Document Zbl 1545.93185

<!doctype html> <html lang="en"> <head> <meta charset="utf-8"> <title>Document Zbl 1545.93185 - 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="/1545.93185?"> <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:1545.93185" aria-label="Search for documents" placeholder="Search for documents" autocomplete="off"> </div> <div class="search-buttons input-group-btn"> <div class="btn-group"> <button class="btn btn-default search" type="submit"><span class="virtual">Search</span> <span class="glyphicon glyphicon-search" style="top: 2px;"></span></button> </div> </div> </span> <span> <div class="search-buttons input-group-btn"> <div class="btn-group"> <div class="btn-group fields"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Fields <i class="caret"></i></button> <ul id="fields" class="dropdown-menu pull-right"> <li><a href="#"><span class="token item">any:</span><span> </span>anywhere (default)</a></li> <li><a href="#"><span class="token item">ab:</span><span>  </span>review text</a></li> <li><a href="#"><span class="token item">an:</span><span>  </span>zbmath id</a></li> <li><a href="#"><span class="token item">any:</span><span>  </span>anywhere</a></li> <li><a href="#"><span class="token item">au:</span><span>  </span>contributor name</a></li> <li><a href="#"><span class="token item">br:</span><span>  </span>biographic reference name</a></li> <li><a href="#"><span class="token item">cc:</span><span>  </span>msc title</a></li> <li><a href="#"><span class="token item">dt:</span><span>  </span>document type</a></li> <li><a href="#"><span class="token item">doi:</span><span>  </span>doi</a></li> <li><a href="#"><span class="token item">en:</span><span>  </span>external id</a></li> <li><a href="#"><span class="token item">la:</span><span>  </span>language</a></li> <li><a href="#"><span class="token item">pu:</span><span>  </span>publisher</a></li> <li><a href="#"><span class="token item">py:</span><span>  </span>year</a></li> <li><a href="#"><span class="token item">rv:</span><span>  </span>reviewer name</a></li> <li><a href="#"><span class="token item">so:</span><span>  </span>source</a></li> <li><a href="#"><span class="token item">sw:</span><span>  </span>software name</a></li> <li><a href="#"><span class="token item">ti:</span><span>  </span>title</a></li> <li><a href="#"><span class="token item">ut:</span><span>  </span>keyword</a></li> </ul> </div> <div class="btn-group operators"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Operators <i class="caret"></i></button> <ul id="operators" class="dropdown-menu pull-right"> <li><a href="#"><span class="token">a <span class="item">&</span> b </span><span> </span>logical and (default)</a></li> <li><a href="#"><span class="token">a <span class="item">|</span> b </span><span> </span>logical or</a></li> <li><a href="#"><span class="token"><span class="item">!</span>ab   </span><span> </span>logical not</a></li> <li><a href="#"><span class="token">abc<span class="item">*</span>  </span><span> </span>right wildcard</a></li> <li><a href="#"><span class="token"><span class="item">"</span>ab c<span class="item">"</span></span><span> </span>phrase</a></li> <li><a href="#"><span class="token"><span class="item">(</span>ab c<span class="item">)</span></span><span> </span>parentheses</a></li> </ul> </div> </div> </div> <div class="special"> <ul class="nav help-button"> <li class="dropdown pull-right"> <a href="#">Help <i class="caret"></i></a> </li> </ul> </div> </span> </div> <div class="help"><h2>Examples</h2> <div id="help-terms" role="table"> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Geometry">Geometry</a></span> <span class="search-explanation" role="cell" role="cell">Search