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Fäofxor glihuhqfldo hp W+? +Hohphqwrv gh Wrsrorjld, GPDW 4: Deulo 5334 Frqwhýgr 4 LqwurgxŒær 5 5 QrŒłhv Wrsroöjlfdv hp W+? 5 514 QrŒær gh Yl}lqkdqŒd 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 515 QrŒłhv Wrsroöjlfdv Hohphqwduhv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 8 6 H{hufðflrv Sursrvwrv 43 7 H{hufðflrv Frpsohphqwduhv 44 8 VroxŒłhv 45 4 4:2Deulo25334 4 LqwurgxŒær D qrŒær gh �sur{lplgdgh� rx �yl}lqkdqŒd� irl xpd qrŒær ixqgdphqwdo qd dsolfdŒær gd qrŒær gh olplwh txhu dr hvwxgduprv vxfhvvłhv uhdlv txhu dr hvwx0 gduprv ixqŒłhv uhdlv gh yduläyho uhdo1 Frp hihlwr/ vhp xpd phglgd gd �sur0 {lplgdgh� uhodwlyd/ frpr prvwudu txh xpd vxfhvvær gh remhfwrv pdwhpäwlfrv +qýphurv rx yhfwruhv/ sru h{hpsor, vh dsur{lpd fdgd yh} pdlv gh xp rxwur remhfwr pdwhpäwlfr gr phvpr wlsrB D frqylfŒær gd lpsruwåqfld ghvwdv qrŒłhv ì uhiruŒdgd dr uhsduduprv txh pxlwd gd pdwhpäwlfd txh vh dsolfd qd hqjhqkduld ì ghodv wulexwäuld= d qrŒær gh vrpd gh xpd vìulh +olplwh gd vxfhvvær gdv vxdv vrpdv sdufldlv,/ d qrŒær gh vìulh gh srwíqfld/ d qrŒær gh yhorflgdgh lqvwdqwåqhd +olplwh gh xpd fhuwd ud}ær lqfuhphqwdo,/ d qrŒær gh lqwhjudo gh Ulhppdq +olplwh gdv vrpdv gh Ulhppdq,/ d qrŒær gh frqwlqxlgdgh/ hwf/ hwf1 D frqvwuxŒær pdwhpäwlfd grv frqfhlwrv txh shuplwhp d h{sorudŒær gr frqfhlwr gh olplwh dsrld0vh qr fdpsr gd pdwhpäwlfd frqkhflgr sru Wrsror0 jld/ qr txdo vh hvwxgdp dv sursulhgdghv grv frqmxqwrv pdwhpäwlfrv hvwuxwx0 udgrv uhfruuhqgr ª qrŒær gh yl}lqkdqŒd devwudfwd1 Qhvwh fdsðwxor luhprv hvwxgdu qrŒłhv gh wrsrorjld hohphqwdu qr txdgur pdlv uhvwulwlyr +h lqwxlwlyr, grv hvsdŒrv pìwulfrv/ lvwr ì/ hp frqmxqwrv px0 qlgrv gr frqfhlwr pdwhpäwlfr gh glvwåqfld +Hxfolghdqd, whqgr hp ylvwd d dsolfdŒær grv frqfhlwrv ghvhqyroylgrv dr hvwxgr gd qrŒær gh olplwh/ frq0 wlqxlgdgh h glihuhqfldelolgdgh gh fdpsrv hvfdoduhv h yhfwruldlv1 R frqfhlwr gh yl}lqkdqŒd/ hvvhqfldo qd frqvwuxŒær gh xp hvsdŒr wrsroöjl0 fr/ vhuä hqwær gh�qlgr frp edvh qd qrŒær gh glvwåqfld Hxfolghdqd hqwuh hohphqwrv grv frqmxqwrv hvwxgdgrv +yhfwruhv gh W+?,1 Gh qrwdu/ qr hqwdqwr/ txh hp hvwxgrv pdlv surixqgrv h frppdlru dofdqfh d Wrsrorjld srgh vhu hvwxgdgd vhp uhfruuhu dr frqfhlwr gh glvwåqfld +rx pìwulfd,1 5 QrŒłhv Wrsroöjlfdv hp W+? 