1P1BEI JiPiOKKIMO bVbEK 2EKIE2 - Finance Departmentfinance.wharton.upenn.edu/~jermann/w4951.pdf ·...
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Transcript of 1P1BEI JiPiOKKIMO bVbEK 2EKIE2 - Finance Departmentfinance.wharton.upenn.edu/~jermann/w4951.pdf ·...
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lUlO qowGic cnucucA 91 113G flLG Lpcq Gxcp9uG L91G j flUC0AGLG UJIGLG2I b9LTIA poq2 9uq
11110 fIG OLG1&U Ci1LLGUCA 113A621113& '1 lU 9 1pLG!u q€bo21 9Uq fIGU c0lThGLiru fIG bLocGGq2 P9CIC
1JAG21G W 9 OWG21C qGbo21 Gdn9p fiG Gxbcclcq LGjRLU2 jLoW COUAGL U fIG qowG2lIC CflLLGIJCA
jJin2e f1UC0AGLG WLGLG2I b9LTIA iii (j) 29A2 11391 113G LGIflW2 Oil 9 flUII O qOWG2IIC CnLLGIJCA
ribou CflLLGUj IU0LW9[J0U1 20 11391 E'() c E(•)
I!ICL9WLG !U MIJ!CP fIG UJ9LJCGI)2 CXbGCI9fOU 0G2 1101 Gdfl9j IPG 2191!211C91 GXbGCI9ITOU c0uqOU9J
cxbGcl9iTou !2 1101 11GCG229L
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LCjC2 io fliC W9 (j LGLC221OU qccpcq pcjoMbLoqricou (nwpA (j)) o uwc ci jpp LcLc2z!ou iis Lrru OL bL2iwouX uq cnciJq pou nJci.c Lc ru qrcLci cnLLGUcIc2 (cwbpcjj uq cJLq (io uq Ufl2iLWJruq HOqLC (J)) jicq oqc LGUILU2 (iozuu UI 9U OLIOU (j))pc 2bLcJq GtMGGU jOUUIIUJpCL O flipOL2 JJAe onuq 1J iJJG2C LGLflUJ2 CIJ pe cxbjueq pA jicq GXCG22 LGInLU2 (Hu2cu
ju biucbc W!2 LcLc22!ou conjq pe LIIU ou uA AL!PIG2 qrn pcjb cxbju cxcc LcuILuz v
v 2fIpacdfIGIJt WGLflLG p iceq tpj uqu oici oipci wbjc bcLloq2 9uq CrILLCUCIC2QBII2OU (JJ) cuJcq JT2 LcLc221oU uq onuq pr nucoicicq IIU;LG21 biuA qoc uo pojq
JJJG G2L LGLC22G2 IJJG CJJUG ru pc cxCpuc LG OU LJJG OLM9L bLcwlrlw:
tOL LPG pcJJA!OL O bLcqrcwpjc LCCfli2 peoii
I MJ 1JJGLCOLG fl2C W12 p2TC Lc2np 2 GUCUJLJC 0L q2Cfl22rn AL1Ofl2 OLTC1IJ cXbjW111O1J2
LcLc2a1Ou ic2r jp aiwbjc pz bLoqnccq cpSjjcuc OL LG2GLCL2 !U ucwsouJ IJ1JUCG
jw (j) rjjnjurgcq pc qcLcc o bLcq1cpjc cxcc LGIrILU AJL1p1J1A nnJ 2rnibfc
VV'
woqcp (jg) cwbpr2icq ! quiwicijA nup rpe qccowbo21iou qccupeq U€W
U i GWLG o bLcqrcwpfc LC[flW2 12 IIJC WO2C qqjjcnji O LGC0UCjC rp ruqtq
wunw pqc e Acu LCUILU2 AJLA LOW OAGL io -obLcqcwpJc LG(flUJ2 qthjiA cou2qcLpic ALfl1PTI11A DY! LCUILIJ2 L1UG LOW oa o bcL
uo SCLO4 pnr po !ApA qicA c ouicuic uet!Ic uq si OGL WJC2 bo2/c JJJLqe fJJG
jpcLcOW cXbJUToIJ2 o GXCG2 OLGT1J pouq LGU1W2 W112i cXbiiJ uoi ouA MJJA pCa; LflLU2 LC
2u!IJcIujA ucte qnLw b o LJA uq M9 2UU1C1UTA bo2Tg1c U
cpcuc 2U qnLpJ pc 2JwbJc Jpc bLcqcrpc GXCG22 LGflL1J2 ou pojqru DY! 01. Acu qcbo2r2 M2
LCUIW2 LC 2uIjcuJA qIjcLcur LOW GLO OACI. 2OWG bcuoq2 !U qic 2wb!c ccouq f jiG LGfIIW2
jpLcc GjflLG2 o pc bLcqccq LGIflLU2 2uq on FLow 11112 suJA212 h!121 we bLcqcrcq
jyc qpcq flUG2 LcbLc2clu pc wuqLq caoz. coujjqcucc puq2 Lonuq tpc bLcqrccq AffJf1G2
= p° + p' ( - + WfJIG JI1IGL bLo1cciou cdritou 1AGU iii y o jpcbLcqrccq LGUILU2 LG pc ctnj LGflLU2 LGLG22G nbou ijic 9LML bLcwinw -2 ccOLqU to
Q
bLwinwipc LCpJTOU2pTb CLrIffA qacupq pA ui COUCGW!U qJc Af4UCC o JJOLiJ GXCp11JC 142C
bLGqicpipjc cxcc LCLIILU2 Mipon urnpu uX I22r1wbiou iporu cxbccjou2 f'iCL I Mfl 2C(T22JGLI q2cne2iou woqrijc i p JUJ (Jf) LG2fl[ WOLC GUGLffA o CI4G
UJ JpG jLGS1ou2p!b fl2TU OGL UoU-qOJL CLO2Z LG2 uq onuq 2WL LcI!oU2p!b2 fO O2G JU2L fiG
fiG JLCUCJJ tLIJC OU fiG OfiGL pUq B JCSG14 Uq HOqLC( (j) pc GX9WIUGq fiG 2WGAcw EOL cxwbjc1 Bo2G2 uq H!II!OU (jj) puq bo2i!AG C II1JC2 oL wo2 CIILLCIJC!C2
JJJT2 LG2flJ 2 VbbiLCU OL 2OWG O fiG CL022 cxcirnuc LG2 MTfJU fiG EflL0bU ouwz.A
AL(bGL) = /L(72'"') - - + ML( - (jjj)jo 2CC MpA uo pj pc AL1UCG o (j) cu pc ,,ii1Gu:
ASL(bGL) > AL(E(V2')) ft io)
CpUG JU OfJGL oLq2e
cowboucu o GXCG22 LGUILU2 GXCGG2 fiG ALUCG o fiG J!IJGL bLGqc1ou oj fiG LG
