Mukhtarbay Otelbayev, Kazakistan\u2019\u0131n Astana kentinde bulunan Avrasya Ulusal \u00dcniversitesi\u2019nde matematik\u00e7i. Otelbayev, g\u00fcn\u00fcm\u00fczde m\u00fchendislikten meteorolojiye kadar pek \u00e7ok alanda ak\u0131\u015fkanlar\u0131 modellemek i\u00e7in kullan\u0131lan Navier-Stokes problemini \u00e7\u00f6zd\u00fc\u011f\u00fcn\u00fc iddia ediyor.<\/p>\n
Navier-Stokes problemi, asl\u0131nda bildi\u011fimiz anlamda bir \u201cproblem\u201d de\u011fil; Navier ve Stokes\u2019un yakla\u015f\u0131k iki y\u00fcz y\u0131l \u00f6nce ortaya koydu\u011fu denklemler, asl\u0131nda i\u015fe yar\u0131yor; fakat denklemlerin olas\u0131 her durumda \u00e7al\u0131\u015ft\u0131\u011f\u0131na ili\u015fkin kan\u0131t yok. Ba\u015fka bir deyi\u015fle bu denklemlerin duvara toslad\u0131\u011f\u0131 ya da ger\u00e7ek\u00e7i sonu\u00e7lar \u00fcretmedi\u011fi durumlar\u0131n olup olmad\u0131\u011f\u0131 bilinmiyor.<\/p>\n
2000\u2019de Clay Matematik Enstit\u00fcs\u00fc, yeni milenyumda matemati\u011fi kutlamak i\u00e7in Yedi Milenyum Problemi belirlemi\u015f ve problemlerin her birinin \u00e7\u00f6z\u00fcm\u00fc i\u00e7in birer milyon dolarl\u0131k \u00f6d\u00fcl konmu\u015ftu. Navier-Stokes problemi de bunlardan biri\u2026<\/p>\n
Otelbayev, Kazakistan\u2019da yay\u0131mlanan Mathematical Journal<\/em> dergisindeki makalesinde bir milyon dolarl\u0131k bu problemin \u00e7\u00f6z\u00fcm\u00fcn\u00fc yay\u0131mlad\u0131. Kazak matematik\u00e7i, problem \u00fczerinde kesintili olarak 30 y\u0131l boyunca u\u011fra\u015ft\u0131\u011f\u0131n\u0131 belirtiyor.<\/p>\n Anla\u015fmak i\u00e7in matematik yetmez<\/strong><\/p>\n Fakat ortada bir sorun var: Her ne kadar matematik, sembollerden olu\u015fan evrensel bir dilse de, ayn\u0131 zamanda b\u00fcy\u00fck \u00f6l\u00e7\u00fcde a\u00e7\u0131klay\u0131c\u0131 metinler de i\u00e7eriyor. Ne var ki,\u00a0 Otelbayev, \u0130ngilizce bilmiyor. \u00dcnl\u00fc problemi \u00e7\u00f6zd\u00fc\u011f\u00fc metin Rus\u00e7a ve hen\u00fcz \u00e7evrilmi\u015f de\u011fil. Bu nedenle uluslararas\u0131 matematik camias\u0131n\u0131n metni de\u011ferlendirmesi \u015fimdilik zor.<\/p>\n Clay Matematik enstit\u00fcs\u00fc i\u00e7in problemin resmi form\u00fclasyonunu yazan Princeton \u00dcniversitesi\u2019nden Charles Fefferman y\u0131llard\u0131r problemi \u00e7\u00f6zd\u00fc\u011f\u00fc iddia edilen makalelerin yanl\u0131\u015f \u00e7\u0131kt\u0131\u011f\u0131n\u0131 hat\u0131rlat\u0131yor; fakat hen\u00fcz makale \u00e7evrilmedi\u011fi i\u00e7in daha fazlas\u0131n\u0131 s\u00f6yleyemeyece\u011fini belirtiyor.<\/p>\n Tahmin edilece\u011fi \u00fczere, milenyum problemlerinin \u00e7\u00f6z\u00fcm\u00fcne y\u00f6nelik, internet \u00fczerinden d\u00fczenli olarak g\u00f6nderilen amat\u00f6r u\u011fra\u015flar mevcut. Bu \u00e7al\u0131\u015fmalar genelde pek yank\u0131 uyand\u0131rm\u0131yor. Fakat Otelbayev\u2019in bir profesyonel olmas\u0131, matematik\u00e7ilerin bu makaleye di\u011ferlerinden daha fazla ilgi g\u00f6stermesine neden oluyor.