Kai Yao - Author Profile

<!doctype html> <html lang="en"> <head> <meta charset="utf-8"> <title>Kai Yao - Author Profile - zbMATH Open</title> <meta name="viewport" content="width=device-width, minimum-scale=0.1, maximum-scale=5.0"> <meta name="robots" content="noarchive"> <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. 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type="text" name="q" value="ai:yao.kai" aria-label="Search for authors" placeholder="Search for authors" 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">ai:</span><span>  </span>author code</a></li> <li><a href="#"><span class="token item">au:</span><span>  </span>author name</a></li> <li><a href="#"><span class="token item">any:</span><span>  </span>anywhere</a></li> <li><a href="#"><span class="token item">aw:</span><span>  </span>award</a></li> <li><a href="#"><span class="token item">cc:</span><span>  </span>main field</a></li> <li><a href="#"><span class="token item">cm:</span><span>  </span>collectives of</a></li> <li><a href="#"><span class="token item">co:</span><span>  </span>in collective</a></li> <li><a href="#"><span class="token item">en:</span><span>  </span>external id type</a></li> <li><a href="#"><span class="token item">fn:</span><span>  </span>first name</a></li> <li><a href="#"><span class="token item">ln:</span><span>  </span>last name</a></li> <li><a href="#"><span class="token item">py:</span><span>  </span>publication year</a></li> <li><a href="#"><span class="token item">rv:</span><span>  </span>reviewer</a></li> <li><a href="#"><span class="token item">st:</span><span>  </span>state</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=Simon+Donald%2A">Simon Donald*</a></span> <span class="search-explanation" role="cell" role="cell">Search in <strong>all parts</strong> of an author's name (results contain <em>Simon, Donald</em> M. and <em>Donald</em>son, <em>Simon</em> Kirwan).</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=ln%3A+Donald%2A+fn%3A+Simon">ln: Donald* fn: Simon</a></span> <span class="search-explanation" role="cell" role="cell">Search for specified family (<strong>ln</strong>) and given (<strong>fn</strong>) name.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=au%3A+Stefan+M%C3%BCller+cc%3A49">au: Stefan Müller cc:49</a></span> <span class="search-explanation" role="cell" role="cell">Combine name search (<strong>au</strong>) with main MSC fields (<strong>cc</strong>).</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=au%3A+Helga+Bunke">au: Helga Bunke</a></span> <span class="search-explanation" role="cell" role="cell">Search results include <strong>name variations</strong>, in particular <strong>name changes</strong>, different <strong>transliterations</strong> and <strong>pseudonyms</strong>. Names of collectives will be displayed as a separate entity.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%28st%3Ar+%26+b%29+%7C+%28st%3Ao%29">(st:r & b) | (st:o)</a></span> <span class="search-explanation" role="cell" role="cell">Search results include all <strong><u>r</u>eviewers</strong> with <strong><u>b</u>iographic information</strong> or <strong>c<u>o</u>llectives</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%28en%3AMGP+%7C+wikidata%29+ln%3Aa%2A">(en:MGP | wikidata) ln:a*</a></span> <span class="search-explanation" role="cell" role="cell">Search results include all authors having either an <strong><u>en</u>try</strong> in the <em>Math Genealogy</em> Project or in <em>Wikidata</em> and whose family name starts with <em>A</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=aw%3A+Fields+Abel">aw: Fields Abel</a></span> <span class="search-explanation" role="cell" role="cell">Search for all <em>Fields Medal</em> <strong><u>aw</u>ard winners</strong> who also received an <em>Abel Prize</em>. The <strong>&</strong> operator is default and ommitted here.</span> </div> </div> <p style="margin-bottom:0.5cm;"></p> <h2>Fields</h2> <div id="help-fields" role="table"> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>ai</strong> </span> <span class="search-explanation" role="cell" role="cell"> zbMATH author ID </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>au</strong> </span> <span class="search-explanation" role="cell" role="cell"> Author name </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>any</strong> </span> <span class="search-explanation" role="cell" role="cell"> Includes ai, au, aw, cc </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>aw</strong> </span> <span class="search-explanation" role="cell" role="cell"> Name of an award (to find laureates) </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>cc</strong> </span> <span class="search-explanation" role="cell" role="cell"> Main Fields of the author (given by first two MSC digits) </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>cm</strong> </span> <span class="search-explanation" role="cell" role="cell"> Name of a collective (to find members of this collective) </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>co</strong> </span> <span class="search-explanation" role="cell" role="cell"> Name of an author (to find collectives the author is a member of) </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>en</strong> </span> <span class="search-explanation" role="cell" role="cell"> External author ID: ORCID, MGP, Wikidata object number and others </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>fn</strong> </span> <span class="search-explanation" role="cell" role="cell"> First name </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>ln</strong> </span> <span class="search-explanation" role="cell" role="cell"> Last name </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>py</strong> </span> <span class="search-explanation" role="cell" role="cell"> Year(s) in which the author has published. Interval search with “-” </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>rv</strong> </span> <span class="search-explanation" role="cell" role="cell"> Reviewer ID </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>st</strong> </span> <span class="search-explanation" role="cell" role="cell"> State: has biographic references (<em>st:b</em>), is cited (<em>st:c</em>), is collective (st:o), has references (<em>st:r</em>) </span> </div> </div> <p style="margin-bottom:0.5cm;"></p> <h2>Operators</h2> <div id="operators-fields" role="table"> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>a & b</strong></span> <span class="search-explanation" role="cell" role="cell">logical and</span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>a | b</strong></span> <span class="search-explanation" role="cell" role="cell">logical or</span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>!ab</strong></span> <span class="search-explanation" role="cell" role="cell">logical not</span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>abc*</strong></span> <span class="search-explanation" role="cell" role="cell">right wildcard</span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>ab c</strong></span> <span class="search-explanation" role="cell" role="cell">phrase</span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>(ab c)</strong></span> <span class="search-explanation" role="cell" role="cell">parentheses</span> </div> </div> <p> See also our <a href="/general-help/">General Help</a>. </p></div> </div> </form> <form class="form-inline" name="authors" method="get" action="/authors/"> <div class="authors structured" 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 two-columns"> <div class="row"> <div class="col-xs-12 col-sm-6"> <div class="form-group field ln"> <label for="ln">Family Name:</label> <input id="ln" name="ln" class="form-control" type="text" value="" placeholder=""> </div> <div class="form-group field fn"> <label for="fn">Given Name:</label> <input id="fn" name="fn" class="form-control" type="text" value="" placeholder=""> </div> <div class="form-group field cc"> <label for="cc">Main Fields:</label> <input id="cc" name="cc" class="form-control" type="text" value="" placeholder=""> <span tabindex="0" class="glyphicon glyphicon-question-sign" title="field given by first two MSC digits" aria-label="field given by first two MSC digits"></span> </div> <div class="form-group field st checkboxes-wrapper"> <label>Status:</label> <div class="checkboxes"> <input type="checkbox" id="st-z" name="st" class="form-control" value="z"> <label for="st-z" title="restrict to Authors who are zbMATH Reviewers"> Reviewer</label><br> <input type="checkbox" id="st-b" name="st" class="form-control" value="b"> <label for="st-b" title="restrict to Authors having Biographic References"> Biographic References</label><br> </div> </div> </div> <div class="col-xs-12 col-sm-6"> <div class="form-group field ai"> <label for="ai">zbMATH Author ID:</label> <input id="ai" name="ai" class="form-control" type="text" value="" placeholder=""> </div> <div class="form-group field en"> <label for="en">External ID:</label> <input id="en" name="en" class="form-control" type="text" value="" placeholder=""> <span tabindex="0" class="glyphicon glyphicon-question-sign" title="e.g. ORCID, MGP, …" aria-label="e.g. ORCID, MGP, ..."