Document Zbl 1550.74220

<!doctype html> <html lang="en"> <head> <meta charset="utf-8"> <title>Document Zbl 1550.74220 - 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="/1550.74220?"> <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:1550.74220" 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/lan.weibin" title="Author Profile">Lan, Weibin</a>; <a href="/authors/fan.shouwen" title="Author Profile">Fan, Shouwen</a>; <a href="/authors/fan.shuai" title="Author Profile">Fan, Shuai</a></div> <h2 class="title"> <strong>A fractal model of elastic-plastic contact between rough surfaces for a low-velocity impact process.</strong> <i>(English)</i> <a class="label nowrap" href="/1550.74220">Zbl 1550.74220</a> </h2> <div class="source"> <a href="/serials/3157" title="Journal Profile">Int. J. Comput. Methods</a> <a href="/?q=in%3A473491" title="Articles in this Issue">18, No. 9, Article ID 2150039, 26 p. (2021)</a>. </div> <div class="abstract">Summary: Under the low-velocity impact conditions, in order to study the contact load variation law of the ellipsoid elastic bodies, an elastic-plastic contact analysis model of rough ellipsoid surfaces is provided based on elastic-plastic fractal theory. A spherical elastic-plastic fractal model considering friction factors is established, and the spherical diameter density distribution function and elastic contact mechanics are used as the solution methods. The two contact surfaces are taken as the research object, and the influence of relevant variables on the contact intensity is analyzed. The analysis results show that the fractal dimension and roughness have a greater effect on contact performance, the contact load is positively related to the surface roughness, and the lower friction coefficient has a weaker effect on the contact load, and the correctness of the present model is verified by comparing finite element simulation results and other studies. The modified spherical contact load function provides a theoretical basis for the friction and wear of the microscopic surface, it can be applied for solving the sliding contact problems with different impact velocities and the surface bearing capacity of the impact parts can be improved.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7446706">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%3A74M15" title="MSC2020">74M15</a> </td> <td class="space"> Contact in solid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74C05" title="MSC2020">74C05</a> </td> <td class="space"> Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74M20" title="MSC2020">74M20</a> </td> <td class="space"> Impact in solid mechanics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Arough+ellipsoid+surface">rough ellipsoid surface</a>; <a href="/?q=ut%3Afractal+model">fractal model</a>; <a href="/?q=ut%3Acontact+load">contact load</a>; <a href="/?q=ut%3Alow-velocity+impact">low-velocity impact</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 1550.74220" data-ciurl="/ci/07446706" data-biburl="/bibtex/07446706.bib" data-amsurl="/amsrefs/07446706.bib" data-xmlurl="/xml/07446706.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07446706.pdf" title="Zbl 1550.74220 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/10.1142/S0219876221500390" aria-label="DOI for “A fractal model of elastic-plastic contact between rough surfaces for a low-velocity impact process”" title="10.1142/S0219876221500390">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">Akemi, N., Tsuha, H. and Cavalca, K. L. [2020] “ Stiffness and damping of elastohydrodynamic line contact applied to cylindrical roller bearing dynamic model,” J. Sound Vib.481, 115-136.