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iovo 11iq 01 qirf2noilslol lcfob orb iii ioivsr1odim boon ow 1dob floqqu2 qlorf 01 qirI2rIoiIslol iorfions

Inuorns lIsm2 s isfil iuo aniut ml .

qirlanoilslol bobbs orb ni noilsiuqol 1nomrnovog orb r1inls1 bns

.mundiliupo ni iovolliqa rf3u olsionog 111w noi13o ni Isrit 01 ls1irni noilsrnlolni ololqmo3ni lo

oW .mnomi2loq bns ogisl iliod od 01 noilsIuqol boog s gninislnism lo iuIonod Ion orb boon o1s oW

olom Isdi isob od 111w II .2oIqmsxo olqmi2 iov omo lo nsom d anoilibno3 oor1J oIsfl2ulIi

.201711 onm orb gnols bol3inl2rIoo od nz 2oIqmsxo olsiodslo

bbs 01 ai ovods lobom orb 01 qiff 200115101 121n1 iorfions bbs 01 '5W lsiviil J2om out hso1D

2o15311q01 1qrni2 rbirlw (I1nuo3 iorlions ni 2loinsd lo quog iorflons flliw qirI2noilsIol Idob iorlions

8

i2nof1 f1i nrD iqx iotd E rni th d qui noi1smioni rh iJ .iar1i ob ioJ .121fi rfJ

iii .arn1nid b quoig 1fIti3 fitiw 213EIinO3 Aeid Ii 'li ii1ilu ni oI ii ifiu irIofnnlovog

quoi fliod fliiw iwrlrto3 LIE ionorl 111w inmnivog lnorf ffl jbom oth to muhdiIiiip nth8 £1 oe 13AnEd lo quoi iorIli 1i udT .g1EI 'I1n3x3ffiua i mrIJ rIiAEo1d Io io3 1i1ifli ffJ ii

ion i 1n3fnfn3Vo 3111 iiirli 31U2 ioI worn! 111w 13)LnEd 0111 i3E1JnO3 to oql iorliio AEOId iriomniovo

inomrnovo E ol bnol iovon 111w 1oInEd lsrb oiIqmi inomtrgrn noiiotibni b1swEd oIqmi2 A .ionor1

lsoid io 13sttno3 ittod lonoll ioiliio 111w 1nornniovo LEmron ofli o3noH ionorf ion i worn! or1i

orb moil rIoililuq31 wr1T .noiiEiuqol ati oo1 ol inomrriovo orb 0UE3 iofllio niAEo1d 03flI jhod

.saiov 331V bus iortio orli ui bovlovni luii orli ol iovo a!liq2 qirf2rioiislol idob ono ui bovlovni 1ui1

idob orli O135 iovo11iq i olorli u1uou1i novo isull 15313 ii 0)!Em b1uoff noil3Oflol inomorn A

idob o1ni orli riliw boiioqqu od bluo3 isfIl idob oio 'Iovii3o1Io lo lovol os ofli Ino qirknoiisIoi

Loborn orb ui nii1us1eb lo atoo orb bus atfionod orb ubod &ni .oiorl boiioqqu od ris qirknoilsloi

anoi2i3ob ILuslob orb i3 oIq ono riJiw lobom euli ui OIII 'or1i Isriw o3iwi 1qmi O1E at33[oIq owl riliw

11E3 idob oiom on iorbons ol qidnoiis1oi Idob ono moñ iovo1Iiq rhiw novo o3noH .bognsrlonu OlE

.oiolod od bluo3 nsrli boiioqqu od

'I1sioi i qiu1noi1s1oi bobbs odi ous33d 1si3oq Jsr1womo i Ii 1if1ou i O13l3X3 irI1 31111W

aI1iq qiul2no!lsIoi idob 3111 ui loivsulod2im ii novo isftt 3O 01 boon oW .ono niiixo orb 01 3i1lomrn

ni o1qrnsxo ioI .idob rloqqu2 ion Effi iovo11iq iu1i q1r12noi1s1ol lo oqi tfIolsThb iov S 01 1OVO

