pravasache vitaran

pravasache vitaran (kinwa gantavya nivadi kinwa vibhagiy aadanpradan vishleshan) haah paramparik chaar-charaniy vahtook andaj modelmadhil dusra ghatak aahe (pravas nirmitinantar, parantu marg nivad aanee marg assignmentpurvi). hii payari 'trip table' vikasit karnyasathi tripmakerschya utpattishi aanee gantvyasthananshi julate, eka matricks joou pratyek mool thikanahun pratyek gantvyasthanakade gantvyasthanakade ekoon sankhya darshavito. aitihasikdrushtya, haah ghatak vahtook niyojan modelcha sarvat qamee vikasit ghatak rahila aahe.
jetheh "t" "ij" = mool "i" pasoon gantvyasthan "j" paryantchya kelelya. lakshat ghya qee karnavaril sahalinche vyavharik moolya, udaa.jee. kshetra 1 teey kshetra 1 paryant, shoonya aahe kaaran aantar-vibhagiy pravas hott nahee.
kamachi sahal vitaran haah pravasachya maganichya pratimananna lock nokri kashee ghetat heey samajoon ghenyacha marg aahe. kirana kharedisathi thikan nivadane yasarkhya itar (kaam nasalelya) upkramansathi sahaliche vitaran model aahet, jeey tyach sanrachaneche anusaran karatat.
itihas.
gelya kahee varshant, modellersney pherii vitaranachya anek vegvegalya sutrancha vapar keela aahe. pahile mhanje fratar kinwa vadhiche model (jeey uddeshane uddeshane farak karat navhate). yaa sanrachanene vadhivar aadharit bhavishyatil aadhar varsh pravas saraniche vistar kele, parantu vadhiv puravatha kinwa pravasachya paddhati aanee garditil badalanmule badalatya sthanik sulbhatecha vichar keela nahee. (sadhe vaadh ghatak model, bhatti model aanee detroit model heey ekach kalavadhit vikasit kelele model aahet)
pudhil vikasit models mhanje gurutvakarshan model aanee madhyavarti sandhee model. sarvat mothya pramanavar vaparale jaanare sootra ajunahi gurutvakarshanache model aahe.
marylandchya baltimoremadhil rahdaricha abhyas kartana, alaan woorheesne jaminichya vaparachya aadhare rahdarichya namunyancha andaj lavnyasathi eka ganiteey sootra vikasit kele. jagbharatil asankhya vahtook aanee sarvajanik bandhkam prakalpanchya rachnet yaa sutrane mahattvapoorn bhoomika bajavali aahe. tyanni "rahdarichya halchalicha eka samanya siddhant" (voreheese, 1956) lihila, jyane pravas vitaranasathi gurutvakarshanache model lagoo kele, jeey eka bhagat nirman jhalelya jhalelya bhashantar eka matrixmadhye karate jeey pratyek mool thikanahun pratyek gantvyasthanaparyantchya ekoon sankhya olakhate, jeey nantar networkwar loaded kele jaau shakate.
1960 chya dashkatil anek pratikruti prakaranchya mulyankanamule assa nishkarsh nighala qee "gurutvakarshan pratikruti aanee madhyavarti sandhee pratikruti yanni washingtonsathi 1948 aanee 1955 chya pherii vitaranache anukaran karnyat samaan vishvasarhata aanee upayuktata siddha kelee.see."(henyu aanee pires 1966). jaminichya vaparat badal hott asalelya bhagat fratar modelmadhye kamjori asalyache disun aale. sanganakeey sulbhatemule, nirikshan kelelya paristhitishi julavun ghenyasathi ektar titkech changle calibrate kele jaau shakate asey modelsmadhil tulana darshavit asalyane, gurutvakarshanache models madhyavarti sandhee modelspeksha adhik vyapakpane pasarale. darmyanchya sandhinchya pratimanatil kahee saiddhantik samasyanvar whiteker aanee west (1968) yanni charcha kelee hotee, jyat eka kshetrat nirman jhalelya serve serve hishob karnyat asamarthatebaddal charcha kelee hotee, jyamule tyache mapan karane adhik katheen hote, jaree maryada hatalanyasathi tantra ruiter (1967) dware vikasit kele gele aahe.