</td> </tr><tr> <td>[2]</td> <td class="space">Anders, E. and Bjorn, A. P. [2019] “ Multiscale modelling of train-track interaction phenomena with focus on contact mechanics,” Wear430, 393-400.</td> </tr><tr> <td>[3]</td> <td class="space">Ang, K. K., Dai, J., Tran, M. T. and Luong, V. H. [2014] “ Analysis of high-speed rail accounting for jumping wheel phenomenon,” Int. J. Comp. Meth-Sing.11(3), 1-12. · <a href="/1359.70053" class="nowrap">Zbl 1359.70053</a></td> </tr><tr> <td>[4]</td> <td class="space">Arnold, W., Hartmann, T. and Rottenkolber, E. [2020] “ Filling the gap between hypervelocity and low velocity impacts,” Int. J. Impact Eng.139, 103531.</td> </tr><tr> <td>[5]</td> <td class="space">Ausloos, M. and Berman, D. H. [1985] “ A multivariate Weierstress-Mandelbrot function,” Proc. R. Soc. London. Series A Math. Phys. Sci.400, 331-350. · <a href="/0576.28010" class="nowrap">Zbl 0576.28010</a></td> </tr><tr> <td>[6]</td> <td class="space">Chang, W. R., Etsion, I. and Bogy, D. B. [1998] “ Static friction coefficient model for metallic rough surfaces,” J. Tribol.-T ASME110, 57-63.</td> </tr><tr> <td>[7]</td> <td class="space">Chao, W. and Dandan, L. [2018] “ Multiscale cohesive zone modeling and simulation of high-speed impact, penetration, and fragmentation,” J. Micromech. Microeng.03(01n02), 1850003.</td> </tr><tr> <td>[8]</td> <td class="space">Chen, Q., Xu, F., Liu, P.et al. [2016] “ Research on fractal model of normal contact stiffness between two spheroidal joint surfaces considering friction factor,” Tribol. Int.97, 253-264.</td> </tr><tr> <td>[9]</td> <td class="space">Dyagel, R. V. and Lapshin, V. V. [2011] “ On a nonlinear viscoelastic model of Hunt-Crossley impact,” Mech. Solids46, 798-806.</td> </tr><tr> <td>[10]</td> <td class="space">Flores, P. [2010] “ A parametric study on the dynamic response of planar multibody systems with multiple clearance joints,” Multibody Syst. Dyn.61(4), 633-653. · <a href="/1204.70008" class="nowrap">Zbl 1204.70008</a></td> </tr><tr> <td>[11]</td> <td class="space">Flores, P., Machado, M., Silva, M. T. and Martins, J. M. [2011(a)] “ On the continuous contact force models for soft materials in multibody dynamics,” Multibody Syst. Dyn.25(3), 357-375. · <a href="/1263.70007" class="nowrap">Zbl 1263.70007</a></td> </tr><tr> <td>[12]</td> <td class="space">Flores, P., Koshy, C. S., Lankarani, H. M., Ambrosio, J. and Claro, J. C. P. [2011(b)] “ Numerical and experimental investigation on multibody systems with revolute clearance joints,” Multibody Syst. Dyn.65(4), 383-398.</td> </tr><tr> <td>[13]</td> <td class="space">Gong, W.et al. [2019] “ Adhesion-fatigue dual mode wear model for fractal surfaces in AISI 1045 cylinder-plane contact pairs,” Wear430-431, 327-339.</td> </tr><tr> <td>[14]</td> <td class="space">Greenwood, J. A. and Johnson, K. L. [2006] “ Oscillatory loading of a viscoelastic adhesive contact,” J. Colloid Interface Sci.296, 284-291.</td> </tr><tr> <td>[15]</td> <td class="space">Greenwood, J. A. and Williamson, J. B. P. [1966] “ Contact of nominally flat surfaces,” Proc. R. Soc. London Series A Math. Phys. Sci.295300-319.</td> </tr><tr> <td>[16]</td> <td class="space">Guo, X., Mac, B. B., Zhu, Y. C. [2019] “ A magnification-based multi-asperity (MBMA) model of rough contact without adhesion,” J. Mech. Phys. Solids133, 1-25.</td> </tr><tr> <td>[17]</td> <td class="space">Han, R. X.et al. [2019] “ Equivalent Method of joint interface based on persson contact theory: Virtual material method,” Materials12, 1-10.</td> </tr><tr> <td>[18]</td> <td class="space">Hanaor, D. A. H.et al. [2016] “ Static friction at fractal interfaces,” Tribol. Int.93, 229-238.