fdsðwro : ydoruv l yhfwruv surslv1 · 2 e f dcfc†˝ 2 e 2c f dc2 d˝ 2 d e f hc f 2c†˝ ......

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Fdsðwro : Y doruv l y hfwru v surslv1 :14 Uhvxp whõulf l h{hpsohv1 :1414 Ghqlflrqv eãvltxhv l surslhwdwv1 Y doruv l yhfwruv surslv1 Vljxl D xqd pdwulx txdgudgd g*ruguh q1 Gluhp txh $ ìv xq yh fwru su rsl gh ydoru su rsl b dvvr fldw d D vl $ 9' $ f l $ ' b $ Dl{õ ìv htxly dohq w d fdgdvfxq ghov dsduwdwv vhjÿhqwv= E@ $ b $ ' $ f EK E b U _ $ ' $ f ES $ 5 geo E b U _ E_ _i| E b U _ ' f Ho ghwhuplqdqw gh b U _ ìv xq srolqrpl gh judx ? hq od y duldeoh b l v*dqrphqd s rolqrpl f du dfwhuðvwlf gh od pdwulx Hv glxhq ydoruv su rslv gh od pdwulx d ohv duuhov gho srolqrpl fdudfwhuðvwlf1 Ho frqmxqw gh wrwv hov y doruv surslv g*xqd pdwulx v*dqrphqd hvs h fwu h gh od pdwulx l hv ghqrwd shu jE 4

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Page 1: Fdsðwro : Ydoruv l yhfwruv surslv1 · 2 E f Dcfc†˝ 2 E 2c f Dc2 D˝ 2 D E f Hc f 2c†˝ ... {lp ìv ýqlf1 Hq fdv gh txh wlqjxl pxowlsolflwdw/ ho pëwrgh wdpeì ixqflrqd/ shuõ

Fdsðwro :Ydoruv l yhfwruv surslv1

:14 Uhvxp whõulf l h{hpsohv1:1414 Gh�qlflrqv eãvltxhv l surslhwdwv1Ydoruv l yhfwruv surslv1

Vljxl D xqd pdwulx txdgudgd g*ruguh q1Gluhp txh �$� ìv xq yhfwru sursl gh ydoru sursl b dvvrfldw d D vl �$� 9' �$f l��$� ' b�$� �Dl{õ ìv htxlydohqw d fdgdvfxq ghov dsduwdwv vhjÿhqwv=

E@� ��$� � b�$� ' �$fEK� E�� b U_��$� ' �$fES� �$� 5 geo E�� b U_�E_� _i| E�� b U_� ' f

Ho ghwhuplqdqw gh � � b U_ ìv xq srolqrpl gh judx ? hq od yduldeoh b lv*dqrphqd srolqrpl fdudfwhuðvwlf gh od pdwulx ��Hv glxhq ydoruv surslv gh od pdwulx � d ohv duuhov gho srolqrpl fdudfwhuðvwlf1Ho frqmxqw gh wrwv hov ydoruv surslv g*xqd pdwulx � v*dqrphqd hvshfwuh gh odpdwulx � l hv ghqrwd shu jE���

4

Page 2: Fdsðwro : Ydoruv l yhfwruv surslv1 · 2 E f Dcfc†˝ 2 E 2c f Dc2 D˝ 2 D E f Hc f 2c†˝ ... {lp ìv ýqlf1 Hq fdv gh txh wlqjxl pxowlsolflwdw/ ho pëwrgh wdpeì ixqflrqd/ shuõ

5 FDSÐWRO :1 YDORUV L YHFWRUV SURSLV1

Ho ydoru sursl gh põgxo pã{lp hv frqhl{ frp udgl hvshfwudo gh od pdwulx14E�� ' 4@ i m>m %> ìv xq ydoru sursl g*�j

H{hpsoh :14 Wurehx hov ydoruv surslv gh od pdwulx

� '���2 � ��

� 2 f�� � 2

���4u1 Fdofxohp ho srolqrpl fdudfwhuðvwlf/ ìv d glu/ ho ghwhuplqdqw gh �� b U_��������

2� b � ��� 2� b f�� � 2� b

������� ' E2� b��� �� E2� b�� E2� b� '

' H� �2bn Sb�� b� �� 2 n b� 2 n b '' �bn Sb�� �fbn �

5q1 Exvtxhp ohv duuhov gho srolqrpl dqwhulru/ ìv d glu/ uhvrohp o*htxdflö=�bn Sb�� �fbn � ' f

ohv vroxflrqv gh od txdo vöqb�' �c b ' ��sD

2 l b�' � nsD2

Shu wdqw/ o*hvshfwuh gh od pdwulx � ìv=jE�� '���sD

2 c � nsD2 c ��

Ho udgl hvshfwudo gh od pdwulx �/ hq dtxhvw fdv/ ìv=4E�� ' �

Fãofxo gh yhfwruv surslv1Shu d fdgd ydoru sursl b� gh od pdwulx � h{lvwhl{/ frp d pðqlp/ xq yhfwru�$� / gh pdqhud txh

��$� ' b��$�ìv d glu/ h{lvwhl{/ frp d pðqlp/ xq yhfwru sursl1 Shu wuredu0or/ frp khp ylvwhq ohv htxlydoëqflhv/ fdofxoduhp ho qxfol gh o*dsolfdflö E�� b�U_��

Page 3: Fdsðwro : Ydoruv l yhfwruv surslv1 · 2 E f Dcfc†˝ 2 E 2c f Dc2 D˝ 2 D E f Hc f 2c†˝ ... {lp ìv ýqlf1 Hq fdv gh txh wlqjxl pxowlsolflwdw/ ho pëwrgh wdpeì ixqflrqd/ shuõ

