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overflow: hidden; text-overflow: ellipsis; -webkit-line-clamp: 3; -webkit-box-orient: vertical; }</style><div class="col-xs-12 clearfix"><div class="u-floatLeft"><h1 class="PageHeader-title u-m0x u-fs30">Pure Mathematics</h1><div class="u-tcGrayDark">43,233 Followers</div><div class="u-tcGrayDark u-mt2x">Recent papers in <b>Pure Mathematics</b></div></div></div></div></div></div><div class="TabbedNavigation"><div class="container"><div class="row"><div class="col-xs-12 clearfix"><ul class="nav u-m0x u-p0x list-inline u-displayFlex"><li class="active"><a href="https://www.academia.edu/Documents/in/Pure_Mathematics">Top Papers</a></li><li><a href="https://www.academia.edu/Documents/in/Pure_Mathematics/MostCited">Most Cited Papers</a></li><li><a href="https://www.academia.edu/Documents/in/Pure_Mathematics/MostDownloaded">Most Downloaded Papers</a></li><li><a href="https://www.academia.edu/Documents/in/Pure_Mathematics/MostRecent">Newest Papers</a></li><li><a class="" href="https://www.academia.edu/People/Pure_Mathematics">People</a></li></ul></div><style type="text/css">ul.nav{flex-direction:row}@media(max-width: 567px){ul.nav{flex-direction:column}.TabbedNavigation li{max-width:100%}.TabbedNavigation li.active{background-color:var(--background-grey, #dddde2)}.TabbedNavigation li.active:before,.TabbedNavigation li.active:after{display:none}}</style></div></div></div><div class="container"><div class="row"><div class="col-xs-12"><div class="u-displayFlex"><div class="u-flexGrow1"><div class="works"><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_55614042" data-work_id="55614042" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/55614042/The_Schur_l1_Theorem_for_filters">The Schur l1 Theorem for filters</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Every theorem of Classical Analysis, Functional Analysis or of the Measure Theory that states a property of sequences leads to a class of filters for which this theorem is valid. Sometimes such class of filters is trivial (say, all... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_55614042" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Every theorem of Classical Analysis, Functional Analysis or of the Measure Theory that states a property of sequences leads to a class of filters for which this theorem is valid. Sometimes such class of filters is trivial (say, all filters or the filters with countable base), but in several ...</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/55614042" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="2acdd81668958027d1cdc017ef9baaef" rel="nofollow" data-download="{"attachment_id":71404009,"asset_id":55614042,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/71404009/download_file?st=MTczMjQxNjA2Nyw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="45413321" href="https://independent.academia.edu/AlexanderLeonov1">Alexander Leonov</a><script data-card-contents-for-user="45413321" type="text/json">{"id":45413321,"first_name":"Alexander","last_name":"Leonov","domain_name":"independent","page_name":"AlexanderLeonov1","display_name":"Alexander Leonov","profile_url":"https://independent.academia.edu/AlexanderLeonov1?f_ri=19997","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_55614042 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="55614042"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 55614042, container: ".js-paper-rank-work_55614042", }); 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Sometimes such class of filters is trivial (say, all filters or the filters with countable base), but in several ...","downloadable_attachments":[{"id":71404009,"asset_id":55614042,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":45413321,"first_name":"Alexander","last_name":"Leonov","domain_name":"independent","page_name":"AlexanderLeonov1","display_name":"Alexander Leonov","profile_url":"https://independent.academia.edu/AlexanderLeonov1?f_ri=19997","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":371,"name":"Functional Analysis","url":"https://www.academia.edu/Documents/in/Functional_Analysis?f_ri=19997","nofollow":false},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics?f_ri=19997","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_30639699" data-work_id="30639699" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/30639699/The_Eckmann_Hilton_argument_and_higher_operads">The Eckmann–Hilton argument and higher operads</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/30639699" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="a4ba83d00ecfa901d7add502ffdc5a79" rel="nofollow" data-download="{"attachment_id":51083357,"asset_id":30639699,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/51083357/download_file?st=MTczMjQxNjA2Nyw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="58340721" href="https://independent.academia.edu/MichaelBatanin">Michael Batanin</a><script data-card-contents-for-user="58340721" type="text/json">{"id":58340721,"first_name":"Michael","last_name":"Batanin","domain_name":"independent","page_name":"MichaelBatanin","display_name":"Michael Batanin","profile_url":"https://independent.academia.edu/MichaelBatanin?f_ri=19997","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_30639699 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="30639699"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 30639699, container: ".js-paper-rank-work_30639699", }); 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By working with several... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_71409482" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">We can regard operations that discard information, like specializing to a particular case or dropping the intermediate steps of a proof, as projections, and operations that reconstruct information as liftings. By working with several projections in parallel we can make sense of statements like “Set is the archetypal Cartesian Closed Category”, which means that proofs about CCCs can be done in the “archetypal language” and then lifted to proofs in the general setting. The method works even when our archetypal language is diagrammatical, has potential ambiguities, is not completely formalized, and does not have semantics for all terms. We illustrate the method with an example from hyperdoctrines and another from synthetic differential geometry.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/71409482" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="07e26a5c21ff6361220f1346f19c472e" rel="nofollow" data-download="{"attachment_id":80764740,"asset_id":71409482,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/80764740/download_file?st=MTczMjQxNjA2Nyw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="1019392" href="https://uff.academia.edu/EduardoNahumOchs">Eduardo Nahum N Ochs</a><script data-card-contents-for-user="1019392" type="text/json">{"id":1019392,"first_name":"Eduardo Nahum","last_name":"Ochs","domain_name":"uff","page_name":"EduardoNahumOchs","display_name":"Eduardo Nahum N Ochs","profile_url":"https://uff.academia.edu/EduardoNahumOchs?f_ri=19997","photo":"https://gravatar.com/avatar/c024e1b07d81571b89d78abf376ebc8c?s=65"}</script></span></span></li><li class="js-paper-rank-work_71409482 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="71409482"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 71409482, container: ".js-paper-rank-work_71409482", }); 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We illustrate the method with an example from hyperdoctrines and another from synthetic differential geometry.","downloadable_attachments":[{"id":80764740,"asset_id":71409482,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":1019392,"first_name":"Eduardo Nahum","last_name":"Ochs","domain_name":"uff","page_name":"EduardoNahumOchs","display_name":"Eduardo Nahum N Ochs","profile_url":"https://uff.academia.edu/EduardoNahumOchs?f_ri=19997","photo":"https://gravatar.com/avatar/c024e1b07d81571b89d78abf376ebc8c?s=65"}],"research_interests":[{"id":10850,"name":"Diagrammatic Reasoning","url":"https://www.academia.edu/Documents/in/Diagrammatic_Reasoning?f_ri=19997","nofollow":false},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics?f_ri=19997","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card 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traced back from the Old Babylonian period at least. According to this idea, there are some signs (omens) which can explain the appearance of all events. These omens... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_53561929" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">In this paper, I show that the idea of logical determinism can be traced back from the Old Babylonian period at least. According to this idea, there are some signs (omens) which can explain the appearance of all events. These omens demonstrate the will of gods and their power realized through natural forces. As a result, each event either necessarily appears or necessarily disappears. This idea can be examined as the first version of eternalism – the philosophical belief that each temporal event (including past and future events) is actual. In divination lists in Akkadian presented as codes we can reconstruct Boolean matrices showing that the Babylonians used some logical-algebraic structures in their reasoning. The idea of logical contingency was introduced within a new mood of thinking presented by the Greek prose – historical as well as philosophical narrations. In the Jewish genre ’aggādōt, the logical determinism is supposed to be in opposition to the Greek prose.