{"id":155545,"date":"2026-01-27T23:12:35","date_gmt":"2026-01-27T21:12:38","guid":{"rendered":"https:\/\/prohoster.info\/blog\/novosti-interneta\/rossijskij-matematik-nashel-klyuch-k-nereshaemym-uravneniyam-xix-veka-eto-uprostit-raschety-v-fizike-i-kosmonavtike"},"modified":"2026-01-30T17:57:27","modified_gmt":"2026-01-30T15:57:27","slug":"rossijskij-matematik-nashel-klyuch-k-nereshaemym-uravneniyam-xix-veka-eto-uprostit-raschety-v-fizike-i-kosmonavtike","status":"publish","type":"post","link":"https:\/\/prohoster.info\/sk\/blog\/news\/rossijskij-matematik-nashel-klyuch-k-nereshaemym-uravneniyam-xix-veka-eto-uprostit-raschety-v-fizike-i-kosmonavtike","title":{"rendered":"Rusk\u00fd matematik na\u0161iel k\u013e\u00fa\u010d k \u201enerozhodnute\u013en\u00fdm\u201c rovnicam 19. storo\u010dia: to zjednodu\u0161\u00ed v\u00fdpo\u010dty v fyzike a kozmonautike.","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"<p>N\u00e1rodn\u00e1 v\u00fdskumn\u00e1 univerzita \u201eVy\u0161\u0161ia \u0161kola ekonomiky\u201c (NIU V\u0160E) <a href=\"https:\/\/www.hse.ru\/news\/science\/1122687898.html\" target=\"_blank\" rel=\"nofollow noopener\">uviedol<\/a>, \u017ee matematik Ivan Remizov z Ni\u017en\u00e9ho Novgorodu na\u0161iel sp\u00f4sob pre podmiene\u010dne jednoduch\u00e9 rie\u0161enie diferenci\u00e1lnych rovn\u00edc druh\u00e9ho r\u00e1du s premenliv\u00fdmi koeficientmi. Po\u010das takmer dvoch storo\u010d\u00ed sa tak\u00e9to rovnice pova\u017eovali za nevyrie\u0161ite\u013en\u00e9. Zatia\u013e v\u0161ak zohr\u00e1va k\u013e\u00fa\u010dov\u00fa \u00falohu v matematike a pr\u00edrodn\u00fdch ved\u00e1ch, preto\u017ee sa pou\u017e\u00edvaj\u00fa na opis dynamick\u00fdch procesov.<\/p>\n<p><img decoding=\"async\" style=\"display: block; margin: 0 auto;\" src=\"\/wp-content\/uploads\/2026\/01\/1dcf3f3559eaa552afaf6ebdedbf6df6.png\" alt=\"Rusk\u00fd matematik na\u0161iel k\u013e\u00fa\u010d k \u201enerozhodnute\u013en\u00fdm\u201c rovnicam 19. storo\u010dia: to zjednodu\u0161\u00ed v\u00fdpo\u010dty v fyzike a kozmonautike.\" \/><\/p>\n<p>Historicky bolo toto obmedzenie spojen\u00e9 s v\u00fdsledkami franc\u00fazskeho matematik Josepha Liouvilla, ktor\u00fd u\u017e v roku 1834 uk\u00e1zal, \u017ee rie\u0161enia podobn\u00fdch rovn\u00edc nemo\u017eno vyjadri\u0165 prostredn\u00edctvom kone\u010dn\u00e9ho po\u010dtu \u0161tandardn\u00fdch oper\u00e1ci\u00ed a element\u00e1rnych funkci\u00ed. Z tohto d\u00f4vodu boli matematiky n\u00faten\u00e9 bu\u010f h\u013eada\u0165 \u010diasto\u010dn\u00e9 rie\u0161enia, alebo pou\u017e\u00edva\u0165 aproxim\u00e1cie, \u010do vyl\u00fa\u010dilo univerz\u00e1lnu metodiku a ve\u013emi s\u0165a\u017eilo v\u00fdpo\u010dty. In\u00fdmi slovami, neexistovala v\u0161eobecn\u00e1 formula, do ktorej by sa jednoducho \u201edoplnili \u010d\u00edsla\u201c a z\u00edskalo sa rie\u0161enie.<\/p>\n<p>Ivan Remizov navrhol nov\u00fd pr\u00edstup, ktor\u00fd roz\u0161\u00edril triedu povolen\u00fdch matematick\u00fdch oper\u00e1ci\u00ed. Nespochyb\u0148oval Liouvilla, ale jednoducho pridal do rovn\u00edc \u010fal\u0161\u00ed matematick\u00fd n\u00e1stroj \u2014 h\u013eadanie limitu postupnosti. Na to matematik vyu\u017eil \u010cernovovu te\u00f3riu a Laplaceovu transform\u00e1ciu. To mu umo\u017enilo vybudova\u0165 univerz\u00e1lnu formulu, ktor\u00e1 form\u00e1lne d\u00e1va rie\u0161enie ak\u00fdchko\u013evek rovn\u00edc \u201enevyrie\u0161ite\u013enej\u201c triedy, obch\u00e1dzaj\u00fac klasick\u00e9 obmedzenia te\u00f3rie.<\/p>\n<p>\u201ePodstata my\u0161lienky spo\u010d\u00edva v tom, \u017ee zlo\u017eit\u00fd, neust\u00e1le sa meniac\u00ed proces sa rozdel\u00ed na nekone\u010dn\u00e9 mno\u017estvo jednoduch\u00fdch krokov. Pre ka\u017ed\u00fd tak\u00fd \u00fasek sa vytvor\u00ed svoje pribl\u00ed\u017eenie \u2014 element\u00e1rny fragment, ktor\u00fd popisuje spr\u00e1vanie syst\u00e9mu v konkr\u00e9tnom bode. Samostatne tieto kusy d\u00e1vaj\u00fa len zjednodu\u0161en\u00fd obraz, ale ke\u010f ich po\u010det smeruje k nekone\u010dnu, bez probl\u00e9mov sa spoja do ide\u00e1lne presn\u00e9ho grafu rie\u0161enia,\u201c vysvet\u013euje sa v tla\u010dovej spr\u00e1ve NIU V\u0160E.