></span> </div> <div class="form-group field any"> <label for="any">Anywhere:</label> <input id="any" name="any" class="form-control" type="text" value="" placeholder=""> </div> <div class="form-group field aw"> <label for="aw">Awards:</label> <select id="aw" name="aw" class="form-control"> <option value=""></option> <option value="Abel Prize">Abel Prize</option> <option value="Breakthrough Prize in Mathematics">Breakthrough Prize in Mathematics</option> <option value="Carl Friedrich Gauss Prize">Carl Friedrich Gauss Prize</option> <option value="Chern Medal">Chern Medal</option> <option value="Clay Research Award">Clay Research Award</option> <option value="EMS Prize">EMS Prize</option> <option value="Fields Medal">Fields Medal</option> <option value="Kyoto Prize in Basic Sciences">Kyoto Prize in Basic Sciences</option> <option value="Nevanlinna Prize">Nevanlinna Prize</option> <option value="Nobel Memorial Prize in Economic Sciences">Nobel Memorial Prize in Economic Sciences</option> <option value="Nobel Prize in Physics">Nobel Prize in Physics</option> <option value="Shaw Prize">Shaw Prize</option> <option value="Turing Award">Turing Award</option> <option value="Wolf Prize">Wolf Prize</option> </select> </div> </div> </div> </div> <div class="clearfix"></div> <div class="container-fluid"> <div class="row buttons"> <div class="col-xs-6"> <a tabindex="0" class="btn btn-default clear-all">Clear all <span class="glyphicon glyphicon-remove"></span></a> </div> <div class="col-xs-12 col-sm-6"> <div class="submit"> <button class="btn btn-default search" type="submit">Search <span class="glyphicon glyphicon-search"></span></button> </div> </div> </div> </div> <div class="clearfix"></div> </div> </form> <div class="clear"></div> </div><div class="content-shadow"></div> </div> </div> <div id="body"> <div id="main"> <div class="messages"> </div> <div id="authors"> <div class="content-main"> <article> <div class="head"> <div class="pull-right"> <a class="btn btn-default matrix edit-profile" type="button" href="/author-profile/edit/yao.kai" target="_blank">Edit Profile <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></a> </div> <h2>Yao, Kai</h2> </div> <div class="erdos pull-right"> <a href="/collaboration-distance/?a=yao.kai&b=erdos.paul" title="Compute Co-Author Distance to Erdős or any other Author"> Co-Author Distance </a> </div> <div class="text" style="max-width: 80%;"> <table> <tr> <td>Author ID:</td> <td>yao.kai <a target="_blank" href="/atom/ai/yao.kai"><img class="feed-icon" alt="Recent zbMATH articles by "Yao, Kai"" src="/static/feed-icon-14x14.png"></a></td> </tr><tr> <td>Published as:</td> <td><span>Yao, Kai</span></td> </tr> </table> </div> <div class="indexed"> <table> <tr> <td>Documents Indexed:</td> <td> <a href="/?q=ia%3Ayao.kai">51 Publications</a> since 1967, including <a href="/?q=ia%3Ayao.kai+dt%3Ab">2 Books</a> </td> </tr> <tr> <td></td> <td> <a href="/?q=ei%3Ayao.kai">2 Contributions as Editor</a> </td> </tr> <tr> <td>Co-Authors:</td> <td> <a href="/authors/?q=ai1%3Ayao.kai">31 Co-Authors</a> with <a href="/?q=ai%3Ayao.kai+ai1%3Ayao.kai"> 26 Joint Publications</a> </td> </tr> <tr><td></td><td> <a href="/authors/?q=ai2%3Ayao.kai">1,244 Co-Co-Authors</a> </td> </table> </div> <div class="profile"> <div class="facet1st"><a tabindex="0" class="more">all <i class="caret"></i></a> <a tabindex="0" class="less">top 5 <i class="caret"></i></a><h3>Co-Authors</h3> <table class="profile"> <tr class="single_authored"> <td class="number"> <a href="/?q=ai%3Ayao.kai+na%3A1" title="Single-Authored Publications">11</a> </td> <td class="text">single-authored</td> </tr><tr> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Ayao.kai" title="Joint Publications">37</a> </td> <td class="text"> <a href="/authors/yao.kai" title="Author Profile"> Yao, Kai </a> </td></tr><tr> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Aqin.zhongfeng" title="Joint Publications">3</a> </td> <td class="text"> <a href="/authors/qin.zhongfeng" title="Author Profile"> Qin, Zhongfeng </a> </td></tr><tr> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Asheng.yuhong" title="Joint Publications">3</a> </td> <td class="text"> <a href="/authors/sheng.yuhong" title="Author Profile"> Sheng, Yuhong </a> </td></tr><tr> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Ayang.xiangfeng" title="Joint Publications">3</a> </td> <td class="text"> <a href="/authors/yang.xiangfeng" title="Author Profile"> Yang, Xiangfeng </a> </td></tr><tr> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Agao.jinwu" title="Joint Publications">2</a> </td> <td class="text"> <a href="/authors/gao.jinwu" title="Author Profile"> Gao, Jinwu </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Agao.yuan.4" title="Joint Publications">2</a> </td> <td class="text"> <a href="/authors/gao.yuan.4" title="Author Profile"> Gao, Yuan </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Ake.hua" title="Joint Publications">2</a> </td> <td class="text"> <a href="/authors/ke.hua" title="Author Profile"> Ke, Hua </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Aliu.baoding" title="Joint Publications">2</a> </td> <td class="text"> <a href="/authors/liu.baoding" title="Author Profile"> Liu, Baoding </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Ani.yaodong" title="Joint Publications">2</a> </td> <td class="text"> <a href="/authors/ni.yaodong" title="Author Profile"> Ni, Yaodong </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Asun.yiyao" title="Joint Publications">2</a> </td> <td class="text"> <a href="/authors/sun.yiyao" title="Author Profile"> Sun, Yiyao </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Achen.jein-shan" title="Joint Publications">1</a> </td> <td class="text"> <a href="/authors/chen.jein-shan" title="Author Profile"> Chen, Jein-Shan </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Achen.xiaowei" title="Joint Publications">1</a> </td> <td class="text"> <a href="/authors/chen.xiaowei" title="Author Profile"> Chen, Xiaowei </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Achevapatrakul.thanaset" title="Joint Publications">1</a> </td> <td class="text"> <a href="/authors/chevapatrakul.thanaset" title="Author Profile"> Chevapatrakul, Thanaset </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Adai.wei.6" title="Joint Publications">1</a> </td> <td class="text"> <a href="/authors/dai.wei.6" title="Author Profile"> Dai, Wei </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Adong.jichang" title="Joint Publications">1</a> </td> <td class="text"> <a href="/authors/dong.jichang" title="Author Profile"> Dong, Jichang </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Afu.zongfei" title="Joint Publications">1</a> </td> <td class="text"> <a href="/authors/fu.zongfei" title="Author Profile"> Fu, Zongfei </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Aguo.jian.2" title="Joint Publications">1</a> </td> <td class="text"> <a href="/authors/guo.jian.2" title="Author Profile"> Guo, Jian </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Ahe.shikai" title="Joint Publications">1</a> </td> <td class="text"> <a href="/authors/he.shikai" title="Author Profile"> He, Shikai </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Aji.xiaoyu" title="Joint Publications">1</a> </td> <td class="text"> <a href="/authors/ji.xiaoyu" title="Author Profile"> Ji, Xiaoyu </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Ajia.liang" title="Joint Publications">1</a> </td> <td class="text"> <a href="/authors/jia.liang" title="Author Profile"> Jia, Liang </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Aliu.yi.19" title="Joint Publications">1</a> </td> <td class="text"> <a href="/authors/liu.yi.19" title="Author Profile"> Liu, Yi </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Amiao.xinhe" title="Joint Publications">1</a> </td> <td class="text"> <a href="/authors/miao.xinhe" title="Author Profile"> Miao, Xinhe </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Apeng.jin" title="Joint Publications">1</a> </td> <td class="text"> <a href="/authors/peng.jin" title="Author Profile"> Peng, Jin </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Aralescu.dan-a" title="Joint Publications">1</a> </td> <td class="text"> <a href="/authors/ralescu.dan-a" title="Author Profile"> Ralescu, Dan A. </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Ashen.yuanyuan" title="Joint Publications">1</a> </td> <td class="text"> <a href="/authors/shen.yuanyuan" title="Author Profile"> Shen, Yuanyuan </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Awei.yuchuan" title="Joint Publications">1</a> </td> <td class="text"> <a href="/authors/wei.yuchuan" title="Author Profile"> Wei, Yuchuan </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Ayan.guangwen" title="Joint Publications">1</a> </td> <td class="text"> <a href="/authors/yan.guangwen" title="Author Profile"> Yan, Guangwen </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Ayang.chingyu" title="Joint Publications">1</a> </td> <td class="text"> <a href="/authors/yang.chingyu" title="Author Profile"> Yang, Chingyu </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Ayin.shiyan" title="Joint Publications">1</a> </td> <td class="text"> <a href="/authors/yin.shiyan" title="Author Profile"> Yin, Shiyan </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Azhang.li.100" title="Joint Publications">1</a> </td> <td class="text"> <a href="/authors/zhang.li.100" title="Author Profile"> Zhang, Li </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Azhang.qishan" title="Joint Publications">1</a> </td> <td class="text"> <a href="/authors/zhang.qishan" title="Author Profile"> Zhang, Qishan </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+ai%3Azhao.hua" title="Joint Publications">1</a> </td> <td class="text"> <a href="/authors/zhao.hua" title="Author Profile"> Zhao, Hua </a> </td></tr> </table> </div> <div class="facet2nd"><a tabindex="0" class="more">all <i class="caret"></i></a> <a tabindex="0" class="less">top 5 <i class="caret"></i></a><h3>Serials</h3> <table class="profile"> <tr> <td class="number"> <a href="/?q=ai%3Ayao.kai+se%3A2352" title="Publications in this Serial">10</a> </td> <td class="text"> <a href="/serials/?q=se%3A2352" title="Serial Profile"> Soft Computing </a> </td></tr><tr> <td class="number"> <a href="/?q=ai%3Ayao.kai+se%3A3151" title="Publications in this Serial">9</a> </td> <td class="text"> <a href="/serials/?q=se%3A3151" title="Serial Profile"> Fuzzy Optimization and Decision Making </a> </td></tr><tr> <td class="number"> <a href="/?q=ai%3Ayao.kai+se%3A2763" title="Publications in this Serial">2</a> </td> <td class="text"> <a href="/serials/?q=se%3A2763" title="Serial Profile"> International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems </a> </td></tr><tr> <td class="number"> <a href="/?q=ai%3Ayao.kai+se%3A9356" title="Publications in this Serial">2</a> </td> <td class="text"> <a href="/serials/?q=se%3A9356" title="Serial Profile"> Springer Uncertainty Research </a> </td></tr><tr> <td class="number"> <a href="/?q=ai%3Ayao.kai+se%3A62" title="Publications in this Serial">1</a> </td> <td class="text"> <a href="/serials/?q=se%3A62" title="Serial Profile"> Computers & Mathematics with Applications </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+se%3A250" title="Publications in this Serial">1</a> </td> <td class="text"> <a href="/serials/?q=se%3A250" title="Serial Profile"> Chaos, Solitons and Fractals </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+se%3A331" title="Publications in this Serial">1</a> </td> <td class="text"> <a href="/serials/?q=se%3A331" title="Serial Profile"> Applied Mathematics and Computation </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+se%3A906" title="Publications in this Serial">1</a> </td> <td class="text"> <a href="/serials/?q=se%3A906" title="Serial Profile"> Insurance Mathematics & Economics </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+se%3A1353" title="Publications in this Serial">1</a> </td> <td class="text"> <a href="/serials/?q=se%3A1353" title="Serial Profile"> Economics Letters </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+se%3A1551" title="Publications in this Serial">1</a> </td> <td class="text"> <a href="/serials/?q=se%3A1551" title="Serial Profile"> Applied Mathematical Modelling </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+se%3A1567" title="Publications in this Serial">1</a> </td> <td class="text"> <a href="/serials/?q=se%3A1567" title="Serial Profile"> Communications in Statistics. Simulation and Computation </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+se%3A1568" title="Publications in this Serial">1</a> </td> <td class="text"> <a href="/serials/?q=se%3A1568" title="Serial Profile"> Communications in Statistics. Theory and Methods </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+se%3A2235" title="Publications in this Serial">1</a> </td> <td class="text"> <a href="/serials/?q=se%3A2235" title="Serial Profile"> Mathematical Problems in Engineering </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+se%3A2967" title="Publications in this Serial">1</a> </td> <td class="text"> <a href="/serials/?q=se%3A2967" title="Serial Profile"> Information </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+se%3A3037" title="Publications in this Serial">1</a> </td> <td class="text"> <a href="/serials/?q=se%3A3037" title="Serial Profile"> Journal of Intelligent and Fuzzy Systems </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+se%3A3222" title="Publications in this Serial">1</a> </td> <td class="text"> <a href="/serials/?q=se%3A3222" title="Serial Profile"> Iranian Journal of Fuzzy Systems </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+se%3A4881" title="Publications in this Serial">1</a> </td> <td class="text"> <a href="/serials/?q=se%3A4881" title="Serial Profile"> International Journal of Operations Research (Taichung) </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+se%3A7351" title="Publications in this Serial">1</a> </td> <td class="text"> <a href="/serials/?q=se%3A7351" title="Serial Profile"> Numerical Algebra, Control and Optimization </a> </td></tr> </table> </div> <div class="facet3rd"><a tabindex="0" class="more">all <i class="caret"></i></a> <a tabindex="0" class="less">top 5 <i class="caret"></i></a><h3>Fields</h3> <table class="profile"> <tr> <td class="number"> <a href="/?q=ai%3Ayao.kai+cc%3A91" title="Publications in this Field">16</a> </td> <td class="text"> <a href="/classification/?q=cc%3A91" title="Mathematics Subject Classification"> Game theory, economics, finance, and other social and behavioral sciences <span style="white-space: nowrap;">(91-XX)</span> </a> </td></tr><tr> <td class="number"> <a href="/?q=ai%3Ayao.kai+cc%3A60" title="Publications in this Field">13</a> </td> <td class="text"> <a