Document Zbl 1443.74055

<!doctype html> <html lang="en"> <head> <meta charset="utf-8"> <title>Document Zbl 1443.74055 - zbMATH Open</title> <meta name="viewport" content="width=device-width, minimum-scale=0.1, maximum-scale=5.0"> <meta name="robots" content="noarchive, noindex"> <meta name="referrer" content="origin-when-cross-origin"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap-theme.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.css" rel="stylesheet" media="screen,print"> <link rel="stylesheet" href="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/css/bootstrap-select.min.css"> <link href="/static/css/smoothness/jquery-ui-1.10.1.custom.min.css" rel="stylesheet" media="screen"> <link href="/static/styles.css?v=20241024" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/zbMathJax/v0.1.38/zbmathjax.css" rel="stylesheet" media="screen,print"> <link rel="shortcut icon" href="/static/zbmath.ico"> <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "Organization", "url": "https://zbmath.org/", "logo": "https://zbmath.org/static/zbMATH.png" } </script> </head> <body> <div id="line"></div> <span id="clear" style="cursor: pointer;">×</span> <div id="page"> <div id="head"> <nav id="menu" class="navbar navbar-default"> <div class="container-fluid"> <div class="navbar-header"> <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#zbnav" aria-expanded="false"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar"></span> <span class="icon-bar"></span> <span class="icon-bar"></span> </button> <a class="navbar-brand" href="#"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open logo"> </a> </div> <div id="zbnav" class="collapse navbar-collapse"> <ul class="nav navbar-nav pages"> <li class="about"> <a href="/about/">About</a> </li> <li class="frequently-asked-questions"> <a href="/frequently-asked-questions/">FAQ</a> </li> <li class="general-help"> <a href="/general-help/">General Help</a> </li> <li class="reviewer-service"> <a href="https://zbmath.org/reviewer-service/" target="_self" >Reviewer Service</a> </li> <li> <a href="/tools-and-resources/">Tools & Resources</a> </li> <li class="contact"> <a href="/contact/">Contact</a> </li> </ul> <ul class="nav navbar-nav navbar-right prefs"> <li class="preferences dropdown"> <a data-toggle="dropdown" href="#">Preferences <i class="caret"></i></a> <ul class="dropdown-menu preferences"> <li> <form id="preferences" class="navbar-form" method="post" action="/preferences/" onsubmit="return confirm('This website uses cookies for the purposes of storing preference information on your device. Do you agree to this?\n\nPlease refer to our Privacy Policy to learn more about our use of cookies.')" > <input type="hidden" name="path" value="/1443.74055?"> <span class=""> <label class="title">Search Form</label> <div class="form-group"> <input id="search-multi-line" type="radio" name="search" value="multi-line" checked> <label for="search-multi-line" class="radio">Multi-Line Search (default)</label> </div> <div class="form-group"> <input id="search-one-line" type="radio" name="search" value="one-line"> <label for="search-one-line" class="radio">One-Line Search</label> </div> </span> <span class="count"> <label class="title">Hits per Page</label> <div class="form-group"> <input id="count-10" type="radio" name="count" value="10"> <label for="count-10" class="radio">10</label> </div> <div class="form-group"> <input id="count-20" type="radio" name="count" value="20"> <label for="count-20" class="radio">20</label> </div> <div class="form-group"> <input id="count-50" type="radio" name="count" value="50"> <label for="count-50" class="radio">50</label> </div> <div class="form-group"> <input id="count-100" type="radio" name="count" value="100" checked> <label for="count-100" class="radio">100 (default)</label> </div> <div class="form-group"> <input id="count-200" type="radio" name="count" value="200"> <label for="count-200" class="radio">200</label> </div> </span> <span class="format"> <label class="title">Display Format</label> <div class="form-group"> <input id="format-mathjax" type="radio" name="format" value="mathjax" checked> <label for="format-mathjax" class="radio">MathJax (default)</label> </div> <div class="form-group"> <input id="format-amstex" type="radio" name="format" value="latex"> <label for="format-amstex" class="radio">LaTeX</label> </div> </span> <span class="ranking"> <label class="title">Documents Sorting</label> <div class="form-group"> <input id="documents-ranking-default" type="radio" name="documents_ranking" value="date" checked> <label