doc/overview1-100.html
<!DOCTYPE html>
<html class="client-nojs" lang="en" dir="ltr">
<head>
<meta charset="UTF-8"/>
<title>Display topics - enwikimath</title>
<script>document.documentElement.className=document.documentElement.className.replace(/(^|\s)client-nojs(\s|$)/,"$1client-js$2");</script>
<script>(window.RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgCanonicalNamespace":"Special","wgCanonicalSpecialPageName":"DisplayTopics","wgNamespaceNumber":-1,"wgPageName":"Special:DisplayTopics","wgTitle":"DisplayTopics","wgCurRevisionId":0,"wgRevisionId":0,"wgArticleId":0,"wgIsArticle":false,"wgIsRedirect":false,"wgAction":"view","wgUserName":"Admin","wgUserGroups":["bureaucrat","sysop","*","user","autoconfirmed"],"wgCategories":[],"wgBreakFrames":true,"wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy","wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgMonthNamesShort":["","Jan","Feb","Mar","Apr","May","Jun","Jul","Aug","Sep","Oct","Nov","Dec"],"wgRelevantPageName":"Special:DisplayTopics","wgRelevantArticleId":0,"wgRequestId":"15292ea991a33a5457cae685","wgUserId":1,"wgUserEditCount":179,"wgUserRegistration":1395732936000,"wgUserNewMsgRevisionId":null,"wgIsProbablyEditable":false,"wgRelevantPageIsProbablyEditable":false});mw.loader.state({"site.styles":"ready","noscript":"ready","user.styles":"ready","user":"ready","user.options":"loading","user.tokens":"loading","ext.math.styles":"ready","ext.smw.style":"ready","ext.smw.tooltip.styles":"ready","skins.vector.styles.responsive":"ready","mediawiki.legacy.shared":"ready","mediawiki.legacy.commonPrint":"ready","mediawiki.sectionAnchor":"ready","mediawiki.skinning.interface":"ready","skins.vector.styles":"ready"});mw.loader.implement("user.options@0bx3ja3",function($,jQuery,require,module){mw.user.options.set({"timecorrection":"Offset|0","watchlisttoken":"21e52c447a8229d2b940db0eb95cb5427c98cfd8"});});mw.loader.implement("user.tokens@06mbv65",function($,jQuery,require,module){mw.user.tokens.set({"editToken":"197163bbdc0decfb6d3f037543ebbfbe5a45ca06+\\","patrolToken":"d0e5293789d2e783909d0e51f244c1975a45ca06+\\","watchToken":"f252491d4c485a1dcb36c3bb749129455a45ca06+\\","csrfToken":"197163bbdc0decfb6d3f037543ebbfbe5a45ca06+\\"});});mw.loader.load(["ext.math.scripts","site","mediawiki.page.startup","mediawiki.user","mediawiki.hidpi","mediawiki.page.ready","jquery.tablesorter","mediawiki.searchSuggest","ext.smw.style","skins.vector.js"]);});</script>
<link rel="stylesheet" href="/w/A.load.php,,qdebug==false,,alang==en,,amodules==ext.math.styles,,P7Cmediawiki.legacy.commonPrint,,P2Cshared,,P7Cmediawiki.sectionAnchor,,P7Cmediawiki.skinning.interface,,P7Cskins.vector.styles,,P7Cskins.vector.styles.responsive,,aonly==styles,,askin==vector+load.php,,qdebug==false,,alang==en,,amodules==ext.smw.style,,P7Cext.smw.tooltip.styles,,aonly==styles,,askin==vector+load.php,,qdebug==false,,alang==en,,amodules==site.styles,,aonly==styles,,askin==vector,Mcc.W0_lySKyC-.css.pagespeed.cf.pJBQ32dAd4.css"/>
<script async="" src="https://en.formulasearchengine.com/w/load.php,qdebug=false,alang=en,amodules=startup,aonly=scripts,askin=vector.pagespeed.jm.0aTVPPbYss.js"></script>
<meta name="ResourceLoaderDynamicStyles" content=""/>
<meta name="generator" content="MediaWiki 1.30.0-alpha"/>
<meta name="robots" content="noindex,nofollow"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<link rel="shortcut icon" href="/w/images/favicon.ico"/>
<link rel="search" type="application/opensearchdescription+xml" href="/w/opensearch_desc.php" title="enwikimath (en)"/>
<link rel="EditURI" type="application/rsd+xml" href="https://en.formulasearchengine.com/w/api.php?action=rsd"/>
<link rel="alternate" type="application/atom+xml" title="enwikimath Atom feed" href="/w/index.php?title=Special:RecentChanges&feed=atom"/>
</head>
<body class="mediawiki ltr sitedir-ltr mw-hide-empty-elt ns--1 ns-special mw-special-DisplayTopics page-Special_DisplayTopics rootpage-Special_DisplayTopics skin-vector action-view"> <div id="mw-page-base" class="noprint"></div>
<div id="mw-head-base" class="noprint"></div>
<div id="content" class="mw-body" role="main">
<a id="top"></a>
<div class="mw-indicators mw-body-content">
</div>
<h1 id="firstHeading" class="firstHeading" lang="en">Display topics</h1>
<div id="bodyContent" class="mw-body-content">
<div id="contentSub"></div>
<div id="jump-to-nav" class="mw-jump">
Jump to: <a href="#mw-head">navigation</a>, <a href="#p-search">search</a>
</div>
<div id="mw-content-text"><p>⧼math-wmc-Queries⧽
</p><table class="wikitable sortable">
<tr>
<th> # </th>
<th> fId </th>
<th> #Var </th>
<th> #matches </th>
<th> query </th>
<th> reference
</th></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/1" title="Special:DisplayTopics/1">1</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/2459#math.2459.3" title="Special:PermanentLink/2459">Van_der_Waerden's_theorem-3</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle W(2,k)>2^{{k}}/k^{{\varepsilon}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">
<mrow id="p1.1.m1.1.13.1" xref="p1.1.m1.1.13.1.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">W</mi>
<mo id="p1.1.m1.1.13.1.1" xref="p1.1.m1.1.13.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.13.1.2c" xref="p1.1.m1.1.13.1.2.cmml">
<mo stretchy="false" id="p1.1.m1.1.13.1.2" xref="p1.1.m1.1.13.1.2.cmml">(</mo>
<mn id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">2</mn>
<mo id="p1.1.m1.1.13.1.2a" xref="p1.1.m1.1.13.1.2.cmml">,</mo>
<mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">k</mi>
<mo stretchy="false" id="p1.1.m1.1.13.1.2b" xref="p1.1.m1.1.13.1.2.cmml">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">></mo>
<mrow id="p1.1.m1.1.13.2" xref="p1.1.m1.1.13.2.cmml">
<msup id="p1.1.m1.1.13.2.1" xref="p1.1.m1.1.13.2.1.cmml">
<mn id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">2</mn>
<mi id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">k</mi>
</msup>
<mo id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">/</mo>
<msup id="p1.1.m1.1.13.2.2" xref="p1.1.m1.1.13.2.2.cmml">
<mi id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">k</mi>
<mi id="p1.1.m1.1.12.1" xref="p1.1.m1.1.12.1.cmml">ε</mi>
</msup>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">
<gt id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
<apply id="p1.1.m1.1.13.1.cmml" xref="p1.1.m1.1.13.1">
<times id="p1.1.m1.1.13.1.1.cmml" xref="p1.1.m1.1.13.1.1"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">W</ci>
<interval closure="open" id="p1.1.m1.1.13.1.2.cmml" xref="p1.1.m1.1.13.1.2">
<cn type="integer" id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">2</cn>
<ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">k</ci>
</interval>
</apply>
<apply id="p1.1.m1.1.13.2.cmml" xref="p1.1.m1.1.13.2">
<divide id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10"/>
<apply id="p1.1.m1.1.13.2.1.cmml" xref="p1.1.m1.1.13.2.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.13.2.1.1.cmml">superscript</csymbol>
<cn type="integer" id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">2</cn>
<ci id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">k</ci>
</apply>
<apply id="p1.1.m1.1.13.2.2.cmml" xref="p1.1.m1.1.13.2.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.13.2.2.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">k</ci>
<ci id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12.1">ε</ci>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle W(2,k)>2^{{k}}/k^{{\varepsilon}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=00cecdd7d2afa32b326e78ff2717120e&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.833ex; width: 16.833ex;" alt="W(2,k)>2^{{k}}/k^{{\varepsilon }}" data-pagespeed-url-hash="3727682694" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W(2,k)>2^{k}/k^{\varepsilon }}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>W</mi>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mo>,</mo>
<mi>k</mi>
<mo stretchy="false">)</mo>
<mo>></mo>
<msup>
<mn>2</mn>
<mrow class="MJX-TeXAtom-ORD">
<mi>k</mi>
</mrow>
</msup>
<mrow class="MJX-TeXAtom-ORD">
<mo>/</mo>
</mrow>
<msup>
<mi>k</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>ε<!-- ε --></mi>
</mrow>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle W(2,k)>2^{k}/k^{\varepsilon }}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/045045535ed2655006f05a36e645307bd33a4e92" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:16.374ex; height:3.176ex;" alt="{\displaystyle W(2,k)>2^{k}/k^{\varepsilon }}" data-pagespeed-url-hash="3022000311" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/2" title="Special:DisplayTopics/2">2</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/4050#math.4050.189" title="Special:PermanentLink/4050">Bounded_variation-189</a>
</td>
<td> 0
</td>
<td> 9
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (X,\Sigma )}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>,</mo>
<mi mathvariant="normal">Σ<!-- Σ --></mi>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle (X,\Sigma )}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=000138f6a2210ff1f9bb5eb7bc25ab6c&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; height: 2.843ex; width: 6.501ex;" alt="{\displaystyle (X,\Sigma)}" data-pagespeed-url-hash="3556134968" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (X,\Sigma )}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>,</mo>
<mi mathvariant="normal">Σ<!-- Σ --></mi>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle (X,\Sigma )}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/63c4fcf15808c3dbf52cc4b3fd473e97e231f53f" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:6.501ex; height:2.843ex;" alt="{\displaystyle (X,\Sigma )}" data-pagespeed-url-hash="1104805632" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/3" title="Special:DisplayTopics/3">3</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/4189#math.4189.50" title="Special:PermanentLink/4189">Lindemann–Weierstrass_theorem-50</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle(p-1)!^{{n}}}">
<semantics id="p1.1.m1.1a">
<msup id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">
<mrow id="p1.1.m1.1.8.2" xref="p1.1.m1.1.8.2.cmml">
<mrow id="p1.1.m1.1.8.2.1b">
<mo stretchy="false" id="p1.1.m1.1.8.2.1">(</mo>
<mrow id="XM1" xref="XM1.cmml">
<mi id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">p</mi>
<mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">-</mo>
<mn id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">1</mn>
</mrow>
<mo stretchy="false" id="p1.1.m1.1.8.2.1a">)</mo>
</mrow>
<mo lspace="0pt" rspace="3.5pt" id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">!</mo>
</mrow>
<mi id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">n</mi>
</msup>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">
<csymbol cd="ambiguous" id="p1.1.m1.1.8.1.cmml">superscript</csymbol>
<apply id="p1.1.m1.1.8.2.cmml" xref="p1.1.m1.1.8.2">
<factorial id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
<apply id="XM1.cmml" xref="XM1">
<minus id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
<ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">p</ci>
<cn type="integer" id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">1</cn>
</apply>
</apply>
<ci id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">n</ci>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle(p-1)!^{{n}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=e83857329ed8c124f7d245398c41ffc6&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.5ex; width: 9.667ex;" alt="(p-1)!^{{n}}" data-pagespeed-url-hash="3576179931" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (p-1)!^{n}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mo stretchy="false">(</mo>
<mi>p</mi>
<mo>−<!-- − --></mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<msup>
<mo>!</mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>n</mi>
</mrow>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle (p-1)!^{n}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/caaaaaab187a02e4be6f46e48ce9b80cd9e5d6d1" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:8.847ex; height:2.843ex;" alt="{\displaystyle (p-1)!^{n}}" data-pagespeed-url-hash="2835232102" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/4" title="Special:DisplayTopics/4">4</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/15332#math.15332.68" title="Special:PermanentLink/15332">Orbit_portrait-68</a>
</td>
<td> 1
</td>
<td> 2
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle f_{\qvar@construct{x0}}(z)=z^{2}+c}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">
<mrow id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml">
<msub id="p1.1.m1.1.11.1.2" xref="p1.1.m1.1.11.1.2.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">f</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">x0</mi>
</msub>
<mo id="p1.1.m1.1.11.1.1" xref="p1.1.m1.1.11.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.11.1.3b">
<mo stretchy="false" id="p1.1.m1.1.11.1.3">(</mo>
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">z</mi>
<mo stretchy="false" id="p1.1.m1.1.11.1.3a">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">=</mo>
<mrow id="p1.1.m1.1.11.2" xref="p1.1.m1.1.11.2.cmml">
<msup id="p1.1.m1.1.11.2.1" xref="p1.1.m1.1.11.2.1.cmml">
<mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">z</mi>
<mn id="p1.1.m1.1.8.1" xref="p1.1.m1.1.8.1.cmml">2</mn>
</msup>
<mo id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">+</mo>
<mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">c</mi>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">
<eq id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
<apply id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1">
<times id="p1.1.m1.1.11.1.1.cmml" xref="p1.1.m1.1.11.1.1"/>
<apply id="p1.1.m1.1.11.1.2.cmml" xref="p1.1.m1.1.11.1.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.11.1.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">f</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">x0</csymbol>
</apply>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">z</ci>
</apply>
<apply id="p1.1.m1.1.11.2.cmml" xref="p1.1.m1.1.11.2">
<plus id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9"/>
<apply id="p1.1.m1.1.11.2.1.cmml" xref="p1.1.m1.1.11.2.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.11.2.1.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">z</ci>
<cn type="integer" id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.1">2</cn>
</apply>
<ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">c</ci>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle f_{\qvar@construct{x0}}(z)=z^{2}+c}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=96dbbd2846e7c7ecb56194a3e6a53732&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.667ex; width: 15.667ex;" alt="f_{\qvar{x0}}(z)=z^{2}+c" data-pagespeed-url-hash="3236431601" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{c}(z)=z^{2}+c}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>f</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>c</mi>
</mrow>
</msub>
<mo stretchy="false">(</mo>
<mi>z</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<msup>
<mi>z</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>+</mo>
<mi>c</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle f_{c}(z)=z^{2}+c}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/191627a3eebdd6608c9b226786defc468b747502" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:14.071ex; height:3.176ex;" alt="{\displaystyle f_{c}(z)=z^{2}+c}" data-pagespeed-url-hash="1019378453" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/5" title="Special:DisplayTopics/5">5</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/391#math.391.114" title="Special:PermanentLink/391">First-order_logic-114</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\forall x\,\forall y\,P(x,y)\Leftrightarrow\forall y\,\forall x% \,P(x,y)}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.26" xref="p1.1.m1.1.26.cmml">
<mrow id="p1.1.m1.1.26.1" xref="p1.1.m1.1.26.1.cmml">
<mo id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">∀</mo>
<mrow id="p1.1.m1.1.26.1.1" xref="p1.1.m1.1.26.1.1.cmml">
<mpadded width="+1.7pt" id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">
<mi id="p1.1.m1.1.2a" xref="p1.1.m1.1.2.cmml">x</mi>
</mpadded>
<mo id="p1.1.m1.1.26.1.1.1" xref="p1.1.m1.1.26.1.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.26.1.1.2" xref="p1.1.m1.1.26.1.1.2.cmml">
<mo id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">∀</mo>
<mrow id="p1.1.m1.1.26.1.1.2.1" xref="p1.1.m1.1.26.1.1.2.1.cmml">
<mpadded width="+1.7pt" id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">
<mi id="p1.1.m1.1.5a" xref="p1.1.m1.1.5.cmml">y</mi>
</mpadded>
<mo id="p1.1.m1.1.26.1.1.2.1.1" xref="p1.1.m1.1.26.1.1.2.1.1.cmml"></mo>
<mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">P</mi>
<mo id="p1.1.m1.1.26.1.1.2.1.1a" xref="p1.1.m1.1.26.1.1.2.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.26.1.1.2.1.2c" xref="p1.1.m1.1.26.1.1.2.1.2.cmml">
<mo stretchy="false" id="p1.1.m1.1.26.1.1.2.1.2" xref="p1.1.m1.1.26.1.1.2.1.2.cmml">(</mo>
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">x</mi>
<mo id="p1.1.m1.1.26.1.1.2.1.2a" xref="p1.1.m1.1.26.1.1.2.1.2.cmml">,</mo>
<mi id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">y</mi>
<mo stretchy="false" id="p1.1.m1.1.26.1.1.2.1.2b" xref="p1.1.m1.1.26.1.1.2.1.2.cmml">)</mo>
</mrow>
</mrow>
</mrow>
</mrow>
</mrow>
<mo id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">⇔</mo>
<mrow id="p1.1.m1.1.26.2" xref="p1.1.m1.1.26.2.cmml">
<mo id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">∀</mo>
<mrow id="p1.1.m1.1.26.2.1" xref="p1.1.m1.1.26.2.1.cmml">
<mpadded width="+1.7pt" id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">
<mi id="p1.1.m1.1.15a" xref="p1.1.m1.1.15.cmml">y</mi>
</mpadded>
<mo id="p1.1.m1.1.26.2.1.1" xref="p1.1.m1.1.26.2.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.26.2.1.2" xref="p1.1.m1.1.26.2.1.2.cmml">
<mo id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">∀</mo>
<mrow id="p1.1.m1.1.26.2.1.2.1" xref="p1.1.m1.1.26.2.1.2.1.cmml">
<mpadded width="+1.7pt" id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">
<mi id="p1.1.m1.1.18a" xref="p1.1.m1.1.18.cmml">x</mi>
</mpadded>
<mo id="p1.1.m1.1.26.2.1.2.1.1" xref="p1.1.m1.1.26.2.1.2.1.1.cmml"></mo>
<mi id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">P</mi>
<mo id="p1.1.m1.1.26.2.1.2.1.1a" xref="p1.1.m1.1.26.2.1.2.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.26.2.1.2.1.2c" xref="p1.1.m1.1.26.2.1.2.1.2.cmml">
<mo stretchy="false" id="p1.1.m1.1.26.2.1.2.1.2" xref="p1.1.m1.1.26.2.1.2.1.2.cmml">(</mo>
<mi id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">x</mi>
<mo id="p1.1.m1.1.26.2.1.2.1.2a" xref="p1.1.m1.1.26.2.1.2.1.2.cmml">,</mo>
<mi id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml">y</mi>
<mo stretchy="false" id="p1.1.m1.1.26.2.1.2.1.2b" xref="p1.1.m1.1.26.2.1.2.1.2.cmml">)</mo>
</mrow>
</mrow>
</mrow>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.26.cmml" xref="p1.1.m1.1.26">
<ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">normal-⇔</ci>
<apply id="p1.1.m1.1.26.1.cmml" xref="p1.1.m1.1.26.1">
<csymbol cd="latexml" id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">for-all</csymbol>
<apply id="p1.1.m1.1.26.1.1.cmml" xref="p1.1.m1.1.26.1.1">
<times id="p1.1.m1.1.26.1.1.1.cmml" xref="p1.1.m1.1.26.1.1.1"/>
<ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">x</ci>
<apply id="p1.1.m1.1.26.1.1.2.cmml" xref="p1.1.m1.1.26.1.1.2">
<csymbol cd="latexml" id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">for-all</csymbol>
<apply id="p1.1.m1.1.26.1.1.2.1.cmml" xref="p1.1.m1.1.26.1.1.2.1">
<times id="p1.1.m1.1.26.1.1.2.1.1.cmml" xref="p1.1.m1.1.26.1.1.2.1.1"/>
<ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">y</ci>
<ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">P</ci>
<interval closure="open" id="p1.1.m1.1.26.1.1.2.1.2.cmml" xref="p1.1.m1.1.26.1.1.2.1.2">
<ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">x</ci>
<ci id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">y</ci>
</interval>
</apply>
</apply>
</apply>
</apply>
<apply id="p1.1.m1.1.26.2.cmml" xref="p1.1.m1.1.26.2">
<csymbol cd="latexml" id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">for-all</csymbol>
<apply id="p1.1.m1.1.26.2.1.cmml" xref="p1.1.m1.1.26.2.1">
<times id="p1.1.m1.1.26.2.1.1.cmml" xref="p1.1.m1.1.26.2.1.1"/>
<ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">y</ci>
<apply id="p1.1.m1.1.26.2.1.2.cmml" xref="p1.1.m1.1.26.2.1.2">
<csymbol cd="latexml" id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">for-all</csymbol>
<apply id="p1.1.m1.1.26.2.1.2.1.cmml" xref="p1.1.m1.1.26.2.1.2.1">
<times id="p1.1.m1.1.26.2.1.2.1.1.cmml" xref="p1.1.m1.1.26.2.1.2.1.1"/>
<ci id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">x</ci>
<ci id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">P</ci>
<interval closure="open" id="p1.1.m1.1.26.2.1.2.1.2.cmml" xref="p1.1.m1.1.26.2.1.2.1.2">
<ci id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22">x</ci>
<ci id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">y</ci>
</interval>
</apply>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\forall x\,\forall y\,P(x,y)\Leftrightarrow\forall y\,\forall x%
\,P(x,y)}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=0853e868640db6db59c7bf82483ae01d&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.5ex; width: 30.5ex;" alt="\forall x\,\forall y\,P(x,y)\Leftrightarrow \forall y\,\forall x\,P(x,y)" data-pagespeed-url-hash="3793527728" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \forall x\,\forall y\,P(x,y)\Leftrightarrow \forall y\,\forall x\,P(x,y)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">∀<!-- ∀ --></mi>
<mi>x</mi>
<mspace width="thinmathspace"/>
<mi mathvariant="normal">∀<!-- ∀ --></mi>
<mi>y</mi>
<mspace width="thinmathspace"/>
<mi>P</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">⇔<!-- ⇔ --></mo>
<mi mathvariant="normal">∀<!-- ∀ --></mi>
<mi>y</mi>
<mspace width="thinmathspace"/>
<mi mathvariant="normal">∀<!-- ∀ --></mi>
<mi>x</mi>
<mspace width="thinmathspace"/>
<mi>P</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \forall x\,\forall y\,P(x,y)\Leftrightarrow \forall y\,\forall x\,P(x,y)}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/b2bd10da835e07d3f2df8a14ea462278e5a23409" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:29.451ex; height:2.843ex;" alt="{\displaystyle \forall x\,\forall y\,P(x,y)\Leftrightarrow \forall y\,\forall x\,P(x,y)}" data-pagespeed-url-hash="4075345840" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/6" title="Special:DisplayTopics/6">6</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/6937#math.6937.5" title="Special:PermanentLink/6937">Clenshaw_algorithm-5</a>
</td>
<td> 0
</td>
<td> 8
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>α<!-- α --></mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \alpha (x)}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=000ad1eb8a2c2182ff048350cc9eb0e8&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; height: 2.843ex; width: 4.668ex;" alt="{\displaystyle \alpha(x)}" data-pagespeed-url-hash="2106747584" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha (x)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>α<!-- α --></mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \alpha (x)}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/43941ef40b4eb751a8daea118d0012ea998f5610" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:4.627ex; height:2.843ex;" alt="{\displaystyle \alpha (x)}" data-pagespeed-url-hash="3005649952" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/7" title="Special:DisplayTopics/7">7</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/25610#math.25610.24" title="Special:PermanentLink/25610">Isolation_lemma-24</a>
</td>
<td> 0
</td>
<td> 8
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>α<!-- α --></mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \alpha (x)}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=000ad1eb8a2c2182ff048350cc9eb0e8&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; height: 2.843ex; width: 4.668ex;" alt="{\displaystyle \alpha(x)}" data-pagespeed-url-hash="2106747584" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha (x)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>α<!-- α --></mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \alpha (x)}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/43941ef40b4eb751a8daea118d0012ea998f5610" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:4.627ex; height:2.843ex;" alt="{\displaystyle \alpha (x)}" data-pagespeed-url-hash="3005649952" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/8" title="Special:DisplayTopics/8">8</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/27419#math.27419.4" title="Special:PermanentLink/27419">Singularity_spectrum-4</a>
</td>
<td> 0
</td>
<td> 8
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>α<!-- α --></mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \alpha (x)}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=000ad1eb8a2c2182ff048350cc9eb0e8&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; height: 2.843ex; width: 4.668ex;" alt="{\displaystyle \alpha(x)}" data-pagespeed-url-hash="2106747584" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha (x)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>α<!-- α --></mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \alpha (x)}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/43941ef40b4eb751a8daea118d0012ea998f5610" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:4.627ex; height:2.843ex;" alt="{\displaystyle \alpha (x)}" data-pagespeed-url-hash="3005649952" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/9" title="Special:DisplayTopics/9">9</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/14488#math.14488.36" title="Special:PermanentLink/14488">Time-evolving_block_decimation-36</a>
</td>
<td> 7
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle|{\Psi}\rangle=\sum_{\qvar@construct{x0}}\Gamma_{{% \qvar@construct{x1}}}^{{[1]i_{1}}}\lambda_{{\alpha_{1}}}^{{[1]}}\Gamma_{{% \alpha_{\qvar@construct{x2}}\alpha_{2}}}^{{[2]i_{\qvar@construct{x3}}}}\lambda% _{\qvar@construct{x4}}^{{\qvar@construct{x5}}}|{i_{1}i_{2}}\rangle|{% \qvar@construct{x6}}\rangle}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.28" xref="p1.1.m1.1.28.cmml">
<mrow id="p1.1.m1.1.28.1b" xref="p1.1.m1.1.28.1.cmml">
<mo fence="true" stretchy="false" id="p1.1.m1.1.28.1" xref="p1.1.m1.1.28.1.cmml">|</mo>
<mi mathvariant="normal" id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">Ψ</mi>
<mo stretchy="false" id="p1.1.m1.1.28.1a" xref="p1.1.m1.1.28.1.cmml">⟩</mo>
</mrow>
<mo id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">=</mo>
<mrow id="p1.1.m1.1.28.2" xref="p1.1.m1.1.28.2.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.28.2.1" xref="p1.1.m1.1.28.2.1.cmml">
<munder id="p1.1.m1.1.28.2.1a" xref="p1.1.m1.1.28.2.1.cmml">
<mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">∑</mo>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">x0</mi>
</munder>
</mstyle>
<mrow id="p1.1.m1.1.28.2.2" xref="p1.1.m1.1.28.2.2.cmml">
<msubsup id="p1.1.m1.1.28.2.2.2" xref="p1.1.m1.1.28.2.2.2.cmml">
<mi mathvariant="normal" id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">Γ</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.8.1" xref="p1.1.m1.1.8.1.cmml">x1</mi>
<mrow id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">
<mrow id="p1.1.m1.1.9.1.7b" xref="p1.1.m1.1.9.1.7.cmml">
<mo stretchy="false" id="p1.1.m1.1.9.1.7" xref="p1.1.m1.1.9.1.7.cmml">[</mo>
<mn id="p1.1.m1.1.9.1.2" xref="p1.1.m1.1.9.1.2.cmml">1</mn>
<mo stretchy="false" id="p1.1.m1.1.9.1.7a" xref="p1.1.m1.1.9.1.7.cmml">]</mo>
</mrow>
<mo id="p1.1.m1.1.9.1.6" xref="p1.1.m1.1.9.1.6.cmml"></mo>
<msub id="p1.1.m1.1.9.1.8" xref="p1.1.m1.1.9.1.8.cmml">
<mi id="p1.1.m1.1.9.1.4" xref="p1.1.m1.1.9.1.4.cmml">i</mi>
<mn id="p1.1.m1.1.9.1.5.1" xref="p1.1.m1.1.9.1.5.1.cmml">1</mn>
</msub>
</mrow>
</msubsup>
<mo id="p1.1.m1.1.28.2.2.1" xref="p1.1.m1.1.28.2.2.1.cmml"></mo>
<msubsup id="p1.1.m1.1.28.2.2.3" xref="p1.1.m1.1.28.2.2.3.cmml">
<mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">λ</mi>
<msub id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml">
<mi id="p1.1.m1.1.11.1.1" xref="p1.1.m1.1.11.1.1.cmml">α</mi>
<mn id="p1.1.m1.1.11.1.2.1" xref="p1.1.m1.1.11.1.2.1.cmml">1</mn>
</msub>
<mrow id="p1.1.m1.1.12.1b" xref="p1.1.m1.1.12.1.cmml">
<mo stretchy="false" id="p1.1.m1.1.12.1" xref="p1.1.m1.1.12.1.cmml">[</mo>
<mn id="p1.1.m1.1.12.1.2" xref="p1.1.m1.1.12.1.2.cmml">1</mn>
<mo stretchy="false" id="p1.1.m1.1.12.1a" xref="p1.1.m1.1.12.1.cmml">]</mo>
</mrow>
</msubsup>
<mo id="p1.1.m1.1.28.2.2.1a" xref="p1.1.m1.1.28.2.2.1.cmml"></mo>
<msubsup id="p1.1.m1.1.28.2.2.4" xref="p1.1.m1.1.28.2.2.4.cmml">
<mi mathvariant="normal" id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">Γ</mi>
<mrow id="p1.1.m1.1.14.1" xref="p1.1.m1.1.14.1.cmml">
<msub id="p1.1.m1.1.14.1.6" xref="p1.1.m1.1.14.1.6.cmml">
<mi id="p1.1.m1.1.14.1.1" xref="p1.1.m1.1.14.1.1.cmml">α</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.14.1.2.1" xref="p1.1.m1.1.14.1.2.1.cmml">x2</mi>
</msub>
<mo id="p1.1.m1.1.14.1.5" xref="p1.1.m1.1.14.1.5.cmml"></mo>
<msub id="p1.1.m1.1.14.1.7" xref="p1.1.m1.1.14.1.7.cmml">
<mi id="p1.1.m1.1.14.1.3" xref="p1.1.m1.1.14.1.3.cmml">α</mi>
<mn id="p1.1.m1.1.14.1.4.1" xref="p1.1.m1.1.14.1.4.1.cmml">2</mn>
</msub>
</mrow>
<mrow id="p1.1.m1.1.15.1" xref="p1.1.m1.1.15.1.cmml">
<mrow id="p1.1.m1.1.15.1.7b" xref="p1.1.m1.1.15.1.7.cmml">
<mo stretchy="false" id="p1.1.m1.1.15.1.7" xref="p1.1.m1.1.15.1.7.cmml">[</mo>
<mn id="p1.1.m1.1.15.1.2" xref="p1.1.m1.1.15.1.2.cmml">2</mn>
<mo stretchy="false" id="p1.1.m1.1.15.1.7a" xref="p1.1.m1.1.15.1.7.cmml">]</mo>
</mrow>
<mo id="p1.1.m1.1.15.1.6" xref="p1.1.m1.1.15.1.6.cmml"></mo>
<msub id="p1.1.m1.1.15.1.8" xref="p1.1.m1.1.15.1.8.cmml">
<mi id="p1.1.m1.1.15.1.4" xref="p1.1.m1.1.15.1.4.cmml">i</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.15.1.5.1" xref="p1.1.m1.1.15.1.5.1.cmml">x3</mi>
</msub>
</mrow>
</msubsup>
<mo id="p1.1.m1.1.28.2.2.1b" xref="p1.1.m1.1.28.2.2.1.cmml"></mo>
<msubsup id="p1.1.m1.1.28.2.2.5" xref="p1.1.m1.1.28.2.2.5.cmml">
<mi id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">λ</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.17.1" xref="p1.1.m1.1.17.1.cmml">x4</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.18.1" xref="p1.1.m1.1.18.1.cmml">x5</mi>
</msubsup>
<mo id="p1.1.m1.1.28.2.2.1c" xref="p1.1.m1.1.28.2.2.1.cmml"></mo>
<mrow id="p1.1.m1.1.28.2.2.6b" xref="p1.1.m1.1.28.2.2.6.cmml">
<mo fence="true" stretchy="false" id="p1.1.m1.1.28.2.2.6" xref="p1.1.m1.1.28.2.2.6.cmml">|</mo>
<mrow id="XM1" xref="XM1.cmml">
<msub id="XM1.2" xref="XM1.2.cmml">
<mi id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">i</mi>
<mn id="p1.1.m1.1.21.1" xref="p1.1.m1.1.21.1.cmml">1</mn>
</msub>
<mo id="XM1.1" xref="XM1.1.cmml"></mo>
<msub id="XM1.3" xref="XM1.3.cmml">
<mi id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">i</mi>
<mn id="p1.1.m1.1.23.1" xref="p1.1.m1.1.23.1.cmml">2</mn>
</msub>
</mrow>
<mo stretchy="false" id="p1.1.m1.1.28.2.2.6a" xref="p1.1.m1.1.28.2.2.6.cmml">⟩</mo>
</mrow>
<mo id="p1.1.m1.1.28.2.2.1d" xref="p1.1.m1.1.28.2.2.1.cmml"></mo>
<mrow id="p1.1.m1.1.28.2.2.7b" xref="p1.1.m1.1.28.2.2.7.cmml">
<mo fence="true" stretchy="false" id="p1.1.m1.1.28.2.2.7" xref="p1.1.m1.1.28.2.2.7.cmml">|</mo>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.26" xref="p1.1.m1.1.26.cmml">x6</mi>
<mo stretchy="false" id="p1.1.m1.1.28.2.2.7a" xref="p1.1.m1.1.28.2.2.7.cmml">⟩</mo>
</mrow>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.28.cmml" xref="p1.1.m1.1.28">
<eq id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4"/>
<apply id="p1.1.m1.1.28.1a.cmml" xref="p1.1.m1.1.28.1">
<csymbol cd="latexml" id="p1.1.m1.1.28.1.cmml" xref="p1.1.m1.1.28.1">ket</csymbol>
<ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">normal-Ψ</ci>
</apply>
<apply id="p1.1.m1.1.28.2.cmml" xref="p1.1.m1.1.28.2">
<apply id="p1.1.m1.1.28.2.1.cmml" xref="p1.1.m1.1.28.2.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.28.2.1.1.cmml">subscript</csymbol>
<sum id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1">x0</csymbol>
</apply>
<apply id="p1.1.m1.1.28.2.2.cmml" xref="p1.1.m1.1.28.2.2">
<times id="p1.1.m1.1.28.2.2.1.cmml" xref="p1.1.m1.1.28.2.2.1"/>
<apply id="p1.1.m1.1.28.2.2.2.cmml" xref="p1.1.m1.1.28.2.2.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.28.2.2.2.1.cmml">superscript</csymbol>
<apply id="p1.1.m1.1.28.2.2.2.2.cmml">
<csymbol cd="ambiguous" id="p1.1.m1.1.28.2.2.2.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">normal-Γ</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.1">x1</csymbol>
</apply>
<apply id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">
<times id="p1.1.m1.1.9.1.6.cmml" xref="p1.1.m1.1.9.1.6"/>
<apply id="p1.1.m1.1.9.1.7a.cmml" xref="p1.1.m1.1.9.1.7">
<csymbol cd="latexml" id="p1.1.m1.1.9.1.7.cmml" xref="p1.1.m1.1.9.1.7">delimited-[]</csymbol>
<cn type="integer" id="p1.1.m1.1.9.1.2.cmml" xref="p1.1.m1.1.9.1.2">1</cn>
</apply>
<apply id="p1.1.m1.1.9.1.8.cmml" xref="p1.1.m1.1.9.1.8">
<csymbol cd="ambiguous" id="p1.1.m1.1.9.1.8.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.9.1.4.cmml" xref="p1.1.m1.1.9.1.4">i</ci>
<cn type="integer" id="p1.1.m1.1.9.1.5.1.cmml" xref="p1.1.m1.1.9.1.5.1">1</cn>
</apply>
</apply>
</apply>
<apply id="p1.1.m1.1.28.2.2.3.cmml" xref="p1.1.m1.1.28.2.2.3">
<csymbol cd="ambiguous" id="p1.1.m1.1.28.2.2.3.1.cmml">superscript</csymbol>
<apply id="p1.1.m1.1.28.2.2.3.2.cmml">
<csymbol cd="ambiguous" id="p1.1.m1.1.28.2.2.3.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">λ</ci>
<apply id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.11.1.3.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.11.1.1.cmml" xref="p1.1.m1.1.11.1.1">α</ci>
<cn type="integer" id="p1.1.m1.1.11.1.2.1.cmml" xref="p1.1.m1.1.11.1.2.1">1</cn>
</apply>
</apply>
<apply id="p1.1.m1.1.12.1a.cmml" xref="p1.1.m1.1.12.1">
<csymbol cd="latexml" id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12.1">delimited-[]</csymbol>
<cn type="integer" id="p1.1.m1.1.12.1.2.cmml" xref="p1.1.m1.1.12.1.2">1</cn>
</apply>
</apply>
<apply id="p1.1.m1.1.28.2.2.4.cmml" xref="p1.1.m1.1.28.2.2.4">
<csymbol cd="ambiguous" id="p1.1.m1.1.28.2.2.4.1.cmml">superscript</csymbol>
<apply id="p1.1.m1.1.28.2.2.4.2.cmml">
<csymbol cd="ambiguous" id="p1.1.m1.1.28.2.2.4.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">normal-Γ</ci>
<apply id="p1.1.m1.1.14.1.cmml" xref="p1.1.m1.1.14.1">
<times id="p1.1.m1.1.14.1.5.cmml" xref="p1.1.m1.1.14.1.5"/>
<apply id="p1.1.m1.1.14.1.6.cmml" xref="p1.1.m1.1.14.1.6">
<csymbol cd="ambiguous" id="p1.1.m1.1.14.1.6.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.14.1.1.cmml" xref="p1.1.m1.1.14.1.1">α</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.14.1.2.1.cmml" xref="p1.1.m1.1.14.1.2.1">x2</csymbol>
</apply>
<apply id="p1.1.m1.1.14.1.7.cmml" xref="p1.1.m1.1.14.1.7">
<csymbol cd="ambiguous" id="p1.1.m1.1.14.1.7.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.14.1.3.cmml" xref="p1.1.m1.1.14.1.3">α</ci>
<cn type="integer" id="p1.1.m1.1.14.1.4.1.cmml" xref="p1.1.m1.1.14.1.4.1">2</cn>
</apply>
</apply>
</apply>
<apply id="p1.1.m1.1.15.1.cmml" xref="p1.1.m1.1.15.1">
<times id="p1.1.m1.1.15.1.6.cmml" xref="p1.1.m1.1.15.1.6"/>
<apply id="p1.1.m1.1.15.1.7a.cmml" xref="p1.1.m1.1.15.1.7">
<csymbol cd="latexml" id="p1.1.m1.1.15.1.7.cmml" xref="p1.1.m1.1.15.1.7">delimited-[]</csymbol>
<cn type="integer" id="p1.1.m1.1.15.1.2.cmml" xref="p1.1.m1.1.15.1.2">2</cn>
</apply>
<apply id="p1.1.m1.1.15.1.8.cmml" xref="p1.1.m1.1.15.1.8">
<csymbol cd="ambiguous" id="p1.1.m1.1.15.1.8.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.15.1.4.cmml" xref="p1.1.m1.1.15.1.4">i</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.15.1.5.1.cmml" xref="p1.1.m1.1.15.1.5.1">x3</csymbol>
</apply>
</apply>
</apply>
<apply id="p1.1.m1.1.28.2.2.5.cmml" xref="p1.1.m1.1.28.2.2.5">
<csymbol cd="ambiguous" id="p1.1.m1.1.28.2.2.5.1.cmml">superscript</csymbol>
<apply id="p1.1.m1.1.28.2.2.5.2.cmml">
<csymbol cd="ambiguous" id="p1.1.m1.1.28.2.2.5.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">λ</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.17.1.cmml" xref="p1.1.m1.1.17.1">x4</csymbol>
</apply>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.18.1.cmml" xref="p1.1.m1.1.18.1">x5</csymbol>
</apply>
<apply id="p1.1.m1.1.28.2.2.6a.cmml" xref="p1.1.m1.1.28.2.2.6">
<csymbol cd="latexml" id="p1.1.m1.1.28.2.2.6.cmml" xref="p1.1.m1.1.28.2.2.6">ket</csymbol>
<apply id="XM1.cmml" xref="XM1">
<times id="XM1.1.cmml" xref="XM1.1"/>
<apply id="XM1.2.cmml" xref="XM1.2">
<csymbol cd="ambiguous" id="XM1.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">i</ci>
<cn type="integer" id="p1.1.m1.1.21.1.cmml" xref="p1.1.m1.1.21.1">1</cn>
</apply>
<apply id="XM1.3.cmml" xref="XM1.3">
<csymbol cd="ambiguous" id="XM1.3.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22">i</ci>
<cn type="integer" id="p1.1.m1.1.23.1.cmml" xref="p1.1.m1.1.23.1">2</cn>
</apply>
</apply>
</apply>
<apply id="p1.1.m1.1.28.2.2.7a.cmml" xref="p1.1.m1.1.28.2.2.7">
<csymbol cd="latexml" id="p1.1.m1.1.28.2.2.7.cmml" xref="p1.1.m1.1.28.2.2.7">ket</csymbol>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.26.cmml" xref="p1.1.m1.1.26">x6</csymbol>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle|{\Psi}\rangle=\sum_{\qvar@construct{x0}}\Gamma_{{%
\qvar@construct{x1}}}^{{[1]i_{1}}}\lambda_{{\alpha_{1}}}^{{[1]}}\Gamma_{{%
\alpha_{\qvar@construct{x2}}\alpha_{2}}}^{{[2]i_{\qvar@construct{x3}}}}\lambda%
_{\qvar@construct{x4}}^{{\qvar@construct{x5}}}|{i_{1}i_{2}}\rangle|{%
\qvar@construct{x6}}\rangle}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=c6484aebbc40e056912beba3d3c0cc59&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.833ex; height: 5.333ex; width: 38.833ex;" alt="|{\Psi}\rangle=\sum_{\qvar{x0}}\Gamma_{{\qvar{x1}}}^{{[1]i_{1}}}\lambda_{{\alpha_{1}}}^{{[1]}}\Gamma_{{\alpha_{\qvar{x2}}\alpha_{2}}}^{{[2]i_{\qvar{x3}}}}\lambda_{\qvar{x4}}^{{\qvar{x5}}}|{i_{1}i_{2}}\rangle|{\qvar{x6}}\rangle" data-pagespeed-url-hash="3328833984" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |{\Psi }\rangle =\sum _{i_{1},i_{2},\alpha _{1},\alpha _{2}}\Gamma _{\alpha _{1}}^{[1]i_{1}}\lambda _{\alpha _{1}}^{[1]}\Gamma _{\alpha _{1}\alpha _{2}}^{[2]i_{2}}\lambda _{{\alpha }_{2}}^{[2]}|{i_{1}i_{2}}\rangle |{\Phi _{\alpha _{2}}^{[3..N]}}\rangle }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">|</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">Ψ<!-- Ψ --></mi>
</mrow>
<mo fence="false" stretchy="false">⟩<!-- ⟩ --></mo>
<mo>=</mo>
<munder>
<mo>∑<!-- ∑ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<msub>
<mi>i</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>i</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
</mrow>
</munder>
<msubsup>
<mi mathvariant="normal">Γ<!-- Γ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<msub>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">[</mo>
<mn>1</mn>
<mo stretchy="false">]</mo>
<msub>
<mi>i</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
</mrow>
</msubsup>
<msubsup>
<mi>λ<!-- λ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<msub>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">[</mo>
<mn>1</mn>
<mo stretchy="false">]</mo>
</mrow>
</msubsup>
<msubsup>
<mi mathvariant="normal">Γ<!-- Γ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<msub>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<msub>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">[</mo>
<mn>2</mn>
<mo stretchy="false">]</mo>
<msub>
<mi>i</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
</mrow>
</msubsup>
<msubsup>
<mi>λ<!-- λ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<msub>
<mrow class="MJX-TeXAtom-ORD">
<mi>α<!-- α --></mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">[</mo>
<mn>2</mn>
<mo stretchy="false">]</mo>
</mrow>
</msubsup>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">|</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<msub>
<mi>i</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<msub>
<mi>i</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
</mrow>
<mo fence="false" stretchy="false">⟩<!-- ⟩ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">|</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<msubsup>
<mi mathvariant="normal">Φ<!-- Φ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<msub>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">[</mo>
<mn>3..</mn>
<mi>N</mi>
<mo stretchy="false">]</mo>
</mrow>
</msubsup>
</mrow>
<mo fence="false" stretchy="false">⟩<!-- ⟩ --></mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle |{\Psi }\rangle =\sum _{i_{1},i_{2},\alpha _{1},\alpha _{2}}\Gamma _{\alpha _{1}}^{[1]i_{1}}\lambda _{\alpha _{1}}^{[1]}\Gamma _{\alpha _{1}\alpha _{2}}^{[2]i_{2}}\lambda _{{\alpha }_{2}}^{[2]}|{i_{1}i_{2}}\rangle |{\Phi _{\alpha _{2}}^{[3..N]}}\rangle }</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/931cab39539ccdf5bce2f96e36c68297e4a5bd54" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.338ex; width:44.834ex; height:6.009ex;" alt="{\displaystyle |{\Psi }\rangle =\sum _{i_{1},i_{2},\alpha _{1},\alpha _{2}}\Gamma _{\alpha _{1}}^{[1]i_{1}}\lambda _{\alpha _{1}}^{[1]}\Gamma _{\alpha _{1}\alpha _{2}}^{[2]i_{2}}\lambda _{{\alpha }_{2}}^{[2]}|{i_{1}i_{2}}\rangle |{\Phi _{\alpha _{2}}^{[3..N]}}\rangle }" data-pagespeed-url-hash="2060406034" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/10" title="Special:DisplayTopics/10">10</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/16784#math.16784.38" title="Special:PermanentLink/16784">Monoidal_t-norm_logic-38</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle z*x\leq y}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
<mrow id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">z</mi>
<mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">*</mo>
<mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">x</mi>
</mrow>
<mo id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">≤</mo>
<mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">y</mi>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">
<leq id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4"/>
<apply id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1">
<times id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">z</ci>
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">x</ci>
</apply>
<ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">y</ci>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle z*x\leq y}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=6ed387d80554ceb6931d9429fed702fc&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.5ex; height: 2.333ex; width: 9ex;" alt="z*x\leq y" data-pagespeed-url-hash="2176594866" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z*x\leq y}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>z</mi>
<mo>∗<!-- ∗ --></mo>
<mi>x</mi>
<mo>≤<!-- ≤ --></mo>
<mi>y</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle z*x\leq y}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/0b0368ccc5d27240cae15c3418da91ab428602f0" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:8.866ex; height:2.343ex;" alt="{\displaystyle z*x\leq y}" data-pagespeed-url-hash="209814257" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/11" title="Special:DisplayTopics/11">11</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/16716#math.16716.20" title="Special:PermanentLink/16716">Differentiation_rules-20</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{{\frac{d}{dx}}}\left(\log_{{c}}x\right)={1\over x\ln c},\qquad c% >0,c\neq 1}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.18a" xref="p1.1.m1.1.18.cmml">
<mrow id="XM4" xref="XM4.cmml">
<mrow id="XM4.1" xref="XM4.1.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">
<mfrac id="p1.1.m1.1.1a" xref="p1.1.m1.1.1.cmml">
<mi id="p1.1.m1.1.1.2" xref="p1.1.m1.1.1.2.cmml">d</mi>
<mrow id="p1.1.m1.1.1.3" xref="p1.1.m1.1.1.3.cmml">
<mi id="p1.1.m1.1.1.3.1" xref="p1.1.m1.1.1.3.1.cmml">d</mi>
<mo id="p1.1.m1.1.1.3.3" xref="p1.1.m1.1.1.3.3.cmml"></mo>
<mi id="p1.1.m1.1.1.3.2" xref="p1.1.m1.1.1.3.2.cmml">x</mi>
</mrow>
</mfrac>
</mstyle>
<mo id="XM4.1.1" xref="XM4.1.1.cmml"></mo>
<mrow id="XM4.1.2b">
<mo id="XM4.1.2">(</mo>
<mrow id="XM1" xref="XM1.cmml">
<msub id="XM1.1" xref="XM1.1.cmml">
<mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">log</mi>
<mi id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">c</mi>
</msub>
<mo id="XM1a" xref="XM1.cmml"></mo>
<mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">x</mi>
</mrow>
<mo id="XM4.1.2a">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">=</mo>
<mstyle displaystyle="true" id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">
<mfrac id="p1.1.m1.1.8a" xref="p1.1.m1.1.8.cmml">
<mn id="p1.1.m1.1.8.2" xref="p1.1.m1.1.8.2.cmml">1</mn>
<mrow id="p1.1.m1.1.8.3" xref="p1.1.m1.1.8.3.cmml">
<mi id="p1.1.m1.1.8.3.1" xref="p1.1.m1.1.8.3.1.cmml">x</mi>
<mo id="p1.1.m1.1.8.3.4" xref="p1.1.m1.1.8.3.4.cmml"></mo>
<mrow id="p1.1.m1.1.8.3.5" xref="p1.1.m1.1.8.3.5.cmml">
<mi id="p1.1.m1.1.8.3.2" xref="p1.1.m1.1.8.3.2.cmml">ln</mi>
<mo id="p1.1.m1.1.8.3.5a" xref="p1.1.m1.1.8.3.5.cmml"></mo>
<mi id="p1.1.m1.1.8.3.3" xref="p1.1.m1.1.8.3.3.cmml">c</mi>
</mrow>
</mrow>
</mfrac>
</mstyle>
</mrow>
<mo rspace="22.5pt" id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">,</mo>
<mrow id="XM5a" xref="XM5.cmml">
<mrow id="XM2" xref="XM2.cmml">
<mi id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">c</mi>
<mo id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">></mo>
<mn id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">0</mn>
</mrow>
<mo id="XM5" xref="XM5.cmml">,</mo>
<mrow id="XM3" xref="XM3.cmml">
<mi id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">c</mi>
<mo id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">≠</mo>
<mn id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">1</mn>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">
<csymbol cd="ambiguous" id="p1.1.m1.1.18a.cmml" xref="p1.1.m1.1.18">formulae-sequence</csymbol>
<apply id="XM4.cmml" xref="XM4">
<eq id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
<apply id="XM4.1.cmml" xref="XM4.1">
<times id="XM4.1.1.cmml" xref="XM4.1.1"/>
<apply id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">
<divide id="p1.1.m1.1.1.1.cmml"/>
<ci id="p1.1.m1.1.1.2.cmml" xref="p1.1.m1.1.1.2">d</ci>
<apply id="p1.1.m1.1.1.3.cmml" xref="p1.1.m1.1.1.3">
<times id="p1.1.m1.1.1.3.3.cmml" xref="p1.1.m1.1.1.3.3"/>
<ci id="p1.1.m1.1.1.3.1.cmml" xref="p1.1.m1.1.1.3.1">d</ci>
<ci id="p1.1.m1.1.1.3.2.cmml" xref="p1.1.m1.1.1.3.2">x</ci>
</apply>
</apply>
<apply id="XM1.cmml" xref="XM1">
<apply id="XM1.1.cmml" xref="XM1.1">
<csymbol cd="ambiguous" id="XM1.1.1.cmml">subscript</csymbol>
<log id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
<ci id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">c</ci>
</apply>
<ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">x</ci>
</apply>
</apply>
<apply id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">
<divide id="p1.1.m1.1.8.1.cmml"/>
<cn type="integer" id="p1.1.m1.1.8.2.cmml" xref="p1.1.m1.1.8.2">1</cn>
<apply id="p1.1.m1.1.8.3.cmml" xref="p1.1.m1.1.8.3">
<times id="p1.1.m1.1.8.3.4.cmml" xref="p1.1.m1.1.8.3.4"/>
<ci id="p1.1.m1.1.8.3.1.cmml" xref="p1.1.m1.1.8.3.1">x</ci>
<apply id="p1.1.m1.1.8.3.5.cmml" xref="p1.1.m1.1.8.3.5">
<ln id="p1.1.m1.1.8.3.2.cmml" xref="p1.1.m1.1.8.3.2"/>
<ci id="p1.1.m1.1.8.3.3.cmml" xref="p1.1.m1.1.8.3.3">c</ci>
</apply>
</apply>
</apply>
</apply>
<apply id="XM5.cmml" xref="XM5">
<csymbol cd="ambiguous" id="XM5a.cmml" xref="XM5">formulae-sequence</csymbol>
<apply id="XM2.cmml" xref="XM2">
<gt id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12"/>
<ci id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">c</ci>
<cn type="integer" id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">0</cn>
</apply>
<apply id="XM3.cmml" xref="XM3">
<neq id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16"/>
<ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">c</ci>
<cn type="integer" id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">1</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{{\frac{d}{dx}}}\left(\log_{{c}}x\right)={1\over x\ln c},\qquad c%
>0,c\neq 1}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=94fbcb157d2396d95a99e839a9a1a07d&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.833ex; height: 5ex; width: 38.333ex;" alt="{{\frac {d}{dx}}}\left(\log _{{c}}x\right)={1 \over x\ln c},\qquad c>0,c\neq 1" data-pagespeed-url-hash="3271900786" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {d}{dx}}\left(\log _{c}x\right)={1 \over x\ln c},\qquad c>0,c\neq 1}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>d</mi>
<mrow>
<mi>d</mi>
<mi>x</mi>
</mrow>
</mfrac>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>log</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>c</mi>
</mrow>
</msub>
<mo>⁡<!-- --></mo>
<mi>x</mi>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mn>1</mn>
<mrow>
<mi>x</mi>
<mi>ln</mi>
<mo>⁡<!-- --></mo>
<mi>c</mi>
</mrow>
</mfrac>
</mrow>
<mo>,</mo>
<mspace width="2em"/>
<mi>c</mi>
<mo>></mo>
<mn>0</mn>
<mo>,</mo>
<mi>c</mi>
<mo>≠<!-- ≠ --></mo>
<mn>1</mn>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\frac {d}{dx}}\left(\log _{c}x\right)={1 \over x\ln c},\qquad c>0,c\neq 1}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/fa7d8d5be70b8858e655f1f25ca058f135ea417a" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.005ex; width:37.444ex; height:5.509ex;" alt="{\displaystyle {\frac {d}{dx}}\left(\log _{c}x\right)={1 \over x\ln c},\qquad c>0,c\neq 1}" data-pagespeed-url-hash="4199171813" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/12" title="Special:DisplayTopics/12">12</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/2875#math.2875.2" title="Special:PermanentLink/2875">Fermat's_spiral-2</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\theta=n\times 137.508^{{\circ}},}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">
<mrow id="p1.1.m1.1.14a" xref="p1.1.m1.1.14.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">θ</mi>
<mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">=</mo>
<mrow id="p1.1.m1.1.14.1" xref="p1.1.m1.1.14.1.cmml">
<mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">n</mi>
<mo id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">×</mo>
<msup id="p1.1.m1.1.14.1.1" xref="p1.1.m1.1.14.1.1.cmml">
<mn id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">137.508</mn>
<mo id="p1.1.m1.1.12.1" xref="p1.1.m1.1.12.1.cmml">∘</mo>
</msup>
</mrow>
</mrow>
<mo id="p1.1.m1.1.14b" xref="p1.1.m1.1.14.cmml">,</mo>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">
<eq id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">θ</ci>
<apply id="p1.1.m1.1.14.1.cmml" xref="p1.1.m1.1.14.1">
<times id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4"/>
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">n</ci>
<apply id="p1.1.m1.1.14.1.1.cmml" xref="p1.1.m1.1.14.1.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.14.1.1.1.cmml">superscript</csymbol>
<cn type="float" id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">137.508</cn>
<compose id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12.1"/>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\theta=n\times 137.508^{{\circ}},}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=560864f77de17632f73e76e0d0840223&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.5ex; height: 2.167ex; width: 17.833ex;" alt="\theta =n\times 137.508^{{\circ }}," data-pagespeed-url-hash="3500341682" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta =n\times 137.508^{\circ },}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>θ<!-- θ --></mi>
<mo>=</mo>
<mi>n</mi>
<mo>×<!-- × --></mo>
<msup>
<mn>137.508</mn>
<mrow class="MJX-TeXAtom-ORD">
<mo>∘<!-- ∘ --></mo>
</mrow>
</msup>