href="/classification/?q=cc%3A60" title="Mathematics Subject Classification"> Probability theory and stochastic processes <span style="white-space: nowrap;">(60-XX)</span> </a> </td></tr><tr> <td class="number"> <a href="/?q=ai%3Ayao.kai+cc%3A34" title="Publications in this Field">9</a> </td> <td class="text"> <a href="/classification/?q=cc%3A34" title="Mathematics Subject Classification"> Ordinary differential equations <span style="white-space: nowrap;">(34-XX)</span> </a> </td></tr><tr> <td class="number"> <a href="/?q=ai%3Ayao.kai+cc%3A62" title="Publications in this Field">5</a> </td> <td class="text"> <a href="/classification/?q=cc%3A62" title="Mathematics Subject Classification"> Statistics <span style="white-space: nowrap;">(62-XX)</span> </a> </td></tr><tr> <td class="number"> <a href="/?q=ai%3Ayao.kai+cc%3A90" title="Publications in this Field">5</a> </td> <td class="text"> <a href="/classification/?q=cc%3A90" title="Mathematics Subject Classification"> Operations research, mathematical programming <span style="white-space: nowrap;">(90-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+cc%3A65" title="Publications in this Field">3</a> </td> <td class="text"> <a href="/classification/?q=cc%3A65" title="Mathematics Subject Classification"> Numerical analysis <span style="white-space: nowrap;">(65-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+cc%3A68" title="Publications in this Field">3</a> </td> <td class="text"> <a href="/classification/?q=cc%3A68" title="Mathematics Subject Classification"> Computer science <span style="white-space: nowrap;">(68-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+cc%3A00" title="Publications in this Field">2</a> </td> <td class="text"> <a href="/classification/?q=cc%3A00" title="Mathematics Subject Classification"> General and overarching topics; collections <span style="white-space: nowrap;">(00-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+cc%3A28" title="Publications in this Field">2</a> </td> <td class="text"> <a href="/classification/?q=cc%3A28" title="Mathematics Subject Classification"> Measure and integration <span style="white-space: nowrap;">(28-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+cc%3A93" title="Publications in this Field">2</a> </td> <td class="text"> <a href="/classification/?q=cc%3A93" title="Mathematics Subject Classification"> Systems theory; control <span style="white-space: nowrap;">(93-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+cc%3A94" title="Publications in this Field">2</a> </td> <td class="text"> <a href="/classification/?q=cc%3A94" title="Mathematics Subject Classification"> Information and communication theory, circuits <span style="white-space: nowrap;">(94-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+cc%3A11" title="Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A11" title="Mathematics Subject Classification"> Number theory <span style="white-space: nowrap;">(11-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+cc%3A35" title="Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A35" title="Mathematics Subject Classification"> Partial differential equations <span style="white-space: nowrap;">(35-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ai%3Ayao.kai+cc%3A74" title="Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A74" title="Mathematics Subject Classification"> Mechanics of deformable solids <span style="white-space: nowrap;">(74-XX)</span> </a> </td></tr> </table> </div> <div class="diagram svg-diagram"> <h3>Publications by Year</h3> <div class="diagram ai-diagram" aria-label="publications by year"></div> <style> rect:hover { fill: steelblue; } .axis path, .axis line { fill: none; stroke: #000; shape-rendering: crispEdges; } .bar { fill: steelblue; } a:hover .bar, a:focus .bar { stroke: black; fill-opacity: 60%; } </style> <script src="/static/js/d3.v3.min.js"></script> <script> var margin = { top: 20, right: 0, bottom: 30, left: 50 }; var width = 930 - margin.left - margin.right; var height = 150 - margin.top - margin.bottom; var svg = d3.selectAll(".ai-diagram").append("svg") .attr("width", width + margin.left + margin.right) .attr("height", height + margin.top + margin.bottom) .append("g") .attr("transform", "translate(" + margin.left + "," + margin.top + ")"); var data = [{ year:2001, frequency:1 },{ year:2011, frequency:1 },{ year:2012, frequency:2 },{ year:2013, frequency:4 },{ year:2014, frequency:3 },{ year:2015, frequency:6 },{ year:2016, frequency:2 },{ year:2017, frequency:1 },{ year:2018, frequency:6 },{ year:2019, frequency:2 },{ year:2020, frequency:3 },{ year:2021, frequency:2 },{ year:2022, frequency:3 },{ year:2023, frequency:1 }]; data.forEach(function(d) { d.year = +d.year; d.frequency = +d.frequency; }); var xScale = d3.scale.ordinal() .rangeRoundBands([0, width], .1); var yScale = d3.scale.linear() .range([height, 0]); // fill if less than 20 years span var zero = d3.max( [ 20 - ( d3.max( data, d => d.year ) + 1 - d3.min( data, d => d.year ) ), 0 ] ); // generate range from min to max xScale.domain( d3.range( d3.min( data, d => d.year ), d3.max( data, d => d.year ) + 1 + zero ) ); yScale.domain( [ 0, d3.max( data, d => d.frequency ) ] ); var xAxis = d3.svg.axis() .scale(xScale) .tickValues( // show ticks every 5 years for range up to 50 years, every 10 // years up to 100 years, and every 20 years above that xScale.domain().filter( function(d, i) { let ticks; if (xScale.domain().length <= 50) { ticks = 5; } else if (xScale.domain().length <= 100) { ticks = 10; } else { ticks = 20; } return !(d % ticks); } ) ) .tickSize(6,3,0) // removes end tick .orient("bottom"); var yAxis = d3.svg.axis() .scale(yScale) .ticks(3) // number of ticks .tickFormat(d3.format("d")) // only integers .tickSize(6,3,0) // removes end tick .orient("left"); svg.selectAll(".bar") .data(data) .enter() .append("a") .attr( "xlink:href", d => "/?q=ai%3Ayao.kai+py%3A" + d.year ) .attr( "title", d => d.frequency + " Publication" + (d.frequency > 1 ? "s" : "") + " in " + d.year ) .append("rect") .attr("class", "bar") .attr("x", d => xScale(d.year)) .attr("width", xScale.rangeBand()) .attr("y", d => yScale(d.frequency)) .attr("height", d => height - yScale(d.frequency)); svg.append("g") .attr("class", "x axis") .attr("transform", "translate(0," + height + ")") .call(xAxis); svg.append("g") .attr("class", "y axis") .call(yAxis) .append("text") .attr("transform", "rotate(-90)") .attr("y", 6) .attr("dy", ".75em") .style("text-anchor", "end") .text(""); </script> </div> </div> <div class="publications sort_by_ci hide_more"><div class="more_less"> <a tabindex="0" class="more">all cited Publications <i class="caret"></i></a> <a tabindex="0" class="less">top 5 cited Publications <i class="caret"></i></a> </div><h3>Citations contained in zbMATH Open</h3> <table> <thead> <tr> <th> <strong>29 Publications have been cited 791 times in <a href="/?q=ra%3Ayao.kai">353 Documents</a> </strong> </th> <th> <a tabindex="0" class="sort_cited">Cited by<span class="pub_ci"> ▼</span></a> </th> <th> <a tabindex="0" class="sort_year">Year<span class="pub_py"> ▼</span></a> </th> </tr> </thead> <tbody> <tr class="pub_ci"> <td> <a class="black" href="/1291.65025">A numerical method for solving uncertain differential equations.</a> <a class="label nowrap" href="/1291.65025">Zbl 1291.65025</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/chen.xiaowei" title="Author Profile">Chen, Xiaowei</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6315211">152</a> </div> </td> <td> <div class="citation_year">2013</div> </td> </tr> <tr class="pub_ci"> <td> <a class="black" href="/1412.60104">Some stability theorems of uncertain differential equation.</a> <a class="label nowrap" href="/1412.60104">Zbl 1412.60104</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/gao.jinwu" title="Author Profile">Gao, Jinwu</a>; <a href="/authors/gao.yuan.4" title="Author Profile">Gao, Yuan</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A7059763">86</a> </div> </td> <td> <div class="citation_year">2013</div> </td> </tr> <tr class="pub_ci"> <td> <a class="black" href="/1468.91175">A new option pricing model for stocks in uncertainty markets.