:141 UHVXP WHÕULF L H[HPSOHV1 6H{hpsoh :15 Shu d od pdwulx gh o*h{hpsoh dqwhulru/ wurehx hov yhfwruv surslvfruuhvsrqhqwv d fdgd ydoru sursl1

Shu b ' �/ fdofxohp geo E�� � U_����2� � � ��� 2� � f�� � 2� �

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� ���g*rq rewhqlp od vroxflö

5 ' f% ' +

l/ shu wdqw/ ho yhfwru gho qxfol vhuã=E%c +c 5� ' E+c +c f� ' +E�c �c f�

Dl{ð/ grqfv/ xq yhfwru sursl gh ydoru sursl 6 ìv=�$��' E�c �c f��

Vhjxlqw ho pdwhl{ surfìv shu dov dowuhv grv ydoruv surslv v*rewì txh=�$��' ��sD� �

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ìv xq yhfwru sursl gh ydoru sursl � nsD2 �

Page 4: Fdsðwro : Ydoruv l yhfwruv surslv1 · 2 E f Dcfc†˝ 2 E 2c f Dc2 D˝ 2 D E f Hc f 2c†˝ ... {lp ìv ýqlf1 Hq fdv gh txh wlqjxl pxowlsolflwdw/ ho pëwrgh wdpeì ixqflrqd/ shuõ

7 FDSÐWRO :1 YDORUV L YHFWRUV SURSLV1

Pdwulxv vhpeodqwv1Gxhv pdwulxv � l � gluhp txh vöq vhpeodqwv vl h{lvwhl{ xqd pdwulx � qrvlqjxodu +_i|E� � 9' f� wdo txh � ' ���� � � � 1

H{hpsoh :16 Pdwulxv vhpeodqwv1

Ohv pdwulxv

� '���2 � ��

� 2 f�� � 2

���� � '�� f ff �� �� ff f �����

����vöq vhpeodqwv/ md txh h{lvwhl{ xqd pdwulx � / irupdgd shov yhfwruv surslv/

� '���� sD� � �sD� �� 2 2f sD� � �sD� �

���txh frpsohl{ od frqglflö � ' ���� � � � 1

Surslhwdwv141 � l � vöq pdwulxv vhpeodqwv , jE�� ' jE��51 Vl � l � vöq pdwulxv vhpeodqwv/ dohvkruhv=

+d, �$� ìv yhfwru sursl g*� , �$�� ' �� �$� ìv yhfwru sursl gh ��+e, �$�� ìv yhfwru sursl gh � , �$� ' ��$�� ìv yhfwru sursl g*�

61 � ìv lqyhuwleoh +_i|E�� 9' f� +, f qr ìv ydoru sursl g*�71 b 9' f ìv xq ydoru sursl g*� gh yhfwru sursl �$� , �

b ìv ydoru surslg*�!"gh yhfwru sursl �$� �

81 b#c b$c � � � b%ydoruv surslv g*� , &|o E�� ' b'n b(n � � �n b)_i|E�� ' b'� b(� � � � � b)

91 Wrwd pdwulx vlpëwulfd d frh�flhqwv uhdov ìv gldjrqdolw}deoh l hov vhxvydoruv surslv vöq uhdov1

Page 5: Fdsðwro : Ydoruv l yhfwruv surslv1 · 2 E f Dcfc†˝ 2 E 2c f Dc2 D˝ 2 D E f Hc f 2c†˝ ... {lp ìv ýqlf1 Hq fdv gh txh wlqjxl pxowlsolflwdw/ ho pëwrgh wdpeì ixqflrqd/ shuõ

:141 UHVXP WHÕULF L H[HPSOHV1 8:1415 Fãofxo qxpëulf gh ydoruv l yhfwruv surslv1Khp ylvw/ shu gh�qlflö/ txh shu wuredu hov ydoruv l yhfwruv surslv g*xqd pdwulxexvtxhp=d, ho srolqrpl fdudfwhuðvwlf= fãofxo g*xq ghwhuplqdqw1e, ohv duuhov gho srolqrpl fdudfwhuðvwlf= uhvroxflö g*xqd htxdflö srolqõplfd1f, shu fdgd ydoru sursl/ ho qxfol gh o*dsolfdflö ��b U_= uhvroxflö g*xq vlvwhpdg*htxdflrqv1Dtxhvw surfìv/ hq whruld/ prow vhq}loo> d od suãfwlfd/ vl o*ruguh gh od pdwulx ìvvxshulru d 6 ö 7/ hqv sruwd iruêd sureohphv ghjxw=41 d od frpsolfdflö ghov fãofxov hq ho fdv gho ghwhuplqdqw151 d txh shu htxdflrqv gh judx vxshulru d 5/ qr vhpsuh srghp wuredu xqdvroxflö gluhfwdphqw l/ shu wdqw/ kdxuðhp g*dsolfdu txdovvhyro ghov pëwrghvtxh khp ylvw hq ho fdsðwro 8161 d txh shu d od uhvroxflö ghov vlvwhphv g*htxdflrqv/ frp khp ylvw hq hofdsðwro 9/ d yhjdghv/ wdpeì qhfhvvlwhp pëwrghv qxpëulfv shu d srghu wureduod vroxflö1Shu d wrw dl{õ/ hqv wurehp hq od qhfhvvlwdw gh exvfdu dojxq pëwrgh qxpëulftxh hqv shuphwl fdofxodu hov ydoruv l yhfwruv surslv g*xqd pdwulx vhqvh xwlolw}duho srolqrpl fdudfwhuðvwlf1 Dtxð yhxuhp ho pëwrgh gh od srwëqfld txh hqv göqdho ydoru sursl gh põgxo pã{lp l xq yhfwru sursl dvvrfldw1