for="documents-ranking-default" class="radio">Newest first (default)</label> </div> <div class="form-group"> <input id="documents-ranking-references" type="radio" name="documents_ranking" value="references"> <label for="documents-ranking-references" class="radio">Citations</label> </div> <div class="form-group"> <input id="documents-ranking-relevance" type="radio" name="documents_ranking" value="relevance"> <label for="documents-ranking-relevance" class="radio">Relevance</label> </div> </span> <span class="ranking"> <label class="title">Authors Sorting</label> <div class="form-group"> <input id="authors-ranking-default" type="radio" name="authors_ranking" value="alpha" checked> <label for="authors-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="authors-ranking-references" type="radio" name="authors_ranking" value="references"> <label for="authors-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Serials Sorting</label> <div class="form-group"> <input id="serials-ranking-default" type="radio" name="serials_ranking" value="alpha" checked> <label for="serials-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="serials-ranking-references" type="radio" name="serials_ranking" value="references"> <label for="serials-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Software Sorting</label> <div class="form-group"> <input id="software-ranking-default" type="radio" name="software_ranking" value="references" checked> <label for="software-ranking-default" class="radio">Citations (default)</label> </div> <div class="form-group"> <input id="software-ranking-alpha" type="radio" name="software_ranking" value="alpha"> <label for="software-ranking-alpha" class="radio">Alphabetically</label> </div> </span> <button type="submit" class="btn btn-default">OK</button> <div class="clearfix"> </form> </li> </ul> </li> </ul> </div> </div> </nav> <div id="tabs"> <h1 class="logo"> <a class="logo" href="/"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open — the first resource for mathematics" > </a> </h1> <nav> <ul class="nav nav-tabs"> <li class="tab-documents active"> <a href="/">Documents</a> </li> <li class="tab-authors"> <a href="/authors/">Authors</a> </li> <li class="tab-serials"> <a href="/serials/">Serials</a> </li> <li class="tab-software"> <a href="/software/">Software</a> </li> <li class="tab-classification"> <a href="/classification/">Classification</a> </li> <li class="tab-formulae"> <a href="/formulae/">Formulæ</a> </li> </ul> </nav> <div class="clearfix"></div> </div> <div class="content-fixed"> <div class="content-formular"> <div style="display: none;"> <div class="row ml-0"id="multi-line-new-line" style="display: none;"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-0-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-0-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input"> <span class="multi-line-value" id="multi-line-type-range"><span style="padding-left: 5px;">from</span> <input name="ml-0-v1" class="form-control multi-line-input" type="text" value="" aria-label="value"> until <input name="ml-0-v2" class="form-control multi-line-input" type="text" value="" aria-label="value"></span> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-la" placeholder="use name or ISO code"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-rv" placeholder="enter name or zbMATH reviewer number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-an" placeholder="Zbl, JFM or ERAM number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-en" placeholder="e.g. DOI, ISBN, arXiv ID"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-sw" placeholder="use * to find all documents using software"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-br" placeholder="find documents about the life or work of a person"> <span class="multi-line-value" id="multi-line-type-multiselect-db"> <select class="multi-line-selectpicker" data-width="100%" multiple> <option value="zbl">Zbl</option> <option value="arxiv">arXiv</option> <option value="jfm">JFM</option> <option value="eram">ERAM</option> </select> <input type="hidden" class="multi-line-input" name="ml-0-v" value=""> </span> </div> <form name="documents" method="GET" action="/" autocomplete="off"> <div class="documents multi-line" style="display: none;"> <div class="forms"> <ul class="nav forms"> <li class="one-line"> <span tabindex="0" class="glyphicon glyphicon-question-sign" title="One-Line Search allows for free logical combinations of search