iu csc nrqu o ' < u jpjc j piJbjG2 ip AL!1JCG o pc bLcqcpJc
MGLG pG jr cdrnqrA tojjom pccnc CoA(c - = o pA COULnc!OU
= - -
= [coA(v" - ) + - - 2)
= - - 2) (Fo)
uo ip ipc bLopupj l O fiG O2 COGWC!CUL
cpiuc iii ipc GXC1WG LC LC!IAG o fiG bLcq1cpJG cowbouGu o LGWLU2TO jo 2G MpA
/.JJGu rpi coicicu cu coUAGA iuouinniou poru pc AILrprp1A ni pc Cxbcclcq
JJJI2 LC2flIL 12 1Th1C9j O( UflIIJA O1CL 2U1qC2 GX91JJUpI fiG 2WC LC!fOU2p!b
fiG C2(WJ(G O ' LG JJ 21UT1CU1jA jc rpu ouc ici fpcA LG ;/u 21 icriiqA IJGfAG
qG Dt BL!1!P bonuq uq iib9uC2G AGU OAGL fiG bGLoq LOW 10 J)g 2 fiG 1jC 2p0M2e
Jpf C JIJQ 'f 2poN2 fiG LG2(f 12 Ot fi!2 LGLC22!OU fl2i1J fiG qOJJL CXC}JBiG LjC2 !1J21
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MCLG v 2 fIG pcJcMLq T[GLGUCC obcunoL wq n41 2 u GLLOL jcLur 4OG flJI1 IP LGLG221OU
= o + j ( - +
WLJCCt2 XbCttT0U2 O GXCJJUC LtC CjJUG2
j pcu iwbjrn2 tpt tpc ALWUCC o tJJG U2JC bLCwrrlw cxccq luG AL!UCG o
= o tp tpc bLGqctip€ bI4 o GXCG LGUILIJbGLD i lnar Gdrni to tp LT2r bLGwInw th jjjc
LG Lt!0Uj uq tpc 2T2ticJ qtLpnlou o tp ccouowA jcuou to tpc UJLfCG iu tpJ czc
lpc L2JC bLGwTnw tG W1GthLCU0II !AGU pA IW (Jo2t) vccoLq to rpi !m GxbGctsL!oU2
Lt tp uotiou rpt tPG GV4OL o bLcqicwpc LGIflLU2 onuq OAG M2 qnc 10
= th +
JJJJT2 ipc GXCG22 LGLflUJ cu pc /ALULGU 2:
- EV2i÷I = (nt)cdrqjpqnw bLGunnw brq 0L WfU WOLG 42C JJJG UWLJCGI2 40LGC2t G1.LOL
dnqou (jj) 2iA2 tpt tpc WLJCGt2 GxbGcicq LGIflLU tOL pojqrn OLGiU qGbo2I2 12 U
— - = Ehi+f - ( - 4). (T•J3)
EOL tJJZ bnLbo2 qu ipG L12JC bLGW!rIW ou IJJG bo21tou Mrtp tp LGWLU iu (nj) a:
iuro lG2G tio onba i i nrq to qccowbo tp jiurn LG&G22!OU COCjjC1GUt flLIpGL
() qic OLG!U GXCJJUG L12fc bLCW!UW OL (p) cxbccttowij GLLOL2 jO 2GG OlA GXb1SUI!OU2 1J
qGJ O LG2GLCJJ OAGL pc bt qGcqc QGUGLflA' tpc GXb1IrntT0U2 cu pc cjnqicq iuo tiio onb2:
MJ'1 GXbJ9U2 IIJG2G LG2flJI2 JJfl2 u !wboLtut J22flG tIrnI P"2 GGU rpc OCfl2 O
y ouu XitouL1G CpUc2
iuq bLcqc1pjc IAGU CIILLGUI 11JoLUJt!oIJ tGL AL1UCG !2 dnitG 1LC LG1I1AG 10 €XbGclGq GXCIUG
JGLGOLG fIG 21LI1CUI coUcffl2iOU tLOW JpjG j 12 1P11 UO oujA 9LG GXCG22 LGIJ1LU2 UOU-SGLO
OLMLq bLGwnur
qcAwtou2 o gpc bLcqctGq ijn L0W LGLG2210U2 0 fIG C}IJG 113 fIG GXCJJUG LtG 0U pG
2ruqLq qi l!ou2 o bLcqictcq GXCGZZ LGj11LU2 LG L0npjA twicc tpc coLLc2bouqru 2tuqLq
JJJ!2 LGI9L!0U211!b cU j20 PC 2CCU (f2U fIG C21TUJ1G2 111 LPIG 'q2 2JJ0/A1J !' b1GI B1 fIG
- - = (T.J)
r1p1atu (vu) uq tpcu (uo) 0L jpC jt-puq qc o (jj) uJbjG2 tpt tpc !uGdnflA Mffl pojq
xcjniuc L wn p couibuecq OL OLCIU xcjrnuc U2JC VCCOLU 10 1j2 XbjUL!0U
pojq toLGxu pouq uq ipcu COUACLI jpc LCLfILU2 CfC iuio OW21C crrLLGucA C 1G tI1I1LQ bLcAu
ouc cxbjuiou tot. bicqcpjc GXCG22 LGIflW2 !2 11J91 qowcatic WAC2IOL2 MO LC MU111J 10
\ptu csiuI qcn GCI 0 IJJG2G GXbjU1i0IJ2 GJ0M
2o-cflGq bczo bLopJcw U wc2rILw ipc cxbcclcq LG1flUJ ju ipe wuqq mA qccLTpcq po,c
bLoppfl11A 011 qjc JTJCGjlJJooq 1G qoJJL onjq LcponlJq 2! UC1u1IA jJIT2 cACIJI !Aofljq WILOqIICG
LCIflLIJ2 EOL cXuibic 1L€L2 pnAiu ?cii 0LML 111 flJG J1C urnX pc bccq ouic10 WG2ITLG cXbcCWjTOU2 2 UI E!r1Lc j WIA U01 fCCrIL1GjA LCUCCI IJJG WLJCG12 cXbGC11I0U oj
cxbccWou2 ot bLcqiqipJc LGWLU2 VCC0LU 10 1JJ2 €XbjfU1!0U1 Ipe L 1G22T0U GdnW0u2 nzcq
V ccouq 20flLC 0 2A21CWfflC tOLGC921 GLLOL2 L!2C2 tLOW qrcfl1ic2 U WG2fl4IJ
2A21CUUJ1TCJIIA iiiou
1101 AG ncq JJ !UtOLUJWOU CtIJCTG1Jq?I uq cXbcClcq 10 urnjcc bLoj12 c/cu 1P0fJ ipeA !AcLC
jU1T0U9j 1LGL2 UI IjJC UJSL!CC1 EOL GXWbJGe 1LGL2 pnAni Acu OLML qrILIiJ 1G jf I I8O2 UrnA
t0LCC21 GLLOL2 corrq L!2C tLOW INtO TCLGUI ITh2 Ot 2011LCG2 QUG 2OI1LCG 12 IJJC bLccucc o aowc
2ccouqe IJJG bLcqcIcq LcInLU UJA LC2fl!I tLOW 2A21cWflC t0LCS2I CLLOL2 JJ1C2G 2A21GW911C
