{"id":14210,"date":"2017-06-13T10:30:17","date_gmt":"2017-06-13T10:30:17","guid":{"rendered":"https:\/\/www.upjs.sk\/prirodovedecka-fakulta\/root\/studium\/doktorandske\/poziadavky-na-prijimacie-konanie\/"},"modified":"2024-04-16T11:02:35","modified_gmt":"2024-04-16T10:02:35","slug":"poziadavky-na-prijimacie-konanie","status":"publish","type":"page","link":"https:\/\/www.upjs.sk\/prirodovedecka-fakulta\/studium\/doktorandske\/poziadavky-na-prijimacie-konanie\/","title":{"rendered":"Po\u017eiadavky na prij\u00edmacie konanie na doktorandsk\u00e9 \u0161t\u00fadium"},"content":{"rendered":"\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n<style>.kadence-column14210_cfed5b-8f > .kt-inside-inner-col,.kadence-column14210_cfed5b-8f > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column14210_cfed5b-8f > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column14210_cfed5b-8f > .kt-inside-inner-col{flex-direction:column;}.kadence-column14210_cfed5b-8f > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column14210_cfed5b-8f > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column14210_cfed5b-8f{position:relative;}@media all and (max-width: 1024px){.kadence-column14210_cfed5b-8f > .kt-inside-inner-col{flex-direction:column;}}@media all and (max-width: 767px){.kadence-column14210_cfed5b-8f > .kt-inside-inner-col{flex-direction:column;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column14210_cfed5b-8f\"><div class=\"kt-inside-inner-col\"><style>.kb-row-layout-id14210_f48c10-70 > .kt-row-column-wrap{align-content:start;}:where(.kb-row-layout-id14210_f48c10-70 > .kt-row-column-wrap) > .wp-block-kadence-column{justify-content:start;}.kb-row-layout-id14210_f48c10-70 > .kt-row-column-wrap{column-gap:var(--global-kb-gap-md, 2rem);row-gap:var(--global-kb-gap-md, 2rem);grid-template-columns:minmax(0, calc(30% - ((var(--global-kb-gap-md, 2rem) * 1 )\/2))) minmax(0, calc(70% - ((var(--global-kb-gap-md, 2rem) * 1 )\/2)));}.kb-row-layout-id14210_f48c10-70 > .kt-row-layout-overlay{opacity:0.30;}@media all and (max-width: 1024px){.kb-row-layout-id14210_f48c10-70 > .kt-row-column-wrap{grid-template-columns:repeat(2, minmax(0, 1fr));}}@media all and (max-width: 767px){.kb-row-layout-id14210_f48c10-70 > .kt-row-column-wrap{grid-template-columns:minmax(0, 1fr);}}<\/style><div class=\"kb-row-layout-wrap kb-row-layout-id14210_f48c10-70 alignnone wp-block-kadence-rowlayout\"><div class=\"kt-row-column-wrap kt-has-2-columns kt-row-layout-right-golden kt-tab-layout-inherit kt-mobile-layout-row kt-row-valign-top\">\n<style>.kadence-column14210_49937c-b6 > .kt-inside-inner-col{display:flex;}.kadence-column14210_49937c-b6 > .kt-inside-inner-col,.kadence-column14210_49937c-b6 > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column14210_49937c-b6 > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column14210_49937c-b6 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_49937c-b6 > .kt-inside-inner-col > .aligncenter{width:100%;}.kt-row-column-wrap > .kadence-column14210_49937c-b6{align-self:center;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_49937c-b6{align-self:auto;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_49937c-b6 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_49937c-b6 > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column14210_49937c-b6{position:relative;}@media all and (max-width: 1024px){.kadence-column14210_49937c-b6 > .kt-inside-inner-col{flex-direction:column;}}@media all and (max-width: 767px){.kadence-column14210_49937c-b6 > .kt-inside-inner-col{flex-direction:column;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column14210_49937c-b6\"><div class=\"kt-inside-inner-col\"><style>.kb-image14210_592bb0-44 .kb-image-has-overlay:after{opacity:0.3;}.kb-image14210_592bb0-44 img.kb-img, .kb-image14210_592bb0-44 .kb-img img{border-top-left-radius:5px;border-top-right-radius:5px;border-bottom-right-radius:5px;border-bottom-left-radius:5px;}<\/style>\n<div class=\"wp-block-kadence-image kb-image14210_592bb0-44\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"200\" src=\"https:\/\/www.upjs.sk\/app\/uploads\/sites\/10\/2023\/10\/odbor-biologia.png\" alt=\"\" class=\"kb-img wp-image-62002\"\/><\/figure><\/div>\n<\/div><\/div>\n\n\n<style>.kadence-column14210_6aa5cc-47 > .kt-inside-inner-col{display:flex;}.kadence-column14210_6aa5cc-47 > .kt-inside-inner-col,.kadence-column14210_6aa5cc-47 > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column14210_6aa5cc-47 > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column14210_6aa5cc-47 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_6aa5cc-47 > .kt-inside-inner-col > .aligncenter{width:100%;}.kt-row-column-wrap > .kadence-column14210_6aa5cc-47{align-self:center;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_6aa5cc-47{align-self:auto;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_6aa5cc-47 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_6aa5cc-47 > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column14210_6aa5cc-47{position:relative;}@media all and (max-width: 1024px){.kadence-column14210_6aa5cc-47 > .kt-inside-inner-col{flex-direction:column;}}@media all and (max-width: 767px){.kadence-column14210_6aa5cc-47 > .kt-inside-inner-col{flex-direction:column;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column14210_6aa5cc-47\"><div class=\"kt-inside-inner-col\"><style>.kt-accordion-id14210_8b339d-1b .kt-accordion-panel-inner{border-top:0px solid transparent;border-right:0px solid transparent;border-bottom:0px solid transparent;border-left:0px solid transparent;padding-top:var(--global-kb-spacing-sm, 1.5rem);padding-right:var(--global-kb-spacing-sm, 1.5rem);padding-bottom:var(--global-kb-spacing-sm, 1.5rem);padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kt-accordion-id14210_8b339d-1b .wp-block-kadence-pane .kt-accordion-header-wrap .kt-blocks-accordion-header{border-top:0px solid #f2f2f2;border-right:0px solid #f2f2f2;border-bottom:0px solid #f2f2f2;border-left:0px solid #f2f2f2;border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;background:#ffffff;color:#008338;padding-top:6px;padding-right:5px;padding-bottom:6px;padding-left:6px;}.kt-accordion-wrap.kt-accordion-id14210_8b339d-1b > .kt-accordion-inner-wrap > .kt-accordion-pane > .kt-accordion-header-wrap{margin-top:0px;}.single-content .wp-block-kadence-pane>h2:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h3:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h4:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h5:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h6:first-child{margin-top:0px;}.kt-accordion-id14210_8b339d-1b:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_8b339d-1b:not( .kt-accodion-icon-style-basiccircle ):not( 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.kt-blocks-accordion-header:focus{color:#000000;background:#ffffff;border-top-color:#eeeeee;border-top-style:solid;border-right-color:#eeeeee;border-right-style:solid;border-bottom-color:#eeeeee;border-bottom-style:solid;border-left-color:#eeeeee;border-left-style:solid;}.kt-accordion-id14210_8b339d-1b:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_8b339d-1b:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before, body:not(.hide-focus-outline) .kt-accordion-id14210_8b339d-1b:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id14210_8b339d-1b:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:before{background:#000000;}.kt-accordion-id14210_8b339d-1b:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger, body:not(.hide-focus-outline) .kt-accordion-id14210_8b339d-1b:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger{background:#000000;}.kt-accordion-id14210_8b339d-1b:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_8b339d-1b:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before, body:not(.hide-focus-outline) .kt-accordion-id14210_8b339d-1b:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id14210_8b339d-1b:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:before{background:#ffffff;}.kt-accordion-id14210_8b339d-1b .kt-accordion-header-wrap .kt-blocks-accordion-header.kt-accordion-panel-active{color:#000000;background:#ffffff;border-top-color:#0e9cd1;border-top-style:solid;border-right-color:#0e9cd1;border-right-style:solid;border-bottom-color:#0e9cd1;border-bottom-style:solid;border-left-color:#0e9cd1;border-left-style:solid;}.kt-accordion-id14210_8b339d-1b:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_8b339d-1b:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before{background:#000000;}.kt-accordion-id14210_8b339d-1b:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger{background:#000000;}.kt-accordion-id14210_8b339d-1b:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_8b339d-1b:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before{background:#ffffff;}@media all and (max-width: 1024px){.kt-accordion-id14210_8b339d-1b .kt-accordion-panel-inner{border-top:0px solid transparent;border-right:0px solid transparent;border-bottom:0px solid transparent;border-left:0px solid transparent;}}@media all and (max-width: 1024px){.kt-accordion-id14210_8b339d-1b .wp-block-kadence-pane .kt-accordion-header-wrap .kt-blocks-accordion-header{border-top:0px solid #f2f2f2;border-right:0px solid #f2f2f2;border-bottom:0px solid #f2f2f2;border-left:0px solid #f2f2f2;}}@media all and (max-width: 1024px){.kt-accordion-id14210_8b339d-1b .kt-accordion-header-wrap .kt-blocks-accordion-header:hover, body:not(.hide-focus-outline) .kt-accordion-id14210_8b339d-1b .kt-accordion-header-wrap .kt-blocks-accordion-header:focus{border-top-color:#eeeeee;border-top-style:solid;border-right-color:#eeeeee;border-right-style:solid;border-bottom-color:#eeeeee;border-bottom-style:solid;border-left-color:#eeeeee;border-left-style:solid;}}@media all and (max-width: 1024px){.kt-accordion-id14210_8b339d-1b .kt-accordion-header-wrap .kt-blocks-accordion-header.kt-accordion-panel-active{border-top-color:#0e9cd1;border-top-style:solid;border-right-color:#0e9cd1;border-right-style:solid;border-bottom-color:#0e9cd1;border-bottom-style:solid;border-left-color:#0e9cd1;border-left-style:solid;}}@media all and (max-width: 767px){.kt-accordion-id14210_8b339d-1b .kt-accordion-panel-inner{border-top:0px solid transparent;border-right:0px solid transparent;border-bottom:0px solid transparent;border-left:0px solid transparent;}.kt-accordion-id14210_8b339d-1b .wp-block-kadence-pane .kt-accordion-header-wrap .kt-blocks-accordion-header{border-top:0px solid #f2f2f2;border-right:0px solid #f2f2f2;border-bottom:0px solid #f2f2f2;border-left:0px solid #f2f2f2;}.kt-accordion-id14210_8b339d-1b .kt-accordion-header-wrap .kt-blocks-accordion-header:hover, body:not(.hide-focus-outline) .kt-accordion-id14210_8b339d-1b .kt-accordion-header-wrap .kt-blocks-accordion-header:focus{border-top-color:#eeeeee;border-top-style:solid;border-right-color:#eeeeee;border-right-style:solid;border-bottom-color:#eeeeee;border-bottom-style:solid;border-left-color:#eeeeee;border-left-style:solid;}.kt-accordion-id14210_8b339d-1b .kt-accordion-header-wrap .kt-blocks-accordion-header.kt-accordion-panel-active{border-top-color:#0e9cd1;border-top-style:solid;border-right-color:#0e9cd1;border-right-style:solid;border-bottom-color:#0e9cd1;border-bottom-style:solid;border-left-color:#0e9cd1;border-left-style:solid;}}<\/style>\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-id14210_8b339d-1b kt-accordion-has-20-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-arrow kt-accodion-icon-side-left\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-15 kt-pane14210_263d58-6a\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Fyziol\u00f3gia rastl\u00edn<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\"has-text-align-justify\"><strong>Fyziol\u00f3gia rastl\u00edn<\/strong>: Vodn\u00fd re\u017eim. Dif\u00fazia, hromadn\u00fd tok a osm\u00f3za. Vodn\u00fd potenci\u00e1l. Pr\u00edjem, translok\u00e1cia xyl\u00e9mom a v\u00fddaj vody. Vodn\u00e1 bilancia. Miner\u00e1lna v\u00fd\u017eiva. \u017diviny v p\u00f4de. Pr\u00edjem miner\u00e1lnych \u017eiv\u00edn a mechanizmy transportu. Biog\u00e9nne prvky. Fotosynt\u00e9za. Stavba fotosyntetick\u00e9ho apar\u00e1tu. Komplexy tylakoidnej membr\u00e1ny. Absorpcia FAR a migr\u00e1cia energie. Elektr\u00f3nov\u00fd transportn\u00fd re\u0165azec a tvorba kysl\u00edka. Prot\u00f3nov\u00fd transport a fotofosforyl\u00e1cia. Metabolizmus uhl\u00edka. Calvinov cyklus a fotorespir\u00e1cia. Hatchov a Slackov, syndr\u00f3m C3, C4 a CAM. Synt\u00e9zy v chloroplastoch a transport asimil\u00e1tov. D\u00fdchanie. Mobiliz\u00e1cia z\u00e1sobn\u00fdch sacharidov. Odb\u00faravanie \u0161krobu. Glykol\u00fdza. Citr\u00e1tov\u00fd cyklus. Pent\u00f3zov\u00fd cyklus. Alternat\u00edvne d\u00fdchanie. Glykozidy. Monosacharidov\u00e9 deriv\u00e1ty. Lipidy. Synt\u00e9za v cytoplazme. Vosky. Synt\u00e9za \u0161trukt\u00farnych lipidov v chloroplastoch. Mobiliz\u00e1cia z\u00e1sobn\u00fdch lipidov. Glyoxal\u00e1tov\u00fd cyklus. Metabolizmus dus\u00edka. Redukcia molekulov\u00e9ho dus\u00edka. Asimil\u00e1cia nitr\u00e1tu, vznik aminokysel\u00edn. Metabolizmus s\u00edry. Asimila\u010dn\u00e1 redukcia sulf\u00e1tu. Metabolizmus cyste\u00ednu a metion\u00ednu. Terpenoidy. Synt\u00e9za v cytoplazme a v plastidoch. Metabolity cesty kyseliny \u0161ikimovej. Jednoduch\u00e9 fenoly, fenylprop\u00e1ny, kumar\u00edny, tan\u00edny, chin\u00f3ny, flavonoidy, a lign\u00edn. Alkaloidy. V\u00fdznam pre rastliny a ekologick\u00e9 interakcie. Regul\u00e1cia v\u00fdvinov\u00fdch procesov. Hodnotenie rastu. Embryon\u00e1lna f\u00e1za rastu. Objemov\u00fd rast. Rast bunkovej steny. Polarita vrcholov\u00e9ho a dif\u00fazneho rastu. Kinetika rastu. Diferenci\u00e1cia buniek, plet\u00edv a org\u00e1nov. Regener\u00e1cia a transplant\u00e1cia. Fotoreceptory. Etiol\u00e1cia a fotomorfogen\u00e9za. Ch\u00e9mia a transform\u00e1cie fytochr\u00f3mov. Fyziologick\u00e9 \u00fa\u010dinky (VLFR, LFR a HIR). Fytochr\u00f3my v zelen\u00fdch rastlin\u00e1ch. Fotoreceptory modr\u00e9ho svetla, kryptochr\u00f3my, a fototrop\u00edny. Regul\u00e1cia zatv\u00e1rania prieduchov svetlom. Horm\u00f3ny rastl\u00edn, percepcia a vedenie sign\u00e1lu. Ch\u00e9mia, metabolizmus a transport; mechanizmus p\u00f4sobenia; fyziologick\u00e9 \u00fa\u010dinky aux\u00ednov, giberel\u00ednov, cytokin\u00ednov, kyseliny abscisovej, etyl\u00e9nu, brasinosteroidov, polypeptidov\u00fdch horm\u00f3nov, kyseliny jasm\u00f3novej, oxidu dusnat\u00e9ho a \u010fal\u0161\u00edch hormon\u00e1lne akt\u00edvnych l\u00e1tok. Biologick\u00e9 rytmy, cirkadi\u00e1nny oscil\u00e1tor, fotoperiodizmus. Dormancia p\u00fa\u010dikov a semien, kl\u00ed\u010denie, regul\u00e1cia mobiliz\u00e1cie z\u00e1sobn\u00fdch l\u00e1tok. Kvitnutie. Expresia reproduk\u010dnej dospelosti. Determin\u00e1cia merist\u00e9mov. Fotoperiodick\u00e1 indukcia kvitnutia a jaroviz\u00e1cia. Kvetn\u00e9 merist\u00e9my a v\u00fdvin kvetn\u00fdch org\u00e1nov. Tuberiz\u00e1cia. Starnutie rastl\u00edn a programovan\u00e1 smr\u0165 bunky. Pohyby rastl\u00edn &#8211; orient\u00e1cia v priestore. Fyziol\u00f3gia stresu.<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-16 kt-pane14210_fcf4ee-e2\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Fyziol\u00f3gia \u017eivo\u010d\u00edchov<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\"has-text-align-justify\"><strong><u>Fyziol\u00f3gia \u017eivo\u010d\u00edchov:<\/u><\/strong>Predmet a z\u00e1kladn\u00e9 \u00fadaje z hist\u00f3rie vedn\u00e9ho odboru. Z\u00e1kladn\u00e9 funk\u010dn\u00e9 princ\u00edpy \u017eivo\u010d\u00ed\u0161neho organizmu. Princ\u00edp dynamickej homeost\u00e1zy. Telesn\u00e9 tekutiny: fylogenetick\u00fd v\u00fdvoj, zlo\u017eenie, funkcie krvn\u00fdch elementov a krvnej plazmy, hematopo\u00e9za a jeho regul\u00e1cia, krvn\u00e9 skupiny. fylogen\u00e9za obehovej s\u00fastavy. Pr\u00e1ca srdca. Nervov\u00e9 a hormon\u00e1lne riadenie krvn\u00e9ho tlaku a \u010dinnosti srdca. pr\u00edjem, tr\u00e1venie a vstreb\u00e1vanie \u017eiv\u00edn. Tr\u00e1viaci syst\u00e9m u bezstavovcov a jednotliv\u00fdch tried stavovcov. Nervov\u00e1 a hormon\u00e1lna regul\u00e1cia procesov tr\u00e1venia a vstreb\u00e1vania. Funkcie pankreasu. Funkcie pe\u010dene. Mechanizmy z\u00e1sobovania buniek kysl\u00edkom &#8211;&nbsp; evolu\u010dn\u00e9 h\u013eadisko. Vonkaj\u0161ie a vn\u00fatorn\u00e9 d\u00fdchanie u stavovcov. Transport d\u00fdchac\u00edch plynov. Mechanizmy vylu\u010dovania vo fylogen\u00e9ze. exkr\u00e9cia u vodn\u00fdch a suchozemsk\u00fdch \u017eivo\u010d\u00edchov. Funkcie obli\u010diek. Hospod\u00e1renie s vodou a miner\u00e1lmi. Horm\u00f3ny \u2013 pojem, rozdelenie, mechanizmy \u00fa\u010dinku, horm\u00f3ny bezstavovcov a stavovcov a ich \u00fa\u010dinky, neurohumor\u00e1lne vz\u0165ahy. Fylogen\u00e9za nervov\u00e9ho syst\u00e9mu. Neur\u00f3n ako z\u00e1kladn\u00e1 jednotka nervov\u00e9ho syst\u00e9mu. Vznik a vedenie nervov\u00fdch vzruchov. Riadenie motoriky na \u00farovni miechy. Reflexy. Receptory &#8211; rozdelenie, mechanizmy prevodu sign\u00e1lu, \u0161pecializ\u00e1cia a adapt\u00e1cia. Funkcie jednotliv\u00fdch \u010dast\u00ed mozgu. Motorick\u00e9 a senzorick\u00e9 funkcie mozgovej k\u00f4ry. Asocia\u010dn\u00e9 funkcie CNS. Geometrick\u00e1 optika oka. Funkcie sietnice. Zrakov\u00e1 dr\u00e1ha. Vedenie a transform\u00e1cia akustickej inform\u00e1cie v strednom a vn\u00fatornom uchu. Mechanizmus frekven\u010dnej citlivosti sluchu. Mechanizmus svalovej kontrakcie. Energetika svalovej kontrakcie. Endokrinn\u00e1 regul\u00e1cia \u010dinnosti sam\u010d\u00edch pohlavn\u00fdch org\u00e1nov. Hormon\u00e1lna regul\u00e1cia ovari\u00e1lneho cyklu. Riadenie pr\u00edjmu potravy u cicavcov. Exotermia a endotermia. Mechanizmy termoregul\u00e1cie u endotermn\u00fdch \u017eivo\u010d\u00edchov. Heterotermia. \u00daloha a mechanizmy celul\u00e1rnej imunity.Vroden\u00e1 imunita -fagocyt\u00f3za, z\u00e1pal.