{"id":20953,"date":"2018-10-17T18:50:32","date_gmt":"2018-10-17T18:50:32","guid":{"rendered":"https:\/\/www.upjs.sk\/prirodovedecka-fakulta\/pracoviska\/umv\/vv\/hov\/"},"modified":"2022-11-13T21:34:22","modified_gmt":"2022-11-13T20:34:22","slug":"hov","status":"publish","type":"cpt_pracoviska","link":"https:\/\/www.upjs.sk\/prirodovedecka-fakulta\/pracoviska\/ustavy-pf\/umat\/vv\/hov\/","title":{"rendered":"Hlavn\u00e9 oblasti v\u00fdskumu"},"content":{"rendered":"<p style=\"text-align: justify;\"><span style=\"font-size:16px\"><strong>Algebra<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\">\u00a0<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family:arial,sans-serif; font-size:10pt\"><font color=\"#000000\">Algebraick\u00fd v\u00fdskum je zameran\u00fd na univerz\u00e1lnu algebru. Univerz\u00e1lna algebra zov\u0161eobec\u0148uje poznatky z\u00edskan\u00e9 v\u00a0r\u00f4znych oblastiach algebry (te\u00f3ria gr\u00fap, line\u00e1rna algebra, te\u00f3ria zv\u00e4zov a\u00a0in\u00e9) a\u00a0sk\u00fama v\u0161eobecn\u00e9 vlastnosti algebraick\u00fdch syst\u00e9mov s\u00a0finit\u00e1rnymi oper\u00e1ciami. Jej v\u00fdsledky a\u00a0postupy poskytuj\u00fa in\u0161pir\u00e1ciu pre r\u00f4zne matematick\u00e9 discipl\u00edny.<\/font><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family:arial,sans-serif; font-size:10pt\"><font color=\"#000000\">Jednotliv\u00ed \u010dlenovia v\u00fdskumnej skupiny s\u00fa zameran\u00ed nasledovne:<\/font><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family:arial,sans-serif; font-size:10pt\"><font color=\"#000000\">Doc. RNDr. Miroslav Plo\u0161\u010dica, CSc.: zv\u00e4zy kongruenci\u00ed algebier, najm\u00e4 v\u00a0kongruen\u010dne distribut\u00edvnych variet\u00e1ch.<\/font><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family:arial,sans-serif; font-size:10pt\"><font color=\"#000000\">Doc. RNDr. Danica Studenovsk\u00e1, CSc.: zv\u00e4zy retraktov a kv\u00e1ziusporiadan\u00ed monoun\u00e1rnych algebier.<\/font><\/span><\/p>\n<p style=\"text-align: justify;\">\u00a0<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size:16px\"><strong>Anal\u00fdza<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\">\u00a0<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family:arial,sans-serif; font-size:10pt\"><font color=\"#000000\">Vedeck\u00e1 \u010dinnos\u0165 je zameran\u00e1 na nasleduj\u00face oblasti:\u00a0<\/font><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family:arial,sans-serif; font-size:10pt\"><font color=\"#000000\">Kvalitat\u00edvna te\u00f3ria diferenci\u00e1lnych rovn\u00edc<\/font><\/span><strong><span style=\"font-family:arial,sans-serif; font-size:10pt\"><font color=\"#000000\">.<\/font><\/span><\/strong><span style=\"font-family:arial,sans-serif; font-size:10pt\"><font color=\"#000000\">\u00a0Vy\u0161etruj\u00fa sa<\/font><\/span><span style=\"color:rgb(0, 0, 0); font-family:arial,sans-serif; font-size:10pt\">\u00a0vlastnost\u00ed rie\u0161en\u00ed, ako s\u00fa oscilatori\u010dnos\u0165, ohrani\u010denos\u0165, konvergencia\u00a0 a pod., r\u00f4znych typov diferenci\u00e1lnych rovn\u00edc a ich syst\u00e9mov.