dh inq - nber.org · rpef (jjglg ew couqiqoue nuqoi. litp!cp vflcji v enpeiqa wipr ectnvjja ejag...

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Page 1: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

ILSIa2 0141)1510W $13814

2HIUI2U T$1O'1X3 0141T1IH-TMa$I 3TAIU3M$l3T4I UHT$1O1MI MA HTIW

TDuuos1q

iwnlirkI Liot inq . dH

8R 1E nbhoW

HD$1A33$1 DIMOMOD3 O UA3$LU8 JAMOITAM un3vA aflur13f3aM OO1

81O AM bhdmD ÔQQI IBu1d1

I1u13ia1 aw floqqu 1i3nEru1 .inrnmo3 1uIqLui ioI aB10 mA AnBth 03 li1 bluow W abtswA nbsn.s3 lo 3n3rnn1vo0 di bits noiisbnuo smijs)1 3di rnmI £w1irI2I slot d bvii

flsq ai iqsq thIT .sidmziloD d2llFIfl lo ii2ivinU 3di is 2.8.I.D mm? inq atsths8 d bits is b2iqx3 2noithqo nA .inmi2vnI bits 3bslT 1snonsrriinI 111 rnsioiq ff3153231 25138T4 lo

.d31s,R 3Imono3H lo us,iu8 Isnolisl4 di lo 32orfi ion bits 2loffius ffi lo 32orli

Ion 1310 2noiie nod2 .b3v13231 aidh hA .1n3q2 .t sisthsfl bits swithckl siot sd ÔQQI © iib313 ilul isdi b3bivmq noi2arrn3q n3ilqx3 Juodliw b3loup 3d '(Sin 2ffqs1s1sq owl b3x3 ol

.mo2 3ffi oi n3vi 2i iion © nibu13ni

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beilqqa 'biadu8 hoqxe na nhsbianoo d suaai aiifi aeiolqxe ieqaq aiiiT

eVIlIteqInoo (133eheqa1i &nedxe eno Ia d3UIW ni thflea a ni boo-Ian1t a ot

boog-lasth aitasinob d beau booB-eiaibeansinl na lo Ha sauboq annfl 313831n0b

o .behoqmi si boog-elaibennelni sift 10 Ha efneiixe isi1io silt Ia baa szsauboiq

ew 3efiam booi-elaibeaneith edt moi1 aniana alaslis lanoiiibba silt 1nala 03 aa

boo*-IanIt ladi jeboin (8Q1) sansq2 baa isbw 1aniho sill in aa ,smuaaa

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3*13tI38 tamiiqo 1Jdzain boo*-oiaibeinieini na lo noiiibba edt dIiW

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aliaeinob bna nwo1 noowled aIe3ubozq boo-Lanfi 3itaemob bna niezo1

-etalbeanetm bna rieubmqbooa-hnl1 neewied boa aieubmq boo-e3albeuneIni

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a taonil ai bnaincbii tcvcwoH .(bnamcb zaenil .g.c) anoilibnoo bnaunb coma

lnct3ffluia cwiqao bluow 3uboiq ctaibennelni cdl nilqquc loqonom nicio1

toven ai '(3iloq a da lath biadua hoqxe na d beiaienc ainci cub lo .lmoqweiv 3daemob a mail eudwzftzow

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Page 6: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

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aa boos 3aib&inein1 eii3 lo 'i bna 833nq 3113 athiai noi3it3qrnoo 3omuo3

d bnamth 113111w Ia sriq thaeI3-IeJham sill (1qmi8 a SIlT .U8V1

uonsobns sd 03 bowolla al 'ill .Iqque alwps atsuboiq boo-Ian11 3ziasmob

.i1qqua sIll 01 boos slaibsnnslnl sill iol bnamsb ni5io1 3113 aslaups Ii

thooD slaibsunslu! bni Inf4 sill iol ?Js*wM sill ni mundili,ma £

ifaaT4-loinuo0 sift ninimsJsb anoilibnoo 5113 jijo 3 3a',jt sW

daaWioinuoZ) sill mqo1svsb so1sd lsAum boo-Ianft 3111 iii mundiliups

.jsiwn b o-s3aibsurislth 3111 in mundiliups

boo* LanlI sill lo 1svi3sqaei baa aluqino submq 1 baa b amiiq

bb — by 51511W 'y + 'Y — Y liJqliJo s3agsa ol 5 nivi ,s3nq silT .iuqiuo nieio1 lalol altsasiqs1 — Y bna luqluo 3iiasmob

= q noiI3mR bnarnsb satevth sill d nsvi ai 33ub0lq lanIl sill lo q bsloasb

81 aialazia sill asia 3113 in siulaislil auoivsiq 3111 in aA .0> (Y)'q sisdw (Y)q

anothoqmq bexñ Bniau bsubmq ai boog-lanIl 5113 laIll galmuaaa id bsllilqmia

lo sthod3 slanqoiqqa na fl .iodal io3a1 15iliona baa boog slaibsurzsith sill lo 5111 10 luw sno lauj laill gnimzmaa in vtilaisnsg lo aaol Ofi ai sisill (8311w

a' iod&L .l3ulxnq hail sill lo 311w das iol bsiiupsi ai boog slaibeiinslni

alaoa sgaw liiw 1131w sgaw inaiano3 a Ia 'ilnuo3 ibas ni laubth sill 03 bsilqqua

•q (13nuo3 ni w baa U nuoo ni 0w d nsvig

iinil 03 bsilqqa biadua 3ItiQeqa a aslonth 'a eisilw ba — gnilIsJ

d nevig (1evii3eqas1 si& I baa 13 annil lo alilmq sill laill awohlol Ii (ahoqxs a'b

(1) .[('w+S)-qJ = ' baa ba - — q rol [('w+o)-aJ = sill (nsvi aa alaVn 10 aluqluo sill gthial lIloiq asaimixam nnil Il3as s3nr