<\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong>Etol\u00f3gia:<\/strong>Hist\u00f3ria, v\u00fdznam a rozdelenie etol\u00f3gie. Metodol\u00f3gia etol\u00f3gie. Vroden\u00e9 spr\u00e1vanie a jeho formy. U\u010denie \u2013 v\u00fdznam, rozdelenie, u\u010denie podmie\u0148ovan\u00edm, in\u0161trument\u00e1lne u\u010denie, imprinting, vy\u0161\u0161ie formy u\u010denia. U\u010denie a vroden\u00e9 spr\u00e1vanie. Soci\u00e1lne spr\u00e1vanie &#8211;&nbsp; met\u00f3dy sk\u00famania, soci\u00e1lne prejavy a vz\u0165ahy, soci\u00e1lne skupiny.&nbsp; Rodi\u010dovsk\u00e9 spr\u00e1vanie. Sexu\u00e1lne spr\u00e1vanie. Hrav\u00e9 spr\u00e1vanie.&nbsp; Komunika\u010dn\u00e9 syst\u00e9my \u017eivo\u010d\u00edchov \u2013 zmena postoja, mimika, ritualizovan\u00e9 spr\u00e1vanie, komunik\u00e1cia chemick\u00fdmi, sveteln\u00fdmi a zvukov\u00fdmi sign\u00e1lmi. Agonistick\u00e9 spr\u00e1vanie a prejavy agresie. Biologick\u00e9 rytmy v spr\u00e1van\u00ed \u017eivo\u010d\u00edchov. Prejavy abnorm\u00e1lneho spr\u00e1vania.<\/p>\n\n\n\n<p class=\"has-text-align-justify\"><em>S\u00fa\u010das\u0165ou prij\u00edmacej sk\u00fa\u0161ky je preuk\u00e1zanie jazykov\u00fdch schopnost\u00ed uch\u00e1dza\u010da o D\u0160 (pr\u00e1ca s cudzojazy\u010dn\u00fdm odborn\u00fdm textom \u2013 angli\u010dtina pr\u00edp.\u010fal\u0161\u00ed svetov\u00fd jazyk, akt\u00edvna komunik\u00e1cia v anglickom jazyku)<\/em><\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-18 kt-pane14210_ef5342-5d\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Molekul\u00e1rna cytol\u00f3gia a genetika<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\"has-text-align-justify\">Od uch\u00e1dza\u010da sa vy\u017eaduje znalos\u0165 cytol\u00f3gie, molekulovej biol\u00f3gie, genetiky a ich subdiscipl\u00edn v rozsahu druh\u00e9ho stup\u0148a vysoko\u0161kolsk\u00e9ho \u0161t\u00fadia. Nutnou podmienkou je schopnos\u0165 pracova\u0165 s odborn\u00fdm textom v jazyku anglickom.<br>Chemick\u00e9 zlo\u017eenie buniek<br>Energia, katal\u00fdza a biosynt\u00e9za (Katal\u00fdza a vyu\u017eitie energie bunkami. Aktivovan\u00e9 nosi\u010dov\u00e9 molekuly a biosynt\u00e9za)<br>Ako bunky z\u00edskavaj\u00fa energiu z potravy (Odb\u00faravanie cukrov a tukov. Ukladanie a zu\u017eitkovanie potravy.)<br>Prote\u00edny: \u0161trukt\u00fara a funkcia<br>DNA (\u0160trukt\u00fara a funkcia DNA. Replik\u00e1cia DNA. Oprava DNA.)<br>Od DNA k prote\u00ednom (Od DNA k RNA. Od RNA k prote\u00ednom. RNA a p\u00f4vod \u017eivota.)<br>Chromoz\u00f3my a regul\u00e1cia g\u00e9nov (\u0160trukt\u00fara eukaryontick\u00fdch chromoz\u00f3mov. Regul\u00e1cia g\u00e9nov.)<br>Genetick\u00e1 rozmanitos\u0165 (Genetick\u00e1 rozmanitos\u0165 u bakt\u00e9ri\u00ed. Zdroje genetick\u00fdch zmien v eukaryontick\u00fdch gen\u00f3moch. Pohlavn\u00e9 rozmno\u017eovanie a reorganiz\u00e1cia g\u00e9nov.)<br>DNA \u2013 technol\u00f3gie (Ako sa DNA molekuly analyzuj\u00fa. Hybridiz\u00e1cia nukleov\u00fdch kysel\u00edn. Klonovanie DNA. G\u00e9nov\u00e9 in\u017einierstvo.)<br>\u0160trukt\u00fara membr\u00e1n (Lipidov\u00e1 dvojvrstva. Membr\u00e1nov\u00e9 prote\u00edny.)<br>Prenos l\u00e1tok cez membr\u00e1ny (Pren\u00e1\u0161a\u010dov\u00e9 prote\u00edny a ich funkcia. I\u00f3nov\u00e9 kan\u00e1ly a membr\u00e1nov\u00fd potenci\u00e1l. I\u00f3nov\u00e9 kan\u00e1ly a signaliz\u00e1cia v nervov\u00fdch bunk\u00e1ch.)<br>Z\u00edskavanie energie v mitochondri\u00e1ch a chloroplastoch<br>Vn\u00fatrobunkov\u00e9 oddiely a transport<br>Komunik\u00e1cie medzi bunkami<br>Cytoskelet<br>Bunkov\u00e9 delenie<br>Kontrola bunkov\u00e9ho delenia a bunkov\u00e1 smr\u0165<br>Tkaniv\u00e1<\/p>\n\n\n\n<p>&nbsp;<strong><u>Genetika:<\/u><\/strong> \u010co je genetika? \u017div\u00e1 pr\u00edroda ako integrovan\u00e9 genetick\u00e9 laborat\u00f3rium. Hist\u00f3ria a s\u00fa\u010dasn\u00fd stav genetiky. Subdiscipl\u00edny genetiky. J. G. Mendel \u2013 zakladate\u013e genetiky. Mendlove genetick\u00e9 princ\u00edpy. Cytologick\u00e9 mechanizmy dedi\u010dnosti. Monohybrid, dihybrid, trihybrid. Mnohon\u00e1sobn\u00e9 alelov\u00e9 s\u00e9rie. Penetrancia a expresivita. G\u00e9nov\u00e9 interakcie. Cytologick\u00e9 z\u00e1klady g\u00e9nov\u00fdch interakci\u00ed. Typy g\u00e9nov\u00fdch interakci\u00ed. Reciprok\u00e1 interakcia, epist\u00e1zy, inhib\u00edcia, kompenz\u00e1cia, komplementarita, duplicitn\u00e9 g\u00e9ny. Dedi\u010dnos\u0165 kvantitat\u00edvnych znakov. Podiel genotypu a prostredia. Heritabilita. Koeficient genetickej determin\u00e1cie. Biometrick\u00e9 hodnotenie. V\u00e4zba g\u00e9nov. Cytologick\u00e9 z\u00e1klady v\u00e4zby. V\u00e4zbov\u00e9 f\u00e1zy. Crossing-over. Pravdepodobn\u00fd molekulov\u00fd mechanizmus crossing-overu. Modely genetickej rekombin\u00e1cie. Chromoz\u00f3mov\u00e9 mapy. Mapovanie genetick\u00fdch lokusov na chromoz\u00f3me. In situ hybridiz\u00e1cia metaf\u00e1zov\u00fdch chromoz\u00f3mov. Mapovanie g\u00e9nov met\u00f3dami molekulovej genetiky. Genetick\u00e1 determin\u00e1cia pohlavia. Stru\u010dn\u00fd fylogenetick\u00fd preh\u013ead. Pohlavn\u00e9 typy a pohlavn\u00e9 chromoz\u00f3my. Gonoz\u00f3mov\u00fd lokus. Lyonovej hypot\u00e9za. Holandrick\u00e1 dedi\u010dnos\u0165. Znaky na pohlavie viazan\u00e9, pohlav\u00edm ovplyvnen\u00e9 a ovl\u00e1dan\u00e9. Extrachromoz\u00f3mov\u00e9 genetick\u00e9 determinanty. Plastidov\u00e1 a mitochonri\u00e1lna DNA. Vn\u00fatrobunkov\u00e1 symbi\u00f3za. Genetick\u00e9 mechanizmy na subcelul\u00e1rnej \u00farovni. Genetika v\u00edrusov. Retrov\u00edrusy. Prov\u00edrus. AIDS. Genetika prokaryotick\u00fdch organizmov. Bakteri\u00e1lny gen\u00f3m. Mechanizmy prenosu bakteri\u00e1lnych g\u00e9nov. Konjug\u00e1cia, transform\u00e1cia, transdukcia. Restrik\u010dno-modifika\u010dn\u00e9 syst\u00e9my. Restrik\u010dn\u00e9 endonukle\u00e1zy a&nbsp; ch v\u00fdznam v g\u00e9nov\u00fdch manipul\u00e1ci\u00e1ch. Cytogenetika. \u0160trukt\u00fara chromoz\u00f3mu. rDNA. Cytogenetick\u00e9 met\u00f3dy. Po\u010det chromoz\u00f3mov, karyotyp, obsah DNA. Mut\u00e1cie a mutagen\u00e9za. Chemick\u00e9 a fyzik\u00e1lne mutag\u00e9ny. Klasifik\u00e1cia mut\u00e1ci\u00ed. Detekcia mut\u00e1ci\u00ed. Materi\u00e1lna podstata g\u00e9nu. \u0160trukt\u00fara a funkcia DNA, mRNA, tRNA, rRNA. Genetick\u00fd k\u00f3d. Replik\u00e1cia DNA. Mechanizmy replik\u00e1cie. Enz\u00fdmy replik\u00e1cie. Transkripcia a transl\u00e1cia. Mechanizmus transkripcie v prokaryotick\u00fdch a eukaryotick\u00fdch organizmoch. Mechanizmus transl\u00e1cie. Posttranskrip\u010dn\u00e9 a posttransla\u010dn\u00e9 modifik\u00e1cie. Regul\u00e1cia g\u00e9novej expresie v prokaryotick\u00fdch a eukaryotick\u00fdch organizmoch. Indukcia a represia. Regul\u00e1cia sp\u00e4tnou v\u00e4zbou. Regula\u010dn\u00e9 mechanizmy eukaryotick\u00fdch organizmov. Funkcia prom\u00f3tora v regul\u00e1cii g\u00e9novej expresie. Z\u00e1klady genetiky \u010dloveka. Met\u00f3dy v genetike \u010dloveka. Genealogick\u00e1 a gemelologick\u00e1 met\u00f3da. Cytogenetick\u00e9, biochemick\u00e9 a molekulovo-genetick\u00e9 met\u00f3dy. Dedi\u010dnos\u0165 niektor\u00fdch norm\u00e1lnych znakov. Dedi\u010dnos\u0165 niektor\u00fdch patologick\u00fdch znakov a chor\u00f4b. \u013dudsk\u00fd karyotyp a d\u00f4sledky jeho zmien. Genetika popul\u00e1ci\u00ed. Hardyho-Weinbergov z\u00e1kon a podmienky jeho platnosti. Genetick\u00e1 rovnov\u00e1ha v popul\u00e1cii. Zmeny frekvencie alel a genotypov a ich genetick\u00e9 d\u00f4sledky. Aplikovan\u00e1 genetika. Genetika v rastlinnej a \u017eivo\u010d\u00ed\u0161nej produkcii. Molekulov\u00e1 evol\u00facia. Poznatky zo sekvenovania eukaryotick\u00fdch gen\u00f3mov. HUGO. Spolo\u010dn\u00e9 a rozdielne genetick\u00e9 charakteristiky. Modelov\u00e9 organizmy v genetike.<\/p>\n\n\n\n<p><strong>Subdiscipl\u00edna genetiky: Pod\u013ea zamerania t\u00e9my dizerta\u010dnej pr\u00e1ce.<\/strong><\/p>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n\n<\/div><\/div><\/div><\/div>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n<style>.kadence-column14210_903504-1d > .kt-inside-inner-col,.kadence-column14210_903504-1d > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column14210_903504-1d > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column14210_903504-1d > .kt-inside-inner-col{flex-direction:column;}.kadence-column14210_903504-1d > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column14210_903504-1d > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column14210_903504-1d{position:relative;}@media all and (max-width: 1024px){.kadence-column14210_903504-1d > .kt-inside-inner-col{flex-direction:column;}}@media all and (max-width: 767px){.kadence-column14210_903504-1d > .kt-inside-inner-col{flex-direction:column;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column14210_903504-1d\"><div class=\"kt-inside-inner-col\"><style>.kb-row-layout-id14210_510f44-87 > .kt-row-column-wrap{align-content:start;}:where(.kb-row-layout-id14210_510f44-87 > .kt-row-column-wrap) > .wp-block-kadence-column{justify-content:start;}.kb-row-layout-id14210_510f44-87 > .kt-row-column-wrap{column-gap:var(--global-kb-gap-md, 2rem);row-gap:var(--global-kb-gap-md, 2rem);grid-template-columns:minmax(0, calc(30% - ((var(--global-kb-gap-md, 2rem) * 1 )\/2))) minmax(0, calc(70% - ((var(--global-kb-gap-md, 2rem) * 1 )\/2)));}.kb-row-layout-id14210_510f44-87 > .kt-row-layout-overlay{opacity:0.30;}@media all and (max-width: 1024px){.kb-row-layout-id14210_510f44-87 > .kt-row-column-wrap{grid-template-columns:repeat(2, minmax(0, 1fr));}}@media all and (max-width: 767px){.kb-row-layout-id14210_510f44-87 > .kt-row-column-wrap{grid-template-columns:minmax(0, 1fr);}}<\/style><div class=\"kb-row-layout-wrap kb-row-layout-id14210_510f44-87 alignnone wp-block-kadence-rowlayout\"><div class=\"kt-row-column-wrap kt-has-2-columns kt-row-layout-right-golden kt-tab-layout-inherit kt-mobile-layout-row kt-row-valign-top\">\n<style>.kadence-column14210_ee1db2-e4 > .kt-inside-inner-col{display:flex;}.kadence-column14210_ee1db2-e4 > .kt-inside-inner-col,.kadence-column14210_ee1db2-e4 > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column14210_ee1db2-e4 > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column14210_ee1db2-e4 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_ee1db2-e4 > .kt-inside-inner-col > .aligncenter{width:100%;}.kt-row-column-wrap > .kadence-column14210_ee1db2-e4{align-self:center;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_ee1db2-e4{align-self:auto;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_ee1db2-e4 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_ee1db2-e4 > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column14210_ee1db2-e4{position:relative;}@media all and (max-width: 1024px){.kadence-column14210_ee1db2-e4 > .kt-inside-inner-col{flex-direction:column;}}@media all and (max-width: 767px){.kadence-column14210_ee1db2-e4 > .kt-inside-inner-col{flex-direction:column;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column14210_ee1db2-e4\"><div class=\"kt-inside-inner-col\"><style>.kb-image14210_d8553a-dc .kb-image-has-overlay:after{opacity:0.3;}.kb-image14210_d8553a-dc img.kb-img, .kb-image14210_d8553a-dc .kb-img img{border-top-left-radius:5px;border-top-right-radius:5px;border-bottom-right-radius:5px;border-bottom-left-radius:5px;}<\/style>\n<div class=\"wp-block-kadence-image kb-image14210_d8553a-dc\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"200\" src=\"https:\/\/www.upjs.sk\/app\/uploads\/sites\/10\/2023\/10\/odbor-Fyzika.png\" alt=\"\" class=\"kb-img wp-image-62022\"\/><\/figure><\/div>\n<\/div><\/div>\n\n\n<style>.kadence-column14210_f5d8da-5d > .kt-inside-inner-col{display:flex;}.kadence-column14210_f5d8da-5d > .kt-inside-inner-col,.kadence-column14210_f5d8da-5d > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column14210_f5d8da-5d > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column14210_f5d8da-5d > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_f5d8da-5d > .kt-inside-inner-col > .aligncenter{width:100%;}.kt-row-column-wrap > .kadence-column14210_f5d8da-5d{align-self:center;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_f5d8da-5d{align-self:auto;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_f5d8da-5d > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_f5d8da-5d > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column14210_f5d8da-5d{position:relative;}@media all and (max-width: 1024px){.kadence-column14210_f5d8da-5d > .kt-inside-inner-col{flex-direction:column;}}@media all and (max-width: 767px){.kadence-column14210_f5d8da-5d > .kt-inside-inner-col{flex-direction:column;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column14210_f5d8da-5d\"><div class=\"kt-inside-inner-col\"><style>.kt-accordion-id14210_40e7f6-ec .kt-accordion-panel-inner{border-top:0px solid transparent;border-right:0px solid transparent;border-bottom:0px solid transparent;border-left:0px solid transparent;padding-top:var(--global-kb-spacing-sm, 1.5rem);padding-right:var(--global-kb-spacing-sm, 1.5rem);padding-bottom:var(--global-kb-spacing-sm, 1.5rem);padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kt-accordion-id14210_40e7f6-ec .wp-block-kadence-pane .kt-accordion-header-wrap .kt-blocks-accordion-header{border-top:0px solid #f2f2f2;border-right:0px solid #f2f2f2;border-bottom:0px solid #f2f2f2;border-left:0px solid #f2f2f2;border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;background:#ffffff;color:#008338;padding-top:6px;padding-right:5px;padding-bottom:6px;padding-left:6px;}.kt-accordion-wrap.kt-accordion-id14210_40e7f6-ec > .kt-accordion-inner-wrap > .kt-accordion-pane > .kt-accordion-header-wrap{margin-top:0px;}.single-content .wp-block-kadence-pane>h2:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h3:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h4:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h5:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h6:first-child{margin-top:0px;}.kt-accordion-id14210_40e7f6-ec:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_40e7f6-ec:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-icon-trigger:before{background:#008338;}.kt-accordion-id14210_40e7f6-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger{background:#008338;}.kt-accordion-id14210_40e7f6-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_40e7f6-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger:before{background:#ffffff;}.kt-accordion-id14210_40e7f6-ec .kt-accordion-header-wrap .kt-blocks-accordion-header:hover, body:not(.hide-focus-outline) .kt-accordion-id14210_40e7f6-ec .kt-accordion-header-wrap .kt-blocks-accordion-header:focus{color:#000000;background:#ffffff;border-top-color:#eeeeee;border-top-style:solid;border-right-color:#eeeeee;border-right-style:solid;border-bottom-color:#eeeeee;border-bottom-style:solid;border-left-color:#eeeeee;border-left-style:solid;}.kt-accordion-id14210_40e7f6-ec:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_40e7f6-ec:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before, body:not(.hide-focus-outline) .kt-accordion-id14210_40e7f6-ec:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id14210_40e7f6-ec:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:before{background:#000000;}.kt-accordion-id14210_40e7f6-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger, body:not(.hide-focus-outline) .kt-accordion-id14210_40e7f6-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger{background:#000000;}.kt-accordion-id14210_40e7f6-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_40e7f6-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before, body:not(.hide-focus-outline) .kt-accordion-id14210_40e7f6-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id14210_40e7f6-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:before{background:#ffffff;}.kt-accordion-id14210_40e7f6-ec .kt-accordion-header-wrap .kt-blocks-accordion-header.kt-accordion-panel-active{color:#000000;background:#ffffff;border-top-color:#0e9cd1;border-top-style:solid;border-right-color:#0e9cd1;border-right-style:solid;border-bottom-color:#0e9cd1;border-bottom-style:solid;border-left-color:#0e9cd1;border-left-style:solid;}.kt-accordion-id14210_40e7f6-ec:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_40e7f6-ec:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before{background:#000000;}.kt-accordion-id14210_40e7f6-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger{background:#000000;}.kt-accordion-id14210_40e7f6-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_40e7f6-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before{background:#ffffff;}@media