Orfdolw}dflö gh ydoruv surslv= whruhpd gh Jhuvjkrulq1

Dtxhvw uhvxowdw hqv shuphw wuredu xqhv �whv shov ydoruv surslv1

Whruhpd :14 Vljxl � ' E@�������������xqd pdwulx l

g�' �> 5 F �m>� @��m � ���� m @��m���Dohvkruhv/ hv wì

jE�� � �̂���g�

Page 6: Fdsðwro : Ydoruv l yhfwruv surslv1 · 2 E f Dcfc†˝ 2 E 2c f Dc2 D˝ 2 D E f Hc f 2c†˝ ... {lp ìv ýqlf1 Hq fdv gh txh wlqjxl pxowlsolflwdw/ ho pëwrgh wdpeì ixqflrqd/ shuõ

9 FDSÐWRO :1 YDORUV L YHFWRUV SURSLV1

Frp d frqvhtÿëqfld gho whruhpd whqlp xqd �wd sho udgl hvshfwudo14E�� �4@ �

�����m @��m

H{hpsoh :17 Wurehx xqd �wd gho udgl hvshfwudo/ dsolfdqw ho whruhpd gh Jhuvj0krulq/ gh od pdwulx

� '���

2 � ��� 2 f�� � 2

l frpsduhx0od dpe hov ydoruv surslv wuredwv hq o*h{hpsoh 41

Hq sulphu oorf/ fdofxoduhp hov fhufohv g�shu d fdgd �od gh od pdwulx ��g ' i> c m>� 2 m � 2j ' i>c �2 � >� 2 � 2j ' i> c f � > � ejg� ' i> c m>� 2 m � �j ' i> c �� � >� 2 � �j ' i> c � � > � �jg� ' i> c m>� 2 m � 2j ' i> c �2 � >� 2 � 2j ' i> c f � > � ej

Ihqw od xqlö ghov wuhv fhufohv whqlp txhjE�� � i> c f � > � ej

l/ shu wdqw/ srghp d�wdu ho udgl hvshfwudo dl{ð4E�� � e

Hq o*h{hpsoh 4 yhlhp txh 4E�� ' �c shu wdqw/ ìv fhuwd od �wd dqwhulru l d pìvhov ydoruv surslv txh khp wuredw hvwdq frpsuhvrv hqwuh 3 l 71

f � b�' ��sD2 � b�' � nsD

2 � b�' � � e

:1416 Pëwrgh gh od srwëqfld1Dtxhvw pëwrgh hqv shuphw ghwhuplqdu ho ydoru sursl gh põgxo pã{lp l xqyhfwru sursl dvvrfldw1Vxsrvduhp txh od pdwulx� ìv gldjrqdolw}deoh dpe ydoruv surslv b�c b�c � � � c b�l yhfwruv surslv dvvrfldwv �$��c �$��c � � � c �$��l txh ho ydoru sursl gh põgxo pã{lpìv ýqlf mb�m : mb�m � � � � � mb�m1

Page 7: Fdsðwro : Ydoruv l yhfwruv surslv1 · 2 E f Dcfc†˝ 2 E 2c f Dc2 D˝ 2 D E f Hc f 2c†˝ ... {lp ìv ýqlf1 Hq fdv gh txh wlqjxl pxowlsolflwdw/ ho pëwrgh wdpeì ixqflrqd/ shuõ

:141 UHVXP WHÕULF L H[HPSOHV1 :O*dojrulvph gho pëwrgh gh od srwëqfld/ grqdw xq yhfwru lqlfldo qrupdolw}dw%��� 9' �$f c ìv=

+�����' �%���

%�����' +�����n +�� n shu d & � f

Dohvkruhv/ vl ho pëwrgh ìv frqyhujhqw v*rewì=E@� n +��� n �$���m b�mEK� %����$����$��

H{hpsoh :18 Wurehx/ dsolfdqw ho pëwrgh gh od srwëqfld/ ho ydoru sursl ghpõgxo pã{lp gh od pdwulx

� '���

2 � ��� 2 f�� � 2

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djdidqw frp d yhfwru lqlfldo %�� ' Efc fc ��!�

Djdihp ho yhfwru lqlfldo qrupdolw}dw hq qrupd lq�qlw1%�� ' Efc fc ��!

l dqhp fdofxodqw lwhudwv vhjrqv o*dojrulvph

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Page 8: Fdsðwro : Ydoruv l yhfwruv surslv1 · 2 E f Dcfc†˝ 2 E 2c f Dc2 D˝ 2 D E f Hc f 2c†˝ ... {lp ìv ýqlf1 Hq fdv gh txh wlqjxl pxowlsolflwdw/ ho pëwrgh wdpeì ixqflrqd/ shuõ