L1IIL1J2 LG Nt0LCIU GXCJI1UG L127C btcwinur
Mpojc its cowbcu2uu WAG2IOL2 tOL I1JC1U Ip!2 b02!1!0W flUCL 1p!2 cXbJUWoUe fliC bLcqc1pc
OflL pouq qnLnJ IJJG J1G jga uq UC9flAG qnL1u Ipe CLjA Th802 pCfl2 IJJc UJLJCG1 e
VCCOLU 10 IJJ!2 GXbjU1!0IJ 1JJ LCI11LU2 Mete bO2IITAG 10 I1JAG2IOL2 Mi1p 1J obeu bo2iITou ru uou-
poq cJ22ujcnou2 ha21 IPG bLcqTclcq LGWUJ2 UJØX pe w OflICOUJG ot ,u cdnpqnw bLocG2
BCJ0M I Mifi qcecupc cXbj1J1!oU2 tOt weCJJA0L O GXC22 LGII1W2 pcq nbou jJJC2G INtO
cuq we fJJ9AJOL 0 bLcqicIpJc XCC22 LGIflL1J2 conjq LG2fl!I tLOW C0Wp1U1I01J 0 IP2G INtO tCL0L2
oCOITL2G IpJJe-AL? U L12JC bLcwT9 uq 2A2IcW1TC t0LGC2L GLLOL2 UOI WnIr1flA cxcjntc
M!UP jieq Wt0LW1!0u
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cdnj 10 11)° 20 GL" = + 3' W 1JJ2 ipc pp ALT10U w bLcqicIpfc CXCG22 LCLITW2
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JJJG aGcouq 2Gf o woqca i j bicauj pGjoM 0Cfl2G2 nbou iuIGLLcwboufl WAG2IWGUI
lC woqcp u tpa onb LG biwj Gdrnppunur
IJJG bLOCG22G2 ojjoq pA GXCS1JG LiG2 !IJIGLG2I LIG2 uq 1UUT0U L1G2 92 GX0G1J0fl2 f2 2J1CJJ
MTJJ qcacupc 1MG LThG2 O LJaJc bLcwrnw w0qGj2 JG UL2L 2G1 0j woqca 12 2111C TU U1flL€ suq jLG12
jjiA i.uip uou-Lo bLGqiclpJG GXCG2a LGjflLU2 G IjJG LG2flII o u Gdnrppqnw bLoccaa
bLcui!nw woqca I Mffl aiujb1A MLIIG LG UJLCG[2 GXbCCL110U2 111 1jJ2 2GCLIOU 72
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To
qeuoteq AL(M) MJiGLG AL' 12 IJiG AILp1ucc couqJtoIrnj nbou 1J1OL1J1flOU JUJOMU ( (TUJG t JJJfl2
flUCtOU qrni f2 wcLc12ru iii tpe weu pnt GCLG12J Hi tpc AUUCG 01 euq-o-bcLToqMGJtJI
V2 MTtp tpe qowG2tIc cv pe IUAG2(0L 12 22L1WG (0 CJJOO2G X' (0 UI9XIWISC JU oplGCtJAe
20 1Ji( L'"' = -
— i (: + a') + (j -x') ' (uio)
boLllopo pi (GLW2 °1 tp uownrnj LG(ru.u:
qoweec piIJ110U L(G qepieq 2 ! tPLG10LG COUAGIITGU( (0 LGMLI(G (PG LGJ LG(I1LU OU fIG
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J + L'' — (( + ')(\J,') i + !-''J + L1 — (I + !'.) b' \ ') + , + -
LG qeteq pA excjn,uc L(G uq bticc jGAGj cpsue2:
jO MU(G (JJ62G LGJ LCUILII2 (GLUJ2 0 0P2G[JP!G2 (JJG11. UoWTIrnJ LG(IILU2 Hi GCJl CflLLGUCA
12 (JIG LGU3LII 0U fIG qowG2(ic 22G( potp LeflSGq t y
MJJ€LG X' 72 (pG 2JJLG 01 j pejq p fIG 10LGU 22G( L,' !2 (JIG LGUILIJ OU (JIG 10LGIJ 22G( uq L1
= X' L' + (j — x') Lt+J (iix)hIG LGfff LC(1'ILU OU (JIG JIOLUG boi4ojio 12
qGCl2Iou IOL (JIG 10LG1IJ WAG2(OL 12 cowbieteiX 2AIJJWG(LIC
L22G( Mffl ITL2( qccupc ipe boLtlopo qeclalou ou ipe bLt 01 (JiG JiOUIG TUAG2(0L JJJG boLqopo
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MJIGLG 12 (JIG LGSJ LG(ILII ou (JIG JJOWG boulopo ILOW t to i+ jo COU2IqGL IP!2 boi.qopo LGIILU
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to iwoqnc (PT2 couiboueu tOll 0M (JiG p21C 1UjA212 pGfOM
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JJ
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(X.1) + x ), ,'W' + ,V1 =
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:a3vL ,3n3m3uiE nfl 9113 03 333qz31 1111w V to 23vilsvFI3b
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=1fl2u lpc qcijiirqou o €L uq ! (oY coA(cL') = /L(72') x' uq COA(CL')
Edfl1!0U (fl4) GXWWC2 OUJA 1MG LJ2JC-(LGG pouq uq IMO TUA20L2 U OLqGL 10 GWOU21LiC
miou qGbcuqJu nbou ip C0AL1UCG p€[ft¼u oiiui TuJJiou uq IIJG GXC}J1UG L1G
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pojqpi O 0LGTU pouq2 uq tOLG!U poqpi O qOUJC2iC pOUq2 /JJJGU 0UJC21TC Lc21qcU12 LC
qcbcuq nbou pc CLCUCG G1MCCU x' i uq (j - x) f4P OL flJG GLGUC G1MCGU qowc2Jc
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EdI1i10U (T9) U TU1flhjTA IU1GLbLG1WOU 2rTbbo2G UL2L iIJC WU1TOU MGLC bcqccq?
