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Level Kinetic Approach in the Case of Strong Vibrational Nonequilibrium for a Pure Diatomic Gas

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(1)Level Kinetic Approach in the Case of Strong Vibrational Nonequilibrium for a Pure Diatomic Gas Elena V. Kustova, François Mallinger. To cite this version: Elena V. Kustova, François Mallinger. Level Kinetic Approach in the Case of Strong Vibrational Nonequilibrium for a Pure Diatomic Gas. [Research Report] RR-3577, INRIA. 1998. �inria-00073104�. HAL Id: inria-00073104 https://hal.inria.fr/inria-00073104 Submitted on 24 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Level kinetic approach in the case of strong vibrational nonequilibrium for a pure diatomic gas. E. V. Kustova , F. Mallinger. No 3577 1998 ` THEME 4. N 0249-6399. apport de recherche.

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(98)    ] ‹ˆ‰,^ ] ‹n^ ] ‹n‹^ ] +Š -- ^ ] +Š -YŠ)^ . =o   O   = = .  . . ] +Š -UŽ^. ] +Š -n ^. @ ( * 2 = 2 o @   = @G ( F.A O  ‚ = o  o u F.A   @ ( * 2 =2 @  =  m   ‚ O  u  FA  u  ! A = = @ ( * = b  o  @    L  ƒ F  = o A = o @G ( F.A t u  O %‚ 2 2 o Z } = o   = o   ! O ~ b =?> @   ƒ F = @ ( * = = =2 2     u      L  t  A } =   =   ! O u % ‚ m  =. @ ( * 2 = 2 o % ~ b @  =o F  =o A @ @G ( F.A =o  =o   O = o r    u   u   u Q % u ‚ =  o  } w ~ % b @ = F = @ ( * 2 =2    @ =  = O L  ‚ m = =  r    u   L   L Q3%   =     }  w ~. @ ( * 2 =  =k= % b @   =k= F  = = A   L ‚ }=k= r   L Q3% =k =  } w L  ƒ F  =o @ ( * 2 = 2 o  b   o  = o  ~ = o b  o @       t u     O u ‚ c= o  u % Z } = o   = o   =o . . =o.   . !! O =k= . ~. ~.   ƒ F  =o A  @ @ G ( .F A  o   u     - L t  L O Z = o   L  ƒ F  = @ ( * b  ?=  > @  2 = 2 ~  b   =   =   =  =k= .   t u      O u ‚ m   = =  L % } =       =    ] Š+-j\ ^ ~ ~. Q ( * 2 = b @ =k= F =k= b  =N > @      L  ƒ F  =    =k =   }  A u    - t u =   u Q   ‚ }= = @ ( * 2 = 2 o  b  =N > @  o  ~   p   ƒ F  = o @ b   ~=    o  = o A   o   L t ] Š+-U‡^ = o   x@ G  ( F.A u   =o O Z } = o  Z  u     O u % ‚ = o    ~  @ ( * @ b @   =~ F  =  = =k=   = 2  #OL   2   O % ‚ m = ( = U  L     =    } =   L ] Š+- * ^ U ~  @ ( * @ = @ k = b #OL   =k =    = Fc=} k= =k= \ L % ‚ 2 = ( = U  = L   } b. VWY[qkuBqvis[.Z hUqkqklBx brh0is[ t isl'ikWY[x.lc[ ¶ x bd[.mˆisq. .  . ] +Š -ˆ‰^. ¦WY[w{k[ ] +Š -n ^ ïï ÛT 

(99)  . . =o. p O m U U . ‚V=‚ ‚. . }. m.  . . bdqoU¦ {kbžiƒis[.m<hnq. op. U m  p  o U AQA O  p.  A. U. . ~. V‚ = =o  o p p O ‚   A U  U U U \k\k\ A G O Q A \ \ AAG2A V‚ =x‚    =   = o L ‚ o. U }. . p.  A. U. .    =  o A U.

