Large eddy simulation of particulate turbulent channel flows
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(19) ÄPò`ó á6âmô`àõöß]â ð. ó àá. Liquid flux [m/s]. 10. 1 dispersed annular flow. bubbly flow slug flow. 0.1. churn flow 0.01 0.01. 0.1. 1. 10. 100. Gas flux [m/s]. $F÷,!øúù]&(ù]& J"I FD c _ \ I M b7 M w N I`e Rnc I c D _ f ² J P [ImY DWa I M b e DWa p \ R ³ SR x M w R J D I N P R Y DQ\ _ R _BI@¯ ½ R a [ Rc Ds ² a [ RnRgu r º s ± f. c I a [ u<:S P Y M D N a I N P [ D J P [ DQP R JÕ o o u a S Y'[ P [ DGP N I \nDQP R I \ ; \nD N eOII`JI N eOI P R Y0IZxx R I a Y D J : I N I a M \ IKx D Y`Y MWN x R JEe P M D ® \¼P I N IKx I N a RnM J M b o D R I N po P M iWI a IK³ S DGP RM J f/X [EI N I \nDQP R I \ ; \nD N eOIIKxx R I a R J P [ R a Y M J P I FqP x$I a R eWJ DGP I P [I a.D c I a RIê I a MON \nD N eOI N P [ D J P [ M a IkY MOc _ D p N D : \ I P M P [I R J P I`e N DQ\\ I`Je P [ a Y DQ\ I R J P [I M w f3X [EI a c DQ\n\ I NKu a S: e NR x a Y DQ\ I¾¯ o » o± IKxx R I a0D N I Y M J a R x$I N IKx P Mk: I R JEx$I`_BI`Jx$I`J P M b/P [I eWI MWc I P N.;@M b/P [I M w D JEx R a M P NM _ R Y f X [I N I b MON I P [I ; Y D J : I cM x$I \ IZx S a R Je D o » o cM x$I \gf PP [I _ N I a I`J PP Rnc I u DQ\P [ MWS eO[ N I aP N.R Y P IKx P MN I \DGP R I \ ; \ M w I N ] I ; J M \ x a J Sct: I N aD JEx a Rc _ \ IteOI MWc I P NR I a u:M P [ÃÕ o o D JExÃL ~ o D N I D : \ I P MN IK_ NM x S YI P [I P Rc ImxI`_BI`JEx$IKJ PP SN.:ES \ IKJ P I \ M Y R P ;® I \ x w R P [ D e M<M x D Y`Y SN D Y ; f X [I+J DGP SN I M b&P SN.:ES \ IKJEYI c I`J P RM JIKx D :BM I w R \n\ : I D [ SN x \ I DQ\a M w [I`J P [EI M w Y M J a R aPa M bP w MEuqMWNcMON I u x R I N I`J P _[ DWa I a uOR f I f R J a M Y DQ\n\ IZx ctS \P R _[ DOa I M w aKf7X SN:S p \ IKJ PhP w M p _[ DWa I M w a u Y M J a R aP R Je M b I f e f e DWahD JEx \ R ³ SR x u e DOahD JExm_ D N P R Y \ I MWN \ R ³ SER x D JEx _ D N P R Y \ I u Y D J : I b MWS Jx DW\ cM aP I I N; w [I N I b N.MOc P [It_ N.M Y`I aa I a R J P [ItJ DGP SN I a S Y'[ DWa P [I Y \ MOS x a R J P [EI a i ;Wu w [ R Y'[[ D II F R aP IKx a R JEY`I \ M Je P Rnc I : I b MWN I c D JEi R JEx D __BI D N IZx M J P [II D N P [ u P M P [I R JEx S aP N.R DQ\ _ NM Y`I aa I a-a S Y'[ DWa R J P [I_ R _BI a R JÔJ S Y \ I D N-N I D Y P MON a w [ R Y'[ w I N I N I DQ\ ûR ê IKx :q; DWaa I ct: \ R JEe cM x$I N J P IZY'[J M \ M e ; f ² J"eWIKJI N DQ\ u x R I N I`J P _[ DOa I a R J P w M p _[ DWa I M w a R J P I N D Y P I D Y'[ M P [I NZu Y'[ D JeOI P [I a [ D _BI M b0P [EI RnNR J P I N b°D YI u D JEx P N D J a R Pb NMWc M JI M w _ DGP.P I N J P M D J M P [I N fÔC MWN P [ R a N I DWa M J u P w M p _[ DWa I M w a D N I S a S DQ\n\ ; x R R x$IKx R J P M x R I N IKJ P M w N I`e Rnc I a u w [ R Y'[ D N I P N I DQP IKx¿x R I N IKJ P.\ ; f e DOa p \ R ³ SR x P w M p _[ DWa I M w a R J D _ R _BI u b MONR J aPD JEYI u Y D J : I Y \DWaa R® IZxÈx$IK_IKJEx R Je M J P [Ive DWat M w N DGP I D JEx P [I \ R ³ SER x M w N DGP I :SE:: \ ;Wu a.\ S e u Y'[ SN J D JEx-x R a _I N a IKx D JJ S \nD N M w N I`e Rc I a u DWa&a [ M w J R J C R e f r f r f&X [I P I Ncvu x R a _BI N a IZx M w a uWc I D J a7P [ DGP M JI M b P [EI0_[ DOa I a I F R aP'a(DWa(D x R a _BI N a IZxm_E[ DWa I f7X [I N I b MON I D :ES:: \ ; M w R a0DW\na M D i R JEx M b x R a _BI N a IZx M w aKf.
(20) ÄPò`ó á6âmô`àõöß]â. $*÷,øýù`&ûþ&. ó àá. ü. JvI FD c _ \ I M b _ D N P R Y S n\ DQP I M w f. ² J P [EI_ N I a I`J P(P [I a R a u P [I a Rnc _ \ I aPP w M p _[ DWa I P SEN.:S \ IKJ P M w§w [ R Y'[Y D J : I aP S x p R IZx M J D@a M \ R x : DOa R a uBR f I f _ D N P R Y S \nDQP I P SN:S \ I`J P M w uBR a Y'[ M a IKJ b MWN P [I a S:¡ IKY PZfX [I _ D N P R Y S \nDQP I M w R aD x R a _BI N a IZx M w w [ R Y'[UY M J a R aP M b4D- SER x DWaP [I Y M J P R J SMWS a _[ DOa I D JEx a M \ R x _ D N P R Y \ I a+DWaP [Ikx R a _I N a IKxÃ_[ DWa I u DOaa [ M w J R J C R e f r f T f o P S x ; M b _ D N P R Y p S \DGP I P SN:S \ I`J P M w a Y D J DW\na M : I D e M<M x aP'D N P R Je _ MWR J Pmb MWNmS JEx$I N aPD JEx R Je M bP [I c IKY'[ D J R a c a M b cMWN IeOI`JI N DW\ ctS \P R _[ DOa I P SEN.:S \ IKJ P M w a`f Õ R É@Y S \P ;@R J S JEx$I N aPD JEx R Je M b _ D N P R Y S \DGP I P SEN.:S \ IKJ P M w a D N.R a I a x S I P M Y MWc _ \ R p Y DQP IKx cM P RnM J M bP [I@_ D N P R Y \ I a \ R JiOIKx P M P [I S JEx$I N \ ;qR Je RnN.N I`e S \D NR P ; M b Y D NNR I N M w P SN:S \ I`JYI =f n JEII F YI`_ P RnM J R a P [I-Y DOa I w [I`J P [EI _ D N P R Y \ I a [ D I R J ® J R P I \ ; \nD N eOI R JI N p P R D Y MWc _ D N IZx P M P [I SR x D JEx¾x M J M P R J P I N D Y P w R P [ P [IkY D NN.R I N SR x f² J P [ DGP Y DOa I _ D N P R Y \ I a Y D J : I P N I DGP IZx a RncR \D N \ ; P M P [I P [I MON.; b MON e DWa cM \ IKY S \ I a u a IKI o S JEx D N D c ¤ M \n\ R J a ¯ r Oq ± f(² J cM aP Y DOa I a w [ R Y'[ D N I M b R J P I N I aP u [ M w I I NKu _ D N P R Y \ I a x M J M P [ D I R J ® J R P I \ ; \D N eWI R JI N P R DvD JEx¾x MvR J P I N D Y P w R P [ P [I@Y D NN.R I N SR x f@X [I N I b MWN I u a RcR \nD N \ ; P M P [I D __ N.M D Y'[ b MWN a R Je \ I0_E[ DWa I P SN.:ES \ IKJ P M w u aPDGP R aP R