:snoilibao3 robto Igril sill laiiaa (Ievii3eqasI I baa b annil 10 aluqluo

() .0 = = '6\'ii6 0 = (w+t)-'q+q =

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8

Mod oi beinuaaa ,ia anoilibaoo iilidaia bna t8blo bnooe *niwollol 3dT

..i :llado1 () ,O < 3-I+M 4 bits (t,b=i) 0 <3-!+it — ' O> "q+'q

'q\qY- — 3 (3e*iam booB-lanft eli) in I &mlI lo cuda ciii) YVY — Lo eieilw

baa (boo* faith 3d) lo ev•w basmeb c-ievth 3d) lo eqoI8 cii) lo 1i3ilaaIc ciii)

.(&inlI boog-lathI lo ,edmua laloi ciii) n+a — 14

Iuq)uo murtdiiupo iomuo3 3di enfleb () saoilibnoo iclno 38th cdT

cii) lo anoi)31w1 89 Icvkkoqaei 1 baa b annit zo1 (&j baa (c alevel

a&nooed 31 I1)iw beliimo ai t) 1803 lathgum 3383111th 10 t-'1 — c lncnoqmoo

1wo14 .(alnsMnoo eu 3d) eotha be))imo eia w °w baa noibo ni cldariav

b&tedmun anol18upe) (.A) mml aevkiavhob laihaq c)oneb 01 alqrtoadu8 gniau

tha)do ew (x1bnqqA ciii ni Its cu ( .A) as () 9tq\(a%.ln)(tn\ba>. = (q)i baz 0> 9'q\1ç = ()b

wb)theninaawoda(t)aA.(()moj10 < 9bna0 <'ciciIw (both 8niblod ba biadua hoqxe 3d) in noii3ubci a to O3fl 3d) ni cascioni

,'q\("f+ 'q)n = Eo-'n on1a ievcwoH .b anfi lo luqluo ciii a&ubct anwIs

71*eirlla 85 a)uqiuo faith 3di awciv 3111 1no baa Ii 80th 1 unIt lo Iuqiuo cdi

novi* buboiq lath 3d) lo )uqiuo Ia)oJ edT .(0 > f+ %q 111 .c.i) aoiuliiadua

conisalla1aawla1,b = iio1(o)'y'n — (q)'Y = 1YciedwY + by — ()Yd (1) thau

() .0 > 4'q\'n = ()Y cub) a18oo laniam in noii3ubei a molt tha b annlt 311a&flOb iciiicdW

.a3luaei )neupoadua cdi lo cmoa zo1 )nahoqmi ed 03 acvmq (biadua iioqxe as 03

d boosl 1603 1animin 3d) in u0i)3ub3t a 8Ql) ebacE 1(d awoda Itsthgho aA

0 > qbY+ 'q(! +bn) :a beaoiqxe 1nommo3 ciom eta anoilibnoo caciff' bcaueiaanoiiibnooowilaifteiff.0 > qY+'q(1+14)bna0> 'qY+'q(1+n)

1ilida3a baa tsenupinu tol baboon ai 38a1 3d) baa aaila3a cviizIaqrno3 cdi n318 01 .((?8Q1) baa (08Q1) cbae2 cea) mundiliupe 10

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Q

mill ne 3d) UI %Mf%-o 381113 bluoo pubni loniuo3 £ UI 8m111 ifs

aid) bthalxe 3vld (QQt) A3dQalidu&$L has t33n3qE .IIi a)IIoiq (13aubni lIsievo

annft n*ieiol to 3biaiuo 311 siodi nsdw thf1ida-ievo lItmq isbianoo 01 aia(Isna

— saflth irifi ew 1d3wnqqs iiib niwoI1o1 .Jnalano3 nismei alao3 moiiw iol

Isafi sift lo e3nq sill no in egnsd3 £ 10 13e113 sift thuassm sifT .nwo a'sno tud aanft isdio ifs lo aluqiuo sift in a3na1f3 duoidt l3ubmq

isiilo to luq)uo s3seis sill eaus bluow c m noii3ubst sli sviiiaoq al xinsi

— *thi3J .saivrnil)o svi3asn bus (ffioiq baa snq thaizi) hit 01 annlt

th&ldo nsdi ew ) baa (1) niau bus

(ô) b313 +'n = — Y 31811W 9\ = —

d nsvxg ak JlImq a'b unit no c1o 1eTIs sill Q) baa () thau (1) moll snsH (V) (+ 1)(c- = + - =

.\[(+1)a-(n+I)J = 4J\(x)+9) = +1 ) bus (E) 2niau ,eieilw

sill aeubei 1803 1anium UI 381813ffi as (V) mrnI ness ed n aA

eni .0 <+ Iii 1no bits Ii (* flida-tevo 311otq )uo gthhn) b sunitlo afficnq

edjli bsubetaiswlsetasl1tmq 0 < +! e3aedbnsO � aei1qmi0 (hla1sneZ ernM .usnil to svuo ak boog lanit sill tol evn, basmeb sstevth

UI 1kxsvnoo teissig neve lud gniffida-tevo JIIotq 1110 shin 01 ilieI3fflUe 81 > 3 .O <'nil bolsbommoooa ed na SVtU3 buarneb 3818Vth ed)

euboiq in baa 11 aunit 3shain boog-elaibeanelni 3113 gnrisbianoo wol4

.CI (iinuoo UI 5158 tot boog e18ibmslUI 3d3 io 1evii3eqa5I "ax baa dx aluqiuo

dxdn — dx eiedw mX+hIX — °X d novig sis CI '(t1nu03 UI aeilqqua s18gsiggA

ngieioi halo) ainoa5iqsl mfn X baa nokt3ubcnq 3ilasmob 11)03 alneaszqei

sill slaqiarias 1hft in bits 11 annit eu sgaia UI luqiuo gullies a! .noII3ubOtq

egals bnooes sill mon gUIana boog eisibennsith 3d) rol (Y basmeb bevnsb

()by .e.i) lqqua iftiw buameb gthusu! .booa lanit sill tol rnundiliupe loinuoZ)