(100) Šw\.   .[

(101)  ,

(102) N

(103)  . ] +Š -U‹^. ± Ul mgqkb t [w{kbdmYœikWY[HD{sqƒimYlnmB² ¨ ] ŠnŠ-^ ¦Wg[.{s[. .  . ŠnŠUŠ^ ]. @ } M  U  @

(104) F \ hjmYbrqkWYbžmg'x.lc[ ¶ x bd[.mˆisqwÁcikWg[n[.mg[.{„hj. }f$qƒuB} qƒik[wZ. . ! O. ŠnŠ@Ž^. . Q A \k\ A!G2A O. @xG  ( F O. = o   A. ~ } }. ~. .  . p p O # U X UX. . G. {k[ t egx.[wqikl.

(105) % m 2 = 2  Q @  =      L =    L 2 = = =   \ O.  !  = ~ ~ } } }~ } }. . =o.

(106).

(107) % 2 = 2 o Q @  = o    L u. =o. VWg[)qkuBqvis[.Z hnqsqƒlBx brh0is[ t iklHikWY[x.lc[ ¶  x bd[.mˆisq ¦Wg[.{s[ ] ŠnŠŒ ^. u. ‚ = A ‚. =o o. ==. . ].

(108)

(109).  !    O  o. m. .   O U J. . r m. . po. Z. p. bdqo¦{kbžiƒis[.m·hnq. V‚ =   = o |  U o X @ ( * "  = A m mp p p Zp p O u ‚ +   o Z U X A 4 U X A QU A U \ | \k\ U A X G A  Q A \ \k\ A!G2A. O  O. . . ‚ =‚ ‚.  . p p A U X. . ‚ =‚    =   = o L ‚ o. U[X.  . p p A U X. .    =  o UX. w. A. }. nŠ Šw\ ^   O   @ F   @  > =} F \ U UX X ´ibdqµln© ¨ bžlUegqikWghji  = op p O = o p p «VWYlUeYnW·bžiµbd-!qµ. }pDlˆqk} qkbd©Yfž[)isl“x lUmgqkb t [w{lnmYfduikWY[ x.lc[ ¶ x bd[.mˆisq !Z   o ÁD¦[ Z h@ux lnmDqƒb t [.{ox.lc[ ¶ x U bd[.X mˆU isX q   o U £¬lUX {<U X @ A 4 F O @  A  F.A @ Q A Q FA @  A Q F «¤VWg[{k[Œqƒegf isbžmY qkuBqvis[.Z x.hjm·©L[ t | [ t egx [ t £¬{slnZ ] ‹j\ ^,ÁYqkeY©gqƒikbžikeBisbžmg bžm·| [wZU hUX x„W[Œªˆegh0isbžlUm¸ÁcikWY[{sbdnWˆiWghjm t qkb t [©cu ]. . .

(110).

(111). @ ( * "  =. ‚V= A uZ ‚ +. A. A. {s[wqkpL[wx,isb ¨ [.fdun« /-bžmDhjfdfžuUÁcikWY[U[.mY[w{shnfSqkuBqvis[.Z hnqsqƒlBx brh0is[ t iklHikWY[x.lc[ ¶ x bd[.mˆisqH; = rb qnb ¨ [wm©cu. .  . ŠnŠ@‡^ ]. ¦Wg[.{s[ ] ŠnŠ * ^. [U X V‚ = Q ; op p @ L    L  =    F.A p p m mp p  L  O ‚ L L L u U X U o U X U U X UX U X U U U X A4 Q A k\ \ \ A G Q A \ \k\ A!G2A. O O =o. . =o. p p O m r U X UX. . . ‚ =‚ ‚.  . p p A U X. . ‚ =‚    =   = o L ‚ o. UX. . . p p A U X. .    =  o U[X. w. A. nŠ Š0‰,^.   O   @ U UX /g{klUZ_ikWg[ t [IHgmgb isbžlUmln£!isWY[©Y{„hnx„®n[.ibdmˆik[wn{„hjfMÁcikWY[). £¬lU} fžfdl0} ¦bžmgœpY{slnpL[.{kivu WYlUf t q =o = ] ŠnŠŒ ^ p p O o p p[\ /geY{kikWY[w{kZ'ln{s[nÁ¸£¬ln{ 4 O  ÁqkuBqvis[.Z ] ŠnŠ@‡^U X bdqU X mYljifdbžU[mYX[ŒU hjX {sfžuŸbžm t [.pL[.m t [wmˆiw«VWgbdq)brqh·x lUmgqƒ[ŒªˆeY[.mgx.['lj£ O isWY[ islji„hjf[.mY[w{kUu§x.lnmgqk[.{ ¨ h0ikbdlnmbdm°h€x.lnfdfžbrqkbžlUm¸&« Óm isWgh0i'x.hUqƒ[UÁ:qƒuBqƒik[.Z ] ŠUŠŒ‡ ^brqœqkeYpYpYfd[.Z'[wmUis[ t ©cu§ikWg[ x.lnmgqƒik{„hjbdmˆi[Œªˆegh0isbžlUm ‚V= ] ŠnŠŒ‹ ^ @ ; = =; = F m ‚ L  L L   O  \ ]. }. F. .

