Document Zbl 1460.90114

<!doctype html> <html lang="en"> <head> <meta charset="utf-8"> <title>Document Zbl 1460.90114 - 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=in%3A459328+ai%3Aanjos.miguel-f"> <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="in:459328 ai:anjos.miguel-f" 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/anjos.miguel-f" title="Author Profile">Anjos, Miguel F.</a>; <a href="/authors/vieira.manuel-v-c" title="Author Profile">Vieira, Manuel V. C.</a></div> <h2 class="title"> <strong>Mathematical optimization approach for facility layout on several rows.</strong> <i>(English)</i> <a class="label nowrap" href="/1460.90114">Zbl 1460.90114</a> </h2> <div class="source"> <a href="/serials/4920" title="Journal Profile">Optim. Lett.</a> <a href="/?q=in%3A459328" title="Articles in this Issue">15, No. 1, 9-23 (2021)</a>. </div> <div class="abstract">Summary: The facility layout problem is concerned with finding an arrangement of non-overlapping indivisible departments within a facility so as to minimize the total expected flow cost. In this paper we consider the special case of multi-row layout in which all the departments are to be placed in three or more rows, and our focus is on, for the first time, solutions for large instances. We first propose a new mixed integer linear programming formulation that uses continuous variables to represent the departments’ location in both $x$ and $y$ coordinates, where $x$ represents the position of a department within a row and $y$ represents the row assigned to the department. We prove that this formulation always achieves an optimal solution with integer values of $y$, but it is limited to solving instances with up to 13 departments. This limitation motivates the application of a two-stage optimization algorithm that combines two mathematical optimization models by taking the output of the first-stage model as the input of the second-stage model. This algorithm is, to the best of our knowledge, the first one in the literature reporting solutions for instances with up to 100 departments.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7315886">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C11" title="MSC2020">90C11</a> </td> <td class="space"> Mixed integer programming </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C90" title="MSC2020">90C90</a> </td> <td class="space"> Applications of mathematical programming </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Afacilities+planning+and+design">facilities planning and design</a>; <a href="/?q=ut%3Aunequal-areas+facility+layout">unequal-areas facility layout</a>; <a href="/?q=ut%3Arow+layout">row layout</a>; <a href="/?q=ut%3Amixed+integer+linear+programming">mixed integer linear programming</a>; <a href="/?q=ut%3Acontinuous+optimization">continuous optimization</a></div> <div class="software"> <h3>Software:</h3><a href="/software/31820">RowLayout</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 1460.90114" data-ciurl="/ci/07315886" data-biburl="/bibtex/07315886.bib" data-amsurl="/amsrefs/07315886.bib" data-xmlurl="/xml/07315886.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07315886.pdf" title="Zbl 1460.90114 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/10.1007/s11590-020-01621-z" aria-label="DOI for “Mathematical optimization approach for facility layout on several rows”" title="10.1007/s11590-020-01621-z">DOI</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Amaral, ARS, A new lower bound for the single row facility layout problem, Discrete Appl. Math., 157, 1, 183-190 (2009) · <a href="/1155.90413" class="nowrap">Zbl 1155.90413</a> · <a href="https://doi.org/10.1016/j.dam.2008.06.002" class="nowrap">doi:10.1016/j.dam.2008.06.002</a></td> </tr><tr> <td>[2]</td> <td