> 5</t年代p一个n></text> </g> </g> </svg>．算法实现的结果<一个href="#algg1">1</一个>汇总于表<一个href="//www.newsama.com/journals/cmmm/2011/674318/tab1/" target="_blank">1</一个>．设置<年代vg height="14.8375" id="M400" style="vertical-align:-3.22282pt;width:59.987499px;" version="1.1" viewbox="0 0 59.987499 14.8375" width="59.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8375)"> <g transform="translate(72,-60.13)"> <text transform="matrix(1,0,0,-1,-71.95,63.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,60.27)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61.11,63.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.530886" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.782387" y="0"> 2</t年代p一个n></text> </g> </g> </svg>，我们有一个有16000个未知数和47个约束条件的LP问题，它由<我>linprog</我>在MATLAB中优化工具箱的代码。一台CPU为2.20 GHz、RAM为0.99 GB的笔记本电脑所需的总CPU时间为17.23分钟。已找到次最佳时间<年代vg height="18.762501" id="M401" style="vertical-align:-5.79958pt;width:75.387497px;" version="1.1" viewbox="0 0 75.387497 18.762501" width="75.387497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.7625)"> <g transform="translate(72,-56.99)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.1499996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-58.16,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.530886" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.782387" y="0"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.033886" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.159637" y="0"> 2</t年代p一个n></text> </g> </g> </svg>．所得到的次优控制和系统对所得到的控制函数的响应如图所示<一个href="//www.newsama.com/journals/cmmm/2011/674318/fig1/" target="_blank">1</一个>和<一个href="//www.newsama.com/journals/cmmm/2011/674318/fig2/" target="_blank">2</一个>，分别。此外,我们发现<年代vg height="18.762501" id="M402" style="vertical-align:-5.79958pt;width:95.087502px;" version="1.1" viewbox="0 0 95.087502 18.762501" width="95.087502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.7625)"> <g transform="translate(72,-56.99)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.4267821" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.590281" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.45,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.1499996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-50.04,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ）</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6268301" y="0"> ＝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.667219" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.918718" y="0"> ．</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.04447" y="0"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.295967" y="0"> 3.</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.54747" y="0"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.798969" y="0"> 0</t年代p一个n></text> </g> </g> </svg>，接近准确值，即5 (<年代vg height="18.262501" id="M403" style="vertical-align:-4.56824pt;width:46.1875px;" version="1.1" viewbox="0 0 46.1875 18.262501" width="46.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.2625)"> <g transform="translate(72,-57.39)"> <text transform="matrix(1,0,0,-1,-71.95,61.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.389513" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.266884" y="0"> 4</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-47.43,67.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> +</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-47.43,57.53)"> <tspan style="font-size: 8.75px; " x="0" y="0"> c</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.8858881" y="0"> r</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.95784" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3908958" y="0"> t</t年代p一个n></text> </g> </g> </svg>%)。注意，成熟CD4+ t细胞的正常水平大约是1000个/<我>μ.。</我>lCD4+t细胞、ctl和病毒在疾病不同阶段的关系如图所示<一个href="//www.newsama.com/journals/cmmm/2011/674318/fig3/" target="_blank">3.</一个>作为相空间图。