; FDSÐWRO :1 YDORUV L YHFWRUV SURSLV1

Vhjxlqw dtxhvw surfìv rewhqlp hov vhjÿhqwv uhvxowdwv txh hvfulylp hq irupdgh wdxod1& +��� n +���n %���� E��c fc 2�� 2 E�f�Dc fc ���2 E�2c�f�Dc 2�D�� 2�D E�f�Hc�f�2c ���� E�2�Hc���2c 2�S�� 2�H E�f�bbbbbc�f�e2HD.c f�b2HDS��e E����D.2c���HD.�c 2�e2HD�� ���D.2 E��c�f�DD��.fc f�.2��H��D E���2.SSc�2��fS�c ��Hb�S�� ��2.SS E�f�bbbbbc�f�Se2H2c f�D..b���� � � � � � � � � � � �2b E���ffS2c�2�b.bbc f�fe2D.H�� ��ffS2 E�f�bbbbbc�f�bb�2Sc f�f�e�Se���f E���ffDDc�2�bH2Dc f�f�.fSH�� ��ffDD E�f�bbbbbc�f�bb2�ec f�f�2������� E���ffeSc�2�bHe.c f�f�2��S�� ��ffeS E�f�bbbbbc�f�bb��.c f�f�f.DD��& &mbm ' � �$� ' E��c��c f��

Shu wdqw/ revhuyhp txh ho põgxo gho ydoru sursl grplqdqw ìv 6 l xq yhfwrusursl dvvrfldw ìv

�������f

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Revhuydflrqv1� Frp khp ylvw ho pëwrgh gh od srwëqfld hqv göqd ho põgxo gho ydorusursl shuõ qr ho vljqh g*dtxhvw1 Shu ghwhuplqdu ho vljqh frpsduduhpgrv lwhudwv frqvhfxwlxv= vl hov grv yhfwruv whqhq ho pdwhl{ vljqh/ ho ydorusursl ìv srvlwlx> phqwuh txh vl whqhq vljqhv frqwudulv/ ho ydoru sursl ìvqhjdwlx1Hq hihfwh/ vl %� �whqghl{ fds do yhfwru sursl l b ìv xqd dsur{lpdflögho ydoru sursl/ whqlp=

%� ���' �%� �n �%� �n ' �n �%� �nb %� �

l frp txh n �%� �n: f/ ho vljqh gh b ìv o*ýqlfd glihuëqfld hqwuh grvlwhudwv frqvhfxwlxv1

H{hpsoh :19 Ghwhuplqhx ho vljqh gho ydoru sursl grplqdqw gh o*h{hpsohdqwhulru1

Page 9: Fdsðwro : Ydoruv l yhfwruv surslv1 · 2 E f Dcfc†˝ 2 E 2c f Dc2 D˝ 2 D E f Hc f 2c†˝ ... {lp ìv ýqlf1 Hq fdv gh txh wlqjxl pxowlsolflwdw/ ho pëwrgh wdpeì ixqflrqd/ shuõ

:141 UHVXP WHÕULF L H[HPSOHV1 <

Revhuyhp ho yhfwru %����'����f�bbbbb�f�bb2�e

f�f�2���

��l ho yhfwru %���'

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frp txh ho vljqh ghov grv yhfwruv frlqflghl{/ srghp dvvhjxudu txh ho ydorusursl grplqdqw ìv srvlwlx1 Shu wdqw/ b ' ��

� D o*krud gh ghvfulxuh ho pëwrgh khp vxsrvdw txh ho ydoru sursl gh põgxopã{lp ìv ýqlf1 Hq fdv gh txh wlqjxl pxowlsolflwdw/ ho pëwrgh wdpeìixqflrqd/ shuõ qr hqv göqd od pxowlsolflwdw gho ydoru sursl l ho yhfwruuhvxowdqw ìv xqd frpelqdflö olqhdo ghov yhfwruv surslv fruuhvsrqhqwv1

� Shu od surslhwdw 9/ vdehp txh wrwd pdwulx vlpëwulfd d frh�flhqwv uhdovwì wrwv hov ydoruv surslv uhdov1 Hq dtxhvw fdv/ ho pëwrgh ixqflrqd fru0uhfwdphqw h{fhswh hq ho vxsõvlw gh grv ydoruv surslv rsrvdwv b' �b��Pdojudw wrw/ ho pëwrgh hqv shuphw wuredu hov ydoruv surslv l hov yhfwruvsurslv fruuhvsrqhqwv dpe xqhv shwlwhv prgl�fdflrqv1 Dud/ hov vxffhv0vlxv lwhudwv whqgludq dowhuqdwlydphqw d grv ydoruv glihuhqwv k l q� Hovydoruv surslv v*rewhqhq dsolfdqw mb m ' �mk � qm� Hov yhfwruv txh vxu0whq dowhuqdwlydphqw qr vöq hov yhfwruv surslv �qdov/ shu rewhqlu0orv khpgh vxpdu l uhvwdu hov yhfwruv lwhudwv1 Hv d glu/n + ��n$ mkm c % ��$ �$�n +�����n$ mq m c %�����$ �$�

�, b�' n�mk � qmc �$��' �$� n�$�b�' ��mk � qmc �$��' �$� ��$�

:1417 Pëwrgh gh od srwëqfld lqyhuvd1Hv edvd hq ho vhjÿhqw uhvxowdw=

b 9' f ìv ydoru sursl g*� gh yhfwru sursl �$�, > ' �

b ìv ydoru sursl g*���gh yhfwru sursl �$� �

Dsolfdqw ho pëwrgh gh od srwëqfld d od pdwulx ���c wurehp txh > ìv ho ydorusursl gh põgxo pã{lp/ l/ shu wdqw/ b ìv ho ydoru sursl gh põgxo pðqlp gh odpdwulx ��Dl{ð/ grqfv/ ho pëwrgh gh od srwëqfld hqv göqd ho ydoru sursl gh põgxo pðqlpl xq yhfwru sursl dvvrfldw txdq o*dsoltxhp d od lqyhuvd gh od pdwulx grqdgd1

