Foriya asinthe. Fast Foriya asinthe. Apawokha Foriya kusandutsa

Foriya kusandulika - kusintha, kusonkhana ntchito winawake wa variable weniweni. Opaleshoni imeneyi imagwiridwa nthawi iliyonse timazindikira phokoso osiyana. Khutu umabala zodziwikiratu "mawerengedwe" imene kukwaniritsa yathu yozindikira angakhoze kokha pambuyo Kupenda gawo masamu apamwamba. kumva limba mu kusinthika anthu yamanga, imene phokoso (ochiritsira vibrational zoyenda wa particles mu sing'anga zotanuka, amene kufalitsa mu mawonekedwe yoweyula mu olimba, madzi kapena gaseous sing'anga) amaperekedwa mu osiyanasiyana mfundo zotsatizana za mlingo buku la malankhulidwe a pamwamba osiyana. Patatha izi, ubongo akutembenukira zambiri mu phokoso zonse bwino.

Masamu Foriya kusandutsa

Kutembenuka mafunde wabwino kapena njira zina kugwedera (by umuna kuwala ndi nyanja mafunde ndi m'zinthu Nyenyezi kapena dzuwa) angathe kuchitidwa ndi mwa njira masamu. Choncho, pogwiritsa ntchito njira imeneyi, ntchito akhoza kukodzedwa mwa kuyambitsa ndondomeko vibrational anapereka zigawo zikuluzikulu sinusoidal, i.e. wavy zokhotakhota amene amapita ku osachepera kuti pazipita ndiyeno kachiwiri asatayike, ngati funde la nyanja. Foriya kusandulika - kusinthika ntchito limene limafotokoza gawo kapena matalikidwe aliyense sinusoid lolingana pafupipafupi makamaka. Gawo ndi poyambira a pamapindikira, ndi matalikidwe - wa msinkhu wake.

Foriya asinthe (zitsanzo tikuonera chithunzi) ndi chida champhamvu kwambiri, amene ntchito zosiyanasiyana za sayansi. Mu zina, ntchito ngati njira maikwezhoni m'malo ovuta amene akufotokoza njira zazikulu zikuchitika mchikakamizo cha kuwala, kutentha kapena mphamvu ya magetsi. Nthawi zina timatha inu kuthandauza kwa zigawo zonse mu waveforms zovuta, chifukwa izi zikhoza kukhala zoona kumasulira kuzipenya zosiyanasiyana komanso mu zimapangidwira, mankhwala ndi zakuthambo.

nkhani za m'mbiri

Munthu woyamba kugwiritsa ntchito njira imeneyi inali French masamu Zhan Batist Fure. Kutembenuka, kenako dzina lake, poyamba ntchito pofotokoza kutentha conduction limagwirira. Foriya moyo wake wonse wamkulu chinkhoswe mu kuphunzira katundu cha kutentha. Iye anapanga zopereka kwambiri kuti chiphunzitso masamu a mtima wa mizu ya maikwezhoni algebraic. Foriya anali katswiri wa kusanthula pa Ecole Polytechnique, Mlembi wa Institute of Egyptology, anali kutumikira lachifumu, omwe anachititsa chipwirikiti pa nthawi ya kumanga msewu wa Turin (motsogozedwa wake chatsanulidwa wa makilomita oposa 80 zikwi lalikulu la zithaphwi malungowa). Komabe, activism izi zonse sanaleke wasayansi chinkhoswe mu kusanthula masamu. Mu 1802 izo anachokera kuti aone kuti pali limene limalongosola kafalitsidwe kutentha mu zolimba. Mu 1807, wasayansi anapeza njira ya kuthetsa aone kuti pali ichi, chimene unadziwika ngati "Foriya kusintha".

matenthedwe kusanthula madutsidwe

Akatswiri ntchito njira masamu kufotokoza kutentha conduction limagwirira. Chitsanzo yabwino, mmene palibe vuto masovedwe ndi kafalitsidwe mphamvu matenthedwe ndi mphete chitsulo, gawo limodzi kumizidwa mu moto. Kuchita zinthu zatsopano Foriya wofiira gawo otentha mphete ndi kumuika m'manda mu mchenga chabwino. Kenako, miyezo kutentha ikuchitika pa mbali zosiyana zace. Poyamba, kutentha yogawa ndi osasamba: mbali ya mphete - ozizira, ndi zina - otentha, pakati mabacteria akhoza kusunga lakuthwa kutentha masinthidwe amtundu. Mnthawi yogawa kutentha kudutsa pamwamba zitsulo, kumakhaladi zambiri yunifolomu. Choncho, posachedwapa, ndondomeko izi zimatengera mtundu wa yoweyula sine. Zithunzi Choyamba pang'onopang'ono kumawonjezera komanso amachepetsa bwino, molondola malamulo a kusintha kwa cosine kapena ntchito sine. Wave pang'onopang'ono equalized ndi chifukwa kutentha amakhala yunifolomu padziko lonse la mphete.

