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Page 1: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

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13 iii A3or12

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l3woI fl1V3if{3E lo 1203 '1B1oqm3l 3rD 2b333x3 bnsrn3b '3nom b3iiolib lo 212o3 13rliE31 .noiisflni

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rioilBIIni lo 31131 3rD iI 3213313r11 ris noiisflni iol b3i2ulbB Ion 2i noilJsi33lq3b 3au13)38

Jn3mqiup3 b3vil-tIorl2 bris 23noin3vni flu ln3rn)23vni 21OV51

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1o noiliaoqmo3 3(11 2llolaib 2ni5g 11311q133 lisnirnon lo bns 123131f1i Isniirriori lo noilf3xl3l 3f{T

.2oiloThoq blorl32uorl

b3rlaiIdsi23 n33d 213(1 noilsflni 10 \li1ils1ov briE 13v31 3rD n33w13d noitsI3l 3rD r1uorll1A 3rD 3113 lull noil13flnilo 213v31 wol 3(1115 23ilqqs 21(1111 15313 Ion 2! ii e23!bUl21o l3drnuJn r ni

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Page 9: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

iii inJ d bluow n&li ivi oi oI iuqiuo irii iiup1 'm bn noilEflni iom ol bEI J3m

.33nq 3IdEi2 lo ioiir1 i diiw 'mono fIE

!fli3nEnil niAIfn no'ni iol 3fliflVfIO3 1ds1bi2no3 i oth3 i bv1 nq 1dEi A

Ldtho1mo3 iv d m iirnono Iir1W .n3rnq bn qi3i iutu1 v!ovrii i1i noi2iDb

fnii iIu3fllib v&J Iqoq 'nim 4nuornL Isi ol li3nimon 8ftii1Vno3 lo oiq rIi ritiw

IEnoiiu1i1ni biE3iiidqo nom nv3 .3i iini1o ii Isi n±1o ii iuodI3 gniAnirli

Il3nimon ru b3tsia niuti iu1u1 lo noiiroiq Iinup5i1 wod !dBA1Em31 i ii ioiavni

.noiiif1ni lo iI31 1ni&I1ib 13V diiw 2boi-1q ivo ni1qx ial3q no bI3d bnE Ern1i

rno dguodi nv noiflifini ni3ub1 lo 2titn3d oc{i lo !1u3 iBuIEv 01 iqm3flE ion Iliw I

noiiEIumu33E !Eflqf3 b1or1auor1 lo aoiq di ni inmvo1qmi dt s 213 3cJ im rnHt lo

in1q ni) 1!Eiinsi2du2 1iinEup I 1Ii 2iflnd1o ie b3i3i1i1 r1T .iusm ob I ii3di

lo iE1 wol rrioil 'ii1idEi2 i1q ot niflg lo 1203 3d1 (31E1 Inuo32ib Idi2u13Iq i uLEv

.noifl$flfli

Hi iiJ noi2uI3no3 3r11 ot noiiE!u3I1 2id1 rrioi! o ot 1v3wod gnoiw d bluow II

o2li3 113 ir1i i&Li 'iiIidioq rIi grui1bi2no3 tuodhiw m1bw 1ri aiini noifl3fIrli ni ruoiiaubi

-iimiiq rIT .ii1id13t2 iiq niv13r1 rusril ifIiB1 noib13fIni lo bE1 wol niunuinoo lo 23f3in13vbB

Jnrrmivo r!i iIi 1310irIi2 rIi 21 iutiruii1 db lu b1uiinbi nd 213d 113f11 nOihl3flni moiI nii

iol bn r1i 23ub1 unvi giioni 2ifIT .noiiE1o riom lo isi idgir1 r1i molt oin bluow xEt doua r1i 22o1 idiwbsb ,rIi i13nirnuI 1o131di bn13 xui \1J3nothoi2ib l3fIbo

b131 di rhiw '12vni imv idb I13noii13n db nioivi lo 1o3 Iso-u r{i noiiibbB nI .1i131r13

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Page 10: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

d 111w ii noitiffini owi í1i gniunuino3 lo E1nEvbE r1i 1o uthv r1T £ .noiiflni

2 bns noii32 ill '1ii3i1qx3 biE1u3IE3

ninismi 3H1 ni bu3ib 3Th r&D agnsrb m1bw 3di1o !1 immmu I !dT

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in3l ni iiui blinU r1l ol t1E bq i1qqJ3 2i1EnE lnnu3 r1T .1ui x131 rIi iu 11w E

.mii bru 2&linuo3 irbo ol olds3iIqqE '1ib 21 2i1EnE1o bof1irn 3rli lud

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bluow 1i1idEl2 iiq oi inmlimmo 2uouidm&1u nh ridi bugrn d rm ii r1uodi1A

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iu virbs ol 1nimu2ni i iiIiunq 1iuiiritoq 8no112 riliw rloiiEgildo IEuJD11no3 i3 io noiiEflni wol

muiidi1iup rI1 uE3d i'n idb1o 1203 in lii ,rIi 23Ubl iEl noilEfini rr1if1 A nrI1 i muimlq noiiEflni 3111 md noilsflni riliw inioq idi lnioq 1i 31131 bnod 1n3mm3vo

noiiiuflni rliiw inioq io1 mnioq flEsh a1 aii 31o1313r11 ii 1i1ni liunicnon 13n 3rIT .xiui ol 133 1du2

.23nu133b 3iJi 13n bi r1i bilE

ni noiiiuflni b 23inEvbE IEurn3moq 3111 no 3luliul3lil 1133u131o3r11 1n331 13 o2113 i 313c{T 213)hlum 3viiii3qrno3 '11h3qmi flu noitsuooIIE 331U0231 21oiqmi 113111 Im gni3ubni

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Page 11: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

I IdiT

noi1iflnI ninJb95t to iTh1 ui1I9W 1I'1 iiIT ot £ moit

(qUa to 1n19q nBdD)

a113 1EoT 111 i1IW lo b113 131iU fmfD 10 nuo ru1 uriv5I lo noi1ioiG b3ub51

.i=c .i=1c .o=c noi1qmuno

Q.0 —

01.0 — £0.1 t.O = nimiT 0.O - .O 8V.O

— 1.O

— V.O 0 =

4ô. I Q. I O.O O.O I$. 1 :0.1 =

I.O 01.0 gniauoH bn&nU

VI.0 —

0.0 —

Q1.0— O.0— 0.O rioM bn13mU

8E.O— 01.0— 8E.O— 01.0— --AM-- i'n1d3U

10.1 1.0 — U.0 — II.! 4.0 = .r IkioT ô.0 OQO

— 0

— 8.0 :0 =

4.1 8.1 80.0 0.0 .I :0.1 =

IdE3i1qqs3 oV1 :AM

rIT .m s iB J(fl di ni ii B 01 2bnoqrIo3 1rn noilBflni in3q A *

.m1bw iii gnEf13 Isunru3 1E 31f btioqi i311 ii1!w

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Page 12: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

Io3 3111 XIf1i 3U2E io1id1 Iliw I 13qiq ir1fIo oçiuq d1 ioI .noill$flniTlo noii3ub5I 2231n!Eq

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d b33ub31 n13d 21 noilERni 11311w boil3q f1 gnuiub uo b ao1 3v11131umu3 3111 213 noiiEflni2ib

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-3110 13 21111 013 ol 1r13313q owl mo-il rIoiIi3flrIi 8r113ub3-r lisril 2311qm1 2irlT •'IQDlo irin3q 3311!)

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Page 13: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

noitqmuno to noitwollA I1r1oqm9hInI dt bnR noitsflnl

io) inoqio r1i IA 'tmm ni 01 nhIJ11 xl3Ilo In 1i 3fD 3UbL noifl3flnl

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anig 1s1iq 1&iimon no biv1 axiI bvI LEubivibni dI IA .1Iiq3 'Iiup bilE Id3b ioI 'q 01

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1E1Iw 13 aiii nivpa ii,dli no ms IEubivibni I1I muii o 1ii d1 ni noi13ub1 A

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fnIx3 3r11 1iIidsia iiq ai 13rIi n3rlw nv noiliolaib ff3ua i13 wsl XEI 3db 33n12 .am .aoI Idi3wbi3b baB13ai i3blo-Ialfl i3 aaus noilEflni d baui notholaib

aI!uai I11 aaol iHgi3wbib 3db (8VQ I ni3tabbI) l3qEq iihi ilE al b3siasrlqm3 I aA

bilE noitqmuano3 10 nimiI 3111 ni noitiolaib gni11uai 311) no abn3q3b a3xEI 3mo3ni 1131iq133 moil

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Page 14: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

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is noiiqmuno3 nmiii asfl31JJq ot (gnuo nr1w) -Iuiibn3qx rh as bo 1rIuoi11 d n&,

•T(1+l)zzr qbo

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noilqmuno3 inmiili ml bnsrnb bisnqrnoo 'li3ubivibni rl1 wod2 I -iui'I .noilqmueno3

m noiib gniv Isdi rnii rh is noiiqmuno3 inrniiii bo i1q rli bo noilonifi s as

(q)

noiiqmuno inomii151 :1 iugi1

bo jq ifI3ffI5Lii35I

noilqrnu2noD

noiiqmunoD 1nrn31ii5I

(D - I) (1q - q) .O + (D - 1D) (0q - 1q) = JWU £ (1q - q) - (D - ) (0q - 1q) = V351 t

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Page 15: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

rI1 bnJ3 0q lo i1q J3 iIqmi niifli lo lsi Iioi di xsl bru noiisflni fitod lo 33rIds 3r11 nI

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3(11 a nwork o1 1di3wbE3b 3111 iuni oh lEubivibili 3(11 23211133 noilqrriu2no3 bn3m31i1i lo 33fl

ni ii dt iol b1Jn3qmo3 3d oh 3vs11 bluow Isubivibni d1 113r11 inuornl3 3111 .3.1 A is b3bsrI2

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lo 31131 3(11 fli2iE51 .A im di oh Ii3up3 bnuomE rrn d tn3mn13vo 3111 'd b313311o3 311fl3V31

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U + D sns 1sbiosqisii c1h 'd 21313f1i won o1 hdgi3wbs3b r1T D oh noibqmu2no3 1n3m31i131

.(— J)(1q —sq) .O+(1D— 1D)(0q —1q)=

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.31Jn3V31 xEl (Ii 23f1&13

ix\11 V\T I . + ( 3

— ) (0q

— 1q) ci noitiobeib !Eloqm3tl3hrIi b33ub31 moll f1i13 315113w lEunnE 311T

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Page 16: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

1n3m31i11 111 3nI3c13 dT (.D —

J ) [(q —cq) .O + (0q q)] = ( 3 —

) ( q —sq) .O

(cq —

1q) (qb\Db) = — biirnixoiqqi 3d n fIoi1qfflUflo3

b3iEn3qmo3 3th i 0> q3 31dw [q \(q —

1q)] q3 D cq \(çq —

1q) (qb\Db) ( CJ \q)

IBilini bndo 3r11 fl biEu1v3 ) 33fl 01 1o3q9I riliw noiiqrr1uno3 1n3mIi131 lo iii1i13

:i noiliolaib IEloqrn3il3fni bub31 mofi nig 3r11 2urIT .(1n3313q owiIo 31131 noiiI3fIni

q\(çq —1q)] q)3 [(1q —sq) .O+(0q —1q) =0 (1)

q \(q —

1q)] q3 D q[ q\( 1q —sq) .0 + q\(0q —

1q)] =

0 ( 0q = 1q) ois ai 31131 floilEfini 3r11 nr1w noitioiib b3oubni x13i on w ii{1 Ii 111 31014

moil n13rk 33fl s lo o1 1r1i3wb3b 3111 ioI E1urmo1 3Ignshl IBnoi1ibsd 3111 ol 1i1qmi blijow

oi 1q

1i3i1aE13 b31rI3qmo3 3r11 113111 3lon buiinm 31d13v-I3do oIl noili3up3 mofi vofn oT

1ian3qo1q 3r11 bnB q)fi 1i3i1asb b31in3qrno3nu nibnoqarIo3 odito irrI3i lii n3fliiw 3d n 31110301 uon3goxo b luo 3V13 ol

+ = 3 () 1o '1i3i11313 3111 1)q = 'd b3113131 m noirqmuno3 1n3m31i131 briE gniv oni 13vo31oM

3111 01 133q31 riliw fl1VS2 b 1i3ii13!3 3111 bris 33fl 1i 01 1qi 1111w noi1qmuno3 1n3m31i131

o1 Icl8i3wbls3b owl 3rlllo E3 3111 r133w13d 33n31311ib 3111 is b31s1 3d bhioD aiflT 13 1rI331q 313ff b32u noi31qx3 3111 kid q bns 1q 33fl 01 gnibnoq311o3 31gfu3i11

