Document Zbl 07905897

<!doctype html> <html lang="en"> <head> <meta charset="utf-8"> <title>Document Zbl 07905897 - 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="/?q=rf%3A7736127+ai%3Ayang.xiangli"> <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="rf:7736127 ai:yang.xiangli" 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%3Aliu.zhe%7Cliu.zhe.1" title="Author Profile">Liu, Zhe</a>; <a href="/authors/?q=ai%3Acao.yu.1%7Ccao.yu" title="Author Profile">Cao, Yu</a>; <a href="/authors/yang.xiangli" title="Author Profile">Yang, Xiangli</a>; <a href="/authors/liu.lusi" title="Author Profile">Liu, Lusi</a></div> <h2 class="title"> <strong>A new uncertainty measure via belief Rényi entropy in Dempster-Shafer theory and its application to decision making.</strong> <i>(English)</i> <a class="label nowrap" href="/7905897">Zbl 07905897</a> </h2> <div class="source"> <a href="/serials/1568" title="Journal Profile">Commun. Stat., Theory Methods</a> <a href="/?q=in%3A516711" title="Articles in this Issue">53, No. 19, 6852-6868 (2024)</a>. </div> <div class="abstract">Summary: Dempster-Shafer theory (DST) has attracted wide attention in many fields thanks to its strong advantages over probability theory. Whereas the uncertainty measure of basic belief assignment (BBA) in DST is an open and essential problem. The main goal of this article is to propose a new belief Rényi entropy for the uncertainty measure of BBA, which is inspired by generalized Rényi entropy in DST. The proposed belief Rényi entropy satisfies some desirable properties of uncertainty measure. Furthermore, the proposed belief Rényi entropy can be degraded to Rényi entropy when BBA is transformed into a probability distribution. Finally, a new decision-making method is designed based on the proposed belief Rényi entropy. The validity of the proposed belief entropy is verified by some numerical examples and its application to decision-making.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62-XX" title="MSC2020">62-XX</a> </td> <td class="space"> Statistics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3ADempster-Shafer+theory">Dempster-Shafer theory</a>; <a href="/?q=ut%3Abelief+entropy">belief entropy</a>; <a href="/?q=ut%3Abasic+belief+assignment">basic belief assignment</a>; <a href="/?q=ut%3AR%C3%A9nyi+entropy">Rényi entropy</a>; <a href="/?q=ut%3Auncertainty+measure">uncertainty measure</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 07905897" data-ciurl="/ci/07905897" data-biburl="/bibtex/07905897.bib" data-amsurl="/amsrefs/07905897.bib" data-xmlurl="/xml/07905897.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07905897.pdf" title="Zbl 07905897 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/10.1080/03610926.2023.2253342" aria-label="DOI for “A new uncertainty measure via belief Rényi entropy in Dempster-Shafer theory and its application to decision making”" title="10.1080/03610926.2023.2253342">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">Allen, M. R., Stott, P. A., Mitchell, J. F., Schnur, R., and Delworth, T. L.. 2000. Quantifying the uncertainty in forecasts of anthropogenic climate change. Nature407 (6804):617-20. 11034207 doi: .</td> </tr><tr> <td>[2]</td> <td class="space">Dempster, A. P.1967. Upper and lower probabilities induced by a multivalued mapping. The Annals of Mathematical Statistics38 (2):325-39. doi: . · <a href="/0168.17501" class="nowrap">Zbl 0168.17501</a></td> </tr><tr> <td>[3]</td> <td class="space">Deng, Y.2016. Deng entropy. Chaos, Solitons & Fractals91:549-53. doi: . · <a href="/1372.94368" class="nowrap">Zbl 1372.94368</a></td> </tr><tr> <td>[4]</td> <td class="space">Deng, Y.2020. Information volume of mass function. International Journal of Computers Communications & Control15 (6).</td> </tr><tr> <td>[5]</td> <td class="space">Deng, Y., Shi, W., Zhu, Z., and Liu, Q.. 2004. Combining belief functions based on distance of evidence. Decision Support Systems38 (3):489-93.