{"id":206,"date":"2019-01-21T09:31:51","date_gmt":"2019-01-21T07:31:51","guid":{"rendered":"https:\/\/yrmath4.conf.uoi.gr\/?page_id=206"},"modified":"2026-05-05T10:01:12","modified_gmt":"2026-05-05T08:01:12","slug":"%ce%b5%cf%80%ce%b9%cf%84%cf%81%ce%bf%cf%80%ce%ad%cf%82","status":"publish","type":"page","link":"https:\/\/yrmath4.conf.uoi.gr\/?page_id=206","title":{"rendered":"\u03a0\u03c1\u03bf\u03c3\u03ba\u03b5\u03ba\u03bb\u03b7\u03bc\u03ad\u03bd\u03bf\u03b9 \u039f\u03bc\u03b9\u03bb\u03b7\u03c4\u03ad\u03c2"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"206\" class=\"elementor elementor-206\" data-elementor-settings=\"[]\">\n\t\t\t<div class=\"elementor-inner\">\n\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t<section class=\"elementor-element elementor-element-63b6edf elementor-section-stretched elementor-section-full_width elementor-section-content-middle elementor-section-height-default elementor-section-height-default elementor-section elementor-top-section\" data-id=\"63b6edf\" data-element_type=\"section\" data-settings=\"{&quot;stretch_section&quot;:&quot;section-stretched&quot;,&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t<div class=\"elementor-element elementor-element-ad36530 elementor-column elementor-col-100 elementor-top-column\" data-id=\"ad36530\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-column-wrap  elementor-element-populated\">\n\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-element elementor-element-95a5a5c elementor-section-boxed elementor-section-height-default elementor-section-height-default elementor-section elementor-top-section\" data-id=\"95a5a5c\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t<div class=\"elementor-element elementor-element-202da4c elementor-column elementor-col-100 elementor-top-column\" data-id=\"202da4c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap  elementor-element-populated\">\n\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t<div class=\"elementor-element elementor-element-e067276 elementor-widget elementor-widget-heading\" data-id=\"e067276\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">\u03a0\u03c1\u03bf\u03c3\u03ba\u03b5\u03ba\u03bb\u03b7\u03bc\u03ad\u03bd\u03bf\u03b9 \u039f\u03bc\u03b9\u03bb\u03b7\u03c4\u03ad\u03c2<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4ca2e99 elementor-widget elementor-widget-divider\" data-id=\"4ca2e99\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-element elementor-element-09f3bc1 elementor-section-boxed elementor-section-height-default elementor-section-height-default elementor-invisible elementor-section elementor-top-section\" data-id=\"09f3bc1\" data-element_type=\"section\" data-settings=\"{&quot;animation&quot;:&quot;fadeInDown&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1213c08 elementor-column elementor-col-50 elementor-top-column\" data-id=\"1213c08\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap  elementor-element-populated\">\n\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2e13106 elementor-position-top elementor-vertical-align-top elementor-widget elementor-widget-image-box\" data-id=\"2e13106\" data-element_type=\"widget\" data-widget_type=\"image-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<div class=\"elementor-image-box-wrapper\"><figure class=\"elementor-image-box-img\"><img width=\"150\" height=\"150\" src=\"https:\/\/yrmath4.conf.uoi.gr\/wp-content\/uploads\/2025\/10\/Giannopoulos-150x150.