Periodic basa: mukuru pfungwa

Kazhinji kudzidza zvakasikwa, zvemakemikari uye zvivako-siyana zvinhu zvokunyama, uyewo kugadzirisa kunzwisisa hwokugadzira matambudziko vasangana pamwe kwemasayendisiti, rutivi rwuri kakawanda, saka pane tsika kudzokorora pashure imwe nguva. Nokuti tsananguro uye kumiririrwa yakajeka cyclicality kwakadaro zvesayenzi, pane kuti basa chinokosha - kwenguva nenguva basa.

Nyore uye kupfuura zvinzwisiswe vose muenzaniso - Mabatirwo redu yakapoteredza Sun, iro nguva dzose kushandura chinhambwe pakati pavo pasi wepagore kutenderera. Saizvozvowo, ari kudzoka chigaro chake, vavesa zvakakwana uyewo turbine chipasa. pezvakaitwa zvose izvi zvinogona ratombonzi kwemasvomhu ukoshi sezvo kwenguva nenguva basa. Kazhinji, nyika yedu iri cyclical. Uye kuti zvinoreva kuti kwenguva nenguva basa anotora nzvimbo inokosha yevanhu puranga.

Kudiwa masvomhu ari nhamba dzidziso, topology, differential equations , uye zvinonyatsochengeta geometrical Masvomhu kwakakonzera kuti chidzoke negore regumi namapfumbamwe remakore, mumwe muboka itsva mashandiro pamwe kujairika ehupfumi. Vaiva nenguva dzirikure mabasa vachitora akafanana tsika pane dzimwe pfungwa zvichikonzerwa transformations dzakaoma. Vari zvino kushandiswa munzvimbo zhinji masvomhu uye sayenzi vamwe. Somuenzaniso, kudzidza migumisiro siyana vibrational chinozunguzirwa wefizikisi.

In siyana kwemasvomhu mabhuku akasiyana tsanangudzo kwenguva nenguva basa. Zvisinei, zvisinei kusiyana izvi mashoko, ivo rinoenderana nerokuti sezvo tsanangura chete ehupfumi pakati mashandiro. The nyore chaizvo pachena chingava tsananguro inotevera. Basa, asi uwandu zvacho zvisingachinji, kana isu wedzera kwavo nharo nhamba asiri zero, vanonzi nguva mashandiro runotaurwa tsamba T vanonzi nguva nenguva. Izvi zvose zvinoreva uchidzidzira?

Somuenzaniso, zviri nyore kushanda muchimiro: y = d (x) ichava nguva nenguva kana X ane mumwe kukosha nguva (T). Kubva tsanangudzo iyi zvinoreva kuti kana kusanganiswa ukoshi basa ane nguva (T) chinorondedzerwa imwe pfungwa (x), kutara wayo anozivikanwa pa X T + X - T. The inokosha pano ndechokuti kana T ndiyo razero anova nokuzivikanwa chaitika. Periodic basa anogona isingaperi nhamba dzakasiyana nguva. In unorema zvakanaka kacho pakati tsika T ariko pakati rakadzika kusanganiswa chakarurama. Inonzi inokosha nguva. Uye vose mumwe netsika T nguva dzose divisible. Uyu mumwe anofadza uye zvikuru nokuti zvakasiyana minda pfuma.

Kuronga kwenguva nenguva basa anewo wandei zvinhu. Somuenzaniso, kana T nderei nguva okuti: y = d (x), ipapo kuronga basa iri, chete zvakakwana kuvaka bazi rimwe nguva kwenguva yakareba, uye ipapo kuibvisa achitevedza X akabatana kuti anotevera tsika: ± T, ± 2T , ± 3T uye zvichingodaro. Mukugumisa, zvinofanira kucherechedzwa kuti havasi vose periodic basa Nde nguva. A klassiske muenzaniso uyu ndiyo German yemasvomhu Dirichlet kushanda zvinotevera chimiro: y = D (x).