for the term <em>Geometry</em> in <strong>any</strong> field. Queries are <strong>case-independent</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Funct%2A">Funct*</a></span> <span class="search-explanation" role="cell"><strong>Wildcard</strong> queries are specified by <strong><u>*</u></strong> (e.g. <em>functions</em>, <em>functorial</em>, etc.). Otherwise the search is <strong>exact</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Topological+group%22">"Topological group"</a></span> <span class="search-explanation" role="cell"><strong>Phrases</strong> (multi-words) should be set in <u>"</u>straight quotation marks<u>"</u>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=au%3A+Bourbaki+%26+ti%3A+Algebra">au: Bourbaki & ti: Algebra</a></span> <span class="search-explanation" role="cell">Search for <strong><u>au</u>thor</strong> and <strong><u>ti</u>tle</strong>. The <strong>and-operator &</strong> is default and can be omitted.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Chebyshev+%7C+Tschebyscheff">Chebyshev | Tschebyscheff</a></span> <span class="search-explanation" role="cell">The <strong>or-operator |</strong> allows to search for <em>Chebyshev</em> or <em>Tschebyscheff</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Quasi%2A+map%2A+py%3A+1989">Quasi* map* py: 1989</a></span> <span class="search-explanation" role="cell">The resulting documents have <strong><u>p</u>ublication <u>y</u>ear</strong> <em>1989</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=so%3A+Eur%2A+J%2A+Mat%2A+Soc%2A+cc%3A+14">so: Eur* J* Mat* Soc* cc: 14</a></span> <span class="search-explanation" role="cell">Search for publications in a particular <strong><u>so</u>urce</strong> with a <strong>Mathematics Subject <u>C</u>lassification <u>c</u>ode (<u>cc</u>)</strong> in <em>14</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Partial+diff%2A+eq%2A%22+%21+elliptic">"Partial diff* eq*" ! elliptic</a></span> <span class="search-explanation" role="cell">The <strong>not</strong>-operator <strong>!</strong> eliminates all results containing the word <em>elliptic</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=dt%3A+b+%26+au%3A+Hilbert">dt: b & au: Hilbert</a></span> <span class="search-explanation" role="cell">The <strong><u>d</u>ocument <u>t</u>ype</strong> is set to books; alternatively: <u>j</u> for <strong>journal articles</strong>, <u>a</u> for <strong>book articles</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=py%3A+2000-2015+cc%3A+%2894A+%7C+11T%29">py: 2000-2015 cc: (94A | 11T)</a></span> <span class="search-explanation" role="cell">Number <strong>ranges</strong> are accepted. Terms can be grouped within <strong><u>(</u>parentheses<u>)</u></strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=la%3A+chinese">la: chinese</a></span> <span class="search-explanation" role="cell">Find documents in a given <strong><u>la</u>nguage</strong>. <a href="http://en.wikipedia.org/wiki/ISO_639-1">ISO 639-1</a> language codes can also be used.</span> </div> </div> <div id="help-fields"> <h2>Fields</h2> <table> <tr> <td class="nowrap padding" role="rowheader"><strong>any</strong></td> <td class="padding">anywhere</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>an</strong></td> <td class="padding">internal document identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>au</strong></td> <td class="padding">author, editor</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ai</strong></td> <td class="padding">internal author identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ti</strong></td> <td class="padding">title</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>la</strong></td> <td