Y DW\ c I P [ M x aD N I P Mm: I N I \ R IZx MJf X [I N I D N I c D R J \ ; P w M x R¼ I N I`J P w D ; a P M x$I DQ\ w R P [ P [I : IK[ D RMON^M b _ D N P R Y S \DGP I P SEN p :S \ I`J P0 M w a ~ S \ I N.R D J p ~ S \ I N.R D J D __ NM D Y'[ D JEx ~ S \ I NR D J p L D e N D Je R D J D __ NM D Y'[ f(X [I ~ S \ I NR D J p ~ S \ I NR D J D __ N.M D Y'[ R a M b P I`J N I b I NN IZx P M DWa&P w M p SR x cM x$I \$D __ NM D Y'[ : IZY D S a I P [I_ D N P R Y \ I-_E[ DWa I R aDW\na M P N I DGP IZx DWaD Y M J P R J SESc f² J P [I ~ S \ I NR D J p L D e N D Je R D J D _ p _ NM D Y'[ u P N D ¡ IKY P MWNR I a M b R JEx R R x S DQ\ _ D N P R Y \ I aD N ImY MWc _ S P IKx D YKY MWN x R Je P M P [EIm_ D N P R Y \ I IK³ S DQP RnM J M b cM P RnM J R J P [EImL D e N D Je R D J b N D c I u w [ R Y'[ w R \n\ : I R J P NM x S YIZx R J ¤ [ D _ P I N f§X [I ~ S \ I NR D J p L D e N D Je R D J D __ NM D Y'[ R a M b P IKJ a Rnc _ \ ;ÔN I b I N.N IKx P M DWa L D e N D JEe R D J _ D N P R Y \ I P N D Y'i R Je¯°L £X ± f<²P R a M b Y MWSN a I_ M aa Rn: \ I P M Y M J a R x$I N L D e N D JEe R D J p L D e N D Je R D J D __ N.M D Y'[ f4j M w I I NKu L D e N D Je R D J D _E_ N.M D Y'[ b MWN P [I SR x ¯I f e fhd M a [ ûR êKS i D I PDQ\f u r O u r O ºO± R a M J \ ;UM J I D N \ ; aP'D eOI M b x$I I \ M _ c I`J PD Jx R a J M P N I DQ\ R aP R Y P M: I S a IKx b MWN P [I Y MOc _ S PDQP RnM J M b/P SN:S \ I`J P M w aKf X [I a Rnc _ \ I aP _ D N P R Y S \nDQP I P SN:S \ I`J P M w R a D [ MOcM eWIKJI MOS ahP SN.:ES \ IKJEYI R J M \n R JEe D_ N P R Y \ I aKf o [ R [ L Sc \ I ; ¯ r º Á ± N IK_ MON P IKx M J a IZY M JEx p MWN x$I N Y \ M a SEN I cM x$I \ R Je M b _ D N P R Y \ IÃx R a _I N a RM J R J D x$IZY D ;<R JEeÇ[ MWcM eOI`JI MWS akP SN:S \ I`JEY`I f X [EI a RcmS \nDQP RnM J w DWa b MWS Jx P M: I R Je M<M x D e N I`I c IKJ P w R P [ P [II F _BI NRc I`J P'DQ\ x DGP'D :<%; ÿ I \n\n{a o P M Y'i@¯ r ºWq± f.
(21) ÄPò`ó á6âmô`àõöß]â ó àá L D e N D Je R D J@_ D N P R Y \ I P N D Y'i R JeY MWS _ \ IZx w R P [vÕ o o ¯gL £X p Õ o o± M b cM P RnM J M b _ D N P R Y \ I a R J D x$IKY D ;<R Je[ MWcM eWI`JEI MWS a0P SN.:ES \ IKJEYI w DWa _BI N b MWNc IZx :<; ~ \ eO[ MW: DOa [ R X NS I a x$I \\ ¯ r W T ± D JEx P [I Rnc _ MWN PD J P ³ S D J P R P R I aa S Y'[ DOa L D e N D Je R D J I \ M Y R P ; D S P M p Y MWNN I \DGP RnM J a D JExvx R S a R R P ;M b/P [I _ D N P R Y \ I a w I N I aP S x R IZx f o [I D N M w aD JEx ¡ I P0 M w aD N I P [ItJI F<Pa Rnc _ \ I aP Y DOa I a : IZY D S a I a M \ R x :MOS JEx D N.R I a JI`IZx¿J M PkP MÇ: I P'D iWIKJ R J P M D Y`Y MOS J PKf o RncM J R J§I PDW\gf ¯ r O W± x$I I \ M _BIKx D
(22) a IKY M JEx p MWN x$I N Y \ M a SN I M bP [I P w M p SER x cM x$I \Eb MWN _ D N P R Y S \DGP I P SEN.:S \ IKJ P a [I D N M w a`f7X [I P Rc I I M \ S P RnM J M b/P [I GD NRMOS a Y MON.N I \DGP RM J a w DWab MOS JEx P M: I R Jve M<M x D e N IKI c I`J P w R P [ P [I RnN x DGP'D Y MWc _ S P IKx S a R JevL D e N D Je R D Jv_ D N P R Y \ I P N D Y'i R JeY MOS _ \ IKx w R P [#L ~ o ¯°L £X p L ~ o± f P SN:S \ I`J P _ D N P R Y S \nDQP I ¡ I P7 M wÔw DWa7a RcmS \nDQP IZx :<; ¤ [I`J ÿ¾M<M xU¯ r ºqW± S a R Je D0P w M p SR 3 x ëì í cM x$I \gf ~ IZY P M b/P [I _ D N P R Y \ I a IR ê I D Jx_ D N P R Y \ I \ M D x R JEe M J P [I-x R a _BI N a RM J w DOaaP S x R IZx :<; Y MOc _ D NR Je P [I a RnctS \nDQP RnM Jx DQPD w R P [ DGD R \nD : \ I0I F _BI NRc I`J P'DQ\ x DGP'D :<; I f e |f v M e S a.\nD w a i R £ M _ R I \ ¯ r qQ ± /u ÿ DQ\n\ I PDQ\f ¯ r º T ± D JEx ½ M xI NN I a.a I PDW\gf ¯ r º s ± f C MON P [Ik_ N D Y P R Y DW\(D __ \ R Y DGP RM J a u a S Y'[ DOa _ N IKx R Y P RM J a M b : IK[ D RMON a M b _ D N P R Y S \DGP I M w a@D __I D NR JEe R J R JEx S aP N.R DQ\a ; aP I c a uR P R a JEIKYI a.aD N; P MÔS JEx$I N aPD JEx P [EI cM P RnM J M b _ D N P R Y \ I a R JÇeWI MWc I P N.R I a w R P [ NR e R x w DQ\n\na u^R f I f w DQ\n\ p :MOS JEx$IZx M w a`f@X [I a Rnc _ \ I aP I FD c _ \ I a w R P [ a S Y'[3eWI MOc I P NR I atD N I aP N D R eO[ P _ R _I a MON Y'[ D JJI \na :BMWS JExIKx w R P [ P w M _ D N DQ\n\ I \ w DW\\aKf ~ F _BI NRc IKJ P'DQ\ w MWN i M J#_ D N P R Y S \DGP I P SN.:ES \ IKJ P M w a R J a S Y'[¾_ R _I a MWN Y'[ D JEJI \a [ DWa : IKI`JÃY D NN.R IKx MOS P :<;vc D J ;vN I a I D N Y'[I N a`f L DWa I N Õ M __I N D JI cMOc I P N;R a P [I cM aP _ M _ S \D N P IZY'[J R ³ S I P M#MO: a I N I P [I cM P RnM J M b _ D N P R Y \ I aD JEx w DOa S a IZx :<; I f e f R a.a I \ c D N ½ M \ I \ S a ¯ r qG ± u ½ D IZx D I P+DW\gf ¯ r º V ± u L&I`I Õ SN aP ¯ r ºErZ± u Xa SG¡R I P-DQ\f ¯ r º s ± u d S \ R Y'ivI P-DQ\f ¯ r W s ± D JEx d DGb P MWNR I P DW\gf ¯ r O O± f [ R eW[ p a _IKIKx R x$I M a ; aP I c w DWa S a IZx :q; I f e f>]0DOa [ R x R I PvDQ\f ¯ r O V ± D JEx o0R J M »+D N Y R D ¯ r W Á ± f*²P w DOa MW: a I N IKx R J P [I@I F _BI NRnc IKJ Pa+P [ DGPmP [IY D NN.R I N SR x P SN:S \ I`JEY`I D N I a S __ N I aa IZx :<; a S a _BI`J a RM J M b a c DQ\n\ _ D N P R Y \ I aD JEx I`J[ D JEYIZx :<; \nD N eOI-_ D N P R Y \ I a`f+j I Pa N.M J R ¯ r º ± D JEx » MWN I ¤ NM w Iï r º ± a Scc D NIR ê IKx P [Ivx DGP'D"b NMWc P [I DGD R \nD : \ II F _BI NRc I`J P'a u D JEx@_ N.M _ M a IZxkY NR P I NR D : I P w IKI`J P [IIKJ[ D JYI c IKJ PD JEx P [I a S _E_ N I a.a RnM J M bP SN:S \ I`JEY`I u w [ R Y'[ w I N I \DGP I N GDQ\ R x DGP IKx P [EI MWN I P R Y DQ\n\ ;3:<; S D J ½ R Y'[ D I \ R xI a ¯ r W T ± f9²P w DWa DQ\a M b MOS JEx
