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714 R Pìwrgr gh Nrorgqhu 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 85 71414 R Sureohpd 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 85 71415 Frqvlghudêøhv Jhudlv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 87 71416 Lqwhjudlv Dqäorjdv drv Srwhqfldlv Vlpsohv h Gxsorv 1 1 1 1 1 1 1 1 1 1 1 1 1 8; 71417 Frqvwuxêær gr Ixqflrqdo Dx{loldu 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 96 71418 Whruhpd gd Uhgxêær 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9; 715 Dsolfdêær 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9< 8 Vroxêøhv Qxpìulfdv sdud d Iurqwhlud hp Prylphqwr :8 814 Fuhvflphqwr gh Suhflslwdgrv Sodqduhv qxpd Pdwul} Lqqlwd 1 1 1 1 1 1 1 1 1 1 1 1 :8 815 Fuhvflphqwr gh Suhflslwdgrv Sodqduhv qxpd Pdwul} Ilqlwd 1 1 1 1 1 1 1 1 1 1 1 1 1 ;3 816 Fuhvflphqwr gh Suhflslwdgrv Hviìulfrv qxpd Pdwul} Lqqlwd 1 1 1 1 1 1 1 1 1 1 1 1 ;7 817 Glvvroxêær gh Suhflslwdgrv Hviìulfrv qxpd Pdwul} Lqqlwd 1 1 1 1 1 1 1 1 1 1 1 1 1 ;< 9 Fuhvflphqwr gh xp Suhflslwdgr Hviìulfr frp d Frqfhqwudêær gd Lqwhuidfh

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515= Ghshqgíqfld gh J hp W sdud d yl}lqkdqêd gd wudqvlêær gh idvh1 1 1 1 1 1 1 1 1 1 1 1 1 1 48 516= Hvtxhpd gh xpd pdwul}1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 49 517= Frpsdudêær hqwuh rv whuprv gd Hqhujld1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4: 518= Ghqlêær gh qýfohr h hpeulær1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4; 519= Fxuyd wðslfd gh Q+U,1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4< 51:= Fxuydv gh Q+U, sdud glihuhqwhv W1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 54 614= Hvtxhpd gdv uhjløhv gh d dwì e sdud ghwhuplqdu J1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 63 615= Srvlêær gd irqwh uhdo h gd fwðfld1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6: 616= Frqfhqwudêær wrwdo rewlgd shodv gxdv irqwhv1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6; 617= Srvlêær gd irqwh fwðfld frpr xp ydoru qhjdwlyr1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6:

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ì gd dsur{lpdêær gr Judglhqwh Olqhdul}dgr1 1 1 1 = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7: 61;= Fuhvflphqwr sdud suhflslwdgrv sodqduhv frpr ixqêær gh mnm1  ì gd vroxêær h{dwd> 2 ì

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7: 61<= Glvvroxêær gh suhflslwdgrv hviìulfrv gh dfrugr frpr d dsur{lpdêær gr fdpsr lqyduldqwh +s @ 3, h d dsur{lpdêær gr wdpdqkr lqyduldqwh +s N 3,1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7< 6143= Glvvroxêær gh suhflslwdgrv hviìulfrv gh dfrugr frpr d dsur{lpdêær gr wdpdqkr lqyduldqwh +olqkd vöolgdv, h d dsur{lpdêær gr uhyhuvhg0jurzwk +olqkdv srqwlokdgdv,1 1 1 1 1 1 1 1 1 7< 714= Iljxud hvtxhpäwlfd gr grpðqlr G-= 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 86

715= Iljxud hvtxhpäwlfd gr grpðqlr m{m  n= 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 99 716= Hl{rv gh frrughqdgd xvdgrv qr fäofxor sdud d iurqwhlud sodqdu1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9< 717= Hl{rv gh frrughqdgdv frp dv yduläyhlv dglphqvlrqdlv1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 :3 814= Hvtxhpd gh loxvwudêær sdud d lqwhjudêær qxpìulfd1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1:9 815= Yduldêær gd yhorflgdgh gd iurqwhlud frp r whpsr sdud @ 3=8= 1 1 1 1 1 1 1 1 1 1 1 1 1 :; 816= Yduldêær gr udlr gd iurqwhlud  frp r whpsr sdud @ 3=8= 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 :< 817= Shuo gd glixvær qd pdwul} lqqlwd fdofxodgd sdud @ 3=8= 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 :< 818= Hl{rv gdv frrughqdgdv xvdgdv qr fäofxor sdud d iurqwhlud sodqdu= +d, qrupdlv> +e, yduläyhlv dglphqvlrqdlv1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ;3 819= Yduldêær gr udlr gd iurqwhlud frp r whpsr sdud +d, @ 3=38 h +e, @ 3=; sdud d iurqwhlud sodqdu1 D fxuyd srqwlokdgd ì d vroxêær lqlfldo1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;5

{lll 81:= Yduldêær gr udlr gd iurqwhlud frp r whpsr sdud +d, @ 3=38 h +e, @ 3=; sdud d iurqwhlud sodqdu1 D fxuyd srqwlokdgd ì d vroxêær lqlfldo1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ;6 81;= Shuo gr fdpsr gd glixvær qxpd pdwul} qlwd fdofxodgd sdud xpd iurqwhlud sodqdu1 @ 3=8= 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ;6 81<= Yduldêær gd frqfhqwudêær gr vroxwr qr fdvr sodqdu frp r whpsr sdud @ 3=38> 3=8 h 3=;1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ;6 8143= Yduldêær gr udlr gr suhflslwdgr frp r whpsr sdud @ 3=4> 3=8 h 3=<1 Dv fxuydv srqwlokdgdv

vær gd dsur{lpdêær gh lqwhuidfh hvwdflrqäuld1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ;: 8144= Yduldêær gd yhorflgdgh gr suhflslwdgr frp r whpsr sdud @ 3=4> 3=8 h 3=<1 Dv fxuydv

srqwlokdgdv vær gd dsur{lpdêær gh lqwhuidfh hvwdflrqäuld1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ;; 8145= Yduldêær gr udlr gr suhflslwdgr frp r whpsr sdud @ 3=4> 3=8 h 3=<1 Dv fxuydv srqwlokdgdv vær sdud r fuhvflphqwr gh udlr }hur1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ;; 8146= Juäfr gd frqfhqwudêær qrupdol}dgd shod glvwåqfld +U,1 1 1 1 1 1 1 = 1 1 1 1 1 1 1 1 1 1 1 ;< 8147= Yduldêær gr udlr suhflslwdgr frp r whpsr sdud @ 3=4> 3=8 h 4=31 Dv fxuydv srqwlokdgdv vær ihlwdv shod dsur{lpdêær gd Lqwhuidfh Hvwdflrqäuld1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 <5 8148= Yduldêær gd yhorflgdgh gd iurqwhlud frp r whpsr sdud @ 3=4> 3=8 h 4=31 Dv fxuydv srqwlokdgdv vær ihlwdv shod dsur{lpdêær gd Lqwhuidfh Hvwdflrqäuld1 1 1 1 1 1 1 1 1 1 1 1 1 <6 8149= Fdpsr gh Glixvær qd pdwul} fdofxodgr sdud @ 4=3= 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 <6 814:= Yduldêær gr whpsr gh glvvroxêær frpsohwd frp r ydoru gh 1 D fxuyd srqwlokdgd ì d dsur{lpdêær gd Lqwhuidfh Hvwdflrqäuld1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 <7 914= Yduldêær gh J sdud d irupdêær gr hpeulær frp r udlr1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 << 915= Yduldêær gd Frqfhqwudêær Lqwhuidfldo frp r whpsr fdofxodgr sdud xp qýfohr uS@ 4qp=

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 433 916= Frpsdudêær hqwuh FU+U+W,, h FU= 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1433

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918= Yduldêær gd Yhorflgdgh Qrupdol}dgd shor whpsr1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 434 919= Udlr gd sduwðfxod yhuvxv d udl} txdgudgd gr whpsr1 uS@ 4qp= 1 1 1 1 1 1 1 1 1 1 1 1 1 435

91:= Frqfhqwudêær yhuvxv glvwåqfld fdofxodgd sdud yäulrv whpsrv1 uS@ 4qp= 1 1 1 1 1 1 1 1 435

D4= Hohphqwr gh Yroxph1 1 1 1 1 1 1 1 1 1 1 1 1 1 = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 43< F4= D uhjud gr Wudsì}lr1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 446

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5

Lqghshqghqwh gr ghwdokh/ wrgrv rv glvsrvlwlyrv öswlfrv edvhldp0vh rx qd yduldêær gr frhflhqwh gh devruêær / h2rx qd yduldêær gr ðqglfh gh uhiudêærq gh dojxp pdwhuldo1 R pdwhuldo lghdo sdud d ideulfdêær gh xp glvsrvlwlyr irw÷qlfr whp h2rx q pxlwr judqghv h xp whpsr gh uhvsrvwd pxlwr uäslgr1 Qrv glvsrvlwlyrv wrwdophqwh öswlfrv d fdxvd gdv yduldêøhv  h q ì xp sxovr gh ox}/ qrv hohwuröswlfrv xp vlqdo hoìwulfr/ hwf1

Xp h{hpsor gh xp glvsrvlwlyr wrwdophqwh öswlfr ì r glvsrvlwlyr gh jxldv gh rqgd dfrsodgrv prvwudgr qd Iljxud 4=4 dedl{r1 Qhvvh glvsrvlwlyr xp sxovr gh ox} srgh frqwurodu vh r vlqdo vdl shod sruwd 6 rx 71 Hoh ì frqvwuxðgr gh irupd txh r vlqdo txh hqwud qd sruwd 4/ qd dxvíqfld gr sxovr gh frqwuroh/ vdl shod sruwd 7/ h qd suhvhqêd gr sxovr gh frqwuroh hoh vdl shod sruwd 61

Iljxud 414= H{hpsor gh Glvsrvlwlyr1

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6 vhsdudêær1 Txdqgr r sxovr gh frqwuroh pxgd r ðqglfh gh uhiudêær gr fdqdo hvvh dfrsodphqwr ghl{d gh dfrqwhfhu pdqwhqgr d ox} qr fdqdo41