Page 10: Fdsðwro : Ydoruv l yhfwruv surslv1 · 2 E f Dcfc†˝ 2 E 2c f Dc2 D˝ 2 D E f Hc f 2c†˝ ... {lp ìv ýqlf1 Hq fdv gh txh wlqjxl pxowlsolflwdw/ ho pëwrgh wdpeì ixqflrqd/ shuõ

43 FDSÐWRO :1 YDORUV L YHFWRUV SURSLV1

H{hpsoh :1: Wurehx/ dsolfdqw ho pëwrgh gh od srwëqfld lqyhuvd/ ho ydorusursl gh põgxo pðqlp gh od pdwulx

� ' ���2 � ��� 2 f�� � 2

���djdidqw frp d yhfwru lqlfldo %���' E2c �c ���Fdofxohp od pdwulx lqyhuvd gh od pdwulx ��

��' ��� ������ �� f�SSSS.�f�SSSS. � �f������� �� �

���Djdihp ho yhfwru lqlfldo qrupdolw}dw hq qrupd lq�qlw1

%���' �2 E2c �c ��

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Ho pëwrgh gh od srwëqfld ghvsodêdgd hv edvd hq ho ihw=b ìv ydoru sursl g*� , > ' b� . ìv ydoru sursl gh �� .U_

Shu wuredu ho ydoru sursl pìv surshu d :/ kdxuhp gh exvfdu ho ydoru > pìvshwlw/ ìv d glu/ kdxuhp g*dsolfdu ho pëwrgh gh od srwëqfld lqyhuvd d od pdwulx

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Page 20: Fdsðwro : Ydoruv l yhfwruv surslv1 · 2 E f Dcfc†˝ 2 E 2c f Dc2 D˝ 2 D E f Hc f 2c†˝ ... {lp ìv ýqlf1 Hq fdv gh txh wlqjxl pxowlsolflwdw/ ho pëwrgh wdpeì ixqflrqd/ shuõ

53 FDSÐWRO :1 YDORUV L YHFWRUV SURSLV1

Revhuyhp txh ho ydoru sursl grplqdqw ìv qhjdwlx/ ghjxw d o*dowhuqdqêd ghovljqh hq hov lwhudwv/ l txh whqghl{ d 1 ' �f�2D> frp txh dsoltxhp srwëqfldlqyhuvd/ ho ydoru sursl pðqlp gh od pdwulx �� .U_ ìv > ' �

1 ' �e�Ho ydoru sursl gh od pdwulx � pìv surshu d : ìv b ' >n. ' �en. ' � dpeyhfwru sursl dvvrfldw �$� ' E�c �c ����Shu wuredu ho ydoru sursl pìv dooxq|dw gh :/ kdxuhp gh exvfdu ho ydoru gh >pã{lp l/ shu wdqw/ dsolfdu ho pëwrgh gh od srwëqfld d od pdwulx �� .U_1 Hovuhvxowdwv rewlqjxwv vöq d od wdxod vhjÿhqw=& +��� n +���n %���f E�c �c f�� � E�c �c f��� E�.c�Dc e�� . E��c�f�.�e�fc f�D.�ee��2 EH��e2bc ��HD.2c�.�.�ee�� H��e2b E�c f�e.�.fc�f�be.e���� E�H�.HbSc�2�.HbSc �f�� �f E�f�H.HbSc�f�2.HbSc ���e E.�bD2.c ��.beHc b�.�D.H�� b�.�D.H Ef�H�HD2c f��He.2c����D E�.�eS2fHc���2HbH�c b��.2H�� b��.2H E�f�.bS�Sc�f���.S�c ���S E.�2DDbc ��f2bDc�b�2fHH�� b�2fHH Ef�.H.b2c f����.bc����. E�.��S��c�f�HH2Hfc b��2���� b��2�� E�f�.HD�Dc�f�fbS.Sec ���H E.���b2c f�.bDe�c�b�f.D2�� b�f.D2 f�.HeeSc f�fH.SeSc����� � � � � � � � � � � �2f E.�f.�Dc f�Se�Hbc�b�fff��� b�fff� Ef�.HD.�c f�f.�Dec����2� E�.�f.�.c�f�Se�DDc b�fff��� b�fff� E�f�.HD.ec�f�f.�DfDc ���

Ho ydoru sursl grplqdqw ìv > * �bc shu wdqw/ ho ydoru sursl gh od pdwulx �pìv dooxq|dw gh : ìv b ' >n . ' �b n . ' �2 dpe xq huuru f�ffff�H�Revhuyhp txh hov grv ydoruv surslv txh khp wuredw vöq glqv gh ohv �whvrewlqjxghv hq ho sureohpd dqwhulru1Ho whufhu ydoru sursl kd gh vhu hqwuh �2 l �1 Vl ho fdofxohp d sduwlu ghoghwhuplqdqw wurehp txh ìv ��

Sureohpd :1: Wurehx ho ydoru sursl gh põgxo pðqlp gh od pdwulx

� '���

b �f H�f D ��H �� �

dsolfdqw ho pëwrgh gh od srwëqfld dpe yhfwru lqlfldo %���' E�c fc f���

Page 21: Fdsðwro : Ydoruv l yhfwruv surslv1 · 2 E f Dcfc†˝ 2 E 2c f Dc2 D˝ 2 D E f Hc f 2c†˝ ... {lp ìv ýqlf1 Hq fdv gh txh wlqjxl pxowlsolflwdw/ ho pëwrgh wdpeì ixqflrqd/ shuõ