.(ÔQQI) Asda3idua$I bus tsaeq2 es2

Page 12: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

! 4P4 1GG U1 j0Cq U 4p 4,OIU C0fluilA HOMQAL' nUqcL ou

MJIGI1 Lo11J ULUJ m vthbiA iutuqittc *ooq' spo uivnj tbIw4!ou

pi4pu o bwjj to uiiqi-Sooq bLoqnc' potp qowic uq oiwbbpq to uiq-8ooq xboL pA conui) D N14p bwicnjvi vgwpou ku o po

JJJ!2 CC0U qGAQ4ob 4pc qowpc MG4W ccj o tpc npwqA a

t V S1P2A 40 ImJ-C0O E0O14

8ooq wijccr) wuq — u,+u (tpo torwi unrnpci ot ugcunGqiwo-8ooq uii)-+ <0 — F+J.E,i> o'k — J4,,+J-> o' (H)

couqisiouw anwoq jo poq 8joptiA: !G LOL IC = p'W

40 4p0 U1tJC4 LOL tP 4!"I 8ooq' 5110 )IJOM!IJ 80c0Uq OUJCL miq wprptA

CflT.AG OL 5170 1Ut0LW0W40 8ooq MJJQLC IT 8itU LOL ,,b-ap.cvui' gpoi? iujoonjA

1t1!U8 E — -XDb,\, IbLocu45110 opopciA o 4)10 obo o spo WAQL9O qQwuq

9\9X1 = b(X) + 1(XD) - = 0 (F = p'ui) (Jo)

couqipou: iow (a)'

iucuuoqijo-8ooq &oqnciou 4)1017 uo to jpo (ojoiiMu 4Lt oiqotM)1CI0 Li — Cp8p8q wuq f — C11,+ f,,,- flO COU4tT74W COIIWO( C0U1b0414017 117

= = XD)-fJxw (e)= [L-(c,-e,)1z, = x)-Li,)J, uq

bto o tui p uq in io i. cr!AQIA 1AGU pA= b() + !1L0ll0MtPttIP0

bioqncriou o po u4ouJJGqJo *ooq uq t1,w bocqc jvui wbooq oii qowctic

p uq c OL tW rn tcbioscu , thocic &npiqA bbpsq to qowoc

y9i81uj bwqncou C0842 11.0 nuioq cou4IU( 14 V fOAGI C LOL 1!UJl

= J\Aq" <0 ''% (Xo) = A,\(Aq% (8)

qowuq cmo pw ut tuq ccouq qoqAwyGWA0L0 qcuuq CITLAG = '(XD) + 4p rntouncqltto ooq JJlc WAOUG= x uq jp9rnAoiaoqc4ucb =b(y)'ipicpwwb =

JO

Page 13: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

Aq\(Aq = O !I! E = E =q E — -Abb LOL iiciz quq IL b = O 'Pa" b. =

io 2bucL uq Knp!ccpGI (IooQ) qouAc jp pouepb psycw En —

L < '1 (Z L> 1 = - z' v.iiwqu%L kw 3c;t1% tyt (nn ott

t' tI %fl%1 % àO14%

j,wboipou j LoW W1mQqWLGJ) horn= - I = - W\k <o (iO= b(qx\q) + i = (r-&M iuq

+1-E> O!0P(!Uqorncc umiiIu!J co o uv$ooq bwqncpou' hOW i. = b(XD) +

Vg t IPG GCI °L 1P xboLt BnpIq) oil q'c bucQ °L qic rnfoullGqIt bwqncc= qAq\q = - \bj1> 0 (13)

oxbo,.t °L qi© bLoqnc rnn jeo usc:

UZ O flJQ WCUDGqI4G ooq W COfl1Jfl) D q Aq = XD OWQC

jij qic CYbOLI 21ipiq)t imc qjc oj anbbj) y — +

HOJL MJp &wrncuc co vuq uoujiut qcwuq x z1, UJVA jjI1L0l!k0L!L91 = = o)qL-JeAoJcnbnI,vuqz_poiprncl.cewc

ooq nbbpt VLG q'uI (avp!cp pojq 'L " 'u qowQ&L0L 9 - (j) pON 'L qcnmuq i puei (! !L E = OL !L I'

= 4i + VUq qz\qRq = -U - ilp9 n\XtJ\kn (J)rj' ui1qi't *ooq !r ! BOMU w (ve) IPWI

1P ILGC °L ° Ipa h!'-II OIUbIU wonq bbjX so sp joctou °L qorncc UUJJ jr

ptc1 qmonp qowcpc ix OL IU5 *orU 50 qoWQc M0q(Lr V UJJIJVL bOWI

m4LbLcfPou onjq LGdIflL pt DOUG Oh 1G bwt om* to iw iii i cbsnLQq

b1u iocci U' sp qowzc conuA jpton*p oirnbi qict rnActulr JP!8C!LCflWUCG' '1 P bo!PIc to wtthLG ni i pQrn owTU-oMucq

11

Page 14: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

.t ti k'ux M%ia* eit i'oh$ iio cd1io bnanIebIiabIodd3ufW I > 31i Ino1oiqthbiaaA

as (bnameb CVMOff 03 baa actht thbul3th) xevnoo 003 Jon ai booa sisibenneith

54110 a1 33fl cdl ais 301 09 IcaIlo 'llsitiaq bi dus ciii 88151301

annlI mml befihila si biadus ciii moil niq cdi lo hsq aunT .boo elaibennclth

(fl .ioioea boog-elaubeancirn cdl ni m baa ii aunfl 01 tobea boo8-InhI cdi iii b

cdi thv,uinam °t cohq cdi aeaactob biadua 3Ioqxe cdl j <'l Ii laat1no3

na3 ew (M) baa (V) niaU .1803 I&nigwn *nnswol in ibiadua ciii lo bdIle

:nnol cdi at tab\b aaeiqxc

(J) U9\UI,4( I) = b\b)(b\rb) = d3udw O < \+I1ikiobna1iaealttftmqabunft (H)mot1nseaedn&eaA

at noii30bet a mon gnifiuda-ievo iIImq tuo cliii ol bctiupct noilibno3 ciii iaul al

iIIotq a'b rn-in no ha lo i3clIc sill iol noiaaciqxc niwollo1 cdT .1803 lsthguirn