Em 2031U0201 oldilausuixo niv1ovni qiularioiisloi £ 01 lovolliqa isili woila ow , (1QQ 1) oorloA bits oloD

ui boibuia qiilanoiisloi boisoqoi Is3iq1 3111 al qiulanoilsloi iorfio orb ii iovowoH .idob iloqqiia ion

rnioq aiili olsflaxjl!i oW .inoioThb od sm ailuaoi orb norli ouflsioii1 'ioorfi oms orb lo us laornls

.insiano3 Sis aifionod bonoq-isq orb floiflw ui qirlanoilslol lodE! bolsoqoi olqmia s gnulobiano3 d aoisnsmo qirlanoiisloi iodsl airiT .Iobom Idob orb 01 qiilanoiisloi iodsl s nibbs iobianoD

lo niumiod orb is boiid aio*row lo iodmun orb 11 .boiioq rf3so ui oldslisvs ai lsrIi 13oo1q s moil

osia Isunixsm s asul i3oo1q ouT ai boiloq omsa isrb luqiuo ai3o01q orb norli T4 ai boilsq orb

ai vJlivii3ubolq rn r1J &! 13o1q iodiL r1i &ü noitqmu iT) .M � 3V1 JEfli on fD fu 14 lo

s sr1 'morIo33 3r!T (.'1no ii3ilqrni 1Enoiron iol i 2boil3q bidmun-bbo ni i33o1q icJib rü

.133[olq rli rnn o thri irI3rrm13vo 8th 211b12 b i1Ei33q fli 8vErL oriw io*iow lo l8dmun

ihow E nii i&1i iriutioqqo 1n3in'o1qm3 3vii&n3iIE ni rL briE 1E1iu3rI-)1i1 i ihow 8th lo

i&li 3U2E 3W .boil3q rbi ni inisti fiuiw atirtu

(8)

ihiW .atniE1Jno3 yiuoi au ol l33ldua iili1u eu nisimixEm a 1r13rnni3vo orb lobom Iliw oW

orb eosrrixrn rnomrnovog orb rloirfw iii ofio ez Loborn orb iqioinioi bluoo ow noiuiuon oiom 311111 E

-riolaib 1 ni aoxii bni oiuOesi boi1ii3oqa nieu d eboo 3iIduq aobivoiq anosi1i3 au lo oithlow

.'EW fIi

nI .awollol CE OlE CnoiiE3oIIE Ofh elfl3friilfflfflO3 iobnu IEIII olofi jIOlllUJfIi lo 3)(E2 orb ioI

I boiioq nI .0 aomuanoo bnli cio*iow 14 coiirl .1 alaovni brni aworiod 1nornrnovo odi 0 boiioq

orb rloiriw lo iuo 1uq1uo lo clinu MA + A lo hilol ii b1oi a133[olq lodEl brni Jnornleovni orb

0 aleovni briE eworiod inernrIievo orIT .M aiohow orli 2'sq briE q aiolriiid orb esq 1norrirnovo

iothil orb i&b ioi1 bohoq boiodmuri-novo 'iIE bnli boiioq nI .M( —

A) + (c— A) eornucno briE

3111 .M(— A) comucrio briE M cio*iow orb asq inomniovo oril rloiriw lo tuo MA cb1oi 133 joiq

= brni ao3nolololq ilionul rhiw noiioo iii cii oioH .ii alcovni bnii I awoiiod oahs lnomniovo

orb b1oi ol ciiw lo 1oiuiiv ii ni bolIfl3InIe od fhE3 1nomrnovo orb d noiuqmucno3 lo nimu1 orb ,

o\ I

.'ii1iuu lo ouhiiv bolnuo3cib omiia

cii orniia orb ci lobom orb lo gnimii orIT .lriorniirnmo3 iuorliiw lobom orb lobieno3 wol4

aioliow lo iodmurx ous1 orb lo rl3EO boiioq rl3iio lo fIifirIi3d orb nI .erioiuibbii oaorli thiw oio1od

orb ol lodE! lo alinu (1wi)3n s1qque ol ciello i io1iow rI3sH .oIubor!32 tnomso1qrno ni ciofto

muunulno3 ii rhiw bolnoilnoD .1 io 0 iorbio ci 3ri oiorfw iiq lo eliriu 1w lo oaimoiq ii iol 1nomfriovo