.noilsfrlixolqqs

('b\Db) 1) —

qo){qb\Db} = qbVJb :noi1ioqmo33b '1a1u1 1suii 3111 mo-il wo11o1 irlT81

2U0fI30X3 111 313313fII 1113 d b33ubni noilqrnu2003 1n3m31i131 01 3E313f1i 3111 i 'b\Db 31311W

b13i z = b\2b = bV)qb = (bVJb)q IsfIl ni1on bnis D\q d ff13111353 niIqi11uM .311103111

.() noi1sup

1 I OO\I.lnI

Page 17: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

wriT .1 — qIT = qI1 d bis1i m noilqmuwo3 ifl3ffl31Ii11O 3i1q

.1D+ qJ1 qD3 (E)

bnj3

(D qI1 I) [q\(1q —q)][q\(.q —sq) .O+ q\(0q —1q)] =0 () .I3(3 li1 r!i1o si hs rli is 1subivibni1o nivs oig rii D 5IflW

is rloiiqmuwo3 iuiuI 1o iiq rIi 1o ismii Is3i1mun 1iupi I noiisup isuIsv oT

gnivs di 1o nivs oi lo isrriii s ILw s xsi 'ns iuorliiw bris isi noiisflni 1niThb

.rnooni wonox lo iiio vi3 ol iinqoIq rlt lo bns ii3iiasI

O\O'I \iV\o I. I . nwbd II3\rIini mii r1i muas I noiJqmuwo3 tnmiiii lo iiq di isIu3Is3 oT

ÔQQ I isindI s is sivs no vs Isubivibni th ;u O i noiiqmuwo3 bns nivs

xsl r{i no bnqb ilo u!sv r1i irIw ot-(i+I) = q urIT .OV gs is vsib rirIi bns

..U rIi ni fsiiqs3 oi niuii Ist xsi5zq rli IQI fIuo1fIi OMI moil .noiisflni 10 isi rIi bns

bns 2biI muitdi1iup3 1sin gniionI .iriiq Q bsivs io1 isioq1o3 Isi3nsnilrlon

lo 33rIds r1I ni lisviq bluow fl3rIi is iq muti mit-132ib r11 lo iuim 3di s irb niAsi

I VO.O = - (QO. I) = 0q i noiiqmu2noD inrnii1i lo iiq nibnoqrno3 rii isril ilqmi xsi I 4 luods bIsup ainrnrnvo 1E3o1 bns isi2 Js1b31 oi 2noiisloqlo3 'd bisq xsT

xsi Isnoiq io1d cnuii in Isi s ni',sI eboiwq 2irll niiub niu1i xs11q li3ioi r1t1o inoiq

IIw s xsi riqoiq nibuIni) xsi us io1d ffioiq1o oiisi r1i i 1n313q .Q ifiT' .)I3o1 Isiiqs3 rii1o uIsv in3m3sIq1 rIi 01 ainmsq iaiini 1n Lsi aulq (axs1 fflO3fl1 as

qqi5I bns noiisIu3Is3Io borIim rIi cJrI3ab (E8Q1) xus1iM-aA3iU bris sdiio niiabbI d niuii airIi ubi bluow exsi i'iqo1q r1t nibuI3x3 .isb ol qu noiisIu31s di ariiid (Q I) .(QQI) kiwms2 bns sdiioq a :atnioq gsinuiq V.0 iuods

I àQ4'OO\I.ThI

Page 18: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

bnidmo r1i1o noits3ibni n13 s niThb bLi ith Lf1 iliw I .(QQI qqi5I) tn1q 4 lo

xi1 r1uor{t riv (in31q is noitsflni biuasm e..1) in313q is noiisflni bns xsi lo i311

rnuii1o isi xsilo in r{T °.Isviini m ? irIi vo bimv noitsflni bns 1si XEI Itn

no sq 2Lsubivibni isril xsi r1i rio 0215 lud 1v1 is1oq1o3 i1i is xsl dli no 'Ino tori 2bnqb

!stiqs3 bns 2bnthivib mo3ni iiini no xsi Ht nibu13ni jnul3i xi$i-t131oq1o3-1fl5 U3f11

lo 2uisi2 xsi i1i no bns no3ni dt lo rrriol r1t no 2bn3qb i13i xI3i Isnigism ii11 dT .nis

lo IE1 xsi 1subivibni Lsnimm s nimuJ3 'd 2idilo us immmu2 lIiw I .Isubivibni sf11

nis r1i1o 2i2Isns r1T .in31q OA ol 1n31q 42 moil mui3l in 1i 3ub1 2irlT .ino1q

10 muii 2iHi lo Iv1 iiq di 01 viii2n ion i noiisflni lo iin muiidi1iup r1i ni3ub1 moil

di rltiw i mno mo 33rii2 muim xsimq in31q .Q rIi bns ii riw1d 33nmflib 2i31q sf11

rIi b Iv1 2i3mq r1i 1mIimi2 .ism xsi vit3T1 no ism noitsilni ni 3n5I11ib Lb i3TI

rIi diiw 21 nino iuo 33ni2 2flo1i511J3153 inTIU3 sf11 01 insrioqifi! Ion 21 3151 XSI 3Vii3113 Isilini

bo tgi muildiliup3 3r11 ni nsrb 3r!i bo iIui s as 2111330 i&li 31s1 XLI 3V1i33113 3rIi rh 3n&13

O.Ibo mut3m i3rI 21fI1 ot 2bnoqr1o3 isrit noiiqmuano3 1n311131i1311o 33fl rfT tr.cioilsflni

airli isrlt a3ts3ibni 3iIq 3rIi no iqhl3adua 3rli 3-ir1w IOLO = or - (OIO. 1) = cq ai in3313q

.1n3313q owl bo 3iE1 noilsllni iis is imq f{i 21n3231q31

xst 3viI33113 3rIi al3woI oi ot in3313q owl moil 3151 rioiisllni muildiliup3 3111 ni3ub35I

fII ni a3nsf13 I3v31 3isloqlo3 ff I IA .a13v31 Isubivibni bns 31510q1o3 3111 rllod 113 31131

noilsi35hq3bbo 3111Ev fi nignsr13 d 31131 xsi 3vi133113 3111 13115 3Iin noiisflni muimdiliup3

in3313q V.4 \11sui3s asw boil3q airli nimub rioilsflni b3muas3m bo 3is1 gs13vL 3rITor

.in3313q V. bo 3151 noitsflni 3irht 3L13VE ns niIqmi

.wol3d b31n3231q ms afhoitsIu3IE3 \iivitian32 ii3iIqx3 3fno2

ôQOO\flnI

Page 19: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

th u8 .2inrnq lrlrii lo noiloubb di lo 3u1Ev r1i nin&b d bnl3 3nEwoILf

i mi li3nimon iii bnflb i ffioiq !dExIi nitI!u3li3 iol bwoII ai JEdI 31ub3ii3 noirEi31qb

di as13r!i 'd5Idt briE noitsi3iqb ril lo uIiv ln1q dl 3ub5I noilnflni lo li irIir{

b 1ui s 'd blsmixo1qqE d nB3 rioiibi idi ili bworf (8VQ 1) r1oEd1uA .lE1 xl viJ113

lo lnioq Eln31q rI3E iol elnioq V.O 'd ffioiq Id13xBi irii lErli dmurh

lriioq J3lfI331q owl s ? lo 31B1 xBl 3mofIi ts1oq1o3 li3rligrnrn r ciliW .rloiiBflni

O4OO.O = (O.O)(V.O).O 'd I3nni3rb idi rLuoirLt fnuli xiilo ln dl iin noilsflni fil nu1ob

lnioq gfiln313q OkO

3rli lii b1i xEl i1h r1i vom noilsflni bnf$ noil3ub3b liini 3d11o noiloiiini dT

niworiod iioqio lEnimon rli isr noilERni lo rnioq in31oq rL3E II .noitoiib iioqqo

no!lknoq-1o Hl lud bn&13rIu i niwonod lo io xEiIq lii di lrIioq Ein331q no d iE1

10 11 r1i lo noiu3ib 3il1En13 riE iol (8VQ 1) iArtir1ar1 bnl3 niD nilb11 .rmwo1113 noilBi331qb lo uIEv 3r11 no noiisflni

flu nJ3r13 ol noqi flu th noiiEi31qb n&b inoD 113r11 bum d lrIim lI 1u8 .b3gnErbnu 3nJ3wo1IE noiiEi1qb lo uIEv ln321q !ii r1i q1 01 l3blo ni noiizflni

flu niI33b r1i O8Q I 1m rLl iii 1ub3r{3 noiiEi31q3b biqsi iom l3En3 bib ignoI1) riguorlilE mrI bns IubfI3 noiiEi1qth gninrIign3! 'd l11o nd Ion d rnhl IEfLI rii noilEflni

.xEl fnoni thoq-io31o lE1 3vil311 grIt flu noil3ub1 i ni blIui moil ml i 31s1 lioini hi 1nElr1o3 E lo iarIioqd IiI gni\ril uorrm1 irIT

-non Ino 3rD Ii Iqmsx3 ioI .iubuil xEl !Eliu3n-rion x3IqrnO3 dhiw rnono cm ni 3IdEliv3ni in3rrIivni HE briE 2ln3mEq tI3lni lErlimon loub3b 01 noilE1oq1o3 lo \fllidE 3rD iw li1E1lu3n

3f11 mii (r-I)\I d ii bluow 31B1 I313irIi lEnimon 3f11 nigmm 3f11 IE ld3b d b33nEnib 313W l3v3worl b3fl2inimib 2i 133113 irLT .31E1 xEi 3IEloqlo3 ioluIEte odD r oiorlw noilEflni ni ogrmrl3

brm 2wofb IsliqE3 IEno!lf3rnolni o3flEflfl 'liup3 noilEi31q3b lo3 3i1olir1 lo noulEnudrrio3 orD

(QVI nEmimH briE EQQI F8I nioIb1oI oo) .IEubivibni orDlo lovol odD li oIui xsl odD

iolovni brm oIiri xzl auoimv 323db lEfli 2120ggu2 o3nObivO oril IiugidmE IE3llOloOfLt orb oliqoU ioio1ni lo olin xf3lolq IEO1 orb qooA ol otf3i2 boiiriU orb ni ooiI3Elq flu lmi3ini loivi3rbd

.(QI) nbIrI2iM oo ;2ognh3rb rIoiiJ3flnhlo olin orb noflw bognEfl3nu \1o1Lrnixo1qq13

V I ôOO\1T1nI

Page 20: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

10 oiisi 1siiqs3-idb 1s3iq'X s diiW .moni 1dsxsi niis1u3Is3 iii noiiubb Isnoiiibbs ns ig noilsflni ni nu13b in313q owl s in3313q lo 3151 xsi 3isloqlo3 iolulsl s bns inI3q 'iio1

.inioq finn3q 8.0 io 8O0.O = (0.0)(0.O).O 'd lsi xsi 3vil3113 r1i 3iSi

01 31o1313r11 i '1ilidsi oiiq 01 isi noiisflni 1n3313q owl s moil nio lo i113 i3n 3dT

1n3313q O4. 3rIi moil inioq sin13q 1.0 'd xsi 3lInoqlo3 l3iIs niuli lo tsi 311l 3iJ31

ol 3vods b31s1u3!53

.13v31 Isubivibni r1i is xi dl i11s 3151 noilsllni l3woI r1i won lx3n 13bino

s i1qmi xsl 3isloqlo3 nL11o 130 niu1i inioq 2 3rD 01 lsi xsl 1ni3q 3rD ni1qqA

32u533d Isubiv'ibni 3rD 01 b13i' bn ni thiioq sIn3313q p0.0 1o B313fli ns ln3313q 1 I .I Io bbi'

315 xsI 3rno3rli Isubivibni us33d noiiibbs 01 .bv3I 3Isioqlo3 3(11 is noilsxsi oh risd3 3rD1o

noiisflni lo 1si 3111 Oh noil3ub3l s nisg Isiiqso Isnirnon bnis in3msq I313lnI Isnimon no b3iv3I

.nlul3l lo 31s1 xsl-13fi5 1s31 3111 isi bns ts•i xsl 3vi133113 3r11 3ubi l3rItluI

3rD Is i313ini Isnirnonlo noilxsi n1I rliiw b3izi3os i Isdi noiisbi thlllo noirioq 3nlT

3isloqlo3 {i Is 133113 3(11 2I3IIslsq isnli 'sw s oh b1srnixoiqqs 3d 1153 Isubivibni n1i lo 13v31