() baa (I) mo-il :liReau acvoiq osla

(at) .(\b) - = lo aiiloiq cdi no ha bisdus ciii 10 130115 cdi gnhcbianoo wol4

icb-io la-in cdl aiaoqmi (Q) moil awollol ii m baa ii snnlt boog-cisibem-iclni

iadI (€1) baa (II) gmau neil baa ((if) anoilibno3

boa a&bn+IaJdx = [((\d )-(b\°Xb))'qx + Ii = (VI) = habVa-b

tail alasvci (VI) nczll (O = = Ii .c.i) l13iinebi s-ia at baa ii annut cdi II . > Ii lao baa Ii 'biadus ciii 03 eanoqas-i at eth alflmq boog-claibcnnelth

= I = 'M duiw 53fl18 icilqqua (loqonofn a tol ablod noilibnoo aidT

= -i CVU3 bnsrncb catcvth ciii Iuo alluda ha biadua cdl cnr .(II) motI 0 laupe as bluow aa losIls cinaa ciii aaut Ii 1Iaalano3 cvziibbs as d h8 + (°X)q

> noilibnoo cdi 3308H .((Q) sea) ' baa 3 alaoo lsthgisrn ciii ni noii3ubcrx

iol befiuda—icvo ton c-is alilotq tail (8QI) cbaca 'd iluaci cdl 01 belatct si

cdl atewol ha iiguodllA . > Ii 'lno baa Ii aIe3uboiq boog-Isnil (l13itncbi)

(I nouiisoqoIdl llaoi) I < neulw boog clsibeuznctth 3113 lo a1 c3nq

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(1

.Juqiuo I3dgiil 10 uaoed th 131ih3v3n affirnq boog-e1aibenn3ni

iev 5d 01 in baa if aunli eauao aeoaaiThb Moo Ianoiiamn3lni Ii nev3

miii boo-e1aib&nieUñ iove lo hftoiq eifi aaiai ibiadu edi ,ia ni 3h15mm1aa

menil-non al bnamthli zevwoH .(0 = " itiiw ('1) moft) usnil al bnamb1i

ni . > "a Ii UV8 (bi8dUa edl moiI eaol annii Moo tsif8td cdl ladi e!diaaoq ai Ii

noiiiaoqcnq aniwollol cdl ahftmq no lo aloelle cdl 01 beqaci illiw ummaa .bcdi1da3ac ai ' tt't,yq %SUSt1 L *U *IK

.0 <+ fl so tgi to-o'a > 'A' %no i& ( ttu

= —

ia1Iew a'U '(llnuoo anoilaoi1qmi cuufew 11azevo cdl 01 3nilnuT

slaibenneini baa IanlI moil beinac hiioiq oiiaemob lalol ciii lauj i W belonsb

:biadua ciii lo Moo ciii ace! noilouboiq boo8

(81) .mXml + 'X'a - byb8 - iLd1 + b.rbn = OW

moiq .(aaeneielqmoo iol (81) in bebuloni cia l lihal ciii baa ds biadua cdT)

biadua hoqxe 8nfiuila-iaci lainliqo ciii 0 > r(b)\aWb *thmuaaa (81)

aoiiailaa (0 = l = 'a ifuiw) beloneb

(21) .0 = (Lj\by)b - bY - (labVwb)dn + (LabVwb)bn = "ab\0Wb

aa beeaciqxe ad 1kftacu nao 1) baa (14) 3niau (21) 3ninanaeS1

(Os) Qby +

[(I_n) +

bab\YbJqby — bth\bYb b bth\byb

in aleioaid ciaups in noiaaeiqze cuT .bY\[(b\olb)bY - "ab\b'n] — 0 cicilw

hoqxe na lo aloelic *cbzii lo amic3 baa 'ois3aula biabnaM cull acwiqao (0) na 01 inlimia 'iev nnol a ax Ieium aboo-lanl1 ciii mo-ft Bnitha biadua

Ma! edT .((8.A) noiiaupe 1QQ!) daiuz1T baa andan)1 d bevncb noiaaczqxc

cdi iol lcham ioxnuo3 cdl b conelaixe cdl lo c€uaoed acaha (0) lo nncl

.boo elaibexxnslth

Page 16: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

abófl. 'ebail to amieY bna '31*et1da edl lo noi3anaIqx Iohd nio2

oil) lo )oófte 3i*oMiia oil) *)noeoiqoi (0) lo miei iath edT .bein&izaw meoa Ii ab\qb)'Y = b\Yb &wiiE .1 annft n*ieiol oil) 10 Iuq)uo oil) no bi8du8

lath nuiuaiie (ti) mml 0 < Y nod) o)u3iJadua 3xeIa138 aa aluqluo woiv I &inlL

03 abir4 aidT .(0 > b\Yb .s.i) biadua oil) 03 eenoqaei ni allal )uqluo iloil)

iol lnomu$u (8Q1) ieoaq2 baa iebaai oil) lo eoiuoa oil) ai baa 0 < Ii (ô8Q1) namaacnD baa no)a d Juo beinioq aa ievowoH .biadua )ioqxe na

no nhovil 0 < habYb ,noifi aJnema1qmo3 31zd8 as aiuq3uo weiv I annit

enD nail) oi al oiodi nodw niana 3oelte tthgd lo annele ouT .xa) 3zoqxo

as3 annfi 3iMornob eoni2 .(0) 10 snio* bnoaea oil) ni beioeflei ai uniI 3ijaetnob

aun1t oiiaainob ed)o lo ahoqxe oil) no ahoqxo uoih lo 3eIIo oil) 10 flU033* on 3Iiaeinob lab) aeaimixam lad) level oil) bnoed ahoqxo abnaqxo b mill ibao

oohq hoqxo oil) aiewol noianaqxo silT .nevii as Iuqiuo nioio1 gnth) aliIoiq

oriiupoi bluow enols noihoisib aid) lo noiiaeiio3 .ebaii lo anne) oil) nineaiow

.xat hoqxe as oil) d novi* as aI3o1fi 'ebaib 1o smio) baa 'ip)ai3a' oil) ninidmo3