<\/span><\/p>\n<p style=\"text-align: justify;\"> <span style=\"font-family:arial,sans-serif; font-size:10pt\"><font color=\"#000000\">Harmonick\u00e1 a funkcion\u00e1lna anal\u00fdza.\u00a0Vy\u0161etruj\u00fa sa dva okruhy probl\u00e9mov &#8211; lebesgueovsk\u00e9 integrovanie a jeho zov\u0161eobecnenia na vektorov\u00e9 funkcie a miery (Banachove priestory a lok\u00e1lne konvexn\u00e9 priestory s \u010fal\u0161\u00edmi \u0161trukt\u00farami). Druhou oblas\u0165ou s\u00fa wavelety (a v\u0161eobecnej\u0161ie koherentn\u00e9 stavy), kde\u00a0 je v\u00fdskum zameran\u00fd na rie\u0161enie ot\u00e1zok s\u00favisiacich s oper\u00e1tormi zalo\u017een\u00fdmi na waveletoch, \u010dasovo-frekven\u010dn\u00fdmi oper\u00e1tormi a sk\u00faman\u00ed symbolov tak\u00fdchto integr\u00e1lnych oper\u00e1torov v r\u00f4znych funkcion\u00e1lnych priestoroch.<\/font><\/span><\/p>\n<p style=\"text-align: justify;\">\u00a0<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size:16px\"><strong>Te\u00f3ria hier a matematick\u00e1 ekon\u00f3mia<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\">\u00a0<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family:arial,sans-serif; font-size:10pt\"><font color=\"#000000\">V tejto oblasti sa s\u00fastre\u010fujeme hlavne na\u00a0<strong>kooperat\u00edvne hry\u00a0<\/strong><em><strong>n<\/strong><\/em><strong>\u00a0hr\u00e1\u010dov s neprenosn\u00fdm \u00fa\u017eitkom<\/strong><\/font><font color=\"#000000\">. Tieto modely maj\u00fa aplik\u00e1cie napr\u00edklad pri vyh\u013ead\u00e1van\u00ed darcov obli\u010diek, priradzovan\u00ed absolventov sk\u00f4r na pracovn\u00e9 poz\u00edcie alebo na \u0161tudijn\u00e9 miesta. \u0160tudovali sme vlastnosti rie\u0161en\u00ed r\u00f4znych variantov tak\u00fdchto hier a algoritmick\u00e9 ot\u00e1zky spojen\u00e9 s nasleduj\u00facimi probl\u00e9mami: rozhodnutie o existencii rie\u0161enia, n\u00e1jdenie rie\u0161enia, popis \u0161trukt\u00fary v\u0161etk\u00fdch rie\u0161en\u00ed. Navrhli sme nieko\u013eko efekt\u00edvnych algoritmov a v pr\u00edpade nieko\u013ek\u00fdch probl\u00e9mov sme uk\u00e1zali ich NP-\u00faplnos\u0165. Z\u00e1kladn\u00fdmi pou\u017e\u00edvan\u00fdmi n\u00e1strojmi s\u00fa okrem te\u00f3rie v\u00fdpo\u010dtovej zlo\u017eitosti aj te\u00f3ria grafov a kombinatorick\u00e1 optimaliz\u00e1cia.<\/font><\/span><\/p>\n<p style=\"text-align: justify;\"> <span style=\"font-family:arial,sans-serif; font-size:10pt\"><font color=\"#000000\">V tejto oblasti spolupracujeme s nasledovn\u00fdmi pracoviskami:<\/font><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family:arial,sans-serif; font-size:10pt\"><font color=\"#000000\">BME Budapest, University of Glasgow, Universidad Aut\u00f3noma de Barcelona, Universidad Carlos III, Madrid<\/font><\/span><\/p>\n<p style=\"text-align: justify;\">\u00a0<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size:16px\"><strong>Pravdepodobnos\u0165 