LG2TqGUi21 LG2bGCLTAG1A 20 1I31 M + = F
!1JJJ1!OU LG ruq M6LG M uq /A' LG 1G 2LG2 O JJG /AOLJ //!LP pjq pA IJOUJG uq IOLG!U
MGL X 2 IpC 2çrnLC 0 0LCIUCL2 /ACj1 1P1 LpcA poq W IPC!L 0/AU 22Gt2 MJJCLC Lt 2 1}JC 0LG!U
bcL'' = b [x' ,, - (j - x') m] ASL'(w) - t[it coi(v' + M' t')J (j)L0ll0M1IJ WC 2uJc 2jCb2 2 P0AG 0L IJJG 0LG!U i1iAC20L flhJbJTC2 €drnppLrnw LCji0U2PJb,Q
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Jpn2 qc iL2i-OLqcL c0Uq1110U2 qcbcuq oujA nbou 1G ALJpTJI1A o cxcpu LI1G2 iuq I1JJJ1IOIr
= \sL'(v2') - ' coA'(v2' ,/+J). (ii)JL0LG cdnstou (j) cu pc iti.iucu 2:
C1MGU XCG22 L1flW2 LT2G2 20j1A L0W pG COUqTIJOU9J C0ALJLJCG G1MGU cxcpu LG21
cou2lq€LGq UGI MJ1P ffCLU cdrI!Ijcucc Wfl21 U01 pojq p1 J!2C2G IJJG couqiouj C0AL1LJC
LG Li2JC-LGG pouq2 III LJJCIL LG2bCjiAG CflLLGUC!2 ypo1 ni oLqGt. tOL oniqc pouq jo p
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y UrIUJpL ot 9110L2 pcic GX9WUG tpc uJbcq G!AIOL o tpc oLc!u ;xcirnuc L12JC
1t1Ucc1 Htt\1
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LGIflLIJ2 WG92flL6 u LG9j tGUJJ2 911q U U0WU9! ICLW2 qo uo1 CJJ9AC AGLA qIjGLG1JflA JJJGLGOLG
U1!UJpGL o 9flt0L2 cJnq EUGI (j) uq CnwpA (jgg) p9zc onuq tpt tp GMOL o cxcc
CXcp9uG L91C2 9uq W9l:iOU 12 dnp 2111911 9U UG9L GL0 92 Nffl G 20MU 111 2GCOU pi 9C1 9
ot tpc CO19U9UCG CtMCGU qic GXC9UG L9IG 9uq wuroIr Ewba!c9ff? pG CA9L19UCG PGIMCGU
H0I IUJbOLj9IJI 12 1p12 cucue wcdntA tGLW CIC9LIA tpi qcbcuq2 nbou rpc rwboucc
tpt IJJC2G ictnw ponjq uot pG cjjcq 9 42C bLcw!nur
ucc bLcqct9pc GXCG22 LGtflLIJ2 9LG UO GL0 GAGU !U tile 92GUCG O 421C 9AGL2OU1 !t W9? pG 9L11G
LGWU1 9LG UO GLO GAGU !AJJGU TUAG2IOL2 9LC L!2JC 9AGL2G CL91!0U2 9LG 2W1I211C9JA nup9eq
(io) uq ucj (Jg) bo1ucq onc tpt qnc to tp icuacu ucdn9j!1A tGLW bLcqIcwpJG
GXCG22 LGtflUI2 9LG 1IOU-GL0 9Uq Gd119j to CO (V?" L') EOL ipi LG&20U1 ELGUtCGI uq jsw
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bcLt = X' A9L'(V2') + - ) cO(v' '')• (J•Q)
JJJG bccucc O iJJ2 tGLW 1U1b11G2 t9t (j) pecowc:
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LGUILU2 GqJcL
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2flIiCiGhJ1fA JJJGnJ1Lcdnu1 2IJ12 G1MGGU UGI qcpgo 10 CLCqIIOL bo2Inou2 11uq 1IJG 1q OIA11LI11PfflIA
MJJU COIIUIL!G2 CJI11U?.C 11.0W IJCI C10L 10 CLcq1oL boeijTou2 01. !ACU couqiioiij A11LI11IJCC2 CJ11UC
112 qGbTcrcq in jflLC 1 H0MACL woqj bLGqc12 1P111 IJJC2C C11U2 in 21U Mifi 111JCG bj11cG oujh
g'Gcjj 11O bLGqcpjc GXCC22 LCIflLIJ2 C11U 2!U 1LCdflCU1jh CACU OAGL 2}JOLL bLoq2
bLqc111pJG LC1flW2
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11L1211J 11.0W WOAGWCU[2 in couqwoirn A11L111UCC2 EU1 11Uq J0qL1nc2 (j) oriuq 1111 CPG J11L21
112 WG11211LC ph CITLLGUj 11CCOIIUI CSUG2 12 oiijh 11POflC J 10 bcL 11UUflUF1 2 IOL AOj111fl1h
H0MGAGL 1G 2111U11L qcAr11CTOu 0 WC112flLG2 0 Ofli2TqG pouqz 11Uq LGI11CTAG MG11J1 bo2!1Jou
C0flIJ1LTG2 CPG MG11J1 2p11LC2e 01. IJJG C0Uq7110U11j A11L!11UC2 11uq COA11L!11UCC2
wq Aw Edn11CIou (J4) 2p0M2 1111 1P!2 A11L!11pU11A Wfl21 COUJQ 11.0W GICJJCL 1JJ 1122CC 211LC2 11CL022
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JLC LGlGcCGq$
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GC COtJ2fIWCL Wfl2 pnA qi qowic ooq tp qowc2ic woucA jbuccj uq oLc!u ooq
cnu.ciu onbsu o ip OLtU ooqe A' OLCIJ wouc? jo pnA ooqe OMGACL
onLbnl o powc ooq j uq GUOMWGIU2 O woucX I'{' !I4JffG PG OLTU COUflU1L LCCC!AC2
cp bqoq qçpicq 9 JJG AcoL: k = (i i.j EAGI.A bGqoq tpc powc COU2IIUJCL LCG!AG2
bLoqncou 21G o couowA 2rwb!G2nbboa ijrn ooq 9LC bLoqncGq GXoCUon2!A irgp onbn2
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LGbccflAcj? courrwcq pA qJ LcvquI o conuuA
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iu rnce woqG1 flJGLC LC LcbLc2cu1i!AG GUj2 /ALJJ qcurIcJ bLccLcucc2 Iii cp 0 MO
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woiircq ALTOn gc2e o Lcpiou2pib2 rpr LG woL ucL9J ipu tp woqcJ EOL I JJ LG0IJ
o cxbjnu ipc GwbIucj pcpsA!oL o IG xcp9uc L[G i€ji IQ wInitiou LOW LI2 woqj
pA uio-conzur.A couib!GI6 W9LICCI woq oj rnc (J yiponp pi woqcj iz oo &qicq
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2rlpaGdnGuI gurXi2 ot LG oi.ciu GXCU uc bLGwrnw p pccu qAGjobcq 11UJ GUGLfJ
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bLfwJ cdnrppuriw w 1JjflLC JJJG GXCIJUG L(G iiq !IJIGLGI L(C bLocG22G2 X0U0fl2 (0 (G
