On the approximation of geometric densities of random closed sets

<!DOCTYPE html> <html lang="it"> <head> <meta charset="utf-8"> <meta http-equiv="X-UA-Compatible" content="IE=edge"> <meta name="viewport" content="width=device-width, initial-scale=1.0"> <link rel="shortcut icon" href="/sr/favicon.ico" /> <link href="/sr/jstree/themes/default/style.min.css" rel="stylesheet" type="text/css"><link rel="stylesheet" href="/sr/jquery-ui/jquery-ui.min.css"> <link rel="stylesheet" type="text/css" href="https://static.cineca.it/jd/npm/jgrowl@1.4.9/jquery.jgrowl.min.css" /> <link rel="stylesheet" href="https://static.cineca.it/jd/npm/select2@4.0.13/dist/css/select2.min.css" /> <link rel="stylesheet" href="https://static.cineca.it/jd/npm/select2-bootstrap-5-theme@1.1.1/dist/select2-bootstrap-5-theme.min.css" /> <link rel="stylesheet" href="/sr/cineca/css/bootstrap-ricerca.min.css"> <link rel="stylesheet" href="/sr/local.css"><title>On the approximation of geometric densities of random closed sets</title> <script src="https://static.cineca.it/jd/npm/jquery@3.7.1/dist/jquery.min.js" integrity="sha512-v2CJ7UaYy4JwqLDIrZUI/4hqeoQieOmAZNXBeQyjo21dadnwR+8ZaIJVT8EE2iyI61OV8e6M8PP2/4hpQINQ/g==" crossorigin="anonymous"></script> <script type="text/javascript" src="/sr/jquery-ui/jquery-ui.min.js"></script> <script type="text/javascript" src="/sr/jquery-ui-i18n/jquery.ui.datepicker-it.latest.js" charset="utf-8"></script> <script src="https://static.cineca.it/jd/npm/bootstrap@5.2.3/dist/js/bootstrap.bundle.min.js" integrity="sha384-kenU1KFdBIe4zVF0s0G1M5b4hcpxyD9F7jL+jjXkk+Q2h455rYXK/7HAuoJl+0I4" crossorigin="anonymous"></script> <script src="https://static.cineca.it/jd/npm/jgrowl@1.4.9/jquery.jgrowl.min.js"></script> <script src="https://static.cineca.it/jd/npm/select2@4.0.13/dist/js/select2.full.min.js"></script> <script src="https://static.cineca.it/jd/npm/blueimp-tmpl@3.20.0/js/tmpl.min.js"></script><script type="text/javascript" src="/sr/jstree/jstree.min.js"></script><script type="text/javascript" src="/sr/jquery/js/jquery.displaytag-ajax-1.2.js"></script> <script src="https://static.cineca.it/jd/npm/js-cookie@3.0.5/dist/js.cookie.min.js" integrity="sha256-WCzAhd2P6gRJF9Hv3oOOd+hFJi/QJbv+Azn4CGB8gfY=" crossorigin="anonymous" referrerpolicy="no-referrer"></script> <script> var JQ = $; var j = $; </script> <script type="text/javascript"> </script> <script type="text/javascript" src="/sr/cineca/js/cilea.js?fwkVersion=24.11.2.0"></script> <script type="text/javascript" src="/sr/cineca/js/fragment.js?fwkVersion=24.11.2.0"></script> <script type="text/javascript" src="/sr/cineca/js/treeview.js?fwkVersion=24.11.2.0"></script> <script type="text/javascript" src="/sr/cineca/js/ap-tool.js?fwkVersion=24.11.2.0"></script> <span style="display:none;" id="rememberToSaveText">Attenzione: i dati modificati non sono ancora stati salvati. Per confermare inserimenti o cancellazioni di voci è necessario confermare con il tasto SALVA/INSERISCI in fondo alla pagina</span> <script type="text/javascript" src="/sr/cineca/js/print.js?fwkVersion=24.11.2.0"></script> <script type="text/javascript" src="/sr/cineca/js/widget.js?fwkVersion=24.11.2.0"></script> <script type="text/javascript" src="/sr/cineca/js/layout.js?fwkVersion=24.11.2.0"></script> <script type="text/javascript"> var authenticatedPersonId=''; var authenticatedUser=false; </script> <script type="text/javascript" src="https://ricerca.sns.it/static/js/utils.js"></script> <script type="text/javascript" src="https://ricerca.sns.it/static/js/choice-support.js"></script> <script type="text/javascript"> j(document).ready(function() { j('body').on('change','#itemxpage', function() { var dspaceObjectId = $('#dspaceObjectId').val(); if (dspaceObjectId != null && dspaceObjectId != '') { $('#modal_display_item').modal('toggle'); showEventLog(dspaceObjectId, '1', this.value); } }); j('body').on('click',"#modal_display_item .pagination li:not('.active') .page-link", function(event) { var pagesize = $('#itemxpage').val(); var dspaceObjectId = $('#dspaceObjectId').val(); var url = new URL(this.href); var page = url.searchParams.get("page"); if (page == null || isNaN(page)){ page = 1; } if (dspaceObjectId != null && dspaceObjectId != '') { $('#modal_display_item').modal('toggle'); showEventLog(dspaceObjectId,page, pagesize); } return false; }); }); function showEventLog(dsoId, page, pagesize) { var url = "/dspaceObjectEventLog/widgetSearch.modal"; jQuery.ajax({ url: url, method: 'GET', data: {dspaceObjectId: dsoId, posting: 1, modalSize: 'xlarge', page: page, pageSize: pagesize}, success: function(data) { var $modal = $(data); $modal.attr('id','modal_display_item'); $('body').append($modal); var myModal = new bootstrap.Modal(document.getElementById('modal_display_item'), {backdrop: true}); myModal.show(); $modal.filter('.modal').on('hidden.bs.modal', function(){ $modal.remove(); }); } }); } </script> <script type"text/javascript"> $(document).ready(function() { checkMoreless(); }); function checkMoreless() { if($('.moreless-more').length) { var more = $('<a class="btn-link"></a>').html(' espandi'); more.click(function(){ var