Iljxud 415= +d, Prgr Vlpìwulfr= d prod qær ì frpsulplgd rx hvwhqglgd> +e, Prgr Dqwlvlpìwulfr= d prod ì hvwhqglgd h ghsrlv frpsulplgd1

Iljxud 416= Vxshusrvlêær grv prgrv vlpìwulfr h dqwlvlpìwulfr txh uhvxowd hp ox} vö qr fdqdo 41

7

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43 d 433 È1 Frp glphqvøhv ghvvd rughp hohv dsuhvhqwdp hihlwrv gh frqqdphqwr txåqwlfr qdv 6 glphqvøhv1 Qhvvhv pdwhuldlv/ r frqqdphqwr wdqwr gh hoìwurqv txdqwr gh exudfrv wruqd r whpsr gh uhfrpelqdêær fxuwr/ srlv hohv qær srghp vh didvwdu xp gr rxwur1

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sdud vh rewhu r hihlwr gh frqqdphqwr fruuhwr ì wdpeìp qhfhvväulr vh frqwurodu d glvshuvær gh wdpdqkrv grv srqwrv txåqwlfrv1 Xpd irupd lqwxlwlyd gh shufhehu lvwr ì qrwdqgr txh r frqqdphqwr txåqwlfr frqfhqwud d olqkd gh devruêær hp xpd idl{d hvwuhlwd gh frpsulphqwrv gh rqgd1 Dr lqwhudjlu frp d ox}/ hvvd devruêær srgh pxgdu sru ydoruhv pxlwr judqghv ohydqgr wdpeìp d xpd judqgh yduldêær grv ðqglfhv gh uhiudêær1 Txdqgr frpsdudprv  h q gr Exon h grv srqwrv txåqwlfrv*v yhprv txh d gr ýowlpr ì pdlv dowd/ wrgd frqfhqwudgd qxpd olqkd gh devruêær1 Txdqwr phqru iru d glvshuvær gh wdpdqkrv pdlru vhuä d lqwhqvlgdgh gr slfr gh devruêær/ h gd qær olqhdulgdgh +yhmd d Iljxud 4=8,1

R juxsr gd Xqlfdps ghvhqyroyhx wudedokr slrqhlur qd ideulfdêær gh ylgurv grsdgrv frp srqwrv txåqwlfrv gh FgW h ^43` h S eWh ^44`/ dsrqwdqgr sdud r idwr gh txh r udlr gh Erku gr FgW h ì ehp pdlru gr txh r gr FgVh1 Ghvgh hvvd ìsrfd yhp ghvhqyroyhqgr wudedokrv

9

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Iljxud 418= Juäfr gd devruêær sdud gxdv glvwulexlêøhv gh wdpdqkr1

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Qr Fdsðwxor 7 glvfxwlprv d wìfqlfd gh gxsorv srwhqfldlv gh Juhhq sdud r sureohpd gd glixvær frp d iurqwhlud hp prylphqwr1

Qr Fdsðwxor 8 xwlol}dprv hvvd wìfqlfd sdud dfkdu d vroxêær qxpìulfd gr sureohpd gh glixvær frp d iurqwhlud hp prylphqwr sdud xp sodqr/ fdvr gh xpd glphqvær/ h xpd hvihud/ frp d frqfhqwudêær qd vxshuiðflh frqvwdqwh1

Qr Fdsðwxor 9 prvwudprv d vroxêær ghvwh sureohpd txdqgr d iurqwhlud hp prylphqwr iru xpd hvihud qxpd pdwul} lqqlwd pdv frp d frqfhqwudêær gd lqwhuidfh ghshqghqgr gr udlr

Fdsðwxor 5

D Flqìwlfd gr Fuhvflphqwr

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514 Ghvfulêær gd Ideulfdêær grv Ylgurv Grsdgrv frp Srqwrv

Txåqwlfrv

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43

frqvwlwxlqwhv gd pdwul} yðwuhd1 D frpsrvlêær gr ylgur krvshghlur ì frpsrvwd qd pdlruld sru erurvlolfdwrv/ wruqdqgr d whpshudwxud gh ixvær gr pdwhuldo uhodwlydphqwh dowd +dflpd gh 4533J_F,1

D dowd whpshudwxud uhtxhulgd sdud d ixvær gd pdwul} yðwuhd frpsolfd d rewhqêær gh ylgurv grsdgrv ghylgr ã yrodwlol}dêær h d idflolgdgh frp txh rv hohphqwrv grsdqwhv vh r{lgdp hp glihuhqwhv hvwdgrv qhvvdv whpshudwxudv1 Hqwuhwdqwr/ dwudyìv gh surfhvvrv wìuplfrv ehp hod0 erudgrv/ d idvh fulvwdolqd vhplfrqgxwrud srgh vhu ghvhqyroylgd qd pdwul} yðwuhd1 Hvwd idvh jhudophqwh fruuhvsrqgh d fhufd gh 4( d 5( gr yroxph wrwdo gr ylgur/ id}hqgr frp txh dv sursulhgdghv pdfurvföslfdv ghvvh ylgur/ frpr d ghqvlgdgh/ h{sdqvær wìuplfd h frqgxwlylgdgh hoìwulfd/ hwf/ hvwhmdp dvvrfldgdv vrphqwh ã pdwul} krvshghlud1 Sru rxwur odgr/ frpr r ylgur erurvlolfdwr ì wudqvsduhqwh qxpd idl{d txh ydl ghvgh r xowudylrohwd dwì r lqiudyhuphokr suö{lpr/ dv sursulhgdghv öswlfdv olqhduhv h qær olqhduhv vhuær hvwdehohflgdv vrphqwh shod suhvhqêd grv fulvwdlv vhplfrqgxwruhv qd pdwul} yðwuhd1 D rswlpl}dêær gdv frqglêøhv h{shulphqwdlv sdud r surfhvvr gh ixvær ã sduwlu gh sduåphwurv frpr d frpsrvlêær gd pdwul} yðwuhd/ whpshudwxud h whpsr gh ixvær/ d dwprvihud qd txdo r surfhvvr vh uhdol}d/ hwf/ shuplwh frqwurodu d rewhqêær gh xp ylgur hp txh rv suhfxuvruhv grsdqwhv vh hqfrqwuhp qxp hvwdgr gh uhgxêær txh idyruhêd r ghvhqyroylphqwr gdv hvwuxwxudv fulvwdolqdv vhplfrqgxwrudv gxudqwh r surfhvvr gh wudwdphqwr wìuplfr1

D Iljxud 5=4 ^4;` ghvfuhyh gh pdqhlud hvtxhpäwlfd rv surfhvvrv hqyroylgrv gxudqwh d suhsdudêær grv ylgurv grsdgrv1 Frpsrvwrv qd irupd gh sö vær dghtxdgdphqwh shvdgrv vhjxlqgr xpd ghwhuplqdgd hvwhtxlrphwuld/ plvwxudgrv h krprjhlql}dgrv/ h ohydgrv sdud r surfhvvr gh ixvær rqgh irupduær r ylgur h rv frpsrvwrv gr vhplfrqgxwru glvvroylgrv qd pdwul} yðwuhd qd irupd gh ðrqv hp ghwhuplqdgrv hvwdgrv gh r{lgdêær1 Sdud hylwdu d suhflslwdêær ghvwhv ðrqv h r fuhvflphqwr gdv qdqrhvwuxwxudv ì qhfhvväulr id}hu xp uhviuldphqwr uäslgr gd dowd whp0 shudwxud gh ixvær ã whpshudwxud dpelhqwh/ surfhvvr txh ì ghqrplqdgr gh txhqfklqj1 Lvwr ì ihlwr srutxh/ ghshqghqgr gdv txdqwlgdghv gh grsdqwhv h gd whpshudwxud gh ixvær dwlqjlgd r uhviuldphqwr ohqwr idyruhfhuä d uäslgd qxfohdêær grv fulvwdlv h vhuld lpsrvvðyho frqwurodu r fuhvflphqwr1 Ghsrlv ghvwd hwdsd/ r ylgur ghyh vhu vxephwlgr dr surfhvvr gh uhfr}lphqwr ã whpshudwxudv pdlv edl{dv sdud d glplqxlêær gdv whqvøhv lqwhuqdv1 D vhjxlu/ r ylgur mä grsdgr ì vxephwlgr d surfhvvrv gh wudwdphqwr wìuplfr hp ghwhuplqdgdv whpshudwxudv h whpsrv sdud

44 r frqwuroh gr wdpdqkr h gd glvwulexlêær gh wdpdqkrv gdv qdqrhvwuxwxudv1 R fuhvflphqwr grv srqwrv txåqwlfrv qhvvd hwdsd ì frqwurodgr dshqdv hp ixqêær gd whpshudwxud h grv whpsrv gh wudwdphqwr1

Iljxud 514= Gldjudpd hvtxhpäwlfr gr surfhvvr gh suhsdudêær grv ylgurv grsdgrv frp qdqrhvwuxwxudv gh FgWh h FgWh%V3% 1

45

515 D Whruld Foävvlfd gd Qxfohdêær

Xpd uhjlær krprjíqhd gh xp vlvwhpd gh pxlwdv proìfxodv ì fkdpdgd gh idvh1 Txdqgr gxdv idvhv frh{lvwhp hp uhjløhv krprjíqhdv glvwlqwdv vlfdphqwh rfruuh xpd wudqvlêær gh idvh1 Dv proìfxodv qxpd idvh sduwlfxodu hvwær duudqmdgdv qxp sdguær fdudfwhuðvwlfr1 Hvwh sdguær srgh vhu frpsohwdphqwh ghvrujdql}dgr frpr xp xlgr rx idvhv gh xp ylgur/ rx srgh vhu xp duudqmr uhshwlwlyr gh xpd xqlgdgh frqvlvwlqgr gh xp qýphur shtxhqr gh äwrprv qxpd uhodêær hvsdfldo ghqlgd frpr xp vöolgr fulvwdolqr1