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" decoding=\"async\" loading=\"lazy\" \/><\/figure><\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5a6f6ac elementor-widget elementor-widget-text-editor\" data-id=\"5a6f6ac\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f41bf4e elementor-column elementor-col-50 elementor-top-column\" data-id=\"f41bf4e\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap  elementor-element-populated\">\n\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t<div class=\"elementor-element elementor-element-a501051 elementor-widget elementor-widget-text-editor\" data-id=\"a501051\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\"><ul><li style=\"text-align: left;\"><strong><a href=\"https:\/\/sites.google.com\/view\/apgiannop\/home?authuser=0\">\u0391\u03c0\u03cc\u03c3\u03c4\u03bf\u03bb\u03bf\u03c2 \u0393\u03b9\u03b1\u03bd\u03bd\u03cc\u03c0\u03bf\u03c5\u03bb\u03bf\u03c2<\/a><a href=\"https:\/\/sites.google.com\/view\/apgiannop\/home?authuser=0\">,<\/a><\/strong><span style=\"font-family: Verdana, sans-serif; font-size: 16px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400;\">\u00a0\u03a3\u03c7\u03bf\u03bb\u03ae \u0395\u03c6\u03b1\u03c1\u03bc\u03bf\u03c3\u03bc\u03ad\u03bd\u03c9\u03bd \u039c\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd &amp; \u03a6\u03c5\u03c3\u03b9\u03ba\u03ce\u03bd \u0395\u03c0\u03b9\u03c3\u03c4\u03b7\u03bc\u03ce\u03bd, \u0395\u03b8\u03bd\u03b9\u03ba\u03cc \u039c\u03b5\u03c4\u03c3\u03cc\u03b2\u03b9\u03bf \u03a0\u03bf\u03bb\u03c5\u03c4\u03b5\u03c7\u03bd\u03b5\u03af\u03bf<br \/><\/span><strong><br \/>\u03a4\u03af\u03c4\u03bb\u03bf\u03c2: <\/strong>\u03a3\u03c5\u03bd\u03b1\u03c1\u03c4\u03b7\u03c3\u03b9\u03b1\u03ba\u03ae \u03c0\u03b5\u03c1\u03af\u03bc\u03b5\u03c4\u03c1\u03bf\u03c2 \u03ba\u03b1\u03b9 \u03b7 \u03b4\u03b9\u03b1\u03c3\u03c4\u03b1\u03c4\u03b9\u03ba\u03ae \u03b1\u03bd\u03b9\u03c3\u03cc\u03c4\u03b7\u03c4\u03b1 Brunn\u2013Minkowski \u03b3\u03b9\u03b1 \u03bb\u03bf\u03b3\u03b1\u03c1\u03b9\u03b8\u03bc\u03b9\u03ba\u03ac \u03ba\u03bf\u03af\u03bb\u03b1 \u03bc\u03ad\u03c4\u03c1\u03b1<br \/><strong><strong><strong>\u03a0\u03b5\u03c1\u03af\u03bb\u03b7\u03c8\u03b7: <\/strong><\/strong><\/strong>\u039c\u03b5\u03bb\u03b5\u03c4\u03ac\u03bc\u03b5 \u03c4\u03b7 \u03b4\u03b9\u03b1\u03c3\u03c4\u03b1\u03c4\u03b9\u03ba\u03ae \u03b1\u03bd\u03b9\u03c3\u03cc\u03c4\u03b7\u03c4\u03b1 Brunn&#8211;Minkowski \u03b3\u03b9\u03b1 \u03bb\u03bf\u03b3\u03b1\u03c1\u03b9\u03b8\u03bc\u03b9\u03ba\u03ac \u03ba\u03bf\u03af\u03bb\u03b1 \u03bc\u03ad\u03c4\u03c1\u03b1 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2 $\\mu$ \u03c3\u03c4\u03bf\u03bd $\\mathbb{R}^n$ \u03bc\u03ad\u03c3\u03c9 \u03bc\u03b9\u03b1\u03c2 \u03b1\u03bd\u03b1\u03bb\u03c5\u03c4\u03b9\u03ba\u03ae\u03c2 \u03c0\u03c1\u03bf\u03c3\u03ad\u03b3\u03b3\u03b9\u03c3\u03b7\u03c2 \u03c0\u03bf\u03c5 \u03b2\u03b1\u03c3\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03c3\u03b5 \u03c4\u03b5\u03bb\u03b5\u03c3\u03c4\u03ad\u03c2 \u03b4\u03b9\u03ac\u03c7\u03c5\u03c3\u03b7\u03c2 \u03ba\u03b1\u03b9 \u03b5\u03ba\u03c4\u03b9\u03bc\u03ae\u03c3\u03b5\u03b9\u03c2 \u03ba\u03bb\u03af\u03c3\u03b7\u03c2. \u0391\u03c0\u03bf\u03b4\u03b5\u03b9\u03ba\u03bd\u03cd\u03bf\u03c5\u03bc\u03b5 \u03cc\u03c4\u03b9 \u03b3\u03b9\u03b1 \u03ba\u03ac\u03b8\u03b5 \u03b6\u03b5\u03cd\u03b3\u03bf\u03c2 \u03c3\u03c5\u03bc\u03bc\u03b5\u03c4\u03c1\u03b9\u03ba\u03ce\u03bd \u03ba\u03c5\u03c1\u03c4\u03ce\u03bd \u03c3\u03c5\u03bd\u03cc\u03bb\u03c9\u03bd $K, L \\subset \\mathbb{R}^n$ \u03ba\u03b1\u03b9 \u03b3\u03b9\u03b1 \u03ba\u03ac\u03b8\u03b5 $\\lambda \\in (0,1)$,\u00a0\\( \\displaystyle \\mu\\big(\\lambda K + (1-\\lambda)L\\big)^{c_n} \\ge \\lambda \\mu(K)^{c_n} + (1-\\lambda)\\mu(L)^{c_n} \\) \u03cc\u03c0\u03bf\u03c5 $c_n \\ge \\frac{c}{n^3 \\ln n}$ \u03b3\u03b9\u03b1 \u03ba\u03ac\u03c0\u03bf\u03b9\u03b1 \u03b1\u03c0\u03cc\u03bb\u03c5\u03c4\u03b7 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ac $c&gt;0$. \u0388\u03bd\u03b1 \u03b2\u03b1\u03c3\u03b9\u03ba\u03cc \u03c3\u03c5\u03c3\u03c4\u03b1\u03c4\u03b9\u03ba\u03cc \u03c4\u03b7\u03c2 \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf \u03b1\u03ba\u03c1\u03b9\u03b2\u03ad\u03c2 \u03ac\u03bd\u03c9 \u03c6\u03c1\u03ac\u03b3\u03bc\u03b1 \\( \\displaystyle \\int_{\\mathbb{R}^n} \\lvert \\nabla \\psi \\rvert \\, d\\mu \\le C n \\) \u03c4\u03bf \u03bf\u03c0\u03bf\u03af\u03bf \u03b1\u03c0\u03bf\u03b4\u03b5\u03b9\u03ba\u03bd\u03cd\u03bf\u03c5\u03bc\u03b5 \u03b3\u03b9\u03b1 \u03b9\u03c3\u03bf\u03c4\u03c1\u03bf\u03c0\u03b9\u03ba\u03ac \u03bb\u03bf\u03b3\u03b1\u03c1\u03b9\u03b8\u03bc\u03b9\u03ba\u03ac \u03ba\u03bf\u03af\u03bb\u03b1 \u03bc\u03ad\u03c4\u03c1\u03b1 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2 $\\mu$ \u03bc\u03b5 \u03c0\u03c5\u03ba\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 $e^{-\\psi}$, \u03ba\u03b1\u03b9 \u03c4\u03bf \u03bf\u03c0\u03bf\u03af\u03bf \u03b5\u03af\u03bd\u03b1\u03b9 \u03b2\u03ad\u03bb\u03c4\u03b9\u03c3\u03c4\u03bf \u03c9\u03c2 \u03c0\u03c1\u03bf\u03c2 \u03c4\u03b7 \u03b4\u03b9\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7. \u0397 \u03b5\u03ba\u03c4\u03af\u03bc\u03b7\u03c3\u03b7 \u03b1\u03c5\u03c4\u03ae \u03c0\u03b1\u03c1\u03ad\u03c7\u03b5\u03b9 \u03b4\u03bf\u03bc\u03b9\u03ba\u03ae \u03c0\u03bb\u03b7\u03c1\u03bf\u03c6\u03bf\u03c1\u03af\u03b1 \u03b3\u03b9\u03b1 \u03c4\u03bf \u03bc\u03ad\u03b3\u03b5\u03b8\u03bf\u03c2 \u03c4\u03c9\u03bd \u03c3\u03c5\u03bd\u03cc\u03bb\u03c9\u03bd \u03c3\u03c4\u03ac\u03b8\u03bc\u03b7\u03c2 \u03c4\u03b7\u03c2 \u03ba\u03bb\u03af\u03c3\u03b7\u03c2 \u03c4\u03b7\u03c2 $\\psi$, \u03ba\u03b1\u03b9 \u03b1\u03c0\u03bf\u03ba\u03b1\u03bb\u03cd\u03c0\u03c4\u03b5\u03b9 \u03ad\u03bd\u03b1 \u03b3\u03b5\u03c9\u03bc\u03b5\u03c4\u03c1\u03b9\u03ba\u03cc \u03b5\u03bc\u03c0\u03cc\u03b4\u03b9\u03bf \u03b3\u03b9\u03b1 \u03c0\u03b5\u03c1\u03b1\u03b9\u03c4\u03ad\u03c1\u03c9 \u03b2\u03b5\u03bb\u03c4\u03b9\u03ce\u03c3\u03b5\u03b9\u03c2 \u03c4\u03bf\u03c5 \u03b5\u03ba\u03b8\u03ad\u03c4\u03b7 \u03c3\u03c4\u03b7\u03bd \u03b1\u03bd\u03b9\u03c3\u03cc\u03c4\u03b7\u03c4\u03b1 Brunn&#8211;Minkowski. \u03a0\u03b1\u03c1\u03bf\u03c5\u03c3\u03b9\u03ac\u03b6\u03bf\u03c5\u03bc\u03b5 \u03b5\u03c0\u03af\u03c3\u03b7\u03c2 \u03b5\u03c6\u03b1\u03c1\u03bc\u03bf\u03b3\u03ad\u03c2 \u03b1\u03c5\u03c4\u03ae\u03c2 \u03c4\u03b7\u03c2 \u03b5\u03ba\u03c4\u03af\u03bc\u03b7\u03c3\u03b7\u03c2 \u03c3\u03c4\u03b7\u03bd \u03c0\u03b5\u03c1\u03af\u03bc\u03b5\u03c4\u03c1\u03bf \u03c4\u03c9\u03bd \u03c3\u03c5\u03bd\u03cc\u03bb\u03c9\u03bd \u03c3\u03c4\u03ac\u03b8\u03bc\u03b7\u03c2, \u03c4\u03b9\u03c2 \u03c0\u03c1\u03bf\u03b2\u03bf\u03bb\u03ad\u03c2, \u03c4\u03b1 \u03bc\u03ad\u03c4\u03c1\u03b1 \u03c1\u03bf\u03c0\u03ce\u03bd \u03ba\u03b1\u03b9 \u03c4\u03b1 \u03bc\u03ad\u03c4\u03c1\u03b1 \u03b5\u03c0\u03b9\u03c6\u03ac\u03bd\u03b5\u03b9\u03b1\u03c2 \u03b9\u03c3\u03bf\u03c4\u03c1\u03bf\u03c0\u03b9\u03ba\u03ce\u03bd \u03bb\u03bf\u03b3\u03b1\u03c1\u03b9\u03b8\u03bc\u03b9\u03ba\u03ac \u03ba\u03bf\u03af\u03bb\u03c9\u03bd \u03c3\u03c5\u03bd\u03b1\u03c1\u03c4\u03ae\u03c3\u03b5\u03c9\u03bd, \u03b1\u03bd\u03b1\u03b4\u03b5\u03b9\u03ba\u03bd\u03cd\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c4\u03bf\u03bd \u03ba\u03b5\u03bd\u03c4\u03c1\u03b9\u03ba\u03cc \u03c1\u03cc\u03bb\u03bf \u03c4\u03b7\u03c2 \u03ba\u03bb\u03af\u03c3\u03b7\u03c2 \u03c4\u03bf\u03c5 \u03bb\u03bf\u03b3\u03b1\u03c1\u03b9\u03b8\u03bc\u03b9\u03ba\u03bf\u03cd \u03b4\u03c5\u03bd\u03b1\u03bc\u03b9\u03ba\u03bf\u03cd \u03c3\u03c4\u03b7\u03bd \u03ba\u03c5\u03c1\u03c4\u03cc\u03c4\u03b7\u03c4\u03b1 \u03bc\u03b5\u03b3\u03ac\u03bb\u03c9\u03bd \u03b4\u03b9\u03b1\u03c3\u03c4\u03ac\u03c3\u03b5\u03c9\u03bd.<p>\u0397 \u03bf\u03bc\u03b9\u03bb\u03af\u03b1 \u03b2\u03b1\u03c3\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03c3\u03b5 \u03ba\u03bf\u03b9\u03bd\u03ae \u03b5\u03c1\u03b3\u03b1\u03c3\u03af\u03b1 \u03bc\u03b5 \u03c4\u03bf\u03c5\u03c2 \u0391\u03bb\u03ad\u03be\u03b1\u03bd\u03b4\u03c1\u03bf \u0395\u03c3\u03ba\u03b5\u03bd\u03ac\u03b6\u03b7 \u03ba\u03b1\u03b9 \u039d\u03b1\u03c4\u03b1\u03bb\u03af\u03b1 \u03a4\u03b6\u03b9\u03ce\u03c4\u03b6\u03b9\u03bf\u03c5.<\/p><hr \/><\/li><\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-element elementor-element-c37645b elementor-section-boxed elementor-section-height-default elementor-section-height-default elementor-invisible elementor-section elementor-top-section\" data-id=\"c37645b\" data-element_type=\"section\" data-settings=\"{&quot;animation&quot;:&quot;fadeInDown&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t<div class=\"elementor-element elementor-element-5e94950 elementor-column elementor-col-50 elementor-top-column\" data-id=\"5e94950\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap  elementor-element-populated\">\n\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t<div class=\"elementor-element elementor-element-604141c elementor-position-top elementor-vertical-align-top elementor-widget elementor-widget-image-box\" data-id=\"604141c\" data-element_type=\"widget\" data-widget_type=\"image-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<div class=\"elementor-image-box-wrapper\"><figure class=\"elementor-image-box-img\"><img width=\"150\" height=\"150\" src=\"https:\/\/yrmath4.conf.uoi.gr\/wp-content\/uploads\/2025\/10\/karlis-150x150.