Woyambitsa njira imeneyi ankaganiza kuti yogawa koyamba ndi osasamba ndithu akhoza decomposed mu angapo mafunde pulayimale sine. Aliyense wa iwo adzakhala gawo lake (udindo koyamba) ndi kutentha kwake pazipita. Choncho aliyense ngati kusintha chigawo ku osachepera kuti pazipita ndi ku kumaliza zisinthe kuzungulira nthawi mphete inteja. Chigawo chimodzi ndi nthawi imene ankatchedwa amgwirizano achikhazikitso, ndi mtengo ndi ziwiri mmasiku Awiri kapena zambiri - wachiwiri ndi zina zotero. Mwachitsanzo, ntchito masamu kuti limafotokoza kutentha pazipita, gawo kapena malo wotchedwa Foriya kusandutsa wa ntchito yogawa. Scientist anabweretsa chigawo umodzi kuti n'zovuta kufotokoza masamu, chifukwa zida zosavuta ntchito - mizere ya sine ndi cosine, kuchuluka kwa kupereka yogawa koyamba.

Akamanena za kuwunika

Kugwiritsa kusanthula izi kutembenuka kwa yogawa kutentha pa chinthu cholimba, kukhala ndi mawonekedwe annular, ndi masamu kuti kuwonjezeka nthawi zigawo sinusoidal kuyambitsa damping ake mofulumira. Izi akuonekera pa harmonics chachikulu ndi wachiwiri. Kutentha komaliza ukufika kawiri mfundo pazipita ndi osachepera mu chiphaso imodzi, choyamba - kamodzi kokha. Iwo likukhalira kuti mtunda anayenda ndi kutentha mu amgwirizano chachiwiri ndi theka la pakati. Komanso, masinthidwe amtundu wa theka lachiwiri kudzakhala steeper kuposa poyamba. Choncho, kuyambira kwambiri matenthedwe kamwazi akudutsa wamasiye mtunda kochepa, ndiye adzakhala damped amgwirizano kanayi mofulumira kuposa zikuluzikulu, monga ntchito za nthawi. Otsatirawa ndondomeko adzakhala mofulumira. Masamu ankakhulupirira kuti njira imeneyi kumatithandiza kudziwa ndondomeko yogawa koyamba kutentha ndi nthawi.

kuitana m'nthawi

Foriya kusandutsa aligorivimu wakhala zovuta maziko ongolankhula wa masamu pa nthawi. Mu zaka za m'ma chakhumi ndi chisanu ndi chinayi, ambiri asayansi otchuka kuphatikizapo Lagrange, Laplace, Poisson, Legendre ndi Biot sanamvere Satana ananena kuti kutentha yogawa koyamba ndi linakwiriridwa m'zigawo mu mawonekedwe a yoweyula wachibadidwe ndi pafupipafupi apamwamba. Komabe, Academy of Sciences sanathe amanyalanyaza zotsatira analandira masamu, ndi kupereka iye Prize kwa chiphunzitso cha kutentha conduction ya malamulo, komanso kuchititsa poyerekeza ake ndi zatsopano thupi. Mu njira Foriya, ndi wokana chachikulu ndi chakuti ntchito discontinuous ukufanizidwa ndi ndalama ntchito angapo sinusoidal, amene mosalekeza. Ndipotu, pofotokoza akuphulikira molunjika ndi yokhota kumapeto mizere. wasayansi Contemporary anali asanawerengepo wakumana ndi lotereli, pamene ntchito discontinuous pofotokoza kuphatikiza mosalekeza, monga quadratic, liniya, sine kapena exhibitor. Kukachitika kuti masamu zoyenera kunena wake, Uwerenge ndi mndandanda wopandamalire ntchito trigonometric ayenera okha liwiro enieni. Ngakhale maganizo amenewa ankaoneka chotheka. Komabe, ngakhale kukayikira ena ofufuza (mwachitsanzo Claude Navier, Sofi Zhermen) kunanditsegula kuchuluka kwa kafukufuku ndi kuwatulutsa ndi kusanthula yogawa kutentha. masamu A, azungu anapitiriza kuvutika funso kaya ndalama ntchito angapo sinusoidal yafupika ndi chizindikiro chenicheni cha akuphulikira.