class="padding">language</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>so</strong></td> <td class="padding">source</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ab</strong></td> <td class="padding">review, abstract</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>py</strong></td> <td class="padding">publication year</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>rv</strong></td> <td class="padding">reviewer</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>cc</strong></td> <td class="padding">MSC code</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ut</strong></td> <td class="padding">uncontrolled term</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>dt</strong></td> <td class="padding" colspan="4">document type (<strong>j</strong>: journal article; <strong>b</strong>: book; <strong>a</strong>: book article)</td> </tr> </table> </div> <div id="help-operators"> <h2>Operators</h2> <table> <tr> <td class="nowrap padding" role="rowheader">a <strong>&</strong> b</td> <td class="padding">logic and</td> </tr> <tr> <td class="nowrap padding" role="rowheader">a <strong>|</strong> b</td> <td class="padding">logic or</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>!</strong>ab</td> <td class="padding">logic not</td> </tr> <tr> <td class="nowrap padding" role="rowheader">abc<strong>*</strong></td> <td class="padding">right wildcard</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>"</strong>ab c<strong>"</strong></td> <td class="padding">phrase</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>(</strong>ab c<strong>)</strong></td> <td class="padding">parentheses</td> </tr> </table> </div> <p> See also our <a href="/general-help/">General Help</a>. </p></div> </div> </form> <div class="clearfix"></div> </div> <div class="content-shadow"></div> </div> </div> <div id="body"> <div id="main"> <div class="messages"> </div> <div id="documents"> <div class="content-main"> <div class="content-item"><div class="item"> <article> <div class="author"><a href="/authors/?q=ai%3Aali.m-syed%7Cali.muhammed-syed" title="Author Profile">Ali, M. Syed</a>; <a href="/authors/tajudeen.m-mubeen" title="Author Profile">Tajudeen, M. Mubeen</a>; <a href="/authors/rajchakit.grienggrai" title="Author Profile">Rajchakit, Grienggrai</a>; <a href="/authors/priya.bandana" title="Author Profile">Priya, Bandana</a>; <a href="/authors/?q=ai%3Athakur.ganeshkumar%7Cthakur.ganesh-kumar" title="Author Profile">Thakur, Ganesh Kumar</a></div> <h2 class="title"> <strong>Adaptive event-triggered pinning synchronization control for complex networks with random saturation subject to hybrid cyber-attacks.</strong> <i>(English)</i> <a class="label nowrap" href="/1545.93185">Zbl 1545.93185</a> </h2> <div class="source"> <a href="/serials/1373" title="Journal Profile">Int. J. Adapt. Control Signal Process.</a> <a href="/?q=in%3A511937" title="Articles in this Issue">37, No. 8, 2041-2062 (2023)</a>. </div> <div class="abstract">Summary: This research is concerned with the problem of pinning based output synchronization control for a complex networks with random saturation vulnerable to hybrid cyber-attacks via an adaptive event-triggered scheme (AETS). The output synchronization error systems are subject to suffer from deception attacks, replay attacks, and denial-of-service attacks. A novel hybrid cyber-attack model is first constructed to integrate the three kinds of attacks into a synchronization of complex network. AETSs based on output synchronization errors with the consideration of hybrid cyber-attacks, have been proposed to reduce the burden of communication. A pinning control strategy is used to decrease the control signal’s input. By constructing a Lyapunov functional and using the linear matrix inequality technique, sufficient conditions are provided to ensure the output synchronization error system. Finally, a numerical simulation results are developed to illustrate the efficacy of the proposed theoretical methodology.