</a> <a class="label nowrap" href="/1468.91175">Zbl 1468.91175</a> <br><a href="/authors/peng.jin" title="Author Profile">Peng, Jin</a>; <a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A7368836">62</a> </div> </td> <td> <div class="citation_year">2011</div> </td> </tr> <tr class="pub_ci"> <td> <a class="black" href="/1378.60009">Uncertain differential equations.</a> <a class="label nowrap" href="/1378.60009">Zbl 1378.60009</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6633066">55</a> </div> </td> <td> <div class="citation_year">2016</div> </td> </tr> <tr class="pub_ci"> <td> <a class="black" href="/1437.60033">Parameter estimation in uncertain differential equations.</a> <a class="label nowrap" href="/1437.60033">Zbl 1437.60033</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/liu.baoding" title="Author Profile">Liu, Baoding</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A7197626">53</a> </div> </td> <td> <div class="citation_year">2020</div> </td> </tr> <tr class="pub_ci more"> <td> <a class="black" href="/1398.62207">Uncertain regression analysis: an approach for imprecise observations.</a> <a class="label nowrap" href="/1398.62207">Zbl 1398.62207</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/liu.baoding" title="Author Profile">Liu, Baoding</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6963297">47</a> </div> </td> <td> <div class="citation_year">2018</div> </td> </tr> <tr class="pub_ci more"> <td> <a class="black" href="/1463.93250">Stability in mean for uncertain differential equation.</a> <a class="label nowrap" href="/1463.93250">Zbl 1463.93250</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/ke.hua" title="Author Profile">Ke, Hua</a>; <a href="/authors/sheng.yuhong" title="Author Profile">Sheng, Yuhong</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6954676">40</a> </div> </td> <td> <div class="citation_year">2015</div> </td> </tr> <tr class="pub_ci more"> <td> <a class="black" href="/1428.60092">Uncertain partial differential equation with application to heat conduction.</a> <a class="label nowrap" href="/1428.60092">Zbl 1428.60092</a> <br><a href="/authors/yang.xiangfeng" title="Author Profile">Yang, Xiangfeng</a>; <a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6955113">39</a> </div> </td> <td> <div class="citation_year">2017</div> </td> </tr> <tr class="pub_ci more"> <td> <a class="black" href="/1429.91333">Uncertain contour process and its application in stock model with floating interest rate.</a> <a class="label nowrap" href="/1429.91333">Zbl 1429.91333</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6954678">35</a> </div> </td> <td> <div class="citation_year">2015</div> </td> </tr> <tr class="pub_ci more"> <td> <a class="black" href="/1379.60003">A formula to calculate the variance of uncertain variable.</a> <a class="label nowrap" href="/1379.60003">Zbl 1379.60003</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6705059">34</a> </div> </td> <td> <div class="citation_year">2015</div> </td> </tr> <tr class="pub_ci more"> <td> <a class="black" href="/1277.60144">Uncertain calculus with renewal process.</a> <a class="label nowrap" href="/1277.60144">Zbl 1277.60144</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6119994">27</a> </div> </td> <td> <div class="citation_year">2012</div> </td> </tr> <tr class="pub_ci more"> <td> <a class="black" href="/1322.91022">Uncertain decision making and its application to portfolio selection problem.</a> <a class="label nowrap" href="/1322.91022">Zbl 1322.91022</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/ji.xiaoyu" title="Author Profile">Ji, Xiaoyu</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6497118">21</a> </div> </td> <td> <div class="citation_year">2014</div> </td> </tr> <tr class="pub_ci more"> <td> <a class="black" href="/1398.91632">Interest rate model in uncertain environment based on exponential Ornstein-Uhlenbeck equation.</a> <a class="label nowrap" href="/1398.91632">Zbl 1398.91632</a> <br><a href="/authors/sun.yiyao" title="Author Profile">Sun, Yiyao</a>; <a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/fu.zongfei" title="Author Profile">Fu, Zongfei</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6960067">15</a> </div> </td> <td> <div class="citation_year">2018</div> </td> </tr> <tr class="pub_ci more"> <td> <a class="black" href="/1371.91185">A mean-reverting currency model in an uncertain environment.</a> <a class="label nowrap" href="/1371.91185">Zbl 1371.91185</a> <br><a href="/authors/shen.yuanyuan" title="Author Profile">Shen, Yuanyuan</a>; <a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6773322">14</a> </div> </td> <td> <div class="citation_year">2016</div> </td> </tr> <tr class="pub_ci more"> <td> <a class="black" href="/1361.60048">Uncertain differential equation with jumps.</a> <a class="label nowrap" href="/1361.60048">Zbl 1361.60048</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6704241">14</a> </div> </td> <td> <div class="citation_year">2015</div> </td> </tr> <tr class="pub_ci more"> <td> <a class="black" href="/1449.91149">A no-arbitrage theorem for uncertain stock model.</a> <a class="label nowrap" href="/1449.91149">Zbl 1449.91149</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6954645">14</a> </div> </td> <td> <div class="citation_year">2015</div> </td> </tr> <tr class="pub_ci more"> <td> <a class="black" href="/1323.94062">Sine entropy for uncertain variables.</a> <a class="label nowrap" href="/1323.94062">Zbl 1323.94062</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/gao.jinwu" title="Author Profile">Gao, Jinwu</a>; <a href="/authors/dai.wei.6" title="Author Profile">Dai, Wei</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6504290">12</a> </div> </td> <td> <div class="citation_year">2013</div> </td> </tr> <tr class="pub_ci more"> <td> <a class="black" href="/1323.90010">A transportation model with uncertain costs and demands.</a> <a class="label nowrap" href="/1323.90010">Zbl 1323.90010</a> <br><a href="/authors/sheng.yuhong" title="Author Profile">Sheng, Yuhong</a>; <a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6499741">12</a> </div> </td> <td> <div class="citation_year">2012</div> </td> </tr> <tr class="pub_ci more"> <td> <a class="black" href="/1318.91127">A modified insurance risk process with uncertainty.</a> <a class="label nowrap" href="/1318.91127">Zbl 1318.91127</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/qin.zhongfeng" title="Author Profile">Qin, Zhongfeng</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6439983">10</a> </div> </td> <td> <div class="citation_year">2015</div> </td> </tr> <tr class="pub_ci more"> <td> <a class="black" href="/1331.60176">Age replacement policy in uncertain environment.</a> <a class="label nowrap" href="/1331.60176">Zbl 1331.60176</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/ralescu.dan-a" title="Author Profile">Ralescu, Dan A.</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6542077">8</a> </div> </td> <td> <div class="citation_year">2013</div> </td> </tr> <tr class="pub_ci more"> <td> <a class="black" href="/1479.91420">Barrier option pricing formulas of an uncertain stock model.</a> <a class="label nowrap" href="/1479.91420">Zbl 1479.91420</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/qin.zhongfeng" title="Author Profile">Qin, Zhongfeng</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A7434885">6</a> </div> </td> <td> <div class="citation_year">2021</div> </td> </tr> <tr class="pub_ci more"> <td> <a class="black" href="/1398.91617">Asian option pricing problems of uncertain mean-reverting stock model.