a \u0161tatistika<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\">\u00a0<\/p>\n<p style=\"text-align: justify;\">Vedeck\u00e1 \u010dinnos\u0165 je zameran\u00e1 na nasleduj\u00face oblasti:<\/p>\n<ul>\n<li style=\"text-align: justify;\">modelovanie extr\u00e9mnych hodn\u00f4t<\/li>\n<li style=\"text-align: justify;\">stochastick\u00e9 procesy a ich aplik\u00e1cie<\/li>\n<li style=\"text-align: justify;\">mnohorozmern\u00e9 line\u00e1rne modely<\/li>\n<li style=\"text-align: justify;\">modelovanie z\u00e1vislost\u00ed v mnohorozmern\u00fdch modeloch<\/li>\n<li style=\"text-align: justify;\">predikcia v \u010dasov\u00fdch radoch pomocou line\u00e1rnej regresie<\/li>\n<li style=\"text-align: justify;\">aplik\u00e1cie \u0161tatistiky v medic\u00edne<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u00a0<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size:16px\"><strong>Te\u00f3ria grafov<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\">\u00a0<\/p>\n<p style=\"text-align: justify;\">V\u00fdskum v te\u00f3rii grafov je zameran\u00fd predov\u0161etk\u00fdm na nasleduj\u00face oblasti:<\/p>\n<ul>\n<li style=\"text-align: justify;\">farebnos\u0165 grafov,<\/li>\n<li style=\"text-align: justify;\">topologick\u00e1 te\u00f3ria grafov,<\/li>\n<li style=\"text-align: justify;\">cykly v grafoch,<\/li>\n<li style=\"text-align: justify;\">aplik\u00e1cie te\u00f3rie grafov,<\/li>\n<li style=\"text-align: justify;\">ohodnoten\u00e9 grafy.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">Pracovn\u00edci zaoberaj\u00faci sa te\u00f3riou grafov s\u00fa zapojen\u00ed do v\u00fdskumn\u00e9ho projektu APVV \u2013 0007 \u2013 07 Vnorenie, zafarbenie a\u00a0ohodnotenie grafov. Na b\u00e1ze vedeck\u00e9ho v\u00fdskumu konan\u00e9ho oddelen\u00edm sa \u00faspe\u0161ne rozv\u00edja doktorandsk\u00e9 \u0161t\u00fadium v\u00a0odbore 9. 1. 6. Diskr\u00e9tna matematika a\u00a0magistersk\u00e9 \u0161t\u00fadium \u0161tudijn\u00e9ho programu Mana\u017e\u00e9rska matematika \u0161tudijn\u00e9ho odboru Matematika.<\/p>\n<p style=\"text-align: justify;\">\u00a0<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size:16px\"><strong>Te\u00f3ria mno\u017e\u00edn a topol\u00f3gia<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\">\u00a0<\/p>\n<p style=\"text-align: justify;\">V\u00fdskumn\u00e1 \u010dinnos\u0165 je zameran\u00e1 na:<\/p>\n<ul>\n<li style=\"text-align: justify;\">mno\u017einovo-teoretick\u00e1 topol\u00f3gia<\/li>\n<li style=\"text-align: justify;\">kombinatorick\u00e1 te\u00f3ria mno\u017e\u00edn<\/li>\n<li style=\"text-align: justify;\">deskript\u00edvna te\u00f3ria mno\u017e\u00edn<\/li>\n<li style=\"text-align: justify;\">aplik\u00e1cie te\u00f3rie mno\u017e\u00edn v re\u00e1lnej anal\u00fdze<\/li>\n<li style=\"text-align: justify;\">booleovsk\u00e9 modely te\u00f3rie mno\u017e\u00edn a forcing<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u00a0<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size:16px\"><strong>Te\u00f3ria