objnrnrou bLopj;w cGq pA jpc LcbLc2GuI,(rAc TUAG2(OL i ic ouc ccouq1 pc woqj 2
bLOW rpcoLcLicsJ bow( 01 A1GM (JJ2 woq 2fl1GL2 ILOW OIGL bLopJGw 2 ftGfl bL2I fIG
LCGL bLoqncrou ccouowAfI2 woqcf BGJCGLi (J) TIJtLOqrICG2 tLU2Ci1OU2 tGcpuO1OA tOL wauGA OjU2 suq bLoAqG2L1tG qGbcuq athou GXbGCtGq tflUILG ASInG2 EUGI (jp) qGLIAG2 fIG L!2J bLGWIIIW u1bHcrioua oAUCG COU2tLIUt /IJITCp TUJbJTG2 bLGcnLouI.A WOITAG tOL poqu UJOUGA iirnjqu fiG GXCjrnUG12 fJGLGtOLG UOt OLLq-aOJcTU 2AGU22OU (jp) 2rhWC2 qCLGIJ tTUI1U O fIG C2p-u-
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fIG L12r bLGwnw !AOlIjq pG GLOiii ipG bbjcoim pA HOqLCJC uq 2L!AtA (j) uq Dow0M!t uq HJC!O (jôg) wbAWOUGWLA 1Jq LG9j qi2wLpucca HG 2OM2 tpt (JIG znwbqou o wOuG(IILA uq Lc3J pIqGbGuqcucc
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= b' b\I1 = [flCs(t)\flC(j)] b\bA = [Cs(C)\C()] [v' A.\JAL' A'] (FBI)
fl2hJ Gdrrhr[10u2 (jg)) (jy uq (naY tJJG UOWTUJ GXCJIUG L(G cu cLut!AG1A G LG!AL!UGU:
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MJIGLG flC uq fl LG (JIG UIL11J(J fl1(JG2 !AifJ LG2bGC( to c uq c. LG2bGcITAGJA VCCOLU (0 (JIG
b' = flC.(I)\flc(iy (u5o)
at ooq A qjucq 2 b 12 IAGU pA:
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L(G2
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twq (PG LT2JC bLcwrnw LGCff Lpi: Lb — 2' - (E'(2') - )\D !AJJGLG E' = cxb() cuq =EUG1 (J5g) GXW1UG (JIG rwbfc(Tau2 a (JIG tOLU GXCJUG LI2JC bLcwInw rh UI!2 WOGf jO
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') uq — (j + !.jpc L1G2 z.C i.cjcq o LC CLflCL qsIutou o utcLc LC2 ccoLqiu o: — (j +
coiLq !UiGLG bLTA uq (j) nnbjX:
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ru couenwbiiou 1PCLCtOLG fl2I1J qJC qCIuou2 OL uq JJC Li!O ot t1UILC O CITLLGIU
JJJC abj CXCJJUC LC i 2niJbfA iC cou(GwboLucon2 L!O O UOUJW LC O flp2ITU1LIOU
MJJCLQ TUAC2IOL2 CUIJO1 jJIflA IU2flLG JJ bonTpjc ewc o ipc oqq pccnc WLC2 LC TucowbjCic
obboLjnuUic2 LC bLG2cur,, v qc2cLrpq pA JftJUJCL (J IJ2 LC1!OU}J!b j2o JJojq2 Hi 2CUTU2
jJJC LCJTO1J2pTb iii dniou () JJOj2 OL iiiA GCOIJOWX FU MpTCJJ UO
tOLCIIJ UOUJTIJ9J TUGLjGWbOLJ LC2 O P!WC!OU
COnUCth13 U OLGIU CrILLCUCA' BGIOM I M7fl C1I '' LCbCCITACA ip OWC2flC uq
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Juq LC2bGC(4AGjA ni bCLioq r-- j 3' i qcucq 2 1C iucLcuJboL91 UWLTUj LG O
MJJGLC cL' iuq J$ LG fIG UOWTU9J UUGLG2 LC 011 Li2JC-LGG qGb01L bAiu OUC flU1 O ,AL
= c.(,L:+J) b*\flc*Ot) b'} —
Et{ flC(kt+I) 4\flc(;) b} —
CCI CflLLGUCA i + j T2 1AGU pA:
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1UAC2IOL W9XHUISG2 ngjiA pA cpooiucouviwbiou uq UAGWGU( OAGL LnJic Miqi DfflA flUCfl0U
1IO#A fIG I0LCIU GXCpu&C 42JC bLGw!nw EU WOLG GUGL1 2CUU !IJ 1141!Cp PC
\ couçnton cc vi ui nmnCOUq11OU2 O fJ2 woqcj poq HI wncp WOLC GU6LJ 2Cf1J2 qc2cLipGq UCW
lu cou2nuJbiou HI CC COnIULA HOMCAGL fIG p2iC JU1flTOU oprucq LOW fiG n21-oLqGL
OLCIU criacucA LCtIILIJ2 2 MT!J pG G2C4G WOLG qct CJORjuqccq tG Lcpwou2JJIba SLC 2o UGUIJ tjrnt tpGA wnt poq OL qowct1c MCff 92
LG1trou2pb CLO22 9fJ 22G LGflW2 BGJOMe G2C4G tMO a%bG2 O tJJG2G GUGLJJ 1G2t2 ipG jitcur
s22nwbI!ou oj bwcn ntipi) IIUCQU2 WOLG GUGL9J izt pcu qcAcjobGq to U 2tJtG tpG
pcpv to bLoqncG tG PGPA!0L O GXCG22 LGU1W2 IAGU pA LJJG qt HOMGAGLe to LGjX tpc
2ncp bniwcuc tG2t2 LG fl2Gj1J OL rTuqcLawuq1J jiOM bwcnjL ritq1A nuctiou wn21
AGL21OU 12 GL0 CUUO[ pG LGlGCtGq
1AGL2!OU bLrwctcL 12 G2t1UJC dnItG ruJbLccT2cjA o tp tpc pThotpc2r2 tpt ipc bILWCtGL O 42J1
OAGL-iqGUtTArU LG2[LICtIOU2 O tJJG woqcj LG UOt LG1GCiGq OL 2OWG flJ2tLflUJGlJt2 tjiG LG!t!AG L12jC
tpc LTpqA o tpc bLcqcwpjc Lcriwa to tjiG L!21c bLcwTrIw woqç jpqc qLj( iJq2 tjrnt
AJL!JPffltA o pc bLGqTcwpc GXCG22 LGtJ1UJ2 JLG WO(IUL2 O LI2JC gAGL2!OU LG LCdnTLGq tO LGCOUCG
GUCLJJA !U L9UG O J O Ø OL W02t 2Gt2 O( tU2tLflUJGUWJ A9LTpjc2 V2 2flC2tG pA qJC JLG
.GIt!!G LT2JC AGL2!O11 U!!!tA HG trurntc ijic b9LU.JGtGL O L12jC 1AGI2TOU to p drntc jLG
A4LfC (Jg) tC2i2 rpG UiGLtGUJbOLSj LG2tL!C1!OU2 N4tji COU2flUJbtIOU OL COLI2RWGL M!tIJ COU2LLJt
uq tjiG WtGLG2t LtG2 iii (J) 2n. 2j2 pt tG2i1U iPG2G LGJtiOU2jJib2 LG iflJtflL1 JL2t 2tGb2
jJJG GUGLfltA o tpc mtci.tcwboL1 L€jt!ou2jJ!b2 GtMGGU ipG WJLUJ L(G2 O 2flp21flt!OU
GXCGG2 tjiG AL!UCG Oj tpc cxbcctGq LWO O UWthU9J LLG2 O 2npat!trItTOu qOUG.
