{"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\/cs\/blog\/news\/rossijskij-matematik-nashel-klyuch-k-nereshaemym-uravneniyam-xix-veka-eto-uprostit-raschety-v-fizike-i-kosmonavtike","title":{"rendered":"Rusk\u00fd matematik na\u0161el kl\u00ed\u010d k 'ne\u0159e\u0161iteln\u00fdm' rovnic\u00edm 19. stolet\u00ed: to zjednodu\u0161\u00ed v\u00fdpo\u010dty ve fyzice a kosmonautice","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"<p>N\u00e1rodn\u00ed v\u00fdzkumn\u00e1 univerzita \u201eVy\u0161\u0161\u00ed ekonomick\u00e1 \u0161kola\u201c (NIU V\u0160E) <a href=\"https:\/\/www.hse.ru\/news\/science\/1122687898.html\" target=\"_blank\" rel=\"nofollow noopener\">uvedl<\/a>, \u017ee matematik Ivan Remizov z Ni\u017en\u00edho Novgorodu na\u0161el zp\u016fsob pro podm\u00edn\u011bn\u011b jednoduch\u00e9 \u0159e\u0161en\u00ed diferenci\u00e1ln\u00edch rovnic druh\u00e9ho \u0159\u00e1du s prom\u011bnn\u00fdmi koeficienty. Po t\u00e9m\u011b\u0159 dv\u011b stolet\u00ed byly tyto rovnice pova\u017eov\u00e1ny za ne\u0159e\u0161iteln\u00e9. Hraj\u00ed v\u0161ak kl\u00ed\u010dovou roli v matematice a p\u0159\u00edrodn\u00edch v\u011bd\u00e1ch, proto\u017ee se pou\u017e\u00edvaj\u00ed k popisu dynamick\u00fdch proces\u016f.<\/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\u0161el kl\u00ed\u010d k &#039;ne\u0159e\u0161iteln\u00fdm&#039; rovnic\u00edm 19. stolet\u00ed: to zjednodu\u0161\u00ed v\u00fdpo\u010dty ve fyzice a kosmonautice\" \/><\/p>\n<p>Historicky bylo toto omezen\u00ed spojeno s v\u00fdsledky francouzsk\u00e9ho matematika Josepha Liouvillea, kter\u00fd ji\u017e v roce 1834 uk\u00e1zal, \u017ee \u0159e\u0161en\u00ed podobn\u00fdch rovnic nelze vyj\u00e1d\u0159it pomoc\u00ed kone\u010dn\u00e9ho po\u010dtu standardn\u00edch operac\u00ed a element\u00e1rn\u00edch funkc\u00ed. Z tohoto d\u016fvodu byli matematikov\u00e9 nuceni bu\u010f hledat d\u00edl\u010d\u00ed \u0159e\u0161en\u00ed, nebo pou\u017e\u00edvat aproximace, co\u017e vylu\u010dovalo univerz\u00e1ln\u00ed metodiku a zna\u010dn\u011b zt\u011b\u017eovalo v\u00fdpo\u010dty. Jin\u00fdmi slovy, neexistoval \u017e\u00e1dn\u00fd obecn\u00fd vzorec, do kter\u00e9ho by bylo mo\u017en\u00e9 jednodu\u0161e dosadit \u201e\u010d\u00edsla\u201c a z\u00edskat \u0159e\u0161en\u00ed.<\/p>\n<p>Ivan Remizov navrhl nov\u00fd p\u0159\u00edstup, kdy\u017e roz\u0161\u00ed\u0159il t\u0159\u00eddu povolen\u00fdch matematick\u00fdch operac\u00ed. Nep\u0159el se s Liouvillem, ale prost\u011b p\u0159idal do rovnic dal\u0161\u00ed matematick\u00fd n\u00e1stroj \u2014 nalezen\u00ed limitu posloupnosti. K tomu matematik vyu\u017eil \u010cernovovu teorii a Laplaceovu transformaci. To mu umo\u017enilo sestavit univerz\u00e1ln\u00ed vzorec, kter\u00fd form\u00e1ln\u011b poskytuje \u0159e\u0161en\u00ed jak\u00e9koli rovnice \u201ene\u0159e\u0161iteln\u00e9ho\u201c typu, obch\u00e1zej\u00edc\u00ed klasick\u00e1 omezen\u00ed teorie.<\/p>\n<p>\u201ePodstatou my\u0161lenky je, \u017ee slo\u017eit\u00fd, neust\u00e1le se m\u011bn\u00edc\u00ed proces je rozd\u011blen na nekone\u010dn\u00e9 mno\u017estv\u00ed jednoduch\u00fdch krok\u016f. Pro ka\u017ed\u00fd takov\u00fd \u00fasek se vytv\u00e1\u0159\u00ed sv\u00e9 p\u0159ibl\u00ed\u017een\u00ed \u2014 element\u00e1rn\u00ed fragment, kter\u00fd popisuje chov\u00e1n\u00ed syst\u00e9mu v konkr\u00e9tn\u00edm bod\u011b. Zvl\u00e1\u0161\u0165 tyto kousky poskytuj\u00ed pouze zjednodu\u0161en\u00fd obraz, ale kdy\u017e jejich po\u010det sm\u011b\u0159uje k nekone\u010dnu, bezprobl\u00e9mov\u011b se spoj\u00ed v dokonale p\u0159esn\u00fd graf \u0159e\u0161en\u00ed,\u201c uv\u00e1d\u00ed se v tiskov\u00e9 zpr\u00e1v\u011b NIU V\u0160E.<\/p>\n<p>Diferenci\u00e1ln\u00ed rovnice druh\u00e9ho \u0159\u00e1du se pou\u017e\u00edvaj\u00ed nejen k modelov\u00e1n\u00ed ud\u00e1lost\u00ed re\u00e1ln\u00e9ho sv\u011bta, ale i k ur\u010dov\u00e1n\u00ed nov\u00fdch funkc\u00ed, kter\u00e9 nelze jin\u00fdm zp\u016fsobem definovat. Pat\u0159\u00ed sem nap\u0159\u00edklad takzvan\u00e9 speci\u00e1ln\u00ed funkce Mathieu a Hilla, kter\u00e9 jsou kriticky d\u016fle\u017eit\u00e9 pro pochopen\u00ed, jak se pohybuj\u00ed satelity na orbit\u011b nebo protony ve Velk\u00e9m hadronov\u00e9m kolideru.<\/p>\n<p>O n\u011bco slo\u017eit\u011bj\u0161\u00edm matematick\u00fdm jazykem o objevu lze <a href=\"https:\/\/www.hse.ru\/news\/science\/1122687898.html\" target=\"_blank\" rel=\"nofollow noopener\">p\u0159e\u010d\u00edst<\/a> nal\u00e9zt na webu NII V\u0160E. V anglick\u00e9m jazyce je pr\u00e1ce <a href=\"https:\/\/www.vmj.ru\/articles\/2025_4_10.pdf#\/\" target=\"_blank\" rel=\"nofollow noopener\">byla vyd\u00e1na<\/a> kompletn\u011b publikov\u00e1na v \u201eVladikavkazsk\u00e9m matematick\u00e9m \u010dasopise\u201c.<\/p>\n<p><strong>Zdroj:<\/strong><\/p>\n<ul class=\"related\">\n<li><a title=\"Nyu VSHE\" href=\"https:\/\/www.hse.ru\" target=\"_blank\" rel=\"nofollow noopener\">Nyu VSHE<\/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 5.0.3 - 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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