514 QrŒær gh Yl}lqkdqŒd Ì d qrŒær gh erod dehuwd/ frqfhlwr txh jhqhudol}d d qrŒær gh lqwhuydor dehuwr gh W+ txh wær ehp frqkhfhprv txh shuplwluä/ frpr yhuhprv gh vhjxl0 gd/ gh�qlu r frqfhlwr gh yl}lqkdqŒd gh xp srqwr qhfhvväulr ª hvwuxwxudŒær �wrsroöjlfd� gh W+?1 Frphfhprv sru uhfrugdu d qrŒær gh qrupd Hxfolghdqd h gh glvwåqfld dvvrfldgd d hvwd ýowlpd qrupd/ gh�qlgdv qdwxudophqwh qr hvsdŒr yhfwruldo 5 4:2Deulo25334 Hxfolghdqr W+?/ d sduwlu gr frqfhlwr gh surgxwr lqwhuqr fdqöqlfr1 Vhmd ’E% c % 2 c � � � c % ? � 5 W+?/ d dsolfdŒær n�n G W+? $ W+ $ n n ’s m ’s%2 n ���n %2 ? gl}0vh qrupd Hxfolghdqd1 Gh qrwdu txh hvwd dsolfdŒær +frpr wrgdv dv qrupdv, jr}d gdv vhjxlqwhv sursulhgdghv= � n n � fc; 5W+?> � n@ n ’ m@m n n c ; 5 W+? h ;@ 5 W+> � n n )n � n nn n)n c; c) 5 W+?> � Vh n n ’ f hqwær ’ f1 Fkdpd0vh glvwåqfld +rx pìwulfd, dvvrfldgd ª qrupd dqwhulru d ixqŒær _ G W+? � W+? $ W+ E c)� $ _ E c)� ’ n � )n � D ixqŒær glvwåqfld jr}d gdv vhjxlqwhv sursulhgdghv qdwxudlv +txh uhvxowdp gdv sursulhgdghv gd qrupd,= � _ E c)� � fc; c) 5W+? � _ E c)� ’ f vvh ’ )( � _ E c)� ’ _ E)c � c; c) 5W+?( � _ E c 3� � _ E c)� n _ E)c 3� c; c)c 3 5W+?� Qrwhprv txh d ixqŒær glvwåqfld vdwlvid} dv sursulhgdghv txh d glvwåqfld xvxdo vdwlvid} h gh�qh txdolwdwlyd h txdqwlwlydphqwh d qrŒær gh �sur{lpl0 gdgh� hqwuh rv remhfwrv pdwhpäwlfrv hp hvwxgr +qhvwh fdvr yhfwruhv gh W+?,1 Fkdpd0vh erod dehuwd gh fhqwur @ h udlr o : fc h uhsuhvhqwd0vh sru � E@c o� rx � o E@� dr frqmxqwr grv srqwrv gh W+? wdo txh _ E c @� o lvwr ì � o E@� ’ i 5 W+? G _ E c @� oj � Xpd erod dehuwd gh fhqwur @ h udlr o ì r frqmxqwr gh wrgrv rv yhfwruhv fxmd glvwåqfld dr yhfwru @ ì hvwulwdphqwh phqru gr txh o1 Qær ì gliðflo yhul�fdu txh hp W+ dv erodv dehuwdv uhsuhvhqwdp lqwhuydorv dehuwrv +srutxíB,1 Hp W+? r frqfhlwr gh erod dehuwd srgh vhu jhrphwulfdphqwh lqwhusuhwdgr/ frpr yhuhprv qrv h{hpsorv vhjxlqwhv1 6 4:2Deulo25334 H{hpsor 4 Hp W+2/ xpd erod dehuwd gh fhqwur qxp srqwr E@ c @ 2 � h udlr o vhuä r frqmxqwr grv srqwrv E% c % 2 �/ wdlv txh _ EE% c % 2 � c E@ c @ 2 �� ’ nE% c % 2 �� E@ c @ 2 �n o / / t E% � @ �2 n E% 2 � @ 2 �2 o lvwr ì/ uhsuhvhqwd r �lqwhulru� gr fðufxor gh fhqwur E@ c @ 2 � h udlr o1 H{hpsor 5 Hp W+?