11nnol oil) ni sae1qxe 0) ovibiniani sill ,(O) lo suuno) ow) baill

(lx) ('sb\Th)\[0 + = as lo oneeda oil) a! (-,Y)'q-

— ,(ô) mall oieulw

(1a88o3en ai0 < Jail) awoila (!) bus 0 = 0 neil) )eI1am boo*-olaibeunoith

luqluo o)aeip edi eauar bhuow in noiiouberi *11.0 < o1 )nei3lfiua baa

Jomuo3 oil) eoiii. ioI b01113 ax biadue a (O <Ii .o.i)lla1 ol annit ieullolo

oil) lqquaiebiw bluow (n,vi* as annit iodlolo Juq)uo oil) athuid) annit 3iiaomob

— ball $nills3o1 .noiiaximixam iiIcnq iniojlo )nioqwoiv oil) mail )eham

'lno baa 110 < lad) awollol oala Ii 0 = 011 ) mall 0 < 9 baa @) mail ,bn I + 'q("'(+'q)n = abeaseiqxoedna3 o (ô)moiI ,03n2 .0< 1i

03th8 awollol auilT" = (t J)(,b(1..b) +,Y)'q = [(bab\bbXIbn) + (tth\Yb)]q

Page 17: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

weiv annft n*ieioi 11 (1no 8vthaoq 3d na Iazfi flua iailimth 3dJ niaJdo 8W

lanoiiibba nA .(0 > "+ 'q 11 1no .3.1) a3iuhiladul oi3aiia aa aluqluo

lnbvelq oP 118m8 (I3nbi31fiu8 3d ainifi 31388mob lo iedmun eili iaili ai 3nmsiiup w bnambb ii e1qmax3 io1 .niiathmob mcxii 'bbIib 31)813 lo ann33 8113

.0< + = DupolbwlabmI boo-3aibeane3th 3111 d boaua3 lbeii3 lanoiiibba 811303 3oqsi jIJiW

3vtiiaoq 0 nivad 1aup3 3813 lii (1) io (0) mcxii neea 3d fl13 a ,ibiwn .0 < .i) 'bi8dIm a ai '(3iIoq hoqxe Iamuiqo 3113 Jaili 1s1il om 31 1am

:aa b38aelqxe ed fl83 0 1) bna (is!) (0) mo () .[(b\°ibro + xb)'qoJ- = bY[(Mib)bY - (bvwb)an] 0

lo aJiioiq 3113 iai bi8dua 3zoqxe 3d1 Ii Jail 8wolll () 1thahcpu8 Poi4

1evewoH .bviiiBoq 0 ,iam 0381)1183 lIdJ a133u1xnq boos 831ib8ffn33th 3iI8bmob

-Ianlt moil beflida 81 iitmq Paul 1n83x8 811303 leaiio 11aiJiaq iaael Ia ai 338118 aidI

ohq 3dainob edl in 388313w na ifuoid3 aubmq booa-83aibburrnlni oi boo*

.('3i3naup in 38831381 na ilguoidJ 13Iuq nadi tediai) boo* 83aibenn8Jth 811310 i ooi Ion ai bnamebii beaaeini 81 °i ehq 8113 1 noi3iaoqoi mcxii woni w aA

3i3amob 0O1 81 vtiaubth boog-e3aib81ln3Jni 3d) nedW .(! > 1i .e.i) xvnoo 338113 bib iadl (1) niau () molt awollol ii (0 = tmn bna I = o n3dw .8.1)

aaw1a 81eoubolq boo-e3aibeuine3th 3138311101) lo aiiloiq 3111 niaiai m ba lo 3111 Ii ,381131103 fl .0 < j\I = (babvixb)q = 0 gnhfRm aeianimob

Iev8nedw bY 11*31181 ('ab\°-ib)- = 0 nail nZi31o1 (1 3118 8i b003-slaibeun3ini

sviliaoq 0 *nblam O > bab\a.ib Iadl eldiaaoq sill 1evbwoH .beas8ffl3rn 81

.3813 ngioiol 0OI 311381 113V3

3111 1&nan ieqaq 81111 lo anoilaeup Iaiiueo 3113 lo o 03 au agnhd suiT

no Paubth boo*-blaibennelth oiiaemob a nauti 131138111*13101 a 3nivad lo 333113

.aeaoqmq *thflida-In&i tol 83tOqxb boog-tanit enibiadua 01 bvxlns3nz 3ila3mob 8113

