Zrcohfc Kcr tlc pchrv @ lhc bccg cgmkp`gi tlc dcn`iltv ko FV@. GF@V hgd v`a`nhr “okrcgv`f‐ T_ vlkyv' Hzhrt orka tlc`r bnhthgt tcgdcgfp tk i`c tlc “ahvv!vzcf‐ ohr tkk asfl h`r!t`ac. hgd trcht `t n`ec tlc ik tk vknst`kg cvzcf`hnnp `g FV@. @ lhc cvzcf`hnnp bccg `gtr`iscd lky tlc acd`fhn c|ha`gcrv hrc hnyhpv tlc zk`gt ko okfsv ylcg vkac kgc bciv tlc xscvt`kg ko t`ac ko dchtl' Ccg tlksil @ lhc akdcnncd ahgp nsazcd fhzhf`thgfc vpvtcav. hgd ccg v`asnhtcd tlca `g V@ASN@GE. @ d`d gkt rchn`vc tlc vknst`kg tk vsfl h zrkbnca yhv h d`rcft hzzn`fht`kg ko Gcytkg‐v Nhy ko Fkkn`gi ! hv @ v`aznp gccr ihc tl`v xscvt`kg asfl tlksilt bcokrc' @g zhrt`fsnhr. @ gd tlc hghnpt`f vknst`kg ko tlc rvt!krdcr KDC xs`tc hg cncihgt vknst`kg tk tl`v zrkbnca. cvzcf`hnnp v`gfc `t `gvthgtnp vlkyv tlc rcvsnt `v tlht ko h dcfhp`gi c|zkgcgt`hn osgft`kg ! hv kgc yksnd c|zcft `t tk bc' H fkazstht`kghn hzzrkhfl tk tlc vknst`kg `v chv`np kbth`gcd bp vkn`gi tlc KDC bp sv`gi Csncr‐v Actlkd' Tl`v thve `v v`aznp hfl`ccd bp hzzrk|`aht`gi tlc dcr`ht`c y`tl tlc g`tc!okryhrd d`oocrcgfc. ylcrc o ,| % l) o ,|) . tlcrcbp kbth`g`gi h rcfsrv`c fkazstht`kghn hnikr`tla' o ,|) 1 n`al : l −
→
— A`flhcn dc V`nh. Kftkbcr 2::0
Fkaacgtv. Fr`t`f`va. hgd Fkgtr`bst`kg Fkgtr`bst`kg @o pks lhc hgp vsiicvt`kgv kr d`vfkcr crrkrv `g tl`v dkfsacgt. yr`tc tk a`flhcnJaydcv`nh'fka tk lcnz ahec tl`v dkfsacgt bcttcr' Tlhgev `g hdhgfc okr pksr fkgtr`bst`kg' Fkgtr`bstkrv y`nn bc hfegkyncdicd `g tl`v dkfsacgt'
A`flhcn A' Y`mctsgic dc V`nh AVf ,D`vt). BCgi ,Lkgv). A@CCC. HA@AcflC,SE) cah`n= a`flhcnJaydcv`nh'fka a`flhcnJaydcv`nh'fka • bnki= bvkda`ec'fka • rcvsa´ c´ vsac= c´ = aydcv`nh'fka
8
O`gd` O`gd`gi gi tlc tlc T`a T`acc ko Dcht Dchtl l ko h Mklg Mklg Dkc Dkc
O`rvt!krdcr n`gchr d`oocrcgt`hn cxsht`kgv hrc y`dcnp svcd bp vf`cgt`vtv hgd cgi`gccrv tk vknc h hr`ctp ko zrkbncav `gkn`gi tcazcrhtsrc'
Gcytkg‐v Nhy ko Fkkn`gi= Tlc rhtc ht yl`fl tlc tcazcrhtsrc T ,t) flhgicv `g h fkkn`gi bkdp `v d`rcftnp zrkzkrt`kghn tk tlc tcazcrhtsrc d`oocrcgfc bctyccg tlc bkdp hgd tlc fkgvthgt tcazcrhtsrc vsrrksgd`gi acd`sa' T v . ko tlc vsrrksgd`gi
Gcytkg‐v Nhy ko Fkkn`gi `v akdcnncd hv h rvt!krdcr `g`t`hn!hnsc zrkbnca.
1 , ,:) 1 dT dt T
e T
−
T v )
,8)
T :
ylcrc T : `v tlc `g`t`hn `g`t`hn tcazcrhtsrc tcazcrhtsrc ko tlc bkdp hgd e `v tlc fkgvthgt ko zrkzkrt`kghn`tp' @o T v `v fkgvthgt. bp vczhrht`gi hr`hbncv.
8 T
−
T v
dT 1 e dt
,2)
@gtcirht`gi bktl v`dcv.
8 T
−
T v
ng ,T
−
T
dT 1
e dt
T v ) 1 et % F
−
,6)
T v 1 cet%F
T ,t) 1 T v % F cet
Hzznp`gi tlc `g`t`hn fkgd`t`kg.
T ,:) 1 T v % F c:
→
F 1 T :
−
T v
,4)
8
A`flhcn A' Y`mctsgic dc V`nh AVf ,D`vt). BCgi ,Lkgv). A@CCC. HA@AcflC,SE) cah`n= a`flhcnJaydcv`nh'fka a`flhcnJaydcv`nh'fka • bnki= bvkda`ec'fka • rcvsa´ c´ vsac= c´ = aydcv`nh'fka
Lcgfc.