</a> <a class="label nowrap" href="/1398.91617">Zbl 1398.91617</a> <br><a href="/authors/sun.yiyao" title="Author Profile">Sun, Yiyao</a>; <a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/dong.jichang" title="Author Profile">Dong, Jichang</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6963298">5</a> </div> </td> <td> <div class="citation_year">2018</div> </td> </tr> <tr class="pub_ci more"> <td> <a class="black" href="/1449.34005">Continuous dependence theorems on solutions of uncertain differential equations.</a> <a class="label nowrap" href="/1449.34005">Zbl 1449.34005</a> <br><a href="/authors/gao.yuan.4" title="Author Profile">Gao, Yuan</a>; <a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6991512">5</a> </div> </td> <td> <div class="citation_year">2014</div> </td> </tr> <tr 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processes.</a> <a class="label nowrap" href="/1448.60004">Zbl 1448.60004</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A7076540">3</a> </div> </td> <td> <div class="citation_year">2019</div> </td> </tr> <tr class="pub_ci more"> <td> <a class="black" href="/1489.65092">Levenberg-Marquardt method for absolute value equation associated with second-order cone.</a> <a class="label nowrap" href="/1489.65092">Zbl 1489.65092</a> <br><a href="/authors/miao.xinhe" title="Author Profile">Miao, Xin-He</a>; <a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/yang.chingyu" title="Author Profile">Yang, Ching-Yu</a>; <a href="/authors/chen.jein-shan" title="Author Profile">Chen, Jein-Shan</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A7471923">2</a> </div> </td> <td> <div class="citation_year">2022</div> </td> </tr> <tr class="pub_ci more"> <td> <a class="black" href="/1495.60020">Continuity and variation analysis of fractional uncertain processes.</a> <a class="label nowrap" href="/1495.60020">Zbl 1495.60020</a> <br><a href="/authors/sheng.yuhong" title="Author Profile">Sheng, Yuhong</a>; <a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/qin.zhongfeng" title="Author Profile">Qin, Zhongfeng</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A7508314">2</a> </div> </td> <td> <div class="citation_year">2020</div> </td> </tr> <tr class="pub_ci more"> <td> <a class="black" href="/1449.28017">Conditional uncertain set and conditional membership function.</a> <a class="label nowrap" href="/1449.28017">Zbl 1449.28017</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6955261">1</a> </div> </td> <td> <div class="citation_year">2018</div> </td> </tr> <tr class="pub_py"> <td> <a class="black" href="/1489.65092">Levenberg-Marquardt method for absolute value equation associated with second-order cone.</a> <a class="label nowrap" href="/1489.65092">Zbl 1489.65092</a> <br><a href="/authors/miao.xinhe" title="Author Profile">Miao, Xin-He</a>; <a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/yang.chingyu" title="Author Profile">Yang, Ching-Yu</a>; <a href="/authors/chen.jein-shan" title="Author Profile">Chen, Jein-Shan</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A7471923">2</a> </div> </td> <td> <div class="citation_year">2022</div> </td> </tr> <tr class="pub_py"> <td> <a class="black" href="/1479.91420">Barrier option pricing formulas of an uncertain stock model.</a> <a class="label nowrap" href="/1479.91420">Zbl 1479.91420</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/qin.zhongfeng" title="Author Profile">Qin, Zhongfeng</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A7434885">6</a> </div> </td> <td> <div class="citation_year">2021</div> </td> </tr> <tr class="pub_py"> <td> <a class="black" href="/1437.60033">Parameter estimation in uncertain differential equations.</a> <a class="label nowrap" href="/1437.60033">Zbl 1437.60033</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/liu.baoding" title="Author Profile">Liu, Baoding</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A7197626">53</a> </div> </td> <td> <div class="citation_year">2020</div> </td> </tr> <tr class="pub_py"> <td> <a class="black" href="/1495.60020">Continuity and variation analysis of fractional uncertain processes.</a> <a class="label nowrap" href="/1495.60020">Zbl 1495.60020</a> <br><a href="/authors/sheng.yuhong" title="Author Profile">Sheng, Yuhong</a>; <a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/qin.zhongfeng" title="Author Profile">Qin, Zhongfeng</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A7508314">2</a> </div> </td> <td> <div class="citation_year">2020</div> </td> </tr> <tr class="pub_py"> <td> <a class="black" href="/1418.60113">First hitting time of uncertain random renewal reward process and its application in insurance risk process.</a> <a class="label nowrap" href="/1418.60113">Zbl 1418.60113</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A7093997">3</a> </div> </td> <td> <div class="citation_year">2019</div> </td> </tr> <tr class="pub_py more"> <td> <a class="black" href="/1448.60004">Uncertain renewal processes.</a> <a class="label nowrap" href="/1448.60004">Zbl 1448.60004</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A7076540">3</a> </div> </td> <td> <div class="citation_year">2019</div> </td> </tr> <tr class="pub_py more"> <td> <a class="black" href="/1398.62207">Uncertain regression analysis: an approach for 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href="/1398.91617">Asian option pricing problems of uncertain mean-reverting stock model.</a> <a class="label nowrap" href="/1398.91617">Zbl 1398.91617</a> <br><a href="/authors/sun.yiyao" title="Author Profile">Sun, Yiyao</a>; <a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/dong.jichang" title="Author Profile">Dong, Jichang</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6963298">5</a> </div> </td> <td> <div class="citation_year">2018</div> </td> </tr> <tr class="pub_py more"> <td> <a class="black" href="/1449.28017">Conditional uncertain set and conditional membership function.</a> <a class="label nowrap" href="/1449.28017">Zbl 1449.28017</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6955261">1</a> </div> </td> <td> <div class="citation_year">2018</div> </td> </tr> <tr class="pub_py more"> <td> <a class="black" href="/1428.60092">Uncertain partial differential equation with application to heat conduction.</a> <a class="label nowrap" href="/1428.60092">Zbl 1428.60092</a> <br><a href="/authors/yang.xiangfeng" title="Author Profile">Yang, Xiangfeng</a>; <a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6955113">39</a> </div> </td> <td> <div class="citation_year">2017</div> </td> </tr> <tr class="pub_py more"> <td> <a class="black" href="/1378.60009">Uncertain differential equations.</a> <a class="label nowrap" href="/1378.60009">Zbl 1378.60009</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6633066">55</a> </div> </td> <td> <div class="citation_year">2016</div> </td> </tr> <tr class="pub_py more"> <td> <a class="black" href="/1371.91185">A mean-reverting currency model in an uncertain environment.</a> <a class="label nowrap" href="/1371.91185">Zbl 1371.91185</a> <br><a href="/authors/shen.yuanyuan" title="Author Profile">Shen, Yuanyuan</a>; <a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6773322">14</a> </div> </td> <td> <div class="citation_year">2016</div> </td> </tr> <tr class="pub_py more"> <td> <a class="black" href="/1463.93250">Stability in mean for uncertain differential equation.</a> <a class="label nowrap" href="/1463.93250">Zbl 1463.93250</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/ke.hua" title="Author Profile">Ke, Hua</a>; <a href="/authors/sheng.yuhong" title="Author Profile">Sheng, Yuhong</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6954676">40</a> </div> </td> <td> <div class="citation_year">2015</div> </td> </tr> <tr class="pub_py more"> <td> <a class="black" href="/1429.91333">Uncertain contour process and its application in stock model with floating interest rate.</a> <a class="label nowrap" href="/1429.91333">Zbl 1429.91333</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6954678">35</a> </div> </td> <td> <div class="citation_year">2015</div> </td> </tr> <tr class="pub_py more"> <td> <a class="black" href="/1379.60003">A formula to calculate the variance of uncertain variable.