fields" aria-label="One-Line Search allows for free logical combinations of search fields" data-placement="bottom"></span> <a style="display: inline-block;" href="#">One-Line Search <span class="glyphicon glyphicon-search"></span></a> </li> </ul> </div> <div class="clearfix"></div> <div class="container-fluid"> <input type="hidden" id="multi-line-ml" name="ml" value="3"> <div id="multi-line-row-wrapper"> <div class="row ml-1"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-1-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-1-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-1-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-2"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-2-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au" selected>Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-2-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-2-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-3"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-3-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti" selected>Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-3-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><div id="multi-line-plus"> <a href="#"><span class="glyphicon glyphicon-plus" aria-hidden="true"></span> add line</a> </div></div> </div> </div> <div class="row"> <div class="col-xs-12 form-inline"> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-test" style="visibility: hidden; position: fixed;"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label title="search for Articles in Journals"> <input type="checkbox" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label title="search for arXiv Preprints"> <input type="checkbox" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-real"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label for="dt-j" title="search for Articles in Journals"> <input type="checkbox" id="dt-j" name="dt" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label for="dt-a" title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" id="dt-a" name="dt" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label for="dt-b" title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" id="dt-b" name="dt" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label for="dt-p" title="search for arXiv Preprints"> <input type="checkbox" id="dt-p" name="dt" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> </div> </div> <div class="row"> <div class="col-xs-12 buttons"> <a tabindex="0" class="btn btn-default clear-all">Reset all <span class="glyphicon glyphicon-remove"></span></a> <div class="submit"> <button class="btn btn-default search" type="submit">Search <span class="glyphicon glyphicon-search"></span></button> </div> </div> </div> </div> </div> </form> <form class="form-inline" name="documents" method="GET" action="/"> <div class="documents one-line" style="display: block;"> <div class="forms"> <ul class="nav forms"> <li class="multi-line"><a href="#">New Multi-Line Search <span class="glyphicon glyphicon-list"></span></a></li> </ul> </div> <div id="search-row" class="input-group box"> <span> <div id="search-field"> <input class="query form-control" type="text" name="q" value="an:1443.74055" aria-label="Search for documents" placeholder="Search for documents" autocomplete="off"> </div> <div class="search-buttons input-group-btn"> <div class="btn-group"> <button class="btn btn-default search" type="submit"><span class="virtual">Search</span> <span class="glyphicon glyphicon-search" style="top: 2px;"></span></button> </div> </div> </span> <span> <div class="search-buttons input-group-btn"> <div class="btn-group"> <div class="btn-group fields"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Fields <i class="caret"></i></button> <ul id="fields" class="dropdown-menu pull-right"> <li><a href="#"><span class="token item">any:</span><span> </span>anywhere (default)</a></li> <li><a href="#"><span class="token item">ab:</span><span>  </span>review text</a></li> <li><a href="#"><span class="token item">an:</span><span>  </span>zbmath id</a></li> <li><a href="#"><span class="token item">any:</span><span>  </span>anywhere</a></li> <li><a href="#"><span class="token item">au:</span><span>  </span>contributor name</a></li> <li><a href="#"><span class="token item">br:</span><span>  </span>biographic reference name</a></li> <li><a href="#"><span class="token item">cc:</span><span>  </span>msc title</a></li> <li><a href="#"><span class="token item">dt:</span><span>  </span>document