(23) ¯ C I aa\ I N I PDQ\f u r W s ± P [ DQPP [I-_ D N P R Y \ I a w R P [ ® J R P I u a c DW\\ R JI N P R DmP IKJEx P M Y M JEYIKJ P N DQP I R J P [I N IKe RnM J a w R P [ \ M w a [I D NR J P [I aP N I D i ; P SN:S \ I`J PtaP NS Y P SN ImJI D N P [I w DQ\n\f X [I MON I P R Y DW\aP S x R I a(D :MOS PhP [I a I w DW\\ p :BMWS JEx$IKxm_ D N P R Y S \nDQP I M w a S a R Je J Sc I NR Y DQ\ a RnctS \nDQP RnM J a [ D I DQ\a M0: I`IKJ N I`_ MWN P IZx f/X [I c D R J N I a I D N Y'[ R J P I N I aP c D ;+: I rZ± P M Y \nD N.R b ; P [Im_[IKJ MWc I`J D M b x$IK_ M a R P RnM J D JExvI`J P N D R J c I`J P M b _ D N P R Y \ I a JI D N P [I w DW\\/D JEx T ± P M _ NM R x$I aPDGP R aP R Y DW\ cMWc I`J Pa M b _ D N P R Y \ I aKf L £X a RnctS \DGP RM J R a M b P IKJ S a IZx b MWN P [EI_ N IZx R Y P RnM J M b x$IK_ M a R P RnM J M b/a c DQ\n\ _ D N P R Y \ I a R J D w DW\\ p :BMWS JEx$IKx P SN:S \ I`J P+ M w f n S J R a I P DW\gf ¯ r O r± N I`_ MWN P IKx M J P [Ikx R a _BI N a RM J D JEx P [Ix$I`_ M a R P RM J M b( I N; a c DQ\n\ _ D N P R Y \ I a S a R JEeL £X p Õ o o f X [I v NM w J R D J cM P RnM J x S I P MR J P I N D Y P RM J : I P w IKI`Jt_ D N P R Y \ I a&D JEx SER x cM \ IZY S \ I a w DWa&DW\na M P'D iWIKJ R J P M D Y`Y MOS J PKf X [I-IKJ P N D R J c IKJ P _ N.M YI a.a w DOaaP S x R IKx :<; o M \¼P'D J R [ c D x R ¯ r O W± S a R Je P [I a.D c I c I P [ M x M \ M e ; f ÕIK_ M a R P RnM J R J D _ R _BI M w w DWaa RnctS \DGP IKx :<;@ÿ R ¡ P.P I w DWDW\8rn\ R I c D J a.
(24) ÄPò`ó á6âmô`àõöß]â ó àá ¯ r W Á ± f ÿ D Je o ³ SRnN I a ¯ r W ÁWD ± S a IKxÃL £X p L ~ o P M aP S x ; _ D N P R Y \ Ix$I`_ M a R P RnM J R J D Y'[ D JEJI \f L R [ c D x R ¯ r W O± aP S x R IKx P [Itx$IK_ M a R P RnM J N DGP I M b _ D N P R Y \ I a R J D Y'[ D JEJI \ S a R Je D ³ S DWa R p P SN:S \ I`J P SR x I \ M Y R P ;#® I \ xÈ_ NM _ M a IKx :q; d N D R Y'[J D J9¯ r q V ± DOamP [I : D Y'i<e N.MOS JEx P SN:S \ I`JEY`I f(X [I aD c I c I P [ M x M \ M e ; w DWaDW\na M D __ \ R IKx P M P [I _ N IKx R Y P RM J M b x$I`_ M a R P RM J N DGP I R J D Y MWc _ \ I F eWI MOc I P N; ¯°L Rgu I PDW\gf u r W q± f¿C MWN P [I Y DOa I a w R P [ I N.; a c DQ\n\ _ D N P R Y \ I a u P [EI a RnctS \DGP RM J a c I`J P RnM JEIKx D :BM IY MWS \ x#_ N IKx R Y P P [I aP'DGP R aP R Y a a S Y'[ DOa x$IK_ M a R P RnM J I \ M Y R P ;3R J e MqM x D YKY SN D Y ; DWa Y MWc _ D N IZx P M P [IÃY MWNN I a _ M Jx R JEe I F _BI NRc I`J P'DQ\ x DGP'D ¯I f e f L RnS e D N w DQ\ u r < s ± D JEx"I c _ RNR Y DQ\ N I \DGP RnM JÔ¯°I f e f ÿ#M<M x u r ºrZ± f L £X>a RnctS \DGP RM J ab MWNN I \nDQP R I \ ; \nD N eOI-_ D N P R Y \ I a R J w DQ\n\ p :MOS JEx$IZx P SEN.:S \ IKJ P M w a [ D I DW\na Mv: IKI`J N I`_ MWN P IKx f£ IKx R J M PP R I PmDQ\f ¯ r W T ± Y D N.NR IKx MOS PtD"a RcmS \nDQP RnM J M b cM p P RnM J M b _ M \ ; aP ;<N I`JI_ D N P R Y \ I a w R P [vx R D c I P I N a M b r TQV prWr VOV µcR J D [ MWNIR ê`M J P'DQ\ w DGP I N Y'[ D JEJI \ S a R Je L £X p Õ o o fWX [EI a RnctS \DGP RM Jx DQPD w DWa Y MOc _ D N IKx w R P [ P [II F _BI NRc IKJ P'DQ\ x DGP'D :<; ]DWa [ R x R I P DQ\f ¯ r W V ± f L D N eWIx R a Y N IK_ D JEY R I a w I N I b MWS JEx f7j M w I I NKu \DGP I NZu £hD J vD JI N°¡ IKI#¯ r W Á ± N I R a R P IKx P [I a.D c I_ NMW: \ I cÂ:<; P'D i R JEe R J P M D Y`Y MWS J PP [I : D Y'i p w D N x R J S I`JEY`I M b _ D N P R Y \ I a M J SR x u<R f I f/P w M pw D ; Y MOS _ \ R Je u D JEx a S Y`Y`I`IZx$IKx MO: PD R J R Je aP'DGP R aP R Y a R J D N I DWa M J D : \ I D e N I`I c IKJ P w R P [ P [II F _BI NRc IKJ P'DQ\ x DQPD :<; ]0DWa [ R x R I P-DQ\f ¯ r W V ± f C MON P [IUY DOa I a w [I N I@_ D N P R Y \ I a [ D I N I \nDQP R I \ ; [ R eO[ R JEI N P R D u a S Y'[ DWa Y DWa I a w R P [ a M \ R x_ D N P R Y \ I a M b MON x$I N(M b r VWVµc R J w DQ\n\ p :BMWS JExIKx D RnN M w a u P [I N I D N I aP R \\ _ NMW: \ I c a N I c D R J R JEe M J P [I w D ; b MON D YKY SN DGP I _ N IKx R Y P RM J S a R JeL £X+fB] MWS a M J ~ DQP M JÔ¯ r O s ± D JEx ÿ D Je o ³ SRnN I a ¯ r W Á : ± _I N b MON.c IKx L £X p Õ o o D Jx L £X p L ~ o uN I a _BIKY P R I \ ;Wu P M a RnctS \DGP I P [I#I F _BI NRc I`J P'a :<; d S \ R Y'iÈI PUDQ\f ¯ r W s ±w [ M aP S x R IZx P [I aP'DGP R aP R Y a M b Vµc e \DWaaD JExà Vmµc _ D N P R Y \ I a R J D I N P R Y DQ\ P SN.:ES \ IKJ P Y'[ D JEJI \ M w f \P [ MOS eW[ e M<M x D e N I`I c IKJ P w DWa/b MWS Jx : I P w I`IKJ P [I a IY MWc _ S PDGP RM J DQ\ N I a S \Pa u \nD N eOI x R a Y N I`_ D JEY R I a w I N I b MOS JEx DWa Y MWc _ D N IZx P M P [I@I F _I N.Rnc I`J PDW\ x DGP'DfC MWN I FD c _ \ I u P [I a RnctS \nDQP RnM J a _ N IKx R Y P IKx cmS Y'[ \ M w I N S Y P S DGP RM J \ I I \ M b _ D N P R Y \ I I \ M Y R P ;R J w DW\\ p J MWNc DQ\ x RN IKY P RnM J f o RncR \D N0N I a S \Pa w I N I N I`_ MWN P IZx :<; a I I N DQ\ N I a I D N Y'[I N a u I f e f7X4D J D i D I PDQ\f ¯ r