</td> </tr><tr> <td>[6]</td> <td class="space">Doshi, H., Kumar, P., and Yerramilli, V.. 2018. Uncertainty, capital investment, and risk management. Management Science64 (12):5769-86. doi: .</td> </tr><tr> <td>[7]</td> <td class="space">Duan, S., Wen, T., and Jiang, W.. 2019. A new information dimension of complex network based on Rényi entropy. Physica A: Statistical Mechanics and Its Applications516:529-42. doi: .</td> </tr><tr> <td>[8]</td> <td class="space">Dubois, D, and Prade, H.. 1985. A note on measures of specificity for fuzzy sets. International Journal of General Systems10 (4):279-83. doi: . · <a href="/0569.94032" class="nowrap">Zbl 0569.94032</a></td> </tr><tr> <td>[9]</td> <td class="space">Gao, X., Liu, F., Pan, L., Deng, Y., and Tsai, S.. 2019. Uncertainty measure based on Tsallis entropy in evidence theory. International Journal of Intelligent Systems34 (11):3105-20. doi: .</td> </tr><tr> <td>[10]</td> <td class="space">George, T, and Pal, N. R.. 1996. Quantification of conflict in dempster-shafer framework: A new approach. International Journal of General Systems24 (4):407-23. doi: . · <a href="/0856.90153" class="nowrap">Zbl 0856.90153</a></td> </tr><tr> <td>[11]</td> <td class="space">Höhle, U.1987. A general theory of fuzzy plausibility measures. Journal of Mathematical Analysis and Applications127 (2):346-64. doi: . · <a href="/0649.60002" class="nowrap">Zbl 0649.60002</a></td> </tr><tr> <td>[12]</td> <td class="space">Huang, H., Liu, Z., Han, X., Yang, X., and Liu, L.. 2023. A belief logarithmic similarity measure based on Dempster-Shafer theory and its application in multi-source data fusion. Journal of Intelligent & Fuzzy Systems45(3): 4935-47. doi: .</td> </tr><tr> <td>[13]</td> <td class="space">Jiang, W.2018. A correlation coefficient for belief functions. International Journal of Approximate Reasoning103:94-106. doi: . · <a href="/1448.68419" class="nowrap">Zbl 1448.68419</a></td> </tr><tr> <td>[14]</td> <td class="space">Jiroušek, R., and Shenoy, P. P.. 2018. A new definition of entropy of belief functions in the Dempster-Shafer theory. International Journal of Approximate Reasoning92:49-65. doi: . · <a href="/1423.68505" class="nowrap">Zbl 1423.68505</a></td> </tr><tr> <td>[15]</td> <td class="space">Khalaj, F., and Khalaj, M.. 2022. Developed cosine similarity measure on belief function theory: An application in medical diagnosis. Communications in Statistics- Theory and Methods51 (9):2858-69. doi: . · <a href="/07535567" class="nowrap">Zbl 07535567</a></td> </tr><tr> <td>[16]</td> <td class="space">Khalaj, M., and Khalaj, F.. 2021. An improvement decision-making method by similarity and belief function theory. Communications in Statistics - Theory and Methods25 (7):2240-58. doi: . · <a href="/07702505" class="nowrap">Zbl 07702505</a></td> </tr><tr> <td>[17]</td> <td class="space">Khalaj, M., Tavakkoli-Moghaddam, R., Khalaj, F., and Siadat, A.. 2020. New definition of the cross entropy based on the Dempster-Shafer theory and its application in a decision-making process. Communications in Statistics- Theory and Methods49 (4):909-23. doi: . · <a href="/07549069" class="nowrap">Zbl 07549069</a></td> </tr><tr> <td>[18]</td> <td class="space">Klir, B., and Parviz, G. J.. 1992. A note on the measure of discord. In Uncertainty in Artificial Intelligence, 138-41.</td> </tr><tr> <td>[19]</td> <td class="space">Klir, G. J., and Ramer, A.. 1990. Uncertainty in the dempster-shafer theory: A critical re-examination. International Journal of General Systems18 (2):155-66. doi: . · <a href="/0732.60004" class="nowrap">Zbl 0732.60004</a></td> </tr><tr> <td>[20]</td> <td class="space">Krylovas, A., Kosareva, N., and Zavadskas, E. K.. 2017. WEBIRA- Comparative Analysis of Weight Balancing Method. International Journal of Computers Communications & Control12 (2):238 doi: .