3s1n3313q no d 31s1 i13inli Isnimon 1i isi noiisflnilo lnioq 351fI3313q 1b5311 .bv31

nllfl3l xst l3fis n1I lud b3ns±nu i idb no nlui3l xsI3lq 1531 1oI23vni Isubivibni 3111 lnioq

r{i nimuA .noiislmni oh nsrk 3111 bns 3151 xsi 1sniiism ioIuisl r1l lo Iouboiq 3111 d 11s1

boI Isliqs3 3Isloqlo3 3(11 iol b3mus I s 1v1 Isubivibni 3(11 15 3lsrk Id3b in3313q 'rio1

3rD b333x3 in3313q r1i iuods Inisii33nu1o niism 3(11 n1uor1Ils isdI 3ioI.4 Ion 3113 iIsns In3TIu3 3(11 1o noiubno3 3nIi in3313q 1.0 lo mui3l oh nsrb b3i51u3153

.mul3l lo 3151 1f13313q Isilini offI lo 13v01 32i331q nhi 01 3viii2n3

d b3A3sd iiaoq3b &isH .Id3b In3nnrri3vo ni In3m13vni Isubivibni 31Of1l ir1T b1or13uor1 3(11 nirDiw nIi3d s b3lorlgi 3d 11133 ( 3gsgi'1ofn 3monl ...3) 2i32s Ansd 3isloql03000

8 1

Page 21: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

niI3b in313q owi £ 1&Ii iIqmi iin xiii 1nilBrn ll3ubivibni 313VE bir1iw in3iq bni

.inioq gEin3q O.0 io 0OO.0 = (O.0)(O1.O).0 d fl31 x131 vii11 fL1 iwo1 noiiiflni ni

IEubivibni lo noirloq 'iiup3 r1i ol rnu1i bcibivib rli no iii xii vii11 3r11 riguorfilA

idgid S (1v1 isioq1o3 di is iuo lo iqx) noiisflni 'd bi3TIs ion i qiH21nwo Isiiqs3

113 bxsi won is nisg Isiiqs3 ñguorlilA .2f1113g 11311q133 lo fIoiisxl3t th asini noill3flni 1o 1rn

rLi is 1n31q 8 lo 1si nisg IsliqED mumixsm s ol qu) fflO3fli irimivfli l3rIio s isi rns r11

.bIo i r1i ndw biv1 '1no i xsi r1i us33d l3woI ei isi xsi viioTI 3rIi (bv1 1rnb1

lsiiq& no isi xi3i Isnigmm 3v1133113 in3q 01 13 mus io113r1i 111w I noiisrnixo-rqqs ns 2A

uIsv Isnimon r1i isi 1v1 nq r1i flu as3ni inioq gEin331q r{3s muidi1iup ru .ruisg

nuf3m1 i1i1idsi1 di lo u1sv If3nifnon rii ni .inioq g1$in31q no d )13oi IEiiqE3 rLt lo

idb r1i i d ir1w 2inioq n3q (d-1)\1 d ii 'iiup3 di1o uIsv li$nirnon 3rIi bgnsrbnu

s .1.0 = lo nisg Isiiqs3 Isnirnon no xsi 1J$nigmm Vii3113 fiB bns t.0 = d illiW .oiisi Isiiq& oX

no riiuti lo isi xoi ifth 1si r1i isi noiisllni lo olsi r1i ni nikb inioq gs1n1q owl

2in321q1 iiup 3rui2 ivwoH .2lnioq gsin31q 0 io E00.0 = b[(d- 1)\ 1] O d iiup3

r1I 22iJ3I x131 2nisg 1siiqs vii11 l3woI rIi oilo1iioq 1rnjbivibni r1i1o inriq 0 1no

gsin5I3q 0.0 io 2inioq gsin31q CE.o 21r{iIo in33q 0 Ino d rnui,ilo iisu 11svo

.einioq

d 1si noilsilni r1i gni3ub1 isth i1qmi 2i311 2nisg Isiiqs3 bns idb rli gninidrno

rIi s rns f{i 21 oiloliioq 21Eubivibni r1i ni idb1o 5113f12 r1i isril noiiqmu2s dT 3loM .noiXslu3Is3 r1t1o iuo qoib oi rrrii (d-1)\1 r1i 2UE3 !sliqs3 is1oq-io ru idb1o mr12

nI311ib r1i rio ebriqth mubi lo isi !2Isubivibni rL1 no noiisflrui lo i3fl 3r11 11sirug .2oiloThoq 2lsubivibni rIi ru bns Isiiqs3 isioqio iii rdb Io iBrl2 rIi nwbd

Q I

Page 22: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

r1i d bv1 iovni Lsubivibni rh t13 th xi vitu13 di 3ubi1 2thiOq sniq ow

urI1 i ivi IBubivibni dt o mifli 1n Ii dT .inioq Ein31q Ok Olo 1n1Eviup

nutq owi i isi noitsfmni r1i nf{w n-iuii li moil 2inioq iniq Q.O qu iniq = (4eO. 1) = 1q i noiiqmuno3 inrniiii lo iiq bi1qrth {T .miigirl inioq

8i1qmi 4 noiiiwp olni noiiqmu2no3 inrniiif1o iiq 3rli iol u113v gniiu1iidu2

!D qIf — 1) O.O = 1D ()

'gth L I . rIt 1i inm1ii11q nnub nivi 3d1 1niq1 noitiup ni lo uIv dT

1U2f3ffl IfIUO33 fflO3fli IEnoiiI$n fII ffloll tfl5I11ib iuo lo i irIT .noitEflni lo 311 gnuiiX

ignuo rh1o griiwa rIi nwid 3n111ib fIi i nivz I&1o21q 3fli2 gniv 1&ioiq1o

.1vEib biiii lo gnivEib rIi briE ivia fIJ bns 2 nwrd noiisIi rh u ol i 2 lo u1Ev rIi gfliiEffllxolqql3 io1 3IE1I nO

nI .rliwoig 'bsi flu mono (113 flu gnivEa lisnoiq lo iuaim ifliJo3OE fflOfli lEnoiJI3n

13 113 woi gnivE mo3ni 01 Irlnoiiloqolq nivs riliw Ibom noiiE1ng gniqqsIivo olqmi r1i

.13w 131iq133 iq ni rliwoig r!i i bni rIiwoi noiisluqoq lo iin r1i i n 5IrIw + ii lo 1E1

ib1o di1o gnivEib 3d1 mii T(g+n+1) i nuo'c Hi1o riiv di tsdi iIqmi irIT

3d1 bnE rnuii x13i1q 3th luodE noi1qmu r1i 01 i!ui 2idi lo 1iviiin rIi i1 oT vii13miIB gniau 3nq noiiqm1Jno 1nmii1i rIi bi13Iu31s1 I 1si x131 3113loqlo3 3v!13Tb vii11 bnidmo3 r11 iol 14.0 bnt$ niu1i x13i-1q 3(11 iol 1fl3313q Q lo 23u113v b3mu2a 3(11 ot

b3gn&13 'Ino 1n3313q 01 ol 1fl3313q .Q moil rnui3l lo 31131 xEI3lq 3(11 grIiiB5I .flsi xf$i iioq1o3 nlui3i b 31131 x1313-iq 3d ni13wo1 ;Q0.0 01 O.O mob noiisup3 lii uIiv aoI idi3wb1b 3(11

3(11 ni13513f1I .OQO.0 oX 3uIBv oI ir1i3wb133b di biwoI inn3q 1.8 01 1n3313q .Q mob (1i bi1id 'Ino .Q1o muI'i xEf3lq i rliiw 0.0 oX 1.0 mo 31131 xEi 3XEloqio3 3vi1o3T13

3111 isfli frnulno3 noifl31u3Ir33 33fIT .ÔQO.O oX Q0.0 moil noilEup3 ni 3uIEv oI 1r1i3wbib iol b3rnuE 3uIBv 32i31q di oX 3vi1in3 Ion i 3i1 noilEfini muhdiliup3 3r11 nirIEr13 lo 133113

.31131 x131 3nuI3i3d 3vi133113 3r11 briE rrIuX3l lo 31131 xEi3lq 3111

0 ôOO\ItnI

Page 23: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

() fIUO\( di lo gnivi f1 ol b1I311 i rnono d1 iii () gnivi I&ioiq 1n euriT

:01 gnib1o3ii

— = 2 (a)

mooni s$w !i5J o 1nIBviup IIEu1q3noo ci bn w isdl 2 lo u1Ev rLT

= + ii nieU bn. OQI nwid 1n3q ô.1o 1ii 1 ei1 biinU rIi iii wi 'biErnixo1qqs d 01 nivie IEnoe1q Aii1 w II 2 ô8. I = 1fi ei1qmi OE = T bLiE

0quD QO.O = 1irIi eiIqrrii in quiin0

1i2n3qoIq d1 21$ mie rD ci (o) mo3ni euonox lo tuo mueno 01 '1ienqo1q c1i 11

.QD Lii cgw1o 1.r3fIe rli ci n iIw (UD * n) \ = z rno3ni 13w1o luo muenoo ol

coilqrni eifD V.O = D riliW

noii1$up ni bdh3eb nig m1bw r11 1i3Iu31E3 01 ibio ni b1EuI1w d 01 rrn1 I1$nfl HT

3i1q fli 3fli .noilqmucno3 1nmii1i lo nq 3f11 01 1qc1 rhiw gnivc 10 1i3iiaI rIi ci

rhiw cgnivc1o 'i3i1c b11$cn3qmo3nu rI1 T(i+I) = q 'd nvi ci noilqmuerlo3 1nfniii5I1o

rh 01 iqe1 riliw '1i3ii21$I fl1$ 21$ b1E1e1 cJ fttS3 noIlqmucrlo3 inmiiii1o rh 01 13qe1

cmo3d noilsup3 curiT •(i+1)\ qClT Ti — = fT :frlubl lo 1isi Iii

2 QO.O =1D (V)

13ihB iirh lo nivEeeib rI1 fliod athul3ni eii151 ibIo rh lo riibriqe fi1 11$di 31oT4 rIi 'Ino ci grIIVC Isnociq 14 .gnivc iirI1 no b3rn1$ V13rI 'rIi lEfil ffl03fIi r1i bnB fI1VB2

.c1vJ$eeib d11o r1ivEccib d1 bns 213VE2 d11o fliv1$2 3r11 nw1d 3n1flib

ci boiiq 4iow rI1 lo rhn! r11 113(11 XIfI031 ol bbn1x d ni AIowrrn311 cirl TOE

cifli ninr1 Id1$iiqqB luoihiw boiiq tnmii1i dh1o r1tn& 3(11 ei3 gnol 21$ iw1 '1r1uoi .11u231

QOO\tnI

Page 24: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

o nvoiq srI mui Tb ii in Iii Hi oi 1qi dhiw gniv1 Tbo \i3itEl fh nu1f3m!I3

-1o-n 1s b3qx Hi gn&k niiuairn Hi bvIovni rn31do1q rh Tbo aus3d ilu3mib iv d .gnivE2 b1J3 sr11 iobi1 idio di £Jb irn mh Hi ni 1nEino3 nibIoc{ ni brn3 rnui xJ$i

rh eirn 1r11i3 niuri lo fli 1i irLir{ B ll3dh 2bnil '1IE1n 13du ir11 no 1uh131iI 1131 ,riT

exJ1 .2.UIo to3 1ETb1w rfi1o 'bui 3iB13 iir1i nI .1IB 113 1Ih3 on io 1si niv

ir1i AJ Iliw I .04.O = 1211 lo (fl3i1aEI nivis is bmuis (8I) 11&IW bnis n3vorf eblISIIJSH

(40.0 1 rhiw) i1qmi V noitsup 2is 2irli cii .'bui2 in3nu d1 iol 3ulisv Imrnr{3n3d 3(11 acs

D — Ti\1i (i+I) + 1) Q0.0 = 0 (8)

quo 0i0.0 = uo (I.O — + I )(0.0) 0.0 =

2i1{T quo lo 1n3313q 0. I oi Isup3 i rfoiiqmu2no3 lo noii'io1ib bub31 mofi niis Isurins i1T

.1 IdisT Tbo WOi 12111 3(11 Hi nwor1 i ,iu11

owl 3nimsx3 o2113 Iliw I T1o 3ulisv rIi 01 isrnui3 2irhlo 'liviii2rI r1i 32is oT

nivis no on 3visnl lisi ii.tni 1isi cii nisrb rbidw cii ais niiimi1 3dT .uIisv irlio

:23iIqrfIi 0 = fi tisril .3.i

— Ti\12f1 (i+1)+ 1) Q0.0 = 0 (Q)

uo V00.0 = uo (SI.— I) (Q0.0) Q0.0 =

quo Tbo 2lnioq 3Bin3313q EV.0 01 IIsup3 fluI3 3113113W lisunmu nis

lusH (dQQI) ni312b1I 8QI) 2n13v3 e(8V1) nithofl jVI) l3bfIiIB 213(110 noms 33t .()QI) 1n1iiW bins (V8QI) wblnisM (V8QI) nblsM (VXQI)

isw!s lomIs 3113 fT Tbo lsmii23 IBOiiiqm3 flsfli 3(11 fl is gnilirnul is 21 2ir1T .0> i lzdi 31dioq 2111 321LJo3Tbo 1o3n11 nil .3vili2oq