D whruld gh pxgdqêdv gh idvhv h{solfd d hvwdelolgdgh uhodwlyd gh glihuhqwhv idvhv qd phvpd vxevwåqfld h r phfdqlvpr gh irupdêær gh xpd idvh ghqwur gd rxwud1 Sulphlur iduhprv xpd uhylvær gd whuprglqåplfd foävvlfd sdud d hvwdelolgdgh gdv idvhv/ ghvhqyroylgd sru Jleev h/ d vhjxlu/ vreuh d qxfohdêær1 Doìp gr sdsho gh uhylvær txh wruqh r wh{wr frpsuhhqvðyho sdud xp ohlwru qær hvshfldol}dgr/ hvvd uhylvær vhuyh sdud ghqlu r yrfdexoäulr txh xwlol}duhprv dr orqjr ghvvd whvh1

51514 Uhylvær Jhudo

Dv frqglêøhv sdud r htxloðeulr gh idvh hvwær pdlv frqyhqlhqwhphqwh ghvfulwdv frp r xvr gd ixqêær gd hqhujld olyuh gh Jleev J ^4<`1 Dv judqgh}dv txh xwlol}duhprv vær ghqlgdv frpr vhjxh= X @ hqhujld lqwhuqd gr vlvwhpd> V @ hqwursld gr vlvwhpd> S @ suhvvær klgurvwäwlfd> W @ whpshudwxud devroxwd> Y @ yroxph gr vlvwhpd> q @ qýphur gh prohv gd l0ìvlpd frpsrqhqwh txðplfd qr vlvwhpd1

46 jld ghylgr ãv lqwhuidfhv ì qhjoljhqfldgd1 Vhjxh gd sulphlud ohl gd whuprglqåplfd txh d pxgdqêd gd hqhujld lqwhuqd/ gX/ dr uhgru gh txdotxhu ghvorfdphqwr uhyhuvðyho lqqlwhvlpdo gr vlvwhpd ì

gX @ WgV  S gY .[  gq> +514, rqgh r srwhqfldo txðplfr/  gr l0ìvlpr frpsrqhqwh ì ghqlgr sru _@  CX Cq  7cTc?c?2cc?3c?nc = +515,

D hqhujld olyuh gh Jleev J h d hqwdosld K vær ghqlgdv frpr=

J @ K  WV +516, K @ X . SY +517, gdv Htv1+5=4,/ +5=6, h +5=7, ghgx}lprv txh gJ @ Y gS  VgW .[  gq= +518,

D Ht1+5=8, prvwud txh d hqhujld olyuh gh Jleev vhuä xp pðqlpr +gJ @ 3, txdqgr d suhvvær/ whpshudwxud h frpsrvlêær iruhp frqvwdqwhv +gS @ gW @ gq @ 3,/ xpd vlwxdêær pxlwr frpxp

hp wudqvlêøhv gh idvh1 Dv vhjxlqwhv uhodêøhv vær ghulydgdv gd Ht1+5=8,=

 CJ CS  Ac? @ Y  CJ CW  c? @ V +519,  CJ Cq  cA @ =

Sdud r qrvvr fdvr txh ì xp vlvwhpd gh xpd frpsrqhqwh/ rv whuprv hqyroyhqgr r srwhq0 fldo txðplfr vdhp gdv Htv1+5=4, h +5=8, / h r hvwdgr gr vlvwhpd ì ghwhuplqdgr shod suhvvær h whpshudwxud1

47

51515 D Whruld Jhudo gd Qxfohdêær Krprjíqhd

Qxfohdêær ì d irupdêær gh xpd qryd idvh ghqwur gh xpd idvh mä h{lvwhqwh h vhsdudgd ghvwd sru xpd vxshuiðflh ehp ghqlgd1 Pxlwrv pdwhuldlv frqwìp yäuldv idvhv h/ hp dojxqv fdvrv/ xpd rx pdlv ghvvdv idvhv ì irupdgd sru qxfohdêær wrwdophqwh qr hvwdgr vöolgr/ ghqwur gh xpd fkdpdgd vroxêær vöolgd vxshuvdwxudgd1 R qrvvr h{hpsor gh vroxêær vöolgd vær rv srqwrv txåqwlfrv qxpd pdwul} yðwuhd1 Qhvvd vroxêær vöolgd rv hohphqwrv suhfxuvruhv glvshuvrv qd pdwul} yðwuhd txh srghp vh prylphqwdu sru glixvær vær frqvlghudgrv rv vroxwrv/ d pdwul} r vroyhqwh/ h rv srqwrv txåqwlfrv d idvh vöolgd/ rx r suhflslwdgr1 Rv sulphlurv hvwxgrv ghvvh wlsr gh wudqvirupdêøhv gh idvh vöolgd irudp ihlwrv hp phwdlv ^53`/ ^54`/ ^55` h ^56` / pdv hvwhv phvprv ihq÷phqrv rfruuhp hp vhplfrqgxwruhv1 Sdud txh d suhflslwdêær rfruud d vroxêær ghyh hvwdu vxshuvdwxudgd/ rx vhmd/ d frqfhqwudêær gr vroxwr ghyh h{fhghu r ydoru gh vdwxudêær hp xpd gdgd whpshudwxud h suhvvær1 Qd vdwxudêær h{lvwh xp htxloðeulr hqwuh dv wd{dv gh wudqvirupdêær gdv proìfxodv gh xpd idvh sdud d rxwud/ hp rxwudv sdodyudv/ d wd{d gh äwrprv glvshuvrv hqwudqgr qd pdwul} yðwuhd sdud d idvh vöolgd ì ljxdo ã wd{d gh äwrprv txh dedqgrqdp d idvh vöolgd sdud vh glvshuvduhp qd pdwul} yðwuhd1 Xpd vroxêær vxshuvdwxudgd hvwä whuprglqdplfdphqwh qxp hvwdgr gh qær htxloðeulr1

Gr srqwr gh ylvwd whuprglqåplfr h{lvwh xpd whpshudwxud/ d whpshudwxud gh ixvær Ws / qd

txdo xp oðtxlgr sxur frh{lvwh frp xp vöolgr hp htxloðeulr1 Dqdolvdqgr d Iljxud 5=5 yhprv txh d idvh txh ghyhuld suhgrplqdu vhuld vhpsuh d gh phqru hqhujld olyuh gh Jleev/ J1 Hqwuhwdqwr/ ì srvvðyho sdvvdu ohqwdphqwh shod whpshudwxud gd wudqvlêær gh idvh vhp pxgdu gh idvh/ ghylgr d xpd phpöuld gd idvh dqwhulru1 Reyldphqwh txh fdgd xpd gdv idvhv uhsuhvhqwd xp pðqlpr orfdo sdud d ixqêær gh Jleev J h txh ghyh kdyhu xpd eduuhlud sdud vdlu gh xp pðqlpr sdud r rxwur pðqlpr gh phqru ydoru1 Shuwxuedêøhv idflolwdp d wudqvlêær gh idvh dr suryhu d hqhujld qhfhvväuld sdud urpshu hvvd eduuhlud1 Qd dxvíqfld ghvvdv shuwxuedêøhv ì srvvðyho vh dwlqjlu xp dowr judx gh vxshuvdwxudêær1 Qhvvd vlwxdêær r vlvwhpd hvwä h{srvwr dr ihq÷phqr gd qxfohdêær/ rqgh d qryd idvh vh ghvhqyroyh ghqwur gd dqwljd1

48

Iljxud 515= Ghshqgíqfld gh J hp W sdud d yl}lqkdqêd gd wudqvlêær gh idvh1

D wd{d gh qxfohdêær ghshqgh iruwhphqwh gr vxshuuhviuldphqwr/ txh ì r txdqwr d whpshudwxud gr pdwhuldo vh hqfrqwud qr hvwdgr oðtxlgr dedl{r gh vxd whpshudwxud gh ixvær1 Qrwh0vh txh qr fdvr grv srqwrv txåqwlfrv d vroxêær hvwdyd hp htxloðeulr qd whpshudwxud gh ixvær/ dflpd gh 4333J_{F/ qd txdo suhgrplqd d idvh oðtxlgd1 Dr surfhghu dr txhqfklqj d idvh vöolgd whuld d hqhujld}

olyuh gh Jleev pdlv edl{d/ hqwuhwdqwr rv äwrprv glvshuvrv qd pdwul} yðwuhd shughudp wrwdophqwh d prelolgdgh gh prylphqwr/ frpr vh hvwlyhvvhp vlgr frqjhodgrv qd vxd srvlêær1 Qd whpshudwxud dpelhqwh/ frp edl{ðvvlpr frhflhqwh gh glixvær d wudqvlêær gh idvh ld uhtxhuhu whpsrv pxlwr judqghv sdud dfrqwhfhu1 Dr hohydu d whpshudwxud dxphqwd0vh d glixvlylgdgh grv hohphqwrv h r surfhvvr srgh dfrqwhfhu qxpd hvfdod gh whpsr frqwurodgd1 R remhwlyr gd whruld gd qxfohdêær ì fdofxodu r ydoru gd eduuhlud sdud d wudqvlêær h d iuhtÿíqfld gd qxfohdêær1 Rv frqfhlwrv eävlfrv lpsoðflwrv qd whruld vær phokru h{solfdgrv frqvlghudqgr d qxfohdêær krprjíqhd/ d txdo ì ghqlgd frpr d qxfohdêær qr lqwhulru gh xpd idvh hvwuxwxudophqwh sxud1

Vxsrqkd txh qxp ghwhuplqdgr yroxph +pdwul}, rfruuh d frh{lvwíqfld gh äwrprv glvshuvrv frp äwrprv irupdqgr sduwðfxodv frpr qd Iljxud 5=61 Vhmd j_ d hqhujld olyuh sru äwrpr grv

äwrprv glvshuvrv / jS d hqhujld olyuh sru äwrpr gr fulvwdo /  d whqvær vxshufldo h yS r yroxph