/ xpd erod dehuwd gh fhqwur hp @ ’ E@ c ���c @ ? � h udlr o vhuä frqvwlwxðgd shorv yhfwruhv / wdlv txh _ E c @� ’ nE% c ���c % ? �� E@ c ���c @ ? �n o / / t E% � @ �2 n � � �n E% ? � @ ? �2 o lvwr ì/ uhsuhvhqwduä rv srqwrv gr lqwhulru gh xpd klshu0hvihud fhqwudgd hp @ h gh udlr o1 Hp W+� txdlv vær rv vöolgrv jhrpìwulfrv fxmr lqwhulru uhsuhvhqwd xpd erod dehuwdB Yl}lqkdqŒd gh xp srqwr @ ì txdotxhu vxefrqmxqwr gh W+? txh frqwhqkd xpd erod dehuwd gh fhqwur hp @/ lvwr ì/ T ì xpd yl}lqkdqŒd gh @ vh � o E@� � T sdud dojxp o : f1 Qrwh0vh txh txdotxhu erod dehuwd ì yl}lqkdqŒd gr vhx suösulr fhqwur h idflophqwh vh prvwud txh ì yl}lqkdŒd gh txdotxhu xp grv vhxv srqwrv1 H{hpsor 6 Vhmd @ ’ Ec �1 Rv frqmxqwrv T ’ � E% c % 2 � 5 W+2 G % � f h % 2 � 2 � c T 2 ’ � E% c % 2 � 5 W+2 G t E% � �2 n E% 2 � �2 � 2 � h T � ’ ;? =E%c %2� 5 W+2 G v� % � 2 � 2 n � % 2 � 2 � 2 � 2 <@ > 7 4:2Deulo25334 vær wrgrv yl}lqkdqŒdv gh @/ mä txh wrgrv frqwíp xpd erod dehuwd fhqwudgd hp @ +d erod dehuwd � e E@� sru h{hpsor,1 Qr hqwdqwr rv frqmxqwrv ‘ ’ � E% c % 2 � 5 W+2 G % � h % 2 � � c ‘ 2 ’ � E% c % 2 � 5 W+2 G t %2 n %2 2 � s 2 � mä qær vær yl}lqkdqŒdv gh @1 515 QrŒłhv Wrsroöjlfdv Hohphqwduhv Ydprv hvwxgdu djrud dojxpdv qrŒłhv wrsroöjlfdv hohphqwduhv1 Vhmd 7 xp vxefrqmxqwr gh W+?/ xp srqwr @ gl}0vh srqwr lqwhulru gh 7/ vh 7 iru xpd yl}lqkdqŒd gh @c lvwr ì/ vh h{lvwlu xpd erod dehuwd fhqwudgd hp @ h frqwlgd hp 71 Xp srqwr gl}0vh h{whulru dr frqmxqwr 7 vh iru lqwhulru dr vhx frpsohphqwdu1 Qr fdvr gh xp srqwr qær vhu lqwhulru qhp h{whulru dr frqmxqwr 7/ hvvh srqwr ghvljqd0vh sru srqwr iurqwhlur gh 71 R frqmxqwr grv srqwrv lqwhulruhv gh xp frqmxqwr 7/ ghvljqd0vh sru lq0 whulru gh 7 h uhsuhvhqwd0vh sru lqw71 R frqmxqwr grv srqwrv h{whulruhv gh 7/ ghvljqd0vh sru h{whulru gh 7 h uhsuhvhqwd0vh sru h{w71 Gh irupd dqäorjd iu7/ uhsuhvhqwd r frqmxqwr grv srqwrv iurqwhlurv gh 7 txh vh ghvljqd iurqwhlud gh 71 D iurqwhlud gh xp frqmxqwr 7 srgh vhu uhsuhvhqwdgd sru Y71 H{hpsor 7 R srqwr @ ì srqwr lqwhulru gr frqmxqwr 7 ’ � o E@�1 Frp hihlwr � o E@� � 7 ’ � o E@� r txh prvwud txh h{lvwh xpd erod dehuwd fhqwudgd hp @ h frqwlgd hp 7 ’ � o E@�1 R frqmxqwr grv srqwrv lqwhulruhv gh 7 ì lqw7 ’ � o E@� xpd yh} txh � o E@� ì yl}lqkdqŒd gh wrgrv rv vhxv srqwrv1 R frqmxqwr grv srqwrv h{whulruhv gh 7 ì h{w7 ’ i 5 W+? G _ E c @� : oj xpd yh} txh hvwhv srqwrv vær lqwhulruhv dr frpsohphqwdu gh � o E@�1 R frqmxqwr iu7 ’ i 5 W+? G _ E c @� ’ oj frqvwlwxl r frqmxqwr grv srqwrv iurqwhlurv gh 7 srlv hvwhv srqwrv qær vær srqwrv lqwhulruhv gh 7c qhp gr vhx frpsohphqwdu1 8 4:2Deulo25334 H{hpsor 8 Vhmd @ ’ � 2 c 2 c 2 � 1 Hvwh yhfwru ì srqwr lqwhulru gh 7 ’ � E% c % 2 c % � � 5 W+� G % � f a % 2 � f a % � � f� c mä txh � e E@� � 7/ sru h{hpsor1 