moretext = $(this).next('.moreless-more'); var lesstext = $(this).prev('.moreless-fixed'); lesstext.html(lesstext.html().substring(0, lesstext.html().length-3)); moretext.toggleClass('hide'); $(this).toggleClass('hide'); var less = $('<a class="btn-link"></a>').html(' comprimi'); less.click(function(){ var moretext = $(this).prev('.moreless-more'); moretext.toggleClass('hide'); $(this).toggleClass('hide'); moretext.prev('a').toggleClass('hide'); var elements = document.getElementsByTagName('span'); for (var i = 0; i < elements.length; i++) { if((elements[i].className).indexOf('moreless-fixed') > -1) { if(elements[i].innerHTML.indexOf('...') == -1){ elements[i].innerHTML=elements[i].innerHTML+'...'; } } } }); moretext.after(less); }); $('.moreless-more').before(more); $('.moreless-more').toggleClass('hide'); } } </script><script> window.customCookieJsonConfigPath='/sr/cookie-config.json'; </script> <script src="https://static.iu.cineca.it/v1/default.js"></script> <script type="text/javascript"> function isThirdPartyCookieEnabled() { var cookieString = Cookies.get('cc_cookie'); if (cookieString==null||cookieString=="") return false; var cookieJson = JSON.parse(cookieString); var retValue = false; $.each(cookieJson.level , function (key, value) { if(value == 'thirdParty') retValue = true; }); return retValue; } $(document).on('click', '.c-bn', function() { Cookies.set('thirdParty',isThirdPartyCookieEnabled(), { path: '/'}); }); Cookies.set('thirdParty',isThirdPartyCookieEnabled(), { path: '/' }); </script> <script type="text/javascript"> $(document).ready(function() { if (typeof trackEventCategoryDone === "undefined") { trackEvent('trackPageView'); } }); </script> <script type="text/javascript" src="/sr/local.js?fwkVersion=24.11.2.0"></script> <link rel="schema.DCTERMS" href="http://purl.org/dc/terms/" /> <link rel="schema.DC" href="http://purl.org/dc/elements/1.1/" /> <meta name="DC.description" content="3" /> <meta name="DC.identifier" content="http://hdl.handle.net/11384/92148" scheme="DCTERMS.URI" /> <meta name="DC.language" content="en" xml:lang="en" scheme="DCTERMS.RFC1766" /> <meta name="DCTERMS.issued" content="2006-05-09" xml:lang="en" scheme="DCTERMS.W3CDTF" /> <meta name="DC.type" content="262" /> <meta name="DC.description" content="Journal article published in: Bernoulli, vol. 15 (2009), 4, 1222-1242, DOI:
10.3150/09-BEJ186, available also at URL http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.bj/1262962233 - The publisher (Bernoulli Society for Mathematical Statistics and Probability) allows to archive the journal publisher's version on any open access repository [source: Sherpa-Romeo at URL http://www.sherpa.ac.uk/romeo/issn/1350-7265/ ]" xml:lang="en" /> <meta name="DCTERMS.available" content="2020-12-14T11:09:36Z" scheme="DCTERMS.W3CDTF" /> <meta name="DC.publisher" content="Bernoulli Society for Mathematical Statistics and Probability" xml:lang="en" /> <meta name="DC.title" content="On the approximation of geometric densities of random closed sets" xml:lang="en" /> <meta name="DC.type" content="1 Contributo su Rivista::1.1 Articolo in rivista" xml:lang="it" /> <meta name="DC.type" content="1.1 Articolo in rivista" /> <meta name="DC.description" content="open" xml:lang="en" /> <meta name="DC.type" content="info:eu-repo/semantics/article" /> <meta name="DC.description" content="Many real phenomena may be modelled as random closed sets in Rd, of different Hausdorff dimensions. The authors have recently revisited the
concept of mean geometric densities of random closed sets θn with Hausdorff dimension n ≤ d with respect to the standard Lebesgue measure
on Rd, in terms of expected values of a suitable class of linear functionals (Delta functions à la Dirac). In many real applications such as fiber
processes, n-facets of random tessellations of dimension n ≤ d in spaces
of dimension d ≥ 1, several problems are related to the estimation of
such mean densities; in order to face such problems in the general setting of spatially inhomogeneous processes, we suggest and analyze here
an approximation of mean densities for sufficiently regular random closed
sets. We will show how some known results in literature follow as particular cases. A series of examples throughout the paper are provided to
exemplify various relevant situations." xml:lang="en" /> <meta name="DC.description" content="open" xml:lang="en" /> <meta name="DC.subject" content="Mathematics" xml:lang="en" /> <meta name="DC.subject" content="Mean Geometric densities" xml:lang="en" /> <meta name="DC.subject" content="Random Distributions" xml:lang="en" /> <meta name="DC.subject" content="Stochastic geometry" xml:lang="en" /> <meta name="DC.contributor" content="Classe di Scienze" xml:lang="*" /> <meta name="DC.contributor" content="22714" xml:lang="*" /> <meta name="DC.subject" content="Mathematics" xml:lang="*" /> <meta name="DC.subject" content="Mean Geometric densities" xml:lang="*" /> <meta name="DC.subject" content="Random Distributions" xml:lang="*" /> <meta name="DC.subject" content="Stochastic geometry" xml:lang="*" /> <meta name="DC.date" content="2023/07/23 