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7844281">Cited in <strong>5</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B70" title="MSC2020">93B70</a> </td> <td class="space"> Networked control </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B36" title="MSC2020">93B36</a> </td> <td class="space"> $H^\infty$-control </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C40" title="MSC2020">93C40</a> </td> <td class="space"> Adaptive control/observation systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93E15" title="MSC2020">93E15</a> </td> <td class="space"> Stochastic stability in control theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aadaptive+event-triggered+pinning+control">adaptive event-triggered pinning control</a>; <a href="/?q=ut%3Acomplex+networks">complex networks</a>; <a href="/?q=ut%3Ahybrid+attacks">hybrid attacks</a>; <a href="/?q=ut%3ALyapunov-functional">Lyapunov-functional</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 1545.93185" data-ciurl="/ci/07844281" data-biburl="/bibtex/07844281.bib" data-amsurl="/amsrefs/07844281.bib" data-xmlurl="/xml/07844281.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07844281.pdf" title="Zbl 1545.93185 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/10.1002/acs.3625" aria-label="DOI for “Adaptive event-triggered pinning synchronization control for complex networks with random saturation subject to hybrid cyber-attacks”" title="10.1002/acs.3625">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">HuT, HeZ, ZhangX, ZhongS, ShiK, ZhangdY. Adaptive fuzzy control for quasi‐synchronization of uncertain complex dynamical networks with time‐varying topology via event‐triggered communication strategy. Inform Sci. 2022;582:704‐724. · <a href="/1530.93193" class="nowrap">Zbl 1530.93193</a></td> </tr><tr> <td>[2]</td> <td class="space">WangY, HuX, ShiK, SongX, ShenH. Network‐based passive estimation for switched complex dynamical networks under persistent dwell‐time with limited signals. J Franklin Inst. 2020;3657(15):10921‐10936. · <a href="/1450.93078" class="nowrap">Zbl 1450.93078</a></td> </tr><tr> <td>[3]</td> <td class="space">AliMS, UshaM, KwonOM, GunasekaranN, ThakurGK. H_∞/passive non‐fragile synchronization of Markovian jump stochastic complex dynamical networks with time‐varying delays. Int J Syst Sci. 2021;52(7):1270‐1283. · <a href="/1483.93142" class="nowrap">Zbl 1483.93142</a></td> </tr><tr> <td>[4]</td> <td class="space">ManiP, JooYH, AssawinchaichotecW. Fuzzy‐logic‐based event‐triggered <br class="zbmathjax-newline">[( {H}_{\infty } \]\) control for networked systems and its application to wind turbine systems. Inform Sci. 2022;585:144‐161. · <a href="/1532.93209" class="nowrap">Zbl 1532.93209</a></td> </tr><tr> <td>[5]</td> <td class="space">LiuYA, TangS, LiuY, KongQ, WangJ. Extended dissipative sliding mode control for nonlinear networked control systems via event‐triggered mechanism with random uncertain measurement. Appl Math Comput. 2021;396:125901. · <a href="/1508.93306" class="nowrap">Zbl 1508.93306</a></td> </tr><tr> <td>[6]</td> <td class="space">GonzalezA, CuencaA, SaltJ, JacobsJ. Robust stability analysis of an energy‐efficient control in a networked control system with application to unmanned ground vehicles. Inform Sci. 2021;578:64‐84. · <a href="/1530.93380" class="nowrap">Zbl 1530.93380</a></td> </tr><tr> <td>[7]</td> <td class="space">WangH, XieS, ZhouB, WangW. Non‐fragile robust <br class="zbmathjax-newline">[( {H}_{\infty } \]\) filtering of Takagi‐Sugeno fuzzy networked control systems with sensor failures. Sensors. 