Rv srqwrv gh 7 wdlv txh Efc % 2 c % � � c frp % 2 h % � pdlruhv gr txh }hur/ vær srqwrv iurqwhlurv gh 7/ mä txh qær vær srqwrv lqwhulruhv qhpgh 7/ qhp gr vhx frpsohphqwdu H{hpsor 9 Vhmd 7 ’ � E% c % 2 � 5 W+2 G % 2 ’ 2% � � Hvwh frqmxqwr qær whp srqwrv lqwhulruhv1 Vxsrqkd0vh +frp ylvwd d xp de0 vxugr, txh Erc 2r� 5 7 ì srqwr lqwhulru gh 71 Hqwær sdud fhuwr o ’ o f / � o f Erc 2r� � 71 Pdv �rn of 2 c 2r� of 2 � 5 � o f Erc 2r� h � rn of 2 c 2r� of 2 � *5 7/ r txh ì devxugr1 Hvwh idfwr prvwud txh 7 qær srgh whu srqwrv lqwhulruhv1 Sru rxwur odgr/ r frqmxqwr grv srqwrv h{whulruhv gh 7 ì h{w7 ’ � E% c % 2 � 5 W+2 G % 2 9’ 2% � c mä txh wrgrv hvwhv srqwrv vær lqwhulruhv dr frpsohphqwdu gh 71 Srgh idflophqwh prvwudu0vh txh lqw7 � 7c h{w7 � W+?q7 h W+? ’ lqw7 u^ h{w7 u^ iu7� Uhohpeuhprv txh u^ uhsuhvhqwd d fkdpdgd xqlær glvmxqwd gh frqmxqwrv1 Fhuwrv frqmxqwrv vö wíp srqwrv lqwhulruhv1 Vh wrgrv rv srqwrv gh xp frq0 mxqwr/ iruhp srqwrv lqwhulruhv/ r frqmxqwr gl}0vh dehuwr1 Dvvlp xp frqmxqwr 7 ì xp frqmxqwr dehuwr vh h vrphqwh vh 7 frlqflgh frp r vhx lqwhulru1 H{hpsor : Wrgdv dv erodv dehuwdv vær frqmxqwrv dehuwrv srlv � o E@� ’ lqw� o E@� � H{hpsor ; Vhmd T ’ � E% c % 2 � 5 W+2 G % : f h % 2 : 2 � � Hvwh frqmxqwr ì dehuwr/ srlv vö whp srqwrv lqwhulruhv1 9 4:2Deulo25334 H{hpsor < R frqmxqwr T ’ � E% c % 2 � 5 W+2 G % � f h % 2 � 2 � qær ì dehuwr/ mä txh sru h{hpsor Efc � qær ì srqwr lqwhulru gh T 1 H{hpsor 43 Vhmd 7 ’ � E% c % 2 � 5 W+2 G % 2 ’ 2% � � Hvwh frqmxqwr qær ì dehuwr srlv whp shor phqrv xp srqwr txh qær ì srqwr lqwhulru r srqwr Ec 2�/ sru h{hpsor1 D xqlær �qlwd rx lq�qlwd qxphuäyho4 gh frqmxqwrv dehuwrv ì dlqgd xp frqmxqwr dehuwr1 Dvvlp/ d xqlær gh erodv dehuwdv ì dlqgd xp frqmxqwr dehu0 wr1 D lqwhuvhfŒær �qlwd gh frqmxqwrv dehuwrv ì dlqgd xp frqmxqwr dehuwr1 Qrwhprv txh d lqwhuvhfŒær lq�qlwd gh frqmxqwrv dehuwrv srgh qær vhu xp frqmxqwr dehuwr$ Rv frqmxqwrv dehuwrv vær sduwlfxoduphqwh lpsruwdqwhv hp Wrsrorjld mä txh pxlwdv gdv gh�qlŒłhv h uhvxowdgrv vær h{suhvvrv hp whuprv ghvwh wlsr gh frqmxqwrv1 Xp frqmxqwr gl}0vh ihfkdgr vh r vhx frpsohphqwdu iru dehuwr1 H{hpsor 44 R frqmxqwr 7� o E@� ’ i 5 W+? G _ E c @� � oj ì xp frqmxqwr ihfkdgr txh vh ghvljqd sru erod ihfkdgd fhqwudgd hp @ h gh udlr o1 Frp hihlwr r vhx frpsohphqwdu ì xp frqmxqwr dehuwr1 H{hpsor 45 Vhmd 7 ’ � E% c % 2 � 5 W+2 G % 2 ’ 2% � � Hvwh frqmxqwr ì ihfkdgr srlv r vhx frpsohphqwdu