[(I + bab\) - ((b\d>.{bth\UTh))q + I](bYVX) = 0 onia swo11o1 ft1))(by\rnX) -

Page 18: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

bIILQIA qowcvpc

bLoqnc; Mc couviqci. tpc civc in MP!CP spc utouucqvtc4ooq uqnvp1 iv

pcpc cowbiuvon itxp qic etwuqviq vuvviv wcotbotvqn* oujA ipc wvj

qccuuwiu spc vi*u o pc czboij vnpvq) nvcq ot IJ1-vpuju* bnthovcr

urctwcqvrc$ooq mqnv& NJ7ctpoL qOWQiQc OL t0Wik ou IPQ lwoiijpc ucx dncvtou v qic cacct o qw bzceicc o v onuio

bwqncciv icqnccv viA qomcvtc Sin ow vucxboig vnpvqA

nTpAcJ) bvnvpjc q' tp't pvwS bwv jcvy to LoicRu ucuuGqvo-tooq

qic qowcvpc IUCQUtIAC tOL ipc vnpvq) .LW' Woboe!t!ou 3 ccuiuiiv tpc

cqncpou in qic bwbotpou 0 qouvqc WtGuThQqVtQ-*ooq bLOqIICcU muit joct

viqiq uvj-Sooq cxboqv vi vpicq go wtcuuqiwgc-*ooq bwqncctv v

Vi J,Lobovipou 3 pu vpoIiI? q vowc o gpc biov Suuoq

> o eiucc = qic touo 6ED

qili iiJJbpcv q3\qq1zw = - t !nncpvuScq cuvnuuS qmg j t qJ\qv vuq q,\qvq vic nuuocgcq jow (j

LI: Hojqi 140 cq' qi', = - qu1 J)ITj Migp 9, = Ø tfl O$PL Av1tpJGv ILC

%fl%1% %1% b.o\t tO nc.Zn% t1$ %*tUtI to %'p3i%-%OO OM% )1W3 OVçh

IV t bOLtOV t.'%OtU tO 'OW&tt %It% 6\ t flflUVOtOO%%OV '4%ThW 9 - = = %*, + U fl\L '4V flIU

o gpcvc nnm pu no cjjccg on bucci OL ongbngv SivqA vimbpw* gpc

covgr pi gpc vpvcucc o ccicucA cccgv v cpvnk in gpc oMucup!b

Iow ccicuc) OILCCfi p) ,unwmS qiug wgcuIJcqrvgo-*ooq VUJJi p vuq in piAc

ocnv bnij) on gpc mc oj gpc nuwvc icjbicug o( qic bwv c vpvgwcg

qowcvgic un poJquS gp rotwi unwpct o ugcuIJcqivgc-Sooq uu 2° Ii

j,toboupon 3 vqqcucv gpv ivvnc p) vnbbo.iut gpi v oicitu w wbjvcce v

IQ

Page 19: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

VI

ti38ubnI booD-e)aiburicin! 3ita9moU 'tbn#I

= .e.i) 3daemob 11* cia &znit boos elaibeiwzelth cdl lash niaoqqu

ucihi baa (Is) ni "9V'M- = bab\qb baa ((SI) mau () moñ) "4j\I = 0 *niau n niaido ew = bab\bYb gj5

() 'n = 'M iol 'Y\['x + Y]- = (bab\bfb)u9\[I + MJ'Y = leimm boo* ciaibeiznelni us lo cncada cdl iii JadJ nilla3e$I .4o = 5tcilw

cdi alncono3 t' aoii1aoqoi 0 < bn3I +n — Ii Ino baa 11 0 < i3aubth Joinuo3 i3aemob 1cwq £ nedw thshs anoilibno3 gnlbnoq8cno3

.boog claibennelth cdl aciIqquB

% t00% JUU SI % (%%)I% fliiba '0*W03 cdJ . 0IYI ô1u'

.0 <t o\ 'uu.a %o1 t 0 +\ = . . 0 < \1Tt t'& 0 <t 1Abao tn K (fi

= .t0 <+ 1J 01( *N t%-WI0 cd

0 <\br 0 <t ncd 100 < i-¼ - 1++'s j 0 <t (

= 1\ (11) .beiiupci Jon alO < iud 0 < \n = 11 0 <b$ (t) mo'i1 (1) :jj (d) baa (a) oe (babtbYb)\[(Idn) - d(+ I)]by = 'a = 1111w (Es) uioiI (1 +'n)(I +n)JbY = b* coals woIIoI (d) baa (a) 0 = "q II (iii) .(U) mon wollol

UaQ .(I +T4)\en-I +a) = ifliw () mon (I +M (Iab\bYb)\[(Idu)bn - i viiaubth boo-e*aibeaneJa1 ciii nedw liii awoda (1)4 noiliaoqoicl

molt 1icvewoH .0 > Ii neve eviiisoq ed nao biadua Jioqxc cdl iiacmob

ciii si doiiIw 0 < An+ I = + I Jail' 'maie3ea ai ii (a)(ii)I noiIisoqoi

113111W ni eaao Iaiaqa cdl a! .b aanll iol niflid8-ievo iftmq iuo gthkri noiiibnoo

cdl Iadl aeiailanoaieb (d)(ii)t noiiiaoqoidl ,Iaioqonosn a ai ii mill oiiaemob cdi

boo-1anft olaemob lo 8IlIoiq cdi caael3n Ii lath aiO< iol lnemaiiupei Ino cdl niMujba d eauaoed Jnavelei Jon as iacav(aq biadua cdl lo iaoo cdT .aanit

Page 20: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

81

ol Iaupe lauj alitoiq behb ew1qao 01 eldn ai lailoqonom edt ,beilqqua v1iinaup

.'ahoqxe lo 'Y = 4x Qi1n&up nevi* a ioi lnetw(aq 'biBdua edt ni eaaeini cdi

eviiiaoq ai '* iaenil al bnaweb nedw eth b annit boo-1an11 lo a1itoq cdi e3n12

iaal aidT .((hi)t noiiiaoqoi cea) lailoqonom 3ilaemob a illiw 8883 iacuil cdl ni

aisdinun eviiaIel cdi no bnsqcb Ion aeob Ii eaua3od niaiaadqms dhow ai IIuae

.aunfl boo-1anlt nieiol bna 3Iisemob lo belimil noa iebiw eldiaaoq won at Ii noithoqatl in lao lea aA

boog-lanil ii ncve eiillew 3ilacmob e&ai 01 biadua lioqxe na ioi anoilibno3

Ie3 ainetnelqrno3 3IgelzzIa aidi iii � 'nil .alnelneIqmo3 3i 18118 eia atuqluo

beftuifr-ievo ai iltolq Mdl uwoila evad (ÔQQI) ici1alidua$1 bun icnaq nedi

ibidw) I = n ii iovewoH .0 < lao aelin (ii)t noiiiaoqol molt d3u1w

molt awolloi ii neili (Iel1e eb&zJ io aimel on ai eledi eau83ed 0 < aiovil

1110 < twft(11.A)