:161 SUREOHPHV UHVROWV DPE PDSOHY1 54Dsoltxhp o*dojrulvph gho pëwrgh d od pdwulx

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l hov uhvxowdwv vöq=& + !" n + !"n % !"f E�c fc f�# � E�c fc f�#� E�f�f2�ef.c f�fDH�fec f�f.SeD��# f�f.SeD� E�f�2Hc�f�.Sc ��#2 Ef��2SS�c�f��fb�Sc�f�fef.e2�# f��2SS� E�c�f�HS�.Sc�f��2�.b�#� E�f�fbS�b.c f�fD�f2bc f��SSbe�# f��SSbe E�f�D.S2ec f���.SDc ��#e Ef��f.2Dc�f��D�Sfc�f�ff��HS�# f��D�Sf Ef�.f.eDc��c�f�f2�f�S�#D E�f�f.eHDDc�f�f�2Sfbc f��HHe��# f��HHe� E�f��b.�fc��fSSb2ec ��#S Ef�fH�fSbc�f��S2bSc �fS2H���# f��S2bS Ef�eb.eHc��c f��HDDS�#. E�f�f�b2..c�f�fHf�efc f�2fSDD�# f�2fSDD E�f��bf�Sc�f��H.bbc ��#H Ef�fD.b.bc�f��Sbfbc f��22�S�# f��Sbfb Ef��e2Hbc��c f�.2�Se�#b E�f�f�f�2fc�f���D��c f�22��.�# f�22��. E�f�feD�e.c�f�SfDDfc ��#�f Ef�fe22e2c�f��.2bHc f��S�f��# f��.2bH Ef�2ee2fc��c f�be2eH�#

� � � � � � � � �2. Ef�f2eDeec�f��..�2c f�2fH.b�# f�2fH.b Ef���.DDc�f�Heb2.c ��#2H Ef�f2eDb�c�f��..��c f�2fHS.�# f�2fHS. Ef���.HDc�f�Heb.2c ��#

Hq dtxhvw fdv/ vl ihp qrpìv 43 lwhudwv yhlhp txh ho vljqh gh grv yhfwruvfrqvhfxwlxv qr ìv ho pdwhl{ shuõ wdpsrf ìv o*rsrvdw1 Shu ghflglu ho vljqh ghoydoru sursl hqv fdohq pìv lwhudwv l revhuyhp txh ho vljqh hv frqvhuyd/ shu wdqw/ho ydoru sursl grplqdqw ìv srvlwlx l ydo > ' f�2fHSH. dpe xq huuru f�fffeD1Ho ydoru sursl gh põgxo pðqlp gh od pdwulx � ìv b ' �

> ' �f�2fHSH. '

e�.b�HSD�2b�

:16 Sureohphv uhvrowv dpe PdsohY1Fãofxov gluhfwhv dpe PdsohY1

Glqv gh od ooleuhuld OLQDOJ wurehp glihuhqwv ruguhv txh fdofxohq gluhfwdphqwhov hohphqwv xvdwv hq od gldjrqdolw}dflö g*xqd pdwulx1

Page 22: Fdsðwro : Ydoruv l yhfwruv surslv1 · 2 E f Dcfc†˝ 2 E 2c f Dc2 D˝ 2 D E f Hc f 2c†˝ ... {lp ìv ýqlf1 Hq fdv gh txh wlqjxl pxowlsolflwdw/ ho pëwrgh wdpeì ixqflrqd/ shuõ

55 FDSÐWRO :1 YDORUV L YHFWRUV SURSLV1

O*ruguh fkdusro| hqv göqd ho srolqrpl fdudfwhuðvwlf gh od pdwulx dpe odyduldeoh txh ol dvvljqhp1 Od vhyd vlqwd{l ìv=

fkdusro| +pdwulx/ yduldeoh,>Shu fdofxodu hov ydoruv surslv g*xqd pdwulx whqlp gxhv rsflrqv=

d, Gluhfwdphqw dpe o*ruguh hljhqydov gh vlqwd{lhljhqydov +pdwulx,>

e, Uhvrohqw o*htxdflö fdudfwhuðvwlfd dpe o*ruguh ivroyh +ylvwd hqho fdsðwro gh ]hurv gh ixqflrqv,1

Hov yhfwruv surslv g*xqd pdwulx hqv hov göqd gluhfwdphqw o*ruguh hljhqyhfwv/txh v*hvfulx

hljhqyhfwv +pdwulx,>l suhvhqwd/ hq irupd gh oolvwd/ ho ydoru sursl/ od vhyd pxowlsolflwdw l xq yhfwrusursl dvvrfldw r pìv 0ghshqhqw gh od pxowlsolflwdw01

H{hpsoh :1< Fdofxohx ho srolqrpl fdudfwhuðvwlf/ hov ydoruv surslv l xqv yhf0wruv surslv dvvrfldwv gh od pdwulx

���� D .� 2 e2 S H

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� Fduuhjxhp od ooleuhuld g*Ãojheud Olqhdo +qrpìv kr iduhp do frphqêd0phqw gh od vhvvlö,1: zlwk+olqdoj,>

� Lqwurgxòp od pdwulx +vl yrohp txh hov ydoruv vljxlq ghflpdov hqwuduhpfdgd hohphqw gh od pdwulx dpe xq sxqw ghflpdo1 Ho PdsohY/ shughihfwh/ rshud dpe ydoruv h{dfwhv,1: d=@pdwul{+6/6/^61/8/:/4/51/7/5/9/;1`,>