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/53561929" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="fcb6b7cebe5c92db5dc1392c6eb89928" rel="nofollow" data-download="{"attachment_id":70348140,"asset_id":53561929,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/70348140/download_file?st=MTczMjQxNjA2Nyw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="47698432" href="https://independent.academia.edu/AndrewSchumann">Andrew Schumann</a><script data-card-contents-for-user="47698432" type="text/json">{"id":47698432,"first_name":"Andrew","last_name":"Schumann","domain_name":"independent","page_name":"AndrewSchumann","display_name":"Andrew Schumann","profile_url":"https://independent.academia.edu/AndrewSchumann?f_ri=19997","photo":"https://0.academia-photos.com/47698432/12733470/14162734/s65_andrew.schumann.jpg"}</script></span></span></li><li class="js-paper-rank-work_53561929 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="53561929"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 53561929, container: ".js-paper-rank-work_53561929", }); });</script></li><li class="js-percentile-work_53561929 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 53561929; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_53561929"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_53561929 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="53561929"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 53561929; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=53561929]").text(description); $(".js-view-count-work_53561929").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_53561929").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="53561929"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i></div><span class="InlineList-item-text u-textTruncate u-pl6x"><a class="InlineList-item-text" data-has-card-for-ri="19997" href="https://www.academia.edu/Documents/in/Pure_Mathematics">Pure Mathematics</a><script data-card-contents-for-ri="19997" type="text/json">{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics?f_ri=19997","nofollow":false}</script></span></li><script>(function(){ if (false) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=53561929]'), work: {"id":53561929,"title":"On the Origin of Logical Determinism in Babylonia","created_at":"2021-09-27T13:14:39.095-07:00","url":"https://www.academia.edu/53561929/On_the_Origin_of_Logical_Determinism_in_Babylonia?f_ri=19997","dom_id":"work_53561929","summary":"In this paper, I show that the idea of logical determinism can be traced back from the Old Babylonian period at least. According to this idea, there are some signs (omens) which can explain the appearance of all events. These omens demonstrate the will of gods and their power realized through natural forces. As a result, each event either necessarily appears or necessarily disappears. This idea can be examined as the first version of eternalism – the philosophical belief that each temporal event (including past and future events) is actual. In divination lists in Akkadian presented as codes we can reconstruct Boolean matrices showing that the Babylonians used some logical-algebraic structures in their reasoning. The idea of logical contingency was introduced within a new mood of thinking presented by the Greek prose – historical as well as philosophical narrations. 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To this aim, we prove an appropriate fixed point... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_10255366" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">We prove the existence and uniqueness of solution for a first-order ordinary differential equation with periodic boundary conditions admitting only the existence of a lower solution. To this aim, we prove an appropriate fixed point theorem in partially ordered sets.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/10255366" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="0967cbee0480bbb6552dbf95a12da901" rel="nofollow" data-download="{"attachment_id":47466523,"asset_id":10255366,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/47466523/download_file?st=MTczMjQxNjA2OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="25106527" href="https://independent.academia.edu/JuanNieto12">Juan Nieto</a><script data-card-contents-for-user="25106527" type="text/json">{"id":25106527,"first_name":"Juan","last_name":"Nieto","domain_name":"independent","page_name":"JuanNieto12","display_name":"Juan Nieto","profile_url":"https://independent.academia.edu/JuanNieto12?f_ri=19997","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_10255366 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="10255366"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 10255366, container: ".js-paper-rank-work_10255366", }); 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To this aim, we prove an appropriate fixed point theorem in partially ordered sets.","downloadable_attachments":[{"id":47466523,"asset_id":10255366,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":25106527,"first_name":"Juan","last_name":"Nieto","domain_name":"independent","page_name":"JuanNieto12","display_name":"Juan Nieto","profile_url":"https://independent.academia.edu/JuanNieto12?f_ri=19997","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics?f_ri=19997","nofollow":false},{"id":181847,"name":"First-Order Logic","url":"https://www.academia.edu/Documents/in/First-Order_Logic?f_ri=19997","nofollow":false},{"id":183513,"name":"Order","url":"https://www.academia.edu/Documents/in/Order?f_ri=19997","nofollow":false},{"id":287143,"name":"Fixed Point 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u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">This paper considers the family $\\mathscr{S}_0$ of smooth affine factorial surfaces of logarithmic Kodaira dimension 0 with trivial units over an algebraically closed field $k$. Our main result (Theorem 4.1) is that the number of... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_82189782" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">This paper considers the family $\\mathscr{S}_0$ of smooth affine factorial surfaces of logarithmic Kodaira dimension 0 with trivial units over an algebraically closed field $k$. Our main result (Theorem 4.1) is that the number of isomorphism classes represented in $\\mathscr{S}_0$ is at least countably infinite. This contradicts the earlier classification of Gurjar and Miyanishi [5] which asserted that $\\mathscr{S}_0$ has at most two elements up to isomorphism when $k=\\mathbb{C}$. Thus, the classification of surfaces in $\\mathscr{S}_0$ for the field $\\mathbb{C}$, long thought to have been settled, is an open problem.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/82189782" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="d4c60bbec0eb0fe0bcd43be7c566999a" rel="nofollow" data-download="{"attachment_id":87974615,"asset_id":82189782,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/87974615/download_file?st=MTczMjQxNjA2OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="97773558" href="https://independent.academia.edu/%E5%AD%9D%E5%85%B8%E9%95%B7%E5%B3%B0">Takanori Nagamine</a><script data-card-contents-for-user="97773558" type="text/json">{"id":97773558,"first_name":"Takanori","last_name":"Nagamine","domain_name":"independent","page_name":"孝典長峰","display_name":"Takanori Nagamine","profile_url":"https://independent.academia.edu/%E5%AD%9D%E5%85%B8%E9%95%B7%E5%B3%B0?f_ri=19997","photo":"https://0.academia-photos.com/97773558/38148223/32022965/s65__._.jpg"}</script></span></span><span class="u-displayInlineBlock InlineList-item-text"> and <span class="u-textDecorationUnderline u-clickable InlineList-item-text js-work-more-authors-82189782">+1</span><div class="hidden js-additional-users-82189782"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://independent.academia.edu/%E7%A7%80%E9%9B%84%E5%BA%AD%E5%B1%B1">秀雄庭山</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-82189782'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-82189782').html(); 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Our main result (Theorem 4.1) is that the number of isomorphism classes represented in $\\\\mathscr{S}_0$ is at least countably infinite. This contradicts the earlier classification of Gurjar and Miyanishi [5] which asserted that $\\\\mathscr{S}_0$ has at most two elements up to isomorphism when $k=\\\\mathbb{C}$. Thus, the classification of surfaces in $\\\\mathscr{S}_0$ for the field $\\\\mathbb{C}$, long thought to have been settled, is an open problem.","downloadable_attachments":[{"id":87974615,"asset_id":82189782,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":97773558,"first_name":"Takanori","last_name":"Nagamine","domain_name":"independent","page_name":"孝典長峰","display_name":"Takanori 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In particular we obtain integrability results for some... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_75484480" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. In particular we obtain integrability results for some families of quadratic vector fields, Li\&#39;enard equations and equations related with special functions such as Hypergeometric and Heun ones. The Poincar\&#39;e problem for some families is also approached.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/75484480" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="4ec531457cad6e811fdb828b82e7a54c" rel="nofollow" data-download="{"attachment_id":83235128,"asset_id":75484480,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/83235128/download_file?st=MTczMjQxNjA2OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="37144956" href="https://independent.academia.edu/JuanMoralesruiz">Juan Morales-ruiz</a><script data-card-contents-for-user="37144956" type="text/json">{"id":37144956,"first_name":"Juan","last_name":"Morales-ruiz","domain_name":"independent","page_name":"JuanMoralesruiz","display_name":"Juan Morales-ruiz","profile_url":"https://independent.academia.edu/JuanMoralesruiz?f_ri=19997","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_75484480 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="75484480"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 75484480, container: ".js-paper-rank-work_75484480", }); 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$(".js-view-count[data-work-id=75484480]").text(description); $(".js-view-count-work_75484480").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_75484480").