2020;20(1):17.</td> </tr><tr> <td>[8]</td> <td class="space">HuF, JiaoC, ChangH, SuX, GuY. Event‐triggered control for networked control system via an improved integral inequality. J Franklin Inst. 2021;358(5):2661‐2682. · <a href="/1459.93105" class="nowrap">Zbl 1459.93105</a></td> </tr><tr> <td>[9]</td> <td class="space">PangZH, FanLZ, SunJ, LiuK, LiuGP. Detection of stealthy false data injection attacks against networked control systems via active data modification. Inform Sci. 2021;546:192‐205.</td> </tr><tr> <td>[10]</td> <td class="space">NagamaniG, KarthikC, JooYH. Event‐triggered observer‐based sliding mode control for T‐S fuzzy systems via improved relaxed‐based integral inequality. J Franklin Inst. 2020;357(14):9543‐9567. · <a href="/1448.93208" class="nowrap">Zbl 1448.93208</a></td> </tr><tr> <td>[11]</td> <td class="space">LiY, SongF, LiuJ, XieX, TianE. Decentralized event‐triggered synchronization control for complex networks with non periodic DoS attacks. Appl Math Comput. 2022;32(3):1633‐1653. · <a href="/1527.93006" class="nowrap">Zbl 1527.93006</a></td> </tr><tr> <td>[12]</td> <td class="space">LiuD, YeaD. Observer‐based synchronization control for complex networks against asynchronous attacks. Inform Sci. 2021;546:753‐768. · <a href="/1478.93582" class="nowrap">Zbl 1478.93582</a></td> </tr><tr> <td>[13]</td> <td class="space">LeeTH, ParkJH. Design of sampled‐data controllers for the synchronization of complex dynamical networks under controller attacks. Adv Differ Equ. 2019;2019:184. · <a href="/1459.93101" class="nowrap">Zbl 1459.93101</a></td> </tr><tr> <td>[14]</td> <td class="space">PradeepC, CaoY, MurugesuR, RakkiyappanR. An event‐triggered synchronization of semi‐Markov jump neural networks with time‐varying delays based on generalized free‐weighting‐matrix approach. Math Comput Simul. 2019;159:41‐56. · <a href="/1540.34103" class="nowrap">Zbl 1540.34103</a></td> </tr><tr> <td>[15]</td> <td class="space">LiuJ, GuY, XieX, YueD, ParkJH. Hybrid‐driven‐based <br class="zbmathjax-newline">[( {\mathcal{E}}_{\infty } \]\) control for networked cascade control systems with actuator saturations and stochastic cyber attacks. IEEE Trans Syst Man Cybern Syst. 2019;49(12):2452‐2463.</td> </tr><tr> <td>[16]</td> <td class="space">AliMS, GunasekaranN, KwonOM. Delay dependent <br class="zbmathjax-newline">[( {H}_{\infty } \]\) performance state estimation of static delayed neural networks using sampled‐data control. Neural Comput Appl. 2018;30(2):539‐550.</td> </tr><tr> <td>[17]</td> <td class="space">CaoY, MaheswariK, DharaniS, SivaranjaniK. New event based <br class="zbmathjax-newline">[( {H}_{\infty } \]\) state estimation for discrete‐time recurrent delayed semi‐Markov jump neural networks via a novel summation inequality. J Artif Intell Soft Comput Res. 2022;12(3):207‐221.</td> </tr><tr> <td>[18]</td> <td class="space">AliMS, VadivelR, KwonOM. Decentralised event‐triggered impulsive synchronization for semi‐Markovian jump delayed neural networks with leakage delay and randomly occurring uncertainties. Inform Sci. 2019;50(8):1636‐1660. · <a href="/1483.93010" class="nowrap">Zbl 1483.93010</a></td> </tr><tr> <td>[19]</td> <td class="space">LiuJ, LiuQ, CaoJ, ZhangY. Adaptive event‐triggered <br class="zbmathjax-newline">[( H\infty \]\) filtering for T‐S fuzzy system with time delay. Neurocomputing. 2015;189:86‐94.