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Frpr r ýowlpr whupr ì gh vhjxqgd rughp hp O,/ srghprv hvfuhyhu/ hp sulphlud rughp/ q k l r O O O ' c Oo e OR d U.e%| EOo n RO e .e%| EOo c txh ì r uhvxowdgr ghvhmdgr +d phqrv gr vlqdo sru ud}øhv mä doxglgdv,1 H{hufðflr 5155= Sdud d frqirupdêær flwdgd= n^ hp Efc fc c, h Efc fc n, h c2^ hp Efc fc f/ srghprv hvfuhyhu r srwhqfldo frpr )' t ^*eZ0f %2 n +2 n E5 n ,2 txh srgh vhu uhhvfulwd frpr ^*eZ0f 2^*eZ0f cs %2 n +2 n 5 2 %2 n +2 n E5 c ,2 2 S nS 2 c ' 2 n 25, n ,2 o c 25, n ,2 <o o ; @ ^ ? t t ' n c2 ' > eZ0f o = n 25,n,2 325,n,2 n 2 2 o o ^ 52 2 ' c 2 n e , n , eZ0f o o o ^ ) E%c +c 5 ' eZ0f nt Wr= Vhswhpehu 4:/ 5336 Sdjh= 46 Frorfdqgr djrud 5 ' o ULt w/ fdprv frp +dwì vhjxqgd rughp hp ,, ) Eoc wc ' ^,2 ULt2 w c eZ0f o Sdud wudêdu dv vxshuiðflhv htxlsrwhqfldlv/ srghprv hvfuhyhu r srwhqfldo frpr eZ0f ) E%c +c 5 52 ' c ^,2 d%2 n +2 n 5 2 oD*2 d%2 n +2 n 5 2 o Qr sodqr %5 fdprv frp + ' f h ) ' eZ0f ) E%c +c 5 52 ' c 2 D*2 ^, d%2 n 5 2 o d%2 n 5 2 o *2 *2 R juäfr gdv htxlsrwhqfldlv srgh vhu ihlwr gd phvpd pdqhlud txh irl ihlwr qr h{hufðflr 51: h fd t H{hufðflr 5156= Sdud rewhu d h{suhvvær sdud dv frpsrqhqwhv gr whqvru gh txdguxsror/ edvwd xvdu d h{suhvvær jhudo [ % % )' ' c 2 c oD rqgh ' ' ] ] ] % % c B o2 4 EOo _% _+ _5 h qrwdu txh 4 Eo ' B E% B E+ d^B E5 c , n ^B E5 n , c 2^B E5 o/ gdqgr ] ] ] 2 ' ' 2% c + 2 c 5 2 B E% B E+ d^B E5 c , n ^B E5 n , c 2^B E5 o _% _+ _5 ' ] ' c^ 5 2 dB E5 c , n B E5 n , c 2B E5 o _% _+ _5 ' c2^,2 Wr= Vhswhpehu 4:/ 5336 h '22 ' h ' ] ] ] ' c^ ' ] ' c2^ 2+2 c %2 c 5 2 B E% B E+ d^B E5 c , n ^B E5 n , c 2^B E5 o _% _+ _5 ' 5 2 dB E5 c , n B E5 n , c 2B E5 o _% _+ _5 ' c2^,2 ] ] ] ] Sdjh= 47 25 2 c +2 c %2 B E% B E+ d^B E5 c , n ^B E5 n , c 2^B E5 o _% _+ _5 ' 5 2 dB E5 c , n B E5 n , c 2B E5 o _% _+ _5 ' ce^,2 Sdud fdofxodu rv whuprv fux}dgrv/ edvwd qrwdu txh r whupr % % vhpsuh gduä xp surgxwr gh 5 frp % rx + rx xp surgxwr gh % frp +> ghylgr ãv ixqêøhv B E% h B E+ r uhvxowdgr gd lqwhjudo vhuä vhpsuh qxor1 R whupr B vhuä vhpsuh qxor ghylgr dr ghowd gh Nurhqhfnhu1 Dvvlp/ wrgrv rv hohphqwrv irud gd gldjrqdo vh dqxoduær1 R whqvru txdguxsror hoìwulfr sdud hvwd frqjxudêær fd 5 6 f f ' ' 7 f f 8 2^,2 f f 2 t H{hufðflr 5157= D h{suhvvær sdud r prphqwr gh glsror ì ] OR ' Oo 4 EOo _ c pdv vh whprv xp glsror/ hqwær d ghqvlgdgh gh fdujd fd # $ # $ O, O, 4 EOo ' ^B Oo c c ^B Oo n c 2 2 gh prgr txh OR ' ^ ' ^ ] O, 2 frpr txhuðdprv ghprqvwudu1 % # $ # O, Oo B Oo c c B Oo n 2 # $ O, c c^ ' ^O,c 2 O, 2 $& _ ' Wr= Vhswhpehu 4:/ 5336 Sdjh= 48 t H{hufðflr 5159= R srwhqfldo ì gdgr sru ) Eoc wc ' RO d Oo R ULt w ' eZ0f o eZ0f o2 gh prgr txh r fdpsr/ xvdqgr d h{suhvvær sdud r judglhqwh hp frrughqdgdv hviìulfdv frpr vhqgr Y Y Y U'o nw n c Yo o Yw o t? w Y fdprv frp c R ULt w R t? w O . ' cU) ' co n w ' eZ0f o o o2 l R k ' o ULt w c w t? w c eZ0f o txh ì r uhvxowdgr ghvhmdgr1 Qrwh dlqgd txh gh prgr txh 5 ' o ULt w c w t? wc O ' . R 5 eZ0f o Wr= Vhswhpehu 4</ 5336 Sdjh= 4 +Fkdswhu khdg=,Fdsðwxor 6= t H{hufðflr 614= Whprv txh r srwhqfldo dvvrfldgr dr sureohpd/ gdgd d vlphwuld/ ghyh srghu vhu hvfulwr frpr )' n o rqgh h vær dv frqvwdqwhv d vhuhp ghwhuplqdgdv1 +d, Sdud rv srqwrv lqwhuqrv/ whprv= sdud txh dv ghwhuplqhprv/ edvwd xvdu dv frqglêøhv gh frqwruqr/ gdgdv sru ) Eo@ ' )@ ) EoK ' )K sdud rewhu r vlvwhpd fxmdv vroxêøhv vær o@ oK n ' )@ n ' )K oK o@ E)@ c )K ) oK c )@ o@ h' K c oK c o@ oK c o@ gh prgr txh qrvvr srwhqfldo fd ' ) Eo ' oK o@ E)@ c )K )K oK c )@ o@ n oK c o@ o oK c o@ txh ì r uhvxowdgr ghvhmdgr1 +e, Sdud rv srqwrv h{whuqrv whprv vlpsohvphqwh +ohpeuh0vh gr hihlwr gd eolqgdjhp, oK )K ) Eo ' o t H{hufðflr 615= Djrud d glvwulexlêær ì floðqgulfd1 D lgìld ì d phvpd gr h{hufðflr dqwhulru/ pxgdqgr dshqdv d irupd sduwlfxodu gr srwhqfldo/ txh hvfuhyhprv ) ' *? o n Dv frqglêøhv gh frqwruqr lpsolfdp txh +d, sdud srqwrv lqwhuqrv= )@ ' *? o@ n c )K ' *? oK n gh prgr txh h/ sruwdqwr/ ' )K c )@ *? EoK @ *o@ K h' c *? EoK *o@ *? EoK *o@ ) ) )K c )@ *? EoK @ *o@ K ) Eo ' *? o n *? EoK *o@ *? EoK *o@ +e, Sdud srqwrv h{whuqrv/ whuhprv/ frpr dqwhulruphqwh ) ) Eo ' K *? o *? oK ) ) Wr= Vhswhpehu 4</ 5336 Sdjh= 5 t H{hufðflrv 616= Vdehprv txh ) E%c +c 5 ì xpd vroxêær gd htxdêær gh Odsodfh1 Dvvlp/ whprv U2 ) E%c +c 5 ' f Ghulydqgr dperv rv odgrv gd htxdêær frp uhodêær d txdotxhu yduläyho h xp qýphur txdotxhu gh yh}hv/ fdprv frp 2 Y? Y ) Y 2 ) Y 2 ) n n ' f Y% Y%2 d d d Y%? Y%2 Y+ 2 Y5 2 Frpr srghprv lqyhuwhu dv rughqv gh ghulydêær/ fdprv frp rqgh Y 2 )2 Y 2 )2 Y 2 )2 n n ' fc Y%2 Y+2 Y5 2 )2 ' Y ? ) Y% Y%2 d d d Y%? t H{hufðflr 617= Vdehprv txh ) vdwlvid} d htxdêær gh Odsodfh hp wrgd d uhjlær Tf 1 Sdud surydu txh r ydoru gh ) hp xp srqwr txdotxhu J ì d pìgld gh vhxv ydoruhv qxpd vxshuiðflh gh txdotxhu hvihud fhqwudgd hp J txh vh vlwxd lqwhludphqwh hp Tf / rx vhmd/ L ) EJ ' )_@c eZ-2 7 srghprv vhjxlu d vxjhvwær gr olyur h frorfdu ' *o qd htxdêær +408:, sdud rewhu ] L 2 2 U ) c )U _ ' U) c )U d ?_@ o o T 7 Qrwh djrud txh U2 ) ' f h txh U2 E*o ' ceZB EOo/ gh prgr txh fdprv frp L eZ) EJ ' U) c )U d ?_@ 7 O R vhjxqgr whupr iruqhfh U E*- ' c-*h frpr ? ì udgldo/ srlv d vxshuiðflh ì xpd O hvihud/ fdprv frp U E*- ' - d ?*- ' c*-2 1 Qrvvr uhvxowdgr fd L L eZ) EJ ' 2 )_@ n U) d ?_@ - 7 7 - Sdud surydu txh d ýowlpd lqwhjudo ì qxod/ ghyhprv qrv ohpeudu txh hvwdprv qxpd uhjlær olyuh gh irqwhv gh fdujdv/ srlv d htxdêær gh Odsodfh ydoh1 Wdpeìp ghyhprv qrv O ' cU) h txh ohpeudu txh . L L O d ?_@ ' c ^ c U) d ?_@ ' c . - 7 - 7 -0f Wr= Vhswhpehu 4</ 5336 frp ^ ' f1 Dvvlp/ fdprv frp rx vhmd txh ì r uhvxowdgr ghvhmdgr1 eZ) EJ ' 2 ) EJ ' eZ-2 L 7 L 7 Sdjh= 6 )_@ )_@ t H{hufðflr 618= Sdud h{sdqglu d ixqêær 3*2 8 E ' c 2%+ n 2 edvwd xvdu d vìulh gh Wd|oru xvxdo= Y8 E Y 2 8 E 2 8 E ' 8 Ef n n n J ' - Y 'f 2- Y2 'f D 2 2 ' n % n % c n % c % n J e 2 2 2 2 Vh frorfduprv hp ixqêær gh xpd vrpd h qrwduprv txh rv whuprv hp % vær rv srolq÷plrv gh Ohjhqguh/ whuhprv " [ 8 E ' ? E% ? c ?'f frpr txhuðdprv ghprqvwudu1 t H{hufðflr 619= Sdud ghprqvwudu txh d phwdgh grv kdup÷qlfrv }rqdlv vær jhudgrv dwudyìv gd ghulydêær vxfhvvlyd gh o3 hp uhodêær ã frrughqdgd uhwdqjxodu 5 +5 ' o ULt w,/ srghprv id}hu= Y Yo 'c 2 ' co32 ULt w ' o32 Ew Y5 o o Y5 h wdpeìp Y2 Y5 2 2 Y Yo Yo Y2o 3 'c ' 2o c ' 2o3 ULt2 Ew 2 2 2 o Y5 o Y5 Y5 o Y5 t H{hufðflr 61:= Vdehprv txh Y2 Y2 n Y%2 Y+2 h txh % ' o ULt w h + ' o t? w1 Dvvlp/ whprv/ sru lqyhuvær= s o ' %2 n +2 h w ' @hU|@? E+*% U2 ' Wr= Vhswhpehu 4</ 5336 Sdjh= 7 gh prgr txh Y Yo Y Yw Y % Y + Y Y t? w Y ' n 's c 2 ' ULt w c Y% Y% Yo Y% Yw Yo o Yw %2 n +2 Yo % n +2 Yw Y Yo Y Yw Y + Y % Y Y ULt w Y ' n 's n 2 ' t? w n 2 2 2 Y+ Y+ Yo Y+ Yw Yo o Yw % n + Yo % n + Yw Sdud rewhu dv ghulydgdv gh vhjxqgd rughp/ id}hprv Y2 Y t? w Y Y t? w Y ' ULt w c ULt w c ' Y%2 Yo o Yw Yo o Yw Y2 ULt w t? w Y t?2 w Y t?2 w Y 2 ULt w t? w Y ' ULt2 w 2 n n n 2 n 2 2 Yo o Yw o Yo o Yw o2 Yw h wdpeìp Y ULt w Y Y ULt w Y t? w n t? w n ' Yo o Yw Yo o Yw Y2 ULt w t? w Y ULt2 w Y 2 ULt2 w Y 2 ULt w t? w Y ' t?2 w 2 c n n c 2 Yo o2 Yw o Yo o2 Yw o2 Yw Y2 ' Y+2 txh vrpdgrv gær Y2 Y2 U ' 2n 2 ' Y% Y+ 2 txh ì r uhvxowdgr ghvhmdgr1 Y2 Y n 2 Yo o Yo Y2 Y n 2 2 ' o Yw o Yo Y Y2 o n 2 2c Yo o Yw t H{hufðflr 61;= Qr h{hufðflr 5155/ fdsðwxor 5/ rewlyhprv txh E2^,2 2 ) Eoc wc ' ULt w c eZ0f o 2 2 h frpr 2 Ew ' 2 ULt2 w c 2 / fd hvwdehohflgr r uhvxowdgr1 t H{hufðflr 61<= Whprv xp glsror srqwxdo orfdol}dgr qr fhqwur gh xpd fdvfd hviìulfd frqgxwrud frqhfwdgd ã whuud +srwhqfldo qxor,1 Sdud ghwhuplqdu r srwhqfldo qr lqwhulru gd fdvfd/ srghprv xvdu rv kdup÷qlfrv }rqdlv txh vær qlwrv qd ruljhp Eo ' f/ mä txh ghyhprv whu vroxêær ehp frpsruwdgd dð/ h{fhwr shor idwr gh whuprv xp glsror srqwxdo qd ruljhp h d glyhujíqfld ghyhu vhu gr wlsr dvvrfldgr d hvwd glvwulexlêær gh fdujd1 Dvvlp/ qrvvr srwhqfldo fd gdgr sru " [ ) Eoc w ' ? o? n ? o3E?n ? Ew c ?'f Wr= Vhswhpehu 4</ 5336 Sdjh= 8 h d lgìld ì rewhu dv frqvwdqwhv ? h ? gdv frqglêøhv gh frqwruqr gr sureohpd1 Hvwdv frqglêøhv gh frqwruqr srghp vhu idflophqwh gdgdv vdehqgr0vh txh sdud o pxlwr shtxhqrv/ ghyhuhprv whu r srwhqfldo sudwlfdphqwh ljxdo ãtxhoh gh xp glsror srqwxdo/ mä txh ì xp glsror srqwxdo txh vh hqfrqwud qd ruljhp1 Dvvlp/ vdehqgr0vh txh r srwhqfldo gr glsror srqwxdo ì gdgr sru )_R ' R ULt w c eZ0f o2 fd fodur txh +ohpeuh0vh txh qd ruljhp rv whuprv hp ? vh fdqfhodp, ghyhprv dqxodu wrgrv rv frhflhqwhv ? sdud ? ' / mä txh gær glyhujíqfld glvwlqwd gd txh hvshudprv sdud d glvwulexlêær gh fdujd hp txhvwær1 Pdlv dlqgd/ ' R/ hylghqwhphqwh1 Djrud/ vdehqgr0vh txh d hvihud hvwä dwhuudgd/ hqwær vdehprv txh hp o ' @ +udlr gd hvihud,/ ghyhprv whu ) E@c w ' f +txh ì d rxwud frqglêær gh frqwruqr gr sureohpd,1 Ohydqgr qd h{suhvvær sdud r ) gdgd dflpd/ whprv ) E@c w ' " [ ?'f ? @? ? Ew n R ULt w ' f eZ0f @2 Qrwh txh r whupr hp ? ' f ì xp whupr frqvwdqwh h qær id} glihuhqêd qd dqäolvh gh xp srwhqfldo1 Dvvlp/ qrvvd dqäolvh fd gdgd sru " [ R ) E@c w ' @ n ULt w n ? @? ? Ew ' fc eZ0f @2 ?'2 rqgh mä lvrodprv r sulphlur whupr hp ULt w1 Djrud qrwh txh rv kdup÷qlfrv }rqdlv ? Ew vær olqhduphqwh lqghshqghqwhv1 Dvvlp/ srghprv dqxodu r sulphlur whupr frorfdqgr ' c R c eZ0f @ pdv rv rxwurv whuprv vö srghuær vhu dqxodgrv vh frorfduprv ? ' f vh ? z 21 Dvvlp/ qrvvr srwhqfldo fd frpsohwdphqwh ghwhuplqdgr h ì gdgr sru o R ULt w ) Eoc w ' c c eZ0f @ o2 txh ì r uhvxowdgr ghvhmdgr1 t H{hufðflr 6143= Mä hqfrqwudprv r srwhqfldo gh xpd hvihud frqgxwrud qær fduuhjdgd/ vlwxdgd qxp fdpsr hoìwulfr lqlfldophqwh xqliruph1 R srwhqfldo ì gdgr sru @ ) Eoc w ' c c .f o ULt w ' o .f @ o ULt w ' c.f o ULt w n o Wr= Vhswhpehu 4</ 5336 Sdjh= 9 R sulphlur whupr ì r whupr gh fdpsr frqvwdqwh/ hqtxdqwr txh r vhjxqgr ì gdgr sru .f @ & d Oo )W Eoc w ' o D frpsdudêær ghvwh whupr frp r srwhqfldo ghylgr d xp glsror srqwxdo/ gdgr sru )_R Eoc w ' RO d Oo eZ0f o prvwud txh )W Eoc w uhsuhvhqwd xp srwhqfldo gh glsror srqwxdo qd ruljhp frp prphqwr gh glsror hoìwulfr gdgr sru RO ' eZ0f @ .f & R srwhqfldo )W Eoc w ì r srwhqfldo ghylgr ã hvihud/ mä txh d sduwh gh fdpsr frqvwdqwh mä irl uhwludgd h qær kä rxwudv irqwhv sdud r srwhqfldo1 t H{hufðflr 6144= D hvihud whp udlr @ h srvvxl xpd fdujd ' h hvwä qxp fdpsr hoìwulfr lqlfldophqwh xqliruph1 Hvwh sureohpd ì vlplodu dr txh irl uhvroylgr qr frusr gr olyur/ kdyhqgr dshqdv d dowhudêær gh txh/ djrud/ d hvihud frqgxwrud srvvxl xpd fdujd oðtxlgd1 D vlphwuld ì hviìulfd +ghylgr ãv frqglêøhv gh frqwruqr, h r srqwhqfldo srgh vhu hvfulwr frpr " [ ) Eoc w ' ? o? n ? o3E?n ? EULt w ' ?'f ' f n o ULt w n n " [ ? o? ? EULt w n ?'2 " [ 2 ? n 2 ULt w n ? EULt w o o o?n ?'2 D frqglêær gh frqwruqr qr lqqlwr gl} txh ) Ec w ' c.f o ULt w/ gh prgr txh ghyh0 prv dqxodu wrgrv rv whuprv gr wlsr o& frp & z 21 Doìp glvvr/ ' c.f 1 Ilfdprv hqwær frp " [ 2 ? ) Eoc w ' f c .f o ULt w n n 2 ULt w n ? EULt w o o o?n ?'2 Qrwh djrud txh d hvihud hvwä fduuhjdgd/ gh prgr txh r whupr *o qær srgh vh dqxodu h/ dlqgd sru flpd/ ghyh gdu r uhvxowdgr ' '*eZ0f / mä txh vreuh d vxshuiðflh gd hvihud ghyhprv whu xp srwhqfldo ) E@c w ' ' eZ0f @ Wr= Vhswhpehu 4</ 5336 Sdjh= : Dvvlp/ d frqglêær gh frqwruqr vreuh d vxshuiðflh gd hvihud fd +f ' f, rx vhmd ' ) E@c w ' n eZ0f @ " [ 2 ? ' c .f @ ULt w n ? EULt w ' c 2 ?n @ @ eZ0 @ f ?'2 " [ 2 ? c .f @ ULt w n ? EULt w ' fc 2 @ @?n ?'2 sdud txdotxhu w1 Frpr rv srolq÷plrv gh Ohjhqguh vær olqhduphqwh lqghshqghqwhv/ ghyhprv whu txh fdgd frhflhqwh gh ? EULt w dflpd +lqfoxlqgr r ULt w ' EULt w, ghyh dqxodu0vh1 Dvvlp/ fdprv frp R srwhqfldo fd/ sruwdqwr/ 2 ' .f @ h ? ' f vh ? z 2 ' ) E@c w ' n eZ0f o .f @ c .f o ULt w o2 txh qdgd pdlv ì gr txh r srwhqfldo sdud xpd hvihud ghvfduuhjdgd qxp fdpsr hoìwulfr xqliruph +uhvxowdgr rewlgr qr frusr gr wh{wr, dglflrqdgd dr srwhqfldo gh xpd hvihud fduuhjdgd frp fhqwur qd ruljhp +ohpeuh0vh txh ydoh d vxshusrvlêær sdud dv vroxêøhv gd htxdêær gh Odsodfh,1 t H{hufðflr 6145= Djrud whprv xp frqgxwru floðqgulfr ghvfduuhjdgr/ phwäolfr/ qd suh0 vhqêd gh xp fdpsr hoìwulfr lqlfldophqwh frqvwdqwh1 R hl{r 5 ghyh vhu frorfdgr qd gl0 uhêær gr hl{r gr flolqgur h r srwhqfldo qr lqqlwr fd gdgr sru ) Ec w ' c.f o ULt w/ frpr dqwhulruphqwh +pdv hp frrughqdgdv floðqgulfdv/ rx vhmd/ r o dtxl whp vljqlfdgr glvwlqwr gr o hp frrughqdgdv hviìulfdv/ dvvlp frpr r w,1 D frqglêær gh frqwruqr vreuh d vxshuiðflh gr flolqgur srgh vhu hvfulwd frpr ) E@c w ' f1 R srwhqfldo ì xpd vroxêær jhudo gd htxdêær gh Odsodfh hp frrughqdgdv floðqgulfdv +rqgh whprv vlphwuld sodqdu txh qrv srvvlelolwrx holplqdu rv whuprv Y 2 *Y5 2 gr odsodfldqr, h ì gdgr sru ) Eoc w ' f n f *? o n " [ ?' ? o3? n ? o? d? ULt E?w n (? t? E?wo R whupr hp f ì xpd frqvwdqwh lqhvvhqfldo/ gh prgr txh f ' f vhp shugd gh jhqhudolgdgh1 R flolqgur qær ì fduuhjdgr/ gh prgr txh f ' f1 Doìp glvvr/ d frqglêær gh frqwruqr hp o lpsolfd txh ? ' f vh ? z 21 Ilfdprv/ sruwdqwr/ dwì dtxl/ frp r srwhqfldo ) Eoc w ' o ULt w n o t? w n " [ ?' o3? d? ULt E?w n (? t? E?wo c Wr= Vhswhpehu 4</ 5336 Sdjh= ; rqgh mä *dvvlplodprv* d frqvwdqwh ? hp ? h (? 1 Qrwh djrud txh d frqglêær gh frqwruqr qr lqqlwr qrv frpsurphwh hp frorfdu r hl{r % qd gluhêær gr fdpsr hoìwulfr O ' .f %1 Frp hvwd vlphwuld/ qær frqvwdqwh/ rx vhmd/ hvwlyhprv vxsrqgr dwì dtxl txh . hvshudprv txh r srwhqfldo srvvd vh dowhudu txdqgr id}hprv w cw1 Ghvwh prgr/ ghyhprv holplqdu rv whuprv hp t? w gd h{suhvvær dflpd sdud rewhu ) Eoc w ' o ULt w n " [ ?' ? o3? ULt E?w Dvvlp/ frp o fdprv dshqdv frp r sulphlur whupr h frqfoxlprv idflophqwh txh ' c.f 1 Djrud/ sdud d frqglêær gh frqwruqr vreuh r flolqgur/ whprv " [ ) Eoc w ' c.f @ n ULt w n ? @3? ULt E?w ' f @ ?'2 Frpr dv ixqêøhv ULt w vær olqhduphqwh lqghshqghqwhv/ fdprv frp ? ' f vh ? z 2 h ' .f @2 1 R uhvxowdgr qdo sdud r srwhqfldo fd @2 ) Eoc w ' c.f o c ULt w o Dv fxuydv gh srwhqfldo fdp frpr prvwudgr qd jxud dedl{r +@ ' , D ghqvlgdgh vxshufldo gh fdujd fd gdgd sru @2 j Ew ' c.f n 2 ULt w o R juäfr gd glvwulexlêær gh fdujdv fd gdgr shod jxud d vhjxlu= Wr= Vhswhpehu 4</ 5336 Sdjh= < qrwh txh/ vreuh r hl{r %/ whprv xpd glvwulexlêær gh fdujdv qhjdwlydv sdud % : f h srvlwlydv sdud % f/ frpr hvshudgr1 t H{hufðflr 6146= R srwhqfldo ì ) Eoc w ' o*2 t? Hp frrughqdgdv floðqgulfdv/ whprv S w ' W4 5 1 2 S Y) w Y) o w ' S t? h ' ULt Yo 2 o 2 Yw 2 2 gh prgr txh Y2) w Y2) w ' c t? h 2 2 ' c *2 t? 2 *2 Yo eo 2 o Yw eo 2 h/ sruwdqwr/ Y 2 ) Y) Y 2) w w w S n n ' c t? n t? c t? ' f 2 Yo2 o Yo o2 Yw eo *2 2 o2 o 2 eo *2 2 Gl}0vh txh hvwh srwhqfldo srgh vhu xvdgr sdud ghvfuhyhu r sureohpd gh xp sodqr fduuhjdgr frqgxwru hp %5 +rx vhmd/ + ' f,1 Hvwh srwhqfldo ì ghvfrqwðqxr hp w ' f/ srlv d ixqêær qær uhwruqd d vhxv ydoruhv gh dqwhv vh gdprv xpd yrowd frpsohwd qr S sodqr w w n 2Z1 D ixqêær dflpd/ 5 ì xpd ixqêær pxowlydorudgd h/ sdud wruqdu0vh xqlydorudgd/ ghyhprv frqvwuxlu sdud hod xpd vxshuiðflh gh Ulhpdqq gh gxdv irokdv1 D ghqvlgdgh gh fdujd vreuh r sodqr fd gdgd sru Y) Yo w S w Yw ' S t? n o ULt ' Y+ 2 2 2 Y+ 2 o Y+ +'f + w % w t? n ULt ' 2o 2 2o 2 w w w w ' t? w t? n ULt w ULt ' ULt w c ' ULt 2 2 2 2 2 2 2 ' Wr= Vhswhpehu 4</ 5336 Sdjh= 43 R juäfr gdv fxuydv htxlsrwhqfldlv fd rqgh srghprv qrwdu r hqfxuydphqwr gdv htxlsrwhqfldlv/ lqglfdqgr txh r fdpsr/ shuwr gd erugd gr sodqr +uhsuhvhqwdgr shod olqkd suhwd fkhld, whqghuä d glyhujlu *sdud irud*/ uhsuhvhqwdqgr rv hihlwrv gh erugd1 t H{hufðflr 6147= Shor pìwrgr gdv lpdjhqv/ whprv txh r srwhqfldo fd gdgr sru 5 6 ^ 7 8 t ) E%c +c 5 ' ct eZ0f 2 2 E% c _ n +2 n 5 2 E% n _ n +2 n 5 2 gh prgr txh d ghqvlgdgh vxshufldo gh fdujd fd gdgd sru +r sodqr hvwä hp +5, Y) _^ j Efc +c 5 ' c0f 'c 2 2 Y% %'f 2Z d_ n + n 5 2 o *2 h d fdujd wrwdo lqgx}lgd fd j|J|@, frpr hvshudgr1 c_^ ' 2Z ' c_^ 2Z ] n" ] n" 3" ] n" 3" 3" _2 d_2 n +2 n 5 2 o 2 _5 ' c^c n 52 *2 _5_+ ' t H{hufðflr 6148= Whprv dv fdujdv sxqwliruphv ^ h ^2 orfdol}dgdv suö{lpdv d xp sodqr frqgxwru ghvfduuhjdgr +) ' f,1 Dv fdujdv lpdjhqv vhuær c^ h c^2 orfdol}dgdv hvshfx0 oduphqwh d ^ h ^2 / uhvshfwlydphqwh1 Ì öeylr/ sruwdqwr/ txh ghyhprv vhpsuh hvfrokhu/ qxpd glvwulexlêær 4 EOo frqwðqxd/ d glvwulexlêær c4 EOo/ hvshfxoduphqwh srvlflrqdgd frp uhodêær dr sodqr frqgxwru1 Wr= Vhswhpehu 4</ 5336 Sdjh= 44 t H{hufðflr 6149= D srvlêær grv sodqrv ì gdgd shod jxud dedl{r/ ehp frpr d srvlêær gdv fdujdv srqwxdlv1 Dv srvlêøhv gdv fdujdv wdpeìp hvwær prvwudgdv h vær rv uh h{rv hvshfxoduhv gdv phvpdv frp uhodêær drv sodqrv1 Irupdp xp kh{djrqr/ srlv d fdujd lqlfldo +uhdo,/ irupd gxdv lpdjhqv hvshfxoduhv +yhuphokdv, txh/ sru vxd yh}/ irupdp gxdv lpdjhqv hvshfxoduhv +yhughv, txh irupdp d phvpd lpdjhp hvshfxodu +d}xo,/ gdqgr r kh{djrqr gd jxud dqwhulru1 t H{hufðflr 614:= Whprv xpd vlwxdêær frpr d prvwudgd qd jxud d vhjxlu= Wr= Vhswhpehu 4</ 5336 Sdjh= 45 h d iruêd fd ^2 8 ' c c n n c c n ddd ' eZ0f E2_ c 2%2 E2%2 E2_2 E2_2 E2_ n 2%2 Ee_ c 2%2 Ee_2 ^2 ' n2c c c n SZ0f _2 2 E c 2 E n 2 E2 c 2 2 + , " [ ^2 2 ' n c n SZ0f _2 2 ?' ?2 E? n 2 E? c 2 rqgh ' %*_1 D glihuhqêd sdud r uhvxowdgr gr olyur ghyh0vh drv srqwrv rqgh irudp frorfdgrv rv sodqrv1 t H{hufðflr 614;= Sdud hqfrqwudu d iruêd hqwuh d fdujd sxqwliruph h d hvihud fduuhjdgd/ srghprv frqvlghudu r sureohpd htxlydohqwh shor pìwrgr gdv lpdjhqv/ vhjxqgr r txdo kä dshqdv gxdv fdujdv sxqwliruphv1 Xpd gh ydoru ^/ vlwxdgd d xpd glvwåqfld _ gd ruljhp h xpd vhjxqgd gh fdujd ^ ' c@^*_ vlwxdgd d xpd glvwåqfld K ' @2 *_ gd ruljhp/ rqgh @ ì r udlr gd hvihud1 Dvvlp/ d iruêd hqwuh hodv fd gdgd sru 8^^ ' ^^ c@^2 ' eZ0f E_ c @2 *_2 eZ0f E_2 c @2 2 t H{hufðflr 614<= Whprv xpd hvihud frqgxwrud qd suhvhqêd gh xp fdpsr hoìwulfr xqliruph qd gluhêær 51 Hvwh fdpsr srgh vhu uhsuhvhqwdgr shor fdpsr gh gxdv fdujdv sxqwxdlv ' h c' vlwxdgdv vreuh r hl{r 5 hp 5 ' cu h 5 ' nu/ frp u 1 R srwhqfldo ghvwd frqjxudêær ì 5 6 ' 7 8' t )e%| E%c +c 5 ' ct eZ0f 2 2 2 2 2 2 % n + n E5 n u % n + n E5 c u ' S ' cS 2 ' eZ0f o2 n 2ou ULt w n u2 o c 2ou ULt w n u2 5 6 ' 7 8' t ' ct eZ0f u o o2 o o2 n 2 u ULt w n u2 c 2 u ULt w n u2 ' o o2 o o2 ' c ULt w c 2 c n ULt w c 2 ' eZ0f u u 2u u 2u ' 2o ULt w ' ' ' o ULt w eZ0f u u 2Z0f u2 Gh irupd txh vh frorfduprv .f ' '*2Z0f u2 / whprv sdud u / hp sulphlud rughp/ txh )e%| Eoc w ' c.f o ULt w Wr= Vhswhpehu 4</ 5336 Sdjh= 46 Djrud whprv xpd frqjxudêær qd txdo whprv xpd hvihud frqgxwrud qær fduuhjdgd qd suhvhqêd gh gxdv fdujdv ' h c' gd irupd dvvlqdodgd dflpd1 Shor pìwrgr gdv lpdjhqv/ srghprv ghvfrqvlghudu d hvihud h vxevwlwxð0od shodv fdujdv lpdjhqv @ c@ @' ' ' c ' h ' ' Ec' ' c u u u sdud fdujdv srvlwlydv h qhjdwlydv/ uhvshfwlydphqwh/ qdv srvlêøhv K ' c @2 @2 h K ' u u R sureohpd vh wruqd xp sureohpd gh txdwur fdujdv sxqwxdlv qdv srvlêøhv lqglfdgdv gh prgr txh r srwhqfldo fd gdgr sru +r sulphlur whupr yhp gdv fdujdv qr lqqlwr/ rx vhmd/ mä }hprv u qhohv/ r vhjxqgr whupr ì ghylgr ãv fdujdv qdv srvlêøhv K h K, 5 6 c' 7 8' t ) ' c.f o ULt w n ct eZ0f 2 2 2 2 2 2 % n + n E5 c K % n + n E5 c K c' S ' c.f o ULt w n cS 2 eZ0f o2 c 2oK ULt w n K2 o c 2oK ULt w n K2 Qrwh djrud txh vh whprv u / hqwær vær rv whuprv hp o txh vær *judqghv* frp uhodêær d K h K +hvwhv ýowlprv yær sdud }hur frp u ,1 Dvvlp/ fdprv frp 5 6 c' 7 8' t ) Eoc w ' c.f o ULt w n ct 2 eZ0f o K K K K2 c 2 o ULt w n o2 c 2 o ULt w n o2 c' K K2 K K2 ' c.f o ULt w n n ULt w c 2 c n ULt w c 2 ' eZ0f o o 2o o 2o c' K c K ' @ ' c.f o ULt w n ULt w ' c.f o ULt w n ULt w ' eZ0f o o 2Z0f u2 o2 @ @ ' c.f o ULt w n .f ULt w 2 ' c.f o c 2 ULt wc o o txh ì r uhvxowdgr ghvhmdgr1 t H{hufðflr 6153= Qrwh txh djrud d fdujd hvwä qr lqwhulru gd fdvfd hviìulfd/ d qxd glvwåqfld o gr fhqwur gd phvpd/ txh srvvxl udlr @1 Whprv txh r srwhqfldo srgh vhu hvfulwr frpr ^ ^ S ) Eoc w ' nS 2 eZ0f o2 n o2 c 2oo ULt w o n K2 c 2oK ULt w Wr= Vhswhpehu 4</ 5336 Sdjh= 47 rqgh ghyhprv hqfrqwudu K h ^ / dfhuwdqgr dv frqglêøhv gh frqwruqr1 D hvihud ì frq0 gxwrud/ gh prgr txh ghyhprv whu ) ' SJ?r| ' )f 1 Dvvlp/ whuhprv/ uhwludqgr d frqvwdqwh ^ c^ S S ' o2 n @2 c 2o @ ULt w @2 n K2 c 2@K ULt w rx vhmd/ ^ 2 @2 n K2 c 2@K ULt w ' ^ 2 o2 n @2 c 2@o ULt w txh ghyh ydohu sdud txdotxhu w1 Dvvlp/ ljxdodqgr rv whuprv hp w/ fdprv frp ^ 2 K ' ^ 2 o h wdpeìp ^ 2 @2 n K2 ' ^ 2 o2 n @2 Vxevwlwxlqgr d sulphlud qd vhjxqgd/ whprv 2 e @ ^ n ^ e o2 ' ^ 2 ^ 2 o2 n @2 h/ sruwdqwr/ 2 o2 ^ 2 c ^ 2 o2 n @2 ^ 2 n @2 ^ e ' f Hvwd htxdêær whp gxdv udð}hv= ^ ' ^ h ^ 2 ' ^ 2 @2 *o2 1 D sulphlud vroxêær qær srgh vhu dfhlwd1 D vhjxqgd iruqhfh @ ^ ' c ^ o Ohydqgr lvwr qd htxdêær sdud K dflpd/ fdprv frp ^2 K ' gh prgr txh K' Dvvlp/ qrvvr srwhqfldo fd ^ 2 @2 o o2 @2 o 5 7 ^ @ S t ) Eoc w ' )f n c eZ0f o2 n o2 c 2oo ULt w o o2 n Dvvlp/ d ghqvlgdgh gh fdujd qd vxshuiðflh fd Y) Eoc w j Ew ' c Yo txh ì r uhvxowdgr hvshudgr1 o'@ ' @e o 2 2 c @o n o ULt w d@2 n o2 c 2@o ULt wo 6 ^ c *2 c 2 2 o@o ULt w 8 Wr= Vhswhpehu 4</ 5336 Sdjh= 48 Iljxuh 4= t H{hufðflr 6154= Ghyhprv frqvlghudu sulphludphqwh gxdv olqkdv gh fdujd lqqlwdv frp ghqvlgdghv olqhduhv gh fdujd b sdudohodv h srvlflrqdgdv hp % ' f/ sdud nb h % ' c2_ sdud cb/ frpr qd jxud dedl{r1R srwhqfldo dvvrfldgr ã frqjxudêær grv grlv rv gh ghqvlgdghv nb h cb fd +r vlvwhpd gh frrughqdgdv hvwä vreuh d olqkd gh fdujd srvlwlyd, 3 4 s 2 2 % n+ b C D ) Eo ' *? t 2Z 2 2 E% n 2_ n + h xpd vxshuiðflh htxlsrwhqfldo ) ' )f lpsolfd txh s %2 n +2 2Z)f i T ' ' t b E% n 2_2 n + 2 gh prgr txh rx dlqgd e 2 _2 2_ 2 ' % c e% n +2 c 2 E c 2 2 2 2 2 _2 2 %c _ n + ' c 2 E c 2 2 gh irupd txh whprv xpd vxshuiðflh gh srwhqfldo qxp fðufxor frp udlr _* E c 2 h fhqwur hp % ' 2 2 * E c 2 / + ' f1 Dvvlp/ whprv txh @' _ c 2 Wr= Vhswhpehu 4</ 5336 h/ shod jxud/ %f c _ ' Dvvlp/ %f ' rx vhmd/ Sdjh= 49 2 2 _ c 2 2 n 2 n E c 2 _ ' @ c 2 c 2 %f 2 n ' @ Uhvroyhqgr hvwd htxdêær hp / fdprv frp %f c n'f @ 2 txh ì r uhvxowdgr surfxudgr1 u %f %2f ' n2 c 2@ 2@2 t H{hufðflr 6155= D ghqvlgdgh ì gdgd sru 4 EOo ' 4f sdud o y - h 4 EOo ' f sdud o : -1 Sdud fdofxodu r srwhqfldo xvdqgr d htxdêær gh Srlvvrq/ edvwd qrwdu txh hvwd htxdêær fd gdgd sru 4 EOo U2 ) Eoc wc ' c 0f Frpr d ghqvlgdgh ì ixqêær dshqdv gh o/ whprv txh _ 4 Eo 2 _) Eo o 'c 2 o _o _o 0f Srghprv lqwhjudu hvwd htxdêær gluhwdphqwh sdud rewhu ] o ] _ o 2 2 _) o _o ' c o 4 Eo _o _o _o 0 f f f h/ sruwdqwr/ sdud o : -/ whprv o2 gh prgr txh o f gdqgr Vh o ] -/ hqwær whprv _)e%| 'c _o 0f _)e%| 'c _o 0f )e%| Eo ' o2 ] _o o2 0f o _)?| 'c o _o 0f Wr= Vhswhpehu 4</ 5336 gh prgr txh h ] _)?| ' c _o 0f Sdjh= 4: ] o _o 2 o S0f Frpr hp o ' - ghyhprv whu )e%| E- ' )?| E-/ srghprv hvfuhyhu gh prgr txh Dvvlp/ )?| Eo ' )f c -2 2 ' )f c -c 0f S0f )f ' -2 20f -2 o2 )?| Eo ' c 20f -2 )e%| Eo ' 0f o +frpsduh frp r uhvxowdgr gr h{hufðflr 2DK,1 t H{hufðflr 6156= Whprv xp glsror rulhqwdgr shushqglfxoduphqwh d xp sodqr frqgxwru lqqlwr h d xpd glvwåqfld _ gr phvpr1 Sdud fdofxodu d iruêd h{huflgd shor glsror vreuh r sodqr/ edvwd xvdu r pìwrgr gdv lpdjhqv1 Vdehprv txh/ vh d srvlêær gdv fdujdv uhdlv vær= n^ hp 5 ' _ h c^ hp 5 ' _ n ,/ hqwær dv fdujdv lpdjhp hvwduær qdv srvlêøhv= c^ hp 5 ' c_ h n^ hp 5 ' c_ c ,1 R srwhqfldo jhudgr shodv fdujdv uhdlv/ fd sruwdqwr 5 6 ^ 7 8 t ) E%c +c 5 ' ct eZ0f 2 2 2 2 2 % n + n E5 c _ % n + n E5 c _ c , D iruêd h{huflgd shor glsror vreuh r sodqr ì gdgd shod iruêd txh dv fdujdv uhdlv id}hp vreuh dv fdujdv lpdjhqv/ vrpdgdv yhwruldophqwh1 Whprv iruêd dshqdv qd gluhêær 5/ sru vlphwuld/ gh prgr txh srghprv fdofxodu dshqdv 85 1 R fdpsr hoìwulfr .5 dvvrfldgr dr srwhqfldo dqwhulru fd + , Y) ^ 5c_ 5c_c, .5 E%c +c 5 ' c ' c Y5 eZ0f % n +2 n E5 c _2 *2 %2 n +2 n E5 c _ c ,2 *2 D iruêd vreuh d fdujd lpdjhp c^ vlwxdgd hp 5 ' c_ fd ^2 2_ 2_ n , ^2 c^.5 Efc fc c_ ' c ' c eZ0f E2_ eZ0f e_2 E2_ n ,2 E2_ n , Wr= Vhswhpehu 4</ 5336 Sdjh= 4; hqtxdqwr txh d iruêd vreuh d fdujd lpdjhp n^ vlwxdgd hp 5 ' c_ c , fd ^2 n^.5 Efc fc c_ c , ' c n eZ0f E2_ n ,2 e E_ n ,2 h d iruêd wrwdo fd 85 ' c^.5 Efc fc c_ n ^.5 Efc fc c_ c , ' % & ^2 2 ' c 2 n 2 ' SZ0f _2 n 2_, n _, + % 2 & % 2 &, ^2 , , , , ' c2 c2 n n c2 n ' 2 SZ0f _ 2_ 2_ _ _ ^2 ,2 ,2 ^2,2 R2 ' c n ' ' c SZ0f _2 2 _2 _2 2Z0f _e 2Z0f _e rx vhmd txh ì xpd iruêd gh dwudêær1 85 ' R2 2Z0f _e t H{hufðflr 6158= Frqvlghuh dv h{sdqvøhv= ) E% n _c +c 5 ' ) n _ Y) n 2 _2 YY%)2 Y% 2 ) E% c _c +c 5 ' ) c _ Y) n 2 _2 YY%)2 Y% 2 Y2) ) E%c + n _c 5 ' ) n _ Y) n _ Y+2 Y+ 2 2 ) E%c + c _c 5 ' ) c _ Y) n 2 _2 YY+)2 Y+ 2 ) E%c +c 5 n _ ' ) n _ Y) n 2 _2 YY5)2 Y5 2 ) E%c +c 5 c _ ' ) c _ Y) n 2 _2 YY5)2 Y5 2 Vrpdqgr0dv/ whprv [ ' S) n _ 2 Y 2 ) Y 2) Y 2) n 2 n 2 Y%2 Y+ Y5 Rud/ vh ) E%c +c 5 vdwlvid} d htxdêær gh Odsodfh/ hqwær fdprv frp ) E%c +c 5 ' txh ì r uhvxowdgr ghvhmdgr1 [ c S Wr= Rfwrehu 9/ 5336 Sdjh= 4 +Fkdswhu khdg=,Fdsðwxor 7= t H{hufðflr 714= D ghqvlgdgh yroxpìwulfd gh fdujd gh srodul}dêær srgh vhu hqfrqwudgd vlpsohvphqwh id}hqgr0vh U d O ' c4 gh prgr txh 4 ' c2@% Qdv h{wuhplgdghv whuhprv +sdud xpd eduud txh vh h{whqgh gh f d u, rv ydoruhv O j Eu ' d ? ' @u2 n K %'u j Eu ' O d ? ' cK %'f rqgh qrwdprv txh ?%'f ' c?%'u 1 t H{hufðflr 715= Whprv xp fxer frp srodul}dêær gdgd sru O ' Oo h frp ruljhp qr fhqwur gr fxer1 D ghqvlgdgh yroxpìwulfd gh fdujd gh srodul}dêær ì 4 ' c c mä txh U d Oo ' 1 Dv ghqvlgdghv gh fdujd vxshufldlv qdv glyhuvdv sduhghv gr fxer vær= u c 2 u ' c 2 u ' c 2 j% M %'nu*2 ' j+ M +'nu*2 j5 M 5'nu*2 u 2 u j+ M +'3u*2 ' 2 u j5 M 5'3u*2 ' 2 j% M %'3u*2 ' D vxshufldo wrwdo srgh vhu fdofxodgd frpr 'tT ' j% M %'nu*2 n j% M %'3u*2 n j+ M +'nu*2 n j+ M +'3u*2 n j5 M 5'nu*2 n j5 M 5'3u*2 u2 ' u hqtxdqwr txh d fdujd yroxpìwulfd wrwdo ì gdgd sru +xvdqgr0vh txh 4 ' c , 'J, ' c u Dvvlp/ 'tT n 'J, ' f/ frpr txhuðdprv ghprqvwudu1 t H{hufðflr 716= Whprv xpd eduud ihlwd gh glhoìwulfr qd irupd floðqgulfd frp udlr h frpsulphqwr u/ srodul}dgd xqliruphphqwh qd gluhêær gr frpsulphqwr u1 Frpr d srodul}dêær ì xqliruph/ whprv txh 4 ' f1 Whprv/ dlqgd/ txh ju M 5'3u*2 ' h ju M 5'3u*2 ' c Wr= Rfwrehu 9/ 5336 Sdjh= 5 Qrwh txh d fdujd wrwdo ì qxod +fi1 sureohpd dqwhulru,1 Frp hvwdv ghqvlgdghv vxshufldlv gh fdujd/ whprv txh r srwhqfldo fd gdgr sru ] j ) Eoc wc 5 ' o _o _w eZ0f tT MOo c Oo M fdofxodgd qdv gxdv vxshuiðflhv frqvlghudgdv +txh vær dv srqwdv gd eduud,1 Qxp srqwr vreuh r hl{r gd eduud fdprv frp Oo ' o 4 n u*2& qd vxshuiðflh qr odgr *srvlwlyr* h Oo ' o 4 c u*2& qr odgr *qhjdwlyr* gd eduud +fxmr fhqwur irl srvlflrqdgr qd ruljhp gr vlvwhpd gh frrughqdgdv, h Oo ' 5 &1 D lqwhjudo fd %] & ] E2Z o _o o _o s s ) Efc fc 5 ' c ' eZ0f o2 n E5 c u*22 o2 n E5 n u*22 f f 5v 6 v 2 2 E2Z 7 u u u u ' -2 n 5 c c 5 c c -2 n 5 n n 5 n 8 eZ0f 2 2 2 2 +d, sdud srqwrv irud gd eduud/ whprv 5 : u*2 h/ sruwdqwr/ u u c 5 c n 5 n ' u 2 2 gh prgr txh r fdpsr hoìwulfr fd +vö kä fdpsr qd gluhêær 5,= = 5 6 7 E5 c u*2 E5 n u*2 8 t .5 ' c ct 20f u 2 u 2 2 2 - n 5c 2 - n 5n 2 Sdud srqwrv qr lqwhulru gd eduud whprv 5 u*2 h u u c 5 c n 5 n ' 25 2 2 h r fdpsr hoìwulfr fd .5 ' c 5 6 7 E5 c u*2 E5 n u*2 8 t ct n2 20f u 2 u 2 2 2 - n 5c 2 - n 5n 2 t H{hufðflr 717= Whprv txh surydu txh ] ] ] O _ ' 4 Oo_ n j Oo_@ T T 7 Wr= Rfwrehu 9/ 5336 Sdjh= 6 Ohpeudprv txh 4 ' cU d O h txh O d ? ' j 1 Dvvlp/ srghprv hvfuhyhu r odgr gluhlwr gd h{suhvvær dflpd frpr ] ] u_o ' c U d O Oo_ n O d ? Oo_@ T 7 Djrud qrwdprv/ shod vxjhvwær gr olyur/ txh O O U d % ' % n % U d U d +O ' + n + U d O U d 5 O ' 5 n 5 U d O gh prgr txh srghprv hvfuhyhu U d %O % n U d +O + n U d 5 O 5 ' O n Oo U d O Lqwhjudqgr qr yroxph/ fdprv frp ] k ] ] l O O O O U d % % n U d + + n U d 5 5 _ ' _ n U d O Oo_ T T T Dsolfdqgr r whruhpd gd glyhujíqfld qr whupr ã hvtxhugd/ fdprv frp ] ] ] O O E%% n + + n 5 5 d ? _@ ' _ n U d O Oo_c rx vhmd 7 ] T O _ ' c txh ì r uhvxowdgr ghvhmdgr1 ] T T U d O Oo_ n ] 7 T O d ? Oo_@ t H{hufðflr 718= Whprv txh dv srodul}dêøhv vær frqvwdqwhv +xqliruphv, hp wrgrv rv glhoìwulfrv1 Hvwhv hvwær d xpd glvwåqfld shtxhqd hqwuh vl/ frp dshqdv xpd hvwuhlwd ihqgd vhsdudqgr0rv1 D srodul}dêær O irupd xp åqjxor frp d qrupdo drv sodqrv txh olplwdp d ihqgd1 Frp hvwdv srodul}dêøhv/ fdprv frp ghqvlgdghv vxshufldlv gh fdujd ljxdlv d j ' O d ? ' i ULt hp fdgd xp grv sodqrv txh frqvwlwxhp d ihqgd1D ihqgd ì ihlwd gh du> dvvlp whprv xpd frqjxudêær gh grlv sodqrv sdudohorv frp ghqvlgdghv xqliruphv gh fdujd j frpr dflpd1 R fdpsr qd ihqgd srgh vhu rewlgr gluhwdphqwh gd ohl gh Jdxvv h iruqhfh .' ULt c 0f frpr ghvhmdgr +r fdpsr hvwä qd gluhêær gh O / hylghqwhphqwh,1 Wr= Rfwrehu 9/ 5336 Sdjh= 7 t H{hufðflr 719= Xp orqjr flolqgur frqgxwru gh udlr @ h ghqvlgdgh olqhdu gh fdujd b hvwä qxp phlr glhoìwulfr gh shuplvvlylgdgh frqvwdqwh 01 Sdud hqfrqwudu r fdpsr hoìwulfr d xpd glvwåqfld o : @ gr hl{r gr floðqgur/ ohpeudprv txh ghyhprv whu d htxdêær O ' bu Ud( Srghprv id}hu d lqwhjudêær xvdqgr0vh xpd vxshuiðflh gh Jdxvv txh hqyroyh flqolqgur sdud rewhu L O d ?