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="75484480"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">7</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="300" href="https://www.academia.edu/Documents/in/Mathematics">Mathematics</a>, <script data-card-contents-for-ri="300" type="text/json">{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=19997","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="305" href="https://www.academia.edu/Documents/in/Applied_Mathematics">Applied Mathematics</a>, <script data-card-contents-for-ri="305" type="text/json">{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics?f_ri=19997","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="19997" href="https://www.academia.edu/Documents/in/Pure_Mathematics">Pure Mathematics</a>, <script data-card-contents-for-ri="19997" type="text/json">{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics?f_ri=19997","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="59542" href="https://www.academia.edu/Documents/in/Galois_Theory">Galois Theory</a><script data-card-contents-for-ri="59542" type="text/json">{"id":59542,"name":"Galois Theory","url":"https://www.academia.edu/Documents/in/Galois_Theory?f_ri=19997","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=75484480]'), work: {"id":75484480,"title":"On the integrability of polynomial fields in the plane by means of Picard-Vessiot theory","created_at":"2022-04-04T22:14:31.504-07:00","url":"https://www.academia.edu/75484480/On_the_integrability_of_polynomial_fields_in_the_plane_by_means_of_Picard_Vessiot_theory?f_ri=19997","dom_id":"work_75484480","summary":"We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. In particular we obtain integrability results for some families of quadratic vector fields, Li\\\u0026#39;enard equations and equations related with special functions such as Hypergeometric and Heun ones. The Poincar\\\u0026#39;e problem for some families is also approached.","downloadable_attachments":[{"id":83235128,"asset_id":75484480,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":37144956,"first_name":"Juan","last_name":"Morales-ruiz","domain_name":"independent","page_name":"JuanMoralesruiz","display_name":"Juan Morales-ruiz","profile_url":"https://independent.academia.edu/JuanMoralesruiz?f_ri=19997","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=19997","nofollow":false},{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics?f_ri=19997","nofollow":false},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics?f_ri=19997","nofollow":false},{"id":59542,"name":"Galois Theory","url":"https://www.academia.edu/Documents/in/Galois_Theory?f_ri=19997","nofollow":false},{"id":135583,"name":"Special functions","url":"https://www.academia.edu/Documents/in/Special_functions?f_ri=19997"},{"id":868912,"name":"Dynamic System","url":"https://www.academia.edu/Documents/in/Dynamic_System?f_ri=19997"},{"id":1010090,"name":"Non linear Partial Differential Equation","url":"https://www.academia.edu/Documents/in/Non_linear_Partial_Differential_Equation?f_ri=19997"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_74992563" data-work_id="74992563" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/74992563/A_note_on_the_real_part_of_complex_chromatic_roots">A note on the real part of complex chromatic roots</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/74992563" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="d928eedf44214cbcdfbddaec0ff559b9" rel="nofollow" data-download="{"attachment_id":82942681,"asset_id":74992563,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/82942681/download_file?st=MTczMjQxNjA2OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="160569672" href="https://independent.academia.edu/JasonBrown160">Jason Brown</a><script data-card-contents-for-user="160569672" type="text/json">{"id":160569672,"first_name":"Jason","last_name":"Brown","domain_name":"independent","page_name":"JasonBrown160","display_name":"Jason Brown","profile_url":"https://independent.academia.edu/JasonBrown160?f_ri=19997","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_74992563 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="74992563"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 74992563, container: ".js-paper-rank-work_74992563", }); 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$(".js-view-count[data-work-id=74992563]").text(description); $(".js-view-count-work_74992563").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_74992563").