<\/p>\n Elbette bunlardan baz\u0131lar\u0131 Rus\u00e7a makaleyi anlama olana\u011f\u0131 olan matematik\u00e7iler. \u00d6rne\u011fin Rus meslekta\u015flar\u0131 ile birlikte \u00e7al\u0131\u015fan Missouri \u00dcniversitesi\u2019nden Stephen Montgomery-Smith makalenin umut vaat etti\u011fini, \u015fimdiye dek okudu\u011fu kadar\u0131n\u0131n de\u011ferli oldu\u011funu fakat hen\u00fcz kan\u0131t\u0131n kalbine ula\u015fm\u0131\u015f gibi hissetmedi\u011fini s\u00f6yl\u00fcyor. Otelbayev ise, Kazakistan\u2019dan \u00fc\u00e7 ve Rusya\u2019dan bir meslekta\u015f\u0131n\u0131n kan\u0131t\u0131n do\u011frulu\u011fu konusunda hemfikir olduklar\u0131n\u0131 s\u00f6yl\u00fcyor.<\/p>\n Kan\u0131tlama y\u00fck\u00fcml\u00fcl\u00fc\u011f\u00fc<\/strong><\/p>\n Bir milyon dolarl\u0131k \u00f6d\u00fcl g\u00f6z \u00f6n\u00fcne al\u0131n\u0131rsa, problem \u00e7\u00f6z\u00fcm\u00fcne dair s\u0131k\u0131 bir kan\u0131t\u0131n istenmesi olduk\u00e7a do\u011fal. Clay Matematik Enstit\u00fcs\u00fc\u2019n\u00fcn kurallar\u0131na g\u00f6re \u00f6d\u00fcl\u00fcn verilmesi i\u00e7in, \u00e7\u00f6z\u00fcm d\u00fcnya \u00e7ap\u0131nda itibar sahibi bir dergide yay\u0131mlanacak ve iki y\u0131l boyunca \u201ctart\u0131\u015fmas\u0131z do\u011fru\u201d kalacak.<\/p>\n Otelbayev makalenin \u00f6\u011frencileri taraf\u0131ndan \u00e7evrilmekte oldu\u011funu, \u0130ngilizce \u00e7evirisinin \u00e7ok yak\u0131nda \u00f6nce bir Kazak dergisinde ve belki daha sonra yurtd\u0131\u015f\u0131ndaki bir dergide yeniden yay\u0131mlanaca\u011f\u0131n\u0131 s\u00f6yl\u00fcyor.<\/p>\n \u0130\u015fin zorlu\u011funu g\u00f6stermesi a\u00e7\u0131s\u0131ndan, bug\u00fcne kadar resmi olarak yaln\u0131zca bir milenyum probleminin \u00e7\u00f6z\u00fclebildi\u011fini hat\u0131rlatal\u0131m. 2003\u2019te Grigori Perelman, Poincar\u00e9 Varsay\u0131m\u0131\u2019n\u0131 kan\u0131tlam\u0131\u015f fakat sonra matematik camias\u0131ndan uzakla\u015farak \u00f6d\u00fcl olan bir milyon dolar\u0131 reddetmi\u015fti.<\/p>\n Ayr\u0131ca \u201cP=NP\u201d olarak bilinen ba\u015fka bir probleme 2010\u2019da gelen olas\u0131 bir \u00e7\u00f6z\u00fcm matematik\u00e7ilerin ilgisini \u00e7ekmi\u015f, ne var ki hatal\u0131 oldu\u011fu bulunmu\u015ftu. Otelbayev\u2019in \u00e7\u00f6z\u00fcm\u00fcn\u00fcn de ayn\u0131 kaderi payla\u015f\u0131p payla\u015fmayaca\u011f\u0131 ise yak\u0131nda g\u00f6r\u00fclecek.<\/p>\n Milenyumun matematik problemleri<\/strong><\/p>\n Clay Matematik Enstit\u00fcs\u00fc\u2019n\u00fcn 2000 y\u0131l\u0131nda, her birinin \u00e7\u00f6z\u00fcm\u00fc i\u00e7in bir milyon dolarl\u0131k \u00f6d\u00fcl koydu\u011fu Navier-Stokes probleminin d\u0131\u015f\u0131ndaki alt\u0131 milenyum problemi \u015funlar:<\/p>\n Yang-Mills teorisi<\/strong><\/p>\n Deneyler ve bilgisayar sim\u00fclasyonlar\u0131 Yang-Mill denklemlerinin kuantum versiyonlar\u0131nda \u201ck\u00fctle aral\u0131\u011f\u0131\u201dn\u0131n varl\u0131\u011f\u0131n\u0131 \u00f6ne s\u00fcrer; fakat bu \u00f6zelli\u011fin bulundu\u011funa ili\u015fkin herhangi bir kan\u0131t yoktur.