Wq ± f o RnctS \DGP RM J a S a R Je M P [I N D __ N.M D Y'[I a&P [ D JkL £X [ D I DQ\a M+: I`I`J N I`_ MWN P IZx f o$w D R \ I a 9] IKI`i a ¯ r W s ± S a IZx D i R JI P R Y P [I MON.; b MON _ D N P R Y S \DGP I M w a ¯ ] IKI`i a u r O rZ± P M a RcmS \DGP I x$I`_ M a R P RnM J M b _ D N P R Y \ I a R J D@P SN:S \ I`J P Y'[ D JJEI \4 M w D JEx MO: PD R JEIKx N I DOa M J D : \ ItxI`_ M p a R P RnM J I \ M Y R P ; f¾X w M p SER x cM x$I \a w I N I S a IZx :<; ] ûR ê i ~ \ eO[ MW: DOa [ R ¯ r º ± u v M \ RM o R JEY \nD RN ¯ r O W± D JEx ¤ D M [ c D x R ¯ r O W± P M aP S x ;ÃM bP SN.:ES \ IKJ P Y'[ D JJEI \7 M w a w R P [ N I \nDQP R I \ ; [I D ; D JEx \nD N eOI_ D N P R Y \ I a`{f v M \ RM I PDW\gf ¯ r W W± DQ\a M D _E_ \ R IKx P [EI a.D c I cM xI \b MWN D Y MWc _ \ I F eOI MWc I P N; w R P [ NR a I N aKfh¤ MOc _ D NR a M J : I P w I`I`J P [I cM x$I \ :<; ] ûR ê i ~ \ eO[ MW: DWa [ R D JExI F _BI NRc I`J P'a :<; ½ D IZx D I PDW\gf ¯ r º V ± D JEx Xa SG¡R I PDW\gf ¯ r º s ± u b MWN R J aP'D JEY`I u a [ M w a0P [ DGPP [EI cM x$I \ :<; ] IR ê i ~ \ eO[ MW: DWa [ R [ DOa _ N IZx R Y P IZx P [EI : I`[ D RnMWN M b _ D N P R Y \ I a(D Jx SR x N I DWa M J D : \ ; w I \n\ R J P [I :S \ i N I`e RM J M b P [IY'[ D JEJI \ u P [ MWS eW[ u x R a p Y N I`_ D JEY R I a Y D J : I b MWS JEx@JI D N P [EI w DQ\n\gf4² J P [EI M P [I N I FD c _ \ I aa RnctS \nDQP R Je-[I D ; D JEx \nD N eOI_ D N P R Y \ I a u P M<MEu a RcR \nD N D e N I`I c I`J PmD JxÈx R a.D e N I`I c IKJ P w R P [ÈI F _I N.Rnc I`J PDW\ x DGPD.
(25) ÄPò`ó á6âmô`àõöß]â ó àá D N I N IK_ MON P IKx f(C MWNcMWN I D YKY SN DGP I_ N IKx R Y P RnM J R JY \ S x R Je P [I D e N I`I c IKJ P JI D N P [I w DQ\n\ u b SN P [I N0Rc _ NM I c I`J P M b/P [I I F R aP R JEe cM x$I \na R a\ R iOI \ ; P M: I JI`IZx$IKx f X M a Scc D N.RIê I P [I N I a S \Pa M b I D N \ R I N _ R IKY`I a M b w MON i u J Sc I NR Y DQ\7a RnctS \DGP RM J a Y D J N_ IKx R Y PP [I aP'DGP R aP R Y a w R P [ D N I DWa M J D : \ I D Y`Y SN D Y ; w [I`J P [I M w R a S J :MOS JEx$IZx u P [I R JEI N P R D M b _ D N P R Y \ I R a@a c DQ\n\ uMONk:M P [ f ÿ [I`J P [EI M w R a :BMWS Jx$IKx D Jx¿Y M J PD R J R Je _ D N P R Y \ I a w R P [¾[ R eW[ R JI N P R D u P [I_ N IKx R Y P'D :R \ R P ;"M bP [I a RcmS \nDQP RnM J a R aaP R \n\ _ M<MWN f-X [I _ M<MON _ N IKx R Y P'D :R \ R P ;M b :BM P [L £X¿a RnctS \DGP RM J D JEx P w M p SR x cM xI \ a RnctS \DGP RM J M b w DQ\n\ p :MOS JEx$IZx P SEN.:S \ IKJ P e DWa p _ D N P R Y \ I M w a0a I`I c a0P M@: Itx S I P MEu DGP\ I DWaP _ D N P.\ ;Wu P [I a.D c I N I DWa M J f X [ DQP R a+D\D Y'i M b R J b MWNc DQP RnM J M J w [ DQP I IZY P'a cmS aP : I PD iOI`J R J P M D YKY MWS J P D JEx w [ DQP Y D J : I JI`e \ IZY P IKx u I a _BIKY R DW\\ ; JI D N P [EI w DW\\a`f X [I ® J DW\ e M DQ\ M bP [ R a w MWN i R a P M aP S x ; P [EI cM P RnM J M b _ D N P R Y \ I a JI D N P [I w DQ\n\ u P [II IZY P M b _ N I a IKJEYI M b _ D N P R Y \ I a M J P [I P SN.:ES \ IKJ P aP NS Y P SN ImJEI D N P [EI w DQ\n\hD JEx P M c D iWI D¾a Rnc _ \ I u(cMWN I D Y`Y SN DQP I cM x$I \ P M _ N IKx R Y Pka S Y'[ M w aKfÔC MON P [I a IU_ SN _ M a I a u D Y MOc _ S PDQP RnM J DW\ Y M x$I P M Y DW\ Y S \DGP I P [I cM P RM J M b _ D N P R Y \ I a R J DvP SN.:ES \ IKJ P Y'[ D JEJI \ M w¿w DOa x$I I \ M _BIKx : DOa IZx M J P [I \nD N eOI IZxx ; a RnctS \nDQP RnM JkY M x$IxI I \ M _IZx :q; D [ N D R I P DQ\f ¯ r W W± f(X [I-Y M x$I w DWa _ N I`_ D N IKx P M D Y`Y MOS J Pb MWN P [EI cM x S \nDQP RnM J M b4P [EI P SN:S \ I`J P SR x I \ M Y R P ;m® I \ xx S I P M P [I+_ N I a I`JYI M b _ D N P R Y \ I aKf D NRMOS a I IZY P'a a S Y'[ DWa _ D N P R Y \ I p _ D N P R Y \ IvY M \n\ R a RM J a uhR JEY N I DWa I M b x N D e¾Y M IÉ@Y R I`J P JI D N P [I w DW\\ u \ R b Pb MON Y`I u v NM w J R D J b MWN YI u I P Y f u D N I R JEY \ S xIKx P M I FD cR JI P [EI RnN Rc _ MWN PD JYI f o P'DGP R aP R Y a :BM P [ M bP [I SR x D JEx M bP [Ik_ D N P R Y \ I atD N IY DQ\ Y S \DGP IKx u w [ R Y'[ w R \\ _ NM R x$I P [IJIKY`I aa.D N.; x DQPDb MWN P [I cM xI \ R Je f X [ R a P [I a R a R a MON e D J IR ê IZx R J P [I b M \n\ M w R Je w D ; f4² J ¤ [ D _ P I NT$u$c D R J R xI DWa : I`[ R JEx P [I \nD N eOI IZxx ; a RnctS \DGP RM J D N I R J P NM x S YIZx {f v DOa R YY M JEYIK_ Pa(D JEx P [I MWN I P R Y DQ\ cM x$I \a M J P [Ik_ D N P R Y \ I cM P RM J b M \\ M w R J ¤ [ D _ P I N f½ M x$I \nab MON Y MWS _ \ R Je : I P w IKI`J¾_[ DOa I aD N I x$I a Y NRn: IZx R J ¤ [ D _ P I N^s f/² J ¤ [ D _ P I N u J SEc I N.R Y DW\ _ NM YIKx SN I aD N I MWS P\ R JIZx {f n I N R I w a M bhP [It_ D _I N aD N I-_ N I a I`J P IZx R J ¤ [ D _ P I N Áf0² xI DWa0b MWN P [I b S P SN I w MON i D N I-_ N I a I`J P IZx R J ¤ [ D _ P I N f0C R J DQ\n\ ;OuR J ¤ [ D _ P I N º u a MOc I-eWIKJI N DQ\ Y M JEY \ S a RnM J aD N I-x N D w J f o _BIKY R® Y P M _ R Y aD N I0x R a Y S aa IKx R J@_ D _BI N a N I \DGP IKx P M P [ R a w MON i f4X [I_ D _I N aD N I DGP.PD Y'[EIKx P M P [ R a R J P N.M x S Y P MON.; J M P I f ~ D Y'[Ã_ D _I N-R a R J D Y MWc _ \ I P I b MWNc D Jx¾Y D J : I N I D x DW\na M DWa D J R Jx$I`_BI`JExI`J PD N P R Y \ I f .