</td> </tr><tr> <td>[21]</td> <td class="space">Lee, H., and Kwon, H.. 2021. DBF: Dynamic belief fusion for combining multiple object detectors. IEEE Transactions on Pattern Analysis and Machine Intelligence43 (5):1499-514. 31722478 doi: .</td> </tr><tr> <td>[22]</td> <td class="space">Li, X., Liu, Z., Han, X., Liu, N., and Yuan, W.. 2023. An intuitionistic fuzzy version of Hellinger distance measure and its application to decision-making process. Symmetry15 (2):500. doi: .</td> </tr><tr> <td>[23]</td> <td class="space">Lin, Y., Li, Y., Yin, X., and Dou, Z.. Multisensor fault diagnosis modeling based on the evidence theory. IEEE Transactions on Reliability67 (2):513-21. doi: .</td> </tr><tr> <td>[24]</td> <td class="space">Liu, Z.2023. An effective conflict management method based on belief similarity measure and entropy for multi-sensor data fusion. Artificial Intelligence Review 1-28. doi: .</td> </tr><tr> <td>[25]</td> <td class="space">Liu, Z., and Huang, H.. 2023. Comment on “New cosine similarity and distance measures for Fermatean fuzzy sets and TOPSIS approach. Knowledge and Information Systems1-7. doi: .</td> </tr><tr> <td>[26]</td> <td class="space">Liu, Z., Huang, H., and Letchmunan, S.. 2023. Adaptive weighted multi-view evidential Clustering. In International Conference on Artificial Neural Networks, , 1-12.</td> </tr><tr> <td>[27]</td> <td class="space">Loeve, M.2017. Probability theory. Courier Dover Publications. · <a href="/1368.60005" class="nowrap">Zbl 1368.60005</a></td> </tr><tr> <td>[28]</td> <td class="space">Ma, Z-F., Liu, Z., Luo, C., and Song, L.. Evidential classification of incomplete instance based on K-nearest centroid neighbor. Journal of Intelligent & Fuzzy Systems41 (6):7101-15. doi: .</td> </tr><tr> <td>[29]</td> <td class="space">Murphy, C. K.2000. Combining belief functions when evidence conflicts. Decision Support Systems29 (1):1-9. doi: .</td> </tr><tr> <td>[30]</td> <td class="space">Pal, N. R., Bezdek, J. C., and Hemasinha, R.. 1992. Uncertainty measures for evidential reasoning I: A review. International Journal of Approximate Reasoning7 (3-4):165-83. doi: . · <a href="/0769.68112" class="nowrap">Zbl 0769.68112</a></td> </tr><tr> <td>[31]</td> <td class="space">Pan, L., and Deng, Y.. 2018. A new belief entropy to measure uncertainty of basic probability assignments based on belief function and plausibility function. Entropy20 (11):842. doi: .</td> </tr><tr> <td>[32]</td> <td class="space">Pan, Q., Zhou, D., Tang, Y., Li, X., and Huang, J.. 2019. A novel belief entropy for measuring uncertainty in Dempster-Shafer evidence theory framework based on plausibility transformation and weighted Hartley entropy. Entropy21 (2):163. doi: .</td> </tr><tr> <td>[33]</td> <td class="space">Qiang, C., Deng, Y., and Cheong, K. H.. 2022. Information fractal dimension of mass function. Fractals30 (06):2250110. doi: . · <a href="/1512.28003" class="nowrap">Zbl 1512.28003</a></td> </tr><tr> <td>[34]</td> <td class="space">Rényi, A.1961. On measures of entropy and information. In Proc. Fourth Berkeley Symp. Math. Stat. and Probability, Vol. 1, 547-61. Berkeley, CA: University of California Press. · <a href="/0106.33001" class="nowrap">Zbl 0106.33001</a></td> </tr><tr> <td>[35]</td> <td class="space">Sarkar, S., Das, S., and Chaudhuri, S. S.. 2016. Hyper-spectral image segmentation using Rényi entropy based multi-level thresholding aided with differential evolution. Expert Systems with Applications50:120-9. doi: .</td> </tr><tr> <td>[36]</td> <td class="space">Shafer, G.2021. A mathematical theory of evidence. Princeton, NJ: Princeton University Press.</td> </tr><tr> <td>[37]</td> <td class="space">Shannon, C. E.2001. A mathematical theory of communication. ACM Sigmobile Mobile Computing and Communications Review5 (1):3-55. doi: .</td> </tr><tr> <td>[38]</td> <td class="space">Su, J, and Deng, Y.. 2022. An interval method to measure the uncertainty of basic probability assignment. Soft Computing26 (13):6041-50. doi: .