Dirichlet kuti Principle. Zviri nyore uye zvakajeka mune mhinduro matambudziko kunosiyana kunzwisisa

yemasvomhu German Gustava Lezhona Dirichlet, Peter (13.02.1805 - 05.05.1859) inozivikanwa se muvambi nheyo, musoro zita rake. Asi kunze dzidziso, rakagara richidudzirwa akatsanangura nomuenzaniso "shiri uye masero", nokuda yokumwe runoenzanirana nhengo St. Petersburg Academy of Sciences, nhengo Royal Society of London, kuti Paris Academy of Sciences, ari Berlin Academy of Sciences, Professor kweBerlin uye University of Göttingen vari mapepa akawanda pamusoro kwemasvomhu kuongorora uye nhamba dzidziso .

Haana kungoita kupinda masvomhu inozivikanwa musimboti, Dirichlet aigona kuratidza munhu theorem no musi isingaperi nhamba inonyanya nhamba kuripo chero svomhu kuchiita integers vane zvimwe zvinhu. A zvimiso ichi ndechokuti wokutanga izwi kwaro uye musiyano - kuwanda nekaupenyu wehurumende.

Akagamuchira kunyatsodzidza mutemo nokuparadzirwa nhamba zvavo, izvo yaingowanikwa svomhu progressions. Dirichlet akatanga dzakatevedzana mashandiro kuti vane chimwe maonero, akabudirira muchidimbu pamusoro kwemasvomhu kuongorora kokutanga zvakarurama zvakajeka uye kuongorora pfungwa zvimiso convergence uye kugadza convergence ane nhamba, kupa zvakaoma uchapupu mukana rwakawedzera kupinda pakati Fourier akatevedzana ari kushanda kuti ane finite nhamba, sezvo ichava nenguva yakanaka uye neyakaoma . Handisi kusiya pasina kuteerera mabasa Dirichlet mibvunzo makanika uye akarongeka wefizikisi (the Dirichlet nhungamiro nokuda harmonic mabasa dzidziso).

nzira musayendisiti angakwanisa yakagadzirwa German raro kutarisana nyore, izvo anotibvumira kudzidza Dirichlet musimboti kuchikoro chepuraimari. Ichiita mabasa akawanda chishandiso zvakawanda mafomu, dzinoshandiswa Uchapupu nyore theorems vari geometry, uye nokuda nekugadzirisa kunzwisisa musoro uye akarongeka matambudziko.

Kuwanikwa uye nyore kushandisa nzira akabvumira kutsanangura zvakajeka kuridza nzira. Complex chivara oma okuti mukuronga Dirichlet musimboti ane chimiro: "Nokuti yakatarwa N zvinhu wakaputsika mumitauro disjoint zvikamu - N (zvakafanana nezvinhu hatisi), Akariritira N> N, pane mumwe mugove ichange iine kupfuura imwe eremendi. " Kwakasarudzwa zvakanaka nepamwe kuti ichi kuti vawane yakajeka, taifanira yokutsiva N mu "tsuro", uye N mu "keji", uye abstruse okuti kuwana Zvinoonekwa: "Rupiwe kuti tsuro kuti dzinenge imwe kupfuura muchitokisi, pane dzimwe nguva dzose kumuduku rimwe muchitokisi, iyo anowana anopfuura maviri uye netsuro. "

nzira iyi pfungwa zvakawanda zvinozivikanwa pamusoro zvinopesana akatanga kuzivikanwa sezvo Dirichlet musimboti. Mabasa anogona kugadziriswa kana rinoshandiswa, yakasiyana siyana. Pasina kupinda rondedzero pamusoro zvinogadzirisa, ari Dirichlet zvinoshandawo zvakafanana zvakanaka uchapupu nyore geometric uye musoro mabasa anoteya hwaro inference kana tichifunga yepamusoro masvomhu matambudziko.

Vanotsigira nzira iyi inoti kuti huru kuoma nzira ndiko kuziva chii umboo akafukidzwa pasi tsanangudzo "tsuro", uye izvo zvinofanira anoonekwa somunhu "muchitokisi."

In dambudziko zvakananga uye netriangle avete chete mundege, kuzviratidza kuti rukoniwe kuyambuka mativi matatu chete, hakugumiri kushandisa chimwe chinhano, kana zvichikodzera - mutsetse asingadi nomunyika chero nokukwirira Triangle. Sezvo "hares" funga kukwirira Triangle, uye "masero" vane mbiri hafu-ndege, izvo okurutivi kana divi mutsetse. Zviri pachena kuti miti dzinenge mbiri zvichava rimwe nehafu ndege, ukuwo, kureba kwenguva kuti dzisanyanya haasi zvakananga woutsinye, sezvo zvaida.

Akangouya uye muchidimbu zvakanga aishandisa Dirichlet nheyo kusvikira musoro dambudziko senhume uye pennants. Panguva kumativi tafura iri nomurwizi pamusoro siyana inoti, asi petsanga kunyika yaiva pedyo mukomberedzo kuitira kuti mumwe mumiririri mukuru kutevera chiratidzo imwe nyika. Zvakakodzera kuratidza kuvapo ezvinhu akadaro, apo dzinenge mbiri mureza achatevera kuti vamiririri venyika hanya. Kana tikagashira vamiririri kuti "shiri" uye "masero" kunan'anura nzvimbo yasara panguva vachishandisa kutenderera patafura (vachava kare mumwe zvichidzika), zvino dambudziko rinouya chisarudzo pachayo.

Mienzaniso miviri aya anopiwa kuenzanisira sei nyore kugadzirisa matambudziko oma kushandisa nzira kugadzirwa German yemasvomhu.