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" decoding=\"async\" loading=\"lazy\" srcset=\"https:\/\/yrmath4.conf.uoi.gr\/wp-content\/uploads\/2025\/10\/karlis-150x150.jpg 150w, https:\/\/yrmath4.conf.uoi.gr\/wp-content\/uploads\/2025\/10\/karlis-300x300.jpg 300w, https:\/\/yrmath4.conf.uoi.gr\/wp-content\/uploads\/2025\/10\/karlis.jpg 400w\" sizes=\"(max-width: 150px) 100vw, 150px\" \/><\/figure><\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e748e77 elementor-widget elementor-widget-text-editor\" data-id=\"e748e77\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-04043a6 elementor-column elementor-col-50 elementor-top-column\" data-id=\"04043a6\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap  elementor-element-populated\">\n\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t<div class=\"elementor-element elementor-element-9cbb7d3 elementor-widget elementor-widget-text-editor\" data-id=\"9cbb7d3\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\"><ul><li style=\"text-align: left;\"><strong><a href=\"https:\/\/www.aueb.gr\/en\/faculty_page\/karlis-dimitrios\">\u0394\u03b7\u03bc\u03ae\u03c4\u03c1\u03b7\u03c2 \u039a\u03b1\u03c1\u03bb\u03ae\u03c2<\/a>, <\/strong><span style=\"font-family: Verdana, sans-serif; font-size: 16px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400;\">\u03a4\u03bc\u03ae\u03bc\u03b1 \u03a3\u03c4\u03b1\u03c4\u03b9\u03c3\u03c4\u03b9\u03ba\u03ae\u03c2,\u00a0\u039f\u03b9\u03ba\u03bf\u03bd\u03bf\u03bc\u03b9\u03ba\u03cc \u03a0\u03b1\u03bd\u03b5\u03c0\u03b9\u03c3\u03c4\u03ae\u03bc\u03b9\u03bf \u0391\u03b8\u03b7\u03bd\u03ce\u03bd<\/span><p><strong><br \/>\u03a4\u03af\u03c4\u03bb\u03bf\u03c2:\u00a0<\/strong>Random Coefficient extensions for integer autoregressive models: a non-parametric approach<span style=\"font-size: 16px;\"><b><br \/><\/b><\/span><strong>\u03a0\u03b5\u03c1\u03af\u03bb\u03b7\u03c8\u03b7:<\/strong> In this talk, we use the class of integer autoregressive (INAR) time series models, widely used to model time series of counts. INAR models extend the idea of classical time series for continuous data in an admissible way to keep the discrete nature of the data. Random Coefficient INteger AutoRegressive (RCINAR) models constitute an important extension of the simple INAR model when the thinning parameters are considered to be random. In the present paper, we propose the case that the thinning parameter follows a discrete distribution with positive probability at a finite number of points. We do not specify any parametric family for the distribution.\u00a0 We provide an EM algorithm to estimate the model while we link the model to the non-parametric Maximum Likelihood estimate of the mixing distribution. The ideas are then extended to the bivariate case where the thinning parameters are now a matrix of random variables. The finite mixture representation helps a lot to account for the extra variability but also extra correlation to the model.<\/p><hr \/><\/li><\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-element elementor-element-65f4f45 elementor-section-boxed elementor-section-height-default elementor-section-height-default elementor-invisible elementor-section elementor-top-section\" data-id=\"65f4f45\" data-element_type=\"section\" data-settings=\"{&quot;animation&quot;:&quot;fadeInDown&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t<div class=\"elementor-element elementor-element-75f0f0d elementor-column elementor-col-50 