2flp2tItfTtIOU TU COU2flWbtiOIJ uq tJJG GXbGCtJtTOIJ Oj tJJ2 LjTO JJJC M1L1UCC Oj tIJ!2 IJGLGUCC
JU OtJJGL MOL2 tpc U2JC bLcwinw 12 tjiG GLGUCG PGtMGGU tjiG utio o GxbGctGq WfL!LJj LtG2 O
- > AL{E'(tD '\O)}• (I?)(jy tpc LG2fljt A2 tjJt: ML(th') > ML(E:V2s+Y) OL
2t+1 (E2t1 - 2t)\t fl2JJ tJJC GXbLG22!0112 OL iJIG 2bOt L1G p1 (j) uq tpc ot.i.q L[G pi
J 2JJOMGq tjJt A9L(L&) 12 LGtGL tjiU j\9L('2) MJJGLG 1J — - ($2+X - ') uqJJJG2G LGpJIT0U2JJ!b2 wA IJOM pc attcq p1 t}JG tOLUJ O JJG JUJ LG2ITJ[ I{CC9II 1jJt JJG
20J1ltIOU OL tpc eboj L(G TU (jj)
2OjAC OL tPG OLML LJ(G fT21U LJJG 2bGC!IJC OLW O IjJC flC92 woqGj LGdflLG2 oujA 2flp2i1tflLjU tpG
4OtG tjrnr 1)JG LCftOIJ2pb PGtMGGU fIG OLML LJjG uq 2b01 LtG ru (j) i dnrtG GUCLj 10
= !�' \ = 2' E'(.')\E'(O'') (iii)
ju OGL MOL2 pc E(xA) = E(X)E(A) + coA(xeA) tOL su? uq K
vqjL uq DflW (J) cou2iqGL ncp su cxcurou OL p€ iu ipn. ibbcuqpr
iuq fl2!U pc qcwou ot ii cdng!ou (J)flc()(J\b)f) = (ff(+I) (i\'') i�t1) pop iqc p? qi jG-jrnuq qc XbLC22!OU
rpc !uLccwboL9-J ptj OLGL couqou OL u ct iiiqi iu? uowiuj bAo
couqou9J COALIUCC
u counwbou ipcA wnai wo, u bLobor.jou 10 ccJJ O1GL icCOLqU £0 £JJ LtTO2 O 1PG2
ucc ictnwe qGbGuq nbou pca couq ouai C0ALIIJCC2 iiitp qic WLTWfJ L1€ o 2flP1!UU10U
= [coAt(ff1 Dy+)\coAQczif+I)] t(+J) (j.)2WCG (j ) pojq tOL ,uA 22cg1 w urnA enpii orij L12!c-tLcc LC ip iuA ZC1 10 Gt:
= -co'(i'Y') I�' (ri)LGMLI€U
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N4JGLG GL — - ! ipc GXCG22 LGIflLIJ OU 22G1 1 OAGL qiG 42JC LC LG 2WCG £G
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2wjG qowc2pc ooq C1 jrponp jpi2 WGMOLJ( conjq G woqijq lo iucjnqc cowbo21G ooq
L022 LG o LG(IILIJ ou ru? S22G1 \ LG9psGq pwc t+y EOL uo/i Miff 1LG couenwbliou
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1° f1UCL2WU 1G p2IC WIlTijiOU pjiniq J12 iG21 UOIG L}MJ1 fiG tTL2r OLqGL couq1ou O
O!PP0U2 uq LCL2OU (io)
(j) uq ii qGAcJobcq 1uqcbcuqGuqX OL bbjjcgiou u "qq CVEJf GUAILOUWGU pX
JJJG j1C1i1 A1LpG G21 bToucGLcq Hi OLG1IJ GXCpJU?JG 2UIqIC2 pA HUU suq OqLIC
I •• rcnutAsL1pJc WOGj2 1Jq Huu-u1pu ponuq2.
1pc LC2LICTOU2 9LG $0 LC1GC1
ot LGUIW2 uq pojqn bcLToq rp 2nqA onuq tp qic 20LL pc poqu bcLIoq qi UIOLC cqXJJG ilJCjfl2iOU O GLW 2LflC1flLG LfGL pu Gdf1A LGU1LU2 coU2qGLIJ UflWpL O C0WP!UfoU2onuq pc LclccIiou 01 A9LiptG L2L4ci!ou2 2 22UAG oujA o ipc poqu bcuoq uotICUJJ 21LnCnL 2 MGJJ 2 qJG 1OLGIU CXCJJ9UG W9L1CGI fGM! (moo)2nLAAcq rJJI2 I1LflLC uqio pc LGlGCtCq Cwbpc uq cjq (j) fl2q LJJLCG wouip LCWLU2 CL0 tJG EIILOCrILLGUCA(j) GXwucq iiqA LCUILU2 uq ncq LGUIW2 ILOW pc ocjc wLJcci uqns rpG Lc21L1c0u2cuq 2L!A (jg) cxbwqGq ipG 21wbjG bcuoq iJq LGGc1Gq LJJG WOqGj Q!OAUUW! wq 101 40UCLO22 21X CflLLGUCTG2 LG1cq1IJ fl112 LG2ILICITOU M!tP UJL!1JI 2TII!T1CJUCG jGAGj2 UGL 2c 04C7C
J-p1J2GU uq OqLCJc (xo8) 1C21G IJJG2G LG2IL!C110U2 11211J UJ0U1iJJ? GXCG22 1OLG1J LGUILIJ2
bctiou2 IOL Ipc AJqA ot GUGL9J cdnpqnw bqc1u woq
LGp1qOu2pb PGIMGGU LGIflLIJ2 JJJGLGOLG lpc 1GLJ1 ALTP!G bbc 100 GUGLJ O qL!A IIA
Gdnpqnw bLicwg LGjjTou2pib pnt i conjq po pc qn to iuX woqj tpt 2flG2t2 bLoboLtou9J
cowo,wcut pGJb cxbjnu LGWLU2 y iu SCtOL LU0Gj corqq pG fJG LG2IIII ol GUGL9j
f2 CPLSC1GL11TOU O tpc pGp9A!OL 01 CXCG22 LGIflLU2 JJJT2 JT1GLU1LG 2JJ0M2 1p1 2OWG 1IC10L2 01.
