{"id":18080,"date":"2002-04-07T00:00:00","date_gmt":"2002-04-07T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/anillos-de-series-generalizadas-y-ecuaciones-diferenciales-ordinarias\/"},"modified":"2002-04-07T00:00:00","modified_gmt":"2002-04-07T00:00:00","slug":"anillos-de-series-generalizadas-y-ecuaciones-diferenciales-ordinarias","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/anillos-de-series-generalizadas-y-ecuaciones-diferenciales-ordinarias\/","title":{"rendered":"Anillos de series generalizadas y ecuaciones diferenciales ordinarias"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Tomas Aranda Guillen <\/strong><\/h2>\n<p>El objetivo de este trabajo es el estudio de los anillos de series de potencias con exponentes reales y de la posibilidad de usar estas series para resolver determinados tipos de ecuaciones algebraicas y diferenciales.  la aparici\u00f3n de series con exponentes en subconjuntos bien ordenados de los n\u00fameros reales r o en determinados subconjuntos de conos de r^n se produce de forma natural dentro de la resoluci\u00f3n de ecuaciones, ya sean algebraicas, diferenciales o funcionales.  el primer cap\u00edtulo est\u00e1 dedicado a la posibilidad de reducir series con exponentes -racionales con denominador acotado- en conos poli\u00e9dricos a series con exponentes enteros y situados en el primer cuadrante, y ello mediante la utilizaci\u00f3n de transformaciones cuadr\u00e1ticas y ramificadas.  el cap\u00edtulo 2 est\u00e1 dedicado a estudiar los anillos de series con exponentes racionales en conos de r^n con denominador acotado. Los conjuntos naturales de exponentes, para mantener la estructura multiplicativa, son los subsemigrupos de (1\/n)z^n. Se estudian y utilizan t\u00e9cnicas de subsemigrupos.  en el tercer cap\u00edtulo se estudian las series derivadas de la aplicaci\u00f3n de t\u00e9cnicas tipo poliedro de newton obteniendo el anillo de series generalizadas. tambi\u00e9n se estudian las series derivadas del uso de valoraciones, obteni\u00e9ndose en este caso el anillo de series de potencias largas. Se demuestra la finitud del n\u00famero de v\u00e9rtices del poliedro de newton relativo a las series generalizadas, y se utilizan estos resultados para hallar expl\u00edcitamente soluciones de ecuaciones algebraicas o diferenciales.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Anillos de series generalizadas y ecuaciones diferenciales ordinarias<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Anillos de series generalizadas y ecuaciones diferenciales ordinarias <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Tomas Aranda Guillen <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Valladolid<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 04\/07\/2002<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Jos\u00e9 Manuel Aroca Hernandez Ros<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Jos\u00e9 Luis Vicente c\u00f3rdoba <\/li>\n<li>benjamin Dugnol \u00e1lvarez (vocal)<\/li>\n<li> P\u00e9rez de vargas luque Alberto (vocal)<\/li>\n<li>julio Castellanos pe\u00f1uela (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Tomas Aranda Guillen El objetivo de este trabajo es el estudio de los anillos de series de [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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