{"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\/et\/blog\/news\/rossijskij-matematik-nashel-klyuch-k-nereshaemym-uravneniyam-xix-veka-eto-uprostit-raschety-v-fizike-i-kosmonavtike","title":{"rendered":"Venemaa matemaatik leidis v\u00f5tme XIX sajandi \u201elahendamatutele\u201c v\u00f5rranditele: see lihtsustab arvutusi f\u00fc\u00fcsikas ja kosmonautikas.","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"<p>Riikliku teadus\u00fclikooli \"K\u00f5rgem majanduskool\" (NIU HSE) <a href=\"https:\/\/www.hse.ru\/news\/science\/1122687898.html\" target=\"_blank\" rel=\"nofollow noopener\">teatas<\/a>, et matemaatik Ivan Remizov Nizhni Novgorodist leidis v\u00f5imaluse tinglikult lihtsaks lahendamiseks teise astme diferentsiaalv\u00f5rranditele muutuvate koefitsientidega. Peaaegu kahe sajandi jooksul on selliseid v\u00f5rrandeid peetud lahendamatuks. Sellegipoolest m\u00e4ngivad need matemaatikas ja loodusteadustes v\u00f5tmerolli, kuna neid kasutatakse d\u00fcnaamiliste protsesside kirjeldamiseks.<\/p>\n<p><img decoding=\"async\" style=\"display: block; margin: 0 auto;\" src=\"\/wp-content\/uploads\/2026\/01\/1dcf3f3559eaa552afaf6ebdedbf6df6.png\" alt=\"Venemaa matemaatik leidis v\u00f5tme XIX sajandi \u201elahendamatutele\u201c v\u00f5rranditele: see lihtsustab arvutusi f\u00fc\u00fcsikas ja kosmonautikas.\" \/><\/p>\n<p>Ajalooliselt oli piirang seotud Prantsuse matemaatiku Joseph Liouville'i tulemustega, kes n\u00e4itas juba 1834. aastal, et selliste v\u00f5rrandite lahendeid ei saa v\u00e4ljendada l\u00f5pliku arvu standardsete operatsioonide ja elementaarfunktsioonide kaudu. Sel p\u00f5hjusel pidid matemaatikud kas otsima osalisi lahendusi v\u00f5i kasutama l\u00e4hendusi, mis v\u00e4listas universaalsete meetodite kasutamise jakeerult raskendas arvutusi. Teisis\u00f5nu, ei olnud olemas \u00fchtegi \u00fcldist valemit, kuhu saaks lihtsalt \"numbrid\" sisse panna ja saada lahendus.<\/p>\n<p>Ivan Remizov pakkus v\u00e4lja uue l\u00e4henemise, laiendades lubatud matemaatiliste operatsioonide klassi. Ta ei hakanud Liouville'iga vaidlema, vaid lisas v\u00f5rranditesse veel \u00fche matemaatilise t\u00f6\u00f6riista \u2014 j\u00e4rjestuse piiri leidmise. Selleks kasutas matemaatik Chernovi teooriat ja Laplace'i transformatsiooni. See v\u00f5imaldas tal koostada universaalse valemi, mis formaalselt annab lahenduse igale \u201elahendamatuks\u201c klassiks peetavale v\u00f5rrandile, m\u00f6\u00f6daminnes klassikalistest teooria piirangutest.<\/p>\n<p>\u201eIdee tuum seisneb selles, et keeruline, pidevalt muutuva protsess l\u00f5hustatakse l\u00f5putuks arvuks lihtsatest sammudest. Iga sellise osa jaoks ehitatakse oma l\u00e4hendus \u2014 elementaarne fragment, mis kirjeldab s\u00fcsteemi k\u00e4itumist konkreetses punktis. \u00dckshaaval annavad need t\u00fckid vaid lihtsustatud pildi, kuid kui nende arv l\u00e4heneb l\u00f5pmatusele, liituvad nad sujuvalt ideaalset t\u00e4pset lahenduse graafikut,\u201c selgitatakse NIU HSE pressiteates.<\/p>\n<p>Teise j\u00e4rgu diferentsiaalv\u00f5rrandeid kasutatakse mitte ainult reaalse maailma s\u00fcndmuste modelleerimiseks, vaid ka uute funktsioonide m\u00e4\u00e4ratlemiseks, mida ei saa muul viisil esitada. Nende hulka kuuluvad n\u00e4iteks nii nimetatud Mathe'i ja Hilli erifunktsioonid, mis on kriitilise t\u00e4htsusega arusaamise jaoks sellest, kuidas satelliidid orbiidil liiguvad v\u00f5i prootonid Suures Hadronite Kollideerijas.<\/p>\n<p>Veidi keerulisema matemaatilise keele abil avastus <a href=\"https:\/\/www.hse.ru\/news\/science\/1122687898.html\" target=\"_blank\" rel=\"nofollow noopener\">lugeda<\/a> NIU HSE veebilehel. Inglise keeles on t\u00f6\u00f6 <a href=\"https:\/\/www.vmj.ru\/articles\/2025_4_10.pdf#\/\" target=\"_blank\" rel=\"nofollow noopener\">avalikustatud<\/a> t\u00e4ielikult \"Vladikavkazi matemaatikaajakirjas\".<\/p>\n<p><strong>Allikas:<\/strong><\/p>\n<ul class=\"related\">\n<li><a title=\"HSE\" href=\"https:\/\/www.hse.ru\" target=\"_blank\" rel=\"nofollow noopener\">HSE<\/a><\/li>\n<\/ul>\n<p><center><center><\/center><center><\/center><\/center><center><\/center><br \/>\nAllikas: <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 5.0.1.1 - 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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