08:57:20" xml:lang="*" scheme="DCTERMS.W3CDTF" /> <meta name="DC.date" content="1690095440542" xml:lang="*" scheme="DCTERMS.W3CDTF" /> <meta name="DC.contributor" content="AREA MIN. 01 - Scienze matematiche e informatiche" xml:lang="*" /> <meta name="DC.description" content="Capasso, Vincenzo; Villa, Elena; Ambrosio, Luigi;" /> <meta name="DC.description" content="Capasso, Vincenzo; Villa, Elena; Ambrosio, Luigi" /> <meta name="citation_title" content="On the approximation of geometric densities of random closed sets" /> <meta name="citation_author" content="Capasso, Vincenzo" /> <meta name="citation_author" content="Villa, Elena" /> <meta name="citation_author" content="Ambrosio, Luigi" /> <meta name="citation_author_email" content="luigi.ambrosio@sns.it" /> <meta name="citation_author_orcid" content="0000-0001-5077-159X" /> <meta name="citation_date" content="2006-05-09" /> <meta name="citation_abstract_html_url" content="https://ricerca.sns.it/handle/11384/92148" /> <meta name="citation_pdf_url" content="https://ricerca.sns.it/bitstream/11384/92148/1/euclid.bj.1262962233.pdf" /> <meta name="citation_language" content="en" /> <meta name="citation_keywords" content="Mathematics; Mean Geometric densities; Random Distributions; Stochastic geometry" /> <meta name="citation_publisher" content="Bernoulli Society for Mathematical Statistics and Probability" /> <script type="text/javascript"> $(document).on('click', '.c-bn', function() { location.reload(); }); </script> </head> <body class="body-default body-anonymous"> <header class="navbar navbar-expand-md navbar-dark sticky-top layout-top bg-primary iu-hide"> <nav class="container-fluid flex-wrap flex-md-nowrap" aria-label="menu top"> <a class="navbar-brand ps-0 pt-0 pb-0 pe-3" href="https://ricerca.sns.it/" aria-label="link homepage" id="uiLogoLink"> <img src="/sr/logo_iris.png" alt="IRIS" id="uiLogoImg" class="d-block my-1 navbar-brand-img"/> </a> <a class="navbar-brand ps-3 pt-0 pb-0 pe-3 me-3" href="" aria-label="link homepage università" id="customerLogoLink"> <img src="/sr/logo_customer.png" alt="IRIS" id="clientLogoImg" class="d-block my-1 navbar-brand-img"/> </a> <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbarSupportedContent" aria-controls="navbarSupportedContent" aria-expanded="false" aria-label="mostra/nascondi menu"> <span class="fas fa-bars"></span> </button> <div class="collapse navbar-collapse" id="navbarSupportedContent"> <ul class="navbar-nav flex-row flex-wrap pt-2 py-md-0"> </ul> <ul class="navbar-nav flex-row flex-wrap ms-md-auto"> <li class="nav-item col-6 col-md-auto " id="topNavHome"> <a class="nav-link p-2" href="https://ricerca.sns.it/">Home</a> </li> <li class="nav-item col-6 col-md-auto dropdown"> <a class="nav-link p-2 dropdown-toggle" href="#" id="navbarDropdownBrowse" role="button" data-bs-toggle="dropdown" aria-haspopup="true" aria-expanded="false"> Sfoglia</a> <div class="dropdown-menu" aria-labelledby="navbarDropdownBrowse"> <a class="dropdown-item" href="https://ricerca.sns.it/community-list">Macrotipologie<br/>& tipologie</a> <div class="dropdown-divider"></div> <a class="dropdown-item" href="https://ricerca.sns.it/browse?type=author">Autore</a> <a class="dropdown-item" href="https://ricerca.sns.it/browse?type=title">Titolo</a> <a class="dropdown-item" href="https://ricerca.sns.it/browse?type=relationJournal">Rivista</a> <a class="dropdown-item" href="https://ricerca.sns.it/browse?type=relationSerie">Serie</a> <a class="dropdown-item" href="https://ricerca.sns.it/browse?type=discipline">Disciplina SNS</a> </div> </li> </ul> <form class="navbar-search-top d-flex" action="https://ricerca.sns.it/simple-search" method="get" role="search"> <div class="input-group p-2"> <input class="form-control bg-primary layout-top-input" type="search" placeholder="Search IRIS" name="query" id="tequery" size="25" aria-label="Search IRIS"> <button class="btn btn-primary layout-top-input-btn" type="submit"><span class="fas fa-search"></span></button> </div> </form> <ul class="navbar-nav flex-row flex-wrap"> <li class="nav-item col-6 col-md-auto dropdown"> <a class="nav-link p-2 dropdown-toggle" href="#" id="navbarDropdownLanguage" role="button" data-bs-toggle="dropdown" aria-haspopup="true" aria-expanded="false"> IT</a> <div class="dropdown-menu dropdown-menu-end" aria-labelledby="navbarDropdownLanguage"> <a class="dropdown-item" href="javascript:reloadLanguageModuleAll('https://ricerca.sns.it',['bi','rm','gw','ma','','saiku','ap'],'/language/change.json','it');" ><img src="/sr/cineca/images/flag/flag_it.png" alt="Italiano" title=""/> Italiano</a> <a class="dropdown-item" href="javascript:reloadLanguageModuleAll('https://ricerca.sns.it',['bi','rm','gw','ma','','saiku','ap'],'/language/change.json','en');" ><img src="/sr/cineca/images/flag/flag_en.png" alt="English" title="English"/> English</a> </div> </li> <li class="nav-item col-6 col-md-auto "> <script type="text/javascript">  </script><noscript><a href="https://wiki.u-gov.it/confluence/x/HJEWAw" target="dspacepopup"><span class="fas fa-question-circle" title="Aiuto"></span></a></noscript> </li> <li