JJJG W11J COUtLTpIItTOU O 1J112 1T1GL1flLG tG2 IJ OL j1GU1 AL!PjG LGjiT0U2p!b2 2GGW2 tO PG
bbcL2 tO Ut tpc qw pGUGL
jjicA uq ijwt uc ctoi woqcj wbcq pA (J30) e LGGciGq jiponp i vio 1CtOL woq€
1U1OLtTOU lu yg ot toLG1u GXCUG uq Gdru(.A LGUIW2 ro tct ip jtut /L!pJG LG2IL!C1!0U2
BG!GL1 9uq HOqLICJC (io) UqLGCtA COU2qGL tpa bonip A pA nm tG UG 21Gb
MIJGIPGL ZJ2 tcuqcucA U01 10 LG1GCt OAGL jOUGL OLS0U 2 Wt1GL 01 IOM boMcL
ibbGL to woic iii bLobowou ouiA OAGL jOUGL J0jqW bcLioq2 HOMGAGL £pc dnciou LGUJUJ2
01 LG1GCflOU UJ pG J1GUt ASLIP!G ft r! (iooi) III jpc L(!02 01 C0AUUCG2 iu (io)
snzrpn.A a2nwbtiou tp coLwucc woi ii, bLobor4iou jo cp OI4JGL C0UtG1U qtp ipc biuGw
cnwpA (jgge iooo) uq jcr (JJ) dnGztiou MGJGL LcGctiou2 cowc ILOW fpG
dntGLJA LGjflL1J2 pm LG 21L0UA LGGCtGq IOL pp tLCdnCU qwe 2ricp f 2
LC21LICt0II2 UJbGq pA LGI1L1J2 W0A!1J bLobo1.tou SLG U0r LG}GCIGq IOL oM LGdncucrG2 2IICJJ 2
1G Lf 102 01 C0AL!IJCG2 Ti3 (J) LG C0U21U1 QGUGLJA 2tnqG2 uq 1}Jt IJJC oAGL-1qcu1Au
2rtp2tItfltIOU iu cou2nWbtIou WOAG Hi bLoboLjjou CL022 22Gt2 OAGL 1!WG flUGL 1P!2 f22flWbtT0U
LC2GLCGL2 221TUJG t}J1 111€ c0uqT11ou9J COA9L113CG2 PGIMGGIJ LGIILIJ2 iiq 111€ WL1UJ L1G 01
P' 0LGL to iG2j tpT2 LG2ILICtIOIJ1 HUGU uq HoqLcJc (Jg-) s 92 w9uA 2np2GdnGuI
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(ioo) ciuurc ipi2 L!2C AGL2!OU COGIjCCUt Wf121 pG OAGL
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ccnjcq [pG L1[TO oj [G (o)\E(o) OL U GXjGU2TOU O tpc fflC2 (J5) uioqcj [0 G ØJ
[pGA uq jrnj ip poriuq LG iii pG icuA O Q [0 H0MCLe eic.i (Jo4)LGUILIJ2 hOL cowpuqou o cdrn[A uq 0LG!U cxcjnwc LGIflLU2 TIJ [JiG fl ITbUa uq
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> E.1 E(GL')1 (J•4)OL
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MJJCLG j2 [JiG AL9UCG 0 CL'' (MJJCIJ CL !2 ACC[0L E P [JIG AL!IJCC-C0A9L1UCC W[LiX) wq MJIGLC
9 = Z.1 [E(O' CL'') - E(O'') E(GL'')] = - E- E(O'') E(GL'') (jj)MJIGLC C 12 [JIG bLolccuou GLLOL JJJGU pA or'2 pC bsLgwc[CL AGC[OL 9 C1J pG [Gt1
cY' = 9° + L' + C' (r4o)OU CL'1
2nbbo2C jpj [JIG IU[GL[GWbOL9T WLIIJ1 L[C 0 2np2[1[t1[1ou CJU pG 12 I JTUGIL bLoICc[iou
E(Y' GL') = (vi)ExbGc!ou2 uq 2np2nw11J ipc 2nbGL2cubr \:
2CC JIOM [JJ12 LG19[0U2JJ1b p qCL1AGq coueIqcL HU Cdns[iou (j) fl21U [jiG r'm o I[CL[G
ponuq OU [JIG AoJ[1JT[A °1 [JIG !u[cLiCwboLg'I W1LWJJ L[C 01 2flp2[1[n 0u rn cou2nwb[1ou ' j0jJIG (H-i) ponuq 112C cowpu[10u2 01 GXCC22 LG[JILU2 o bLoAtqc
rwbJ1c[rou2 IOL [JIG 10LGiU GXCJiUG LT2JC bLcwlnur
oL1WffA bbflCq [0 fl2 j-rfj L[G 2111CC [jiGp2!C 1LWCM0LJC pOjq2 OL LG[flL1J2 ! CjGLJA 1fl12
ot suA OUG woq Ji2 p€u bLoAiqGq lii [JIG b1oucGLw MOLJ( o HU2GU uq upiu (jj)
V fl2Gjflj M9A [0 cowb1LG [JIG Aiqp[A 01 bLcqTc[ipJG CXCC2Z LC[flLlJ2 M
LGCGU 2flLAC? 2GG q20U (J
xcjrnuc LjG 2GL!62 2 LJJG Gquc2qA LLG LGboLcq p1 LpG JGqcLJ I�G2GL! PrIIJCnUJJJC IUiCLAC1UTOU 2G14G2 MS2 2nbbJq pA tpc JGGLJ G2GLAG p0Lq o Q0ALIJ0L2 uq rp
uJouGrn.A bopcA 1LGUU iii QLWUA 9uq OLJJCL COrIUrL!G2
P!1 L-Bffl2 obu-uiL!cG obGLjTouz' jp12 2rcLIpi1ou bLocqnL 12 CLL1 otu qJLOflp
CGC2 nbou pc woucA 2nbb!A j9 i gpcA iionjq oac qccpuc !U ipc wouGA 2nbbjA pA
jpc qojjL bnLcp2c hOL q.112 LG2OU tpGA iionjq pcu nuqcrjcc ccouq 2Gb o II21CLJTCI, LJJ
10oJc uo flLJCL ciiou ipcu f pp-boMGLGq wouA 2nbbJA Monjq qccpu pA pG jwonui o
hP pcA tikozljq pnA qoje uq aJ Au LG2€LAG2 ff3 iG 1OLG!1J GXCjiUC WJLj( 11 luG fl[pOL!G2
couqric OffL bnLcp2!u obGLi1ou2 jpcac obGLiou2 cu p nuqcL2ooq uio 21Gb bLocGqnLc
rpr tpc fl npoL!1!c2 iionjq jij jo 2nbboLj 1G Jru21 1G AGLr ju flhT2 cc ipcA onjq
Lc2GLCpGL2 hOL 1P!2 bntho2 COU2IqGL rThICJ oicu cxcpuc ucuc1u!ou obGLsciow 2nbbo2c
!uJbo1U O JL2t flUGL21U MpA jpc cjucn o UIGLAGUOU bb,L2 20 bn1iu o
BGtOLG qcwpu po# uzc bLcw!nw cu bwiiqc L1OUJG 0L ii UIIOUe !1 !2
IJJG GXCUG L1G OUG Gxbju1!ou qGb€uq2 nbou 1G bLG2GUcG o 42jC bLGwrnur
OpArOfl2 C JGq LC2GLCGL2 jo 2GLC)J IOL LG2OU2 MpA 1J1GLAGUOU wrA G GGc1!AG p1 CJJJ1JU
cwbiucj LG2cLCp31 J4GAGLGjG22 !1 12 CjGL LJJ1 CG1J1Lj PIJtCGL2 COUITUJIG 10 IJICLAGUG JjJ!2
NJJG1IJGL 1G2G U[GLAGIJlTOU2 sGcr IJJG GXCUG LG OL U01 LGUJH1J2 U 122flG 01 C11AG