<mo>,</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \theta =n\times 137.508^{\circ },}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/de0a699a99e559ac5f6d1ffe3dcf4463689702f5" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:17.747ex; height:2.676ex;" alt="{\displaystyle \theta =n\times 137.508^{\circ },}" data-pagespeed-url-hash="1090891597" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/13" title="Special:DisplayTopics/13">13</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/9319#math.9319.2" title="Special:PermanentLink/9319">Consistency_criterion-2</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle s_{{V}}({{\mathcal{R}}})}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
<msub id="p1.1.m1.1.6.2" xref="p1.1.m1.1.6.2.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">s</mi>
<mi id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">V</mi>
</msub>
<mo id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml"></mo>
<mrow id="p1.1.m1.1.6.3b">
<mo stretchy="false" id="p1.1.m1.1.6.3">(</mo>
<mi class="ltx_font_mathcaligraphic" id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">ℛ</mi>
<mo stretchy="false" id="p1.1.m1.1.6.3a">)</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">
<times id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1"/>
<apply id="p1.1.m1.1.6.2.cmml" xref="p1.1.m1.1.6.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.6.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">s</ci>
<ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">V</ci>
</apply>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">ℛ</ci>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle s_{{V}}({{\mathcal{R}}})}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=cb760930876680b64d100aaafb303bd0&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.5ex; width: 6.833ex;" alt="s_{{V}}({{\mathcal {R}}})" data-pagespeed-url-hash="791287746" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s_{V}({\mathcal {R}})}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>s</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>V</mi>
</mrow>
</msub>
<mo stretchy="false">(</mo>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi class="MJX-tex-caligraphic" mathvariant="script">R</mi>
</mrow>
</mrow>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle s_{V}({\mathcal {R}})}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/abbe00466c7e94d9eba0fc82cfc7b9d08ac68a92" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:6.366ex; height:2.843ex;" alt="{\displaystyle s_{V}({\mathcal {R}})}" data-pagespeed-url-hash="4026424029" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/14" title="Special:DisplayTopics/14">14</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/21982#math.21982.43" title="Special:PermanentLink/21982">Basis_(universal_algebra)-43</a>
</td>
<td> 0
</td>
<td> 2
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\ell(m)}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">
<mi mathvariant="normal" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">ℓ</mi>
<mo id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml"></mo>
<mrow id="p1.1.m1.1.5.2b">
<mo stretchy="false" id="p1.1.m1.1.5.2">(</mo>
<mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">m</mi>
<mo stretchy="false" id="p1.1.m1.1.5.2a">)</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">
<times id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">normal-ℓ</ci>
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">m</ci>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\ell(m)}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=0019c83f9d0e4f79dbb27fa6520759ef&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.5ex; width: 5.167ex;" alt="\ell (m)" data-pagespeed-url-hash="2698208378" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ell (m)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>ℓ<!-- ℓ --></mi>
<mo stretchy="false">(</mo>
<mi>m</mi>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \ell (m)}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/b3a47e90aa8e63b909b4ff6740cd8b5f5055d874" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:4.819ex; height:2.843ex;" alt="{\displaystyle \ell (m)}" data-pagespeed-url-hash="1750558891" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/15" title="Special:DisplayTopics/15">15</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/26321#math.26321.4" title="Special:PermanentLink/26321">Adequality-4</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle bx-x^{{2}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
<mrow id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">b</mi>
<mo id="p1.1.m1.1.6.1.1" xref="p1.1.m1.1.6.1.1.cmml"></mo>
<mi id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">x</mi>
</mrow>
<mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">-</mo>
<msup id="p1.1.m1.1.6.2" xref="p1.1.m1.1.6.2.cmml">
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">x</mi>
<mn id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">2</mn>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">
<minus id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
<apply id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1">
<times id="p1.1.m1.1.6.1.1.cmml" xref="p1.1.m1.1.6.1.1"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">b</ci>
<ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">x</ci>
</apply>
<apply id="p1.1.m1.1.6.2.cmml" xref="p1.1.m1.1.6.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.6.2.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">x</ci>
<cn type="integer" id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1">2</cn>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle bx-x^{{2}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=95c282154e3a6188b91dba20bef85f5e&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.167ex; height: 2ex; width: 7.667ex;" alt="bx-x^{{2}}" data-pagespeed-url-hash="126753537" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle bx-x^{2}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>b</mi>
<mi>x</mi>
<mo>−<!-- − --></mo>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle bx-x^{2}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/e13a2194147f14ded5f84a6114a7e19c9ab5b8fd" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.505ex; width:7.552ex; height:2.843ex;" alt="{\displaystyle bx-x^{2}}" data-pagespeed-url-hash="4254177220" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/16" title="Special:DisplayTopics/16">16</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/13492#math.13492.85" title="Special:PermanentLink/13492">Mason–Weaver_equation-85</a>
</td>
<td> 0
</td>
<td> 6
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\omega_{{{k}}}}">
<semantics id="p1.1.m1.1a">
<msub id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">ω</mi>
<mi id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">k</mi>
</msub>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
<csymbol cd="ambiguous" id="p1.1.m1.1.3.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">ω</ci>
<ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">k</ci>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\omega_{{{k}}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=507e69b4e9f4e0b3911edc90cce5f4fb&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.5ex; height: 1.5ex; width: 2.5ex;" alt="\omega _{{{k}}}" data-pagespeed-url-hash="28649793" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{k}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>ω<!-- ω --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>k</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \omega _{k}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/4e636bf7531cecd91206a36f038cf869e7934932" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:2.535ex; height:2.009ex;" alt="{\displaystyle \omega _{k}}" data-pagespeed-url-hash="2475715415" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/17" title="Special:DisplayTopics/17">17</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/27275#math.27275.2" title="Special:PermanentLink/27275">Kernel_Fisher_discriminant_analysis-2</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{{\mathbf{m}}}_{{1}}}">
<semantics id="p1.1.m1.1a">
<msub id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">𝐦</mi>
<mn id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">1</mn>
</msub>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
<csymbol cd="ambiguous" id="p1.1.m1.1.3.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝐦</ci>
<cn type="integer" id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">1</cn>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{{\mathbf{m}}}_{{1}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=77e4cccdf1e63263f898167c45e4dde1&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.5ex; height: 1.5ex; width: 3.333ex;" alt="{{\mathbf {m}}}_{{1}}" data-pagespeed-url-hash="2079944963" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {m} _{1}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="bold">m</mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \mathbf {m} _{1}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/2fdce6547b8891574df3b8a1f6609b2ec85d4d6a" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:3.28ex; height:2.009ex;" alt="{\displaystyle \mathbf {m} _{1}}" data-pagespeed-url-hash="3991126705" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/18" title="Special:DisplayTopics/18">18</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/15283#math.15283.17" title="Special:PermanentLink/15283">Implicit_solvation-17</a>
</td>
<td> 0
</td>
<td> 16
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle r_{{{ij}}}}">
<semantics id="p1.1.m1.1a">
<msub id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">r</mi>
<mrow id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">
<mi id="p1.1.m1.1.2.1.1" xref="p1.1.m1.1.2.1.1.cmml">i</mi>
<mo id="p1.1.m1.1.2.1.3" xref="p1.1.m1.1.2.1.3.cmml"></mo>
<mi id="p1.1.m1.1.2.1.2" xref="p1.1.m1.1.2.1.2.cmml">j</mi>
</mrow>
</msub>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
<csymbol cd="ambiguous" id="p1.1.m1.1.3.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">r</ci>
<apply id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">
<times id="p1.1.m1.1.2.1.3.cmml" xref="p1.1.m1.1.2.1.3"/>
<ci id="p1.1.m1.1.2.1.1.cmml" xref="p1.1.m1.1.2.1.1">i</ci>
<ci id="p1.1.m1.1.2.1.2.cmml" xref="p1.1.m1.1.2.1.2">j</ci>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle r_{{{ij}}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=fe801f95e20cf8d385671fa4bd84e0ad&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.833ex; height: 1.833ex; width: 2.5ex;" alt="r_{{{ij}}}" data-pagespeed-url-hash="663961602" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r_{ij}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>r</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle r_{ij}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/857845aef8b93395ad10279211c6c49180bb8791" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.005ex; width:2.526ex; height:2.343ex;" alt="{\displaystyle r_{ij}}" data-pagespeed-url-hash="140034616" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/19" title="Special:DisplayTopics/19">19</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/3897#math.3897.2" title="Special:PermanentLink/3897">Partition_function_(statistical_mechanics)-2</a>
</td>
<td> 1
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle Z=\sum_{{j}}g_{j}\cdot{\mathrm{e}}^{{\qvar@construct{x0}}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">Z</mi>
<mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">=</mo>
<mrow id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.10.1.1" xref="p1.1.m1.1.10.1.1.cmml">
<munder id="p1.1.m1.1.10.1.1a" xref="p1.1.m1.1.10.1.1.cmml">
<mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">∑</mo>
<mi id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">j</mi>
</munder>
</mstyle>
<mrow id="p1.1.m1.1.10.1.2" xref="p1.1.m1.1.10.1.2.cmml">
<msub id="p1.1.m1.1.10.1.2.1" xref="p1.1.m1.1.10.1.2.1.cmml">
<mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">g</mi>
<mi id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">j</mi>
</msub>
<mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">⋅</mo>
<msup id="p1.1.m1.1.10.1.2.2" xref="p1.1.m1.1.10.1.2.2.cmml">
<mi mathvariant="normal" id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">e</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">x0</mi>
</msup>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">
<eq id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">Z</ci>
<apply id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">
<apply id="p1.1.m1.1.10.1.1.cmml" xref="p1.1.m1.1.10.1.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.10.1.1.1.cmml">subscript</csymbol>
<sum id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
<ci id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">j</ci>
</apply>
<apply id="p1.1.m1.1.10.1.2.cmml" xref="p1.1.m1.1.10.1.2">
<ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">normal-⋅</ci>
<apply id="p1.1.m1.1.10.1.2.1.cmml" xref="p1.1.m1.1.10.1.2.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.10.1.2.1.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">g</ci>
<ci id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1">j</ci>
</apply>
<apply id="p1.1.m1.1.10.1.2.2.cmml" xref="p1.1.m1.1.10.1.2.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.10.1.2.2.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">normal-e</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">x0</csymbol>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle Z=\sum_{{j}}g_{j}\cdot{\mathrm{e}}^{{\qvar@construct{x0}}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=de949ba18cdc347261678ecfa6669821&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.167ex; height: 5.5ex; width: 15.333ex;" alt="Z=\sum_{{j}}g_{j}\cdot{\mathrm{e}}^{{\qvar{x0}}}" data-pagespeed-url-hash="3199676867" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z=\sum _{j}g_{j}\cdot \mathrm {e} ^{-\beta E_{j}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>Z</mi>
<mo>=</mo>
<munder>
<mo>∑<!-- ∑ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>j</mi>
</mrow>
</munder>
<msub>
<mi>g</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>j</mi>
</mrow>
</msub>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">e</mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>−<!-- − --></mo>
<mi>β<!-- β --></mi>
<msub>
<mi>E</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>j</mi>
</mrow>
</msub>
</mrow>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle Z=\sum _{j}g_{j}\cdot \mathrm {e} ^{-\beta E_{j}}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/bff33cdaffc76f2c5c2ded90a9cf993c3394a95f" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.338ex; width:17.631ex; height:5.843ex;" alt="{\displaystyle Z=\sum _{j}g_{j}\cdot \mathrm {e} ^{-\beta E_{j}}}" data-pagespeed-url-hash="1781328753" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/20" title="Special:DisplayTopics/20">20</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/8808#math.8808.39" title="Special:PermanentLink/8808">Color_balance-39</a>
</td>
<td> 0
</td>
<td> 48
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1" class="ltx_Math" alttext="{\displaystyle S^{{\prime}}}" xml:id="p1.1.m1.1" xref="p1.1.m1.1.cmml">
<semantics xml:id="p1.1.m1.1a" xref="p1.1.m1.1.cmml">
<msup xml:id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
<mi xml:id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">S</mi>
<mo xml:id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">′</mo>
</msup>
<annotation-xml encoding="MathML-Content" xml:id="p1.1.m1.1.cmml" xref="p1.1.m1.1">
<apply xml:id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
<csymbol cd="ambiguous" xml:id="p1.1.m1.1.3.1.cmml">superscript</csymbol>
<ci xml:id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">S</ci>
<ci xml:id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">normal-′</ci>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" xml:id="p1.1.m1.1b" xref="p1.1.m1.1.cmml">{\displaystyle S^{{\prime}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=93383c212e2b016a5e66f30d1fc0dd83&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="width: 2.25ex; height: 2ex; vertical-align: -0.25ex; margin-top: 1px; margin-right: 0px; margin-bottom: 1px; margin-left: 0px; position: static; width: 10;" alt="S^{{\prime }}" data-pagespeed-url-hash="2435268494" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S'}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msup>
<mi>S</mi>
<mo>′</mo>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle S'}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/bf9961844d1f539adee019e432dc18aa2a7ede59" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:2.206ex; height:2.509ex;" alt="{\displaystyle S'}" data-pagespeed-url-hash="2004084909" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/21" title="Special:DisplayTopics/21">21</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/17336#math.17336.30" title="Special:PermanentLink/17336">Hilbert's_theorem_(differential_geometry)-30</a>
</td>
<td> 0
</td>
<td> 48
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1" class="ltx_Math" alttext="{\displaystyle S^{{\prime}}}" xml:id="p1.1.m1.1" xref="p1.1.m1.1.cmml">
<semantics xml:id="p1.1.m1.1a" xref="p1.1.m1.1.cmml">
<msup xml:id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
<mi xml:id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">S</mi>
<mo xml:id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">′</mo>
</msup>
<annotation-xml encoding="MathML-Content" xml:id="p1.1.m1.1.cmml" xref="p1.1.m1.1">
<apply xml:id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
<csymbol cd="ambiguous" xml:id="p1.1.m1.1.3.1.cmml">superscript</csymbol>
<ci xml:id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">S</ci>
<ci xml:id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">normal-′</ci>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" xml:id="p1.1.m1.1b" xref="p1.1.m1.1.cmml">{\displaystyle S^{{\prime}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=93383c212e2b016a5e66f30d1fc0dd83&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="width: 2.25ex; height: 2ex; vertical-align: -0.25ex; margin-top: 1px; margin-right: 0px; margin-bottom: 1px; margin-left: 0px; position: static; width: 10;" alt="S^{{\prime }}" data-pagespeed-url-hash="2435268494" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S'}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msup>
<mi>S</mi>
<mo>′</mo>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle S'}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/bf9961844d1f539adee019e432dc18aa2a7ede59" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:2.206ex; height:2.509ex;" alt="{\displaystyle S'}" data-pagespeed-url-hash="2004084909" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/22" title="Special:DisplayTopics/22">22</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/4416#math.4416.4" title="Special:PermanentLink/4416">Mayer–Vietoris_sequence-4</a>
</td>
<td> 1
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\text{Ker}}(k_{*}-l_{*})\cong{\text{\qvar@construct{x0}}}(i_{*}% ,j_{*}).}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">
<mrow id="p1.1.m1.1.20a" xref="p1.1.m1.1.20.cmml">
<mrow id="p1.1.m1.1.20.1" xref="p1.1.m1.1.20.1.cmml">
<mtext id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">Ker</mtext>
<mo id="p1.1.m1.1.20.1.1" xref="p1.1.m1.1.20.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.20.1.2b">
<mo stretchy="false" id="p1.1.m1.1.20.1.2">(</mo>
<mrow id="XM1" xref="XM1.cmml">
<msub id="XM1.1" xref="XM1.1.cmml">
<mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">k</mi>
<mo id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">*</mo>
</msub>
<mo id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">-</mo>
<msub id="XM1.2" xref="XM1.2.cmml">
<mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">l</mi>
<mo id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">*</mo>
</msub>
</mrow>
<mo stretchy="false" id="p1.1.m1.1.20.1.2a">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">≅</mo>
<mrow id="p1.1.m1.1.20.2" xref="p1.1.m1.1.20.2.cmml">
<mrow id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml"/>
<mo id="p1.1.m1.1.20.2.1" xref="p1.1.m1.1.20.2.1.cmml"></mo>
<mi mathcolor="red" id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">x0</mi>
<mo id="p1.1.m1.1.20.2.1a" xref="p1.1.m1.1.20.2.1.cmml"></mo>
<mrow id="p1.1.m1.1.20.2.2c" xref="p1.1.m1.1.20.2.2.cmml">
<mo stretchy="false" id="p1.1.m1.1.20.2.2" xref="p1.1.m1.1.20.2.2.cmml">(</mo>
<msub id="XM2" xref="XM2.cmml">
<mi id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">i</mi>
<mo id="p1.1.m1.1.14.1" xref="p1.1.m1.1.14.1.cmml">*</mo>
</msub>
<mo id="p1.1.m1.1.20.2.2a" xref="p1.1.m1.1.20.2.2.cmml">,</mo>
<msub id="XM3" xref="XM3.cmml">
<mi id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">j</mi>
<mo id="p1.1.m1.1.17.1" xref="p1.1.m1.1.17.1.cmml">*</mo>
</msub>
<mo stretchy="false" id="p1.1.m1.1.20.2.2b" xref="p1.1.m1.1.20.2.2.cmml">)</mo>
</mrow>
</mrow>
</mrow>
<mo id="p1.1.m1.1.20b" xref="p1.1.m1.1.20.cmml">.</mo>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">
<approx id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9"/>
<apply id="p1.1.m1.1.20.1.cmml" xref="p1.1.m1.1.20.1">
<times id="p1.1.m1.1.20.1.1.cmml" xref="p1.1.m1.1.20.1.1"/>
<mtext id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">Ker</mtext>
<apply id="XM1.cmml" xref="XM1">
<minus id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/>
<apply id="XM1.1.cmml" xref="XM1.1">
<csymbol cd="ambiguous" id="XM1.1.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">k</ci>
<times id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1"/>
</apply>
<apply id="XM1.2.cmml" xref="XM1.2">
<csymbol cd="ambiguous" id="XM1.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">l</ci>
<times id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1"/>
</apply>
</apply>
</apply>
<apply id="p1.1.m1.1.20.2.cmml" xref="p1.1.m1.1.20.2">
<times id="p1.1.m1.1.20.2.1.cmml" xref="p1.1.m1.1.20.2.1"/>
<mtext id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10"/>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">x0</csymbol>
<interval closure="open" id="p1.1.m1.1.20.2.2.cmml" xref="p1.1.m1.1.20.2.2">
<apply id="XM2.cmml" xref="XM2">
<csymbol cd="ambiguous" id="XM2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">i</ci>
<times id="p1.1.m1.1.14.1.cmml" xref="p1.1.m1.1.14.1"/>
</apply>
<apply id="XM3.cmml" xref="XM3">
<csymbol cd="ambiguous" id="XM3.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">j</ci>
<times id="p1.1.m1.1.17.1.cmml" xref="p1.1.m1.1.17.1"/>
</apply>
</interval>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\text{Ker}}(k_{*}-l_{*})\cong{\text{\qvar@construct{x0}}}(i_{*}%
,j_{*}).}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=55c6253e73dd11e8d9b51cead4ae6e86&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1ex; height: 3ex; width: 126.333ex;" alt="{\text{Ker}}(k_{*}-l_{*})\cong{\text{\qvar{x0}}}(i_{*},j_{*})." data-pagespeed-url-hash="2523754427" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{Ker}}(k_{*}-l_{*})\cong {\text{Im}}(i_{*},j_{*}).}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mtext>Ker</mtext>
</mrow>
<mo stretchy="false">(</mo>
<msub>
<mi>k</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>∗<!-- ∗ --></mo>
</mrow>
</msub>
<mo>−<!-- − --></mo>
<msub>
<mi>l</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>∗<!-- ∗ --></mo>
</mrow>
</msub>
<mo stretchy="false">)</mo>
<mo>≅<!-- ≅ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mtext>Im</mtext>
</mrow>
<mo stretchy="false">(</mo>
<msub>
<mi>i</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>∗<!-- ∗ --></mo>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>j</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>∗<!-- ∗ --></mo>
</mrow>
</msub>
<mo stretchy="false">)</mo>
<mo>.</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\text{Ker}}(k_{*}-l_{*})\cong {\text{Im}}(i_{*},j_{*}).}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/598298bd9e4c4b6819ebea274f45cea0655bfe7b" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:25.648ex; height:2.843ex;" alt="{\displaystyle {\text{Ker}}(k_{*}-l_{*})\cong {\text{Im}}(i_{*},j_{*}).}" data-pagespeed-url-hash="2211582807" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/23" title="Special:DisplayTopics/23">23</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/25343#math.25343.3" title="Special:PermanentLink/25343">Graphlets-3</a>
</td>
<td> 2
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle D(G,H)=\sum_{{i=1}}^{{\qvar@construct{x0}}}|F_{i}(G)-F_{% \qvar@construct{x1}}(H)|}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml">
<mrow id="p1.1.m1.1.24.1" xref="p1.1.m1.1.24.1.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">D</mi>
<mo id="p1.1.m1.1.24.1.1" xref="p1.1.m1.1.24.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.24.1.2c" xref="p1.1.m1.1.24.1.2.cmml">
<mo stretchy="false" id="p1.1.m1.1.24.1.2" xref="p1.1.m1.1.24.1.2.cmml">(</mo>
<mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">G</mi>
<mo id="p1.1.m1.1.24.1.2a" xref="p1.1.m1.1.24.1.2.cmml">,</mo>
<mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">H</mi>
<mo stretchy="false" id="p1.1.m1.1.24.1.2b" xref="p1.1.m1.1.24.1.2.cmml">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">=</mo>
<mrow id="p1.1.m1.1.24.2" xref="p1.1.m1.1.24.2.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.24.2.1" xref="p1.1.m1.1.24.2.1.cmml">
<munderover id="p1.1.m1.1.24.2.1a" xref="p1.1.m1.1.24.2.1.cmml">
<mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">∑</mo>
<mrow id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">
<mi id="p1.1.m1.1.9.1.1" xref="p1.1.m1.1.9.1.1.cmml">i</mi>
<mo id="p1.1.m1.1.9.1.2" xref="p1.1.m1.1.9.1.2.cmml">=</mo>
<mn id="p1.1.m1.1.9.1.3" xref="p1.1.m1.1.9.1.3.cmml">1</mn>
</mrow>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">x0</mi>
</munderover>
</mstyle>
<mrow id="p1.1.m1.1.24.2.2b" xref="p1.1.m1.1.24.2.2.cmml">
<mo stretchy="false" id="p1.1.m1.1.24.2.2" xref="p1.1.m1.1.24.2.2.cmml">|</mo>
<mrow id="XM1" xref="XM1.cmml">
<mrow id="XM1.1" xref="XM1.1.cmml">
<msub id="XM1.1.2" xref="XM1.1.2.cmml">
<mi id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">F</mi>
<mi id="p1.1.m1.1.13.1" xref="p1.1.m1.1.13.1.cmml">i</mi>
</msub>
<mo id="XM1.1.1" xref="XM1.1.1.cmml"></mo>
<mrow id="XM1.1.3b">
<mo stretchy="false" id="XM1.1.3">(</mo>
<mi id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">G</mi>
<mo stretchy="false" id="XM1.1.3a">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">-</mo>
<mrow id="XM1.2" xref="XM1.2.cmml">
<msub id="XM1.2.2" xref="XM1.2.2.cmml">
<mi id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">F</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.19.1" xref="p1.1.m1.1.19.1.cmml">x1</mi>
</msub>
<mo id="XM1.2.1" xref="XM1.2.1.cmml"></mo>
<mrow id="XM1.2.3b">
<mo stretchy="false" id="XM1.2.3">(</mo>
<mi id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">H</mi>
<mo stretchy="false" id="XM1.2.3a">)</mo>
</mrow>
</mrow>
</mrow>
<mo stretchy="false" id="p1.1.m1.1.24.2.2a" xref="p1.1.m1.1.24.2.2.cmml">|</mo>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">
<eq id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
<apply id="p1.1.m1.1.24.1.cmml" xref="p1.1.m1.1.24.1">
<times id="p1.1.m1.1.24.1.1.cmml" xref="p1.1.m1.1.24.1.1"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">D</ci>
<interval closure="open" id="p1.1.m1.1.24.1.2.cmml" xref="p1.1.m1.1.24.1.2">
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">G</ci>
<ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">H</ci>
</interval>
</apply>
<apply id="p1.1.m1.1.24.2.cmml" xref="p1.1.m1.1.24.2">
<apply id="p1.1.m1.1.24.2.1.cmml" xref="p1.1.m1.1.24.2.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.24.2.1.1.cmml">superscript</csymbol>
<apply id="p1.1.m1.1.24.2.1.2.cmml">
<csymbol cd="ambiguous" id="p1.1.m1.1.24.2.1.2.1.cmml">subscript</csymbol>
<sum id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8"/>
<apply id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">
<eq id="p1.1.m1.1.9.1.2.cmml" xref="p1.1.m1.1.9.1.2"/>
<ci id="p1.1.m1.1.9.1.1.cmml" xref="p1.1.m1.1.9.1.1">i</ci>
<cn type="integer" id="p1.1.m1.1.9.1.3.cmml" xref="p1.1.m1.1.9.1.3">1</cn>
</apply>
</apply>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">x0</csymbol>
</apply>
<apply id="p1.1.m1.1.24.2.2a.cmml" xref="p1.1.m1.1.24.2.2">
<abs id="p1.1.m1.1.24.2.2.cmml" xref="p1.1.m1.1.24.2.2"/>
<apply id="XM1.cmml" xref="XM1">
<minus id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17"/>
<apply id="XM1.1.cmml" xref="XM1.1">
<times id="XM1.1.1.cmml" xref="XM1.1.1"/>
<apply id="XM1.1.2.cmml" xref="XM1.1.2">
<csymbol cd="ambiguous" id="XM1.1.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">F</ci>
<ci id="p1.1.m1.1.13.1.cmml" xref="p1.1.m1.1.13.1">i</ci>
</apply>
<ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">G</ci>
</apply>
<apply id="XM1.2.cmml" xref="XM1.2">
<times id="XM1.2.1.cmml" xref="XM1.2.1"/>
<apply id="XM1.2.2.cmml" xref="XM1.2.2">
<csymbol cd="ambiguous" id="XM1.2.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">F</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.19.1.cmml" xref="p1.1.m1.1.19.1">x1</csymbol>
</apply>
<ci id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">H</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle D(G,H)=\sum_{{i=1}}^{{\qvar@construct{x0}}}|F_{i}(G)-F_{%
\qvar@construct{x1}}(H)|}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=3d48b154ec77e37fa634b6e691dcc1eb&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.833ex; height: 7ex; width: 34.333ex;" alt="D(G,H)=\sum_{{i=1}}^{{\qvar{x0}}}|F_{i}(G)-F_{\qvar{x1}}(H)|" data-pagespeed-url-hash="1070409438" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D(G,H)=\sum _{i=1}^{29}|F_{i}(G)-F_{i}(H)|}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>D</mi>
<mo stretchy="false">(</mo>
<mi>G</mi>
<mo>,</mo>
<mi>H</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<munderover>
<mo>∑<!-- ∑ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>29</mn>
</mrow>
</munderover>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">|</mo>
</mrow>
<msub>
<mi>F</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
</mrow>
</msub>
<mo stretchy="false">(</mo>
<mi>G</mi>
<mo stretchy="false">)</mo>
<mo>−<!-- − --></mo>
<msub>
<mi>F</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
</mrow>
</msub>
<mo stretchy="false">(</mo>
<mi>H</mi>
<mo stretchy="false">)</mo>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">|</mo>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle D(G,H)=\sum _{i=1}^{29}|F_{i}(G)-F_{i}(H)|}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/967e4607d29e85a265525cef7d2b79bbbdca9b36" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.005ex; width:31.73ex; height:7.343ex;" alt="{\displaystyle D(G,H)=\sum _{i=1}^{29}|F_{i}(G)-F_{i}(H)|}" data-pagespeed-url-hash="442756807" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/24" title="Special:DisplayTopics/24">24</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/566#math.566.28" title="Special:PermanentLink/566">Kinetic_energy-28</a>
</td>
<td> 2
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle E_{{\text{\qvar@construct{x0}}}}=E_{t}+E_{{\qvar@construct{x1}}% }\,}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">
<msub id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">E</mi>
<mrow id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">
<mrow id="p1.1.m1.1.2.1.1" xref="p1.1.m1.1.2.1.1.cmml"/>
<mo id="p1.1.m1.1.2.1.3" xref="p1.1.m1.1.2.1.3.cmml"></mo>
<mi mathcolor="red" id="p1.1.m1.1.2.1.2" xref="p1.1.m1.1.2.1.2.cmml">x0</mi>
</mrow>
</msub>
<mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">=</mo>
<mrow id="p1.1.m1.1.10.2" xref="p1.1.m1.1.10.2.cmml">
<msub id="p1.1.m1.1.10.2.1" xref="p1.1.m1.1.10.2.1.cmml">
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">E</mi>
<mi id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">t</mi>
</msub>
<mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">+</mo>
<mpadded width="+1.7pt" id="p1.1.m1.1.10.2.2" xref="p1.1.m1.1.10.2.2.cmml">
<msub id="p1.1.m1.1.10.2.2a" xref="p1.1.m1.1.10.2.2.cmml">
<mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">E</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.8.1" xref="p1.1.m1.1.8.1.cmml">x1</mi>
</msub>
</mpadded>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">
<eq id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
<apply id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.10.1.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">E</ci>
<apply id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">
<times id="p1.1.m1.1.2.1.3.cmml" xref="p1.1.m1.1.2.1.3"/>
<mtext id="p1.1.m1.1.2.1.1.cmml" xref="p1.1.m1.1.2.1.1"/>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.2.1.2.cmml" xref="p1.1.m1.1.2.1.2">x0</csymbol>
</apply>
</apply>
<apply id="p1.1.m1.1.10.2.cmml" xref="p1.1.m1.1.10.2">
<plus id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
<apply id="p1.1.m1.1.10.2.1.cmml" xref="p1.1.m1.1.10.2.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.10.2.1.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">E</ci>
<ci id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1">t</ci>
</apply>
<apply id="p1.1.m1.1.10.2.2.cmml" xref="p1.1.m1.1.10.2.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.10.2.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">E</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.1">x1</csymbol>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle E_{{\text{\qvar@construct{x0}}}}=E_{t}+E_{{\qvar@construct{x1}}%
}\,}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=4122d0f45374afb48de4935bc5baa488&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.5ex; height: 2ex; width: 16.667ex;" alt="E_{{\text{\qvar{x0}}}}=E_{t}+E_{{\qvar{x1}}}\," data-pagespeed-url-hash="2484615410" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\text{k}}=E_{t}+E_{\text{r}}\,}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>E</mi>
<mrow class="MJX-TeXAtom-ORD">
<mtext>k</mtext>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>E</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>t</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>E</mi>
<mrow class="MJX-TeXAtom-ORD">
<mtext>r</mtext>
</mrow>
</msub>
<mspace width="thinmathspace"/>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle E_{\text{k}}=E_{t}+E_{\text{r}}\,}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/d02acf771c5c5e88525a9b5895990cdc5302a350" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:14.275ex; height:2.509ex;" alt="{\displaystyle E_{\text{k}}=E_{t}+E_{\text{r}}\,}" data-pagespeed-url-hash="1976339683" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/25" title="Special:DisplayTopics/25">25</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/22618#math.22618.22" title="Special:PermanentLink/22618">Lattice_problem-22</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\lambda(L(B))\leq d}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">
<mrow id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">λ</mi>
<mo id="p1.1.m1.1.10.1.1" xref="p1.1.m1.1.10.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.10.1.2b">
<mo stretchy="false" id="p1.1.m1.1.10.1.2">(</mo>
<mrow id="XM1" xref="XM1.cmml">
<mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">L</mi>
<mo id="XM1.1" xref="XM1.1.cmml"></mo>
<mrow id="XM1.2b">
<mo stretchy="false" id="XM1.2">(</mo>
<mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">B</mi>
<mo stretchy="false" id="XM1.2a">)</mo>
</mrow>
</mrow>
<mo stretchy="false" id="p1.1.m1.1.10.1.2a">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">≤</mo>
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">d</mi>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">
<leq id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8"/>
<apply id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">
<times id="p1.1.m1.1.10.1.1.cmml" xref="p1.1.m1.1.10.1.1"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">λ</ci>
<apply id="XM1.cmml" xref="XM1">
<times id="XM1.1.cmml" xref="XM1.1"/>
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">L</ci>
<ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">B</ci>
</apply>
</apply>
<ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">d</ci>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\lambda(L(B))\leq d}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=2d793a758f787981775929782a75d2ca&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.5ex; width: 13.5ex;" alt="\lambda (L(B))\leq d" data-pagespeed-url-hash="754771858" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda (L(B))\leq d}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>λ<!-- λ --></mi>
<mo stretchy="false">(</mo>
<mi>L</mi>
<mo stretchy="false">(</mo>
<mi>B</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">)</mo>
<mo>≤<!-- ≤ --></mo>
<mi>d</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \lambda (L(B))\leq d}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/7191449065b5d0f3d771a02e92368d805a0c72b7" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:12.635ex; height:2.843ex;" alt="{\displaystyle \lambda (L(B))\leq d}" data-pagespeed-url-hash="1149454859" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/26" title="Special:DisplayTopics/26">26</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/485#math.485.10" title="Special:PermanentLink/485">Huffman_coding-10</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle L\left(C\right)\leq L\left(T\right)}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">
<mrow id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">L</mi>
<mo id="p1.1.m1.1.10.1.1" xref="p1.1.m1.1.10.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.10.1.2b">
<mo id="p1.1.m1.1.10.1.2">(</mo>
<mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">C</mi>
<mo id="p1.1.m1.1.10.1.2a">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">≤</mo>
<mrow id="p1.1.m1.1.10.2" xref="p1.1.m1.1.10.2.cmml">
<mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">L</mi>
<mo id="p1.1.m1.1.10.2.1" xref="p1.1.m1.1.10.2.1.cmml"></mo>
<mrow id="p1.1.m1.1.10.2.2b">
<mo id="p1.1.m1.1.10.2.2">(</mo>
<mi id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">T</mi>
<mo id="p1.1.m1.1.10.2.2a">)</mo>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">
<leq id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/>
<apply id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">
<times id="p1.1.m1.1.10.1.1.cmml" xref="p1.1.m1.1.10.1.1"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">L</ci>
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">C</ci>
</apply>
<apply id="p1.1.m1.1.10.2.cmml" xref="p1.1.m1.1.10.2">
<times id="p1.1.m1.1.10.2.1.cmml" xref="p1.1.m1.1.10.2.1"/>
<ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">L</ci>
<ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">T</ci>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle L\left(C\right)\leq L\left(T\right)}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=6d116e62c20fd0d61cf31e3ab8b70303&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.5ex; width: 14.167ex;" alt="L\left(C\right)\leq L\left(T\right)" data-pagespeed-url-hash="763319691" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L\left(C\right)\leq L\left(T\right)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>L</mi>
<mrow>
<mo>(</mo>
<mi>C</mi>
<mo>)</mo>
</mrow>
<mo>≤<!-- ≤ --></mo>
<mi>L</mi>
<mrow>
<mo>(</mo>
<mi>T</mi>
<mo>)</mo>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle L\left(C\right)\leq L\left(T\right)}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/6e6665e9af506721382168d97210f1ae13d39a40" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:14.06ex; height:2.843ex;" alt="{\displaystyle L\left(C\right)\leq L\left(T\right)}" data-pagespeed-url-hash="1964797772" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/27" title="Special:DisplayTopics/27">27</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/2623#math.2623.0" title="Special:PermanentLink/2623">Dispersion_(optics)-0</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle v={{\frac{c}{n}}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">v</mi>
<mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">=</mo>
<mstyle displaystyle="true" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
<mfrac id="p1.1.m1.1.3a" xref="p1.1.m1.1.3.cmml">
<mi id="p1.1.m1.1.3.2" xref="p1.1.m1.1.3.2.cmml">c</mi>
<mi id="p1.1.m1.1.3.3" xref="p1.1.m1.1.3.3.cmml">n</mi>
</mfrac>
</mstyle>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">
<eq id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">v</ci>
<apply id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
<divide id="p1.1.m1.1.3.1.cmml"/>
<ci id="p1.1.m1.1.3.2.cmml" xref="p1.1.m1.1.3.2">c</ci>
<ci id="p1.1.m1.1.3.3.cmml" xref="p1.1.m1.1.3.3">n</ci>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle v={{\frac{c}{n}}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=282482f29b5c344df9559aeffe1d29f1&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.667ex; height: 4.333ex; width: 6.5ex;" alt="v={{\frac {c}{n}}}" data-pagespeed-url-hash="1695102123" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v={\frac {c}{n}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>v</mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>c</mi>
<mi>n</mi>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle v={\frac {c}{n}}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/6d5004b06289deee6cb0c0b7d310ed0f7b192ac4" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.838ex; width:6.457ex; height:4.676ex;" alt="{\displaystyle v={\frac {c}{n}}}" data-pagespeed-url-hash="3237660153" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/28" title="Special:DisplayTopics/28">28</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/1227#math.1227.93" title="Special:PermanentLink/1227">Allan_variance-93</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\sigma_{{y}}^{{2}}(\tau)={{\frac{2\pi^{{2}}\tau}{3}}}h_{{{-2}}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">
<mrow id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml">
<msubsup id="p1.1.m1.1.11.1.2" xref="p1.1.m1.1.11.1.2.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">σ</mi>
<mi id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">y</mi>
<mn id="p1.1.m1.1.3.1" xref="p1.1.m1.1.3.1.cmml">2</mn>
</msubsup>
<mo id="p1.1.m1.1.11.1.1" xref="p1.1.m1.1.11.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.11.1.3b">
<mo stretchy="false" id="p1.1.m1.1.11.1.3">(</mo>
<mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">τ</mi>
<mo stretchy="false" id="p1.1.m1.1.11.1.3a">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">=</mo>
<mrow id="p1.1.m1.1.11.2" xref="p1.1.m1.1.11.2.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">
<mfrac id="p1.1.m1.1.8a" xref="p1.1.m1.1.8.cmml">
<mrow id="p1.1.m1.1.8.2" xref="p1.1.m1.1.8.2.cmml">
<mn id="p1.1.m1.1.8.2.1" xref="p1.1.m1.1.8.2.1.cmml">2</mn>
<mo id="p1.1.m1.1.8.2.5" xref="p1.1.m1.1.8.2.5.cmml"></mo>
<msup id="p1.1.m1.1.8.2.6" xref="p1.1.m1.1.8.2.6.cmml">
<mi id="p1.1.m1.1.8.2.2" xref="p1.1.m1.1.8.2.2.cmml">π</mi>
<mn id="p1.1.m1.1.8.2.3.1" xref="p1.1.m1.1.8.2.3.1.cmml">2</mn>
</msup>
<mo id="p1.1.m1.1.8.2.5a" xref="p1.1.m1.1.8.2.5.cmml"></mo>
<mi id="p1.1.m1.1.8.2.4" xref="p1.1.m1.1.8.2.4.cmml">τ</mi>
</mrow>
<mn id="p1.1.m1.1.8.3" xref="p1.1.m1.1.8.3.cmml">3</mn>
</mfrac>
</mstyle>
<mo id="p1.1.m1.1.11.2.1" xref="p1.1.m1.1.11.2.1.cmml"></mo>
<msub id="p1.1.m1.1.11.2.2" xref="p1.1.m1.1.11.2.2.cmml">
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">h</mi>
<mrow id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">
<mo id="p1.1.m1.1.10.1.1" xref="p1.1.m1.1.10.1.1.cmml">-</mo>
<mn id="p1.1.m1.1.10.1.2" xref="p1.1.m1.1.10.1.2.cmml">2</mn>
</mrow>
</msub>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">
<eq id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
<apply id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1">
<times id="p1.1.m1.1.11.1.1.cmml" xref="p1.1.m1.1.11.1.1"/>
<apply id="p1.1.m1.1.11.1.2.cmml" xref="p1.1.m1.1.11.1.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.11.1.2.1.cmml">superscript</csymbol>
<apply id="p1.1.m1.1.11.1.2.2.cmml">
<csymbol cd="ambiguous" id="p1.1.m1.1.11.1.2.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">σ</ci>
<ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">y</ci>
</apply>
<cn type="integer" id="p1.1.m1.1.3.1.cmml" xref="p1.1.m1.1.3.1">2</cn>
</apply>
<ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">τ</ci>
</apply>
<apply id="p1.1.m1.1.11.2.cmml" xref="p1.1.m1.1.11.2">
<times id="p1.1.m1.1.11.2.1.cmml" xref="p1.1.m1.1.11.2.1"/>
<apply id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">
<divide id="p1.1.m1.1.8.1.cmml"/>
<apply id="p1.1.m1.1.8.2.cmml" xref="p1.1.m1.1.8.2">
<times id="p1.1.m1.1.8.2.5.cmml" xref="p1.1.m1.1.8.2.5"/>
<cn type="integer" id="p1.1.m1.1.8.2.1.cmml" xref="p1.1.m1.1.8.2.1">2</cn>
<apply id="p1.1.m1.1.8.2.6.cmml" xref="p1.1.m1.1.8.2.6">
<csymbol cd="ambiguous" id="p1.1.m1.1.8.2.6.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.8.2.2.cmml" xref="p1.1.m1.1.8.2.2">π</ci>
<cn type="integer" id="p1.1.m1.1.8.2.3.1.cmml" xref="p1.1.m1.1.8.2.3.1">2</cn>
</apply>
<ci id="p1.1.m1.1.8.2.4.cmml" xref="p1.1.m1.1.8.2.4">τ</ci>
</apply>
<cn type="integer" id="p1.1.m1.1.8.3.cmml" xref="p1.1.m1.1.8.3">3</cn>
</apply>
<apply id="p1.1.m1.1.11.2.2.cmml" xref="p1.1.m1.1.11.2.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.11.2.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">h</ci>
<apply id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">
<minus id="p1.1.m1.1.10.1.1.cmml" xref="p1.1.m1.1.10.1.1"/>
<cn type="integer" id="p1.1.m1.1.10.1.2.cmml" xref="p1.1.m1.1.10.1.2">2</cn>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\sigma_{{y}}^{{2}}(\tau)={{\frac{2\pi^{{2}}\tau}{3}}}h_{{{-2}}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=3093d27bb443222909e9ea4014f02053&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.833ex; height: 5.333ex; width: 18.667ex;" alt="\sigma _{{y}}^{{2}}(\tau )={{\frac {2\pi ^{{2}}\tau }{3}}}h_{{{-2}}}" data-pagespeed-url-hash="103528131" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma _{y}^{2}(\tau )={\frac {2\pi ^{2}\tau }{3}}h_{-2}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msubsup>
<mi>σ<!-- σ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>y</mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msubsup>
<mo stretchy="false">(</mo>
<mi>τ<!-- τ --></mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mn>2</mn>
<msup>
<mi>π<!-- π --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mi>τ<!-- τ --></mi>
</mrow>
<mn>3</mn>
</mfrac>
</mrow>
<msub>
<mi>h</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>−<!-- − --></mo>
<mn>2</mn>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \sigma _{y}^{2}(\tau )={\frac {2\pi ^{2}\tau }{3}}h_{-2}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/0c588e5aabecf62f18a94156c6080444dd60adfe" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.838ex; width:17.755ex; height:5.676ex;" alt="{\displaystyle \sigma _{y}^{2}(\tau )={\frac {2\pi ^{2}\tau }{3}}h_{-2}}" data-pagespeed-url-hash="4250818243" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/29" title="Special:DisplayTopics/29">29</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/21692#math.21692.5" title="Special:PermanentLink/21692">Superconducting_radio_frequency-5</a>
</td>
<td> 1
</td>
<td> 6
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle R_{{s\ normal}}={\sqrt{\qvar@construct{x0}}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">
<msub id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">R</mi>
<mrow id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">
<mpadded width="+5pt" id="p1.1.m1.1.2.1.1" xref="p1.1.m1.1.2.1.1.cmml">
<mi id="p1.1.m1.1.2.1.1a" xref="p1.1.m1.1.2.1.1.cmml">s</mi>
</mpadded>
<mo id="p1.1.m1.1.2.1.9" xref="p1.1.m1.1.2.1.9.cmml"></mo>
<mi id="p1.1.m1.1.2.1.3" xref="p1.1.m1.1.2.1.3.cmml">n</mi>
<mo id="p1.1.m1.1.2.1.9a" xref="p1.1.m1.1.2.1.9.cmml"></mo>
<mi id="p1.1.m1.1.2.1.4" xref="p1.1.m1.1.2.1.4.cmml">o</mi>
<mo id="p1.1.m1.1.2.1.9b" xref="p1.1.m1.1.2.1.9.cmml"></mo>
<mi id="p1.1.m1.1.2.1.5" xref="p1.1.m1.1.2.1.5.cmml">r</mi>
<mo id="p1.1.m1.1.2.1.9c" xref="p1.1.m1.1.2.1.9.cmml"></mo>
<mi id="p1.1.m1.1.2.1.6" xref="p1.1.m1.1.2.1.6.cmml">m</mi>
<mo id="p1.1.m1.1.2.1.9d" xref="p1.1.m1.1.2.1.9.cmml"></mo>
<mi id="p1.1.m1.1.2.1.7" xref="p1.1.m1.1.2.1.7.cmml">a</mi>
<mo id="p1.1.m1.1.2.1.9e" xref="p1.1.m1.1.2.1.9.cmml"></mo>
<mi id="p1.1.m1.1.2.1.8" xref="p1.1.m1.1.2.1.8.cmml">l</mi>
</mrow>
</msub>
<mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">=</mo>
<msqrt id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.4.2" xref="p1.1.m1.1.4.2.cmml">x0</mi>
</msqrt>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">
<eq id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
<apply id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.5.1.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">R</ci>
<apply id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">
<times id="p1.1.m1.1.2.1.9.cmml" xref="p1.1.m1.1.2.1.9"/>
<ci id="p1.1.m1.1.2.1.1.cmml" xref="p1.1.m1.1.2.1.1">s</ci>
<ci id="p1.1.m1.1.2.1.3.cmml" xref="p1.1.m1.1.2.1.3">n</ci>
<ci id="p1.1.m1.1.2.1.4.cmml" xref="p1.1.m1.1.2.1.4">o</ci>
<ci id="p1.1.m1.1.2.1.5.cmml" xref="p1.1.m1.1.2.1.5">r</ci>
<ci id="p1.1.m1.1.2.1.6.cmml" xref="p1.1.m1.1.2.1.6">m</ci>
<ci id="p1.1.m1.1.2.1.7.cmml" xref="p1.1.m1.1.2.1.7">a</ci>
<ci id="p1.1.m1.1.2.1.8.cmml" xref="p1.1.m1.1.2.1.8">l</ci>
</apply>
</apply>
<apply id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">
<root id="p1.1.m1.1.4a.cmml" xref="p1.1.m1.1.4"/>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.4.2.cmml" xref="p1.1.m1.1.4.2">x0</csymbol>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle R_{{s\ normal}}={\sqrt{\qvar@construct{x0}}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=840c1706ca9ae55c8527fa5d82130bd4&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.5ex; height: 2.5ex; width: 17ex;" alt="R_{{s\ normal}}={\sqrt{\qvar{x0}}}" data-pagespeed-url-hash="3672726228" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{s\ normal}={\sqrt {\frac {\omega \mu _{0}}{2\sigma }}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>R</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>s</mi>
<mtext> </mtext>
<mi>n</mi>
<mi>o</mi>
<mi>r</mi>
<mi>m</mi>
<mi>a</mi>
<mi>l</mi>
</mrow>
</msub>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mfrac>
<mrow>
<mi>ω<!-- ω --></mi>
<msub>
<mi>μ<!-- μ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>0</mn>
</mrow>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<mi>σ<!-- σ --></mi>
</mrow>
</mfrac>
</msqrt>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle R_{s\ normal}={\sqrt {\frac {\omega \mu _{0}}{2\sigma }}}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/58e8c2efe66b484d47f3715b7cdfcf6d51ac2808" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.505ex; width:18.836ex; height:6.176ex;" alt="{\displaystyle R_{s\ normal}={\sqrt {\frac {\omega \mu _{0}}{2\sigma }}}}" data-pagespeed-url-hash="181049970" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/30" title="Special:DisplayTopics/30">30</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/24277#math.24277.5" title="Special:PermanentLink/24277">Vienna_rectifier-5</a>
</td>
<td> 1
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\phi_{1}=-30^{\circ}...+30^{\qvar@construct{x0}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">
<msub id="p1.1.m1.1.15.1" xref="p1.1.m1.1.15.1.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">ϕ</mi>
<mn id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">1</mn>
</msub>
<mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">=</mo>
