Umgaqo Dirichlet kaThixo. Ecacile nelula kwi ngesisombululo iingxaki yokuntsonkotha nelula

yezibalo German Gustava Lezhona Dirichlet, Peter (13.02.1805 - 05.05.1859) yaziwa ngokuba ngunozala umgaqo, itayitile igama lakhe. Kodwa ukongezelela kwithiyori, ngokwesiko awucacise umzekelo 'iintaka kunye neeseli ", ngenxa yokuba esihambelanayo ilungu langaphandle le-St Petersburg Academy of Sciences, ilungu le-Royal Society of London, i-Paris Academy of Sciences, i-Berlin Academy of Sciences, uNjingalwazi eBerlin kunye University of Göttingen kukho amaphepha amaninzi kucalulo lwezibalo theory nenombolo .

Akazange nje afake kwimathematika umgaqo ezaziwayo-kakuhle, Dirichlet nazo Makazicikide theorem kwi inani olungenasiphelo amanani inkulumbuso ezikhoyo nayiphi na ukuqhubela phambili lokubala eliguqukayo integers kunye neemeko ezithile. Yimeko kuba oku kukuba kwikota yokuqala ka kwakhe umahluko - inani inkulumbuso kakhulu.

Wafumana isifundo ngokucokisekileyo umthetho lonikezelo kwamanani eziqhelekileyo, ezo abayinqobo ukuba izibalo progressions. Dirichlet laqalisa uthotho lwemisebenzi abe nembono ethile, waphumelela inxalenye uhlalutyo zezibalo okokuqala ngokuchanekileyo livakalise kwaye bahlole isigama ukuhlangabezana enemiqathango kunye nokuseka ukuhlangabezana lwenani, ukunika ubungqina olungqongqo yethuba kwandiswa ukuya kwi Fourier kuthotho umsebenzi ukuba unalo amanani anesiphelo, njengoko nowakho nezibuhlungu . I musa ukuhamba ngaphandle ingqalelo imisebenzi imibuzo Dirichlet yokulungisa kunye physics lweMathematika (i Dirichlet siseko ukuze theory imisebenzi harmonic).

Isazinzulu yakhelwe indlela German yinto elula yayo ezibonwayo, esivumela ukuba afunde lo mgaqo Dirichlet kwisikolo aphantsi. isixhobo Onemisebenzi ngakubhalileyo ngokoluhlu olubanzi kwezicelo, ezithi zisetyenziswe njengobungqina ukuba theorems elula geometry, nangenxa zokusombulula iingxaki ezinzima zilandelelana kunye zemathematika.

Ukufumaneka kunye lula kokusebenzisa indlela eye wavumela ukuba ukuyicacisa udlala ngokucacileyo indlela. Enzima kunye bantwana ezididayo abaseke umgaqo Dirichlet, oko kukuthi: "Kuba iseti ye N elements, kwaphulwa kwinani iindawo disjoint - n (izinto eziqhelekileyo abangekhoyo), ngaphandle N> n, ubuncinane enye inxalenye uya kuba ngaphezu kwesinye element. " Kwagqitywa kakuhle phinda oku ukuze afumane ingcaciso, kwafuneka ukuba indawo N kwi "nomvundla", yaye n kwi "ebuhlanti", yaye ibinzana abstruse ukuze ufumane ukhangelo: "Ngaphandle kokuba imivundla enye ubuncinane ngaphezu iseli, kukho lisoloko ubuncinane enye iseli, nto leyo ngaphezu ababini kunye nomvundla. "

Le ndlela yokuqiqa ngakumbi yaziwa phezu koko, waba sasisaziwa umgaqo Dirichlet. Imisebenzi ingasombululwa xa isetyenziselwe, iintlobo ngeentlobo. Ngaphandle eyaya inkcazelo eneenkcukacha sezisombululo, lo mgaqo Dirichlet isebenza kakuhle ngokufanayo ngenxa wazimisa ephilile imisebenzi ezilula zejometri kunye ubhalo kwaye kwenza isiseko okufanayo xa sijonga iingxaki eziphezulu imathematika.

Abaxhasi le ndlela ithi ukuba ubunzima iphambili yale ndlela ukuqonda oko data ziphantsi kwenkcazo 'nomvundla ", kwaye kufuneka ithathwe njenge" cell. "

Xa ingxaki ngqo kunye nonxantathu lulele-moya enye, ukuba kuyimfuneko, ukungqina ukuba kuyiwela kumacala amathathu ekunene, isetyenziswa njenge umda imeko enye - kumgca akuthethi kudlula nayiphi unxantathu ukuphakama. Njengoko "imivundla" cinga ukuphakama unxantathu, yaye "iiseli" asuke-moya ezimbini, leyo ulale ngapha nangapha lomgca. Kucacile ukuba eziphakamileyo ubuncinane ezimbini iya kuba ngomnye kwisiqingatha-moya, ngokulandelelana, ubude bexesha ukuba umda akukho imiswa ngqo, njengoko kuyimfuneko.

Njengoko elula ecacisa umgaqo ingxaki Dirichlet kwi-logic unozakuzaku kunye pennants. Etafileni ngeenxa ifumaneka emazantsi ithi ezahlukeneyo, kodwa iindwe kumazwe ibekwe ecaleni kwebala ukuze ngunozakuzaku nganye ecaleni njengomfuziselo kwilizwe langaphandle. Kuyimfuneko ukuba ubungqina xa ubuncinane ezimbini iflegi iya kuba ecaleni abameli kumazwe ezichaphazelekayo ubukho kwimeko enjalo,. Ukuba siyayamkela makhumsha ukuba "iintaka" kunye "iiseli" ukuze achaze imeko eseleyo ngexesha njengokujikeleza itafile (sele baya kuba mnye ngaphantsi), ngoko ke ingxaki oza isigqibo ngokwalo.

Le mizekelo mibini banikwa ukubonisa indlela yokucombulula lula iingxaki entsonkothileyo usebenzisa indlela eyenziwe yi sezibalo waseJamani.