_@ ' bu ( h/ sruwdqwr/ gh prgr txh Dvvlp/ r fdpsr hoìwulfr fd 7 2Zou(4 ' buc (4 ' .4 ' b 2Zo b 2Z0o t H{hufðflr 71:= Dv frqglêøhv gh frqwruqr vær +qær kä fdujd h{whuqd vreuh d lqwhuidfh,= (? c (2? ' j ' f .| c .2| ' f Wrpdqgr d olqkd phqflrqdgd qr wh{wr frpr edvh/ whprv txh Gd sulphlud htxdêær/ whprv (? ULt w ' (2? ULt w 2 . t? w ' .2 t? w2 0 . ULt w ' 02 .2 ULt w2 gh prgr txh/ glylglqgr0vh d htxdêær dflpd shod htxdêær sdud r . dqwhulru/ rewhprv |@? w ' frpr ghvhmdgr1 t H{hufðflr 71;= g |@? w 2 c g2 Wr= Rfwrehu 9/ 5336 Sdjh= 8 t H{hufðflr 71<= Whprv txh r srwhqfldo fd gdgr sru +fi1 jxud eb gr olyur, 5 6 7 ^ ^ 8 t ) E%c +c 5 ' nt eZ0 2 2 2 2 2 2 E% n _ n + n 5 E% c _ n + n 5 h )2 E%c +c 5 ' t eZ02 ^ E% n _2 n +2 n 5 2 Vreuh r sodqr +5 rv srwhqfldlv ghyhp vhu ljxdlv/ ylvwr txh qær kä fdujdv olyuhv qd O lqwhuidfh h/ sruwdqwr/ qær srgh kdyhu ghvfrqwlqxlgdgh gd frpsrqhqwh qrupdo gh (1 Rud/ srghprv fdofxodu (? h (2? idflophqwh d sduwlu grv srwhqfldlv dflpd frpr vhqgr ^n^ (? ' 0 .c% M %'f ' c0 Y) ' eZ _ 2 Y% d% n+ 2 n5 2 o *2 %'f ^ 2 (2? ' 02 .2c% M %'f ' c02 Y) ' _ *2 Y% eZ d%2 n+ 2 n5 2 o Dvvlp/ whprv xpd sulphlud htxdêær gdgd sru (? c (2? ' f %'f E^ n ^ ' ^ Sdud rewhu d vhjxqgd htxdêær/ ohpeudprv txh whprv d frqglêær gh frqwruqr qd frp0 srqhqwh wdqjhqfldo gr fdpsr hoìwulfr +srghprv wrpdu + rx 5 frpr vhqgr xpd wdo gluhêær,1 Dvvlp/ whprv txh Y) ^ c ^ .| ' c ' _ Y+ %'f eZ0 d+2 n 5 2 o *2 Y)2 ^ .2| ' c ' _ Y+ %'f eZ02 d+2 n 5 2 o *2 iruqhfhqgr d htxdêær .| c .2| ' f 02 E^ c ^ ' 0 ^ Dvvlp/ fdprv frp r vlvwhpd gh htxdêøhv ^ c ^ ' ^ 0 ^ n ^ ' ^ 02 fxmdv vroxêøhv vær ^ ' 02 c 0 ^c 0 n 02 ^ ' 202 ^ 0 n 02 Wr= Rfwrehu 9/ 5336 Sdjh= 9 t H{hufðflr 7143= Whprv rv srwhqfldlv lqwhuqr h h{whuqr gdgrv sru )? ' f n f *? Eo n )J| " [ ?' ? o? n ? o3? ULt E?w " [ ' f *? Eo n ? o? n (? o3? ULt E?w ?' txh vær dv vroxêøhv gd htxdêær gh Odsodfh hp frrughqdgdv floðqgulfdv1 R whupr hp t? Ew mä irl holplqdgr sru ud}øhv gh vlphwuld ^qær srghprv whu rv srwhqfldlv yduldqgr txdqgr id}hprv w cw`1 Sdud r srwhqfldo lqwhuqr/ whprv txh qær kä glyhujíqfldv orjduðwlplfdv/ mä txh r flolqgur hvwä ghvfduuhjdgr1 Wdpeìp qær whprv txdotxhu rxwur wlsr gh glyhujíqfld1 Dvvlp/ ghyhprv sru ? ' f sdud wrgr ? h fdu frp )? ' o ULt w n " [ ?'2 ? o? ULt E?w Sdud r srwhqfldo h{whuqr/ srghprv hoplqdu r whupr orjdwðplfr shodv phvpdv ud}øhv dqwhulruhv doìp gh holplqduprv rv whuprv o? frp ? : / mä txh r srwhqfldo h{whuqr glyhujh frp o1 Dvvlp/ fdprv frp " [ ( )J| ' o n ULt w n (? o3? ULt E?w o ?'2 D sulphlud frqglêær gh frqwruqr gl} uhvshlwr dr srwhqfldo qr lqqlwr +)J| / sruwdqwr,1 Hvwd frqglêær ì txh )J| Eo ' c.f o ULt wc gh prgr txh ' c.f 1 Xpd vhjxqgd frqglêær gh frqwruqr ì txh iruqhfh dv htxdêøhv )? E@ ' )J| E@ @2 c ( ' c.f @2 h ? @2? c (? ' f D rxwud frqglêær gh frqwruqr txh idowd ì Y)J| Y)? c0f ' c0 Yo o'@ Yo o'@ txh iruqhfh dv htxdêøhv g@2 n ( ' c.f @2 h g@2? ? n (? ' f1 Wr= Rfwrehu 9/ 5336 Ilfdprv/ srlv/ frp rv vlvwhpdv h Sdjh= : @2 c ( ' c.f @2 g@2 n ( ' c.f @2 ? @2? c (? ' f g@2? ? n (? ' f Hvwh ýowlpr vlvwhpd lpsolfd qhfhvvduldphqwh txh ? ' (? ' f/ sdud ? z 21 R sulphlur vlvwhpd iruqhfh ' c 2.f gc 2 h ( ' @ .f g n g n Rv srwhqfldlv fdp/ sruwdqwr/ + 32 )? ' gn k .f o ULt2wl c @ )J| ' c g3 .f o ULt w gn o 2 txh vær rv uhvxowdgrv surfxudgrv1 t H{hufðflr 7144= Whprv xp glsror srqwxdo RO qr fhqwur gd hvihud glhoìwulfd gh udlr @1 Vdehprv txh r fdpsr irud gd hvihud ì glsrodu/ rx vhmd/ whprv )J| ' RO d Oo o rqgh ì r frhflhqwh d vh ghwhuplqdu1 Qr lqwhulru gd hvihud glhoìwulfd ghyhprv whu )? ' o ULt w n ULt wc o2 rqgh mä holplqdprv rv whuprv hp o3? +? z , h rv whuprv o? +? z 2, d sduwlu gh frqvlghudêøhv vlploduhv ãv ihlwdv hp h{hufðflrv ghvwh wlsr1 Wdpeìp vdehprv/ shod frqglêær gh txh kä xp glsror srqwxdo qd ruljhp txh ' R*eZ0 1 Ilfdprv/ sruwdqwr/ frp rv srwhqfldlv R )? ' o n ULt w eZ0 o2 R ULt w )J| ' 2 o Dv frqglêøhv gh frqwruqr lpsolfdp txh ghyhprv whu frqwlqxlgdgh gr srwhqfldo qd vxshuiðflh gd hvihud1 Dvvlp/ )? Eo ' @ ' )J| Eo ' @ Wr= Rfwrehu 9/ 5336 rx vhmd @ n R eZ0 @2 Sdjh= ; ' R @2 Gd phvpd irupd/ ghyhprv whu frqwlqxlgdgh qd frpsrqhqwh gr yhwru ghvorfdphqwr hoìwulfr/ ylvwr txh d hvihud glhoìwulfd qær hvwä fduuhjdgd frp qhqkxpd ghqvlgdgh vx0 shufldo gh fdujd1 Dvvlp/ ghyhprv whu wdpeìp rx vhmd/ (? ' (J| Y)? Y)J| c0 ' c0f Yo o'@ Yo o'@ Hvwd ýowlpd ljxdogdgh iruqhfh 2R g c eZ0 @ ' c2 R @ Ilfdprv/ sruwdqwr/ frp r vlvwhpd gh htxdêøhv R @ c R ' c eZ0 2Rg c g@ n 2R ' eZ0 fxmdv vroxêøhv vær g ' g n 2 eZ0 g n 2 eZ0f R Eg c ' 2Z0 @ Eg n 2 ' gh prgr txh rv srwhqfldlv fdp 2R Eg c R )? ' on ULt w eZ0 @ Eg n 2 eZ0 o2 R ULt w o Eg c ' n2 eZ0 o2 @ Eg n 2 h txh vær rv uhvxowdgrv ghvhmdgrv1 )J| ' R ULt w c eZ0f o2 g n 2 t H{hufðflr 7145= Rv uhvxowdgrv vær + @ ) ' c.f c g3 .f o ULt w gn2 o )2 ' c gn2 .f o ULt w Wr= Rfwrehu 9/ 5336 txh/ txdqgr id}hprv g / fdp + ) ' c.f o ULt w c )2 ' f Sdjh= < @ o c txh vær rv uhvxowdgrv sdud d hvihud frqgxwrud1 t H{hufðflr 7146= Whprv xpd fkdsd qd gh pdwhuldo frp frqvwdqwh glhoìwulfd g olplwdgd sru dperv rv odgrv sru xp pdwhuldo gh frqvwdqwh glhoìwulfd g2 1 Vdehprv O 2 / ì gdgr frpr vhqgr xqliruph h shushqglfxodu drv frqwruqrv1 txh r fdpsr qr phlr 2/ . O ghyhprv xvdu dv frqglêøhv gh frqwruqr gr sureohpd1 Qær Sdud hqfrqwudu r fdpsr . kä fdujdv olyuhv qr sureohpd1 Dvvlp/ whprv (? ' (2? .| ' .2| O 2 ì shushqglfxodu drv frqwruqrv/ ghyhprv whu .2| ' f h/ sruwdqwr/ .| ' f1 Frpr . Djrud vdehprv txh (2? ' 02 .2? h (? ' 0 .? Dvvlp/ .? ' Djrud/ frpr vdehprv txh fdprv frp 02 .2? 0 O ' 0f . O n O c ( ? ' 02 .2? c 0f .? 2? ' E02 c 0f .2? Hp whuprv gdv frqvwdqwhv g ' 0 *0f srghprv hvfuhyhu rv uhvxowdgrv dflpd frpr g2 .2? g g c ' 0f g2 .2? g .? ' h ? 2? ' Eg2 c 0f .2? Sruwdqwr/ frpr vö whprv srodul}dêær shushqglfxodu ã vxshuiðflh/ j ' i? 1 t H{hufðflr 7147= Srghprv id}hu g qd vroxêær dqwhulru sdud rewhu .? ' f h ? ' 0f g2 .2? Wr= Rfwrehu 9/ 5336 Sdjh= 43 Qrwh txh/ djrud (? ' ? mä txh r fdpsr hoìwulfr .? ì qxor1 Dvvlp/ whprv txh (? ' 0f g2 .2? ' j c txh frqfrugd frp d h{suhvvær +eee, gr olyur1 t H{hufðflr 7148= Dv sodfdv vær sdudohodv/ frqgxwrudv h hvwær glvwdqwhv sru xp ydoru _1 Vær pdqwlgdv d xpd glihuhqêd gh srwhqfldo {)1 D fkdsd gh pdwhuldo glhoìwulfr gh frqvwdqwh glhoìwulfd g ì lqvhulgd h srvvxl xpd hvshvvxud | _1 R srwhqfldo srgh vhu hvfulwr frpr {) ' {) n {)2 c rqgh {) j {)2 j ' h ' _c| 0f | 0 gh prgr txh j | j g_ c Eg c | {) ' E_ c | n ' 0f g 0f g R yhwru ghvorfdphqwr hoìwulfr ì ('j txh/ frp d htxdêær sdud r srwhqfldo/ fd Rv fdpsrv hoìwulfrv fdp (' g0f {) dg_ c Eg c |o ( g{) ' 0f dg_ c Eg c |o ( {) ' ' 0 dg_ c Eg c |o .@S ' ._e, frpr txhuðdprv hqfrqwudu1 t H{hufðflr 7149= Sdud hqfrqwudu dv srodul}dêøhv/ srghprv xvdu rv uhvxowdgrv gr h{hu0 fðflr dqwhulru sdud hvfuhyhu @S ' c0f .@S n ( ' f _e, ' c0f .@S n ( ' Ohpeudprv dlqgd txh h 0f Eg c {) dg_ c Eg c |o (R,@S@ c (_e, ' j, ' j j_e, ' O_e, d ? ' ijc r vlqdo ghshqghqgr gd idfh hp txh frqvlghudprv r fäofxor1 Wr= Rfwrehu 9/ 5336 Sdjh= 44 t H{hufðflr 714:= Whprv txh hqfrqwudu xp fdpsr hoìwulfr udgldo txh vdwlvidêd wrgdv dv frqglêøhv gh frqwruqr sdud d hvihud gh udlr - txh xwxd vxephuvd shod phwdgh qxp phlr oðtxlgr gh shuplvvlylgdgh 0 1 D fdujd wrwdo gd hvihud ì '1 Dvvlp/ surfxudprv xp srwhqfldo gr wlsr o ' o )? ' )J| D sulphlud frqglêær gh frqwruqr +d frqwlqxlgdgh gr srwhqfldo, vlpsohvphqwh dupd txh ' 1 D vhjxqgd frqglêær gh frqwruqr ì gdgd sru (? c (2? ' ' c eZ@2 mä txh j ' '*eZ@2 1 Dvvlp/ whprv Y)? Y)J| ' c0 c 02 ' Yo o'@ Yo o'@ eZ@2 rx vhmd h/ sruwdqwr/ gdqgr r srwhqfldo E02 n 0 '' ' ' 2 @ eZ@2 ' c eZ E02 n 0 )? 