<mrow id="p1.1.m1.1.15.2" xref="p1.1.m1.1.15.2.cmml">
<mrow id="p1.1.m1.1.15.2.1" xref="p1.1.m1.1.15.2.1.cmml">
<mo id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">-</mo>
<mrow id="p1.1.m1.1.15.2.1.1" xref="p1.1.m1.1.15.2.1.1.cmml">
<msup id="p1.1.m1.1.15.2.1.1.2" xref="p1.1.m1.1.15.2.1.1.2.cmml">
<mn id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">30</mn>
<mo id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">∘</mo>
</msup>
<mo id="p1.1.m1.1.15.2.1.1.1" xref="p1.1.m1.1.15.2.1.1.1.cmml"></mo>
<mi mathvariant="normal" id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">…</mi>
</mrow>
</mrow>
<mo id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">+</mo>
<msup id="p1.1.m1.1.15.2.2" xref="p1.1.m1.1.15.2.2.cmml">
<mn id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">30</mn>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.14.1" xref="p1.1.m1.1.14.1.cmml">x0</mi>
</msup>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">
<eq id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
<apply id="p1.1.m1.1.15.1.cmml" xref="p1.1.m1.1.15.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.15.1.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">ϕ</ci>
<cn type="integer" id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">1</cn>
</apply>
<apply id="p1.1.m1.1.15.2.cmml" xref="p1.1.m1.1.15.2">
<plus id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11"/>
<apply id="p1.1.m1.1.15.2.1.cmml" xref="p1.1.m1.1.15.2.1">
<minus id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4"/>
<apply id="p1.1.m1.1.15.2.1.1.cmml" xref="p1.1.m1.1.15.2.1.1">
<times id="p1.1.m1.1.15.2.1.1.1.cmml" xref="p1.1.m1.1.15.2.1.1.1"/>
<apply id="p1.1.m1.1.15.2.1.1.2.cmml" xref="p1.1.m1.1.15.2.1.1.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.15.2.1.1.2.1.cmml">superscript</csymbol>
<cn type="integer" id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">30</cn>
<compose id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1"/>
</apply>
<ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">normal-…</ci>
</apply>
</apply>
<apply id="p1.1.m1.1.15.2.2.cmml" xref="p1.1.m1.1.15.2.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.15.2.2.1.cmml">superscript</csymbol>
<cn type="integer" id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">30</cn>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.14.1.cmml" xref="p1.1.m1.1.14.1">x0</csymbol>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\phi_{1}=-30^{\circ}...+30^{\qvar@construct{x0}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=afee66ff339d7526099698a9dc1910d3&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.5ex; height: 2.667ex; width: 20.833ex;" alt="\phi_{1}=-30^{\circ}...+30^{\qvar{x0}}" data-pagespeed-url-hash="428640305" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi _{1}=-30^{\circ }...+30^{\circ }}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>ϕ<!-- ϕ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<mo>−<!-- − --></mo>
<msup>
<mn>30</mn>
<mrow class="MJX-TeXAtom-ORD">
<mo>∘<!-- ∘ --></mo>
</mrow>
</msup>
<mo>.</mo>
<mo>.</mo>
<mo>.</mo>
<mo>+</mo>
<msup>
<mn>30</mn>
<mrow class="MJX-TeXAtom-ORD">
<mo>∘<!-- ∘ --></mo>
</mrow>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \phi _{1}=-30^{\circ }...+30^{\circ }}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/269c68e677d36ca3b4594df622220dd277172588" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:19.015ex; height:2.676ex;" alt="{\displaystyle \phi _{1}=-30^{\circ }...+30^{\circ }}" data-pagespeed-url-hash="3954681361" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/31" title="Special:DisplayTopics/31">31</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/3625#math.3625.19" title="Special:PermanentLink/3625">Modigliani–Miller_theorem-19</a>
</td>
<td> 0
</td>
<td> 54
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{c}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>c</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle T_{c}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=77dafb06f9703e07915e68e4b07e5d81&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; height: 2.509ex; width: 2.302ex;" alt="{\displaystyle T_{c}}" data-pagespeed-url-hash="1727865232" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{c}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>c</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle T_{c}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/66261e3cbed8035b2bf7a9ccb878c786cf7556c6" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:2.302ex; height:2.509ex;" alt="{\displaystyle T_{c}}" data-pagespeed-url-hash="2918242607" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/32" title="Special:DisplayTopics/32">32</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/17517#math.17517.2" title="Special:PermanentLink/17517">Proximity_effect_(superconductivity)-2</a>
</td>
<td> 0
</td>
<td> 54
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{c}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>c</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle T_{c}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=77dafb06f9703e07915e68e4b07e5d81&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; height: 2.509ex; width: 2.302ex;" alt="{\displaystyle T_{c}}" data-pagespeed-url-hash="1727865232" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{c}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>c</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle T_{c}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/66261e3cbed8035b2bf7a9ccb878c786cf7556c6" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:2.302ex; height:2.509ex;" alt="{\displaystyle T_{c}}" data-pagespeed-url-hash="2918242607" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/33" title="Special:DisplayTopics/33">33</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/22538#math.22538.9" title="Special:PermanentLink/22538">Multicritical_point-9</a>
</td>
<td> 1
</td>
<td> 54
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle T_{\qvar@construct{x0}}}">
<semantics id="p1.1.m1.1a">
<msub id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">T</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">x0</mi>
</msub>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
<csymbol cd="ambiguous" id="p1.1.m1.1.3.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">T</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">x0</csymbol>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle T_{\qvar@construct{x0}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=73d7f89bf4a37aba4c0c260dc4d0968a&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.5ex; height: 2ex; width: 3.333ex;" alt="T_{\qvar{x0}}" data-pagespeed-url-hash="1491583333" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{c}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>c</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle T_{c}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/66261e3cbed8035b2bf7a9ccb878c786cf7556c6" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:2.302ex; height:2.509ex;" alt="{\displaystyle T_{c}}" data-pagespeed-url-hash="2918242607" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/34" title="Special:DisplayTopics/34">34</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/17497#math.17497.55" title="Special:PermanentLink/17497">Jenkins–Traub_algorithm-55</a>
</td>
<td> 1
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle P_{1}(X)=P(X)/(X-\alpha_{\qvar@construct{x0}})}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">
<mrow id="p1.1.m1.1.18.1" xref="p1.1.m1.1.18.1.cmml">
<msub id="p1.1.m1.1.18.1.2" xref="p1.1.m1.1.18.1.2.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">P</mi>
<mn id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">1</mn>
</msub>
<mo id="p1.1.m1.1.18.1.1" xref="p1.1.m1.1.18.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.18.1.3b">
<mo stretchy="false" id="p1.1.m1.1.18.1.3">(</mo>
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">X</mi>
<mo stretchy="false" id="p1.1.m1.1.18.1.3a">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">=</mo>
<mrow id="p1.1.m1.1.18.2" xref="p1.1.m1.1.18.2.cmml">
<mrow id="p1.1.m1.1.18.2.1" xref="p1.1.m1.1.18.2.1.cmml">
<mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">P</mi>
<mo id="p1.1.m1.1.18.2.1.1" xref="p1.1.m1.1.18.2.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.18.2.1.2b">
<mo stretchy="false" id="p1.1.m1.1.18.2.1.2">(</mo>
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">X</mi>
<mo stretchy="false" id="p1.1.m1.1.18.2.1.2a">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">/</mo>
<mrow id="p1.1.m1.1.18.2.2b">
<mo stretchy="false" id="p1.1.m1.1.18.2.2">(</mo>
<mrow id="XM1" xref="XM1.cmml">
<mi id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">X</mi>
<mo id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">-</mo>
<msub id="XM1.1" xref="XM1.1.cmml">
<mi id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">α</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.16.1" xref="p1.1.m1.1.16.1.cmml">x0</mi>
</msub>
</mrow>
<mo stretchy="false" id="p1.1.m1.1.18.2.2a">)</mo>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">
<eq id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
<apply id="p1.1.m1.1.18.1.cmml" xref="p1.1.m1.1.18.1">
<times id="p1.1.m1.1.18.1.1.cmml" xref="p1.1.m1.1.18.1.1"/>
<apply id="p1.1.m1.1.18.1.2.cmml" xref="p1.1.m1.1.18.1.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.18.1.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">P</ci>
<cn type="integer" id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">1</cn>
</apply>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">X</ci>
</apply>
<apply id="p1.1.m1.1.18.2.cmml" xref="p1.1.m1.1.18.2">
<divide id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11"/>
<apply id="p1.1.m1.1.18.2.1.cmml" xref="p1.1.m1.1.18.2.1">
<times id="p1.1.m1.1.18.2.1.1.cmml" xref="p1.1.m1.1.18.2.1.1"/>
<ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">P</ci>
<ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">X</ci>
</apply>
<apply id="XM1.cmml" xref="XM1">
<minus id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14"/>
<ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">X</ci>
<apply id="XM1.1.cmml" xref="XM1.1">
<csymbol cd="ambiguous" id="XM1.1.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">α</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.16.1.cmml" xref="p1.1.m1.1.16.1">x0</csymbol>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle P_{1}(X)=P(X)/(X-\alpha_{\qvar@construct{x0}})}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=0d1843701946690b33d9df4d12050984&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.5ex; width: 28ex;" alt="P_{1}(X)=P(X)/(X-\alpha_{\qvar{x0}})" data-pagespeed-url-hash="3404803517" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{1}(X)=P(X)/(X-\alpha _{1})}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>P</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>P</mi>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo stretchy="false">)</mo>
<mrow class="MJX-TeXAtom-ORD">
<mo>/</mo>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo>−<!-- − --></mo>
<msub>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle P_{1}(X)=P(X)/(X-\alpha _{1})}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/8abf0becc00090f1cefaa754eb6e1d02059ba84f" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:25.303ex; height:2.843ex;" alt="{\displaystyle P_{1}(X)=P(X)/(X-\alpha _{1})}" data-pagespeed-url-hash="3599427371" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/35" title="Special:DisplayTopics/35">35</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/5626#math.5626.4" title="Special:PermanentLink/5626">Doomsday_argument-4</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle={{\frac{k}{n}}}.}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">
<mrow id="p1.1.m1.1.4a" xref="p1.1.m1.1.4.cmml">
<mi id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml"/>
<mo id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">=</mo>
<mstyle displaystyle="true" id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">
<mfrac id="p1.1.m1.1.2a" xref="p1.1.m1.1.2.cmml">
<mi id="p1.1.m1.1.2.2" xref="p1.1.m1.1.2.2.cmml">k</mi>
<mi id="p1.1.m1.1.2.3" xref="p1.1.m1.1.2.3.cmml">n</mi>
</mfrac>
</mstyle>
</mrow>
<mo id="p1.1.m1.1.4b" xref="p1.1.m1.1.4.cmml">.</mo>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">
<eq id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1"/>
<csymbol cd="latexml" id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">absent</csymbol>
<apply id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">
<divide id="p1.1.m1.1.2.1.cmml"/>
<ci id="p1.1.m1.1.2.2.cmml" xref="p1.1.m1.1.2.2">k</ci>
<ci id="p1.1.m1.1.2.3.cmml" xref="p1.1.m1.1.2.3">n</ci>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle={{\frac{k}{n}}}.}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=89afb99a82a8e7e3e0a672a27a798ff3&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.667ex; height: 4.833ex; width: 4.667ex;" alt="={{\frac {k}{n}}}." data-pagespeed-url-hash="119175044" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ={\frac {k}{n}}.}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>k</mi>
<mi>n</mi>
</mfrac>
</mrow>
<mo>.</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle ={\frac {k}{n}}.}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/bb0f89bd7b0a370574e7e3f3d743f7381cfc5747" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.838ex; width:5.331ex; height:5.343ex;" alt="{\displaystyle ={\frac {k}{n}}.}" data-pagespeed-url-hash="1708568601" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/36" title="Special:DisplayTopics/36">36</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/4630#math.4630.12" title="Special:PermanentLink/4630">Divisor_function-12</a>
</td>
<td> 1
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle n=\prod_{{i=1}}^{r}p_{i}^{{\qvar@construct{x0}}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">n</mi>
<mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">=</mo>
<mrow id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.9.1.1" xref="p1.1.m1.1.9.1.1.cmml">
<munderover id="p1.1.m1.1.9.1.1a" xref="p1.1.m1.1.9.1.1.cmml">
<mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">∏</mo>
<mrow id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">
<mi id="p1.1.m1.1.4.1.1" xref="p1.1.m1.1.4.1.1.cmml">i</mi>
<mo id="p1.1.m1.1.4.1.2" xref="p1.1.m1.1.4.1.2.cmml">=</mo>
<mn id="p1.1.m1.1.4.1.3" xref="p1.1.m1.1.4.1.3.cmml">1</mn>
</mrow>
<mi id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">r</mi>
</munderover>
</mstyle>
<msubsup id="p1.1.m1.1.9.1.2" xref="p1.1.m1.1.9.1.2.cmml">
<mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">p</mi>
<mi id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">i</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.8.1" xref="p1.1.m1.1.8.1.cmml">x0</mi>
</msubsup>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">
<eq id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">n</ci>
<apply id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">
<apply id="p1.1.m1.1.9.1.1.cmml" xref="p1.1.m1.1.9.1.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.9.1.1.1.cmml">superscript</csymbol>
<apply id="p1.1.m1.1.9.1.1.2.cmml">
<csymbol cd="ambiguous" id="p1.1.m1.1.9.1.1.2.1.cmml">subscript</csymbol>
<csymbol cd="latexml" id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">product</csymbol>
<apply id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">
<eq id="p1.1.m1.1.4.1.2.cmml" xref="p1.1.m1.1.4.1.2"/>
<ci id="p1.1.m1.1.4.1.1.cmml" xref="p1.1.m1.1.4.1.1">i</ci>
<cn type="integer" id="p1.1.m1.1.4.1.3.cmml" xref="p1.1.m1.1.4.1.3">1</cn>
</apply>
</apply>
<ci id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1">r</ci>
</apply>
<apply id="p1.1.m1.1.9.1.2.cmml" xref="p1.1.m1.1.9.1.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.9.1.2.1.cmml">superscript</csymbol>
<apply id="p1.1.m1.1.9.1.2.2.cmml">
<csymbol cd="ambiguous" id="p1.1.m1.1.9.1.2.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">p</ci>
<ci id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">i</ci>
</apply>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.1">x0</csymbol>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle n=\prod_{{i=1}}^{r}p_{i}^{{\qvar@construct{x0}}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=5145b5149bd3848fb2110616a35c26a4&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.833ex; height: 6.5ex; width: 11.167ex;" alt="n=\prod_{{i=1}}^{r}p_{i}^{{\qvar{x0}}}" data-pagespeed-url-hash="1075310570" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=\prod _{i=1}^{r}p_{i}^{a_{i}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>n</mi>
<mo>=</mo>
<munderover>
<mo>∏<!-- ∏ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi>r</mi>
</mrow>
</munderover>
<msubsup>
<mi>p</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<msub>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
</mrow>
</msub>
</mrow>
</msubsup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle n=\prod _{i=1}^{r}p_{i}^{a_{i}}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/838611821c9b7161f6f5db4db73a4058a51d757b" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.005ex; width:10.746ex; height:6.843ex;" alt="{\displaystyle n=\prod _{i=1}^{r}p_{i}^{a_{i}}}" data-pagespeed-url-hash="1342617759" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/37" title="Special:DisplayTopics/37">37</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/8338#math.8338.87" title="Special:PermanentLink/8338">LTI_system_theory-87</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle H(j\omega)={{\mathcal{F}}}\{h(t)\}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">
<mrow id="p1.1.m1.1.14.1" xref="p1.1.m1.1.14.1.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">H</mi>
<mo id="p1.1.m1.1.14.1.1" xref="p1.1.m1.1.14.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.14.1.2b">
<mo stretchy="false" id="p1.1.m1.1.14.1.2">(</mo>
<mrow id="XM1" xref="XM1.cmml">
<mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">j</mi>
<mo id="XM1.1" xref="XM1.1.cmml"></mo>
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">ω</mi>
</mrow>
<mo stretchy="false" id="p1.1.m1.1.14.1.2a">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">=</mo>
<mrow id="p1.1.m1.1.14.2" xref="p1.1.m1.1.14.2.cmml">
<mi class="ltx_font_mathcaligraphic" id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">ℱ</mi>
<mo id="p1.1.m1.1.14.2.1" xref="p1.1.m1.1.14.2.1.cmml"></mo>
<mrow id="p1.1.m1.1.14.2.2b" xref="p1.1.m1.1.14.2.2.cmml">
<mo stretchy="false" id="p1.1.m1.1.14.2.2" xref="p1.1.m1.1.14.2.2.cmml">{</mo>
<mrow id="XM2" xref="XM2.cmml">
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">h</mi>
<mo id="XM2.1" xref="XM2.1.cmml"></mo>
<mrow id="XM2.2b">
<mo stretchy="false" id="XM2.2">(</mo>
<mi id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">t</mi>
<mo stretchy="false" id="XM2.2a">)</mo>
</mrow>
</mrow>
<mo stretchy="false" id="p1.1.m1.1.14.2.2a" xref="p1.1.m1.1.14.2.2.cmml">}</mo>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">
<eq id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
<apply id="p1.1.m1.1.14.1.cmml" xref="p1.1.m1.1.14.1">
<times id="p1.1.m1.1.14.1.1.cmml" xref="p1.1.m1.1.14.1.1"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">H</ci>
<apply id="XM1.cmml" xref="XM1">
<times id="XM1.1.cmml" xref="XM1.1"/>
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">j</ci>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">ω</ci>
</apply>
</apply>
<apply id="p1.1.m1.1.14.2.cmml" xref="p1.1.m1.1.14.2">
<times id="p1.1.m1.1.14.2.1.cmml" xref="p1.1.m1.1.14.2.1"/>
<ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">ℱ</ci>
<set id="p1.1.m1.1.14.2.2.cmml" xref="p1.1.m1.1.14.2.2">
<apply id="XM2.cmml" xref="XM2">
<times id="XM2.1.cmml" xref="XM2.1"/>
<ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">h</ci>
<ci id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">t</ci>
</apply>
</set>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle H(j\omega)={{\mathcal{F}}}\{h(t)\}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=698695593978da27478094ef15004f7a&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.5ex; width: 19.333ex;" alt="H(j\omega )={{\mathcal {F}}}\{h(t)\}" data-pagespeed-url-hash="1290077784" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H(j\omega )={\mathcal {F}}\{h(t)\}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>H</mi>
<mo stretchy="false">(</mo>
<mi>j</mi>
<mi>ω<!-- ω --></mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi class="MJX-tex-caligraphic" mathvariant="script">F</mi>
</mrow>
</mrow>
<mo fence="false" stretchy="false">{</mo>
<mi>h</mi>
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
<mo fence="false" stretchy="false">}</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle H(j\omega )={\mathcal {F}}\{h(t)\}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/8243cf79c3eccf125bb67646e818c2f70e18ad17" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:17.615ex; height:2.843ex;" alt="{\displaystyle H(j\omega )={\mathcal {F}}\{h(t)\}}" data-pagespeed-url-hash="1424426398" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/38" title="Special:DisplayTopics/38">38</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/1320#math.1320.31" title="Special:PermanentLink/1320">Phase-shift_keying-31</a>
</td>
<td> 0
</td>
<td> 10
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi /4}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>π<!-- π --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>/</mo>
</mrow>
<mn>4</mn>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \pi /4}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=003f7619ae0c1da19bd1ae62e01dcd2d&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; height: 2.843ex; width: 3.657ex;" alt="{\displaystyle \pi/4}" data-pagespeed-url-hash="1920204722" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi /4}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>π<!-- π --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>/</mo>
</mrow>
<mn>4</mn>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \pi /4}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/1707aa0fec2c8ef008b9e30b6045fbf95dab9e20" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:3.657ex; height:2.843ex;" alt="{\displaystyle \pi /4}" data-pagespeed-url-hash="1852535301" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/39" title="Special:DisplayTopics/39">39</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/133#math.133.6" title="Special:PermanentLink/133">Binomial_theorem-6</a>
</td>
<td> 3
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle(x+y)^{n}=\sum_{{\qvar@construct{x0}}}^{n}{n\choose k}x^{{n-k}}y% ^{k}=\sum_{{\qvar@construct{x1}}}^{n}{n\choose k}x^{{\qvar@construct{x2}}}y^{{% n-k}}.}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.26" xref="p1.1.m1.1.26.cmml">
<mrow id="p1.1.m1.1.26a" xref="p1.1.m1.1.26.cmml">
<msup id="p1.1.m1.1.26.2" xref="p1.1.m1.1.26.2.cmml">
<mrow id="p1.1.m1.1.26.2.2b">
<mo stretchy="false" id="p1.1.m1.1.26.2.2">(</mo>
<mrow id="XM5" xref="XM5.cmml">
<mi id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">x</mi>
<mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">+</mo>
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">y</mi>
</mrow>
<mo stretchy="false" id="p1.1.m1.1.26.2.2a">)</mo>
</mrow>
<mi id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">n</mi>
</msup>
<mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">=</mo>
<mrow id="p1.1.m1.1.26.3" xref="p1.1.m1.1.26.3.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.26.3.1" xref="p1.1.m1.1.26.3.1.cmml">
<munderover id="p1.1.m1.1.26.3.1a" xref="p1.1.m1.1.26.3.1.cmml">
<mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">∑</mo>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">x0</mi>
<mi id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">n</mi>
</munderover>
</mstyle>
<mrow id="p1.1.m1.1.26.3.2" xref="p1.1.m1.1.26.3.2.cmml">
<mrow id="p1.1.m1.1.11h" xref="p1.1.m1.1.11.cmml">
<mo id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">(</mo>
<mstyle displaystyle="true" id="p1.1.m1.1.11a" xref="p1.1.m1.1.11.cmml">
<mtable columnspacing="0.4em" rowspacing="0.2ex" id="p1.1.m1.1.11b" xref="p1.1.m1.1.11.cmml">
<mtr id="p1.1.m1.1.11c" xref="p1.1.m1.1.11.cmml">
<mtd id="p1.1.m1.1.11d" xref="p1.1.m1.1.11.cmml">
<mi id="p1.1.m1.1.11.3.2" xref="p1.1.m1.1.11.3.2.cmml">n</mi>
</mtd>
</mtr>
<mtr id="p1.1.m1.1.11e" xref="p1.1.m1.1.11.cmml">
<mtd id="p1.1.m1.1.11f" xref="p1.1.m1.1.11.cmml">
<mi id="p1.1.m1.1.11.3.3" xref="p1.1.m1.1.11.3.3.cmml">k</mi>
</mtd>
</mtr>
</mtable>
</mstyle>
<mo id="p1.1.m1.1.11g" xref="p1.1.m1.1.11.cmml">)</mo>
</mrow>
<mo id="p1.1.m1.1.26.3.2.1" xref="p1.1.m1.1.26.3.2.1.cmml"></mo>
<msup id="p1.1.m1.1.26.3.2.2" xref="p1.1.m1.1.26.3.2.2.cmml">
<mi id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">x</mi>
<mrow id="p1.1.m1.1.13.1" xref="p1.1.m1.1.13.1.cmml">
<mi id="p1.1.m1.1.13.1.1" xref="p1.1.m1.1.13.1.1.cmml">n</mi>
<mo id="p1.1.m1.1.13.1.2" xref="p1.1.m1.1.13.1.2.cmml">-</mo>
<mi id="p1.1.m1.1.13.1.3" xref="p1.1.m1.1.13.1.3.cmml">k</mi>
</mrow>
</msup>
<mo id="p1.1.m1.1.26.3.2.1a" xref="p1.1.m1.1.26.3.2.1.cmml"></mo>
<msup id="p1.1.m1.1.26.3.2.3" xref="p1.1.m1.1.26.3.2.3.cmml">
<mi id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">y</mi>
<mi id="p1.1.m1.1.15.1" xref="p1.1.m1.1.15.1.cmml">k</mi>
</msup>
</mrow>
</mrow>
<mo id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">=</mo>
<mrow id="p1.1.m1.1.26.4" xref="p1.1.m1.1.26.4.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.26.4.1" xref="p1.1.m1.1.26.4.1.cmml">
<munderover id="p1.1.m1.1.26.4.1a" xref="p1.1.m1.1.26.4.1.cmml">
<mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">∑</mo>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.18.1" xref="p1.1.m1.1.18.1.cmml">x1</mi>
<mi id="p1.1.m1.1.19.1" xref="p1.1.m1.1.19.1.cmml">n</mi>
</munderover>
</mstyle>
<mrow id="p1.1.m1.1.26.4.2" xref="p1.1.m1.1.26.4.2.cmml">
<mrow id="p1.1.m1.1.20h" xref="p1.1.m1.1.20.cmml">
<mo id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">(</mo>
<mstyle displaystyle="true" id="p1.1.m1.1.20a" xref="p1.1.m1.1.20.cmml">
<mtable columnspacing="0.4em" rowspacing="0.2ex" id="p1.1.m1.1.20b" xref="p1.1.m1.1.20.cmml">
<mtr id="p1.1.m1.1.20c" xref="p1.1.m1.1.20.cmml">
<mtd id="p1.1.m1.1.20d" xref="p1.1.m1.1.20.cmml">
<mi id="p1.1.m1.1.20.3.2" xref="p1.1.m1.1.20.3.2.cmml">n</mi>
</mtd>
</mtr>
<mtr id="p1.1.m1.1.20e" xref="p1.1.m1.1.20.cmml">
<mtd id="p1.1.m1.1.20f" xref="p1.1.m1.1.20.cmml">
<mi id="p1.1.m1.1.20.3.3" xref="p1.1.m1.1.20.3.3.cmml">k</mi>
</mtd>
</mtr>
</mtable>
</mstyle>
<mo id="p1.1.m1.1.20g" xref="p1.1.m1.1.20.cmml">)</mo>
</mrow>
<mo id="p1.1.m1.1.26.4.2.1" xref="p1.1.m1.1.26.4.2.1.cmml"></mo>
<msup id="p1.1.m1.1.26.4.2.2" xref="p1.1.m1.1.26.4.2.2.cmml">
<mi id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">x</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.22.1" xref="p1.1.m1.1.22.1.cmml">x2</mi>
</msup>
<mo id="p1.1.m1.1.26.4.2.1a" xref="p1.1.m1.1.26.4.2.1.cmml"></mo>
<msup id="p1.1.m1.1.26.4.2.3" xref="p1.1.m1.1.26.4.2.3.cmml">
<mi id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">y</mi>
<mrow id="p1.1.m1.1.24.1" xref="p1.1.m1.1.24.1.cmml">
<mi id="p1.1.m1.1.24.1.1" xref="p1.1.m1.1.24.1.1.cmml">n</mi>
<mo id="p1.1.m1.1.24.1.2" xref="p1.1.m1.1.24.1.2.cmml">-</mo>
<mi id="p1.1.m1.1.24.1.3" xref="p1.1.m1.1.24.1.3.cmml">k</mi>
</mrow>
</msup>
</mrow>
</mrow>
</mrow>
<mo id="p1.1.m1.1.26b" xref="p1.1.m1.1.26.cmml">.</mo>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.26.cmml" xref="p1.1.m1.1.26">
<and id="p1.1.m1.1.26a.cmml" xref="p1.1.m1.1.26"/>
<apply id="p1.1.m1.1.26b.cmml" xref="p1.1.m1.1.26">
<eq id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
<apply id="p1.1.m1.1.26.2.cmml" xref="p1.1.m1.1.26.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.26.2.1.cmml">superscript</csymbol>
<apply id="XM5.cmml" xref="XM5">
<plus id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
<ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">x</ci>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">y</ci>
</apply>
<ci id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1">n</ci>
</apply>
<apply id="p1.1.m1.1.26.3.cmml" xref="p1.1.m1.1.26.3">
<apply id="p1.1.m1.1.26.3.1.cmml" xref="p1.1.m1.1.26.3.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.26.3.1.1.cmml">superscript</csymbol>
<apply id="p1.1.m1.1.26.3.1.2.cmml">
<csymbol cd="ambiguous" id="p1.1.m1.1.26.3.1.2.1.cmml">subscript</csymbol>
<sum id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8"/>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">x0</csymbol>
</apply>
<ci id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">n</ci>
</apply>
<apply id="p1.1.m1.1.26.3.2.cmml" xref="p1.1.m1.1.26.3.2">
<times id="p1.1.m1.1.26.3.2.1.cmml" xref="p1.1.m1.1.26.3.2.1"/>
<apply id="p1.1.m1.1.11a.cmml" xref="p1.1.m1.1.11">
<csymbol cd="latexml" id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">binomial</csymbol>
<ci id="p1.1.m1.1.11.3.2.cmml" xref="p1.1.m1.1.11.3.2">n</ci>
<ci id="p1.1.m1.1.11.3.3.cmml" xref="p1.1.m1.1.11.3.3">k</ci>
</apply>
<apply id="p1.1.m1.1.26.3.2.2.cmml" xref="p1.1.m1.1.26.3.2.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.26.3.2.2.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">x</ci>
<apply id="p1.1.m1.1.13.1.cmml" xref="p1.1.m1.1.13.1">
<minus id="p1.1.m1.1.13.1.2.cmml" xref="p1.1.m1.1.13.1.2"/>
<ci id="p1.1.m1.1.13.1.1.cmml" xref="p1.1.m1.1.13.1.1">n</ci>
<ci id="p1.1.m1.1.13.1.3.cmml" xref="p1.1.m1.1.13.1.3">k</ci>
</apply>
</apply>
<apply id="p1.1.m1.1.26.3.2.3.cmml" xref="p1.1.m1.1.26.3.2.3">
<csymbol cd="ambiguous" id="p1.1.m1.1.26.3.2.3.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">y</ci>
<ci id="p1.1.m1.1.15.1.cmml" xref="p1.1.m1.1.15.1">k</ci>
</apply>
</apply>
</apply>
</apply>
<apply id="p1.1.m1.1.26c.cmml" xref="p1.1.m1.1.26">
<eq id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16"/>
<share href="#p1.1.m1.1.26.3.cmml" id="p1.1.m1.1.26d.cmml" xref="p1.1.m1.1.26"/>
<apply id="p1.1.m1.1.26.4.cmml" xref="p1.1.m1.1.26.4">
<apply id="p1.1.m1.1.26.4.1.cmml" xref="p1.1.m1.1.26.4.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.26.4.1.1.cmml">superscript</csymbol>
<apply id="p1.1.m1.1.26.4.1.2.cmml">
<csymbol cd="ambiguous" id="p1.1.m1.1.26.4.1.2.1.cmml">subscript</csymbol>
<sum id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17"/>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.18.1.cmml" xref="p1.1.m1.1.18.1">x1</csymbol>
</apply>
<ci id="p1.1.m1.1.19.1.cmml" xref="p1.1.m1.1.19.1">n</ci>
</apply>
<apply id="p1.1.m1.1.26.4.2.cmml" xref="p1.1.m1.1.26.4.2">
<times id="p1.1.m1.1.26.4.2.1.cmml" xref="p1.1.m1.1.26.4.2.1"/>
<apply id="p1.1.m1.1.20a.cmml" xref="p1.1.m1.1.20">
<csymbol cd="latexml" id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">binomial</csymbol>
<ci id="p1.1.m1.1.20.3.2.cmml" xref="p1.1.m1.1.20.3.2">n</ci>
<ci id="p1.1.m1.1.20.3.3.cmml" xref="p1.1.m1.1.20.3.3">k</ci>
</apply>
<apply id="p1.1.m1.1.26.4.2.2.cmml" xref="p1.1.m1.1.26.4.2.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.26.4.2.2.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">x</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.22.1.cmml" xref="p1.1.m1.1.22.1">x2</csymbol>
</apply>
<apply id="p1.1.m1.1.26.4.2.3.cmml" xref="p1.1.m1.1.26.4.2.3">
<csymbol cd="ambiguous" id="p1.1.m1.1.26.4.2.3.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">y</ci>
<apply id="p1.1.m1.1.24.1.cmml" xref="p1.1.m1.1.24.1">
<minus id="p1.1.m1.1.24.1.2.cmml" xref="p1.1.m1.1.24.1.2"/>
<ci id="p1.1.m1.1.24.1.1.cmml" xref="p1.1.m1.1.24.1.1">n</ci>
<ci id="p1.1.m1.1.24.1.3.cmml" xref="p1.1.m1.1.24.1.3">k</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle(x+y)^{n}=\sum_{{\qvar@construct{x0}}}^{n}{n\choose k}x^{{n-k}}y%
^{k}=\sum_{{\qvar@construct{x1}}}^{n}{n\choose k}x^{{\qvar@construct{x2}}}y^{{%
n-k}}.}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=64cf17c57c6a8ddba04ebb06afd1114b&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.833ex; height: 6.5ex; width: 49.667ex;" alt="(x+y)^{n}=\sum_{{\qvar{x0}}}^{n}{n\choose k}x^{{n-k}}y^{k}=\sum_{{\qvar{x1}}}^{n}{n\choose k}x^{{\qvar{x2}}}y^{{n-k}}." data-pagespeed-url-hash="1794201729" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x+y)^{n}=\sum _{k=0}^{n}{n \choose k}x^{n-k}y^{k}=\sum _{k=0}^{n}{n \choose k}x^{k}y^{n-k}.}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>+</mo>
<mi>y</mi>
<msup>
<mo stretchy="false">)</mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>n</mi>
</mrow>
</msup>
<mo>=</mo>
<munderover>
<mo>∑<!-- ∑ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>k</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi>n</mi>
</mrow>
</munderover>
<mrow class="MJX-TeXAtom-ORD">
<mrow>
<mrow class="MJX-TeXAtom-OPEN">
<mo maxsize="2.047em" minsize="2.047em">(</mo>
</mrow>
<mfrac linethickness="0">
<mi>n</mi>
<mi>k</mi>
</mfrac>
<mrow class="MJX-TeXAtom-CLOSE">
<mo maxsize="2.047em" minsize="2.047em">)</mo>
</mrow>
</mrow>
</mrow>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>n</mi>
<mo>−<!-- − --></mo>
<mi>k</mi>
</mrow>
</msup>
<msup>
<mi>y</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>k</mi>
</mrow>
</msup>
<mo>=</mo>
<munderover>
<mo>∑<!-- ∑ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>k</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi>n</mi>
</mrow>
</munderover>
<mrow class="MJX-TeXAtom-ORD">
<mrow>
<mrow class="MJX-TeXAtom-OPEN">
<mo maxsize="2.047em" minsize="2.047em">(</mo>
</mrow>
<mfrac linethickness="0">
<mi>n</mi>
<mi>k</mi>
</mfrac>
<mrow class="MJX-TeXAtom-CLOSE">
<mo maxsize="2.047em" minsize="2.047em">)</mo>
</mrow>
</mrow>
</mrow>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>k</mi>
</mrow>
</msup>
<msup>
<mi>y</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>n</mi>
<mo>−<!-- − --></mo>
<mi>k</mi>
</mrow>
</msup>
<mo>.</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle (x+y)^{n}=\sum _{k=0}^{n}{n \choose k}x^{n-k}y^{k}=\sum _{k=0}^{n}{n \choose k}x^{k}y^{n-k}.}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/689f5d27fa52a8ff3f89bed50e7d6625d5c35aaa" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.171ex; width:46.178ex; height:7.009ex;" alt="{\displaystyle (x+y)^{n}=\sum _{k=0}^{n}{n \choose k}x^{n-k}y^{k}=\sum _{k=0}^{n}{n \choose k}x^{k}y^{n-k}.}" data-pagespeed-url-hash="316396317" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/40" title="Special:DisplayTopics/40">40</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/9082#math.9082.33" title="Special:PermanentLink/9082">Rate_equation-33</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\ [A]_{{t}}=-kt+[A]_{{0}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">
<msub id="p1.1.m1.1.15.1" xref="p1.1.m1.1.15.1.cmml">
<mrow id="p1.1.m1.1.15.1.2b" xref="p1.1.m1.1.15.1.2.cmml">
<mo lspace="7.5pt" stretchy="false" id="p1.1.m1.1.15.1.2" xref="p1.1.m1.1.15.1.2.cmml">[</mo>
<mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">A</mi>
<mo stretchy="false" id="p1.1.m1.1.15.1.2a" xref="p1.1.m1.1.15.1.2.cmml">]</mo>
</mrow>
<mi id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">t</mi>
</msub>
<mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">=</mo>
<mrow id="p1.1.m1.1.15.2" xref="p1.1.m1.1.15.2.cmml">
<mrow id="p1.1.m1.1.15.2.1" xref="p1.1.m1.1.15.2.1.cmml">
<mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">-</mo>
<mrow id="p1.1.m1.1.15.2.1.1" xref="p1.1.m1.1.15.2.1.1.cmml">
<mi id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">k</mi>
<mo id="p1.1.m1.1.15.2.1.1.1" xref="p1.1.m1.1.15.2.1.1.1.cmml"></mo>
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">t</mi>
</mrow>
</mrow>
<mo id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">+</mo>
<msub id="p1.1.m1.1.15.2.2" xref="p1.1.m1.1.15.2.2.cmml">
<mrow id="p1.1.m1.1.15.2.2.2b" xref="p1.1.m1.1.15.2.2.2.cmml">
<mo stretchy="false" id="p1.1.m1.1.15.2.2.2" xref="p1.1.m1.1.15.2.2.2.cmml">[</mo>
<mi id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">A</mi>
<mo stretchy="false" id="p1.1.m1.1.15.2.2.2a" xref="p1.1.m1.1.15.2.2.2.cmml">]</mo>
</mrow>
<mn id="p1.1.m1.1.14.1" xref="p1.1.m1.1.14.1.cmml">0</mn>
</msub>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">
<eq id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
<apply id="p1.1.m1.1.15.1.cmml" xref="p1.1.m1.1.15.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.15.1.1.cmml">subscript</csymbol>
<apply id="p1.1.m1.1.15.1.2a.cmml" xref="p1.1.m1.1.15.1.2">
<csymbol cd="latexml" id="p1.1.m1.1.15.1.2.cmml" xref="p1.1.m1.1.15.1.2">delimited-[]</csymbol>
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">A</ci>
</apply>
<ci id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1">t</ci>
</apply>
<apply id="p1.1.m1.1.15.2.cmml" xref="p1.1.m1.1.15.2">
<plus id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10"/>
<apply id="p1.1.m1.1.15.2.1.cmml" xref="p1.1.m1.1.15.2.1">
<minus id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
<apply id="p1.1.m1.1.15.2.1.1.cmml" xref="p1.1.m1.1.15.2.1.1">
<times id="p1.1.m1.1.15.2.1.1.1.cmml" xref="p1.1.m1.1.15.2.1.1.1"/>
<ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">k</ci>
<ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">t</ci>
</apply>
</apply>
<apply id="p1.1.m1.1.15.2.2.cmml" xref="p1.1.m1.1.15.2.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.15.2.2.1.cmml">subscript</csymbol>
<apply id="p1.1.m1.1.15.2.2.2a.cmml" xref="p1.1.m1.1.15.2.2.2">
<csymbol cd="latexml" id="p1.1.m1.1.15.2.2.2.cmml" xref="p1.1.m1.1.15.2.2.2">delimited-[]</csymbol>
<ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">A</ci>
</apply>
<cn type="integer" id="p1.1.m1.1.14.1.cmml" xref="p1.1.m1.1.14.1">0</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\ [A]_{{t}}=-kt+[A]_{{0}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=ccc8f109cf83a4114b3c6e547e95e823&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.833ex; height: 2.5ex; width: 19.667ex;" alt="\ [A]_{{t}}=-kt+[A]_{{0}}" data-pagespeed-url-hash="3284528329" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ [A]_{t}=-kt+[A]_{0}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mtext> </mtext>
<mo stretchy="false">[</mo>
<mi>A</mi>
<msub>
<mo stretchy="false">]</mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>t</mi>
</mrow>
</msub>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mi>k</mi>
<mi>t</mi>
<mo>+</mo>
<mo stretchy="false">[</mo>
<mi>A</mi>
<msub>
<mo stretchy="false">]</mo>
<mrow class="MJX-TeXAtom-ORD">
<mn>0</mn>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \ [A]_{t}=-kt+[A]_{0}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/989476d225b1fd0996646a5eb831e1b75d505eca" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:18.332ex; height:2.843ex;" alt="{\displaystyle \ [A]_{t}=-kt+[A]_{0}}" data-pagespeed-url-hash="2530356788" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/41" title="Special:DisplayTopics/41">41</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/3545#math.3545.1" title="Special:PermanentLink/3545">Martingale_(betting_system)-1</a>
</td>
<td> 1
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle q^{{\qvar@construct{x0}}}}">
<semantics id="p1.1.m1.1a">
<msup id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">q</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">x0</mi>
</msup>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
<csymbol cd="ambiguous" id="p1.1.m1.1.3.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">q</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">x0</csymbol>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle q^{{\qvar@construct{x0}}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=e7f4dfd85f7c266cea532301eb2e5a3a&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.5ex; height: 2.5ex; width: 3.167ex;" alt="q^{{\qvar{x0}}}" data-pagespeed-url-hash="1544120347" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q^{42}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msup>
<mi>q</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>42</mn>
</mrow>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle q^{42}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/75a835fc74838d9ecbcfc8954f079c8b2031af1c" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:2.956ex; height:3.009ex;" alt="{\displaystyle q^{42}}" data-pagespeed-url-hash="3928511352" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/42" title="Special:DisplayTopics/42">42</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/15433#math.15433.5" title="Special:PermanentLink/15433">Borsuk's_conjecture-5</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\alpha(d)\leq\left({{\sqrt{3/2}}}+\varepsilon\right)^{{d}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">
<mrow id="p1.1.m1.1.12.1" xref="p1.1.m1.1.12.1.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">α</mi>
<mo id="p1.1.m1.1.12.1.1" xref="p1.1.m1.1.12.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.12.1.2b">
<mo stretchy="false" id="p1.1.m1.1.12.1.2">(</mo>
<mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">d</mi>
<mo stretchy="false" id="p1.1.m1.1.12.1.2a">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">≤</mo>
<msup id="p1.1.m1.1.12.2" xref="p1.1.m1.1.12.2.cmml">
<mrow id="p1.1.m1.1.12.2.2b">
<mo id="p1.1.m1.1.12.2.2">(</mo>
<mrow id="XM1" xref="XM1.cmml">
<msqrt id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">
<mrow id="p1.1.m1.1.7.2" xref="p1.1.m1.1.7.2.cmml">
<mn id="p1.1.m1.1.7.2.1" xref="p1.1.m1.1.7.2.1.cmml">3</mn>
<mo id="p1.1.m1.1.7.2.2" xref="p1.1.m1.1.7.2.2.cmml">/</mo>
<mn id="p1.1.m1.1.7.2.3" xref="p1.1.m1.1.7.2.3.cmml">2</mn>
</mrow>
</msqrt>
<mo id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">+</mo>
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">ε</mi>
</mrow>
<mo id="p1.1.m1.1.12.2.2a">)</mo>
</mrow>
<mi id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml">d</mi>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">
<leq id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/>
<apply id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12.1">
<times id="p1.1.m1.1.12.1.1.cmml" xref="p1.1.m1.1.12.1.1"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">α</ci>
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">d</ci>
</apply>
<apply id="p1.1.m1.1.12.2.cmml" xref="p1.1.m1.1.12.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.12.2.1.cmml">superscript</csymbol>
<apply id="XM1.cmml" xref="XM1">
<plus id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8"/>
<apply id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">
<root id="p1.1.m1.1.7a.cmml" xref="p1.1.m1.1.7"/>
<apply id="p1.1.m1.1.7.2.cmml" xref="p1.1.m1.1.7.2">
<divide id="p1.1.m1.1.7.2.2.cmml" xref="p1.1.m1.1.7.2.2"/>
<cn type="integer" id="p1.1.m1.1.7.2.1.cmml" xref="p1.1.m1.1.7.2.1">3</cn>
<cn type="integer" id="p1.1.m1.1.7.2.3.cmml" xref="p1.1.m1.1.7.2.3">2</cn>
</apply>
</apply>
<ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">ε</ci>
</apply>
<ci id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1">d</ci>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\alpha(d)\leq\left({{\sqrt{3/2}}}+\varepsilon\right)^{{d}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=66401ea763d9a3d08eab5ebd3aad7cfe&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.833ex; height: 3.5ex; width: 21.167ex;" alt="\alpha (d)\leq \left({{\sqrt {3/2}}}+\varepsilon \right)^{{d}}" data-pagespeed-url-hash="2715170355" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha (d)\leq \left({\sqrt {3/2}}+\varepsilon \right)^{d}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>α<!-- α --></mi>
<mo stretchy="false">(</mo>
<mi>d</mi>
<mo stretchy="false">)</mo>
<mo>≤<!-- ≤ --></mo>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>3</mn>
<mrow class="MJX-TeXAtom-ORD">
<mo>/</mo>
</mrow>
<mn>2</mn>
</msqrt>
</mrow>
<mo>+</mo>
<mi>ε<!-- ε --></mi>
</mrow>
<mo>)</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi>d</mi>
</mrow>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \alpha (d)\leq \left({\sqrt {3/2}}+\varepsilon \right)^{d}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/2007cb276376e55f3a9f4c26655af02d3db4ece0" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.838ex; width:21.214ex; height:5.343ex;" alt="{\displaystyle \alpha (d)\leq \left({\sqrt {3/2}}+\varepsilon \right)^{d}}" data-pagespeed-url-hash="267310380" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/43" title="Special:DisplayTopics/43">43</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/12471#math.12471.96" title="Special:PermanentLink/12471">Theoretical_motivation_for_general_relativity-96</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle f^{{\mu}}=-8\pi{G\over{3c^{4}}}\left({A\over 2}T_{{\alpha\beta}% }+{B\over 2}T\eta_{{\alpha\beta}}\right)\left(\delta_{{\nu}}^{{\mu}}+u^{{\mu}}% u_{{\nu}}\right)u^{{\alpha}}x^{{\nu}}u^{{\beta}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.34" xref="p1.1.m1.1.34.cmml">
<msup id="p1.1.m1.1.34.1" xref="p1.1.m1.1.34.1.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">f</mi>
<mi id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">μ</mi>
</msup>
<mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">=</mo>
<mrow id="p1.1.m1.1.34.2" xref="p1.1.m1.1.34.2.cmml">
<mo id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">-</mo>
<mrow id="p1.1.m1.1.34.2.1" xref="p1.1.m1.1.34.2.1.cmml">
<mn id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">8</mn>
<mo id="p1.1.m1.1.34.2.1.1" xref="p1.1.m1.1.34.2.1.1.cmml"></mo>
<mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">π</mi>
<mo id="p1.1.m1.1.34.2.1.1a" xref="p1.1.m1.1.34.2.1.1.cmml"></mo>
<mstyle displaystyle="true" id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">
<mfrac id="p1.1.m1.1.7a" xref="p1.1.m1.1.7.cmml">
<mi id="p1.1.m1.1.7.2" xref="p1.1.m1.1.7.2.cmml">G</mi>
<mrow id="p1.1.m1.1.7.3" xref="p1.1.m1.1.7.3.cmml">
<mn id="p1.1.m1.1.7.3.1" xref="p1.1.m1.1.7.3.1.cmml">3</mn>
<mo id="p1.1.m1.1.7.3.4" xref="p1.1.m1.1.7.3.4.cmml"></mo>
<msup id="p1.1.m1.1.7.3.5" xref="p1.1.m1.1.7.3.5.cmml">
<mi id="p1.1.m1.1.7.3.2" xref="p1.1.m1.1.7.3.2.cmml">c</mi>
<mn id="p1.1.m1.1.7.3.3.1" xref="p1.1.m1.1.7.3.3.1.cmml">4</mn>
</msup>
</mrow>
</mfrac>
</mstyle>
<mo id="p1.1.m1.1.34.2.1.1b" xref="p1.1.m1.1.34.2.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.34.2.1.2b">
<mo id="p1.1.m1.1.34.2.1.2">(</mo>
<mrow id="XM1" xref="XM1.cmml">
<mrow id="XM1.1" xref="XM1.1.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">
<mfrac id="p1.1.m1.1.9a" xref="p1.1.m1.1.9.cmml">
<mi id="p1.1.m1.1.9.2" xref="p1.1.m1.1.9.2.cmml">A</mi>
<mn id="p1.1.m1.1.9.3" xref="p1.1.m1.1.9.3.cmml">2</mn>
</mfrac>
</mstyle>
<mo id="XM1.1.1" xref="XM1.1.1.cmml"></mo>
<msub id="XM1.1.2" xref="XM1.1.2.cmml">
<mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">T</mi>
<mrow id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml">
<mi id="p1.1.m1.1.11.1.1" xref="p1.1.m1.1.11.1.1.cmml">α</mi>
<mo id="p1.1.m1.1.11.1.3" xref="p1.1.m1.1.11.1.3.cmml"></mo>
<mi id="p1.1.m1.1.11.1.2" xref="p1.1.m1.1.11.1.2.cmml">β</mi>
</mrow>
</msub>
</mrow>
<mo id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">+</mo>
<mrow id="XM1.2" xref="XM1.2.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">
<mfrac id="p1.1.m1.1.13a" xref="p1.1.m1.1.13.cmml">
<mi id="p1.1.m1.1.13.2" xref="p1.1.m1.1.13.2.cmml">B</mi>
<mn id="p1.1.m1.1.13.3" xref="p1.1.m1.1.13.3.cmml">2</mn>
</mfrac>
</mstyle>
<mo id="XM1.2.1" xref="XM1.2.1.cmml"></mo>
<mi id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">T</mi>
<mo id="XM1.2.1a" xref="XM1.2.1.cmml"></mo>
<msub id="XM1.2.2" xref="XM1.2.2.cmml">
<mi id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">η</mi>
<mrow id="p1.1.m1.1.16.1" xref="p1.1.m1.1.16.1.cmml">
<mi id="p1.1.m1.1.16.1.1" xref="p1.1.m1.1.16.1.1.cmml">α</mi>
<mo id="p1.1.m1.1.16.1.3" xref="p1.1.m1.1.16.1.3.cmml"></mo>
<mi id="p1.1.m1.1.16.1.2" xref="p1.1.m1.1.16.1.2.cmml">β</mi>
</mrow>
</msub>
</mrow>
</mrow>
<mo id="p1.1.m1.1.34.2.1.2a">)</mo>
</mrow>
<mo id="p1.1.m1.1.34.2.1.1c" xref="p1.1.m1.1.34.2.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.34.2.1.3b">
<mo id="p1.1.m1.1.34.2.1.3">(</mo>
<mrow id="XM2" xref="XM2.cmml">
<msubsup id="XM2.1" xref="XM2.1.cmml">
<mi id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">δ</mi>
<mi id="p1.1.m1.1.20.1" xref="p1.1.m1.1.20.1.cmml">ν</mi>
<mi id="p1.1.m1.1.21.1" xref="p1.1.m1.1.21.1.cmml">μ</mi>
</msubsup>
<mo id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">+</mo>
<mrow id="XM2.2" xref="XM2.2.cmml">
<msup id="XM2.2.2" xref="XM2.2.2.cmml">
<mi id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">u</mi>
<mi id="p1.1.m1.1.24.1" xref="p1.1.m1.1.24.1.cmml">μ</mi>
</msup>
<mo id="XM2.2.1" xref="XM2.2.1.cmml"></mo>
<msub id="XM2.2.3" xref="XM2.2.3.cmml">
<mi id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">u</mi>
<mi id="p1.1.m1.1.26.1" xref="p1.1.m1.1.26.1.cmml">ν</mi>
</msub>
</mrow>
</mrow>
<mo id="p1.1.m1.1.34.2.1.3a">)</mo>
</mrow>
<mo id="p1.1.m1.1.34.2.1.1d" xref="p1.1.m1.1.34.2.1.1.cmml"></mo>
<msup id="p1.1.m1.1.34.2.1.4" xref="p1.1.m1.1.34.2.1.4.cmml">
<mi id="p1.1.m1.1.28" xref="p1.1.m1.1.28.cmml">u</mi>
<mi id="p1.1.m1.1.29.1" xref="p1.1.m1.1.29.1.cmml">α</mi>
</msup>
<mo id="p1.1.m1.1.34.2.1.1e" xref="p1.1.m1.1.34.2.1.1.cmml"></mo>
<msup id="p1.1.m1.1.34.2.1.5" xref="p1.1.m1.1.34.2.1.5.cmml">
<mi id="p1.1.m1.1.30" xref="p1.1.m1.1.30.cmml">x</mi>
<mi id="p1.1.m1.1.31.1" xref="p1.1.m1.1.31.1.cmml">ν</mi>
</msup>
<mo id="p1.1.m1.1.34.2.1.1f" xref="p1.1.m1.1.34.2.1.1.cmml"></mo>
<msup id="p1.1.m1.1.34.2.1.6" xref="p1.1.m1.1.34.2.1.6.cmml">
<mi id="p1.1.m1.1.32" xref="p1.1.m1.1.32.cmml">u</mi>
<mi id="p1.1.m1.1.33.1" xref="p1.1.m1.1.33.1.cmml">β</mi>
</msup>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.34.cmml" xref="p1.1.m1.1.34">
<eq id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
<apply id="p1.1.m1.1.34.1.cmml" xref="p1.1.m1.1.34.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.34.1.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">f</ci>
<ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">μ</ci>
</apply>
<apply id="p1.1.m1.1.34.2.cmml" xref="p1.1.m1.1.34.2">
<minus id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4"/>
<apply id="p1.1.m1.1.34.2.1.cmml" xref="p1.1.m1.1.34.2.1">
<times id="p1.1.m1.1.34.2.1.1.cmml" xref="p1.1.m1.1.34.2.1.1"/>
<cn type="integer" id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">8</cn>
<ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">π</ci>
<apply id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">
<divide id="p1.1.m1.1.7.1.cmml"/>
<ci id="p1.1.m1.1.7.2.cmml" xref="p1.1.m1.1.7.2">G</ci>
<apply id="p1.1.m1.1.7.3.cmml" xref="p1.1.m1.1.7.3">
<times id="p1.1.m1.1.7.3.4.cmml" xref="p1.1.m1.1.7.3.4"/>
<cn type="integer" id="p1.1.m1.1.7.3.1.cmml" xref="p1.1.m1.1.7.3.1">3</cn>
<apply id="p1.1.m1.1.7.3.5.cmml" xref="p1.1.m1.1.7.3.5">
<csymbol cd="ambiguous" id="p1.1.m1.1.7.3.5.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.7.3.2.cmml" xref="p1.1.m1.1.7.3.2">c</ci>
<cn type="integer" id="p1.1.m1.1.7.3.3.1.cmml" xref="p1.1.m1.1.7.3.3.1">4</cn>
</apply>
</apply>
</apply>
<apply id="XM1.cmml" xref="XM1">
<plus id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12"/>
<apply id="XM1.1.cmml" xref="XM1.1">
<times id="XM1.1.1.cmml" xref="XM1.1.1"/>
<apply id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">
<divide id="p1.1.m1.1.9.1.cmml"/>
<ci id="p1.1.m1.1.9.2.cmml" xref="p1.1.m1.1.9.2">A</ci>
<cn type="integer" id="p1.1.m1.1.9.3.cmml" xref="p1.1.m1.1.9.3">2</cn>
</apply>
<apply id="XM1.1.2.cmml" xref="XM1.1.2">
<csymbol cd="ambiguous" id="XM1.1.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">T</ci>
<apply id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1">
<times id="p1.1.m1.1.11.1.3.cmml" xref="p1.1.m1.1.11.1.3"/>
<ci id="p1.1.m1.1.11.1.1.cmml" xref="p1.1.m1.1.11.1.1">α</ci>
<ci id="p1.1.m1.1.11.1.2.cmml" xref="p1.1.m1.1.11.1.2">β</ci>
</apply>
</apply>
</apply>
<apply id="XM1.2.cmml" xref="XM1.2">
<times id="XM1.2.1.cmml" xref="XM1.2.1"/>