</td> </tr><tr> <td>[39]</td> <td class="space">Wang, D., Gao, J., and Wei, D.. 2019. A new belief entropy based on Deng entropy. Entropy21 (10):987. doi: .</td> </tr><tr> <td>[40]</td> <td class="space">Wang, J., Hu, Y., Xiao, F., Deng, X., and Deng, Y.. 2016. A novel method to use fuzzy soft sets in decision making based on ambiguity measure and Dempster-Shafer theory of evidence: An application in medical diagnosis. Artificial Intelligence in Medicine69:1-11. 27235800 doi: .</td> </tr><tr> <td>[41]</td> <td class="space">Xiao, F.2019. Multi-sensor data fusion based on the belief divergence measure of evidences and the belief entropy. Information Fusion46:23-32. doi: .</td> </tr><tr> <td>[42]</td> <td class="space">Xiao, F., Cao, Z., and Jolfaei, A.. A novel conflict measurement in decision-making and its application in fault diagnosis. IEEE Transactions on Fuzzy Systems29 (1):186-97. doi: .</td> </tr><tr> <td>[43]</td> <td class="space">Xiao, F, and Ding, W.. 2019. Divergence measure of Pythagorean fuzzy sets and its application in medical diagnosis. Applied Soft Computing79:254-67. doi: .</td> </tr><tr> <td>[44]</td> <td class="space">Yager, R. R.1983. Entropy and specificity in a mathematical theory of evidence. International Journal of General Systems9 (4):249-60. doi: . · <a href="/0521.94008" class="nowrap">Zbl 0521.94008</a></td> </tr><tr> <td>[45]</td> <td class="space">Yager, R. R.2019. Generalized Dempster-Shafer structures. IEEE Transactions on Fuzzy Systems27 (3):428-35. doi: .</td> </tr><tr> <td>[46]</td> <td class="space">Yan, H., and Deng, Y.. 2020. An improved belief entropy in evidence theory. IEEE Access. 8:57505-16. doi: .</td> </tr><tr> <td>[47]</td> <td class="space">Yin, L., and Deng, Y.. 2018. Toward uncertainty of weighted networks: An entropy-based model. Physica A: Statistical Mechanics and Its Applications508:176-86. doi: .</td> </tr><tr> <td>[48]</td> <td class="space">Yu, R., and Deng, Y.. 2022. A generalization of Rényi entropy for basic probability assignment. Communications in Statistics - Theory and Methods52 (17):6991-7008. doi: . · <a href="/07736127" class="nowrap">Zbl 07736127</a></td> </tr><tr> <td>[49]</td> <td class="space">Zhang, Z., Liu, T., Chen, D., and Zhang, W.. 2014. Novel algorithm for identifying and fusing conflicting data in wireless sensor networks. Sensors (Basel, Switzerland)14 (6):9562-81. 24887039 doi: .</td> </tr><tr> <td>[50]</td> <td class="space">Zhao, Y., Ji, D., Yang, X., Fei, L., and Zhai, C.. 2019. An improved belief entropy to measure uncertainty of basic probability Aassignments based on Deng entropy and belief interval. Entropy21 (11):1122. doi: .</td> </tr><tr> <td>[51]</td> <td class="space">Zhou, D., Tang, Y., and Jiang, W.. 2017. An improved belief entropy and its application in decision-making. Complexity2017:1-15. doi: . · <a href="/1367.93332" class="nowrap">Zbl 1367.93332</a></td> </tr><tr> <td>[52]</td> <td class="space">Zhou, M., Zhu, S.-S., Chen, Y.-W., Wu, J., and Herrera-Viedma, E.. A generalized belief entropy with nNonspecificity and structural conflict. IEEE Transactions on Systems, Man, and Cybernetics: Systems52 (9):5532-45. doi: .</td> </tr><tr> <td>[53]</td> <td class="space">Zhou, Q., and Deng, Y.. 2021. Belief eXtropy: Measure uncertainty from negation. Communications in Statistics - Theory and Methods52 (11):3825-47. doi: . · <a href="/07706270" class="nowrap">Zbl 07706270</a></td> </tr><tr> <td>[54]</td> <td class="space">Zhou, Q., and Deng, Y.. 2022. Higher order information volume of mass function. Information Sciences586:501-13. doi: . · <a href="/1532.94022" class="nowrap">Zbl 1532.94022</a></td> </tr><tr> <td>[55]</td> <td class="space">Zhu, C., Xiao, F., and Cao, Z.. 2022. A generalized Rényi divergence for multi-source information fusion with its application in EEG data analysis. Information Sciences605:225-43. doi: . · <a href="/07814681" class="nowrap">Zbl 07814681</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 07905897 - zbMATH Open