logit aanee itar swatantra nivad tantranchya vikasasah, pravasachya maganisathi naveen, loksankhyechya drushtine vibhedak drushtikonacha prayatna karnyat aala. pravasachi sambhavyata nishchit karnyasathi pravasachya velevyatirikt itar chalancha samavesh karoon, tyat pravasachya vartanacha changla andaj asane apekshit aahe. loggit model aanee gurutva model heey willson (1967) yanni moolatah sankhyikeey yantrikimadhye, entropy maximization modelmadhye vaparlya jaanarya swarupache asalyache darshavile aahe. yaa pratimancha vapar sankalpanet vegala aahe, kaaran gurutvakarshan pratiman pravasachya velenusar, kadachit samajik-aarthik chalandware starikrut, pravasachi sambhavyata nirdharit karnyasathi pratibadha vaparte, tarr swatantra nivad drushtikon tyaa chalanna upayuktata kinwa pratibadha karyat aanato. swatantra nivad modelsna andaj lavnyasathi adhik mahitee aanee adhik sanganakeey velechi aavashyakta asate.
baine-aakiva aanee lerman (1985) yanni kaam aanee kaam nasalelya sahalinsathi loggit formulation vapar karoon gantavya nivad aanee mode nivad modelsche sanyojan vikasit kele aahe. sanganakeey tivratemule, yaa sutranmadhye andajanusar mothya jilhyanmadhye kinwa vartulanmadhye vahtook kshetra ektrit karnyacha cull hota. sadhyachya vaparat, udaharanarth portland, oregonmadhye vaparlya jaanarya vahtook niyojan models kahee model gantavya nivadisathi loggit formulation vapartat. elon (1984) yanni pravas vitaranasathi sammishra pratibadha nirdharit karnyasathi loggit aadharit mode nivad modelmadhil upayuktata vaparlya. tathapi, mode nivad logg-samcha vapar karoon tyaa drushtikonatun asey soochit hote qee gantavya nivadichi paddhat nivadanyapramanech tyach chalanvar avalambun asate. levinson aanee kumar (1995) heey vajan ghatak mhanoon mode nivad sambhavyatecha vapar karatat aanee kaam aanee kaam nasalelya sahalichya uddeshansathi pratyek modasathi vishisht pratibadha karya kinwa "eff-vakr" vikasit karatat.
ganeet.
vahtook niyojan prakriyechya yaa tappyavar, kshetriy aadanpradan vishleshanachi mahitee mool-gantavya taktyat aayojit kelee jaate. davikade pratyek vibhagat tayar kelelya kelelya soochibaddha aahet. varchya bajula kshetranchi yadee aahe aanee pratyek kshetrasathi aamhi tyache aakarshan soochibaddha karato. takta "n" x "n" aahe, jethe "n" = kshetranchi sankhya.
aaplya tablemadhil pratyek kakshat 'i' teey 'j' yaa kshetraparyantchya ekoon sankhya asane aavashyak aahe. jaree aaplyakade pankti aanee stambhanchi ekoon sankhya asali taree, aaplyajaval adyap yaa aatalya peshichya sankhya naheet. asha prakare deta aayojit kelyane, "tii" = 1 yaa shirshakachya sarnyansathi peshi bharane heey aamche kaam aahe, udaharanarth "tii" = "aine".
pratyakshat, gharguti mulakhatichya pravas sarvekshan deta aanee aakarshan vishleshanatun aamchyakade 'tii' = 1 sathee peshi mahitee aahe. deta eka namuna aahe, mhanoon aamhi namuna vishvasathi samanya karato. vibhagiy aadanpradan vishleshanasathi vaparali jaanari tantre "tii" = 1 detala basnara anubhavjanya niyam shodhatat. tyanantar too niyam 'tii' = 2, 'tii' = 3, 'tii' = 4, ityadinsathi peshi deta tayar karnyasathi vaparla jaato., teey "tii" = "aine".
vibhagiy aadanpradan model karnyasathi vikasit kelelya pahilya tantrat yasarkhe model samavisht aaheh
kutheh
zoan "i" mule "t" i "trips tayar hotat; zoan" j "madhye kitee jaatil? teey serve thikananchya aakarshanachya tulanet 'jeey' chya aakarshanavar avalambun asate; kshetra 'aay' pasoonchya antarachya aadhare aakarshan qamee hote. aapan serve thikananchya tulanet 'jeey' chya apurnankachi ganana karato aanee 'tii'; 'aay' laa tyacha gunakar karato.