<\/p>\n Riemann hipotezi<\/strong><\/p>\n Asal say\u0131 teorisi asal say\u0131lar\u0131n ortalama da\u011f\u0131l\u0131m\u0131n\u0131 belirler. Riemann hipotezi ise ortalamadan deviasyonu (sapma) verir. Riemann\u2019\u0131n 1859 y\u0131l\u0131nda yazd\u0131\u011f\u0131 makalesinde form\u00fcle edilmi\u015f bu hipotez, \u03b6(s) = 0 denkleminin t\u00fcm kompleks \u00e7\u00f6z\u00fcmlerinin reel k\u0131s\u0131mlar\u0131n\u0131n 1\/2 oldu\u011funu \u00f6ne s\u00fcrer.<\/p>\n P=NP problemi<\/strong><\/p>\n E\u011fer bir problemin \u00e7\u00f6z\u00fcm\u00fcn\u00fcn do\u011fru oldu\u011fu kolayca kontrol edilabiliyorsa, problemi \u00e7\u00f6zmek de kolayd\u0131r, de\u011fil mi? Bu soru, P=NP probleminin temeli. NP problemlerinin tipik bir \u00f6rne\u011fi Hamilton yolu problemidir: N \u015fehir verilidir, bir ki\u015fi bir \u015fehre iki defa gitmeden nas\u0131l \u015fehirlerin tamam\u0131na gidebilir? E\u011fer bana bir \u00e7\u00f6z\u00fcm sunarsan\u0131z, kolayca do\u011fru oldu\u011funu ispatlar\u0131m. Fakat yan\u0131t\u0131 o kadar kolay bulamam.<\/p>\n Poincar\u00e9 varsay\u0131m\u0131<\/strong><\/p>\n 1904\u2019te Frans\u0131z matematik\u00e7i Henri Poincar\u00e9, \u00fc\u00e7 boyutlu bir k\u00fcreyi basit bile\u015fmi\u015f \u00fc\u00e7 manifold olarak karakterize edebilir miyiz? sorusunu sordu. Bu soru, Thurston\u2019\u0131n varsay\u0131m\u0131n\u0131n \u00f6zel bir durumuna ili\u015fkindi. Rus matematik\u00e7i Grigori Perelman, \u00f6nce Thurston varsay\u0131m\u0131n\u0131 daha sonra Poincar\u00e9 varsay\u0131m\u0131n\u0131 kan\u0131tlad\u0131.<\/p>\n Birch ve Swinnerton-Dyer varsay\u0131m\u0131<\/strong><\/p>\n Olduk\u00e7a deneysel bir kan\u0131tla desteklenen bu varsay\u0131m, yaln\u0131zca belirli bir de\u011ferde L-fonksiyonunun s\u0131f\u0131r olmas\u0131 halinde bir e\u011fri \u00fczerinde sonsuz say\u0131da rasyonel nokta bulunaca\u011f\u0131n\u0131 iddia eder.<\/p><\/blockquote>\n U\u00e7ak yap\u0131m\u0131ndan \u00e7evre kirlili\u011fi analizine\u2026\u00a0<\/strong>Navier-Stokes denklemleri <\/strong><\/p>\n Frans\u0131z fizik\u00e7i ve m\u00fchendis Claude-Louis Navier ile \u0130rlandal\u0131 matematik\u00e7i ve fizik\u00e7i George Gabriel Stokes taraf\u0131ndan 19. y\u00fczy\u0131lda olu\u015fturulan denklemler, ak\u0131\u015fkan hareketlerini tan\u0131mlar. Navier-Stokes denklemleri Newton\u2019un ikinci yasas\u0131n\u0131n ak\u0131\u015fkan hareketlerine uygulanmas\u0131yla olu\u015fturulur. Denklemler, ak\u0131\u015fkan i\u00e7indeki birim k\u00fctleye d\u00fc\u015fen momentumun, viskoz kuvvetlerin toplam\u0131na e\u015fit oldu\u011fu varsay\u0131m\u0131nda bulunur.<\/p>\n B\u00fct\u00fcnl\u00fckl\u00fc ve basit formlar\u0131yla Navier-Stokes denklemleri, \u00e7ok \u00e7e\u015fitli alanlarda biliminsanlar\u0131na yard\u0131mc\u0131 olur. U\u00e7ak ve otomobil yap\u0131m\u0131nda, kan ak\u0131\u015f\u0131n\u0131 inceleyen \u00e7al\u0131\u015fmalarda, hava durumu tahminlerinde, g\u00fc\u00e7 istasyonlar\u0131n\u0131n tasar\u0131m\u0131nda, \u00e7evre kirlili\u011finin analizinde vs. kullan\u0131labilir. Ayr\u0131ca Maxwell\u2019in denklemleri ile birlikte manyetohidrodinamik alan\u0131nda yap\u0131lan \u00e7al\u0131\u015fma ve modellemelerde kullan\u0131l\u0131r. New Statesman<\/em> dergisinden Micheal