class="space">Amaral, ARS, Optimal solutions for the double row layout problem, Optim. Lett., 7, 2, 407-413 (2013) · <a href="/1267.90116" class="nowrap">Zbl 1267.90116</a> · <a href="https://doi.org/10.1007/s11590-011-0426-8" class="nowrap">doi:10.1007/s11590-011-0426-8</a></td> </tr><tr> <td>[3]</td> <td class="space">Amaral, ARS, A mixed-integer programming formulation for the double row layout of machines in manufacturing systems, Int. J. Prod. Res., 57, 1, 34-47 (2019) · <a href="https://doi.org/10.1080/00207543.2018.1457811" class="nowrap">doi:10.1080/00207543.2018.1457811</a></td> </tr><tr> <td>[4]</td> <td class="space">Anjos, MF; Kennings, A.; Vannelli, A., A semidefinite optimization approach for the single-row layout problem with unequal dimensions, Discrete Optim., 2, 2, 113-122 (2005) · <a href="/1077.90046" class="nowrap">Zbl 1077.90046</a> · <a href="https://doi.org/10.1016/j.disopt.2005.03.001" class="nowrap">doi:10.1016/j.disopt.2005.03.001</a></td> </tr><tr> <td>[5]</td> <td class="space">Anjos, MF; Vannelli, A., An attractor-repeller approach to floor planning, Math. Methods Oper. Res., 56, 1, 3-27 (2002) · <a href="/1023.90036" class="nowrap">Zbl 1023.90036</a> · <a href="https://doi.org/10.1007/s001860200197" class="nowrap">doi:10.1007/s001860200197</a></td> </tr><tr> <td>[6]</td> <td class="space">Anjos, MF; Vannelli, A., A new mathematical-programming framework for facility-layout design, INFORMS J. Comput., 18, 1, 111-118 (2006) · <a href="/1241.90075" class="nowrap">Zbl 1241.90075</a> · <a href="https://doi.org/10.1287/ijoc.1040.0103" class="nowrap">doi:10.1287/ijoc.1040.0103</a></td> </tr><tr> <td>[7]</td> <td class="space">Anjos, MF; Vannelli, A., Computing globally optimal solutions for single-row layout problems using semidefinite programmingand cutting planes, INFORMS J. Comput., 20, 4, 611-617 (2008) · <a href="/1243.90174" class="nowrap">Zbl 1243.90174</a> · <a href="https://doi.org/10.1287/ijoc.1080.0270" class="nowrap">doi:10.1287/ijoc.1080.0270</a></td> </tr><tr> <td>[8]</td> <td class="space">Anjos, MF; Vieira, MV, An improved two-stage optimization-based framework for unequal-areas facility layout, Optim. Lett., 10, 7, 1379-1392 (2016) · <a href="/1355.90096" class="nowrap">Zbl 1355.90096</a> · <a href="https://doi.org/10.1007/s11590-016-1008-6" class="nowrap">doi:10.1007/s11590-016-1008-6</a></td> </tr><tr> <td>[9]</td> <td class="space">Anjos, MF; Vieira, MVC, Mathematical optimization approaches for facility layout problems: the state-of-the-art and future research directions, Eur. J. Oper. Res., 261, 1, 1-16 (2017) · <a href="/1403.90467" class="nowrap">Zbl 1403.90467</a> · <a href="https://doi.org/10.1016/j.ejor.2017.01.049" class="nowrap">doi:10.1016/j.ejor.2017.01.049</a></td> </tr><tr> <td>[10]</td> <td class="space">Anjos, MF; Yen, G., Provably near-optimal solutions for very large single-row facility layout problems, Optim. Methods Softw., 24, 4, 805-817 (2009) · <a href="/1180.90258" class="nowrap">Zbl 1180.90258</a> · <a href="https://doi.org/10.1080/10556780902917735" class="nowrap">doi:10.1080/10556780902917735</a></td> </tr><tr> <td>[11]</td> <td class="space">Chae, J.; Regan, AC, A mixed integer programming model for a double row layout problem, Comput. Ind. Eng., 140, 106244 (2020) · <a href="https://doi.org/10.1016/j.cie.2019.106244" class="nowrap">doi:10.1016/j.cie.2019.106244</a></td> </tr><tr> <td>[12]</td> <td class="space">Chung, J.; Tanchoco, JMA, The double row layout problem, Int. J. Prod. Res., 48, 3, 709-727 (2010) · <a href="/1197.90282" class="nowrap">Zbl 1197.90282</a> · <a href="https://doi.org/10.1080/00207540802192126" class="nowrap">doi:10.1080/00207540802192126</a></td> </tr><tr> <td>[13]</td> <td