kauchi-kowalewski pramey

ganitat, kauchi-kovlevskya pramey (kauchi-kovlevsky pramey mhanoon dekhil lihile jaate) heey kauchi prarambhik moolya samasyanshi sambandhit vishleshanatmak aanshik vibhedak samikaranansathi mukhya sthanik astitva aanee advitiyata pramey aahe. eka vishesh prakaran siddha jhaale aanee sampoorn parinam siddha jhaala.
pratham kram kauchi-kovlevskya pramey.
heey pramey jevha gunank vishleshanatmak karye asatat tevha 'aine' parimananmadhil 'emm' vibhedak samikarananchya pranalichya upayanchya astitvabaddal aahe. pramey aanee tyacha purava ektar vastavik kinwa jatil chalanchya vishleshanatmak karyansathi vaidh aahet.
k" heey ektar vastavik kinwa jatil sankhyanche kshetra darshavu dya aanee "v" = "k" "m" aanee "" w "=" "k" "n" asey mhanuya ". aaa" 1, asey mhanuya..., a" "n" "−1 hii vishleshanatmak karye aahet jee" "w" "×" "v" "madheel (0,0) chya kahee shejaravar paribhashit kelee jaatat aanee" "m" "×" "m" "matrixmadhye moolye ghetat aanee" "b" "heey tyach shejarvar paribhashit kelelya" "v" "madheel moolyansah vishleshanatmak karya asoo dya". mug 'doubleu' madhye 0 chaa eka shejari aahe jyavar quasilinear kachee samasya aahe
prarambhik sthitisah
atiuchch prushthbhagavar
tyache eka adviteey vishleshanatmak uttar aahe "f": "w" → "v" 0 chya jawal aahe.
leviche udaharan darshavite qee heey pramey serve gulgulit karyansathi adhik samanyatah vaidh nahee.
heey pramey amoort (vastavik kinwa jatil) vector spacemadhye dekhil sangitale jaau shakate. v" aanee "w" heey "n" = diim "w" saha maryadit-aayami vastavik kinwa jatil vector space asoo dya. aaa" 1, asey mhanuya..., a" "n" "−1 heey shevati (" "v" ") moolyansah vishleshanatmak karye aanee" "b" "heey" "v" "madheel moolyansah vishleshanatmak karya aahe, jeey" "w" "×" "v" "madhye (0,0) chya kahee shejari paribhashit kele aahe". yaa prakaranat, samaan parinam lagoo hoto.
vishleshanatmak mothya pramanadvare purava.
aanshik vibhedak samikaranachya donhi bajunna aupcharik shakti malika mhanoon vistarle jaau shakate aanee "f" sathee aupcharik shakti malikechya gunankansathi punaravrutti sambandh dile jaau shakatat jeey advitiyapane gunank nirdharit karatat. a" "i" aanee "b" chey teller maliketil gunank heey matricks aanee vector normmadhye eka sadhya scalar tarksangat vishleshanatmak karyadvare pramukh kele jaatat. yaa karyacha samavesh asalelya sambandhit scalar kauchi samasyemadhye "a" i "aanee" b "aivaji eka spasht sthanik vishleshanatmak upay aahe. tyachya gunankanchi paripoorn moolye mool samasyechya nikashanna pramukh banavtat; mhanoon aupcharik shakti malikeche samadhan ektrit hone aavashyak aahe.
jethe scalar dravan ekatra yete.
uchch-kramatil kachee-kovlevskya pramey.
jarr 'f' aanee 'f' j 'hii 0 chya jawalchi vishleshanatmak karye asateel, tarr naun-linier cotchy samasya
prarambhik attins
0 chya jawal eka adviteey vishleshanatmak upay aahe.
heey pahilya kramankachya samasyepasun pudhe yete, jyamadhye ujavya bajula bajula "etch" chya vyutpananna vector-moolya karyache ghatak mhanoon vicharat ghetale jaate.
udaharanadakhal.
ushnateche samikaran
attis
eka adviteey aupcharik shakti malika upay aahe (sumare vistarit (0,0)). tathapi, hii aupcharik shakti malika "tii" chya konatyahi shunyetar mulyansathi ektrit hott nahee, mhanoon moolchya parisarat konatehi vishleshanatmak upay naheet. yavarun hii sthitee disun yete ."aaa". + "jeey" ≤ "keey" varr sodale jaau shakat nahee. (heey udaharan kovalevskimule aahe.)
kauchi-kovlevskya-kashiwara pramey.
vishleshanatmak gunank asalelya rekheey aanshik vibhedak samikarananchya pranalinsathi, kauchi-kovlevskya-kashiwara pramey, yache vyapak samanyikaran aahe, kaaran
. yaa prameyamadhye dii-moduleschya bhashet sadar kelelya samaroop rachanacha samavesh aahe. astitva sthitimadhye pratyek samikaranachya eksandh nasalelya bhaganmadhye susangatata sthitee aanee vyutpann functor sootra _ 8 gayab hone samavisht aahe.
udaharanadakhal.
sootra _ 9. sootra _ 10 nishchit qaraa. jarr aanee susangatatechya atinche sootra _ 13 satyapit kele asel tarach pranali sootra _ 11 chey samadhan sootra _ 12 aahe. eka adviteey upay midvinyasathi aapan prarambhik sthitee sootra _ 14 samavisht karane aavashyak aahe, jethe sootra _ 15 aahe.