<apply id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">
<divide id="p1.1.m1.1.13.1.cmml"/>
<ci id="p1.1.m1.1.13.2.cmml" xref="p1.1.m1.1.13.2">B</ci>
<cn type="integer" id="p1.1.m1.1.13.3.cmml" xref="p1.1.m1.1.13.3">2</cn>
</apply>
<ci id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">T</ci>
<apply id="XM1.2.2.cmml" xref="XM1.2.2">
<csymbol cd="ambiguous" id="XM1.2.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">η</ci>
<apply id="p1.1.m1.1.16.1.cmml" xref="p1.1.m1.1.16.1">
<times id="p1.1.m1.1.16.1.3.cmml" xref="p1.1.m1.1.16.1.3"/>
<ci id="p1.1.m1.1.16.1.1.cmml" xref="p1.1.m1.1.16.1.1">α</ci>
<ci id="p1.1.m1.1.16.1.2.cmml" xref="p1.1.m1.1.16.1.2">β</ci>
</apply>
</apply>
</apply>
</apply>
<apply id="XM2.cmml" xref="XM2">
<plus id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22"/>
<apply id="XM2.1.cmml" xref="XM2.1">
<csymbol cd="ambiguous" id="XM2.1.1.cmml">superscript</csymbol>
<apply id="XM2.1.2.cmml">
<csymbol cd="ambiguous" id="XM2.1.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">δ</ci>
<ci id="p1.1.m1.1.20.1.cmml" xref="p1.1.m1.1.20.1">ν</ci>
</apply>
<ci id="p1.1.m1.1.21.1.cmml" xref="p1.1.m1.1.21.1">μ</ci>
</apply>
<apply id="XM2.2.cmml" xref="XM2.2">
<times id="XM2.2.1.cmml" xref="XM2.2.1"/>
<apply id="XM2.2.2.cmml" xref="XM2.2.2">
<csymbol cd="ambiguous" id="XM2.2.2.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">u</ci>
<ci id="p1.1.m1.1.24.1.cmml" xref="p1.1.m1.1.24.1">μ</ci>
</apply>
<apply id="XM2.2.3.cmml" xref="XM2.2.3">
<csymbol cd="ambiguous" id="XM2.2.3.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25">u</ci>
<ci id="p1.1.m1.1.26.1.cmml" xref="p1.1.m1.1.26.1">ν</ci>
</apply>
</apply>
</apply>
<apply id="p1.1.m1.1.34.2.1.4.cmml" xref="p1.1.m1.1.34.2.1.4">
<csymbol cd="ambiguous" id="p1.1.m1.1.34.2.1.4.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.28.cmml" xref="p1.1.m1.1.28">u</ci>
<ci id="p1.1.m1.1.29.1.cmml" xref="p1.1.m1.1.29.1">α</ci>
</apply>
<apply id="p1.1.m1.1.34.2.1.5.cmml" xref="p1.1.m1.1.34.2.1.5">
<csymbol cd="ambiguous" id="p1.1.m1.1.34.2.1.5.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.30.cmml" xref="p1.1.m1.1.30">x</ci>
<ci id="p1.1.m1.1.31.1.cmml" xref="p1.1.m1.1.31.1">ν</ci>
</apply>
<apply id="p1.1.m1.1.34.2.1.6.cmml" xref="p1.1.m1.1.34.2.1.6">
<csymbol cd="ambiguous" id="p1.1.m1.1.34.2.1.6.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.32.cmml" xref="p1.1.m1.1.32">u</ci>
<ci id="p1.1.m1.1.33.1.cmml" xref="p1.1.m1.1.33.1">β</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle f^{{\mu}}=-8\pi{G\over{3c^{4}}}\left({A\over 2}T_{{\alpha\beta}%
}+{B\over 2}T\eta_{{\alpha\beta}}\right)\left(\delta_{{\nu}}^{{\mu}}+u^{{\mu}}%
u_{{\nu}}\right)u^{{\alpha}}x^{{\nu}}u^{{\beta}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=69b20a62698d014b79bced90d50c49ce&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.333ex; height: 5.667ex; width: 57.333ex;" alt="f^{{\mu}}=-8\pi{G\over{3c^{4}}}\left({A\over 2}T_{{\alpha\beta}}+{B\over 2}T\eta_{{\alpha\beta}}\right)\left(\delta_{{\nu}}^{{\mu}}+u^{{\mu}}u_{{\nu}}\right)u^{{\alpha}}x^{{\nu}}u^{{\beta}}" data-pagespeed-url-hash="1034251715" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f^{\mu }=-8\pi {G \over {3c^{4}}}\left({A \over 2}T_{\alpha \beta }+{B \over 2}T\eta _{\alpha \beta }\right)\left(\delta _{\nu }^{\mu }+u^{\mu }u_{\nu }\right)u^{\alpha }x^{\nu }u^{\beta }}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msup>
<mi>f</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>μ<!-- μ --></mi>
</mrow>
</msup>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mn>8</mn>
<mi>π<!-- π --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>G</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
<msup>
<mi>c</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>4</mn>
</mrow>
</msup>
</mrow>
</mfrac>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>A</mi>
<mn>2</mn>
</mfrac>
</mrow>
<msub>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>α<!-- α --></mi>
<mi>β<!-- β --></mi>
</mrow>
</msub>
<mo>+</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>B</mi>
<mn>2</mn>
</mfrac>
</mrow>
<mi>T</mi>
<msub>
<mi>η<!-- η --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>α<!-- α --></mi>
<mi>β<!-- β --></mi>
</mrow>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<msubsup>
<mi>δ<!-- δ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>ν<!-- ν --></mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi>μ<!-- μ --></mi>
</mrow>
</msubsup>
<mo>+</mo>
<msup>
<mi>u</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>μ<!-- μ --></mi>
</mrow>
</msup>
<msub>
<mi>u</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>ν<!-- ν --></mi>
</mrow>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<msup>
<mi>u</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>α<!-- α --></mi>
</mrow>
</msup>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>ν<!-- ν --></mi>
</mrow>
</msup>
<msup>
<mi>u</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>β<!-- β --></mi>
</mrow>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle f^{\mu }=-8\pi {G \over {3c^{4}}}\left({A \over 2}T_{\alpha \beta }+{B \over 2}T\eta _{\alpha \beta }\right)\left(\delta _{\nu }^{\mu }+u^{\mu }u_{\nu }\right)u^{\alpha }x^{\nu }u^{\beta }}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/81c623d109d724eccd4cc0992d19820976b21fb2" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.505ex; width:54.993ex; height:6.176ex;" alt="{\displaystyle f^{\mu }=-8\pi {G \over {3c^{4}}}\left({A \over 2}T_{\alpha \beta }+{B \over 2}T\eta _{\alpha \beta }\right)\left(\delta _{\nu }^{\mu }+u^{\mu }u_{\nu }\right)u^{\alpha }x^{\nu }u^{\beta }}" data-pagespeed-url-hash="1171490505" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/44" title="Special:DisplayTopics/44">44</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/27611#math.27611.0" title="Special:PermanentLink/27611">Q-Vectors-0</a>
</td>
<td> 1
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\frac{D_{g}u_{\qvar@construct{x0}}}{Dt}}-f_{{0}}v_{a}-\beta yv_% {g}=0}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">
<mrow id="p1.1.m1.1.14.1" xref="p1.1.m1.1.14.1.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">
<mfrac id="p1.1.m1.1.1a" xref="p1.1.m1.1.1.cmml">
<mrow id="p1.1.m1.1.1.2" xref="p1.1.m1.1.1.2.cmml">
<msub id="p1.1.m1.1.1.2.6" xref="p1.1.m1.1.1.2.6.cmml">
<mi id="p1.1.m1.1.1.2.1" xref="p1.1.m1.1.1.2.1.cmml">D</mi>
<mi id="p1.1.m1.1.1.2.2.1" xref="p1.1.m1.1.1.2.2.1.cmml">g</mi>
</msub>
<mo id="p1.1.m1.1.1.2.5" xref="p1.1.m1.1.1.2.5.cmml"></mo>
<msub id="p1.1.m1.1.1.2.7" xref="p1.1.m1.1.1.2.7.cmml">
<mi id="p1.1.m1.1.1.2.3" xref="p1.1.m1.1.1.2.3.cmml">u</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.1.2.4.1" xref="p1.1.m1.1.1.2.4.1.cmml">x0</mi>
</msub>
</mrow>
<mrow id="p1.1.m1.1.1.3" xref="p1.1.m1.1.1.3.cmml">
<mi id="p1.1.m1.1.1.3.1" xref="p1.1.m1.1.1.3.1.cmml">D</mi>
<mo id="p1.1.m1.1.1.3.3" xref="p1.1.m1.1.1.3.3.cmml"></mo>
<mi id="p1.1.m1.1.1.3.2" xref="p1.1.m1.1.1.3.2.cmml">t</mi>
</mrow>
</mfrac>
</mstyle>
<mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">-</mo>
<mrow id="p1.1.m1.1.14.1.1" xref="p1.1.m1.1.14.1.1.cmml">
<msub id="p1.1.m1.1.14.1.1.2" xref="p1.1.m1.1.14.1.1.2.cmml">
<mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">f</mi>
<mn id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">0</mn>
</msub>
<mo id="p1.1.m1.1.14.1.1.1" xref="p1.1.m1.1.14.1.1.1.cmml"></mo>
<msub id="p1.1.m1.1.14.1.1.3" xref="p1.1.m1.1.14.1.1.3.cmml">
<mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">v</mi>
<mi id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">a</mi>
</msub>
</mrow>
<mo id="p1.1.m1.1.2a" xref="p1.1.m1.1.2.cmml">-</mo>
<mrow id="p1.1.m1.1.14.1.2" xref="p1.1.m1.1.14.1.2.cmml">
<mi id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">β</mi>
<mo id="p1.1.m1.1.14.1.2.1" xref="p1.1.m1.1.14.1.2.1.cmml"></mo>
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">y</mi>
<mo id="p1.1.m1.1.14.1.2.1a" xref="p1.1.m1.1.14.1.2.1.cmml"></mo>
<msub id="p1.1.m1.1.14.1.2.2" xref="p1.1.m1.1.14.1.2.2.cmml">
<mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">v</mi>
<mi id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml">g</mi>
</msub>
</mrow>
</mrow>
<mo id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">=</mo>
<mn id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">0</mn>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">
<eq id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12"/>
<apply id="p1.1.m1.1.14.1.cmml" xref="p1.1.m1.1.14.1">
<minus id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
<apply id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">
<divide id="p1.1.m1.1.1.1.cmml"/>
<apply id="p1.1.m1.1.1.2.cmml" xref="p1.1.m1.1.1.2">
<times id="p1.1.m1.1.1.2.5.cmml" xref="p1.1.m1.1.1.2.5"/>
<apply id="p1.1.m1.1.1.2.6.cmml" xref="p1.1.m1.1.1.2.6">
<csymbol cd="ambiguous" id="p1.1.m1.1.1.2.6.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.2.1.cmml" xref="p1.1.m1.1.1.2.1">D</ci>
<ci id="p1.1.m1.1.1.2.2.1.cmml" xref="p1.1.m1.1.1.2.2.1">g</ci>
</apply>
<apply id="p1.1.m1.1.1.2.7.cmml" xref="p1.1.m1.1.1.2.7">
<csymbol cd="ambiguous" id="p1.1.m1.1.1.2.7.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.2.3.cmml" xref="p1.1.m1.1.1.2.3">u</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.1.2.4.1.cmml" xref="p1.1.m1.1.1.2.4.1">x0</csymbol>
</apply>
</apply>
<apply id="p1.1.m1.1.1.3.cmml" xref="p1.1.m1.1.1.3">
<times id="p1.1.m1.1.1.3.3.cmml" xref="p1.1.m1.1.1.3.3"/>
<ci id="p1.1.m1.1.1.3.1.cmml" xref="p1.1.m1.1.1.3.1">D</ci>
<ci id="p1.1.m1.1.1.3.2.cmml" xref="p1.1.m1.1.1.3.2">t</ci>
</apply>
</apply>
<apply id="p1.1.m1.1.14.1.1.cmml" xref="p1.1.m1.1.14.1.1">
<times id="p1.1.m1.1.14.1.1.1.cmml" xref="p1.1.m1.1.14.1.1.1"/>
<apply id="p1.1.m1.1.14.1.1.2.cmml" xref="p1.1.m1.1.14.1.1.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.14.1.1.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">f</ci>
<cn type="integer" id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">0</cn>
</apply>
<apply id="p1.1.m1.1.14.1.1.3.cmml" xref="p1.1.m1.1.14.1.1.3">
<csymbol cd="ambiguous" id="p1.1.m1.1.14.1.1.3.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">v</ci>
<ci id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1">a</ci>
</apply>
</apply>
<apply id="p1.1.m1.1.14.1.2.cmml" xref="p1.1.m1.1.14.1.2">
<times id="p1.1.m1.1.14.1.2.1.cmml" xref="p1.1.m1.1.14.1.2.1"/>
<ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">β</ci>
<ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">y</ci>
<apply id="p1.1.m1.1.14.1.2.2.cmml" xref="p1.1.m1.1.14.1.2.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.14.1.2.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">v</ci>
<ci id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1">g</ci>
</apply>
</apply>
</apply>
<cn type="integer" id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">0</cn>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\frac{D_{g}u_{\qvar@construct{x0}}}{Dt}}-f_{{0}}v_{a}-\beta yv_%
{g}=0}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=247c0f627195d45a028a29397cc3a28f&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.833ex; height: 5.333ex; width: 26.333ex;" alt="{\frac{D_{g}u_{\qvar{x0}}}{Dt}}-f_{{0}}v_{a}-\beta yv_{g}=0" data-pagespeed-url-hash="1822866140" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {D_{g}u_{g}}{Dt}}-f_{0}v_{a}-\beta yv_{g}=0}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<msub>
<mi>D</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>g</mi>
</mrow>
</msub>
<msub>
<mi>u</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>g</mi>
</mrow>
</msub>
</mrow>
<mrow>
<mi>D</mi>
<mi>t</mi>
</mrow>
</mfrac>
</mrow>
<mo>−<!-- − --></mo>
<msub>
<mi>f</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>0</mn>
</mrow>
</msub>
<msub>
<mi>v</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>a</mi>
</mrow>
</msub>
<mo>−<!-- − --></mo>
<mi>β<!-- β --></mi>
<mi>y</mi>
<msub>
<mi>v</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>g</mi>
</mrow>
</msub>
<mo>=</mo>
<mn>0</mn>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\frac {D_{g}u_{g}}{Dt}}-f_{0}v_{a}-\beta yv_{g}=0}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/d2ff20a5b6f880b1bb4711bcfe52581b7173e3e4" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.838ex; width:25.134ex; height:5.509ex;" alt="{\displaystyle {\frac {D_{g}u_{g}}{Dt}}-f_{0}v_{a}-\beta yv_{g}=0}" data-pagespeed-url-hash="1752285693" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/45" title="Special:DisplayTopics/45">45</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/22412#math.22412.10" title="Special:PermanentLink/22412">Stencil_code-10</a>
</td>
<td> 0
</td>
<td> 8
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle I_{{c}}}">
<semantics id="p1.1.m1.1a">
<msub id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">I</mi>
<mi id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">c</mi>
</msub>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
<csymbol cd="ambiguous" id="p1.1.m1.1.3.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">I</ci>
<ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">c</ci>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle I_{{c}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=4006a349031978100ce21d157d728a78&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.5ex; height: 2ex; width: 2ex;" alt="I_{{c}}" data-pagespeed-url-hash="2504087308" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{c}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>I</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>c</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle I_{c}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/7463de5fff5fee0c540ac1d8cd1aca43f4852c65" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:1.967ex; height:2.509ex;" alt="{\displaystyle I_{c}}" data-pagespeed-url-hash="610963764" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/46" title="Special:DisplayTopics/46">46</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/460#math.460.81" title="Special:PermanentLink/460">Geometric_algebra-81</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\,A\mapsto M\alpha(A)M^{{{-1}}},}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">
<mrow id="p1.1.m1.1.12a" xref="p1.1.m1.1.12.cmml">
<mpadded lspace="1.7pt" width="+1.7pt" id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">
<mi id="p1.1.m1.1.2a" xref="p1.1.m1.1.2.cmml">A</mi>
</mpadded>
<mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">↦</mo>
<mrow id="p1.1.m1.1.12.1" xref="p1.1.m1.1.12.1.cmml">
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">M</mi>
<mo id="p1.1.m1.1.12.1.1" xref="p1.1.m1.1.12.1.1.cmml"></mo>
<mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">α</mi>
<mo id="p1.1.m1.1.12.1.1a" xref="p1.1.m1.1.12.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.12.1.2b">
<mo stretchy="false" id="p1.1.m1.1.12.1.2">(</mo>
<mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">A</mi>
<mo stretchy="false" id="p1.1.m1.1.12.1.2a">)</mo>
</mrow>
<mo id="p1.1.m1.1.12.1.1b" xref="p1.1.m1.1.12.1.1.cmml"></mo>
<msup id="p1.1.m1.1.12.1.3" xref="p1.1.m1.1.12.1.3.cmml">
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">M</mi>
<mrow id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">
<mo id="p1.1.m1.1.10.1.1" xref="p1.1.m1.1.10.1.1.cmml">-</mo>
<mn id="p1.1.m1.1.10.1.2" xref="p1.1.m1.1.10.1.2.cmml">1</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mo id="p1.1.m1.1.12b" xref="p1.1.m1.1.12.cmml">,</mo>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">
<csymbol cd="latexml" id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">maps-to</csymbol>
<ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">A</ci>
<apply id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12.1">
<times id="p1.1.m1.1.12.1.1.cmml" xref="p1.1.m1.1.12.1.1"/>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">M</ci>
<ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">α</ci>
<ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">A</ci>
<apply id="p1.1.m1.1.12.1.3.cmml" xref="p1.1.m1.1.12.1.3">
<csymbol cd="ambiguous" id="p1.1.m1.1.12.1.3.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">M</ci>
<apply id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">
<minus id="p1.1.m1.1.10.1.1.cmml" xref="p1.1.m1.1.10.1.1"/>
<cn type="integer" id="p1.1.m1.1.10.1.2.cmml" xref="p1.1.m1.1.10.1.2">1</cn>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\,A\mapsto M\alpha(A)M^{{{-1}}},}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=998c425fea7158ac6259fb2ad1e10588&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.667ex; width: 19.667ex;" alt="\,A\mapsto M\alpha (A)M^{{{-1}}}," data-pagespeed-url-hash="4095142383" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \,A\mapsto M\alpha (A)M^{-1},}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mspace width="thinmathspace"/>
<mi>A</mi>
<mo stretchy="false">↦<!-- ↦ --></mo>
<mi>M</mi>
<mi>α<!-- α --></mi>
<mo stretchy="false">(</mo>
<mi>A</mi>
<mo stretchy="false">)</mo>
<msup>
<mi>M</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</msup>
<mo>,</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \,A\mapsto M\alpha (A)M^{-1},}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/7018cc821be15a65b15532ded4c57fd4f1485ad2" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:18.705ex; height:3.176ex;" alt="{\displaystyle \,A\mapsto M\alpha (A)M^{-1},}" data-pagespeed-url-hash="1835678460" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/47" title="Special:DisplayTopics/47">47</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/16803#math.16803.53" title="Special:PermanentLink/16803">Stochastic_game-53</a>
</td>
<td> 0
</td>
<td> 2
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\Gamma_{{{\infty}}}}">
<semantics id="p1.1.m1.1a">
<msub id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
<mi mathvariant="normal" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">Γ</mi>
<mi mathvariant="normal" id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">∞</mi>
</msub>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
<csymbol cd="ambiguous" id="p1.1.m1.1.3.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">normal-Γ</ci>
<infinity id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1"/>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\Gamma_{{{\infty}}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=01a9ef823e63198b513b36029bd3b8b2&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.5ex; height: 2ex; width: 3.333ex;" alt="\Gamma _{{{\infty }}}" data-pagespeed-url-hash="482034294" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Gamma _{\infty }}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi mathvariant="normal">Γ<!-- Γ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">∞<!-- ∞ --></mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \Gamma _{\infty }}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/2fec865d9875533fcbec721889a34a217f5492a7" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:3.328ex; height:2.509ex;" alt="{\displaystyle \Gamma _{\infty }}" data-pagespeed-url-hash="2887538393" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/48" title="Special:DisplayTopics/48">48</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/15858#math.15858.3" title="Special:PermanentLink/15858">331_model-3</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle Y=\beta T_{{8}}+IX}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">Y</mi>
<mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">=</mo>
<mrow id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">
<mrow id="p1.1.m1.1.9.1.1" xref="p1.1.m1.1.9.1.1.cmml">
<mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">β</mi>
<mo id="p1.1.m1.1.9.1.1.1" xref="p1.1.m1.1.9.1.1.1.cmml"></mo>
<msub id="p1.1.m1.1.9.1.1.2" xref="p1.1.m1.1.9.1.1.2.cmml">
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">T</mi>
<mn id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">8</mn>
</msub>
</mrow>
<mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">+</mo>
<mrow id="p1.1.m1.1.9.1.2" xref="p1.1.m1.1.9.1.2.cmml">
<mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">I</mi>
<mo id="p1.1.m1.1.9.1.2.1" xref="p1.1.m1.1.9.1.2.1.cmml"></mo>
<mi id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">X</mi>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">
<eq id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">Y</ci>
<apply id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">
<plus id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
<apply id="p1.1.m1.1.9.1.1.cmml" xref="p1.1.m1.1.9.1.1">
<times id="p1.1.m1.1.9.1.1.1.cmml" xref="p1.1.m1.1.9.1.1.1"/>
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">β</ci>
<apply id="p1.1.m1.1.9.1.1.2.cmml" xref="p1.1.m1.1.9.1.1.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.9.1.1.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">T</ci>
<cn type="integer" id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1">8</cn>
</apply>
</apply>
<apply id="p1.1.m1.1.9.1.2.cmml" xref="p1.1.m1.1.9.1.2">
<times id="p1.1.m1.1.9.1.2.1.cmml" xref="p1.1.m1.1.9.1.2.1"/>
<ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">I</ci>
<ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">X</ci>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle Y=\beta T_{{8}}+IX}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=6dcb0896bf62e5ba5077b79a10387a4e&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.5ex; height: 2.167ex; width: 14.667ex;" alt="Y=\beta T_{{8}}+IX" data-pagespeed-url-hash="877166289" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y=\beta T_{8}+IX}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>Y</mi>
<mo>=</mo>
<mi>β<!-- β --></mi>
<msub>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>8</mn>
</mrow>
</msub>
<mo>+</mo>
<mi>I</mi>
<mi>X</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle Y=\beta T_{8}+IX}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/f448b07b8df04f535cb31b8304c3f6c2bc7c9ae9" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:14.608ex; height:2.509ex;" alt="{\displaystyle Y=\beta T_{8}+IX}" data-pagespeed-url-hash="2362319233" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/49" title="Special:DisplayTopics/49">49</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/7473#math.7473.12" title="Special:PermanentLink/7473">Sigma_additivity-12</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\mu(A)={{\begin{cases}1&{{\mbox{ if }}}0\in A\\ 0&{{\mbox{ if }}}0\notin A.\end{cases}}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">
<mrow id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">μ</mi>
<mo id="p1.1.m1.1.9.1.1" xref="p1.1.m1.1.9.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.9.1.2b">
<mo stretchy="false" id="p1.1.m1.1.9.1.2">(</mo>
<mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">A</mi>
<mo stretchy="false" id="p1.1.m1.1.9.1.2a">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">=</mo>
<mrow id="p1.1.m1.1.8h" xref="p1.1.m1.1.8.cmml">
<mo id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">{</mo>
<mtable id="p1.1.m1.1.8a" xref="p1.1.m1.1.8.cmml">
<mtr id="p1.1.m1.1.8b" xref="p1.1.m1.1.8.cmml">
<mtd columnalign="left" id="p1.1.m1.1.8c" xref="p1.1.m1.1.8.cmml">
<mn id="p1.1.m1.1.7.1.1.1" xref="p1.1.m1.1.7.1.1.1.cmml">1</mn>
</mtd>
<mtd columnalign="left" id="p1.1.m1.1.8d" xref="p1.1.m1.1.8.cmml">
<mrow id="p1.1.m1.1.7.1.2.1" xref="p1.1.m1.1.7.1.2.1.cmml">
<mrow id="p1.1.m1.1.7.1.2.1.5" xref="p1.1.m1.1.7.1.2.1.5.cmml">
<mtext id="p1.1.m1.1.7.1.2.1.1" xref="p1.1.m1.1.7.1.2.1.1.cmml"> if </mtext>
<mo id="p1.1.m1.1.7.1.2.1.5.1" xref="p1.1.m1.1.7.1.2.1.5.1.cmml"></mo>
<mn id="p1.1.m1.1.7.1.2.1.2" xref="p1.1.m1.1.7.1.2.1.2.cmml">0</mn>
</mrow>
<mo id="p1.1.m1.1.7.1.2.1.3" xref="p1.1.m1.1.7.1.2.1.3.cmml">∈</mo>
<mi id="p1.1.m1.1.7.1.2.1.4" xref="p1.1.m1.1.7.1.2.1.4.cmml">A</mi>
</mrow>
</mtd>
</mtr>
<mtr id="p1.1.m1.1.8e" xref="p1.1.m1.1.8.cmml">
<mtd columnalign="left" id="p1.1.m1.1.8f" xref="p1.1.m1.1.8.cmml">
<mn id="p1.1.m1.1.7.2.1.1" xref="p1.1.m1.1.7.2.1.1.cmml">0</mn>
</mtd>
<mtd columnalign="left" id="p1.1.m1.1.8g" xref="p1.1.m1.1.8.cmml">
<mrow id="p1.1.m1.1.7.2.2.1" xref="p1.1.m1.1.7.2.2.1.cmml">
<mrow id="p1.1.m1.1.7.2.2.1a" xref="p1.1.m1.1.7.2.2.1.cmml">
<mrow id="p1.1.m1.1.7.2.2.1.6" xref="p1.1.m1.1.7.2.2.1.6.cmml">
<mtext id="p1.1.m1.1.7.2.2.1.1" xref="p1.1.m1.1.7.2.2.1.1.cmml"> if </mtext>
<mo id="p1.1.m1.1.7.2.2.1.6.1" xref="p1.1.m1.1.7.2.2.1.6.1.cmml"></mo>
<mn id="p1.1.m1.1.7.2.2.1.2" xref="p1.1.m1.1.7.2.2.1.2.cmml">0</mn>
</mrow>
<mo id="p1.1.m1.1.7.2.2.1.3" xref="p1.1.m1.1.7.2.2.1.3.cmml">∉</mo>
<mi id="p1.1.m1.1.7.2.2.1.4" xref="p1.1.m1.1.7.2.2.1.4.cmml">A</mi>
</mrow>
<mo id="p1.1.m1.1.7.2.2.1b" xref="p1.1.m1.1.7.2.2.1.cmml">.</mo>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">
<eq id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/>
<apply id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">
<times id="p1.1.m1.1.9.1.1.cmml" xref="p1.1.m1.1.9.1.1"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">μ</ci>
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">A</ci>
</apply>
<apply id="p1.1.m1.1.8a.cmml" xref="p1.1.m1.1.8">
<csymbol cd="latexml" id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">cases</csymbol>
<cn type="integer" id="p1.1.m1.1.7.1.1.1.cmml" xref="p1.1.m1.1.7.1.1.1">1</cn>
<apply id="p1.1.m1.1.7.1.2.1.cmml" xref="p1.1.m1.1.7.1.2.1">
<in id="p1.1.m1.1.7.1.2.1.3.cmml" xref="p1.1.m1.1.7.1.2.1.3"/>
<apply id="p1.1.m1.1.7.1.2.1.5.cmml" xref="p1.1.m1.1.7.1.2.1.5">
<times id="p1.1.m1.1.7.1.2.1.5.1.cmml" xref="p1.1.m1.1.7.1.2.1.5.1"/>
<mtext id="p1.1.m1.1.7.1.2.1.1.cmml" xref="p1.1.m1.1.7.1.2.1.1"> if </mtext>
<cn type="integer" id="p1.1.m1.1.7.1.2.1.2.cmml" xref="p1.1.m1.1.7.1.2.1.2">0</cn>
</apply>
<ci id="p1.1.m1.1.7.1.2.1.4.cmml" xref="p1.1.m1.1.7.1.2.1.4">A</ci>
</apply>
<cn type="integer" id="p1.1.m1.1.7.2.1.1.cmml" xref="p1.1.m1.1.7.2.1.1">0</cn>
<apply id="p1.1.m1.1.7.2.2.1.cmml" xref="p1.1.m1.1.7.2.2.1">
<notin id="p1.1.m1.1.7.2.2.1.3.cmml" xref="p1.1.m1.1.7.2.2.1.3"/>
<apply id="p1.1.m1.1.7.2.2.1.6.cmml" xref="p1.1.m1.1.7.2.2.1.6">
<times id="p1.1.m1.1.7.2.2.1.6.1.cmml" xref="p1.1.m1.1.7.2.2.1.6.1"/>
<mtext id="p1.1.m1.1.7.2.2.1.1.cmml" xref="p1.1.m1.1.7.2.2.1.1"> if </mtext>
<cn type="integer" id="p1.1.m1.1.7.2.2.1.2.cmml" xref="p1.1.m1.1.7.2.2.1.2">0</cn>
</apply>
<ci id="p1.1.m1.1.7.2.2.1.4.cmml" xref="p1.1.m1.1.7.2.2.1.4">A</ci>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\mu(A)={{\begin{cases}1&{{\mbox{ if }}}0\in A\\
0&{{\mbox{ if }}}0\notin A.\end{cases}}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=9e5b29ee42bc8eaadeff7b40f36b1803&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.333ex; height: 5.833ex; width: 23ex;" alt="\mu (A)={{\begin{cases}1&{{\mbox{ if }}}0\in A\\0&{{\mbox{ if }}}0\notin A.\end{cases}}}" data-pagespeed-url-hash="4098667354" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu (A)={\begin{cases}1&{\mbox{ if }}0\in A\\0&{\mbox{ if }}0\notin A.\end{cases}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>μ<!-- μ --></mi>
<mo stretchy="false">(</mo>
<mi>A</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mrow>
<mo>{</mo>
<mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false">
<mtr>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="false" scriptlevel="0">
<mtext> if </mtext>
</mstyle>
</mrow>
<mn>0</mn>
<mo>∈<!-- ∈ --></mo>
<mi>A</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="false" scriptlevel="0">
<mtext> if </mtext>
</mstyle>
</mrow>
<mn>0</mn>
<mo>∉<!-- ∉ --></mo>
<mi>A</mi>
<mo>.</mo>
</mtd>
</mtr>
</mtable>
<mo fence="true" stretchy="true" symmetric="true"></mo>
</mrow>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \mu (A)={\begin{cases}1&{\mbox{ if }}0\in A\\0&{\mbox{ if }}0\notin A.\end{cases}}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/da363046af529f9d167c7e08421ff03545dc15ce" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.505ex; width:22.945ex; height:6.176ex;" alt="{\displaystyle \mu (A)={\begin{cases}1&{\mbox{ if }}0\in A\\0&{\mbox{ if }}0\notin A.\end{cases}}}" data-pagespeed-url-hash="3332635334" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/50" title="Special:DisplayTopics/50">50</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/12130#math.12130.56" title="Special:PermanentLink/12130">Marcus_theory-56</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\lambda_{{{in}}}}">
<semantics id="p1.1.m1.1a">
<msub id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">λ</mi>
<mrow id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">
<mi id="p1.1.m1.1.2.1.1" xref="p1.1.m1.1.2.1.1.cmml">i</mi>
<mo id="p1.1.m1.1.2.1.3" xref="p1.1.m1.1.2.1.3.cmml"></mo>
<mi id="p1.1.m1.1.2.1.2" xref="p1.1.m1.1.2.1.2.cmml">n</mi>
</mrow>
</msub>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
<csymbol cd="ambiguous" id="p1.1.m1.1.3.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">λ</ci>
<apply id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">
<times id="p1.1.m1.1.2.1.3.cmml" xref="p1.1.m1.1.2.1.3"/>
<ci id="p1.1.m1.1.2.1.1.cmml" xref="p1.1.m1.1.2.1.1">i</ci>
<ci id="p1.1.m1.1.2.1.2.cmml" xref="p1.1.m1.1.2.1.2">n</ci>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\lambda_{{{in}}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=07e69f6a926f8048174d66a3c14b922f&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.5ex; height: 2ex; width: 3.167ex;" alt="\lambda _{{{in}}}" data-pagespeed-url-hash="3038610139" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda _{in}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>λ<!-- λ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
<mi>n</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \lambda _{in}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/783bc8059136ee996a4672a36580aaf04aed71fb" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:3.141ex; height:2.509ex;" alt="{\displaystyle \lambda _{in}}" data-pagespeed-url-hash="2373386551" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/51" title="Special:DisplayTopics/51">51</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/16788#math.16788.2" title="Special:PermanentLink/16788">Centrifugal_fan-2</a>
</td>
<td> 1
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle rpm_{{\qvar@construct{x0}}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">r</mi>
<mo id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml"></mo>
<mi id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">p</mi>
<mo id="p1.1.m1.1.5.1a" xref="p1.1.m1.1.5.1.cmml"></mo>
<msub id="p1.1.m1.1.5.2" xref="p1.1.m1.1.5.2.cmml">
<mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">m</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">x0</mi>
</msub>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">
<times id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">r</ci>
<ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">p</ci>
<apply id="p1.1.m1.1.5.2.cmml" xref="p1.1.m1.1.5.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.5.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">m</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">x0</csymbol>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle rpm_{{\qvar@construct{x0}}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=39cc4991d946e96e90a858352fbfcb17&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.5ex; height: 1.667ex; width: 6.333ex;" alt="rpm_{{\qvar{x0}}}" data-pagespeed-url-hash="637592972" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle rpm_{motor}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>r</mi>
<mi>p</mi>
<msub>
<mi>m</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>m</mi>
<mi>o</mi>
<mi>t</mi>
<mi>o</mi>
<mi>r</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle rpm_{motor}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/f53e5854d1a8ec9a7b9b036fc4123811f8880474" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:8.863ex; height:2.009ex;" alt="{\displaystyle rpm_{motor}}" data-pagespeed-url-hash="2056219215" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/52" title="Special:DisplayTopics/52">52</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/21960#math.21960.157" title="Special:PermanentLink/21960">Backstepping-157</a>
</td>
<td> 16
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\underbrace{u_{1}({\mathbf{\qvar@construct{x0}}},z_{1})=v_{1}+{% \dot{u}}_{x}}_{\qvar@construct{x1}}=\overbrace{-{\frac{\partial V_{x}}{% \partial{\qvar@construct{x2}}}}g_{x}({\mathbf{\qvar@construct{x3}}})-k_{1}(% \underbrace{z_{1}-u_{x}({\mathbf{x}})}_{\qvar@construct{x4}})}^{{v_{1}}}\,+\,% \overbrace{{\frac{\qvar@construct{x5}}{\partial{\qvar@construct{x6}}}}(% \underbrace{f_{\qvar@construct{x7}}({\qvar@construct{x8}})+g_{x}({\mathbf{% \qvar@construct{x9}}})z_{1}}_{{{\qvar@construct{x10}}{\text{ (i.e., }}{\frac{% \operatorname{d}{\mathbf{\qvar@construct{x11}}}}{\operatorname{\qvar@construct% {x12}}t}}{\text{\qvar@construct{x13}}}}})}^{{{\qvar@construct{x14}}_{x}{\text{% (i.e., }}{\frac{\operatorname{d}u_{\qvar@construct{x15}}}{\operatorname{d}t}}% {\text{)}}}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">
<munder id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml">
<munder accentunder="true" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">
<mrow id="p1.1.m1.1.1.2" xref="p1.1.m1.1.1.2.cmml">
<mrow id="p1.1.m1.1.1.2.15" xref="p1.1.m1.1.1.2.15.cmml">
<msub id="p1.1.m1.1.1.2.15.2" xref="p1.1.m1.1.1.2.15.2.cmml">
<mi id="p1.1.m1.1.1.2.1" xref="p1.1.m1.1.1.2.1.cmml">u</mi>
<mn id="p1.1.m1.1.1.2.2.1" xref="p1.1.m1.1.1.2.2.1.cmml">1</mn>
</msub>
<mo movablelimits="false" id="p1.1.m1.1.1.2.15.1" xref="p1.1.m1.1.1.2.15.1.cmml"></mo>
<mrow id="p1.1.m1.1.1.2.15.3c" xref="p1.1.m1.1.1.2.15.3.cmml">
<mo movablelimits="false" stretchy="false" id="p1.1.m1.1.1.2.15.3" xref="p1.1.m1.1.1.2.15.3.cmml">(</mo>
<mi mathcolor="red" id="p1.1.m1.1.1.2.4" xref="p1.1.m1.1.1.2.4.cmml">𝐱𝟎</mi>
<mo movablelimits="false" id="p1.1.m1.1.1.2.15.3a" xref="p1.1.m1.1.1.2.15.3.cmml">,</mo>
<msub id="XM1" xref="XM1.cmml">
<mi id="p1.1.m1.1.1.2.6" xref="p1.1.m1.1.1.2.6.cmml">z</mi>
<mn id="p1.1.m1.1.1.2.7.1" xref="p1.1.m1.1.1.2.7.1.cmml">1</mn>
</msub>
<mo movablelimits="false" stretchy="false" id="p1.1.m1.1.1.2.15.3b" xref="p1.1.m1.1.1.2.15.3.cmml">)</mo>
</mrow>
</mrow>
<mo movablelimits="false" id="p1.1.m1.1.1.2.9" xref="p1.1.m1.1.1.2.9.cmml">=</mo>
<mrow id="p1.1.m1.1.1.2.16" xref="p1.1.m1.1.1.2.16.cmml">
<msub id="p1.1.m1.1.1.2.16.1" xref="p1.1.m1.1.1.2.16.1.cmml">
<mi id="p1.1.m1.1.1.2.10" xref="p1.1.m1.1.1.2.10.cmml">v</mi>
<mn id="p1.1.m1.1.1.2.11.1" xref="p1.1.m1.1.1.2.11.1.cmml">1</mn>
</msub>
<mo movablelimits="false" id="p1.1.m1.1.1.2.12" xref="p1.1.m1.1.1.2.12.cmml">+</mo>
<msub id="p1.1.m1.1.1.2.16.2" xref="p1.1.m1.1.1.2.16.2.cmml">
<mover accent="true" id="p1.1.m1.1.1.2.13" xref="p1.1.m1.1.1.2.13.cmml">
<mi id="p1.1.m1.1.1.2.13.2" xref="p1.1.m1.1.1.2.13.2.cmml">u</mi>
<mo movablelimits="false" id="p1.1.m1.1.1.2.13.1" xref="p1.1.m1.1.1.2.13.1.cmml">˙</mo>
</mover>
<mi id="p1.1.m1.1.1.2.14.1" xref="p1.1.m1.1.1.2.14.1.cmml">x</mi>
</msub>
</mrow>
</mrow>
<mo movablelimits="false" id="p1.1.m1.1.1.1" xref="p1.1.m1.1.1.1.cmml">⏟</mo>
</munder>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">x1</mi>
</munder>
<mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">=</mo>
<mrow id="p1.1.m1.1.11.2" xref="p1.1.m1.1.11.2.cmml">
<mpadded width="+1.7pt" id="p1.1.m1.1.11.2.1" xref="p1.1.m1.1.11.2.1.cmml">
<mover id="p1.1.m1.1.11.2.1a" xref="p1.1.m1.1.11.2.1.cmml">
<mover accent="true" id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">
<mrow id="p1.1.m1.1.4.2" xref="p1.1.m1.1.4.2.cmml">
<mrow id="p1.1.m1.1.4.2.15" xref="p1.1.m1.1.4.2.15.cmml">
<mo movablelimits="false" id="p1.1.m1.1.4.2.1" xref="p1.1.m1.1.4.2.1.cmml">-</mo>
<mrow id="p1.1.m1.1.4.2.15.1" xref="p1.1.m1.1.4.2.15.1.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.4.2.2" xref="p1.1.m1.1.4.2.2.cmml">
<mfrac id="p1.1.m1.1.4.2.2a" xref="p1.1.m1.1.4.2.2.cmml">
<mrow id="p1.1.m1.1.4.2.2.2" xref="p1.1.m1.1.4.2.2.2.cmml">
<mo movablelimits="false" id="p1.1.m1.1.4.2.2.2.1" xref="p1.1.m1.1.4.2.2.2.1.cmml">∂</mo>
<mo movablelimits="false" id="p1.1.m1.1.4.2.2.2a" xref="p1.1.m1.1.4.2.2.2.cmml"></mo>
<msub id="p1.1.m1.1.4.2.2.2.4" xref="p1.1.m1.1.4.2.2.2.4.cmml">
<mi id="p1.1.m1.1.4.2.2.2.2" xref="p1.1.m1.1.4.2.2.2.2.cmml">V</mi>
<mi id="p1.1.m1.1.4.2.2.2.3.1" xref="p1.1.m1.1.4.2.2.2.3.1.cmml">x</mi>
</msub>
</mrow>
<mrow id="p1.1.m1.1.4.2.2.3" xref="p1.1.m1.1.4.2.2.3.cmml">
<mo movablelimits="false" id="p1.1.m1.1.4.2.2.3.1" xref="p1.1.m1.1.4.2.2.3.1.cmml">∂</mo>
<mo movablelimits="false" id="p1.1.m1.1.4.2.2.3a" xref="p1.1.m1.1.4.2.2.3.cmml"></mo>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.4.2.2.3.2" xref="p1.1.m1.1.4.2.2.3.2.cmml">x2</mi>
</mrow>
</mfrac>
</mstyle>
<mo movablelimits="false" id="p1.1.m1.1.4.2.15.1.1" xref="p1.1.m1.1.4.2.15.1.1.cmml"></mo>
<msub id="p1.1.m1.1.4.2.15.1.2" xref="p1.1.m1.1.4.2.15.1.2.cmml">
<mi id="p1.1.m1.1.4.2.3" xref="p1.1.m1.1.4.2.3.cmml">g</mi>
<mi id="p1.1.m1.1.4.2.4.1" xref="p1.1.m1.1.4.2.4.1.cmml">x</mi>
</msub>
<mo movablelimits="false" id="p1.1.m1.1.4.2.15.1.1a" xref="p1.1.m1.1.4.2.15.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.4.2.15.1.3b">
<mo movablelimits="false" stretchy="false" id="p1.1.m1.1.4.2.15.1.3">(</mo>
<mi mathcolor="red" id="p1.1.m1.1.4.2.6" xref="p1.1.m1.1.4.2.6.cmml">𝐱𝟑</mi>
<mo movablelimits="false" stretchy="false" id="p1.1.m1.1.4.2.15.1.3a">)</mo>
</mrow>
</mrow>
</mrow>
<mo movablelimits="false" id="p1.1.m1.1.4.2.8" xref="p1.1.m1.1.4.2.8.cmml">-</mo>
<mrow id="p1.1.m1.1.4.2.16" xref="p1.1.m1.1.4.2.16.cmml">
<msub id="p1.1.m1.1.4.2.16.2" xref="p1.1.m1.1.4.2.16.2.cmml">
<mi id="p1.1.m1.1.4.2.9" xref="p1.1.m1.1.4.2.9.cmml">k</mi>
<mn id="p1.1.m1.1.4.2.10.1" xref="p1.1.m1.1.4.2.10.1.cmml">1</mn>
</msub>
<mo movablelimits="false" id="p1.1.m1.1.4.2.16.1" xref="p1.1.m1.1.4.2.16.1.cmml"></mo>
<mrow id="p1.1.m1.1.4.2.16.3b">
<mo movablelimits="false" stretchy="false" id="p1.1.m1.1.4.2.16.3">(</mo>
<munder id="XM2" xref="XM2.cmml">
<munder accentunder="true" id="p1.1.m1.1.4.2.12" xref="p1.1.m1.1.4.2.12.cmml">
<mrow id="p1.1.m1.1.4.2.12.2" xref="p1.1.m1.1.4.2.12.2.cmml">
<msub id="p1.1.m1.1.4.2.12.2.9" xref="p1.1.m1.1.4.2.12.2.9.cmml">
<mi id="p1.1.m1.1.4.2.12.2.1" xref="p1.1.m1.1.4.2.12.2.1.cmml">z</mi>
<mn id="p1.1.m1.1.4.2.12.2.2.1" xref="p1.1.m1.1.4.2.12.2.2.1.cmml">1</mn>
</msub>
<mo movablelimits="false" id="p1.1.m1.1.4.2.12.2.3" xref="p1.1.m1.1.4.2.12.2.3.cmml">-</mo>
<mrow id="p1.1.m1.1.4.2.12.2.10" xref="p1.1.m1.1.4.2.12.2.10.cmml">
<msub id="p1.1.m1.1.4.2.12.2.10.2" xref="p1.1.m1.1.4.2.12.2.10.2.cmml">
<mi id="p1.1.m1.1.4.2.12.2.4" xref="p1.1.m1.1.4.2.12.2.4.cmml">u</mi>
<mi id="p1.1.m1.1.4.2.12.2.5.1" xref="p1.1.m1.1.4.2.12.2.5.1.cmml">x</mi>
</msub>
<mo movablelimits="false" id="p1.1.m1.1.4.2.12.2.10.1" xref="p1.1.m1.1.4.2.12.2.10.1.cmml"></mo>
<mrow id="p1.1.m1.1.4.2.12.2.10.3b">
<mo movablelimits="false" stretchy="false" id="p1.1.m1.1.4.2.12.2.10.3">(</mo>
<mi id="p1.1.m1.1.4.2.12.2.7" xref="p1.1.m1.1.4.2.12.2.7.cmml">𝐱</mi>
<mo movablelimits="false" stretchy="false" id="p1.1.m1.1.4.2.12.2.10.3a">)</mo>
</mrow>
</mrow>
</mrow>
<mo movablelimits="false" id="p1.1.m1.1.4.2.12.1" xref="p1.1.m1.1.4.2.12.1.cmml">⏟</mo>
</munder>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.4.2.13.1" xref="p1.1.m1.1.4.2.13.1.cmml">x4</mi>
</munder>
<mo movablelimits="false" stretchy="false" id="p1.1.m1.1.4.2.16.3a">)</mo>
</mrow>
</mrow>
</mrow>
<mo movablelimits="false" id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">⏞</mo>
</mover>
<msub id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">
<mi id="p1.1.m1.1.5.1.1" xref="p1.1.m1.1.5.1.1.cmml">v</mi>
<mn id="p1.1.m1.1.5.1.2.1" xref="p1.1.m1.1.5.1.2.1.cmml">1</mn>
</msub>
</mover>
</mpadded>
<mo rspace="4.2pt" id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">+</mo>
<mover id="p1.1.m1.1.11.2.2" xref="p1.1.m1.1.11.2.2.cmml">
<mover accent="true" id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">
<mrow id="p1.1.m1.1.9.2" xref="p1.1.m1.1.9.2.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.9.2.1" xref="p1.1.m1.1.9.2.1.cmml">
<mfrac id="p1.1.m1.1.9.2.1a" xref="p1.1.m1.1.9.2.1.cmml">
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.9.2.1.2" xref="p1.1.m1.1.9.2.1.2.cmml">x5</mi>
<mrow id="p1.1.m1.1.9.2.1.3" xref="p1.1.m1.1.9.2.1.3.cmml">
<mo movablelimits="false" id="p1.1.m1.1.9.2.1.3.1" xref="p1.1.m1.1.9.2.1.3.1.cmml">∂</mo>
<mo movablelimits="false" id="p1.1.m1.1.9.2.1.3a" xref="p1.1.m1.1.9.2.1.3.cmml"></mo>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.9.2.1.3.2" xref="p1.1.m1.1.9.2.1.3.2.cmml">x6</mi>
</mrow>
</mfrac>
</mstyle>
<mo movablelimits="false" id="p1.1.m1.1.9.2.6" xref="p1.1.m1.1.9.2.6.cmml"></mo>
<mrow id="p1.1.m1.1.9.2.7b">
<mo movablelimits="false" stretchy="false" id="p1.1.m1.1.9.2.7">(</mo>
<munder id="XM3" xref="XM3.cmml">
<munder accentunder="true" id="p1.1.m1.1.9.2.3" xref="p1.1.m1.1.9.2.3.cmml">
<mrow id="p1.1.m1.1.9.2.3.2" xref="p1.1.m1.1.9.2.3.2.cmml">
<mrow id="p1.1.m1.1.9.2.3.2.14" xref="p1.1.m1.1.9.2.3.2.14.cmml">
<msub id="p1.1.m1.1.9.2.3.2.14.2" xref="p1.1.m1.1.9.2.3.2.14.2.cmml">
<mi id="p1.1.m1.1.9.2.3.2.1" xref="p1.1.m1.1.9.2.3.2.1.cmml">f</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.9.2.3.2.2.1" xref="p1.1.m1.1.9.2.3.2.2.1.cmml">x7</mi>
</msub>
<mo movablelimits="false" id="p1.1.m1.1.9.2.3.2.14.1" xref="p1.1.m1.1.9.2.3.2.14.1.cmml"></mo>
<mrow id="p1.1.m1.1.9.2.3.2.14.3b">
<mo movablelimits="false" stretchy="false" id="p1.1.m1.1.9.2.3.2.14.3">(</mo>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.9.2.3.2.4" xref="p1.1.m1.1.9.2.3.2.4.cmml">x8</mi>
<mo movablelimits="false" stretchy="false" id="p1.1.m1.1.9.2.3.2.14.3a">)</mo>
</mrow>
</mrow>
<mo movablelimits="false" id="p1.1.m1.1.9.2.3.2.6" xref="p1.1.m1.1.9.2.3.2.6.cmml">+</mo>
<mrow id="p1.1.m1.1.9.2.3.2.15" xref="p1.1.m1.1.9.2.3.2.15.cmml">
<msub id="p1.1.m1.1.9.2.3.2.15.2" xref="p1.1.m1.1.9.2.3.2.15.2.cmml">
<mi id="p1.1.m1.1.9.2.3.2.7" xref="p1.1.m1.1.9.2.3.2.7.cmml">g</mi>
<mi id="p1.1.m1.1.9.2.3.2.8.1" xref="p1.1.m1.1.9.2.3.2.8.1.cmml">x</mi>
</msub>
<mo movablelimits="false" id="p1.1.m1.1.9.2.3.2.15.1" xref="p1.1.m1.1.9.2.3.2.15.1.cmml"></mo>
<mrow id="p1.1.m1.1.9.2.3.2.15.3b">
<mo movablelimits="false" stretchy="false" id="p1.1.m1.1.9.2.3.2.15.3">(</mo>
<mi mathcolor="red" id="p1.1.m1.1.9.2.3.2.10" xref="p1.1.m1.1.9.2.3.2.10.cmml">𝐱𝟗</mi>
<mo movablelimits="false" stretchy="false" id="p1.1.m1.1.9.2.3.2.15.3a">)</mo>
</mrow>
<mo movablelimits="false" id="p1.1.m1.1.9.2.3.2.15.1a" xref="p1.1.m1.1.9.2.3.2.15.1.cmml"></mo>
<msub id="p1.1.m1.1.9.2.3.2.15.4" xref="p1.1.m1.1.9.2.3.2.15.4.cmml">
<mi id="p1.1.m1.1.9.2.3.2.12" xref="p1.1.m1.1.9.2.3.2.12.cmml">z</mi>
<mn id="p1.1.m1.1.9.2.3.2.13.1" xref="p1.1.m1.1.9.2.3.2.13.1.cmml">1</mn>
</msub>
</mrow>
</mrow>
<mo movablelimits="false" id="p1.1.m1.1.9.2.3.1" xref="p1.1.m1.1.9.2.3.1.cmml">⏟</mo>
</munder>
<mrow id="p1.1.m1.1.9.2.4.1" xref="p1.1.m1.1.9.2.4.1.cmml">
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.9.2.4.1.1" xref="p1.1.m1.1.9.2.4.1.1.cmml">x10</mi>
<mo movablelimits="false" id="p1.1.m1.1.9.2.4.1.6" xref="p1.1.m1.1.9.2.4.1.6.cmml"></mo>
<mtext id="p1.1.m1.1.9.2.4.1.2" xref="p1.1.m1.1.9.2.4.1.2.cmml"> (i.e., </mtext>
<mo movablelimits="false" id="p1.1.m1.1.9.2.4.1.6a" xref="p1.1.m1.1.9.2.4.1.6.cmml"></mo>
<mfrac id="p1.1.m1.1.9.2.4.1.3" xref="p1.1.m1.1.9.2.4.1.3.cmml">
<mrow id="p1.1.m1.1.9.2.4.1.3.2" xref="p1.1.m1.1.9.2.4.1.3.2.cmml">
<mo movablelimits="false" id="p1.1.m1.1.9.2.4.1.3.2.1" xref="p1.1.m1.1.9.2.4.1.3.2.1.cmml">d</mo>
<mo movablelimits="false" id="p1.1.m1.1.9.2.4.1.3.2a" xref="p1.1.m1.1.9.2.4.1.3.2.cmml"></mo>
<mi mathcolor="red" id="p1.1.m1.1.9.2.4.1.3.2.2" xref="p1.1.m1.1.9.2.4.1.3.2.2.cmml">𝐱𝟏𝟏</mi>
</mrow>
<mrow id="p1.1.m1.1.9.2.4.1.3.3" xref="p1.1.m1.1.9.2.4.1.3.3.cmml">
<mo mathcolor="red" movablelimits="false" id="p1.1.m1.1.9.2.4.1.3.3.1" xref="p1.1.m1.1.9.2.4.1.3.3.1.cmml">x12</mo>
<mo movablelimits="false" id="p1.1.m1.1.9.2.4.1.3.3a" xref="p1.1.m1.1.9.2.4.1.3.3.cmml"></mo>
<mi id="p1.1.m1.1.9.2.4.1.3.3.2" xref="p1.1.m1.1.9.2.4.1.3.3.2.cmml">t</mi>
</mrow>
</mfrac>
<mo movablelimits="false" id="p1.1.m1.1.9.2.4.1.6b" xref="p1.1.m1.1.9.2.4.1.6.cmml"></mo>
<mrow id="p1.1.m1.1.9.2.4.1.4" xref="p1.1.m1.1.9.2.4.1.4.cmml"/>
<mo movablelimits="false" id="p1.1.m1.1.9.2.4.1.6c" xref="p1.1.m1.1.9.2.4.1.6.cmml"></mo>
<mi mathcolor="red" id="p1.1.m1.1.9.2.4.1.5" xref="p1.1.m1.1.9.2.4.1.5.cmml">x13</mi>
</mrow>
</munder>
<mo movablelimits="false" stretchy="false" id="p1.1.m1.1.9.2.7a">)</mo>
</mrow>
</mrow>
<mo movablelimits="false" id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">⏞</mo>
</mover>
<mrow id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">
<msub id="p1.1.m1.1.10.1.7" xref="p1.1.m1.1.10.1.7.cmml">
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.10.1.1" xref="p1.1.m1.1.10.1.1.cmml">x14</mi>
<mi id="p1.1.m1.1.10.1.2.1" xref="p1.1.m1.1.10.1.2.1.cmml">x</mi>
</msub>
<mo id="p1.1.m1.1.10.1.6" xref="p1.1.m1.1.10.1.6.cmml"></mo>
<mtext id="p1.1.m1.1.10.1.3" xref="p1.1.m1.1.10.1.3.cmml"> (i.e., </mtext>
<mo id="p1.1.m1.1.10.1.6a" xref="p1.1.m1.1.10.1.6.cmml"></mo>
<mfrac id="p1.1.m1.1.10.1.4" xref="p1.1.m1.1.10.1.4.cmml">
<mrow id="p1.1.m1.1.10.1.4.2" xref="p1.1.m1.1.10.1.4.2.cmml">
<mo id="p1.1.m1.1.10.1.4.2.1" xref="p1.1.m1.1.10.1.4.2.1.cmml">d</mo>
<mo id="p1.1.m1.1.10.1.4.2a" xref="p1.1.m1.1.10.1.4.2.cmml"></mo>
<msub id="p1.1.m1.1.10.1.4.2.4" xref="p1.1.m1.1.10.1.4.2.4.cmml">
<mi id="p1.1.m1.1.10.1.4.2.2" xref="p1.1.m1.1.10.1.4.2.2.cmml">u</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.10.1.4.2.3.1" xref="p1.1.m1.1.10.1.4.2.3.1.cmml">x15</mi>
</msub>
</mrow>
<mrow id="p1.1.m1.1.10.1.4.3" xref="p1.1.m1.1.10.1.4.3.cmml">
<mo id="p1.1.m1.1.10.1.4.3.1" xref="p1.1.m1.1.10.1.4.3.1.cmml">d</mo>
<mo id="p1.1.m1.1.10.1.4.3a" xref="p1.1.m1.1.10.1.4.3.cmml"></mo>
<mi id="p1.1.m1.1.10.1.4.3.2" xref="p1.1.m1.1.10.1.4.3.2.cmml">t</mi>
</mrow>
</mfrac>
<mo id="p1.1.m1.1.10.1.6b" xref="p1.1.m1.1.10.1.6.cmml"></mo>
<mtext id="p1.1.m1.1.10.1.5" xref="p1.1.m1.1.10.1.5.cmml">)</mtext>
</mrow>
</mover>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">
<eq id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
<apply id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.11.1.1.cmml">subscript</csymbol>
<apply id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">
<ci id="p1.1.m1.1.1.1.cmml" xref="p1.1.m1.1.1.1">normal-⏟</ci>
<apply id="p1.1.m1.1.1.2.cmml" xref="p1.1.m1.1.1.2">
<eq id="p1.1.m1.1.1.2.9.cmml" xref="p1.1.m1.1.1.2.9"/>
<apply id="p1.1.m1.1.1.2.15.cmml" xref="p1.1.m1.1.1.2.15">
<times id="p1.1.m1.1.1.2.15.1.cmml" xref="p1.1.m1.1.1.2.15.1"/>
<apply id="p1.1.m1.1.1.2.15.2.cmml" xref="p1.1.m1.1.1.2.15.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.1.2.15.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.2.1.cmml" xref="p1.1.m1.1.1.2.1">u</ci>
<cn type="integer" id="p1.1.m1.1.1.2.2.1.cmml" xref="p1.1.m1.1.1.2.2.1">1</cn>
</apply>
<interval closure="open" id="p1.1.m1.1.1.2.15.3.cmml" xref="p1.1.m1.1.1.2.15.3">
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.1.2.4.cmml" xref="p1.1.m1.1.1.2.4">x0</csymbol>
<apply id="XM1.cmml" xref="XM1">
<csymbol cd="ambiguous" id="XM1.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.2.6.cmml" xref="p1.1.m1.1.1.2.6">z</ci>
<cn type="integer" id="p1.1.m1.1.1.2.7.1.cmml" xref="p1.1.m1.1.1.2.7.1">1</cn>
</apply>
</interval>
</apply>
<apply id="p1.1.m1.1.1.2.16.cmml" xref="p1.1.m1.1.1.2.16">
<plus id="p1.1.m1.1.1.2.12.cmml" xref="p1.1.m1.1.1.2.12"/>
<apply id="p1.1.m1.1.1.2.16.1.cmml" xref="p1.1.m1.1.1.2.16.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.1.2.16.1.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.2.10.cmml" xref="p1.1.m1.1.1.2.10">v</ci>
<cn type="integer" id="p1.1.m1.1.1.2.11.1.cmml" xref="p1.1.m1.1.1.2.11.1">1</cn>
</apply>
<apply id="p1.1.m1.1.1.2.16.2.cmml" xref="p1.1.m1.1.1.2.16.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.1.2.16.2.1.cmml">subscript</csymbol>
<apply id="p1.1.m1.1.1.2.13.cmml" xref="p1.1.m1.1.1.2.13">
<ci id="p1.1.m1.1.1.2.13.1.cmml" xref="p1.1.m1.1.1.2.13.1">normal-˙</ci>
<ci id="p1.1.m1.1.1.2.13.2.cmml" xref="p1.1.m1.1.1.2.13.2">u</ci>
</apply>
<ci id="p1.1.m1.1.1.2.14.1.cmml" xref="p1.1.m1.1.1.2.14.1">x</ci>
</apply>
</apply>
</apply>
</apply>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">x1</csymbol>
</apply>
<apply id="p1.1.m1.1.11.2.cmml" xref="p1.1.m1.1.11.2">
<plus id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
<apply id="p1.1.m1.1.11.2.1.cmml" xref="p1.1.m1.1.11.2.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.11.2.1.1.cmml">superscript</csymbol>
<apply id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">
<ci id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">normal-⏞</ci>
<apply id="p1.1.m1.1.4.2.cmml" xref="p1.1.m1.1.4.2">
<minus id="p1.1.m1.1.4.2.8.cmml" xref="p1.1.m1.1.4.2.8"/>
<apply id="p1.1.m1.1.4.2.15.cmml" xref="p1.1.m1.1.4.2.15">
<minus id="p1.1.m1.1.4.2.1.cmml" xref="p1.1.m1.1.4.2.1"/>
<apply id="p1.1.m1.1.4.2.15.1.cmml" xref="p1.1.m1.1.4.2.15.1">
<times id="p1.1.m1.1.4.2.15.1.1.cmml" xref="p1.1.m1.1.4.2.15.1.1"/>
<apply id="p1.1.m1.1.4.2.2.cmml" xref="p1.1.m1.1.4.2.2">
<divide id="p1.1.m1.1.4.2.2.1.cmml"/>
<apply id="p1.1.m1.1.4.2.2.2.cmml" xref="p1.1.m1.1.4.2.2.2">
<partialdiff id="p1.1.m1.1.4.2.2.2.1.cmml" xref="p1.1.m1.1.4.2.2.2.1"/>
<apply id="p1.1.m1.1.4.2.2.2.4.cmml" xref="p1.1.m1.1.4.2.2.2.4">
<csymbol cd="ambiguous" id="p1.1.m1.1.4.2.2.2.4.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.4.2.2.2.2.cmml" xref="p1.1.m1.1.4.2.2.2.2">V</ci>
<ci id="p1.1.m1.1.4.2.2.2.3.1.cmml" xref="p1.1.m1.1.4.2.2.2.3.1">x</ci>
</apply>
</apply>
<apply id="p1.1.m1.1.4.2.2.3.cmml" xref="p1.1.m1.1.4.2.2.3">
<partialdiff id="p1.1.m1.1.4.2.2.3.1.cmml" xref="p1.1.m1.1.4.2.2.3.1"/>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.4.2.2.3.2.cmml" xref="p1.1.m1.1.4.2.2.3.2">x2</csymbol>
</apply>
</apply>
<apply id="p1.1.m1.1.4.2.15.1.2.cmml" xref="p1.1.m1.1.4.2.15.1.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.4.2.15.1.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.4.2.3.cmml" xref="p1.1.m1.1.4.2.3">g</ci>
<ci id="p1.1.m1.1.4.2.4.1.cmml" xref="p1.1.m1.1.4.2.4.1">x</ci>
</apply>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.4.2.6.cmml" xref="p1.1.m1.1.4.2.6">x3</csymbol>
</apply>
</apply>
<apply id="p1.1.m1.1.4.2.16.cmml" xref="p1.1.m1.1.4.2.16">
<times id="p1.1.m1.1.4.2.16.1.cmml" xref="p1.1.m1.1.4.2.16.1"/>
<apply id="p1.1.m1.1.4.2.16.2.cmml" xref="p1.1.m1.1.4.2.16.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.4.2.16.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.4.2.9.cmml" xref="p1.1.m1.1.4.2.9">k</ci>
<cn type="integer" id="p1.1.m1.1.4.2.10.1.cmml" xref="p1.1.m1.1.4.2.10.1">1</cn>
</apply>
<apply id="XM2.cmml" xref="XM2">
<csymbol cd="ambiguous" id="XM2.1.cmml">subscript</csymbol>
<apply id="p1.1.m1.1.4.2.12.cmml" xref="p1.1.m1.1.4.2.12">
<ci id="p1.1.m1.1.4.2.12.1.cmml" xref="p1.1.m1.1.4.2.12.1">normal-⏟</ci>
<apply id="p1.1.m1.1.4.2.12.2.cmml" xref="p1.1.m1.1.4.2.12.2">
<minus id="p1.1.m1.1.4.2.12.2.3.cmml" xref="p1.1.m1.1.4.2.12.2.3"/>
<apply id="p1.1.m1.1.4.2.12.2.9.cmml" xref="p1.1.m1.1.4.2.12.2.9">
<csymbol cd="ambiguous" id="p1.1.m1.1.4.2.12.2.9.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.4.2.12.2.1.cmml" xref="p1.1.m1.1.4.2.12.2.1">z</ci>
<cn type="integer" id="p1.1.m1.1.4.2.12.2.2.1.cmml" xref="p1.1.m1.1.4.2.12.2.2.1">1</cn>
</apply>
<apply id="p1.1.m1.1.4.2.12.2.10.cmml" xref="p1.1.m1.1.4.2.12.2.10">
<times id="p1.1.m1.1.4.2.12.2.10.1.cmml" xref="p1.1.m1.1.4.2.12.2.10.1"/>
<apply id="p1.1.m1.1.4.2.12.2.10.2.cmml" xref="p1.1.m1.1.4.2.12.2.10.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.4.2.12.2.10.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.4.2.12.2.4.cmml" xref="p1.1.m1.1.4.2.12.2.4">u</ci>
<ci id="p1.1.m1.1.4.2.12.2.5.1.cmml" xref="p1.1.m1.1.4.2.12.2.5.1">x</ci>
</apply>
<ci id="p1.1.m1.1.4.2.12.2.7.cmml" xref="p1.1.m1.1.4.2.12.2.7">𝐱</ci>
</apply>
</apply>
</apply>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.4.2.13.1.cmml" xref="p1.1.m1.1.4.2.13.1">x4</csymbol>
