Isimiso Dirichlet sika. Kucaca kanye lula in ikhambi zezinkinga yinkimbinkimbi nelula

sezibalo German Gustava Lezhona Dirichlet, uPetru (13.02.1805 - 05.05.1859) is njengoba umsunguli isimiso, isihloko igama lakhe laziwe. Kodwa ngaphezu theory, ngokwesiko alichaza isibonelo "izinyoni namaseli", ngenxa ilungu langaphandle ohambelana we Petersburg Academy of Sciences, ilungu iRoyal Society of London, Paris Academy of Sciences, Berlin Academy of Sciences, uProfesa Berlin kanye University of Gottingen kukhona amaphepha amaningi ku umqulusizinda kanye nenombolo theory .

Akazange nje afake ku-mathematics isimiso owaziwa, Dirichlet ungase futhi afakazele a ifayela echaza ifomu ku-isibalo esingapheliyo izinombolo eziyinhloko ezikhona iyiphi inchubekelembili izibalo ka integers nezimiso ezithile. Isimo kule iwukuthi leli gama lokuqala wakhe kanye nomehluko - isibalo kuqhathaniswa eyinhloko.

Wathola balifundisise umthetho wokusabalalisa izinombolo ezejwayelekile, okuyizinto eziyizici izibalo Progressions. Dirichlet esethula uchungechunge lwezinkulumo imisebenzi ukuthi anombono ethile, waphumelela ngokwengxenye sokuhlaziya zezibalo okokuqala ngokunembile isho uphinde uhlole umqondo tekuhlangani okunemibandela futhi ngimise isihlalo convergence inombolo, ukunikeza ubufakazi zamandla kungenzeka enwetshiwe ku le-Fourier uchungechunge umsebenzi linenani ezilinganiselwe, njengoba kusenjalo ngizithole nezikhathi ezijabulisayo nezibuhlungu . Angazi ukushiya ngaphandle ukunakekela imisebenzi imibuzo Dirichlet ka Mechanics yemvelo zezibalo (the Dirichlet isimiso kwemisebenzi harmonic theory).

Usosayensi ekhethekile German ndlela alula ezibukwayo, okuvumela ukuba ukufunda isimiso Dirichlet esikoleni sabaqalayo. ithuluzi Anhlobonhlobo eziningi ezahlukahlukene kwezicelo, ezisetshenziswa njengoba ubufakazi theorems elula geometry, futhi ukuxazulula izinkinga eziyinkimbinkimbi ngekulandzelana zezibalo.

Ukutholakala kalula ukusetshenziswa indlela ukuvumele ukukuchazela ukudlala ngokucacile indlela. Inkulumo Complex futhi kancane eyinkimbinkimbi Ekuthathweni isimiso Dirichlet ine uhlobo: "Ngenxa iqoqo izakhi N ngobugebengu ku ngetincenye disjoint - n (izakhi ezivamile bengekho), inqobo N> n, okungenani libe linye sizoqukatha angaphezu kwelilodwa isici. " Kwanqunywa kahle uhlalisa kuhle okutjhiwo salokhu ukuze bathole ukucaciseleka, kuye kwadingeka ukuba esikhundleni N e "nonogwaja", futhi n ku "yezinyoni", futhi inkulumo abstruse ukuthola ukubukeka: "Inqobo nje uma onogwaja okungenani ezingaphezu kuka iseli, kukhona njalo okungenani oyedwa cell, okuyinto uthola engaphezu kwemibili futhi owawuhlala. "

Le ndlela yokucabanga okwengeziwe kunalokho aziwa, kepha baziwa kakhulu isimiso Dirichlet. Imisebenzi ukuthi zingaxazululwa uma isetshenziswa, ezihlukahlukene. Ngaphandle kokuya incazelo eningiliziwe izixazululo, isimiso Dirichlet osebenza kahle ngokufanayo bonakaliso imisebenzi elula be-Jomethri ngekulandzelana uyisisekelo inshokutsi lapho ucabangela ephakeme izinkinga wezibalo.

Abasekeli balobu indlela uthi ubunzima eyinhloko indlela iwukuba ukunquma ukuthi iyiphi idatha ezivikelwe ngaphansi kwencazelo "nonogwaja", futhi lapho kufanele kuthathwe njengendlela "cell."

Ngo inkinga ka eqondile unxantathu ungephansi kwemandla indiza efanayo, ukufakazela ukuthi akunakuba ukuwela izinhlangothi ezintathu nje, kungagcini usebenzise umbandela owodwa, uma kunesidingo - umugqa aluphumeleli ngokusebenzisa yimuphi unxantathu ukuphakama. Njengoba "onogwaja" cabangela ukuphakama unxantathu, futhi "amaseli" ezimbili nengxenye-izindiza, okuyinto amanga nhlangothi zombili emgqeni. Kuyacaca ukuthi okungenani ezimbili eziphakeme kuyoba kwelinye isigamu-indiza, ngokulandelana, ubude besikhathi ukuthi ubeke umkhawulo akuyona ukuyiveza ngqo, njengoba kudingeka.

Njengoba nje ne-ngamafuphi kusetshenziswa isimiso Dirichlet senkinga okunengqondo amanxusa pennants. Etafuleni round itholakala ezansi ezifundazweni ezihlukahlukene, kodwa amafulegi lamazwe esemgwaqweni ipherimitha ukuze inxusa ngamunye owelama uphawu ezweni langaphandle. Kuyadingeka ukuba ukufakazela ukuba khona kwamandla Esimweni esinjalo, uma okungenani ababili ifulege kuyoba eduze bameleli amazwe ukhathazekile. Uma samukela izithunywa ukuze "izinyoni" futhi "amaseli" ekuchazeni isikhundla ezisele phakathi ukujikeleza etafuleni (bona bayobe sebekhona kakade eyodwa ngaphansi), khona-ke inkinga kuziwa isinqumo ngokwalo.

Lezi zibonelo ezimbili banikwa ukuze acacise indlela lula ukuxazulula izinkinga eyinkimbinkimbi kusetshenziswa indlela akhiwa sezibalo German.