niyam anekada gurutvakarshanachya swarupacha asatoh
kutheh
parantu kshetriy vinimay paddhatimadhye, aapan loksankhyeaivaji pravasachya utpattishi ("tii"; "aay") aanee pravasachya gantavye ("tii"; "jeey") sambandhit sankhya vaparato.
anek pratikruti prakar aahet kaaran aapan vajan aanee vishesh calibration parameters vaparu shakato, udaa.jee., asey lihile jaau shakateh
kinwa
kutheh
gurutvakarshan model.
gurutvakarshanache model thikananmadhil (udaharanarth ghare aanee kamachya thikani) sthool sambandh spasht karate. done thikananmadhil parasparsanvad tyanchya darmyanchya vadhatya (antar, vel aanee kharch) pramananusar qamee hoto, parantu pratyek thikanchya kriyakalapanchya pramanasah sakaratmakpane sambandhit aahe (issard, 1956) asey asey kalapasoon manale jaate. bhautikshastrashi sadrushya sadhatana, releene (1929) relicha kirkol gurutvakarshanacha niyam tayar keela aanee jeey. kyu. stuartne (1948) jansankhyikiy gurutvakarshan, shakti, urja aanee sambhavyatechya vyakhya tayar kelya, jyanna aata sulabhata mhanatat (hanson, 1959). 1/antaracha antar kshay ghatak samanyikrut kharchachya adhik vyapak karyat adyayavat keela gela aahe, joou aavashyakpane resheey nahee-nakaratmak ghatank haah pasantiche swaroop asato.
gurutvakarshanachya pratimechi moolbhut antarnihit ektrit sambandh mhanoon anek vela pushti kelee gelee aahe (scott 1988, servero 1989, levinson aanee kumar 1995). parasparsanvadachya ghasaranicha darr (jyala paryayipane, pratibadha kinwa gharshan ghatak kinwa upayogita kinwa pravrutti karya mhanatat) anubhavjanyapane mojala pahije aanee sandarbhanusar badalato.
gurutvakarshanachya pratimanachi upayuktata maryadit karane heey tyache ekoon swaroop aahe. dhoran jaree ektrit patalivarhi karya karat asale, taree adhik achook vishleshan shakya titka vel mahitichi sarvat tapshilvar patali rakhoon thewel. mothya sankhyene vyaktinchi nivad spasht karnyat gurutvakarshanache model khoop yashasvi asale taree, konatyahi vyaktichi nivad andajit mulyapeksha khoop badalate. shahari pravasachya maganichya sandarbhat lagoo kelyapramane, visangati pramukhyane vel, antar aanee kharch aahet, jaree kahivela adhik vistrut upayuktata abhivyaktinchya vaparasah swatantra nivad models vaparali jaatat, tasech utpann kinwa vahanachya malkidware starikaran kele jaate.
ganitiyadrushtya, gurutvakarshanache model anekada asey swaroop dharan karateh
kuthe? 
heey duppat maryadit aahe, yaa arthane qee konatyahi 'aay' sathee modelane andaj lavalelya 'aay' pasoon ekoon ekoon sankhya nehmi (yantrikdrushtya, konatyahi parameter mulyansathi) 'aay' pasoon ekoon ekoon sankhya asate. tyachpramane, modelane andaj lavalelya 'jeey' chya ekoon ekoon sankhya konatyahi 'jeey' sathee 'jeey' chya ekoon ekoon vastavik sankhyeitaki aahe.
entropy vishleshan.
willson (1970) haah vibhagiy devanghevanichya samasyebaddal vichar karnyacha aanakhi eka marg deto. yaa vibhagat willsonchya karyapaddhaticha vichar karoon madhyavarti kalpana samajoon ghetalya jaatat.
suruvat karnyasathi, kahee sahali vicharat ghya jithe mool kshetrat saat lock gantavya kshetranmadhye saat saat pravas karatat. asha sahalichi eka rachana ashee aselah
0 kuthe! = 1.
tee rachana 1,260 prakare disu shakate. aapan pravasanche swaroop kitee prakare ghadale asave yachee ganana kelee aahe aanee ganana spasht karnyasathi, prathamik aakadevarimadhye khoop kahee bolalya gelelya naane fekanyachya prayoganchi aathvan karoon deuya.