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(30) . ÛéØ2Ú. ÌKÏgÍÍOÒ4ÍWËqÐ4ÑKÌ. m. ÌKÏgÍ#Ë8$ÑKÏgÒ4Ì[X [Ie M I N J R Je@IK³ S DQP RnM J b MWN P [I cM P RM J M b D J R JY MWc p _ N I aa Rn: \ I SR x w R P [ D x$I`J a R P ; D JEx D i R JI c DQP R Y R a Y M a R P ; u Y D J : II F _ N I a.a IKx w R P [ m(m. P [I-Y M J P R J SR P ; IK³ S QD P RnM J u. !" !%$. # ¹ V #. ¯ rZ±. D JEx P [I o D R I N päo P M iOI a IK³ S GD P RM J u !%" # ¹ ! ( " " r ',+ T-/. '10 f ¯T ± # !%& !%$' ì # ' ì )%* # w [I N I " # D JEx ) D N I P [I I \ M Y R P ; D JEx P [EIk_ N I a.a SN I u^N I a _BIKY P R I \ ; f@X [I@xI b MWNc DGP RM J N DQP I P IKJ a MWNZ2u . # ' uR a x$I ® JIKx DOa r !" # + !%" ' f . #' ¹ 4 ¯ O± T 3 !%$/' !%$ #5 m SÊUÏÎGË<ÍQ6 Ñ 87ÔËqÎÏgGÍ /9BÌZ:Ï 7;<9($ÑKÏgÒ = M w : IKY MWc I a^P SN:S \ I`J P R J-Y DOa I a w [I N I P [IJ M J \ R JEI D N P I Nc R J P [EI o D R I N po P M iWI a IZ³ S DGP RnM J u ~ ³ f ¯ T ± uQR aha S É@Y R I`J P\ ; \D N eWI N P [ D J P [I R a Y MWS aP I Nc fkX SN:S \ I`JEY`IY M J a R aP'a M b IZxx R I a w R P [ w R xI N D JeWI M b \ IKJe P [ a Y DW\ I a`f X [I \D N eWI aPka Y DQ\ I R a N I \DGP IZx P M D Y'[ D N D Y P I NR aP R Y \ I`JEe P [ R J P [I a ; aP I cvu x$IKJ M P IKx DWa = fX [I a c DQ\n\ I aPa Y DQ\ I uES JEx$I N w [ R Y'[ P [Imi R JI P R Y-IKJI N e ;M b7P [ImIKxx R I a x R aa R _ DGP I a R J P M P [I N.c DW\ IKJI N e ;Ou R a Y DW\\ IKx d M \ cM e MON.M \ IKJe P [ a Y DW\ I u xI`J M P IKx DWa =1> )f v I P w I`I`J P [I a I P w M \ I`Je P [ a Y DQ\ I a u = D JEx =1> u Dka Y DW\ I N I \DGP RnM J u = > ¶+B· A üDC u ¯s ± =@? E [ M \ x aKfÀj I N I u ¶+· E R aP [I ] I ; J M \ x a J Sct: I N@: DWa IKx M J = ,u D JEx P [I Y'[ D N D Y P I N.R aP R Y I \ M Y R P ;@M b/P [I cM aP IKJI N eWI P R YIKxx R I a u " uR f I f ¶· E ¹ " = f ¯ W± X [I cM aP _ N.RncR P R I D JEx D Y`Y SN DGP I w D ; P M Y MOc _ S P I DP SN:S \ I`J Ph I \ M Y R P ; ® I \ x R a4P M PD iWI P [I a ûR ê I M b^P [I Y MWc _ S P'DGP RnM J DQ\ c I a [ a c DW\\ I N P [ D J =1> D JEx R J P I`e N DGP I P [I o D R I N p o P M iWI a IK³ S DQP RnM JÔx RnN IZY P\ ; fUX [ R a c I P [ M x M \ M e ;ÃR a Y DQ\n\ IZx
(31) x RN IKY P J Sc I NR Y DQ\a RnctS \DGP RM J ¯°Õ o o± f a Y D J : IJ M P R YIZx b NMWc P [I a Y DQ\ I N I \nDQP RnM J u ~ ³ f ¯ s ± u P [IJ Scm: I NmM b c I a [ F.
(32) 2H JI àõãKLGàôMK | 2ô Nã3ã.õõOBä ó I*ö%K | â ó àá _ MOR J P'a JI`IZx$IKx b MON Õ o o R JY N I DWa I a R J _ NM _ MWN P RnM J P M ¶+· üPE C R J§I D Y'[§x R N IKY P RnM J f9²b D P ; _ R Y DQ\ x S Y Pk M w M b D RnNkR akPD iOI`J b MWN I FD c _ \ I D JEx = ¹ r V A Ä cUu " ¹ r cRQ akD JEx ¹ r V A c ð Q a-D N I DWaa SEc IZx u P [I@J Scm: I N-M b c I a [¾_ MWR J Pa R J M JEI@x RN IKY P RnM JÇY D J : I I aP Rnc DGP IZx DWa = ñ =1> ? ¶+· üDE C S r V ü f² J DUP [ N I`I@x Rnc I`J a RnM J DW\a _ D YI u&M JI a [ MOS \ x S a I r V-T c I a [v_ MWR J P'a :<; D N.MOS eW[I aP Rnc DGP I f G. ð ò â 6ã. U0ÎWVBË ËYX8X<Z ÌZÏ:7;<9($ÑKÏgÒ=X [I N I D N I R J P I N I aP R JeÇY'[ D N D Y P I NR aP R Y a-b MON P [ I KI xx R I ama c DQ\n\ I N P [ D J D Y`I N PD R J a Y DQ\ I u w [ R Y'[ÔY MON.N I a _ M JEx a P M D w D I`J Sct: I NZu ë-[ u7M J m p. P [I R JI N P R DW\^a S:EN D JeWI M b4P [I d M \ cM e MWNM 6ï a I`JI N e ; a _BIKY P NSc f o c DQ\n\^a Y DQ\ I+IKxx R I aD N I N DQP [I N [ MOcM eWIKJI MOS aD JEx R a M P NM _ R Y N I`e D N x \ I a.a M b e \ MO: DQ\ Y M J aP N D R J Pa0a S Y'[ DWa eOI MOc I P p N.R Y DW\b°D Y P MON a u w [ R \ I P [I#Y'[ D N D Y P I NR aP R Y a M b+P [I \D N eWI N IKxx R I aD N IU[ R eO[ \ ; x$IK_IKJEx$I`J P M J P [EI M w Y M JEx R P RnM J f@X [I a RnctS \nDQP RnM J c I P [ M x M \ M e ; w [ R Y'[ S P R \ Rûê I a-a S Y'[ S J R I N aDQ\ Y'[ D N D Y P I N.R aP R Y a M ba c DQ\n\4a Y DW\ ItIKxx R I a R a Y DQ\n\ IZx \nD N eOI-IKxEx ; a RnctS \DGP RM Jȯ°L ~ o± f² J¾L ~ o P [I c I a [ a IR ê I R a Y'[ M a IKJ a S Y'[ P [ DGP R P Y D J N I a M \ I P [EI \D N eWI NKu eOI MWc I P N; p D Jx M wp x$I`_BI`Jx$I`J P IKxEx R I a`f3X [I a c DQ\n\ I NZu(R a M P N.M _ R Y@IKxEx R I akD N I cM x$I \ IKx :<; D#a S: e N.R x a Y DW\ I ¯ o » oE± cM x$I \gf v ; x MOR Je P [ DGP u P [IJ Scm: I N M b Y MWc _ S P'DGP RM J DQ\ YI \\a Y D J : I N IZx S YIZx f o S Y'[x$IKY MWc _ M a R P RnM J R J P M e N.R x a Y DQ\ I ® I \ x D JEx a S: e N.R x a Y DQ\ I ® I \ x w DWa ®EN aP _ N.M _ M a IZx :<; o c D e MWNR J a i ; ¯ r Á q±w [ M aP S x R IKx D ³ S DOa R p P w M p x Rnc I`J a RM J DQ\ DGP cM a _[I NR Y P SN:S \ I`JEY`I f