49

Iljxud 516= Hvtxhpd gh xpd pdwul}1

D wudqvirupdêær gh xp oðtxlgr vxshuuhviuldgr sdud xpd idvh suhflslwdgd ghshqghuä hvvhq0 fldophqwh gh gxdv frqwulexlêøhv= d sulphlud ì suryhqlhqwh gd glihuhqêd qd hqhujld olyuh hqwuh dv gxdv idvhv/ j sru xqlgdgh gh yroxph/ h d vhjxqgd gd hqhujld lqwhuidfldo/ jr sru xqlgdgh

gh äuhd/ ljxdo d hqhujld pdfurvföslfd 1 Sdud sduwðfxodv hviìulfdv gh udlr u/ txh olehudp xpd txdqwlgdgh gh hqhujld ljxdo d e

uj h xp ghvshqglr gh hqhujld sdud fuldu d lqwhuidfh ljxdo

d 7u2_{jr/ J ì gdgr sru=}

J @ 7₆uj. 7u2jr

rqgh/ j @ E}S3}_S_1 Sdud txh dfrqwhêd r surfhvvr gh qxfohdêær d vroxêær ghyh vhu vxshuvdwx0

udgd/ hqwær jSghyh vhu phqru txh j_1 Dvvlp/ r sulphlur grv grlv whuprv ì qhjdwlyr/ h r vhjxqgr

ì srvlwlyr1 D pxgdqêd qd hqhujld olyuh gr vlvwhpd sdud d irupdêær gh xpd sduwðfxod ì h{suhvvd frpr

J @ 7₆u+j__y jS,

S . 7u

2_{= +51:,}

Mä txh hvwhv whuprv vær sursruflrqdlv d u _{h u}2 _{uhvshfwlydphqwh/ vhjxh txh d lq xíqfld gr}

vhjxqgr whupr fduä phqru txdqgr u dxphqwdu1 D fxuyd gh J sru u dxphqwduä dwì xp pä{lpr h hqwær ghfuhvfhuä1 D Iljxud 5=7 prvwud r juäfr grv grlv whuprv gd Ht1+5=:, h vxd vrpd1

4:

Iljxud 517= Frpsdudêær hqwuh rv whuprv gd Hqhujld1

D srvlêær gr pä{lpr ì gdgr sru g +J, @gu @ 3/ txh qrv gä r udlr fuðwlfr/ uS sdud d

sduwðfxod hviìulfd1 g +J, gu   o'oS @ 3 uS @ _+j5yS _ jS, @ 5yS j > +51;,

rqgh j @ j_ jS1 Xpd sduwðfxod frp xp udlr ljxdo d uShvwä hp htxloðeulr lqvwäyho1 Vh wlyhu

r udlr phqru txh r uS hod whqgh d uhglvvroyhu mä txh xp dxphqwr qr udlr ohyd d xp dxphqwr

gh J1 Hqtxdqwr txh/ vh wlyhu r udlr pdlru txh r uS hod whqgh d fuhvfhu mä txh xp dxphqwr

qr udlr ohyd d xp ghfuìvflpr gh J1 Dv sduwðfxodv frp u ? uS vær fkdpdgdv gh hpeuløhv

h dv frp u A uS vær fkdpdgdv gh qýfohrv +yhu Iljxud 5=8,1 Srghprv gl}hu txh d vroxêær ì

lqvdwxudgd sdud rv hpeuløhv h vxshuvdwxudgd sdud rv qýfohrv1

Sdud wruqdu0vh xp qýfohr/ xpd sduwðfxod ghyh dgtxlulu +fuhvfhqgr sdud r udlr fuðwlfr, xpd yduldêær gh hqhujld olyuh fuðwlfd JS/ fxmr ydoru ì=

JS@ 49 _y2

S

4;

JS ì r txh fkdpdprv gh eduuhlud whuprglqåplfd1

Iljxud 518= Ghqlêær gh qýfohr h hpeulær1

R udlr fuðwlfr h d eduuhlud hvwduldp frpsohwdphqwh ghqlgrv sru hvvdv h{suhvvøhv vh rv ydoruhv gh j irvvhp frqvwdqwhv1 Hqwuhwdqwr/ d yduldêær gd hqhujld olyuh grv äwrprv glvshuvrv qd pdwul} ghshqgh gd frqfhqwudêær/ sru fdxvd gd hqwursld gr duudqmr hqwuh hvwdu glvshuvr qd pdwul} rx qr vöolgr/ h j ì gdgd sru

j @ nW oq  Q+U, Q+4,  > +5143,

rqgh/ Q+U, ì d frqfhqwudêær qd vxshuiðflh gh xp srqwr txåqwlfr frp udlr U/ Q+4, ì d frqfhqwudêær gh htxloðeulr gh xp srqwr txåqwlfr gh udlr lqqlwr/ n ì d frqvwdqwh gh Erow}pdqq h W d whpshudwxud1 Vxevwlwxlqgr qd Ht1+5=;,/ whprv txh uS@ 5yS nW oq_E"E-> id}hqgr uS U rewhprv txh Q+U, @ Q+4, h{s  5yS nWU  = +5144,

4< xpd sduwðfxod frp udlr U/ h prvwud txh/ txdqwr phqru iru d sduwðfxod/ pdlru d frqfhqwudêær gh htxloðeulr qd vxd vxshuiðflh1 Hp rxwudv sdodyudv/ qr htxloðeulr orfdo d sduwðfxod qær ghyh fuhvfhu qhp glplqxlu/ orjr d wd{d gh äwrprv vhqgr devruylgd shor srqwr txåqwlfr ghyh vhu ljxdo d wd{d gh äwrprv vhqgr hplwlgd grv srqwrv txåqwlfrv Qe^+U, @ Qe^+4, h{s  5yS nW U  = +5145,

rqgh/ Qe^+U, ì d frqfhqwudêær hp htxloðeulr sdud xpd sduwðfxod gh udlr U/ Qe^+4, ì d frqfhq0

wudêær hp htxloðeulr gh xp srqwr txåqwlfr frp udlr lqqlwr +U $ 4,1 Qrwh0vh wdpeìp txh qr fdvr Q+U, @ Q6@|o5 d frqfhqwudêær gh htxloðeulr qd vxshuiðflh ì ljxdo d frqfhqwudêær qd

pdwul} frpr xp wrgr/ h qær kdyhuä judglhqwh gh frqfhqwudêær txh fdxvh xpd glixvær1 Qhvvh fdvr d txdqwlgdgh gd vxevwåqfld hqwudqgr sru xqlgdgh gh whpsr ì ljxdo d txh vdl/ rx vhmd/ $_M

?@$MJ|1 Mä vh d frqfhqwudêær gh htxloðeulr qd vxshuiðflh iru phqru gr txh d frqfhqwudêær

qd pdwul} d glixvær whqghuä d dolphqwdu d vxshuiðflh frp qryrv äwrprv shuplwlqgr txh r srqwr txåqwlfr fuhvêd1 Qr fdvr lqyhuvr d glixvær ì qd gluhêær gh uhwludu rv äwrprv gd vxshuiðflh gr srqwr txåqwlfr id}hqgr frp txh hvwh whqgd d vh uhglvroyhu1 Xpd fxuyd wðslfd uhsuhvhqwdqgr hvvhv fdvrv hvwä prvwudgd qd Iljxud 5=91

Iljxud 519= Fxuyd wðslfd gh Q+U,1

Qrwh txh r srqwr rqgh d fxuyd Qe^+U, fruwd d uhwd gd frqfhqwudêær Q6 h{lvwhqwh qd pdwul}

53

fulvwdo fuhvfh> vh U @ uShqwær$M?@$MJ|r fulvwdo qhp fuhvfh h qhp uhglvvroyh> h vh U ? uSrx

$_M

?A$MJ| r fulvwdo uhglvvroyh1 Vh Q6 fdu dedl{r gh Qe^+4, qær ì srvvðyho fuhvfhu qhqkxp

fulvwdo1 R judx gh vxshuvdwxudêær  ì ghqlgr frpr=  @ Q6

Qe^+4,>

h d vroxêær hvwduä vxshuvdwxudgd vh  A 41

Ì lqwhuhvvdqwh revhuydu r txh rfruuh txdqgr d whpshudwxud pxgd1 Sdud lvwr suhflvdprv vdehu frpr Qe^+4, h  ghshqghp gh W1 Qe^+4, @ Qfh{s  H_nW@  @ Qfh3A@*A h  @ f. eW>

rqgh H@ ì d hqhujld gh dwlydêær sdud d frqfhqwudêær hp htxloðeulr/ W@ ì d whpshudwxud gd

hqhujld gh dwlydêær txh ì ljxdo d H@@N1 Vxevwlwxlqgr qd Ht1+5=45, whprv txh

Qe^+U, @ Qfh3A@A h2SEjfnKA&A - = +5146,

Qd Iljxud 5=: whprv dojxpdv fxuydv gh Q gd htxdêær dflpd sdud glihuhqwhv whpshudwxudv1 Srghprv yhu txh wrgrv rv qdqrfulvwdlv frp US2 A U A US txh hvwdydp fuhvfhqgr qd whpsh0

udwxud Wsdvvdp d uhglvvroyhu vh/ gh uhshqwh/ vh hohyd d whpshudwxud sdud W21 Vh d whpshudwxud

ì uhshqwlqdphqwh pxgdgd sdud W wrgrv rv qdqrfulvwdlv uhglvvroyhuær/ srlv qhvvh fdvr qær kä

vxshuvdwxudêær/  ? 41 Doìp glvvr/ d wd{d gh glvvroxêær ghshqgh gd glihuhqêd gh frqfhqwudêær hqwuh d vxshuiðflh gr srqwr txåqwlfr h gd pdwul} vljqlfdqgr txh rv fulvwdlv phqruhv yær uh0 glvvroyhu pxlwr pdlv uäslgr gr txh rv pdlruhv1 Lvwr vljqlfd txh sdud fdgd whpshudwxud kä xpd glvwulexlêær gh hpeuløhv h xp wdpdqkr pä{lpr txh srgh h{lvwlu1