OO\iinI

Page 25: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

O.4 molt muii lo i1n sf11 niaE13ni i&Ii .i 0. I = ft fl3d1 bstni 3fflU2 3w II

ot tn3313q owi molt isi noitiRiii rI1 riiqqoib lo ifl b3timii 3f11) in13q ot tnn3q

quo N 10.0 = 0 21 f11S 3113113w 3ff! 1f13313q 1.01 ol 1n3313q Q Ii niva 3111 2321131 (oi lo gthmil 3111 no t3TI3 3113113w lEnoilibEll 3111 111 ta3u2 anoilEIu3IE3 32311T

nw1d b3bnuod \dEdo1q at ois 01 1n3313q owl molt 31131 noilBiliti 3111 rIi3ub31 lo noilqmuano3

bno33a d1 ni itwoik m aiufl 3a3rIT .qUDIo 1n3313q N. I bits quoi0 atnioq 131n3313q V.0

.1 3IdsT 1o awoi bunt bits

o xV isti wwoX \o w1 V\T oiX

at lull no 3d! bnis 2fl0i1S111311$3 3113113w ni floitqmhJaafS lsnoilibsil 3111 13i1m3 blon I aA

mua qrnul 'd 132110 3d 11133 133113 3U113V31 'ns isnIl at , I . nOilo3a lo noiislu3Is3 3111 ni ti3iIqmi

fflOflO33 .2.U 3111 nj IOn 21 h3!3 ii 25 3UI1 ton at ainil fI3f{W .2131211511 bits a3Xsi

usnotho1aib irlio nil noit3ubu aIirrn3q ii 32u1333d striovbs 3mlbw l3fIrnJt s asH 31JI13V31 xsl

ol 23x1$1 isnoiriotaib 131110 gniau 1o 1203 3113113w s eoilqmi 3U113V51 xsl lo aaol 13 31111w 23x131

3(11 d bisq 3Ufl3V xsl no 1o3113 3111 sluo1s nIoii3a in3a1q 3nlT .3un3v31 lao! 3f11 33s1q31

2322u321b bits 3151 noilsf.tni 1n3313q owl it null l3nltnn 'Ii1ids1a 331 nivsnI 1o noitsl3n3g Iitilmi

.3m1L3w 31111011033 no 1113 nibnoqa3rIo3 3111

31o1313f11 bits aiVEa ol mul3l 1si 3111 a3aisu noiloflni lo 31131 muildiliup3 3(11 ni3ub351

abn3q3b 3Ufl3V31 In3mn13vo no ainil lo 133113 3nIT .noilqmuano3 !n3m31i131 1o i1q 3(11 233ub31

3(11 IA .oviu bnsm3b b3Isan3qmo3 dI d b3ilqmi noilqmuano3 1n3m311131 111 3c1uI3 3111 110

23x51 131110 3Iof1w 13 213 a13sqXsi iol 32uS33d b3au at 3V1U3 bnsm3b b3tsanI3qmo3 3f1T r1s3 uol nollIsan3qmo3 13sx3 Ion ai ainli n1uor1I1A .lnstano3 3LJfl3V31 Iltiol q33A 01 b3iau[bs 3Th

3111 null 3lsrlqolqqs 11s3n uom d3IJnn at 3V1U3 bnsm3b b3lsan3qmo3 3d1 13'sqxSl

oQtoo\:tn1

Page 26: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

1Uj\O5O4Q

nucouJbcu2cq qcuJuq CflL1G

°' 'P = 00ô 0Db 2 qcuAcq 1I�EA = — 0003Q 0Db

a = oi (& qcuicq iu ciiou J) JG GUCIJJILJCccojJ rujbji qjç = —

— {oog(i +(J+L)JJ\Lj—a)—iyJ3jQ}

(13) qiii= oo(i _jJ2b _a)_Ø•J3J}

b°=030) iwbJJc2

npJrniu bucqLiiq rn bLcAion2 ciou (b° =ooi b' = O5Qf iuq

(ii) q IEA = 2 {[ (b—

b°) \b )] [ (b3—

b') \b5)](J — jyb —a)

—(b— b')\b5 }

JGbJ1cru b5 c5 pA uq LccijJiu ijow cdrnwou () Ct) = + a — j Aicq

= (b'—b°)(b1 _b3)cC')(C5\b3)_(b3_bI)C3

= (b'—

b°) (b — b5) (q\qb) (b \ c5)(c5 \b3) — (b—

b') c5

=(b'—b°)(q\qb)(b' —b5)—(b5—b')C5

(io) q WEA = (b'—

b°)(—

C3)—

(b5— b') c5

ju bLGu cac cp cjrnuc tu LACUflC cu p cjcricq :

UG CICC OIJ LGAGUfTG (b' — b°)('—

c3)—

(b5— b1) c cu ru tpcoi.A p Jfp boWAc 01.

o,i.umcu cojjcc qqwourj LACUfTC dnq o (b1 — b°)(C'—

c5Y E/GU c5 <C fG oiLj

LciLcWCU counwbrou CJf1C2 LCILGWGU cou2nuJbrou o !uCL2C L0UJ O

Lf1CC2 LG1cunc (i nucq op rurrrj ruJc) pA (b3 — b') c IUJ ijj ru pc bucc oi

ruJ!gJ jcicj oi LG1LGuJu couanwbpou Lcqncru bucc oj jrinccou2nwbiou JLOW b5 o b

Page 27: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

iIqmi 0.1 =fT IiHw cIUD 00.0 — = V351b iIqrni 0 =T lo gniiirnil f{T

.quoEloo.o =V351b

lo iE1 3f11 01 i3q21 riliw niv lo 'li3il2EI b nqmonu 1l no nibnq3b uf1T

ithi, d ns '1iIidsl riq 01 noilfmni ffi31q owl moiI gnifiirl2 lo if1 unvi rIi el5rlni

.vili2oq io vi1n co

rli diiw (Q bru3 8 2noiisup1o O) nii 1E11w lEnoilibsil r1i nidmo won ns W

lo isilob rks II .(! bns 11 2noiisup3 lo VT5Ib) 3nf$f{3 unv1 3r11 lo 3flJJ2fIO3 5uiIbw

3isIbw ln fLl lo 2201 1ff iwbsb s vIovni xsl idlo mofi bisi d l2um isril unvi 21 'li1idsi 3fl 01 noiisflni ino13q owl moul nil1iff 2 lo niz

.1.0 =.i 11 qUO [ 00.0 —

010.0] = O (sU)

hs1imi

0 =c li cIUD [ 00.0 —

V00.0] = D (dU)

bns

.0.1=i 1icIUD[AEI00.0+4$I0.0} = D (aEl)

ni 2nsfb 01 12u1b5 01 b2u 21 isrIl 2xs1 ni nsfL3 3ff1 no 2bnqb A lo uIv dT

01 1born mundi1iup 1sin 1ds1uqmo3 i bu (8Q1) '11sn1W bnis nvon12 bisIIsH .unvi f1l isfil bbu13no3 bns noiiIoqolq ms2 3f11 ill 2xsl 115 fI12E313fL1 lo i311 ff I 3151 u3153

no nibn3q3b 2ln33 bns 2in3 OE nwi3d 2BW 3Ufl3V31 lo isl lob iq 2201 Inli3wbsb

in 3rD isifI 23ilqmi 2inIl ni2U .01.0 = A 'd gnsi 21r11 1n3251q31 111w I .2no11q1nu225 il3ms1sq

nJJ ni cIUO lo 3n13313q Q.0 215up3 0i 01 1n13313q owl moil noilsflnii 8ni3ubi lo nis 3m113w

OO\tnI

Page 28: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

i (quo lo th313q 01.0-) 3UII3V31 bubi lo txfl tth13w r1T ..O = ji 1o &i hsrnrbrid

uo lo in331q .0 lo tI1 515113w b3nidmoo 3r11 bits I 3ldsT lo nmulo3 bno3o 3d1 iii nwor1

I IdsT lo fiffIlJIO3 II! f1WOfI i 315 kO = o rnbnoqiio3 nis 3lslbw in r1t 23B3 gnuiimil owi 13db 3r11 iii

3db ill nwofl2 315 33dT .0.1 =.i ilbiw quoi bnn3q Q1.1 bits 0 =i rhiw quoi0 br13313q

.1 3ldsTlo nrnulo3lo woi bilili bits bnoc

rio bsi xsi ir1id1o ao1 blfgi3wbs3b 3db bsrnii (8QI).1s .b bislisfilo i1sns 3r{T

13r1id1o bI13 ,rhlo n3Asb i briuoos o4 .nivs bits 1qqu iodsl ni noirioiib 3r1bO 2i25d 3fh

flu mooni gn1v13331 io 2m3ti 3ldii3ub3b rio gnibn3q rlguoirll 33rIsbiovs xsb rio bsi xsi

nibb1I) iqsq bn31 s iii noiiibno3 gnbhow 1331(1 4flon3d nui1) 2rrnol 3Idsxsbnon

b3rns1o rloib3ubsi Isnoibibrnb 3db s 113w 25 33nsbiov's xsllo 2rrnol 3db bsrh b3worl2 I (QQ1

23b51 XIII 3ffl03fl1 ru 2nsrb1o ol brlgi3wbs3b 3rIblo 11011131u3153 3db ni b3buI3ni 3d f153 3mo3ni

b3asll .3iI xsblo bn 3r11 ob b3oqe3l rlbiw 3rnO3ni 3Idsxsilo bi3iis13 b3Isarl3qmo3 orb niu 'd

obsi xsb 8(1 rh iofth bits siolod wro'sqxs omorii r1irf1o ononoqxo or{blo 2i2\15ns its no

3db iij vji3iI2sIo 2irIb ni2U .(bQ I niobEbIoI) 10. I od ob 'Ii3ibsIo Isrh boiBrnil2o I rtoibuboi

xsb omooni lsubivibrii us ni osoioni bno3loq nob s isrh bobsmii2o noiib I Jobom MI2XAT 5I18L4

orb 33(112 ;213v31 omo3ni 4Q I Is noillid I4 biods lo o1 3r1iowbsob £ OU5 bluow 23i51

= 21 lo 3u15v boilqrrri odb noiIlid I od bluow osoiorii OUrIOVOi nibnoqaoi-io

2325313n1 3151 xsi EQ( I 3(11 no b325d (QQ I g13dn33I bits niob2bIo1) 'bui2 bnoupo2du2 A

oulsv 0.I orlblo bsob2ni 8.0 Iuodslo 'Ii3ib2s1o bobserloqrno3 13115m2 isdwomo2 s

21 bui2 EQQ 1 3db bsrh 1351 3db 133fl31 \sm 33f131311ib 21db r1uor111A .bui2 l3ihso orb ni boviiob

ooo\:tnI

Page 29: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

wo1 i fflU22E bnI3 3viticnno3 d Iliw I Ino is iii di niiub 33fIi1qx rI1 no baBd

= lo u1Bv oI 1iIgiwbib

:1mi1 nii i1bw1o nsi ibiw i Iqrni L duoic1i i1 noiiup .1 = rhiW

1n1q E.O d 5IEIbwlo Iv1 1unnE rIi iini o ot innq owl moil noi1flni ni3ub1

10 o1 1If3ff1 ii i l311 ln r1t 0 =i rhiW .4.O =T lo )hErnrL3nd fl lo 1n31q 4ô.11o niig 1siinEidu i iT1 1n r1i 0.1 rhiw Iir1w qcjoi0 iniq 0.0

.1 LdsT1o 3vfl bn ir1i anmulo3 ni nwork ii uli3v rIT •quo

noiiEooIIE Isioqmtilni ive no noill3flni lo ai311 lEunnE di 1u1iuo1o U3 3r1T

biow l3ild B 'f3 ol Iuiu i ii noiiEflni 10 11 irho rh 01 8nimtJl ioI8 .noilqmuno3 lo

.vEanon tuod

on vir1 bIofb2uor1 lo rioii3Bil gm! idl i bIofIJJod nB3i1mA iuodi lJ31 niAht A

1rt on b&1 oi bi bir1 dliw b1or1uor1 ..IJ lo Jnoiq 0 tom1A .1h lB thinEnfl

3rI1 ;00E8 ibnu bzd 2b1or1uorI bu21o iri31q 0 bnB IQQI ni IIB 113 1J3 113i3n13n11