o R JEYI P [EI _ RM JI`I N.R Je w MON i :<; ÕI D N x MON ¯ r q V ±(w [ M D __ \ R IKxUL ~ o P M D Y'[ D JJEI \ M w u L ~ o [ DWa : IKY MWc I D JkI aa IKJ P R DW\$P M<M \P M aP S x ; [ R eO[I N ] I ; J M \ x a J SEct: I N P SN:S \ I`J P( M w a P [ D J w [ DGP Õ o o Y D J[ D JEx \ I f X [I_ N.M YI a.a(P M a I`_ D N DGP I P [I \nD N eOI NZu e NR x a Y DQ\ IIKxEx R I aD JEx a c DW\\ I NZu o » o IKxEx R I a R a Y DW\\ IKx ® \P I N.R Je f4² JkeOI`JI N DW\ u P [I ® \¼P I NR JEe-_ NM Y`I aa M b^D ® I \ x u " # ]¯ $8\ ^_& ± u Y D J : II F _ N I aa IZx w R P [ D ® \¼P I NR JEe b S JEY P RM J u ` ]¯ $ \ ì %\$ a ± uR f I f " # ]¯ $<\ ^b& ± d ¹ c " # ¯ \$ ae^b& ± ` ]¯ $ \ ì \$ a g± f \$ a u ¯Á ± w [I N I " # ¯]$8\ ^_& ± R a P [EI ® \¼P I N IKx uER f I f e N.R x a Y DW\ I uq® I \ x f cM JEe c D J ; b MON.c a M b ® \¼P I NR Je b S JEY P RnM J3_ N.M _ M a IZx R J P [Iv_ DWaP u P [I »+D S aa R D J ® \P I NZu P [I a [ D N _@Y S P p MW® \P I N D JEx P [I :BM F ® \P I N D N I P [ M a I cM aP\ ;S a IKx f a R a J D c IZx u P [I a [ D _BI M b `#M bBP [I »+D S aa R D J ® \P I NR aD-»+D S a.a R D J b S JEY P RnM J fhX [I a [ D N _kY S P p MQ® \¼P I N [ DWa+a S Y'[ D@b MWNc P [ DQP+P [IIKxx R I a w R P [¾[ R eW[I N w D IKJ Sct: I N P [ D J ë [ D N IY MWc _ \ I P I \ ; ® \P I N IKx MOS P R J P [I w D IKJ Sct: I N a _ D Y`I f7X [I :BM F ® \P I N w MON i ahDOa7P [I M \ Sc I D I N D e R Je R J P [IY MWc _ S P'DGP RnM J DQ\ Y`I \n\naKi f ha I M b x R I N IKJ P ® \¼P I N a-\ I D x a+P M JIKIKx M b x R¼ I N I`J P o » o cM xI \a`fk²b P [I »+D S aa R D J ® \P I NtR a S a IKx u P [EI o » o cM xI \ R JEY \ S x$I a a M p Y DQ\n\ IZx#L&I M J D N x D JExÃY NM aaaP N I aa I a R J D xx R P RM J P M ] I ; J M \ x a p \ R iWI aP N I aaK f ha I M b(P [I :M F ® \P I NN I a S \Pa R J Da S: e NR x cM x$I \ Y \ M a I P M P [I-Y \nDOa.a R Y DQ\ IZxx ; R a Y M a R P ; Y M JEY`I`_ PZf(X [I-x R I N IKJEYI a R J ® \P I N IKx³ S D J P R P R I a x S I P M Y'[ MWR YI M b ® \¼P I NR Je M _BI N DGP MWN w I N I aP S x R IZx :<; £ RnMWc I \n\ R I P DQ\f ¯ r ºWºq± f mIzRj8kJjml^ÏgÌKÍOÒÌZÏPÑ Z __ \ ;<R JEe P [I :M F ® \P I N.R Je u b MONR J aPD JYI u P M P [I o D R I N p o P M iWI a IK³ S DQP RnM J u ~ ³ f ¯ T ± uM JI-Y D J MW: PD R J D JvIZ³ S DGP RnM J b MON P [I ® \¼P I N IKx ® I \ x u w NR P.P I`J.
(33) ]N nI. K T. ð ò ä ä àõã. DWa. ! " # ¹ ! ( " " ' !%& !%$' ì #. r. ! ( " a " ' a 0 u , ' + 1 ' o 0 + . T # # !%$' ì # )*. ì. ¯ ±. w [I N I P [I M I N p \ R JII F _ N I a.a I amP [EIv³ S D J P R P ;Ç® \P I N IKx :<; P [EI :M F ® \¼P I N D Jx P [I " # a x$I`J M P I aP [I o » o I \ M Y R P ; f-X [I \DWaPP I N.cR aP [I ] I ; J M \ x a p \ R iOI aP N I aa0P I Nc D JEx#Y D J : I cM x$I \ IZx a RncR \D N \ ; P M P [I £ N D JEx P.\£ï a cR F R JEe \ I`JEe P [ cM x$I \ ¯ £ N D Jx P.\ u r T W± DWa ¶ # ' ¹ " # a " ' a ì pr * # ' " q a " q a ¹ ì T-sr . # ' f ¯ ºO± j I N I u r R aP [I o » o R a Y M a R P ; w [ R Y'[ [ DWaP M: I cM x$I \ IKx S a R Je P [I D N.R D : \ I a M J P [I ® \P I N IKx a Y DW\ I f Rj8kJjt7ÔÒuX4Ë9. S. c M $x I \ u Y QD \n\ ZI x o c D e WM NR J a i ; Rjp7/VBÒEÎGÏ:4Ì]vZw7ÔÒuX4Ë90X [I a PD J x D N x o » o . S(m. cM xI \ u Y D J : Ix$I N.R IZx DWahP [I b M \\ M w R JEe f7X [I P N D J a _ MWN P IK³ S DQP RnM J b MON P [I o » o i R JI P R Y I`JI N e ;Wu x$I ® JZI x :<; · r ¹ Tr " q a " q a u ¯g ± Y D J : I w NR P.P I`J DWa ! · r + " ' ! · r y ! r' r f r ¹ x ì ¯rV ± !%& !%$ ' !%$ 'uz ìîí X [I ®EN aPP I Nc M J P [EI N.R eW[ P p [ D JEx p a R x$I R a Y DQ\n\ IZx_ N.M x S Y P RnM J P I N.cvu x r ¹ ì " # a " ' a . # ' f ¯ rWrZ± o R JEYI P [I-x$I b MWNc DQP RnM J P IKJ a MONK%u . # ' uR aP N D Y`I \ I aa : IZY D S a I M b/P [I R JEY MOc _ N I a.a R:ER \ R P ;Ou ~ ³ f ¯ r± u P [I _ NM x S Y P RM J P I Nc Y D J : I N I w NR P.P I`J S a R JEe ¶ # ' DOa x r ¹ ì ¶ #' . #' f ¯rT ± X [I a IKY M JEx P I Nc R J ~ ³ f ¯ r V ± R a P [I P N D J a _ MWN PP I Ncvu rz ' ¹ Tr " ' a " q a " q a + r ) a{" ' a ì BT . a# ' " # a u ¯ rKO± D JEx P [I \nDOaPP I Nc R a P [I R a Y MWS a x R aa R _ DGP RM J P I Ncvu a r ¹ BT . a# ' %! !%" $ # ' f. ¯rs ± aa SEcR Je P [It_ N.M x S Y P RnM J P I Nc D JEx x R aa R _ DGP RM J P I N.c [ D I ctS 'Y [ \D N We I 0N c D eWJ R p P S xI P [ D J P [I P N D J a _ MWN PP I Nc a S Y'[ P [ DQPP [I ;: DW\nD JEYI+I D Y'[ M P [I NKu$R f I f x r ¹ í rÇu ¯ rZW± P [I i R JI P R Y+IKJI N e ; P N D J a _ MON P IK³ S DQP RnM J u ~ ³ f ¯ r V ± u$N IKx S YI a P M a a ì " # " ' . # ' ¹ í r f ¯rÁ ± í.