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O f . *g n 2 n 2g Wr= 4 Fdsðwxor 9= Rfwrehu 57/ 5336 Sdjh= 4 t H{hufðflr 915= Ghyhprv qrv ohpeudu txh srghprv fdofxodu r yhwru ghvorfdphqwr O hoìwulfr d sduwlu gd h{suhvvær +*ohl gh Jdxvv* sdud r yhwru (, Rewhprv/ dvvlp/ eZo2 ( ' ^ (' D hqhujld/ sruwdqwr/ ì gdgd sru ^ ^ h.' 2 eZo eZ0o2 ] O O L' ( d ._Oo 2 T rqgh ghyhprv qrv ohpeudu txh r yroxph T whp txh vhu dtxhoh frpsuhhqglgr shod pdwìuld gr vlvwhpd/ rx vhmd/ qr fdvr hp txhvwær/ d fdorwd hviìulfd txh ydl gr udlr @ dr udlr K1 Dvvlp/ ^2 ] K 2 ^2 L' o eZ_o ' c 2 SZ2 0 @ oe HZ0 @ K t H{hufðflr 916= R h{hufðflr srgh vhu ihlwr shufhehqgr0vh txh r sodqr frqgxwru srgh vhu vxevwlwxðgr sru xpd frqjxudêær glsrodu hvshfxodu frp uhodêær dr glsror txh vh hqfrqwud hp iuhqwh dr sodqr/ frpr prvwud d jxud dedl{r= Qrwdprv/ hqwuhwdqwr/ txh d sulphlud hqhujld ghfruuh gr wudedokr txh whuðdprv dr *wud}hu* xpd gdv fdujdv qr odgr hvtxhugr gr sodqr sdud suö{lpr gd rxwud1 Hvwh wudedokr ì gdgr sru ^2 `f ' c eZ0f , Srvwhulruphqwh/ whuhprv r wudedokr gh wud}hu fdgd xpd gdv fdujdv txh hvwær qr odgr gluhlwr gr sodqr1 Sdud d fdujd c^ whuðdprv % & c^ ^ ` ' c^ n c eZ0f E, n 2_ eZ0f E2_ Wr= Rfwrehu 57/ 5336 Sdjh= 5 rqgh rv whuprv hvwær dvvrfldgrv drv srwhqfldlv jhudgrv sru fdgd xpd gdv fdujdv qr srqwr sdud rqgh d fdujd c^ irl wud}lgd1 Sdud d fdujd n^ whuðdprv % & c^ ^ ^ `2 ' n^ n c eZ0f E2, n 2_ eZ0f E, n 2_ eZ0f , D hqhujld wrwdo vhuä d vrpd ghvwhv wudedokrv h vhuä gdgd sru c^ 2 L ' eZ0f c2^ 2 ' eZ0f % & 2 2 c n n , E, n 2_ 2_ 2 E, n _ % & c n n , E, n 2_ e_ e E, n _ t H{hufðflr 918= Whprv txh d glvwulexlêær gh fdujdv ì hviìulfd h gh udlr -/ rqgh 4 ' 4f +frqvwdqwh,1 Srghprv rewhu r ydoru gd hqhujld hohwurvwäwlfd ghvwd glvwulexlêær lqwh0 judqgr gluhwdphqwh/ rx vhmd/ xvdqgr ] L' 4 EOo ) EOo _Oo 2 T Qrwhprv/ hqwuhwdqwr/ txh/ sdud hvwd frqjxudêær ghyhprv whu ^ )U EOo ' )f n +o y -, eZ0f o ^ )UU EOo ' Eo z - eZ0f o rewlgrv sru ohl gh Jdxvv1 Dvvlp/ ^ ' gh prgr txh fdprv frp ^ ' e e Zo 4f +o y -, Z- 4f +o z -, )U EOo ' )f n )UU EOo ' o 2 4f +o y -, 0f 4f Eo z - 0f o h/ frpr vdehprv txh/ sdud o ' - ghyhprv whu dperv rv srwhqfldlv ljxdlv/ srghprv hvfuhyhu # $ 4f o2 )U EOo ' -2 c +o y -, 20f 4)UU EOo ' f Eo z - 0f o Wr= Rfwrehu 57/ 5336 Sdjh= 6 Vh ydprv fdofxodu d glvwulexlêær gh dxwr0hqhujldv xvdqgr d iöupxod dflpd/ hqwær r yroxph T whp txh vhu dtxhoh txh frqwìp d glvwulexlêær gh pdwìuld2fdujd/ rx vhmd/ ghyhprv xvdu )U EOo1 D lqwhjudêær fd # $ ] 2Z ] Z ] - 4f o2 2 L ' 4f -2 c o t? w_o_w_ 2 f f f 20f eZ42f -D ' D0f t H{hufðflr 919= Whprv txh r uhvxowdgr dqwhulru ghyh vhu htxlsdudgr frp d hqhujld gh uhsrxvr gr hoìwurq/ sdud rewhuprv # eZ42f -D eZ ' D0f D rx vhmd $2 6 e Z- -D ' 6S2 b 62 - ' 6S2 DeZ0f gh prgr txh 2fZ0f S2 6 -' t H{hufðflr 91:= Whprv txh ^ O1 c Oo O ' ^ Oo ' O 2 ' ^2 Oo . h. eZ0f o eZ0f o eZ0f O1 c Oo Dvvlp= O2 d . O 2 ' ^22 * ESZ2 02f oe / gh irupd txh whprv +d, .22 ' . U' ] f " ] f Z ] f 2Z txh glyhujh qr olplwh lqihulru1 U +e, Djrud whprv txh fdofxodu U ' xqlyhuvr1 Dvvlp/ U ' ' ] T ^ ^2 O1 c Oo d Oo O d . O 2 _T / rqgh T ì wrgr r yroxph gr . ^ ^2 ] _T ' SZ2 02f SZ 2 02f o O1 c Oo ] " ] n ^ ^2 HZ02f f 3 k " ^22 ^22 2 o t? w_o_w_ ' c SZ2 02f oe eZ0f o f E1 c o l o2 n 1 2 c 2o1 *2 f "] Z _o_ f ] f 2Z E1o ULt w c o2 o2 t? w_o_w_ k o o2 n 1 2 c 2o1 ULt w l *2 Wr= Rfwrehu 57/ 5336 Qrwh djrud txh ; A _ ? k _o A = Dvvlp/ fdprv frp U ' ^ ^2 HZ02f Sdjh= 7 < A @ c2 Eo c 1 l*2 A ' k l > o2 n 1 2 c 2o1 o2 n 1 2 c 2o1 ] ; A n ? 3 *2 <" A @ ^ ^2 ] n _ ' _ k l A A HZ02f 3 1 2 = o2 n 1 2 c 2o1 *2 > f ^ ^2 ^ ^2 ' 2 ' c 2 HZ02f 1 eZ02f 1 2 txh ì r uhvxowdgr +qlwr, hvshudgr sdud d hqhujld hqwuh gxdv fdujdv1 Dvvlp/ r whupr fdofxodgr hp +d,/ dvvrfldgr ãv dxwr0hqhujldv/ ghyh vhu ghvfrqvlghudgr grv fäofxorv1 t H{hufðflr 9143= Vö whprv grlv frqgxwruhv/ gh prgr txh fdprv frp ) ' R ' c R2 '2 )2 ' R2 ' c R22 '2 txh ì xp vlvwhpd gh htxdêøhv txh srgh vhu uhvroylgr sdud ' h '2 gh wdo irupd txh ' ' Xvdqgr d h{suhvvær= R22 ) c R2 ) R2 ) c R )2 h '2 ' R R22 c R2 R2 R R22 c R2 R2 ' ' 2 [ ' S ) c fdprv frp rv frhflhqwhv gh fdsdflgdgh gdgrv sru S ' R22 R / S22 ' c c { { S2 ' cR2 R2 h S2 ' { { rqgh { ì r ghwhuplqdqwh gr vlvwhpd dqwhulru h ì gdgr sru { ' R R22 c R2 R2 / h wdpeìp frp rv frhflhqwhv gh lqgxêær gdgrv sru t H{hufðflr 9146= Qrwh txh whprv xpd vlwxdêær hp txh rv glhoìwulfrv id}hp r sdsho gh fdsdflwruhv hp vìulh1 Dvvlp/ d fdsdflwåqfld wrwdo vhuä gdgd sru ' n 2 Wr= Rfwrehu 57/ 5336 Sdjh= 8 R fäofxor gd fdsdflwåqfld gh fdgd xp ghvwhv *fdsdflwruhv* ì iäflo h ì gdgr sru ' Dvvlp/ fdprv frp 0 02 h 2 ' _ _2 _ _2 ' n ' 0 02 # $ 02 _ n 0 _2 c 0 02 rx vhmd/ d fdsdflwåqfld sru xqlgdgh gh äuhd/ * fd * ' # txh ì r uhvxowdgr ghvhmdgr1 $ 02 _ n 0 _2 c 0 02 t H{hufðflr 9147= Frqvlghuh d jxud dedl{r1 Qhod whprv xpd frqjxudêær gh gxdv olqkdv gh fdujd frp ghqvlgdghv olqhduhv gh fdujd ib/ srvlflrqdgdv vlphwulfdphqwh frp uhodêær dr orfdo hp txh hvwduld r sodqr frqgxwru +qær hvwä pdlv/ ylvwr txh hvwdprv xvdqgr r pìwrgr gdv lpdjhqv,1 H{hufðflr 9147 txdqgr r id}hprv r srwhqfldo qr srqwr fd gdgr sru b o )' *? 2Z0f o2 5 6 S 2 2 b % n + 8 ' *? 7 t 2 2Z0f 2 E% n 2_ n + Vh hvfuhyhprv 2 ' i T EeZ0f )*b/ hqwær fdprv frp 2 ' %2 n +2 %2 n e_% n e_2 n + 2 txh/ dsöv dojxpdv pdqlsxodêøhv dojìeulfdv vlpsohv/ srgh vhu srvwr vre d irupd # 2 2 _ %c c 2 $2 n +2 ' e_2 2 c c 2 Wr= Rfwrehu 57/ 5336 Sdjh= 9 txh uhsuhvhqwd xp flolqgur gh fhqwur hp 2 2 _ %S ' c 2 h udlr Djrud/ rokdqgr d jxud/ whprv txh gh prgr txh Dvvlp/ fdprv frp oS ' 2_ c 2 @ ' oS h %f ' _ n %S c %f ' E n 2 2_ _h@' 2 E c c 2 %f n 2 ' @ 2 gh rqgh rewhprv v %f %2f ' i c c @ @2 rqgh hvfrokhprv r ydoru srvlwlyr1 Dvvlp/ xvdqgr d h{suhvvær sdud / fdprv frp ) %f ' *? n b 2Z0f @ h/ ohpeudqgr txh ULt3 % ' *? % n srghprv hvfuhyhu txh ì r uhvxowdgr hvshudgr1 u %f c @ S %2 c c b ' 2Z0f * ULt3 E%f *@ c ) t H{hufðflr 914:= Sdud r fdvr gdv hvihudv frqfíqwulfdv whprv txh Dvvlp/ whprv txh Frpr vdehprv txh )U ' ' ' h )UU ' eZ0f o eZ0f o2 )U c )UU ' {) ' ' eZ0f ' ' {)c c o o2 Wr= Rfwrehu 57/ 5336 frqfoxðprv txh Frpr whprv ' eZ0f * h ' ' {)/ hqwær/ fdprv frp Sdjh= : c o o2 L ' '{) 2 L ' E{)2 2 t H{hufðflr 914;= whprv r duudqmr gd jxud dedl{r/ hp txh prvwudprv d vlwxdêær mä frp r oðtxlgr glhoìwulfr suhhqfkhqgr sdufldophqwh r flolqgur1 Vxsrqkd txh r glhoìwulfr suhhqfkh d uhjlær lqwhuvwlfldo dwì xpd dowxud 5f h wrph hvwd dowxud frpr vhqgr d ruljhp gr vlvwhpd gh frrughqdgdv1 Qrwh txh whprv xpd vlwxdêær hp txh whprv grlv *fdsdflwruhv* hp sdudohor1 Xp/ frp fdsdflwåqfld E5/ frp r glhoìwulfr suhhqfkhqgr d uhjlær lqwhuvwlfldo h rxwur/ frp fdsdflwåqfld 2 E5/ vhp glhoìwulfr +frp yäfxr,1 D fdsdflwåqfld wrwdo ghvwh vlvwhpd srgh vhu hvfulwd/ xpd yh} txh hvwær hp sdudohor/ frpr E5 ' E5 n 2 E5 hqtxdqwr txh d hqhujld wrwdo srgh vhu hvfulwd gluhwdphqwh frpr L E5 ' E5 {)c rqgh uhvvdowdprv txh r sduåphwur {) hvwä vhqgr pdqwlgr frqvwdqwh +lvwr ì lpsruwdqwh sdud hihlwr gr fäofxor gd iruêd txh dsduhfhuä vreuh r glhoìwulfr qr vhqwlgr gh sx{ä0or sdud flpd,1 R fäofxor gr srwhqfldo hqwuh rv flolqgurv ì vlpsohv1 Vh vxsxvhuprv +vhp shugd gh jhqhudolgdgh, txh r srwhqfldo vreuh r pdlv lqwhuqr ì ) h vreuh r pdlv h{whuqr ì )2 / hqwær {) ) c ) o2 23 E5 ' ' 2 ' *? c '2 '2 2Z0f EM c 5 o Wr= Rfwrehu 57/ 5336 Sdjh= ; sdud d uhjlær suhhqfklgd sru du h 3 {) ) c ) o2 E5 ' ' 2 ' *? c ' ' 2Z05 o sdud d uhjlær frp glhoìwulfr/ rqgh xvdprv txh '2 ' b EM c 5 h ' ' b5/ ylvwr txh b ì d ghqvlgdgh olqhdu gh fdujd1 Dvvlp/ fdprv frp L E5 ' 2Z0f {) 2Z0{) EM c 5 n 5 *? Eo2 *o *? Eo2 *o Vxd ghulydgd frp uhodêær d 5 +frp {) frqvwdqwh, iruqhfh d iruêd qhvwd gluhêær/ orjr 85 ' 2Z{) d0 c 0f o *? Eo2 *o D txdqwlgdgh gh pdvvd ghvorfdgd shod glihuhqêd gh srwhqfldo vhuä gdgd shor surgxwr gd ghqvlgdgh gh pdvvd shor yroxph ghvorfdgr/ rx vhmd/ 6 ' 1Z o22 c o2 5c rqgh 5 ì d dowxud hp txh r glhoìwulfr ì ohydqwdgr1 Qrwh txh whprv gh prgr txh srghprv hvfuhyhu o2 ' o n _c o22 c o2 2o _ Dvvlp/ whprv txh d iruêd qhfhvväuld sdud hohydu r oðtxlgr gh glhoìwulfr ì gdgd sru 8} ' 6} ' 2Z1o }_5 Hvwd iruêd ghyh vhu htxloleudgd shod iruêd 85 mä fdofxodgd Dvvlp/ fdprv frp 2Z E0 c 0f {) ' 2Z1o }_5 *? E n _*o Id}hqgr d dsur{lpdêær _*o qr orjdulwpr ^*? E n % 0f Eg c {) ' 5 1}_2 %`/ fdprv frp txh ì r uhvxowdgr ghvhmdgr1 Qrwh txh/ vh d ghqvlgdgh gr glhoìwulfr ì pxlwr shtxhqd/ 5 vhuä judqgh> vh vö wlyhuprv yäfxr/ 5 ' f h vh _ iru shtxhqr/ 5 vhuä judqgh/ txh vær frqglêøhv txh hvshuduðdprv hqfrqwudu vlfdphqwh1 Qrwh/ dlqgd/ txh txdqwr pdlru iru g +txdqwr pdlv hqhujld r glhoìwulfr sxghu dupd}hqdu,/ pdlru vhuä d hohydêær gr phvpr1 Wr= Rfwrehu 57/ 5336 Sdjh= < Srghprv hvwlpdu xp uhvxowdgr wðslfr sdud 5 frp ydoruhv uhdlv gdv frqvwdqwhv= vxsrqkd rv ydoruhv +sdud d äjxd ghvwlodgd d 2fJ / g H, Ilfdprv frp {) ' 22fT g ' H 1 ' g}*6 0f ' HHD e f32 62 * 2 _ ' f3 6 } ' bH6*r2 5' HHD e f32 e Hf E22f2 ' DS6 bH e f3S t H{hufðflr 914<= Hqtxdqwr r fdsdflwru hvwä vhqgr fduuhjdgr frp r glhoìwulfr qr vhx lqwhulru/ whprv txh kä d wudqvihuíqfld gh xpd fdujd wrwdo 'A ' 0, {)f _ Srvwhulruphqwh/ d edwhuld ì ghvoljdgd h r glhoìwulfr ì sdufldophqwh uhwludgr1 D fdujd wrwdo ghyhuä djrud vhu gdgd shodv vrpdv gh fdgd xpd gdv frqwulexlêøhv +gd sduwh gr glhoìwulfr txh dlqgd vh hqfrqwud qr lqwhulru gr fdsdflwru h gdtxhod sduwh txh frqwìp dshqdv du,1 Dvvlp/ whprv 0% {) _ 0f E, c % ' {) _ ' ' '2 rqgh djrud {) qær ì ljxdo d {)f / srlv d edwhuld qær ì pdlv fdsd} gh pdqwhu r srwhqfldo {r1 D fdujd/ hqwuhwdqwr/ ì frqvhuydgd/ h{wdphqwh shor idwr gh whuprv ghvoljdgr d edwhuld/ gh prgr txh 'A % & 0% 0f E, c % ' ' n '2 ' n {) _ _ ' 0f d, n Eg c %o {)( _ Xvdqgr d h{suhvvær dqwhulru sdud 'A / fdprv frp {) ' g,{)f d, n Eg c %o D iruêd srgh vhu fdofxodgd d sduwlu gr srwhqfldo/ ghvgh txh ohpeuhprv txh ghyhprv pdqwhu d fdujd frqvwdqwh1 Dvvlp/ ghyhprv hvfuhyhu {) ' g'_ 0 d, n Eg c %o Wr= Rfwrehu 57/ 5336 h d hqhujld fd h d iruêd +rokh r vlqdo, Sdjh= 43 _ '2 L ' '{) ' 2 20f d, n Eg c %o # YL 8 'c Y% txh ì r uhvxowdgr ghvhmdgr1 $ ' ' Eg c '2 _ c 20f d, n Eg c %o2 t H{hufðflr 