Document Zbl 1542.93341

<!doctype html> <html lang="en"> <head> <meta charset="utf-8"> <title>Document Zbl 1542.93341 - 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="/1542.93341?"> <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:1542.93341" 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/liu.can" title="Author Profile">Liu, Can</a>; <a href="/authors/mao.xiang" title="Author Profile">Mao, Xiang</a>; <a href="/authors/zheng.qunxian" title="Author Profile">Zheng, Qunxian</a>; <a href="/authors/zhang.hongbin" title="Author Profile">Zhang, Hongbin</a></div> <h2 class="title"> <strong>Unified stability criteria for continuous-time switched T-S fuzzy systems.</strong> <i>(English)</i> <a class="label nowrap" href="/1542.93341">Zbl 1542.93341</a> </h2> <div class="source"> <a href="/serials/6633" title="Journal Profile">IET Control Theory Appl.</a> <a href="/?q=in%3A455568" title="Articles in this Issue">14, No. 16, 2455-2461 (2020)</a>. </div> <div class="abstract">Summary: This study explores the unified stability problem for a class of continuous-time switched non-linear systems, in which the non-linearities are described by the Takagi-Sugeno (T-S) fuzzy models. The ‘unified’ means that the switched system can be arbitrarily composed of either stable or unstable subsystems. Firstly, mode-dependent average dwell time switching strategies are introduced, and the fast switching strategy is improved by a mode-dependent bounded maximum average dwell time. Then, the subsystems are reclassified into ‘switching-stable’ and ‘switching-unstable’ subsystems. The state divergence will be absorbed by the ‘switching-stable’ subsystems. Moreover, by constructing a time-scheduled multiple Lyapunov function, the unified stability conditions are established. Finally, the effectiveness of the achieved results is validated by numerical examples.<br class="zbmathjax-paragraph">© 2021 The Authors. IET Control Theory & Applications published by John Wiley & Sons, Ltd. on behalf of The Institution of Engineering and Technology</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93D30" title="MSC2020">93D30</a> </td> <td class="space"> Lyapunov and storage functions </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C30" title="MSC2020">93C30</a> </td> <td class="space"> Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C42" title="MSC2020">93C42</a> </td> <td class="space"> Fuzzy control/observation systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C10" title="MSC2020">93C10</a> </td> <td class="space"> Nonlinear systems in control theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Astability">stability</a>; <a href="/?q=ut%3Anonlinear+control+systems">nonlinear control systems</a>; <a href="/?q=ut%3Acontrol+system+synthesis">control system synthesis</a>; <a href="/?q=ut%3Atime-varying+systems">time-varying systems</a>; <a href="/?q=ut%3Astability+criteria">stability criteria</a>; <a href="/?q=ut%3Afuzzy+control">fuzzy control</a>; <a href="/?q=ut%3Alinear+systems">linear systems</a>; <a href="/?q=ut%3ALyapunov+methods">Lyapunov methods</a>; <a href="/?q=ut%3Acontinuous+time+systems">continuous time systems</a>; <a href="/?q=ut%3Aasymptotic+stability">asymptotic stability</a>; <a href="/?q=ut%3Afuzzy+systems">fuzzy systems</a>; <a href="/?q=ut%3Aunified+stability+criteria">unified stability criteria</a>; <a href="/?q=ut%3AT-S+fuzzy+systems">T-S fuzzy systems</a>; <a href="/?q=ut%3Aunified+stability+problem">unified stability problem</a>; <a href="/?q=ut%3Anonlinear+systems">nonlinear systems</a>; <a href="/?q=ut%3Anonlinearities">nonlinearities</a>; <a href="/?q=ut%3ATakagi-Sugeno">Takagi-Sugeno</a>; <a href="/?q=ut%3Afuzzy+models">fuzzy models</a>; <a href="/?q=ut%3Aunified+means">unified means</a>; <a href="/?q=ut%3Aswitched+system">switched system</a>; <a href="/?q=ut%3Aunstable+subsystems">unstable subsystems</a>; <a