class="nav-item col-6 col-md-auto dropdown"><a class="nav-link p-2" href="https://ricerca.sns.it/securityLanding.htm">LOGIN</a></li> </ul> </div> </nav> </header> <div class="site-header iu-hide bg-secondary text-white"> <div class="site-title CinecaSiteIntroduction" id="headerText"> <div> <p class="CinecaSiteIntroduction"></p></div> </div> </div> <div class="container-xxl ps-0 pe-0 layout-no-sidebar" id="mainContainerDiv"> <main class="layout-main" id="content"> <div class="container-fluid page-content"> <nav aria-label="breadcrumb" class="mt-2 iu-hide"> <form name="breadCrumbsForm" id="breadCrumbsForm" method="post"> <ol class="breadcrumb rounded"> <li class="breadcrumb-item"><a href="/">IRIS</a></li> <li class="breadcrumb-item"><a href="/handle/11384/55738">Catalogo Ricerca</a></li> <li class="breadcrumb-item"><a href="/handle/11384/55739">1 Contributo su Rivista</a></li> <li class="breadcrumb-item"><a href="/handle/11384/55700">1.1 Articolo in rivista</a></li></ol> </form> </nav> <p class="searchIndexItemDescription abstractEng">Many real phenomena may be modelled as random closed sets in Rd, of different Hausdorff dimensions. The authors have recently revisited the concept of mean geometric densities of random closed sets θn with Hausdorff dimension n ≤ d with respect to the standard Lebesgue measure on Rd, in terms of expected values of a suitable class of linear functionals (Delta functions à la Dirac). In many real applications such as fiber processes, n-facets of random tessellations of dimension n ≤ d in spaces of dimension d ≥ 1, several problems are related to the estimation of such mean densities; in order to face such problems in the general setting of spatially inhomogeneous processes, we suggest and analyze here an approximation of mean densities for sufficiently regular random closed sets. We will show how some known results in literature follow as particular cases. A series of examples throughout the paper are provided to exemplify various relevant situations.</p> <div class="row"> <div class="col-lg-12 col-xl-9"> <div class="card"> <div class="card-body"> <div> <h3 class="mb-1 text-secondary">On the approximation of geometric densities of random closed sets</h3> <h5> <em><span class="contributor internalContributor internalContributore3aace00-c9eb-4c98-e053-3705fe0acb7e m-1"><a href="/cris/rp/rp13228" class="authority author">Capasso, Vincenzo</a>;</span><span class="contributor internalContributor internalContributore3aace00-c9eb-4c98-e053-3705fe0acb7e m-1"><a href="/cris/rp/rp18728" class="authority author">Villa, Elena</a>;</span><span class="contributor internalContributor internalContributore3aace00-c9eb-4c98-e053-3705fe0acb7e m-1"><a href="/cris/rp/rp01440" class="authority author">Ambrosio, Luigi</a></span></em> </h5> <h5>2006</h5> <hr/> <h4 class="mb-1">Abstract</h4> Many real phenomena may be modelled as random closed sets in Rd, of different Hausdorff dimensions. The authors have recently revisited the concept of mean geometric densities of random closed sets θn with Hausdorff dimension n ≤ d with respect to the standard Lebesgue measure on Rd, in terms of expected values of a suitable class of linear functionals (Delta functions à la Dirac). In many real applications such as fiber processes, n-facets of random tessellations of dimension n ≤ d in spaces of dimension d ≥ 1, several problems are related to the estimation of such mean densities; in order to face such problems in the general setting of spatially inhomogeneous processes, we suggest and analyze here an approximation of mean densities for sufficiently regular random closed sets. We will show how some known results in literature follow as particular cases. A series of examples throughout the paper are provided to exemplify various relevant situations. </div> <div class="dspace-display-item tabbable page-tabs mt-3"> <h5> <ul class="nav nav-tabs border-bottom fw-bold"> <li class="nav-item"><a class="nav-link active" href="#tab_default" onclick="changeItemView('simple');" data-bs-toggle="tab">Scheda breve</a></li> <li class="nav-item"><a class="nav-link " href="#tab_default" onclick="changeItemView('complete');" data-bs-toggle="tab">Scheda completa</a></li> <li class="nav-item"><a class="nav-link " href="#tab_default" onclick="changeItemView('full');" data-bs-toggle="tab">Scheda completa (DC)</a></li> <li class="nav-item"><a class="nav-link" onclick="location.href='/cris/item/11384/92148/statistics'" data-bs-toggle="tab"><span class="far fa-chart-bar"></span></a></li> </ul> </h5> <div class="tab-content"> <div class="tab-pane active fade show" id="tab_default"> <div class="itemDisplayTable container-fluid g-3"> <div class="line form-group row metadataFieldValue pt-2 pb-2 dc_date_issued" id="dc.date.issued_line" > <div class="line-label col-md-12"><label for="dc.date.issued" class="control-label metadataFieldLabel dc_date_issued"> <span class="line-label-text">Anno di pubblicazione</span> </label></div> <div class="line-content col-sm-12" id="dc.date.issued_content"> <em>9-mag-2006</em> </div> </div> <div class="line form-group row