elementor-top-column\" data-id=\"75f0f0d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap  elementor-element-populated\">\n\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t<div class=\"elementor-element elementor-element-ea67a5f elementor-position-top elementor-vertical-align-top elementor-widget elementor-widget-image-box\" data-id=\"ea67a5f\" data-element_type=\"widget\" data-widget_type=\"image-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<div class=\"elementor-image-box-wrapper\"><figure class=\"elementor-image-box-img\"><img decoding=\"async\" src=\"https:\/\/yrmath4.conf.uoi.gr\/wp-content\/uploads\/elementor\/thumbs\/platis-rdtcls4qrbfbs93ctddid129yy08l2hadhdh4v8if4.jpg\" title=\"platis\" alt=\"platis\" \/><\/figure><\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0b03032 elementor-widget elementor-widget-text-editor\" data-id=\"0b03032\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-03e91dc elementor-column elementor-col-50 elementor-top-column\" data-id=\"03e91dc\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap  elementor-element-populated\">\n\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t<div class=\"elementor-element elementor-element-8d610d0 elementor-widget elementor-widget-text-editor\" data-id=\"8d610d0\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\"><ul><li style=\"text-align: left;\"><strong><a href=\"https:\/\/thalis.math.upatras.gr\/~idplatis\/\">\u0399\u03c9\u03ac\u03bd\u03bd\u03b7\u03c2 \u03a0\u03bb\u03b1\u03c4\u03ae\u03c2,<\/a><\/strong><span style=\"font-family: Verdana, sans-serif; font-size: 16px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400;\">\u00a0\u03a4\u03bc\u03ae\u03bc\u03b1 \u039c\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd, \u03a0\u03b1\u03bd\u03b5\u03c0\u03b9\u03c3\u03c4\u03ae\u03bc\u03b9\u03bf \u03a0\u03b1\u03c4\u03c1\u03ce\u03bd<\/span><p><strong><br \/>\u03a4\u03af\u03c4\u03bb\u03bf\u03c2: <\/strong>\u039f\u03c1\u03b9\u03b6\u03cc\u03bd\u03c4\u03b9\u03b5\u03c2 \u03ba\u03b1\u03bc\u03c0\u03c5\u03bb\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03b5\u03c0\u03b9\u03c6\u03b1\u03bd\u03b5\u03b9\u03ce\u03bd \u03c3\u03b5 \u03c4\u03c1\u03b9\u03c3\u03b4\u03b9\u03ac\u03c3\u03c4\u03b1\u03c4\u03b5\u03c2, \u03c5\u03c0\u03bf-\u03a1\u03b9\u03bc\u03ac\u03bd\u03b5\u03b9\u03b5\u03c2 \u03bf\u03bc\u03ac\u03b4\u03b5\u03c2 Lie \u03b5\u03c0\u03b1\u03c6\u03ae\u03c2.<strong style=\"font-size: 16px;\"><br \/><\/strong><strong>\u03a0\u03b5\u03c1\u03af\u03bb\u03b7\u03c8\u03b7:<\/strong> \u03a3\u03b5 \u03b1\u03c5\u03c4\u03ae\u03bd \u03c4\u03b7\u03bd \u03bf\u03bc\u03b9\u03bb\u03af\u03b1 \u03bc\u03b5\u03bb\u03b5\u03c4\u03ac\u03bc\u03b5 \u03bf\u03c1\u03b9\u03b6\u03cc\u03bd\u03c4\u03b9\u03b5\u03c2 \u03ba\u03b1\u03bc\u03c0\u03c5\u03bb\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03b3\u03b9\u03b1 \u03b5\u03c0\u03b9\u03c6\u03ac\u03bd\u03b5\u03b9\u03b5\u03c2 \u03b5\u03bc\u03c6\u03c5\u03c4\u03b5\u03c5\u03bc\u03ad\u03bd\u03b5\u03c2 \u03c3\u03b5 \u03c4\u03c1\u03b9\u03c3\u03b4\u03b9\u03ac\u03c3\u03c4\u03b1\u03c4\u03b5\u03c2 \u03c5\u03c0\u03bf-\u03a1\u03b9\u03bc\u03ac\u03bd\u03bd\u03b5\u03b9\u03b5\u03c2 \u03bf\u03bc\u03ac\u03b4\u03b5\u03c2 Lie \u03b5\u03c0\u03b1\u03c6\u03ae\u03c2. \u03a7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03ce\u03bd\u03c4\u03b1\u03c2 \u03ad\u03bd\u03b1 \u03a1\u03b9\u03bc\u03ac\u03bd\u03bd\u03b5\u03b9\u03bf \u03c0\u03c1\u03bf\u03c3\u03b5\u03b3\u03b3\u03b9\u03c3\u03c4\u03b9\u03ba\u03cc\u03c3\u03c7\u03ae\u03bc\u03b1 \u03b5\u03af\u03bc\u03b1\u03c3\u03c4\u03b5 \u03c3\u03b5 \u03b8\u03ad\u03c3\u03b7 \u03bd\u03b1 \u03b5\u03be\u03b1\u03b3\u03ac\u03b3\u03bf\u03c5\u03bc\u03b5 \u03b1\u03ba\u03c1\u03b9\u03b2\u03b5\u03af\u03c2 \u03c4\u03cd\u03c0\u03bf\u03c5\u03c2 \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03bf\u03c1\u03b9\u03b6\u03cc\u03bd\u03c4\u03b9\u03b1 \u03ba\u03b1\u03bc\u03c0\u03c5\u03bb\u03cc\u03c4\u03b7\u03c4\u03b1 Gauss, \u03c4\u03b7\u03bd \u03bf\u03c1\u03b9\u03b6\u03cc\u03bd\u03c4\u03b9\u03b1 \u03bc\u03ad\u03c3\u03b7 \u03ba\u03b1\u03bc\u03c0\u03c5\u03bb\u03cc\u03c4\u03b7\u03c4\u03b1 \u03ba\u03b1\u03b9 \u03c4\u03b7\u03bd \u03c3\u03c5\u03bc\u03c0\u03bb\u03b5\u03ba\u03c4\u03b9\u03ba\u03ae \u03c0\u03b1\u03c1\u03b1\u03bc\u03cc\u03c1\u03c6\u03c9\u03c3\u03b7 \u03b5\u03c0\u03b9\u03c6\u03b1\u03bd\u03b5\u03b9\u03ce\u03bd \u03b5\u03bc\u03c6\u03c5\u03c4\u03b5\u03c5\u03bc\u03ad\u03bd\u03c9\u03bd \u03c3\u03b5 \u03c4\u03c1\u03b9\u03c3\u03b4\u03b9\u03ac\u03c3\u03c4\u03b1\u03c4\u03b5\u03c2 \u03bf\u03bc\u03ac\u03b4\u03b5\u03c2 Lie \u03bc\u03b5 \u03c5\u03c0\u03bf-\u03a1\u03b9\u03bc\u03ac\u03bd\u03bd\u03b5\u03b9\u03b1 \u03b4\u03bf\u03bc\u03ae \u03c0\u03bf\u03c5 \u03bb\u03b1\u03bc\u03b2\u03ac\u03bd\u03b5\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc \u03bc\u03b9\u03b1 \u03bc\u03bf\u03c1\u03c6\u03ae \u03b5\u03c0\u03b1\u03c6\u03ae\u03c2. \u0395\u03c3\u03c4\u03b9\u03ac\u03b6\u03bf\u03c5\u03bc\u03b5 \u03c3\u03b5 \u03b4\u03cd\u03bf \u03ba\u03cd\u03c1\u03b9\u03b1 \u03c0\u03b1\u03c1\u03b1\u03b4\u03b5\u03af\u03b3\u03bc\u03b1\u03c4\u03b1: \u03c4\u03b7\u03bd \u03bf\u03bc\u03ac\u03b4\u03b1 Heisenberg \u03ba\u03b1\u03b9 \u03c4\u03b7\u03bd \u03b1\u03c6\u03b9\u03bd\u03b9\u03ba\u03ae-\u03c0\u03c1\u03bf\u03c3\u03b8\u03b5\u03c4\u03b9\u03ba\u03ae \u03bf\u03bc\u03ac\u03b4\u03b1. \u03a4\u03b1\u03be\u03b9\u03bd\u03bf\u03bc\u03bf\u03cd\u03bc\u03b5 \u03b5\u03c0\u03b9\u03c6\u03ac\u03bd\u03b5\u03b9\u03b5\u03c2 \u03c0\u03b5\u03c1\u03b9\u03c3\u03c4\u03c1\u03bf\u03c6\u03ae\u03c2 \u03b5\u03bd\u03c4\u03cc\u03c2 \u03b1\u03c5\u03c4\u03ce\u03bd \u03c4\u03c9\u03bd \u03bf\u03bc\u03ac\u03b4\u03c9\u03bd \u03c0\u03bf\u03c5 \u03b5\u03bc\u03c6\u03b1\u03bd\u03af\u03b6\u03bf\u03c5\u03bd \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ad\u03c2 \u03bf\u03c1\u03b9\u03b6\u03cc\u03bd\u03c4\u03b9\u03b5\u03c2 \u03ba\u03b1\u03bc\u03c0\u03c5\u03bb\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2, \u03c3\u03c5\u03c7\u03bd\u03ac \u03b5\u03ba\u03c6\u03c1\u03ac\u03b6\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c4\u03b1 \u03c0\u03c1\u03bf\u03c6\u03af\u03bb \u03c4\u03bf\u03c5\u03c2 \u03bc\u03ad\u03c3\u03c9 \u03c3\u03c4\u03bf\u03b9\u03c7\u03b5\u03b9\u03c9\u03b4\u03ce\u03bd \u03ae \u03b5\u03bb\u03bb\u03b5\u03b9\u03c0\u03c4\u03b9\u03ba\u03ce\u03bd \u03bf\u03bb\u03bf\u03ba\u03bb\u03b7\u03c1\u03c9\u03bc\u03ac\u03c4\u03c9\u03bd.