3EW hEuIJ3ilhEq 3fflOC CO3fIUOffflE lnorfiffloVOg orb jE3iirIobi OlE rkñilw lo liii co1uborf3a ogiiw rI3ua lo

ioilA .'1ohiiibomrrn bosihsoi ci 13ooiq orb lo uuquuo oriT .T4 qii iriomo1qmo ni riuiw ior1uooi 3w

0I

.ihow 1J bni 11nEd r1i flflw 13E1inO eli ionorf ol ion 10 ir1idw ebi3b inomnvo ri1 4&fJ

Cinisliano3 i1T .al3sflno3 locfBL bns idb di niionoil ol bnoqerio3 I = x bni I = lI W

ii lnmnivo dl 'd bi1 114A + 3x3A � I41wx + d,5Is (Q)

fitiW 13f113g01

,frI1ws — 3d,5I&

— 114A + 3x1A = — x + (01)

bnii

.14 � 314bn 1 � i+1 (11)

.,M ci eieAiow b isdmun cr11 1fli b3muec vJ3r1 w (O1) fT

lo cqi owl 5I)r1T .31ob3d Iliffi 01 islirnic ci ainmnivo oth 10 noils3fli33qe rfT

IEIiusn-)Ian ci inmrrrvo \wo A .1n8ffm1vo icrIoff ifs bns ifI3mffl5v0 Ismion s :1rrsrrifr13vo

rnsc f1i emsiic noiiqmueno3 c3lsIJIsv8 if18rnffl3vo os\ nA .E\ iwi is 3liflth 3111 atrluo3eib fins

niAs31d 01 ii1iiucib 3gm! s cniecs ocis ln3mn13vo ie3noil ns md in3mn13vo himion rfi es

3w is1u3irisq nI .135111103 iods! fi io tsilnoo id3b r1i 131i1i3 ci Isrim b3rIie esri ii 135111103 'ens

25 1f13frffl18Vo ic3norf flE to 233r1313131q 3111 3111W 1153

[M(s— 1) —

dM_ 1) - 3 () 01 bnoqc11o3 I = s bns I = s Isril 1153351) .el3drnun ovilicoq gisI 31S M brIE dM 313r1w

323111 no nil1us13b 01 bnoqe3lio3 0 = bits 0 = s bits aloslino3 iodsl fins id3b 3111 niionor1

blorl 213*10w bits eiLnsd ifoa .noiisfrnotni 3isvhq ci in3mn15vo 3111 to 3q'i i1T (.2135111103

3111 gnie l3ñs chiI3d 323111 3isbqu '&1i fins ci inemnlevog 3111 q'i isrfw luods 1i1ed 3vil3eiduc

.1nemrnevo 3111 to 2n01135

ns m isth ei3r! 1s313 elsm bluoffc cqirlcnoilzlei ideb owl ifliw evods becu ew 3io1 emse silT

ciosnno3 iocfsl fins id3b us lonofi Iliw 1nsrrIrnevo 125110ff sf11 jsfiom ziril to muiidiliupe risics'sH

eisvnq £ Ii euflT .3ui1 ed 01 emuces rfflo1e3nerf Iliw 3w rf3irlw eis1 1in3i3ffiuc 31E M bits dM ii

II

1flOE OuiI i3B1iflO3 lo oq1 i3r!iio 110 IILJE1OI) inomrnovo oril oo iohow £ io io{nd iorliio 1no

1nomuiE noil3ubni biiwI3id olqmi2 A .1onorI Ion 21 1riomniovo orli 111111 31U2 iol wonl Iliw

Ion i worDi or1i isril 1nomrnovo £ o1 bnol ioAnid io riot *iow iovon 11kw io*iow 313th oi1qmi

031112 r1iod no 11utob io 1flno3 rllod ionorl iorllio Iliw Inomniovo kmion orb o3rI3H .Iorior1

orb moil noi1iIuq51 orb ur1T .noiisluqoi 1 3201 ol 1nomrriovo 3111 ono iorbio no nii1uitob

lodE! orb ni bovlovni Iuii orb 03 lovo 211iq2 1n 2203011 qirI2noiIIlIol Idob orb 11k bovlovni 121n3