Mbiri 200 chaka

Chiphunzitsochi ali kusanduka zaka mazana awiri, lero ndi potsiriza anapanga. Mothandizidwa ndi ntchito okhudza malo kapena zosatha osweka m'zigawo sinusoidal kuti ndi pafupipafupi, gawo ndi matalikidwe. kutembenuka Izi akamagwira njira ziwiri zosiyana masamu. The oyamba ntchito ngati pamene gwero ndi ntchito mosalekeza, ndipo chachiwiri - mu choncho kumene ukufanizidwa ndi kuchuluka kwa kusintha apawokha payekha. Ngati akuti ndi kuwapeza mfundo zomwe anafotokozedwa pa intervals apawokha, zikhoza kugawidwa mu angapo apawokha sinusoidal mafurikwense mawu - kuchokera ku chotsikitsitsa kenako kawiri, katatu, ndi zina zotero pamwamba wofunikila. ndalamazo amatchedwa ndi Foriya zino. Ngati mawu koyamba amapereka phindu la nambala iliyonse weniweni, izo zikhoza unagwa mu mafurikwense angapo sinusoidal n'kotheka. Iwo akutchedwa Foriya integral, ndi chigamulo zikusonyeza wasinthika kugwira ntchito yofunika. Kaya njira chopezera kusintha chilichonse pafupipafupi zisonyeze manambala awiri: matalikidwe ndi pafupipafupi. mfundo izi chimaonetsera limodzi chiwerengero zovuta. Mawu ovuta zosintha chiphunzitso pamodzi ndi Foriya kusandulika kuchita kuwerengetsera analola kapangidwe madera osiyanasiyana magetsi, ndi kusanthula Phokoso makina, kuphunzira limagwirira yoweyula kafalitsidwe ndi mzake.

Foriya kusandutsa lero

Masiku ano, kuphunzira ndondomeko kwenikweni inali kupeza njira zothandiza kusintha kwa ntchito kutembenuza ilo mmbuyo kwa maganizo. njira imeneyi imatchedwa Foriya mwachindunji ndi osiyanitsidwa asinthe. Kodi zikutanthauza chiyani? Pofuna kudziwa yofunika ndi kupanga Foriya mwachindunji asinthe, mungathe kugwiritsa ntchito njira masamu, koma mukhoza analytic. Ngakhale kuti pamene ntchito mchitidwe pali mavuto ena, integrals kwambiri kale apezeka ndi kulowa mu mabukhu masamu. Ndi mawu thandizo la njira n'zosangalatsa kumva kuchita masamu, mawonekedwe a ozikidwa pa deta komanso ntchito amene integrals mu magome zikusowa, ndipo iwo ndi ovuta taganizani mu maonekedwe mawunikidwe.

Pamaso pa Kubwera kwa kuwerengetsera kompyuta zomangamanga masinthidwe akhala yosasangalatsa kwambiri, iwo amafuna Buku kuphedwa kwa ambiri ntchito masamu kuti zimadalira chiwerengero cha mfundo kufotokoza ntchito yoweyula. Magawowa kuthetsa lero, pali zochitika zapadera amaloledwa kugwiritsa latsopano njira mawunikidwe. Choncho, mu 1965, Dzheyms Kuli ndi Dzhon Tyuki analenga mapulogalamu anatchedwa "Fast Foriya Sinthani". Iwo amapulumutsa nthawi ya mawerengedwe ndi kuchepetsa chiwerengero cha multiplications mu kusanthula pamapindikira. "Fast Foriya Sinthani" njira mogwirizana ndi kugawa pamapindikira mu chiwerengero chachikulu cha mfundo yunifolomu nyemba. Choncho, chiwerengero cha multiplications yafupika ndi theka pa yomweyo kuchepetsa chiwerengero cha mfundo.

Kugwiritsa ntchito Foriya kusandutsa

Zimenezi ntchito zosiyanasiyana: Mu chiphunzitso chiwerengero, sayansi, processing chizindikiro combinatorics, chiphunzitso Mwina, cryptography, ziwerengero oceanography, Optics, zowulutsira, ndi geometries ena. mwayi wolemera ntchito zake zochokera zingapo zochititsa zothandiza, ndipo amatchedwa "katundu wa Foriya kusandulika." Tiyeni tione iwo.