.iii1idEi! li$i3ru3nfl moi anoi1BiIdo gB11om buI3x 2ui1

io Isnoilirni 1i3 IE1Jbivibni lBrh 'Iqmi Ion ob gniv 1Eilnsldu2 lo onacIB dT

l1thn3d ii1u3 11313o2 ni .noilqmu2no3 1nrnii1i 33nEnul ol bn ñ1 rhiw brn3no3nu

mi11iI nthbrn bEn 13n1 ofiw iAiow i iol mo3ni xil i1h3 lo 2biH1-ow1 ni3fh 3lom

h3i3o ol noitibbE flu 1nm'Eq noinq 1Evi1q iBqi3i1nrn n oIqrn ni3m bnrn flifl1E

13'3-1!I lEnoilEl rhiw ln31ainlo3 d 'im 2i13 I13ianwnfl lsnoilibbE 1o 3ndE n!1 inu3

Page 30: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

.mumiiqo b3niE1no3 B in31qi nivi ois 1subivibni ioI .ioiv&!d

oi noiiflni wo! moiI fiur! d1 iuia Isi3o bnB noinq flvnq lo niq fD nI

'm niv flu J35I3fli t1i bnB oJ b1orIuoH r1flo mo &n ii1idB 3nq

I i&Ii bs1u3IE3 nii m1bw th oni .ounvi xBi Isior ii bn 5IJ31Iw iirh ni i!iow inm1i1--iq d gniv lo inuorrrn r1i oi LBnoirloqolq i noii idi ni ii1m bioqi

.1vBnofl 1nT1u3 oi nig IJ3itnJoq fli ioni ii

2ifll &h '1qmi mo3ni dgirl iir1i bni3 vnon lo idmun gmI rIi r1uothIA

'IIsub13 bluow niuti 1o si b13ni woil bu1 oi w on vsr1 I inBJ-loqrni d bIuo3 io11

rn iuIi iIqmi i iir1i nion 1no anoiiBIu3IE3 f1t 10 mo 21dm vi1 31o113r1i I .1oivEdd i311B

.bu1Bv13brnJ mnix 2idi at i noimnflni woI rnofi nii 1TI1 lo iEfflui23

niuoH b3iquO l3nwO io1 bnIm9U 9dflo nothotiU II1noihRuI

.xi1 rnoni !Eno21q rIi ibnu irIrnh13i1 1Bi3q2 2Vi331 ni2uor1 biqu33o inwO

dm no boqmi i xiii on iud bt3ubb m xiJ h3qo1q 1133o1 brrn 2inm'q iai1ni ttoM

oat 3ubni bluow mnrnmB1m eirlT .i-iqoiq rIJ iii btvni IEiiqB3 di no rnuti IB1n mi3ilqmi

.noimEflni lo ndB fli ni nv iri ni2uod1o noiiqmLJ2no3 rburn

no dT owm ni 2iV1 ni2uod b3iqu33o nwo1o 12o r1i 23ub1 noimBflnl

'1snoi1uE31q d m 2lBubivibni 113u21o 3nBIsd ISiOftBnfl IIEm2 brido rIT rIm ni1i oi Idinib d bluow ml .inq d noo Iliw milfim 2bnul Oo1i2nE1m bim rn 3nsIBd

2nivB2 mnuo33E fflo3ni IBnoimsn IsurtnB ffm lo rno IBril xinoi at noim3 airli lo 2fl0iiBIU3IB)

dr nimEIi noi22iqx frnol b2ok '1ot3B12iifia on 21 icIm 3fli2 .oqiuq '1BnoimuB1q iol m noiiBIu3IB3 iBdi bu21uq ion vEd I i25I3ini lo 3iBl rIi ol fl1VE2 'mnoiiuB351q iol bnBrn3b

di moil wi11ib Jud (Q I bnJ3 48 I) I3d11o9 ni 2!21Bf1B dt rnoil tind noi1332 2iHT .EW 1o dmun ni ir1i b2u A10Wfr1B1l

8

Page 31: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

I't\O5Oô(

JJJG2G AJfl2 °L I iuq 9 JLG FLOW LOfCLP (iooY

flLJCL JC GX12JLJ f9X LIIjG2 LOL i conbj mpo 1GW1G fpcJL WY LCUILU:

iu COIJfLf2 qrn cou bouqiu iwbJiGq co bcL qoj o pof12!u cbif

bL qojJrL oLpon2ru cbrj

o05 uq 9 = ØØ5 ° = oJ5 qic LGUW co oLo1wci occnbicq porI2Ju onq pc ccu

LJ} L&G O LCIIILU Oh cibii Iii JJC UOUIJJ1JC11j COLbOLC 2GCOL MCGU j suq j cf) Iii =

qojjLoponu c1bJWJ iuq 9 ! LG oqcbLcciJow 1yiqi b =ooa (we cLc bLe1x

/A}JCLC b i pc LCII LcWW ou cibij JU fjJ IJOJJJJOf12HJ 2CCOL 111 12 we CO2 O hJJHUCU1UCG beL

(J) °=b+w +9

(g°) LCG2 qic obbonurA co o pc Lc2onLcc2:

ju {G 2GUCG oi wxc pe iuibpeq LGUWJ eo o poniu beL qoj o poniu cgbi1

-o ecc too own.fC pon21u 2np2!qA bLo/Tqe2 iu iqqJ!ouiJ M1TLG iw

LGAIJF1 i L121U LGACLJflC IIJAOjAG2 f qe1qMcip JO22 qJi2 LGqncJou TU IjJ j022 OJ WY LCACUI1C O

CXCG22JAG qcuiiiq LOL pOn2iIJ 2CLATCC2 JJJ iqqwou J i0/ 1IJJIOU LC LGf1C2 11JG 1° °L WY

jçcqfIciu pc LSG O 1IJ1OU pecjpe LeqnCC2 qcqMcp 1022 flJ1 L2fIJ12 LLOUJ

JUAG2WJGW2 iu pe qcp uq cdrn o coLbouJou2

qqwou iuIJJou iucLc12c2 qJG qGwJuq LOL OMIJCL occribicq JJOuI2IU pA Lcqf1ciu JJG LWW Oh

qeqnciOu JIJCLcJ2c2 qe 2np2JqA iUeLcI2c2 uq qJc uc CO2 °L 2CLAICC2 qecpUc2 lu

OJjpG UOUJJ1J IJJOLIG TUGLG2 bAuJcu2 iuce pc LhfG LCuJTu2 nucprncq hpJJc pe wx

JJf 2 CGU pc ocna oupe IPGLWLc ou qJJ2 2cTp1ec (e 102GUe J?) 12 1UCL2q qeqncjiou

Page 32: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

IUUt\O5O4ôQ30

ECOUOW JuqicC qJC LWO O IJOUJG UJO14RC qcpl ID 11JflG O OMUCL-OCCflbiCq LC1J GCWOLC2 pn ou ocj o€ woi.c o iujiiu Wxb?L 1P 2JJGC2 OL WC fl

f()JjJC LCIG/U T L!O 12 UO qJ'I OU IJCM hO C2 OL OIJ qJC O1CL9fl 2IOC O J

ipoi LOL fJJC LCOU nc pi JbbLox!InWowJpC 22rIuJbiou qiq = i 22r1wbiou wq LU 2CCPOU 5 2CC LOOWOC

CCU JOMGL

iupuiou L1fG oj j j bcxcuç JJ1JC biciion LUC2 MGLC pJpCL 2np2cdncIu !uu1ou Ic pcLPC ChI LO PX 31 bCLCU JOW DGCCWPGL I àôO O DCCCWPCL j j j iwb1Aiu i

E01jOM1U BOCLP1 (ioos) j 92flWC =

2CCflLLJC2 MJJGIJ = 003 /A'P AbicIii IJJOL JC-O-AjfhC ULPO ITJJOU I W1CL h =0RO

2cciou 5 C1JAC = LOL ipc LC1j uc LGWLU ou z boi.qojio oj qcp uq GdniA

¶J22nmbiOu q i = j twbp w W iionjq PC 0085 ¶If 1IJ 1U1OU L1C OT = 0053o

12{C Oh COUACUPOU UJOLLC2 M2 1" = flJq JC hUG O TUJ1OU M2 = O01 JJJG

lu Aci OL Mp!CJJ OJCL q'w ou pon2ju ncq tu p1 cciou MGLG qcucq fC

waiucuucc [in] uq qcbLccJwou [2] JG2 fpc iuijwou A iu ou bLobcI.A [.c}

jocq bLobCI.A wx LCqIICCq pA fJJC /&JnG opC coacbouqiu wx qcqncJou [(i— o) bjb1n2 JJC

(i - o) I bJn2 obboI4nuiA co opc cdniA iu/caGq in jJG Of12G [( j — h) (LU + c)] b1r12 JJC

MLUU LI OjjL1L2 MOLIJJ OpOr12iU 12 IJC 2fIUJ OUIJG IJG OULIX WOLLIC 1UGLC2 bLIXmcu2 h [

2LIUJC J9L ooq2 in GUGLLIj LIuq ponc bLicc2) jp cdnpou &A2 pL qic LIUUflLIJ coat Oi

bL0bGUA in 9 LILG qcucq poi LIuq 12 fG LLIC oT, UOU (2nLucq ID pc fJJG

UJOLLIC LU j JJG LGLII IJC LLIG OLCU1LIJ LIALIIILIpIC ou bowojio Iu/C2uiCu Lb LLUG oJ

ALIJfIG O1 IJJC JJOfl2G 9 ! JJG WLIL1ULIJ IUCOIJJC CLIX LLIC 1W 12 1UGLC2I LLIIG bLIiq ou

IIpGLG }fl iuqicLriC2 JLI J 12 JG LCUILIJ CO2 OJ LIU 1CW1GL h 12 iJJC LLIJO O JJC UJOLfLIC ID

(j) id = (J_O)!w+( j —h)( +i)+(J_9)Lb+w +9 —

Page 33: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

IUI\OO4ô 3

nc L!0U2 jpc LC2I12 OUJJI2 2CiOU JLG U0 2cu2ii/\c o pc bLcci2c JGACJ oup12 bILUJCGL0WGOMUGL2 LG i1GW!CL2 TUq JJIf IJJO2G MJJO qo icwic TLG jqcjA 0 pAC jJ1pGL woIic-fo-

iucccq o .3 beLceuf ill oor I 112C pipcL ijnc fo Lcjcc pc jrn UOf

2fICp u0uJfGuJJcL2 inoi.ic !uCLC2 bAwcu2 iuq pc bLobcI4A x biüwciua 1LC uo JOUCL ix

qLJAG tIJG coLLc2bouqJu cxbLc2eiou2 JOL OUJC0I1JJL2 MO qo UOf !cmic pcJL qcqncfIou2 J0L

BG0LC ciJcnpil1u fpc qciqmciju 1022 cIj.cc2 oupe cqnccq iuijiou !i !2 ucCc22LA fo

2UJI1IcL qi2oW0u

JOMGL LG oj iUJ10u Jmbjic2 pipcL LGUV1J CO2 bcL nui °L pon2Ju cbij uq pcLcjoLc

ooaa iwo bcLccu Juiou q\q = — os !WbPc2 WI' = 0J048 cL0 JUJ1OU jpc

icuiiiu 0UJOMUL ip woi.ic o /ijnc L1O oj o q\q = — Ø'5' iucc jj5 =

q(L' + ) \ qiC = OX22 jpJl2 "PP 0 03 qWI\q =0 T + (1 — h)—

j OL JU

qcp qccLc&2c oin LU= = 0 io LL ooo = oos !c qLU\ q = — ost uq

JUCLC2 p?\ ouc bcLccuWc boiu pc Lcq uc LC o LGf1LU ou boI.oiio o cothouic cdrn ruq

cciou 2OMG qcicp bcLcculrc boiu 1UCLGi2G in pc LG ojjujriou Lfl22 pc LU oi

() qBiq = (1- 0) qiw \qit + ( j—

h) q(L' + it) \ qit —

OMUGL occnbicq poniu:

oIJ2q uoii pc ccc oj i GCLC2C !U pc LIC o juiou OU jJJ2 iwbpci LCUWJ CO2 O

C021 1LOW J33 CGU2 bcL qoju opon2iu cbij o g ccu2 beL qojpii ojpoff2iu cbii

JJJII2 Jc cOmplinwou opc wx UIIG2 uq mo bcLccu Jujiou LUC Lcqncc pc LGU

CO2 bcL qoJJL opon2!u c&brWl OL u JCW1GL pcu qic iupwou uc 12 iMO bcLccu !2 WI =

IJJTL1UJ UX LC oi e = os bLobcI. wx Lc oc' = in = oo iiq 9 = oos pc LCU1J

Page 34: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

Iujj\()5O4

JfGwiS bLobcLA x qqriciiou CACU ponp rpA no lOUGL p/c &uo iGWJG n jj uq fPGLGLOL qo uo qcqnc bLobcA x bAwu owc xbAc w&A in

,jjJ!2 OLWflJ1f!OU 2flWC2 JJ9 WXLAL2 MO qo UO I1CW1G UJOLIC qcqncpoua qo

HOn2!U C0UflWbf0U

H° H' H3

icbL O H°11EdIIJ/JGU1I{G1JW1

I)

EJnL : How0uL2P!b JUAWGU

cJbit1 qcmuqcq o i.uij co oj ncp poniu ip no wxc ° =Ø j 3 uq pc iwonu

jjJ jfTL bLCCIUa pc cowbcu2q qcannJq cnuc Lcjuiu pc dnuijA o poniu

EJf1LC 5 2JJON IJJG UJ1LC OUJJC MGJILG IU 1LOW LGqf1ciu JUIOU OL IxbAL2 MJJO

q2I41J2 LC cqnccq MGU pC LG o iuuErion qccJiuc LOUJ MO bLccu o CLO

fLC p!pcL p1u JJG coLLc2bOuqiu AJflC2 J9L 1CW1GL2 pm Of IUJbJA 2F12JUJ

MIjfIC LJO 1WOU UOUJCUJJC12 oijr JuJbpc2 icii3= ooo cuq J�I'l' =oJi BOP

jpc L&LIIJJGLIC ¶1nwb1!ou2 wiqc J0L !M!L2 woqJcq oujA pA 2nuJjug jOMGL UJOL O

(J) = hiw+(J_h)(Lu+)++w +9 —'

qqncipjG !I.UbIA!u

Page 35: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

233ub51 noiflifini oi s Im xsi niiix di lo noiiEnidrno3 dT .