.1lov ooiv bn qirf2rloiIEIol

orb oluqmoo 01 i niwoiiod 1riomniovo 1oI 2noxIE3ilqml 2lobom orb o1Eri1$ 01 'w 3110

orno qolovob 01 2i 'w Inoinovno3 oiom i iovowoH .1101131111111 blEwI3Ed 'd '113olib mijiidiliupo

lobi2no3 ow :311111 13 b1i13Ed 1iiI ow flr1i ob oT .'1i3o1Ibni rnuhdiliupo orb Io 2othoqolq olqmie

to 0111Ev orb iol fl0125lXO lIE lobom IErb iii qolovob 111113 13oo1q lodl3I s 1no a1r1 1irb lobom

lodEl bns idob orb rbod rhiw lobom orb lobi2rio3 norb oW .0110113 qiff2rroilElol lodEl orb 11k noilsIuqol

lodEl offi 01 ievo 211iq2 qirlanoilElol idob orb ni 12u11 ni2o! 313th 1111201 Orli 0211 oW .2qirf2rIoir1o1

.bolloqqu2 od nii Idob o 1ov1 Inomlirnrno3 IhJt orli won worl2 01 qiff2nortJsIol

13 lo noilinflob lEmlol onIT .1 1113 iof 0 d = 1o Ow rloinlw ru lobom orb lobi2noD

.'11EffrIo1ni oiom boo3olq ow oiorl ;noiloo2 uoivoiq orb 111 0110 orb 01 ishirni2 21 muhdiliupo nEL2oEH

0113 Inomn-ievog orb luodE 1oi1od io*tow orb Iobi2no3 OW iErb rnuiidiliupo nJ3i2o\EH orb nI

li$noilibno3 21111 oionob oW .I2onorl 21 Inomrnovo orb Illrb 3ilid13do1q lilnoilibno3 d boshirrirnu

(ro12ir1 orb muiidi1iupo 2irb nI .Inornrnovo orb o orb 11 11i bnus 1q d 1113 1i1idEdo1q

orfT .q 1i1idsdoiq Iznoilibno3 orb d bosilEfrlrrlu2 211 boiioq lo gninniod orb u thiovo 1213q 10

b0111133o bEo11E ovEff 113111 211011313 orb rbiw lorboo1 jq no bnoqob ol bowollE 3m 21nos lo eoio113112

21obom ouT .(qwi),n 213 noIIiiw od ns I io*tow lo noi2i3ob *iow orb 2LJrfT .boiioq orb nirbiw

10 iorborlw iovo io nisimobnsi Insrr1fn3vo orb ovlovni 01 Iuo nIm l3ndiliupo r1ii2o1o1ni

orb 21011011 1rIomnlovo Ismiort orb 113111 3i1id13do1q orb olonob IoJ .1313111103 all ioniocf 01 Ion

InogE rI3uuo o32 oIdi22oq '(tovo IA : 2lnlomoliupol owl 213ff oluqrnoo ow muhdiliupo oniT .1313111103

ol nib1o331 b3lsbqu ri 1i1cJ bni 1ns idio lo 13iIc1 briE ir1 rLi nvi 11irnu1qo 13E

(1 ) 213siino3 no 2llushb 1vn 1n3rrIrn3vo inor1 r11 ni .1dioq 13v31311w Lxn i1 no Isrioiiibnoo

, I + I fl InorI i Inmnvog th IiriJ sIi1idEdo1q rfi Iirfi iIqmi 311n I8

i boiisq uoivoiq 1I bnr) I Ii 13ff 11n03 fl nuionori

_____________ = 13q (U) (,q—I) +

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1n3rnn1vo LErrnon rIJ bni 2I1ino3 1onof1 wIs 1nrnrnvog 1onor1 r1J 11 01 trnJp 10 nirIi

to iw b313fIo ni I nrfi 'IilidEdo1q riliw mrIJ ionorI

=Iw (14) 'o(3q—I) +

rft io1 1cIffioiq sd Irio 111w is.*iow thiiH . lo siiw bsI3sqxs ns Vi5351 Iliw ishow srli

Ii i I&b 13sto1q srli no nuflsi eth fIEfli sl i sIii ow sill ti Insrnnlsvog Isnorf