(112). .   @  }> = F \ X. =. U. U. û¬ü ï ßû ý.

(113) Š@‡.  

(114)   . Ómpg{shUx,ikbrx [UÁŒqkuBqvis[.Z ] ŠnŠ@‡^Lbrq!qklnf ¨ [ t £¬lU{C@ A 4 F O @ Q A  F.A @  A Q F Á@bd[n«!lUmYfduoikWg[ Hg{„qvi¸mglnm ¨ hjmYbrqƒWgbžmYox.lc[ ¶ x bd[.mˆisq bdmikWY[[.ycpDhjmgqkbžlUm ] - ^hn{k[)x lUmgqkb t [w{k[ t « š b isW·ikWY[pg{k[ ¨ bdlneDqWcucpLljikWg[wqkbdqwÁB¦[)¦{sb is[. . V‚ = L A G Q A \k\k\ A!G2A  ; o  F O O    u ‚ L L U  L o   ŠŒŽ,- ^ U U  ‚V= L  = = = o o o o A G Q A \ \k\ A!G \ @  ; ; F m O A  L       O ‚ L UL  L  o  £ßik[.{qƒbdZ'pYfž[hnfžU[.©Y{„hYÁBx.lˆ[.¶ x bd[.mˆisqln£-qkucqƒik[wZ ] ŠŒŽ,- :^ Z h@u U ©L[[ U yB pY{s[wqsqk[ t hnq   = ŠŒŽBŠ)^ @G ( F.A  o  O 2 = 2 o  =  o   L b @  = o F = o  A O   u ~ }   == ŠŒŽnŽ^   O m 2 = 2   =    L b @  =  F =   L % 2 = b @  = = F =k= A   = ~ } } } =. o ŠŒŽj ^ @ o F @ =o F =o A @xG ( FA % =   O    O u 2 2 o b = =    ŠŒŽ0\ ^ = @ = F @ = F = % 2 = b @ =k= F =k= A %       O u m  = 2 2 b u } } =o  = F F A . F A ŠŒŽn‡^ @ = @ =  @ G   ( o   o O  O 2 2 o b k = =   ŠŒŽ * ^ = % 2 = b @ =F =k= \   O  m 2 = 2 b @  = F L    = } } }. . ] (. . m. @ = o  ;  o    L. =o. . . ]. . . ] ]. . . ]. . ] ]. . . . . . . . . . . . . . . š ·[ pDlUbžmˆi lneBi'isWgh0i lnmgfžu mY[w¦ t [ Hg mYbžikbdlnmgq'Wgh ¨ [©L[.[wm°bdmˆik{sl t egx [ t isl¢[.ycpg{k[ŒqkqœikWg[·x.lc[ ¶ x bd[.mˆisqHln£oikWY[ t b S[.{s[.mˆiµqƒuBqƒik[wZ'qwÁBmYl hjpgpY{kl@yBbdZ h0ikbdlnmWghnq©L[.[wm·Z'h t [h0iisWYbdqofž[ ¨ [.fM«  -   ./&) 

(115)  