dwimukh naane kitee prakare yeu shakate heey sootra _ 26 aahe, jethe n mhanje aapan naane kitee vela fekato. jarr aapan ekada naane fekale tarr teey sheersh kinwa shepativar yeu shakate, sootra _ 27. jarr aapan teey donada fekale tarr teey etch. etch., etch. tii., tii. etch., kinwa tii. tii., chaar marganni aanee sootra _ 28 varr yeu shakate. chaar nanee serve shirshanvar yet aahet yabaddal vishisht prashna vicharanyasathi, aapan sootra _ 29 mojato. done sheersh aanee done shepati sootra _ 30 asateel. aapan samikaran sodavat aahot.
eka mahattvacha muddah assa aahe qee jasjase 'aine' mothe hott jaate, tasatase aapale vitaran adhikadhik shikharavar pohochate aanee sambhavya sthiticha vichar karane adhikadhik vajvi tharate.
tathapi, bahudha sthitichi kalpana yaa vicharatoon yet nahee; tee sankhyikeey yantrikimadhun yete, jeey willsonla changle dnyat aahe aanee vahtook niyojakanna itake changle dnyat nahee. sankhyikeey yantrikicha parinam assa aahe qee avarohi malika asanyachi shakyata jaast aahe. vargatil divyanmadhun divyanmadhun urjecha vargatil havevar kassa parinam hott aahe yacha vichar qaraa. jarr parinam chadhatya maliket jhaala tarr anek anoo aanee renunvar khoop parinam hoil aanee kahee anoonvar thoda parinam hoil. utaratya malikecha anekanvar farsa parinam jhaala nasata kinwa farsa jhaala nasata aanee keval kahee mojkyach lokanvar khoop parinam jhaala asata. aapan urjechi dileli patali gheu shakato aanee chadhatya aanee utaratya maliket uttejana patalichi ganana karoo shakato. vareel sootra vaparoon, aapan vishisht malika ghadanyachya marganchi ganana karoo aanee aapan assa nishkarsh kadhu qee avarohi malika varchasva gajavate.
too qamee-adhik boltzmancha niyam aahe,
mhanjech, konatyahi vishisht uttejana patalivaril kann "jeey" heey jaminivaril avasthetil kananche nakaratmak ghatankiy karya, sootra _ 33, uttejana patali, sootra _ 34 aanee eka mapdand sootra _ 35 asel, jeey pranalitil kananna upalabdh asalelya (sarasari) urjeche karya aahe.
vareel done parichhed heey yaa nondinchya aavakyabahercha vishay asalelya gibsney vikasit kelelya gananechya ektrit paddhatinshi sambandhit aahet.
oo-dii matrixkade parat jaatana, lakshat ghya qee oo aanee dii sarvekshanatun aanee trip generationvaril aamchya purvichya kamatoon aamhala jitaki mahitee milel titaki aamhi vaparali nahee. purvi vaparlya gelelya oo-dii matrixmadhil tyach pravas namunyasathi, aamchyakade pankti aanee stambhanchi ekoon sankhya asel, i.eae.:
charahi lock kase pravas kartil yacha vichar qaraa, 4!/(2!1!1!) = 12; teen lokancha vichar qaraa, 3!/(0!2!1!) = 3. serve pravas 12 × 3 = 36 marganni ekatra keela jaau shakato. asha prakare, ferichi sambhavya rachana stambh aanee panktichya ekoon sankhyemule khoop maryadit asalyache disun yete.
aapan haah muddah aaplya matricks purvichya kamasah aanee aaplyala asey mhanayache aahe qee bahudha sthitichya kalpanesah ekatra thevato
yaa vishayat
kutheh
aanee hii samasya aahe jee aapan varr sodavali aahe.
willson aanakhi eka vichar jodato; too pranalila upalabdh urjechya pramanat maryadit karato (i.eae., paisa), aanee aamchyakade atirikt maryada aahe,
jethe "see" heey upalabdh sansadhananche praman aahe aanee sootra _ 13 heey "aay" teey "jeey" paryantchya pravasacha kharch aahe.
aataparyantchya charchet willsonchya karyatil madhyavarti kalpana aahet, parantu aapan adyap tyaa thikani pohochalelo nahee jithe vachak model olakhel kaaran teey willsonne tayar kele aahe.
pratham, lagrangian gunak vaparoon jastit jaast karnyasathi sootra _ 41 karya lihinyasathi, aamchyakade aaheh
jethe sootra _ 43 aanee sootra _ 35 heey lagrange gunak aahet, sootra _ 35 urja bhavna asalele aahet.