all and (max-width: 1024px){.kt-accordion-id14210_40e7f6-ec .kt-accordion-panel-inner{border-top:0px solid transparent;border-right:0px solid transparent;border-bottom:0px solid transparent;border-left:0px solid transparent;}}@media all and (max-width: 1024px){.kt-accordion-id14210_40e7f6-ec .wp-block-kadence-pane .kt-accordion-header-wrap .kt-blocks-accordion-header{border-top:0px solid #f2f2f2;border-right:0px solid #f2f2f2;border-bottom:0px solid #f2f2f2;border-left:0px solid #f2f2f2;}}@media all and (max-width: 1024px){.kt-accordion-id14210_40e7f6-ec .kt-accordion-header-wrap .kt-blocks-accordion-header:hover, body:not(.hide-focus-outline) .kt-accordion-id14210_40e7f6-ec .kt-accordion-header-wrap .kt-blocks-accordion-header:focus{border-top-color:#eeeeee;border-top-style:solid;border-right-color:#eeeeee;border-right-style:solid;border-bottom-color:#eeeeee;border-bottom-style:solid;border-left-color:#eeeeee;border-left-style:solid;}}@media all and (max-width: 1024px){.kt-accordion-id14210_40e7f6-ec .kt-accordion-header-wrap .kt-blocks-accordion-header.kt-accordion-panel-active{border-top-color:#0e9cd1;border-top-style:solid;border-right-color:#0e9cd1;border-right-style:solid;border-bottom-color:#0e9cd1;border-bottom-style:solid;border-left-color:#0e9cd1;border-left-style:solid;}}@media all and (max-width: 767px){.kt-accordion-id14210_40e7f6-ec .kt-accordion-panel-inner{border-top:0px solid transparent;border-right:0px solid transparent;border-bottom:0px solid transparent;border-left:0px solid transparent;}.kt-accordion-id14210_40e7f6-ec .wp-block-kadence-pane .kt-accordion-header-wrap .kt-blocks-accordion-header{border-top:0px solid #f2f2f2;border-right:0px solid #f2f2f2;border-bottom:0px solid #f2f2f2;border-left:0px solid #f2f2f2;}.kt-accordion-id14210_40e7f6-ec .kt-accordion-header-wrap .kt-blocks-accordion-header:hover, body:not(.hide-focus-outline) .kt-accordion-id14210_40e7f6-ec .kt-accordion-header-wrap .kt-blocks-accordion-header:focus{border-top-color:#eeeeee;border-top-style:solid;border-right-color:#eeeeee;border-right-style:solid;border-bottom-color:#eeeeee;border-bottom-style:solid;border-left-color:#eeeeee;border-left-style:solid;}.kt-accordion-id14210_40e7f6-ec .kt-accordion-header-wrap .kt-blocks-accordion-header.kt-accordion-panel-active{border-top-color:#0e9cd1;border-top-style:solid;border-right-color:#0e9cd1;border-right-style:solid;border-bottom-color:#0e9cd1;border-bottom-style:solid;border-left-color:#0e9cd1;border-left-style:solid;}}<\/style>\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-id14210_40e7f6-ec kt-accordion-has-21-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-arrow kt-accodion-icon-side-left\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-4 kt-pane14210_b5a5e0-04\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Biofyzika<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\"has-text-align-justify\">Na prij\u00edmac\u00edch pohovoroch bud\u00fa vy\u017eadovan\u00e9 znalosti, v z\u00e1vislosti na zvolenej t\u00e9me dizerta\u010dnej pr\u00e1ce,&nbsp; v rozsahu \u0161t\u00e1tnych z\u00e1vere\u010dn\u00fdch sk\u00fa\u0161ok v \u0161tudijn\u00fdch odboroch biofyziky, bioch\u00e9mie alebo molekulovej biol\u00f3gie. V pr\u00edpade absolventa medic\u00edny bud\u00fa po\u017eadovan\u00e9 v\u0161eobecn\u00e9 znalosti a orient\u00e1cia v bioch\u00e9mii a molekulovej biol\u00f3gii.<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-5 kt-pane14210_e6c251-ae\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Fyzika kondenzovan\u00fdch l\u00e1tok<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\"has-text-align-justify\"><strong><u>Te\u00f3ria fyziky kondenzovan\u00fdch l\u00e1tok:<\/u><\/strong> Adiabatick\u00e1 a jednoelektr\u00f3nov\u00e1 aproxim\u00e1cia. Jednoelektr\u00f3nov\u00e9 stavy energie v kry\u0161t\u00e1li. Elektr\u00f3n v periodickom poli. Aproxim\u00e1cia takmer vo\u013en\u00fdch elektr\u00f3nov.&nbsp; Met\u00f3da efekt\u00edvnej hmotnosti. Klasifik\u00e1cia tuh\u00fdch l\u00e1tok na z\u00e1klade spektra energie jednoelektr\u00f3nov\u00fdch stavov. Elektr\u00f3nov\u00e9 mern\u00e9 teplo. Kmity at\u00f3mov kry\u0161talickej mrie\u017eky. Line\u00e1rna mrie\u017eka s jedn\u00fdm at\u00f3mom v element\u00e1rnej bunke. Fon\u00f3ny. Mern\u00e9 teplo kry\u0161t\u00e1lov. Magn\u00f3ny. V\u00fdmenn\u00e1 interakcia a Heisenbergov hamiltoni\u00e1n.&nbsp; Magn\u00f3nov\u00e9 mern\u00e9 teplo. Elektr\u00f3novo-fon\u00f3nov\u00e1 interakcia. Cooperove p\u00e1ry-v\u00e4zbov\u00e1 energia. Z\u00e1kladn\u00fd stav supravodi\u010da (BCS model). Supratekutos\u0165. Hustota elektr\u00f3nov\u00fdch stavov. Koncentr\u00e1cia elektr\u00f3nov a dier v polovodi\u010doch. Fermiho energia. Boltzmannova kinetick\u00e1 rovnica, kinetick\u00e9 koeficienty.&nbsp; Termoelektrick\u00e9 a galvanomagnetick\u00e9 javy.<\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong>Experiment\u00e1lna fyzika kondenzovan\u00fdch l\u00e1tok:<\/strong> Fyzik\u00e1lny princ\u00edp a stavba elektr\u00f3nov\u00e9ho mikroskopu.&nbsp; Experiment\u00e1lne met\u00f3dy rtg. difraktografie. Vznik a vlastnosti rtg \u017eiarenia. Braggov z\u00e1kon. Laueho difrak\u010dn\u00e9 podmienky. Recipro\u010dn\u00e1 mrie\u017eka. Neutr\u00f3nov\u00e1 difrakcia.&nbsp; Rastrovacia tunelov\u00e1 mikroskopia (STM). At\u00f3mov\u00e1 silov\u00e1 mikroskopia (AFM).&nbsp; Elektrick\u00e1 vodivos\u0165 polovodi\u010dov. Met\u00f3dy merania elektrickej vodivosti. Meranie Hallovej kon\u0161tanty.&nbsp;<br>Ur\u010denie orbit\u00e1lneho a spinov\u00e9ho magnetick\u00e9ho momentu.&nbsp; Met\u00f3dy merania intenzity a indukcie magnetick\u00e9ho po\u013ea. (induk\u010dn\u00e9 met\u00f3dy, magnetometrick\u00e9 met\u00f3dy, Hallov jav). Met\u00f3dy zaznamen\u00e1vania krivky magnetiz\u00e1cie a hyster\u00e9znej slu\u010dky. Jadrov\u00e1 magnetick\u00e1 rezonancia. Elektr\u00f3nov\u00e1 paramagnetick\u00e1 rezonancia. M\u00f6ssbauerova spektroskopia. Infra\u010derven\u00e1 spektroskopia. Met\u00f3dy z\u00edskavanie a merania n\u00edzkych (do l K) a ve\u013emi n\u00edzkych tepl\u00f4t (pod l K).&nbsp; Met\u00f3dy merania tepelnej vodivosti a tepelnej kapacity. Supravodivos\u0165. Supratekutos\u0165. Termodynamika f\u00e1zov\u00fdch transform\u00e1ci\u00ed. Termodynamick\u00e1 podmienka rovnov\u00e1hy. Rozdelenie kondenzovan\u00fdch l\u00e1tok pod\u013ea ich magnetick\u00fdch vlastnost\u00ed. Orbit\u00e1lny magnetick\u00fd moment. Spinov\u00fd magnetick\u00fd moment. Magnetick\u00e9 vlastnosti at\u00f3mu s jedn\u00fdm a viacer\u00fdmi elektr\u00f3nmi, Russelova-Sanndersova v\u00e4zba. Hundov\u00e9 pravidl\u00e1.&nbsp; Feromagnetizmus.&nbsp;&nbsp; F\u00e1zov\u00e9 prechody 2. druhu ( prechod z feromagnetick\u00e9ho do paramagnetick\u00e9ho stavu). Antiferomagnetizmus. Ferimagnetizmus. Druhy energie feromagnet\u00edk. Dom\u00e9nov\u00e1 \u0161trukt\u00fara feromagnet\u00edk.<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-7 kt-pane14210_408486-24\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Fyzika<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\"has-text-align-justify\"><strong>Astrofyzika:<\/strong>Stavov\u00e1 rovnica hviezdnej l\u00e1tky, excit\u00e1cia, Boltzmanova rovnica, ioniz\u00e1cia, Sahova rovnica. Stavba hviezd, hydrostatick\u00e1 a \u017eiariv\u00e1 rovnov\u00e1ha, prenos energie \u017eiaren\u00edm, veden\u00edm a konvekciou. Prenos energie v atmosf\u00e9re hviezd. Rovnica prenosu \u017eiarenia. Vznik spektra a z\u00e1kladn\u00e9 vlastnosti. Z\u00e1kladn\u00e9 rovnice stavby hviezd a ich rie\u0161enie. Zdroje energie vo hviezdach. Vznik a evol\u00facia hviezd. Kone\u010dn\u00e9 \u0161t\u00e1dia hviezdneho v\u00fdvoja, model degenerovanej hviezdy, bieli trpasl\u00edci, neutr\u00f3nov\u00e9 hviezdy, pulzary, \u010dierne diery. Premenn\u00e9 hviezdy a ich delenie , pr\u00ed\u010diny premennosti, z\u00e1kladne typy premenn\u00fdch hviezd<\/p>\n\n\n\n<p class=\"has-text-align-justify\">Princ\u00edp geometrickej optiky, optick\u00e9 chyby a ich korekcia, typy \u010falekoh\u013eadov ich kon\u0161trukcia, r\u00e1dioteleskopy, dru\u017eicov\u00e9 UV a X \u010falekoh\u013eady, detektory svetla: CCD, CMOS, z\u00e1klady fotometrie, spektroskopie a polarimetrie<\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong>Jadrov\u00e1 a subjadrov\u00e1 fyzika<\/strong>: Na prij\u00edmac\u00edch pohovoroch bud\u00fa vy\u017eadovan\u00e9 znalosti v rozsahu \u0161t\u00e1tnej z\u00e1vere\u010dnej sk\u00fa\u0161ky v \u0161tudijnom odbore jadrov\u00e1 a subjadrov\u00e1 fyzika.<\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong>Matematick\u00e1 a po\u010d\u00edta\u010dov\u00e1 fyzika:<\/strong> Komplexn\u00e1 premenn\u00e1, analytick\u00e9 funkcie, Cauchyho integr\u00e1lne vety, te\u00f3ria rez\u00eddu\u00ed. Diferenci\u00e1lne rovnice, oby\u010dajn\u00e9 diferenci\u00e1lne rovnice druh\u00e9ho r\u00e1du s kon\u0161tantn\u00fdmi koeficientmi, Eulerova rovnica. Eulerova met\u00f3da rie\u0161enia diferenci\u00e1lnych rovn\u00edc separ\u00e1ciou premenn\u00fdch. Sturmova-Liouvillova \u00faloha, okrajov\u00e9 podmienky a \u00falohy. Besselove funkcie, Legendrove, Laguerrove a Hermitove polyn\u00f3my. Rie\u0161enie Laplaceovej rovnice vo sf\u00e9rick\u00fdch s\u00faradniciach, sf\u00e9rick\u00e9 funkcie. Klasifik\u00e1cia diferenci\u00e1lnych rovn\u00edc druh\u00e9ho r\u00e1du, charakteristick\u00e1 rovnica. Numerick\u00e9 rie\u0161enie syst\u00e9mov algebraick\u00fdch rovn\u00edc, kon\u0161trukcia numerick\u00fdch kvadrat\u00far pre s\u00fastavy diferenci\u00e1lnych rovn\u00edc a parci\u00e1lne diferenci\u00e1lne rovnice. Klasifik\u00e1cia dynamick\u00fdch syst\u00e9mov pomocou invariantn\u00fdch mier, identifik\u00e1cia chaosu. Diskr\u00e9tna Fourierova transform\u00e1cia. Met\u00f3da Monte Carlo, generovanie rozde\u013eovac\u00edch funkci\u00ed v s\u00faboroch \u0161tatistickej fyziky, aplik\u00e1cie v te\u00f3rii magnetizmu. Met\u00f3da molekulovej dynamiky. Stochastick\u00e9 diferenci\u00e1lne rovnice. Modelovanie zalo\u017een\u00e9 na celul\u00e1rnych automatoch a auton\u00f3mnych agentoch. Funkcion\u00e1lne stabiln\u00e9 rozde\u013eovacie funkcie. Optimaliza\u010dn\u00e9 met\u00f3dy.\u00a0<\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong>Teoretick\u00e1 fyzika:<\/strong> Z\u00e1kladn\u00e9 princ\u00edpy klasickej mechaniky: princ\u00edp virtu\u00e1lnych pr\u00e1c, d\u2019Alembertov princ\u00edp a Hamiltonov princ\u00edp. Lagrangeove a Hamiltonove\u00a0 kanonick\u00e9 rovnice. Princ\u00edp relativity, Lorentzova transform\u00e1cia, vlastn\u00fd \u010das, interval v \u0161tvorrozmernom priestore, \u0161tvorvektor\u00a0 hybnosti, relativistick\u00e9 pohybov\u00e9 rovnice. S\u00fastava Maxwellov\u00fdch rovn\u00edc vo v\u00e1kuu a v l\u00e1tkovom prostred\u00ed. Potenci\u00e1ly elektromagnetick\u00e9ho po\u013ea. Kalibra\u010dn\u00e1 invariantnos\u0165. \u0160tvorrozmern\u00fd vektor hustoty pr\u00fadu a \u0161tvorrozmern\u00fd potenci\u00e1l. S\u00fastava Maxwellov\u00fdch rovn\u00edc vo v\u00e1kuu v kovariantnom tvare, tenzor elektromagnetick\u00e9ho po\u013ea. Elektrostatick\u00e9 pole, stacion\u00e1rne magnetick\u00e9 pole a kv\u00e1zistacion\u00e1rne elektromagnetick\u00e9 pole. Elektromagnetick\u00e9 vlny. Rovinn\u00e1 monochromatick\u00e1 vlna a jej polariz\u00e1cia. Z\u00e1kladn\u00e9 pojmy kvantovej mechaniky: princ\u00edp neur\u010ditosti, princ\u00edp superpoz\u00edcie, stavy a veli\u010diny v kvantovej mechanike, oper\u00e1tory z\u00e1kladn\u00fdch fyzik\u00e1lnych veli\u010d\u00edn. Schr\u00f6dingerova rovnica, hamiltoni\u00e1n. Jednoduch\u00e9 kvantovomechanick\u00e9 s\u00fastavy: \u010dastica v potenci\u00e1lovej jame, prechod \u010dastice potenci\u00e1lovou bari\u00e9rou, harmonick\u00fd oscil\u00e1tor, at\u00f3m vod\u00edka.\u00a0 Spin, Pauliho vylu\u010dovac\u00ed princ\u00edp. \u0160tatistick\u00e9 s\u00fabory a rozdelenia. Mikrokanonick\u00e9, kanonick\u00e9 a grandkanonick\u00e9 rozdelenia v klasickej a kvantovej \u0161tatistickej fyzike. Boltzmannovo, Boseho-Einsteinovo a Fermiho-Diracovo rozdelenie. Kv\u00e1zi\u010dastice v tuh\u00fdch l\u00e1tkach, fon\u00f3ny a magn\u00f3ny. Mern\u00e9 teplo. F\u00e1zov\u00e9 prechody, klasifik\u00e1cia f\u00e1zov\u00fdch prechodov. Landauova te\u00f3ria f\u00e1zov\u00fdch prechodov.<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-8 kt-pane14210_2e596c-af\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Te\u00f3ria vyu\u010dovania fyziky<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p><strong>V\u0161eobecn\u00e1 a teoretick\u00e1 fyzika<\/strong><\/p>\n\n\n\n<ol>\n<li>Mechanika hmotn\u00e9ho bodu a tuh\u00e9ho telesa<\/li>\n\n\n\n<li>Gravita\u010dn\u00e9 pole. Pr\u00e1ca, v\u00fdkon, energia, z\u00e1kony zachovania<\/li>\n\n\n\n<li>Mechanika tekut\u00edn<\/li>\n\n\n\n<li>Mechanick\u00e9 kmitanie a vlnenie<\/li>\n\n\n\n<li>Kinetick\u00e1 te\u00f3ria plynov a termodynamika<\/li>\n\n\n\n<li>Elektrostatick\u00e9 pole.<\/li>\n\n\n\n<li>Elektrick\u00fd pr\u00fad. Elektrick\u00e9 obvody<\/li>\n\n\n\n<li>Stacion\u00e1rne magnetick\u00e9 pole<\/li>\n\n\n\n<li>Elektromagnetick\u00e1 indukcia<\/li>\n\n\n\n<li>Striedav\u00e9 elektrick\u00e9 pr\u00fady. Vlastn\u00e9 a vyn\u00faten\u00e9 kmity. Rezonancia<\/li>\n\n\n\n<li>Elektromagnetick\u00e9 vlnenie. Svetlo. \u0160\u00edrenie svetla<\/li>\n\n\n\n<li>Kvantov\u00e9 vlastnosti svetla<\/li>\n\n\n\n<li>\u0160trukt\u00fara at\u00f3mu a kvantovanie energetick\u00fdch hlad\u00edn<\/li>\n\n\n\n<li>Klasifik\u00e1cia element\u00e1rnych \u010dast\u00edc. Jadrov\u00e9 reakcie<\/li>\n<\/ol>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p><strong>Didaktika fyziky<\/strong><\/p>\n\n\n\n<ol>\n<li>\u0160kolsk\u00fd fyzik\u00e1lny experiment, jeho funkcie, metodika pr\u00edpravy, realiz\u00e1cia a fyzik\u00e1lna interpret\u00e1cia, anal\u00fdza vybran\u00e9ho fyzik\u00e1lneho experimentu.<\/li>\n\n\n\n<li>Fyzik\u00e1lne \u00falohy, ich klasifik\u00e1cia, v\u00fdznam, met\u00f3dy rie\u0161enia a metodika zaradenia do fyzik\u00e1lneho vzdel\u00e1vania, rozbor vybranej fyzik\u00e1lnej \u00falohy.<\/li>\n\n\n\n<li>Graf fyzik\u00e1lnej z\u00e1vislosti, prvky grafu, zru\u010dnosti \u0161tudentov pre pr\u00e1cu s grafmi, vyu\u017eitie grafov vo fyzik\u00e1lnom vzdel\u00e1van\u00ed, popis vzdel\u00e1vacej aktivity s vyu\u017eit\u00edm grafu fyzik\u00e1lnej z\u00e1vislosti.<\/li>\n\n\n\n<li>Modern\u00e9 vyu\u010dovacie met\u00f3dy, akt\u00edvne pozn\u00e1vanie, b\u00e1date\u013esk\u00fd pr\u00edstup vo fyzik\u00e1lnom pozn\u00e1van\u00ed, uk\u00e1\u017eka spr\u00edstupnenia vybranej fyzik\u00e1lnej t\u00e9my interakt\u00edvnou met\u00f3dou.<\/li>\n\n\n\n<li>N\u00e1stroje sp\u00e4tnej v\u00e4zby, objektiviz\u00e1cia hodnotenia vzdel\u00e1vac\u00edch v\u00fdsledkov, modifik\u00e1cia vyu\u010dovacieho postupu na z\u00e1klade z\u00edskan\u00fdch v\u00fdsledkov sp\u00e4tnej v\u00e4zby, uk\u00e1\u017eka vlastnej tvorby ot\u00e1zok didaktick\u00e9ho testu.<\/li>\n\n\n\n<li>Modely a modelovanie vo fyzik\u00e1lnom vzdel\u00e1van\u00ed, charakteristika, metodika pou\u017eitia modelov, met\u00f3da dynamick\u00e9ho modelovania, rozbor vybran\u00e9ho modelu fyzik\u00e1lneho javu.<\/li>\n\n\n\n<li>Modern\u00e1 didaktick\u00e1 technika, jej pr\u00ednos pre fyzik\u00e1lne vzdel\u00e1vanie, mo\u017enosti vyu\u017eitia pri akt\u00edvnom \u017eiackom b\u00e1dan\u00ed, uk\u00e1\u017eka konkr\u00e9tnej aplik\u00e1cie a rozbor mo\u017enost\u00ed jej vyu\u017eitia.<\/li>\n\n\n\n<li>Po\u010d\u00edta\u010dom podporovan\u00e9 fyzik\u00e1lne vzdel\u00e1vanie, aktu\u00e1lne mo\u017enosti, \u0161pecifik\u00e1, v\u00fdznam pre pochopenie podstaty fyzik\u00e1lnych javov \u0161tudentmi.<\/li>\n\n\n\n<li>Pr\u00e1ca s talentovanou ml\u00e1de\u017eou, neform\u00e1lne vzdel\u00e1vanie, vyu\u017e\u00edvanie prvotn\u00fdch poznatkov a budovanie vedeckej gramotnosti \u017eiakov, rozbor vybran\u00e9ho fyzik\u00e1lneho probl\u00e9mu.<\/li>\n\n\n\n<li>On-line informa\u010dn\u00e9 zdroje a vyu\u017e\u00edvanie multim\u00e9di\u00ed vo fyzik\u00e1lnom vzdel\u00e1van\u00ed, n\u00e1stroje, mo\u017enosti a pr\u00ednos e-vzdel\u00e1vania, predstavenie konkr\u00e9tneho rie\u0161enia na vybranej t\u00e9me.<\/li>\n<\/ol>\n\n\n\n<p>Op\u00ed\u0161te v\u00e1\u0161 pr\u00edstup k fyzik\u00e1lnemu vzdel\u00e1vaniu.<br>V \u010dom by ste radi prispeli k skvalitneniu fyzik\u00e1lneho vzdel\u00e1vania va\u0161ou dizerta\u010dnou pr\u00e1cou.<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-9 kt-pane14210_34618f-80\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Progres\u00edvne materi\u00e1ly<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<ol>\n<li>Typy v\u00e4zieb v&nbsp;TL.<\/li>\n\n\n\n<li>\u0160trukt\u00fara TL, z\u00e1klady kry\u0161talografie (prvky symetrie, oper\u00e1cie symetrie, bodov\u00e9 a priestorov\u00e9 grupy).