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="74992563"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">5</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="305" href="https://www.academia.edu/Documents/in/Applied_Mathematics">Applied Mathematics</a>, <script data-card-contents-for-ri="305" type="text/json">{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics?f_ri=19997","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="19997" href="https://www.academia.edu/Documents/in/Pure_Mathematics">Pure Mathematics</a>, <script data-card-contents-for-ri="19997" type="text/json">{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics?f_ri=19997","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="37345" href="https://www.academia.edu/Documents/in/Discrete_Mathematics">Discrete Mathematics</a>, <script data-card-contents-for-ri="37345" type="text/json">{"id":37345,"name":"Discrete Mathematics","url":"https://www.academia.edu/Documents/in/Discrete_Mathematics?f_ri=19997","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="525222" href="https://www.academia.edu/Documents/in/Chromatic_polynomial">Chromatic polynomial</a><script data-card-contents-for-ri="525222" type="text/json">{"id":525222,"name":"Chromatic polynomial","url":"https://www.academia.edu/Documents/in/Chromatic_polynomial?f_ri=19997","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=74992563]'), work: {"id":74992563,"title":"A note on the real part of complex chromatic roots","created_at":"2022-03-30T10:23:43.252-07:00","url":"https://www.academia.edu/74992563/A_note_on_the_real_part_of_complex_chromatic_roots?f_ri=19997","dom_id":"work_74992563","summary":null,"downloadable_attachments":[{"id":82942681,"asset_id":74992563,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":160569672,"first_name":"Jason","last_name":"Brown","domain_name":"independent","page_name":"JasonBrown160","display_name":"Jason Brown","profile_url":"https://independent.academia.edu/JasonBrown160?f_ri=19997","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics?f_ri=19997","nofollow":false},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics?f_ri=19997","nofollow":false},{"id":37345,"name":"Discrete Mathematics","url":"https://www.academia.edu/Documents/in/Discrete_Mathematics?f_ri=19997","nofollow":false},{"id":525222,"name":"Chromatic polynomial","url":"https://www.academia.edu/Documents/in/Chromatic_polynomial?f_ri=19997","nofollow":false},{"id":2999418,"name":"Chromatic Scale","url":"https://www.academia.edu/Documents/in/Chromatic_Scale?f_ri=19997"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_74110649" data-work_id="74110649" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/74110649/The_Distance_Between_Crossing_Points_as_a_Parameter_in_Edge_Coloring_Problems_for_Cubic_Graphs">The Distance Between Crossing Points as a Parameter in Edge Coloring Problems for Cubic Graphs</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">We investigate the 3-edge coloring problem, based on the idea to give an algorithm, that attempts to minimize the use of color 4 (in a 4-edge coloring), and to study the factors that force it to fail. More specific, we introduce the... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_74110649" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">We investigate the 3-edge coloring problem, based on the idea to give an algorithm, that attempts to minimize the use of color 4 (in a 4-edge coloring), and to study the factors that force it to fail. More specific, we introduce the notion of the ”position” of crossing points (or crossing edges) and the notion of the ”connection by bicolor paths”. A first result of this approach is that we can always assign a 4-edge coloring in a connected, bridgeless and cubic graph G using the fourth color only in crossing edges. Furthermore, color 4 is needed at most in half of these pairs of crossing edges. Finally, we bound the number of times color 4 is required in terms of the distance between the crossing points in the drawing of the graph.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/74110649" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="2ec060906382f0fe71da2ceb27ed49a3" rel="nofollow" data-download="{"attachment_id":82428445,"asset_id":74110649,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/82428445/download_file?st=MTczMjQxNjA2OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="7887836" href="https://independent.academia.edu/dkoreas">diamantis koreas</a><script data-card-contents-for-user="7887836" type="text/json">{"id":7887836,"first_name":"diamantis","last_name":"koreas","domain_name":"independent","page_name":"dkoreas","display_name":"diamantis koreas","profile_url":"https://independent.academia.edu/dkoreas?f_ri=19997","photo":"https://0.academia-photos.com/7887836/4326679/82862605/s65_diamantis.koreas.jpg"}</script></span></span></li><li class="js-paper-rank-work_74110649 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="74110649"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 74110649, container: ".js-paper-rank-work_74110649", }); 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$(".js-view-count[data-work-id=74110649]").text(description); $(".js-view-count-work_74110649").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_74110649").