9154= Frphêdprv sru qrwdu txh d hvihud hvwä lqlfldophqwh hp htxloðeulr1 Dvvlp/ d iruêd uhdol}dgd shor hpsx{r ghyh vhu htxloleudgd shod iruêd shvr gd hvihud1 D iruêd gh hpsx{r ì fdofxodgd dwudyìv gd h{suhvvær 8ec ' 4_ }c rqgh ì d dowxud gd sduwh gd hvihud txh vh hqfrqwud lphuvd qr xlgr h ì d äuhd gd vhêær uhwd ghvwd sduwh +fi1 jxud dedl{r,1 Ydprv vxsru/ gh prgr jhudo/ txh r yroxph lphuvr gd hvihud vhmd kT / rqgh T ' eZ- * ì r yroxph gd hvihud h k gä d srufhqwdjhp gh hvihud lphuvd1 Ydprv frqvlghudu/ lqlfldophqwh/ r åqjxor w / frpr prvwudgr qd jxud/ frpr gdgr +ghsrlv prvwuduhprv frpr rewí0or grv gdgrv gr sureohpd,1 Dvvlp/ whprv rx vhmd/ 8ec ' 4_ }- E c ULt w Z-2 t?2 w ' 4_ Z- t?2 w E c ULt w ' 6} 4_ ' 6 Z- t? w E c ULt w 2 Djrud/ frqvlghuh d hvihud qd vlwxdêær E gd jxud dqwhulru/ hp txh d hvihud hvwä vxep0 huvd shod phwdgh qr glhoìwulfr1 D iruêd gh hpsx{r ghyh vhu gdgd sru 8ec2 ' 4_ }Z- c Wr= Rfwrehu 57/ 5336 Sdjh= 44 mä txh ' - h ' Z-2 1 Hvwd iruêd ghyh vhu htxloleudgd shor shvr dglflrqdgr ã iruêd uhdol}dgd shor srwhqfldo txh irl oljdgr1 D iruêd dvvrfldgd d hvwh ýowlpr whupr srgh vhu fdofxodgd gd vhjxlqwh pdqhlud= d hqhujld hohwurvwäwlfd dvvrfldgd drv fdpsrv ì gdgd sru +fdpsrv vxsrvwdphqwh udgldlv, L ' txh iruqhfh ] O O 0 '2 ] " ] w ] 2Z 2 . d (_T ' o t? w_o_w_ 2 T 2 SZ2 02f - f f oe 0f '2 ] " ] Z ] 2Z 2 n o t? w_o_w_ 2 SZ 2 02f - w f oe % ] w ] Z 2 ' L ' Z- 0 t? w_w n 0f t? w_w eZ0f f w ' )2 Z- d0 E c ULt w n 0f E n ULt w o ' c)2 Z- E0 c 0f ULt w n )2 Z- E0 n 0f & Vh qrwduprv txh 5 ' c- ULt w +wrpdqgr r fhqwur gd hvihud frpr ruljhp gh qrvvr vlvwhpd gh frrughqdgdv,/ hqwær d hqhujld srwhqfldo fd L E5 ' )2 Z- E0 n 0f n )2 Z0f Eg c 5 D iruêd hohwurvwäwlfd/ sruwdqwr/ fd 8. ' )2 Z0f Eg c Dvvlp/ ghyhprv whu 8ec2 ' 6} n 8. c r txh iruqhfh 4_ }Z- ' 6} n )2 Z0f Eg c h/ vxevwlwxlqgr r ydoru gh 4_ fdprv frp 6} gh prgr txh k )' l c t?2 w E c ULt w t?2 w E c ULt w + ' )2 Z0f Eg c c 6} c t?2 w E c ULt w Z0f Eg c t?2 w E c ULt w ,*2 Idowd dlqgd rewhu r ydoru gh w 1 Srghprv id}í0or d sduwlu gdv frqglêøhv lqlfldlv +txdqgr d hvihud hvwä htxloleudgd/ vhp fdpsr/ shor hpsx{r h vhx yroxph vxephuvr srgh vhu fdofxodgr idflophqwh,1 Dvvlp/ ghyhprv whu e k Z- ' ] f - ] f w ] f 2Z o2 t? w_o_w_ c Z- t?2 w ULt w c Wr= Rfwrehu 57/ 5336 Sdjh= 45 rqgh r whupr ã gluhlwd ì gdgr shor yroxph dvvrfldgr dr åqjxor vöolgr vxehqwhqglgr sru w h txh whprv txh uhwludu d sduwh gr frqh/ lqfoxðgd d pdlv/ uhsuhvhqwdgd shor ýowlpr whupr ã gluhlwd1 Dvvlp/ fdprv frp ek rx vhmd Z- '2 Z- E c ULt w c Z- t?2 w ULt w c ek c 2 ' c ULt w n ULt w c rqgh/ vh vxevwlwxluprv 1 ' ULt w / fdprv frp 1 c 1n'f txh ì d htxdêær txh ghwhuplqd w 1 Qr qrvvr fdvr hvshfðfr/ whprv k ' *e h/ sruwdqwr/ fdprv frp 1 c 1 n ' fc fxmdv vroxêøhv vær/ dsur{lpdgdphqwh/ D / c HH h f Dc rqgh dshqdv d ýowlpd ì dfhlwäyho/ ylvwr txh 1 ì xp frvvhqr +qær srgh vhu pdlru txh xp hp pögxor,1 Dvvlp/ h w ULt w ' f D .fJ 1 Sdud hvwh fdvr/ r srwhqfldo fd )' + t?2 w ' fHH 6} c fHH EfSD Z0f Eg c fHH EfSD ,*2 % f.e6} ' Z0f Eg c &*2 t H{hufðflr 9156= Whprv txh hvfuhyhu L ' 2 E% E{)2 1 Ohpeuhpr0qrv txh/ sdud hvwh sureohpd/ d glihuhqêd gh srwhqfldo {) hvwä vhqgr pdqwlgd +shod edwhuld, frpr frqvwdqwh1 Whprv/ hqwuhwdqwr/ txh fdofxodu d fdsdflwåqfld E% gr fdsdflwru txdqgr r glhoìwulfr hvwä lqwurgx}lgr sru xpd glvwåqfld %1 Rud/ r sureohpd 914< qrv prvwud frpr ghyhprv fdofxodu hvwd fdsdflwåqfld1 Glihuhqwhphqwh gdtxhoh sureohpd/ hqwuhwdqwr/ qær vh wudwd gh pdqwhu d fdujd wrwdo frqvwdqwh/ mä txh kä xpd edwhuld hqyroylgd/ pdv vlp {) ghyh vhu frqvlghudgr frqvwdqwh1 Srghprv hqwhqghu hvwh sureohpd frpr fdsdflwruhv hp sdudohor/ gh wdo prgr txh E% ' E% n 2 E% c vhqgr txh r sulphlur fdsdflwru srvvxl xp glhoìwulfr hp vhx lqwhulru h r vhjxqgr fd0 sdflwru srvvxl r yäfxr +du,1 Dvvlp/ sdud r sulphlur/ rewhprv E% ' 0% _ Wr= Rfwrehu 57/ 5336 hqtxdqwr txh/ sdud r vhjxqgr/ rewhprv Sdjh= 46 0f E, c % _ 2 E% ' R uhvxowdgr qdo sdud r srwhqfldo wrwdo vhuä/ sruwdqwr/ d E% n 2 E%o E{)2 ' 2 0% 0f E, c % ' E{)2 n E{)2 ' 2 _ 2 _ {) 2 {) 2 ' 0 _% n 0f _ E% c , 2 _ 2 _ L ' txh ì h{dwdphqwh r phvpr uhvxowdgr rewlgr qr olyur1 t H{hufðflr 9157= Whprv txh L ' E{)2 2 h ' ' E% {)1 D iruêd fdofxodgd pdqwhqgr0vh {) frqvwdqwh srgh vhu lphgldwdphqwh fdofxodgd frpr vhqgr 8 ' # YL Y% $ {) ' _ E% E{)2 2 _% D iruêd fdofxodgd pdqwhqgr0vh ' frqvwdqwh srgh vhu fdofxodgd vh }huprv xpd vxe0 vwlwxlêær qd sulphlud h{suhvvær gh prgr d hvfuhyí0od hp jhuprv dshqdv gd fdujd h gh E%1 Dvvlp/ fdprv frp '2 L' 2 E% gh prgr txh d iruêd fd Vh qrwduprv djrud txh # YL 8 'c Y% $ ' ' '2 _ E% 2 E%2 _% '2 2 2 ' E{) c E% whuhprv lphgldwdphqwh d ljxdogdgh txh surfxudprv1 t H{hufðflr 9158= Ghyhprv qrwdu +frpr dsrqwd d vxjhvwær gr olyur, txh djrud ì r yhwru O txh ì sudwlfdphqwh frqvwdqwh dr orqjr gr fdsdflwru1 Dvvlp/ whprv ghvorfdphqwr ( (' 0f {) _ Wr= Rfwrehu 57/ 5336 Sdjh= 47 h d hqhujld hohwurvwäwlfd fd ] 2 E{)2 2 E{)2 2 L' ( _Oo ' 0f % n 0 E, c % 20 T 20 _ 20f f _ rqgh r sulphlur whupr srvvxl xp 0 qr ghqrplqdgru sru hvwduprv qr lqwhulru gr glhoìwulfr/ hqtxdqwr txh r vhjxqgr srvvxl xp 0f sru hvwduprv qr du +qrwh/ hqwuhwdqwr/ txh ( ì vhpsuh r phvpr/ hp dperv rv fdvrv,1 D iruêd/ sruwdqwr/ fd 8% # $ YL 0f 0f c 0 ' ' Y% {) 2 0 ' c 0f . 2 c 2 g {) _ 2 _ rqgh ' _ h . 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RO ' ] T Sdjh= 6 ] T O OoU d a_T Oo4 EOo _T ] _OR _ ] Y4 EOo ' Oo4 EOo _T ' Oo _T _| _|] T Y| T O ' c OoU d a_T T Frpr aO ì qxor qd vxshuiðflh 7/ hqwær srghprv xvdu d h{suhvvær dqwhulru sdud hvfuhyhu ] T O a_T 'c ] T O OoU d a_Tc mä txh d lqwhjudo vreuh 7 vh dqxod1 Hqwær/ shor uhvxowdgr dqwhulru txh ì r uhvxowdgr hvshudgr1 _O R ] O ' a_Tc _| T t H{hufðflr :1:= Dv fdvfdv floðqgulfdv wíp udlrv o h o2 / o2 : o h vær pdqwlgdv ã glihuhqêd gh srwhqfldo {)1 Hqwuh dv fdvfdv kä xp phlr gh frqgxwlylgdgh }1 Vdehprv O txh lpsolfd/ frpr mä ylprv/ txh txh ydoh d Ohl gh Rkp aO ' } .cr U' {) - h suhflvdprv fdofxodu -1 Sdud fdofxoä0or/ qrwdprv txh whprv h gh prgr txh Dvvlp/ qdophqwh ' ' {) - ' -' U' 0 } 0 } }{) 0 Wr= Rfwrehu 57/ 5336 Sdjh= 7 h suhflvdprv phudphqwh fdofxodu sdud d frqjxudêær hp txhvwær1 Qrwh txh whprv gh prgr txh )' b *? Eo*o n )f c 2Z0 {) ' rx vhmd ' Dvvlp/ fdprv frp b *? Eo2 *o c 2Z0 b 2Z0 ' {) *? Eo2 *o U' 2Z}{) c *? Eo2 *o txh hud r uhvxowdgr surfxudgr1 R h{hufðflr irl ihlwr vhp xvdu d Ohl gh Rkp gluhwdphqwh1 O h fdofxodu . O sdud hvwd Sdud xvä0od/ vhuld qhfhvväulr sduwluU gluhwdphqwh gd ohl aO ' } . O e _@1 Dvvlp/ fdprv frp frqjxudêær/ ohpeudqgr txh U ' 7 a d ? 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+ ' R+ c ^% 6 26 22 ^ R ' R c ^e6 % A % + A 26 A = R ' 3^ R c ^2 2 + + 26 % e6 Frqvwuxd djrud r yhwru vlpsoìwlfr O# gdgr sru +ydprv wuhlqdu dtxl xp srxfr gh phfåqlfd foävlfd, 3 4 % E + F F O# ' E C R% D R+ wdo txh 4 3 ^ f % 26 ^ E + F E f E c 26 E F 22 O# ' C 'E R% D C c ^e6 f ^2 2 R+ f c e6 3 6 f f 3^ 26 Rud/ vdehprv txh d vroxêær gh xp sureohpd gr wlsr 43 4 % FE F 6 FE + F ^ F C R% D 26 D R+ f f rqgh ì xp whqvru/ ì gdgd sru O# ' dO# O# ' O# f i T Eb| c rqgh b ì xp dxwrydoru gd pdwul} 1 Qrwh txh/ qhvwh fdvr/ whprv rv dxwrydoruhv h dxwryhwruhv +ghjhqhuhvfíqfld gxsod hp f, ^ ^ bc2 ' fc O# ' c fc fc c O# 2 ' fc c c c f 2 2 ^ ^ ^ b ' cO# ' c c c cc 6 2 2 c^ ^ ^ be ' c O# e ' c cc cc 6 2 2 gh prgr txh whuhprv vroxêøhv gr wlsr +sdud rv dxwrydoruhv b h2rx be txh glihuhp dshqdv shod gluhêær gr prylphqwr flufxodu, ^ ^ % ' - t? | n B % c + ' - ULt | n B+ c 6 6 frp yhorflgdgh dqjxodu /' ^ 6 Wr= Rfwrehu 57/ 5336 Sdjh= 6 Pdv qrwh txh /- ' z / gh prgr txh z ^ ' 6 -' 6z c ^ frpr hvshudgr1 Qrwh txh R5 ' SJ?r|/ rx vhmd/ r prylphqwr qd gluhêær 5 vh gä frp yhorflgdgh frqvwdqwh1 t H{hufðflr ;17= Whprv txh d iöupxod +;158, ì gdgd sru k l L L _O, e _O,2 e EOo2 c Oo > 8O2 ' f U U2 eZ MOo2 c Oo M 2 Srghprv id}hu r surgxwr yhwruldo wulsor lqglfdgr sdud rewhu k l _O, e _O,2 e EOo2 c Oo ' _O,2 _O, d EOo2 c Oo c EOo2 c Oo _O, d _O,2 Dvvlp/ whprv > 8O2 ' c f U U2 eZ Qrwh/ djrud/ txh L L 2 EOo2 c Oo O O _, d _,2 n MOo2 c Oo M L U MOo2 c Oo M L 2 _O,2 L U MOo2 c Oo M d _O, d _O, ' fc ylvwr txh d lqwhjudo gh olqkd ì wrpdgd vreuh xpd fxuyd ihfkdgd1 Dvvlp/ fdprv frp L L >f EOo2 c Oo O O O 82 ' c U U2 _, d _,2 c eZ o2 c Oo M 2 MO txh ì r uhvxowdgr hvshudgr1 t H{hufðflr ;18= +hp dqgdphqwr, Whprv txh L O O EOo2 c 8 ' U2 _O,2 e ylvwr txh 2 O EOo2 ' >f U eZ L h rqgh xvdprv d ohl gh Elrw h Vdyduw1 Hwf1 _O, e EOo2 c Oo MOo2 c Oo M t H{hufðflr ;1:= Srghprv xvdu rv uhvxowdgrv mä rewlgrv d sduwlu gr wh{wr gr olyur/ qrwdqgr djrud txh whprv rv åqjxorv w ' SfJ h w2 ' 2fJ h txh @ @ |@? 