</apply>
</apply>
</apply>
</apply>
<apply id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.5.1.3.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.5.1.1.cmml" xref="p1.1.m1.1.5.1.1">v</ci>
<cn type="integer" id="p1.1.m1.1.5.1.2.1.cmml" xref="p1.1.m1.1.5.1.2.1">1</cn>
</apply>
</apply>
<apply id="p1.1.m1.1.11.2.2.cmml" xref="p1.1.m1.1.11.2.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.11.2.2.1.cmml">superscript</csymbol>
<apply id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">
<ci id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">normal-⏞</ci>
<apply id="p1.1.m1.1.9.2.cmml" xref="p1.1.m1.1.9.2">
<times id="p1.1.m1.1.9.2.6.cmml" xref="p1.1.m1.1.9.2.6"/>
<apply id="p1.1.m1.1.9.2.1.cmml" xref="p1.1.m1.1.9.2.1">
<divide id="p1.1.m1.1.9.2.1.1.cmml"/>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.9.2.1.2.cmml" xref="p1.1.m1.1.9.2.1.2">x5</csymbol>
<apply id="p1.1.m1.1.9.2.1.3.cmml" xref="p1.1.m1.1.9.2.1.3">
<partialdiff id="p1.1.m1.1.9.2.1.3.1.cmml" xref="p1.1.m1.1.9.2.1.3.1"/>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.9.2.1.3.2.cmml" xref="p1.1.m1.1.9.2.1.3.2">x6</csymbol>
</apply>
</apply>
<apply id="XM3.cmml" xref="XM3">
<csymbol cd="ambiguous" id="XM3.1.cmml">subscript</csymbol>
<apply id="p1.1.m1.1.9.2.3.cmml" xref="p1.1.m1.1.9.2.3">
<ci id="p1.1.m1.1.9.2.3.1.cmml" xref="p1.1.m1.1.9.2.3.1">normal-⏟</ci>
<apply id="p1.1.m1.1.9.2.3.2.cmml" xref="p1.1.m1.1.9.2.3.2">
<plus id="p1.1.m1.1.9.2.3.2.6.cmml" xref="p1.1.m1.1.9.2.3.2.6"/>
<apply id="p1.1.m1.1.9.2.3.2.14.cmml" xref="p1.1.m1.1.9.2.3.2.14">
<times id="p1.1.m1.1.9.2.3.2.14.1.cmml" xref="p1.1.m1.1.9.2.3.2.14.1"/>
<apply id="p1.1.m1.1.9.2.3.2.14.2.cmml" xref="p1.1.m1.1.9.2.3.2.14.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.9.2.3.2.14.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.9.2.3.2.1.cmml" xref="p1.1.m1.1.9.2.3.2.1">f</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.9.2.3.2.2.1.cmml" xref="p1.1.m1.1.9.2.3.2.2.1">x7</csymbol>
</apply>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.9.2.3.2.4.cmml" xref="p1.1.m1.1.9.2.3.2.4">x8</csymbol>
</apply>
<apply id="p1.1.m1.1.9.2.3.2.15.cmml" xref="p1.1.m1.1.9.2.3.2.15">
<times id="p1.1.m1.1.9.2.3.2.15.1.cmml" xref="p1.1.m1.1.9.2.3.2.15.1"/>
<apply id="p1.1.m1.1.9.2.3.2.15.2.cmml" xref="p1.1.m1.1.9.2.3.2.15.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.9.2.3.2.15.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.9.2.3.2.7.cmml" xref="p1.1.m1.1.9.2.3.2.7">g</ci>
<ci id="p1.1.m1.1.9.2.3.2.8.1.cmml" xref="p1.1.m1.1.9.2.3.2.8.1">x</ci>
</apply>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.9.2.3.2.10.cmml" xref="p1.1.m1.1.9.2.3.2.10">x9</csymbol>
<apply id="p1.1.m1.1.9.2.3.2.15.4.cmml" xref="p1.1.m1.1.9.2.3.2.15.4">
<csymbol cd="ambiguous" id="p1.1.m1.1.9.2.3.2.15.4.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.9.2.3.2.12.cmml" xref="p1.1.m1.1.9.2.3.2.12">z</ci>
<cn type="integer" id="p1.1.m1.1.9.2.3.2.13.1.cmml" xref="p1.1.m1.1.9.2.3.2.13.1">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply id="p1.1.m1.1.9.2.4.1.cmml" xref="p1.1.m1.1.9.2.4.1">
<times id="p1.1.m1.1.9.2.4.1.6.cmml" xref="p1.1.m1.1.9.2.4.1.6"/>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.9.2.4.1.1.cmml" xref="p1.1.m1.1.9.2.4.1.1">x10</csymbol>
<mtext id="p1.1.m1.1.9.2.4.1.2.cmml" xref="p1.1.m1.1.9.2.4.1.2"> (i.e., </mtext>
<apply id="p1.1.m1.1.9.2.4.1.3.cmml" xref="p1.1.m1.1.9.2.4.1.3">
<divide id="p1.1.m1.1.9.2.4.1.3.1.cmml"/>
<apply id="p1.1.m1.1.9.2.4.1.3.2.cmml" xref="p1.1.m1.1.9.2.4.1.3.2">
<ci id="p1.1.m1.1.9.2.4.1.3.2.1.cmml" xref="p1.1.m1.1.9.2.4.1.3.2.1">normal-d</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.9.2.4.1.3.2.2.cmml" xref="p1.1.m1.1.9.2.4.1.3.2.2">x11</csymbol>
</apply>
<apply id="p1.1.m1.1.9.2.4.1.3.3.cmml" xref="p1.1.m1.1.9.2.4.1.3.3">
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.9.2.4.1.3.3.1.cmml" xref="p1.1.m1.1.9.2.4.1.3.3.1">x12</csymbol>
<ci id="p1.1.m1.1.9.2.4.1.3.3.2.cmml" xref="p1.1.m1.1.9.2.4.1.3.3.2">t</ci>
</apply>
</apply>
<mtext id="p1.1.m1.1.9.2.4.1.4.cmml" xref="p1.1.m1.1.9.2.4.1.4"/>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.9.2.4.1.5.cmml" xref="p1.1.m1.1.9.2.4.1.5">x13</csymbol>
</apply>
</apply>
</apply>
</apply>
<apply id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">
<times id="p1.1.m1.1.10.1.6.cmml" xref="p1.1.m1.1.10.1.6"/>
<apply id="p1.1.m1.1.10.1.7.cmml" xref="p1.1.m1.1.10.1.7">
<csymbol cd="ambiguous" id="p1.1.m1.1.10.1.7.1.cmml">subscript</csymbol>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.10.1.1.cmml" xref="p1.1.m1.1.10.1.1">x14</csymbol>
<ci id="p1.1.m1.1.10.1.2.1.cmml" xref="p1.1.m1.1.10.1.2.1">x</ci>
</apply>
<mtext id="p1.1.m1.1.10.1.3.cmml" xref="p1.1.m1.1.10.1.3"> (i.e., </mtext>
<apply id="p1.1.m1.1.10.1.4.cmml" xref="p1.1.m1.1.10.1.4">
<divide id="p1.1.m1.1.10.1.4.1.cmml"/>
<apply id="p1.1.m1.1.10.1.4.2.cmml" xref="p1.1.m1.1.10.1.4.2">
<ci id="p1.1.m1.1.10.1.4.2.1.cmml" xref="p1.1.m1.1.10.1.4.2.1">normal-d</ci>
<apply id="p1.1.m1.1.10.1.4.2.4.cmml" xref="p1.1.m1.1.10.1.4.2.4">
<csymbol cd="ambiguous" id="p1.1.m1.1.10.1.4.2.4.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.10.1.4.2.2.cmml" xref="p1.1.m1.1.10.1.4.2.2">u</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.10.1.4.2.3.1.cmml" xref="p1.1.m1.1.10.1.4.2.3.1">x15</csymbol>
</apply>
</apply>
<apply id="p1.1.m1.1.10.1.4.3.cmml" xref="p1.1.m1.1.10.1.4.3">
<ci id="p1.1.m1.1.10.1.4.3.1.cmml" xref="p1.1.m1.1.10.1.4.3.1">normal-d</ci>
<ci id="p1.1.m1.1.10.1.4.3.2.cmml" xref="p1.1.m1.1.10.1.4.3.2">t</ci>
</apply>
</apply>
<mtext id="p1.1.m1.1.10.1.5.cmml" xref="p1.1.m1.1.10.1.5">)</mtext>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\underbrace{u_{1}({\mathbf{\qvar@construct{x0}}},z_{1})=v_{1}+{%
\dot{u}}_{x}}_{\qvar@construct{x1}}=\overbrace{-{\frac{\partial V_{x}}{%
\partial{\qvar@construct{x2}}}}g_{x}({\mathbf{\qvar@construct{x3}}})-k_{1}(%
\underbrace{z_{1}-u_{x}({\mathbf{x}})}_{\qvar@construct{x4}})}^{{v_{1}}}\,+\,%
\overbrace{{\frac{\qvar@construct{x5}}{\partial{\qvar@construct{x6}}}}(%
\underbrace{f_{\qvar@construct{x7}}({\qvar@construct{x8}})+g_{x}({\mathbf{%
\qvar@construct{x9}}})z_{1}}_{{{\qvar@construct{x10}}{\text{ (i.e., }}{\frac{%
\operatorname{d}{\mathbf{\qvar@construct{x11}}}}{\operatorname{\qvar@construct%
{x12}}t}}{\text{\qvar@construct{x13}}}}})}^{{{\qvar@construct{x14}}_{x}{\text{%
(i.e., }}{\frac{\operatorname{d}u_{\qvar@construct{x15}}}{\operatorname{d}t}}%
{\text{)}}}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=9f8221a45f0696330d0ac9028f3e73d6&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -5.833ex; height: 14.333ex; width: 89.833ex;" alt="\underbrace{u_{1}({\mathbf{\qvar{x0}}},z_{1})=v_{1}+{\dot{u}}_{x}}_{\qvar{x1}}=\overbrace{-{\frac{\partial V_{x}}{\partial{\qvar{x2}}}}g_{x}({\mathbf{\qvar{x3}}})-k_{1}(\underbrace{z_{1}-u_{x}({\mathbf{x}})}_{\qvar{x4}})}^{{v_{1}}}\,+\,\overbrace{{\frac{\qvar{x5}}{\partial{\qvar{x6}}}}(\underbrace{f_{\qvar{x7}}({\qvar{x8}})+g_{x}({\mathbf{\qvar{x9}}})z_{1}}_{{{\qvar{x10}}{\text{ (i.e., }}{\frac{\operatorname{d}{\mathbf{\qvar{x11}}}}{\operatorname{\qvar{x12}}t}}{\text{\qvar{x13}}}}})}^{{{\qvar{x14}}_{x}{\text{ (i.e., }}{\frac{\operatorname{d}u_{\qvar{x15}}}{\operatorname{d}t}}{\text{)}}}}" data-pagespeed-url-hash="2018474013" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \underbrace {u_{1}(\mathbf {x} ,z_{1})=v_{1}+{\dot {u}}_{x}} _{{\text{By definition of }}v_{1}}=\overbrace {-{\frac {\partial V_{x}}{\partial \mathbf {x} }}g_{x}(\mathbf {x} )-k_{1}(\underbrace {z_{1}-u_{x}(\mathbf {x} )} _{e_{1}})} ^{v_{1}}\,+\,\overbrace {{\frac {\partial u_{x}}{\partial \mathbf {x} }}(\underbrace {f_{x}(\mathbf {x} )+g_{x}(\mathbf {x} )z_{1}} _{{\dot {\mathbf {x} }}{\text{ (i.e., }}{\frac {\operatorname {d} \mathbf {x} }{\operatorname {d} t}}{\text{)}}})} ^{{\dot {u}}_{x}{\text{ (i.e., }}{\frac {\operatorname {d} u_{x}}{\operatorname {d} t}}{\text{)}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<munder>
<mrow class="MJX-TeXAtom-OP MJX-fixedlimits">
<munder>
<mrow>
<msub>
<mi>u</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<mo stretchy="false">(</mo>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="bold">x</mi>
</mrow>
<mo>,</mo>
<msub>
<mi>z</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<mo stretchy="false">)</mo>
<mo>=</mo>
<msub>
<mi>v</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>u</mi>
<mo>˙<!-- ˙ --></mo>
</mover>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi>x</mi>
</mrow>
</msub>
</mrow>
<mo>⏟<!-- ⏟ --></mo>
</munder>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mtext>By definition of </mtext>
</mrow>
<msub>
<mi>v</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
</mrow>
</munder>
<mo>=</mo>
<mover>
<mrow class="MJX-TeXAtom-OP MJX-fixedlimits">
<mover>
<mrow>
<mo>−<!-- − --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<msub>
<mi>V</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>x</mi>
</mrow>
</msub>
</mrow>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="bold">x</mi>
</mrow>
</mrow>
</mfrac>
</mrow>
<msub>
<mi>g</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>x</mi>
</mrow>
</msub>
<mo stretchy="false">(</mo>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="bold">x</mi>
</mrow>
<mo stretchy="false">)</mo>
<mo>−<!-- − --></mo>
<msub>
<mi>k</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<mo stretchy="false">(</mo>
<munder>
<mrow class="MJX-TeXAtom-OP MJX-fixedlimits">
<munder>
<mrow>
<msub>
<mi>z</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<mo>−<!-- − --></mo>
<msub>
<mi>u</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>x</mi>
</mrow>
</msub>
<mo stretchy="false">(</mo>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="bold">x</mi>
</mrow>
<mo stretchy="false">)</mo>
</mrow>
<mo>⏟<!-- ⏟ --></mo>
</munder>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<msub>
<mi>e</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
</mrow>
</munder>
<mo stretchy="false">)</mo>
</mrow>
<mo>⏞<!-- ⏞ --></mo>
</mover>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<msub>
<mi>v</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mover>
<mspace width="thinmathspace"/>
<mo>+</mo>
<mspace width="thinmathspace"/>
<mover>
<mrow class="MJX-TeXAtom-OP MJX-fixedlimits">
<mover>
<mrow>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<msub>
<mi>u</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>x</mi>
</mrow>
</msub>
</mrow>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="bold">x</mi>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo stretchy="false">(</mo>
<munder>
<mrow class="MJX-TeXAtom-OP MJX-fixedlimits">
<munder>
<mrow>
<msub>
<mi>f</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>x</mi>
</mrow>
</msub>
<mo stretchy="false">(</mo>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="bold">x</mi>
</mrow>
<mo stretchy="false">)</mo>
<mo>+</mo>
<msub>
<mi>g</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>x</mi>
</mrow>
</msub>
<mo stretchy="false">(</mo>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="bold">x</mi>
</mrow>
<mo stretchy="false">)</mo>
<msub>
<mi>z</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mo>⏟<!-- ⏟ --></mo>
</munder>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="bold">x</mi>
</mrow>
<mo>˙<!-- ˙ --></mo>
</mover>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mtext> (i.e., </mtext>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi mathvariant="normal">d</mi>
<mo>⁡<!-- --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="bold">x</mi>
</mrow>
</mrow>
<mrow>
<mi mathvariant="normal">d</mi>
<mo>⁡<!-- --></mo>
<mi>t</mi>
</mrow>
</mfrac>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mtext>)</mtext>
</mrow>
</mrow>
</munder>
<mo stretchy="false">)</mo>
</mrow>
<mo>⏞<!-- ⏞ --></mo>
</mover>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<msub>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>u</mi>
<mo>˙<!-- ˙ --></mo>
</mover>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi>x</mi>
</mrow>
</msub>
<mrow class="MJX-TeXAtom-ORD">
<mtext> (i.e., </mtext>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi mathvariant="normal">d</mi>
<mo>⁡<!-- --></mo>
<msub>
<mi>u</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>x</mi>
</mrow>
</msub>
</mrow>
<mrow>
<mi mathvariant="normal">d</mi>
<mo>⁡<!-- --></mo>
<mi>t</mi>
</mrow>
</mfrac>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mtext>)</mtext>
</mrow>
</mrow>
</mover>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \underbrace {u_{1}(\mathbf {x} ,z_{1})=v_{1}+{\dot {u}}_{x}} _{{\text{By definition of }}v_{1}}=\overbrace {-{\frac {\partial V_{x}}{\partial \mathbf {x} }}g_{x}(\mathbf {x} )-k_{1}(\underbrace {z_{1}-u_{x}(\mathbf {x} )} _{e_{1}})} ^{v_{1}}\,+\,\overbrace {{\frac {\partial u_{x}}{\partial \mathbf {x} }}(\underbrace {f_{x}(\mathbf {x} )+g_{x}(\mathbf {x} )z_{1}} _{{\dot {\mathbf {x} }}{\text{ (i.e., }}{\frac {\operatorname {d} \mathbf {x} }{\operatorname {d} t}}{\text{)}}})} ^{{\dot {u}}_{x}{\text{ (i.e., }}{\frac {\operatorname {d} u_{x}}{\operatorname {d} t}}{\text{)}}}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/07392ae0eb769e7c529d384af883357347f973a7" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -6.005ex; margin-right: -0.028ex; width:78.218ex; height:14.509ex;" alt="{\displaystyle \underbrace {u_{1}(\mathbf {x} ,z_{1})=v_{1}+{\dot {u}}_{x}} _{{\text{By definition of }}v_{1}}=\overbrace {-{\frac {\partial V_{x}}{\partial \mathbf {x} }}g_{x}(\mathbf {x} )-k_{1}(\underbrace {z_{1}-u_{x}(\mathbf {x} )} _{e_{1}})} ^{v_{1}}\,+\,\overbrace {{\frac {\partial u_{x}}{\partial \mathbf {x} }}(\underbrace {f_{x}(\mathbf {x} )+g_{x}(\mathbf {x} )z_{1}} _{{\dot {\mathbf {x} }}{\text{ (i.e., }}{\frac {\operatorname {d} \mathbf {x} }{\operatorname {d} t}}{\text{)}}})} ^{{\dot {u}}_{x}{\text{ (i.e., }}{\frac {\operatorname {d} u_{x}}{\operatorname {d} t}}{\text{)}}}}" data-pagespeed-url-hash="3246962273" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/53" title="Special:DisplayTopics/53">53</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/14318#math.14318.10" title="Special:PermanentLink/14318">Stochastic_volatility-10</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle E\left[{{\hat{\sigma}}}^{{2}}\right]={{\frac{n-1}{n}}}\sigma^{{% 2}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">
<mrow id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">E</mi>
<mo id="p1.1.m1.1.10.1.1" xref="p1.1.m1.1.10.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.10.1.2b" xref="p1.1.m1.1.10.1.2.cmml">
<mo id="p1.1.m1.1.10.1.2" xref="p1.1.m1.1.10.1.2.cmml">[</mo>
<msup id="XM1" xref="XM1.cmml">
<mover accent="true" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
<mi id="p1.1.m1.1.3.2" xref="p1.1.m1.1.3.2.cmml">σ</mi>
<mo stretchy="false" id="p1.1.m1.1.3.1" xref="p1.1.m1.1.3.1.cmml">^</mo>
</mover>
<mn id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">2</mn>
</msup>
<mo id="p1.1.m1.1.10.1.2a" xref="p1.1.m1.1.10.1.2.cmml">]</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">=</mo>
<mrow id="p1.1.m1.1.10.2" xref="p1.1.m1.1.10.2.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">
<mfrac id="p1.1.m1.1.7a" xref="p1.1.m1.1.7.cmml">
<mrow id="p1.1.m1.1.7.2" xref="p1.1.m1.1.7.2.cmml">
<mi id="p1.1.m1.1.7.2.1" xref="p1.1.m1.1.7.2.1.cmml">n</mi>
<mo id="p1.1.m1.1.7.2.2" xref="p1.1.m1.1.7.2.2.cmml">-</mo>
<mn id="p1.1.m1.1.7.2.3" xref="p1.1.m1.1.7.2.3.cmml">1</mn>
</mrow>
<mi id="p1.1.m1.1.7.3" xref="p1.1.m1.1.7.3.cmml">n</mi>
</mfrac>
</mstyle>
<mo id="p1.1.m1.1.10.2.1" xref="p1.1.m1.1.10.2.1.cmml"></mo>
<msup id="p1.1.m1.1.10.2.2" xref="p1.1.m1.1.10.2.2.cmml">
<mi id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">σ</mi>
<mn id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">2</mn>
</msup>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">
<eq id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
<apply id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">
<times id="p1.1.m1.1.10.1.1.cmml" xref="p1.1.m1.1.10.1.1"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">E</ci>
<apply id="p1.1.m1.1.10.1.2a.cmml" xref="p1.1.m1.1.10.1.2">
<csymbol cd="latexml" id="p1.1.m1.1.10.1.2.cmml" xref="p1.1.m1.1.10.1.2">delimited-[]</csymbol>
<apply id="XM1.cmml" xref="XM1">
<csymbol cd="ambiguous" id="XM1.1.cmml">superscript</csymbol>
<apply id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
<ci id="p1.1.m1.1.3.1.cmml" xref="p1.1.m1.1.3.1">normal-^</ci>
<ci id="p1.1.m1.1.3.2.cmml" xref="p1.1.m1.1.3.2">σ</ci>
</apply>
<cn type="integer" id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">2</cn>
</apply>
</apply>
</apply>
<apply id="p1.1.m1.1.10.2.cmml" xref="p1.1.m1.1.10.2">
<times id="p1.1.m1.1.10.2.1.cmml" xref="p1.1.m1.1.10.2.1"/>
<apply id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">
<divide id="p1.1.m1.1.7.1.cmml"/>
<apply id="p1.1.m1.1.7.2.cmml" xref="p1.1.m1.1.7.2">
<minus id="p1.1.m1.1.7.2.2.cmml" xref="p1.1.m1.1.7.2.2"/>
<ci id="p1.1.m1.1.7.2.1.cmml" xref="p1.1.m1.1.7.2.1">n</ci>
<cn type="integer" id="p1.1.m1.1.7.2.3.cmml" xref="p1.1.m1.1.7.2.3">1</cn>
</apply>
<ci id="p1.1.m1.1.7.3.cmml" xref="p1.1.m1.1.7.3">n</ci>
</apply>
<apply id="p1.1.m1.1.10.2.2.cmml" xref="p1.1.m1.1.10.2.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.10.2.2.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">σ</ci>
<cn type="integer" id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">2</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle E\left[{{\hat{\sigma}}}^{{2}}\right]={{\frac{n-1}{n}}}\sigma^{{%
2}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=90bba4456ea2c776498e8816f065022e&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.667ex; height: 4.833ex; width: 19ex;" alt="E\left[{{\hat {\sigma }}}^{{2}}\right]={{\frac {n-1}{n}}}\sigma ^{{2}}" data-pagespeed-url-hash="579011414" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E\left[{\hat {\sigma }}^{2}\right]={\frac {n-1}{n}}\sigma ^{2}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>E</mi>
<mrow>
<mo>[</mo>
<msup>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>σ<!-- σ --></mi>
<mo stretchy="false">^<!-- ^ --></mo>
</mover>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>]</mo>
</mrow>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi>n</mi>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</mfrac>
</mrow>
<msup>
<mi>σ<!-- σ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle E\left[{\hat {\sigma }}^{2}\right]={\frac {n-1}{n}}\sigma ^{2}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/d5c5c168bcd9bd7510cd6321a59d7cb2377a7234" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.838ex; width:18.203ex; height:5.176ex;" alt="{\displaystyle E\left[{\hat {\sigma }}^{2}\right]={\frac {n-1}{n}}\sigma ^{2}}" data-pagespeed-url-hash="3049204863" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/54" title="Special:DisplayTopics/54">54</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/13072#math.13072.63" title="Special:PermanentLink/13072">Separation_logic-63</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{{\mathsf{fv}}}}">
<semantics id="p1.1.m1.1a">
<mi id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">𝖿𝗏</mi>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">𝖿𝗏</ci>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{{\mathsf{fv}}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=bea887d9b7fd216eb2bf57290354a815&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.167ex; height: 1.667ex; width: 1.833ex;" alt="{{\mathsf {fv}}}" data-pagespeed-url-hash="1309002212" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathsf {fv}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="sans-serif">f</mi>
<mi mathvariant="sans-serif">v</mi>
</mrow>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\mathsf {fv}}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/7c015e66dcf04760b4af9837f182731888c5e945" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.879ex; height:2.176ex;" alt="{\displaystyle {\mathsf {fv}}}" data-pagespeed-url-hash="3627860797" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/55" title="Special:DisplayTopics/55">55</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/10050#math.10050.2" title="Special:PermanentLink/10050">Image_moment-2</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\sum_{{x}}\sum_{{y}}I(x,y)\,\!}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.13.1" xref="p1.1.m1.1.13.1.cmml">
<munder id="p1.1.m1.1.13.1a" xref="p1.1.m1.1.13.1.cmml">
<mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">∑</mo>
<mi id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">x</mi>
</munder>
</mstyle>
<mrow id="p1.1.m1.1.13.2" xref="p1.1.m1.1.13.2.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.13.2.1" xref="p1.1.m1.1.13.2.1.cmml">
<munder id="p1.1.m1.1.13.2.1a" xref="p1.1.m1.1.13.2.1.cmml">
<mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">∑</mo>
<mi id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">y</mi>
</munder>
</mstyle>
<mrow id="p1.1.m1.1.13.2.2" xref="p1.1.m1.1.13.2.2.cmml">
<mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">I</mi>
<mo id="p1.1.m1.1.13.2.2.1" xref="p1.1.m1.1.13.2.2.1.cmml"></mo>
<mrow id="p1.1.m1.1.13.2.2.2c" xref="p1.1.m1.1.13.2.2.2.cmml">
<mo stretchy="false" id="p1.1.m1.1.13.2.2.2" xref="p1.1.m1.1.13.2.2.2.cmml">(</mo>
<mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">x</mi>
<mo id="p1.1.m1.1.13.2.2.2a" xref="p1.1.m1.1.13.2.2.2.cmml">,</mo>
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">y</mi>
<mo stretchy="false" id="p1.1.m1.1.13.2.2.2b" xref="p1.1.m1.1.13.2.2.2.cmml">)</mo>
</mrow>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">
<apply id="p1.1.m1.1.13.1.cmml" xref="p1.1.m1.1.13.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.13.1.1.cmml">subscript</csymbol>
<sum id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1"/>
<ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">x</ci>
</apply>
<apply id="p1.1.m1.1.13.2.cmml" xref="p1.1.m1.1.13.2">
<apply id="p1.1.m1.1.13.2.1.cmml" xref="p1.1.m1.1.13.2.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.13.2.1.1.cmml">subscript</csymbol>
<sum id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
<ci id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">y</ci>
</apply>
<apply id="p1.1.m1.1.13.2.2.cmml" xref="p1.1.m1.1.13.2.2">
<times id="p1.1.m1.1.13.2.2.1.cmml" xref="p1.1.m1.1.13.2.2.1"/>
<ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">I</ci>
<interval closure="open" id="p1.1.m1.1.13.2.2.2.cmml" xref="p1.1.m1.1.13.2.2.2">
<ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">x</ci>
<ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">y</ci>
</interval>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\sum_{{x}}\sum_{{y}}I(x,y)\,\!}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=31d46ec4b4668215e91f16ad114d296c&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.167ex; height: 5.333ex; width: 14.5ex;" alt="\sum _{{x}}\sum _{{y}}I(x,y)\,\!" data-pagespeed-url-hash="1201888902" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{x}\sum _{y}I(x,y)\,\!}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<munder>
<mo>∑<!-- ∑ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>x</mi>
</mrow>
</munder>
<munder>
<mo>∑<!-- ∑ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>y</mi>
</mrow>
</munder>
<mi>I</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo stretchy="false">)</mo>
<mspace width="thinmathspace"/>
<mspace width="negativethinmathspace"/>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \sum _{x}\sum _{y}I(x,y)\,\!}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/0eb0d68fa66330d1c2968c1767931198d24f98e6" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.338ex; margin-right: -0.387ex; width:14.371ex; height:5.843ex;" alt="{\displaystyle \sum _{x}\sum _{y}I(x,y)\,\!}" data-pagespeed-url-hash="3035604787" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/56" title="Special:DisplayTopics/56">56</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/5363#math.5363.5" title="Special:PermanentLink/5363">Geostrophic_wind-5</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{{\boldsymbol{F}}}_{{r}}}">
<semantics id="p1.1.m1.1a">
<msub id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">𝑭</mi>
<mi id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">r</mi>
</msub>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
<csymbol cd="ambiguous" id="p1.1.m1.1.3.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝑭</ci>
<ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">r</ci>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{{\boldsymbol{F}}}_{{r}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=7afb8aa5362f2b837c148fcfd5a08a52&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.5ex; height: 2ex; width: 2.667ex;" alt="{{\boldsymbol {F}}}_{{r}}" data-pagespeed-url-hash="790625094" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {F}}_{r}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="bold-italic">F</mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi>r</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {F}}_{r}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/e4560a7578e12f06e2ced0aef062ff806fc1347d" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:2.575ex; height:2.509ex;" alt="{\displaystyle {\boldsymbol {F}}_{r}}" data-pagespeed-url-hash="2494933184" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/57" title="Special:DisplayTopics/57">57</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/6693#math.6693.9" title="Special:PermanentLink/6693">Ext_functor-9</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle 0\rightarrow B\rightarrow A\oplus B\rightarrow A\rightarrow 0.}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">
<mn id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">0</mn>
<mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">→</mo>
<mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">B</mi>
<mo id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">→</mo>
<mrow id="p1.1.m1.1.13.2" xref="p1.1.m1.1.13.2.cmml">
<mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">A</mi>
<mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">⊕</mo>
<mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">B</mi>
</mrow>
<mo id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">→</mo>
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">A</mi>
<mo id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">→</mo>
<mn id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">0.</mn>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">
<and id="p1.1.m1.1.13a.cmml" xref="p1.1.m1.1.13"/>
<apply id="p1.1.m1.1.13b.cmml" xref="p1.1.m1.1.13">
<ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">normal-→</ci>
<cn type="integer" id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">0</cn>
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">B</ci>
</apply>
<apply id="p1.1.m1.1.13c.cmml" xref="p1.1.m1.1.13">
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">normal-→</ci>
<share href="#p1.1.m1.1.3.cmml" id="p1.1.m1.1.13d.cmml" xref="p1.1.m1.1.13"/>
<apply id="p1.1.m1.1.13.2.cmml" xref="p1.1.m1.1.13.2">
<csymbol cd="latexml" id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">direct-sum</csymbol>
<ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">A</ci>
<ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">B</ci>
</apply>
</apply>
<apply id="p1.1.m1.1.13e.cmml" xref="p1.1.m1.1.13">
<ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">normal-→</ci>
<share href="#p1.1.m1.1.13.2.cmml" id="p1.1.m1.1.13f.cmml" xref="p1.1.m1.1.13"/>
<ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">A</ci>
</apply>
<apply id="p1.1.m1.1.13g.cmml" xref="p1.1.m1.1.13">
<ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">normal-→</ci>
<share href="#p1.1.m1.1.9.cmml" id="p1.1.m1.1.13h.cmml" xref="p1.1.m1.1.13"/>
<cn type="float" id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">0.</cn>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle 0\rightarrow B\rightarrow A\oplus B\rightarrow A\rightarrow 0.}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=4b8d06622b8fbb3b9857de8850d1b7a9&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.333ex; height: 2ex; width: 27.333ex;" alt="0\rightarrow B\rightarrow A\oplus B\rightarrow A\rightarrow 0." data-pagespeed-url-hash="1365815601" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0\rightarrow B\rightarrow A\oplus B\rightarrow A\rightarrow 0.}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mn>0</mn>
<mo stretchy="false">→<!-- → --></mo>
<mi>B</mi>
<mo stretchy="false">→<!-- → --></mo>
<mi>A</mi>
<mo>⊕<!-- ⊕ --></mo>
<mi>B</mi>
<mo stretchy="false">→<!-- → --></mo>
<mi>A</mi>
<mo stretchy="false">→<!-- → --></mo>
<mn>0.</mn>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle 0\rightarrow B\rightarrow A\oplus B\rightarrow A\rightarrow 0.}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/a87480d391182ea8a48f7fda5ad54e80c90839a7" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.505ex; width:27.283ex; height:2.343ex;" alt="{\displaystyle 0\rightarrow B\rightarrow A\oplus B\rightarrow A\rightarrow 0.}" data-pagespeed-url-hash="1458364082" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/58" title="Special:DisplayTopics/58">58</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/4787#math.4787.50" title="Special:PermanentLink/4787">Covariant_derivative-50</a>
</td>
<td> 1
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle(\nabla_{Y}T)(\alpha_{1},\alpha_{2},\ldots,X_{1},X_{2},\ldots)=Y% (T(\alpha_{1},\alpha_{2},\ldots,X_{\qvar@construct{x0}},X_{2},\ldots))}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.45" xref="p1.1.m1.1.45.cmml">
<mrow id="p1.1.m1.1.45.1" xref="p1.1.m1.1.45.1.cmml">
<mrow id="p1.1.m1.1.45.1.2b">
<mo stretchy="false" id="p1.1.m1.1.45.1.2">(</mo>
<mrow id="XM1" xref="XM1.cmml">
<msub id="XM1.1" xref="XM1.1.cmml">
<mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">∇</mo>
<mi id="p1.1.m1.1.3.1" xref="p1.1.m1.1.3.1.cmml">Y</mi>
</msub>
<mo id="XM1a" xref="XM1.cmml"></mo>
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">T</mi>
</mrow>
<mo stretchy="false" id="p1.1.m1.1.45.1.2a">)</mo>
</mrow>
<mo id="p1.1.m1.1.45.1.1" xref="p1.1.m1.1.45.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.45.1.3g" xref="p1.1.m1.1.45.1.3.cmml">
<mo stretchy="false" id="p1.1.m1.1.45.1.3" xref="p1.1.m1.1.45.1.3.cmml">(</mo>
<msub id="XM2" xref="XM2.cmml">
<mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">α</mi>
<mn id="p1.1.m1.1.8.1" xref="p1.1.m1.1.8.1.cmml">1</mn>
</msub>
<mo id="p1.1.m1.1.45.1.3a" xref="p1.1.m1.1.45.1.3.cmml">,</mo>
<msub id="XM3" xref="XM3.cmml">
<mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">α</mi>
<mn id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml">2</mn>
</msub>
<mo id="p1.1.m1.1.45.1.3b" xref="p1.1.m1.1.45.1.3.cmml">,</mo>
<mi mathvariant="normal" id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">…</mi>
<mo id="p1.1.m1.1.45.1.3c" xref="p1.1.m1.1.45.1.3.cmml">,</mo>
<msub id="XM4" xref="XM4.cmml">
<mi id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">X</mi>
<mn id="p1.1.m1.1.16.1" xref="p1.1.m1.1.16.1.cmml">1</mn>
</msub>
<mo id="p1.1.m1.1.45.1.3d" xref="p1.1.m1.1.45.1.3.cmml">,</mo>
<msub id="XM5" xref="XM5.cmml">
<mi id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">X</mi>
<mn id="p1.1.m1.1.19.1" xref="p1.1.m1.1.19.1.cmml">2</mn>
</msub>
<mo id="p1.1.m1.1.45.1.3e" xref="p1.1.m1.1.45.1.3.cmml">,</mo>
<mi mathvariant="normal" id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">…</mi>
<mo stretchy="false" id="p1.1.m1.1.45.1.3f" xref="p1.1.m1.1.45.1.3.cmml">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">=</mo>
<mrow id="p1.1.m1.1.45.2" xref="p1.1.m1.1.45.2.cmml">
<mi id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml">Y</mi>
<mo id="p1.1.m1.1.45.2.1" xref="p1.1.m1.1.45.2.1.cmml"></mo>
<mrow id="p1.1.m1.1.45.2.2b">
<mo stretchy="false" id="p1.1.m1.1.45.2.2">(</mo>
<mrow id="XM18" xref="XM18.cmml">
<mi id="p1.1.m1.1.26" xref="p1.1.m1.1.26.cmml">T</mi>
<mo id="XM18.1" xref="XM18.1.cmml"></mo>
<mrow id="XM18.2g" xref="XM18.2.cmml">
<mo stretchy="false" id="XM18.2" xref="XM18.2.cmml">(</mo>
<msub id="XM14" xref="XM14.cmml">
<mi id="p1.1.m1.1.28" xref="p1.1.m1.1.28.cmml">α</mi>
<mn id="p1.1.m1.1.29.1" xref="p1.1.m1.1.29.1.cmml">1</mn>
</msub>
<mo id="XM18.2a" xref="XM18.2.cmml">,</mo>
<msub id="XM15" xref="XM15.cmml">
<mi id="p1.1.m1.1.31" xref="p1.1.m1.1.31.cmml">α</mi>
<mn id="p1.1.m1.1.32.1" xref="p1.1.m1.1.32.1.cmml">2</mn>
</msub>
<mo id="XM18.2b" xref="XM18.2.cmml">,</mo>
<mi mathvariant="normal" id="p1.1.m1.1.34" xref="p1.1.m1.1.34.cmml">…</mi>
<mo id="XM18.2c" xref="XM18.2.cmml">,</mo>
<msub id="XM16" xref="XM16.cmml">
<mi id="p1.1.m1.1.36" xref="p1.1.m1.1.36.cmml">X</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.37.1" xref="p1.1.m1.1.37.1.cmml">x0</mi>
</msub>
<mo id="XM18.2d" xref="XM18.2.cmml">,</mo>
<msub id="XM17" xref="XM17.cmml">
<mi id="p1.1.m1.1.39" xref="p1.1.m1.1.39.cmml">X</mi>
<mn id="p1.1.m1.1.40.1" xref="p1.1.m1.1.40.1.cmml">2</mn>
</msub>
<mo id="XM18.2e" xref="XM18.2.cmml">,</mo>
<mi mathvariant="normal" id="p1.1.m1.1.42" xref="p1.1.m1.1.42.cmml">…</mi>
<mo stretchy="false" id="XM18.2f" xref="XM18.2.cmml">)</mo>
</mrow>
</mrow>
<mo stretchy="false" id="p1.1.m1.1.45.2.2a">)</mo>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.45.cmml" xref="p1.1.m1.1.45">
<eq id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23"/>
<apply id="p1.1.m1.1.45.1.cmml" xref="p1.1.m1.1.45.1">
<times id="p1.1.m1.1.45.1.1.cmml" xref="p1.1.m1.1.45.1.1"/>
<apply id="XM1.cmml" xref="XM1">
<apply id="XM1.1.cmml" xref="XM1.1">
<csymbol cd="ambiguous" id="XM1.1.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">normal-∇</ci>
<ci id="p1.1.m1.1.3.1.cmml" xref="p1.1.m1.1.3.1">Y</ci>
</apply>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">T</ci>
</apply>
<vector id="p1.1.m1.1.45.1.3.cmml" xref="p1.1.m1.1.45.1.3">
<apply id="XM2.cmml" xref="XM2">
<csymbol cd="ambiguous" id="XM2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">α</ci>
<cn type="integer" id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.1">1</cn>
</apply>
<apply id="XM3.cmml" xref="XM3">
<csymbol cd="ambiguous" id="XM3.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">α</ci>
<cn type="integer" id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1">2</cn>
</apply>
<ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">normal-…</ci>
<apply id="XM4.cmml" xref="XM4">
<csymbol cd="ambiguous" id="XM4.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">X</ci>
<cn type="integer" id="p1.1.m1.1.16.1.cmml" xref="p1.1.m1.1.16.1">1</cn>
</apply>
<apply id="XM5.cmml" xref="XM5">
<csymbol cd="ambiguous" id="XM5.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">X</ci>
<cn type="integer" id="p1.1.m1.1.19.1.cmml" xref="p1.1.m1.1.19.1">2</cn>
</apply>
<ci id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">normal-…</ci>
</vector>
</apply>
<apply id="p1.1.m1.1.45.2.cmml" xref="p1.1.m1.1.45.2">
<times id="p1.1.m1.1.45.2.1.cmml" xref="p1.1.m1.1.45.2.1"/>
<ci id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">Y</ci>
<apply id="XM18.cmml" xref="XM18">
<times id="XM18.1.cmml" xref="XM18.1"/>
<ci id="p1.1.m1.1.26.cmml" xref="p1.1.m1.1.26">T</ci>
<vector id="XM18.2.cmml" xref="XM18.2">
<apply id="XM14.cmml" xref="XM14">
<csymbol cd="ambiguous" id="XM14.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.28.cmml" xref="p1.1.m1.1.28">α</ci>
<cn type="integer" id="p1.1.m1.1.29.1.cmml" xref="p1.1.m1.1.29.1">1</cn>
</apply>
<apply id="XM15.cmml" xref="XM15">
<csymbol cd="ambiguous" id="XM15.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.31.cmml" xref="p1.1.m1.1.31">α</ci>
<cn type="integer" id="p1.1.m1.1.32.1.cmml" xref="p1.1.m1.1.32.1">2</cn>
</apply>
<ci id="p1.1.m1.1.34.cmml" xref="p1.1.m1.1.34">normal-…</ci>
<apply id="XM16.cmml" xref="XM16">
<csymbol cd="ambiguous" id="XM16.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.36.cmml" xref="p1.1.m1.1.36">X</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.37.1.cmml" xref="p1.1.m1.1.37.1">x0</csymbol>
</apply>
<apply id="XM17.cmml" xref="XM17">
<csymbol cd="ambiguous" id="XM17.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.39.cmml" xref="p1.1.m1.1.39">X</ci>
<cn type="integer" id="p1.1.m1.1.40.1.cmml" xref="p1.1.m1.1.40.1">2</cn>
</apply>
<ci id="p1.1.m1.1.42.cmml" xref="p1.1.m1.1.42">normal-…</ci>
</vector>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle(\nabla_{Y}T)(\alpha_{1},\alpha_{2},\ldots,X_{1},X_{2},\ldots)=Y%
(T(\alpha_{1},\alpha_{2},\ldots,X_{\qvar@construct{x0}},X_{2},\ldots))}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=4d647c4b4afbc7317b314b581f2bf17b&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.5ex; width: 65.5ex;" alt="(\nabla_{Y}T)(\alpha_{1},\alpha_{2},\ldots,X_{1},X_{2},\ldots)=Y(T(\alpha_{1},\alpha_{2},\ldots,X_{\qvar{x0}},X_{2},\ldots))" data-pagespeed-url-hash="1698881525" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (\nabla _{Y}T)(\alpha _{1},\alpha _{2},\ldots ,X_{1},X_{2},\ldots )=Y(T(\alpha _{1},\alpha _{2},\ldots ,X_{1},X_{2},\ldots ))}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mo stretchy="false">(</mo>
<msub>
<mi mathvariant="normal">∇<!-- ∇ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>Y</mi>
</mrow>
</msub>
<mi>T</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<msub>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
<mo>,</mo>
<mo>…<!-- … --></mo>
<mo>,</mo>
<msub>
<mi>X</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>X</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
<mo>,</mo>
<mo>…<!-- … --></mo>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>Y</mi>
<mo stretchy="false">(</mo>
<mi>T</mi>
<mo stretchy="false">(</mo>
<msub>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>α<!-- α --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
<mo>,</mo>
<mo>…<!-- … --></mo>
<mo>,</mo>
<msub>
<mi>X</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>X</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
<mo>,</mo>
<mo>…<!-- … --></mo>
<mo stretchy="false">)</mo>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle (\nabla _{Y}T)(\alpha _{1},\alpha _{2},\ldots ,X_{1},X_{2},\ldots )=Y(T(\alpha _{1},\alpha _{2},\ldots ,X_{1},X_{2},\ldots ))}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/dec7dc721d60d753d7ef99078f63cb8906657c43" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:62.892ex; height:2.843ex;" alt="{\displaystyle (\nabla _{Y}T)(\alpha _{1},\alpha _{2},\ldots ,X_{1},X_{2},\ldots )=Y(T(\alpha _{1},\alpha _{2},\ldots ,X_{1},X_{2},\ldots ))}" data-pagespeed-url-hash="3570195808" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/59" title="Special:DisplayTopics/59">59</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/10209#math.10209.4" title="Special:PermanentLink/10209">Anderson_localization-4</a>
</td>
<td> 1
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\sum_{{n\in{\qvar@construct{x0}}^{d}}}|\psi(t,n)|^{2}|n|\leq C}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">
<mrow id="p1.1.m1.1.17.1" xref="p1.1.m1.1.17.1.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.17.1.1" xref="p1.1.m1.1.17.1.1.cmml">
<munder id="p1.1.m1.1.17.1.1a" xref="p1.1.m1.1.17.1.1.cmml">
<mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">∑</mo>
<mrow id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">
<mi id="p1.1.m1.1.2.1.1" xref="p1.1.m1.1.2.1.1.cmml">n</mi>
<mo id="p1.1.m1.1.2.1.2" xref="p1.1.m1.1.2.1.2.cmml">∈</mo>
<msup id="p1.1.m1.1.2.1.5" xref="p1.1.m1.1.2.1.5.cmml">
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.2.1.3" xref="p1.1.m1.1.2.1.3.cmml">x0</mi>
<mi id="p1.1.m1.1.2.1.4.1" xref="p1.1.m1.1.2.1.4.1.cmml">d</mi>
</msup>
</mrow>
</munder>
</mstyle>
<mrow id="p1.1.m1.1.17.1.2" xref="p1.1.m1.1.17.1.2.cmml">
<msup id="p1.1.m1.1.17.1.2.2" xref="p1.1.m1.1.17.1.2.2.cmml">
<mrow id="p1.1.m1.1.17.1.2.2.2b" xref="p1.1.m1.1.17.1.2.2.2.cmml">
<mo stretchy="false" id="p1.1.m1.1.17.1.2.2.2" xref="p1.1.m1.1.17.1.2.2.2.cmml">|</mo>
<mrow id="XM1" xref="XM1.cmml">
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">ψ</mi>
<mo id="XM1.1" xref="XM1.1.cmml"></mo>
<mrow id="XM1.2c" xref="XM1.2.cmml">
<mo stretchy="false" id="XM1.2" xref="XM1.2.cmml">(</mo>
<mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">t</mi>
<mo id="XM1.2a" xref="XM1.2.cmml">,</mo>
<mi id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">n</mi>
<mo stretchy="false" id="XM1.2b" xref="XM1.2.cmml">)</mo>
</mrow>
</mrow>
<mo stretchy="false" id="p1.1.m1.1.17.1.2.2.2a" xref="p1.1.m1.1.17.1.2.2.2.cmml">|</mo>
</mrow>
<mn id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml">2</mn>
</msup>
<mo id="p1.1.m1.1.17.1.2.1" xref="p1.1.m1.1.17.1.2.1.cmml"></mo>
<mrow id="p1.1.m1.1.17.1.2.3b" xref="p1.1.m1.1.17.1.2.3.cmml">
<mo stretchy="false" id="p1.1.m1.1.17.1.2.3" xref="p1.1.m1.1.17.1.2.3.cmml">|</mo>
<mi id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">n</mi>
<mo stretchy="false" id="p1.1.m1.1.17.1.2.3a" xref="p1.1.m1.1.17.1.2.3.cmml">|</mo>
</mrow>
</mrow>
</mrow>
<mo id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">≤</mo>
<mi id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">C</mi>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">
<leq id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15"/>
<apply id="p1.1.m1.1.17.1.cmml" xref="p1.1.m1.1.17.1">
<apply id="p1.1.m1.1.17.1.1.cmml" xref="p1.1.m1.1.17.1.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.17.1.1.1.cmml">subscript</csymbol>
<sum id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1"/>
<apply id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">
<in id="p1.1.m1.1.2.1.2.cmml" xref="p1.1.m1.1.2.1.2"/>
<ci id="p1.1.m1.1.2.1.1.cmml" xref="p1.1.m1.1.2.1.1">n</ci>
<apply id="p1.1.m1.1.2.1.5.cmml" xref="p1.1.m1.1.2.1.5">
<csymbol cd="ambiguous" id="p1.1.m1.1.2.1.5.1.cmml">superscript</csymbol>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.2.1.3.cmml" xref="p1.1.m1.1.2.1.3">x0</csymbol>
<ci id="p1.1.m1.1.2.1.4.1.cmml" xref="p1.1.m1.1.2.1.4.1">d</ci>
</apply>
</apply>
</apply>
<apply id="p1.1.m1.1.17.1.2.cmml" xref="p1.1.m1.1.17.1.2">
<times id="p1.1.m1.1.17.1.2.1.cmml" xref="p1.1.m1.1.17.1.2.1"/>
<apply id="p1.1.m1.1.17.1.2.2.cmml" xref="p1.1.m1.1.17.1.2.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.17.1.2.2.1.cmml">superscript</csymbol>
<apply id="p1.1.m1.1.17.1.2.2.2a.cmml" xref="p1.1.m1.1.17.1.2.2.2">
<abs id="p1.1.m1.1.17.1.2.2.2.cmml" xref="p1.1.m1.1.17.1.2.2.2"/>
<apply id="XM1.cmml" xref="XM1">
<times id="XM1.1.cmml" xref="XM1.1"/>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">ψ</ci>
<interval closure="open" id="XM1.2.cmml" xref="XM1.2">
<ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">t</ci>
<ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">n</ci>
</interval>
</apply>
</apply>
<cn type="integer" id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1">2</cn>
</apply>
<apply id="p1.1.m1.1.17.1.2.3a.cmml" xref="p1.1.m1.1.17.1.2.3">
<abs id="p1.1.m1.1.17.1.2.3.cmml" xref="p1.1.m1.1.17.1.2.3"/>
<ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">n</ci>
</apply>
</apply>
</apply>
<ci id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">C</ci>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\sum_{{n\in{\qvar@construct{x0}}^{d}}}|\psi(t,n)|^{2}|n|\leq C}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=c1354d147a2a0f1d01f87b1d7f203621&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.333ex; height: 5.667ex; width: 22.5ex;" alt="\sum_{{n\in{\qvar{x0}}^{d}}}|\psi(t,n)|^{2}|n|\leq C" data-pagespeed-url-hash="2921613736" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{n\in \mathbb {Z} ^{d}}|\psi (t,n)|^{2}|n|\leq C}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<munder>
<mo>∑<!-- ∑ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>n</mi>
<mo>∈<!-- ∈ --></mo>
<msup>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="double-struck">Z</mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi>d</mi>
</mrow>
</msup>
</mrow>
</munder>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">|</mo>
</mrow>
<mi>ψ<!-- ψ --></mi>
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo>,</mo>
<mi>n</mi>
<mo stretchy="false">)</mo>
<msup>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">|</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">|</mo>
</mrow>
<mi>n</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">|</mo>
</mrow>
<mo>≤<!-- ≤ --></mo>
<mi>C</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \sum _{n\in \mathbb {Z} ^{d}}|\psi (t,n)|^{2}|n|\leq C}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/7e9dc23b5e9756751b1000f25a7179721fbb0ea1" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.505ex; width:20.92ex; height:6.009ex;" alt="{\displaystyle \sum _{n\in \mathbb {Z} ^{d}}|\psi (t,n)|^{2}|n|\leq C}" data-pagespeed-url-hash="134043570" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/60" title="Special:DisplayTopics/60">60</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/9833#math.9833.26" title="Special:PermanentLink/9833">Trajectory_of_a_projectile-26</a>
</td>
<td> 5
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle p={{\frac{-x\pm{\sqrt{x^{\qvar@construct{x0}}-4({% \qvar@construct{x1}})({\frac{\qvar@construct{x2}}{\qvar@construct{x3}}}-y)}}}{% 2({\frac{-gx^{2}}{\qvar@construct{x4}}})}}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">p</mi>
<mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">=</mo>
<mstyle displaystyle="true" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
<mfrac id="p1.1.m1.1.3a" xref="p1.1.m1.1.3.cmml">
<mrow id="p1.1.m1.1.3.2" xref="p1.1.m1.1.3.2.cmml">
<mrow id="p1.1.m1.1.3.2.5" xref="p1.1.m1.1.3.2.5.cmml">
<mo id="p1.1.m1.1.3.2.1" xref="p1.1.m1.1.3.2.1.cmml">-</mo>
<mi id="p1.1.m1.1.3.2.2" xref="p1.1.m1.1.3.2.2.cmml">x</mi>
</mrow>
<mo id="p1.1.m1.1.3.2.3" xref="p1.1.m1.1.3.2.3.cmml">±</mo>
<msqrt id="p1.1.m1.1.3.2.4" xref="p1.1.m1.1.3.2.4.cmml">
<mrow id="p1.1.m1.1.3.2.4.2" xref="p1.1.m1.1.3.2.4.2.cmml">
<msup id="p1.1.m1.1.3.2.4.2.13" xref="p1.1.m1.1.3.2.4.2.13.cmml">
<mi id="p1.1.m1.1.3.2.4.2.1" xref="p1.1.m1.1.3.2.4.2.1.cmml">x</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.3.2.4.2.2.1" xref="p1.1.m1.1.3.2.4.2.2.1.cmml">x0</mi>
</msup>
<mo id="p1.1.m1.1.3.2.4.2.3" xref="p1.1.m1.1.3.2.4.2.3.cmml">-</mo>
<mrow id="p1.1.m1.1.3.2.4.2.14" xref="p1.1.m1.1.3.2.4.2.14.cmml">
<mn id="p1.1.m1.1.3.2.4.2.4" xref="p1.1.m1.1.3.2.4.2.4.cmml">4</mn>
<mo id="p1.1.m1.1.3.2.4.2.14.1" xref="p1.1.m1.1.3.2.4.2.14.1.cmml"></mo>
<mrow id="p1.1.m1.1.3.2.4.2.14.2b">
<mo stretchy="false" id="p1.1.m1.1.3.2.4.2.14.2">(</mo>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.3.2.4.2.6" xref="p1.1.m1.1.3.2.4.2.6.cmml">x1</mi>
<mo stretchy="false" id="p1.1.m1.1.3.2.4.2.14.2a">)</mo>
</mrow>
<mo id="p1.1.m1.1.3.2.4.2.14.1a" xref="p1.1.m1.1.3.2.4.2.14.1.cmml"></mo>
<mrow id="p1.1.m1.1.3.2.4.2.14.3b">
<mo stretchy="false" id="p1.1.m1.1.3.2.4.2.14.3">(</mo>
<mrow id="XM1" xref="XM1.cmml">
<mfrac id="p1.1.m1.1.3.2.4.2.9" xref="p1.1.m1.1.3.2.4.2.9.cmml">
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.3.2.4.2.9.2" xref="p1.1.m1.1.3.2.4.2.9.2.cmml">x2</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.3.2.4.2.9.3" xref="p1.1.m1.1.3.2.4.2.9.3.cmml">x3</mi>
</mfrac>
<mo id="p1.1.m1.1.3.2.4.2.10" xref="p1.1.m1.1.3.2.4.2.10.cmml">-</mo>
<mi id="p1.1.m1.1.3.2.4.2.11" xref="p1.1.m1.1.3.2.4.2.11.cmml">y</mi>
</mrow>
<mo stretchy="false" id="p1.1.m1.1.3.2.4.2.14.3a">)</mo>
</mrow>
</mrow>
</mrow>
</msqrt>
</mrow>
<mrow id="p1.1.m1.1.3.3" xref="p1.1.m1.1.3.3.cmml">
<mn id="p1.1.m1.1.3.3.1" xref="p1.1.m1.1.3.3.1.cmml">2</mn>
<mo id="p1.1.m1.1.3.3.5" xref="p1.1.m1.1.3.3.5.cmml"></mo>
<mrow id="p1.1.m1.1.3.3.6b">
<mo stretchy="false" id="p1.1.m1.1.3.3.6">(</mo>
<mfrac id="p1.1.m1.1.3.3.3" xref="p1.1.m1.1.3.3.3.cmml">
<mrow id="p1.1.m1.1.3.3.3.2" xref="p1.1.m1.1.3.3.3.2.cmml">
<mo id="p1.1.m1.1.3.3.3.2.1" xref="p1.1.m1.1.3.3.3.2.1.cmml">-</mo>
<mrow id="p1.1.m1.1.3.3.3.2.5" xref="p1.1.m1.1.3.3.3.2.5.cmml">
<mi id="p1.1.m1.1.3.3.3.2.2" xref="p1.1.m1.1.3.3.3.2.2.cmml">g</mi>
<mo id="p1.1.m1.1.3.3.3.2.5.1" xref="p1.1.m1.1.3.3.3.2.5.1.cmml"></mo>
<msup id="p1.1.m1.1.3.3.3.2.5.2" xref="p1.1.m1.1.3.3.3.2.5.2.cmml">
<mi id="p1.1.m1.1.3.3.3.2.3" xref="p1.1.m1.1.3.3.3.2.3.cmml">x</mi>
<mn id="p1.1.m1.1.3.3.3.2.4.1" xref="p1.1.m1.1.3.3.3.2.4.1.cmml">2</mn>
</msup>
</mrow>
</mrow>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.3.3.3.3" xref="p1.1.m1.1.3.3.3.3.cmml">x4</mi>
</mfrac>
<mo stretchy="false" id="p1.1.m1.1.3.3.6a">)</mo>
</mrow>
</mrow>
</mfrac>
</mstyle>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">
<eq id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">p</ci>
<apply id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
<divide id="p1.1.m1.1.3.1.cmml"/>
<apply id="p1.1.m1.1.3.2.cmml" xref="p1.1.m1.1.3.2">
<csymbol cd="latexml" id="p1.1.m1.1.3.2.3.cmml" xref="p1.1.m1.1.3.2.3">plus-or-minus</csymbol>
<apply id="p1.1.m1.1.3.2.5.cmml" xref="p1.1.m1.1.3.2.5">
<minus id="p1.1.m1.1.3.2.1.cmml" xref="p1.1.m1.1.3.2.1"/>
<ci id="p1.1.m1.1.3.2.2.cmml" xref="p1.1.m1.1.3.2.2">x</ci>
</apply>
<apply id="p1.1.m1.1.3.2.4.cmml" xref="p1.1.m1.1.3.2.4">
<root id="p1.1.m1.1.3.2.4a.cmml" xref="p1.1.m1.1.3.2.4"/>
<apply id="p1.1.m1.1.3.2.4.2.cmml" xref="p1.1.m1.1.3.2.4.2">
<minus id="p1.1.m1.1.3.2.4.2.3.cmml" xref="p1.1.m1.1.3.2.4.2.3"/>
<apply id="p1.1.m1.1.3.2.4.2.13.cmml" xref="p1.1.m1.1.3.2.4.2.13">
<csymbol cd="ambiguous" id="p1.1.m1.1.3.2.4.2.13.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.3.2.4.2.1.cmml" xref="p1.1.m1.1.3.2.4.2.1">x</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.3.2.4.2.2.1.cmml" xref="p1.1.m1.1.3.2.4.2.2.1">x0</csymbol>
</apply>
<apply id="p1.1.m1.1.3.2.4.2.14.cmml" xref="p1.1.m1.1.3.2.4.2.14">
<times id="p1.1.m1.1.3.2.4.2.14.1.cmml" xref="p1.1.m1.1.3.2.4.2.14.1"/>
<cn type="integer" id="p1.1.m1.1.3.2.4.2.4.cmml" xref="p1.1.m1.1.3.2.4.2.4">4</cn>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.3.2.4.2.6.cmml" xref="p1.1.m1.1.3.2.4.2.6">x1</csymbol>
<apply id="XM1.cmml" xref="XM1">
<minus id="p1.1.m1.1.3.2.4.2.10.cmml" xref="p1.1.m1.1.3.2.4.2.10"/>
<apply id="p1.1.m1.1.3.2.4.2.9.cmml" xref="p1.1.m1.1.3.2.4.2.9">
<divide id="p1.1.m1.1.3.2.4.2.9.1.cmml"/>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.3.2.4.2.9.2.cmml" xref="p1.1.m1.1.3.2.4.2.9.2">x2</csymbol>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.3.2.4.2.9.3.cmml" xref="p1.1.m1.1.3.2.4.2.9.3">x3</csymbol>
</apply>
<ci id="p1.1.m1.1.3.2.4.2.11.cmml" xref="p1.1.m1.1.3.2.4.2.11">y</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="p1.1.m1.1.3.3.cmml" xref="p1.1.m1.1.3.3">
<times id="p1.1.m1.1.3.3.5.cmml" xref="p1.1.m1.1.3.3.5"/>
<cn type="integer" id="p1.1.m1.1.3.3.1.cmml" xref="p1.1.m1.1.3.3.1">2</cn>
<apply id="p1.1.m1.1.3.3.3.cmml" xref="p1.1.m1.1.3.3.3">
<divide id="p1.1.m1.1.3.3.3.1.cmml"/>
<apply id="p1.1.m1.1.3.3.3.2.cmml" xref="p1.1.m1.1.3.3.3.2">
<minus id="p1.1.m1.1.3.3.3.2.1.cmml" xref="p1.1.m1.1.3.3.3.2.1"/>
<apply id="p1.1.m1.1.3.3.3.2.5.cmml" xref="p1.1.m1.1.3.3.3.2.5">
<times id="p1.1.m1.1.3.3.3.2.5.1.cmml" xref="p1.1.m1.1.3.3.3.2.5.1"/>
<ci id="p1.1.m1.1.3.3.3.2.2.cmml" xref="p1.1.m1.1.3.3.3.2.2">g</ci>
<apply id="p1.1.m1.1.3.3.3.2.5.2.cmml" xref="p1.1.m1.1.3.3.3.2.5.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.3.3.3.2.5.2.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.3.3.3.2.3.cmml" xref="p1.1.m1.1.3.3.3.2.3">x</ci>
<cn type="integer" id="p1.1.m1.1.3.3.3.2.4.1.cmml" xref="p1.1.m1.1.3.3.3.2.4.1">2</cn>
</apply>
</apply>
</apply>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.3.3.3.3.cmml" xref="p1.1.m1.1.3.3.3.3">x4</csymbol>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle p={{\frac{-x\pm{\sqrt{x^{\qvar@construct{x0}}-4({%
\qvar@construct{x1}})({\frac{\qvar@construct{x2}}{\qvar@construct{x3}}}-y)}}}{%
2({\frac{-gx^{2}}{\qvar@construct{x4}}})}}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=4d84896bc8187f9dc954a0bc3396d3b8&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -4.167ex; height: 9.833ex; width: 35ex;" alt="p={{\frac{-x\pm{\sqrt{x^{\qvar{x0}}-4({\qvar{x1}})({\frac{\qvar{x2}}{\qvar{x3}}}-y)}}}{2({\frac{-gx^{2}}{\qvar{x4}}})}}}" data-pagespeed-url-hash="1485898347" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p={\frac {-x\pm {\sqrt {x^{2}-4({\frac {-gx^{2}}{2v^{2}}})({\frac {-gx^{2}}{2v^{2}}}-y)}}}{2({\frac {-gx^{2}}{2v^{2}}})}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>p</mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mo>−<!-- − --></mo>