type</a></li> <li><a href="#"><span class="token item">doi:</span><span>  </span>doi</a></li> <li><a href="#"><span class="token item">en:</span><span>  </span>external id</a></li> <li><a href="#"><span class="token item">la:</span><span>  </span>language</a></li> <li><a href="#"><span class="token item">pu:</span><span>  </span>publisher</a></li> <li><a href="#"><span class="token item">py:</span><span>  </span>year</a></li> <li><a href="#"><span class="token item">rv:</span><span>  </span>reviewer name</a></li> <li><a href="#"><span class="token item">so:</span><span>  </span>source</a></li> <li><a href="#"><span class="token item">sw:</span><span>  </span>software name</a></li> <li><a href="#"><span class="token item">ti:</span><span>  </span>title</a></li> <li><a href="#"><span class="token item">ut:</span><span>  </span>keyword</a></li> </ul> </div> <div class="btn-group operators"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Operators <i class="caret"></i></button> <ul id="operators" class="dropdown-menu pull-right"> <li><a href="#"><span class="token">a <span class="item">&</span> b </span><span> </span>logical and (default)</a></li> <li><a href="#"><span class="token">a <span class="item">|</span> b </span><span> </span>logical or</a></li> <li><a href="#"><span class="token"><span class="item">!</span>ab   </span><span> </span>logical not</a></li> <li><a href="#"><span class="token">abc<span class="item">*</span>  </span><span> </span>right wildcard</a></li> <li><a href="#"><span class="token"><span class="item">"</span>ab c<span class="item">"</span></span><span> </span>phrase</a></li> <li><a href="#"><span class="token"><span class="item">(</span>ab c<span class="item">)</span></span><span> </span>parentheses</a></li> </ul> </div> </div> </div> <div class="special"> <ul class="nav help-button"> <li class="dropdown pull-right"> <a href="#">Help <i class="caret"></i></a> </li> </ul> </div> </span> </div> <div class="help"><h2>Examples</h2> <div id="help-terms" role="table"> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Geometry">Geometry</a></span> <span class="search-explanation" role="cell" role="cell">Search for the term <em>Geometry</em> in <strong>any</strong> field. Queries are <strong>case-independent</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Funct%2A">Funct*</a></span> <span class="search-explanation" role="cell"><strong>Wildcard</strong> queries are specified by <strong><u>*</u></strong> (e.g. <em>functions</em>, <em>functorial</em>, etc.). Otherwise the search is <strong>exact</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Topological+group%22">"Topological group"</a></span> <span class="search-explanation" role="cell"><strong>Phrases</strong> (multi-words) should be set in <u>"</u>straight quotation marks<u>"</u>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=au%3A+Bourbaki+%26+ti%3A+Algebra">au: Bourbaki & ti: Algebra</a></span> <span class="search-explanation" role="cell">Search for <strong><u>au</u>thor</strong> and <strong><u>ti</u>tle</strong>. The <strong>and-operator &</strong> is default and can be omitted.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Chebyshev+%7C+Tschebyscheff">Chebyshev | Tschebyscheff</a></span> <span class="search-explanation" role="cell">The <strong>or-operator |</strong> allows to search for <em>Chebyshev</em> or <em>Tschebyscheff</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Quasi%2A+map%2A+py%3A+1989">Quasi* map* py: 1989</a></span> <span class="search-explanation" role="cell">The resulting documents have <strong><u>p</u>ublication <u>y</u>ear</strong> <em>1989</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=so%3A+Eur%2A+J%2A+Mat%2A+Soc%2A+cc%3A+14">so: Eur* J* Mat* Soc* cc: 14</a></span> <span class="search-explanation" role="cell">Search for publications in a particular <strong><u>so</u>urce</strong> with a <strong>Mathematics Subject <u>C</u>lassification <u>c</u>ode (<u>cc</u>)</strong> in <em>14</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Partial+diff%2A+eq%2A%22+%21+elliptic">"Partial diff* eq*" ! elliptic</a></span> <span class="search-explanation" role="cell">The <strong>not</strong>-operator <strong>!