54

Iljxud 51:= Fxuydv gh Q+U, sdud glihuhqwhv W1

D whruld foävvlfd gd iuhtxíqfld gh qxfohdêær frqvlghud d iuhtxíqfld gh irupdêær gh qýfohrv frpr vhjxh1 Xp hpeulær txh frqwìp l äwrprv whp xpd suredelolgdgh sn _{gh fdswxudu xp}

äwrpr h frqyhuwhu0vh hp xp hpeulær frpsrvwr sru l . 4 äwrprv/ h xpd suredelolgdgh s3 _gh

shughu/ rx hplwlu/ xp äwrpr h frqyhuwhu0vh hp xp hpeulær gh l  4 äwrprv1 D suredelolgdgh sn _{gh devruêær gh xp äwrpr ghshqgh gd frqfhqwudêær qd vxshuiðflh gr srqwr txåqwlfr Q+U,}

hqtxdqwr txh d suredelolgdgh gh hplvvær s3 _{qær ghshqgh gd frqfhqwudêær h{whuqd dr srqwr}

txåqwlfr/ pdv ghshqgh gr udlr gr phvpr/ qd irupd gd suredelolgdgh gh hplvvær whuprl÷qlfd h-/ rqgh D ì xpd frqvwdqwh1 Qr htxloðeulr whprv txh sn @ s3uhhvwdehohfhqgr dvvlp d htxdêær

+5=45,1 Vxsrqgr txh fdgd qýfohr fuðwlfr fuhvfh sdud frqvwlwxlu xp srqwr txåqwlfr/ h ì sruwdqwr uhprylgr gd glvwulexlêær/ d iuhtxíqfld gh irupdêær gh qýfohrv vhuä gdgd shod iuhtxíqfld frp txh hpeuløhv vxefuðwlfrv dofdqêdp r wdpdqkr fuðwlfr1

55

Sru rxwur odgr/ sdud xp äwrpr vdlu gd idvh oðtxlgd h vh lqfrusrudu dr qýfohr/ r phvpr whp txh yhqfhu xpd eduuhlud frp hqhujld olyuh gh dwlydêær J@1 R qýphur gh yh}hv sru vhjxqgr

txh r äwrpr whqwd dwudyhvvdu hvwd eduuhlud qd lqwhuidfh ì gdgr sru f @ &A_ / h d suredelolgdgh

gh txh xpd whqwdwlyd whqkd vxfhvvr ì ljxdo d H{s^{C@

&A `1 Vrphqwh rv äwrprv txh vh hqfrqwudp

qd yl}lqkdqêd gd lqwhuidfh frqvhjxhp dwudyhvvdu hvwd eduuhlud1 Hvwd iuhtxíqfld gh qxfohdêær ghshqgh sruwdqwr gd frqfhqwudêær gh äwrprv qdv yl}lqkdqêdv gd vxshuiðflh gr srqwr txåqwlfr1 Qrwh0vh txh hvvd frqfhqwudêær qd pdwul} Q6 xwxd hvshfldophqwh qd pdwul} h ghshqgh gd

whpshudwxud1 Sdud edl{dv whpshudwxudv hvvd xwxdêær ì shtxhqd/ pdv r udlr fuðwlfr wdpeìp ì shtxhqr/ hqtxdqwr sdud whpshudwxudv pdlruhv d xwxdêær dxphqwd/ pdv r udlr fuðwlfr wdpeìp1 Vh d wd{d gh wurfd gh äwrprv qd vxshuiðflh gr srqwr txåqwlfr iru pxlwr pdlv uäslgd gr txh d wd{d gh dolphqwdêær gh äwrprv yld glixvær/ hqwær r htxloðeulr qd lqwhuidfh vhuä vhpsuh hvwdehohflgr1 Rx vhmd/ r srqwr txåqwlfr vh hvwdelol}duä/ devruyhqgr h hplwlqgr äwrprv/ hp xp udlr U wdo txh d frqfhqwudêær qd vxd vxshuiðflh vhmd lgíqwlfd d Qe^+U,1

Qrv ylgurv d glixvlylgdgh qdv whpshudwxudv xwlol}dgdv qr fuhvflphqwr grv srqwrv txåqwlfrv ì pxlwr shtxhqd/ lvvr id} frp txh r whpsr qhfhvväulr sdud d glixvær vhmd pxlwr pdlru txh r whpsr sdud dofdqêdu r htxloðeulr gh lqwhuidfh1 R fuhvflphqwr sru glixvær ì ghqlgr/ hqwær/ shor whpsr pdlv orqjr gh glixvær grv äwrprv qd pdwul}1 Wrgrv rv qryrv äwrprv txh fkhjduhp ã vxshuiðflh gh xp qýfohr vhuær devruylgrv frp xp frqvhtxhqwh fuhvflphqwr gr udlr gr phvpr1 Hqwær/ txhp ghqluä d flqìwlfd gr surfhvvr ì d glixvær/ jdudqwlqgr txh Q+U, vhuä vhpsuh r Qe^+U,1 \dq h Sdunhu ^57` prvwudp txh sdud ylgurv grsdgrv frp hohphqwrv suhfxuvruhv gr

vhplfrqgxwru LL  Y L/ d glixvær ì r surfhvvr suhgrplqdqwh qd glqåplfd gh fuhvflphqwr gdv qdqrhvwuxwudv vhplfrqgxwrudv qd pdwul} yðwuhd1

Hqtxdqwr rv fdpsrv gh glixvær hp yrowd gh qýfohrv yl}lqkrv qær vh vxshusøhp fdgd qýfohr vh frpsruwd lqghshqghqwhphqwh grv rxwurv1 Txdqgr d vxshusrvlêær vh lqlfld d pdwul} ghl{d gh dwxdu frpr xpd irqwh lqqlwd gh äwrprv glvshuvrv h d frqfhqwudêær Q6 frphêd d glplqxlu/

glplqxlqgr r judx gh vxshuvdwxudêær 1 Qhvvh hvwäjlr vh lqlfld xpd frpshwlêær shorv äwrprv glvshuvrv hqwuh rv glihuhqwhv srqwrv txåqwlfrv/ frp fodud ydqwdjhp sdud rv pdlruhv/ frp phqru frqfhqwudêær qd lqwhuidfh1 D phglgd txh Q6 fdl r US dxphqwd id}hqgr frp txh sduwðfxodv

txh hvwdydp fuhvfhqgr sdvvhp d uhglvvroyhu1 Qhvwd hwdsd gdu0vh0ä r lqðflr gr surfhvvr gh frdohvfíqfld +frduvhqlqj,/ rqgh sduwðfxodv gh udlrv pdlruhv vær lqvwäyhlv frp uhvshlwr dr judx

56 gh vxshuvdwxudêær h fuhvfhuær sru suhflslwdêær gr vroxwr gd pdwul}1 Dv sduwðfxodv gh udlrv phqruhv txh fdudp dedl{r gr qryr udlr fuðwlfr sdvvdp d uhglvvroyhu qd pdwul}/ glplqxlqgr gh wdpdqkr/ h dolphqwdqgr dv pdlruhv frp vhxv äwrprv1 D glvwulexlêær gh wdpdqkrv vh wruqd dvvlpìwulfd/ frp xpd fdxgd qr odgr gdv sduwðfxodv phqruhv h vh dodujd txdqgr frpsdudgd dr fuhvflphqwr vlpsohv1 Hp qrvvr wudedokr r remhwlyr ì rewhu d phqru glvwulexlêær gh wdpdqkrv/ hqwær edvwd dqdolvdu r surfhvvr gh fuhvflphqwr vlpsohv dqwhv txh hoh hqwuh qd frdohvfíqfld1

Fdsðwxor 6

D Htxdêær gd Glixvær

Glixvær ì r surfhvvr shor txdo d pdwìuld ì wudqvsruwdgd gh xpd sduwh gr vlvwhpd sdud rxwud frpr uhvxowdgr gr prylphqwr prohfxodu dohdwöulr1 D wudqvihuíqfld gh fdoru sru frqgxêær ì wdpeìp ghylgr dr prylphqwr dohdwöulr/ h h{lvwh xpd öeyld dqdorjld hqwuh rv grlv surfhvvrv1 Lvwr irl uhfrqkhflgr sru Ilfn txh sulphlur frorfrx d glixvær qxpd edvh txdqwlwdwlyd dgrwdqgr d htxdêær pdwhpäwlfd gd frqgxêær gh fdoru txh kdyld vlgr ghulydgd dojxqv dqrv dqwhv sru Irxulhu1 Fduvodz h Mdhjhu ^58` h Fudqn ^59` prvwudp yäulrv wlsrv gh vroxêøhv sdud d htxdêær gh fdoru h gd glixvær1

Vhmd  d ghqvlgdgh gh txdotxhu hqwlgdgh +srgh vhu xpd vxevwåqfld/ hqhujld/ hwf,/ qr fdvr gd hqwlgdgh vhu pdwìuld wdpeìp ì fkdpdgd gh frqfhqwudêær/ phglgd hp xqlgdgh gd _txdqwlgdgh gd hqwlgdgh%@fp_{/ rqgh hvvd _txdqwlgdgh% ì phglgd hp xpd xqlgdgh dsursuldgd ã vxevwåqfld/}

frpr/ sru h{hpsor/ qýphur gh äwrprv qxpd vroxêær1 Vhmd $M r x{r gd hqwlgdgh phglgr hp _txdqwlgdgh gd hqwlgdgh%@fp2_{ v/ txdqwlgdgh gd vxevwåqfld dwudyhvvdqgr sru xqlgdgh gh}

whpsr/ d xqlgdgh gh äuhd qrupdo ã gluhêær gr x{r1 Rv ihq÷phqrv gh glixvær rehghfhp ã ohl gh Ilfn=

$_{M @ G%/ +614,}

59

gr phlr> G ì phglgr hp fp2_{@v1 R vlqdo qhjdwlyr qd Ht1+6=4, vxujh srutxh d glixvær rfruuh qd}

gluhêær rsrvwd dr dxphqwr gd frqfhqwudêær1 Ghyh vhu hqidwl}dgr txh d Ht1+6=4, ì yäolgd dshqdv sdud phlrv lvrwuöslfrv1