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' c t? w_w! e- 3- 5 2 n @ E52 *2 e- f Dvvlp/ r fdpsr wrwdo qr fhqwur gd hvihud fd gdgr sru ] Z ] Z > U > U f f O Efc fc f ' c t? w_w ' c c ULt2 w t? w_w e- f e- f >f U e > U ' ' f eQrwh txh/ qr olyur/ d uhvsrvwd ì gdgd sru xp idwru e qr ghqrplqdgru/ qær frpr hqfrqwudprv1 Qær fuhlr/ hqwuhwdqwr/ txh d uhvroxêær dtxl ghvhqyroylgd hvwhmd huudgd/ d glihuhqêd ghyhqgr0vh/ sruwdqwr/ d xp srvvðyho huur ruwrjuäfr gr olyur1 Wr= Rfwrehu 57/ 5336 Sdjh= 8 t H{hufðflr ;144= Qrwh txh whprv sulphludphqwh txh rewhu r fdpsr ghylgr d xpd hvslud txdgudgd gh odgr @1 Dvvlp/ frqvlghuh d jxud d vhjxlu Ydprv uhvroyhu hvwh h{hufðflr xvdqgr qrwdêær yhwruldo wrxw frxuw/ frpr irupd gh dsol0 fdêær gd ohl gh Elrw Vdyduw1 Dvvlp/ frqvlghudqgr d jxud/ yhprv txh/ sdud r r gd gluhlwd whprv @ E_ E_ E_ _O, ' c_%=c Oo ' %= n Hc Oo2 ' @& 2 @ EOo2 c Oo E_ ' c%= c H n 5 & k 2 l @ @ E_ E_ O _, e EOo2 c Oo ' c_% = e c%= c H n 5 & ' _%& n 5_%H 2 2 hqtxdqwr txh sdud r r gd hvtxhugd whprv @ Ee Ee Ee _O, ' _%=c Oo ' %= c Hc Oo2 ' @& 2 @ EOo2 c Oo Ee ' c%= n H n 5 & k 2 l @ @ Ee Ee O _, e EOo2 c Oo ' c_% = e c%= n H n 5 & ' c _%& n 5_%H 2 2 vhqgr txh qr r gd gluhlwd hvwdprv lqwhjudqgr gh @*2 dwì c@*2/ hqtxdqwr txh qr udpr gd hvtxhugd hvwdprv lqwhjudqgr gh c@*2 dwì @*21 Dvvlp/ fdprv frp r whupr O gdqgr dvvrfldgr ã frqwulexlêær grv grlv rv ã lqgxêær pdjqìwlfd ] ] E_ Ee >f U 3@*2 _O, e EOo2 c Oo E_ >f U n@*2 _O, e EOo2 c Oo Ee O E5 ' n eZ n@*2 eZ 3@*2 MOo2 c Oo M MOo2 c Oo M ] 3@*2 ] n@*2 c@*2& n 5 H _% @*2 & n 5 H _% >f U >f U ' n eZ n@*2 d%2 n 5 2 n @2 *eo *2 eZ 3@*2 d%2 n 5 2 n @2 *eo *2 ] c>f U@ n@*2 _% ' & *2 2 2 eZ 3@*2 d% n 5 n @2 *eo Wr= Rfwrehu 57/ 5336 Sdjh= 9 Djrud/ sdud rv rv txh hvwær *dwuäv* h *qd iuhqwh* gd hvslud whuðdprv h{dwdphqwh d phvpd frqvwuxêær/ h{fhwr shor dsduhflphqwr gd yduläyho + qr oxjdu gh %1 Dvvlp/ fdprv frp d frqwulexlêær wrwdo gd hvslud gdgd sru ] c>f U@ n@*2 _% O E5 ' &c *2 2 2 2Z 3@*2 d% n 5 n @2 *eo fxmr uhvxowdgr/ dsöv lqwhjudêær/ fd @ O E5 ' c>f U@ *2 & 2 @ @2 2Z 2 2 n 5 n 5 e 2 2 c>f U @ ' & 2 2Z @ n 5 2 @2 n 5 2 *2 e 2 Djrud/ hvwd ì d lqgxêær pdjqìwlfd qr srqwr 5 ghylgr d xpd ýqlfd hvslud txdgudgd1 Vh whprv xp vrohqölgh frpsulgr +lqqlwr,/ frp hvsludv/ hqwær/ qr frpsulphqwr _5 whprv _5*u hvsludv h d frqwulexlêær gr hohphqwr _5 sdud d lqgxêær pdjqìwlfd gr vrohqölgh fd O E5f ' _ gh prgr txh c>f U @2 _5 & 2Zu @2 n E5 c 5f 2 @2 n E5 c 5f 2 *2 e 2 2 O E5f ' c>f U@ 2Zu ] Sdud id}hu hvwd lqwhjudo/ frortxh sdud fdu frp n" 3" @2 e _5 2 *2 & n E5 c 5f 2 @2 n E5 c 5f 2 @ @ 5 c 5f ' S |@? 1c _5 ' S tiU2 1_1 2 2 O E5f ' c>f U Zu ] nZ*2 3Z*2 2 tiU 1 c>f U _1 & ' &c 2 u n |@? 1 txh ì r uhvxowdgr hvshudgr/ d phqrv gh xp vlqdo ghylgr ã hvfrokd gd gluhêær gd fruuhqwh/ reyldphqwh +qd uhvsrvwd gr olyur idowd r whupr u txh whp txh dsduhfhu/ hylghqwhphqwh/ mä txh/ fdvr frqwuäulr/ whuðdprv xp sureohpd gh glphqvlrqdolgdgh sdud d lqgxêær pdjqìwlfd,1 t H{hufðflr ;145= Whprv txh/ hp frrughqdgdv hviìulfdv >f U @2 O E5 ' 2 E5 2 n @2 *2 !c Wr= Rfwrehu 57/ 5336 Sdjh= : Srghprv hvfuhyhu r glyhujhqwh/ hp frrughqdgdv floðqgulfdv frpr vhqgr O ' Ud gh prgr txh fdprv frp Y Yw Y5 Eoo n n ' fc o Yo o Yw Y5 Y >U 5@2 o Eoo ' c f Yo 2 E5 2 n @2 D*2 Djrud/ frpr o 5/ srghprv/ hp sulphlud dsur{lpdêær/ frorfdu qd h{suhvvær dflpd/ 5 ' o sdud fdu frp Y >U o2 @2 Eoo ' c f Yo 2 Eo2 n @2 D*2 txh/ sru lqwhjudêær/ fdprv frp o Rx vhmd/ @2 >f U ' c o 2 ] o2 _o Eo2 n @2 D*2 >f U o >f U o2 ' ' 2o Eo2 n @2 *2 S Eo2 n @2 o ' >f U o2 S Eo2 n @2 *2 *2 t H{hufðflr ;146= Vdehprv txh 5 E4c 5 ì ghfuhvfhqwh frp 41 Dvvlp/ ã phgld hp txh ydprv vdlqgr sdud rv odgrv gr pdjqhwr wudsh}rlgdo/ d lqgxêær pdjqìwlfd qd gluhêær 5 ydl glplqxlqgr +frqud d jxud d vhjxlu,1 O whprv txh +d, Wrpdqgr r urwdflrqdo gh O ' Ue h/ sruwdqwr/ Y5 Yw c 4 Yw Y5 4n Y4 Y5 c Y5 Y4 wn 4 Y E4w Y4 c Y4 Yw &'f Y4 Y5 ' f1 Y5 Y4 Dvvlp/ frqfoxðprv txh 4 ghfuhvfh frp 51 Djrud frqvlghuh d jxud dqwhulru rqgh dsuhvhqwdprv xpd ýqlfd olqkd gh lqgxêær pdjqìwlfd1 Vdehprv txh vreuh r sodqr phgldqr whprv 4 ' f h wdpeìp txh Y4 *Y5 ' f1 Hqwær/ ghyhprv whu/ dflpd gr sodqr phgldqr/ xpd frpsrqhqwh 4 : f h/ dedl{r gr sodqr/ 4 f/ h{dwdphqwh frpr prvwudgr dol1 D olqkd gh fdpsr ì d frpsrvlêær ghvwd frpsrqhqwh 4 frp d frpsrqhqwh 5 / r txh gä r irupdwr ghvhmdgr sdud d olqkd gh lqgxêær1 Wr= Rfwrehu 57/ 5336 Sdjh= ; +e, Qd jxud dqwhulru wdpeìp dsuhvhqwdprv gxdv srvvlelolgdghv sdud d fruuhqwh U +dtxl qær lpsruwd d gluhêær gr prylphqwr gd sduwðfxod/ rx vxd fdujd/ pdv dshqdv d gluhêær gd fruuhqwh/ txh ì d phvpd gluhêær gh _O,1 Vdehprv txh d iruêd ì gdgd sru L O O e _O,( 8 ' cU dvvlp/ ì iäflo yhu sdud dv gxdv fruuhqwhv dol dsuhvhqwdgdv/ txh vhpsuh whuhprv d iruêd 8O qd gluhêær gr sodqr phgldqr +ghylgr ã dowhudêær gd gluhêær gd lqgxêær pdjqìwlfd/ txdqgr sdvvdprv shor sdoqr,1 Dv rxwudv gxdv srvvlelolgdghv hvwduldp uhodflrqdgdv frp dv gluhêøhv rsrvwdv gd fruuhqwh1 R ohlwru srgh yhulfdu txh r uhvxowdgr vhuä r phvpr1 O ' f1 Vh wlyhuprv t H{hufðflr ;147= +d, Whprv txh d htxdêær +;163, ì gdgd sru U d hqwær/ whuhprv O ' Oo e U} E%c +c 5 c o Oo Oo Oo O Ud 'Ud e U} E%c +c 5 ' U e d U} c dU e U}o d o o o Ohpeudqgr txh U e EOo*o ' f h txh r urwdflrqdo gh xp judglhqwh ì qxor/ whprv r uhvxowdgr qdo1 +e, Sdud hqfrqwudu d ghqvlgdgh gh fruuhqwh/ edvwd txh idêdprv Dvvlp/ O >f aO ' U e O o >f aO ' U e e U} E%c +c 5 ' o Oo Oo Oo Oo ' EU d U} c U d U} n EU} d U c d U U} ' o o o o 2 Oo Oo ' U} n eZB EOo U} n U} n U} d U Oo c d U U} o o o o Dojxpdv vlpsolfdêøhv wdoyh} srvvdp vhu ihlwdv1 Ghl{dprv d fder gr ohlwru whqwä0odv1 Ohpeuh0vh txh ghyhprv whu U d U} ' U2 } ' f1 Dvvlp/ O o O o Oo >f aO ' eZB EOo n c d U U} c U} d o o o o2 Wr= Rfwrehu 57/ 5336 Sdjh= < t H{hufðflr ;148= Hvwh ì xp h{hufðflr h{wuhpdphqwh vlpsohv1 Mä vdehprv txh ghyhprv whu +vh hvwlyhuprv qd dsur{lpdêær gh fruuhqwhv hvwdflrqäuldv/ rx vhmd/ vh U d aO ' cY4*Y| ' f, O ' >f ac O Ue gh prgr txh/ wrpdqgr r urwdflrqdo gh dperv rv odgrv/ whprv O 'U Ud O c U2 O ' >f U e a O Ue Ue O Qrwh txh vö sxghprv wrpdu Ue >f a ' >f Ue aO ghylgr ã lvrwursld h krprjhqhlgdgh gr phlr pdjqìwlfr1 Djrud qrwh txh/ sdud xp phlr frpr r frqvlghudgr/ whprv/ shod Ohl gh Rkp/ O aO ' }.c gh prgr txh O ' U e a O }U e . 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O ' fc U2 frpr txhuðdprv ghprqvwudu1 t H{hufðflr ;149= Qhvwh fdvr whprv xpd vlwxdêær frpr d prvwudgd qd jxud d vhjxlu= h srghprv dsolfdu d ohl flufxlwdo gh Dpsëuh1 Vdehprv txh d lqgxêær pdjqìwlfd/ sru ud}øhv gh vlphwuld/ ghyh vhu gluhflrqdgd wdqjhqfldophqwh ã txdotxhu flufxqihuíqfld fhqwudgd qr hl{r txh sdvvd shor fhqwur gr frqgxwru1 Dvvlp/ d irupd pdwhpäwlfd gd ohl fd +_O, ' o_ww, L ] O d _O, ' 2Z f o_w ' >f Uc Wr= Rfwrehu 57/ 5336 Sdjh= 43 rqgh U ì d fruuhqwh txh sdvvd shor r frqvlghudgr1 Qrwh/ hqwuhwdqwr/ txh d fruuhqwh U ì gdgd sru ] U' aO d ?_@c 7 rqgh 7 ì d vhêær uhwd olplwdgd sru 1 Dvvlp/ vh o : -/ rqgh - ì r udlr gr frqgxwru/ hqwær hvwdprv wrpdqgr wrgd d vhêær uhwd gr frqgxwru h d fruuhqwh U ì d fruuhqwh wrwdo1 Orjr >U E2Zo ' >f U ' f c o z - 2Zo Sru rxwur odgr/ vh whprv o y -/ hqwær dshqdv sduwh gd fruuhqwh hvwä vhqgr frqvlghudgd +d sduwh lqwhuqd ã flufxqihuíqfld frp udlr o,1 Qhvwh fdvr/ whprv Zo2 c Z-2 rqgh r whupr ã gluhlwd iruqhfh d srufhqwdjhp gh fruuhqwh vhqgr frqvlghudgd +r r ì frqvlghudgr phwdo krprjíqhr,1 Orjr/ qhvwh fdvr/ fdprv frp U? ' U o2 >U ' f oc o y - 2Z Ilfd fodur ghvwd htxdêær txh ' f vh o ' f/ rx vhmd/ d lqgxêær pdjqìwlfd vh dqxod vreuh r hl{r gr r1 E2Zo ' >f t H{hufðflr ;14:= Frqvlghuh d jxud d vhjxlu= Dgrwdqgr d vxjhvwær gr olyur h dvvxplqgr txh d fdylgdgh fduuhjd ghqvlgdgh gh fru0 O hqtxdqwr txh r flolqgur fduuhjd ghqvlgdgh gh fruuhqwh a/ O fdprv frp uhqwh ca/ +frqvlghudqgr0vh d fxuyd , L O d _O, ' >f aZr2 c Wr= Rfwrehu 57/ 5336 Sdjh= 44 rqgh }hprv U ' Zr2 a/ xpd yh} txh hvwdprv frqvlghudqgr d fxuyd gr flolqgur +frpsohwr, gh udlr K sdud r txdo d ghqvlgdgh gh fruuhqwh ì a h hvwd fxuyd sdvvd shor fhqwur gd fdylgdgh/ txh fd d xpd glvwåqfld r gr fhqwur gr flolqgur gh udlr K1 D fdylgdgh qær frqwulexl/ ylvwr txh r fdpsr hp vhx hl{r ì qxor +yhmd h{hufðflr dqwhulru,1 Dvvlp/ wrpdqgr d fxuyd whprv E2Zo ' >f Zr2 a rx vhmd ' frpr txhuðdprv ghprqvwudu1 >f r2 a c 2 t H{hufðflr ;14;= Vh qrvvr vrohqölgh lqqlwr srgh vhu frqvlghudgr wdo txh d lqgxêær pdjqìwlfd vö srvvxl frpsrqhqwh qd gluhêær 5 +phvpd gluhêær gh rulhqwdêær gr vrohqölgh,/ hqwær srghprv frqvwuxlu xpd fxuyd frpr d dsuhvhqwdgd qd jxud d vhjxlu sdud r O fäofxor gh 1 Gh dfrugr frp d jxud/ whprv txh r fäofxor gd lqwhjudo L L O O O d _O, ' >f U d _, ' ghyh vhu r phvpr wdqwr sdud r shufxuvr txdqwr sdud r fdplqkr / xpd yh} txh d txdqwlgdgh gh fruuhqwh hqyroylgd hp dperv rv fdvrv ì h{dwdphqwh d phvpd1 Qrwh txh hvwhv grlv fdplqkrv sdvvdp vhpsuh shor hl{r gr vrohqölgh1 Dvvlp/ vh r vrohqölgh whp xp frpsulphqwr u/ hqwær whprv txh ] u ] f 5 E4 ' f _5 c 5 E4 ' @ _5 ' >f Uc f u Wr= Rfwrehu 57/ 5336 Sdjh= 45 vhqgr txh @ yduld sdud r sulphlur rx vhjxqgr fdplqkrv1 Wrph djrud @ ' > vh 5 E4 ' ' f/ hqwær r uhvxowdgr gr fäofxor dqwhulru fd ] u f 5 E4 ' f _5 ' >f Uc gh prgr txh r fdpsr qr lqwhulru gr vrohqölgh ghyh vhu frqvlghudgr frqvwdqwh gh irupd d rewhuprv > U u ' >f U ' f c u frqfrugdqgr frp r uhvxowdgr mä rewlgr qr olplwh @*u 1 Rud/ frpr rv fäofxorv dwudyìv gh h gh gær r phvpr uhvxowdgr h d glihuhqêd hqwuh rv fdplqkrv vh ghyh drv ydoruhv txh 5 srgh wrpdu qrv srqwrv 4 irud gr vrohqölgh/ hvwhv ydoruhv ghyhp vhu ljxdlv/ lpsolfdqgr txh qær srgh yduldu frp 4 irud gr vrohqölgh1 Frpr r vrohqölgh ì lqqlwr/ 5 qær srgh yduldu frp 5/ sru vlphwuld/ lpsolfdqgr/ sruwdqwr/ txh whp txh vhu frqvwdqwh1 t H{hufðflr ;14<= +d, Qrwh txh whprv d frqjxudêær gd jxud d vhjxlu= D vlphwuld gr sureohpd qrv lqirupd txh vö srghprv whu d frpsrqhqwh w gd lqgxêær pdjqìwlfd1 Dvvlp/ srghprv hvfrokhu xpd fxuyd frpr d dsuhvhqwdgd qd jxud dqwhulru/ gh udlr o/ gh irupd txh qr vhx lqwhulru sdvvd xpd fruuhqwh U +fdgd hvslud frpsduhfh frp xp U h vær hvsludv,1 Dvvlp/ shod ohl gh Dpsëuh/ fdprv frp +sdud d fxuyd qr lqwhulru gr vrohqölgh, L O d _O, ' 2Z4w ' >f U gh prgr txh w ' >f U c 2Z4 txh ì r phvpr uhvxowdgr gh xp r orqjr +frp fruuuhqwh U,1 Sdud 4 @ whprv O txh U ' f h/ sruwdqwr/ ' f1 Gd phvpd irupd/ sdud 4 : K/ whprv U fruuhqwhv Wr= Rfwrehu 57/ 5336 Sdjh= 46 *sdud flpd* h U fruuhqwhv *sdud edl{r*/ gdqgr xp oðtxlgr gh U|J| ' f/ gh prgr txh/ O ' f1 qrydphqwh/ +e, Dvvlp/ qrv srqwrv 4 ' @ h 4 ' K whprv w E@ ' >f U > U c w EK ' f 2Z@ 2ZK h txhuhprv txh r ydoru gh w EK qær vhmd phqru gr txh w E@ sru pdlv gh 2DI1 Dvvlp/ whprv w EK @ @ 'c 'c ' e w E@ K K e r txh gä K e ' c @ hp frqfrugåqfld frp r olyur1 t H{hufðflr ;153= Xpd pdqhlud gh uhvroyhu hvwh sureohpd ì xwlol}dqgr r uhvxowdgr mä frqkhflgr gd lqgxêær pdjqìwlfd sdud r fdvr gh xp r frpsulgr1 Dvvlp/ whprv O E4 ' >f U wc 2Z4 hp frrughqdgdv floðqgulfdv1 Djrud/ vdehprv txh rx vhmd O E4 ' U e c O Y5 Yw c 4 Yw Y5 >f U ' w 2Z4 O ' Ue 4n Y4 Y5 c Y5 Y4 wn 4 Y E4w Y4 c Y4 Yw & Qrwdqgr txh/ sru vlphwuld/ 5 +dvvlp frpr qhqkxpd rxwud frpsrqhqwh srgh ghshqghu gh w rx 5, / fdprv frp c Y5 Y E4w >U wn & ' f w Y4 4 Y4 2Z4 Gd phvpd pdqhlud/ sru vlphwuld/ qær srghprv whu w glihuhqwh gh }hur1 Sruwdqwr c h fdprv frp 5 E4 ' c ] 4 Y5 >U ' f Y4 2Z4 @ >f U >U _4 ' f *? 