<\/li>\n\n\n\n<li>Fyzik\u00e1lny princ\u00edp vzniku X-ray,&nbsp; Recipro\u010dn\u00e1 mrie\u017eka, Laueho difrak\u010dn\u00e9 z\u00e1kony, Braggov z\u00e1kon.<\/li>\n\n\n\n<li>Mechanick\u00e9 vlastnosti materi\u00e1lov: typy por\u00fach v re\u00e1lnych materi\u00e1loch, z\u00e1kladn\u00e9 pevnostn\u00e9 parametre<\/li>\n\n\n\n<li>Elektrick\u00e9 vlastnosti TL: klasifik\u00e1cia TL, kovy, polovodi\u010de, izol\u00e1tory &#8211; z\u00e1kladn\u00e9 vlastnosti, kovy- p\u00e1smov\u00fd model vodivosti.<\/li>\n\n\n\n<li>Magnetick\u00e9 vlastnosti: klasifik\u00e1cia l\u00e1tok pod\u013ea magnetick\u00fdch vlastnost\u00ed (dia, para, fero, feri, antifero), druhy energie feromagnet\u00edk, dom\u00e9nov\u00e1 \u0161trukt\u00fara feromagnet\u00edk.<\/li>\n\n\n\n<li>Met\u00f3dy \u0161trukt\u00farnej anal\u00fdzy: X-ray: vybran\u00e9 metodiky, Elektr\u00f3nov\u00e1 mikroskopia: princ\u00edp TEM a REM, pr\u00edpadne \u010fal\u0161ie metodiky pod\u013ea po\u017eiadaviek t\u00e9my DzP.<\/li>\n\n\n\n<li>Tepeln\u00e9 vlastnosti TL: mern\u00e9 teplo TL.<\/li>\n\n\n\n<li>F\u00e1zov\u00e9 rovnov\u00e1hy, F\u00e1zov\u00e9 diagramy, Jednozlo\u017ekov\u00e1 s\u00fastava, Kvapaln\u00e9 dvojzlo\u017ekov\u00e9 s\u00fastavy, Kondenzovan\u00e9 s\u00fastavy.<\/li>\n\n\n\n<li>Heterog\u00e9nna katal\u00fdza, Adsorpcia.<\/li>\n\n\n\n<li>Povrchy a tenk\u00e9 vrstvy (metodiky charakteriz\u00e1cie povrchov AFM,&nbsp; STM, pr\u00edprava tek\u00fdch vrstiev, PVD met\u00f3dy, Langmuir Blodgett, SAMs)<\/li>\n\n\n\n<li>Litografick\u00e9 met\u00f3dy pr\u00edpravy nano\u0161trukt\u00far. (optick\u00e1 a elektr\u00f3nov\u00e1 litografia, rezisty, prenos \u0161trukt\u00far)<\/li>\n<\/ol>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p><strong>Odpor\u00fa\u010dan\u00e1 literat\u00fara:<\/strong><\/p>\n\n\n\n<ol>\n<li>P. Sov\u00e1k et al, Vybran\u00e9 met\u00f3dy \u0161trukt\u00farnej anal\u00fdzy kovov, UPJ\u0160, 2007<\/li>\n\n\n\n<li>Zdroj Hajko , Potock\u00fd, Zentko, Magnetiza\u010dn\u00e9 procesy, Alfa, 1982.<\/li>\n\n\n\n<li>V. Kave\u010dansk\u00fd, Fyzika TL, UPJ\u0160, 1983<\/li>\n\n\n\n<li>D.R. Askeland, P. Phule, The Science and Engineering of Materials, Thomson,&nbsp; 2002.<\/li>\n\n\n\n<li>V. Kell\u00f6 \u2013 A. Tk\u00e1\u010d: Fyzik\u00e1lna ch\u00e9mia, Alfa, Bratislava, 1977.<\/li>\n\n\n\n<li>P.W. Atkins: Fyzik\u00e1lna ch\u00e9mia, Oxford \/STU Bratislava, 1999.<\/li>\n<\/ol>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n\n<\/div><\/div><\/div><\/div>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n<style>.kadence-column14210_927ddc-d1 > .kt-inside-inner-col,.kadence-column14210_927ddc-d1 > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column14210_927ddc-d1 > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column14210_927ddc-d1 > .kt-inside-inner-col{flex-direction:column;}.kadence-column14210_927ddc-d1 > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column14210_927ddc-d1 > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column14210_927ddc-d1{position:relative;}@media all and (max-width: 1024px){.kadence-column14210_927ddc-d1 > .kt-inside-inner-col{flex-direction:column;}}@media all and (max-width: 767px){.kadence-column14210_927ddc-d1 > .kt-inside-inner-col{flex-direction:column;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column14210_927ddc-d1\"><div class=\"kt-inside-inner-col\"><style>.kb-row-layout-id14210_b3cd6d-2d > .kt-row-column-wrap{align-content:start;}:where(.kb-row-layout-id14210_b3cd6d-2d > .kt-row-column-wrap) > .wp-block-kadence-column{justify-content:start;}.kb-row-layout-id14210_b3cd6d-2d > .kt-row-column-wrap{column-gap:var(--global-kb-gap-md, 2rem);row-gap:var(--global-kb-gap-md, 2rem);grid-template-columns:minmax(0, calc(30% - ((var(--global-kb-gap-md, 2rem) * 1 )\/2))) minmax(0, calc(70% - ((var(--global-kb-gap-md, 2rem) * 1 )\/2)));}.kb-row-layout-id14210_b3cd6d-2d > .kt-row-layout-overlay{opacity:0.30;}@media all and (max-width: 1024px){.kb-row-layout-id14210_b3cd6d-2d > .kt-row-column-wrap{grid-template-columns:repeat(2, minmax(0, 1fr));}}@media all and (max-width: 767px){.kb-row-layout-id14210_b3cd6d-2d > .kt-row-column-wrap{grid-template-columns:minmax(0, 1fr);}}<\/style><div class=\"kb-row-layout-wrap kb-row-layout-id14210_b3cd6d-2d alignnone wp-block-kadence-rowlayout\"><div class=\"kt-row-column-wrap kt-has-2-columns kt-row-layout-right-golden kt-tab-layout-inherit kt-mobile-layout-row kt-row-valign-top\">\n<style>.kadence-column14210_108f2d-6e > .kt-inside-inner-col{display:flex;}.kadence-column14210_108f2d-6e > .kt-inside-inner-col,.kadence-column14210_108f2d-6e > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column14210_108f2d-6e > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column14210_108f2d-6e > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_108f2d-6e > .kt-inside-inner-col > .aligncenter{width:100%;}.kt-row-column-wrap > .kadence-column14210_108f2d-6e{align-self:center;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_108f2d-6e{align-self:auto;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_108f2d-6e > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_108f2d-6e > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column14210_108f2d-6e{position:relative;}@media all and (max-width: 1024px){.kadence-column14210_108f2d-6e > .kt-inside-inner-col{flex-direction:column;}}@media all and (max-width: 767px){.kadence-column14210_108f2d-6e > .kt-inside-inner-col{flex-direction:column;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column14210_108f2d-6e\"><div class=\"kt-inside-inner-col\"><style>.kb-image14210_6e824d-93 .kb-image-has-overlay:after{opacity:0.3;}.kb-image14210_6e824d-93 img.kb-img, .kb-image14210_6e824d-93 .kb-img img{border-top-left-radius:5px;border-top-right-radius:5px;border-bottom-right-radius:5px;border-bottom-left-radius:5px;}<\/style>\n<div class=\"wp-block-kadence-image kb-image14210_6e824d-93\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"200\" src=\"https:\/\/www.upjs.sk\/app\/uploads\/sites\/10\/2023\/10\/odbor-Chemia.png\" alt=\"\" class=\"kb-img wp-image-62026\"\/><\/figure><\/div>\n<\/div><\/div>\n\n\n<style>.kadence-column14210_24aa83-f0 > .kt-inside-inner-col{display:flex;}.kadence-column14210_24aa83-f0 > .kt-inside-inner-col,.kadence-column14210_24aa83-f0 > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column14210_24aa83-f0 > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column14210_24aa83-f0 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_24aa83-f0 > .kt-inside-inner-col > .aligncenter{width:100%;}.kt-row-column-wrap > .kadence-column14210_24aa83-f0{align-self:center;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_24aa83-f0{align-self:auto;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_24aa83-f0 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_24aa83-f0 > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column14210_24aa83-f0{position:relative;}@media all and (max-width: 1024px){.kadence-column14210_24aa83-f0 > .kt-inside-inner-col{flex-direction:column;}}@media all and (max-width: 767px){.kadence-column14210_24aa83-f0 > .kt-inside-inner-col{flex-direction:column;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column14210_24aa83-f0\"><div class=\"kt-inside-inner-col\"><style>.kt-accordion-id14210_76d68c-17 .kt-accordion-panel-inner{border-top:0px solid transparent;border-right:0px solid transparent;border-bottom:0px solid transparent;border-left:0px solid transparent;padding-top:var(--global-kb-spacing-sm, 1.5rem);padding-right:var(--global-kb-spacing-sm, 1.5rem);padding-bottom:var(--global-kb-spacing-sm, 1.5rem);padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kt-accordion-id14210_76d68c-17 .wp-block-kadence-pane .kt-accordion-header-wrap .kt-blocks-accordion-header{border-top:0px solid #f2f2f2;border-right:0px solid #f2f2f2;border-bottom:0px solid #f2f2f2;border-left:0px solid #f2f2f2;border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;background:#ffffff;color:#008338;padding-top:10px;padding-right:5px;padding-bottom:6px;padding-left:6px;}.kt-accordion-wrap.kt-accordion-id14210_76d68c-17 > .kt-accordion-inner-wrap > .kt-accordion-pane > .kt-accordion-header-wrap{margin-top:0px;}.single-content .wp-block-kadence-pane>h2:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h3:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h4:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h5:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h6:first-child{margin-top:0px;}.kt-accordion-id14210_76d68c-17:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_76d68c-17:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-icon-trigger:before{background:#008338;}.kt-accordion-id14210_76d68c-17:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger{background:#008338;}.kt-accordion-id14210_76d68c-17:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_76d68c-17:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger:before{background:#ffffff;}.kt-accordion-id14210_76d68c-17 .kt-accordion-header-wrap .kt-blocks-accordion-header:hover, body:not(.hide-focus-outline) .kt-accordion-id14210_76d68c-17 .kt-accordion-header-wrap .kt-blocks-accordion-header:focus{color:#000000;background:#ffffff;border-top-color:#eeeeee;border-top-style:solid;border-right-color:#eeeeee;border-right-style:solid;border-bottom-color:#eeeeee;border-bottom-style:solid;border-left-color:#eeeeee;border-left-style:solid;}.kt-accordion-id14210_76d68c-17:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_76d68c-17:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before, body:not(.hide-focus-outline) .kt-accordion-id14210_76d68c-17:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id14210_76d68c-17:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:before{background:#000000;}.kt-accordion-id14210_76d68c-17:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger, body:not(.hide-focus-outline) .kt-accordion-id14210_76d68c-17:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger{background:#000000;}.kt-accordion-id14210_76d68c-17:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_76d68c-17:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before, body:not(.hide-focus-outline) .kt-accordion-id14210_76d68c-17:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id14210_76d68c-17:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:before{background:#ffffff;}.kt-accordion-id14210_76d68c-17 .kt-accordion-header-wrap .kt-blocks-accordion-header.kt-accordion-panel-active{color:#000000;background:#ffffff;border-top-color:#0e9cd1;border-top-style:solid;border-right-color:#0e9cd1;border-right-style:solid;border-bottom-color:#0e9cd1;border-bottom-style:solid;border-left-color:#0e9cd1;border-left-style:solid;}.kt-accordion-id14210_76d68c-17:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_76d68c-17:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before{background:#000000;}.kt-accordion-id14210_76d68c-17:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger{background:#000000;}.kt-accordion-id14210_76d68c-17:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_76d68c-17:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before{background:#ffffff;}@media all and (max-width: 1024px){.kt-accordion-id14210_76d68c-17 .kt-accordion-panel-inner{border-top:0px solid transparent;border-right:0px solid transparent;border-bottom:0px solid transparent;border-left:0px solid transparent;}}@media all and (max-width: 1024px){.kt-accordion-id14210_76d68c-17 .wp-block-kadence-pane .kt-accordion-header-wrap .kt-blocks-accordion-header{border-top:0px solid #f2f2f2;border-right:0px solid #f2f2f2;border-bottom:0px solid #f2f2f2;border-left:0px solid #f2f2f2;}}@media all and (max-width: 1024px){.kt-accordion-id14210_76d68c-17 .kt-accordion-header-wrap .kt-blocks-accordion-header:hover, body:not(.hide-focus-outline) .kt-accordion-id14210_76d68c-17 .kt-accordion-header-wrap .kt-blocks-accordion-header:focus{border-top-color:#eeeeee;border-top-style:solid;border-right-color:#eeeeee;border-right-style:solid;border-bottom-color:#eeeeee;border-bottom-style:solid;border-left-color:#eeeeee;border-left-style:solid;}}@media all and (max-width: 1024px){.kt-accordion-id14210_76d68c-17 .kt-accordion-header-wrap .kt-blocks-accordion-header.kt-accordion-panel-active{border-top-color:#0e9cd1;border-top-style:solid;border-right-color:#0e9cd1;border-right-style:solid;border-bottom-color:#0e9cd1;border-bottom-style:solid;border-left-color:#0e9cd1;border-left-style:solid;}}@media all and (max-width: 767px){.kt-accordion-id14210_76d68c-17 .kt-accordion-panel-inner{border-top:0px solid transparent;border-right:0px solid transparent;border-bottom:0px solid transparent;border-left:0px solid transparent;}.kt-accordion-id14210_76d68c-17 .wp-block-kadence-pane .kt-accordion-header-wrap .kt-blocks-accordion-header{border-top:0px solid #f2f2f2;border-right:0px solid #f2f2f2;border-bottom:0px solid #f2f2f2;border-left:0px solid #f2f2f2;}.kt-accordion-id14210_76d68c-17 .kt-accordion-header-wrap .kt-blocks-accordion-header:hover, body:not(.hide-focus-outline) .kt-accordion-id14210_76d68c-17 .kt-accordion-header-wrap .kt-blocks-accordion-header:focus{border-top-color:#eeeeee;border-top-style:solid;border-right-color:#eeeeee;border-right-style:solid;border-bottom-color:#eeeeee;border-bottom-style:solid;border-left-color:#eeeeee;border-left-style:solid;}.kt-accordion-id14210_76d68c-17 .kt-accordion-header-wrap .kt-blocks-accordion-header.kt-accordion-panel-active{border-top-color:#0e9cd1;border-top-style:solid;border-right-color:#0e9cd1;border-right-style:solid;border-bottom-color:#0e9cd1;border-bottom-style:solid;border-left-color:#0e9cd1;border-left-style:solid;}}<\/style>\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-id14210_76d68c-17 kt-accordion-has-21-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-arrow kt-accodion-icon-side-left\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-11 kt-pane14210_e56415-a0\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Analytick\u00e1 ch\u00e9mia<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\"has-text-align-justify\">Od uch\u00e1dza\u010da sa vy\u017eaduje znalos\u0165 ch\u00e9mie v rozsahu prv\u00e9ho stup\u0148a vysoko\u0161kolsk\u00e9ho \u0161t\u00fadia v odbore Ch\u00e9mia a analytickej ch\u00e9mie v rozsahu druh\u00e9ho stup\u0148a vysoko\u0161kolsk\u00e9ho \u0161t\u00fadia v odbore Analytick\u00e1 ch\u00e9mia. Nutnou podmienkou je schopnos\u0165 pracova\u0165 s odborn\u00fdm textom v jazyku anglickom.<\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong><u>Analytick\u00e1 ch\u00e9mia:<\/u><\/strong><br>Analytick\u00e1 ch\u00e9mia. Z\u00e1kladn\u00e9 pojmy. Kvalitat\u00edvna a kvantitat\u00edvna anal\u00fdza. Analytick\u00e1 met\u00f3da, spracovanie v\u00fdsledkov stanovenia. Citlivos\u0165 a selektivita reakci\u00ed. Skupinov\u00e9, selekt\u00edvne a \u0161pecifick\u00e9 reakcie. Princ\u00edp a vyu\u017eitie v\u00e1\u017ekovej anal\u00fdzy. Odmern\u00e1 anal\u00fdza. Klasifik\u00e1cia odmern\u00fdch met\u00f3d: acidob\u00e1zick\u00e9, oxida\u010dno-reduk\u010dn\u00e9, komplexotvorn\u00e9 a zr\u00e1\u017eacie titr\u00e1cie. V\u00fdpo\u010det v\u00fdsledkov odmernej anal\u00fdzy. In\u0161trument\u00e1lne analytick\u00e9 met\u00f3dy. Klasifik\u00e1cia, z\u00e1kladn\u00e9 pojmy a terminol\u00f3gia. Z\u00e1kladn\u00e9 \u010dasti analytick\u00fdch pr\u00edstrojov. Absol\u00fatne a relat\u00edvne met\u00f3dy. Line\u00e1rny a neline\u00e1rny sign\u00e1l. Chyby analytick\u00fdch meran\u00ed a spracovanie v\u00fdsledkov. Rozli\u0161ovacia schopnos\u0165, rozsah stanovenia, detek\u010dn\u00fd limit. Kalibra\u010dn\u00fd graf. Spektr\u00e1lne a optick\u00e9 analytick\u00e9 met\u00f3dy (princ\u00edp, z\u00e1kony a z\u00e1kladn\u00e9 matematick\u00e9 vz\u0165ahy, pr\u00edstroje, detektory, pou\u017eitie). Z\u00e1kladn\u00e9 \u010dast\u00ed pr\u00edstrojov v spektr\u00e1lnej anal\u00fdze. Zdroje \u017eiarenia. Monochromatiz\u00e1cia. Absorbancia. UV-VIS spektrofotometria. Luminiscen\u010dn\u00e1 anal\u00fdza. Infra\u010derven\u00e1 a Ramanova spektroskopia. At\u00f3mov\u00e1 absorb\u010dn\u00e1 a at\u00f3mov\u00e1 emisn\u00e1 spektroskopia. Plame\u0148ov\u00e1 fotometria. Hmotnostn\u00e1 spektroskopia. Refraktometria. Polarimetria. Optick\u00e1 rota\u010dn\u00e1 disperzia. Cirkul\u00e1rny dichroizmus. Analytick\u00e9 met\u00f3dy, zalo\u017een\u00e9 na vyu\u017eit\u00ed RTG \u017eiarenia. NMR spektroskopia. R\u00e1diochemick\u00e1 anal\u00fdza. Aktiva\u010dn\u00e1 anal\u00fdza. Kinetick\u00e9 met\u00f3dy anal\u00fdzy. Termick\u00e1 anal\u00fdza. Separa\u010dn\u00e9 a predkoncentra\u010dn\u00e9 met\u00f3dy (princ\u00edp, z\u00e1kony a z\u00e1kladn\u00e9 matematick\u00e9 vz\u0165ahy, pr\u00edstroje, detektory, pou\u017eitie). Destil\u00e1cia. Extrakcia. Plynov\u00e1, kvapalinov\u00e1, i\u00f3nov\u00fdmenn\u00e1, papierov\u00e1 chromatografia. Elektrochemick\u00e9 met\u00f3dy (princ\u00edp, z\u00e1kony a z\u00e1kladn\u00e9 matematick\u00e9 vz\u0165ahy, pr\u00edstroje, pou\u017eitie). Potenciometria. Elektrogravimetrick\u00e9 met\u00f3dy. Konduktometria. Coulometria. Voltamp\u00e9rometria. Polarografia. Amp\u00e9rometrick\u00e1 titr\u00e1cia.