T ,t) 1 T v % ,T :
−
T v ) cet
,3)
cet 1 :' Tlcrcokrc. n`at @o e > :. n`at ko `tv vsrrksgd`giv' →∗
→∗
T ,t) 1 T v . hgd tlc tcazcrhtsrc ko tlc bkdp hzzrkhflcv tlht
C|haznc= Ht 0 ha kg Kftkbcr 80. 2::0 h bkdp yhv oksgd `g rkka 629 ht tlc Sg`crv`tp Fcgtcr' Tlc rkka `v eczt ht h fkgvthgt tcazcrhtsrc ko 92 O' Tlc acd`fhn c|ha`gcr yhv fhnncd hgd lc hrr`cd `g c`ilt a`gstcv' Tlc rvt tl`gi lc d`d yhv tk thec tlc tcazcrhtsrc ko tlc bkdp' @t yhv <6 O' Tl`rtp a`gstcv nhtcr tlc tcazcrhtsrc ko tlc bkdp yhv thecg hih`g hgd `t yhv gky 9< O' Lcnz tlc zkn`fc bp tcnn`gi tlca ylcg tlc zcrvkg yhv asrdcrcd' ◯
◯
◯
Vknst`kg=
Tlc `g`t`hn fkgd`t`kg `v thecg vsfl tlht T : 1 <6 hgd T v 1 92 ht 0=:< ha' Vsbvt`tst`gi tlcvc hnscv `gtk Cxsht`kg ,3 ,3). yc kbth`g T ,t) 1 92 % ,<6 92) cet 1 92 % 88cet ' −
Ht :0=6< ylcg tlc acd`fhn c|ha`gcr tkke tlc bkd`cv tcazcrhtsrc T ,6:) 1 9< hgd T v 1 92' Vsbvt`tst`kg. kgfc hih`g p`cndv 9< 1 92 % ,88) c6:e ' Vkn`gi okr e . tlc fkgvthgt ko zrkzkrt`kghn`tp.
ng e1
? 88 6:
1
,?)
:':2:2
−
Vsbvt`tst`gi e `gtk Cxsht`kg ,3 ,3) p`cndv T ,t) 1 92 % ,88 ,88)) c c|zkgcgt`hn dcfhp dsc tk `tv gciht`c c|zkgcgt.
:':2:2t
−
' Tl`v cxsht`kg cxsht`kg y`nn thec thec tlc okra ko
V`gfc tlc acd`fhn c|ha`gcr y`vlcv tk egky tlc t`ac ko dchtl. h vknst`kg okr t `v oksgd bp vctt`gi tlc tcazcrhtsrc ko tlc bkdp ht 0<'? O. gkrahn bkdp tcazcrhtsrc' Vkn`gi 0<'? 1 92 % ,88) c :':2:2t okr t. ◯
2? ? '
88
:':2:2t
1c
−
ng t1
→
88
2?'? :':2:2
ng
−
88 2?'?
1 :':2:2t ,9)
1
46'9
−
Vsbtrhft`gi Vsbtrhft`gi 46 a`gstcv orka :0=:< ha i`cv i`cv tlc t`ac ko dchtl hv :<=23 ha'
@gtcirht`gi tlc rvt!krdcr n`gchr d`oocrcgt`hn cxsht`kg rcvsntcd `g h n`gchr cxsht`kg `g Cxsht`kg ,6 , 6).
ng ,T
−
T v ) 1 et % F
,<)
@t `v fnchr tlc hbkc `v fkazhrhbnc tk p 1 a| % f' Fkgv`dcr`gi T ,:) 1 T : .
ng ,0<'?
−
92) 1 e,:) % F
→
F 1 ng ,2?'?)
,0)
V`gfc T ,<) 1 <6 hgd T ,6<) 1 9<. yc kbth`g tyk n`gchr cxsht`kgv orka Cxsht`kg , <) ylcrc t `v gsabcr ko a`gstcv bctyccg dchtl hgd :0=:< ha hgd tlc ktlcr `v tlc gsabcr ko a`gstcv bctyccg dchtl hgd :0=6< ha. ,`) ng,88) 1 et % ng ,2?'?) hgd ,``) ng,?) 1 e,t % 6:) % ng ,2?'?)' Vkn`gi okr e y`tl ,`).
ng,88) 1 et % ng ,2?'?)
e1
→
8 88 ng
t
,8:)
2?'?
Vsbvt`tst`gi tl`v rcvsnt.
8 88 ,?) 1 , % 6:) % ,2? ?) 2? ? 88 6: 88 ,?) 1 % % ,2? ?) 2? ? 2? ? ? 88 6: 88 1 % 2? ? 2? ? ? 2? ? 2? ? 1 ? 1 6: 88 88 88 2? ? 2? ? 88 6: 2? ? ? 1 46 9 1 ng
t
ng
ng
ng
ng ng
'
'
ng
t
'
'
t
'
t
ng
t
ng
ng
'
ng
ng
'
ng
'
'
,88)
'
'
ng
'
t
ng
¹
'
88
Fkgra`gi tlc rcvsnt kbth`gcd zrc`ksvnp. tlc t`ac ko dchtl `v 46 a`gstcv bcokrc :0=:< ha. lcgfc. :<=23 ha'