(lS) .('q+'ci)n(I+4n)- > "q'+'q Ii neve blod bluoo (l) anoi)ibnoo iebio bnooea cdl molt 0> "q'+'q s3nia

cbiabnnd1ifghcdinedletha,1 =n=niiIelifciomaiaidT.0 < cf+q ii luiqled ai Ii noiiiaoqoi d be1cfl5I aa oatA .eviisgen 8881 81 () lo . molt lncieThb ev Ion ' gsth1rrr alaoo lalimia cvad 'l bun U aci11nuoo

0 <t i% . = = . ttoics 01 00% hu � \(> ( (.)l WO r + \\\ > a > > � .

1WVc > a> n=*s=\ i'WO +\\ > a>\ .0 < \ + +'\- — .t

= .)j gniau O > 3o-'nTh alneinelqmoo 3rg8181i8 818 aboog hull 831118 :gfl i'cioI 1+ii+'n> a> "ii+1n = = iievzdew 0 < a1+n+bn acilqrni d3idw t\(1 + 'n) > 'iV ii 1no blod acilifaupeth eaedT .I,b = ji baa

= (QI)inoi1bna'Y = 'x = 'ab\',b 1)moi1ncdI ,1 = =

Page 21: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

ou fIG GZhOLj tnptqAcc tn) (ioot) LOt tUtJ)tIt OL fIG LLGC1 0 fIG jGAQJ °L WIL8JUt CO8(

LGfflCU fIG wduitnqc' OL uHf ttI8UI* fIG (U - AA 0 fiGunbGqcI cowbgiou uitpc j(b) < L,k') L' mA iur unpmq) JGAQJ'

CLG84Oq CCtUtQ qio pipct bucc cjmtq jot qic IUtcuJiGqittC btoqnci nuqci.

pqpu btoju 40 fIG !UICUJJGqJ8IG &)Oq tnbbJICLt HOMGA1' vuJpim4A !8

bOuAG 4CLW' UtUJGft' MjJCp U°t fiG CjJGC1 Oj 80 GXb0L4 unpeiqh iii

() Miqi ( it 811D!Jti 10 L0U 40 L cccbj *ptt it put 80 uqqipoutj

MJJICJJ !8 bOtipAG !L uuq oujA !L o — = u1+ J-°E0-14 > 0 CWt)UU

3q Aqo)3o\Aqo)' ()0 uuq qb\qu,1 = -i m (j)' fiG obqwuj cxbotj unpcqA

combC1AC ,ptuc cutc, ititpv unbcz8cub( 1G1O' tpcul b0 — C, - 8q euq 8Gt4!U a

umtutj cout tcqnc'uS fIG UJU!tPqG °j jutJ-*0Oq CXb01481,, DG10fWS fIG

cOwbGppOu 84 fIG 1IJ4GWJGIt4G-O0 RMG 8QUC8 10 1J8G fiG bqcc t tpOAG

t bijccqA cowbc mc couuuu cou uqnui) JP!t !t pcctnuc wbQLjct

HICGUI!AG jOt 80 GxbOLf toptiqA IGItt!AQ (0 ptAuJ ipc iuictwcqiu-tooq bi.oqnooq

CowbCppOu pc Iu4CLwGqitc-ooq 8MG W8 WctcvtGq (ot tGqflccq) ipc

JJIG VpOAG uutj)uta !u 004 unwcioug to qctci.wwc MPC(pGI. comuOr

7 uuq U, = 14 = 4111 COUqI(OU8 (!) 01. (!!) (5ED

4 VHf I\ <B' 4pGt1101 < F co jOff0M tQ1fUS)\A =<UQ + UJftLj) COUqI4IOUV (ii) tiC &flWC!I( 810CC Tj u1(u1+ j) <)tq\A1

+ < B (!G 0I11iUt 1J 84'8M!° co1iiG11Ist) 1I > 0 uHJCC E

tLG VDWCIGII 8111CC !L I q\A < 3 Hf '1\ = U1+)q?1 < E 1GU I\0q = 4

MGLC }q\) < ,iubpGt i. — (3-A\))\[u(u+i) + )q\AJ > 0 C0Hf!4!OU8 (i)

q > 0 i1 B < (uo.)[u1(u+ i) +Th[u(u,+ i) + ?\?tJ =u + .'7' G Op4tlU

> 0 !I.LE < [u('4+j) + 3]\[Q(1I,+J)+Q] 11801* = Lot U =

uQI+i) < q\ < s jot; = r 4.1 = u,q; = 1' t' (vii)'Jo

Page 22: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

B( JIBJ( $)JQ rntctuJcq1vj-*Ooq WVLrQt.

+!Uq> 0 !B BSTIJCJQIJt (OL h> 0 !L (1 °"1 !( (1OUBtC BflbbJJQL2 COUtLO!