21 bbrIEmb gni2uorI lo

12o3 xiq Ii oni2 .

1H 01 bnEmb fIi2uofI 22E13fl1 bris 801 .0 = I5J ol 1203 lEin3l rli

o! ir1gi3wbEb B aifqrni noil&iidmo3 noi1Bflni-xi1 rIi ,

5I i 1i1iqB3 gni2uorf nibivoiq lo

th bnE ni2uor1 IEnoilibbs dli gnibivoiq lo 1203 r1i nwi,d IJ3 rli .i A d nwof1

I5I 01 idiiiu1 ni2uorI lo 12o3 !1ni di 3ub1 1n31q owl ol noi1iflni ni ii A .V1U3 bnl$rrrnb

£Th fli i 22o1 idi3wbBb lEnoilibbE rIT H 01 nieuorf iol bnEm3b 3r11 2f13fl1 bn6 8QQO.0 =

21U I ol u1zv r11 bnf3 ni2uod b fi3fli rf1 gnibivoiqlo 1o xBt1q 1r dI nwid U + J

.3V1U3 bnf$mb r11 'd bIniqi 213

01 noirlol2ib dI ni3ub1 moi 11ui iErIi o1 lrLiwbb rli rn noi13ub1 rL1 ur(T

i ois ol ifl31q owl moil 2nu13b 1zi noi1iflni di ri1w bnEmth grli2uorl

.(1H— cH)(51 151).0+(1H— cH)(151 —

5i)= D (81)

MoiiJ$mixolqql3 m3niI £ HIIW

(5J— 5I)(5Ib\Hb)(5I —51).0+(51— 51)(5Ib\Hb)(151— 51)= O (?1)

H 51{c51(51 —51) .O + [ 5I \(5I —

51 )][ 5I \( 51 — 5I ) ]} (51b\I-lb) ( (FI\5i ) — =

lo \1i3ii213I b3lE2n3qmo3 3r13 lo u1Ev 1u1o2dB d1 iol (51b\Hb) ( H\51 ) — = 3 gniiiiW

SI lo 23u113v bv12do lo 2u1Ev bvido r11 113) iiq IE1n1 d1 ol l3q21 riliw bn13mb niauod

b1,i' 1EqxEl riiim1i ni iol 23u113v 1E1n1 3r11 nitu1it2du2 bn13 (H briE

IH J51 {(0e0.0) .0 + (00.0 )(EV.0) } = 1D (Is)

JH I5I 51H3 QNO.0

ôQOO\flnJ

Page 36: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

bbi inwomorI gniirniinon ioI noilIuoI13 m1imi i Mfl E-5' 5tH3 OO.O = E140 ()

3Th bnEmb lo ili3ilsI b3iEnqmo rfl 1ith noilqmuas th no owl th ninidmoD

rioitrolaib b3ub1 r1l moft nii m1Iw islol r1l vig ixirnlinon brrn isimli ioTl r1l

:oi ol lnnq owl moil noiiz[thi muiidiLiup gni3ubi mofi i1ui tdl bnl3m3b niuor! lo

[fr1H 145I ôOO.O + EIfl J51 tO.O] 5tH3 = (0 (Es)

oilM uIEv 01 iiiom sf11 lnuos olni 3)1131 3l131 Iln31 3f11 b 2no11131u31133 3r11 ni2 gniauod b3iqu33o inwo f1l lo JJI5tv 13)1mm 1131o1 3rD 3m(MH bilE IH lo iuim 1n1w3131 3rD

bns 1inu ni2uod b3iqu33o inwo rioillim O w 313r11 ,

I QQ I nI .13sim31inOn bilE 13ifn31i 10

inwo lo 3ulisv I QQ 1 Islol ri1 33flI .2noi13ub3b ghomn bimn3ii omiw 1sqxs1 noillimn

owl .3) amorI 1ims1 3Igni2 lwl nsrD iom bu13ni noillid O$ lo 31sl liui b3iqu33o

-nwo 3rD nibu13ni) e3morl b3iqu33o nwo 10 3111Ev 3rD li3i I (acmns1 bns a3morl 1imth

33PI3 3un3v351 IEnl3lrII m{T .noillid OOO 3d 01 (mod '1irris1-ow1bo noilloq 13iqu33o

!noillid w noi13ub3b 3gshom 01 3ub I QQ I ni noi13ub31 3Ui3V3i xsi 3(11 isril b3rIoq3l

noillid OOO iuodf3 5101313(11 bus anoilaub3b sjtiom lo rioillid O) I \131Emixo1qqf3 grti1qmi

1h13rr1 3rD IsrIl iIqmi .O=v\mn1o 11fn31i flOff1S 011131 3u15v 01 iiiom r1T .itiomriIo

lo 3111Ev 3(11 113mb 3i1qmi ir1T .noillid OOO = JH i 13imn31i d b3nwo niuorFbo 3u113v

.noillid OOO = T4H 21 2l3Mrn3linon 'd b3nwo ni2uor1

ob 2l3nwo3rnorl imm lr3rIl 1351 3(11 21331131 231ui1 owl 323r!1 n33w13d 33n31311ib 3rIT 1113n3d 3mb isdl 2si-Iom I!13m2 r13u2 3vsrl 3rI1 ,2u1333d) 2fIoil3ub3b ihorn im31i Ion

2l3nwo3morl 'nsm 113(11 bns (1113 Is 38138tIom on 3vlsrI io noil3ub3b blsbnsi2 3f11 niu mou1 iom .33r13bi251 3no (113(11 3lom nwo

oo\:tnI

Page 37: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

(8Q0 1.0 = j451 bn 8QO.0 = J51 diiw) noii&ip oil! iBmii2 r1i niiuii1dij

X1i ai1qmi

.noillid 5tH3 [) () ni noiiflni di gni3ub! moiI ni ir1i ih i1qrni 8.0 = 3 lo i&nii (8 1) no51 gniU

rn1q 01.0 i mEg ifli rtoi11id aw UD 1Q1 3f11 3ni2 1Q1 i riolilid Q. i .quo0

o"cX sO i'K o o oX\o i1 .E

ion ob UlV31 xEi ni 2grzEr13 113d1 noiiqmu2s lEnoilibEli r1i no bd i nitg E0 r1T

dT .1knE1i bnE xzi mu qrnul l3rlio 'd iTto d lEO !i uE33d 3m1iw oimonoo iofls

'unoiiio1ib idio ni noii3ub31 iirn1q 3UlVI xiii ni e aE3loni i1i noiiqmu oiii1ii oiom

atIuoi i1i gniuod ot bidu xii boubi r1i o1E tE1u31s3 ol lruthoqmi i ii i1i oi1qmi xJ3i

.noiiiflni 'lo iin iwo1 i mofi

ni noiXubi r1i thmiw ol inoix odi no bnqb gn13r1o unvor r1i lo buiing&n orIT

ou I 2irli 3if3mii oT .ioto niaud 3rIi ol gniEuod biquooo iriwo moi1 IEtiqso fIiH noiflflni

inoiq r1T .8.0 = uIEv hini orli 01 i3qai thiw gniuor1 1o iioiib biinqrrioo r1i

= i 8QQO.0 = 15I moil aixim1i io1 gniworl biquooo inwo lo ooilq 1Ein1 ofli Iii asioni

to boi muhdifiup 1i ru ni1ob inoioq I s ai1qmi noiizllni oi iE 801.0 = 151 ol 0.0

ioi '1m1imia .(21v3I 1Q1 IB) noillid 0I82 01 noillid 000 moif gniuor1 biquooo-inwo

= 1V151 ol 0.0 = i i 8Q01.0 = 45I molt oiiq lEinol r11 flu E5I3n! innq E r11 ioirniinon

urivi IEioJ qA 01 b31u[bE oiu xsi iu1io uE3d iioi11o b3iEnoqmo3 3f11 u 1 . ion1od1 o2 .inEino3

ôQtOO\I-tnI

Page 38: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

-inwo1o Aooi muiidi1iup iiodl ni onibb Q. iIqrni noifl11ni oi j3 V 11.0

.(Iv1 I QQ I i) noillid I ol noillid 000 moil niuor1 b3iqu33o

bole niuof{ niniErf15I1o noilhid 048E r1l rio 'bidu b3ub1 r1i iiil ibino3

= J lo oiiwi u1Ev ol iriom sb noilqmu22s r1i ninislnisM .isqxsl niimii d bnwo

lnioq nnq owl r1T .iBflqs3 niuo1 ir1i no noillid 0Q, I bo 2sgt1om Islol ai1qmi .0

bns noithid d 2inrnsq li3irii gsi-1om 3ubi noiisflni bo izi dli ru nu13b

.noillid 'd unvi xsi sini lsi xsl Isnigi&n in313q s gnimuE

ni urivi i31th iol aeniud rhl ol niuof1 biqu33o inwo mofi lsliqs3 lo fflr1 dT

di no noxl3ubb xsi 'n3qo1q bns noii3ubb iiom dt 2o1 iicnli rh lii1 .sw irLi

08 Tb agsgiIom 01 bnoqeno !sliqs3 bubi r1T .Isliqs3 niwor1 b3ubi bo noillid 0ô I

.8 bo noilubb iilni sgJiom bo ln1q owl lo lsi noiisflni Isitini r1t is bns noillid

o1s niauod biqu33o inwo lo bo b3ubi r1T .noillid io noillid 08 eith lo in31q

.noilhid N1! io niuor1 noio1bo noillid 0ôIbo ln13q 'd 2noii3ubb x131 tIqoiq 31rb1

li3nigisrn s rii1qqs bns (noillid ô.0 I ) noibubb bsimii ni rioibubi owl rli ninidmoD

.noillid nis unvi s i1qmi ln31q bo lsi xsl

8 aulq 1sim3ii moil noilhid 0ô I ) iolo aniud rli ni lsliqs3 bs13ni r1J bno3

01 b1i xsi-1o-in s bivoiq lud inuiq .Q lo niuii xsl1q s rns (iimlinon moiI noillid

xsl dl i 3n31311ib dT .oi i tsi noilsflni di nifw ln3iq 4Q 'Ino bo iolvrii

bo rioihlid io IsiiqsD 2niaudbo noihlid 81 Isnoilibbs rIi rio tn31q à.Jbo noii3h1o3

.ur1v31 fsnoiiibbs

01 Isup3 3UflVi xsi 'iqoiqbo o! s aus lsl!qs3 gniuor1 bubi r1l biir1T

.noillid io Istiqs3 niuor1 ni noit3ub-i noillid 81 rt1bo lfIu1q

Page 39: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

io noillid Q.ôlZIo nii unvi in B iIqrni unvi no iiI irIi 3di ninidmo

.(Iv! IQQI Is) 'lUDlo Iniq OLO V\ i.tX io zoW. is"1 . E

niauof1 c11 no fIOiIEIIfll muiidi1iup iwo1 lo 1b r11 mo-il nisg is113w Islol 3rlT

niuor1 ol noii-ioIib boubi r1I rnoil nis m11w Isnoilibsil HJ (1)10 mu r1i i 1oi3

noiHid Q1 ih1o nupno m11w dI () bni3 ;'lUDio rn31q 01.0 flOifflUflO3

ir11o moil bisi ,unvi lo isliob r1s II .'lUD lo lnnq OLO lo nis unvi s nisg unv in3iq iuol moul nifiid 1o nis m1bw Isiol idli A lo o1 Ir1iwbsb 13 v1ovni xsI