</p><div class="floats-partial-section partial-other-wrapper" data-section="tab1"> <div class="floats-partial-content fig-content-tab1"> <table class="table-group" id="tab1"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="4"> <hr></td> </tr> <tr class="thead"> <td align="left"><span style="width: 9.3374996px;"> <svg height="13" id="M404" style="vertical-align:-3.22282pt" version="1.1" viewbox="0 0 9.3374996 13" width="9.3374996" 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,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg></span></td> <td align="center"><span style="width: 10.825px;"> <svg height="12.9875" id="M405" style="vertical-align:-3.21404pt" version="1.1" viewbox="0 0 10.825 12.9875" width="10.825" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.9875)"> <g transform="translate(72,-61.61)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg></span></td> <td align="center"><span style="width: 7.9749999px;"> <svg height="7.1750002" id="M406" style="vertical-align:-0.1254pt" 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p一个n></text> </g> </g> </svg></span></td> <td align="center"><span style="width: 31.275px;"> <svg height="18.762501" id="M407" style="vertical-align:-5.79958pt" version="1.1" viewbox="0 0 31.275 18.762501" width="31.275" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.7625)"> <g transform="translate(72,-56.99)"> <text transform="matrix(1,0,0,-1,-71.95,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-68.04,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.1499996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61.63,62.83)"> <tspan style="font-size: 12.50px; " x="0" y="0"> （</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.440005" y="0"> ）</t年代p一个n></text> </g> </g> </svg></span></td> </tr> <tr> <td class="thead-hr" colspan="4"> <hr></td> </tr> <tr> <td align="left">0</td> <td align="center">5297.45</td> <td align="center">2648.72</td> <td align="center">3370.06</td> </tr> <tr> <td align="left">2648.72</td> <td align="center">5297.45</td> <td align="center">3973.08</td> <td align="center">不可行</td> </tr> <tr> <td align="left">2648.72</td> <td align="center">3973.08</td> <td align="center">3310.90</td> <td align="center">3595.25</td> </tr> <tr> <td align="left">3310.90</td> <td align="center">3973.08</td> <td align="center">3641.99</td> <td align="center">3709.73</td> </tr> <tr> <td align="left">3641.99</td> <td align="center">3973.08</td> <td align="center"></td> <td align="center"></td> </tr> <tr class="table-tr"> <td colspan="4"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表1</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/cmmm/2011/674318/tab1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 实施算法的结果<一个href="#algg1">1</一个>．</div> </div> </div> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig1"> <div class="floats-partial-content fig-content-fig1"> <div class="partial-carousel--single-image"> <img alt="" name="674318.fig.001" src="https://static-01.hindawi.com/articles/cmmm/volume-2011/674318/figures/674318.fig.001.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图1</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/cmmm/2011/674318/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="7.1624999" id="M408" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 7.5374999 7.1624999" width="7.5374999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg> <table> 近似次最优分段常数控制．</t一个ble> </div> </div> </div> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig2"> <div class="floats-partial-content fig-content-fig2"> <div class="partial-carousel--single-image"> <img alt="(一)＂n一个米e＝＂6743.18．fig.002a" src="https://static-01.hindawi.com/articles/cmmm/volume-2011/674318/figures/674318.fig.002a.jpg"> <br> <strong>(一)</年代tr在g> </div> <div class="partial-carousel--single-image"> <img alt="(b)＂n一个米e＝＂6743.18．