href="/?q=ut%3Amode-dependent+average">mode-dependent average</a>; <a href="/?q=ut%3Atime+switching+strategies">time switching strategies</a>; <a href="/?q=ut%3Afast+switching+strategy">fast switching strategy</a>; <a href="/?q=ut%3Amode-dependent+bounded+maximum+average">mode-dependent bounded maximum average</a>; <a href="/?q=ut%3Aswitching-stable+subsystems">switching-stable subsystems</a>; <a href="/?q=ut%3Atime-scheduled+multiple+Lyapunov+function">time-scheduled multiple Lyapunov function</a>; <a href="/?q=ut%3Aunified+stability+conditions">unified stability conditions</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 1542.93341" data-ciurl="/ci/07916944" data-biburl="/bibtex/07916944.bib" data-amsurl="/amsrefs/07916944.bib" data-xmlurl="/xml/07916944.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07916944.pdf" title="Zbl 1542.93341 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/10.1049/iet-cta.2019.1421" aria-label="DOI for “Unified stability criteria for continuous-time switched T-S fuzzy systems”" title="10.1049/iet-cta.2019.1421">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">Lian, J.; Li, C.; Xia, B., Sampled‐data control of switched linear systems with application to an f‐18 aircraft, IEEE Trans. Ind. Electron., 64, 2, 1332-1340, 2017</td> </tr><tr> <td>[2]</td> <td class="space">Donkers, M. C.F.; Heemels, W. P.M. H.; Wouw, N. V.D., Stability analysis of networked control systems using a switched linear systems approach, IEEE Trans. Autom. Control, 56, 9, 2101-2115, 2011 · <a href="/1368.93465" class="nowrap">Zbl 1368.93465</a></td> </tr><tr> <td>[3]</td> <td class="space">Ma, Y.; Kawakami, H.; Tse, C. K., Bifurcation analysis of switched dynamical systems with periodically moving borders, IEEE Trans. Circuits Syst. I, Reg. Pap., 51, 6, 1184-1193, 2004 · <a href="/1374.37068" class="nowrap">Zbl 1374.37068</a></td> </tr><tr> <td>[4]</td> <td class="space">di Bernardo, M.; Garefalo, F.; Glielmo, L., Switchings, bifurcations, and chaos in DC/DC converters, IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 45, 2, 133-141, 1998</td> </tr><tr> <td>[5]</td> <td class="space">Tanaka, K.; Hori, T.; Wang, H. O., A multiple Lyapunov function approach to stabilization of fuzzy control systems, IEEE Trans. Fuzzy Syst., 11, 4, 582-589, 2003</td> </tr><tr> <td>[6]</td> <td class="space">Feng, G., A survey on analysis and design of model‐based fuzzy control systems, IEEE Trans. Fuzzy Syst., 14, 5, 676-697, 2006</td> </tr><tr> <td>[7]</td> <td class="space">Chang, X. H.; Yang, G. H., Nonfragile $H_{\operatorname{\infty}}$ filtering of continuous‐time fuzzy systems, IEEE Trans. Signal Process., 59, 4, 1528-1538, 2011 · <a href="/1391.93134" class="nowrap">Zbl 1391.93134</a></td> </tr><tr> <td>[8]</td> <td class="space">Shi, S.; Fei, Z.; Shi, P., Asynchronous filtering for discrete‐time switched T‐S fuzzy systems, IEEE Trans. Fuzzy Syst., PP, c, 1-11, 2019</td> </tr><tr> <td>[9]</td> <td class="space">Shi, S.; Fei, Z.; Wang, T., Filtering for switched T‐S fuzzy systems with persistent dwell time, IEEE Trans. Cybern., 49, 5, 1923-1931, 2019</td> </tr><tr> <td>[10]</td> <td class="space">Xiang, W.; Xiao, J., $H_{\operatorname{\infty}}$ finite‐time control for switched nonlinear discrete‐time systems with norm‐bounded disturbance, J. Franklin Inst., 348, 2, 331-352, 2011 · <a href="/1214.93043" class="nowrap">Zbl 1214.93043</a></td> </tr><tr> <td>[11]</td> <td class="space">Zheng, Q.; Zhang, H., Asynchronous $H_{\operatorname{\infty}}$ fuzzy control for a class of switched nonlinear systems via switching fuzzy Lyapunov function approach, Neurocomputing, 182, 178-186, 2016</td> </tr><tr> <td>[12]</td> <td class="space">Wang, J.; Liang, J.; Dobaie, A. M., Controller synthesis for switched T‐S fuzzy positive systems described by the Fornasini‐Marchesini second model, Nonlinear Anal., Hybrid Syst., 29, 247-260, 2018 · <a href="/1388.93054" class="nowrap">Zbl 