metadataFieldValue pt-2 pb-2 dspace_collection" id="dspace_collection_line" > <div class="line-label col-md-12"><label for="dspace_collection" class="control-label metadataFieldLabel dspace_collection"> <span class="line-label-text">Appare nelle tipologie:</span> </label></div> <div class="line-content col-sm-12" id="dspace_collection_content"> <a href="/handle/11384/55700">1.1 Articolo in rivista</a> </div> </div> </div> </div> </div> </div></div> </div> <script type="text/x-tmpl" id="tmpLicenseDetail"> <div class="d-flex align-items-center"> {% if (o.licenseImage != null) { %} <div class="flex-shrink-0"> <img src="{%= o.licenseImage %}" /> </div> {% } %} <div class="flex-grow-1 ms-3"> {%# o.licenseName %} </div> </div> </script> <div id="bitstreams" class="card bg-white mt-2"> <div class="card-header">File in questo prodotto:</div> <table class="table card-body"> <tr> <th id="t1" class="standard">File</th> <th id="t3" class="standard d-none d-sm-table-cell">Dimensione</th> <th id="t4" class="standard d-none d-sm-table-cell">Formato</th> <th id="t5" class="standard d-none d-sm-table-cell"> </th> </tr> <tr> <td headers="t1" class="standard break-all"> <a target="_blank" rel="noopener" href="/retrieve/e3aacdfe-c102-4c98-e053-3705fe0acb7e/euclid.bj.1262962233.pdf">euclid.bj.1262962233.pdf</a> <p class="badge bg-info">accesso aperto</p> <div class="col-12 mb-2"> Descrizione: journal article full text </div> <div class="col-12 mb-2"> Tipologia: Altro materiale allegato </div> <div class="col-12 mb-2"> Licenza: Solo Lettura </div> <div class="col-12 mb-2 d-block d-sm-none"> Dimensione 172.81 kB </div> <div class="col-12 mb-2 d-block d-sm-none"> Formato Adobe PDF </div> <div class="col-12 mb-2 d-block d-sm-none"> </div> </td> <td headers="t3" class="standard d-none d-sm-table-cell">172.81 kB</td> <td headers="t4" class="standard d-none d-sm-table-cell">Adobe PDF</td> <td class="standard d-none d-sm-table-cell"> </td> </tr> </table> </div> <div class="col-lg-12 mt-2"> </div> <div class="col-lg-12 mt-2"> <p class="submitFormHelp alert alert-info">I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.</p> </div> </div> <div class="col-lg-12 col-xl-3" id="itemInformationsDiv"> <div id="_line" > <div class="accordion" id="accordion_"> <div class="accordion-item"> <h5 class="accordion-header" id="heading_"> <button class="accordion-button bg-info bg-opacity-25 collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapse_" aria-expanded="false" aria-controls="collapse_"><i class="fas fa-info-circle"></i> Informazioni</button> </h5> <div id="collapse_" class="accordion-collapse collapse show" aria-labelledby="heading_" data-bs-parent="#accordion_"> <div class="accordion-body"> Utilizza questo identificativo per citare o creare un link a questo documento: <code>https://hdl.handle.net/11384/92148</code> </div> </div> </div> </div> </div> <script type="text/javascript"> runningExternal=false; </script> <div class="card border-white mt-2" > <div class="card-header bg-white text-primary"><h5>Citazioni</h5></div> <ul class="list-group list-group-flush"> <li class="list-group-item d-flex justify-content-between align-items-start"> <a href="#" ><img src="https://ricerca.sns.it/sr/cineca/images/thirdparty/pmc_small.png" style="height: 18px;" alt="???jsp.display-item.citation.pmc???"/></a> <span class="badge bg-secondary rounded-pill" data-bs-toggle="tooltip" data-bs-placement="left" id="pmcCitedResultTotal" title="" >ND</span> </li> <script type="text/javascript"> var pmcChartData = []; pmcChartData[0] = 0; pmcChartData[1] = 0; pmcChartData[2] = 0; pmcChartData[3] = 0; pmcChartData[4] = 0; pmcChartData[5] = 0; function pmcUpdateCitationQueue(forceUpdate) { //console.log('call pmcUpdateCitation'); if (runningExternal) { var rnd=Math.floor(Math.random() * (2000 + 1) + 1000); //console.log('wait pmcUpdateCitation for '+rnd); setTimeout(() => { pmcUpdateCitationQueue(forceUpdate); }, rnd); } else { //console.log('executing pmcUpdateCitation'); runningExternal=true; pmcUpdateCitation(forceUpdate) } } function pmcUpdateCitation(forceUpdate) { $('#pmcCitedResultTotal').append('<div class="spinner-border spinner-border-sm ms-2" role="status"></div>'); $.ajax({ url: '/itemExternalCitation/pmc/get.json', dataType: 'json', data: { discriminator: 'pmc', itemId: 'e3aace00-c9eb-4c98-e053-3705fe0acb7e', forceUpdate: forceUpdate } }).done(function(adata) { $('#pmcCitedResultTotal').tooltip('dispose'); $('#pmcCitedResultTotal').prop("onclick", null).off("click"); if (adata.total==null){ $('#pmcCitedResultTotal').html('ND'); } else { $('#pmcCitedResultTotal').html(adata.total); } var year=new Date().getFullYear(); pmcChartData[0] = (adata.yearTotalMap[''+(year-5)]!=null ? adata.yearTotalMap[''+(year-5)] : 0); pmcChartData[1] = (adata.yearTotalMap[''+(year-4)]!=null ? adata.yearTotalMap[''+(year-4)] : 0); pmcChartData[2] = (adata.yearTotalMap[''+(year-3)]!=null ? adata.yearTotalMap[''+(year-3)] : 0); pmcChartData[3] = (adata.yearTotalMap[''+(year-2)]!=null ? adata.yearTotalMap[''+(year-2)] : 0); pmcChartData[4] = (adata.yearTotalMap[''+(year-1)]!