fig.002b" src="https://static-01.hindawi.com/articles/cmmm/volume-2011/674318/figures/674318.fig.002b.jpg"> <br> <strong>(b)</年代tr在g> </div> <div class="partial-carousel--single-image"> <img alt="(c)＂n一个米e＝＂6743.18．fig.002c" src="https://static-01.hindawi.com/articles/cmmm/volume-2011/674318/figures/674318.fig.002c.jpg"> <br> <strong>(c)</年代tr在g> </div> <div class="partial-carousel--single-image"> <img alt="(d)＂n一个米e＝＂6743.18．fig.002d" src="https://static-01.hindawi.com/articles/cmmm/volume-2011/674318/figures/674318.fig.002d.jpg"> <br> <strong>(d)</年代tr在g> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig2"> <button class="partial-carousel-dot" aria-label="(a)"><img alt="(一)＂n一个米e＝＂6743.18．fig.002a" src="https://static-01.hindawi.com/articles/cmmm/volume-2011/674318/figures/674318.fig.002a.jpg"><br><strong>(一)</年代tr在g></button> <button class="partial-carousel-dot" aria-label="(b)"><img alt="(b)＂n一个米e＝＂6743.18．fig.002b" src="https://static-01.hindawi.com/articles/cmmm/volume-2011/674318/figures/674318.fig.002b.jpg"><br><strong>(b)</年代tr在g></button> <button class="partial-carousel-dot" aria-label="(c)"><img alt="(c)＂n一个米e＝＂6743.18．fig.002c" src="https://static-01.hindawi.com/articles/cmmm/volume-2011/674318/figures/674318.fig.002c.jpg"><br><strong>(c)</年代tr在g></button> <button class="partial-carousel-dot" aria-label="(d)"><img alt="(d)＂n一个米e＝＂6743.18．fig.002d" src="https://static-01.hindawi.com/articles/cmmm/volume-2011/674318/figures/674318.fig.002d.jpg"><br><strong>(d)</年代tr在g></button> </div> <div class="partial-carousel-next-prev fig-nav-fig2"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图2</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/cmmm/2011/674318/fig2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="15.4875" id="M409" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.75 15.4875" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.4875)"> <g transform="translate(72,-59.61)"> <g> <path d="m -71.95,70.71 9.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg> <svg height="10.325" id="M410" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.75 10.325" width="11.75" 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p一个n></text> </g> </g> </svg> <svg height="7.1750002" id="M411" style="vertical-align:-0.1254pt" 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p一个n></text> </g> </g> </svg> <svg height="10.6125" id="M412" style="vertical-align:-0.15048pt" 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p一个n></text> </g> </g> </svg> <table> 状态变量的动态行为，，和未治疗(虚线)和已治疗的感染患者(实线)的对比时间。</t一个ble> </div> </div> </div> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig3"> <div class="floats-partial-content fig-content-fig3"> <div class="partial-carousel--single-image"> <img alt="(一)＂n一个米e＝＂6743.18．fig.003a" src="https://static-01.hindawi.com/articles/cmmm/volume-2011/674318/figures/674318.fig.003a.jpg"> <br> <strong>(一)</年代tr在g> </div> <div class="partial-carousel--single-image"> <img alt="(b)＂n一个米e＝＂6743.18．fig.003b" src="https://static-01.hindawi.com/articles/cmmm/volume-2011/674318/figures/674318.fig.003b.jpg"> <br> <strong>(b)</年代tr在g> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig3"> <button class="partial-carousel-dot" aria-label="(a)"><img alt="(一)＂n一个米e＝＂6743.18．fig.003a" src="https://static-01.hindawi.com/articles/cmmm/volume-2011/674318/figures/674318.fig.003a.jpg"><br><strong>(一)</年代tr在g></button> <button class="partial-carousel-dot" aria-label="(b)"><img alt="(b)＂n一个米e＝＂6743.18．fig.003b" src="https://static-01.hindawi.com/articles/cmmm/volume-2011/674318/figures/674318.fig.003b.jpg"><br><strong>(b)</年代tr在g></button> </div> <div class="partial-carousel-next-prev fig-nav-fig3"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图3</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/cmmm/2011/674318/fig3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="10.325" id="M413" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.75 10.325" width="11.75" 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p一个n></text> </g> </g> </svg> <svg height="10.6125" id="M414" style="vertical-align:-0.15048pt" 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p一个n></text> </g> </g> </svg> <table> CD4+ t细胞的相空间图(）和ctl (）．