</strong> eliminates all results containing the word <em>elliptic</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=dt%3A+b+%26+au%3A+Hilbert">dt: b & au: Hilbert</a></span> <span class="search-explanation" role="cell">The <strong><u>d</u>ocument <u>t</u>ype</strong> is set to books; alternatively: <u>j</u> for <strong>journal articles</strong>, <u>a</u> for <strong>book articles</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=py%3A+2000-2015+cc%3A+%2894A+%7C+11T%29">py: 2000-2015 cc: (94A | 11T)</a></span> <span class="search-explanation" role="cell">Number <strong>ranges</strong> are accepted. Terms can be grouped within <strong><u>(</u>parentheses<u>)</u></strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=la%3A+chinese">la: chinese</a></span> <span class="search-explanation" role="cell">Find documents in a given <strong><u>la</u>nguage</strong>. <a href="http://en.wikipedia.org/wiki/ISO_639-1">ISO 639-1</a> language codes can also be used.</span> </div> </div> <div id="help-fields"> <h2>Fields</h2> <table> <tr> <td class="nowrap padding" role="rowheader"><strong>any</strong></td> <td class="padding">anywhere</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>an</strong></td> <td class="padding">internal document identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>au</strong></td> <td class="padding">author, editor</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ai</strong></td> <td class="padding">internal author identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ti</strong></td> <td class="padding">title</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>la</strong></td> <td class="padding">language</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>so</strong></td> <td class="padding">source</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ab</strong></td> <td class="padding">review, abstract</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>py</strong></td> <td class="padding">publication year</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>rv</strong></td> <td class="padding">reviewer</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>cc</strong></td> <td class="padding">MSC code</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ut</strong></td> <td class="padding">uncontrolled term</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>dt</strong></td> <td class="padding" colspan="4">document type (<strong>j</strong>: journal article; <strong>b</strong>: book; <strong>a</strong>: book article)</td> </tr> </table> </div> <div id="help-operators"> <h2>Operators</h2> <table> <tr> <td class="nowrap padding" role="rowheader">a <strong>&</strong> b</td> <td class="padding">logic and</td> </tr> <tr> <td class="nowrap padding" role="rowheader">a <strong>|</strong> b</td> <td class="padding">logic or</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>!</strong>ab</td> <td class="padding">logic not</td> </tr> <tr> <td class="nowrap padding" role="rowheader">abc<strong>*</strong></td> <td class="padding">right wildcard</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>"</strong>ab c<strong>"</strong></td> <td class="padding">phrase</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>(</strong>ab c<strong>)</strong></td> <td class="padding">parentheses</td> </tr> </table> </div> <p> See also our <a href="/general-help/">General Help</a>. </p></div> </div> </form> <div class="clearfix"></div> </div> <div class="content-shadow"></div> </div> </div> <div id="body"> <div id="main"> <div class="messages"> </div> <div id="documents"> <div class="content-main"> <div class="content-item"><div class="item"> <article> <div class="author"><a href="/authors/?q=ai%3Aheydari.abbas%7Cheydari.abbas.1" title="Author Profile">Heydari, Abbas</a>; <a href="/authors/jalali.abdolrahim" title="Author Profile">Jalali, Abdolrahim</a>; <a href="/authors/nemati.ali" title="Author Profile">Nemati, Ali</a></div> <h2 class="title"> <strong>Buckling analysis of circular functionally graded plate under uniform radial compression including shear deformation with linear and quadratic thickness variation on the Pasternak elastic foundation.</strong> <i>(English)</i> <a class="label nowrap" href="/1443.74055">Zbl 1443.74055</a> </h2> <div class="source"> <a href="/serials/1551" title="Journal Profile">Appl. Math. Modelling</a> <a href="/?q=in%3A444036" title="Articles in this Issue">41, 494-507 (2017)</a>. </div> <div class="abstract">Summary: A numerical scheme for buckling analysis of functionally graded circular plate (FGCP) subjected to uniform radial compression including shear deformation rested on Pasternak elastic foundation is presented. The linear and quadratic thickness variation patterns with various boundary conditions are considered. A modified Euler-Lagrange equation is achieved and then solved by converting differential equation to a nonlinear algebraic system of equations. Also, based on traction-free surface without using shear correction factor, a new approach by considering shear deformation for buckling analysis of FGCP rested on elastic foundation is carried out. The stability equation based on shear stress-free surface is solved by the spectral Ritz method. The spectral Ritz method has good flexibility in the sense of satisfying the boundary conditions. The effects of both linear and quadratic thickness variations and Poisson’s ratio are investigated. By taking small numbers of the basis, the outcomes in literature are improved.