<\/p><hr \/><\/li><\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>\u03a0\u03c1\u03bf\u03c3\u03ba\u03b5\u03ba\u03bb\u03b7\u03bc\u03ad\u03bd\u03bf\u03b9 \u039f\u03bc\u03b9\u03bb\u03b7\u03c4\u03ad\u03c2 \u0391\u03c0\u03cc\u03c3\u03c4\u03bf\u03bb\u03bf\u03c2 \u0393\u03b9\u03b1\u03bd\u03bd\u03cc\u03c0\u03bf\u03c5\u03bb\u03bf\u03c2,\u00a0\u03a3\u03c7\u03bf\u03bb\u03ae \u0395\u03c6\u03b1\u03c1\u03bc\u03bf\u03c3\u03bc\u03ad\u03bd\u03c9\u03bd \u039c\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd &amp; \u03a6\u03c5\u03c3\u03b9\u03ba\u03ce\u03bd \u0395\u03c0\u03b9\u03c3\u03c4\u03b7\u03bc\u03ce\u03bd, \u0395\u03b8\u03bd\u03b9\u03ba\u03cc \u039c\u03b5\u03c4\u03c3\u03cc\u03b2\u03b9\u03bf \u03a0\u03bf\u03bb\u03c5\u03c4\u03b5\u03c7\u03bd\u03b5\u03af\u03bf\u03a4\u03af\u03c4\u03bb\u03bf\u03c2: \u03a3\u03c5\u03bd\u03b1\u03c1\u03c4\u03b7\u03c3\u03b9\u03b1\u03ba\u03ae \u03c0\u03b5\u03c1\u03af\u03bc\u03b5\u03c4\u03c1\u03bf\u03c2 \u03ba\u03b1\u03b9 \u03b7 \u03b4\u03b9\u03b1\u03c3\u03c4\u03b1\u03c4\u03b9\u03ba\u03ae \u03b1\u03bd\u03b9\u03c3\u03cc\u03c4\u03b7\u03c4\u03b1 Brunn\u2013Minkowski \u03b3\u03b9\u03b1 \u03bb\u03bf\u03b3\u03b1\u03c1\u03b9\u03b8\u03bc\u03b9\u03ba\u03ac \u03ba\u03bf\u03af\u03bb\u03b1 \u03bc\u03ad\u03c4\u03c1\u03b1\u03a0\u03b5\u03c1\u03af\u03bb\u03b7\u03c8\u03b7: \u039c\u03b5\u03bb\u03b5\u03c4\u03ac\u03bc\u03b5 \u03c4\u03b7 \u03b4\u03b9\u03b1\u03c3\u03c4\u03b1\u03c4\u03b9\u03ba\u03ae \u03b1\u03bd\u03b9\u03c3\u03cc\u03c4\u03b7\u03c4\u03b1 Brunn&#8211;Minkowski \u03b3\u03b9\u03b1 \u03bb\u03bf\u03b3\u03b1\u03c1\u03b9\u03b8\u03bc\u03b9\u03ba\u03ac \u03ba\u03bf\u03af\u03bb\u03b1 \u03bc\u03ad\u03c4\u03c1\u03b1 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2 $mu$ \u03c3\u03c4\u03bf\u03bd $mathbb{R}^n$ \u03bc\u03ad\u03c3\u03c9 \u03bc\u03b9\u03b1\u03c2 \u03b1\u03bd\u03b1\u03bb\u03c5\u03c4\u03b9\u03ba\u03ae\u03c2 \u03c0\u03c1\u03bf\u03c3\u03ad\u03b3\u03b3\u03b9\u03c3\u03b7\u03c2 \u03c0\u03bf\u03c5 \u03b2\u03b1\u03c3\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03c3\u03b5 \u03c4\u03b5\u03bb\u03b5\u03c3\u03c4\u03ad\u03c2 \u03b4\u03b9\u03ac\u03c7\u03c5\u03c3\u03b7\u03c2 \u03ba\u03b1\u03b9 \u03b5\u03ba\u03c4\u03b9\u03bc\u03ae\u03c3\u03b5\u03b9\u03c2 \u03ba\u03bb\u03af\u03c3\u03b7\u03c2. \u0391\u03c0\u03bf\u03b4\u03b5\u03b9\u03ba\u03bd\u03cd\u03bf\u03c5\u03bc\u03b5 \u03cc\u03c4\u03b9 \u03b3\u03b9\u03b1 \u03ba\u03ac\u03b8\u03b5 \u03b6\u03b5\u03cd\u03b3\u03bf\u03c2 \u03c3\u03c5\u03bc\u03bc\u03b5\u03c4\u03c1\u03b9\u03ba\u03ce\u03bd \u03ba\u03c5\u03c1\u03c4\u03ce\u03bd [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/yrmath4.conf.uoi.gr\/index.php?rest_route=\/wp\/v2\/pages\/206"}],"collection":[{"href":"https:\/\/yrmath4.conf.uoi.gr\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/yrmath4.conf.uoi.gr\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/yrmath4.conf.uoi.gr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/yrmath4.conf.uoi.gr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=206"}],"version-history":[{"count":71,"href":"https:\/\/yrmath4.conf.uoi.gr\/index.php?rest_route=\/wp\/v2\/pages\/206\/revisions"}],"predecessor-version":[{"id":2795,"href":"https:\/\/yrmath4.conf.uoi.gr\/index.php?rest_route=\/wp\/v2\/pages\/206\/revisions\/2795"}],"wp:attachment":[{"href":"https:\/\/yrmath4.conf.uoi.gr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=206"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}