1388.93054</a></td> </tr><tr> <td>[13]</td> <td class="space">Zheng, Q.; Xu, S.; Zhang, Z., Nonfragile quantized $H_{\operatorname{\infty}}$ filtering for discrete‐time switched T‐S fuzzy systems with local nonlinear models, IEEE Trans. Fuzzy Syst., 2020 · <a href="https://doi.org/10.1109/TFUZZ.2020.2979675" class="nowrap">doi:10.1109/TFUZZ.2020.2979675</a></td> </tr><tr> <td>[14]</td> <td class="space">Du, S.; Qiao, J., Stability analysis and $L_1$ ‐gain controller synthesis of switched positive T-S fuzzy systems with time‐varying delays, Neurocomputing, 275, 2616-2623, 2018</td> </tr><tr> <td>[15]</td> <td class="space">Du, S.; Qiao, J.; Zhao, X., Stability and $L_1$ ‐gain analysis for switched positive T-S fuzzy systems under asynchronous switching, J. Franklin Inst., 355, 13, 5912-5927, 2018 · <a href="/1451.93321" class="nowrap">Zbl 1451.93321</a></td> </tr><tr> <td>[16]</td> <td class="space">Principle, T. L., Basic problems in stability and design of switched systems, IEEE Control Syst., 19, 5, 59-70, 1999 · <a href="/1384.93064" class="nowrap">Zbl 1384.93064</a></td> </tr><tr> <td>[17]</td> <td class="space">Allerhand, L. I.; Shaked, U., Robust stability and stabilization of linear switched systems with dwell time, IEEE Trans. Autom. Control, 56, 2, 381-386, 2011 · <a href="/1368.93487" class="nowrap">Zbl 1368.93487</a></td> </tr><tr> <td>[18]</td> <td class="space">Li, Y.; Zhang, H.; Zhang, L., Equivalence of several stability conditions for switched linear systems with dwell time, Int. J. Robust Nonlinear Control, 29, 1, 306-331, 2019 · <a href="/1411.93143" class="nowrap">Zbl 1411.93143</a></td> </tr><tr> <td>[19]</td> <td class="space">Zhang, L.; Shi, P., Stability, $L_2$ ‐gain and asynchronous $H_{\operatorname{\infty}}$ control of discrete‐time switched systems with average dwell time, IEEE Trans. Autom. Control, 54, 9, 2192-2199, 2009 · <a href="/1367.93191" class="nowrap">Zbl 1367.93191</a></td> </tr><tr> <td>[20]</td> <td class="space">Yin, Y.; Zong, G.; Zhao, X., Improved stability criteria for switched positive linear systems with average dwell time switching, J. Franklin Inst., 354, 8, 3472-3484, 2017 · <a href="/1364.93693" class="nowrap">Zbl 1364.93693</a></td> </tr><tr> <td>[21]</td> <td class="space">Zhao, X.; Zhang, L.; Shi, P., Stability and stabilization of switched linear systems with mode‐dependent average dwell time, IEEE Trans. Autom. Control, 57, 7, 1809-1815, 2012 · <a href="/1369.93290" class="nowrap">Zbl 1369.93290</a></td> </tr><tr> <td>[22]</td> <td class="space">Zhai, G.; Hu, B.; Yasuda, K., Stability analysis of switched systems with stable and unstable subsystems: an average dwell time approach, Int. J. Syst. Sci., 32, 8, 1055-1061, 2001 · <a href="/1022.93043" class="nowrap">Zbl 1022.93043</a></td> </tr><tr> <td>[23]</td> <td class="space">Mao, Y.; Zhang, H.; Xu, S., The exponential stability and asynchronous stabilization of a class of switched nonlinear system via the T‐S fuzzy model, IEEE Trans. Fuzzy Syst., 22, 4, 817-828, 2014</td> </tr><tr> <td>[24]</td> <td class="space">Zheng, Q.; Zhang, H.; Zheng, D., Stability and asynchronous stabilization for a class of discrete‐time switched nonlinear systems with stable and unstable subsystems, Int. J. Control Autom. Syst., 15, 3, 986-994, 2017</td> </tr><tr> <td>[25]</td> <td class="space">Yin, Y.; Zhao, X.; Zheng, X., New stability and stabilization conditions of switched systems with mode‐dependent average dwell time, Circuits Syst. Signal Process., 36, 1, 82-98, 2017 · <a href="/1368.93581" class="nowrap">Zbl 1368.93581</a></td> </tr><tr> <td>[26]</td> <td class="space">Li, L.; Liu, L.; Yin, Y., Stability analysis for discrete‐time switched nonlinear system under MDADT switching, IEEE Access, 5, 18646-18653, 2017</td> </tr><tr> <td>[27]</td> <td class="space">Zhao, X.; Shi, P.; Yin, Y., New results on stability of slowly switched systems: a multiple discontinuous lyapunov function approach, IEEE Trans. Autom. Control, 62, 7, 3502-3509, 2017 · <a href="/1370.34108" class="nowrap">Zbl 1370.34108</a></td> </tr><tr> <td>[28]</td> <td class="space">Zhang, H.; Xie, D.; Zhang, H., Stability analysis for discrete‐time switched systems with unstable subsystems by a mode‐dependent average dwell time approach, ISA Trans., 53, 4, 1081-1086, 2014</td> </tr><tr> <td>[29]</td> <td class="space">Xie, D.; Zhang, H.; Zhang, H., Exponential stability of switched systems with unstable subsystems: a mode‐dependent average dwell time approach, Circuits Syst. Signal Process., 32, 6, 3093-3105, 2013</td> </tr><tr> <td>[30]</td> <td class="space">Xiang, W.; Xiao, J., Stabilization of switched continuous‐time systems with all modes unstable via dwell time switching, Automatica, 50, 3, 940-945, 2014 · <a href="/1298.93283" class="nowrap">Zbl 1298.93283</a></td> </tr><tr> <td>[31]</td> <td class="space">Zhao, X.; Yin, Y.; Niu, B., Stabilization for a class of switched nonlinear systems with novel average dwell time switching by T‐S fuzzy modeling, IEEE Trans. Cybern., 46, 8, 1952-1957, 2016</td> </tr><tr> <td>[32]</td> <td class="space">Mao, Y.; Zhang, H.; Zhang, Z., Finite‐time stabilization of discrete‐time switched nonlinear systems without stable subsystems via optimal switching signal design, IEEE Trans. Fuzzy Syst., 25, 1, 172-180, 2017</td> </tr><tr> <td>[33]</td> <td class="space">Zhao, X.; Yin, Y.; Zhang, L., Control of switched nonlinear systems via T‐S fuzzy modeling, IEEE Trans. Fuzzy Syst., 24, 1, 235-241, 2016</td> </tr><tr> <td>[34]</td> <td class="space">Mao, X.; Zhu, H.; Chen, W., New results on stability of switched continuous‐time systems with all subsystems unstable, ISA Trans., 87, 28-33, 2019</td> </tr><tr> <td>[35]</td> <td class="space">Mao, X.; Zhu, H.; Chen, W., Results on stability of switched discrete‐time systems with all subsystems unstable, IET Control Theory Appl., 13, 1, 152-158, 2019 · <a href="/1434.93069" class="nowrap">Zbl 1434.93069</a></td> </tr><tr> <td>[36]</td> <td class="space">Liu, C.; Mao, X.; Xu, X., Stability analysis of discrete‐time switched T‐S fuzzy systems with all subsystems unstable, IEEE Access, 7, 50412-50418, 2019</td> </tr><tr> <td>[37]</td> <td class="space">Xu, X.; Mao, X.; Li, Y., New result on robust stability of switched systems with all subsystems unstable, IET Control Theory Appl., 13, 13, 2138-2145, 2019 · <a href="/1544.93614" class="nowrap">Zbl 1544.93614</a></td> </tr><tr> <td>[38]</td> <td class="space">Luo, S.; Deng, F.; Chen, W. H., Unified dwell time‐based stability and stabilization criteria for switched linear stochastic systems and their application to intermittent control, Int. J. Robust Nonlinear Control, 28, 6, 2014-2030, 2018 · <a href="/1390.93841" class="nowrap">Zbl 1390.93841</a></td> </tr><tr> <td>[39]</td> <td class="space">Fei, Z.; Shi, S.; Wang, T., Improved stability criteria for discrete‐time switched T‐S fuzzy systems, IEEE Trans. Syst. Man Cybernet., Syst., PP, 1-9, 2019</td> </tr><tr> <td>[40]</td> <td class="space">Zhao, X.; Yin, S.; Li, H., Switching stabilization for a class of slowly switched systems, IEEE Trans. Autom. Control, 60, 1, 221-226, 2015 · <a href="/1360.93584" class="nowrap">Zbl 1360.93584</a></td> </tr><tr> <td>[41]</td> <td class="space">Zhai, G.; Hu, B.; Yasuda, K., Stability analysis of switched systems with stable and unstable subsystems: an average dwell time approach, Int. J. Syst. Sci., 32, 8, 1055-1061, 2001 · <a href="/1022.93043" class="nowrap">Zbl 1022.93043</a></td> </tr><tr> <td>[42]</td> <td class="space">Xiang, W.; Xiao, J., Stabilization of switched continuous‐time systems with all modes unstable via dwell time switching, Automatica, 50, 3, 940-945, 2014 · <a href="/1298.93283" class="nowrap">Zbl 1298.93283</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 1542.93341 - zbMATH Open