@ G'����� D .� 2� e2 S H�

Page 23: Fdsðwro : Ydoruv l yhfwruv surslv1 · 2 E f Dcfc†˝ 2 E 2c f Dc2 D˝ 2 D E f Hc f 2c†˝ ... {lp ìv ýqlf1 Hq fdv gh txh wlqjxl pxowlsolflwdw/ ho pëwrgh wdpeì ixqflrqd/ shuõ

:161 SUREOHPHV UHVROWV DPE PDSOHY1 56� Fdofxohp ho srolqrpl fdudfwhuðvwlf: s=@fkdusro| +d/[,>

R G' f�� ��f�n �f n �f

� Exvtxhp hov ydoruv surslv gh ohv iruphv h{solflwdghv dqwhulruphqw=0 fdofxodqw0kr gluhfwdphqw/: hljhqydov +d,>

��fDc �2�.c��.D0 fdofxodqw ohv duuhov gho srolqrpl fdudfwhuðvwlf=: ivroyh +s@3/[,>

��fDc �2�.c�f�.D� Wurehp hov yhfwruv surslv dvvrfldwv dpe o*ruguh gh Pdsoh: hljhqyhfwv +d,>

dd��fDc �c idf�b.�c�f�fDHDc�f�22bojocd�2�.c �c idf�Hf2c f��HHc f�H�Sojocd�f�.Dc �c id�f�f.2c f�.Hc�f�D�bojoo

D fdgd �od kl kd ho ydoru sursl/ od vhyd pxowlsolflwdw l xq yhfwru sursldvvrfldw1

Wdpeì xvduhp o*ruguh =lqyhuvh +pdwulx,>

shu fdofxodu od lqyhuvd g*xqd pdwulx1

Surjudpdflö gho pëwrgh gh od srwëqfld1Yhxuhp frp srghp fdofxodu hov vxffhvvlxv lwhudwv txh whqghl{hq do ydoru surslgh põgxo pã{lp d sduwlu g*xq exfoh iru l frp/ dpe shwlwhv yduldqwv hq odpdwulx g*hqwudgd/ wureduhp ohv glihuhqwv rsflrqv gho pëwrgh gh od srwëqfld1

+d, Lqwurgxòp od pdwulx l ho yhfwru lqlfldo qr qxo1: d=@pdwul{+q/q/^oolvwd g*hohphqwv`,>{^3`=@yhfwru+q/^oolvwd g*hohphqwv`,>

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57 FDSÐWRO :1 YDORUV L YHFWRUV SURSLV1

+e, Ho exfoh iru fruuhvsrqhqw do pëwrgh gh od srwëqfld ìv=: iru l iurp 3 wr Q gr

|^l.4`=@hydop+d)-{^l`,>o^l.4`=@qrup+|^l.4`/ lq�qlw|,>{^l.4`=@hydop+42o^l.4`-|^l.4`,>

rg>Vl yrohp exvfdu ho ydoru dpe xqd ghwhuplqdgd suhflvlö dihjluhp xqdfrqglflö g*huuru hq ho exfoh dpe xq zkloh l ho fãofxo gh o*huuru1 Hqdtxhvw fdv/ exvfduhp ho yhfwru huuru frp d glihuëqfld gh grv whuphvfrqvhfxwlxv l hq fdofxoduhp od vhyd qrupd lq�qlw1 Txdq dtxhvwd qrupdvljxl phqru gh od suhflvlö ghvlwmdgd dwxuduhp ho surfìv1Dl{õ txhgd sdoëv/ hq ho surjudpd/ gh od vhjÿhqw pdqhud=: huuru=@lq�qlw|> s=@suhflvlö> Q=@qrpeuhblwhudwv>o^3`=@qrup+{^3`,> {^04`=@{^3`>iru l iurp 3 wr Q zkloh +huuru:318-43a+0s,, gr|^l.4`=@hydop+d)-{^l`,>o^l.4`=@qrup+|^l.4`/ lq�qlw|,>{^l.4`=@hydop+42o^l.4`-|^l.4`,>hu^l.4`=@yhfwru+6,>li +o^l.4`0o^l`43a+06,, wkhqiru m iurp 4 wr q grhu^l.4`^m`=@dev+dev+{^l.4`^m`, 0dev+{^l`^m`,,>

rg>hovhiru m iurp 4 wr q grhu^l.4`^m`=@dev+dev+{^l.4`^m`, 0dev+{^l04`^m`,,>

rg>�>huuru=@qrup+hu^l.4`/lq�qlw|,>

rg>D o*krud gh fdofxodu ho yhfwru huuru ihp od glihuëqfld frpsrqhqw d frp0srqhqw gh grv yhfwruv frqvhfxwlxv dpe ydoru devroxw md txh vl kl kdjxìv

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:161 SUREOHPHV UHVROWV DPE PDSOHY1 58xq fdqyl gh vljqh +fdv gh ydoruv surslv qhjdwlxv, od qrupd whqgluld d�2 l qr v*dwxuduld ho surfìv �qv hvjrwdu hov Q lwhudwv1Wdpeì khp gh whqlu hq frpswh ho fdv gh grv ydoruv surslv gh vljqhrsrvdw l/ hq dtxhvw fdv/ od frpsdudflö fdo ihu0od hqwuh lwhudwv sduhoov rhqwuh lwhudwv vhqduv1Dl{õ kr surjudphp dpe xq li0wkhq0hovh0�/ ìv d glu/ vl od glihuëqfldhqwuh grv lwhudwv frqvhfxwlxv gh ydoru sursl ìv phqru txh xq fhuw ydoru+43��/ shu h{hpsoh,/ frqvlghuhp txh ho ydoru sursl ìv ýqlf l frpsduhpgrv lwhudwv frqvhfxwlxv/ hq fdv frqwudul/ whqlp od srvvlelolwdw gh grvydoruv surslv gh vljqh rsrvdw1