</td> </tr><tr> <td>[19]</td> <td class="space">Jackon, R. L. and Itzhak, G. [2005] “ A finite element study of elasto-plastic hemispherical contact against a rigid flat,” J. Tribol.-T. Asme.127, 343-354.</td> </tr><tr> <td>[20]</td> <td class="space">Jbily, D., Guingand, M. and de Vaujany, J. P. [2016] “ A wear model for worm gear,” P I Mech. Eng. M-J Eng.230(7-8), 1290-1302.</td> </tr><tr> <td>[21]</td> <td class="space">Kogut, L. and Etsion, I. [1998] “ A static friction model for elastic-plastic contacting rough surfaces,” J. Tribol.-T Asmel.126, 34-40.</td> </tr><tr> <td>[22]</td> <td class="space">Korayem, M. H. and Taheri, M. [2014] “ Modeling of various contact theories for the manipulation of different biological micro/nanoparticles based on AFM,” J. Nanopart. Res.16(1), 1-13.</td> </tr><tr> <td>[23]</td> <td class="space">Korayem, M. H., Mahmoodi, Z., Taheri, M. and Saraee, M. B. [2015a] “ Three-dimensional modeling and simulation of the AFM-based manipulation of spherical biological micro/nanoparticles with the consideration of contact mechanics theories,” P I Mech. Eng. K-J Mul.229, 370-382.</td> </tr><tr> <td>[24]</td> <td class="space">Korayem, M. H., Saraee, M. B., Mahmoodi, Z. and Dehghani, S. [2015b] “ Modeling and simulation of three dimensional manipulations of biological micro/nanoparticles by applying cylindrical contact mechanics models by means of AFM,” J. Nanopart. Res.17, 1-17.</td> </tr><tr> <td>[25]</td> <td class="space">Korayem, M. H. and Khaksar, H., [2019] “ Investigating the impact models for nanoparticles manipulation based on atomic force microscope (according to contact mechanics),” Powder Technol.344, 17-26.</td> </tr><tr> <td>[26]</td> <td class="space">Kudra, G. and Awrejcewicz, J. [2015] “ Application and experimental validation of new computational models of friction forces and rolling resistance,” Acta Mech.226(8), 2831-2848. · <a href="/1329.74210" class="nowrap">Zbl 1329.74210</a></td> </tr><tr> <td>[27]</td> <td class="space">Liu, P., Browning, R. L., Sue, H. J.et al. [2011] “ Quantitative scratch visibility assessment of polymers based on Erichsen and ASTM/ISO scratch testing methodologies,” Polym. Test.30(5), 633-640.</td> </tr><tr> <td>[28]</td> <td class="space">Liu, W. W., Wang, Y. H., Li, X. B., Huang, C. M., Yang, J. F., Pan, G. Z. and Ding, X. J. [2017] “ A theoretical contact mechanics model of machine joint interfaces based on fractal theory,” 4th Int. Conf. Manufacturing and Industrial Technologies (ICMIT), Lisbon, Portugal, .</td> </tr><tr> <td>[29]</td> <td class="space">Liu, Y., Wang, Y. S., Chen, X. and Yu, H. C. [2018] “ A spherical conformal contact model considering frictional and microscopic factors based on fractal theory,” Chaos Soliton Fract.111, 96-107.</td> </tr><tr> <td>[30]</td> <td class="space">Liu, Y. Q., Wang, W. Z., Liang, H.et al. [2020] “ Nonlinear dynamic behavior of angular contact ball bearings under microgravity and gravity,” Int. J. Mech. Sci.20, 1-33.</td> </tr><tr> <td>[31]</td> <td class="space">Liu, Z. F.et al. [2018] “ Time-varying stiffness model of spur gear considering the effect of surface morphology characteristics,” P I Mech. Eng. E-J Pro.233, 242-253.</td> </tr><tr> <td>[32]</td> <td class="space">Majumdar, A. and Bhushan, B. [1991] “ Fractal model of elastic-plastic contact between rough surfaces,” J. Tribol.113, 1-11.</td> </tr><tr> <td>[33]</td> <td class="space">Megalingam, A. and Hanumanth, K. S. [2020] “ A complete elastic-plastic spherical asperity contact model with the effect of isotropic strain hardening,” P I Mech. Eng. C-J Mec.234, 1-10.