dusare mhanje, sootra _ 46 aivaji naisargik logg (ln) jastit jaast karane soyiche aahe, tyasathi aapan sterlingcha andaj vaparu shakato.
tyamule
tisare, jastit jaast moolyamapan kartana, aamchyakade aahe
upayasah
shevati, sootra _ 2 chey heey moolya aaplya nirbandh samikarananmadhye parat badaloon, aamchyakade aaheh
aanee, sthir gunankanna yog chinhachya baher gheuun
jaau dya.
aamchyakade aahe.
jeey mhanate qee sahalichya sarvat sambhavya vitarnamadhye gurutva modelche swaroop aahe, sootra _ 2 heey sahalichya utpattichya aanee gantvyasthananchya pramanat aahe. sthirank sootra _ 58, sootra _ 59 aanee sootra _ 35 heey nirbandh purn jhaale aahet yachee khatri karatat.
aata gananekade valalyas, aaplyala eka mothee samasya aahe. pratham, aamhala 'see' chey moolya mahit nahee, jeey aamhi aadhi sangitale hote qee upalabdh paishanshi sambandhit hote, tee eka kharch maryada hotee. parinami, aaplyala sootra _ 35 vegvegalya mulyansathi nishchit karave lagel aanee nantar sootra _ 58 aanee sootra _ 59 sathee mulyancha sarvottam sanch shodhava lagel. aaplyala sootra _ 35 mhanje kaay heey mahit aahe-sootra _ 35 chey moolya jitke jaast asel, pravas kelelya sarasari antarachi kimmat titaki qamee asel. (aadhi namood kelelya boltzmanchya niyamatil sootra _ 35 chee tulana qaraa.) dusare mhanje, sootra _ 58 aanee sootra _ 59 chee moolye ekmekanvar avalambun asatat. mhanoon sootra _ 35 chya pratyek mulyasathi, aapan punaravrutti upay vaparla pahije. heey karnyasathi sanganak karyakram aahet.
vilasanachi paddhat laurie modelver lagoo karnyat aalee aahe.
prashna.
gardi.
anek suruvatichya modelschya vaparamadhil eka pramukh tota mhanje done thikananchya darmyan pravas karanyachi sambhavyata nirdharit karnyat rastyanchya jaalyavaril gardichya pravasacha vel vicharat ghenyat asamarthata. jaree volne 1963 chya suruvatilach abhipray yantrana kinwa "niyukt kinwa vitarit praman, pravasacha vel (kinwa pravas 'pratikar') aanee marg kinwa pranali kshamata yanchyatil parasparavalamban" yaa sanshodhanachi nond kelee asali, taree heey kaam abhisaranachya kathor chachanyansah kinwa tathakathit "santulan" kinwa "sanyukt" upayasah (boyce ett all) mothya pramanat sweekarle gele nahee. 1994). hanny (1972) suchavatat qee magani vikasit karnyasathi vaparlya jaanarya pravas velebaddal antargat gruhitak tyaa maganichya marg niyojanachya utpadan pravas veleshi susangat asale pahije. moolbhut varshatil paristhiticha andaj ghenyasathi lahan paddhatshir visangati hii eka samasya asali taree, puravatha aanee magani yanchyatil abhipray samajoon ghetalyashivay andaj aanakhi ksheen hoto. suruvatila huristic paddhati irvin aanee wonn cube aanee itaranni vikasit kelya hotya aanee nantar suzanne evance yanni aupcharik ganiteey programming tantre sthapit kelee. 
pravasachya velechi sthirata.
gharguti utpann, jameen vaparachi paddhat, kautumbik rachana aanee kamgaranchya sahbhagamadhye lakshaniy badal hounahi washington mahanagar pradeshat gelya tees varshant pravasacha kaal sthir rahila aahe, haah aadhichya sanshodhanat aadhalalela nishkarsh haah abhiprayanche vishleshan karnyacha eka mahattvacha muddah aahe. julya shaharanmadhyehi asech parinam aadhalun aale aahet
gelya teen dashkanmadhil pravasacha vel aanee vitaran vakranchi sthirata tulanene dirghakalin andajasathi ekoon pravas vitaran modelchya vaparasathi changla aadhar dete. yacha arth assa nahee qee pravasasathichya veleche satatche andajpatrak aahe.