Brooks, bu denklemler sayesinde Ocak ay\u0131nda Kuzey Amerika\u2019da dondurucu so\u011fuklara neden olan \u201ckutbi girdap\u201d ad\u0131 verilen meteorolojik olay\u0131 anlayabildi\u011fimizi ya da okyanuslardaki karbondioksit deri\u015fiminin artmas\u0131n\u0131n nelere sebep olabilece\u011fini bildi\u011fimizi belirtiyor. Brooks hava yolculu\u011fu s\u0131ras\u0131nda farkl\u0131 hava katmanlar\u0131n\u0131n etkile\u015fimiyle ger\u00e7ekle\u015fen a\u00e7\u0131k hava t\u00fcrb\u00fclans\u0131nda karbondioksit emiliminin etkisini \u00f6rnekleyerek devam ediyor: \u201cBu, karbondioksit konsantrasyonun art\u0131r\u0131r. \u00c7\u00f6z\u00fcm\u00fc hakk\u0131nda Navier-Stokes denklemleri bize t\u00fcrb\u00fclans\u0131n y\u00fcksek enlemlere do\u011fru hareket etti\u011fini s\u00f6yler. Denklemlerin \u00e7\u00f6z\u00fcm\u00fc, transatlantik u\u00e7u\u015flarda izlenecek rotay\u0131 do\u011frudan belirler.\u201d<\/p>\n Dolay\u0131s\u0131yla denklemlerin her ko\u015fulda do\u011frulu\u011funun kan\u0131tlanmas\u0131 ya da bu denklemlere ne kadar g\u00fcvenebilece\u011fimizin ortaya konmas\u0131, sadece akademik de\u011fil, prati\u011fi de etkileyen bir ba\u015far\u0131.<\/p>\n Kaynak<\/strong><\/p>\n 1) Jacob Aron, Katia Moskvitch, “Kazakh mathematician may have solved $1 million puzzle” New Scientist<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":" Mukhtarbay Otelbayev, Kazakistan\u2019\u0131n Astana kentinde bulunan Avrasya Ulusal \u00dcniversitesi\u2019nde matematik\u00e7i. Otelbayev, g\u00fcn\u00fcm\u00fczde m\u00fchendislikten meteorolojiye kadar pek \u00e7ok alanda ak\u0131\u015fkanlar\u0131 modellemek i\u00e7in kullan\u0131lan Navier-Stokes problemini \u00e7\u00f6zd\u00fc\u011f\u00fcn\u00fc iddia ediyor. Navier-Stokes problemi, asl\u0131nda bildi\u011fimiz anlamda bir \u201cproblem\u201d de\u011fil; Navier ve Stokes\u2019un yakla\u015f\u0131k iki y\u00fcz y\u0131l \u00f6nce ortaya koydu\u011fu denklemler, asl\u0131nda i\u015fe yar\u0131yor; fakat denklemlerin olas\u0131 her durumda \u00e7al\u0131\u015ft\u0131\u011f\u0131na […]<\/p>\n","protected":false},"author":448,"featured_media":26665,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[158,19,25],"tags":[208,3449,1572],"class_list":["post-26659","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-121-sayi","category-bilim-gundemi","category-matematik","tag-matematik","tag-navier-stokes-problemi","tag-problemler"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/posts\/26659","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/users\/448"}],"replies":[{"embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/comments?post=26659"}],"version-history":[{"count":0,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/posts\/26659\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/media\/26665"}],"wp:attachment":[{"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/media?parent=26659"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/categories?post=26659"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/tags?post=26659"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}