class="space">Dahlbeck, M.; Fischer, A.; Fischer, F., Decorous combinatorial lower bounds for row layout problems, Eur. J. Oper. Res., 286, 3, 929-944 (2020) · <a href="/1443.90238" class="nowrap">Zbl 1443.90238</a> · <a href="https://doi.org/10.1016/j.ejor.2020.04.010" class="nowrap">doi:10.1016/j.ejor.2020.04.010</a></td> </tr><tr> <td>[14]</td> <td class="space">Etawil, H., Areibi, S., Vannelli, A.: Attractor-repeller approach for global placement. In: Proceedings of the 1999 IEEE/ACM International Conference on Computer-Aided Design, pp. 20-24 (1999)</td> </tr><tr> <td>[15]</td> <td class="space">Fischer, A.; Fischer, F.; Hungerländer, P., New exact approaches to row layout problems, Math. Program. Comput., 11, 4, 703-754 (2019) · <a href="/1432.90085" class="nowrap">Zbl 1432.90085</a> · <a href="https://doi.org/10.1007/s12532-019-00162-6" class="nowrap">doi:10.1007/s12532-019-00162-6</a></td> </tr><tr> <td>[16]</td> <td class="space">Gen, M.; Cheng, R., Genetic Algorithms and Engineering Design (1997), New York: Wiley, New York</td> </tr><tr> <td>[17]</td> <td class="space">Guan, C.; Zhang, Z.; Li, Y., A flower pollination algorithm for the double-floor corridor allocation problem, Int. J. Prod. Res., 57, 20, 6506-6527 (2019) · <a href="https://doi.org/10.1080/00207543.2019.1566673" class="nowrap">doi:10.1080/00207543.2019.1566673</a></td> </tr><tr> <td>[18]</td> <td class="space">Heragu, SS; Kusiak, A., Machine layout problem in flexible manufacturing systems, Oper. Res., 36, 2, 258-268 (1988) · <a href="https://doi.org/10.1287/opre.36.2.258" class="nowrap">doi:10.1287/opre.36.2.258</a></td> </tr><tr> <td>[19]</td> <td class="space">Heragu, SS; Kusiak, A., Efficient models for the facility layout problem, Eur. J. Oper. Res., 53, 1, 1-13 (1991) · <a href="/0726.90024" class="nowrap">Zbl 0726.90024</a> · <a href="https://doi.org/10.1016/0377-2217(91)90088-D" class="nowrap">doi:10.1016/0377-2217(91)90088-D</a></td> </tr><tr> <td>[20]</td> <td class="space">Heragu, SS, Facilities Design (2008), Boca Raton: CRC Press, Boca Raton</td> </tr><tr> <td>[21]</td> <td class="space">Hosseini-Nasab, H.; Fereidouni, S.; Fatemi Ghomi, SMT; Fakhrzad, MB, Classification of facility layout problems: a review study, Int. J. Adv. Manuf. Technol., 94, 1-4, 957-977 (2018) · <a href="https://doi.org/10.1007/s00170-017-0895-8" class="nowrap">doi:10.1007/s00170-017-0895-8</a></td> </tr><tr> <td>[22]</td> <td class="space">Hungerländer, P., Anjos, M. F.: A Semidefinite Optimization Approach to Space-Free Multi-Row Facility Layout. Cahier du GERAD G-2012-03 (2012) · <a href="/1346.90500" class="nowrap">Zbl 1346.90500</a></td> </tr><tr> <td>[23]</td> <td class="space">Hungerländer, P.; Rendl, F., A computational study and survey of methods for the single-row facility layout problem, Comput. Optim. Appl., 55, 1, 1-20 (2013) · <a href="/1272.90070" class="nowrap">Zbl 1272.90070</a> · <a href="https://doi.org/10.1007/s10589-012-9505-8" class="nowrap">doi:10.1007/s10589-012-9505-8</a></td> </tr><tr> <td>[24]</td> <td class="space">Hungerländer, P.; Anjos, MF, A semidefinite optimization-based approach for global optimization of multi-row facility layout, Eur. J. Oper. Res., 245, 1, 46-61 (2015) · <a href="/1346.90500" class="nowrap">Zbl 1346.90500</a> · <a href="https://doi.org/10.1016/j.ejor.2015.02.049" class="nowrap">doi:10.1016/j.ejor.2015.02.049</a></td> </tr><tr> <td>[25]</td> <td class="space">Jankovits, I.; Luo, C.; Anjos, MF; Vannelli, A., A convex optimisation framework for the unequal-areas facility layout problem, Eur. J. Oper. Res., 214, 2, 199-215 (2011) · <a href="/1218.90102" class="nowrap">Zbl 1218.90102</a> · <a href="https://doi.org/10.1016/j.ejor.2011.04.013" class="nowrap">doi:10.1016/j.ejor.2011.04.013</a></td> </tr><tr> <td>[26]</td> <td