4 n c 2Z4 2Z Wr= Rfwrehu 57/ 5336 Sdjh= 47 rqgh ì xpd frqvwdqwh txh gä r qðyho gh hqhujld txh vh hvwä dgrwdqgr1 Dvvlp/ fdgd r whp xp srwhqfldo yhwruldo pdjqìwlfr frpr r rewlgr dflpd +qd gluhêær 5/ reyldphqwh,1 Djrud/ sdud xp srqwr txh hvwhmd d xpd glvwåqfld 4 h 42 gh grlv rv/ fdgd txdo frp fruuhqwh qxp vhqwlgr/ fdprv/ sru vxshusrvlêær >f U >f U >f U 4 5 E ' *? 4 c *? 42 ' *? c 2Z 2Z 2Z 42 frpr txhuðdprv ghprqvwudu1 t H{hufðflr ;054= Mä ylprv txh xpd vlwxdêær frpr d ghvfulwd qr sureohpd +gh xp fder frd{ldo, srvxl xpd frqjxudêær gh fdpsr +rewlgd shod ohl gh Dpsëuh, gdgd sru >f U / sdud 4 K 2Z4 ' f/ sdud 4 : Kc E?| ' Ee%| xpd yh} txh qær kä fruuhqwh wrwdo txdqgr hvwdprv irud gr fder frd{ldo1 D sulphlud lqgxêær pdjqìwlfd +frpr ylprv qr sureohpd dqwhulru, jhud xp srwhqfldo yhwru pdj0 qìwlfr gdgr sru >U E?| E4 ' f *? 4 n c 5 2Z hqtxdqwr txh d vhjxqgd jhud 5 prgr txh Ee%| rx vhmd E4 ' f1 Qr srqwr 4 ' K hodv ghyhp vhu ljxdlv/ gh >f U *? K n ' f 2Z 'c h/ sruwdqwr/ frpr txhuðdprv ghprqvwudu1 E?| ' 5 >f U *? K 2Z >f U 4 *? c 2Z K ^Qrwh txh vh i÷vvhprv fdofxodu r srwhqfldo yhwru pdjqìwlfr xvdqgr gluhwdphqwh d vxd ghqlêær lqwhjudo/ whuðdprv ] aO EOo >f U nu _5 _ ' MOo c Oo M eZ 3u 42 n E5 c 5 2 *2 nu t >f U 2 ' *? E5 c 5 n 42 n E5 c 5 2Z 3u O EOo ' >f eZ ] txh glyhujh vh }huprv rv olplwhv whqghu sdud lqqlwr u 1` Wr= Rfwrehu 57/ 5336 Sdjh= 48 K O d _O, ' x edvwd txh qrwhprv txh +7 ì t H{hufðflr ;155= +d, sdud ghprqvwudu txh vxshuiðflh dehuwd txh ghqh d fxuyd , ] ] L O O O d _O,c x ' d ?_@ ' U e d ?_@ ' 7 frpr ghvhmdgr1 7 O ' f + O ' 5 & qr qrvvr +e, Sdud xpd glvwåqfld 4 irud gr vrohqölgh/ vdehprv txh fdvr,1 Vh wrpduprv rv flufxlwrv txh xwlol}dprv dqwhulruphqwh +h{hufðflr 4;,/ hqwær d vxshuiðflh olplwdgd shor flufxlwr +frp 4 , whqghuä sdud lqqlwr h frpr r fdpsr qr h{whulru gr flolqgur ì qxor/ fdprv frp ] L O O d _O,c d ?_@ ' 7 rqgh 7 ì d vxshuiðflh olplwdgd sru xpd fxuyd 1 Qrwh/ hqwuhwdqwr/ txh hvwd vxshuiðflh whp rulhqwdêær _O@ ' &_@/ rx vhmd/ hvwä qxp sodqr shushqglfxodu dr hl{r gr vrohqölgh +5 ' SJ?r|,1 Dvvlp/ _O,/ sdud lqfoxlu dwì r srqwr 4 gr vrohqölgh/ ghyh vhu ljxdo d _O, ' 4_ww h fdprv frp ] 5 Z42 ' 2Z f w 4_w Frpr/ sru vlphwuld/ w qær srgh ghshqghu gh w/ whprv txh w E?| qr lqwhulru gr vrohqölgh1 E4 ' 5 > U 4' f 4c 2 2u Irud gr vrohqölgh/ whuhprv xpd olplwdêær qd äuhd 7/ ylvwr txh d lqgxêær pdjqìwlfd ì qxod qr h{whulru1 Dvvlp/ fdprv frp ] 2Z 2 5 Z@ ' w 4_w f sdud rewhu w Ee%| +f, Vdehprv txh gh irupd txh + >f U @2 2u 4 U E?| E4 ' >f2u 4 w Ee%| >f U @2 c w E4 ' 2u 4 Y5 Yw Y4 Y5 Y E4w Y4 c 4n c wn c & 4 Yw Y5 Y5 Y4 4 Y4 Yw Y >f U > U ' f 4 n fw n 4 4 &' f & 4 Y4 2u u O E?| ' Ue E4 ' Wr= Rfwrehu 57/ 5336 Sdjh= 49 txh ì r ydoru gd lqgxêær pdjqìwlfd qr lqwhulru gr vrohqölgh1 Gd phvpd pdqhlud/ sdud r h{whulru/ fdprv frp Y5 Yw Y4 Y5 Y E4w Y4 Ee%| O Ue ' c 4n c wn c & 4 Yw Y5 Y5 Y4 4 Y4 Yw Y >f U @2 ' f4 n fw n 4 & ' f& ' fc 4 Y4 2u 4 frpr mä kdyðdprv frqvlghudgr1 t H{hufðflr ;156= +d, D htxdêær +;194, ì O EOo ' >f eZ ] T aO EOo _ MOo c Oo M Wrpdqgr r glyhujhqwh +vreuh Oo/ qdwxudophqwh,/ fdprv frp % & ] O > a EO o O EOo ' f Ud Ud _ c eZ T MOo c Oo M pdv % aO EOo U d MOo c Oo M & U d aO EOo O ' n a EOo d U MOo c Oo M MOo c Oo M U d aO EOo O ' c a EOo d U MOo c Oo M MOo c Oo M ' caO EOo d U MOo c Oo M % & aO EOo ' cU d MOo c Oo M +xvdprv r idwr gh txh U d aO EOo ' f/ yäolgr sdud fruuhqwhv hvwdflrqäuldv, gh prgr txh srghprv hvfuhyhu % & ] L O O > a EO o a EOo d ?_@ f O EOo ' c Ud U d _ ' c c eZ T MOo c Oo M MOo c Oo M 7 rqgh 7 ì d vxshuiðflh txh *ihfkd* r yroxph T 1 Qrwh djrud txh srghprv *ohydu* 7 sdud r lqqlwr/ rqgh aO EOo vh dqxod/ gh prgr txh frpr txhuðdprv ghprqvwudu1 O EOo ' fc Ud Wr= Rfwrehu 57/ 5336 +e, Djrud whprv r vhjxlqwh fdvr frpr vhpsuh/ h Sdjh= 4: O ' U e c O O 'Ue Ue O 'U Ud O c U2 O ' >f a O Ue O vhmd wdo txh U d O ' f +vxsrqkd txh U d O ' , h ydprv Djrud ydprv vxsru txh O wdo txh U2 O ' c>f a/ O frp U d O ' f1 prvwudu txh srghuðdprv hvfrokhu xp rxwur O vhqgr xp urwdflrqdo gh / O qrv shuplwh xpd olehugdgh gh Gh idwr/ qrwhprv txh / hvfrokd +xpd fdoleudjhp, gr wlsr O' O n Ubc rqgh b ì xpd ixqêær hvfdodu txdotxhu +txh luhprv hvfrokhu fdoleududghtxdgdphqwh,1 O ' Ue O ' Ue O shupdqhfh d Frpr r urwdflrqdo gh xp judglhqwh ì qxor/ d htxdêær O ghqlgd sru O rx sru O ì d phvpd1 Wrphprv phvpd/ rx vhmd/ d lqgxêær pdjqìwlfd O O djrud r urwdflrqdo gh / hvfulwr hp whuprv gh > fdprv frp O c U2 O ' >f a O U Ud Qrwh/ djrud/ txh O ' U d O c U2Ob Ud Djrud hvfrokhprv d ixqêær hvfdodu b gh prgr txh sdud rewhu frp U2 b ' O ' c>f aO U2 O ' f Ud Rud/ frpr qrvvd hvfrokd gh b ì wrwdophqwh olyuh/ srghuðdprv whu frphêdgr mä frp hvwh O h rewlgr dv gxdv ýowlpdv htxdêøhv1 O srgh whu txdotxhu glyhujhqwh +f, Gh idwr/ frpr b ì duelwuäulr/ r srwhqfldo yhwruldo gh ghvhmdgr1 t H{hufðflr ;157= +d, Vhmdp rv srwhqfldlv yhwruldlv= O ' c+=c O 2 ' %H h O ' c Oo e O 2 Wr= Rfwrehu 57/ 5336 Sdjh= 4; Sdud prvwudu txh wrgrv vær srvvðyhlv srwhqfldlv yhwruldlv gd lqgxêær pdjqìwlfd xql0 iruph O ' & O uhvxowd qhvwd lqgxêær1 suhflvdprv dshqdv prvwudu txh r fäofxor gr urwdflrqdo grv Dvvlp/ fdprv frp O ' c Y% & ' & Ue Y+ O 2 ' Y+ & ' & U e Y% k l O O O O n EOo d U Oc O d U Oo U e ' c 2 U e Oo e ' c 2 U d Oo c EU d Oo k l O c f c Y Oo ' O ' & ' c 2 f c Y5 +e, Djrud/ wrpdqgr r glyhujhqwh/ fdprv frp O ' Y% n Y+ n Y5 ' f Ud Y% Y+ Y5 O ' Y% n Y+ n Y5 ' f Ud c Y5 Y% k Y+ l O O O O U d ' c 2 U d Oo e ' c 2 EU e Oo d c U e d Oo ' f rx vhmd/ wrgrv rv srwhqfldlv yhwruldlv srvvxhp glyhujíqfld qxod1 O ' O c O 2 1 Dvvlp/ +f, Vhmd djrud O ' c+= c %H ' c E+= n %H ' cU E%+ O ' U/ frp ' c%+1 Ghvwd pdqhlud/ t H{hufðflr ;158= Wrphprv r judglhqwh/ hp frrughqdgdv floðqgulfdv/ gr srwhqfldo pdj0 qìwlfr )W / gdgr sru cU )W ' w 2Z Ilfdprv frp # $ Y w Y Y >U O ' c>f U)W ' c 4 n n )W ' f c Y4 4 Yw Y5 2Z4 txh ì r srwhqfldo gh xp r uhwr h frpsulgr/ frqgx}lqgr xpd fruuhqwh U1 Qrwh/ hqwuhwdqwr/ txh d ixqêær )W qær ì xqlydorudgd/ ylvwr txh/ dr frpsohwduprv xpd yrowd/ vhx ydoru qær uhwruqd dr ydoru gd yrowd dqwhulru/ pdv ì dfuhvflgr gh 2Z1 Dvvlp/ rv phvprv srqwrv gr hvsdêr fruuhvsrqghp d glvwlqwrv ydoruhv gh )W 1 Lqwhuhvvdqwhphqwh/ mä txh r sureohpd whp vlphwuld sodqdu/ srghuðdprv shqvdu hp ghqlu r srwhqfldo )W frpr vhqgr U )W ' c uJ}~c 2Z Wr= Rfwrehu 57/ 5336 Sdjh= 4< rqgh ~ ì d yduläyho frpsoh{d ~ ' 4 i T Ew1 Qhvwh fdvr/ whuðdprv +qrwh txh i T Ew ' i T d Ew n 2&Zo, cU U )W& ' *L} 4 c Ew n 2&Z 2Z 2Z gh prgr txh O ' +i Ic>f U)W& J ' W4 Ic>f U)W& J h r fduäwhu pxowlydorudgr gd ixqêær fd hvwdehohflgr lphgldwdphqwh d sduwlu gd pxowl0 ydorudêær gr orjduðwlpr gh xpd yduläyho frpsoh{d1 Qhvwh fdvr/ r xvr gh vxshuiðflhv gh Ulhpdqq sdud wruqdu d ixqêær xqlydorudgd srgh vhu xpd srvvlelolgdgh sdud holplqdu r sureohpd1 Ì lqwhuhvvdqwh prvwudu hvvd srvvlelolgdgh srutxh hod qrv wruqd d frp0 sdudêær frp r fdvr hohwurvwäwlfr pxlwr pdlv suö{lpd +ohpeuh0vh txh hp hohwurvwäwlfd r srwhqfldo vhuld gdgr sru ^ )' *? 4,1 2Z0f Sdud sureohpdv sodqduhv d vroxêær dflpd srgh vhu h{wuhpdphqwh lpsruwdqwh/ mä txh srghprv xvdu r pìwrgr gh wudqvirupdêøhv frqiruphv sdud wudwdu sudwlfdphqwh gh txdotxhu frqglêær gh frqwruqr1 Dvvlp/ sureohpdv txh hqyroyhuldp rv frp frqglêøhv gh frqwruqr duelwuäuldv srghuldp vhu wudwdgrv ghvwd pdqhlud1 t H{hufðflr ;15:= +d, Vdehprv txh d lqgxêær pdjqìwlfd +vreuh r hl{r 5, sdud xpd hvslud ì gdgd sru @2 O E5 ' >f U & 2 E5 2 n @2 *2 h txh ghyhprv whu O E5 ' c>f U)W Dvvlp/ gh prgr txh U)W ' ) W cU @2 2 E5 2 n @2 *2 &c 5 ] cU@2 _5 cU@2 5 S ' ' 2 2 @2 5 2 n @2 5'" E5 2 n @2 *2 U 5 ' c S c 2 5 2 n @2 txh ì r uhvxowdgr hvshudgr1 +e h f, Djrud/ vxsrqgr txh 5 @/ srghprv hvfuhyhu 5 6 2 e U7 5 U 5 5 5 W 8' ) E5 ' c t c c 2 n e nddd 2 @ 52 n 2 @ 2@ H@ @2 o o D U o D ' c ULt w n ULt Ew c ULt Ew n d d d 2 @ 2 @ H @ Wr= Rfwrehu 57/ 5336 Djrud ydprv hvfuhyhu Sdjh= 53 U [ @ 3? ) Eoc w ' S? ? 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