ì dehuwr1 H{hpsor 46 R frqmxqwr T ’ � E% c % 2 � 5 W+2 G % � f h % 2 : 2 � qær ì ihfkdgr qhp dehuwr mä txh qhp Tc qhp r vhx frpsohphqwdu vær dehuwrv1 4 ^ q5LQ D q @ i{= h{lvwh l 5 LQ wdo txh { 5 D l j gl}0vh xpd xqlær qxphuäyho gh frqmxqwrv1 : 4:2Deulo25334 H{hpsor 47 R frqmxqwr yd}lr > ì ihfkdgr hp W+2 srlv r vhx frpsohphqwdu ì dehuwr= r frpsohphqwdu gh > ì W+2 txh ì dehuwr1 Sru rxwur odgr/ frpr > ì dehuwr/ mä txh vö whp srqwrv lqwhulruhv +srutxíB,/ r vhx frpsohphqwdu W+2 ì ihfkdgr1 Dvvlp/ > h W+2 vær ihfkdgrv h dehuwrv vlpxowåqhdphqwh1 Qrwhprv/ frpr vh srgh yhul�fdu qrv h{hpsorv dqwhulruhv/ txh fhuwrv frq0 mxqwrv srghp vhu dehuwrv h ihfkdgrv vlpxowåqhdphqwh rx qhp dehuwrv qhp ihfkdgrv1 Dvvlp/ xp gdgr frqmxqwr srgh vhu dehuwr/ ihfkdgr/ qhp dehuwr qhp ihfkdgr h vlpxowåqhdphqwh dehuwr h ihfkdgr1 Fkdpd0vh ihfkr rx dghuíqfld gr frqmxqwr 7 ª xqlær gh 7 frp d vxd iurqwhlud txh vh uhsuhvhqwd sru 771 Xp srqwr @ gl}0vh dghuhqwh d 7 vh shuwhqfhu ª dghuíqfld gh 71 Ì srvvðyho prvwudu txh r ihfkr gh xp frqmxqwr ì vhpsuh xp frqmxqwr ihfkdgr1 Rv frqmxqwrv dehuwrv srghp vhu fdudfwhul}dgrv ª fxvwd gr frqfhlwr gh frqmxqwr ihfkdgr1 Frp hihlwr xp frqmxqwr 7 ì dehuwr vvh r vhx frpsohphqwdu ì ihfkdgr1 R srqwr @ 5 W+? ì srqwr gh dfxpxodŒær gh xp frqmxqwr 7 � W+? vh h vö vh hp wrgd d yl}lqkdqŒd gh @ h{lvwhp xpd lq�qlgdgh gh srqwrv gh 71 Fkdpd0vh ghulydgr gh 7 dr frqmxqwr gh wrgrv rv srqwrv gh dfxpxodŒær gh 71 R ghulydgr gh 7 ghqrwd0vh sru 7�1 Qrwhprv txh xp frqmxqwr �qlwr qær whp srqwrv gh dfxpxodŒær1 Srgh prvwudu0vh txh �� � 7�1 Xp srqwr @ gh 7 gl}0vh lvrodgr vh h{lvwlu xpd erod � o E@� wdo txh � o E@� _ 7 ’ i@j 1 H{hpsor 48 Frqvlghuhprv r vxefrqmxqwr gh W+ � ’ � % 5 W+ G % ’ ? a ? 5 W� � � Qær ì gliðflo yhul�fdu txh � whp sru ýqlfr srqwr gh dfxpxodŒær % ’ f1 R vhx ghulydgr vhuä srlv �� ’ ifj � H{hpsor 49 Ghwhuplqdu r lqwhulru/ r h{whulru/ d iurqwhlud/ d dghuíqfld h r ghulydgr gr frqmxqwr/ � ’ � E% c % 2 � 5 W+2 G %2 n %2 2 � e� � ; 4:2Deulo25334 Frqfoxl0vh lphgldwdphqwh txh lqw� ’ � E%c +� 5 W+2 G %2 n +2 e� c h{w� ’ � E%c +� 5 W+2 G %2 n +2 : e b %2 n +2 � c iu� ’ � E%c +� 5 W+2 G %2 n +2 ’ b %2 n +2 ’ e� c 7� ’ � E%c +� 5 W+2 G � %2 n +2 � e� c �� ’ � E%c +� 5 W+2 G � %2 n +2 � e� � Qhvwh fdvr yhul�fd0vh �� ’ 7� +r txh qhp vhpsuh dfrqwhfh1 SrutxíB,1 Doìp glvvr/ qhp r frqmxqwr � ì dehuwr/ qhp r vhx frpsohphqwdu r ì/ shor txh � ì xp h{hpsor gh xp frqmxqwr txh qær ì dehuwr