Periodic muaj nuj nqi: general tswv yim

Feem ntau nyob rau hauv txoj kev tshawb no ntawm tej yam ntuj tso phenomena, tshuaj thiab lub cev thaj chaw ntawm ntau yam tshuaj, raws li zoo li nyob rau hauv kev daws txoj kev teeb meem ces yuav tsum nrog cov txheej txheem, ib tug feature uas yog cov zaus, ces muaj yog ib tug ib txwm kom rov hais dua tom qab ib tug tej lub sij hawm ntawm lub sij hawm. Rau cov hauj lwm thiab cov duab sawv cev ntawm xws cyclicality nyob rau hauv science, muaj ib tug tshwj xeeb zoo muaj nuj nqi - ib tug periodic muaj nuj nqi.

Qhov yooj yim thiab feem ntau to taub rau txhua leej txhua tus ib qho piv txwv - kev kho mob ntawm peb ntiaj chaw nyob ib ncig ntawm lub hnub, nyob rau hauv uas tag nrho cov sij hawm hloov qhov kev ncua deb nruab nrab ntawm lawv yog kev kawm mus rau lub xyoo voj voog. Ib yam li ntawd, nws yog rov qab mus nws lub rooj zaum, uas tau ua ib tug tag nrho lem, tus turbine hniav. Tag nrho cov dab yuav tau piav los ntawm ib tug zauv tus nqi raws li ib tug periodic muaj nuj nqi. By thiab loj, peb lub ntiaj teb yog cyclical. Thiab uas txhais tau hais tias ib tug periodic function yuav siv sij hawm ib qho tseem ceeb qhov chaw nyob rau hauv tib neeg lub cev.

Qhov yuav tsum tau rau kev kawm txog zauv nyob rau hauv kev tshawb xav tooj, topology, differential sib npaug , thiab leej geometrical suav coj mus rau lub rov tshwm sim nyob rau hauv lub puas tawm xyoo, ib tug tshiab qeb ntawm kev khiav dej num nrog txawv txawv zog. Lawv periodic zog noj tib yam qhov tseem ceeb ntawm cov ntsiab lus raws li ib tug tshwm sim ntawm txoj transformations. Lawv tam sim no siv nyob rau hauv ntau qhov chaw ntawm kev kawm txog zauv thiab lwm yam sciences. Piv txwv li, nyob rau hauv kev kawm cov teebmeem ntawm ntau yam vibrational yoj physics.

Nyob rau hauv ntau yam xyuam xim kev qhia no yog sib txawv cov ntsiab lus txhais ntawm ib tug periodic muaj nuj nqi. Txawm li cas los, tsis hais txog ntawm cov kev txawv no nyob rau hauv hais, lawv yog sib npaug, vim lawv piav tib yam thaj chaw ntawm cov nuj nqi. Qhov yooj yim thiab feem ntau pom tseeb tej zaum yuav cov nram qab no txhais. Muaj nuj nqi, tus nqi ntawm uas yog tsis raug hloov, yog hais tias peb ntxiv rau lawv sib cav ib tug xov tooj lwm yam tshaj pes tsawg, qhov thiaj li hu ua lub sij hawm ntawm cov nuj nqi denoted los ntawm tsab ntawv T yog hu ua periodic. Li cas tag nrho cov no txhais tau hais tias nyob rau hauv kev xyaum?

Piv txwv li, ib tug yooj yim muaj nuj nqi ntawm daim ntawv no: y = f (x) yuav los ua ib tug periodic yog X muaj ib tug tej yam muaj nuj nqis ntawm lub sij hawm (T). Los ntawm no txhais nws li nram no uas yog hais tias tus zauv tus nqi ntawm ib tug muaj nuj nqi muaj ib lub sij hawm (T) yog txhais nyob rau hauv ib tug ntawm cov ntsiab lus (x), ces nws cov nuj nqis kuj yuav paub x T + x - T. Qhov tseem ceeb point no yog hais tias thaum T yog pes tsawg yuav ib tug qhia tias yog leejtwg muaj nuj nqi. Periodic muaj nuj nqi yuav muaj ib tug infinite xov tooj ntawm txawv sij hawm. Nyob rau hauv lub ib thooj ntawm zoo tus neeg qhov tseem ceeb T tshwm sim nruab nrab ntawm tus nqi qis tshaj txog zauv qhia. Nws yog hu ua tus yuav tsum muaj lub sij hawm. Thiab tag nrho cov lwm yam tseem ceeb ntawm T nws yog ib txwm divisible. Qhov no yog lwm nthuav thiab tseem ceeb heev rau txawv teb cov cuab yeej.

Teem ib tug periodic function kuj muaj ntau yam zoo. Piv txwv li, yog tias T yog qhov yooj yim lub sij hawm ntawm cov kev qhia: y = f (x), ces los ntawm plotting no muaj nuj nqi, cia li txaus los tsim kom tau ib tug ceg nyob rau hauv ib tug ntawm lub sij hawm ntawm lub sij hawm ntev, thiab ces txav nws raws x axis rau nram qab no qhov tseem ceeb: ± T, ± 2T , ± 3T thiab thiaj li nyob. Nyob rau hauv xaus, nws yuav tsum tau muab sau tseg tias tsis tag nrho cov periodic function yog lub ntsiab lub sij hawm. Ib tug classic piv txwv ntawm no yog German mathematician Dirichlet muaj nuj nqi ntawm cov hauv qab no daim ntawv: y = d (x).