</a> <a class="label nowrap" href="/1379.60003">Zbl 1379.60003</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6705059">34</a> </div> </td> <td> <div class="citation_year">2015</div> </td> </tr> <tr class="pub_py more"> <td> <a class="black" href="/1361.60048">Uncertain differential equation with jumps.</a> <a class="label nowrap" href="/1361.60048">Zbl 1361.60048</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6704241">14</a> </div> </td> <td> <div class="citation_year">2015</div> </td> </tr> <tr class="pub_py more"> <td> <a class="black" href="/1449.91149">A no-arbitrage theorem for uncertain stock model.</a> <a class="label nowrap" href="/1449.91149">Zbl 1449.91149</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6954645">14</a> </div> </td> <td> <div class="citation_year">2015</div> </td> </tr> <tr class="pub_py more"> <td> <a class="black" href="/1318.91127">A modified insurance risk process with uncertainty.</a> <a class="label nowrap" href="/1318.91127">Zbl 1318.91127</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/qin.zhongfeng" title="Author Profile">Qin, Zhongfeng</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6439983">10</a> </div> </td> <td> <div class="citation_year">2015</div> </td> </tr> <tr class="pub_py more"> <td> <a class="black" href="/1322.91022">Uncertain decision making and its application to portfolio selection problem.</a> <a class="label nowrap" href="/1322.91022">Zbl 1322.91022</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/ji.xiaoyu" title="Author Profile">Ji, Xiaoyu</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6497118">21</a> </div> </td> <td> <div class="citation_year">2014</div> </td> </tr> <tr class="pub_py more"> <td> <a class="black" href="/1449.34005">Continuous dependence theorems on solutions of uncertain differential equations.</a> <a class="label nowrap" href="/1449.34005">Zbl 1449.34005</a> <br><a href="/authors/gao.yuan.4" title="Author Profile">Gao, Yuan</a>; <a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6991512">5</a> </div> </td> <td> <div class="citation_year">2014</div> </td> </tr> <tr class="pub_py more"> <td> <a class="black" href="/1334.62013">Entropy operator for membership function of uncertain set.</a> <a class="label nowrap" href="/1334.62013">Zbl 1334.62013</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/ke.hua" title="Author Profile">Ke, Hua</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6574925">5</a> </div> </td> <td> <div class="citation_year">2014</div> </td> </tr> <tr class="pub_py more"> <td> <a class="black" href="/1291.65025">A numerical method for solving uncertain differential equations.</a> <a class="label nowrap" href="/1291.65025">Zbl 1291.65025</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/chen.xiaowei" title="Author Profile">Chen, Xiaowei</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6315211">152</a> </div> </td> <td> <div class="citation_year">2013</div> </td> </tr> <tr class="pub_py more"> <td> <a class="black" href="/1412.60104">Some stability theorems of uncertain differential equation.</a> <a class="label nowrap" href="/1412.60104">Zbl 1412.60104</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/gao.jinwu" title="Author Profile">Gao, Jinwu</a>; <a href="/authors/gao.yuan.4" title="Author Profile">Gao, Yuan</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A7059763">86</a> </div> </td> <td> <div class="citation_year">2013</div> </td> </tr> <tr class="pub_py more"> <td> <a class="black" href="/1323.94062">Sine entropy for uncertain variables.</a> <a class="label nowrap" href="/1323.94062">Zbl 1323.94062</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/gao.jinwu" title="Author Profile">Gao, Jinwu</a>; <a href="/authors/dai.wei.6" title="Author Profile">Dai, Wei</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6504290">12</a> </div> </td> <td> <div class="citation_year">2013</div> </td> </tr> <tr class="pub_py more"> <td> <a class="black" href="/1331.60176">Age replacement policy in uncertain environment.</a> <a class="label nowrap" href="/1331.60176">Zbl 1331.60176</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a>; <a href="/authors/ralescu.dan-a" title="Author Profile">Ralescu, Dan A.</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6542077">8</a> </div> </td> <td> <div class="citation_year">2013</div> </td> </tr> <tr class="pub_py more"> <td> <a class="black" href="/1277.60144">Uncertain calculus with renewal process.</a> <a class="label nowrap" href="/1277.60144">Zbl 1277.60144</a> <br><a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6119994">27</a> </div> </td> <td> <div class="citation_year">2012</div> </td> </tr> <tr class="pub_py more"> <td> <a class="black" href="/1323.90010">A transportation model with uncertain costs and demands.</a> <a class="label nowrap" href="/1323.90010">Zbl 1323.90010</a> <br><a href="/authors/sheng.yuhong" title="Author Profile">Sheng, Yuhong</a>; <a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A6499741">12</a> </div> </td> <td> <div class="citation_year">2012</div> </td> </tr> <tr class="pub_py more"> <td> <a class="black" href="/1468.91175">A new option pricing model for stocks in uncertainty markets.</a> <a class="label nowrap" href="/1468.91175">Zbl 1468.91175</a> <br><a href="/authors/peng.jin" title="Author Profile">Peng, Jin</a>; <a href="/authors/yao.kai" title="Author Profile">Yao, Kai</a></td> <td> <div class="citation_count"> <a href="/?q=rf%3A7368836">62</a> </div> </td> <td> <div class="citation_year">2011</div> </td> </tr> </tbody> </table><div class="more_less"> <a tabindex="0" class="more">all cited Publications <i class="caret"></i></a> <a tabindex="0" class="less">top 5 cited Publications <i class="caret"></i></a> </div></div> <div class="profile"> <div class="facet1st"><a tabindex="0" class="more">all <i class="caret"></i></a> <a tabindex="0" 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control <span style="white-space: nowrap;">(93-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A65" title="Citing Publications in this Field">25</a> </td> <td class="text"> <a href="/classification/?q=cc%3A65" title="Mathematics Subject Classification"> Numerical analysis <span style="white-space: nowrap;">(65-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A49" title="Citing Publications in this Field">15</a> </td> <td class="text"> <a href="/classification/?q=cc%3A49" title="Mathematics Subject Classification"> Calculus of variations and optimal control; optimization <span style="white-space: nowrap;">(49-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A92" title="Citing Publications in this Field">15</a> </td> <td class="text"> <a href="/classification/?q=cc%3A92" title="Mathematics Subject Classification"> Biology and other natural sciences <span style="white-space: nowrap;">(92-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A68" title="Citing Publications in this Field">13</a> </td> <td class="text"> <a href="/classification/?q=cc%3A68" title="Mathematics Subject Classification"> Computer science <span style="white-space: nowrap;">(68-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A26" title="Citing Publications in this Field">12</a> </td> <td class="text"> <a href="/classification/?q=cc%3A26" title="Mathematics Subject Classification"> Real functions <span style="white-space: nowrap;">(26-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A28" title="Citing Publications in this Field">12</a> </td> <td class="text"> <a href="/classification/?q=cc%3A28" title="Mathematics Subject Classification"> Measure and integration <span style="white-space: nowrap;">(28-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A35" title="Citing Publications in this Field">11</a> </td> <td class="text"> <a href="/classification/?q=cc%3A35" title="Mathematics Subject Classification"> Partial differential equations <span style="white-space: nowrap;">(35-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A94" title="Citing