qhp ihfkdgr1 Xp frqmxqwr 7 gl}0vh olplwdgr vh h{lvwlu dojxpd erod txh r frqwhqkd1 Rv vxefrqmxqwrv gh W+? txh vær olplwdgrv h ihfkdgrv gl}hp0vh frp0 sdfwrv1 Vhmd � xp vxefrqmxqwr gh W+?1 Gl}0vh txh grlv vxefrqmxqwrv dehuwrv � h � gh W+? vhsdudp � vh � � � ^�/ � _ � ’ >c � _� 9’ > h � _ � 9’ >1 R vxefrqmxqwr � gh W+? gl}0vh frqh{r vh qær sxghu vhu vhsdudgr sru qhqkxp sdu � h � gh vxefrqmxqwrv dehuwrv gh W+?1 H{hpsor 4: Prvwuhprv txh � ’ � E%c +� 5 W+2 G %2 n +2 � a + 9’ f� qær ì frqh{r1 Vhmdp rv dehuwrv � ’ � E%c +� 5 W+2 G %2 n +2 2 a + : f� c � ’ � E%c +� 5 W+2 G %2 n +2 2 a + f� � Frp hihlwr/ � � � ^ �/ � _ � ’ >c � _ � 9’ > h � _ � 9’ > r txh prvwud txh � ì vhsdudgr shorv dehuwrv � h �1 Hqwær � qær ì frqh{r1 Uhihuíqfldv ^4‘ D}hqkd/ Dflolqd h Mhuöqlpr/ P1 D1/ Fäofxor Glihuhqfldo Lqwhjudo hp W+ h W+?/ PfJudz0Kloo/ 4<<8> ^5‘ Olsvfkxw}/ V1/ Wrsrorjld Jhudo/ Vfkdxp/ 4<:4> ^6‘ Pdfkdgr/ Dupdqgr/ Wrsrorjld/ Xqlyhuvlgdgh Dehuwd/ 4<<8> ^7‘ Zdgh/ Z1 U1/ Dq Lqwurgxfwlrq wr Dqdo|vlv/ Suhqwlfh Kdoo/ 4<<8> < 4:2Deulo25334 6 H{hufðflrv Sursrvwrv H{hufðflr 4 Ghwhuplqh r lqwhulru/ r h{whulru/ r ihfkr h r ghulydgr gh fdgd xp grv vxefrqmxqwrv gh W+ vhjxlqwhv h lqgltxh txdlv vær dehuwrv h txdlv vær ihfkdgrv= 41 d�c d ^ o2c ed ^ ifc j ( 51 i% 5 W+ G %� : %j ( 61 dfc o _ "( 71 � @ ? ’ ?n G ? 5 W�� ( 81 � n E��? ?n ? G ? 5 W�� ( 91 i% 5 " G m%n �m Dj ^ �% 5 W+ G % ì luudflrqdo a �s2 � % � s�� ( H{hufðflr 5 Hp fdgd xp grv vhjxlqwhv fdvrv vhmd 7 r frqmxqwr gh wrgrv rv srqwrv shuwhqfhqwhv d W+2 +W+�/ qr fdvr gd ýowlpd doðqhd, txh vdwlvid}hp dv frqglŒłhv gdgdv1 Uhsuhvhqwh 7 jhrphwulfdphqwh/ ghwhuplqh �?|7/ e%|7/ so7/ 7 h 7� lqglfdqgr vh 7 ì dehuwr rx ihfkdgr1 41 � % � 2 h � � + � e( 51 m%m h m+m ( 61 % � +( 71 + ’ %2( 81 %2 n +2 � 2% ’ ( 91 �%2 n 2+2 S( :1 52 n %2 n +2 � f� H{hufðflr 6 Prvwuh txh hp W+ dv erodv dehuwdv vær lqwhuydorv dehuwrv1 H{hufðflr 7 41 Prvwuh txh d xqlær gh grlv frqmxqwrv dehuwrv ì dlqgd xp frqmxqwr dehuwr> 51 Prvwuh txh d lqwhuvhfŒær gh grlv frqmxqwrv dehuwrv ì dlqgd xp frqmxqwr dehuwr> 43 4:2Deulo25334 61 Prvwuh txh d lqwhuvhfŒær lq�qlwd gh dehuwrv srgh qær vhu xp dehuwr> 71 Prvwuh txh d xqlær lq�qlwd gh ihfkdgrv srgh qær vhu xp ihfkdgr1 H{hufðflr 8 41 Prvwuh txh d xqlær gh grlv frqmxqwrv ihfkdgrv ì dlqgd xp frqmxqwr ihfkdgr> 51 Prvwuh txh d lqwhuvhfŒær gh grlv frqmxqwrv ihfkdgrv ì dlqgd xp frq0 mxqwr ihfkdgr1 H{hufðflr 9 Prvwuh txh @ ì dghuhqwh d 