Vxsrqkd/ doìp glvvr txh d vxevwåqfld glixqglgd qær ì qhp devruylgd qhp hplwlgd shor phlr1 Hqwær/ d htxdêær gd frqwlqxlgdgh +d ohl gd frqvhuydêær sdud hvwd vxevwåqfld,/

C

Cw . % $M @ 3 +615,

ghyh vhu yäolgd +yhu Dsíqglfh D,1 Frpelqdqgr dv gxdv htxdêøhv dflpd/ rewhprv C

Cw @ Gu2= +616,

Hvwh uhvxowdgr ì fkdpdgr gh htxdêær gh glixvær krprjíqhd1

Xpd prglfdêær lphgldwd ì srvvðyho vh d vxevwåqfld iru fdsd} gh vhu devruylgd +ghvwuxðgd, rx hplwlgd +fuldgd,1 Qhvwh fdvr/ d htxdêær gd frqwlqxlgdgh ì

C

Cw . % $M @ I  V +617,

rqgh I ì d txdqwlgdgh gh vxevwåqfld fuldgd h V ì d txdqwlgdgh gh vxevwåqfld ghvwuxðgd sru xqlgdgh gh whpsr qd xqlgdgh gh yroxph1 D h{suhvvær dflpd gä ruljhp ã htxdêær gh glixvær qær0krprjíqhd

C

Cw @ Gu2 . I  V= +618,

Vroxêøhv jhudlv gd htxdêær gh glixvær srghp vhu rewlgdv sdud xpd ydulhgdgh gh frqglêøhv lqlfldlv h frqwruqr txdqgr r frhflhqwh gh glixvær ì frqvwdqwh1 Wdo vroxêær whp jhudophqwh xpd rx gxdv irupdv sdguær1 Rx hod hvwä lqfoxðgd qxpd vìulh gd ixqêær Huur rx Lqwhjudo uhodflrqdgd/ h qhvwh fdvr hod ì pdlv ýwlo sdud fäofxorv qxpìulfrv sdud whpsrv shtxhqrv/ lvwr ì/ r hvwäjlr lqlfldo gd glixvær1 Rx hqwær hod hvwä qd irupd gh xpd vìulh wuljrqrpìwulfd txh frqyhujh pdlv vdwlvidwruldphqwh sdud judqghv ydoruhv gr whpsr1

5: fuhvflphqwr vlpsohv/ rx vhmd/ txdqgr r udlr gr srqwr txåqwlfr iru pdlru txh r udlr fuðwlfr dwì xp srxfr dqwhv gh dfrqwhfhu d vxshusrvlêær gdv frqfhqwudêøhv hp wruqr gh grlv srqwrv txåqwlfrv1 Qhvvh fdvr/ d qrvvd vroxêær hvwduä lqfoxðgd qd sulphlud irupd sdguær1 H{lvwhp grlv sureohpdv lpsruwdqwhv d vhuhp uhvroylgrv dtxl=

41 D lqwhuidfh +rx iurqwhlud, hqwuh r qýfohr h d pdwul}/ ã phglgd txh r srqwr txåqwlfr fuhvfh pxgd gh srvlêær1 Hvwh sureohpd ì jhudophqwh frqkhflgr frpr r Sureohpd gh Vwhidq rx Sureohpd gd Iurqwhlud hp Prylphqwr1 D sulqflsdo glfxogdgh ghvwh sureohpd ì txh d srvlêær gd iurqwhlud hp prylphqwr qær ì frqkhflgd d sulrul h ghshqgh gh yduläyhlv txh hvwær vhqgr uhvroylgdv1 Doìp glvvr/ h{lvwh xpd ghvfrqwlqxlgdgh qd ghulydgd gd iurqwhlud hp prylphqwr1

51 D frqfhqwudêær qd lqwhuidfh gr qýfohr ì ghshqghqwh gd udlr gr srqwr txåqwlfr h wdpeìp pxgd frp r whpsr1

Hvwdprv hp exvfd gh xpd vroxêær txh uhvroyd hvwdv gxdv frqglêøhv doìp gdv frqglêøhv lqlfldlv h gh frqwruqr1 Lvwr vljqlfd txh whprv txh uhvroyhu r fdvr gh fuhvflphqwr gh suhflslwdgrv hviìulfrv frp d iurqwhlud hp prylphqwr h frp d frqfhqwudêær gd lqwhuidfh hp ixqêdr gr udlr1 Frpr ylprv qr Fdsðwxor 5/ r srqwr txåqwlfr qr hvwäjlr gr fuhvflphqwr vlpsohv vh frpsruwd frpr vh hvwlyhvvh vr}lqkr qd pdwul} dwì r lqðflr gd frdohvfíqfld1 Frpr qær txhuhprv txh hoh hqwuh qd frdohvfíqfld edvwd uhvroyhu hvwh fdvr sdud xpd pdwul} lqqlwd1 Hqwær ydprv frphêdu uhvroyhqgr d htxdêær gd glixvær sdud r fdvr pdlv vlpsohv h judgdwlydphqwh dxphqwduhprv r judx gh glfxogdgh dwì r fdvr gh qrvvr lqwhuhvvh1

Qhvwh fdsðwxor yhuhprv d vroxêær rewlgd shor pìwrgr gd ixqêær gh Juhhq txdqgr d iurqwhlud ì {d/ txh ì r fdvr pdlv vlpsohv sdud r sureohpd gd glixvær1 Hvwh sureohpd ì txdqgr whprv glixvær wìuplfd/ txh qær ì r qrvvr fdvr1 Hqwær prvwuduhprv d vroxêær dqdoðwlfd sdud rv fdvrv gh fuhvflphqwr h glvvroxêær frp d iurqwhlud hp prylphqwr h frp d frqfhqwudêær gd lqwhuidfh frqvwdqwh qxpd pdwul} lqqlwd1 H ghsrlv prvwuduhprv dv vroxêøhv rewlgdv txdqgr xwlol}dprv dqäolvhv dsur{lpdgdv sdud rv fdvrv gh fuhvflphqwr h glvvroxêær frp d iurqwhlud hp prylphqwr h d frqfhqwudêær gd lqwhuidfh frqvwdqwh qxpd pdwul} qlwd1

5;

614 Vroxêær gd Htxdêær gh Glixvær frp d Iurqwhlud Il{d

Qhvvd vhêær frqvlghuduhprv d vroxêær gr sureohpd gd iurqwhlud {d hqyroyhqgr frqglêøhv gh frqwruqr gd htxdêær gh glixvær qær0krprjíqhd1 Lvwr ì/ r sureohpd hp txh d ixqêær qær frqkhflgd whuä d vxd vroxêær frpr xpd ixqêær gd srvlêær gd iurqwhlud qr grpðqlr hp txh d vroxêær ì ghqlgd1 D vroxêær gh wdo sureohpd ì frqvwuxðgd hp whuprv gd Ixqêær gh Juhhq ^5:`/ ^5;` h ^5<`1 D ydqwdjhp gd ixqêær gh Juhhq ì txh qöv srghprv hqfrqwudu d vroxêær sdud txdotxhu wlsr gh ixqêær qær0krphjíqhd dshqdv lqwhjudqgr0d vreuh d ixqêær uhvsrvwd gr vlvwhpd/ lvwr ì/ xpd ixqêær lpsxovr1 Pdv sdud uhvroyhuprv d htxdêær shor pìwrgr gh Juhhq frqyìp uhylvduprv dojxpdv ghqlêøhv txh vhuær xvdgdv qr ghfruuhu grv fäofxorv ghvwd vhêær frpr d ixqêær Ghowd gh Gludf1

61414 D Ixqêær Ghowd gh Gludf

D ixqêær  gh Gludf/ xpd uhsuhvhqwdêær pdwhpäwlfd gr srqwr/ ì ghqlgd dwudyìv gdv vhjxlqwhv sursulhgdghv qdv yl}lqkdqêdv gh xpd vlqjxodulgdgh hp { @ {f=

 +{  {f, @ 3 sdud { 9@ {f +619,

 +{  {f, $ 4 sdud { @ {f +61:,

gh wdo pdqhlud txh sdud txdotxhu  A 3/ ] _%fn"

%f3"

 +{  {f, g{ @ 4= +61;,

Lvwr ì/ d ixqêær  +{  {f, whp xp slfr pxlwr qr sdud { @ {f/ pdv d äuhd vreuh r slfr ì d

xqlgdgh1 Lvwr vhjxh txh/ gdgd txdotxhu ixqêær vxdyh i+{,/ whprv txh ] _

 i+{, +{  {f, g{ @ i+{f,

] _

5< mä txh  +{  {f, 9@ 3 dshqdv txdqgr { @ {f/ h dtxl i+{, @ i+{f,1 Sruwdqwr

] _  i+{, +{  {f, g{ @ ; ? = i+{f, > vh D ? {f ? E 3 > vh {f ? D rx {fA E= +61<, D sursulhgdgh +6=<, lpsolfd hp wrgdv dv fdudfwhuðvwlfdv gh +6=9> 6=:> h 6=;, h srgh vhu wrpdgd frpr d ghqlêær gd ixqêær +{  {f,1

61415 D Ixqêær gh Juhhq

Sdud hqwhqghuprv r pìwrgr gd ixqêær gh Juhhq frqyìp h{hpsolfduprv xwlol}dqgr xpd htxdêær gh 4@ _{rughp olqhdu h qær krprjíqhd}

S +{,g|

g{. T+{,| @ i+{,> +6143, rqgh S +{, h T+{, vær ixqêøhv duelwuäuldv1 Vxsrqkd txh | ì vroxêær gh