vyu\u010dovania matematiky<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\">\u00a0<\/p>\n<p style=\"text-align: justify;\">V\u00fdskumn\u00e1 \u010dinnos\u0165 je zameran\u00e1 na:<\/p>\n<ul>\n<li style=\"text-align: justify;\">problematiku matematick\u00fdch k\u013e\u00fa\u010dov\u00fdch kompetenci\u00ed<\/li>\n<li style=\"text-align: justify;\">e-learningov\u00fa podporu vyu\u010dovania matematiky<\/li>\n<li style=\"text-align: justify;\">postavenie diskr\u00e9tnej matematiky v r\u00e1mci \u0161kolskej matematiky<\/li>\n<li style=\"text-align: justify;\">vyu\u010dovanie anal\u00fdzy d\u00e1t v matematike z\u00e1kladnej a strednej \u0161koly<\/li>\n<li style=\"text-align: justify;\">matematick\u00fa pr\u00edpravu bud\u00facich vysoko\u0161kol\u00e1kov<\/li>\n<li style=\"text-align: justify;\">problematiku rie\u0161enia slovn\u00fdch \u00faloh<\/li>\n<\/ul>\n","protected":false},"author":1,"featured_media":0,"parent":20952,"menu_order":0,"template":"","meta":{"_editorskit_title_hidden":false,"_editorskit_reading_time":0,"_editorskit_is_block_options_detached":false,"_editorskit_block_options_position":"{}"},"categories":[],"tags":[],"tax_aktuality":[],"acf":{"acf_link_na_externy_obsah":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Hlavn\u00e9 oblasti v\u00fdskumu - Pr\u00edrodovedeck\u00e1 fakulta | UPJ\u0160<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.upjs.sk\/prirodovedecka-fakulta\/pracoviska\/ustavy-pf\/umat\/vv\/hov\/\" \/>\n<meta property=\"og:locale\" content=\"sk_SK\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Hlavn\u00e9 oblasti v\u00fdskumu - Pr\u00edrodovedeck\u00e1 fakulta | UPJ\u0160\" \/>\n<meta property=\"og:description\" content=\"Algebra \u00a0 Algebraick\u00fd v\u00fdskum je zameran\u00fd na univerz\u00e1lnu algebru. Univerz\u00e1lna algebra zov\u0161eobec\u0148uje poznatky z\u00edskan\u00e9 v\u00a0r\u00f4znych oblastiach algebry (te\u00f3ria gr\u00fap, line\u00e1rna algebra, te\u00f3ria zv\u00e4zov a\u00a0in\u00e9) a\u00a0sk\u00fama v\u0161eobecn\u00e9 vlastnosti algebraick\u00fdch syst\u00e9mov s\u00a0finit\u00e1rnymi oper\u00e1ciami. Jej v\u00fdsledky a\u00a0postupy poskytuj\u00fa in\u0161pir\u00e1ciu pre r\u00f4zne matematick\u00e9 discipl\u00edny. Jednotliv\u00ed \u010dlenovia v\u00fdskumnej skupiny s\u00fa zameran\u00ed nasledovne: Doc. 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Univerz\u00e1lna algebra zov\u0161eobec\u0148uje poznatky z\u00edskan\u00e9 v\u00a0r\u00f4znych oblastiach algebry (te\u00f3ria gr\u00fap, line\u00e1rna algebra, te\u00f3ria zv\u00e4zov a\u00a0in\u00e9) a\u00a0sk\u00fama v\u0161eobecn\u00e9 vlastnosti algebraick\u00fdch syst\u00e9mov s\u00a0finit\u00e1rnymi oper\u00e1ciami. Jej v\u00fdsledky a\u00a0postupy poskytuj\u00fa in\u0161pir\u00e1ciu pre r\u00f4zne matematick\u00e9 discipl\u00edny. Jednotliv\u00ed \u010dlenovia v\u00fdskumnej skupiny s\u00fa zameran\u00ed nasledovne: Doc. 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