<mi>x</mi>
<mo>±<!-- ± --></mo>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>−<!-- − --></mo>
<mn>4</mn>
<mo stretchy="false">(</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mo>−<!-- − --></mo>
<mi>g</mi>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
</mrow>
<mrow>
<mn>2</mn>
<msup>
<mi>v</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
</mrow>
</mfrac>
</mrow>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mo>−<!-- − --></mo>
<mi>g</mi>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
</mrow>
<mrow>
<mn>2</mn>
<msup>
<mi>v</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
</mrow>
</mfrac>
</mrow>
<mo>−<!-- − --></mo>
<mi>y</mi>
<mo stretchy="false">)</mo>
</msqrt>
</mrow>
</mrow>
<mrow>
<mn>2</mn>
<mo stretchy="false">(</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mo>−<!-- − --></mo>
<mi>g</mi>
<msup>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
</mrow>
<mrow>
<mn>2</mn>
<msup>
<mi>v</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
</mrow>
</mfrac>
</mrow>
<mo stretchy="false">)</mo>
</mrow>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle p={\frac {-x\pm {\sqrt {x^{2}-4({\frac {-gx^{2}}{2v^{2}}})({\frac {-gx^{2}}{2v^{2}}}-y)}}}{2({\frac {-gx^{2}}{2v^{2}}})}}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/68f7949992caca793da79d8c14b21415fe4ac2ec" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -4.338ex; margin-left: -0.089ex; width:36.848ex; height:11.509ex;" alt="{\displaystyle p={\frac {-x\pm {\sqrt {x^{2}-4({\frac {-gx^{2}}{2v^{2}}})({\frac {-gx^{2}}{2v^{2}}}-y)}}}{2({\frac {-gx^{2}}{2v^{2}}})}}}" data-pagespeed-url-hash="3715786138" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/61" title="Special:DisplayTopics/61">61</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/8877#math.8877.7" title="Special:PermanentLink/8877">Cusp_neighborhood-7</a>
</td>
<td> 1
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\left\{z\in H:\left|z\right|>1,\,\left|\,{\mbox{\qvar@construct{% x0}}}(z)\,\right|<{\frac{1}{2}}\right\}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.24c" xref="p1.1.m1.1.24.cmml">
<mo id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml">{</mo>
<mrow id="XM4" xref="XM4.cmml">
<mi id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">z</mi>
<mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">∈</mo>
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">H</mi>
</mrow>
<mo id="p1.1.m1.1.24a" xref="p1.1.m1.1.24.cmml">:</mo>
<mrow id="XM5a" xref="XM5.cmml">
<mrow id="XM2" xref="XM2.cmml">
<mrow id="XM2.1b" xref="XM2.1.cmml">
<mo id="XM2.1" xref="XM2.1.cmml">|</mo>
<mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">z</mi>
<mo id="XM2.1a" xref="XM2.1.cmml">|</mo>
</mrow>
<mo id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">></mo>
<mn id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">1</mn>
</mrow>
<mo rspace="4.2pt" id="XM5" xref="XM5.cmml">,</mo>
<mrow id="XM3" xref="XM3.cmml">
<mrow id="XM3.1b" xref="XM3.1.cmml">
<mo rspace="4.2pt" id="XM3.1" xref="XM3.1.cmml">|</mo>
<mrow id="XM1" xref="XM1.cmml">
<mtext mathcolor="red" id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">x0</mtext>
<mo id="XM1.1" xref="XM1.1.cmml"></mo>
<mrow id="XM1.2b">
<mo stretchy="false" id="XM1.2">(</mo>
<mi id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">z</mi>
<mo rspace="4.2pt" stretchy="false" id="XM1.2a">)</mo>
</mrow>
</mrow>
<mo id="XM3.1a" xref="XM3.1.cmml">|</mo>
</mrow>
<mo id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml"><</mo>
<mstyle displaystyle="true" id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">
<mfrac id="p1.1.m1.1.22a" xref="p1.1.m1.1.22.cmml">
<mn id="p1.1.m1.1.22.2" xref="p1.1.m1.1.22.2.cmml">1</mn>
<mn id="p1.1.m1.1.22.3" xref="p1.1.m1.1.22.3.cmml">2</mn>
</mfrac>
</mstyle>
</mrow>
</mrow>
<mo id="p1.1.m1.1.24b" xref="p1.1.m1.1.24.cmml">}</mo>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.24a.cmml" xref="p1.1.m1.1.24">
<csymbol cd="latexml" id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">conditional-set</csymbol>
<apply id="XM4.cmml" xref="XM4">
<in id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
<ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">z</ci>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">H</ci>
</apply>
<apply id="XM5.cmml" xref="XM5">
<csymbol cd="ambiguous" id="XM5a.cmml" xref="XM5">formulae-sequence</csymbol>
<apply id="XM2.cmml" xref="XM2">
<gt id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9"/>
<apply id="XM2.1a.cmml" xref="XM2.1">
<abs id="XM2.1.cmml" xref="XM2.1"/>
<ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">z</ci>
</apply>
<cn type="integer" id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">1</cn>
</apply>
<apply id="XM3.cmml" xref="XM3">
<lt id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21"/>
<apply id="XM3.1a.cmml" xref="XM3.1">
<abs id="XM3.1.cmml" xref="XM3.1"/>
<apply id="XM1.cmml" xref="XM1">
<times id="XM1.1.cmml" xref="XM1.1"/>
<mtext id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">x0</mtext>
<ci id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">z</ci>
</apply>
</apply>
<apply id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22">
<divide id="p1.1.m1.1.22.1.cmml"/>
<cn type="integer" id="p1.1.m1.1.22.2.cmml" xref="p1.1.m1.1.22.2">1</cn>
<cn type="integer" id="p1.1.m1.1.22.3.cmml" xref="p1.1.m1.1.22.3">2</cn>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\left\{z\in H:\left|z\right|>1,\,\left|\,{\mbox{\qvar@construct{%
x0}}}(z)\,\right|<{\frac{1}{2}}\right\}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=ab87a20370f2e82fa0b154bb26382ea8&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.333ex; height: 5.667ex; width: 33.833ex;" alt="\left\{z\in H:\left|z\right|>1,\,\left|\,{\mbox{\qvar{x0}}}(z)\,\right|<{\frac{1}{2}}\right\}" data-pagespeed-url-hash="1552328517" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\{z\in H:\left|z\right|>1,\,\left|\,{\mbox{Re}}(z)\,\right|<{\frac {1}{2}}\right\}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow>
<mo>{</mo>
<mrow>
<mi>z</mi>
<mo>∈<!-- ∈ --></mo>
<mi>H</mi>
<mo>:</mo>
<mrow>
<mo>|</mo>
<mi>z</mi>
<mo>|</mo>
</mrow>
<mo>></mo>
<mn>1</mn>
<mo>,</mo>
<mspace width="thinmathspace"/>
<mrow>
<mo>|</mo>
<mrow>
<mspace width="thinmathspace"/>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="false" scriptlevel="0">
<mtext>Re</mtext>
</mstyle>
</mrow>
<mo stretchy="false">(</mo>
<mi>z</mi>
<mo stretchy="false">)</mo>
<mspace width="thinmathspace"/>
</mrow>
<mo>|</mo>
</mrow>
<mo><</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</mrow>
</mrow>
<mo>}</mo>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \left\{z\in H:\left|z\right|>1,\,\left|\,{\mbox{Re}}(z)\,\right|<{\frac {1}{2}}\right\}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/a2322e1380ba0ca2f77f5c183e8b887d3bb9734e" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.505ex; width:32.285ex; height:6.176ex;" alt="{\displaystyle \left\{z\in H:\left|z\right|>1,\,\left|\,{\mbox{Re}}(z)\,\right|<{\frac {1}{2}}\right\}}" data-pagespeed-url-hash="2583425818" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/62" title="Special:DisplayTopics/62">62</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/2951#math.2951.17" title="Special:PermanentLink/2951">Spectrum_(functional_analysis)-17</a>
</td>
<td> 0
</td>
<td> 4
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>T</mi>
<mo>−<!-- − --></mo>
<mi>λ<!-- λ --></mi>
<mi>I</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle T-\lambda I}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=0069fd5cf07098f5022e7b98d242e05b&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align:-.338ex; height: 2.176ex; width: 7.045ex;" alt="{\displaystyle T-\lambda I}" data-pagespeed-url-hash="897550394" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T-\lambda I}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>T</mi>
<mo>−<!-- − --></mo>
<mi>λ<!-- λ --></mi>
<mi>I</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle T-\lambda I}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/a1851957e0e104ea3a266ef2ff75e0530485755c" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.505ex; width:7.004ex; height:2.343ex;" alt="{\displaystyle T-\lambda I}" data-pagespeed-url-hash="957760244" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/63" title="Special:DisplayTopics/63">63</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/1588#math.1588.20" title="Special:PermanentLink/1588">Multivariate_normal_distribution-20</a>
</td>
<td> 4
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle y\left(x\right)={{\mathop{\qvar@construct{x0}}}}\left({{\rho}}% \right){\frac{{{\qvar@construct{x1}}}}{{{\qvar@construct{x2}}}}}\left({x-{% \qvar@construct{x3}}}\right)+{\mu_{y}}.}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">
<mrow id="p1.1.m1.1.20a" xref="p1.1.m1.1.20.cmml">
<mrow id="p1.1.m1.1.20.1" xref="p1.1.m1.1.20.1.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">y</mi>
<mo id="p1.1.m1.1.20.1.1" xref="p1.1.m1.1.20.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.20.1.2b">
<mo id="p1.1.m1.1.20.1.2">(</mo>
<mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">x</mi>
<mo id="p1.1.m1.1.20.1.2a">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">=</mo>
<mrow id="p1.1.m1.1.20.2" xref="p1.1.m1.1.20.2.cmml">
<mrow id="p1.1.m1.1.20.2.1" xref="p1.1.m1.1.20.2.1.cmml">
<mo mathcolor="red" mathvariant="italic" id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">x0</mo>
<mrow id="p1.1.m1.1.20.2.1.1" xref="p1.1.m1.1.20.2.1.1.cmml">
<mrow id="p1.1.m1.1.20.2.1.1.2b">
<mo id="p1.1.m1.1.20.2.1.1.2">(</mo>
<mi id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">ρ</mi>
<mo id="p1.1.m1.1.20.2.1.1.2a">)</mo>
</mrow>
<mo id="p1.1.m1.1.20.2.1.1.1" xref="p1.1.m1.1.20.2.1.1.1.cmml"></mo>
<mstyle displaystyle="true" id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">
<mfrac id="p1.1.m1.1.10a" xref="p1.1.m1.1.10.cmml">
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.10.2" xref="p1.1.m1.1.10.2.cmml">x1</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.10.3" xref="p1.1.m1.1.10.3.cmml">x2</mi>
</mfrac>
</mstyle>
<mo id="p1.1.m1.1.20.2.1.1.1a" xref="p1.1.m1.1.20.2.1.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.20.2.1.1.3b">
<mo id="p1.1.m1.1.20.2.1.1.3">(</mo>
<mrow id="XM1" xref="XM1.cmml">
<mi id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">x</mi>
<mo id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">-</mo>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">x3</mi>
</mrow>
<mo id="p1.1.m1.1.20.2.1.1.3a">)</mo>
</mrow>
</mrow>
</mrow>
<mo id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">+</mo>
<msub id="p1.1.m1.1.20.2.2" xref="p1.1.m1.1.20.2.2.cmml">
<mi id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">μ</mi>
<mi id="p1.1.m1.1.18.1" xref="p1.1.m1.1.18.1.cmml">y</mi>
</msub>
</mrow>
</mrow>
<mo id="p1.1.m1.1.20b" xref="p1.1.m1.1.20.cmml">.</mo>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">
<eq id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/>
<apply id="p1.1.m1.1.20.1.cmml" xref="p1.1.m1.1.20.1">
<times id="p1.1.m1.1.20.1.1.cmml" xref="p1.1.m1.1.20.1.1"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">y</ci>
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">x</ci>
</apply>
<apply id="p1.1.m1.1.20.2.cmml" xref="p1.1.m1.1.20.2">
<plus id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16"/>
<apply id="p1.1.m1.1.20.2.1.cmml" xref="p1.1.m1.1.20.2.1">
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">x0</csymbol>
<apply id="p1.1.m1.1.20.2.1.1.cmml" xref="p1.1.m1.1.20.2.1.1">
<times id="p1.1.m1.1.20.2.1.1.1.cmml" xref="p1.1.m1.1.20.2.1.1.1"/>
<ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">ρ</ci>
<apply id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">
<divide id="p1.1.m1.1.10.1.cmml"/>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.10.2.cmml" xref="p1.1.m1.1.10.2">x1</csymbol>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.10.3.cmml" xref="p1.1.m1.1.10.3">x2</csymbol>
</apply>
<apply id="XM1.cmml" xref="XM1">
<minus id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13"/>
<ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">x</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">x3</csymbol>
</apply>
</apply>
</apply>
<apply id="p1.1.m1.1.20.2.2.cmml" xref="p1.1.m1.1.20.2.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.20.2.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">μ</ci>
<ci id="p1.1.m1.1.18.1.cmml" xref="p1.1.m1.1.18.1">y</ci>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle y\left(x\right)={{\mathop{\qvar@construct{x0}}}}\left({{\rho}}%
\right){\frac{{{\qvar@construct{x1}}}}{{{\qvar@construct{x2}}}}}\left({x-{%
\qvar@construct{x3}}}\right)+{\mu_{y}}.}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=e7e8f3221314bbf7edfc34e4abaebdba&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.833ex; height: 4.833ex; width: 32.833ex;" alt="y\left(x\right)={{\mathop{\qvar{x0}}}}\left({{\rho}}\right){\frac{{{\qvar{x1}}}}{{{\qvar{x2}}}}}\left({x-{\qvar{x3}}}\right)+{\mu_{y}}." data-pagespeed-url-hash="3420677223" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y\left(x\right)={\mathop {\rm {sgn}} }\left({\rho }\right){\frac {\sigma _{y}}{\sigma _{x}}}\left({x-{\mu _{x}}}\right)+{\mu _{y}}.}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>y</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-OP">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">s</mi>
<mi mathvariant="normal">g</mi>
<mi mathvariant="normal">n</mi>
</mrow>
</mrow>
</mrow>
<mrow>
<mo>(</mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>ρ<!-- ρ --></mi>
</mrow>
<mo>)</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<msub>
<mi>σ<!-- σ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>y</mi>
</mrow>
</msub>
<msub>
<mi>σ<!-- σ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>x</mi>
</mrow>
</msub>
</mfrac>
</mrow>
<mrow>
<mo>(</mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>x</mi>
<mo>−<!-- − --></mo>
<mrow class="MJX-TeXAtom-ORD">
<msub>
<mi>μ<!-- μ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>x</mi>
</mrow>
</msub>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mrow class="MJX-TeXAtom-ORD">
<msub>
<mi>μ<!-- μ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>y</mi>
</mrow>
</msub>
</mrow>
<mo>.</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle y\left(x\right)={\mathop {\rm {sgn}} }\left({\rho }\right){\frac {\sigma _{y}}{\sigma _{x}}}\left({x-{\mu _{x}}}\right)+{\mu _{y}}.}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/306908a0a414abd98839126a9f6175d9eb192677" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.171ex; width:33.152ex; height:5.343ex;" alt="{\displaystyle y\left(x\right)={\mathop {\rm {sgn}} }\left({\rho }\right){\frac {\sigma _{y}}{\sigma _{x}}}\left({x-{\mu _{x}}}\right)+{\mu _{y}}.}" data-pagespeed-url-hash="2943036686" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/64" title="Special:DisplayTopics/64">64</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/15120#math.15120.56" title="Special:PermanentLink/15120">Algebraically_closed_group-56</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle x=b\ }">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">x</mi>
<mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">=</mo>
<mpadded width="+5pt" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
<mi id="p1.1.m1.1.3a" xref="p1.1.m1.1.3.cmml">b</mi>
</mpadded>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">
<eq id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">x</ci>
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">b</ci>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle x=b\ }</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=5d5b6779186293e151ba023d40e783d1&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.167ex; height: 1.667ex; width: 6.667ex;" alt="x=b\ " data-pagespeed-url-hash="538169189" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x=b\ }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>x</mi>
<mo>=</mo>
<mi>b</mi>
<mtext> </mtext>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle x=b\ }</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/6cbd94ab7dd23e6e6dbeec826c0168bb936551fb" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:6.006ex; height:2.176ex;" alt="{\displaystyle x=b\ }" data-pagespeed-url-hash="1481381218" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/65" title="Special:DisplayTopics/65">65</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/6392#math.6392.10" title="Special:PermanentLink/6392">Analytic_capacity-10</a>
</td>
<td> 1
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle H^{1}(K)={\qvar@construct{x0}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">
<mrow id="p1.1.m1.1.8.1" xref="p1.1.m1.1.8.1.cmml">
<msup id="p1.1.m1.1.8.1.2" xref="p1.1.m1.1.8.1.2.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">H</mi>
<mn id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">1</mn>
</msup>
<mo id="p1.1.m1.1.8.1.1" xref="p1.1.m1.1.8.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.8.1.3b">
<mo stretchy="false" id="p1.1.m1.1.8.1.3">(</mo>
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">K</mi>
<mo stretchy="false" id="p1.1.m1.1.8.1.3a">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">=</mo>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">x0</mi>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">
<eq id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
<apply id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.1">
<times id="p1.1.m1.1.8.1.1.cmml" xref="p1.1.m1.1.8.1.1"/>
<apply id="p1.1.m1.1.8.1.2.cmml" xref="p1.1.m1.1.8.1.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.8.1.2.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">H</ci>
<cn type="integer" id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">1</cn>
</apply>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">K</ci>
</apply>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">x0</csymbol>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle H^{1}(K)={\qvar@construct{x0}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=e04fed12140bf702a2a9466a9e5d1401&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.667ex; width: 13.167ex;" alt="H^{1}(K)={\qvar{x0}}" data-pagespeed-url-hash="1344955591" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H^{1}(K)={\sqrt {2}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msup>
<mi>H</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msup>
<mo stretchy="false">(</mo>
<mi>K</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>2</mn>
</msqrt>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle H^{1}(K)={\sqrt {2}}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/d1a5bf3e85f8f32f5e722fc74d158691dfa54f5d" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:13.23ex; height:3.176ex;" alt="{\displaystyle H^{1}(K)={\sqrt {2}}}" data-pagespeed-url-hash="3439466924" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/66" title="Special:DisplayTopics/66">66</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/2482#math.2482.8" title="Special:PermanentLink/2482">Block_cipher_mode_of_operation-8</a>
</td>
<td> 2
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle P_{\qvar@construct{x0}}={\mbox{\qvar@construct{x1}}}(E_{K}(S_{{% i-1}}),x)\oplus C_{i}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">
<msub id="p1.1.m1.1.18.1" xref="p1.1.m1.1.18.1.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">P</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">x0</mi>
</msub>
<mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">=</mo>
<mrow id="p1.1.m1.1.18.2" xref="p1.1.m1.1.18.2.cmml">
<mrow id="p1.1.m1.1.18.2.1" xref="p1.1.m1.1.18.2.1.cmml">
<mtext mathcolor="red" id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">x1</mtext>
<mo id="p1.1.m1.1.18.2.1.1" xref="p1.1.m1.1.18.2.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.18.2.1.2c" xref="p1.1.m1.1.18.2.1.2.cmml">
<mo stretchy="false" id="p1.1.m1.1.18.2.1.2" xref="p1.1.m1.1.18.2.1.2.cmml">(</mo>
<mrow id="XM2" xref="XM2.cmml">
<msub id="XM2.2" xref="XM2.2.cmml">
<mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">E</mi>
<mi id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">K</mi>
</msub>
<mo id="XM2.1" xref="XM2.1.cmml"></mo>
<mrow id="XM2.3b">
<mo stretchy="false" id="XM2.3">(</mo>
<msub id="XM1" xref="XM1.cmml">
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">S</mi>
<mrow id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">
<mi id="p1.1.m1.1.10.1.1" xref="p1.1.m1.1.10.1.1.cmml">i</mi>
<mo id="p1.1.m1.1.10.1.2" xref="p1.1.m1.1.10.1.2.cmml">-</mo>
<mn id="p1.1.m1.1.10.1.3" xref="p1.1.m1.1.10.1.3.cmml">1</mn>
</mrow>
</msub>
<mo stretchy="false" id="XM2.3a">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.18.2.1.2a" xref="p1.1.m1.1.18.2.1.2.cmml">,</mo>
<mi id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">x</mi>
<mo stretchy="false" id="p1.1.m1.1.18.2.1.2b" xref="p1.1.m1.1.18.2.1.2.cmml">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">⊕</mo>
<msub id="p1.1.m1.1.18.2.2" xref="p1.1.m1.1.18.2.2.cmml">
<mi id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">C</mi>
<mi id="p1.1.m1.1.17.1" xref="p1.1.m1.1.17.1.cmml">i</mi>
</msub>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">
<eq id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
<apply id="p1.1.m1.1.18.1.cmml" xref="p1.1.m1.1.18.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.18.1.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">P</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">x0</csymbol>
</apply>
<apply id="p1.1.m1.1.18.2.cmml" xref="p1.1.m1.1.18.2">
<csymbol cd="latexml" id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">direct-sum</csymbol>
<apply id="p1.1.m1.1.18.2.1.cmml" xref="p1.1.m1.1.18.2.1">
<times id="p1.1.m1.1.18.2.1.1.cmml" xref="p1.1.m1.1.18.2.1.1"/>
<mtext id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">x1</mtext>
<interval closure="open" id="p1.1.m1.1.18.2.1.2.cmml" xref="p1.1.m1.1.18.2.1.2">
<apply id="XM2.cmml" xref="XM2">
<times id="XM2.1.cmml" xref="XM2.1"/>
<apply id="XM2.2.cmml" xref="XM2.2">
<csymbol cd="ambiguous" id="XM2.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">E</ci>
<ci id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">K</ci>
</apply>
<apply id="XM1.cmml" xref="XM1">
<csymbol cd="ambiguous" id="XM1.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">S</ci>
<apply id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">
<minus id="p1.1.m1.1.10.1.2.cmml" xref="p1.1.m1.1.10.1.2"/>
<ci id="p1.1.m1.1.10.1.1.cmml" xref="p1.1.m1.1.10.1.1">i</ci>
<cn type="integer" id="p1.1.m1.1.10.1.3.cmml" xref="p1.1.m1.1.10.1.3">1</cn>
</apply>
</apply>
</apply>
<ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">x</ci>
</interval>
</apply>
<apply id="p1.1.m1.1.18.2.2.cmml" xref="p1.1.m1.1.18.2.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.18.2.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">C</ci>
<ci id="p1.1.m1.1.17.1.cmml" xref="p1.1.m1.1.17.1">i</ci>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle P_{\qvar@construct{x0}}={\mbox{\qvar@construct{x1}}}(E_{K}(S_{{%
i-1}}),x)\oplus C_{i}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=c2490bce81f35cd3b8a9bdbf5339b31d&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.5ex; width: 29.333ex;" alt="P_{\qvar{x0}}={\mbox{\qvar{x1}}}(E_{K}(S_{{i-1}}),x)\oplus C_{i}" data-pagespeed-url-hash="3241082718" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{i}={\mbox{head}}(E_{K}(S_{i-1}),x)\oplus C_{i}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>P</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="false" scriptlevel="0">
<mtext>head</mtext>
</mstyle>
</mrow>
<mo stretchy="false">(</mo>
<msub>
<mi>E</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>K</mi>
</mrow>
</msub>
<mo stretchy="false">(</mo>
<msub>
<mi>S</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</msub>
<mo stretchy="false">)</mo>
<mo>,</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>⊕<!-- ⊕ --></mo>
<msub>
<mi>C</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle P_{i}={\mbox{head}}(E_{K}(S_{i-1}),x)\oplus C_{i}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/296992edaa117dae6d00d760b09adb66105e87d1" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:29.188ex; height:2.843ex;" alt="{\displaystyle P_{i}={\mbox{head}}(E_{K}(S_{i-1}),x)\oplus C_{i}}" data-pagespeed-url-hash="3144796110" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/67" title="Special:DisplayTopics/67">67</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/1666#math.1666.30" title="Special:PermanentLink/1666">Partial_derivative-30</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{{\frac{\partial f}{\partial x}}}=f_{{x}}=\partial_{{x}}f.}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">
<mrow id="p1.1.m1.1.10a" xref="p1.1.m1.1.10.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">
<mfrac id="p1.1.m1.1.1a" xref="p1.1.m1.1.1.cmml">
<mrow id="p1.1.m1.1.1.2" xref="p1.1.m1.1.1.2.cmml">
<mo id="p1.1.m1.1.1.2.1" xref="p1.1.m1.1.1.2.1.cmml">∂</mo>
<mo id="p1.1.m1.1.1.2a" xref="p1.1.m1.1.1.2.cmml"></mo>
<mi id="p1.1.m1.1.1.2.2" xref="p1.1.m1.1.1.2.2.cmml">f</mi>
</mrow>
<mrow id="p1.1.m1.1.1.3" xref="p1.1.m1.1.1.3.cmml">
<mo id="p1.1.m1.1.1.3.1" xref="p1.1.m1.1.1.3.1.cmml">∂</mo>
<mo id="p1.1.m1.1.1.3a" xref="p1.1.m1.1.1.3.cmml"></mo>
<mi id="p1.1.m1.1.1.3.2" xref="p1.1.m1.1.1.3.2.cmml">x</mi>
</mrow>
</mfrac>
</mstyle>
<mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">=</mo>
<msub id="p1.1.m1.1.10.2" xref="p1.1.m1.1.10.2.cmml">
<mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">f</mi>
<mi id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">x</mi>
</msub>
<mo id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">=</mo>
<mrow id="p1.1.m1.1.10.3" xref="p1.1.m1.1.10.3.cmml">
<msub id="p1.1.m1.1.10.3.1" xref="p1.1.m1.1.10.3.1.cmml">
<mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">∂</mo>
<mi id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">x</mi>
</msub>
<mo id="p1.1.m1.1.10.3a" xref="p1.1.m1.1.10.3.cmml"></mo>
<mi id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">f</mi>
</mrow>
</mrow>
<mo id="p1.1.m1.1.10b" xref="p1.1.m1.1.10.cmml">.</mo>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">
<and id="p1.1.m1.1.10a.cmml" xref="p1.1.m1.1.10"/>
<apply id="p1.1.m1.1.10b.cmml" xref="p1.1.m1.1.10">
<eq id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
<apply id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">
<divide id="p1.1.m1.1.1.1.cmml"/>
<apply id="p1.1.m1.1.1.2.cmml" xref="p1.1.m1.1.1.2">
<partialdiff id="p1.1.m1.1.1.2.1.cmml" xref="p1.1.m1.1.1.2.1"/>
<ci id="p1.1.m1.1.1.2.2.cmml" xref="p1.1.m1.1.1.2.2">f</ci>
</apply>
<apply id="p1.1.m1.1.1.3.cmml" xref="p1.1.m1.1.1.3">
<partialdiff id="p1.1.m1.1.1.3.1.cmml" xref="p1.1.m1.1.1.3.1"/>
<ci id="p1.1.m1.1.1.3.2.cmml" xref="p1.1.m1.1.1.3.2">x</ci>
</apply>
</apply>
<apply id="p1.1.m1.1.10.2.cmml" xref="p1.1.m1.1.10.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.10.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">f</ci>
<ci id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">x</ci>
</apply>
</apply>
<apply id="p1.1.m1.1.10c.cmml" xref="p1.1.m1.1.10">
<eq id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/>
<share href="#p1.1.m1.1.10.2.cmml" id="p1.1.m1.1.10d.cmml" xref="p1.1.m1.1.10"/>
<apply id="p1.1.m1.1.10.3.cmml" xref="p1.1.m1.1.10.3">
<apply id="p1.1.m1.1.10.3.1.cmml" xref="p1.1.m1.1.10.3.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.10.3.1.1.cmml">subscript</csymbol>
<partialdiff id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
<ci id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">x</ci>
</apply>
<ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">f</ci>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{{\frac{\partial f}{\partial x}}}=f_{{x}}=\partial_{{x}}f.}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=ee71880454515e7f5119bb026555c5ba&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.833ex; height: 5.333ex; width: 17.167ex;" alt="{{\frac {\partial f}{\partial x}}}=f_{{x}}=\partial _{{x}}f." data-pagespeed-url-hash="1975383855" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\partial f}{\partial x}}=f_{x}=\partial _{x}f.}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mi>f</mi>
</mrow>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mi>x</mi>
</mrow>
</mfrac>
</mrow>
<mo>=</mo>
<msub>
<mi>f</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>x</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>x</mi>
</mrow>
</msub>
<mi>f</mi>
<mo>.</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\frac {\partial f}{\partial x}}=f_{x}=\partial _{x}f.}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/42767773f9f263f879422debf6966ea6a9340dad" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.005ex; width:16.325ex; height:5.676ex;" alt="{\displaystyle {\frac {\partial f}{\partial x}}=f_{x}=\partial _{x}f.}" data-pagespeed-url-hash="2613403356" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/68" title="Special:DisplayTopics/68">68</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/27027#math.27027.0" title="Special:PermanentLink/27027">Poset_game-0</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle P_{{x}}=P-\{a\mid a\geq x\}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">
<msub id="p1.1.m1.1.13.1" xref="p1.1.m1.1.13.1.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">P</mi>
<mi id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">x</mi>
</msub>
<mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">=</mo>
<mrow id="p1.1.m1.1.13.2" xref="p1.1.m1.1.13.2.cmml">
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">P</mi>
<mo id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">-</mo>
<mrow id="p1.1.m1.1.13.2.1c" xref="p1.1.m1.1.13.2.1.cmml">
<mo stretchy="false" id="p1.1.m1.1.13.2.1" xref="p1.1.m1.1.13.2.1.cmml">{</mo>
<mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">a</mi>
<mo id="p1.1.m1.1.13.2.1a" xref="p1.1.m1.1.13.2.1.cmml">∣</mo>
<mrow id="XM1" xref="XM1.cmml">
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">a</mi>
<mo id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">≥</mo>
<mi id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">x</mi>
</mrow>
<mo stretchy="false" id="p1.1.m1.1.13.2.1b" xref="p1.1.m1.1.13.2.1.cmml">}</mo>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">
<eq id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
<apply id="p1.1.m1.1.13.1.cmml" xref="p1.1.m1.1.13.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.13.1.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">P</ci>
<ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">x</ci>
</apply>
<apply id="p1.1.m1.1.13.2.cmml" xref="p1.1.m1.1.13.2">
<minus id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">P</ci>
<apply id="p1.1.m1.1.13.2.1a.cmml" xref="p1.1.m1.1.13.2.1">
<csymbol cd="latexml" id="p1.1.m1.1.13.2.1.cmml" xref="p1.1.m1.1.13.2.1">conditional-set</csymbol>
<ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">a</ci>
<apply id="XM1.cmml" xref="XM1">
<geq id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10"/>
<ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">a</ci>
<ci id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">x</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle P_{{x}}=P-\{a\mid a\geq x\}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=58543128839366f7309eb33a3b89fd50&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.5ex; width: 21.667ex;" alt="P_{{x}}=P-\{a\mid a\geq x\}" data-pagespeed-url-hash="1494573664" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{x}=P-\{a\mid a\geq x\}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>P</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>x</mi>
</mrow>
</msub>
<mo>=</mo>
<mi>P</mi>
<mo>−<!-- − --></mo>
<mo fence="false" stretchy="false">{</mo>
<mi>a</mi>
<mo>∣<!-- ∣ --></mo>
<mi>a</mi>
<mo>≥<!-- ≥ --></mo>
<mi>x</mi>
<mo fence="false" stretchy="false">}</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle P_{x}=P-\{a\mid a\geq x\}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/7279763bcbfae06e3b5ad301519fb48cfa1460b6" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:21.499ex; height:2.843ex;" alt="{\displaystyle P_{x}=P-\{a\mid a\geq x\}}" data-pagespeed-url-hash="4174279509" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/69" title="Special:DisplayTopics/69">69</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/15167#math.15167.0" title="Special:PermanentLink/15167">Engine_efficiency-0</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\eta={{\frac{work\ done}{heat\ absorbed}}}={{\frac{Q1-Q2}{Q1}}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">η</mi>
<mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">=</mo>
<mstyle displaystyle="true" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
<mfrac id="p1.1.m1.1.3a" xref="p1.1.m1.1.3.cmml">
<mrow id="p1.1.m1.1.3.2" xref="p1.1.m1.1.3.2.cmml">
<mi id="p1.1.m1.1.3.2.1" xref="p1.1.m1.1.3.2.1.cmml">w</mi>
<mo id="p1.1.m1.1.3.2.10" xref="p1.1.m1.1.3.2.10.cmml"></mo>
<mi id="p1.1.m1.1.3.2.2" xref="p1.1.m1.1.3.2.2.cmml">o</mi>
<mo id="p1.1.m1.1.3.2.10a" xref="p1.1.m1.1.3.2.10.cmml"></mo>
<mi id="p1.1.m1.1.3.2.3" xref="p1.1.m1.1.3.2.3.cmml">r</mi>
<mo id="p1.1.m1.1.3.2.10b" xref="p1.1.m1.1.3.2.10.cmml"></mo>
<mpadded width="+5pt" id="p1.1.m1.1.3.2.4" xref="p1.1.m1.1.3.2.4.cmml">
<mi id="p1.1.m1.1.3.2.4a" xref="p1.1.m1.1.3.2.4.cmml">k</mi>
</mpadded>
<mo id="p1.1.m1.1.3.2.10c" xref="p1.1.m1.1.3.2.10.cmml"></mo>
<mi id="p1.1.m1.1.3.2.6" xref="p1.1.m1.1.3.2.6.cmml">d</mi>
<mo id="p1.1.m1.1.3.2.10d" xref="p1.1.m1.1.3.2.10.cmml"></mo>
<mi id="p1.1.m1.1.3.2.7" xref="p1.1.m1.1.3.2.7.cmml">o</mi>
<mo id="p1.1.m1.1.3.2.10e" xref="p1.1.m1.1.3.2.10.cmml"></mo>
<mi id="p1.1.m1.1.3.2.8" xref="p1.1.m1.1.3.2.8.cmml">n</mi>
<mo id="p1.1.m1.1.3.2.10f" xref="p1.1.m1.1.3.2.10.cmml"></mo>
<mi id="p1.1.m1.1.3.2.9" xref="p1.1.m1.1.3.2.9.cmml">e</mi>
</mrow>
<mrow id="p1.1.m1.1.3.3" xref="p1.1.m1.1.3.3.cmml">
<mi id="p1.1.m1.1.3.3.1" xref="p1.1.m1.1.3.3.1.cmml">h</mi>
<mo id="p1.1.m1.1.3.3.14" xref="p1.1.m1.1.3.3.14.cmml"></mo>
<mi id="p1.1.m1.1.3.3.2" xref="p1.1.m1.1.3.3.2.cmml">e</mi>
<mo id="p1.1.m1.1.3.3.14a" xref="p1.1.m1.1.3.3.14.cmml"></mo>
<mi id="p1.1.m1.1.3.3.3" xref="p1.1.m1.1.3.3.3.cmml">a</mi>
<mo id="p1.1.m1.1.3.3.14b" xref="p1.1.m1.1.3.3.14.cmml"></mo>
<mpadded width="+5pt" id="p1.1.m1.1.3.3.4" xref="p1.1.m1.1.3.3.4.cmml">
<mi id="p1.1.m1.1.3.3.4a" xref="p1.1.m1.1.3.3.4.cmml">t</mi>
</mpadded>
<mo id="p1.1.m1.1.3.3.14c" xref="p1.1.m1.1.3.3.14.cmml"></mo>
<mi id="p1.1.m1.1.3.3.6" xref="p1.1.m1.1.3.3.6.cmml">a</mi>
<mo id="p1.1.m1.1.3.3.14d" xref="p1.1.m1.1.3.3.14.cmml"></mo>
<mi id="p1.1.m1.1.3.3.7" xref="p1.1.m1.1.3.3.7.cmml">b</mi>
<mo id="p1.1.m1.1.3.3.14e" xref="p1.1.m1.1.3.3.14.cmml"></mo>
<mi id="p1.1.m1.1.3.3.8" xref="p1.1.m1.1.3.3.8.cmml">s</mi>
<mo id="p1.1.m1.1.3.3.14f" xref="p1.1.m1.1.3.3.14.cmml"></mo>
<mi id="p1.1.m1.1.3.3.9" xref="p1.1.m1.1.3.3.9.cmml">o</mi>
<mo id="p1.1.m1.1.3.3.14g" xref="p1.1.m1.1.3.3.14.cmml"></mo>
<mi id="p1.1.m1.1.3.3.10" xref="p1.1.m1.1.3.3.10.cmml">r</mi>
<mo id="p1.1.m1.1.3.3.14h" xref="p1.1.m1.1.3.3.14.cmml"></mo>
<mi id="p1.1.m1.1.3.3.11" xref="p1.1.m1.1.3.3.11.cmml">b</mi>
<mo id="p1.1.m1.1.3.3.14i" xref="p1.1.m1.1.3.3.14.cmml"></mo>
<mi id="p1.1.m1.1.3.3.12" xref="p1.1.m1.1.3.3.12.cmml">e</mi>
<mo id="p1.1.m1.1.3.3.14j" xref="p1.1.m1.1.3.3.14.cmml"></mo>
<mi id="p1.1.m1.1.3.3.13" xref="p1.1.m1.1.3.3.13.cmml">d</mi>
</mrow>
</mfrac>
</mstyle>
<mo id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">=</mo>
<mstyle displaystyle="true" id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">
<mfrac id="p1.1.m1.1.5a" xref="p1.1.m1.1.5.cmml">
<mrow id="p1.1.m1.1.5.2" xref="p1.1.m1.1.5.2.cmml">
<mrow id="p1.1.m1.1.5.2.6" xref="p1.1.m1.1.5.2.6.cmml">
<mi id="p1.1.m1.1.5.2.1" xref="p1.1.m1.1.5.2.1.cmml">Q</mi>
<mo id="p1.1.m1.1.5.2.6.1" xref="p1.1.m1.1.5.2.6.1.cmml"></mo>
<mn id="p1.1.m1.1.5.2.2" xref="p1.1.m1.1.5.2.2.cmml">1</mn>
</mrow>
<mo id="p1.1.m1.1.5.2.3" xref="p1.1.m1.1.5.2.3.cmml">-</mo>
<mrow id="p1.1.m1.1.5.2.7" xref="p1.1.m1.1.5.2.7.cmml">
<mi id="p1.1.m1.1.5.2.4" xref="p1.1.m1.1.5.2.4.cmml">Q</mi>
<mo id="p1.1.m1.1.5.2.7.1" xref="p1.1.m1.1.5.2.7.1.cmml"></mo>
<mn id="p1.1.m1.1.5.2.5" xref="p1.1.m1.1.5.2.5.cmml">2</mn>
</mrow>
</mrow>
<mrow id="p1.1.m1.1.5.3" xref="p1.1.m1.1.5.3.cmml">
<mi id="p1.1.m1.1.5.3.1" xref="p1.1.m1.1.5.3.1.cmml">Q</mi>
<mo id="p1.1.m1.1.5.3.3" xref="p1.1.m1.1.5.3.3.cmml"></mo>
<mn id="p1.1.m1.1.5.3.2" xref="p1.1.m1.1.5.3.2.cmml">1</mn>
</mrow>
</mfrac>
</mstyle>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">
<and id="p1.1.m1.1.6a.cmml" xref="p1.1.m1.1.6"/>
<apply id="p1.1.m1.1.6b.cmml" xref="p1.1.m1.1.6">
<eq id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">η</ci>
<apply id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
<divide id="p1.1.m1.1.3.1.cmml"/>
<apply id="p1.1.m1.1.3.2.cmml" xref="p1.1.m1.1.3.2">
<times id="p1.1.m1.1.3.2.10.cmml" xref="p1.1.m1.1.3.2.10"/>
<ci id="p1.1.m1.1.3.2.1.cmml" xref="p1.1.m1.1.3.2.1">w</ci>
<ci id="p1.1.m1.1.3.2.2.cmml" xref="p1.1.m1.1.3.2.2">o</ci>
<ci id="p1.1.m1.1.3.2.3.cmml" xref="p1.1.m1.1.3.2.3">r</ci>
<ci id="p1.1.m1.1.3.2.4.cmml" xref="p1.1.m1.1.3.2.4">k</ci>
<ci id="p1.1.m1.1.3.2.6.cmml" xref="p1.1.m1.1.3.2.6">d</ci>
<ci id="p1.1.m1.1.3.2.7.cmml" xref="p1.1.m1.1.3.2.7">o</ci>
<ci id="p1.1.m1.1.3.2.8.cmml" xref="p1.1.m1.1.3.2.8">n</ci>
<ci id="p1.1.m1.1.3.2.9.cmml" xref="p1.1.m1.1.3.2.9">e</ci>
</apply>
<apply id="p1.1.m1.1.3.3.cmml" xref="p1.1.m1.1.3.3">
<times id="p1.1.m1.1.3.3.14.cmml" xref="p1.1.m1.1.3.3.14"/>
<ci id="p1.1.m1.1.3.3.1.cmml" xref="p1.1.m1.1.3.3.1">h</ci>
<ci id="p1.1.m1.1.3.3.2.cmml" xref="p1.1.m1.1.3.3.2">e</ci>
<ci id="p1.1.m1.1.3.3.3.cmml" xref="p1.1.m1.1.3.3.3">a</ci>
<ci id="p1.1.m1.1.3.3.4.cmml" xref="p1.1.m1.1.3.3.4">t</ci>
<ci id="p1.1.m1.1.3.3.6.cmml" xref="p1.1.m1.1.3.3.6">a</ci>
<ci id="p1.1.m1.1.3.3.7.cmml" xref="p1.1.m1.1.3.3.7">b</ci>
<ci id="p1.1.m1.1.3.3.8.cmml" xref="p1.1.m1.1.3.3.8">s</ci>
<ci id="p1.1.m1.1.3.3.9.cmml" xref="p1.1.m1.1.3.3.9">o</ci>
<ci id="p1.1.m1.1.3.3.10.cmml" xref="p1.1.m1.1.3.3.10">r</ci>
<ci id="p1.1.m1.1.3.3.11.cmml" xref="p1.1.m1.1.3.3.11">b</ci>
<ci id="p1.1.m1.1.3.3.12.cmml" xref="p1.1.m1.1.3.3.12">e</ci>
<ci id="p1.1.m1.1.3.3.13.cmml" xref="p1.1.m1.1.3.3.13">d</ci>
</apply>
</apply>
</apply>
<apply id="p1.1.m1.1.6c.cmml" xref="p1.1.m1.1.6">
<eq id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4"/>
<share href="#p1.1.m1.1.3.cmml" id="p1.1.m1.1.6d.cmml" xref="p1.1.m1.1.6"/>
<apply id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">
<divide id="p1.1.m1.1.5.1.cmml"/>
<apply id="p1.1.m1.1.5.2.cmml" xref="p1.1.m1.1.5.2">
<minus id="p1.1.m1.1.5.2.3.cmml" xref="p1.1.m1.1.5.2.3"/>
<apply id="p1.1.m1.1.5.2.6.cmml" xref="p1.1.m1.1.5.2.6">
<times id="p1.1.m1.1.5.2.6.1.cmml" xref="p1.1.m1.1.5.2.6.1"/>
<ci id="p1.1.m1.1.5.2.1.cmml" xref="p1.1.m1.1.5.2.1">Q</ci>
<cn type="integer" id="p1.1.m1.1.5.2.2.cmml" xref="p1.1.m1.1.5.2.2">1</cn>
</apply>
<apply id="p1.1.m1.1.5.2.7.cmml" xref="p1.1.m1.1.5.2.7">
<times id="p1.1.m1.1.5.2.7.1.cmml" xref="p1.1.m1.1.5.2.7.1"/>
<ci id="p1.1.m1.1.5.2.4.cmml" xref="p1.1.m1.1.5.2.4">Q</ci>
<cn type="integer" id="p1.1.m1.1.5.2.5.cmml" xref="p1.1.m1.1.5.2.5">2</cn>
</apply>
</apply>
<apply id="p1.1.m1.1.5.3.cmml" xref="p1.1.m1.1.5.3">
<times id="p1.1.m1.1.5.3.3.cmml" xref="p1.1.m1.1.5.3.3"/>
<ci id="p1.1.m1.1.5.3.1.cmml" xref="p1.1.m1.1.5.3.1">Q</ci>
<cn type="integer" id="p1.1.m1.1.5.3.2.cmml" xref="p1.1.m1.1.5.3.2">1</cn>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\eta={{\frac{work\ done}{heat\ absorbed}}}={{\frac{Q1-Q2}{Q1}}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=b4d577b10c4752d6d8be0daae84acb81&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.167ex; height: 5.5ex; width: 32.5ex;" alt="\eta ={{\frac {work\ done}{heat\ absorbed}}}={{\frac {Q1-Q2}{Q1}}}" data-pagespeed-url-hash="1130894223" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \eta ={\frac {work\ done}{heat\ absorbed}}={\frac {Q1-Q2}{Q1}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>η<!-- η --></mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi>w</mi>
<mi>o</mi>
<mi>r</mi>
<mi>k</mi>
<mtext> </mtext>
<mi>d</mi>
<mi>o</mi>
<mi>n</mi>
<mi>e</mi>
</mrow>
<mrow>
<mi>h</mi>
<mi>e</mi>
<mi>a</mi>
<mi>t</mi>
<mtext> </mtext>
<mi>a</mi>
<mi>b</mi>
<mi>s</mi>
<mi>o</mi>
<mi>r</mi>
<mi>b</mi>
<mi>e</mi>
<mi>d</mi>
</mrow>
</mfrac>
</mrow>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi>Q</mi>
<mn>1</mn>
<mo>−<!-- − --></mo>
<mi>Q</mi>
<mn>2</mn>
</mrow>
<mrow>
<mi>Q</mi>
<mn>1</mn>
</mrow>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \eta ={\frac {work\ done}{heat\ absorbed}}={\frac {Q1-Q2}{Q1}}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/dd2cc536e498a99c82bfd41f0990657977a3a0c6" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.338ex; width:31.744ex; height:5.843ex;" alt="{\displaystyle \eta ={\frac {work\ done}{heat\ absorbed}}={\frac {Q1-Q2}{Q1}}}" data-pagespeed-url-hash="96147911" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/70" title="Special:DisplayTopics/70">70</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/4480#math.4480.29" title="Special:PermanentLink/4480">Legendre_transformation-29</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle df={\partial f\over\partial x}dx+{\partial f\over\partial y}dy=% pdx+vdy}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">
<mrow id="p1.1.m1.1.19.2" xref="p1.1.m1.1.19.2.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">d</mi>
<mo id="p1.1.m1.1.19.2.1" xref="p1.1.m1.1.19.2.1.cmml"></mo>
<mi id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">f</mi>
</mrow>
<mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">=</mo>
<mrow id="p1.1.m1.1.19.3" xref="p1.1.m1.1.19.3.cmml">
<mrow id="p1.1.m1.1.19.3.1" xref="p1.1.m1.1.19.3.1.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">
<mfrac id="p1.1.m1.1.4a" xref="p1.1.m1.1.4.cmml">
<mrow id="p1.1.m1.1.4.2" xref="p1.1.m1.1.4.2.cmml">
<mo id="p1.1.m1.1.4.2.1" xref="p1.1.m1.1.4.2.1.cmml">∂</mo>
<mo id="p1.1.m1.1.4.2a" xref="p1.1.m1.1.4.2.cmml"></mo>
<mi id="p1.1.m1.1.4.2.2" xref="p1.1.m1.1.4.2.2.cmml">f</mi>
</mrow>
<mrow id="p1.1.m1.1.4.3" xref="p1.1.m1.1.4.3.cmml">
<mo id="p1.1.m1.1.4.3.1" xref="p1.1.m1.1.4.3.1.cmml">∂</mo>
<mo id="p1.1.m1.1.4.3a" xref="p1.1.m1.1.4.3.cmml"></mo>
<mi id="p1.1.m1.1.4.3.2" xref="p1.1.m1.1.4.3.2.cmml">x</mi>
</mrow>
</mfrac>
</mstyle>
<mo id="p1.1.m1.1.19.3.1.1" xref="p1.1.m1.1.19.3.1.1.cmml"></mo>
<mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">d</mi>
<mo id="p1.1.m1.1.19.3.1.1a" xref="p1.1.m1.1.19.3.1.1.cmml"></mo>
<mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">x</mi>
</mrow>
<mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">+</mo>
<mrow id="p1.1.m1.1.19.3.2" xref="p1.1.m1.1.19.3.2.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">
<mfrac id="p1.1.m1.1.8a" xref="p1.1.m1.1.8.cmml">
<mrow id="p1.1.m1.1.8.2" xref="p1.1.m1.1.8.2.cmml">
<mo id="p1.1.m1.1.8.2.1" xref="p1.1.m1.1.8.2.1.cmml">∂</mo>
<mo id="p1.1.m1.1.8.2a" xref="p1.1.m1.1.8.2.cmml"></mo>
<mi id="p1.1.m1.1.8.2.2" xref="p1.1.m1.1.8.2.2.cmml">f</mi>
</mrow>
<mrow id="p1.1.m1.1.8.3" xref="p1.1.m1.1.8.3.cmml">
<mo id="p1.1.m1.1.8.3.1" xref="p1.1.m1.1.8.3.1.cmml">∂</mo>
<mo id="p1.1.m1.1.8.3a" xref="p1.1.m1.1.8.3.cmml"></mo>
<mi id="p1.1.m1.1.8.3.2" xref="p1.1.m1.1.8.3.2.cmml">y</mi>
</mrow>
</mfrac>
</mstyle>
<mo id="p1.1.m1.1.19.3.2.1" xref="p1.1.m1.1.19.3.2.1.cmml"></mo>
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">d</mi>
<mo id="p1.1.m1.1.19.3.2.1a" xref="p1.1.m1.1.19.3.2.1.cmml"></mo>
<mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">y</mi>
</mrow>
</mrow>
<mo id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">=</mo>
<mrow id="p1.1.m1.1.19.4" xref="p1.1.m1.1.19.4.cmml">
<mrow id="p1.1.m1.1.19.4.1" xref="p1.1.m1.1.19.4.1.cmml">
<mi id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">p</mi>
<mo id="p1.1.m1.1.19.4.1.1" xref="p1.1.m1.1.19.4.1.1.cmml"></mo>
<mi id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">d</mi>
<mo id="p1.1.m1.1.19.4.1.1a" xref="p1.1.m1.1.19.4.1.1.cmml"></mo>
<mi id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">x</mi>
</mrow>
<mo id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">+</mo>
<mrow id="p1.1.m1.1.19.4.2" xref="p1.1.m1.1.19.4.2.cmml">
<mi id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">v</mi>
<mo id="p1.1.m1.1.19.4.2.1" xref="p1.1.m1.1.19.4.2.1.cmml"></mo>
<mi id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">d</mi>
<mo id="p1.1.m1.1.19.4.2.1a" xref="p1.1.m1.1.19.4.2.1.cmml"></mo>
<mi id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">y</mi>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">
<and id="p1.1.m1.1.19a.cmml" xref="p1.1.m1.1.19"/>
<apply id="p1.1.m1.1.19b.cmml" xref="p1.1.m1.1.19">
<eq id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
<apply id="p1.1.m1.1.19.2.cmml" xref="p1.1.m1.1.19.2">
<times id="p1.1.m1.1.19.2.1.cmml" xref="p1.1.m1.1.19.2.1"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">d</ci>
<ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">f</ci>
</apply>
<apply id="p1.1.m1.1.19.3.cmml" xref="p1.1.m1.1.19.3">
<plus id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
<apply id="p1.1.m1.1.19.3.1.cmml" xref="p1.1.m1.1.19.3.1">
<times id="p1.1.m1.1.19.3.1.1.cmml" xref="p1.1.m1.1.19.3.1.1"/>
<apply id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">
<divide id="p1.1.m1.1.4.1.cmml"/>
<apply id="p1.1.m1.1.4.2.cmml" xref="p1.1.m1.1.4.2">
<partialdiff id="p1.1.m1.1.4.2.1.cmml" xref="p1.1.m1.1.4.2.1"/>
<ci id="p1.1.m1.1.4.2.2.cmml" xref="p1.1.m1.1.4.2.2">f</ci>
</apply>
<apply id="p1.1.m1.1.4.3.cmml" xref="p1.1.m1.1.4.3">
<partialdiff id="p1.1.m1.1.4.3.1.cmml" xref="p1.1.m1.1.4.3.1"/>
<ci id="p1.1.m1.1.4.3.2.cmml" xref="p1.1.m1.1.4.3.2">x</ci>
</apply>
</apply>
<ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">d</ci>
<ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">x</ci>
</apply>
<apply id="p1.1.m1.1.19.3.2.cmml" xref="p1.1.m1.1.19.3.2">
<times id="p1.1.m1.1.19.3.2.1.cmml" xref="p1.1.m1.1.19.3.2.1"/>
<apply id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">
<divide id="p1.1.m1.1.8.1.cmml"/>
<apply id="p1.1.m1.1.8.2.cmml" xref="p1.1.m1.1.8.2">
<partialdiff id="p1.1.m1.1.8.2.1.cmml" xref="p1.1.m1.1.8.2.1"/>
<ci id="p1.1.m1.1.8.2.2.cmml" xref="p1.1.m1.1.8.2.2">f</ci>
</apply>
<apply id="p1.1.m1.1.8.3.cmml" xref="p1.1.m1.1.8.3">
<partialdiff id="p1.1.m1.1.8.3.1.cmml" xref="p1.1.m1.1.8.3.1"/>
<ci id="p1.1.m1.1.8.3.2.cmml" xref="p1.1.m1.1.8.3.2">y</ci>
</apply>
</apply>
<ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">d</ci>
<ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">y</ci>
</apply>
</apply>
</apply>
<apply id="p1.1.m1.1.19c.cmml" xref="p1.1.m1.1.19">
<eq id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11"/>
<share href="#p1.1.m1.1.19.3.cmml" id="p1.1.m1.1.19d.cmml" xref="p1.1.m1.1.19"/>
<apply id="p1.1.m1.1.19.4.cmml" xref="p1.1.m1.1.19.4">
<plus id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15"/>
<apply id="p1.1.m1.1.19.4.1.cmml" xref="p1.1.m1.1.19.4.1">
<times id="p1.1.m1.1.19.4.1.1.cmml" xref="p1.1.m1.1.19.4.1.1"/>
<ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">p</ci>
<ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">d</ci>
<ci id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">x</ci>
</apply>
<apply id="p1.1.m1.1.19.4.2.cmml" xref="p1.1.m1.1.19.4.2">
<times id="p1.1.m1.1.19.4.2.1.cmml" xref="p1.1.m1.1.19.4.2.1"/>
<ci id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">v</ci>
<ci id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">d</ci>
<ci id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">y</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle df={\partial f\over\partial x}dx+{\partial f\over\partial y}dy=%
pdx+vdy}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=d21dde8adc6ac786c7369d6bc607fa23&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.333ex; height: 5.667ex; width: 35ex;" alt="df={\partial f \over \partial x}dx+{\partial f \over \partial y}dy=pdx+vdy" data-pagespeed-url-hash="2206005358" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle df={\partial f \over \partial x}dx+{\partial f \over \partial y}dy=pdx+vdy}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>d</mi>
<mi>f</mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mi>f</mi>
</mrow>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mi>x</mi>
</mrow>
</mfrac>
</mrow>
<mi>d</mi>
<mi>x</mi>
<mo>+</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mi>f</mi>
</mrow>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mi>y</mi>
</mrow>
</mfrac>
</mrow>
<mi>d</mi>
<mi>y</mi>
<mo>=</mo>
<mi>p</mi>
<mi>d</mi>
<mi>x</mi>
<mo>+</mo>
<mi>v</mi>
<mi>d</mi>
<mi>y</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle df={\partial f \over \partial x}dx+{\partial f \over \partial y}dy=pdx+vdy}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/dbbf599b5e9b58bf16cf485168a9fb8c8c63c945" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.505ex; width:33.42ex; height:6.176ex;" alt="{\displaystyle df={\partial f \over \partial x}dx+{\partial f \over \partial y}dy=pdx+vdy}" data-pagespeed-url-hash="1401748340" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/71" title="Special:DisplayTopics/71">71</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/17690#math.17690.4" title="Special:PermanentLink/17690">Cooperative_diversity-4</a>
</td>
<td> 1
</td>
<td> 2
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle h_{{\qvar@construct{x0}}}}">
<semantics id="p1.1.m1.1a">
<msub id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">h</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">x0</mi>
</msub>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
<csymbol cd="ambiguous" id="p1.1.m1.1.3.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">h</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">x0</csymbol>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle h_{{\qvar@construct{x0}}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=5c95e2dce4fb764fd166ed8fbacfe333&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.5ex; height: 2.167ex; width: 3.333ex;" alt="h_{{\qvar{x0}}}" data-pagespeed-url-hash="3546520093" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h_{r,s}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>h</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>r</mi>
<mo>,</mo>
<mi>s</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle h_{r,s}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/f7e4d78a27e43fc0f4e145a0289656ef0fa0211c" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.005ex; width:3.541ex; height:2.843ex;" alt="{\displaystyle h_{r,s}}" data-pagespeed-url-hash="1922516070" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/72" title="Special:DisplayTopics/72">72</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/5763#math.5763.20" title="Special:PermanentLink/5763">Algebraic_K-theory-20</a>
</td>
<td> 2
</td>
<td> 2
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle K_{\qvar@construct{x0}}^{\qvar@construct{x1}}(k):=T^{*}(k^{% \times})/(a\otimes(1-a))}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">
<mrow id="p1.1.m1.1.25.1" xref="p1.1.m1.1.25.1.cmml">
<msubsup id="p1.1.m1.1.25.1.2" xref="p1.1.m1.1.25.1.2.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">K</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">x0</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.3.1" xref="p1.1.m1.1.3.1.cmml">x1</mi>
</msubsup>
<mo id="p1.1.m1.1.25.1.1" xref="p1.1.m1.1.25.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.25.1.3b">
<mo stretchy="false" id="p1.1.m1.1.25.1.3">(</mo>
<mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">k</mi>
<mo stretchy="false" id="p1.1.m1.1.25.1.3a">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">:=</mo>
<mrow id="p1.1.m1.1.25.2" xref="p1.1.m1.1.25.2.cmml">
<mrow id="p1.1.m1.1.25.2.1" xref="p1.1.m1.1.25.2.1.cmml">
<msup id="p1.1.m1.1.25.2.1.2" xref="p1.1.m1.1.25.2.1.2.cmml">
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">T</mi>
<mo id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">*</mo>
</msup>
<mo id="p1.1.m1.1.25.2.1.1" xref="p1.1.m1.1.25.2.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.25.2.1.3b">
<mo stretchy="false" id="p1.1.m1.1.25.2.1.3">(</mo>
<msup id="XM1" xref="XM1.cmml">
<mi id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">k</mi>
<mo id="p1.1.m1.1.13.1" xref="p1.1.m1.1.13.1.cmml">×</mo>
</msup>
<mo stretchy="false" id="p1.1.m1.1.25.2.1.3a">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">/</mo>
<mrow id="p1.1.m1.1.25.2.2b">
<mo stretchy="false" id="p1.1.m1.1.25.2.2">(</mo>
<mrow id="XM3" xref="XM3.cmml">
<mi id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">a</mi>
<mo id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">⊗</mo>
<mrow id="XM3.1b">
<mo stretchy="false" id="XM3.1">(</mo>
<mrow id="XM2" xref="XM2.cmml">
<mn id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">1</mn>
<mo id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">-</mo>
<mi id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">a</mi>
</mrow>
<mo stretchy="false" id="XM3.1a">)</mo>
</mrow>
</mrow>
<mo stretchy="false" id="p1.1.m1.1.25.2.2a">)</mo>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25">
<csymbol cd="latexml" id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">assign</csymbol>
<apply id="p1.1.m1.1.25.1.cmml" xref="p1.1.m1.1.25.1">
<times id="p1.1.m1.1.25.1.1.cmml" xref="p1.1.m1.1.25.1.1"/>
<apply id="p1.1.m1.1.25.1.2.cmml" xref="p1.1.m1.1.25.1.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.25.1.2.1.cmml">superscript</csymbol>
<apply id="p1.1.m1.1.25.1.2.2.cmml">
<csymbol cd="ambiguous" id="p1.1.m1.1.25.1.2.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">K</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">x0</csymbol>
</apply>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.3.1.cmml" xref="p1.1.m1.1.3.1">x1</csymbol>
</apply>
<ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">k</ci>
</apply>
<apply id="p1.1.m1.1.25.2.cmml" xref="p1.1.m1.1.25.2">
<divide id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15"/>
<apply id="p1.1.m1.1.25.2.1.cmml" xref="p1.1.m1.1.25.2.1">
<times id="p1.1.m1.1.25.2.1.1.cmml" xref="p1.1.m1.1.25.2.1.1"/>
<apply id="p1.1.m1.1.25.2.1.2.cmml" xref="p1.1.m1.1.25.2.1.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.25.2.1.2.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">T</ci>
<times id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1"/>
</apply>
<apply id="XM1.cmml" xref="XM1">
<csymbol cd="ambiguous" id="XM1.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">k</ci>
<times id="p1.1.m1.1.13.1.cmml" xref="p1.1.m1.1.13.1"/>
</apply>
</apply>
<apply id="XM3.cmml" xref="XM3">
<csymbol cd="latexml" id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">tensor-product</csymbol>
<ci id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">a</ci>
<apply id="XM2.cmml" xref="XM2">
<minus id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21"/>
<cn type="integer" id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">1</cn>
<ci id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22">a</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle K_{\qvar@construct{x0}}^{\qvar@construct{x1}}(k):=T^{*}(k^{%
\times})/(a\otimes(1-a))}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=fa13153ff57474ef10014d6708a55825&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.833ex; height: 2.833ex; width: 33.833ex;" alt="K_{\qvar{x0}}^{\qvar{x1}}(k):=T^{*}(k^{\times})/(a\otimes(1-a))" data-pagespeed-url-hash="3946046028" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{*}^{M}(k):=T^{*}(k^{\times })/(a\otimes (1-a))}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msubsup>
<mi>K</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>∗<!-- ∗ --></mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi>M</mi>
</mrow>
</msubsup>
<mo stretchy="false">(</mo>
<mi>k</mi>
<mo stretchy="false">)</mo>
<mo>:=</mo>
<msup>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>∗<!-- ∗ --></mo>
</mrow>
</msup>
<mo stretchy="false">(</mo>
<msup>
<mi>k</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>×<!-- × --></mo>
</mrow>
</msup>
<mo stretchy="false">)</mo>
<mrow class="MJX-TeXAtom-ORD">
<mo>/</mo>
</mrow>
<mo stretchy="false">(</mo>
<mi>a</mi>
<mo>⊗<!-- ⊗ --></mo>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>−<!-- − --></mo>
<mi>a</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle K_{*}^{M}(k):=T^{*}(k^{\times })/(a\otimes (1-a))}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/507658eaa3612ed1cef5a416bb6fa5a7f27adf5e" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:32.208ex; height:3.009ex;" alt="{\displaystyle K_{*}^{M}(k):=T^{*}(k^{\times })/(a\otimes (1-a))}" data-pagespeed-url-hash="914343390" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/73" title="Special:DisplayTopics/73">73</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/21482#math.21482.45" title="Special:PermanentLink/21482">Cone_of_curves-45</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\{C:K_{{X}}\cdot C=0\}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.11c" xref="p1.1.m1.1.11.cmml">
<mo stretchy="false" id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">{</mo>
<mi id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">C</mi>
<mo id="p1.1.m1.1.11a" xref="p1.1.m1.1.11.cmml">:</mo>
<mrow id="XM1" xref="XM1.cmml">
<mrow id="XM1.1" xref="XM1.1.cmml">
<msub id="XM1.1.1" xref="XM1.1.1.cmml">
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">K</mi>
<mi id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">X</mi>
</msub>
<mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">⋅</mo>
<mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">C</mi>
</mrow>
<mo id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">=</mo>
<mn id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">0</mn>
</mrow>
<mo stretchy="false" id="p1.1.m1.1.11b" xref="p1.1.m1.1.11.cmml">}</mo>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.11a.cmml" xref="p1.1.m1.1.11">
<csymbol cd="latexml" id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">conditional-set</csymbol>
<ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">C</ci>
<apply id="XM1.cmml" xref="XM1">
<eq id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8"/>
<apply id="XM1.1.cmml" xref="XM1.1">
<ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">normal-⋅</ci>
<apply id="XM1.1.1.cmml" xref="XM1.1.1">
<csymbol cd="ambiguous" id="XM1.1.1.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">K</ci>
<ci id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1">X</ci>
</apply>
<ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">C</ci>
</apply>
<cn type="integer" id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">0</cn>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\{C:K_{{X}}\cdot C=0\}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=c762c133fcc7e1324e22767bfb8caa40&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.5ex; width: 17.5ex;" alt="\{C:K_{{X}}\cdot C=0\}" data-pagespeed-url-hash="2145386433" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \{C:K_{X}\cdot C=0\}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mo fence="false" stretchy="false">{</mo>
<mi>C</mi>
<mo>:</mo>
<msub>
<mi>K</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>X</mi>
</mrow>
</msub>
<mo>⋅<!-- ⋅ --></mo>
<mi>C</mi>
<mo>=</mo>
<mn>0</mn>
<mo fence="false" stretchy="false">}</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \{C:K_{X}\cdot C=0\}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/58eb88a4c7ed840ffe0a0e1422a68024a3181a31" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:17.34ex; height:2.843ex;" alt="{\displaystyle \{C:K_{X}\cdot C=0\}}" data-pagespeed-url-hash="1041754311" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/74" title="Special:DisplayTopics/74">74</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/28602#math.28602.8" title="Special:PermanentLink/28602">Geometrothermodynamics-8</a>
</td>
<td> 1
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\Theta\wedge(d\Theta)^{\qvar@construct{x0}}\neq 0}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">
<mrow id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">
<mi mathvariant="normal" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">Θ</mi>
<mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">∧</mo>
<msup id="p1.1.m1.1.10.1.1" xref="p1.1.m1.1.10.1.1.cmml">
<mrow id="p1.1.m1.1.10.1.1.2b">
<mo stretchy="false" id="p1.1.m1.1.10.1.1.2">(</mo>
<mrow id="XM1" xref="XM1.cmml">
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">d</mi>
<mo id="XM1.1" xref="XM1.1.cmml"></mo>
<mi mathvariant="normal" id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">Θ</mi>
</mrow>
<mo stretchy="false" id="p1.1.m1.1.10.1.1.2a">)</mo>
</mrow>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">x0</mi>
</msup>
</mrow>
<mo id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">≠</mo>
<mn id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">0</mn>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">
<neq id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8"/>
<apply id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">
<and id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">normal-Θ</ci>
<apply id="p1.1.m1.1.10.1.1.cmml" xref="p1.1.m1.1.10.1.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.10.1.1.1.cmml">superscript</csymbol>
<apply id="XM1.cmml" xref="XM1">
<times id="XM1.1.cmml" xref="XM1.1"/>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">d</ci>
<ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">normal-Θ</ci>
</apply>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">x0</csymbol>
</apply>
</apply>
<cn type="integer" id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">0</cn>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\Theta\wedge(d\Theta)^{\qvar@construct{x0}}\neq 0}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=619507e7141f4a92d285eac60d8bad07&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.833ex; width: 15.667ex;" alt="\Theta\wedge(d\Theta)^{\qvar{x0}}\neq 0" data-pagespeed-url-hash="517924261" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Theta \wedge (d\Theta )^{n}\neq 0}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">Θ<!-- Θ --></mi>
<mo>∧<!-- ∧ --></mo>
<mo stretchy="false">(</mo>
<mi>d</mi>
<mi mathvariant="normal">Θ<!-- Θ --></mi>
<msup>
<mo stretchy="false">)</mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>n</mi>
</mrow>
</msup>
<mo>≠<!-- ≠ --></mo>
<mn>0</mn>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \Theta \wedge (d\Theta )^{n}\neq 0}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/91556658fe4689e7b6315e237ce7b48587124213" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:14.703ex; height:2.843ex;" alt="{\displaystyle \Theta \wedge (d\Theta )^{n}\neq 0}" data-pagespeed-url-hash="3911674060" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/75" title="Special:DisplayTopics/75">75</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/6724#math.6724.5" title="Special:PermanentLink/6724">Darcy's_law-5</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle D\left(\rho u_{{i}}\right)/Dt\approx 0}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">
<mrow id="p1.1.m1.1.12.1" xref="p1.1.m1.1.12.1.cmml">
<mrow id="p1.1.m1.1.12.1.2" xref="p1.1.m1.1.12.1.2.cmml">
<mrow id="p1.1.m1.1.12.1.2.1" xref="p1.1.m1.1.12.1.2.1.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">D</mi>
<mo id="p1.1.m1.1.12.1.2.1.1" xref="p1.1.m1.1.12.1.2.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.12.1.2.1.2b">
<mo id="p1.1.m1.1.12.1.2.1.2">(</mo>
<mrow id="XM1" xref="XM1.cmml">
<mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">ρ</mi>
<mo id="XM1.1" xref="XM1.1.cmml"></mo>
<msub id="XM1.2" xref="XM1.2.cmml">
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">u</mi>
<mi id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">i</mi>
</msub>
</mrow>
<mo id="p1.1.m1.1.12.1.2.1.2a">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">/</mo>
<mi id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">D</mi>
</mrow>
<mo id="p1.1.m1.1.12.1.1" xref="p1.1.m1.1.12.1.1.cmml"></mo>
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">t</mi>
</mrow>
<mo id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">≈</mo>
<mn id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">0</mn>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">
<approx id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10"/>
<apply id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12.1">
<times id="p1.1.m1.1.12.1.1.cmml" xref="p1.1.m1.1.12.1.1"/>
<apply id="p1.1.m1.1.12.1.2.cmml" xref="p1.1.m1.1.12.1.2">
<divide id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
<apply id="p1.1.m1.1.12.1.2.1.cmml" xref="p1.1.m1.1.12.1.2.1">
<times id="p1.1.m1.1.12.1.2.1.1.cmml" xref="p1.1.m1.1.12.1.2.1.1"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">D</ci>
<apply id="XM1.cmml" xref="XM1">
<times id="XM1.1.cmml" xref="XM1.1"/>
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">ρ</ci>
<apply id="XM1.2.cmml" xref="XM1.2">
<csymbol cd="ambiguous" id="XM1.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">u</ci>
<ci id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1">i</ci>
</apply>
</apply>
</apply>
<ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">D</ci>
</apply>
<ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">t</ci>
</apply>
<cn type="integer" id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">0</cn>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle D\left(\rho u_{{i}}\right)/Dt\approx 0}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=79fb88a01a287fa09e78c650802672c1&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.5ex; width: 16.167ex;" alt="D\left(\rho u_{{i}}\right)/Dt\approx 0" data-pagespeed-url-hash="1124465876" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D\left(\rho u_{i}\right)/Dt\approx 0}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>D</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>ρ<!-- ρ --></mi>
<msub>
<mi>u</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
</mrow>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>/</mo>
</mrow>
<mi>D</mi>
<mi>t</mi>
<mo>≈<!-- ≈ --></mo>
<mn>0</mn>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle D\left(\rho u_{i}\right)/Dt\approx 0}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/a81d823426783548554205f769acb0871a2d31fb" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:16.026ex; height:2.843ex;" alt="{\displaystyle D\left(\rho u_{i}\right)/Dt\approx 0}" data-pagespeed-url-hash="2671354675" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/76" title="Special:DisplayTopics/76">76</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/10488#math.10488.25" title="Special:PermanentLink/10488">Unit_root-25</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle z_{{{t}}}=\lambda_{{{1}}}z_{{{t-1}}}+\varepsilon_{{{t}}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">
<msub id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">z</mi>
<mi id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">t</mi>
</msub>
<mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">=</mo>
<mrow id="p1.1.m1.1.11.2" xref="p1.1.m1.1.11.2.cmml">
<mrow id="p1.1.m1.1.11.2.1" xref="p1.1.m1.1.11.2.1.cmml">
<msub id="p1.1.m1.1.11.2.1.2" xref="p1.1.m1.1.11.2.1.2.cmml">
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">λ</mi>
<mn id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">1</mn>
</msub>
<mo id="p1.1.m1.1.11.2.1.1" xref="p1.1.m1.1.11.2.1.1.cmml"></mo>
<msub id="p1.1.m1.1.11.2.1.3" xref="p1.1.m1.1.11.2.1.3.cmml">
<mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">z</mi>
<mrow id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">
<mi id="p1.1.m1.1.7.1.1" xref="p1.1.m1.1.7.1.1.cmml">t</mi>
<mo id="p1.1.m1.1.7.1.2" xref="p1.1.m1.1.7.1.2.cmml">-</mo>
<mn id="p1.1.m1.1.7.1.3" xref="p1.1.m1.1.7.1.3.cmml">1</mn>
</mrow>
</msub>
</mrow>
<mo id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">+</mo>
<msub id="p1.1.m1.1.11.2.2" xref="p1.1.m1.1.11.2.2.cmml">
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">ε</mi>
<mi id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">t</mi>
</msub>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">
<eq id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
<apply id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.11.1.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">z</ci>
<ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">t</ci>
</apply>
<apply id="p1.1.m1.1.11.2.cmml" xref="p1.1.m1.1.11.2">
<plus id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8"/>
<apply id="p1.1.m1.1.11.2.1.cmml" xref="p1.1.m1.1.11.2.1">
<times id="p1.1.m1.1.11.2.1.1.cmml" xref="p1.1.m1.1.11.2.1.1"/>
<apply id="p1.1.m1.1.11.2.1.2.cmml" xref="p1.1.m1.1.11.2.1.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.11.2.1.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">λ</ci>
<cn type="integer" id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1">1</cn>
</apply>
<apply id="p1.1.m1.1.11.2.1.3.cmml" xref="p1.1.m1.1.11.2.1.3">
<csymbol cd="ambiguous" id="p1.1.m1.1.11.2.1.3.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">z</ci>
<apply id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">
<minus id="p1.1.m1.1.7.1.2.cmml" xref="p1.1.m1.1.7.1.2"/>
<ci id="p1.1.m1.1.7.1.1.cmml" xref="p1.1.m1.1.7.1.1">t</ci>
<cn type="integer" id="p1.1.m1.1.7.1.3.cmml" xref="p1.1.m1.1.7.1.3">1</cn>
</apply>
</apply>
</apply>
<apply id="p1.1.m1.1.11.2.2.cmml" xref="p1.1.m1.1.11.2.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.11.2.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">ε</ci>
<ci id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">t</ci>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle z_{{{t}}}=\lambda_{{{1}}}z_{{{t-1}}}+\varepsilon_{{{t}}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=71ec5283852713f4fb9fd60432b2c825&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.5ex; height: 2ex; width: 16.333ex;" alt="z_{{{t}}}=\lambda _{{{1}}}z_{{{t-1}}}+\varepsilon _{{{t}}}" data-pagespeed-url-hash="1505516313" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z_{t}=\lambda _{1}z_{t-1}+\varepsilon _{t}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>z</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>t</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>λ<!-- λ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<msub>
<mi>z</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>t</mi>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>ε<!-- ε --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>t</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle z_{t}=\lambda _{1}z_{t-1}+\varepsilon _{t}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/bbe11304b15997f7a317cece39b9aae473bdd0c1" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:16.173ex; height:2.509ex;" alt="{\displaystyle z_{t}=\lambda _{1}z_{t-1}+\varepsilon _{t}}" data-pagespeed-url-hash="346718789" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/77" title="Special:DisplayTopics/77">77</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/22206#math.22206.83" title="Special:PermanentLink/22206">Drucker–Prager_yield_criterion-83</a>
</td>
<td> 0
</td>
<td> 4
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle b_{3}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=ec3d19dec8eecd49e8ec21bb2b5dea63&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; height: 2.509ex; width: 2.07ex;" alt="{\displaystyle b_{3}}" data-pagespeed-url-hash="379694542" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b_{3}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle b_{3}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/dd1031a09c81052cc099119c78507c89e6ff9b27" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:2.052ex; height:2.509ex;" alt="{\displaystyle b_{3}}" data-pagespeed-url-hash="2098442045" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/78" title="Special:DisplayTopics/78">78</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/23061#math.23061.9" title="Special:PermanentLink/23061">Antiplane_shear-9</a>
</td>
<td> 0
</td>
<td> 4
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle b_{3}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=ec3d19dec8eecd49e8ec21bb2b5dea63&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; height: 2.509ex; width: 2.07ex;" alt="{\displaystyle b_{3}}" data-pagespeed-url-hash="379694542" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b_{3}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle b_{3}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/dd1031a09c81052cc099119c78507c89e6ff9b27" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:2.052ex; height:2.509ex;" alt="{\displaystyle b_{3}}" data-pagespeed-url-hash="2098442045" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/79" title="Special:DisplayTopics/79">79</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/15872#math.15872.32" title="Special:PermanentLink/15872">Table_of_thermodynamic_equations-32</a>
</td>
<td> 2
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\Delta W=\int_{{V_{\qvar@construct{x0}}}}^{{V_{2}}}p{% \qvar@construct{x1}}V\,\!}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">
<mrow id="p1.1.m1.1.12.1" xref="p1.1.m1.1.12.1.cmml">
<mi mathvariant="normal" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">Δ</mi>
<mo id="p1.1.m1.1.12.1.1" xref="p1.1.m1.1.12.1.1.cmml"></mo>
<mi id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">W</mi>
</mrow>
<mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">=</mo>
<mrow id="p1.1.m1.1.12.2" xref="p1.1.m1.1.12.2.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.12.2.1" xref="p1.1.m1.1.12.2.1.cmml">
<msubsup id="p1.1.m1.1.12.2.1a" xref="p1.1.m1.1.12.2.1.cmml">
<mo largeop="true" symmetric="true" id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">∫</mo>
<msub id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">
<mi id="p1.1.m1.1.5.1.1" xref="p1.1.m1.1.5.1.1.cmml">V</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.5.1.2.1" xref="p1.1.m1.1.5.1.2.1.cmml">x0</mi>
</msub>
<msub id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">
<mi id="p1.1.m1.1.6.1.1" xref="p1.1.m1.1.6.1.1.cmml">V</mi>
<mn id="p1.1.m1.1.6.1.2.1" xref="p1.1.m1.1.6.1.2.1.cmml">2</mn>
</msub>
</msubsup>
</mstyle>
<mrow id="p1.1.m1.1.12.2.2" xref="p1.1.m1.1.12.2.2.cmml">
<mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">p</mi>
<mo id="p1.1.m1.1.12.2.2.1" xref="p1.1.m1.1.12.2.2.1.cmml"></mo>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">x1</mi>
<mo id="p1.1.m1.1.12.2.2.1a" xref="p1.1.m1.1.12.2.2.1.cmml"></mo>
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">V</mi>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">
<eq id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
<apply id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12.1">
<times id="p1.1.m1.1.12.1.1.cmml" xref="p1.1.m1.1.12.1.1"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">normal-Δ</ci>
<ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">W</ci>
</apply>
<apply id="p1.1.m1.1.12.2.cmml" xref="p1.1.m1.1.12.2">
<apply id="p1.1.m1.1.12.2.1.cmml" xref="p1.1.m1.1.12.2.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.12.2.1.1.cmml">superscript</csymbol>
<apply id="p1.1.m1.1.12.2.1.2.cmml">
<csymbol cd="ambiguous" id="p1.1.m1.1.12.2.1.2.1.cmml">subscript</csymbol>
<int id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4"/>
<apply id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.5.1.3.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.5.1.1.cmml" xref="p1.1.m1.1.5.1.1">V</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.5.1.2.1.cmml" xref="p1.1.m1.1.5.1.2.1">x0</csymbol>
</apply>
</apply>
<apply id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.6.1.3.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.6.1.1.cmml" xref="p1.1.m1.1.6.1.1">V</ci>
<cn type="integer" id="p1.1.m1.1.6.1.2.1.cmml" xref="p1.1.m1.1.6.1.2.1">2</cn>
</apply>
</apply>
<apply id="p1.1.m1.1.12.2.2.cmml" xref="p1.1.m1.1.12.2.2">
<times id="p1.1.m1.1.12.2.2.1.cmml" xref="p1.1.m1.1.12.2.2.1"/>
<ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">p</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">x1</csymbol>
<ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">V</ci>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\Delta W=\int_{{V_{\qvar@construct{x0}}}}^{{V_{2}}}p{%
\qvar@construct{x1}}V\,\!}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=646df341e8e4c73b55d89cc740fc5831&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.5ex; height: 6.167ex; width: 18.667ex;" alt="\Delta W=\int_{{V_{\qvar{x0}}}}^{{V_{2}}}p{\qvar{x1}}V\,\!" data-pagespeed-url-hash="1937155878" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta W=\int _{V_{1}}^{V_{2}}p\mathrm {d} V\,\!}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">Δ<!-- Δ --></mi>
<mi>W</mi>
<mo>=</mo>
<msubsup>
<mo>∫<!-- ∫ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<msub>
<mi>V</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<msub>
<mi>V</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
</mrow>
</msubsup>
<mi>p</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">d</mi>
</mrow>
<mi>V</mi>
<mspace width="thinmathspace"/>
<mspace width="negativethinmathspace"/>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \Delta W=\int _{V_{1}}^{V_{2}}p\mathrm {d} V\,\!}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/c6059f5b63d6a41e79beda56eae8b32a04ab8fcc" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.671ex; margin-right: -0.387ex; width:16.979ex; height:6.509ex;" alt="{\displaystyle \Delta W=\int _{V_{1}}^{V_{2}}p\mathrm {d} V\,\!}" data-pagespeed-url-hash="2451805766" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/80" title="Special:DisplayTopics/80">80</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/13966#math.13966.2" title="Special:PermanentLink/13966">Fulton–Hansen_connectedness_theorem-2</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\dim f(Z)>n}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">
<mrow id="p1.1.m1.1.8.1" xref="p1.1.m1.1.8.1.cmml">
<mo id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">dim</mo>
<mo id="p1.1.m1.1.8.1a" xref="p1.1.m1.1.8.1.cmml"></mo>
<mrow id="p1.1.m1.1.8.1.1" xref="p1.1.m1.1.8.1.1.cmml">
<mi id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">f</mi>
<mo id="p1.1.m1.1.8.1.1.1" xref="p1.1.m1.1.8.1.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.8.1.1.2b">
<mo stretchy="false" id="p1.1.m1.1.8.1.1.2">(</mo>
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">Z</mi>
<mo stretchy="false" id="p1.1.m1.1.8.1.1.2a">)</mo>
</mrow>
</mrow>
</mrow>
<mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">></mo>
<mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">n</mi>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">
<gt id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
<apply id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.1">
<csymbol cd="latexml" id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">dimension</csymbol>
<apply id="p1.1.m1.1.8.1.1.cmml" xref="p1.1.m1.1.8.1.1">
<times id="p1.1.m1.1.8.1.1.1.cmml" xref="p1.1.m1.1.8.1.1.1"/>
<ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">f</ci>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">Z</ci>
</apply>
</apply>
<ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">n</ci>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\dim f(Z)>n}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=386bfc2694f8e2e58cea8aa6936819d7&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.5ex; width: 14ex;" alt="\dim f(Z)>n" data-pagespeed-url-hash="4222153621" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \dim f(Z)>n}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>dim</mi>
<mo>⁡<!-- --></mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>Z</mi>
<mo stretchy="false">)</mo>
<mo>></mo>
<mi>n</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \dim f(Z)>n}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/c15a4a7ce64bc4b394400d90f99f08c1401c9eef" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:13.524ex; height:2.843ex;" alt="{\displaystyle \dim f(Z)>n}" data-pagespeed-url-hash="3044957748" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/81" title="Special:DisplayTopics/81">81</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/335#math.335.16" title="Special:PermanentLink/335">E_(mathematical_constant)-16</a>
</td>
<td> 2
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\frac{d}{dt}}\log_{e}t={\frac{\qvar@construct{x0}}{% \qvar@construct{x1}}}.}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">
<mrow id="p1.1.m1.1.8a" xref="p1.1.m1.1.8.cmml">
<mrow id="p1.1.m1.1.8.1" xref="p1.1.m1.1.8.1.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">
<mfrac id="p1.1.m1.1.1a" xref="p1.1.m1.1.1.cmml">
<mi id="p1.1.m1.1.1.2" xref="p1.1.m1.1.1.2.cmml">d</mi>
<mrow id="p1.1.m1.1.1.3" xref="p1.1.m1.1.1.3.cmml">
<mi id="p1.1.m1.1.1.3.1" xref="p1.1.m1.1.1.3.1.cmml">d</mi>
<mo id="p1.1.m1.1.1.3.3" xref="p1.1.m1.1.1.3.3.cmml"></mo>
<mi id="p1.1.m1.1.1.3.2" xref="p1.1.m1.1.1.3.2.cmml">t</mi>
</mrow>
</mfrac>
</mstyle>
<mo id="p1.1.m1.1.8.1.1" xref="p1.1.m1.1.8.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.8.1.2" xref="p1.1.m1.1.8.1.2.cmml">
<msub id="p1.1.m1.1.8.1.2.1" xref="p1.1.m1.1.8.1.2.1.cmml">
<mi id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">log</mi>
<mi id="p1.1.m1.1.3.1" xref="p1.1.m1.1.3.1.cmml">e</mi>
</msub>
<mo id="p1.1.m1.1.8.1.2a" xref="p1.1.m1.1.8.1.2.cmml"></mo>
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">t</mi>
</mrow>
</mrow>
<mo id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">=</mo>
<mstyle displaystyle="true" id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
<mfrac id="p1.1.m1.1.6a" xref="p1.1.m1.1.6.cmml">
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.6.2" xref="p1.1.m1.1.6.2.cmml">x0</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.6.3" xref="p1.1.m1.1.6.3.cmml">x1</mi>
</mfrac>
</mstyle>
</mrow>
<mo id="p1.1.m1.1.8b" xref="p1.1.m1.1.8.cmml">.</mo>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">
<eq id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/>
<apply id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.1">
<times id="p1.1.m1.1.8.1.1.cmml" xref="p1.1.m1.1.8.1.1"/>
<apply id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">
<divide id="p1.1.m1.1.1.1.cmml"/>
<ci id="p1.1.m1.1.1.2.cmml" xref="p1.1.m1.1.1.2">d</ci>
<apply id="p1.1.m1.1.1.3.cmml" xref="p1.1.m1.1.1.3">
<times id="p1.1.m1.1.1.3.3.cmml" xref="p1.1.m1.1.1.3.3"/>
<ci id="p1.1.m1.1.1.3.1.cmml" xref="p1.1.m1.1.1.3.1">d</ci>
<ci id="p1.1.m1.1.1.3.2.cmml" xref="p1.1.m1.1.1.3.2">t</ci>
</apply>
</apply>
<apply id="p1.1.m1.1.8.1.2.cmml" xref="p1.1.m1.1.8.1.2">
<apply id="p1.1.m1.1.8.1.2.1.cmml" xref="p1.1.m1.1.8.1.2.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.8.1.2.1.1.cmml">subscript</csymbol>
<log id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
<ci id="p1.1.m1.1.3.1.cmml" xref="p1.1.m1.1.3.1">e</ci>
</apply>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">t</ci>
</apply>
</apply>
<apply id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">
<divide id="p1.1.m1.1.6.1.cmml"/>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.6.2.cmml" xref="p1.1.m1.1.6.2">x0</csymbol>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.6.3.cmml" xref="p1.1.m1.1.6.3">x1</csymbol>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\frac{d}{dt}}\log_{e}t={\frac{\qvar@construct{x0}}{%
\qvar@construct{x1}}}.}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=f7c7fdde81db0b208bd57310dc728e96&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.833ex; height: 5ex; width: 16.5ex;" alt="{\frac{d}{dt}}\log_{e}t={\frac{\qvar{x0}}{\qvar{x1}}}." data-pagespeed-url-hash="3107208296" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {d}{dt}}\log _{e}t={\frac {1}{t}}.}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>d</mi>
<mrow>
<mi>d</mi>
<mi>t</mi>
</mrow>
</mfrac>
</mrow>
<msub>
<mi>log</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>e</mi>
</mrow>
</msub>
<mo>⁡<!-- --></mo>
<mi>t</mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mn>1</mn>
<mi>t</mi>
</mfrac>
</mrow>
<mo>.</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\frac {d}{dt}}\log _{e}t={\frac {1}{t}}.}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/30b471c130e941cf7453d06feca4fea662aa4652" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.005ex; width:14.219ex; height:5.509ex;" alt="{\displaystyle {\frac {d}{dt}}\log _{e}t={\frac {1}{t}}.}" data-pagespeed-url-hash="3214477104" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/82" title="Special:DisplayTopics/82">82</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/17232#math.17232.32" title="Special:PermanentLink/17232">BrownBoost-32</a>
</td>
<td> 1
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle h_{i}:X\to\{\qvar@construct{x0}\}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">
<msub id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">h</mi>
<mi id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">i</mi>
</msub>
<mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">:</mo>
<mrow id="p1.1.m1.1.9.2" xref="p1.1.m1.1.9.2.cmml">
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">X</mi>
<mo id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">→</mo>
<mrow id="p1.1.m1.1.9.2.1b" xref="p1.1.m1.1.9.2.1.cmml">
<mo stretchy="false" id="p1.1.m1.1.9.2.1" xref="p1.1.m1.1.9.2.1.cmml">{</mo>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">x0</mi>
<mo stretchy="false" id="p1.1.m1.1.9.2.1a" xref="p1.1.m1.1.9.2.1.cmml">}</mo>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">normal-:</ci>
<apply id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.9.1.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">h</ci>
<ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">i</ci>
</apply>
<apply id="p1.1.m1.1.9.2.cmml" xref="p1.1.m1.1.9.2">
<ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">normal-→</ci>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">X</ci>
<set id="p1.1.m1.1.9.2.1.cmml" xref="p1.1.m1.1.9.2.1">
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">x0</csymbol>
</set>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle h_{i}:X\to\{\qvar@construct{x0}\}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=89f93b413f4cc3036ca10c411005e740&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.5ex; width: 14.667ex;" alt="h_{i}:X\to\{\qvar{x0}\}" data-pagespeed-url-hash="97706793" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h_{i}:X\to \{-1,+1\}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>h</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
</mrow>
</msub>
<mo>:</mo>
<mi>X</mi>
<mo stretchy="false">→<!-- → --></mo>
<mo fence="false" stretchy="false">{</mo>
<mo>−<!-- − --></mo>
<mn>1</mn>
<mo>,</mo>
<mo>+</mo>
<mn>1</mn>
<mo fence="false" stretchy="false">}</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle h_{i}:X\to \{-1,+1\}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/94f4afefcf0ae550383fb18bf4d5289514f42890" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:18.97ex; height:2.843ex;" alt="{\displaystyle h_{i}:X\to \{-1,+1\}}" data-pagespeed-url-hash="3717966887" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/83" title="Special:DisplayTopics/83">83</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/21545#math.21545.2" title="Special:PermanentLink/21545">List_of_RNA_structure_prediction_software-2</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle 2\leq seqs\leq 6}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">
<mn id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">2</mn>
<mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">≤</mo>
<mrow id="p1.1.m1.1.9.2" xref="p1.1.m1.1.9.2.cmml">
<mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">s</mi>
<mo id="p1.1.m1.1.9.2.1" xref="p1.1.m1.1.9.2.1.cmml"></mo>
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">e</mi>
<mo id="p1.1.m1.1.9.2.1a" xref="p1.1.m1.1.9.2.1.cmml"></mo>
<mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">q</mi>
<mo id="p1.1.m1.1.9.2.1b" xref="p1.1.m1.1.9.2.1.cmml"></mo>
<mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">s</mi>
</mrow>
<mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">≤</mo>
<mn id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">6</mn>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">
<and id="p1.1.m1.1.9a.cmml" xref="p1.1.m1.1.9"/>
<apply id="p1.1.m1.1.9b.cmml" xref="p1.1.m1.1.9">
<leq id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
<cn type="integer" id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">2</cn>
<apply id="p1.1.m1.1.9.2.cmml" xref="p1.1.m1.1.9.2">
<times id="p1.1.m1.1.9.2.1.cmml" xref="p1.1.m1.1.9.2.1"/>
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">s</ci>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">e</ci>
<ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">q</ci>
<ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">s</ci>
</apply>
</apply>
<apply id="p1.1.m1.1.9c.cmml" xref="p1.1.m1.1.9">
<leq id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
<share href="#p1.1.m1.1.9.2.cmml" id="p1.1.m1.1.9d.cmml" xref="p1.1.m1.1.9"/>
<cn type="integer" id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">6</cn>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle 2\leq seqs\leq 6}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=ead4fdf2870967051660a108a512df24&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.5ex; height: 2.167ex; width: 13ex;" alt="2\leq seqs\leq 6" data-pagespeed-url-hash="3290708389" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2\leq seqs\leq 6}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mn>2</mn>
<mo>≤<!-- ≤ --></mo>
<mi>s</mi>
<mi>e</mi>
<mi>q</mi>
<mi>s</mi>
<mo>≤<!-- ≤ --></mo>
<mn>6</mn>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle 2\leq seqs\leq 6}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/58a2363e45f91a9603b3fe5b18382cd524f9426b" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:12.856ex; height:2.509ex;" alt="{\displaystyle 2\leq seqs\leq 6}" data-pagespeed-url-hash="272470616" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/84" title="Special:DisplayTopics/84">84</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/28184#math.28184.6" title="Special:PermanentLink/28184">Projections_onto_convex_sets-6</a>
</td>
<td> 1
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle F=\{\qvar@construct{x0}\}.}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">
<mrow id="p1.1.m1.1.7a" xref="p1.1.m1.1.7.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">F</mi>
<mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">=</mo>
<mrow id="p1.1.m1.1.7.1b" xref="p1.1.m1.1.7.1.cmml">
<mo stretchy="false" id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">{</mo>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">x0</mi>
<mo stretchy="false" id="p1.1.m1.1.7.1a" xref="p1.1.m1.1.7.1.cmml">}</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.7b" xref="p1.1.m1.1.7.cmml">.</mo>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">
<eq id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">F</ci>
<set id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">x0</csymbol>
</set>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle F=\{\qvar@construct{x0}\}.}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=82c402af3a339570be3d568d531972f8&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.5ex; width: 10.833ex;" alt="F=\{\qvar{x0}\}." data-pagespeed-url-hash="952731684" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F=\{(x,y):x\in {\mathcal {R}}^{b},\,y\in {\mathcal {R}}^{n},\;x=y\}.}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>F</mi>
<mo>=</mo>
<mo fence="false" stretchy="false">{</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo stretchy="false">)</mo>
<mo>:</mo>
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<msup>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi class="MJX-tex-caligraphic" mathvariant="script">R</mi>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi>b</mi>
</mrow>
</msup>
<mo>,</mo>
<mspace width="thinmathspace"/>
<mi>y</mi>
<mo>∈<!-- ∈ --></mo>
<msup>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi class="MJX-tex-caligraphic" mathvariant="script">R</mi>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi>n</mi>
</mrow>
</msup>
<mo>,</mo>
<mspace width="thickmathspace"/>
<mi>x</mi>
<mo>=</mo>
<mi>y</mi>
<mo fence="false" stretchy="false">}</mo>
<mo>.</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle F=\{(x,y):x\in {\mathcal {R}}^{b},\,y\in {\mathcal {R}}^{n},\;x=y\}.}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/cf8ef09fac3b77aebd2a7f9e70c7fa80880141ec" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:38.024ex; height:3.176ex;" alt="{\displaystyle F=\{(x,y):x\in {\mathcal {R}}^{b},\,y\in {\mathcal {R}}^{n},\;x=y\}.}" data-pagespeed-url-hash="1971530269" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/85" title="Special:DisplayTopics/85">85</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/4212#math.4212.21" title="Special:PermanentLink/4212">Almost_surely-21</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle X_{{i}}(\omega)=\omega_{{i}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">
<mrow id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">
<msub id="p1.1.m1.1.9.1.2" xref="p1.1.m1.1.9.1.2.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">X</mi>
<mi id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">i</mi>
</msub>
<mo id="p1.1.m1.1.9.1.1" xref="p1.1.m1.1.9.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.9.1.3b">
<mo stretchy="false" id="p1.1.m1.1.9.1.3">(</mo>
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">ω</mi>
<mo stretchy="false" id="p1.1.m1.1.9.1.3a">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">=</mo>
<msub id="p1.1.m1.1.9.2" xref="p1.1.m1.1.9.2.cmml">
<mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">ω</mi>
<mi id="p1.1.m1.1.8.1" xref="p1.1.m1.1.8.1.cmml">i</mi>
</msub>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">
<eq id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
<apply id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">
<times id="p1.1.m1.1.9.1.1.cmml" xref="p1.1.m1.1.9.1.1"/>
<apply id="p1.1.m1.1.9.1.2.cmml" xref="p1.1.m1.1.9.1.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.9.1.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">X</ci>
<ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">i</ci>
</apply>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">ω</ci>
</apply>
<apply id="p1.1.m1.1.9.2.cmml" xref="p1.1.m1.1.9.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.9.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">ω</ci>
<ci id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.1">i</ci>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle X_{{i}}(\omega)=\omega_{{i}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=6ac987e6f52a362cbe9410c9c873c704&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.5ex; width: 11.833ex;" alt="X_{{i}}(\omega )=\omega _{{i}}" data-pagespeed-url-hash="1809308502" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{i}(\omega )=\omega _{i}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>X</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
</mrow>
</msub>
<mo stretchy="false">(</mo>
<mi>ω<!-- ω --></mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<msub>
<mi>ω<!-- ω --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle X_{i}(\omega )=\omega _{i}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/a3c8bbc4425a8cd3c9268847c8ba596076bcd85e" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:11.323ex; height:2.843ex;" alt="{\displaystyle X_{i}(\omega )=\omega _{i}}" data-pagespeed-url-hash="2078589872" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/86" title="Special:DisplayTopics/86">86</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/24328#math.24328.67" title="Special:PermanentLink/24328">Lagrangian_mechanics-67</a>
</td>
<td> 3
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\partial{L}\over\partial q_{i}}={\qvar@construct{x0}}{\partial{% \qvar@construct{x1}}\over\partial{{\qvar@construct{x2}}}}.}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
<mrow id="p1.1.m1.1.6a" xref="p1.1.m1.1.6.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">
<mfrac id="p1.1.m1.1.1a" xref="p1.1.m1.1.1.cmml">
<mrow id="p1.1.m1.1.1.2" xref="p1.1.m1.1.1.2.cmml">
<mo id="p1.1.m1.1.1.2.1" xref="p1.1.m1.1.1.2.1.cmml">∂</mo>
<mo id="p1.1.m1.1.1.2a" xref="p1.1.m1.1.1.2.cmml"></mo>
<mi id="p1.1.m1.1.1.2.2" xref="p1.1.m1.1.1.2.2.cmml">L</mi>
</mrow>
<mrow id="p1.1.m1.1.1.3" xref="p1.1.m1.1.1.3.cmml">
<mo id="p1.1.m1.1.1.3.1" xref="p1.1.m1.1.1.3.1.cmml">∂</mo>
<mo id="p1.1.m1.1.1.3a" xref="p1.1.m1.1.1.3.cmml"></mo>
<msub id="p1.1.m1.1.1.3.4" xref="p1.1.m1.1.1.3.4.cmml">
<mi id="p1.1.m1.1.1.3.2" xref="p1.1.m1.1.1.3.2.cmml">q</mi>
<mi id="p1.1.m1.1.1.3.3.1" xref="p1.1.m1.1.1.3.3.1.cmml">i</mi>
</msub>
</mrow>
</mfrac>
</mstyle>
<mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">=</mo>
<mrow id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">x0</mi>
<mo id="p1.1.m1.1.6.1.1" xref="p1.1.m1.1.6.1.1.cmml"></mo>
<mstyle displaystyle="true" id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">
<mfrac id="p1.1.m1.1.4a" xref="p1.1.m1.1.4.cmml">
<mrow id="p1.1.m1.1.4.2" xref="p1.1.m1.1.4.2.cmml">
<mo id="p1.1.m1.1.4.2.1" xref="p1.1.m1.1.4.2.1.cmml">∂</mo>
<mo id="p1.1.m1.1.4.2a" xref="p1.1.m1.1.4.2.cmml"></mo>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.4.2.2" xref="p1.1.m1.1.4.2.2.cmml">x1</mi>
</mrow>
<mrow id="p1.1.m1.1.4.3" xref="p1.1.m1.1.4.3.cmml">
<mo id="p1.1.m1.1.4.3.1" xref="p1.1.m1.1.4.3.1.cmml">∂</mo>
<mo id="p1.1.m1.1.4.3a" xref="p1.1.m1.1.4.3.cmml"></mo>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.4.3.2" xref="p1.1.m1.1.4.3.2.cmml">x2</mi>
</mrow>
</mfrac>
</mstyle>
</mrow>
</mrow>
<mo id="p1.1.m1.1.6b" xref="p1.1.m1.1.6.cmml">.</mo>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">
<eq id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
<apply id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">
<divide id="p1.1.m1.1.1.1.cmml"/>
<apply id="p1.1.m1.1.1.2.cmml" xref="p1.1.m1.1.1.2">
<partialdiff id="p1.1.m1.1.1.2.1.cmml" xref="p1.1.m1.1.1.2.1"/>
<ci id="p1.1.m1.1.1.2.2.cmml" xref="p1.1.m1.1.1.2.2">L</ci>
</apply>
<apply id="p1.1.m1.1.1.3.cmml" xref="p1.1.m1.1.1.3">
<partialdiff id="p1.1.m1.1.1.3.1.cmml" xref="p1.1.m1.1.1.3.1"/>
<apply id="p1.1.m1.1.1.3.4.cmml" xref="p1.1.m1.1.1.3.4">
<csymbol cd="ambiguous" id="p1.1.m1.1.1.3.4.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.3.2.cmml" xref="p1.1.m1.1.1.3.2">q</ci>
<ci id="p1.1.m1.1.1.3.3.1.cmml" xref="p1.1.m1.1.1.3.3.1">i</ci>
</apply>
</apply>
</apply>
<apply id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1">
<times id="p1.1.m1.1.6.1.1.cmml" xref="p1.1.m1.1.6.1.1"/>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">x0</csymbol>
<apply id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">
<divide id="p1.1.m1.1.4.1.cmml"/>
<apply id="p1.1.m1.1.4.2.cmml" xref="p1.1.m1.1.4.2">
<partialdiff id="p1.1.m1.1.4.2.1.cmml" xref="p1.1.m1.1.4.2.1"/>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.4.2.2.cmml" xref="p1.1.m1.1.4.2.2">x1</csymbol>
</apply>
<apply id="p1.1.m1.1.4.3.cmml" xref="p1.1.m1.1.4.3">
<partialdiff id="p1.1.m1.1.4.3.1.cmml" xref="p1.1.m1.1.4.3.1"/>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.4.3.2.cmml" xref="p1.1.m1.1.4.3.2">x2</csymbol>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\partial{L}\over\partial q_{i}}={\qvar@construct{x0}}{\partial{%
\qvar@construct{x1}}\over\partial{{\qvar@construct{x2}}}}.}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=dcd8ae836b7f802a7f2b9522ca47a808&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.333ex; height: 5.5ex; width: 16.833ex;" alt="{\partial{L}\over\partial q_{i}}={\qvar{x0}}{\partial{\qvar{x1}}\over\partial{{\qvar{x2}}}}." data-pagespeed-url-hash="2545564034" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\partial {L} \over \partial q_{i}}={\mathrm {d} \over \mathrm {d} t}{\partial {L} \over \partial {\dot {q_{i}}}}.}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>L</mi>
</mrow>
</mrow>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<msub>
<mi>q</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
</mrow>
</msub>
</mrow>
</mfrac>
</mrow>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">d</mi>
</mrow>
<mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">d</mi>
</mrow>
<mi>t</mi>
</mrow>
</mfrac>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>L</mi>
</mrow>
</mrow>
<mrow>
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<msub>
<mi>q</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
</mrow>
</msub>
<mo>˙<!-- ˙ --></mo>
</mover>
</mrow>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>.</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\partial {L} \over \partial q_{i}}={\mathrm {d} \over \mathrm {d} t}{\partial {L} \over \partial {\dot {q_{i}}}}.}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/a8cfac601a8a9227afdd3315f707d40c08c4a370" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.338ex; width:14.695ex; height:5.843ex;" alt="{\displaystyle {\partial {L} \over \partial q_{i}}={\mathrm {d} \over \mathrm {d} t}{\partial {L} \over \partial {\dot {q_{i}}}}.}" data-pagespeed-url-hash="1304001294" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/87" title="Special:DisplayTopics/87">87</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/24263#math.24263.100" title="Special:PermanentLink/24263">Near_sets-100</a>
</td>
<td> 1
</td>
<td> 2
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle x_{\qvar@construct{x0}}}">
<semantics id="p1.1.m1.1a">
<msub id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">x</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">x0</mi>
</msub>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
<csymbol cd="ambiguous" id="p1.1.m1.1.3.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">x</ci>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">x0</csymbol>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle x_{\qvar@construct{x0}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=f9a66711a63141b76990dbf2b0cb30a2&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.5ex; height: 1.5ex; width: 3.333ex;" alt="x_{\qvar{x0}}" data-pagespeed-url-hash="1759804012" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{7}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>7</mn>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle x_{7}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/954c46116945ae4026c359eec235f65b6c408df8" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:2.384ex; height:2.009ex;" alt="{\displaystyle x_{7}}" data-pagespeed-url-hash="1734109823" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/88" title="Special:DisplayTopics/88">88</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/2926#math.2926.30" title="Special:PermanentLink/2926">Polynomial_interpolation-30</a>
</td>
<td> 0
</td>
<td> 6
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\Pi_{{n}}}">
<semantics id="p1.1.m1.1a">
<msub id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
<mi mathvariant="normal" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">Π</mi>
<mi id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">n</mi>