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7151216">Cited in <strong>6</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A74-10" title="MSC2020">74-10</a> </td> <td class="space"> Mathematical modeling or simulation for problems pertaining to mechanics of deformable solids </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74K20" title="MSC2020">74K20</a> </td> <td class="space"> Plates </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74G60" title="MSC2020">74G60</a> </td> <td class="space"> Bifurcation and buckling </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Abuckling">buckling</a>; <a href="/?q=ut%3Afunctionally+graded+circular+plate">functionally graded circular plate</a>; <a href="/?q=ut%3Ahigher+order+shear+deformation+theory">higher order shear deformation theory</a>; <a href="/?q=ut%3APasternak+elastic+foundation">Pasternak elastic foundation</a>; <a href="/?q=ut%3AEuler-Lagrange">Euler-Lagrange</a>; <a href="/?q=ut%3Aspectral+Ritz+method">spectral Ritz method</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1443.74055" data-ciurl="/ci/07151216" data-biburl="/bibtex/07151216.bib" data-amsurl="/amsrefs/07151216.bib" data-xmlurl="/xml/07151216.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07151216.pdf" title="Zbl 1443.74055 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.apm.2016.09.012" aria-label="DOI for “Buckling analysis of circular functionally graded plate under uniform radial compression including shear deformation with linear and quadratic thickness variation on the Pasternak elastic foundation”" title="10.1016/j.apm.2016.09.012">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Suresh, S.; Mortensen, A., Fundamentals of Functionally Graded Materials (1998), Maney: Maney London</td> </tr><tr> <td>[2]</td> <td class="space">Miyamoto, Y.; Kaysser, W. A.; Rabin, B. H.; Kawasaki, A.; Ford, R. G., Functionally graded materials: Design, Processing and Applications (1999), Springer-Verlag: Springer-Verlag New York</td> </tr><tr> <td>[3]</td> <td class="space">Gasik, M.; Zhang, B.; Biest, O.; Vleugels, J.; Put, S., Design and fabrication of symmetric FGM plates, Mater. Sci. Forum, 423-425, 23-28 (2003)</td> </tr><tr> <td>[4]</td> <td class="space">Movchan, B. A.; Yu, K., Yakovchukgraded thermal barrier coatings, deposited by EB-PVD, Surf. Coatings Technol., 188-189, 85-92 (2004)</td> </tr><tr> <td>[5]</td> <td class="space">Vecchio, K. S., Synthetic multifunctional metallic-intermetallic laminate composites, J. Miner. Metals Mater. Soc., 57, 25-31 (2005)</td> </tr><tr> <td>[6]</td> <td class="space">EL-Wazery, M. S.; EL-Desouky, A. R., A review on functionally graded ceramic-metal materials, J. Mater. Environ. Sci., 6, 1369-1376 (2015)</td> </tr><tr> <td>[7]</td> <td class="space">Brush, D.; Almroth, B., Bucking of Bars, Plates and Shells (1975), McGraw-Hill: McGraw-Hill New York · <a href="/0352.73040" class="nowrap">Zbl 0352.73040</a></td> </tr><tr> <td>[8]</td> <td class="space">Zheng, X. J., The Theory and Application for Large Deflection of Circular Plate, Jilin Science Technology Press, 45-90 (1990)</td> </tr><tr> <td>[9]</td> <td class="space">Chen, J. W.; Liu, Y. Q.; Liu, W.; Su, X. Y., Thermal buckling analysis of truss-core sandwich plates, Appl. Math. Mech. Eng., 34, 1177-1186 (2013)</td> </tr><tr> <td>[10]</td> <td class="space">Chu, F.; He, J.; Wang, L.; Zhong, Z., Buckling analysis of functionally graded thin plate with in-plane material inhomogeneity, Eng. Anal. Bound. Elem., 65, 112-125 (2016) · <a href="/1403.74031" class="nowrap">Zbl 1403.74031</a></td> </tr><tr> <td>[11]</td> <td class="space">Mohammadi, M.; Saidi, A. R.; Jomehzadeh, E., A novel analytical approach for the buckling analysis of moderately thick functionally graded rectangular plates with two simply supported opposite edges, Proc. Inst. Mech. Eng. C J. Mech., 224, 1831-1841 (2010)</td> </tr><tr> <td>[12]</td> <td