.A � 3w (I) no1iW-qsiA b1EbnE1 sill ni sob ii E '1l3Ex5 Isbom irIi flu aAiow noii3ubni b1EwI3EH

boiisq ol b1IwI3idI rriv1o .xobwisq sroIa nxEfI3 sill to 1sbom (8Q I) aiioc1o5I-moiliM briE (8Q I)

:noilondl 5111Ev niwo11dt srli svi 0

I � � A\ Ii MAT + M(—A)E\

A\ > � (A\) Ii MAI_TE\ + M(—A)

= (T0q)0V (I) l_T(A\) > � T(\ç) li MA + M(—A)

T(A\) > � '"(A\c) ii MA

!+T(A\) > ii 0

bsnftsb noigs1 I2swoI eu nI .loivEfisd muuidiliups gniwollot sill 01 thnoqasllos noil3nrfl 5111Ev irlT

wol bnE A > 0w sgsw E svi 01 iluons rlirl riloci i 'Ii1idEdo1q gnixim on T(A\w) > 0q d

El

IE how ion ob ihow 3nH .noii idirI-1xn r11 olni ionq bohq ixn qii ffuq 01 ffguon

boimq is *iow ion ob ihow bns 0q = 1q ridi bns wioiiq iierfi iV31 ion ob ihoW .0 bohoq

> 0q � I+T(A\) riliw noii iilid-ixn 3d1 nI .oie ijrfi i 'iiIiiu lo oulsv r1T .no oa bns ,

I

eli no griillushb Iinrtuo newi8cI ineieThbni ldul ci in5rrIn1evo 3r11 bns how ciLiow T(A\)

rfiiw noig1 iciiirI-lx3n 1i iii .VIA ci Jiliiu to uIsv 3rD curiT .11 griiionorl bus lsiino3

tisic bns boil8q cirli 13511fl03 afl loflOfi 01 I31Iq 11oiiie lrI3rnn13vo 3rD ,

I_T(A\) > q � T(A\)

3rli no woliomol moit :noilqrnucno3 to ciinu M(— A) cig ii sboi cur1T .boil3q lx3n 3rD nixim

3rD noi3i 1csr1ir1-lx3n 3rD io9 .MA\ + 4(t— A) ci li1ilii Isiol cii bus ;MA ci iiIiiu cli to 3u11w

cvi floirlw nixim lisle 113th bns cbon3q owl iol iosilnOo orb ioriorl 01 eioloiq 1lon1c lnorrlffloVOg

.no oc bns J4A + M(—A) + I4(—A) 1o 1i1ifli Islol s ii

.anorfJno1 nosiiorl ofnii orb as 0q ioiiq boxfi £ iot ioivsulod miiidiIiupo orb won iobienoD

lsth none ioo1ni nis ci 1 ocoqqu

.A(A\) > 0q � '(A\) (VI)

I + 1 —

T eboiioq uI .cbohoq 1 —

T icifi orb ru OIJJC iot closilnoo cii eionoii Inornniovo orb noril

r1ino1 orb coob oc iono1 clog T cA .iIustob 111w Ii T boiioq ui bus xim 111w Ii ,

I — T rlguoirll

1OVOII 1ri3rnrn3vo orb 1imi1 3111 111 bns oiuc iot alowilaoo cli cionorl Inorrlniovog orb isth Omil to

cilustob

(0q)1 lol 0 < 0q ionq Isilini 'ns noviD .iolsl ocu 111w ow lsrli oiinsol s esrl muiidiliupo cifIT

lnoiofhbrn leuL ci inomrnovog orli (0q)A —

T boiioq ui eu11T .eblorf (VI) isrii flouc io31ni orli od

ioi1iso boiioq onO MA ci ioiluio to oiJIsv orli bns elowulnoo cli gniionod bus no nil1ustob noowlod

io J4A\ + 14(—A) ci rwionori to oulsv orli J — (0q)1 — T Is

.M(—A) + MA (81)

eiosilnoo nu1onof1 to oulsv ocli !boiioq 3110 losd ovom ow as isdi oc < I < A rnoilqmueas 'H

ovilicoq 'I1oii1c £ 2! oiorll cuffT .MA Is boxil cnismoi gniilustob to oulsv orb oliriw cocsoioni '11oiiie