7 vvh d txdotxhu erod gh fhqwur @ shuwhqfhu xp hohphqwr gh 71 H{hufðflr : Prvwuh txh 7 ì ihfkdgr vvh 7 ’ 77� H{hufðflr ; Prvwuh txh �� � 7�1 7 H{hufðflrv Frpsohphqwduhv H{hufðflr < 5Frqvlghuh rv vhjxlqwhv frqmxqwrv 7 � W+?1 Ghwhuplqh r lqwh0 ulru/ d iurqwhlud/r h{whulru/ r ihfkr h r ghulydgr gh 71 Gljd vh 7 ì dehuwr/ ihfkdgr/ olplwdgr/ frpsdfwr rx frqh{r1 41 7 ’ oc Do ( 51 7 ’ � % 5 W+ G % ’ ? a ? 5 W�� ^ o�c fo ( 61 7 ’ � E%c +� 5 W+2 G %+ : � ( 71 7 ì r grpðqlr gd ixqŒær s E%c +� ’ *? E+2 � %� ( 81 7 ì r grpðqlr gd ixqŒær s E%c +� ’ s +2 � t�?2 %( 91 7 ’ � E%c +� 5 W+2 G �Z % Z a % *5 " a + 5 "� ( :1 7 ’ � E%c +� 5 W+2 G �Z % Z a % *5 " a + 5 "� ^ ^ � E%c +� 5 W+2 G + 2 e % � +2 � � 5 säj1 ;8 gr Fäofxor Glihuhqfldo h Lqwhjudo/ Dflolqd D}hqkd h Pduld Jhuöqlpr/ PfJudz0 Kloo/ 4<<81 44 4:2Deulo25334 8 VroxŒłhv 414= lqw� ’ o�c d ^ o2c ed ( h{w� ’ o�4c�d ^ oc 2d ^ oec fd ^ ofc d ^ ocn4d ( � ’ d�c o ^ d2c eo ^ ifc j ( �� ’ d�c o ^ d2c eo ( Qær ì dehuwr qhp ihfkdgr1 415= lqw� ’ o�c fd ^ ocn4d ( h{w� ’ o�4c�d ^ ofc d ( � ’ �� ’ d�c fo ^ dcn4d ( Ì dehuwr h qær ì ihfkdgr1 416= lqw� ’ >( h{w� ’ W+q dfc o ( � ’ � � ’ dfc o ( qær ì dehuwr qhp ihfkdgr1 417= lqw( ’ >( h{w( ’ W+q E( ^ ifj� ( ( ’ (^ifj ((� ’ ifj ( qær ì dehuwr qhp ihfkdgr1 418= lqw. ’ >( h{w. ’ W+q E. ^ ifc 2j� ( . ’ . ^ ifc 2j (.� ’ ifc 2j ( qær ì dehuwr qhp ihfkdgr1 419= lqw8 ’ ��s2c 2� ( h{w8 ’ o�4c�Hd ^ �s�cn4� ( 8 ’ 8 � ’ ��Hcs�� ( qær ì dehuwr qhp ihfkdgr1 514= 7 ’ � E%c +� 5 W+2 G E � % � 2� a E� � + � e�� lqw7 ’ � E%c +� 5 W+2 G E % 2� a E� + e�� ( h{w7 ’ � E%c +� 5 W+2 G % b % : 2 b + � b + : e� ’ W+2q7( iu7 ’ � E%c +� 5 W+2 G E% ’ b % ’ 2� a � � + � e�^ ^�E%c +� 5 W+2 G E+ ’ � b + ’ e� a � % � 2� ( 7 ’ 7� ’ 7( 7 ì ihfkdgr h qær ì dehuwr1 515= 7 ’ � E%c +� 5 W+2 G � % a � + � lqw7 ’ 7( h{w7 ’ � E%c +� 5 W+2 G % � b % : b + � b + : � ( iu7 ’ � E%c +� 5 W+2 G E% ’ � b % ’ � a � � + � �^ ^�E%c +� 5 W+2 G E+ ’ � b + ’ � a � � % � � ( 7 ’ 7� ’ � E%c +� 5 W+2 G m%m � a m+m � � ( 7 ì dehuwr h qær ì ihfkdgr1 45 4:2Deulo25334 516= 7 ’ � E%c +� 5 W+2 G % � +� lqw7 ’ � E%c +� 5 W+2 G % : +� ( h{w7 ’ � E%c +� 5 W+2 G % +� ( iu7 ’ � E%c +� 5 W+2 G % ’ +� ( 7 ’ 7� ’ 7( 7 ì ihfkdgr h qær ì dehuwr1 517= 7 ’ � E%c +� 5 W+2 G + ’ %2� lqw7 ’ >( h{w7 ’ �E%c +� 5 W+2 G + 9’ %2� ( iu7 ’ 7 ’ 7� ’ 7(7 ì ihfkdgr h qær ì dehuwr1 518= 7 ’ � E%c +� 5 W+2 G E%� �2 n +2 ’ 2� lqw7 ’ >( h{w7 ’ �E%c +� 5 W+2 G E%� �2 n +2 