2i noilsilni in3q owl 01 noilsllni

.quo [A OOO. + oioo.oj = o (1)

rIi isdi 23ilqmi 1.0 = A lo ismi1 (8Q1) I1&1W bns nvor12 bis1lisH vi1svino dT

riliW .quo 1o lnoiq .0 i oi ol Ir11q owl moil noilsilni ni3ub1 lo nis 31s11w Isiol

bisod r1l aois iis lo 111, rI1 iol 1ismil 1sioivsHd rIi d biIqmi . I = A lo u1sv 3r11

owl molt noill3flni griioubi1o nina 51s1Iw li3Iol r1I 1si xsl fflO3fli Isno13q 1113 lii i3ifl1

.1 1dsT lo 1 woi ni nwork m r1T •'IUD lo In331q .0 i 01 01 1niiq

bns nivs lo noilsxsl d1 ni n&1o di mofi nisg r1i iltiw idt gnidrno3 iob8

iwoI s fbif{w iii asw irho owl 01 n-iul I eflOl13flfl nbubilo io rIl 01 mu fIl nnsqmo

1bud lnmrrrnvog ,rf1 Hguouh is11w 3ifflOflO3 213&l1s noilsflni lo Isi muiidi1iup

.IfIiB1If10

bnkm9tl inoM to noitiotiU dt bon 9wioini .4

3ns1sd nom niisd-1iini-non gniblodlo too di aisi noilsilni ni 313313fli nA

rfi rfuof1I1A .1vf Ismilqo r!I wobd 3nBt13d doug -iol bnsrnb 3r11 ubi 31o11r!1 bns

QOO\Iin1

Page 40: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

ii11w ,rli no 1uiJ31li1 ili lo 2u3oI '1&ni1q r1i nd &{ noi1iflni lo oJ Mgi3wbb gnilIui

1o bn&nb '3flOm ito b&I1 rti iqiq nu1noiq (ôQI) 'IiEEI nl2 noilEflnilo T1 v&1 1iih 3it 13db 3th ol 3viiI31 IIsrn2 i oi 01 1n3313q owl mofi n31 noibEflni 3db ni3Ub31

idi ni b2u3aib nd lb noitiobib rli bi 12111 nb1ooI 'd briE 2noii3 b Alow3mthI 3db 2woIIol noib 2irIT

lo gniblor! 3r11 no xE1 noibEfini Hr lo 3fl3UitO3 3Ufl3V31 db bi nril bits 'nom iol bnl3rn3b

.233f113b3d 'nom

tiM oV\o ii'1 nV \

3db nisini 01 ioo Ist on 21 313db 33ni2 bion asH (QQ 1) nsmb3il1 nobliM aA

3db ob bab3 3db 231sn1m113 '13131qmo3 Ii bsrlb rf3ua 21 bsi rioibsflni Ismibqo 3db nom lb bibnsup

fsthrnon 3db bsdb d3u2 3d bluorla 31s1 noilsflni 3ffb .3.i a33ns1sd nom gniblod lb Isubivibni

3151 noibsfmni Ismibqo 3rIb mb3ni Isbiqs3 no aoxsl oct rlbiw morio its .oi 21 bsi ba313!ni

ii 1113n3g 3loM .q — = *it :Isiiqsc rio rnub3llo 3151 1531 3H11o 3vibs3n 3rIb 3d 31o1313r1b bluow

xsb-i3fh3 Isnurnon 3db 113db rkua ai 31131 noibsflni h3mibqo 3db 23xBb lo 33f1312ix3 3db 3ino331 3W

.o13 2i 2132213 Isi3nsnfl 3vibf3nl3bIfl no mub3l

bits OO.O = ai oitoThoq 'iiup3-1d3b 3rD no nlub3i b3n 1s31 3rD O.O = r Is bsrfb II&s51

ni b3ugls I aA .133113 !Eub3qi3q 13 al bi jlsfna 13m31bx3 2ib33113 Isunns 3db rfuor{biA uo lb noib3sul 11131-na '13v B 113V3 lb nis Isui3ql3q

13 'rnono riiwoig cii (QVQ 1) ni31ab13I r1uon3 wol ai 3bJn inuo3aIb 3!silqolqqs 3db Ii noitsfbni ni3ub31 10 1203 3db r1i3wbuo sm

13v3wor1 iqsq bn3llu3 3db lb bx3bno3 3db nI .dbwoi 3imonoo3 31s31ggs lb 31s1 3db 01 3vi113b1

2b3113 3113113w 3db 01 3vib13131 lisma '(13v at bnsm3b '3nom cii noib3ub3l 3db lo 133113 3113113w 3d! .awsl xsl 3db bits noibsflni 10 noib3sl3bni 3db lo 321rn33d iuo bsrlt

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Page 41: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

lUUf\OOtô

C{MGCU 1XG2 uq !UU!0ULu > > — b 12 I!J(GJA 10 LWJ1U TU UJOLG cxic CJCnJIOIJ LGUGC1LJ flJG TUjCLCTOU22J1UJb1JoIJ o pUGLI w uo pe bbLobuc OAGL pc CULC iuc pc pic bLobcI.A

qLhJ \ qL LCWI1U2 COU2fTJ IIJG ObPLJJ Lfc OLJUUPOU 12 3* = — ooo V1P°P p12

poq!u ujoucA pqucc uq L' --=

12 pc Gj2ici o woucA qcuJuq MJp LG2bcc o pc uowiUJ obboI4nUiA CO2 o

= 000080 j.t ( Lu )

= — 00?30 [q IAI\ q (LU + )] (ooiJ)

OO3O(VI' —LAT5)

() o' = oot (v'i'— + o (ooo — oot) (vi'

ouc? DGWUqV'T5 YI'

ii:4

000

W03

hJr1Lc 3: youc? curnuq mJq 2S1UOL1C

wouA qcwuq cnuc uq lpc cLo obboI.wUi C021 Jrnc:

2fTbbJ)JU iJJoLJG? 12 GLO C MGftL iU FLOW Lcqnciu 1UJPOU 12 qJC LC C+ D pcCCUpc

LU + = 00Q0? 10 pc A&jfIc OJ Lu g = O ! Lu = ØØf 31ucc pc obbonut CO2 oj

JL0w = o pcLcpA Lcqnc1u pc obboi.jriui CO22 ojpojq1u uoucX prjucce ow

L1nLG 3 iJJfl2Uc2 JJG LcqrtcJou lU WC qcqMcJp J022 1}JU LC211112 JUlie !UU!OU LG !2 cqnccq

qLu \ q =—

jjJc obiuiii iujiou LC iu pJ2 coucx 12 2flC LU + =

+ r

Page 42: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

-non niiid tiini 11sin won i 1Mo 1nnoqmo ioqb bnEmb r1i ni u1q '3nTIu3 I iii )IfIBd 2u1q 3flT1U3 ILBiiu12 won i 'nom nid-1iini

lo mii1o nsi biw i i rIT .TUD IO.0 = M uriT .quoi0 rn331q I .ô iw v-ii niThb bns 'nom lo 2noiinu1b iniThb oi nibnoqno3 brismb 'nom lo i3i1Eb rli

ihiw xinoo 1nTIu3 rh nk iEiqoiqqI3 d &n .0 = M31o rrii1 nA .noi1ibno3 3imono3

.quo 1000.0 = D nohqmii dh rhiW vii lnsd u1q onnu bnifb 'norn

oI ir1iwbEb 3rD bu i 'Iqqu2 'nom IEmitqo th iol bisbni nsmb3i1I n3rlw fl3V3 iir1T

.quo 000.0 'Irio i ni31&J 'nom io1 bnEm3b b3i1oiib 3rD ol 311b

fil nOii3ub5I 3Lrh iiI idh Iii 3U331 tn3rnrn3vo b11f3 riohiflni ni 3nuID3b 3rIT

b3iEi3o2e fiB io1rLi bnl3 B1Oin1 Io o1 B ni flui nB1Ed nom no xEi rloiiEfmni rh

jnuuldiliup3 nI .(ER I aq1d) xBi noirioib i3rho d 3Ufi3V31 niiin 10 aoI 5u31bw

3rD iin i noilBflni 3rD gnif3313nI .M 3 01 IEup3 3iJfI3V31 3iiqmi Jt 3iBi J13 fIodf3fmni

3Ufi331 3B10irIi3

(t b\Mb) + M = b\3ioni b (à)

I M ni d-13i3ini-norI iol blirIl-3no lo ii3i1!3 fiB b3mu13 I (QVQ 1) ni31bI31 nI won i norn nii d-trni-non 3rD 1irh tzth 3r11 1fl31 01 WOfi 3uh1v wof rh u I .aliaoq3b

bnBm3b Ii n&h 3viii2n 123131ni aI 3d ol 'I9Ii1 31E 323r1T .n31 lnsd JJIq 3fI3TiLJ3 1LJ giiib{od 1o 1o3 iin1thoqqo 3rD n3rlw = M3 113rh noilqmu2aB 3rIT

. I M lo rrl3noqrrlo3 iioq3b

11i ni 3E313ni lnioq 33Bin3313q 3rlo i lEnD 3iIqrni 0.0 I3iEmixrnqqE i 33ru31Ed '3nom f1ES 3rD nia .1o '1i3i1BI3-im3 B F0.0 = ô0.0\(10.0) . \3lBmixo1qqB 'd M e33ub31

= M1 noi13313 3rD 0 I = 1 o E I rnoil b3nz1 ii3i1!-im inh lo 3iBmii23 (Q I) .3v!1Ev13nO3 3liup 3d \E ix3lno3 IfI3TIIJ3 3rD nI

04 à4OO\4InI

Page 43: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

lt \O5Oô

!uo pnetuc cbij q12cn22cq lu ccioui iirnoon o fG LC/CUf1C nu 22ocifGq MJ pC 2pijj o Ci2 ow poneiu

O1CLIJUJCU2 ipijiA fO anP2fifnfc fJJC JucLcJ2cq wouc? flJCG OJ I4 — jAj OL 1UfGL2f puu

jJJC T!UJJ LACUf1C CJGCf OjJJC CJU HJ f}JC qGuJrnJq jOL IJJOUA 12 f}JC LC2rJf OJPC

000Q bLccuf °1.ODb MP11 MIf}J = J fJJC j022 !2 0051 bcLcuf °ODb

fpi2 GXfLI LGAGUfIG oojt bGLCGUf °1.ODW #1!P Y = Of f}JC MCftILC J022 FLOW fpJ2 2OflLCG 12

°T.ODb ILUbJJC2 LGAGUI1G J22 oLOO4Q(O3O) = bciccu °J.GDh LPC MCJJJLC &HU JLOUJ

bL2ouJ Wx bAwu2 o bcLccuç ybbjAiu fpJ2 io pc 1ucLcmcuf1 cibirj oj bLcuf

oij3 bcLccuf pn UGf ouix i.nuJ oIoIJ1A bcLccu jjJ qijcLcucc i pc coLboLfc uq

bLcuf O GDW //JJIJ fC2 22Cf2 iuAc2fcq JU pn21uc22 cbij fpX 1LU LC&J bLcWx LWLU

iu fG mouG? 2focje ij'—

+ )] (jj) j1j (L -- ) = oo

pIJUCC2 pow opci bLoqrlcpAc 122Cf2 JJJ GCLS2G JU fifl2JU22 ccbij La GdnJ o JUCLC2C

1IJ accouq LGACUfIG CUPCf !2 fJJC LCACUf1 j022 WU LG2flJf 2 TLOW 2jJ1JIU cbij o woucA

2GJLJOLG 12 y j bcLccuf OJ ODb

oupe 102f 2G1UOLgC 12 ØJQ beLceuf °WDh #PP y =j tiJe IGJ9LC C02f OfJJC JO2

ipe coacabouqiu McJJILc J022 0 j y beLceuf o ODW /A'P = Ot fP /llLc C02f

CI12C2 JO22 OJ 2G1U0LG o j j beLceuf OJ 0Db

iuibpca fPU q( 2c$uoLc) \q = OO8 GDb y qcccac O1,iUIJfiOU JLOW .c = 003 f° = 0

R!fP It'! = OOQJ GDW =o q(L" + lt)\ q = = oo uq L" + = ooQo cdniou

= v! { i—

[q(i." + c)\ q ] (L') - }

= + [qyq( + ) ][q (LU +) \ q ]