=null ? adata.yearTotalMap[''+(year-1)] : 0); pmcChartData[5] = (adata.yearTotalMap[''+year]!=null ? adata.yearTotalMap[''+year] : 0); drawChart(); }).always(function(adata){ //console.log('end pmcUpdateCitation'); runningExternal=false; }); } </script> <li class="list-group-item d-flex justify-content-between align-items-start"> <a href="#" ><img src="https://ricerca.sns.it/sr/cineca/images/thirdparty/scopus_small.png" style="height: 18px;" alt="Scopus"/></a> <span class="badge bg-secondary rounded-pill" data-bs-toggle="tooltip" data-bs-placement="left" id="scopusCitedResultTotal" title="" >ND</span> </li> <script type="text/javascript"> var scopusChartData = []; scopusChartData[0] = 0; scopusChartData[1] = 0; scopusChartData[2] = 0; scopusChartData[3] = 0; scopusChartData[4] = 0; scopusChartData[5] = 0; function scopusUpdateCitationQueue(forceUpdate) { //console.log('call scopusUpdateCitation'); if (runningExternal) { var rnd=Math.floor(Math.random() * (2000 + 1) + 1000); //console.log('wait scopusUpdateCitation for '+rnd); setTimeout(() => { scopusUpdateCitationQueue(forceUpdate); }, rnd); } else { //console.log('executing scopusUpdateCitation'); runningExternal=true; scopusUpdateCitation(forceUpdate) } } function scopusUpdateCitation(forceUpdate) { $('#scopusCitedResultTotal').append('<div class="spinner-border spinner-border-sm ms-2" role="status"></div>'); $.ajax({ url: '/itemExternalCitation/scopus/get.json', dataType: 'json', data: { discriminator: 'scopus', itemId: 'e3aace00-c9eb-4c98-e053-3705fe0acb7e', forceUpdate: forceUpdate } }).done(function(adata) { $('#scopusCitedResultTotal').tooltip('dispose'); $('#scopusCitedResultTotal').prop("onclick", null).off("click"); if (adata.total==null){ $('#scopusCitedResultTotal').html('ND'); } else { $('#scopusCitedResultTotal').html(adata.total); } var year=new Date().getFullYear(); scopusChartData[0] = (adata.yearTotalMap[''+(year-5)]!=null ? adata.yearTotalMap[''+(year-5)] : 0); scopusChartData[1] = (adata.yearTotalMap[''+(year-4)]!=null ? adata.yearTotalMap[''+(year-4)] : 0); scopusChartData[2] = (adata.yearTotalMap[''+(year-3)]!=null ? adata.yearTotalMap[''+(year-3)] : 0); scopusChartData[3] = (adata.yearTotalMap[''+(year-2)]!=null ? adata.yearTotalMap[''+(year-2)] : 0); scopusChartData[4] = (adata.yearTotalMap[''+(year-1)]!=null ? adata.yearTotalMap[''+(year-1)] : 0); scopusChartData[5] = (adata.yearTotalMap[''+year]!=null ? adata.yearTotalMap[''+year] : 0); drawChart(); }).always(function(adata){ //console.log('end scopusUpdateCitation'); runningExternal=false; }); } </script> <li class="list-group-item d-flex justify-content-between align-items-start"> <a href="#" ><img src="https://ricerca.sns.it/sr/cineca/images/thirdparty/isi_small.png" style="height: 18px;" alt="???jsp.display-item.citation.isi???"/></a> <span class="badge bg-secondary rounded-pill" data-bs-toggle="tooltip" data-bs-placement="left" id="isiCitedResultTotal" title="" >ND</span> </li> <script type="text/javascript"> var isiChartData = []; isiChartData[0] = 0; isiChartData[1] = 0; isiChartData[2] = 0; isiChartData[3] = 0; isiChartData[4] = 0; isiChartData[5] = 0; function isiUpdateCitationQueue(forceUpdate) { //console.log('call isiUpdateCitation'); if (runningExternal) { var rnd=Math.floor(Math.random() * (2000 + 1) + 1000); //console.log('wait isiUpdateCitation for '+rnd); setTimeout(() => { isiUpdateCitationQueue(forceUpdate); }, rnd); } else { //console.log('executing isiUpdateCitation'); runningExternal=true; isiUpdateCitation(forceUpdate) } } function isiUpdateCitation(forceUpdate) { $('#isiCitedResultTotal').append('<div class="spinner-border spinner-border-sm ms-2" role="status"></div>'); $.ajax({ url: '/itemExternalCitation/isi/get.json', dataType: 'json', data: { discriminator: 'isi', itemId: 'e3aace00-c9eb-4c98-e053-3705fe0acb7e', forceUpdate: forceUpdate } }).done(function(adata) { $('#isiCitedResultTotal').tooltip('dispose'); $('#isiCitedResultTotal').prop("onclick", null).off("click"); if (adata.total==null){ $('#isiCitedResultTotal').html('ND'); } else { $('#isiCitedResultTotal').html(adata.total); } var year=new Date().getFullYear(); isiChartData[0] = (adata.yearTotalMap[''+(year-5)]!=null ? adata.yearTotalMap[''+(year-5)] : 0); isiChartData[1] = (adata.yearTotalMap[''+(year-4)]!=null ? adata.yearTotalMap[''+(year-4)] : 0); isiChartData[2] = (adata.yearTotalMap[''+(year-3)]!=null ? adata.yearTotalMap[''+(year-3)] : 0); isiChartData[3] = (adata.yearTotalMap[''+(year-2)]!=null ? adata.yearTotalMap[''+(year-2)] : 0); isiChartData[4] = (adata.yearTotalMap[''+(year-1)]!=null ? adata.yearTotalMap[''+(year-1)] : 0); isiChartData[5] = (adata.yearTotalMap[''+year]!