<\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong><u>Spektr\u00e1lne analytick\u00e9 met\u00f3dy:<\/u><\/strong>Optick\u00e9 analytick\u00e9 met\u00f3dy, princ\u00edpy, rozdelenie. at\u00f3mov\u00e9 spektr\u00e1, vznik, analytick\u00e9 vyu\u017eitie. Z\u00e1kladn\u00e9 rozdiely emisn\u00fdch a absorp\u010dn\u00fdch met\u00f3d. Budiace zdroje; zdroje \u017eiarenia v AAS (obl\u00fakov\u00fd a iskrov\u00fd v\u00fdboj, tlejiv\u00fd v\u00fdboj, plazmov\u00e9 budiace zdroje; dut\u00e1 kat\u00f3da, bezelektr\u00f3dov\u00e9 zdroje \u017eiarenia v AAS). Rozklad \u017eiarenia v at\u00f3movej spektroch\u00e9mii. Modern\u00e9 zariadenia rozkladu \u017eiarenia. Detekcia \u017eiarenia v at\u00f3movej spektroch\u00e9mii. Historick\u00fd v\u00fdvoja modern\u00e9 trendy. Fotografick\u00e1 detekcia a jej zvl\u00e1\u0161tnosti. Meranie a transform\u00e1cie s\u010dernan\u00ed. Typick\u00e9 postupy spektrografickej anal\u00fdzy, matricov\u00e9 efekty a ich elimin\u00e1cia. Met\u00f3da porovn\u00e1vaj\u00faceho prvku. Met\u00f3dy a postupy roztokovej anal\u00fdzy. Rozpra\u0161ovanie roztokov a jeho \u00fa\u010dinnos\u0165. Tlejiv\u00fd v\u00fdboj z plochou kat\u00f3dou, mo\u017enosti kvantitat\u00edvnej anal\u00fdzy a anal\u00fdzy povrchov. Anal\u00fdza nekovov\u00fdch pr\u00e1\u0161kov\u00fdch vzoriek. \u0160peci\u00e1lne mo\u017enosti pou\u017eitia dutej kat\u00f3dy. Spektrometrick\u00e1 anal\u00fdza s plazmov\u00fdm zdrojom, vn\u00e1\u0161anie pr\u00e1\u0161kov do plazmy, pr\u00edklady vyu\u017eitia v oblasti anal\u00fdz ne\u0161tandardn\u00fdch materi\u00e1lov. Realiz\u00e1cia analytickej kalibr\u00e1cie v at\u00f3movej spektroch\u00e9mii, modelov\u00e9 vzorky, referen\u010dn\u00e9 materi\u00e1ly. At\u00f3mov\u00e1 absorp\u010dn\u00e1 spektrometria, plame\u0148ov\u00e9 a bezplame\u0148ov\u00e9&nbsp; met\u00f3dy. Mo\u017enosti priamej anal\u00fdzy pr\u00e1\u0161kov. Matricov\u00e9 modifik\u00e1tory a ich p\u00f4sobenie. At\u00f3mov\u00e1 absorp\u010dn\u00e1 spektrometria s priamym vn\u00e1\u0161an\u00edm pr\u00e1\u0161kov\u00fdch vzoriek, r\u00f4zne typy elektrochemickej atomiz\u00e1cie, probl\u00e9my homogenity vzoriek. Met\u00f3dy zalo\u017een\u00e9 na interakcii RTG \u017eiarenia so vzorkou: WDXRF, EDXRF, TXRF &#8211; v\u00fdhody, nev\u00fdhody, aplik\u00e1cie. UV-VIS a IR spektrofotometria. Princ\u00edp. Sch\u00e9ma pr\u00edstroja. Monochromatiz\u00e1cia \u017eiarenia. Detektory. Vyu\u017eitie (kvalitat\u00edvna, kvantitat\u00edvna a \u0161trukt\u00farna anal\u00fdza). Luminiscen\u010dn\u00e1 anal\u00fdza. Princ\u00edp. Sch\u00e9ma pr\u00edstroja. Molekulov\u00e1 \u0161trukt\u00fara fluoreskuj\u00facej l\u00e1tky. Fluorescencia. Fosforescencia. Vyu\u017eitie v analytickej ch\u00e9mii.<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-12 kt-pane14210_59fc40-ed\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Anorganick\u00e1 ch\u00e9mia<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\"has-text-align-justify\"><strong><u>Anorganick\u00e1 ch\u00e9mia:<\/u><\/strong> Systematick\u00e1 anorganick\u00e1 ch\u00e9mia, periodicita vlastnost\u00ed prvkov a zl\u00fa\u010den\u00edn.V\u0161eobecn\u00e1 charakteristika kovov, ch\u00e9mia prvkov 1. a 2. skupiny a ostatn\u00fdch kovov\u00fdch prvkov 13. a\u017e 16. skupiny. Ch\u00e9mia prechodn\u00fdch prvkov, lantanoidov , aktinoidov a ich zl\u00fa\u010den\u00edn.&nbsp; Heterocyklick\u00e9 anorganick\u00e9 zl\u00fa\u010deniny. Ch\u00e9mia nekovov. Typy koordina\u010dn\u00fdch zl\u00fa\u010den\u00edn, donorno-akceptorov\u00e1 v\u00e4zba v koordina\u010dn\u00fdch zl\u00fa\u010denin\u00e1ch, te\u00f3ria kry\u0161t\u00e1lov\u00e9ho po\u013ea, te\u00f3ria MO, spektr\u00e1lne a magnetick\u00e9 vlastnosti, \u0161trukt\u00fara koordina\u010dn\u00fdch zl\u00fa\u010den\u00edn, trans-efekt, substitu\u010dn\u00e9 a redoxn\u00e9 reakcie koordina\u010dn\u00fdch zl\u00fa\u010den\u00edn. Prvky v biosyst\u00e9moch &#8211; biokovy, ich funkcia a transport. Anorganick\u00e9 line\u00e1rne polym\u00e9ry S, Se, Te, (SN)x. Chalkogenidov\u00e9 skl\u00e1, BN, borit\u00e9 skl\u00e1, kremenn\u00e9 sklo a kremi\u010dit\u00e9 skl\u00e1,&nbsp; kry\u0161talick\u00e9 kremi\u010ditany a hlinitokremi\u010ditany. Bor\u00e1ny a heterobor\u00e1ny, polyvanadi\u010dnany. Hetero a izopolyzl\u00fa\u010deniny. Klasifik\u00e1cia chemick\u00fdch reakci\u00ed z h\u013eadiska reak\u010dn\u00fdch mechanizmov, \u0161pecifick\u00e9 reakcie koordina\u010dn\u00fdch zl\u00fa\u010den\u00edn, kinetick\u00e9 a termodynamick\u00e9 pr\u00edstupy k chemick\u00fdm reakci\u00e1m, reak\u010dn\u00e9 mechanizmy SN1, SN2, SE1, SE2. Mechanizmy v koordina\u010dn\u00fdch a inkluz\u00edvnych zl\u00fa\u010denin\u00e1ch. \u00da\u010dinky jedov a ich klasifik\u00e1cia, mechanizmus premien toxick\u00fdch l\u00e1tok v organizme, toxikokinetika a toxikodynamika, toxikol\u00f3gia prvkov a anorganick\u00fdch zl\u00fa\u010den\u00edn.<\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong>Fyzik\u00e1lnochemick\u00e9 met\u00f3dy pre charakteriz\u00e1ciu anorganick\u00fdch l\u00e1tok:<\/strong> Vznik a v\u00fdznam rtg. \u017eiarenia pre \u0161t\u00fadium \u0161trukt\u00fary l\u00e1tok. Symetria kry\u0161t\u00e1lov a z\u00e1kladnej bunky, priestorov\u00e9 grupy s\u00famernosti. Recipro\u010dn\u00e1 mrie\u017eka,&nbsp; difrakcia rtg. l\u00fa\u010dov, Braggova a Laueho rovnica. Monokry\u0161t\u00e1lov\u00e9&nbsp; a polykry\u0161t\u00e1lov\u00e9 met\u00f3dy met\u00f3dy \u0161t\u00fadia kry\u0161t\u00e1lovej \u0161trukt\u00fary. S\u00favis medzi intenzitou difraktovan\u00e9ho \u017eiarenia a \u0161trukt\u00farou l\u00e1tok, At\u00f3mov\u00fd a \u0161trukt\u00farny faktor. Chemick\u00e1 interpret\u00e1cia v\u00fdsledkov \u0161trukt\u00farnej anal\u00fdzy, v\u00e4zbov\u00e9 d\u013a\u017eky uhly, \u010fal\u0161ie geometrick\u00e9 inform\u00e1cie o \u0161trukt\u00fare. Termick\u00e1 anal\u00fdza a jej met\u00f3dy&nbsp; (TG\/DTG, DTA, TMA, ETA, EGD, EGA a pod.),&nbsp; procesy ktor\u00e9 sa odohr\u00e1vaj\u00fa v tuh\u00fdch l\u00e1tkach po\u010das ohrevu,&nbsp; reak\u010dn\u00e1 kinetika&nbsp; rozkladn\u00fdch reakcii, aplik\u00e1cii TA pre \u0161t\u00fadium anorganick\u00fdch a organick\u00fdch zl\u00fa\u010den\u00edn a vyu\u017eitie mikropo\u010d\u00edta\u010dov v termickej anal\u00fdze. Fyzik\u00e1lna podstata UV spektroskopie, Ramanovej spektroskopie, I\u010c spektroskopie, jadrovej magnetickej rezonan\u010dnej a hmotnostnej spektroskopie.<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-13 kt-pane14210_7e8c7c-53\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Bioch\u00e9mia<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\"has-text-align-justify\"><strong>Bioch\u00e9mia a molekulov\u00e1 biol\u00f3gia:<\/strong> Bunka, funkcie organel. \u0160trukt\u00fara prote\u00ednov. Aminokyseliny \u2013 fyzik\u00e1lno-chemick\u00e9 vlastnosti. Enz\u00fdmy \u2013 podstata enz\u00fdmovej katal\u00fdzy. Enz\u00fdmov\u00e1 kinetika \u2013 vplyv koncentr\u00e1cie substr\u00e1tu na po\u010diato\u010dn\u00fa r\u00fdchlos\u0165. Rovnica Michaelis-Mentenovej. Charakteriz\u00e1cia Km a met\u00f3dy experiment\u00e1lneho stanovenia. Regul\u00e1cia enz\u00fdmovej aktivity. Alosterick\u00e1 regul\u00e1cia aktivity enz\u00fdmu. Nukleov\u00e9 kyseliny \u2013 funkcie a prim\u00e1rna \u0161trukt\u00fara DNA a RNA. Mechanizmus replik\u00e1cie DNA. Mechanizmus transkripcie DNA. Transl\u00e1cia \u2013 mechanizmus, jednotliv\u00e9 stupne procesu. Met\u00f3dy g\u00e9nov\u00e9ho in\u017einierstva \u2013 pr\u00edprava rekombinantnej DNA. Vyu\u017eitie plazmidov, bakteriof\u00e1gov, restrikt\u00e1z a reverznej transkript\u00e1zy v g\u00e9novom in\u017einierstve. Z\u00e1kladn\u00e9 princ\u00edpy metabolizmu. Glykol\u00fdza, glukoneogen\u00e9za, pent\u00f3zofosf\u00e1tov\u00e1 dr\u00e1ha, citr\u00e1tov\u00fd cyklus. Oxida\u010dn\u00e1 fosforyl\u00e1cia \u2013 chemiosmotick\u00e1 te\u00f3ria synt\u00e9zy ATP. Fotosynt\u00e9za. Tr\u00e1venie tukov a prenos mastn\u00fdch kysel\u00edn do bunky, aktiv\u00e1cia mastn\u00fdch kysel\u00edn. Karnit\u00ednov\u00fd cyklus a beta-oxid\u00e1cia mastn\u00fdch kysel\u00edn. Glyoxal\u00e1tov\u00fd cyklus. Fix\u00e1cia dus\u00edka. Metabolizmus aminokysel\u00edn. Mo\u010dovinov\u00fd cyklus.<\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong>Biofyzik\u00e1lna ch\u00e9mia:<\/strong> Z\u00e1kladn\u00e9 separa\u010dn\u00e9 met\u00f3dy \u2013 chromatografia, elektrofor\u00e9za. Spektr\u00e1lne met\u00f3dy \u2013 ich vyu\u017eitie pri \u0161t\u00fadiu biomakromolek\u00fal. Fluorescencia. Kalorimetria. Met\u00f3dy na ur\u010denie ve\u013ekosti biomakromolek\u00fal, oligom\u00e9rneho stavu, lok\u00e1lnej a glob\u00e1lnej stability, dynamiky.<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-21 kt-pane14210_213e0e-8c\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Fyzik\u00e1lna ch\u00e9mia<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p>Od uch\u00e1dza\u010da sa vy\u017eaduje znalos\u0165 fyzik\u00e1lnej ch\u00e9mie v rozsahu prv\u00e9ho stup\u0148a vysoko\u0161kolsk\u00e9ho \u0161t\u00fadia v odbore Ch\u00e9mia a Fyzik\u00e1lna ch\u00e9mia v rozsahu druh\u00e9ho stup\u0148a vysoko\u0161kolsk\u00e9ho \u0161t\u00fadia v odbore Fyzik\u00e1lna ch\u00e9mia.<\/p>\n\n\n\n<p class=\"has-text-align-justify\">Fyzik\u00e1lna ch\u00e9mia:<br>Okruhy ot\u00e1zok pre pr\u00edjmaciu sk\u00fa\u0161ku na doktorandsk\u00fd \u0161tudijn\u00fd program Fyzik\u00e1lna ch\u00e9mia pozost\u00e1vaj\u00fa&nbsp; z nasledovn\u00fdch okruhov: chemick\u00e1 termodynamika a chemick\u00e1 kinetika reakci\u00ed, chemick\u00e1 v\u00e4zba, heterog\u00e9nna katal\u00fdza, adsorpcia l\u00e1tok, i\u00f3niz\u00e1cia l\u00e1tok, roztoky elektrolytov, elektrochemick\u00fd dej, elektrochemick\u00e9 vylu\u010dovanie, spektroskopick\u00e9 met\u00f3dy ( UV-VIS, IR, NMR, Ramanova spektroskopia), hmotnostn\u00e1 spektrometria, ch\u00e9mia povrchov a koloidov, interakcia molek\u00fal na povrchu, met\u00f3dy \u0161trukt\u00farnej anal\u00fdzy a Anglick\u00fd jazyk \u010d\u00edtan\u00edm a prekladom odborn\u00e9ho textu.<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-14 kt-pane14210_0ad3c0-d5\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Organick\u00e1 ch\u00e9mia<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\"has-text-align-justify\"><strong>Organick\u00e1 ch\u00e9mia<\/strong><strong>:<\/strong> Nenas\u00fdten\u00e9 uh\u013eovod\u00edky, alk\u00e9ny, elektr\u00f3novo-donorov\u00e9 vlastnosti alk\u00e9nov, reakcie, ad\u00edcia halog\u00e9nov, halog\u00e9novod\u00edkov\u00fdch kysel\u00edn, ad\u00edcia kyseliny s\u00edrovej, ad\u00edcia organick\u00fdch kysel\u00edn, hydrobor\u00e1cia, ad\u00edcia oxidu uho\u013enat\u00e9ho, radik\u00e1lov\u00e9 adi\u010dn\u00e9 reakcie, hydrat\u00e1cia, ad\u00edcia alkoholov, ad\u00edcia organokovov\u00fdch zl\u00fa\u010den\u00edn, oxid\u00e1cia, epoxid\u00e1cia, ad\u00edcia oz\u00f3nu, hydroxyl\u00e1cia, di\u00e9ny a\u017e poly\u00e9ny, reakcie, izomeriz\u00e1cia, tvorba sol\u00ed, pericyklick\u00e9 reakcie, elektrocyklick\u00e9 reakcie, cykloadi\u010dn\u00e9 reakcie, cykloalk\u00e9ny. Alk\u00edny.&nbsp; Aromatick\u00e9 uh\u013eovod\u00edky, vlastnosti, benzenoidn\u00e9 uh\u013eovod\u00edky, n\u00e1zvoslovie. Elektrofiln\u00e9 substitu\u010dn\u00e9 reakcie, nitr\u00e1cia, sulfon\u00e1cia, halogen\u00e1cia, alkyl\u00e1cia, acyl\u00e1cia, orientuj\u00faci vplyv substituentov, mechanizmus a energetick\u00fd diagram, radik\u00e1lov\u00e9 adi\u010dn\u00e9 a substitu\u010dn\u00e9 nukleofiln\u00e9 reakcie, oxid\u00e1cia, nebenzenoidn\u00e9 aromatick\u00e9 uh\u013eovod\u00edky. Halog\u00e9nderiv\u00e1ty, reaktivita a reakcie, nukleofiln\u00e9 substitu\u010dn\u00e9 reakcie, vplyv alkylovej skupiny na mechanizmus reakcie, mechanizmus SN1 a SN2 reakcie, nuleofiln\u00e9 substit\u00facie halog\u00e9nalk\u00e1nov ani\u00f3nmi, hydrol\u00fdza a alkohol\u00fdza, substit\u00facia ani\u00f3nmi C, N, O, S, molekulov\u00e9 pre\u0161myky, elimina\u010dn\u00e9 reakcie, E1 a E2 reakcie, substitu\u010dn\u00e9 reakcie halog\u00e9nar\u00e9nov, reakcie halog\u00e9nar\u00e9nov s kovmi. Hydroxyderiv\u00e1ty. Reakcie hydroxyderiv\u00e1tov ako kysel\u00edn a z\u00e1sad. Tautom\u00e9ria. Elimina\u010dn\u00e9 a oxida\u010dn\u00e9 reakcie, dioly ich vlastnosti a reakcie. Dehydrat\u00e1cia diolov. Pinakol\u00ednov\u00fd pre\u0161myk. Substitu\u010dn\u00e9 elektrofiln\u00e9 a oxida\u010dn\u00e9 reakcie fenolov. Sigmatr\u00f3pne pre\u0161myky. Karbonylov\u00e9 zl\u00fa\u010deniny. Aldehydy a ket\u00f3ny, adi\u010dn\u00e9 nukleofiln\u00e9, kondenza\u010dn\u00e9, oxida\u010dn\u00e9 a reduk\u010dn\u00e9 reakcie. Adi\u010dn\u00e9 reakcie na konjugovan\u00e9 karbonylov\u00e9 skupiny. Reakcie C-ani\u00f3nov karbonylov\u00fdch zl\u00fa\u010den\u00edn. Aldolov\u00e1 kondenz\u00e1cia a pr\u00edbuzn\u00e9 reakcie. Skr\u00ed\u017een\u00e1 aldolov\u00e1 kondenz\u00e1cia. Alkyl\u00e1cia a acyl\u00e1cia karbonylov\u00fdch zl\u00fa\u010den\u00edn. Met\u00f3dy pr\u00edpravy karbonylov\u00fdch zl\u00fa\u010den\u00edn. Benzilov\u00fd pre\u0161myk. Karboxylov\u00e9 kyseliny \u2013 charakteristika, n\u00e1zvoslovie, fyzik\u00e1lno-chemick\u00e9 vlastnosti a reakcie. Funk\u010dn\u00e9 a substitu\u010dn\u00e9 deriv\u00e1ty karboxylov\u00fdch kysel\u00edn \u2013 acylhalogenidy, anhydridy, estery a amidy. Reakcie acetoctanu etylov\u00e9ho. Ketotvorn\u00e9 a kyselinotvorn\u00e9 \u0161tiepenie. Halog\u00e9n, hydroxykarboxylov\u00e9 kyseliny, lakt\u00f3ny, aminokyseliny. Organick\u00e9 zl\u00fa\u010deniny dus\u00edka. Am\u00edny, diazozl\u00fa\u010deniny, nitro a nitr\u00f3zozl\u00fa\u010deniny, hydroxylam\u00edny, ox\u00edmy a hydraz\u00edny. Beckmanov pre\u0161myk. Heterocyklick\u00e9 zl\u00fa\u010deniny. P\u00e4\u0165\u010dl\u00e1nkov\u00e9 heterocyklick\u00e9 zl\u00fa\u010deniny: fur\u00e1n, pyrol, tiof\u00e9n, pyrazol, imidazol, tiazol, benzofur\u00e1n, indol a tionaft\u00e9n. \u0160es\u0165\u010dl\u00e1nkov\u00e9 heterocyklick\u00e9 zl\u00fa\u010deniny: pyrid\u00edn, chinol\u00edn, izochinol\u00edn, akrid\u00edn, pyridaz\u00edn, pyrimid\u00edn, pyraz\u00edn, pur\u00edn a pterid\u00edn<\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong><u>\u0160trukt\u00fara a reaktivita organick\u00fdch zl\u00fa\u010den\u00edn:<\/u><\/strong> V\u00e4zby v organick\u00fdch zl\u00fa\u010denin\u00e1ch, i\u00f3nov\u00e1 a kovalentn\u00e1 v\u00e4zba, energia v\u00e4zby, at\u00f3mov\u00e9 orbit\u00e1ly, te\u00f3ria molekulov\u00fdch orbit\u00e1lov, hybridiz\u00e1cia, donorno-akcept\u00f3rna v\u00e4zba, vod\u00edkov\u00e9 v\u00e4zby, polarita v\u00e4zby, polarizovate\u013enos\u0165, stereoch\u00e9mia, izom\u00e9ria, optick\u00e1 aktivita, chiralita, konfigur\u00e1cia, enantiom\u00e9ry, diastereoizom\u00e9ry, racem\u00e1ty. Reakcie organick\u00fdch zl\u00fa\u010den\u00edn, chemick\u00e1 rovnov\u00e1ha, termodynamika reakci\u00ed, reak\u010dn\u00e9 teplo, entropia, entalpia, vo\u013en\u00e1 aktiva\u010dn\u00e1 energia, tranzitn\u00e9 stavy, r\u00fdchlos\u0165 reakcie, reak\u010dn\u00e1 rovnov\u00e1ha, termodynamicky a kineticky kontrolovan\u00e9 reakcie, mechanizny organick\u00fdch reakci\u00ed, homolytick\u00e9 a heterolytick\u00e9 \u0161tiepenie v\u00e4zieb, medziprodukty, s\u00fa\u010dinn\u00e9 a viacstup\u0148ov\u00e9 reakcie, katal\u00fdza, vplyv rozp\u00fa\u0161\u0165adla, typy reakci\u00ed. Ultrafialov\u00e1 a vidite\u013en\u00e1 spektroskopia. Infra\u010derven\u00e1 spektroskopia. Ramanova spektroskopia Hmotnostn\u00e1 spektroskopia. Nukle\u00e1rna magnetick\u00e1 rezonan\u010dn\u00e1 spektroskopia. Jednorozmern\u00e1 (1D) 1H NMR spektroskopia. Dvojrozmern\u00e1 (2D) NMR spektroskopia. Princ\u00edpy a meracie techniky. Prezent\u00e1cia spektier. Korelovan\u00e9 2D NMR spektr\u00e1 (H,H-COSY, H,C-COSY, TOCSY, NOESY, INADEQUATE, korel\u00e1cia \u010falek\u00e9ho dosahu). Kinetika organick\u00fdck reakci\u00ed. R\u00fdchlostn\u00e1 kon\u0161tanta a kinetick\u00e1 rovnica. Met\u00f3dy pou\u017e\u00edvan\u00e9 pri sledovan\u00ed r\u00fdchlost\u00ed reakci\u00ed. Postupy pou\u017e\u00edvan\u00e9 pri ur\u010dovan\u00ed kinetick\u00fdch rovn\u00edc a r\u00fdchlostn\u00fdch kon\u0161t\u00e1nt. Acidob\u00e1zick\u00e1 katal\u00fdza. Line\u00e1rne vz\u0165ahy vo\u013en\u00fdch energi\u00ed.