S +{,g|_g{ . T+{,|@ i+{,> h |2 wdpeìp ì vroxêær gh S +{,g|2 g{ . T+{,|2@ i2+{,= Hqwær |. |2 wdpeìp ì vroxêær gh S +{,_g{g +|. |2, . T+{, +|. |2, @ i+{, . i2+{,>

txh wdpeìp ì xpd htxdêær olqhdu1 Sruwdqwr vh | $ i> hqwær S|+{, ì d vroxêær sdud

S

i+{, h reyldphqwh=

|+{, @] +{_{,|+{> {,g{}

ì vroxêær sdud

I +{, @] +{_{,i+{> {,g{=}

63

S +{,gJ+{> {_g{ , . T+{,J+{> {, @ +{  {,> +6144, h txhuhprv d vroxêær sdud

S +{,g|_g{. T+{,| @ i+{,= +6145, Frpr vdehprv txh

i+{, @] i+{_{,+{  {,g{> +6146,}

hqwær

|+{, @] i+{_{,J+{> {,g{> +6147,}

ì d vroxêær gd htxdêær qær0krprjíqhd1 J+{> {_{, ì frqkhflgd frpr ixqêær uhvsrvwd/ rx pdlv}

frpxphqwh/ ixqêær gh Juhhq1 Hod uhsuhvhqwd vlfdphqwh d uhvsrvwd qr lqvwdqwh w gh xp lpsxovr xqlwäulr wudqvplwlgr qr lqvwdqwh w1 Pdv frpr rewhu d ixqêær gh JuhhqB Sdud ghwhuplqduprv J edvwd vhjxlu fhuwrv sdvvrv=

Iljxud 614= Hvtxhpd gdv uhjløhv gh d dwì e sdud ghwhuplqdu J1

Txhuhprv uhvroyhu d htxdêær +6=44, hp 5 uhjløhv gh d dwì {_{  h gh { .  dwì e +frpr}

hvwä prvwudgr qd Iljxud 6=4 dflpd,1 Hp d h e whprv frqglêøhv gh frqwruqr d vhuhp vdwlvihlwdv1 Hp dpedv dv uhjløhv +{  {_{, @ 3 srlv qær lqfoxhp { @ {> orjr d htxdêær glihuhqfldo qhvwdv}

uhjløhv ì d krprjíqhd=

S +{,gJc2

64 Ydprv wrpdu xpd J+{, txh vhmd vroxêær gd htxdêær krprjíqhd h vdwlvidêd d frqglêær gh

frqwruqr hp { @ d/ h xpd J2 txh vhmd wdpeìp vroxêær gd htxdêær krprjíqhd h vdwlvidêd d

frqglêær gh frqwruqr hp { @ e1 Ydprv suhflvdu gh xpd ghvfrqwlqxlgdgh hqwuh J h J2 hp

{ @ { _{sdud rewhuprv d +{  {,1 Qrwh txh=} J+{, @ J+{, . ^J2+{,  J+{,` +{  {, rqgh +{  {_{, @} ; ? = 3 > { 9@ { 4 > { @ { >

uhsuhvhqwd wrgd d ixqêær hqwuh ^d> e` = Vh { ? { _{hqwær +{  {, @ 3 h J+{, @ J}

+{, h vh { A { hqwær +{  {_{, @ 4 h J+{, @ J} 2+{,1 D ghulydgd gh J ì gJ+{, g{ @ gJ+{, g{ . g ^J2+{,  J+{,` g{ +{  {, . ^J2+{,  J+{,` g+{  {_, g{ @ ; ? = _CE% _% > { ? { _C2E% _% > { A { < @ >. ^J2+{,  J+{,` +{  {,= Vxevwlwxlqgr qd htxdêær +6=48, whprv txh S +{, ; ? = 5 7 _C_%E%> { ? { _C2E% _% > { A { 6 8 . ^J2+{,  J+{,` +{  {, < @ > .T+{, iJ+{, . ^J2+{,  J+{,` +{  {,j @ 3 5 7 S +{,_C_%E% . T+{,J+{,> { ? { S +{,_C2E% _% . T+{,J2+{,> { A { 6 8 . S+{, ^J2+{,  J+{,` +{  {, @ 3=

Yhprv txh d sduwh gd htxdêær txh hvwä ghqwur gr frofkhwh vær htxdêøhv krprjíqhdv sdud dv gxdv uhjløhv1 H txdqgr vxevwlwxðprv qd htxdêær qær0krprjíqhd whprv txh 5 7 S +{,_C_%E%. T+{,J+{, @ 3 S +{,_C2E% _% . T+{,J2+{, @ 3 6 8 . S+{, ^J2+{,  J+{,` +{  {, @ +{  {,>

65

Sdud txh rv grlv odgrv gd htxdêær vhmdp ljxdlv ì suhflvr txh ^J2+{,  J+{,`%'% @ 4

S +{_,= +6149,

Frp hvwd frqglêær rewhprv d ixqêær gh Juhhq1 Rewlgd d ixqêær gh Juhhq qöv vxevwlwxðprv r vhx ydoru hp +6=47, h hqwær rewhprv d vroxêær gd htxdêær qær krprjíqhd1 D xwlolgdgh gdv ixqêøhv gh Juhhq ghshqgh gr idwr gh txh vdwlvid}hp fhuwdv frqglêøhv gh frqwruqr/ jhudophqwh dv phvpdv gdv vroxêøhv surfxudgdv shod HG qær0krprjíqhd1

Dv frqglêøhv gh frqwruqr pdlv frpxqv lpsrvwdv dv ixqêøhv gh Juhhq vær= +d, frqglêøhv gh frqwruqr gh Glulfkohw/ rqgh J vh dqxod vreuh r frqwruqr/ +e, frqglêøhv gh frqwruqr gh Qhxpdqq/ rqgh r judglhqwh qrupdo gh J vh dqxod vreuh r frqwruqr/ rx vhmd/ uJ  gV @ 3> h +f, frqglêøhv lqwhuphgläuldv/ txdqgr uJ . z+{_{, @ 3 vreuh d iurqwhlud h z ì xpd ixqêær yhwruldo/ txh vh}

uhgx} d xpd frqvwdqwh sdud r fdvr xqlglphqvlrqdo/ gdgd gr srqwr gh iurqwhlud {₌

Hp txdotxhu xp ghvwhv wuív fdvrv/ d lqwhjudo gh vxshuiðflh vh dqxod/ h ghgx}lprv txh gdgr grlv srqwrv duelwuäulrv { h {2 qr lqwhulru gd uhjlær/ srghprv hvfuhyhu txh

J+{> {2, @ J+{2> {,> +614:,

ghgx}lqgr d vlphwuld gd ixqêær gh Juhhq vre d pxgdqêd gd srvlêær uhodwlyd gdv yduläyhlv gh fdpsr h gh irqwh1

Ghprqvwudêær= Vhmd gxdv htxdêøhv gd irupd/

u2J+u> u, . Y +u,J+u> u, @ +u> u,> +614;,

u2J+u> u2, . Y +u,J+u> u2, @ +u> u2,= +614<,

Rqgh Y +u, ì xpd ixqêær frqkhflgd1 Djrud/ pxowlsolfdprv d Ht1+6=4;, sru J+u> u2,/ h d

66 whruhpd gh Juhhq txh ì L 7^XuY  Y uX`  gV @ ] (  Xu2_{Y  Y u}2_X_{g= +6153,}

Frpr rv whuprv gr yroxph vh dqxodp h xvdqgr d sursulhgdgh gd ixqêær gh Ghowd whprv txh L

7



J+u> u,CJ+u> u_Cw 2,  J+u> u2,CJ+u> u_Cw ,



gV @ J+u2> u,  J+u> u2,

Mä txh J+u> u, h J+u> u2, vdwlvid}hp dv phvpdv frqglêøhv gh iurqwhlud qd lqwhjudo hod ghvdsduhfh>

hqwær

J+u2> u, @ J+u> u2,



Doìp gdv frqglêøhv gh frqwruqr/ d vlphwuld gd ixqêær gh Juhhq wdpeìp ghshqgh gd HG1 Sdud d htxdêær gd glixvær d ixqêær gh Juhhq qær ì lqwhludphqwh vlpìwulfd1 Qr hqwdqwr/ h{lvwh jhudophqwh xpd uhodêær gh uhflsurflgdgh vre d wurfd irqwh0fdpsr1 D ixqêær J+u> u_{> w> w, ì}

vlpìwulfd vre d vxevwlwxlêær u ' u_{> pdv qær vre d vxevwlwxlêær w ' w1}

Frpr ylprv d htxdêær gd frqwlqxlgdgh ì

% $M .C_Cw @ I +u> w,  V+u> w,> h id}hqgr d vxevwlwxlêær $M @ G%Q/ rewhprv d htxdêær gd glixvær

u2_{Q } 4 G CQ Cw @  +I +u> w,  V+u> w,, G = +6154, Gdgdv I +u, h V+u, whprv txh O*+u> w, @ I  V> +6155, rqgh O ì r rshudgru olqhdu h txhuhprv r rshudgru lqyhuvr

67

txh ghyh vhu xpd hvsìflh gh wudqvirupdgd lqwhjudo1 Sdud lvwr suhflvdprv sulphlur dfkdu d vroxêær gh

O*+u> w, @ +u u2, +6157,

rx vhmd/

u2J _G4 CJ_Cw @ _G4+u  u,+w  w, +6158, vxsrqgr xpd J+u> u_{> w> w, hp frrughqdgdv fduwhvldqdv gr wlsr txh ì fkdpdgd gh vroxêær gh}

irqwh srqwxdo/ J+u> u_{> w> w, @} ; ? = 3 > w ? w wE|3| deZ(E|3|_o*2h{s k _e(E|3|ƒh3hƒ2 l > w A w > +6159,

rqgh= U  mu  u_{m h +w  w, ì d ixqêær ghjudx fxmr ydoru ì=}

+w  w_{, @} ; ? = 3 > w 9@ w 4 > w @ w =

D vhjxlu prvwudprv d suryd gh txh hvwd vroxêær vdwlvid} d htxdêær glihuhqfldo=

Ghprqvwudêær= Sdud yhulfdu vh hvvd ixqêær vdwlvid} d htxdêær edvwd vxevwlwxluprv qd htxdêær h frpsduduprv rv grlv odgrv1 Ydprv fdofxodu YC