<\/p>\n<p>\u201eDiferenci\u00e1lne rovnice druh\u00e9ho r\u00e1du sa pou\u017e\u00edvaj\u00fa nielen na modelovanie udalost\u00ed re\u00e1lneho sveta, ale aj na definovanie nov\u00fdch funkci\u00ed, ktor\u00e9 nemo\u017eno ur\u010di\u0165 in\u00fdm sp\u00f4sobom. Sem patr\u00ed napr\u00edklad takzvan\u00e9 \u0161peci\u00e1lne funkcie Mathieu a Hilla, ktor\u00e9 s\u00fa kriticky d\u00f4le\u017eit\u00e9 na pochopenie toho, ako sa pohybuj\u00fa dru\u017eice na orbite alebo prot\u00f3ny vo Ve\u013ekom hadr\u00f3novom ur\u00fdch\u013eova\u010di.\u201c<\/p>\n<p>Trochu zlo\u017eitej\u0161\u00edm matematick\u00fdm jazykom o objave sa d\u00e1 <a href=\"https:\/\/www.hse.ru\/news\/science\/1122687898.html\" target=\"_blank\" rel=\"nofollow noopener\">pre\u010d\u00edta\u0165<\/a> n\u00e1js\u0165 na str\u00e1nke N\u00e1rodn\u00e9ho v\u00fdskumn\u00e9ho univerzity \u201eVysok\u00e1 \u0161kola ekonomick\u00e1\u201c. Pr\u00e1ca je v angli\u010dtine <a href=\"https:\/\/www.vmj.ru\/articles\/2025_4_10.pdf#\/\" target=\"_blank\" rel=\"nofollow noopener\">bola publikovan\u00e1<\/a> \u00faplne vo \u201eVladikavkazskom matematickom \u010dasopise\u201c.<\/p>\n<p><strong>Zdroj:<\/strong><\/p>\n<ul class=\"related\">\n<li><a title=\"NIU V\u0160E\" href=\"https:\/\/www.hse.ru\" target=\"_blank\" rel=\"nofollow noopener\">NIU V\u0160E<\/a><\/li>\n<\/ul>\n<p><center><center><\/center><center><\/center><\/center><center><\/center><br \/>\nZdroj: <a rel=\"nofollow\" href=\"https:\/\/3dnews.ru\/1135924\">3dnews.ru<\/a><\/p>","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"<p>\u041d\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0439 \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u0441\u043a\u0438\u0439 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u00ab\u0412\u044b\u0441\u0448\u0430\u044f \u0448\u043a\u043e\u043b\u0430 \u044d\u043a\u043e\u043d\u043e\u043c\u0438\u043a\u0438\u00bb (\u041d\u0418\u0423 \u0412\u0428\u042d) \u0441\u043e\u043e\u0431\u0449\u0438\u043b, \u0447\u0442\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a \u0418\u0432\u0430\u043d \u0420\u0435\u043c\u0438\u0437\u043e\u0432 \u0438\u0437 \u041d\u0438\u0436\u043d\u0435\u0433\u043e \u041d\u043e\u0432\u0433\u043e\u0440\u043e\u0434\u0430 \u043d\u0430\u0448\u0451\u043b \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u044c \u0434\u043b\u044f \u0443\u0441\u043b\u043e\u0432\u043d\u043e \u043f\u0440\u043e\u0441\u0442\u043e\u0433\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u0432\u0442\u043e\u0440\u043e\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0430 \u0441 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u043c\u0438 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u0430\u043c\u0438. \u041d\u0430 \u043f\u0440\u043e\u0442\u044f\u0436\u0435\u043d\u0438\u0438 \u043f\u043e\u0447\u0442\u0438 \u0434\u0432\u0443\u0445 \u0441\u0442\u043e\u043b\u0435\u0442\u0438\u0439 \u0442\u0430\u043a\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0441\u0447\u0438\u0442\u0430\u043b\u0438\u0441\u044c \u043d\u0435\u0440\u0435\u0448\u0430\u0435\u043c\u044b\u043c\u0438. \u041c\u0435\u0436\u0434\u0443 \u0442\u0435\u043c, \u043e\u043d\u0438 \u0438\u0433\u0440\u0430\u044e\u0442 \u043a\u043b\u044e\u0447\u0435\u0432\u0443\u044e \u0440\u043e\u043b\u044c \u0432 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u0438 \u0435\u0441\u0442\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0445 \u043d\u0430\u0443\u043a\u0430\u0445, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044e\u0442\u0441\u044f \u0434\u043b\u044f \u043e\u043f\u0438\u0441\u0430\u043d\u0438\u044f \u0434\u0438\u043d\u0430\u043c\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u043e\u0432. [&hellip;]<\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":8,"featured_media":155546,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[702],"tags":[],"class_list":["post-155545","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-news"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.4 - aioseo.com -->\n\t<meta name=\"description\" content=\"\u041d\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0439 \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u0441\u043a\u0438\u0439 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u00ab\u0412\u044b\u0441\u0448\u0430\u044f \u0448\u043a\u043e\u043b\u0430 \u044d\u043a\u043e\u043d\u043e\u043c\u0438\u043a\u0438\u00bb (\u041d\u0418\u0423 \u0412\u0428\u042d) \u0441\u043e\u043e\u0431\u0449\u0438\u043b, 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