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="74110649"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">4</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="305" href="https://www.academia.edu/Documents/in/Applied_Mathematics">Applied Mathematics</a>, <script data-card-contents-for-ri="305" type="text/json">{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics?f_ri=19997","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="19997" href="https://www.academia.edu/Documents/in/Pure_Mathematics">Pure Mathematics</a>, <script data-card-contents-for-ri="19997" type="text/json">{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics?f_ri=19997","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="556845" href="https://www.academia.edu/Documents/in/Numerical_Analysis_and_Computational_Mathematics">Numerical Analysis and Computational Mathematics</a>, <script data-card-contents-for-ri="556845" type="text/json">{"id":556845,"name":"Numerical Analysis and Computational Mathematics","url":"https://www.academia.edu/Documents/in/Numerical_Analysis_and_Computational_Mathematics?f_ri=19997","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="1210260" href="https://www.academia.edu/Documents/in/Edge_Coloring">Edge Coloring</a><script data-card-contents-for-ri="1210260" type="text/json">{"id":1210260,"name":"Edge Coloring","url":"https://www.academia.edu/Documents/in/Edge_Coloring?f_ri=19997","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=74110649]'), work: {"id":74110649,"title":"The Distance Between Crossing Points as a Parameter in Edge Coloring Problems for Cubic Graphs","created_at":"2022-03-19T23:57:33.205-07:00","url":"https://www.academia.edu/74110649/The_Distance_Between_Crossing_Points_as_a_Parameter_in_Edge_Coloring_Problems_for_Cubic_Graphs?f_ri=19997","dom_id":"work_74110649","summary":"We investigate the 3-edge coloring problem, based on the idea to give an algorithm, that attempts to minimize the use of color 4 (in a 4-edge coloring), and to study the factors that force it to fail. More specific, we introduce the notion of the ”position” of crossing points (or crossing edges) and the notion of the ”connection by bicolor paths”. A first result of this approach is that we can always assign a 4-edge coloring in a connected, bridgeless and cubic graph G using the fourth color only in crossing edges. Furthermore, color 4 is needed at most in half of these pairs of crossing edges. Finally, we bound the number of times color 4 is required in terms of the distance between the crossing points in the drawing of the graph.","downloadable_attachments":[{"id":82428445,"asset_id":74110649,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":7887836,"first_name":"diamantis","last_name":"koreas","domain_name":"independent","page_name":"dkoreas","display_name":"diamantis koreas","profile_url":"https://independent.academia.edu/dkoreas?f_ri=19997","photo":"https://0.academia-photos.com/7887836/4326679/82862605/s65_diamantis.koreas.jpg"}],"research_interests":[{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics?f_ri=19997","nofollow":false},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics?f_ri=19997","nofollow":false},{"id":556845,"name":"Numerical Analysis and Computational Mathematics","url":"https://www.academia.edu/Documents/in/Numerical_Analysis_and_Computational_Mathematics?f_ri=19997","nofollow":false},{"id":1210260,"name":"Edge Coloring","url":"https://www.academia.edu/Documents/in/Edge_Coloring?f_ri=19997","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_73644030" data-work_id="73644030" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/73644030/Visibility_queries_in_a_polygonal_region">Visibility queries in a polygonal region</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm 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})();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_69891994" data-work_id="69891994" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/69891994/The_spectra_of_Banach_algebras_of_holomorphic_functions_on_polydisk_type_domains">The spectra of Banach algebras of holomorphic functions on polydisk type domains</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">In 2012, R.M. Aron, D. Carando, T.W. Gamelin, S. Lassalle, and M. Maestre presented that the Cluster Value Theorem in the infinite dimensional Banach space setting holds for the Banach algebra $\mathcal{H}^\infty (B_{c_0})$. On the other... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_69891994" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">In 2012, R.M. Aron, D. Carando, T.W. Gamelin, S. Lassalle, and M. Maestre presented that the Cluster Value Theorem in the infinite dimensional Banach space setting holds for the Banach algebra $\mathcal{H}^\infty (B_{c_0})$. On the other hand, B.J. Cole and T.W. Gamelin showed in 1986 that $\mathcal{H}^\infty (\ell_2 \cap B_{c_0})$ is isometrically isomorphic to $\mathcal{H}^\infty (B_{c_0})$ in the sense of an algebra. Motivated by this work, we are interested in a class of open subsets $U$ of a Banach space $X$ for which $\mathcal{H}^\infty (U)$ is isometrically isomorphic to $\mathcal{H}^\infty (B_{c_0})$. We prove that there exist polydisk type domains $U$ of any infinite dimensional Banach space $X$ with a Schauder basis such that $\mathcal{H}^\infty (U)$ is isometrically isomorphic to $\mathcal{H}^\infty (B_{c_0})$, which also generalizes the result by Cole and Gamelin. We also show that the Cluster Value Theorem is true for $\mathcal{H}^\infty (U)$. As the dual space $X^*$ is...