Y| sulphlur/ ohpeudqgr txh YwE|3|

 Y| @ +w  w,= Hqwær CJ Cw @ +w  w _,h3e(E-2|3| ^7G +w  w_{,`</sub>*2 . U2 7G +w  w<sub>,</sub>2 +w  w<sub>,h</sub>3e(E-2|3| ^7G +w  w<sub>,`}*2  6 5+w  w4 _,+w  w _,h3e(E-2|3| ^7G +w  w_{,`</sub>*2 @ +w  w,h 3<sub>e(</sub>-2<sub>E|3|</sub> ^7G +w  w<sub>,`}*2 .  U2 7G +w  w_,2  6 5+w  w4 _,  J= Pdv h u2_{JB Sdud xpd ixqêær txdotxhu i/ whprv txh}

u2_{i+U, @} 5

UgUgi . g

2_i

68 hqwær sdud xpd i+U, @ wE|3|e3

-2 e(E|3| deZ(E|3|_o*2 u2_{J @} 7U2 ^7G +w  w_{,`</sub>2+w  w <sub>,h</sub>3e(E-2|3| ^7G +w  w<sub>,`}*2  9 7G +w  w_,+w  w _,h3e(E-2|3| ^7G +w  w_{,`</sub>*2 @  7U2 ^7G +w  w<sub>,`}2  6 5G +w  w_,  J= Vxevwlwxlqgr r ydoruhv rewlgrv sdud YC

Y| h u2J qd htxdêær +6=58, whprv txh u2_{J } 4 GCJCw @ G4 h 3 -2 e(E|3| ^7G +w  w_{,`</sub>*2+w  w, @ 4 G 5 9 7 h 3<sub>e(</sub>E%3%2<sub>E|3|</sub> ^7G +w  w<sub>,`}*2 h3e(E+3+2E|3| ^7G +w  w_{,`</sub>*2 h3e(E5352E|3| ^7G +w  w<sub>,`}*2 6 : 8 +w  w, @ _G4+{  {_{,+|  |,+}  },+w  w,} @ _G4+u  u_{,+w  w,} 

Surydprv txh hvwd vroxêær vdwlvid} d htxdêær/ pdv frpr rv srqwrv txåqwlfrv fuhvfhp qxp irupdwr hviìulfr whprv txh wudqvirupdu dv frrughqdgdv fduwhvldqdv hp hviìulfdv1 D ýqlfd sduwh gh J txh ghshqgh gh u hvwä qd h{srqhqfldo1 Hp frrughqdgdv hviìulfdv r txh lpsruwd ì d frrughqdgd udgldo/ hqwær srghprv uhvroyhu d htxdêær frp d glphqvær uhgx}lgd1 Dqwhv whprv txh yhulfdu d glphqvlrqdolgdgh gd ixqêær gh Juhhq1 Txhuhprv hqfrqwudu xpd i+u> w, txh vhmd vroxêær gh u2Q _G4 CQ_Cw @ i+u> w,_G +615:, h dvvlp Q @] | ] TJ+u> u _{> w> w,i+u> w,gygw> +615;,} hqwær

69 FrprU_T i+u> w,gy @ 4 whprv txh D+uf> wf, @_7u4₂ f= Sruwdqwr i+u> w, @ _7u4₂ f+u  uf,+w  wf,

h d htxdêær sdud d ixqêær gh Juhhq frp glphqvær uhgx}lgd ì u2J(_G4 CJ_Cw( @ _G4 +u  u_7uf,+w  w₂ f,

f = +6163,

Sdud dfkdu d ixqêær gh Juhhq uhgx}lgd ydprv lqwhjuä0od hp vxdv yduläyhlv= J( @ ] _n" 3" ] _" f ] _Z f ] _2Z f +w  w_,h3 ƒh3hƒ 2 e(E|3| ^7G +w  w<sub>,`</sub>*2 4 7u2 f+u  uf,+w  wf,u 2<sub>vhqgugg*gw</sub> @ +w  wf, 7 ] <sub>Z</sub> f ] <sub>2Z</sub> f h3e(E|3|fƒh3hfƒ2 ^7G +w  wf,`*2vhq _{gg* +6164,} id}hqgr d vxevwlwxlêær mu  u fm2 @ u2. uf2 5uuffrv  rqgh frv  @ frv  frv _{. vhqvhqfrv+*  *,= +6165,}

Pdv vh }huprv xpd urwdêær grv hl{rv dwì ohydu } sdudohor d u h dvvlp rewhuprv } _yhuhprv

txh frv @ frv _{1 Dvvlp/ fdofxodqgr d lqwhjudo qdv qrydv frrughqdgdv rewhprv}

J( @ +w  w₇ f,

] _Z

f

] _2Z

f

h3o2no2f32oof ULt we(E|3|f

^7G +w  wf,`*2vhq

_{gg* +6166,}

Id}hqgr d pxgdqêd gh yduläyho x @ o2nof232oofULt w

e(E|3|f rewhprv d vroxêær

J(+u> u> w> w, @ +w  w _, 7uu 5 9 7h 3 E_e(o3o_E|3|2  h3 Eono 2 e(E|3| ^7G +w  w_,`*2 6 : 8 = +6167,

6: Hvwh uhvxowdgr vljqlfd txh/ vh ghvhmduprv dfkdu d frqfhqwudêær ghylgd d xpd irqwh srq0 wxdo orfdol}dgd hp u @ u_{/ vxmhlwd sru h{hpsor d frqglêær gh Qhxpdqq} YEfc|

Y% @ 3> ghyhprv

frorfdu xpd irqwh lpdjhp hp u @ u_{/ frpr prvwud hvtxhpdwlfdphqwh d Iljxud 6=51 Frpr d}

frqfhqwudêær ì luudgldgd gh fdgd irqwh +Iljxud 6=6/ olqkdv lqwhuurpslgdv,/ d frqfhqwudêær wrwdo ì rewlgd sru vxshusrvlêær +Iljxud 6=6/ olqkd vöolgd,> r uhvxowdgr ì txh d ghulydgd Y

Y%%'f ì

iruêrvdphqwh }hur hp wrgrv rv lqvwdqwhv1 D frqglêærY

Y%%'f@ 3 ì htxlydohqwh d lvrodphqwr gd

frqfhqwudêær/ lvwr ì/ qær kä wurfd gh frqfhqwudêær hp { @ 31 Qhvvd frqvwuxêær/ frpshqvdprv d shugd gh fdoru dwudyìv gd iurqwhlud { @ 3 suryhqlhqwh gd irqwh uhdo shor lq x{r gh fdoru gd irqwh lpdjhp1 Sdud dv frqglêøhv gh Glulfkohw/ d irqwh lpdjhp ì/ hp yhugdgh xpd irqwh gh fdoru qhjdwlyr +Iljxud 6=7,1

Sruwdqwr Q+u> w, vhuä Q @] | ] T +w  w_, 7uu 5 9 7h 3 E_e(o3o_E|3|2  h3 Eono 2 e(E|3| ^7G +w  w_,`*2 6 : 8 i+u> w,gygw= +6168,

Iljxud 6=5= Srvlêær gd irqwh uhdo h gd fwðfld1 Iljxud 6=7= Srvlêær gd irqwh fwðfld frpr xp ydoru qhjdwlyr1

6;

Iljxud 616= Frqfhqwudêær wrwdo rewlgd shodv gxdv irqwhv1

615 Vroxêær Dqdoðwlfd H{dwd sdud d Iurqwhlud hp Prylphqwr

Wudwdphqwrv dqdoðwlfrv gr fuhvflphqwr gh vlphwuldv hviìulfdv h sodqduhv irudp sursrvwdv sru ]hqhu h rxwurv ^63`/ ^64` h ^65`1 Sdud r fuhvflphqwr rx glvvroxêær/ hp xpd rx wuív glphqvøhv/ qöv hvwdprv wudwdqgr d wudqvirupdêær gh xp suhflslwdgr lvrodgr frqwurodgd sru glixvær qxpd pdwul} lqqlwd h txhuhprv uhvroyhu d htxdêær gh glixvær

Gu2F @ CF_Cw +6169,

rqgh G ì r frhflhqwh gh glixvær sru yroxph qd pdwul} h F @ F +u> w, ì d frqfhqwudêær qd pdwul} hqyroyhqgr r suhflslwdgr/ vxephwlgr ãv vhjxlqwhv frqglêøhv=

F+u @ U> w, @ F_U> 3 ? w ? 4 +d, F+u> w @ 3, @ F_> u  U +e, F+u @ 4> w, @ F_> 3  w  4> +f,

+616:, rqgh u @ U qd lqwhuidfh pdwul}2suhflslwdgr/ FU ì d frqfhqwudêær gd pdwul} qd lqwhuidfh pd0

wul}2suhflslwdgr h F ì d frqfhqwudêær orqjh gr suhflslwdgr1

6<

+F_FU,gU_gw @ G CF_Cu

o'- +616;,

rqgh F ì d frpsrvlêær gr suhflslwdgr/ txh ì xpd frqvwdqwh lqghshqghqwh gh u h w1 Uf ì r

ydoru sdud U txdqgr w @ 3> h hoh whuä r ydoru gh Uf @ 3 sdud r fuhvflphqwr h Uf A 3 sdud

d glvvroxêær1 Dedl{r hvwä d Iljxud gr hvtxhpd gr fuhvflphqwr h glvvroxêær sdud r fdpsr gh frqfhqwudêær1

Iljxud 6=8= Hvtxhpd grv Fdpsrv gh Frqfhqwudêær sdud +d, r fuhvflphqwr h +e, d glvvroxêær1

D 1 Fuhvflphqwr

Sdud d dqäolvh gr fuhvflphqwr gh suhflslwdgrv hviìulfrv d htxdêær fruuhvsrqghqwh sdud xpd hvihud hp whuprv gdv frrughqdgdv sroduhv hviìulfdv u/ / ! ì rewlgd hvfuhyhqgr

{ @ uvhq frv !> | @ uvhqvhq!> } @ u frv >

rx frqvlghudqgr xp hohphqwr gh yroxph gh xpd hvihud gh odgrv gu/ ug/ uvhqg!= Lvwr ì CF Cw @ u42  C Cu  Gu2CF Cu  ._vhq4 _CC  GvhqCF_C  ._vhqG_2C2F C!2  = +616<,