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(117) › ./& Óm'isWYbdq¤qƒ[Œx,ikbdlnm!Án¦[ t [IHgmY[µ{k[wfdhjyBhjikbdlnm ikbdZH[Œq.Áˆhnq t lnmY[©cu ! YŠ#MÁˆhnqsqƒeYZ'bdmYikWghji:Z'lnfd[wx egfž[ŒqêbžmHisWY[ t bL[w{k[wmˆi }<lU{k[wl ¨ [w{wÁishn®cbžmY°bžmˆisl#hUx.x lUeYmˆih tgt b isbžlUmghjf ¨pYbdWc©YuB{sqkhjbdikxwbdhjlnfmghnhnpYfpYfd{s[ l@¨ yB[.bžfrZ qh0hnis{kbž[ŸlUmgZHqwÁBlUegfž[Œqƒx [ eYt fd[w©cqu lj! £ YŠ.t #´b ÁLS¦[.{s[[.mˆUi<b [qƒpLqƒ[wbdZ'x.bž[ŒpYq.fd«_ t [ yBpY{s[wqsqkbžlUmgq£¬ln{µikWY[HqƒuBqƒik[.Z qUb ¨ [.m<bdm·ikWY[  b g H [ ¨ pY{s[ ¨ bdlnegqqk[wx ikbdlnm¸« ± lnmgqkb t [.{sbžmg ikWghjilUmYfdu“isWY[ is[.{sZ hnqsqƒlBx brh0is[ t isl . =?>œ{s[.Z hnbžmgq t bL[w{k[wmUi£¬{slnZ ¡.[.{sl“bdm<isWY[ ± WDhjpYZ hjmY² ³:mDqƒ®Uln t brqvis{kbd©YeBisbžlUm ! YŠ #MÁ ! Š@+‰ #´ÁY¦[)¦{kbžik[ Q  Q ] ŠŒŽU‰ ^ ;=N> ; =N>  @ * F @ – A 'ADEF Q. @ F ; =     @  > = F ;  =   F M \  O ‚

(118)   ‚  u 7 u 7 X J .} } VWY[wm¸ÁYbž£-¦[)fžbdmY[Œhj{sbž¡w[isWY[}€hjyc¦[.fdfdbdhnmBd² $lUf is¡.Z hjmYm t bdqƒik{sbd©YeBikbdlnm . .

(119). ]. ŠŒŽj ^. = R> # @ M - . / V‚ @ * = = F >= 30 254 F A t } = u87 u (9* = w. r u %6( * } U U U U U = * Áˆhjm t {slji„h0ikbdlnmDhjf * Ánis[.Z'pD[w{shjikeY{s[wqwÁUhnm t bž£¸¦[bdm t [wmUisb £¬uHisWY[o{s[wqkeYf isbžmg. # ; ?= >  O ' % ) & U J ( *. ¦bžikW t b S[.{s[.mˆi:is{shnmgqƒfrh0isbžlUmghjf$Á [ŒqƒpY{s[wqsqkbžlUmgq¦b isW ] ŠŒŽˆ‰,^,ÁB¦[)Z h@u U ¦{kbžik[ ]. ŠŒŽj‹ ^. @*. . @* = * F ; =   O  ‚ \ *U u.  .  . ïï ÛT 

(120)  . U. U. *u. * F. O. ; =   A  ‚.