class="space">Keller, B.; Buscher, U., Single row layout models, Eur. J. Oper. Res., 245, 3, 629-644 (2015) · <a href="/1346.90501" class="nowrap">Zbl 1346.90501</a> · <a href="https://doi.org/10.1016/j.ejor.2015.03.016" class="nowrap">doi:10.1016/j.ejor.2015.03.016</a></td> </tr><tr> <td>[27]</td> <td class="space">Kothari, R.; Ghosh, D., The single row facility layout problem: state of the art, Opsearch, 49, 4, 442-462 (2012) · <a href="/1260.90004" class="nowrap">Zbl 1260.90004</a> · <a href="https://doi.org/10.1007/s12597-012-0091-4" class="nowrap">doi:10.1007/s12597-012-0091-4</a></td> </tr><tr> <td>[28]</td> <td class="space">Luo, C.; Anjos, MF; Vannelli, A., A nonlinear optimization methodology for VLSI fixed-outline floorplanning, J. Comb. Optim., 16, 4, 378-401 (2008) · <a href="/1163.90715" class="nowrap">Zbl 1163.90715</a> · <a href="https://doi.org/10.1007/s10878-008-9148-y" class="nowrap">doi:10.1007/s10878-008-9148-y</a></td> </tr><tr> <td>[29]</td> <td class="space">Maganha, I.; Silva, C.; Ferreira, LMDF, The layout design in reconfigurable manufacturing systems: a literature review, Int. J. Adv. Manuf. Technol., 105, 1-4, 683-700 (2019) · <a href="https://doi.org/10.1007/s00170-019-04190-3" class="nowrap">doi:10.1007/s00170-019-04190-3</a></td> </tr><tr> <td>[30]</td> <td class="space">Nemhauser, G., Wolsey, L.: Integral polyhedra. In: Nemhauser, G., Wolsey, L. (eds.) Integer and Combinatorial Optimization (2014)</td> </tr><tr> <td>[31]</td> <td class="space">Safarzadeh, S., Koosha: Solving an extended multi-row facility layout problem with fuzzy clearances using GA, Appl Soft Comput, 61, 819-831 (2017) · <a href="https://doi.org/10.1016/j.asoc.2017.09.003" class="nowrap">doi:10.1016/j.asoc.2017.09.003</a></td> </tr><tr> <td>[32]</td> <td class="space">Secchin, LD; Amaral, ARS, An improved mixed-integer programming model for the double row layout of facilities, Optim. Lett., 13, 193-199 (2019) · <a href="/1417.90105" class="nowrap">Zbl 1417.90105</a> · <a href="https://doi.org/10.1007/s11590-018-1263-9" class="nowrap">doi:10.1007/s11590-018-1263-9</a></td> </tr><tr> <td>[33]</td> <td class="space">Simmons, DM, One-dimensional space allocation: an ordering algorithm, Oper. Res., 17, 5, 812-826 (1969) · <a href="/0182.53304" class="nowrap">Zbl 0182.53304</a> · <a href="https://doi.org/10.1287/opre.17.5.812" class="nowrap">doi:10.1287/opre.17.5.812</a></td> </tr><tr> <td>[34]</td> <td class="space">Yang, X.; Cheng, W.; Smith, AE; Amaral, ARS, An improved model for the parallel row ordering problem, J. Oper. Res. Soc., 71, 3, 475-490 (2020) · <a href="https://doi.org/10.1080/01605682.2018.1556570" class="nowrap">doi:10.1080/01605682.2018.1556570</a></td> </tr><tr> <td>[35]</td> <td class="space">Zhang, Z.; Mao, L.; Guan, C.; Zhu, L.; Wang, Y., An improved scatter search algorithm for the corridor allocation problem considering corridor width, Soft. Comput., 24, 1, 461-481 (2020) · <a href="https://doi.org/10.1007/s00500-019-03925-4" class="nowrap">doi:10.1007/s00500-019-03925-4</a></td> </tr><tr> <td>[36]</td> <td class="space">Zhang, Z.; Murray, CC, A corrected formulation for the double row layout problem, Int. J. Prod. Res., 50, 15, 4220-4223 (2012) · <a href="https://doi.org/10.1080/00207543.2011.603371" class="nowrap">doi:10.1080/00207543.2011.603371</a></td> </tr><tr> <td>[37]</td> <td class="space">Zuo, X.; Gao, S.; Zhou, M.; Yang, X.; Zhao, X., A three-stage approach to a multirow parallel machine layout problem, IEEE Trans. Autom. Sci. Eng., 16, 1, 433-447 (2019) · <a href="https://doi.org/10.1109/TASE.2018.2866377" class="nowrap">doi:10.1109/TASE.2018.2866377</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 1460.90114 - zbMATH Open