</td> </tr><tr> <td>[20]</td> <td class="space">ChenX, WangY, HuS. Event‐triggered quantized <br class="zbmathjax-newline">[( {H}_{\infty } \]\) control for networked control systems in the presence of denial‐of‐service jamming attacks. Nonlinear Anal Hybrid Syst. 2019;33:265‐281. · <a href="/1429.93087" class="nowrap">Zbl 1429.93087</a></td> </tr><tr> <td>[21]</td> <td class="space">AliMS, VadivelR, KwonOM, MuruganK. Event triggered finite time H? Boundedness of uncertain Markov jump neural networks with distributed time varying delays. Neural Process Lett. 2019;49:1649‐1680.</td> </tr><tr> <td>[22]</td> <td class="space">CaoL, LiH, WangN, ZhouQ. Observer‐based event‐triggered adaptive decentralized fuzzy control for nonlinear large‐scale systems. IEEE Trans Fuzzy Syst. 2019;27(6):1201‐1214.</td> </tr><tr> <td>[23]</td> <td class="space">Syed AliM, VadivelR, AlsaediA, AhmadB. Extended dissipativity and event‐triggered synchronization for T‐S fuzzy Markovian jumping delayed stochastic neural networks with leakage delays via fault‐tolerant control. Soft Comput. 2020;24:3675‐3694. · <a href="/1436.93004" class="nowrap">Zbl 1436.93004</a></td> </tr><tr> <td>[24]</td> <td class="space">AliMS, VadivelR, KwonOM. Decentralized event‐triggered stability analysis of neutral‐type BAM neural networks with Markovian jump parameters and mixed time varying delays. Int J Control Autom Syst. 2018;16:983‐993.</td> </tr><tr> <td>[25]</td> <td class="space">LiM, ZhaoJ, XiaJ, ZhuangG, ZhangW. Extended dissipative analysis and synthesis for network control systems with an event‐triggered scheme. Neurocomputing. 2018;312(27):34‐40.</td> </tr><tr> <td>[26]</td> <td class="space">KazemyA, LamJ, ChangZ. Adaptive event‐triggered mechanism for networked control systems under deception attacks with uncertain occurring probability. Int J Syst Sci. 2021;52(7):1426‐1439. · <a href="/1483.93286" class="nowrap">Zbl 1483.93286</a></td> </tr><tr> <td>[27]</td> <td class="space">PanR, TanaY, DuD, FeiS. Adaptive event‐triggered synchronization control for complex networks with quantization and cyber‐attacks. Neurocomputing. 2020;382:249‐258.</td> </tr><tr> <td>[28]</td> <td class="space">XieW, ZhuQ. Input‐to‐state stability of stochastic nonlinear fuzzy Cohen‐Grossberg neural networks with the event‐triggered control. Int J Control. 2020;93(9):2043‐2052. · <a href="/1453.93208" class="nowrap">Zbl 1453.93208</a></td> </tr><tr> <td>[29]</td> <td class="space">RatnaveluK, KalpanaM, BalasubramaniamP. Stability analysis of fuzzy genetic regulatory networks with various time delays. Bull Malays Math Sci Soc. 2018;41:491‐505. · <a href="/1387.93131" class="nowrap">Zbl 1387.93131</a></td> </tr><tr> <td>[30]</td> <td class="space">QiY, ZhaoX, HuangJ. H_∞ filtering for switched systems subject to stochastic cyber attacks: a double adaptive storage event‐triggering communication. Appl Math Comput. 2021;394:125789. · <a href="/1508.93307" class="nowrap">Zbl 1508.93307</a></td> </tr><tr> <td>[31]</td> <td class="space">ZhouX, GuZ, YangF. Resilient event‐triggered output feedback control for load frequency control systems subject to cyber attacks. IEEE Access. 2019;7:58951‐58958.</td> </tr><tr> <td>[32]</td> <td class="space">ZhangL, GuoG. Observer‐based adaptive event‐triggered sliding mode control of saturated nonlinear networked systems with cyber‐attacks. Inform Sci. 2021;543(8):180‐201. · <a href="/1478.93431" class="nowrap">Zbl 1478.93431</a></td> </tr><tr> <td>[33]</td> <td class="space">SunL, WangY, FengG. Control design for a class of affine non‐linear descriptor systems with actuator saturation. IEEE Trans Automat Contr. 2015;60(8):2195‐2200. · <a href="/1360.93302" class="nowrap">Zbl 1360.93302</a></td> </tr><tr> <td>[34]</td> <td class="space">LiuJ, SuoW, XieX, YueD, CaoJ. Quantized control for a class of neural networks with adaptive event‐triggered scheme and complex cyber‐attacks. Int J Robust Nonlinear Control. 