</td> </tr><tr> <td>[34]</td> <td class="space">Mandelbrot, B. [1967] “ How long is the coast of Britain? Statistical self similarity and fractional dimension,” Science (New York, NY)156, 636-638.</td> </tr><tr> <td>[35]</td> <td class="space">Osama, M. [2012] “ Thermal creep model of rough fractal surfaces in contact: Viscoelastic standard linear solid,” Ind. Lubr. Tribol.64, 208-216.</td> </tr><tr> <td>[36]</td> <td class="space">Pan, W. J., Li, X. P. and Guo, N. [2017(a)] “ Three-dimensional fractal model of normal contact damping of dry-friction rough surface,” Adv. Mech. Eng.9(3) 1-11.</td> </tr><tr> <td>[37]</td> <td class="space">Pan, W. J., Li, X. P. and Wang, L. L. [2017(b)] “ A normal contact stiffness fractal prediction model of dryfriction rough surface and experimental verification,” Eur. J. Mech. A/Solids66, 94-102. · <a href="/1406.74512" class="nowrap">Zbl 1406.74512</a></td> </tr><tr> <td>[38]</td> <td class="space">Pan, W. J., Li, X. P. and Wang, L. L. [2017(c)] “ Influence of surface topography on three-dimensional fractal model of sliding friction,” AIP Adv.7(8), 309-321.</td> </tr><tr> <td>[39]</td> <td class="space">Pan, W. J., Li, X. P., Wang, L. L., Mu, J. X. and Yang, Z. M. [2018] “ A loading fractal prediction model developed for dry-friction rough joint surfaces considering elastic-plastic contact,” Acta Mech.229(5), 2149-2162. · <a href="/1390.74145" class="nowrap">Zbl 1390.74145</a></td> </tr><tr> <td>[40]</td> <td class="space">Pan, W. J., Li, X. P. and Wang, X. [2020] “ Contact mechanics of elastic-plastic fractal surfaces and static friction analysis of asperity scale,” Eng. Comput.7, 1-20.</td> </tr><tr> <td>[41]</td> <td class="space">Sista, S. N. B. [2014] Dry Static Friction in Metals: Experiments and Micro-Asperity Based Modeling (University of Cincinnati, Cincinnati).</td> </tr><tr> <td>[42]</td> <td class="space">Tanaka, N. [2001] “ A new calculation method of Hertz elliptical contact pressure,” J. Tribol.-T Asme.123(4), 887-889.</td> </tr><tr> <td>[43]</td> <td class="space">Tran, M. T., Ang, K. K. and Luong, V. H. [2017] “ Vertical dynamic response of high-speed rails during sudden deceleration,” Int. J. Comp. Meth-Sing.14(2), 1-14. · <a href="/1404.74119" class="nowrap">Zbl 1404.74119</a></td> </tr><tr> <td>[44]</td> <td class="space">Wang, S. and Komvopoulos, K. [1994] “ A fractal theory of the interfacial temperature distribution in the slow sliding regime: Part I Elastic contact and heat transfer analysis,” J. Tribol.-T ASME116, 812-823.</td> </tr><tr> <td>[45]</td> <td class="space">Yan, J. and Mi, C. W. [2020] “ On the receding contact between a homogeneous elastic layer and a half-plane substrate coated with functionally graded materials,” Int. J. Comp. Meth-Sing17(1), 1-21. · <a href="/1466.74031" class="nowrap">Zbl 1466.74031</a></td> </tr><tr> <td>[46]</td> <td class="space">Yang, Y. F., Feng, H. B., Chen, H. and Wu, M. J. [2016] “ Dynamical analysis of the flexible beam-cam oblique-impact system,” Acta Phys. Sin-Ch. Ed.65(24), 1-7.</td> </tr><tr> <td>[47]</td> <td class="space">Yeo, C. D., Katta, R. R. and Polycarpou, A. A. [2009] “ Improved elastic contact model accounting for asperity and bulk substrate deformation,” Tribol. Lett.35(3), 191-203.</td> </tr><tr> <td>[48]</td> <td class="space">You, J. M. and Chen, T. N. [2010] “ Statistical model of static friction coefficient,” J. Shock Vib.29, 26-29.</td> </tr><tr> <td>[49]</td> <td class="space">Zhang, Y., He, N. and Hou, Y. B. [2020] “ Crashworthiness optimization of a vertex fractal hexagonal structure,” Int. J. Comp. Meth-Sing, 17(6), 1-15. · <a href="/1550.74332" class="nowrap">Zbl 1550.74332</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 1550.74220 - zbMATH Open