=null ? adata.yearTotalMap[''+year] : 0); drawChart(); }).always(function(adata){ //console.log('end isiUpdateCitation'); runningExternal=false; }); } </script> <li class="list-group-item d-flex justify-content-between align-items-start"> <a href="#" ><img src="https://ricerca.sns.it/sr/cineca/images/thirdparty/openalex_small.png" style="height: 18px;" alt="OpenAlex"/></a> <span class="badge bg-secondary rounded-pill" data-bs-toggle="tooltip" data-bs-placement="left" id="openalexCitedResultTotal" title="" >ND</span> </li> <script type="text/javascript"> var openalexChartData = []; openalexChartData[0] = 0; openalexChartData[1] = 0; openalexChartData[2] = 0; openalexChartData[3] = 0; openalexChartData[4] = 0; openalexChartData[5] = 0; function openalexUpdateCitationQueue(forceUpdate) { //console.log('call openalexUpdateCitation'); if (runningExternal) { var rnd=Math.floor(Math.random() * (2000 + 1) + 1000); //console.log('wait openalexUpdateCitation for '+rnd); setTimeout(() => { openalexUpdateCitationQueue(forceUpdate); }, rnd); } else { //console.log('executing openalexUpdateCitation'); runningExternal=true; openalexUpdateCitation(forceUpdate) } } function openalexUpdateCitation(forceUpdate) { $('#openalexCitedResultTotal').append('<div class="spinner-border spinner-border-sm ms-2" role="status"></div>'); $.ajax({ url: '/itemExternalCitation/openalex/get.json', dataType: 'json', data: { discriminator: 'openalex', itemId: 'e3aace00-c9eb-4c98-e053-3705fe0acb7e', forceUpdate: forceUpdate } }).done(function(adata) { $('#openalexCitedResultTotal').tooltip('dispose'); $('#openalexCitedResultTotal').prop("onclick", null).off("click"); if (adata.total==null){ $('#openalexCitedResultTotal').html('ND'); } else { $('#openalexCitedResultTotal').html(adata.total); } var year=new Date().getFullYear(); openalexChartData[0] = (adata.yearTotalMap[''+(year-5)]!=null ? adata.yearTotalMap[''+(year-5)] : 0); openalexChartData[1] = (adata.yearTotalMap[''+(year-4)]!=null ? adata.yearTotalMap[''+(year-4)] : 0); openalexChartData[2] = (adata.yearTotalMap[''+(year-3)]!=null ? adata.yearTotalMap[''+(year-3)] : 0); openalexChartData[3] = (adata.yearTotalMap[''+(year-2)]!=null ? adata.yearTotalMap[''+(year-2)] : 0); openalexChartData[4] = (adata.yearTotalMap[''+(year-1)]!=null ? adata.yearTotalMap[''+(year-1)] : 0); openalexChartData[5] = (adata.yearTotalMap[''+year]!=null ? adata.yearTotalMap[''+year] : 0); drawChart(); }).always(function(adata){ //console.log('end openalexUpdateCitation'); runningExternal=false; }); } </script> <li class="list-group-item d-flex justify-content-between align-items-start" style="display: none;" id="citation_chart_panel"> <div id="citation_chart" style="width: 100%;"></div> <script type="text/javascript"> $('#citation_chart').html('<span class="fas fa-shield" title="il componente non può essere visualizzato perché i cookie di terze parti sono stati disabilitati. Riabilitarli tramite il pannello Utilizzo dei cookie situato a fondo pagina"><span> '); </script> </li> </ul> </div> <div class="card border-white mt-2" > <div class="card-header bg-white text-primary"><h5>social impact</h5></div> <ul class="list-group list-group-flush"> <li class="list-group-item d-flex justify-content-between align-items-start"> <a id="plumx" href="https://plu.mx/plum/a/?" class="plumx-plum-print-popup"></a> <script type="text/javascript"> if (isThirdPartyCookieEnabled()) { $.getScript("//cdn.plu.mx/widget-popup.js", function() { }); } else { $('#plumx').attr('href','#').html('<span class="fas fa-shield" title="il componente non può essere visualizzato perché i cookie di terze parti sono stati disabilitati. Riabilitarli tramite il pannello Utilizzo dei cookie situato a fondo pagina"><span> '); } </script> </li> </ul> </div> </div> </div> <div id="dialog-confirm-delete" class="modal"> <div class="modal-dialog "> <div class="modal-content"> <div class="modal-header bg-success text-white"> <h5 id="dialog-confirm-delete_title" class="modal-title"> Conferma cancellazione </h5> <button type="button" class="btn-close" data-bs-dismiss="modal" aria-label="Close"></button> </div> <div id="dialog-confirm-delete_content" class="modal-body with-padding"> <p class="message">Sei sicuro che questo prodotto debba essere cancellato?</p> </div> <div id="dialog-confirm-delete_footer" class="modal-footer bg-light"> <button type="button" class="btn btn-secondary " data-bs-dismiss="modal"> Chiudi </button> <button type="button" id="button-confirm-delete" class="btn btn-secondary " > Elimina </button> </div> </div> </div> </div> <script type="text/javascript"> var modeNow; function changeItemView(mode) { $('#tab_default').html('<i class="fas fa-spinner fa-pulse fa-3x fa-fw mt-3"></i>'); $.ajax({ url: '/fragment/handle/11384/92148', data: { mode: mode, descriptionAbstractUsedField: 'dc.description.abstracteng' } }).done(function(data) { modeNow=mode; $('#tab_default').html(data); //change url //var href="/handle/11384/92148"; var href=window.location.href; if (!href.includes("mode=")) { if (!href.includes("?")) href+='?mode='+mode; else href+='&mode='+mode; } else href=href.replace( /(mode=)[a-z]+/ig, '$1'+mode ); window.history.pushState("", "", href); }); } function getUrlVars() { var vars = {}; var parts = window.location.href.replace(/[?