2021;31(10):4705‐4728. · <a href="/1525.93173" class="nowrap">Zbl 1525.93173</a></td> </tr><tr> <td>[35]</td> <td class="space">MaYS, CheWW, DengC. Dynamic event‐triggered model‐free adaptive control for nonlinear CPSs under aperiodic DoS attacks. Inform Sci. 2022;589:790‐801. · <a href="/1541.93218" class="nowrap">Zbl 1541.93218</a></td> </tr><tr> <td>[36]</td> <td class="space">LuH, DengY, XuY, ZhouW. Event‐triggered <br class="zbmathjax-newline">[( H\infty \]\) filtering for networked systems under hybrid probability deception attacks. IEEE Access. 2020;8:192030‐192040.</td> </tr><tr> <td>[37]</td> <td class="space">ZhuY, PanR, TanY, FeiS. Adaptive event‐based non‐fragile output pinning synchronization control for complex networks with random saturations and cyber‐attacks. IEEE Access. 2021;9:122712‐122722.</td> </tr><tr> <td>[38]</td> <td class="space">DingD, TangZ, WangY, JiaZ. Secure synchronization of complex networks under deception attacks against vulnerable nodes. Appl Math Comput. 2021;399:126017. · <a href="/1508.94129" class="nowrap">Zbl 1508.94129</a></td> </tr><tr> <td>[39]</td> <td class="space">GuZ, ParkJH, YueD, WuZG, XieX. Event‐triggered security output feedback control for networked interconnected systems subject to cyber‐attacks. IEEE Trans Syst Man Cybern. 2021;51(10):6197‐6206.</td> </tr><tr> <td>[40]</td> <td class="space">YinT, GuZ. Security control for adaptive event‐triggered networked control systems under deception attacks. IEEE Access. 2021;9:10789‐10796.</td> </tr><tr> <td>[41]</td> <td class="space">ZhaoL, YangGH. Cooperative adaptive fault‐tolerant control for multi‐agent systems with deception attacks. J Franklin Inst. 2020;357(6):3419‐3433. · <a href="/1437.93026" class="nowrap">Zbl 1437.93026</a></td> </tr><tr> <td>[42]</td> <td class="space">TahounAH, ArafaaM. Cooperative control for cyber‐physical multi‐agent networked control systems with unknown false data‐injection and replay cyber‐attacks. ISA Trans. 2021;110(21):1‐14.</td> </tr><tr> <td>[43]</td> <td class="space">PengC, SunH. Switching‐like event‐triggered control for networked control systems under malicious denial of service attacks. IEEE Trans Automat Contr. 2020;65(9):3943‐3949. · <a href="/1533.93493" class="nowrap">Zbl 1533.93493</a></td> </tr><tr> <td>[44]</td> <td class="space">LiuJ, ZhangN, LiY, XieX. H_∞ filter design for discrete‐time networked systems with adaptive event‐triggered mechanism and hybrid cyber attacks. J Franklin Inst. 2021;358(17):9325‐9345. · <a href="/1478.93152" class="nowrap">Zbl 1478.93152</a></td> </tr><tr> <td>[45]</td> <td class="space">LiuJ, WeiL, XieX, TianE, FeiS. Quantized stabilization for T‐S fuzzy systems with hybrid‐triggered mechanism and stochastic cyber‐attacks. IEEE Trans Fuzzy Syst. 2018;26(6):3820‐3834.</td> </tr><tr> <td>[46]</td> <td class="space">ZhangZ, ChenZ, ShengZ, LiD, WangJ. Static output feedback secure synchronization control for Markov jump neural networks under hybrid cyber‐attacks. Appl Math Comput. 2022;430:127274. · <a href="/1510.93299" class="nowrap">Zbl 1510.93299</a></td> </tr><tr> <td>[47]</td> <td class="space">DengY, LuH, ZhouW. Security even‐triggered control for Markovian jump neural network against actuator saturation and hybrid cyber attacks. J Franklin Inst. 2021;358:7096‐7188. · <a href="/1471.93174" class="nowrap">Zbl 1471.93174</a></td> </tr><tr> <td>[48]</td> <td class="space">LiuJ, WangY, CaoJ, YueD, XieX. Secure adaptive‐event‐triggered filter design with input constraint and hybrid cyber attack. IEEE Trans Cybern. 2021;51(8):4000‐4010.</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 1545.93185 - zbMATH Open