Publications in this Field">8</a> </td> <td class="text"> <a href="/classification/?q=cc%3A94" title="Mathematics Subject Classification"> Information and communication theory, circuits <span style="white-space: nowrap;">(94-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A05" title="Citing Publications in this Field">4</a> </td> <td class="text"> <a href="/classification/?q=cc%3A05" title="Mathematics Subject Classification"> Combinatorics <span style="white-space: nowrap;">(05-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A37" title="Citing Publications in this Field">4</a> </td> <td class="text"> <a href="/classification/?q=cc%3A37" title="Mathematics Subject Classification"> Dynamical systems and ergodic theory <span style="white-space: nowrap;">(37-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A40" title="Citing Publications in this Field">4</a> </td> <td class="text"> <a href="/classification/?q=cc%3A40" title="Mathematics Subject Classification"> Sequences, series, summability <span style="white-space: nowrap;">(40-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A82" title="Citing Publications in this Field">4</a> </td> <td class="text"> <a href="/classification/?q=cc%3A82" title="Mathematics Subject Classification"> Statistical mechanics, structure of matter <span style="white-space: nowrap;">(82-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A70" title="Citing Publications in this Field">3</a> </td> <td class="text"> <a href="/classification/?q=cc%3A70" title="Mathematics Subject Classification"> Mechanics of particles and systems <span style="white-space: nowrap;">(70-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A00" title="Citing Publications in this Field">2</a> </td> <td class="text"> <a href="/classification/?q=cc%3A00" title="Mathematics Subject Classification"> General and overarching topics; collections <span style="white-space: nowrap;">(00-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A03" title="Citing Publications in this Field">2</a> </td> <td class="text"> <a href="/classification/?q=cc%3A03" title="Mathematics Subject Classification"> Mathematical logic and foundations <span style="white-space: nowrap;">(03-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A39" title="Citing Publications in this Field">2</a> </td> <td class="text"> <a href="/classification/?q=cc%3A39" title="Mathematics Subject Classification"> Difference and functional equations <span style="white-space: nowrap;">(39-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A45" title="Citing Publications in this Field">2</a> </td> <td class="text"> <a href="/classification/?q=cc%3A45" title="Mathematics Subject Classification"> Integral equations <span style="white-space: nowrap;">(45-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A80" title="Citing Publications in this Field">2</a> </td> <td class="text"> <a href="/classification/?q=cc%3A80" title="Mathematics Subject Classification"> Classical thermodynamics, heat transfer <span style="white-space: nowrap;">(80-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A33" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A33" title="Mathematics Subject Classification"> Special functions <span style="white-space: nowrap;">(33-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A41" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A41" title="Mathematics Subject Classification"> Approximations and expansions <span style="white-space: nowrap;">(41-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A44" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A44" title="Mathematics Subject Classification"> Integral transforms, operational calculus <span style="white-space: nowrap;">(44-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A46" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A46" title="Mathematics Subject Classification"> Functional analysis <span style="white-space: nowrap;">(46-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A47" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A47" title="Mathematics Subject Classification"> Operator theory <span style="white-space: nowrap;">(47-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A74" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A74" title="Mathematics Subject Classification"> Mechanics of deformable solids <span style="white-space: nowrap;">(74-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A76" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A76" title="Mathematics Subject Classification"> Fluid mechanics <span style="white-space: nowrap;">(76-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=ra%3Ayao.kai+cc%3A86" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A86" title="Mathematics Subject Classification"> Geophysics <span style="white-space: nowrap;">(86-XX)</span> </a> </td></tr> </table> </div> <div class="diagram svg-diagram"> <h3>Citations by Year</h3> <div class="diagram ci-diagram" aria-label="citations by year"></div> <style> rect:hover { fill: steelblue; } .axis path, .axis line { fill: none; stroke: #000; shape-rendering: crispEdges; } .bar { fill: steelblue; } a:hover .bar, a:focus .bar { stroke: black; fill-opacity: 60%; } </style> <script> var margin = { top: 20, right: 0, bottom: 30, left: 50 }; var width = 930 - margin.left - margin.right; var height = 150 - margin.top - margin.bottom; var svg = d3.selectAll(".ci-diagram").append("svg") .attr("width", width + margin.left + margin.right) .attr("height", height + margin.top + margin.bottom) .append("g") .attr("transform", "translate(" + margin.left + "," + margin.top + ")"); var data = [{ year:2012, frequency:1 },{ year:2013, frequency:7 },{ year:2014, frequency:10 },{ year:2015, frequency:19 },{ year:2016, frequency:13 },{ year:2017, frequency:19 },{ year:2018, frequency:40 },{ year:2019, frequency:31 },{ year:2020, frequency:48 },{ year:2021, frequency:70 },{ year:2022, frequency:31 },{ year:2023, frequency:33 },{ year:2024, frequency:27 },{ year:2025, frequency:4 }]; data.forEach(function(d) { d.year = +d.year; d.frequency = +d.frequency; }); var xScale = d3.scale.ordinal() .rangeRoundBands([0, width], .1); var yScale = d3.scale.linear() .range([height, 0]); // fill if less than 20 years span var zero = d3.max( [ 20 - ( d3.max( data, d => d.year ) + 1 - d3.min( data, d => d.year ) ), 0 ] ); // generate range from min to max xScale.domain( d3.range( d3.min( data, d => d.year ), d3.max( data, d => d.year ) + 1 + zero ) ); yScale.domain( [ 0, d3.max( data, d => d.frequency ) ] ); var xAxis = d3.svg.axis() .scale(xScale) .tickValues( // show ticks every 5 years for range up to 50 years, every 10 // years up to 100 years, and every 20 years above that xScale.domain().filter( function(d, i) { let ticks; if (xScale.domain().length <= 50) { ticks = 5; } else if (xScale.domain().length <= 100) { ticks = 10; } else { ticks = 20; } return !(d % ticks); } ) ) .tickSize(6,3,0) // removes end tick .orient("bottom"); var yAxis = d3.svg.axis() .scale(yScale) .ticks(3) // number of ticks .tickFormat(d3.format("d")) // only integers .tickSize(6,3,0) // removes end tick .orient("left"); svg.selectAll(".bar") .data(data) .enter() .append("a") .attr( "xlink:href", d => "/?q=ra%3Ayao.kai+py%3A" + d.year ) .attr( "title", d => d.frequency + " Citation" + (d.frequency > 1 ? "s" : "") + " in " + d.year ) .append("rect") .attr("class", "bar") .attr("x", d => xScale(d.year)) .attr("width", xScale.rangeBand()) .attr("y", d => yScale(d.frequency)) .attr("height", d => height - yScale(d.frequency)); svg.append("g") .attr("class", "x axis") .attr("transform", "translate(0," + height + ")") .call(xAxis); svg.append("g") .attr("class", "y axis") .call(yAxis) .append("text") .attr("transform", "rotate(-90)") .attr("y", 6) .attr("dy", ".75em") .style("text-anchor", "end") .text(""); </script> </div> </div> </article> </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>

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