(121) Š* (.   .[

(122)  ,

(123) N

(124)  . ߣ ik[w{µqƒlUZ'[)hnfžU[.©Y{„hYÁUikWg[{k[wfdhjyBhjikbdlnm[wªˆegh0isbžlUm“£¬lU{ R = rb q¦{kbžiƒis[.m<hnq U = ] Šw-^ R D O m 2 o ( ‚ b @   = F  = o * = u # . | U |. o. }. U. u. *. U.  \. Vl t [w{kb ¨ [ [<Z h t [€ikWg[¢hjpgpY{kl@yBbdZ h0ikbdlnm#isWgh0i·x lnZ'pYfd[ y x lUfžfdbrqƒbdlnmgqhj{s[€{„hj{s[n« ± lnZ'pYfd[ y x.lnfdfžbrqkbžlUmgqêhj{s[ikWYlˆqƒ[bdm ¨ lnf ¨¨ bžmgZ'lU{k[ikWDhjm hqƒbdmYUfž[oªˆeghnmUiseYZ |vegZHp!«%Óm pDhj{kikbrx eYfrhj{ŒÁj¦[Wgh ¨ [ikWg[{k[wfdhjikbdlnm = £¬ln{ G  ( €« /YeY{kikWY[w{kZ'lU{k[UÁn¦[µWgh [µhnqsqƒegZH[ t ikWDh0i ¨ bd©Y{„h0ikbdlnmDhjfg{s[.frh0yYhjikbdlnm brq ¨ [.{suHqkfžl0¦ hnm t t lˆ [Œq mY ljo iµO h L [Œx,iik=Wg[O {klnish0isbžlUmghjfS{s[.frh0yYh0isbžlUm¸« ¨ VWY[)[.mg[.{snu R brq t [ HgmY[ t ©cu isWY[{k[wfdhjikbdlnm U Q = = ] ŠwgŠ ^ R > ; =N>  @ Q L  =?> F \ R O = m ] Šw-^ Á¦[¢Wgh. P. U. > q. |. VWg['x.ln{s{k[ŒqƒpLlnm t bžmg“ªˆeghjmˆikbživu<[ ¨ hnfžeghjik[ t ¦bžikWhjm¢[wªˆeYbdfžbd©Y{sbžeYZ t bdqƒik{sbd©YeBikbdlnm¢£¬eYmgx ikbdlnm¢£¬ln{hjm§hj{s©Ybžik{„hj{su is[.Z'pL[.{„h0ikeg{k[ *  bdq Q = = ] ŠwˆŽ ^ R > ; =N>  \ R  @ *  F O = m > q. P. | ] ´i£¬lUfžfdl0¦oqikWghjio[wªˆeghjikbdlnm Šw-^Z h@u ©L[¦{kbžiƒis[.m = ] ŠwU^ R D O Q = R = R =   A u _ u | U U U | ¦Wg[.{s[isWY[{s[.frh0yYh0isbžlUm ikbdZ'[ _ =kÁc£¬ln{ikWg[cGOisW ¨ bd©Y{„h0isbžlUmghjfSfd[ ¨ [wfOÁBbrqUb ¨ Q 2 o A ] Šwn\ ^ = O m = _ o _ o U. [.m“©cu. ¦Wg[.{s[ Q (‚ ] Šwˆ‡ ^ @ =F =o A  = O #OL  = b   _ o } brqisWY[x {slUqsq{k[wfdhjyYh0ikbdlnm“ikbdZ'[n«C/glnfdfžl0¦bdmY'}€hnqklnUm [ ihjfM« ! gŠ.#´ÁY¦[bdmˆik{sl t egx [h x.lnfdfžbrqƒbdlnmmceYZ ©L[.{ŒÁY{s[.frh0is[ t islHikWY[x.{klˆqkq{s[.frh0yYh0isbžlUm ikbdZ'[nÁY©cu isWY[{s[.frh0ikbdlnm 4 _ =o A ] Šw * ^ =  o O & =  o ¦bžikW  = o h HDx,isb isbžlUegq ¨ bdqsx lˆqƒbživu t [ HgmY[ t hUq ( * ] Šwc,‰ ^ =o  O     \ . . =o ~ } }. Óm·pY{„hnx ikbrx [UÁ  = o Z h@u ©L[ t [ is[.{sZHbdmY[ t ©cu ] ŠwU ^ P% = o O @   = o = o \  š [hjfrqƒlHWgh ¨ [UÁBeYm t [w{ikWY[hnpYpY{sl@yBbžZ h0isbžlUm“ln£{„hj{s[ x.lnZ'pYfd[ yx.lnfdfžbrqƒbdlnmDq.ÁcisWY[)£¬lnfdfžl0¦bdmYH{k[wfdhjikbdlnmgq = Q % * ] ŠwU‹ ^ b @   =k= F  =k= O # & L = =  = = A  U  } hnm t = Q * ] Š.\ -^ b   =  =o  =o O # & L =  = \ U  o. . o. û¬ü ï ßû ý.

(125) Š0‰.  