class="space">Tung, H. V.; Duc, N. D., Nonlinear analysis of stability for functionally graded plates under mechanical and thermal loads, Compos. Struct., 92, 1184-1191 (2010)</td> </tr><tr> <td>[13]</td> <td class="space">Bedroud, M.; Nazemnezhad, R.; Hosseini-Hashemi, S.; Valixani, M., Buckling of FG circular/annular mindlin nanoplates with an internal ring support using nonlocal elasticity, Appl. Math. Model., 40, 3185-3210 (2016) · <a href="/1452.74043" class="nowrap">Zbl 1452.74043</a></td> </tr><tr> <td>[14]</td> <td class="space">Sepiani, H. A.; Rastgoo, A.; Ebrahimi, F.; Arani, A. G., Vibration and buckling analysis of two-layered functionally graded cylindrical shell, considering the effects of transverse shear and rotary inertia, Mater. Des., 31, 1063-1069 (2010)</td> </tr><tr> <td>[15]</td> <td class="space">Naderi, A.; Saidi, A. R., On pre-buckling configuration of functionally graded mindlin rectangular plates, Mech. Res. Commun., 37, 535-538 (2010) · <a href="/1272.74201" class="nowrap">Zbl 1272.74201</a></td> </tr><tr> <td>[16]</td> <td class="space">Kulkarni, K.; Singh, B. N.; Maiti, D. K., Analytical solution for bending and buckling analysis of functionally graded plates using inverse trigonometric shear deformation theory, Compos. Struct., 134, 147-157 (2015)</td> </tr><tr> <td>[17]</td> <td class="space">Mojahedina, A.; Jabbari, M.; Khorshidvand, A. R.; Eslamic, M. R., Buckling analysis of functionally graded circular plates made of saturated porous materials based on higher order shear deformation theory, Thin Walled Struct., 99, 83-90 (2016)</td> </tr><tr> <td>[18]</td> <td class="space">Bodaghi, M.; Saidi, A. R., Levy-type solution for buckling analysis of thick functionally graded rectangular plates based on the higher-order shear deformation plate theory, Appl. Math. Model., 34, 3659-3673 (2010) · <a href="/1201.74185" class="nowrap">Zbl 1201.74185</a></td> </tr><tr> <td>[19]</td> <td class="space">Bagherizadeh, E.; Kiani, Y.; Eslami, M. R., Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation, Compos. Struct., 93, 063-3071 (2011)</td> </tr><tr> <td>[20]</td> <td class="space">Kiani, Y.; Eslami, M. R., An exact solution for thermal buckling of annular FGM plates on an elastic medium, Compos. Part B Eng., 45, 101-110 (2013)</td> </tr><tr> <td>[21]</td> <td class="space">Ghomshei, M. M.; Abbasi, V., Thermal buckling analysis of annular FGM plate having variable thickness under thermal load of arbitrary distribution by finite element method, J. Mech. Sci. Technol., 27, 1031-1039 (2013)</td> </tr><tr> <td>[22]</td> <td class="space">Aghelinejad, M.; Zare, K.; Ebrahimi, F.; Rastgoo, A., Nonlinear thermomechanical post-buckling analysis of thin functionally graded annular plates based on von-Karman’s plate theory, Mech. Adv. Mater. Struct., 18, 319-326 (2011)</td> </tr><tr> <td>[23]</td> <td class="space">Ghiasian, S. E.; Kiani, Y.; Sadighi, M.; Eslami, M. R., Thermal buckling of shear deformable temperature dependent circular/annular FGM plates, Int. J. Mech. Sci., 81, 137-148 (2014)</td> </tr><tr> <td>[24]</td> <td class="space">Kiani, Y.; Eslami, M. R., Instability of heated circular FGM plates on a partial winkler-type foundation, Acta Mech., 224, 1045-1060 (2013) · <a href="/1398.74209" class="nowrap">Zbl 1398.74209</a></td> </tr><tr> <td>[25]</td> <td class="space">Kiani, Y.; Eslami, M. R., Thermal postbuckling of imperfect circular functionally graded material plates: Examination of Voigt, Mori-Tanaka, and self-consistent schemes, J. Press. Vessel Technol., 137, 021201 (2014)</td> </tr><tr> <td>[26]</td> <td class="space">Li, S.-R.; Zhang, J.-H.; Zhao, Y.-G., Nonlinear thermomechanical post-buckling of circular FGM plate with geometric imperfection, Thin Walled Struct., 45, 528-536 (2007)</td> </tr><tr> <td>[27]</td> <td class="space">Kiani, Y.; Eslami, M. R., Nonlinear thermo-inertial stability of thin circular FGM plates, J. Frankl. Inst., 351, 1057-1073 (2014) · <a href="/1293.74281" class="nowrap">Zbl 1293.74281</a></td> </tr><tr> <td>[28]</td> <td class="space">Ma, L. S.; Wang, T. J., Nonlinear bending and post-buckling of a functionally graded circular plate under mechanical and thermal loadings, Int. J. Solids Struct., 40, 3311-3330 (2003) · <a href="/1038.74547" class="nowrap">Zbl 1038.74547</a></td> </tr><tr> <td>[29]</td> <td class="space">Nguyen, T.