</msub>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
<csymbol cd="ambiguous" id="p1.1.m1.1.3.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">normal-Π</ci>
<ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">n</ci>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\Pi_{{n}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=84d1564838474b2bdd6b9529caee006a&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.5ex; height: 2ex; width: 3ex;" alt="\Pi _{{n}}" data-pagespeed-url-hash="2820909805" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Pi _{n}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi mathvariant="normal">Π<!-- Π --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>n</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \Pi _{n}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/09f95d02eefa1f08f4a994ebf0d60aad2c122dd9" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:2.962ex; height:2.509ex;" alt="{\displaystyle \Pi _{n}}" data-pagespeed-url-hash="3272569889" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/89" title="Special:DisplayTopics/89">89</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/26177#math.26177.10" title="Special:PermanentLink/26177">Mutual_fund_separation_theorem-10</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\sigma^{{2}}=X^{{T}}VX,}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">
<mrow id="p1.1.m1.1.9a" xref="p1.1.m1.1.9.cmml">
<msup id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">σ</mi>
<mn id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">2</mn>
</msup>
<mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">=</mo>
<mrow id="p1.1.m1.1.9.2" xref="p1.1.m1.1.9.2.cmml">
<msup id="p1.1.m1.1.9.2.2" xref="p1.1.m1.1.9.2.2.cmml">
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">X</mi>
<mi id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">T</mi>
</msup>
<mo id="p1.1.m1.1.9.2.1" xref="p1.1.m1.1.9.2.1.cmml"></mo>
<mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">V</mi>
<mo id="p1.1.m1.1.9.2.1a" xref="p1.1.m1.1.9.2.1.cmml"></mo>
<mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">X</mi>
</mrow>
</mrow>
<mo id="p1.1.m1.1.9b" xref="p1.1.m1.1.9.cmml">,</mo>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">
<eq id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
<apply id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.9.1.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">σ</ci>
<cn type="integer" id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">2</cn>
</apply>
<apply id="p1.1.m1.1.9.2.cmml" xref="p1.1.m1.1.9.2">
<times id="p1.1.m1.1.9.2.1.cmml" xref="p1.1.m1.1.9.2.1"/>
<apply id="p1.1.m1.1.9.2.2.cmml" xref="p1.1.m1.1.9.2.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.9.2.2.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">X</ci>
<ci id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1">T</ci>
</apply>
<ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">V</ci>
<ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">X</ci>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\sigma^{{2}}=X^{{T}}VX,}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=b80f38b8c7d5dbc3aa87cdc29e4a5862&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.5ex; height: 2.5ex; width: 13.333ex;" alt="\sigma ^{{2}}=X^{{T}}VX," data-pagespeed-url-hash="3280610040" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma ^{2}=X^{T}VX,}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msup>
<mi>σ<!-- σ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>=</mo>
<msup>
<mi>X</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>T</mi>
</mrow>
</msup>
<mi>V</mi>
<mi>X</mi>
<mo>,</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \sigma ^{2}=X^{T}VX,}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/ab385eabc7a90426449ad69a22c1d5cf9e197a9f" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:13.283ex; height:3.009ex;" alt="{\displaystyle \sigma ^{2}=X^{T}VX,}" data-pagespeed-url-hash="1440838095" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/90" title="Special:DisplayTopics/90">90</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/22382#math.22382.3" title="Special:PermanentLink/22382">Coarea_formula-3</a>
</td>
<td> 1
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\int_{{{\mathbb{R}}^{n}}}f\,dx=\int_{0}^{\infty}\left\{\int_{% \qvar@construct{x0}}f\,dS\right\}\,dr.}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">
<mrow id="p1.1.m1.1.23a" xref="p1.1.m1.1.23.cmml">
<mrow id="p1.1.m1.1.23.1" xref="p1.1.m1.1.23.1.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.23.1.1" xref="p1.1.m1.1.23.1.1.cmml">
<msub id="p1.1.m1.1.23.1.1a" xref="p1.1.m1.1.23.1.1.cmml">
<mo largeop="true" symmetric="true" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">∫</mo>
<msup id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">
<mi id="p1.1.m1.1.2.1.1" xref="p1.1.m1.1.2.1.1.cmml">ℝ</mi>
<mi id="p1.1.m1.1.2.1.2.1" xref="p1.1.m1.1.2.1.2.1.cmml">n</mi>
</msup>
</msub>
</mstyle>
<mrow id="p1.1.m1.1.23.1.2" xref="p1.1.m1.1.23.1.2.cmml">
<mpadded width="+1.7pt" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
<mi id="p1.1.m1.1.3a" xref="p1.1.m1.1.3.cmml">f</mi>
</mpadded>
<mo id="p1.1.m1.1.23.1.2.1" xref="p1.1.m1.1.23.1.2.1.cmml"></mo>
<mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">d</mi>
<mo id="p1.1.m1.1.23.1.2.1a" xref="p1.1.m1.1.23.1.2.1.cmml"></mo>
<mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">x</mi>
</mrow>
</mrow>
<mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">=</mo>
<mrow id="p1.1.m1.1.23.2" xref="p1.1.m1.1.23.2.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.23.2.1" xref="p1.1.m1.1.23.2.1.cmml">
<msubsup id="p1.1.m1.1.23.2.1a" xref="p1.1.m1.1.23.2.1.cmml">
<mo largeop="true" symmetric="true" id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">∫</mo>
<mn id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">0</mn>
<mi mathvariant="normal" id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">∞</mi>
</msubsup>
</mstyle>
<mrow id="p1.1.m1.1.23.2.2" xref="p1.1.m1.1.23.2.2.cmml">
<mrow id="p1.1.m1.1.23.2.2.2b" xref="p1.1.m1.1.23.2.2.2.cmml">
<mo id="p1.1.m1.1.23.2.2.2" xref="p1.1.m1.1.23.2.2.2.cmml">{</mo>
<mrow id="XM1" xref="XM1.cmml">
<mstyle displaystyle="true" id="XM1.1" xref="XM1.1.cmml">
<msub id="XM1.1a" xref="XM1.1.cmml">
<mo largeop="true" symmetric="true" id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">∫</mo>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.13.1" xref="p1.1.m1.1.13.1.cmml">x0</mi>
</msub>
</mstyle>
<mrow id="XM1.2" xref="XM1.2.cmml">
<mpadded width="+1.7pt" id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">
<mi id="p1.1.m1.1.14a" xref="p1.1.m1.1.14.cmml">f</mi>
</mpadded>
<mo id="XM1.2.1" xref="XM1.2.1.cmml"></mo>
<mi id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">d</mi>
<mo id="XM1.2.1a" xref="XM1.2.1.cmml"></mo>
<mi id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">S</mi>
</mrow>
</mrow>
<mo rspace="4.2pt" id="p1.1.m1.1.23.2.2.2a" xref="p1.1.m1.1.23.2.2.2.cmml">}</mo>
</mrow>
<mo id="p1.1.m1.1.23.2.2.1" xref="p1.1.m1.1.23.2.2.1.cmml"></mo>
<mi id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">d</mi>
<mo id="p1.1.m1.1.23.2.2.1a" xref="p1.1.m1.1.23.2.2.1.cmml"></mo>
<mi id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">r</mi>
</mrow>
</mrow>
</mrow>
<mo id="p1.1.m1.1.23b" xref="p1.1.m1.1.23.cmml">.</mo>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">
<eq id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
<apply id="p1.1.m1.1.23.1.cmml" xref="p1.1.m1.1.23.1">
<apply id="p1.1.m1.1.23.1.1.cmml" xref="p1.1.m1.1.23.1.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.23.1.1.1.cmml">subscript</csymbol>
<int id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1"/>
<apply id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.2.1.3.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.2.1.1.cmml" xref="p1.1.m1.1.2.1.1">ℝ</ci>
<ci id="p1.1.m1.1.2.1.2.1.cmml" xref="p1.1.m1.1.2.1.2.1">n</ci>
</apply>
</apply>
<apply id="p1.1.m1.1.23.1.2.cmml" xref="p1.1.m1.1.23.1.2">
<times id="p1.1.m1.1.23.1.2.1.cmml" xref="p1.1.m1.1.23.1.2.1"/>
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">f</ci>
<ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">d</ci>
<ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">x</ci>
</apply>
</apply>
<apply id="p1.1.m1.1.23.2.cmml" xref="p1.1.m1.1.23.2">
<apply id="p1.1.m1.1.23.2.1.cmml" xref="p1.1.m1.1.23.2.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.23.2.1.1.cmml">superscript</csymbol>
<apply id="p1.1.m1.1.23.2.1.2.cmml">
<csymbol cd="ambiguous" id="p1.1.m1.1.23.2.1.2.1.cmml">subscript</csymbol>
<int id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8"/>
<cn type="integer" id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">0</cn>
</apply>
<infinity id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1"/>
</apply>
<apply id="p1.1.m1.1.23.2.2.cmml" xref="p1.1.m1.1.23.2.2">
<times id="p1.1.m1.1.23.2.2.1.cmml" xref="p1.1.m1.1.23.2.2.1"/>
<set id="p1.1.m1.1.23.2.2.2.cmml" xref="p1.1.m1.1.23.2.2.2">
<apply id="XM1.cmml" xref="XM1">
<apply id="XM1.1.cmml" xref="XM1.1">
<csymbol cd="ambiguous" id="XM1.1.1.cmml">subscript</csymbol>
<int id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12"/>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.13.1.cmml" xref="p1.1.m1.1.13.1">x0</csymbol>
</apply>
<apply id="XM1.2.cmml" xref="XM1.2">
<times id="XM1.2.1.cmml" xref="XM1.2.1"/>
<ci id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">f</ci>
<ci id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">d</ci>
<ci id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">S</ci>
</apply>
</apply>
</set>
<ci id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">d</ci>
<ci id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">r</ci>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\int_{{{\mathbb{R}}^{n}}}f\,dx=\int_{0}^{\infty}\left\{\int_{%
\qvar@construct{x0}}f\,dS\right\}\,dr.}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=76513e964132136a2ad3f63ff3fe363b&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.333ex; height: 5.667ex; width: 32.167ex;" alt="\int_{{{\mathbb{R}}^{n}}}f\,dx=\int_{0}^{\infty}\left\{\int_{\qvar{x0}}f\,dS\right\}\,dr." data-pagespeed-url-hash="2624574415" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int _{\mathbb {R} ^{n}}f\,dx=\int _{0}^{\infty }\left\{\int _{\partial B(x_{0};r)}f\,dS\right\}\,dr.}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mo>∫<!-- ∫ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<msup>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="double-struck">R</mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi>n</mi>
</mrow>
</msup>
</mrow>
</msub>
<mi>f</mi>
<mspace width="thinmathspace"/>
<mi>d</mi>
<mi>x</mi>
<mo>=</mo>
<msubsup>
<mo>∫<!-- ∫ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mn>0</mn>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">∞<!-- ∞ --></mi>
</mrow>
</msubsup>
<mrow>
<mo>{</mo>
<mrow>
<msub>
<mo>∫<!-- ∫ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">∂<!-- ∂ --></mi>
<mi>B</mi>
<mo stretchy="false">(</mo>
<msub>
<mi>x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>0</mn>
</mrow>
</msub>
<mo>;</mo>
<mi>r</mi>
<mo stretchy="false">)</mo>
</mrow>
</msub>
<mi>f</mi>
<mspace width="thinmathspace"/>
<mi>d</mi>
<mi>S</mi>
</mrow>
<mo>}</mo>
</mrow>
<mspace width="thinmathspace"/>
<mi>d</mi>
<mi>r</mi>
<mo>.</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \int _{\mathbb {R} ^{n}}f\,dx=\int _{0}^{\infty }\left\{\int _{\partial B(x_{0};r)}f\,dS\right\}\,dr.}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/c295e95049870e8ec707617ee17fbb87cd2ae6a0" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.671ex; width:35.994ex; height:6.343ex;" alt="{\displaystyle \int _{\mathbb {R} ^{n}}f\,dx=\int _{0}^{\infty }\left\{\int _{\partial B(x_{0};r)}f\,dS\right\}\,dr.}" data-pagespeed-url-hash="651520639" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/91" title="Special:DisplayTopics/91">91</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/18056#math.18056.74" title="Special:PermanentLink/18056">Dirac_bracket-74</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\{x,p_{{x}}\}_{{{DB}}}=\{y,p_{{y}}\}_{{{DB}}}={{\frac{1}{2}}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">
<msub id="p1.1.m1.1.18.2" xref="p1.1.m1.1.18.2.cmml">
<mrow id="p1.1.m1.1.18.2.2c" xref="p1.1.m1.1.18.2.2.cmml">
<mo stretchy="false" id="p1.1.m1.1.18.2.2" xref="p1.1.m1.1.18.2.2.cmml">{</mo>
<mi id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">x</mi>
<mo id="p1.1.m1.1.18.2.2a" xref="p1.1.m1.1.18.2.2.cmml">,</mo>
<msub id="XM2" xref="XM2.cmml">
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">p</mi>
<mi id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">x</mi>
</msub>
<mo stretchy="false" id="p1.1.m1.1.18.2.2b" xref="p1.1.m1.1.18.2.2.cmml">}</mo>
</mrow>
<mrow id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">
<mi id="p1.1.m1.1.7.1.1" xref="p1.1.m1.1.7.1.1.cmml">D</mi>
<mo id="p1.1.m1.1.7.1.3" xref="p1.1.m1.1.7.1.3.cmml"></mo>
<mi id="p1.1.m1.1.7.1.2" xref="p1.1.m1.1.7.1.2.cmml">B</mi>
</mrow>
</msub>
<mo id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">=</mo>
<msub id="p1.1.m1.1.18.3" xref="p1.1.m1.1.18.3.cmml">
<mrow id="p1.1.m1.1.18.3.2c" xref="p1.1.m1.1.18.3.2.cmml">
<mo stretchy="false" id="p1.1.m1.1.18.3.2" xref="p1.1.m1.1.18.3.2.cmml">{</mo>
<mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">y</mi>
<mo id="p1.1.m1.1.18.3.2a" xref="p1.1.m1.1.18.3.2.cmml">,</mo>
<msub id="XM4" xref="XM4.cmml">
<mi id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">p</mi>
<mi id="p1.1.m1.1.13.1" xref="p1.1.m1.1.13.1.cmml">y</mi>
</msub>
<mo stretchy="false" id="p1.1.m1.1.18.3.2b" xref="p1.1.m1.1.18.3.2.cmml">}</mo>
</mrow>
<mrow id="p1.1.m1.1.15.1" xref="p1.1.m1.1.15.1.cmml">
<mi id="p1.1.m1.1.15.1.1" xref="p1.1.m1.1.15.1.1.cmml">D</mi>
<mo id="p1.1.m1.1.15.1.3" xref="p1.1.m1.1.15.1.3.cmml"></mo>
<mi id="p1.1.m1.1.15.1.2" xref="p1.1.m1.1.15.1.2.cmml">B</mi>
</mrow>
</msub>
<mo id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">=</mo>
<mstyle displaystyle="true" id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">
<mfrac id="p1.1.m1.1.17a" xref="p1.1.m1.1.17.cmml">
<mn id="p1.1.m1.1.17.2" xref="p1.1.m1.1.17.2.cmml">1</mn>
<mn id="p1.1.m1.1.17.3" xref="p1.1.m1.1.17.3.cmml">2</mn>
</mfrac>
</mstyle>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">
<and id="p1.1.m1.1.18a.cmml" xref="p1.1.m1.1.18"/>
<apply id="p1.1.m1.1.18b.cmml" xref="p1.1.m1.1.18">
<eq id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8"/>
<apply id="p1.1.m1.1.18.2.cmml" xref="p1.1.m1.1.18.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.18.2.1.cmml">subscript</csymbol>
<set id="p1.1.m1.1.18.2.2.cmml" xref="p1.1.m1.1.18.2.2">
<ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">x</ci>
<apply id="XM2.cmml" xref="XM2">
<csymbol cd="ambiguous" id="XM2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">p</ci>
<ci id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1">x</ci>
</apply>
</set>
<apply id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">
<times id="p1.1.m1.1.7.1.3.cmml" xref="p1.1.m1.1.7.1.3"/>
<ci id="p1.1.m1.1.7.1.1.cmml" xref="p1.1.m1.1.7.1.1">D</ci>
<ci id="p1.1.m1.1.7.1.2.cmml" xref="p1.1.m1.1.7.1.2">B</ci>
</apply>
</apply>
<apply id="p1.1.m1.1.18.3.cmml" xref="p1.1.m1.1.18.3">
<csymbol cd="ambiguous" id="p1.1.m1.1.18.3.1.cmml">subscript</csymbol>
<set id="p1.1.m1.1.18.3.2.cmml" xref="p1.1.m1.1.18.3.2">
<ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">y</ci>
<apply id="XM4.cmml" xref="XM4">
<csymbol cd="ambiguous" id="XM4.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">p</ci>
<ci id="p1.1.m1.1.13.1.cmml" xref="p1.1.m1.1.13.1">y</ci>
</apply>
</set>
<apply id="p1.1.m1.1.15.1.cmml" xref="p1.1.m1.1.15.1">
<times id="p1.1.m1.1.15.1.3.cmml" xref="p1.1.m1.1.15.1.3"/>
<ci id="p1.1.m1.1.15.1.1.cmml" xref="p1.1.m1.1.15.1.1">D</ci>
<ci id="p1.1.m1.1.15.1.2.cmml" xref="p1.1.m1.1.15.1.2">B</ci>
</apply>
</apply>
</apply>
<apply id="p1.1.m1.1.18c.cmml" xref="p1.1.m1.1.18">
<eq id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16"/>
<share href="#p1.1.m1.1.18.3.cmml" id="p1.1.m1.1.18d.cmml" xref="p1.1.m1.1.18"/>
<apply id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">
<divide id="p1.1.m1.1.17.1.cmml"/>
<cn type="integer" id="p1.1.m1.1.17.2.cmml" xref="p1.1.m1.1.17.2">1</cn>
<cn type="integer" id="p1.1.m1.1.17.3.cmml" xref="p1.1.m1.1.17.3">2</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\{x,p_{{x}}\}_{{{DB}}}=\{y,p_{{y}}\}_{{{DB}}}={{\frac{1}{2}}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=42627d67d7f005d2daefda905ec9f9ce&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.667ex; height: 4.833ex; width: 27.833ex;" alt="\{x,p_{{x}}\}_{{{DB}}}=\{y,p_{{y}}\}_{{{DB}}}={{\frac {1}{2}}}" data-pagespeed-url-hash="3925117644" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \{x,p_{x}\}_{DB}=\{y,p_{y}\}_{DB}={\frac {1}{2}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mo fence="false" stretchy="false">{</mo>
<mi>x</mi>
<mo>,</mo>
<msub>
<mi>p</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>x</mi>
</mrow>
</msub>
<msub>
<mo fence="false" stretchy="false">}</mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>D</mi>
<mi>B</mi>
</mrow>
</msub>
<mo>=</mo>
<mo fence="false" stretchy="false">{</mo>
<mi>y</mi>
<mo>,</mo>
<msub>
<mi>p</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>y</mi>
</mrow>
</msub>
<msub>
<mo fence="false" stretchy="false">}</mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>D</mi>
<mi>B</mi>
</mrow>
</msub>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \{x,p_{x}\}_{DB}=\{y,p_{y}\}_{DB}={\frac {1}{2}}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/1fc80760724cc8949828b933f0c5646d0a4b6a0e" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.838ex; width:27.64ex; height:5.176ex;" alt="{\displaystyle \{x,p_{x}\}_{DB}=\{y,p_{y}\}_{DB}={\frac {1}{2}}}" data-pagespeed-url-hash="4157348925" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/92" title="Special:DisplayTopics/92">92</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/26815#math.26815.17" title="Special:PermanentLink/26815">Pickands–Balkema–de_Haan_theorem-17</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle G_{{{k,\sigma}}}(y)=1-(1+ky/\sigma)^{{{-1/k}}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">
<mrow id="p1.1.m1.1.18.1" xref="p1.1.m1.1.18.1.cmml">
<msub id="p1.1.m1.1.18.1.2" xref="p1.1.m1.1.18.1.2.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">G</mi>
<mrow id="p1.1.m1.1.2.1a" xref="p1.1.m1.1.2.1.cmml">
<mi id="p1.1.m1.1.2.1.1" xref="p1.1.m1.1.2.1.1.cmml">k</mi>
<mo id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">,</mo>
<mi id="p1.1.m1.1.2.1.3" xref="p1.1.m1.1.2.1.3.cmml">σ</mi>
</mrow>
</msub>
<mo id="p1.1.m1.1.18.1.1" xref="p1.1.m1.1.18.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.18.1.3b">
<mo stretchy="false" id="p1.1.m1.1.18.1.3">(</mo>
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">y</mi>
<mo stretchy="false" id="p1.1.m1.1.18.1.3a">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">=</mo>
<mrow id="p1.1.m1.1.18.2" xref="p1.1.m1.1.18.2.cmml">
<mn id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">1</mn>
<mo id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">-</mo>
<msup id="p1.1.m1.1.18.2.1" xref="p1.1.m1.1.18.2.1.cmml">
<mrow id="p1.1.m1.1.18.2.1.2b">
<mo stretchy="false" id="p1.1.m1.1.18.2.1.2">(</mo>
<mrow id="XM1" xref="XM1.cmml">
<mn id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">1</mn>
<mo id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">+</mo>
<mrow id="XM1.1" xref="XM1.1.cmml">
<mrow id="XM1.1.1" xref="XM1.1.1.cmml">
<mi id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">k</mi>
<mo id="XM1.1.1.1" xref="XM1.1.1.1.cmml"></mo>
<mi id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">y</mi>
</mrow>
<mo id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">/</mo>
<mi id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">σ</mi>
</mrow>
</mrow>
<mo stretchy="false" id="p1.1.m1.1.18.2.1.2a">)</mo>
</mrow>
<mrow id="p1.1.m1.1.17.1" xref="p1.1.m1.1.17.1.cmml">
<mo id="p1.1.m1.1.17.1.1" xref="p1.1.m1.1.17.1.1.cmml">-</mo>
<mrow id="p1.1.m1.1.17.1.5" xref="p1.1.m1.1.17.1.5.cmml">
<mn id="p1.1.m1.1.17.1.2" xref="p1.1.m1.1.17.1.2.cmml">1</mn>
<mo id="p1.1.m1.1.17.1.3" xref="p1.1.m1.1.17.1.3.cmml">/</mo>
<mi id="p1.1.m1.1.17.1.4" xref="p1.1.m1.1.17.1.4.cmml">k</mi>
</mrow>
</mrow>
</msup>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">
<eq id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
<apply id="p1.1.m1.1.18.1.cmml" xref="p1.1.m1.1.18.1">
<times id="p1.1.m1.1.18.1.1.cmml" xref="p1.1.m1.1.18.1.1"/>
<apply id="p1.1.m1.1.18.1.2.cmml" xref="p1.1.m1.1.18.1.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.18.1.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">G</ci>
<list id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">
<ci id="p1.1.m1.1.2.1.1.cmml" xref="p1.1.m1.1.2.1.1">k</ci>
<ci id="p1.1.m1.1.2.1.3.cmml" xref="p1.1.m1.1.2.1.3">σ</ci>
</list>
</apply>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">y</ci>
</apply>
<apply id="p1.1.m1.1.18.2.cmml" xref="p1.1.m1.1.18.2">
<minus id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8"/>
<cn type="integer" id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">1</cn>
<apply id="p1.1.m1.1.18.2.1.cmml" xref="p1.1.m1.1.18.2.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.18.2.1.1.cmml">superscript</csymbol>
<apply id="XM1.cmml" xref="XM1">
<plus id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11"/>
<cn type="integer" id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">1</cn>
<apply id="XM1.1.cmml" xref="XM1.1">
<divide id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14"/>
<apply id="XM1.1.1.cmml" xref="XM1.1.1">
<times id="XM1.1.1.1.cmml" xref="XM1.1.1.1"/>
<ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">k</ci>
<ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">y</ci>
</apply>
<ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">σ</ci>
</apply>
</apply>
<apply id="p1.1.m1.1.17.1.cmml" xref="p1.1.m1.1.17.1">
<minus id="p1.1.m1.1.17.1.1.cmml" xref="p1.1.m1.1.17.1.1"/>
<apply id="p1.1.m1.1.17.1.5.cmml" xref="p1.1.m1.1.17.1.5">
<divide id="p1.1.m1.1.17.1.3.cmml" xref="p1.1.m1.1.17.1.3"/>
<cn type="integer" id="p1.1.m1.1.17.1.2.cmml" xref="p1.1.m1.1.17.1.2">1</cn>
<ci id="p1.1.m1.1.17.1.4.cmml" xref="p1.1.m1.1.17.1.4">k</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle G_{{{k,\sigma}}}(y)=1-(1+ky/\sigma)^{{{-1/k}}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=330c2c46109df4d69f8d7f6af22d3b7d&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.833ex; height: 3.167ex; width: 29.667ex;" alt="G_{{{k,\sigma }}}(y)=1-(1+ky/\sigma )^{{{-1/k}}}" data-pagespeed-url-hash="4079497992" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G_{k,\sigma }(y)=1-(1+ky/\sigma )^{-1/k}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>G</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>k</mi>
<mo>,</mo>
<mi>σ<!-- σ --></mi>
</mrow>
</msub>
<mo stretchy="false">(</mo>
<mi>y</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>1</mn>
<mo>−<!-- − --></mo>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>+</mo>
<mi>k</mi>
<mi>y</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>/</mo>
</mrow>
<mi>σ<!-- σ --></mi>
<msup>
<mo stretchy="false">)</mo>
<mrow class="MJX-TeXAtom-ORD">
<mo>−<!-- − --></mo>
<mn>1</mn>
<mrow class="MJX-TeXAtom-ORD">
<mo>/</mo>
</mrow>
<mi>k</mi>
</mrow>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle G_{k,\sigma }(y)=1-(1+ky/\sigma )^{-1/k}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/55172bddb23e7a370f4bfb33962aef18c42ce800" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.005ex; width:29.061ex; height:3.509ex;" alt="{\displaystyle G_{k,\sigma }(y)=1-(1+ky/\sigma )^{-1/k}}" data-pagespeed-url-hash="1269710864" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/93" title="Special:DisplayTopics/93">93</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/7260#math.7260.15" title="Special:PermanentLink/7260">Quantum_channel-15</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle L(H_{{B}})\otimes C(X)}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">
<mrow id="p1.1.m1.1.11.2" xref="p1.1.m1.1.11.2.cmml">
<mrow id="p1.1.m1.1.11.2.1" xref="p1.1.m1.1.11.2.1.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">L</mi>
<mo id="p1.1.m1.1.11.2.1.1" xref="p1.1.m1.1.11.2.1.1.cmml"></mo>
<mrow id="p1.1.m1.1.11.2.1.2b">
<mo stretchy="false" id="p1.1.m1.1.11.2.1.2">(</mo>
<msub id="XM1" xref="XM1.cmml">
<mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">H</mi>
<mi id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">B</mi>
</msub>
<mo stretchy="false" id="p1.1.m1.1.11.2.1.2a">)</mo>
</mrow>
</mrow>
<mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">⊗</mo>
<mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">C</mi>
</mrow>
<mo id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml"></mo>
<mrow id="p1.1.m1.1.11.3b">
<mo stretchy="false" id="p1.1.m1.1.11.3">(</mo>
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">X</mi>
<mo stretchy="false" id="p1.1.m1.1.11.3a">)</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">
<times id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1"/>
<apply id="p1.1.m1.1.11.2.cmml" xref="p1.1.m1.1.11.2">
<csymbol cd="latexml" id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">tensor-product</csymbol>
<apply id="p1.1.m1.1.11.2.1.cmml" xref="p1.1.m1.1.11.2.1">
<times id="p1.1.m1.1.11.2.1.1.cmml" xref="p1.1.m1.1.11.2.1.1"/>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">L</ci>
<apply id="XM1.cmml" xref="XM1">
<csymbol cd="ambiguous" id="XM1.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">H</ci>
<ci id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">B</ci>
</apply>
</apply>
<ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">C</ci>
</apply>
<ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">X</ci>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle L(H_{{B}})\otimes C(X)}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=86d61949fb22d1143ab009c0eddb76cb&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.5ex; width: 16ex;" alt="L(H_{{B}})\otimes C(X)" data-pagespeed-url-hash="349408779" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L(H_{B})\otimes C(X)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>L</mi>
<mo stretchy="false">(</mo>
<msub>
<mi>H</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>B</mi>
</mrow>
</msub>
<mo stretchy="false">)</mo>
<mo>⊗<!-- ⊗ --></mo>
<mi>C</mi>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle L(H_{B})\otimes C(X)}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/9681ae66153d81647b4c8f8b1c5506054964bf8a" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:15.199ex; height:2.843ex;" alt="{\displaystyle L(H_{B})\otimes C(X)}" data-pagespeed-url-hash="60743366" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/94" title="Special:DisplayTopics/94">94</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/22755#math.22755.2" title="Special:PermanentLink/22755">Ehrenfest_model-2</a>
</td>
<td> 1
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\pi_{i}=2^{\qvar@construct{x0}}{{\textstyle\left({{N}\atop{i}}% \right)}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">
<msub id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">π</mi>
<mi id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">i</mi>
</msub>
<mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">=</mo>
<mrow id="p1.1.m1.1.7.2" xref="p1.1.m1.1.7.2.cmml">
<msup id="p1.1.m1.1.7.2.2" xref="p1.1.m1.1.7.2.2.cmml">
<mn id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">2</mn>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">x0</mi>
</msup>
<mo id="p1.1.m1.1.7.2.1" xref="p1.1.m1.1.7.2.1.cmml"></mo>
<mrow id="p1.1.m1.1.6h" xref="p1.1.m1.1.6.cmml">
<mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">(</mo>
<mstyle scriptlevel="+1" id="p1.1.m1.1.6a" xref="p1.1.m1.1.6.cmml">
<mtable columnspacing="0.4em" rowspacing="0.2ex" id="p1.1.m1.1.6b" xref="p1.1.m1.1.6.cmml">
<mtr id="p1.1.m1.1.6c" xref="p1.1.m1.1.6.cmml">
<mtd id="p1.1.m1.1.6d" xref="p1.1.m1.1.6.cmml">
<mi id="p1.1.m1.1.6.3.2" xref="p1.1.m1.1.6.3.2.cmml">N</mi>
</mtd>
</mtr>
<mtr id="p1.1.m1.1.6e" xref="p1.1.m1.1.6.cmml">
<mtd id="p1.1.m1.1.6f" xref="p1.1.m1.1.6.cmml">
<mi id="p1.1.m1.1.6.3.3" xref="p1.1.m1.1.6.3.3.cmml">i</mi>
</mtd>
</mtr>
</mtable>
</mstyle>
<mo id="p1.1.m1.1.6g" xref="p1.1.m1.1.6.cmml">)</mo>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">
<eq id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
<apply id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">
<csymbol cd="ambiguous" id="p1.1.m1.1.7.1.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">π</ci>
<ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">i</ci>
</apply>
<apply id="p1.1.m1.1.7.2.cmml" xref="p1.1.m1.1.7.2">
<times id="p1.1.m1.1.7.2.1.cmml" xref="p1.1.m1.1.7.2.1"/>
<apply id="p1.1.m1.1.7.2.2.cmml" xref="p1.1.m1.1.7.2.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.7.2.2.1.cmml">superscript</csymbol>
<cn type="integer" id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">2</cn>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1">x0</csymbol>
</apply>
<apply id="p1.1.m1.1.6a.cmml" xref="p1.1.m1.1.6">
<csymbol cd="latexml" id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">binomial</csymbol>
<ci id="p1.1.m1.1.6.3.2.cmml" xref="p1.1.m1.1.6.3.2">N</ci>
<ci id="p1.1.m1.1.6.3.3.cmml" xref="p1.1.m1.1.6.3.3">i</ci>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\pi_{i}=2^{\qvar@construct{x0}}{{\textstyle\left({{N}\atop{i}}%
\right)}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=f3488b6e0ba565b98555ee4c134683db&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.667ex; height: 4.333ex; width: 13.833ex;" alt="\pi_{i}=2^{\qvar{x0}}{\tbinom{N}{i}}" data-pagespeed-url-hash="3070572282" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi _{i}=2^{-N}{\tbinom {N}{i}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>π<!-- π --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<msup>
<mn>2</mn>
<mrow class="MJX-TeXAtom-ORD">
<mo>−<!-- − --></mo>
<mi>N</mi>
</mrow>
</msup>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="false" scriptlevel="0">
<mrow>
<mrow class="MJX-TeXAtom-OPEN">
<mo maxsize="1.2em" minsize="1.2em">(</mo>
</mrow>
<mfrac linethickness="0">
<mi>N</mi>
<mi>i</mi>
</mfrac>
<mrow class="MJX-TeXAtom-CLOSE">
<mo maxsize="1.2em" minsize="1.2em">)</mo>
</mrow>
</mrow>
</mstyle>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \pi _{i}=2^{-N}{\tbinom {N}{i}}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/b3d7a23fb7f8e6e337d26306bf0f417718a0f8df" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.005ex; width:12.945ex; height:3.343ex;" alt="{\displaystyle \pi _{i}=2^{-N}{\tbinom {N}{i}}}" data-pagespeed-url-hash="3873313881" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/95" title="Special:DisplayTopics/95">95</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/14285#math.14285.1" title="Special:PermanentLink/14285">Fidelity_of_quantum_states-1</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle({{\sqrt{p_{{1}}}}},\cdots,{{\sqrt{p_{{n}}}}})}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.8d" xref="p1.1.m1.1.8.cmml">
<mo stretchy="false" id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">(</mo>
<msqrt id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">
<msub id="p1.1.m1.1.2.2" xref="p1.1.m1.1.2.2.cmml">
<mi id="p1.1.m1.1.2.2.1" xref="p1.1.m1.1.2.2.1.cmml">p</mi>
<mn id="p1.1.m1.1.2.2.2.1" xref="p1.1.m1.1.2.2.2.1.cmml">1</mn>
</msub>
</msqrt>
<mo id="p1.1.m1.1.8a" xref="p1.1.m1.1.8.cmml">,</mo>
<mi mathvariant="normal" id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">⋯</mi>
<mo id="p1.1.m1.1.8b" xref="p1.1.m1.1.8.cmml">,</mo>
<msqrt id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
<msub id="p1.1.m1.1.6.2" xref="p1.1.m1.1.6.2.cmml">
<mi id="p1.1.m1.1.6.2.1" xref="p1.1.m1.1.6.2.1.cmml">p</mi>
<mi id="p1.1.m1.1.6.2.2.1" xref="p1.1.m1.1.6.2.2.1.cmml">n</mi>
</msub>
</msqrt>
<mo stretchy="false" id="p1.1.m1.1.8c" xref="p1.1.m1.1.8.cmml">)</mo>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<vector id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">
<apply id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">
<root id="p1.1.m1.1.2a.cmml" xref="p1.1.m1.1.2"/>
<apply id="p1.1.m1.1.2.2.cmml" xref="p1.1.m1.1.2.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.2.2.3.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.2.2.1.cmml" xref="p1.1.m1.1.2.2.1">p</ci>
<cn type="integer" id="p1.1.m1.1.2.2.2.1.cmml" xref="p1.1.m1.1.2.2.2.1">1</cn>
</apply>
</apply>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">normal-⋯</ci>
<apply id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">
<root id="p1.1.m1.1.6a.cmml" xref="p1.1.m1.1.6"/>
<apply id="p1.1.m1.1.6.2.cmml" xref="p1.1.m1.1.6.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.6.2.3.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.6.2.1.cmml" xref="p1.1.m1.1.6.2.1">p</ci>
<ci id="p1.1.m1.1.6.2.2.1.cmml" xref="p1.1.m1.1.6.2.2.1">n</ci>
</apply>
</apply>
</vector>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle({{\sqrt{p_{{1}}}}},\cdots,{{\sqrt{p_{{n}}}}})}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=febae75a4b223873406deddcfb91e11a&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1ex; height: 2.667ex; width: 15.167ex;" alt="({{\sqrt {p_{{1}}}}},\cdots ,{{\sqrt {p_{{n}}}}})" data-pagespeed-url-hash="2872729190" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ({\sqrt {p_{1}}},\cdots ,{\sqrt {p_{n}}})}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mo stretchy="false">(</mo>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<msub>
<mi>p</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
</msqrt>
</mrow>
<mo>,</mo>
<mo>⋯<!-- ⋯ --></mo>
<mo>,</mo>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<msub>
<mi>p</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>n</mi>
</mrow>
</msub>
</msqrt>
</mrow>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle ({\sqrt {p_{1}}},\cdots ,{\sqrt {p_{n}}})}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/8eb5b8ef67fe63fd33b87f30f58b001dd5a51043" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.171ex; width:15.471ex; height:3.176ex;" alt="{\displaystyle ({\sqrt {p_{1}}},\cdots ,{\sqrt {p_{n}}})}" data-pagespeed-url-hash="1969524420" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/96" title="Special:DisplayTopics/96">96</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/15596#math.15596.27" title="Special:PermanentLink/15596">Yield_surface-27</a>
</td>
<td> 0
</td>
<td> 5
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{{\boldsymbol{s}}}}">
<semantics id="p1.1.m1.1a">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">𝒔</mi>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝒔</ci>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{{\boldsymbol{s}}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=61e303354984601fa55c6acaadbdf001&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.167ex; height: 1.167ex; width: 1.167ex;" alt="{{\boldsymbol {s}}}" data-pagespeed-url-hash="2079449788" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {s}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="bold-italic">s</mi>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {s}}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/adfccdf93cc6115ade3deffbbbf062d6849a1f38" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.234ex; height:1.676ex;" alt="{\displaystyle {\boldsymbol {s}}}" data-pagespeed-url-hash="2060203017" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/97" title="Special:DisplayTopics/97">97</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/21658#math.21658.67" title="Special:PermanentLink/21658">Non-linear_least_squares-67</a>
</td>
<td> 0
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{{\mathbf{J^{{T}}W\ \Delta y}}}}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">
<msup id="p1.1.m1.1.7.2" xref="p1.1.m1.1.7.2.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">𝐉</mi>
<mi id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">𝐓</mi>
</msup>
<mo id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml"></mo>
<mpadded width="+5pt" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
<mi id="p1.1.m1.1.3a" xref="p1.1.m1.1.3.cmml">𝐖</mi>
</mpadded>
<mo id="p1.1.m1.1.7.1a" xref="p1.1.m1.1.7.1.cmml"></mo>
<mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">𝚫</mi>
<mo id="p1.1.m1.1.7.1b" xref="p1.1.m1.1.7.1.cmml"></mo>
<mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">𝐲</mi>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">
<times id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1"/>
<apply id="p1.1.m1.1.7.2.cmml" xref="p1.1.m1.1.7.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.7.2.1.cmml">superscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝐉</ci>
<ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">𝐓</ci>
</apply>
<ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">𝐖</ci>
<ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">𝚫</ci>
<ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">𝐲</ci>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{{\mathbf{J^{{T}}W\ \Delta y}}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=4c386c3f9d5ebab1d5fb668a1425e3e1&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.5ex; height: 2.667ex; width: 10.5ex;" alt="{{\mathbf {J^{{T}}W\ \Delta y}}}" data-pagespeed-url-hash="139225770" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {J^{T}W\ \Delta y} }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<msup>
<mi mathvariant="bold">J</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="bold">T</mi>
</mrow>
</msup>
<mi mathvariant="bold">W</mi>
<mtext mathvariant="bold"> </mtext>
<mi mathvariant="bold">Δ<!-- Δ --></mi>
<mi mathvariant="bold">y</mi>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \mathbf {J^{T}W\ \Delta y} }</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/f7c42792c498219eff4f7caa0c612a314417793a" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:9.908ex; height:3.009ex;" alt="{\displaystyle \mathbf {J^{T}W\ \Delta y} }" data-pagespeed-url-hash="2498249115" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/98" title="Special:DisplayTopics/98">98</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/7629#math.7629.87" title="Special:PermanentLink/7629">Markov_decision_process-87</a>
</td>
<td> 0
</td>
<td> 2
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{{\bar{V}}}^{{*}}}">
<semantics id="p1.1.m1.1a">
<msup id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
<mover accent="true" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">
<mi id="p1.1.m1.1.1.2" xref="p1.1.m1.1.1.2.cmml">V</mi>
<mo stretchy="false" id="p1.1.m1.1.1.1" xref="p1.1.m1.1.1.1.cmml">¯</mo>
</mover>
<mo id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">*</mo>
</msup>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
<csymbol cd="ambiguous" id="p1.1.m1.1.3.1.cmml">superscript</csymbol>
<apply id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">
<ci id="p1.1.m1.1.1.1.cmml" xref="p1.1.m1.1.1.1">normal-¯</ci>
<ci id="p1.1.m1.1.1.2.cmml" xref="p1.1.m1.1.1.2">V</ci>
</apply>
<times id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1"/>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{{\bar{V}}}^{{*}}}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=4d7781983de8c8a2b8252bec5bba52ed&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.167ex; height: 2.333ex; width: 2.833ex;" alt="{{\bar {V}}}^{{*}}" data-pagespeed-url-hash="1856518120" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {V}}^{*}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msup>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>V</mi>
<mo stretchy="false">¯<!-- ¯ --></mo>
</mover>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>∗<!-- ∗ --></mo>
</mrow>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\bar {V}}^{*}}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/469a7ee0366792acb671e6eb13fc755a09b15c1c" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:2.841ex; height:2.676ex;" alt="{\displaystyle {\bar {V}}^{*}}" data-pagespeed-url-hash="3596187388" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/99" title="Special:DisplayTopics/99">99</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/14812#math.14812.9" title="Special:PermanentLink/14812">Hilbert_series_and_Hilbert_polynomial-9</a>
</td>
<td> 2
</td>
<td> 1
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\;{\frac{\qvar@construct{x0}}{\qvar@construct{x1}}}\;}">
<semantics id="p1.1.m1.1a">
<mpadded lspace="2.8pt" width="+5.6pt" id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">
<mstyle displaystyle="true" id="p1.1.m1.1.2a" xref="p1.1.m1.1.2.cmml">
<mfrac id="p1.1.m1.1.2b" xref="p1.1.m1.1.2.cmml">
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.2.2" xref="p1.1.m1.1.2.2.cmml">x0</mi>
<mi mathcolor="red" mathvariant="italic" id="p1.1.m1.1.2.3" xref="p1.1.m1.1.2.3.cmml">x1</mi>
</mfrac>
</mstyle>
</mpadded>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">
<divide id="p1.1.m1.1.2.1.cmml"/>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.2.2.cmml" xref="p1.1.m1.1.2.2">x0</csymbol>
<csymbol cd="mws" name="qvar" id="p1.1.m1.1.2.3.cmml" xref="p1.1.m1.1.2.3">x1</csymbol>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\;{\frac{\qvar@construct{x0}}{\qvar@construct{x1}}}\;}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=3d9e7193900e8cf7f11f4551a92eced2&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.667ex; height: 4.833ex; width: 4.667ex;" alt="\;{\frac{\qvar{x0}}{\qvar{x1}}}\;" data-pagespeed-url-hash="847772212" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;{\frac {(n+\delta -1)(n+\delta -2)\cdots n}{(\delta -1)!}}\;}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mspace width="thickmathspace"/>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mo stretchy="false">(</mo>
<mi>n</mi>
<mo>+</mo>
<mi>δ<!-- δ --></mi>
<mo>−<!-- − --></mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mi>n</mi>
<mo>+</mo>
<mi>δ<!-- δ --></mi>
<mo>−<!-- − --></mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
<mo>⋯<!-- ⋯ --></mo>
<mi>n</mi>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mi>δ<!-- δ --></mi>
<mo>−<!-- − --></mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo>!</mo>
</mrow>
</mfrac>
</mrow>
<mspace width="thickmathspace"/>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \;{\frac {(n+\delta -1)(n+\delta -2)\cdots n}{(\delta -1)!}}\;}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/910273d0889b6cd19544d1a08d0a395f0c5408c2" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.671ex; width:29.21ex; height:6.509ex;" alt="{\displaystyle \;{\frac {(n+\delta -1)(n+\delta -2)\cdots n}{(\delta -1)!}}\;}" data-pagespeed-url-hash="3595951387" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr>
<tr>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics/100" title="Special:DisplayTopics/100">100</a>
</td>
<td> <a href="https://en.formulasearchengine.com/wiki/Special:PermanentLink/17319#math.17319.15" title="Special:PermanentLink/17319">Overlap–add_method-15</a>
</td>
<td> 0
</td>
<td> 3
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle y_{{k}}[n]}">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
<msub id="p1.1.m1.1.6.2" xref="p1.1.m1.1.6.2.cmml">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">y</mi>
<mi id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">k</mi>
</msub>
<mo id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml"></mo>
<mrow id="p1.1.m1.1.6.3b" xref="p1.1.m1.1.6.3.cmml">
<mo stretchy="false" id="p1.1.m1.1.6.3" xref="p1.1.m1.1.6.3.cmml">[</mo>
<mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">n</mi>
<mo stretchy="false" id="p1.1.m1.1.6.3a" xref="p1.1.m1.1.6.3.cmml">]</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
<apply id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">
<times id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1"/>
<apply id="p1.1.m1.1.6.2.cmml" xref="p1.1.m1.1.6.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.6.2.1.cmml">subscript</csymbol>
<ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">y</ci>
<ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">k</ci>
</apply>
<apply id="p1.1.m1.1.6.3a.cmml" xref="p1.1.m1.1.6.3">
<csymbol cd="latexml" id="p1.1.m1.1.6.3.cmml" xref="p1.1.m1.1.6.3">delimited-[]</csymbol>
<ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">n</ci>
</apply>
</apply>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle y_{{k}}[n]}</annotation>
</semantics>
</math></span><img src="https://en.formulasearchengine.com/w/index.php?title=Special:MathShowImage&hash=35f2fcd46bdf8702cd2b9d0c5bc08dd6&mode=latexml" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.667ex; height: 2.5ex; width: 5.333ex;" alt="y_{{k}}[n]" data-pagespeed-url-hash="2748496380" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td>
<td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=""><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y_{k}[n]}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>y</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>k</mi>
</mrow>
</msub>
<mo stretchy="false">[</mo>
<mi>n</mi>
<mo stretchy="false">]</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle y_{k}[n]}</annotation>
</semantics>
</math></span><img src="https://api.formulasearchengine.com/v1/media/math/render/svg/510488c42185dcb9ae020abf4162b1a53fcb8d0c" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:4.916ex; height:2.843ex;" alt="{\displaystyle y_{k}[n]}" data-pagespeed-url-hash="1903081576" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></span>
</td></tr></table>
</div> <div class="printfooter">
Retrieved from "<a dir="ltr" href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics">https://en.formulasearchengine.com/wiki/Special:DisplayTopics</a>" </div>
<div id="catlinks" class="catlinks catlinks-allhidden" data-mw="interface"></div> <div class="visualClear"></div>
</div>
</div>
<div id="mw-navigation">
<h2>Navigation menu</h2>
<div id="mw-head">
<div id="p-personal" role="navigation" class="" aria-labelledby="p-personal-label">
<h3 id="p-personal-label">Personal tools</h3>
<ul>
<li id="pt-userpage"><a href="https://en.formulasearchengine.com/wiki/User:Admin" dir="auto" title="Your user page [.]" accesskey=".">Admin</a></li><li id="pt-mytalk"><a href="https://en.formulasearchengine.com/wiki/User_talk:Admin" class="new" title="Your talk page [n]" accesskey="n">Talk</a></li><li id="pt-preferences"><a href="https://en.formulasearchengine.com/wiki/Special:Preferences" title="Your preferences">Preferences</a></li><li id="pt-watchlist"><a href="https://en.formulasearchengine.com/wiki/Special:Watchlist" title="A list of pages you are monitoring for changes [l]" accesskey="l">Watchlist</a></li><li id="pt-mycontris"><a href="https://en.formulasearchengine.com/wiki/Special:Contributions/Admin" title="A list of your contributions [y]" accesskey="y">Contributions</a></li><li id="pt-logout"><a href="https://en.formulasearchengine.com/w/index.php?title=Special:UserLogout&returnto=Special%3ADisplayTopics&returntoquery=action%3Dparse" title="Log out">Log out</a></li> </ul>
</div>
<div id="left-navigation">
<div id="p-namespaces" role="navigation" class="vectorTabs" aria-labelledby="p-namespaces-label">
<h3 id="p-namespaces-label">Namespaces</h3>
<ul>
<li id="ca-nstab-special" class="selected"><span><a href="https://en.formulasearchengine.com/wiki/Special:DisplayTopics?action=parse" title="This is a special page, and it cannot be edited">Special page</a></span></li>
</ul>
</div>
<div id="p-variants" role="navigation" class="vectorMenu emptyPortlet" aria-labelledby="p-variants-label">
<h3 id="p-variants-label">
<span>Variants</span><a href="#"></a>
</h3>
<div class="menu">
<ul>
</ul>
</div>
</div>
</div>
<div id="right-navigation">
<div id="p-views" role="navigation" class="vectorTabs emptyPortlet" aria-labelledby="p-views-label">
<h3 id="p-views-label">Views</h3>
<ul>
</ul>
</div>
<div id="p-cactions" role="navigation" class="vectorMenu emptyPortlet" aria-labelledby="p-cactions-label">
<h3 id="p-cactions-label"><span>More</span><a href="#"></a></h3>
<div class="menu">
<ul>
</ul>
</div>
</div>
<div id="p-search" role="search">
<h3>
<label for="searchInput">Search</label>
</h3>
<form action="/w/index.php" id="searchform">
<div id="simpleSearch">
<input type="search" name="search" placeholder="Search enwikimath" title="Search enwikimath [f]" accesskey="f" id="searchInput"/><input type="hidden" value="Special:Search" name="title"/><input type="submit" name="fulltext" value="Search" title="Search the pages for this text" id="mw-searchButton" class="searchButton mw-fallbackSearchButton"/><input type="submit" name="go" value="Go" title="Go to a page with this exact name if it exists" id="searchButton" class="searchButton"/> </div>
</form>
</div>
</div>
</div>
<div id="mw-panel">
<div id="p-logo" role="banner"><a class="mw-wiki-logo" href="/wiki/Main_Page" title="Visit the main page"></a></div>
<div class="portal" role="navigation" id='p-navigation' aria-labelledby='p-navigation-label'>
<h3 id='p-navigation-label'>Navigation</h3>
<div class="body">
<ul>
<li id="n-mainpage-description"><a href="https://en.formulasearchengine.com/wiki/Main_Page" title="Visit the main page [z]" accesskey="z">Main page</a></li><li id="n-recentchanges"><a href="https://en.formulasearchengine.com/wiki/Special:RecentChanges" title="A list of recent changes in the wiki [r]" accesskey="r">Recent changes</a></li><li id="n-randompage"><a href="https://en.formulasearchengine.com/wiki/Special:Random" title="Load a random page [x]" accesskey="x">Random page</a></li><li id="n-help"><a href="https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents" title="The place to find out">Help</a></li> </ul>
</div>
</div>
<div class="portal" role="navigation" id='p-tb' aria-labelledby='p-tb-label'>
<h3 id='p-tb-label'>Tools</h3>
<div class="body">
<ul>
<li id="t-upload"><a href="https://en.formulasearchengine.com/wiki/Special:Upload" title="Upload files [u]" accesskey="u">Submit Results</a></li><li id="t-specialpages"><a href="https://en.formulasearchengine.com/wiki/Special:SpecialPages" title="A list of all special pages [q]" accesskey="q">Special pages</a></li><li id="t-print"><a href="https://en.formulasearchengine.com/w/index.php?title=Special:DisplayTopics&action=parse&printable=yes" rel="alternate" title="Printable version of this page [p]" accesskey="p">Printable version</a></li> </ul>
</div>
</div>
</div>
</div>
<div id="footer" role="contentinfo">
<ul id="footer-places">
<li id="footer-places-privacy"><a href="https://en.formulasearchengine.com/wiki/enmath:Privacy_policy" title="enmath:Privacy policy">Privacy policy</a></li>
<li id="footer-places-about"><a href="https://en.formulasearchengine.com/wiki/enmath:About" title="enmath:About">About enwikimath</a></li>
<li id="footer-places-disclaimer"><a href="https://en.formulasearchengine.com/wiki/enmath:General_disclaimer" title="enmath:General disclaimer">Disclaimers</a></li>
</ul>
<ul id="footer-icons" class="noprint">
<li id="footer-poweredbyico">
<a href="https://en.formulasearchengine.com//www.mediawiki.org/"><img src="https://en.formulasearchengine.com/w/resources/assets/poweredby_mediawiki_88x31.png.pagespeed.ce.gmntWCYHG0.png" alt="Powered by MediaWiki" srcset="/w/resources/assets/poweredby_mediawiki_132x47.png.pagespeed.ce.L1zE4_p3Ii.png 1.5x, /w/resources/assets/poweredby_mediawiki_176x62.png.pagespeed.ce.LE9xjEBgUS.png 2x" width="88" height="31" data-pagespeed-url-hash="3503995514" onload="pagespeed.CriticalImages.checkImageForCriticality(this);"/></a> </li>
</ul>
<div style="clear:both"></div>
</div>
<!-- Web analytics code inclusion is disabled for this user. -->
<script>(window.RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgBackendResponseTime":2530});});</script>
</body>
</html>