(126)   . kq qkeYZ'bžmg'ikWghjiikWY[bdmˆik[.{smghnfShnm t ik{„hjmgqkfrh0ikbdlnmZ'ljikbdlnm·hj{s[)eYmgx.ln{s{k[wfdhjik[ t ÁUisWY[)£¬lnfdfdl0¦bžmYH[wªˆeghnfžbžikbd[wqWglnf t ] Š.\gŠ)^  L  ƒ F =o A A A b  =? >  @  t  U Y u  Y t  O  ] Š.\ˆŽ ^ @G ( F \  p  L  ƒ F =o A b  =? >  @  o   O U Z Y u  oZ  Y t  O  š b isW·ikWY[pg{k[ ¨ bdlneDqhnpYpY{sl@yBbžZ h0isbžlUmgqwÁUisWY[)Z h0ik{sbžy Z h@u ©L[¦{kbžiƒis[.m (. x@ G ( F.A ( * 2 = 2 o L * & 2 = = 2 o #OL =  = L #OL  o M A O =o =o  U o  U o J     

(127) 2 =2  Q 2 = 2  #OL  = #OL   # L = A M L  & * 2 =k= = O  = =  O ( * m    L ( & =   L = =   U. =   = =   J  U  }  U  . % * 2 = 2 o #=L  o A = o  @xG  ( F.A O   O u & =o U o   %* 2 = 2  #=L  =  * 2 = #=L  = A = =    O u & m = =  U=  u & = } =  U=    . =o A @xG ( F.A O  O  2 = 2  #=L  =  * 2 = #OL  = A = =   *   O & m = =  U=  L & = } =  U=    . Z h@u ©D[¦{sbžiƒik[wm = o  O   u. Š.\U ^ ]. isWY[Z h0ik{sbžy ] Š.\n\ ^ Š.\ˆ‡^ ] ]. Š.\ * ^ ]. Š.\c‰^ ]. .Š \U ^ ] Š.\U‹ ^ ] ŠŒ‡,- ^. . . . @ (9* 2 = 2 o A =o @xG ( FA O  A!A O u % ‚ = o @ ( * 2 =2  A =k= % ‚ m  = =   !!A O @ ( * 2 = 2 o @   = F.A =o @G ( F.A  O  ‚ =o  o u  !! O   @ ( * 2 =2 @  = =k=   m   O  u  FA ‚  !  A   u  = = =o A   ! O  @ ( * 2 = 2 o  %    = o #OL  = #=L  o M A =o @ x@ G  ( FA =o  =o   O O   u  ‚ c= o    u   u   u @ ( & J  U=  L U  o  @ ( * %    =  #OL  = #=L   M 2 =2   =k =    @ =  =  O  ‚ m = =     u   L   L @ ( & J  U=  L U       L. @ ( * 2 =  % =k= %    = = #OL  = A L %‚ =k=   L @ ( & = }. ]. ŠŒ‡BŠ)^. ïï ÛT 

(128)  . . @*. . U. = # L o A = 2 2 o O    O u ‚ &   o = o  U o  =o. . @xG ( FA O.

(129) ŠŒ ]. ŠŒ‡UŽ^ ]. ŠŒ‡n^ ].   .[

(130)  ,

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(132)   @* =  = =  2 2  #OL   O U=  u u ‚ & m =  c=     = o  A @G O    O  @* = @* k= =  . O # L   =   O % ‚ m = 2 2 = U    L % ‚ 2 U . =  = Q '* 2 =  2  #OL  L ‚ & m =  c= =U   =k=. . ŠŒ‡j\ ^. . hnm t ikWY[Z h0is{kbžy Z h@u ©D[¦{sbžiƒik[wm  =o ] ŠŒ‡U‡^ A O. . '*. ‚ &.  . ( F.A = #=L. # L = A == 2 = = }= =  U= . = = U  = L } U = Q 5* = = 2 = #OL  A L ‚ &  =} = U=  . . .