</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/69891994" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="6442de2c6af301b7f9388ab5fdb3fc8d" rel="nofollow" data-download="{"attachment_id":79815153,"asset_id":69891994,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/79815153/download_file?st=MTczMjQxNjA2OCw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="37376148" href="https://uv.academia.edu/ManuelMaestre">Manuel Maestre</a><script data-card-contents-for-user="37376148" type="text/json">{"id":37376148,"first_name":"Manuel","last_name":"Maestre","domain_name":"uv","page_name":"ManuelMaestre","display_name":"Manuel Maestre","profile_url":"https://uv.academia.edu/ManuelMaestre?f_ri=19997","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_69891994 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="69891994"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 69891994, container: ".js-paper-rank-work_69891994", }); });</script></li><li class="js-percentile-work_69891994 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 69891994; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_69891994"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_69891994 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="69891994"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 69891994; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=69891994]").text(description); $(".js-view-count-work_69891994").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_69891994").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="69891994"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i></div><span class="InlineList-item-text u-textTruncate u-pl6x"><a class="InlineList-item-text" data-has-card-for-ri="19997" href="https://www.academia.edu/Documents/in/Pure_Mathematics">Pure Mathematics</a><script data-card-contents-for-ri="19997" type="text/json">{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics?f_ri=19997","nofollow":false}</script></span></li><script>(function(){ if (false) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=69891994]'), work: {"id":69891994,"title":"The spectra of Banach algebras of holomorphic functions on polydisk type domains","created_at":"2022-01-29T03:09:12.160-08:00","url":"https://www.academia.edu/69891994/The_spectra_of_Banach_algebras_of_holomorphic_functions_on_polydisk_type_domains?f_ri=19997","dom_id":"work_69891994","summary":"In 2012, R.M. Aron, D. Carando, T.W. Gamelin, S. Lassalle, and M. Maestre presented that the Cluster Value Theorem in the infinite dimensional Banach space setting holds for the Banach algebra $\\mathcal{H}^\\infty (B_{c_0})$. On the other hand, B.J. Cole and T.W. Gamelin showed in 1986 that $\\mathcal{H}^\\infty (\\ell_2 \\cap B_{c_0})$ is isometrically isomorphic to $\\mathcal{H}^\\infty (B_{c_0})$ in the sense of an algebra. Motivated by this work, we are interested in a class of open subsets $U$ of a Banach space $X$ for which $\\mathcal{H}^\\infty (U)$ is isometrically isomorphic to $\\mathcal{H}^\\infty (B_{c_0})$. We prove that there exist polydisk type domains $U$ of any infinite dimensional Banach space $X$ with a Schauder basis such that $\\mathcal{H}^\\infty (U)$ is isometrically isomorphic to $\\mathcal{H}^\\infty (B_{c_0})$, which also generalizes the result by Cole and Gamelin. We also show that the Cluster Value Theorem is true for $\\mathcal{H}^\\infty (U)$. As the dual space $X^*$ is...","downloadable_attachments":[{"id":79815153,"asset_id":69891994,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":37376148,"first_name":"Manuel","last_name":"Maestre","domain_name":"uv","page_name":"ManuelMaestre","display_name":"Manuel Maestre","profile_url":"https://uv.academia.edu/ManuelMaestre?f_ri=19997","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics?f_ri=19997","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_68924086" data-work_id="68924086" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" 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href="https://www.academia.edu/61061386/Counting_labeled_claw_free_cubic_graphs_by_connectivity">Counting labeled claw-free cubic graphs by connectivity</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/61061386" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="c4d0867ce19073d63b3d654b977debda" rel="nofollow" data-download="{"attachment_id":74234127,"asset_id":61061386,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button 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class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/49988382/On_the_Continuity_of_the_Eigenvalues_of_a_Sublaplacian">On the Continuity of the Eigenvalues of a Sublaplacian</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest">We study the behavior of the eigenvalues of a sublaplacian Δ b on a compact strictly pseudoconvex CR manifold M, as functions on the set P + of positively oriented contact forms on M by endowing P + with a natural metric topology.</div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/49988382" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li 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