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(11) + MA (QI) E\— I

fli brIE gniionorl lo oulsv r1i nw1x1 qsg ecu wifT .MA Iqmi i gni1!uiIeb b eulEY eiii eliriw

— T mon emil ni 13Ed evom ew is eini Ilfs3ino1onom gniiluiIteb bo eulflv

11 ill erli illiw ebi3nio3 fl3ifIw noils3ollE griisqei bus gnilevni gniwoiiod 1in1enoo Iliw eW

erno neviO .emsg erb bo bne ecU is boiieq b iedmun elirifi bexfi is lud His iol level iffefflhlffllflO3

eioled anoils3olIs inernflrrtrno3 lUll orli wollob inemrrievog orb isrli vh33q noils3oHs oaerli lel ,

'A

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lsioi lo iuo isrli 1i3oq2 noilsoollis oerb lel 'A — T = I iob bbo i 'A —

T isit f13u2 noorl3 'A

gniwoiiod bo bsoini woM .Mt is*iow sq bus ioAnscf sqoi Inomniovog orb j4A + A iuqluo

I + 'A —

T bohoq nI .loi orb omuano bns o\I ovs iriomnievog orb ioi orb gnimuno3 bus 0

bris iooIq iodsl orb moll MA oviooi inominovog erli ioi1soioth boiieq boiodmun-riovo rl3so bus

boiioq cii .M(—A) omuno bus io*iow M oiirf j a1ovni inomniovog ocLT .gnivs orb molt I

bo iuqiuo Isiol is 20V10301 inemniovog erli ol1seioth bonoq boiedmun-bbo flso Uris + 'A —

T

iomsn ioi orb muno bus c\I ovs j4 ieAiow assq 0 ioArisd sqoi j4A + A

.(T'li—A) + (c\I—A)

idob £ rbod ifhiw lobom noiiziuqol orb cii botroqqu od noils3olhi oorIi ns 'A isriw ioT

lebiarlo3 bris iriomom £ io1 ievoIiiq siongi iodrmrn airb oiuqmo3 oT ¶i3oio1q iodsl is bns 13oo1q

boneq ns cii .aioArisd ofli rliiw isflno3 iclob orli no griiiluätob lo 1fioriod bris hoc 1301th orli 1no

bou bruil bo gnivz ecu 'qlqrrii2 015 blslino3 ideb orb no gniilusbeb bo atfiened ion orb 'A — T � I

griiilusbob lo atfionod ion oil o nsol on oiz eiorli 'A — T < I ioI .c Iemsri nso! orli 'sqoi 01

I + (0q)A = 'A io ow Ii 0q loilq novig omo ioi .at3oIlo ievolIiq ecu iii )135d bbs woM .oi3 oiis

rnerb no gmiluslob bus at3sIirIo3 iodsl bus ideb dod gnhonorl lo oulsv orb rioowiod eoriioThb orb

bo atfionod ion orb irb oiobod boheq beiedrnun-bbo ns nI .o — M(w—A) 2k 'A —

T boiieq iii

bnE niionori noowl3cl qig 3fli 3iiffw lornEn rn rli i3Enno3 id3b ii no niludtb

urli bns d3b on i x3rli boi13q b 3dmun-n3v3 'RE fiT .232313f1! 1ino3 iodEl orb no niilus1ob

no niiius1ob lo 2iflonod ion orli o idob on 2i oioth bonoq iofll nI .niilud1ob ol lilonod on

ii ufiT .oios luoivdo oi Ii

j4(—A\) > c (Os)

'A —

T boiioq duoiri1 0 boiioq moil anoii3ol1E lnorniirnrnoo lid! orb hoqqu2 01 oldiaoq i Ii norli

ion orb lEril riou ioo1ni iifl orb od (E\)j lol E\ novig iol iIsiono oioM I + (0q)A = 'A thiw

orb niq moil ni ion orli nsrb ioi1sm on 1311ino3 idob orli no nu1IuE1ob lo ifionod

lomin

1(-A) > (Ii) E\— I

.1 — ()L + (0q)A = 'A iol oaiwiorIio bni )i + (0q)A = 'A iol bbo i [(\) + (0q)A] —

T II

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