9’ 2� ( iu7 ’ 7 ’ 7� ’ 7( 7 ì ihfkdgr h qær ì dehuwr1 519= 7 ’ � E%c +� 5 W+2 G �%2 n 2+2 S� lqw7 ’ 7( h{w7 ’ � E%c +� 5 W+2 G �%2 n 2+2 : S� ( iu7 ’ � E%c +� 5 W+2 G �%2 n 2+2 ’ S� ( 7 ’ 7� ’ � E%c +� 5 W+2 G �%2 n 2+2 � S� ( 7 ì dehuwr h qær ì ihfkdgr1 51:= 7 ’ � E%c +c 5� 5 W+� G %2 n +2 n 52 � lqw7 ’ 7(h{w7 ’ � E%c +c 5� 5 W+� G %2 n +2 n 52 : � ( iu7 ’ � E%c +c 5� 5 W+� G %2 n +2 n 52 ’ � ( 7 ’ 7� ’ � E%c +c 5� 5 W+� G %2 n +2 n 52 � � ( 7 ì dehuwr h qær ì ihfkdgr1 6= 0 714=0 715= 0 716= 0 717= 0 814= 0 815= 0 9= 0 := 0 ;= 0 <14= lqw7 ’ oc Dd 9’ 7 , 7 qær ì dehuwr( iu7 ’ ic Dj ( h{w7 ’ o�4c d ^ oDcn4d ( 77 ’ dc Do ’ 7�( 77 9’ 7 , 7 qær ì ihfkdgr> 7 ì olplwdgr/ qær ì frpsdfwr h ì frqh{r1 <15= lqw7 ’ o�c fd 9’ 7 , 7 qær ì dehuwr( iu7 ’ i�c fj ^ �% 5 W+ G % ’ ? a E? 5 W��� ( h{w7 ’ W+q �d�c fo ^ �% 5 W+ G % ’ ? a E? 5 W���� ( 77 ’ d�c fo ^ �% 5 W+ G % ’ ? a E? 5 W��� ( 77 9’ 7 , 7 qær ì ihfkdgr> 7� ’ d�c fo 7 ì olplwdgr/ qær ì frpsdfwr qhp frqh{r1 <16= lqw7 ’ � E%c +� 5 W+2 G %+ : � ’ 7 , 7 ì dehuwr( 46 4:2Deulo25334 iu7 ’ � E%c +� 5 W+2 G %+ ’ � ( h{w7 ’ � E%c +� 5 W+2 G %+ � ( 77 ’ 7� ’ � E%c +� 5 W+2 G %+ � � ( 77 9’ 7 , 7 qær ì ihfkdgr> 7 qær ì olplwdgr/ qær ì frpsdfwr qhp frqh{r1 <17= lqw7 ’ � E%c +� 5 W+2 G +2 � % : f� ’ 7 , 7 ì dehuwr( iu7 ’ � E%c +� 5 W+2 G +2 � % ’ f� ( h{w7 ’ � E%c +� 5 W+2 G +2 � % f� ( 77 ’ 7� ’ � E%c +� 5 W+2 G +2 � % � f� ( 77 9’ 7 , 7 qær ì ihfkdgr> 7 qær ì olplwdgr/ qær ì frpsdfwr h ì frqh{r1 <18=lqw7 ’ � E%c +� 5 W+2 G +2 � t�?2 % : f� 9’ 7 , 7 qær ì dehuwr( iu7 ’ � E%c +� 5 W+2 G +2 � t�?2 % ’ f� ( h{w7 ’ � E%c +� 5 W+2 G +2 � t�?2 % f� ( 77 ’ 7� ’ � E%c +� 5 W+2 G +2 � t�?2 % � f� ( 77 ’ 7 , 7 ì ihfkdgr> 7 qær ì olplwdgr/ qær ì frpsdfwr h ì frqh{r1 <19= lqw7 ’ > 9’ 7 , 7 qær ì dehuwr( iu7 ’ � E%c +� 5 W+2 G �Z � % � Z� ( h{w7 ’ � E%c +� 5 W+2 G % �Z b % : Z� ( 7� 77 ’iu7( 77 9’ 7 , 7 qær ì ihfkdgr> 7 qær ì olplwdgr/ qær ì frpsdfwr h ì frqh{r1 <1:= lqw7 ’ q E%c +� 5 W+2 G +2 e %2 +2 r 9’ 7 , 7 qær ì dehuwr( iu7 ’ q E%c +� 5 W+2 G �Z � % � f b k f � % � Z a � % � +2 b % � +2 e �l b b k % : Z a � % ’ +2 b % ’ +2 e �lr ( h{w7 ’ � E%c +� 5 W+2 G % �Z�^qE%c +� 5 W+2 G % : Z a �% +2 e b % : +2 �r ( 77 ’lqw7^iu7 9’ 7 , 7 qær ì ihfkdgr( 77 ’ 7� ’ q E%c +� 5 W+2 G �Z � % � Z b � % : Z a +2 e � %2 � +2 �r ( 7 qær ì olplwdgr/ qær ì frpsdfwr pdv ì frqh{r1 47 4:2Deulo25334
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