(34) Ä | ð ò â2H6ãJI àõãKLGàôMK | ô2Nã3ã.õõOBä ó I*ö%K | â ó àá ha R JEe ~ ³ f ¯ ºO± D JEx ~ ³ f ¯ r Á ± u M JI MW: P'D R J aD J I F _ N I aa RnM J b MON P [I o » o R a Y M a R P ; DOaD b S JEY P RnM J M b4P [I-x R aa R _ DQP RnM J N DQP I D JEx P [EI ® \¼P I N IKxvx$I b MWNc DQP RnM J N DQP I u w [ R Y'[ N I D x a r ¹ T} .í r ' } f ¯r± # ð C NMWc D x Rnc I`J a RM J DQ\D J DW\ ; a R a u í r Y D J : II aP Rc DQP IKx S a R Je } . # ' } D JEx P [I \ I`JEe P [ a Y DQ\ I M b o » o IKxx R I a u =]r u DWa ü í r ¯ rKºO± ? } . # ' } = ðr u P[ S a r ? = ð~ } . # ' } f ¯r ± ² J P [I MWNR e R J DW\ o c D e MON.R J a i ;¾cM x$I \ u = r3R amP'D iWIKJ DOa-P [I a IR ê I M b0P [I"Y S:R Y :M F u f ÿ [I`J P [IvY MOc _ S PDQP RnM J DW\ Y`I \n\ R a J M PD Y S: I :S PkD _ D N DQ\n\ I \ M _ R _BIKx M J u R a S a S DW\\ ; ¯ ½ Rn; D iWI u r W T ± PD iWI`J DWa ¹ ¯ $ Ä $ ð $ ü ± Ä CPü u ¯ TQV ± w [I N I $ # R aP [EI a IR ê I R i J p x RnN IZY P RnM J M b4P [I-Y`I \n\gfh² J P [ DGP Y DOa I 2u r Y D J : I cM x$I \ IKx DOa Br d ¹ T ¯ r ± ð } . # ' } f ¯ T rZ± X [I-Y M J aPD J P u r uR a Y DW\\ IKx o c D e MWNR J a i ; Y M J aP'D J PKf L R \\ ; ¯ r Á ± b MWS JEx P [ DGP r R a IZ³ S DQ\P M¾V f V ºO S JEx$I N P [I Y M JEx R P RnM J w [I N I P [I MY Oc _ S PDQP RnM J DW\ c I a [ R aa S É@Y R I`J P\ ;"® JI D JEx DQ\n\7P [I a S: e N.R x a Y DW\ IIKxEx R I a D N I R J P [I S J R I N aDQ\ N D JeOI f&² JJ Sc I NR Y DQ\$a RcmS \DGP RnM J a u r R a S a S DQ\n\ ; PD iWI`J : I P w I`I`J V f r D JEx V f T x$I`_BI`Jx R JEe M J P [I-Y'[ D N D Y P I NR aP R Y a M b/P [I M w ¯ ½ R; D iWI u r O T ± f ² J D Y'[ D JJI \7 M w u r
(35) R a S a S DQ\n\ ; PD iWI`J D NMWS JEx V f r T$u P [ MWS eO[ u&R P R a iqJ M w J P [ DGP P [I o c D e MWNR J a i ;vcM x$I \ M I N I aP Rnc DQP I a0P [I a S: e NR x a Y DQ\ I I \ M Y R P ;"R J P [I R Y R J R P ;"M b w DW\\f(X [ R aa [ MWN P Y MOcR Je R a S a S DQ\n\ ;@® F IKx :<;@S a I M b7D x D c _ R JEe b S JEY P RM J a S Y'[ DWa sr ¯ ± ¹ Br ( r ì¾I F _^¯ ì T ± 0 f ¯ TWT ± S S Ê Zu!/7ÈÏ°; Í j8kJj7ÔuÒ X4YË 9ª aD J D __ NM D Y'[ P M D MWR x D N P R® Y R DQ\4D x ¡S aP c IKJ Pa M b o » o R a Y M a R P ;Wu a S Y'[ DWa S a I M bED x D c _ R Je b S JEY P RnM J u » I N.c D J M I P7DQ\f ¯ r W rZ± _ N.M _ M a IZx D x ; J D cR Y o » o cM x$I \fX [I c D R J b I DQP SN I M b4P [Imx ; J D cR Y o » o cM xI \ R a S a I M b4P w M x R I N IKJ P ® \¼P I N a u^R f I f@D e NR x ® \P I N D JEx DP I aP ® \P I N w R P [ D\D N eWI N a RIê I fkX [I GDW\ S I M b r Y D J P [I`J : I@x ; J D cR Y DQ\n\ ; Y MOc _ S P IZx S a R Je P [I N I \DGP RM J : I P w I`I`J P [I a Ikx R¼ I N I`J P ® \P I N aKf X [Ix ; J D cR Y o » o cM x$I \ : DOa IZx M J P [EI o c D e MON.R J a i ;vcM x$I \ Y D J : Ikx$I NR IKx DWa P [I b M \n\ M w R Je fX [EI a ûR ê I M bP [I P I aP ® \¼P I N+R a Y'[ M a IKJ DWa D JEx P [I³ S D J P R P ;U® \P I N IKx :<; P [ R a R a I F _ N I aa IKx DOa I f e f " # f(X [I a S: e N.R x aP N I a.a u I F _ N I aa IZx DOa # ' ¹ " # " ' ì " # " ' u ¯ T O±.
(36) ]N nI. K. ð ò ä ä àõã. ÄÄ. Y D J : I ® \P I N IZx :<; P [I P I aP ® \P I N P MN I D x # ' d ¹ " # " ' ìd" # " ' f ¯ TGs ± n J P [I M P [EI N [ D JEx u P [I@Y MWcm:R J DGP RnM J M b P [Ike NR x ® \¼P I N D JEx P [I P I aP ® \P I N \ I D x a+P M D J M P [I N a SE: e NR x aP N I aa u w NR P.P IKJ DOa # ' ¹ " # " ' ì" # " ' f ¯ T W± X [I D S F R \D N; ³ S D J P R P ;Wu ¯T Á ± # ' ¹ " # " ' ì " # " ' u Y D J P [I`J : I I F _ N I aa IZx DOa ¯T ± # ' ¹ # ' ì # ' f X [ R a N I \DGP RnM J R a Y DW\\ IKx DWa» I Nc D J M R x$I`J P R P ; f7C R J DQ\n\ ;OuO:<; _BI N b MWNcR JEe a RncR \D N P N D J ab MON p c DGP RnM J a7P M P [ M a I0x M JI b MWN P [I0x$I N.R GDGP RnM J M b o c D e MON.R J a i ; cM x$I \ uqM JI ® JEx a(D N I \DGP RM J : I P w IKI`J P [EI o c D e MON.R J a i ; Y M J aPD J P u r/u D JEx P [EI-³ S D J P R P ;Wu # ' u DWa r ¯ T ºO± # ' ì qq ¹ T r%ð # ' f j I N I # ' R a x$I ® JIZx DOa # ' ¹ ¯ ± ð } . # ' } . # ' ì ð } . # ' } . # ' f ¯T ± a Y D J : I a I`I`J u P [ R aa I P M b IK³ S DGP RM J a [ D I P M<Mkc D J ;R JEx$IK_IKJEx$IKJ PD N.R D : \ I ab MWN P [Ix$I P I NcR J DQP RnM J M b M JI GD NR D : \ I u r f o S Y'[ c DQP [I c DGP R Y DW\ R \\ p _ M a IZx$JI aa R a S a S DW\\ ; ® F IKx :<;UctS \P R _ \ ;<R Je . # ' ¯ » I N.c D J M I P+DQ\ u r O r± uMON # ' ¯°L R \n\ ;Ou r W T ± M J :BM P ["[ D JEx a R x$I a M b ~ ³ f ¯ T ± f ² J P [I"_ N I a I`J P@aP S x ;Ou [ M w I I NZu P [EIvx ; J D cR Y o » o cM x$I \ R a J M PD x M _ P IZx ¡S aP : IZY D S a I P [EI P SN:S \ I`J P I \ M Y R P ;® I \ x#Y D J : IkY MWc _ S P IKx w R P [ D e M<M x D Y`Y SEN D Y ;vS a R Je P [I cM x R® IKx o c D e MWNR J a i ;cM x$I \ uR J P NM x S YIZx R J P [I b M \n\ M w R Je u w R P [ MOS P S a I M bD J ; x D c _ R Je b S JY P RnM JvJI D N P [I w DW\\f S pRj8kJj7Ôu Ò X4Ë 9 Ï ]Ñ 4Ë Ð4ÎGËqÌZË Ñ9ÌK]Ñ 8XpZ² J P [IÇ_ N I a I`J P"aP S x ;Wu D [ R eW[ \ ; D J R a M P NM _ R YY MOc _ S PDQP RnM J DW\ c I a [ a ; aP I c R a S a IKx b MWN P [IkIÉ@Y R I`JY ; D JEx D Y`Y SN D Y ;"M b P [IY MOc _ S PDQP RnM J M b(DP SN:S \ I`J P Y'[ D JJI \ M w f0X [I N I b MWN I u D cM x R® IKx I N a RM J M b7P [I o c D e MWNR J a i ;ÇcM xI \0D _E_ N.M _ NR DQP I b MWN a S Y'[ D c I a [ a ; aP I c ¯ D [ N D R I PDW\gf u r W O± R a S a IKx f C M \\ M w R JEeÕI D N x MON ¯ r q V ± u P [I \ M Y DQ\ x RBS a R R P ;R J kx RnN IZY P RM J 2u r ' uR aDWaa Sc IZx P M x$IK_IKJEx M J P [I ® \¼P I N IKxUx R aa R _ DQP RnM J u í r D JEx P [I Y S P p MQ \ I`Je P [ a Y DQ\ I R J kx RN IKY P RnM J u =]r ' uR f I f r ' ¹ í rÄ CPü = r CP' ü f ¯ V ±.