Page 44: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

IUU$\O5Otô

1JJGLC1OLG 0G2 UO CJJUC 1IJG LLGJX C02 qcp 2LAJC PfULGflC2 JJ X LGAIJflG OU

MpLJG !11U0U bLcunnw 12 2r1p1cC 0 1X & qJG bcL2ou&1 J'1 V jOMCL LUiOU L

CO2 OCCFIL2 pGCrn2c LuJiOU JG1A2 1JG LGj bLwx JUCLC2 L1 OIJ 0AGLIJUJCU qcp iiiJcpUcq

umouij qcp pu LG2fTI2 LOW i Lqnciou LU JJ L1 OJ LIJULULOU jpi2 p1JJCL qp 2GLIJCG

JJJG 1J7} G©c O] cqnccq LujjioiJ ipi I MJJJ cou2JqGL 12 IJJC LJJL LG1 CO2 01 2CLAJCJU&

DP L1!CG iuq 4J16 COAGLUWGUI BUqG4 COU4LJ!UI

wouc? qwuq cijcci

Cou2LqcLJU qJL2 2UJ1Jj LCflCPOU LU LUJ&1OU JJ bPCIb2 LC/ Ufl GTjGC 0UJ1U{C2 ipc njcA

qJ2OI4LOu o wouc? qcw&uq uq ?ft1 °L 222 o xbiu pn2JUG22 JIJA2WJCU42 //JJU

1022 IL0UJ LGqflcCq 2CJUOLC LGACUflC 12 UJflCJJ JLL f1J fJJC MGJLG LU L0W JJC cqnccq

V1{JJoc1p jj ojpc GJJGC2 jrn qcbcuq OU qJG qciiuiuq j0L wouc? 2UJJJ pc MGftLG

bLcUoJ0Db ft =o wq otyj bcLccuf OGDb ft JR

CO1IIP1IJ!JJ JJG2C JJ1CC GJJCC12 A1GJq2 1 UC ICJJ1LG 1022 qri 0 qccLGf2cq LAUflG o oo

VIY JR

!pc C01JC2bOUqiU MCI11LC iLU2 ooos bLccu o 0Db = uq ooo bGLccu oj 0Db

00JW IP cqriccq qp 2GLAJCC C02 LU bGLbGUTL !2 JfI2 (—

v'15 ) = ooooot 0Db

f22flUJG wx LfG o HJq i JJ LIJUJOU uic bcLcciu 12 = o(ooQJ)—

C2JJUJ9C O L' p2Gq OU IJJC 02LAG J LI0 0 LIJ 121 baAuiu2 10 ULOU qcp o 00Q I

orn2wuqiU qcp UC OTJJJC WX 1JJU i COJIGCI2 OU 11J02C JIJiCLG2 bAuu2 COU2GLMWAG

LGLUJUGUJX p? LU ( J.AJ' — tAI ) MCL LU 12 LfJ TJUGLC2f LC barq p? pc OAGunJJGU ou 12

OAQUJUJIJf qpi jponp pi 12 OUC iwc 2np2ijnioU i Lqnca OAGLUWCU qcp 2CLAJCG

Page 45: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

1.xE1 u3noitio1ib l3rlio lo bvI 1IgifI 1$

1iup1 mu ni idT .inm'q idb nmnivog

ni 3s13ni di izdf on ivi db lo io3 n ifi no noi1flni lo J11 3di oT

nttiiw d n (8) Jdb in3fnrnvoa lo A3o gnibnii1uo th

fl(+ i)1O—T—D+8(ir+ i) =8tx (Vi)

ii vi13u1 rIr i O bnE idb inmmvo lo in tiini xsbiq Linimon r1i i (t + t) irEw

fli no nrnq t23Thtn1 3f11 21 H (ir + i) 2uflT .2iftffI'Eq 123131fli r13u2 no xEi lo

idio LIE i 0 .td3b &li no 1iini ri rLi i 8 (t + i) (0 —

I) briE idb nrnmvog

th gnixi moil b13IIo3 unvi rI1 nirI idbo unvi xsi lIE i T bnJ3 nibnq2 1fifnmvo

.Jdob nrnnivo no

uo lEnirnon 213 131 ilt ii woi urn tdb tnrrirrivo lo bo rli jnuiidiIiup nI

rliwoig lo Xii 3rIi i bns noiEIuqoq lo cftwoig b Jii rh i n 13rIw ( r + + 11) 8 HA .i

aiLqmi V noiup dtiw noilibno3 muildiLiup3 2irLl ninidmoD .flJqiuo 1311q133 13q

n- (0-r)]+quo\D=quo\T (8)

.(U0\8) 0 — = tb \(U0\T)b uHT

i'ri db lo 1203 11331 3r11 23213313111 ois ol 1n3313q owl moil 31131 noill3flni 3th ni3ub35I

.8 0 O.O 'd (011131 UD\id3b nui2ix3 3111 nislniisrn ol b3liup3l 23x1311o I3v3L 3fh

lnioq 3sin3313q owl 3111 .O = qUD\810 oiiin UO ol id3b irinu 3111 bni .O = 8 riliW

3113113w 33ub31 31o1313f11 bluow briE uo lo 1n3313q ?..O d 3Uf13V31 x131 33ub31 bluow noil3ub3l

n33w13d 31o1313r11 i iv'i id3b bn b3213313ni 1o 1203 3113113w 3rIT .quo 1o 1r13313q A .O d

noilIlflni-xEl 3111 rfguoisfl) 3UI3VI XIII 3ni2ud no noiiEflni 1o 133113 3ff I 113111 31ot4 23X131 lo noi22u32ib 3vod13 3111 ril b3Inuo3 n33d 213ff (ld3b 311310q103 bn13 noiIl$1331q3b no rloil3El3Ini

lo iu1xirn 3111 ril 23gnErL3 1o 133113 3d1 brrn 2fl1fflIS3 b3n113131 1o 3101 3r11 1origi 2irIT .f1iVE2 bris .3un3v31 xlIl LIEl3vo 3r11 no In3ml23vni 3lEloq-103

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Page 46: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

m iui1 3r1T .1o 3uh3v 3d no nibn3q3b '1UD1o niq 8.0 bn quoi0 irI313q 01.0

.1 31d13T lo ô woi ni nwo

9111113W nmono33 no f1OiItflflI i9woJ lo JTLI YI nIT

nd 3v&1 ifi noiiiifmni bub31 lo i3T13 !13v ,d idJoJ niid won nj W

1uquo 3mui-3no r1i diw md mqmo bns flguoirli flO13 ni bEu1Ev3 bn b3iIiin3bi

I noit ni b2u32ib 313w iErI noi3ub31 noitcflni iEth 3v3irbi oi b3liup3l 3oI noiiioaib b33ub31 lo 2o3113 iib 3d gnir1iuni1ib 11 iuol di simmmu I 1dT

io1 fl3vi m 3uIEv 3imq32 .3Ufl3V3i ni n&{3 Li f1uoirIi iuo &li ai113 331ibr1i 3rD bns

rli iol bru (0.1 = i bni 0 = .'t , f.0 = .i) ii3iiI3 brlBrn3b gnivE 3vill3n13i113 3db

3vi&n3t1E duotdb b32i131 3Ufl3V3I Tb mibob iq oI Mgi3wbib 3db lo 3I3mii3 3viJ3fn3th3

.(. I = bni I.0 = ) xii nihoiib

3rD iD di Iimmiiq bfl31 noDsflrii bub31 moil nii m1 '13viiEI31 323r1T

lo 33ndE 3rD lii nv 3oI 1r1i3wbb m1 ooqmi noiflxr 1siq3 lo m31 gnu1ix3

.noiflni d b3iEdlo3Ex3 m 322oI dgi3wbE3b 3rI1 li3dr bn noirif1ni

rIif m1Iw li3unnE 3ubo1q noiriflni lo 3i131 3db rIi13WO1 'd noifloib 3rI1 8ni3ub351

3viii2oq 11I3ffI (13V £ 21 31311i 5I3fIW 32E3 gnivll2 )Imrnrbn3d 3d ni GO lo fl3313 . I. I lo

22o1 irlgi3wbll3b 3rIT .(.0 = .iT) i2313in1 lo trn i3n 1ii 3rD bn fliV2 n33wd nofl!i

uo lo 1n3313q 8.0 m , I nmulo3 lo mollod 3d 113 nworl2 o2113 owl l3rIlo 3db ni 2noirloThib

.GO1oin3313q I bnJl

lo rnoflod 3db b3simmrnu2 3ufl3v31 ni 23n13u131o 2133113 3113113w lEnoitibbll 3rIT

1331ib 3db nErD 131113rn2 is 33n13113d no lud 3vili2oq io 3viisgn 13rDi3 3d n (4 brIE C 2nrnuIo3

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Page 47: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

3ub1 iI unvi 1itol r1I O = i lo A1&nr13nd r1l iii .noitiol2ib b3ub1 lo 11

= iB R.O —

bnE 1.0 = ii 1.0 —

nwl3d) I1m !viiEIi 2noiioIJb1 r11 iud 1E1Iw

nh1 E 31o11r1i ai oi ol irt313q owl moil noiii$flni ni3ub1 lo i11 rB1bw lElol r1T

£ uo lo innq 10.1 bn m qUO lo ln3iq ô.O riowld lo niv *umf13nd r1t fli

.li 23ub1 noqai gniva wo1 ii 1ir1w nii in dl 32E313nf noqi nivui 1f{id A .m vil13tumuD mil-no ii ox ol lnnq owl moil olin noiliiflni ofh ni3ub31 lo lO3 r1l II

b3iBmui r1l 3i1qmi I nOii32 ni bauaib 2i1EnE (QQ1) 11E8 quoi0 lnoq xialo oI iom m fl1vF2 II lr1io 01 xi nidliw ioo 2idi laflo bluow *u$rr1r1oncJ di ni fliE

gniv1i Ii IriO .'b!3iup iom nv io 3c11 l11o bluow li1idsi nq moil ni fIl vi2noq1

bl1$miie 3r11 2ob ao1 I iwbb r1ir1 £ air1 niisi unvi bnE oii2E13n! liini i3Iqmo3 ei

UD io1 f1i b3x 01 bs3b E nEfil iom 1Bl bluow 2fIiE i11w fh i&1I '1qmi i3113 Iiiiol

IEunnhi di1o 3u1iv Iniq r1l idl ni riv3 .'Ii1idEI2 oiiq virb ol biiupi i i&1l

IiInd gniwo1 di ii uo 1iIini 1i lo ln313q 01 ab3x noilElini gniinimib lo ii1nd

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d iodi iii bluow ir1i 1if1W xEi f1l nixbni d iuqiuo lo o1 s luofiliw bvi±ni

ol 3viiErnI1E IE3iI3Biq £ Ion i ftirli rfw noatii f1I1o 3filO niBIqx Iliw noiI3 ir1I 31dioq

.noill3lIfli fIi3ub1

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Page 48: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

xit rIi xbrii ol lioqoiq1o 'io1iri gno! el irLi i&1t iatuo rit mouI bion d bluorla ii

ru baauib q'i u1i 1o oI ir1iwbib 1i ubi 01 iib r1t d '1no ion bivitom m3i'

anqx bnI3 mo3ni IJiiiqE3 lEnimon no xJ3t J3d 113d1 m3t xit i u33d oli3 Jud iqq irli

Iii v&f Ht1i nv xi ni !Eiiqil3 'q 1ubivibnI .11131nu '1tnis1ni as bb1131 i '1no i tsi 'ioiutste di Ii nv tn313q 001 box im mo3ni iifni no isi xiii vi1TI r1T

3ub31 Ihiiuinii1du ns inmqiup bnii inE!q no noiiiii31qb hinimori Ino niwo11A .tn1q

ui r1i1o HA .noiusflni r1ir1 'bvihs1i1o 2mii niiub inmtvni ni2ud rio ITI1LJI31 f1I

nr1w 08Q I hs bnii 2OVQ I usI rIi ni noiln3fls hEnoi21oiq bnii 3ilduq b3nirIgiri b3vi331

.1r1331q 01 b3b3x usi noiisflni .2.U

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iojuim on nI .mo3ni hEuiqs3 lo noiflixiit 3r11 nixbni ion ni riohs tori i 1EI biiriU r1T

hsi iol 1no bwoI1ii anoii3ubb bns rno3rIi Iso-i no 'Irio boivol xsi om 'çiinuJoc, Ithiiaubni

ii n&rnoD ru as truiiq bnii ovihsitinirnbii 1riiiq jsoinrlooi Iruisq oiii noasoi oriT noqxo

.noasoi lo oq'i rbso no inornmoo 111w noiio icIT .fIoii3iVnoo fJi3iiiIoq lo iofl&n

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Page 51: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

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Page 53: JOLU JTbCL 4Q - NBERlo noilsflni no rh 1si 1n niubi 01 .nivs 2i1IT eioIib h noiis3olls lo mii1iI noiqmuno nw1d '1it3 ait bns i1sI .iso noii tsuisv 3f11 idiwbsb o1 isril a1!ui moiI

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