
sthanikikaran pramey

ganitamadhye, visheshtah avibhajya gananat, sthanikikaran pramey, vishisht atinmadhye, keval tyachya satatya aanee tyachya avibhajya mulyabaddal mahitee dilyas, karyachya shunyatecha andaj lavnyas anumati deto.
vastavik reshechya kahee khulya madhyantaravar paribhashit kelele vastavik-moolya asalele karya asoo dya jeey ω madhye akhand aahe. d haah ω madhye samavisht asalela eka aniyantrit up-antaral asoo dya. pramey khaleel soochitarth sangatoh
sootra _ 1
eka sadha purava khalilpramane aaheh jarr ω madhye x0 haah bindu asel, jyasathi, tarr x0 chya satatyasathi, jyache moolya shoonya nasalele asel, aanee visheshtah x0 peksha samaan chinhache astitva aavashyak asel. kaaran assa shejari n, joou aniyantritpane lahan manla jaau shakato, too vastavik reshevar shoonya nasalela rundicha asala pahije, tarr n peksha jaast avibhajya heey shoonya nasalele moolya mojel. tathapi, x0 haah "open" sanch ω chaa bhag asalyane, x0 chya ω chya simevaril antarapeksha lahan asalelya x0 chya serve parisarancha tyat samavesh keela jaato aanee mhanoon tyanchya vareel avibhajya bhagache moolyankan shunyavar karane aavashyak aahe. shoonya aanee shunyetar donhi asane aavashyak asalelya virodhabhasaparyant pohochalyanantar, prarambhik gruhitak chukiche asale pahije aanee tyamule ω madhye x0 nahee.
heey pramey sahajpane bahuvidh prakaranchya karyanmadhye samanyikrut kele jaate, jyachya jaagi antaranchi jaaga jodalelya khulya sanchanchya adhik samanya sankalpanesah, mhanje domens aanee mool karyasah, konatyahi upkshetravaril tyachya avibhajya bhagachi satatya aanee shunyatechya nirbandhansah ghetali jaate. purava haah ekach chull prakaranashi purnapane samaan aahe aanee assa bindu shodhane ashakya aahe.
udaharanadakhal.
bhautikshastrat yaa pramey vaparnyache eka udaharan mhanje dravpadarthansathi vastuman sanvardhanacha niyam, jyamadhye asey mhatale aahe qee konatyahi dravpadarthachya aakarmanache vastuman badaloo nayeh
sootra _ 2
reinolds vahtook pramey lagoo karoon, ekhada vyakti aniyantrit (drav nasalelya) niyantran khand vhee. see. chaa sandarbh badaloo shakato. pudhe asey gruheet dharale qee ghanata karya satat aahe (i.eae. aapala drav monophasic aanee thermodynamically metastable aahe) aanee nivadalelya sandarbh pranalichya sapeksh vhee. see. halat nahee, asey samikaran banateh
sootra _ 3
samikaran jase asha konatyahi niyantran aakarmanasathi asate, tase sthanikikaran pramey lagoo hote, jeey monophage dravpadarthanmadhil vastumanachya sanvardhanasathi samanya aanshik vibhedak samikaran prastut karateh
sootra _ 4