uq GJLjA Jôjic uq pJ jg ipqc qojJL brrLcp2c2 toojc bjcc MGU TG OflL MS2 MGlCCL 2flCJi 2 p1 TÔ
JUIGLACIJI!0U2 10 2CJJ 0L2 bbcLGq to tjc€ bIcG !I4JGU IJJG qOIIL M2 LGJT11AGJA 21L0U 2flCJJ 2 113
pu!ce MGLG GJu woi.c 9C1!AG!A JAOJAG tu uuGLAcuiTou qnpi 1P!2 bGuoq ffonpJA 2bGJqu
'OIPGL Wl•0L CGULLj UC2 2flCp 2 JJG flUJC 01 JbIJ SUq 1G rluqG2puJe IPG QGUJU CGIILL9j
T13IGLAGUI!OU M2 nuqcL JcGu OIJJGL bcLioqa 2f1C jgg MCLG wLjccq pA cdncut wrcucutiow
GXCUG LS1G2 LGabGct!AGIA yjiqc 1p fl iut 1pLonp bGLToq2 2ncp 2 p1 pcp U0
EIRLG2 qcbicr IU[GLAGU(IOU pA IJJG fl fltIJ0Lit!G2 qsTLp1 JÔ8 t° JôôO 1U21 1G DV{\Z uq i\z
GxcpIuc p1ICLAGuIT0U pA CGUILSJ psuccL2 jO flfl21LiG 2OWG LGCGUI 10LG1U GXCUG C1A!1A
JJJG t0LGT1 GXCJUG L12JC bLcwrnw Jrn2 j20 pccU neq to GXbpTnJ tG bobr1jJLTtA °1 1OLG!1J
uq }jCJJGI2U (jy wou OJJCL2 EOL qacntou c LU2OU uq CUGL2OU (Jjpc bo.qopo pjucc bbLocp M92 qcAGJobGq pA KOfiL! (JQ) BLUOU (juq
O 1JJ!2 flGLflL 2GG cp9bIGI. pA hLUICG! uq J�02C (1aa2) !U ornw1JJ9 1flLC woucA /ATJJ cirnuc wqncni U mJw6qc LC2bOU2C Iii cxcpuc Lrc2 OLJJJLGtOLC GAGtJ iJJOnp cnLLcu woucA 2flbbjj2 LC UOj 9JICLCq tJJLOfl T1UCLACIJUOU 1LL2 PCITCIC2flG22 tjrnt cni.Lcuc 2IcLflscq u ucuuou T2 coLLGq Mtp riru.c cpiuc lu qic wouch 2rlbbjX
tc cxbJcwwoU 12 G oLX' jpi u..ucnjcq pA fl? (ioi)
pc cxbccgcq Gxcc Lcgnw ou oLcu pouq wng UCLG2c
buA,gc 2GCjOL mIJJ pe poqiu LC!t1AG1A WOLG OLG!U pouq iiq J22 0flL p0Vq2 JJJCLCOLG
4OM 2nbbO2c CGUL9J piujccI2 iutcucuc pA bnLcp92ni qojjL2 P.' gpl2 CI2G x' MIII TUCL2C 2TIJCC gJJC
- + E'V2'' = X' AL(V2) - coA(V2I.) (•)cdnfflpL!nw woqc qc2cLIpcq U 2Ct0U J J'ccff pr J2 LGUILU ii2 MLIUCU 2:
L(TAC bL! 0 P0'F coUaqGL rp!2 LGJt!Ac cxbcCGq LC O LCUILIJ !IJ fIG C0UCX1 0 fIGbLufJJJG 2jLGUJJ Oj gji CIJIJGJ LGLGOLG qGbGUq2 nbou po wncp U LAGU1U qGci2 gpc
POLG fIG UflCIAGUjIOU
20 p0i fIGAJflG 0 i.'q LG 0 LCUIW ou OflL pouq t uoii pipcL LGI1JAG o Acu pouq gpu
bLcAiorI2 LGJ11AC L[G 0 LCgIILU o3 M9A go ggu rp cdnflpL1nw OL gpc qoj go bbLcc!gc
1IJ[GLAGU[101J CLG[C2 u GCC22 2flbbjA 01 Acu pouq uq u GXCG22 qcwuq oL OflSLpouq [ [PG
qcuownrnglou 01 !r boi.qopo rpc LGjiAG LG[nw ou gjJGG ZGg wng cpuc 2bcc!c9'JJA ipe
pqj uq WOLG Acu iugGLc2g-pcLiu 22Gj2 flUJG22 gpc bL!AsgG 2GC[OL 12 1UTGLCUt io pc CflLLGUcA
TjGL tpc gcLipcq wgcucu ou qcacqpcq 9poAce gp bLTAuc 2GC[OL 12 jG[ pojqn.' fG22 fl2 1-
uog ccgcq rWqGL 2[Gl4flG GLAGUfOU !1 2 LnQq1 prig LGj[AG 2flbbj!G2 O IJ[GLG2i-pGL!1J 22G[2
jjic boi.goo pucc cxbjiiwou i 2[L}JqOLMLq3 i !2 [LflG gp ujoucA 2nbbpc2 LG
bLobo2cq u2MGL: gpc boi.qopo pucc,, 1LOfl LT2C bLcwinw
GcgGq JGLGOLG 0M cu gpc rugGL!cu[iou bLocc borpjA qccg gpc cxcpuc L[c JJIG
WOUIG2 HOdL [G ccouq 2gGb ot 2gcLrpsg1ou Iwbpc2 qrng gpc u.'oucA 2rIbbpG2 LG IJOi
woucA 2nbbJA jcq go u ibbLGc1ig1ou Ti.' [Gqop 2UICG JIG cxcpruc L[G 2 fIG Lcjgyc bLTcG 01
pc cxcrnuc L[G owcug1ou9J qcwiuq uq 2rlbbjA wrnou 2flG2[2 qccpuc lii rpc fl2
Jj112 egGLrpTg1ou bL9cgIcc bLoqrlcG2 cpjjcuc IOL cxbinuiu OM 1u[GLAGUfOU ciu IGC[
pucc woqcj jj pojqUOi WCLC2C 2f1C1CUqA 20 LJJ JJG CflUCU 2b0 LG TUCLG2C2 WG p21C fLr1CWCU1 O }IC boLqoo
Jp nnwbou 2UOUCL Ipu uccqcq v ou pc cxbCcq jJUflLC Cxcpfu LG 0C2
LCjfl!0U2p!b 2CC BLU20U uq CUCL2OU (jgqLCcqX 2111CC flJC2C 2LC2 LC WC211LC U flUt2 0 qOWC2C C(ILLCUCA LOL WOLC 011
u qJ crnici 2boI L1G CJLJ j20 O112C WC JCLGS2C U OLCIJ pouq boLitoflo 2LC2
uq Ei.uJcc1 (j) ic 2nucA q 2 WG2flLC O CIbGCi!0U2 2 2 !1UCLACUIOU 2
LGjU pouq 2nbbHc2 o IJJG2JTLC o pc OLG!1J CXcpU LC bLcw!nw HOMCAGLe DOW UflGT
pcu qic tOCfl2 o jJJC 2Iflqk V2 qccupcq IpCLC WCLflLC J2 pCCU 2nWU31LUA nuencccntnj P1
0 JJC 2!C P1LGW0U1 cyjJ/4 COu2IqCLGq U 2CC0U J CAGU flJ0rIp !IUCLAGIU!OU UJA uo
2U11C2 fl2C2 (pG LC2(LTC(10112 (0 GXUI1UC IjITZ LCj10U2pTb C!GLIA (p12 2C( flJCJnG2 fl 2(flC2
2nWcICu(IA WGJ2L1C IIJ(GLAGIJ(10U morijq GCL GXbGCGq LCJ L(C2 o LG(flLU y €couq 2GL o
LC2(LIC(10U2 iii ( ooi (J4) wq f42 (jgr) uq uo G/TqCucG rp poiiq qGW1Jq2 LC
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01 C0HuILA 2IOCJC piqcxc uq GXCUG L1G2 11.0W fIG IOU 13UU1 3jU2 OACL fiG bGuoq 11.0W
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