(37) 2H JI àõãKLGàôMK | ô2Nã3ã.õõOBä ó I*ö%K | â ó àá X [I x R a.a R _ DGP RnM J N DQP I u í r u$R a I aP Rnc DGP IKx S a R Je P [IeWI MWc I P N.R Y c I D J M b^P [I a R x$I p \ I`Je P [ a M b4P [I-Y`I \n\ u% $ Ä u $ ð u $ ü u DOa ü CPü í r ¯ rZ± ? }. #' } ¯ $ Ä $ ð $ ü ± ð f X [I \ IKJe P [ a Y DQ\ I R J p x RnN IZY P RnM J u = r ' u$R a J DGP SEN DW\\ ; I aP Rnc DQP IZx :<; P [I a c DW\\ I aP N I a M \n IZx a Y DQ\ I R JR p x RN IKY P RnM J u2 $/' f o S: aP R P S P R Je P [I a I I aP Rnc DGP RnM J a R J P M ~ ³ f ¯ V ± uBr ' Y D J : I. Äð. cM xI \ KI x DWa. ð ò â 6ã. r ' ¹ T r ð ¯ $ Ä $ ð $ ü ± ð C T ¯ $ ' ± CPü } . # ' } f X [I c M x$I \ Y M J aPD J P _ N.M _ M a IZx :<; D [ N D R I P0DQ\f ¯ r W W± R a ¹ /V V º f. ¯ T ±.
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(44) Ä. 2H JI àõãKLGàôMK | N ô | áN ó | á;¿ |. ü ò â 6ã. /K. ô/â ó ß Gã@âmô. | /ß À ó á N. P I N.c f o S Y'["Y DWa I M YKY SN a w [I`J P [EI _ D N P R Y \ I ] I ; J M \ x a J Scm: I NKu ¶· ¤ ¹ } " \ ìÁ" \ ¤ } f ^ ¯ OW± w [I N I f R a0P [It_ D N P R Y \ Imx R D c I P I NKuBR a cmS Y'[ \ I aaP [ D J S J R P ; fX [Ix N D e b MWN YI u © # ¥Â«PD®P¯ § u D Y P R Je M J D J M J p D Y`Y`I \ I N DGP R Je#_ D N P R Y \ I R J DÇaP I D x ; D JEx S J R b MWNc M w Y D J P [IKJ : I MW: P'D R JIKx S a R Je P [I o P M iOI aaP N I D c b S JEY P RM J DWa © # ¥¬«PD®¨¯ § ¹ r " " ¤ ± f ¯ Á ± ä ¯ # ì # X [I-Y M I`ÉkY R IKJ P u à ¤ uR a Y DW\\ IKx o P M iWI a N I \nDQF$DQP RnM J P Rnc I u x$I ® JIKx DOa f ¯ ± à ¤ ¹ rZðź Ä u w [I N I Ä R a P [I-x$I`J a R P ;N DGP RMM b _ D N P R Y \ I P M SR x uR f I f Ä ¹ ¤ f ¯ WºO± S SÆ Ë 8$ÑKÏgÒ ='v DOa.a I P ¯ rKºOºWºq± u v MOS a.a R JI a ³¯ r V O± D JEx na I`IKJ ¯ r T ± I F p D cR JIKx P [I cM P RnM J M bD@a _[I N I a I PP.\ R Jex M w J R J Dk SR x x S I P M e N D R P'DGP RM J DQ\b MON Y`I f X [Iv_ D N P R Y \ IIZ³ S DGP RM J M b cM P RnM J¿x$I I \ M _BIKx :<; P [I c R a Y DW\\ IKx v DOa.a I P p v MOS a.a R JI a ³ p na IKI`J ¯ v*vn ± IZ³ S DGP RM J f¿X Y'[EI`J*¯ r s ± I F<P I`JEx$IZx P [I v*v n IK³ S DQP RnM J a S Y'[ P [ DQP R P Y MOS \ x"xI a Y NR: I P [EI-_ D N P R Y \ I cM P RM J R J D J S J aP I D x ; M w f ~ F<P I`J a RnM J w DWa0DW\na M I FD c p R JEIKx b MON J M J p S J R b MON.c M w a u P [ MWS eO[ u7R P [ D x a MWc I R JEY M J a R aP I`JY ; DOa _ MWR J P IKx MOS P :<; ¤ MWNN a R J L SEc \ I ; ¯ r Á ± f L DQP I NKu v S I R Y'[Ô¯ r ÁOÁ ± D JEx ] R \ I ; ¯ r q rZ± c D x$I D Y MWNN IKY p P RnM J P M X Y'[IKJ ï a I F _ N I aa RnM J f ½ DGF I ; ] R \ I ; ¯ r ºWO± _ N I a I`J P IZx D _ D N P R Y \ IIZ³ S DGP RnM J M b cM P RnM J b MONmS J aP I D x ; J M J S J R b MON.c M w u w [ R Y'[ N I D x a f " ¤# ¹ r " " ¤ + r f " # ì # TQs ðÅÈð #pÉ f& à ¤iÇ. + r " & # ÄËÊ Ê + T r f f & " # Ä Ç. " ¤# + Os r V f ð È ð " u# É ì. " # ¯ & a ± ì " ¤# ¯ & a ± + GT r s f ð È ð " # ¯ & a ± É ² g & a f + f c f & a¾ÌÍÍÎ Ç ]Ï Ð ¯ & ì &ga ±PÑ Ä C ð Ä | ±ÒÔ ÓÓ + (r ì. r 0 Õ u Ä #. f. ¯ ±.
(45) ð ò. ¿|. /K /Ö |. ô/â ó ß ãã ö. LiI àâ. â ó àáBà. ó àá. Ä. w [ I N I " ¤# N IK_ N I a I`J Pa/P [EI R J aP'D J PD JI MOS a _ D N P R Y \ I I \ M Y R P ;Wu D JEx " # R ahP [I R J aPD J P'D JI MWS a SR x I \ M Y R P ; DGPP [I"YIKJ P I NM b0P [Iv_ D N P R Y \ I R bP [EIU_ D N P R Y \ I w I N IJ M P _ N I a IKJ PZfÈX [I M _BI N DGP MWNZu ñ & uN I`_ N I a I`J PaD x$I NR GDQP R I DQ\ M Je P [I SER x3_ DGP [ u w [ R \ I f ñ f & R aP [ DGP DQ\ M Je P [I _ Ê D N ÊP R Y \ I P N D ¡ IZY P MON.; f X [I ® I P I N.c a M J P [I N.R eW[ P [ D JEx a R x$I M b P [IIK³ S DGP RM J D N I S a S DQ\n\ ;N I b I NN IZx P M DOa r f x N D e b MWN YIO´ T f SR x D YKYI \ I N DGP RM J^´ fD xEx$IKx c DWaa ´ s f [ R aP MWN; I IKY P ´ f e N D R P'DGP RM J DQ\b MWN YI f X [ R a I F _ N I aa RnM J R a N I \ I GD J Pb MWN P [I o P M iWI a M w N I`e Rnc I f o0M P I P [ DGP R J P [EI-x N D e b MON Y`I u P [I D xxIKx c DWaaD Jx P [I-[ R aP MON.; I IKY PP I Nc a M b ~ ³ f ¯ ± u D Y MWNN IZY P RM J P I Nc x S I P M P [I I \ M Y R P ; Y SN GDGP SN I M bhP [EIY D NN.R I N SR xÃY DQ\n\ IKx CDGFI`H J Y MWNN IZY P RM J
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