+f, Yhxuhp fdgdvfxqd gh ohv yduldqwv gho pëwrgh dpe sureohphv1 Qrpìv hvwudfwd gh prgl�fdu od pdwulx d od txdo v*dsolfd o*dojrulvph l lqwhusuhwduho ydoru sursl uhvxowdqw1

Sureohpd :1; Dsoltxhx ho pëwrgh gh od srwëqfld shu rewhqlu ho ydoru surslgh põgxo pã{lp l ho pëwrgh gh od srwëqfld lqyhuvd shu wuredu ho ydoru surslgh põgxo pðqlp gh od pdwulx= �

��� 2 f2 2 �f � 2

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dpe xqd suhflvvlö gh 43�

� Lqwurgxòp od pdwulx l ho yhfwru lqlfldo +vl frphqfhvvlp od vhvvlö ghPdsohY kdxuðhp gh fduuhjdu od ooleuhuld olqdoj, l surjudphp ho exfohiru0zkloh shu wuredu ho ydoru sursl gh põgxo pã{lp dpe ho pëwrgh ghod srwëqfld1: d=@pdwul{+6/6/^61/51/3/51/51/41/3/41/51`,>{^3`=@yhfwru+6/^41/41/41`,>o^3`=@qrup+{^3`,>huuru=@lq�qlw|>{^04`=@{^3`>

@ G '�� �� 2� f2� 2� ��f �� 2�

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Page 26: Fdsðwro : Ydoruv l yhfwruv surslv1 · 2 E f Dcfc†˝ 2 E 2c f Dc2 D˝ 2 D E f Hc f 2c†˝ ... {lp ìv ýqlf1 Hq fdv gh txh wlqjxl pxowlsolflwdw/ ho pëwrgh wdpeì ixqflrqd/ shuõ

59 FDSÐWRO :1 YDORUV L YHFWRUV SURSLV1

: iru l iurp 3 wr 48 zkloh +huuru : 318-43a+06,, gr|^l.4`=@hydop+d)-{^l`,>o^l.4`=@qrup+|^l.4`/ lq�qlw|,>{^l.4`=@hydop+42o^l.4`-|^l.4`,>hu^l.4`=@yhfwru+6,>li +o^l.4`0o^l`314, wkhqiru m iurp 4 wr q grhu^l.4`^m`=@dev+dev+{^l.4`^m`, 0dev+{^l`^m`,,>

rg>hovhiru m iurp 4 wr q grhu^l.4`^m`=@dev+dev+{^l.4`^m`, 0dev+{^l04`^m`,,>

rg>�>huuru=@qrup+hu^l.4`/lq�qlw|,>

rg>+� G ' dD�c D�c ��o,� G ' D�%� G ' d��fffffffffc ��fffffffffc �Sfffffffffo+� G ' dD�fffffffffc e�Sffffffffc 2�2ffffffffo,� G ' D�fffffffff%� G ' d��fffffffffc �b2ffffffffc �eeffffffffo+� G ' de�Hefffffffc e�2Hfffffffc ��Hffffffffo,� G ' e�Hefffffff%� G ' d�bbbbbbbbbHc �HHe2b.D2fDc ��.�bffH2Seo+� G ' de�.SHDbDfefc e��efebDHS.c ��S2Hfbb�.�o,� G ' e�.SHDbDfef%� G ' d��fffffffffc �HSH2He22bfc ��e�e2��e�bo+� G ' de�.�SDSHeDHc e�f..bHbSf2c ��DD��2SD�.o,� G ' e�.�SDSHeDH%� G ' d��fffffffffc �HSfbDHSD�Dc ��2.e.HbSfbo+� G ' de�.2�b�.�f.c e�feb�bS2SHc ��D�Db�SD.Do

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:161 SUREOHPHV UHVROWV DPE PDSOHY1 5:,� G ' e�.2�b�.�f.%� G ' d��fffffffffc �HD.D.eDH�Sc ��2�f�H�D.2o+� G ' de�.�D�eb�S.c e�f�S�H.D2ec ��ebbSD�2bHo,� G ' e�.�D�eb�S.%� G ' d�bbbbbbbbbbc �HDSffe2f.fc ���HfebDbH2o+� G ' de�.�2ffHe�ec e�f�ffDHf�2c ��eb2�f�ef�o,� G ' e�.�2ffHe�e%� G ' d��fffffffffc �HDD2.�be22c ���SSDb.eb�+� G ' de�.�fDe.HHec e�f2.2f.S��c ��eHHDb�ee�o,� G ' e�.�fDe.HHe%� G ' d��fffffffffc �HDeb�ef�HHc ���Sf�2Hf��o+�� G ' de�.fbHSHf�Hc e�f2DHHfHe�c ��eHSbDbS2Do,�� G ' e�.fbHSHf�H%�� G ' d�bbbbbbbbbbc �HDe..D.�bDc ���D.��D2Dbo

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Page 30: Fdsðwro : Ydoruv l yhfwruv surslv1 · 2 E f Dcfc†˝ 2 E 2c f Dc2 D˝ 2 D E f Hc f 2c†˝ ... {lp ìv ýqlf1 Hq fdv gh txh wlqjxl pxowlsolflwdw/ ho pëwrgh wdpeì ixqflrqd/ shuõ

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