1. Ntchito kutembenuka ndi liniya woyendetsa ndi normalization lolingana ndi unitary. katundu Ichi chikudziwika ngati Parseval Lingaliro Lovomerezeka, kapena mu nkhani zambiri, Lingaliro Lovomerezeka Plansherelja kapena Pontrjagin dualism.

2. Kutembenuka ndi kusintha. Komanso, zotsatira zosiyana ndi mawonekedwe zayamba zofanana mu mwachindunji akulankhula.

3. sinusoidal mawu zofunika udindo wawo kusiyanitsidwa. Izi zikutanthauza kuti chifaniziro zimasintha maikwezhoni liniya ndi koefishienti zonse mu algebraic ochiritsira.

4. Malinga "convolution" Lingaliro Lovomerezeka, ndondomeko amapanga opaleshoni lovuta chulutsa pulayimale.

5. apawokha Foriya Sinthani akhoza msanga cholinga pa kompyuta ntchito "mwamphamvu" njira.

Kusiyana kwa Foriya ndi kusandutsa

1. Nthawi zambiri mawuwa amagwiritsidwa ntchito ponena kusintha mosalekeza, kupereka chilichonse akuti quadratically integrable monga Uwerenge zovuta kwakukulu kwambiri akuti ndi mafurikwense yeniyeni okhota ndi amplitudes. mtundu ali mitundu yosiyanasiyana amene angakhale osiyana koefishienti zonse. The njira yothandizira zikuphatikizapo tebulo kutembenuka, amene angapezeke mu mabukhu masamu. Nkhani zowombetsa mkota ndi kutembenuka fractional, umene Ntchito imeneyi adzaukitsidwa kuti kufunika mphamvu yeniyeni.

2. The njira yothandizira ndi generalization wa njira kale za Foriya mndandanda kumatanthauza kuti aliyense ntchito nthawi kapena mawu, zomwe zili mwa malo ochepa ndipo zikuimira iwo monga mndandanda wa sinusoids.

3. apawokha Foriya asinthe. Njira ntchito kompyuta kwa masovedwe sayansi ndi processing digito chizindikiro. Kugwira mtundu wa mawerengedwe chofunika kuti ntchito kudziwa pa apawokha ya mfundo munthu, nthawi kapena zochepa dera m'malo mosalekeza Foriya integrals. Signal kutembenuka Pankhaniyi ankayimiridwa ngati Uwerenge sinusoids. Ntchito "mwamphamvu" njira chizathandiza ntchito njira digito zolinga zonse zopindulitsa.

4. zenera Foriya asinthe ndi view zowombetsa mkota njira yakale. Mosiyana ndi njira muyezo pamene mbendera sipekitiramu ntchito amene walandiridwa mu uthunthu wonse wa kuli variable izi ndi chidwi makamaka kuno yekha m'dera pafupipafupi yogawa pokhalabe ndi variable pachiyambi (nthawi).

5. Foriya ziwiri ooneka enieni asinthe. Njira ntchito ntchito ndi magulu awiri azithunzi omwe tikunena deta. Zikatero, kutembenuka imagwiridwa mu njira imodzi, ndiyeno - mu ena.

Pomaliza

Masiku ano, njira Foriya litakhazi- mizu minda zosiyanasiyana za sayansi. Mwachitsanzo, mu 1962 zinatipatsa mawonekedwe a DNA awiri helix ntchito Foriya kusanthula molumikizana ndi X-ray mapindidwe akuwala. timibulu Recent lolunjika pa ulusi DNA, chifukwa mu fano amene analandira ndi mapindidwe akuwala, olembedwa pa filimu. chithunzi ichi anapereka mfundo za ubwino matalikidwe ndi ntchito Foriya kusandutsa dongosolo lino krustalo. deta gawo akamagwira kuyerekezera makadi DNA mapindidwe akuwala ndi makadi kuti analandira mu kusanthula nyumba ofanana mankhwala. Chifukwa cha zimenezi, akatswiri anabwezeretsa dongosolo galasi - ntchito pachiyambi.

Foriya kusandutsa kumathandiza yaikulu mu phunziro la m'mlengalenga, zakuthambo zipangizo michenga yopangira zida zamagetsi ndi madzi, zowulutsira mayikirowevu, oceanography, Rada, seismology ndi mayeso zachipatala.