</t一个ble> </div> </div> </div> <h4 id="conclusion">6.结论</h4><p>在本文中，我们考虑了一个动力学系统，它描述了HIV与免疫系统相互作用的各个方面，以构建一个最优控制问题，使患者的生存时间最大化。一种测量理论方法被用来解决这类问题。该方法不需要迭代，不需要任何解的初始猜想，数值结果证实了该方法的有效性。</p><p>数值结果表明，在治疗的存在下，患者的生存时间可以大大延长。从数据<一个href="//www.newsama.com/journals/cmmm/2011/674318/fig2/" target="_blank">2 (b)</一个>和<一个href="//www.newsama.com/journals/cmmm/2011/674318/fig2/" target="_blank">2 (c)</一个>，它的结论是，在存在治疗(实线)，病毒控制到非常低的水平，CD4+ t细胞维持在较高水平相对较长时间。从图<一个href="//www.newsama.com/journals/cmmm/2011/674318/fig2/" target="_blank">2 (d)</一个>，CTL的增加发生响应治疗。</p><p>数字<一个href="//www.newsama.com/journals/cmmm/2011/674318/fig3/" target="_blank">3(一个)</一个>CD4+t细胞和病毒颗粒呈负相关。此外,图<一个href="//www.newsama.com/journals/cmmm/2011/674318/fig3/" target="_blank">3 (b)</一个>显示了血液中ctl水平与HIV进展之间的明显相关性。随着病毒在最初感染时的增加，ctl增加，以减少病毒。但是这种情况在大约1000天后由于CD4+ t细胞的破坏而改变。因为这些细胞在刺激免疫反应中起着至关重要的作用，并向其他免疫细胞发出信号，通过杀死被感染的细胞来消除感染。1642天后，可以观察到免疫反应的增加，这是由于CD4+ t细胞对治疗的反应恢复。在停止治疗后，免疫反应会增加一段时间，但最终会消失。</p></div> <div 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Zarei等人。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 becpDt hrTitleRef">更多相关文章</h4><div id="biblio_widget" class="biblio__BiblioWrapper-sc-1nou1lz-1 bvnCfh"></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"> <div class="sc-cBdUnI hRnXob article_top_toolbar"> <a class="sc-htpNat bUhGXt link sc-jtRfpW dIjoCg sc-exkUMo hymroZ pdf_desktop button__group" href="//www.newsama.com/downloads/journals/cmmm/2011/674318.pdf" aria-label="" target="_blank" id="toolbar__dcNavSmall"><span><img alt="" class="sc-EHOje 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src="data:image/svg+xml;base64,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" height="24"><span class="text">下载引用</年代p一个n></年代p一个n><span class="sc-htoDjs bqeMOy sc-dqBHgY cQgXqt fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a> <a class="sc-htpNat bUhGXt link sc-jtRfpW dIjoCg sc-BngTV hmDWcT ref_desktop" href="//www.newsama.com/journals/cmmm/2011/674318.ris" aria-label="" target="" id="toolbar__dcNavSmall"><span><img alt="" class="sc-EHOje jOLhQl sc-kTUwUJ eujois" title="" role="presentation" src="data:image/svg+xml;base64,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" height="24"><span class="text">引用</年代p一个n></年代p一个n><span class="sc-htoDjs bqeMOy sc-dqBHgY cQgXqt fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a> </div> </div> <div class="journal_article__ArticleStickyBottomToolbar-sc-12fk6zy-1 isgRZA article_sticky_bottom_toolbar"> <div class="sc-cTjmhe ihmyEq article_bottom_toolbar"> <div class="sc-cugefK itFKcQ accordion" property="background-color" color="#D8D8D8" id="toolbar__dofNav"> <span><img alt="" class="sc-EHOje jOLhQl sc-bfYoXt cGuwDn" title="" role="presentation" src="data:image/svg+xml;base64,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" height="24"><span class="sc-dRFtgE jrsDZP">下载其他格式</年代p一个n><年代p一个nclass="sc-gkFcWv gWTCXQ">更多的</年代p一个n></年代p一个n> <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/cmmm/2011/674318.xml" aria-label="XML" property="background-color" color="#D8D8D8"> <div class="sc-eAKXzc WHkfb"> XML</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p一个n><年代p一个nclass="sc-gkFcWv gWTCXQ">命令</年代p一个n></年代p一个n><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p一个n>882</年代p一个n></div> <div> 下载<年代p一个n>780</年代p一个n></div> </div> <div> <div class="sc-drKuOJ kxdGAZ"> <span class="__dimensions_badge_embed__" data-doi="10.1155/2011/674318" 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/10.1155/2011/674318&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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