<\/p>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n\n<\/div><\/div><\/div><\/div>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n<style>.kadence-column14210_769b9f-4d > .kt-inside-inner-col,.kadence-column14210_769b9f-4d > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column14210_769b9f-4d > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column14210_769b9f-4d > .kt-inside-inner-col{flex-direction:column;}.kadence-column14210_769b9f-4d > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column14210_769b9f-4d > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column14210_769b9f-4d{position:relative;}@media all and (max-width: 1024px){.kadence-column14210_769b9f-4d > .kt-inside-inner-col{flex-direction:column;}}@media all and (max-width: 767px){.kadence-column14210_769b9f-4d > .kt-inside-inner-col{flex-direction:column;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column14210_769b9f-4d\"><div class=\"kt-inside-inner-col\"><style>.kb-row-layout-id14210_fa4e4d-de > .kt-row-column-wrap{align-content:start;}:where(.kb-row-layout-id14210_fa4e4d-de > .kt-row-column-wrap) > .wp-block-kadence-column{justify-content:start;}.kb-row-layout-id14210_fa4e4d-de > .kt-row-column-wrap{column-gap:var(--global-kb-gap-md, 2rem);row-gap:var(--global-kb-gap-md, 2rem);grid-template-columns:minmax(0, calc(30% - ((var(--global-kb-gap-md, 2rem) * 1 )\/2))) minmax(0, calc(70% - ((var(--global-kb-gap-md, 2rem) * 1 )\/2)));}.kb-row-layout-id14210_fa4e4d-de > .kt-row-layout-overlay{opacity:0.30;}@media all and (max-width: 1024px){.kb-row-layout-id14210_fa4e4d-de > .kt-row-column-wrap{grid-template-columns:repeat(2, minmax(0, 1fr));}}@media all and (max-width: 767px){.kb-row-layout-id14210_fa4e4d-de > .kt-row-column-wrap{grid-template-columns:minmax(0, 1fr);}}<\/style><div class=\"kb-row-layout-wrap kb-row-layout-id14210_fa4e4d-de alignnone wp-block-kadence-rowlayout\"><div class=\"kt-row-column-wrap kt-has-2-columns kt-row-layout-right-golden kt-tab-layout-inherit kt-mobile-layout-row kt-row-valign-top\">\n<style>.kadence-column14210_68f7d6-2d > .kt-inside-inner-col{display:flex;}.kadence-column14210_68f7d6-2d > .kt-inside-inner-col,.kadence-column14210_68f7d6-2d > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column14210_68f7d6-2d > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column14210_68f7d6-2d > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_68f7d6-2d > .kt-inside-inner-col > .aligncenter{width:100%;}.kt-row-column-wrap > .kadence-column14210_68f7d6-2d{align-self:center;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_68f7d6-2d{align-self:auto;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_68f7d6-2d > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_68f7d6-2d > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column14210_68f7d6-2d{position:relative;}@media all and (max-width: 1024px){.kadence-column14210_68f7d6-2d > .kt-inside-inner-col{flex-direction:column;}}@media all and (max-width: 767px){.kadence-column14210_68f7d6-2d > .kt-inside-inner-col{flex-direction:column;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column14210_68f7d6-2d\"><div class=\"kt-inside-inner-col\"><style>.kb-image14210_ce4d46-21 .kb-image-has-overlay:after{opacity:0.3;}.kb-image14210_ce4d46-21 img.kb-img, .kb-image14210_ce4d46-21 .kb-img img{border-top-left-radius:5px;border-top-right-radius:5px;border-bottom-right-radius:5px;border-bottom-left-radius:5px;}<\/style>\n<div class=\"wp-block-kadence-image kb-image14210_ce4d46-21\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"200\" src=\"https:\/\/www.upjs.sk\/app\/uploads\/sites\/10\/2023\/10\/odbory-Geoinformatika.png\" alt=\"\" class=\"kb-img wp-image-62033\"\/><\/figure><\/div>\n<\/div><\/div>\n\n\n<style>.kadence-column14210_af36f7-39 > .kt-inside-inner-col{display:flex;}.kadence-column14210_af36f7-39 > .kt-inside-inner-col,.kadence-column14210_af36f7-39 > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column14210_af36f7-39 > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column14210_af36f7-39 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_af36f7-39 > .kt-inside-inner-col > .aligncenter{width:100%;}.kt-row-column-wrap > .kadence-column14210_af36f7-39{align-self:center;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_af36f7-39{align-self:auto;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_af36f7-39 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_af36f7-39 > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column14210_af36f7-39{position:relative;}@media all and (max-width: 1024px){.kadence-column14210_af36f7-39 > .kt-inside-inner-col{flex-direction:column;}}@media all and (max-width: 767px){.kadence-column14210_af36f7-39 > .kt-inside-inner-col{flex-direction:column;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column14210_af36f7-39\"><div class=\"kt-inside-inner-col\"><style>.kt-accordion-id14210_278fac-ec .kt-accordion-panel-inner{border-top:0px solid transparent;border-right:0px solid transparent;border-bottom:0px solid transparent;border-left:0px solid transparent;padding-top:var(--global-kb-spacing-sm, 1.5rem);padding-right:var(--global-kb-spacing-sm, 1.5rem);padding-bottom:var(--global-kb-spacing-sm, 1.5rem);padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kt-accordion-id14210_278fac-ec .wp-block-kadence-pane .kt-accordion-header-wrap .kt-blocks-accordion-header{border-top:0px solid #f2f2f2;border-right:0px solid #f2f2f2;border-bottom:0px solid #f2f2f2;border-left:0px solid #f2f2f2;border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;background:#ffffff;color:#008338;padding-top:6px;padding-right:5px;padding-bottom:6px;padding-left:6px;}.kt-accordion-wrap.kt-accordion-id14210_278fac-ec > .kt-accordion-inner-wrap > .kt-accordion-pane > .kt-accordion-header-wrap{margin-top:0px;}.single-content .wp-block-kadence-pane>h2:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h3:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h4:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h5:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h6:first-child{margin-top:0px;}.kt-accordion-id14210_278fac-ec:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_278fac-ec:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-icon-trigger:before{background:#008338;}.kt-accordion-id14210_278fac-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger{background:#008338;}.kt-accordion-id14210_278fac-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_278fac-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger:before{background:#ffffff;}.kt-accordion-id14210_278fac-ec .kt-accordion-header-wrap .kt-blocks-accordion-header:hover, body:not(.hide-focus-outline) .kt-accordion-id14210_278fac-ec .kt-accordion-header-wrap .kt-blocks-accordion-header:focus{color:#000000;background:#ffffff;border-top-color:#eeeeee;border-top-style:solid;border-right-color:#eeeeee;border-right-style:solid;border-bottom-color:#eeeeee;border-bottom-style:solid;border-left-color:#eeeeee;border-left-style:solid;}.kt-accordion-id14210_278fac-ec:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_278fac-ec:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before, body:not(.hide-focus-outline) .kt-accordion-id14210_278fac-ec:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id14210_278fac-ec:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:before{background:#000000;}.kt-accordion-id14210_278fac-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger, body:not(.hide-focus-outline) .kt-accordion-id14210_278fac-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger{background:#000000;}.kt-accordion-id14210_278fac-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_278fac-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before, body:not(.hide-focus-outline) .kt-accordion-id14210_278fac-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id14210_278fac-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:before{background:#ffffff;}.kt-accordion-id14210_278fac-ec .kt-accordion-header-wrap .kt-blocks-accordion-header.kt-accordion-panel-active{color:#000000;background:#ffffff;border-top-color:#0e9cd1;border-top-style:solid;border-right-color:#0e9cd1;border-right-style:solid;border-bottom-color:#0e9cd1;border-bottom-style:solid;border-left-color:#0e9cd1;border-left-style:solid;}.kt-accordion-id14210_278fac-ec:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_278fac-ec:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before{background:#000000;}.kt-accordion-id14210_278fac-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger{background:#000000;}.kt-accordion-id14210_278fac-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_278fac-ec:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before{background:#ffffff;}@media all and (max-width: 1024px){.kt-accordion-id14210_278fac-ec .kt-accordion-panel-inner{border-top:0px solid transparent;border-right:0px solid transparent;border-bottom:0px solid transparent;border-left:0px solid transparent;}}@media all and (max-width: 1024px){.kt-accordion-id14210_278fac-ec .wp-block-kadence-pane .kt-accordion-header-wrap .kt-blocks-accordion-header{border-top:0px solid #f2f2f2;border-right:0px solid #f2f2f2;border-bottom:0px solid #f2f2f2;border-left:0px solid #f2f2f2;}}@media all and (max-width: 1024px){.kt-accordion-id14210_278fac-ec .kt-accordion-header-wrap .kt-blocks-accordion-header:hover, body:not(.hide-focus-outline) .kt-accordion-id14210_278fac-ec .kt-accordion-header-wrap .kt-blocks-accordion-header:focus{border-top-color:#eeeeee;border-top-style:solid;border-right-color:#eeeeee;border-right-style:solid;border-bottom-color:#eeeeee;border-bottom-style:solid;border-left-color:#eeeeee;border-left-style:solid;}}@media all and (max-width: 1024px){.kt-accordion-id14210_278fac-ec .kt-accordion-header-wrap .kt-blocks-accordion-header.kt-accordion-panel-active{border-top-color:#0e9cd1;border-top-style:solid;border-right-color:#0e9cd1;border-right-style:solid;border-bottom-color:#0e9cd1;border-bottom-style:solid;border-left-color:#0e9cd1;border-left-style:solid;}}@media all and (max-width: 767px){.kt-accordion-id14210_278fac-ec .kt-accordion-panel-inner{border-top:0px solid transparent;border-right:0px solid transparent;border-bottom:0px solid transparent;border-left:0px solid transparent;}.kt-accordion-id14210_278fac-ec .wp-block-kadence-pane .kt-accordion-header-wrap .kt-blocks-accordion-header{border-top:0px solid #f2f2f2;border-right:0px solid #f2f2f2;border-bottom:0px solid #f2f2f2;border-left:0px solid #f2f2f2;}.kt-accordion-id14210_278fac-ec .kt-accordion-header-wrap .kt-blocks-accordion-header:hover, body:not(.hide-focus-outline) .kt-accordion-id14210_278fac-ec .kt-accordion-header-wrap .kt-blocks-accordion-header:focus{border-top-color:#eeeeee;border-top-style:solid;border-right-color:#eeeeee;border-right-style:solid;border-bottom-color:#eeeeee;border-bottom-style:solid;border-left-color:#eeeeee;border-left-style:solid;}.kt-accordion-id14210_278fac-ec .kt-accordion-header-wrap .kt-blocks-accordion-header.kt-accordion-panel-active{border-top-color:#0e9cd1;border-top-style:solid;border-right-color:#0e9cd1;border-right-style:solid;border-bottom-color:#0e9cd1;border-bottom-style:solid;border-left-color:#0e9cd1;border-left-style:solid;}}<\/style>\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-id14210_278fac-ec kt-accordion-has-20-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-arrow kt-accodion-icon-side-left\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-11 kt-pane14210_997bdd-d4\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong><strong>Geoinformatika a dia\u013ekov\u00fd prieskum Zeme<\/strong><\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\"has-text-align-justify\">Na \u0161tudijn\u00fd program Geoinformatika a dia\u013ekov\u00fd prieskum Zeme m\u00f4\u017eu by\u0165 prijat\u00ed absolventi magistersk\u00e9ho \u0161t\u00fadia v \u0161tudijnom odbore Geografia, medziodborov\u00e9ho a u\u010dite\u013esk\u00e9ho \u0161t\u00fadia v kombin\u00e1cii s geografiou, ale aj absolventi pr\u00edbuzn\u00fdch \u0161tudijn\u00fdch odborov. Pr\u00edbuznos\u0165 \u0161tudijn\u00fdch odborov pos\u00fadi garant \u0161tudijn\u00e9ho programu.<\/p>\n\n\n\n<p class=\"has-text-align-justify\">Prij\u00edmacia komisia pos\u00fadi komplexne predpoklady uch\u00e1dza\u010da na z\u00e1klade jeho \u0161tudijn\u00fdch v\u00fdsledkov na ni\u017e\u0161\u00edch stup\u0148och vzdel\u00e1vania a jeho doteraj\u0161ej v\u00fdskumnej a publika\u010dnej \u010dinnosti. Osobitne sa kladie d\u00f4raz na v\u00fdsledky \u00fa\u010dasti na \u0161tudentskej vedeckej konferencii a na v\u00fdskumn\u00fdch projektoch. V\u00edtan\u00e9 s\u00fa odpor\u00fa\u010dacie listy jeho predch\u00e1dzaj\u00facich \u0161kolite\u013eov, ktor\u00e9 by zd\u00f4vod\u0148ovali predpoklady uch\u00e1dza\u010da na absolvovanie doktorandsk\u00e9ho \u0161t\u00fadia. V \u00fastnej \u010dasti prij\u00edmacej sk\u00fa\u0161ky uch\u00e1dza\u010d predstav\u00ed svoj odborn\u00fd profil a svoj v\u00fdskumn\u00fd z\u00e1mer vo v\u00e4zbe na vybran\u00fa t\u00e9mu dizerta\u010dnej pr\u00e1ce. \u010clenovia komisie m\u00f4\u017eu kl\u00e1s\u0165 ot\u00e1zky, ktor\u00e9 s\u00favisia s vybranou t\u00e9mou a ktor\u00e9 by preuk\u00e1zali dostato\u010dn\u00fa odborn\u00fa sp\u00f4sobilos\u0165 uch\u00e1dza\u010da. Pokia\u013e si to charakter ot\u00e1zky vy\u017eaduje, uch\u00e1dza\u010d m\u00f4\u017ee po\u017eiada\u0165 o primeran\u00fd \u010das na pr\u00edpravu odpovede. Komisia tie\u017e m\u00f4\u017ee po\u017eiada\u0165 uch\u00e1dza\u010da o preuk\u00e1zanie akt\u00edvnej znalosti cudzieho jazyka.<\/p>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n\n<\/div><\/div><\/div><\/div>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n<style>.kadence-column14210_210ce2-23 > .kt-inside-inner-col,.kadence-column14210_210ce2-23 > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column14210_210ce2-23 > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column14210_210ce2-23 > .kt-inside-inner-col{flex-direction:column;}.kadence-column14210_210ce2-23 > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column14210_210ce2-23 > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column14210_210ce2-23{position:relative;}@media all and (max-width: 1024px){.kadence-column14210_210ce2-23 > .kt-inside-inner-col{flex-direction:column;}}@media all and (max-width: 767px){.kadence-column14210_210ce2-23 > .kt-inside-inner-col{flex-direction:column;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column14210_210ce2-23\"><div class=\"kt-inside-inner-col\"><style>.kb-row-layout-id14210_8747bf-ed > .kt-row-column-wrap{align-content:start;}:where(.kb-row-layout-id14210_8747bf-ed > .kt-row-column-wrap) > .wp-block-kadence-column{justify-content:start;}.kb-row-layout-id14210_8747bf-ed > .kt-row-column-wrap{column-gap:var(--global-kb-gap-md, 2rem);row-gap:var(--global-kb-gap-md, 2rem);grid-template-columns:minmax(0, calc(30% - ((var(--global-kb-gap-md, 2rem) * 1 )\/2))) minmax(0, calc(70% - ((var(--global-kb-gap-md, 2rem) * 1 )\/2)));}.kb-row-layout-id14210_8747bf-ed > .kt-row-layout-overlay{opacity:0.30;}@media all and (max-width: 1024px){.kb-row-layout-id14210_8747bf-ed > .kt-row-column-wrap{grid-template-columns:repeat(2, minmax(0, 1fr));}}@media all and (max-width: 767px){.kb-row-layout-id14210_8747bf-ed > .kt-row-column-wrap{grid-template-columns:minmax(0, 1fr);}}<\/style><div class=\"kb-row-layout-wrap kb-row-layout-id14210_8747bf-ed alignnone wp-block-kadence-rowlayout\"><div class=\"kt-row-column-wrap kt-has-2-columns kt-row-layout-right-golden kt-tab-layout-inherit kt-mobile-layout-row kt-row-valign-top\">\n<style>.kadence-column14210_479f0d-45 > .kt-inside-inner-col{display:flex;}.kadence-column14210_479f0d-45 > .kt-inside-inner-col,.kadence-column14210_479f0d-45 > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column14210_479f0d-45 > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column14210_479f0d-45 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_479f0d-45 > .kt-inside-inner-col > .aligncenter{width:100%;}.kt-row-column-wrap > .kadence-column14210_479f0d-45{align-self:center;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_479f0d-45{align-self:auto;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_479f0d-45 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_479f0d-45 > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column14210_479f0d-45{position:relative;}@media all and (max-width: 1024px){.kadence-column14210_479f0d-45 > .kt-inside-inner-col{flex-direction:column;}}@media all and (max-width: 767px){.kadence-column14210_479f0d-45 > .kt-inside-inner-col{flex-direction:column;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column14210_479f0d-45\"><div class=\"kt-inside-inner-col\"><style>.kb-image14210_e6c16c-51 .kb-image-has-overlay:after{opacity:0.3;}.kb-image14210_e6c16c-51 img.kb-img, .kb-image14210_e6c16c-51 .kb-img img{border-top-left-radius:5px;border-top-right-radius:5px;border-bottom-right-radius:5px;border-bottom-left-radius:5px;}<\/style>\n<div class=\"wp-block-kadence-image kb-image14210_e6c16c-51\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"200\" src=\"https:\/\/www.upjs.sk\/app\/uploads\/sites\/10\/2023\/10\/odbor-Informatika.png\" alt=\"\" class=\"kb-img wp-image-62040\"\/><\/figure><\/div>\n<\/div><\/div>\n\n\n<style>.kadence-column14210_ef45e2-bd > .kt-inside-inner-col{display:flex;}.kadence-column14210_ef45e2-bd > .kt-inside-inner-col,.kadence-column14210_ef45e2-bd > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column14210_ef45e2-bd > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column14210_ef45e2-bd > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_ef45e2-bd > .kt-inside-inner-col > .aligncenter{width:100%;}.kt-row-column-wrap > .kadence-column14210_ef45e2-bd{align-self:center;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_ef45e2-bd{align-self:auto;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_ef45e2-bd > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_ef45e2-bd > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column14210_ef45e2-bd{position:relative;}@media all and (max-width: 1024px){.kadence-column14210_ef45e2-bd > .kt-inside-inner-col{flex-direction:column;}}@media all and (max-width: 767px){.kadence-column14210_ef45e2-bd > .kt-inside-inner-col{flex-direction:column;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column14210_ef45e2-bd\"><div class=\"kt-inside-inner-col\"><style>.kt-accordion-id14210_d86fa7-5e .kt-accordion-panel-inner{border-top:0px solid transparent;border-right:0px solid transparent;border-bottom:0px solid transparent;border-left:0px solid transparent;padding-top:var(--global-kb-spacing-sm, 1.5rem);padding-right:var(--global-kb-spacing-sm, 1.5rem);padding-bottom:var(--global-kb-spacing-sm, 1.5rem);padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kt-accordion-id14210_d86fa7-5e .wp-block-kadence-pane .kt-accordion-header-wrap .kt-blocks-accordion-header{border-top:0px solid #f2f2f2;border-right:0px solid #f2f2f2;border-bottom:0px solid #f2f2f2;border-left:0px solid #f2f2f2;border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;background:#ffffff;color:#008338;padding-top:6px;padding-right:5px;padding-bottom:6px;padding-left:6px;}.kt-accordion-wrap.kt-accordion-id14210_d86fa7-5e > .kt-accordion-inner-wrap > .kt-accordion-pane > .kt-accordion-header-wrap{margin-top:0px;}.single-content .wp-block-kadence-pane>h2:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h3:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h4:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h5:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h6:first-child{margin-top:0px;}.kt-accordion-id14210_d86fa7-5e:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_d86fa7-5e:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-icon-trigger:before{background:#008338;}.kt-accordion-id14210_d86fa7-5e:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger{background:#008338;}.kt-accordion-id14210_d86fa7-5e:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_d86fa7-5e:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger:before{background:#ffffff;}.kt-accordion-id14210_d86fa7-5e .kt-accordion-header-wrap .kt-blocks-accordion-header:hover, body:not(.hide-focus-outline) .kt-accordion-id14210_d86fa7-5e .kt-accordion-header-wrap .kt-blocks-accordion-header:focus{color:#000000;background:#ffffff;border-top-color:#eeeeee;border-top-style:solid;border-right-color:#eeeeee;border-right-style:solid;border-bottom-color:#eeeeee;border-bottom-style:solid;border-left-color:#eeeeee;border-left-style:solid;}.kt-accordion-id14210_d86fa7-5e:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_d86fa7-5e:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before, body:not(.hide-focus-outline) .kt-accordion-id14210_d86fa7-5e:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id14210_d86fa7-5e:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:before{background:#000000;}.kt-accordion-id14210_d86fa7-5e:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger, body:not(.hide-focus-outline) .kt-accordion-id14210_d86fa7-5e:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger{background:#000000;}.kt-accordion-id14210_d86fa7-5e:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_d86fa7-5e:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before, body:not(.hide-focus-outline) .kt-accordion-id14210_d86fa7-5e:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id14210_d86fa7-5e:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:before{background:#ffffff;}.kt-accordion-id14210_d86fa7-5e .kt-accordion-header-wrap .kt-blocks-accordion-header.kt-accordion-panel-active{color:#000000;background:#ffffff;border-top-color:#0e9cd1;border-top-style:solid;border-right-color:#0e9cd1;border-right-style:solid;border-bottom-color:#0e9cd1;border-bottom-style:solid;border-left-color:#0e9cd1;border-left-style:solid;}.kt-accordion-id14210_d86fa7-5e:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_d86fa7-5e:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before{background:#000000;}.kt-accordion-id14210_d86fa7-5e:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger{background:#000000;}.kt-accordion-id14210_d86fa7-5e:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_d86fa7-5e:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before{background:#ffffff;}@media all and (max-width: 1024px){.kt-accordion-id14210_d86fa7-5e .kt-accordion-panel-inner{border-top:0px solid transparent;border-right:0px solid transparent;border-bottom:0px solid transparent;border-left:0px solid transparent;}}@media all and (max-width: 1024px){.kt-accordion-id14210_d86fa7-5e .wp-block-kadence-pane .kt-accordion-header-wrap .kt-blocks-accordion-header{border-top:0px solid #f2f2f2;border-right:0px solid #f2f2f2;border-bottom:0px solid #f2f2f2;border-left:0px solid #f2f2f2;}}@media all and (max-width: 1024px){.kt-accordion-id14210_d86fa7-5e .kt-accordion-header-wrap .kt-blocks-accordion-header:hover, body:not(.hide-focus-outline) .kt-accordion-id14210_d86fa7-5e .kt-accordion-header-wrap .kt-blocks-accordion-header:focus{border-top-color:#eeeeee;border-top-style:solid;border-right-color:#eeeeee;border-right-style:solid;border-bottom-color:#eeeeee;border-bottom-style:solid;border-left-color:#eeeeee;border-left-style:solid;}}@media all and (max-width: 1024px){.kt-accordion-id14210_d86fa7-5e .kt-accordion-header-wrap .kt-blocks-accordion-header.kt-accordion-panel-active{border-top-color:#0e9cd1;border-top-style:solid;border-right-color:#0e9cd1;border-right-style:solid;border-bottom-color:#0e9cd1;border-bottom-style:solid;border-left-color:#0e9cd1;border-left-style:solid;}}@media all and (max-width: 767px){.kt-accordion-id14210_d86fa7-5e .kt-accordion-panel-inner{border-top:0px solid transparent;border-right:0px solid transparent;border-bottom:0px solid transparent;border-left:0px solid transparent;}.kt-accordion-id14210_d86fa7-5e .wp-block-kadence-pane .kt-accordion-header-wrap .kt-blocks-accordion-header{border-top:0px solid #f2f2f2;border-right:0px solid #f2f2f2;border-bottom:0px solid #f2f2f2;border-left:0px solid #f2f2f2;}.kt-accordion-id14210_d86fa7-5e .kt-accordion-header-wrap .kt-blocks-accordion-header:hover, body:not(.hide-focus-outline) .kt-accordion-id14210_d86fa7-5e .kt-accordion-header-wrap .kt-blocks-accordion-header:focus{border-top-color:#eeeeee;border-top-style:solid;border-right-color:#eeeeee;border-right-style:solid;border-bottom-color:#eeeeee;border-bottom-style:solid;border-left-color:#eeeeee;border-left-style:solid;}.kt-accordion-id14210_d86fa7-5e .kt-accordion-header-wrap .kt-blocks-accordion-header.kt-accordion-panel-active{border-top-color:#0e9cd1;border-top-style:solid;border-right-color:#0e9cd1;border-right-style:solid;border-bottom-color:#0e9cd1;border-bottom-style:solid;border-left-color:#0e9cd1;border-left-style:solid;}}<\/style>\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-id14210_d86fa7-5e kt-accordion-has-20-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-arrow kt-accodion-icon-side-left\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-11 kt-pane14210_fe95b9-9b\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong><strong><strong>Informatika<\/strong><\/strong><\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\"has-text-align-justify\"><strong><u>Didaktika informatiky:<\/u><\/strong> Cie\u013e, obsah, didaktick\u00e9 prostriedky vyu\u010dovania \u0161kolskej informatiky. Pojmotvorn\u00fd proces v \u0161kolskej informatike. \u00davod do metodol\u00f3gie pedagogick\u00e9ho v\u00fdskumu v \u0161kolskej informatike. Stanovovanie u\u010debn\u00fdch cie\u013eov. Maturitn\u00fd \u0161tandard z informatiky. Postavenie \u00faloh v \u0161kolskej informatike, didaktick\u00e9 funkcie a formul\u00e1cie \u00faloh, tvorba syst\u00e9mov \u00faloh. Hodnotenie \u017eiackych v\u00fdkonov, didaktick\u00e9 testy. Tvorba didaktick\u00fdch projektov. V\u00fdu\u010dba \u0161trukt\u00farovan\u00e9ho a objektov\u00e9ho programovania. Aritmetika po\u010d\u00edta\u010da. Matematick\u00e9 modelovanie a simul\u00e1cie. V\u00fdu\u010dba tematick\u00fdch oblast\u00ed: Inform\u00e1cie okolo n\u00e1s, Po\u010d\u00edta\u010dov\u00e9 syst\u00e9my, Informa\u010dn\u00e1 spolo\u010dnos\u0165, Oblasti vyu\u017eitia informatiky (kancel\u00e1rsky bal\u00edk, Internet, multim\u00e9di\u00e1).<\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong><u>Datab\u00e1zov\u00e9 syst\u00e9my:<\/u><\/strong> \u00davod \u2013 hist\u00f3ria, z\u00e1kladn\u00e9 princ\u00edpy. Z\u00e1klady SQL \u2013 pr\u00e1ca s jednou tabu\u013ekou, agrega\u010dn\u00e9 funkcie, vnoren\u00e9 dopyty, modifik\u00e1cia d\u00e1t, integritn\u00e9 obmedzenia, modifik\u00e1cia \u0161trukt\u00fary tabu\u013eky.<\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong>Kombinatorick\u00e9 algoritmy:<\/strong> \u00davod do orientovan\u00fdch i neorientovan\u00fdch grafov. \u00davod do algoritmov, algoritmick\u00e1 zlo\u017eitos\u0165. Triediace algoritmy. Vyh\u013ead\u00e1vacie algoritmy. Kladn\u00e9 algoritmy. NP-\u00faplnos\u0165. Stromy a kostry &#8211; kore\u0148ov\u00e9 stromy. Vyh\u013eadanie v\u0161etk\u00fdch kostier grafu. \u00daloha o minim\u00e1lnej kostre. Vzdialenos\u0165 v grafoch. \u00daloha o najkrat\u0161ej ceste. \u00daloha o najspo\u013eahlivej\u0161ej ceste. \u00daloha o naj\u0161ir\u0161ej ceste. \u00davod do sie\u0165ovej anal\u00fdzy. Rozmiest\u0148ovacie \u00falohy. \u00dalohy o maxim\u00e1lnych tokoch. \u00daloha o najlacnej\u0161\u00edch tokoch. P\u00e1rovacie a pr\u00edra\u010fovacie probl\u00e9my. \u00daloha \u010d\u00ednskeho po\u0161t\u00e1ra. Probl\u00e9m obchodn\u00e9ho cestuj\u00faceho. Dopravn\u00e9 \u00falohy.<\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong>Programovanie, algoritmy a zlo\u017eitos\u0165:<\/strong> Algoritmick\u00fd probl\u00e9m a jeho rie\u0161enie. Pr\u00edklady konkr\u00e9tnych algoritmov, z\u00e1pis algoritmu v dohodnutom formalizme. Spr\u00e1vnos\u0165 algoritmu a testovanie algoritmov. Vlastnosti programovac\u00edch jazykov vy\u0161\u0161ieho typu. Z\u00e1kladn\u00e9 \u00fadajov\u00e9 a pr\u00edkazov\u00e9 \u0161trukt\u00fary programovacieho jazyka PASCAL. Proced\u00fary, funkcie, kni\u017enice proced\u00far a funkci\u00ed. Dynamick\u00e9 \u00fadajov\u00e9 \u0161trukt\u00fary, typ smern\u00edk. Zlo\u017eitos\u0165 algoritmov. Rekurzia, met\u00f3da s n\u00e1vratom (backtracking). Algoritmick\u00fd probl\u00e9m triedenia, algoritmy a zlo\u017eitos\u0165. D\u00f4le\u017eit\u00e9 \u00fadajov\u00e9 \u0161trukt\u00fary &#8211; z\u00e1sobn\u00edk, rad, graf. Algoritmy na grafoch.<\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong><u>\u00davod do kryptol\u00f3gie:<\/u><\/strong> Kryptografick\u00e9 modely, konven\u010dn\u00e1 symetrick\u00e1 kryptografia, met\u00f3dy a mo\u017enosti kryptoanal\u00fdzy. Asymetrick\u00e9 kryptografick\u00e9 syst\u00e9my, elementy te\u00f3rie \u010d\u00edsel, autentiz\u00e1cia, ha\u0161ovacie funkcie a syst\u00e9my elektronick\u00e9ho podpisu. Generovanie a distrib\u00facia k\u013e\u00fa\u010dov, autentiza\u010dn\u00e9 protokoly a ich zranite\u013enos\u0165. Certifik\u00e1cia, bezpe\u010dn\u00e9 elektronick\u00e9 platobn\u00e9 syst\u00e9my.<\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong>V\u00fdpo\u010dtov\u00e1 logika:<\/strong> \u00davodn\u00e1 motiv\u00e1cia o potrebe logiky v informatike. Alternat\u00edvne metamatematick\u00e9 z\u00e1klady: te\u00f3ria mno\u017e\u00edn, slov\u00e1 a \u010d\u00edsla a reprezent\u00e1cia d\u00e1tov\u00fdch \u0161trukt\u00far (rel\u00e1cie &#8211; typovan\u00e9 s atrib\u00fatmi, funkcie, ordin\u00e1lne \u010d\u00edsla, stromy). Z\u00e1kladn\u00e9 \u0161trukt\u00fary a pojmy v\u00fdrokov\u00e9ho a predik\u00e1tov\u00e9ho po\u010dtu: syntax (syntaktick\u00e9 stromy, vytv\u00e1raj\u00face postupnosti, d\u00f4kazy) a s\u00e9mantika (\u0161trukt\u00fary a pravdivos\u0165). Korektnos\u0165 v\u00fdrokov\u00e9ho a predik\u00e1tov\u00e9ho po\u010dtu (korektnos\u0165 axi\u00f3my o substituovate\u013enosti a zaveden\u00ed kvantifik\u00e1tora). Algoritmick\u00e9 aspekty syntaxe. S\u00favislos\u0165 s\u00e9mantiky s datab\u00e1zami. Vety o dedukcii, \u00faplnos\u0165 a kompaktnos\u0165. S\u00e9mantick\u00e9 tableaux, dedukt\u00edvne syst\u00e9my a algoritmy.<\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong>V\u00fdpo\u010dtov\u00e1 zlo\u017eitos\u0165:<\/strong> Pojem nedeterministick\u00e9ho algoritmu pracuj\u00faceho v polynomi\u00e1lnom \u010dase, NP-\u00faplnos\u0165. Deterministick\u00e1 simul\u00e1cia nedeterministick\u00fdch Turingov\u00fdch strojov. Probl\u00e9m splnite\u013enosti boolovskej formuly. \u010eal\u0161ie NP-\u00fapln\u00e9 probl\u00e9my (splnite\u013enos\u0165 boolovskej formuly v konjunkt\u00edvnom norm\u00e1lnom tvare, 3-splnite\u013enos\u0165, 3-zafarbite\u013enos\u0165 grafu, 3-zafarbite\u013enos\u0165 plan\u00e1rneho grafu, plnenie ruksaku, vyva\u017eovanie&#8230;). Pam\u00e4\u0165ovo ohrani\u010den\u00e9 algoritmy, triedy LOG-space a P-space. Deterministick\u00e1 simul\u00e1cia (Savitchova veta). Uzavretos\u0165 na komplement (Immerman-Szelepcs\u00e9nyiho veta).<\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong>V\u00fdpo\u010dtov\u00e9 u\u010denie:<\/strong> U\u010diace algoritmy, koncepcie, hypot\u00e9zy. Booleovsk\u00e9 formuly a ich reprezent\u00e1cia. Pravdepodobnostn\u00e9 u\u010denie, konzistentn\u00e9 algoritmy a u\u010denie, efekt\u00edvne u\u010denie, redukovatelnos\u0165 v PAC u\u010den\u00ed, u\u010denie kone\u010dn\u00fdch automatov pomocou experimentov. U\u010denie v neur\u00f3nov\u00fdch sie\u0165ach.<\/p>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n\n<\/div><\/div><\/div><\/div>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n<style>.kadence-column14210_ae1881-dc > .kt-inside-inner-col,.kadence-column14210_ae1881-dc > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column14210_ae1881-dc > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column14210_ae1881-dc > .kt-inside-inner-col{flex-direction:column;}.kadence-column14210_ae1881-dc > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column14210_ae1881-dc > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column14210_ae1881-dc{position:relative;}@media all and (max-width: 1024px){.kadence-column14210_ae1881-dc > .kt-inside-inner-col{flex-direction:column;}}@media all and (max-width: 767px){.kadence-column14210_ae1881-dc > .kt-inside-inner-col{flex-direction:column;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column14210_ae1881-dc\"><div class=\"kt-inside-inner-col\"><style>.kb-row-layout-id14210_a19da5-a6 > .kt-row-column-wrap{align-content:start;}:where(.kb-row-layout-id14210_a19da5-a6 > .kt-row-column-wrap) > .wp-block-kadence-column{justify-content:start;}.kb-row-layout-id14210_a19da5-a6 > .kt-row-column-wrap{column-gap:var(--global-kb-gap-md, 2rem);row-gap:var(--global-kb-gap-md, 2rem);grid-template-columns:minmax(0, calc(30% - ((var(--global-kb-gap-md, 2rem) * 1 )\/2))) minmax(0, calc(70% - ((var(--global-kb-gap-md, 2rem) * 1 )\/2)));}.kb-row-layout-id14210_a19da5-a6 > .kt-row-layout-overlay{opacity:0.30;}@media all and (max-width: 1024px){.kb-row-layout-id14210_a19da5-a6 > .kt-row-column-wrap{grid-template-columns:repeat(2, minmax(0, 1fr));}}@media all and (max-width: 767px){.kb-row-layout-id14210_a19da5-a6 > .kt-row-column-wrap{grid-template-columns:minmax(0, 1fr);}}<\/style><div class=\"kb-row-layout-wrap kb-row-layout-id14210_a19da5-a6 alignnone wp-block-kadence-rowlayout\"><div class=\"kt-row-column-wrap kt-has-2-columns kt-row-layout-right-golden kt-tab-layout-inherit kt-mobile-layout-row kt-row-valign-top\">\n<style>.kadence-column14210_419ab0-44 > .kt-inside-inner-col{display:flex;}.kadence-column14210_419ab0-44 > .kt-inside-inner-col,.kadence-column14210_419ab0-44 > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column14210_419ab0-44 > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column14210_419ab0-44 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_419ab0-44 > .kt-inside-inner-col > .aligncenter{width:100%;}.kt-row-column-wrap > .kadence-column14210_419ab0-44{align-self:center;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_419ab0-44{align-self:auto;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_419ab0-44 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_419ab0-44 > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column14210_419ab0-44{position:relative;}@media all and (max-width: 1024px){.kadence-column14210_419ab0-44 > .kt-inside-inner-col{flex-direction:column;}}@media all and (max-width: 767px){.kadence-column14210_419ab0-44 > .kt-inside-inner-col{flex-direction:column;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column14210_419ab0-44\"><div class=\"kt-inside-inner-col\"><style>.kb-image14210_8788d8-f6 .kb-image-has-overlay:after{opacity:0.3;}.kb-image14210_8788d8-f6 img.kb-img, .kb-image14210_8788d8-f6 .kb-img img{border-top-left-radius:5px;border-top-right-radius:5px;border-bottom-right-radius:5px;border-bottom-left-radius:5px;}<\/style>\n<div