&]+([^=&]+)=([^&]*)/gi, function(m,key,value) { vars[key] = value; }); return vars; } j('#button-confirm-delete').click(function() { location.href='/item/version/reinstateOrWithdraw.htm?itemId=' + 'e3aace00-c9eb-4c98-e053-3705fe0acb7e'; }); j('#button-confirm-force-delete').click(function() { location.href='/item/version/reinstateOrWithdraw.htm?forceWithdraw=true&itemId=' + 'e3aace00-c9eb-4c98-e053-3705fe0acb7e'; }); function getSOLR() { $('li a.nav-link active').removeClass('active'); $('#linkSOLR').addClass('active'); $('#tab_default').html('<i class="fas fa-spinner fa-pulse fa-3x fa-fw mt-3"></i>'); $.ajax('/itemSolr/get.json?itemUUID=e3aace00-c9eb-4c98-e053-3705fe0acb7e') .done(function(data) { $('#tab_default').html('<pre>'+JSON.stringify(data, null,' ')+'</pre>'); }); } </script> <script type="text/javascript"> function showAbout() { jQuery.ajax({ url: "/about.modal", type: 'GET', success: function(data) { var $modal = jQuery(data); jQuery('body').append($modal); $modal.filter('.modal').modal('show'); $modal.filter('.modal').on('hidden.bs.modal', function(){ $modal.remove(); }); $modal.attr('id','modal_about'); $modal.modal('show') }, error: function(data,extStatus, errorThrown) { $.jGrowl('errore generico di comunicazione', { sticky: true, theme: 'bg-danger text-white' }); } }); } function showCookies() { showCookieSettings(); } function showPrivacyInfo() { window.open('/aboutPrivacyInfo.htm', '_blank').focus(); } </script> <script type="text/javascript"> function asn1820List() { jQuery('#asn1820-div').modal('show'); } </script> <div class="modal fade" id="asn1820-div" tabindex="-1" role="dialog" aria-labelledby="asn1820Label" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <h4 class="modal-title" id="asn1820Label">simulazione ASN</h4> <button type="button" class="btn-close" data-bs-dismiss="modal" aria-hidden="true"></button> </div> <div class="modal-body with-padding"> Il report seguente simula gli indicatori relativi alla propria produzione scientifica in relazione alle soglie ASN 2023-2025 del proprio SC/SSD. Si ricorda che il superamento dei valori soglia (almeno 2 su 3) è requisito necessario ma non sufficiente al conseguimento dell'abilitazione.<br/>La simulazione si basa sui dati IRIS e sugli indicatori bibliometrici alla data indicata e non tiene conto di eventuali periodi di congedo obbligatorio, che in sede di domanda ASN danno diritto a incrementi percentuali dei valori. La simulazione può differire dall'esito di un’eventuale domanda ASN sia per errori di catalogazione e/o dati mancanti in IRIS, sia per la variabilità dei dati bibliometrici nel tempo. Si consideri che Anvur calcola i valori degli indicatori all'ultima data utile per la presentazione delle domande.<br/><br/>La presente simulazione è stata realizzata sulla base delle specifiche raccolte sul tavolo ER del Focus Group IRIS coordinato dall’Università di Modena e Reggio Emilia e delle regole riportate nel DM 589/2018 e allegata Tabella A. Cineca, l’Università di Modena e Reggio Emilia e il Focus Group IRIS non si assumono alcuna responsabilità in merito all’uso che il diretto interessato o terzi faranno della simulazione. Si specifica inoltre che la simulazione contiene calcoli effettuati con dati e algoritmi di pubblico dominio e deve quindi essere considerata come un mero ausilio al calcolo svolgibile manualmente o con strumenti equivalenti.</div> <div class="modal-footer"> <button type="button" class="btn btn-secondary" data-bs-dismiss="modal">Annulla</button> <button type="button" class="btn btn-primary" onclick="location.href='/bi/asn1820/widgetSearch.htm?CLEAR&dataType=MV'">procedi</button> </div> </div> </div> </div> <div class="modal fade" id="genericFragmentErrorModal" tabindex="-1" role="dialog" aria-labelledby="modal-title" aria-hidden="true" style="z-index: 10000"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <h4 class="modal-title">Errore</h4> <button aria-hidden="true" data-bs-dismiss="modal" class="btn-close" type="button"></button> </div> <div class="modal-body with-padding"> <div class="callout alert bg-danger"> <h5>Errore</h5> <p id="genericFragmentErrorModalContent"></p> </div> </div> </div> </div> </div> <script type="text/javascript"> var forceLogindModuleMap = reloadInit(['bi','rm','gw','ma','','saiku','ap']); </script> </div> </main> </div> <div class="clearfix"></div> <footer class="bd-footer py-2 mt-2 bg-light d-flex justify-content-between fw-bold iu-hide"> <div class="ms-2"> Powered by <a class="text-decoration-none" href="https://www.cineca.it/sistemi-informativi-universita/ricerca/iris-la-gestione-della-ricerca">IRIS</a> <span style="margin-left: 10px; margin-right: 10px;">-</span> <a class="text-decoration-none" onclick="showAbout();" href="#">about IRIS</a> <span style="margin-left: 10px; margin-right: 10px;">-</span> <a class="text-decoration-none" onclick="showCookies();" href="#">Utilizzo dei cookie</a> <span style="margin-left: 10px; margin-right: 10px;">-</span> <a class="text-decoration-none" onclick="showPrivacyInfo();" href="#">Privacy</a> </div> <div class="me-2"> <a href="http://www.cineca.it" target="_blank"><img alt="Logo CINECA" height="15px;" src="/sr/cineca/images/interface/logo-cineca-small-white.png"></a> <span> Copyright © 2024 </span><a href="/htmlmap" style="display:none;"></a></div> </footer></body> </html>

CINXE.COM

On the approximation of geometric densities of random closed sets