-K.; Vo, T. P.; Thai, H. T., Vibration and buckling analysis of functionally graded sandwich plates with improved transverse shear stiffness based on the first-order shear deformation theory, J. Mech. Eng. Sci., 228, 2110-2131 (2014)</td> </tr><tr> <td>[30]</td> <td class="space">Thai, H. T.; Choi, D. H., An efficient and simple refined theory for buckling analysis of functionally graded plates, Appl. Math. Model., 36, 1008-1022 (2012) · <a href="/1243.74044" class="nowrap">Zbl 1243.74044</a></td> </tr><tr> <td>[31]</td> <td class="space">Thai, H.-T.; Vo, T. P., A new sinusoidal shear deformation theory for bending, buckling, and vibration of functionally graded plates, Appl. Math. Model., 37, 3269-3281 (2013) · <a href="/1351.74034" class="nowrap">Zbl 1351.74034</a></td> </tr><tr> <td>[32]</td> <td class="space">Naderi, A.; Saidi, A. R., Exact solution for stability analysis of moderately thick functionally graded sector plates on elastic foundation, Compos. Struct., 93, 629-638 (2011)</td> </tr><tr> <td>[33]</td> <td class="space">Fadaee, M., Buckling analysis of a defective annular graphene sheet in elastic medium, Appl. Math. Model., 40, 1863-1872 (2016) · <a href="/1446.74013" class="nowrap">Zbl 1446.74013</a></td> </tr><tr> <td>[34]</td> <td class="space">Mechab, B.; Mechab, I.; Benaissa, S.; Ameri, M.; Serier, B., Probabilistic analysis of effect of the porosities in functionally graded material nanoplate resting on Winkler-Pasternak elastic foundations, Appl. Math. Model., 40, 738-749 (2016) · <a href="/1446.74036" class="nowrap">Zbl 1446.74036</a></td> </tr><tr> <td>[35]</td> <td class="space">Wattanasakulpong, N.; Chaikittiratana, A., Exact solutions for static and dynamic analyses of carbon nanotube-reinforced composite plates with Pasternak elastic foundation, Appl. Math. Model., 39, 5459-5472 (2015) · <a href="/1443.74125" class="nowrap">Zbl 1443.74125</a></td> </tr><tr> <td>[36]</td> <td class="space">Zhang, D.-G., Nonlinear bending analysis of FGM elliptical plates resting on two-parameter elastic foundations, Appl. Math. Model., 37, 8292-8309 (2013) · <a href="/1426.74209" class="nowrap">Zbl 1426.74209</a></td> </tr><tr> <td>[37]</td> <td class="space">Xu, X. J.; Deng, Z. C., Variational principles for buckling and vibration of MWCNTs modeled by strain gradient theory, Appl. Math. Mech., 35, 1115-1128 (2014) · <a href="/1298.74091" class="nowrap">Zbl 1298.74091</a></td> </tr><tr> <td>[38]</td> <td class="space">Mashayekhi, S., Hybrid Functions in Fractional Calculus (2015), Mississippi State University, Ph.D thesis · <a href="/1403.65034" class="nowrap">Zbl 1403.65034</a></td> </tr><tr> <td>[39]</td> <td class="space">Canuto, C.; Hussaini, M. Y.; Quarteroni, A.; Zang, T. A., Spectral methods: Fundamentals in single domains, Scientific Computation (2006), Springer-Verlag: Springer-Verlag Berlin · <a href="/1093.76002" class="nowrap">Zbl 1093.76002</a></td> </tr><tr> <td>[40]</td> <td class="space">Nemati, A.; Yousefi, S. A., A numerical scheme for solving two-dimensional fractional optimal control problems by the Ritz method combined with fractional operational matrix, IMA J. Math. Control Inf., 1-20 (2016)</td> </tr><tr> <td>[41]</td> <td class="space">Lebedev, L. P.; Cloud, M. J., Basic Calculus of Variations, the Calculus of Variations and Functional Analysis, World Scintific, 1-98 (2003) · <a href="/1042.49001" class="nowrap">Zbl 1042.49001</a></td> </tr><tr> <td>[42]</td> <td class="space">Boyd, J. P., Chebyshev and FourierSpectral Methods (2000), Dover Publications, Inc.: Dover Publications, Inc. New York</td> </tr><tr> <td>[43]</td> <td class="space">Naei, M. H.; Masoumi, M.; Shamekhi, A., Buckling analysis of circular functionally graded material plate having variable thickness under uniform compression by finite-element method, J. Mech. Eng. Sci., 221, 1241-1247 (2007)</td> </tr><tr> <td>[44]</td> <td class="space">Najafizadeh, M. M.; Heydari, H. R., An exact solution for buckling of functionally graded circular plates based on higher order shear deformation plate theory under uniform radial compression, Int. J. Mech. Sci., 50, 603-612 (2008) · <a href="/1264.74065" class="nowrap">Zbl 1264.74065</a></td> </tr><tr> <td>[45]</td> <td class="space">Kreyszig, E., Introductory Functional Analysis with Applications (1978), John Wiley and Sons Inc. · <a href="/0368.46014" class="nowrap">Zbl 0368.46014</a></td> </tr><tr> <td>[46]</td> <td class="space">Rivlin, T. J., An Introduction to the Approximation of Function (1981), Dover Publication · <a href="/0489.41001" class="nowrap">Zbl 0489.41001</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

CINXE.COM

Document Zbl 1443.74055 - zbMATH Open