class=\"wp-block-kadence-image kb-image14210_8788d8-f6\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"200\" src=\"https:\/\/www.upjs.sk\/app\/uploads\/sites\/10\/2023\/10\/odbor-Matematika.png\" alt=\"\" class=\"kb-img wp-image-62044\"\/><\/figure><\/div>\n<\/div><\/div>\n\n\n<style>.kadence-column14210_3cc84a-b5 > .kt-inside-inner-col{display:flex;}.kadence-column14210_3cc84a-b5 > .kt-inside-inner-col,.kadence-column14210_3cc84a-b5 > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column14210_3cc84a-b5 > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column14210_3cc84a-b5 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_3cc84a-b5 > .kt-inside-inner-col > .aligncenter{width:100%;}.kt-row-column-wrap > .kadence-column14210_3cc84a-b5{align-self:center;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_3cc84a-b5{align-self:auto;}.kt-inner-column-height-full:not(.kt-has-1-columns) > .wp-block-kadence-column.kadence-column14210_3cc84a-b5 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}.kadence-column14210_3cc84a-b5 > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column14210_3cc84a-b5{position:relative;}@media all and (max-width: 1024px){.kadence-column14210_3cc84a-b5 > .kt-inside-inner-col{flex-direction:column;}}@media all and (max-width: 767px){.kadence-column14210_3cc84a-b5 > .kt-inside-inner-col{flex-direction:column;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column14210_3cc84a-b5\"><div class=\"kt-inside-inner-col\"><style>.kt-accordion-id14210_35b318-06 .kt-accordion-panel-inner{border-top:0px solid transparent;border-right:0px solid transparent;border-bottom:0px solid transparent;border-left:0px solid transparent;padding-top:var(--global-kb-spacing-sm, 1.5rem);padding-right:var(--global-kb-spacing-sm, 1.5rem);padding-bottom:var(--global-kb-spacing-sm, 1.5rem);padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kt-accordion-id14210_35b318-06 .wp-block-kadence-pane .kt-accordion-header-wrap .kt-blocks-accordion-header{border-top:0px solid #f2f2f2;border-right:0px solid #f2f2f2;border-bottom:0px solid #f2f2f2;border-left:0px solid #f2f2f2;border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;background:#ffffff;color:#008338;padding-top:6px;padding-right:5px;padding-bottom:6px;padding-left:6px;}.kt-accordion-wrap.kt-accordion-id14210_35b318-06 > .kt-accordion-inner-wrap > .kt-accordion-pane > .kt-accordion-header-wrap{margin-top:0px;}.single-content .wp-block-kadence-pane>h2:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h3:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h4:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h5:first-child,\n\t\t\t.single-content .wp-block-kadence-pane>h6:first-child{margin-top:0px;}.kt-accordion-id14210_35b318-06:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_35b318-06:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-icon-trigger:before{background:#008338;}.kt-accordion-id14210_35b318-06:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger{background:#008338;}.kt-accordion-id14210_35b318-06:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_35b318-06:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger:before{background:#ffffff;}.kt-accordion-id14210_35b318-06 .kt-accordion-header-wrap .kt-blocks-accordion-header:hover, body:not(.hide-focus-outline) .kt-accordion-id14210_35b318-06 .kt-accordion-header-wrap .kt-blocks-accordion-header:focus{color:#000000;background:#ffffff;border-top-color:#eeeeee;border-top-style:solid;border-right-color:#eeeeee;border-right-style:solid;border-bottom-color:#eeeeee;border-bottom-style:solid;border-left-color:#eeeeee;border-left-style:solid;}.kt-accordion-id14210_35b318-06:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_35b318-06:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before, body:not(.hide-focus-outline) .kt-accordion-id14210_35b318-06:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id14210_35b318-06:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:before{background:#000000;}.kt-accordion-id14210_35b318-06:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger, body:not(.hide-focus-outline) .kt-accordion-id14210_35b318-06:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger{background:#000000;}.kt-accordion-id14210_35b318-06:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_35b318-06:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before, body:not(.hide-focus-outline) .kt-accordion-id14210_35b318-06:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id14210_35b318-06:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:focus .kt-blocks-accordion-icon-trigger:before{background:#ffffff;}.kt-accordion-id14210_35b318-06 .kt-accordion-header-wrap .kt-blocks-accordion-header.kt-accordion-panel-active{color:#000000;background:#ffffff;border-top-color:#0e9cd1;border-top-style:solid;border-right-color:#0e9cd1;border-right-style:solid;border-bottom-color:#0e9cd1;border-bottom-style:solid;border-left-color:#0e9cd1;border-left-style:solid;}.kt-accordion-id14210_35b318-06:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_35b318-06:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before{background:#000000;}.kt-accordion-id14210_35b318-06:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger{background:#000000;}.kt-accordion-id14210_35b318-06:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id14210_35b318-06:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before{background:#ffffff;}@media all and (max-width: 1024px){.kt-accordion-id14210_35b318-06 .kt-accordion-panel-inner{border-top:0px solid transparent;border-right:0px solid transparent;border-bottom:0px solid transparent;border-left:0px solid transparent;}}@media all and (max-width: 1024px){.kt-accordion-id14210_35b318-06 .wp-block-kadence-pane .kt-accordion-header-wrap .kt-blocks-accordion-header{border-top:0px solid #f2f2f2;border-right:0px solid #f2f2f2;border-bottom:0px solid #f2f2f2;border-left:0px solid #f2f2f2;}}@media all and (max-width: 1024px){.kt-accordion-id14210_35b318-06 .kt-accordion-header-wrap .kt-blocks-accordion-header:hover, body:not(.hide-focus-outline) .kt-accordion-id14210_35b318-06 .kt-accordion-header-wrap .kt-blocks-accordion-header:focus{border-top-color:#eeeeee;border-top-style:solid;border-right-color:#eeeeee;border-right-style:solid;border-bottom-color:#eeeeee;border-bottom-style:solid;border-left-color:#eeeeee;border-left-style:solid;}}@media all and (max-width: 1024px){.kt-accordion-id14210_35b318-06 .kt-accordion-header-wrap .kt-blocks-accordion-header.kt-accordion-panel-active{border-top-color:#0e9cd1;border-top-style:solid;border-right-color:#0e9cd1;border-right-style:solid;border-bottom-color:#0e9cd1;border-bottom-style:solid;border-left-color:#0e9cd1;border-left-style:solid;}}@media all and (max-width: 767px){.kt-accordion-id14210_35b318-06 .kt-accordion-panel-inner{border-top:0px solid transparent;border-right:0px solid transparent;border-bottom:0px solid transparent;border-left:0px solid transparent;}.kt-accordion-id14210_35b318-06 .wp-block-kadence-pane .kt-accordion-header-wrap .kt-blocks-accordion-header{border-top:0px solid #f2f2f2;border-right:0px solid #f2f2f2;border-bottom:0px solid #f2f2f2;border-left:0px solid #f2f2f2;}.kt-accordion-id14210_35b318-06 .kt-accordion-header-wrap .kt-blocks-accordion-header:hover, body:not(.hide-focus-outline) .kt-accordion-id14210_35b318-06 .kt-accordion-header-wrap .kt-blocks-accordion-header:focus{border-top-color:#eeeeee;border-top-style:solid;border-right-color:#eeeeee;border-right-style:solid;border-bottom-color:#eeeeee;border-bottom-style:solid;border-left-color:#eeeeee;border-left-style:solid;}.kt-accordion-id14210_35b318-06 .kt-accordion-header-wrap .kt-blocks-accordion-header.kt-accordion-panel-active{border-top-color:#0e9cd1;border-top-style:solid;border-right-color:#0e9cd1;border-right-style:solid;border-bottom-color:#0e9cd1;border-bottom-style:solid;border-left-color:#0e9cd1;border-left-style:solid;}}<\/style>\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-id14210_35b318-06 kt-accordion-has-20-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-arrow kt-accodion-icon-side-left\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-1 kt-pane14210_5323a7-1e\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Aplikovan\u00e1 matematika<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\"has-text-align-justify\">V tomto \u0161tudijnom programe si \u0161tudent vyber\u00e1 t\u00e9mu dizerta\u010dnej pr\u00e1ce z jednej z troch \u0161pecializovan\u00fdch oblast\u00ed (vi\u010f uveden\u00e9 ni\u017e\u0161ie) a preto je d\u00f4raz kladen\u00fd na vedomosti z vybranej oblasti zhruba v rozsahu vyu\u010dovanom na prv\u00fdch dvoch stup\u0148och vysoko\u0161kolsk\u00e9ho \u0161t\u00fadia matematiky. Uch\u00e1dza\u010d by mal okrem z\u00e1ujmu o uveden\u00fa oblas\u0165 vedy preuk\u00e1za\u0165 schopnos\u0165 analytick\u00e9ho a kritick\u00e9ho myslenia, samostatnej formul\u00e1cie nov\u00fdch matematick\u00fdch tvrden\u00ed a algoritmov. Vzh\u013eadom na aplika\u010dn\u00fd charakter viacer\u00fdch t\u00e9m sa vy\u017eaduj\u00fa program\u00e1torsk\u00e9 zru\u010dnosti resp. schopnos\u0165 pracova\u0165 s aplika\u010dn\u00fdmi softv\u00e9rov\u00fdmi bal\u00edkmi. Schopnos\u0165 samostatne \u0161tudova\u0165 cudzojazy\u010dn\u00fa (hlavne&nbsp; anglick\u00fa) vedeck\u00fa matematick\u00fa&nbsp; literat\u00faru je samozrejmos\u0165ou.<\/p>\n\n\n\n<p><strong>Diskr\u00e9tne modely v te\u00f3rii hier, matematickej ekon\u00f3mii a opera\u010dnom v\u00fdskume:<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-justify\">Line\u00e1rne a konvexn\u00e9 programovanie: vlastnosti konvexn\u00fdch mno\u017e\u00edn, simplexov\u00e1 met\u00f3da a jej varianty, dualita, Kuh-Tuckerova te\u00f3ria.<br>Kombinatorick\u00e1 optimaliz\u00e1cia: algoritmy na grafoch, toky v sie\u0165ach, anal\u00fdza zlo\u017eitosti algoritmov, NP-\u00fapln\u00e9 \u00falohy.<br>Z\u00e1klady te\u00f3rie hier: hry v extenz\u00edvnom tvare, maticov\u00e9 a bimaticov\u00e9 hry, kooperat\u00edvne hry n hr\u00e1\u010dov.<\/p>\n\n\n\n<p><strong>Te\u00f3ria pravdepodobnosti a \u0161tatistika:<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-justify\">Te\u00f3ria pravdepodobnosti: N\u00e1hodn\u00e9 vektory, ich rozdelenia a charakteristiky. Charakteristick\u00e9 funkcie. Z\u00e1kony ve\u013ek\u00fdch \u010d\u00edsel a centr\u00e1lne limitn\u00e9 vety. N\u00e1hodn\u00e9 procesy, ich rozdelenia a charakteristiky. Markovove procesy, Poissonov proces, proces vzniku a z\u00e1niku.<br>Matematick\u00e1 \u0161tatistika: Met\u00f3dy odhadu nezn\u00e1mych parametrov. Testovanie hypot\u00e9z. Maticov\u00fd po\u010det pou\u017e\u00edvan\u00fd v \u0161tatistike, g-inverzieVlastnosti a pou\u017eitie line\u00e1rneho modelu (regresia, ANOVA, ANCOVA). Generovanie n\u00e1hodn\u00fdch \u010d\u00edsel a simul\u00e1cie.&nbsp; \u010casov\u00e9 rady.<\/p>\n\n\n\n<p><strong>Diferenci\u00e1lne rovnice a funkcion\u00e1lna anal\u00fdza<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-justify\">Diferenci\u00e1lne rovnice: Element\u00e1rne met\u00f3dy rie\u0161enia diferenci\u00e1lnych rovn\u00edc. Existencia a jednozna\u010dnos\u0165 rie\u0161enia. Z\u00e1kladn\u00e9 vlastnosti rie\u0161en\u00ed line\u00e1rneho diferenci\u00e1lneho syst\u00e9mu a line\u00e1rnej diferenci\u00e1lnej rovnice. Porovn\u00e1vacie vety.<br>Integr\u00e1lny po\u010det funkci\u00ed viac premenn\u00fdch: defin\u00edcia integr\u00e1lu na intervale, niektor\u00e9 vlastnosti a v\u00fdpo\u010det integr\u00e1lu na intervale,&nbsp; integr\u00e1l na mno\u017eine, niektor\u00e9 vlastnosti a v\u00fdpo\u010det integr\u00e1lu na mno\u017eine, dvojn\u00e9 a trojn\u00e9 integr\u00e1ly. Nevlastn\u00e9 integr\u00e1ly \u2013 defin\u00edcia, vety o existencii a met\u00f3dy v\u00fdpo\u010dtu nevlastn\u00fdch integr\u00e1lov. Parametrick\u00e9 integr\u00e1ly \u2013 vlastnosti funkcie danej parametrick\u00fdm integr\u00e1lom, pr\u00edklady v\u00fdpo\u010dtu integr\u00e1lov, funkcie gama a beta, Stirlingov vzorec.<br>Funkcion\u00e1lna anl\u00fdza: Line\u00e1rne priestory. Algebraick\u00e1 b\u00e1za a dimenzia. Line\u00e1rne zobrazenie a funkcion\u00e1l. Algebraick\u00fd du\u00e1lny priestor. Line\u00e1rny topologick\u00fd priestor. Lok\u00e1lne konvexn\u00fd priestor. Line\u00e1rny normovan\u00fd priestor. L(p)-priestory. Du\u00e1lne priestory k priestorom L(p). Hilbertov priestor. Aplik\u00e1cie Baireovej vety o kateg\u00f3rii. Veta o otvorenom zobrazen\u00ed. Veta o uzavretom grafe. Hahnova-Banachova veta. Spektrum line\u00e1rneho kompaktn\u00e9ho oper\u00e1tora.<\/p>\n\n\n\n<p class=\"has-text-align-justify\">&nbsp;<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-2 kt-pane14210_e68a13-ef\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"> <strong>Diskr\u00e9tna matematika<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\"has-text-align-justify\">Od uch\u00e1dza\u010da sa vy\u017eaduje znalos\u0165 ni\u017e\u0161ie uveden\u00fdch predmetov v rozsahu prv\u00fdch dvoch stup\u0148ov vysoko\u0161kolsk\u00e9ho \u0161t\u00fadia. D\u00f4raz je pritom kladen\u00fd na predmety bl\u00edzke k t\u00e9me, o ktor\u00fa m\u00e1 uch\u00e1dza\u010d z\u00e1ujem. Nutnou podmienkou je schopnos\u0165 pracova\u0165 s odborn\u00fdm matematick\u00fdm textom v jazyku anglickom.<\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong><u>Kombinatorika a te\u00f3ria grafov:<\/u><\/strong> Klasick\u00e1 kombinatorika. Z\u00e1kladn\u00e9 kombinatorick\u00e9 princ\u00edpy. Rekurz\u00edvne met\u00f3dy. Enumer\u00e1cia kombinatorick\u00fdch objektov. Klasick\u00e1 te\u00f3ria grafov \u2013 farebnos\u0165, nez\u00e1vislos\u0165, hamiltonovskos\u0165 grafov. Tur\u00e1nova veta, Ramseyova veta. Grafov\u00e9 algoritmy. Orientovan\u00e9 grafy. \u00davod do topologickej te\u00f3rie grafov.<\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong><u>Diskr\u00e9tna optimaliz\u00e1cia a algebraick\u00e9 \u0161trukt\u00fary:<\/u><\/strong> Line\u00e1rne a celo\u010d\u00edseln\u00e9 programovanie. Te\u00f3ria ohodnoten\u00fdch grafov a siet\u00ed. Te\u00f3ria hier. Te\u00f3ria syst\u00e9mov. Opera\u010dn\u00e1 anal\u00fdza. Line\u00e1rna algebra. Usporiadan\u00e9 algebraick\u00e9 \u0161trukt\u00fary. Te\u00f3ria kone\u010dn\u00fdch gr\u00fap. Kone\u010dn\u00e9 polia. Boolove algebry.<\/p>\n\n\n\n<p><\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-3 kt-pane14210_e615fe-9b\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Te\u00f3ria vyu\u010dovania matematiky<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\"has-text-align-justify\"><strong>Didaktika matematiky:<\/strong> Predmet didaktiky matematiky, v\u00fdvoj matematiky a vyu\u010dovania matematiky. Ciele a \u00falohy vyu\u010dovania matematiky. Ciele a \u00falohy vyu\u010dovania matematiky.<br>Pl\u00e1novanie vo vyu\u010dovan\u00ed matematiky. Logicko-didaktick\u00e1 anal\u00fdza u\u010diva. Ur\u010dovanie u\u010debn\u00fdch cie\u013eov. Didaktick\u00e9 princ\u00edpy, met\u00f3dy a formy vo vyu\u010dovan\u00ed matematiky.<br>Hodnotenie u\u010debn\u00fdch v\u00fdsledkov, tvorba didaktick\u00fdch testov. Matematick\u00e9 \u00falohy, syst\u00e9my \u00faloh. Hodnotenie vo vyu\u010dovan\u00ed matematiky, didaktick\u00e9 testy. \u00dalohy vo vyu\u010dovan\u00ed matematiky, tvorba syst\u00e9mov \u00faloh. Obsah a rozsah pojmu, triedenie a klasifik\u00e1cia pojmov.<\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong><u>Elementy matematickej logiky a stredo\u0161kolsk\u00e1 matematika:<\/u><\/strong> V\u00fdroky, oper\u00e1cie s v\u00fdrokmi. Defin\u00edcie, po\u017eiadavky na defin\u00edcie. Pojem d\u00f4kazu, met\u00f3dy d\u00f4kazu. Vz\u0165ah dok\u00e1zate\u013enosti a pravdivosti. Matematick\u00e9 vety. D\u00f4kazy matematick\u00fdch viet. Indukcia a dedukcia, anal\u00f3gia. Rozv\u00edjanie pojmu \u010d\u00edslo v \u0161kolskej matematike. Rel\u00e1cie, zobrazenia a funkcie v \u0161kolskej matematike. Goniometria a trigonometria v \u0161kolskej matematike. Planimetria a stereometria v \u0161kolskej matematike. Vektorov\u00e1 algebra v \u0161kolskej matematike. Infinitezim\u00e1lny po\u010det v \u0161kolskej matematike. Kombinatorika, pravdepodobnos\u0165 a \u0161tatistika v \u0161kolskej matematike.<\/p>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n\n<\/div><\/div><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"parent":12908,"menu_order":10,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_editorskit_title_hidden":false,"_editorskit_reading_time":0,"_editorskit_is_block_options_detached":false,"_editorskit_block_options_position":"{}","footnotes":""},"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>Po\u017eiadavky na prij\u00edmacie konanie na doktorandsk\u00e9 \u0161t\u00fadium - 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\/studium\/doktorandske\/poziadavky-na-prijimacie-konanie\/\" \/>\n<meta property=\"og:locale\" content=\"sk_SK\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Po\u017eiadavky na prij\u00edmacie konanie na doktorandsk\u00e9 \u0161t\u00fadium - 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