(133) @xG  ( FA ( 9* 2 = = 2 o Q A O u @   = o L   o  2 =2 

(134) 2 = =k=. ( *   L Q L % (9* = = \   m O  = A   @ =   =   } bdmY“ikWY[Œqƒ[HmY[.¦]x lc[ ¶ x bd[.mˆi„q.ÁLikWg[ £¬lU fžfdl0¦bžmghjpgpY{kl@yBbdZ h0ikbdlnm<¦hnqhnqkeYZ'[ t 1  = o. ŠŒ‡ * ^ Óm t [.{sb ¨ brqhnpYpY{sl@yBbžZ h0is[ t ©cu  = = O =k« ( i¤isWYbrqfd[ [.fDb ibdqªˆeYbžik[µbdZ'pDlˆqkqkbd©Yfž[µiklHx lnZ'pYeYik[oisWY[)x lc[ ¶ x bd[.mˆi„q:lj£$isWY[pY{k[ bžlUegq¤qkuBqvis[.Z q t eg[µislikWg[ x.lnZ'pYfd[ yBbživuœln¨ £$ikWY[x lnfdfdbdqkbžlUm bžmˆis[.n{„hjfrqw«oegZH[w{kbrx.hnf ¨ hnfžeY[Œq:ln£!x lnfdfdbdqkbžlUm bžmˆis[.n{„hjfr¨q:hn{k[omgljih ¨ hnbžfrhj©Yfd[obdm ikWg[ fdbžik[.{„h0iseY{s[bdmikWY[U[.mY[w{shnfSxwhnqk[n« $[ £¬lU{k[:[wm tYt bdmYµikWYbrqqƒ[Œx,ikbdlnm!ÁŒ¦[¤¦hjmˆi¸islµbdmˆik{sl t egx [¤ikWY[hjpYpg{kl@yBbdZ'hjikbdlnmgq!x lnZ'Z'lnmgfžuegqk[ t bdm pY{„hnx ikbrx [U« VWg[.u“hn{k[ ] Š ^ ( pYpg{kl@yBbdZ'hjikbdlnm ln£µ{sljishjikbdlnmghnf t b Segqƒbdlnm#x lc[ ¶ x.bž[wmUi„q =  o ©ˆu lU{ t bžmghn{ku t b LeDqƒbdlnm#x lc[ ¶ x bd[.mˆi„q =o Á U ] Ž ^hjpYpg{kl@yBbdZ'hjikbdlnm°lj£x.lnfdfžbrqkbžlUm°bdmˆik[.U{shnfdq =  o   ] hjm t ikWcegq = o Á = o Á  = o ^H©cu¯xwhjfrx eYfrh0is[ t [.frhnqƒikbrx    U Y ¨ hjfdeY[wqw« ~ /Yeg{ƒisWY[.{sZ'ln{s[nÁikWg[¢x lUfžfdbrqƒbdlnm bdmˆik[.U{shnfdq =  o   hj{s[<mYln{sZ hjfdbž¡w[ t ©cu#ikWY[§x lU{k{s[wqkpDlUm t bdmY ¨ hjfdeY[nÁomgljik[ t U l Y t [.f¸hjm t Ub [.m©ˆu ' Z =  o    ÁDx lnZ'pYeYik[ t £¬lU{ikWY[{sbžUb t qkpYWY[.{s[) ~ ¨ U Y ~  @ ( * M Q F

(135) Q @ QF ] ŠŒ‡ˆ,‰ ^ L L u U & =o A Q t = o    O . % QF } u % @ U Y # & ]. . Q. ~. . J. L. { }. F brqisWY[ qk[.pghn{shjikbdlnmlj£ikWY[œx [.mˆis[.{oln£-isWY[iv¦l Z'lnfd[wx egfž[Œq.ÁD¦WYlUqk[ t brhjZ'[ is[.{„qohj{s[ @ = L o { o {s[wqkpL[w{ x,isb ¨ [.fd{ un«êVWcegqwÁB¦[)Z h@u ¦{sb is[ { { = o   ] ŠŒ‡n^ =  o   O U Y U Y ~ = o   ~ U Y  š ['xwhjm¢mYl0¦ {s[.¦{sb is[ isWY[ HDx,isbžlUegq ¨ brqsx lUqkbživu  = o hj~ m t ikWg[ t b SegqkbžlUm§x.lˆ[.¶ x bd[.mˆisq = o Á¸egqkbžmY·hjpgpY{kl@yBbž² Z hjikbdlnm ] Ž ^ Á @ & # ( * F  ] ŠŒ‡n‹^ A =o  O Q  & = o = o  . }  { @ & } # ~ ( *} } F  @ ] Š * -^ =o O  ‚ # & = =     . }  \ o o { } ~. ¦Wg[.{s[ =:hjm t. =o. O %. . û¬ü ï ßû ý.

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