UIJB j,wboBIpoU (i) (ecc pcJoM) B0M& pv iii v J1UIL quiuq U =

EXtq!U* qnB BUWJ)BIB to IffOM (OL potJI (OWI*U 111(1 qowcec UuUcq1(Q-*O0q

ccbi.c,ou 0( () LGAIB tp* ip' !B uo gp ci MGU tjj anbbpcu vtc

u* 0((1GUJIU(1 couqtpou wcJnq!u* 1!" qwuq (bLobotou y)) jpç

BiG III (1OWGBPC (c j,zoboipou 4(1))' aiuc q1\qa lB bosipio flU(1GL I

= V1WOfl1 — k' > 0!BBITWC!tLOLh > 01PflbbllQLB= Ag[4n + I (3En)]\n((1Aq\(1Bq) ()= Jiq[\314n - lEq)]\4n((1Aq\q)

cxbott npB!q rpcu pjjo = -(D\F) = -(I-E)\ iu = o iLOW (3j) nw* (I4Y tpc obtimq

IUtUDGII *00(1 BiG Wt!LGI (OLM*u' i pjjo iow ()tuq (I4) tpvt

jnu,w* to t COUBIqGLZtTOU o oqit xwu iii pcp bioqncc

LOL1*U I1GUuGqT1fc-SoOq $OqflC2

Itt [(14+ I-E)+0.EI3p1\u, < E0 (iED

ho> O!Lt(+I1q> EoH3q >LWW ( h > 0 !ttU+I-> [-(1i+I-E)+u,]u mtq iow (J'

O1->o.

W flZ% Ufl% t'd MZ%V1 > 0 (fl11(OTc*wot u towrnt to bcAtt n n-%ooç

Q %nbbO% \ = =

COUqIt!0U lB IIMIAB BUTBIJG(1 MJIGU qGuIluq II flUGVV

CBBGB IUMJflCp4pGGXbOLiBnpBlqAlBb0BIpAc'I8BGontwJ,wbowpcUQ JJIB

C0111.UOt WqflBfl) bLOqnCIU* (JIG JUIQLWGq!1IG *00(1 MOIljq WCLGIBG (JiG IU*G O(

JJJG *CUCLIJ COUqIpOU IIU(1Gt ispicp (JIG IUtLOqIPCflOII 0( I (1OUJGIPC

WlIGt (OL (PG JU!J *00(11018 (0 IILGCL (JIG A!JflG OJ U W1I1AG (OUQ

Page 23: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

8111 ilqqu I8ioqonofn n$i81o aibkdw ax aa 5111 gansbiano3 wol4

nsdw lath awod8 (ii) noiiiaoqoi11 (1 = = MM .s.i) boos siaibennsith

nnaqmoo aui1T .bsxai sd bluoda hoqxs boo-1an1 3ilasmob iaoth1 Bk biwnsb

iii i1oqoiiom nwto1 £ 01 3ilBemob a molt hula a (d)Qii)4 noiiiaoqoL illiw

molt d3liwa ol 'iloq hoqxe gthilida-Insi sill asauao '(IqqUB boo-s3&ibeuns1ni

() 10 noiaasiqxs iaaI sill 10 noanaqmoa a IIaiens stoM .xal a 01 biadua a

sill (Iqqua affIñ 3daemOb 11* naIl tsiliax n*istoI ila nivad lath alasvet () 1131w

baa Ii ahoqxe boog-IanIt sibiadua 01 svilnsni sIl asoubsi boos slaibsnneith

baa 'taaasoon i 0 < (i1) 01l8 q molt 3tha .0 < "a-s Ii i1no

aidi wieilqqua boo*-eiaibeanelni laollnsbi lo alñoiq sill saiai 01 ba tol insiofflua

s3iiseozq agisiol tsiast £ 113111W asbnu (€ noiJiaoqm 881) noilibnoo sill Jaul ai

.ahoqxe eaibiadua 01 evijne3m sill atswol 1qqua boog-slaibsunstni ax

.0 = "q, . hriooI .0 <t I M � t%1 0 <4+'ai =

.0> tn = = usd1 0 = "qi! .(bab\bYbr\[04 + "MJ"Y = '1 Q4) baa (1) motI (1)

baa (th101 = JmO baa (M) (1) () moti) = 0 baa (I+4)\ = s3tha awoflol Iluast 8111

(Vs) .(bab\bYb)(1 +T4)\[(!+w)(1-) + 14Jby = nialdo sw O = ko baa I = = 111kw (Vs) mot (ii)

UIQ .0> (b\bYb)(I +14)\bybn = 1 sth'I fl2i91&I &oaobua 2

sbam ai boo* staibeunelth sill to 'i s3hq nisto1 sill noi33ea audI ni

'(tinuo3 iii b annft as IIsw as 1 ml aun?t laill nimuaaa d auonsobns

.aieilqqua lb quot emsa sill molt boos slaibeansith sill sasibwq (I

boog-lanil sill lnsasiqst ol t = baa ('o) = nithW Ii (() anoilibnoo astno lath sIt molt) '(lsvibeqast 1 baa b annhl lo atuqluo

tall (4k) ol lauogo1ana awoI1ot

Page 24: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

(8) bna 0 > 9%q\b =

(be3ninge€) edJ in boos s3aibeirn&th edt o 1qqu diiw bnafn8b ni3aupe 1lxeM

btii 'X = (11irY bna aX = (iY gth33e .e.i a3eiiam tiaieiol bna aiJemob

+ X1X)4 = oviu bniunth e1bvth edt aenlIcb Iauocim1Iumi8 gthvloa

aA .1evi1eq8ei leiwn niciot bn& oil8emOb edt in (X10X)'4 = 'i bna

:acviiavhcb Iaihaq ovad'4 bna a4 ,(I .A) in nwolI8

,0 > n\q = '4 10 > bn\bq = a'4

(Q) ."cf'+ 'q = '4 baa "q+ 'q = a4

i1qqua tnuo3 eno na th eaacith na 3&dl acilqmi (2S) 1bebeqxe ed Ji1im aA

c3hq ciii tail baa inuo3 ladi ni c3nq B&ubei aawh boo* ctaibeimelth cdi 1 hid 1achzdIi8du8 31p1f118 cii BhiJqhiJO booa-IanIt Ii 811*1081* (iinuo3 il3o cdl in

.atnomclqmoo 3tpifd8 cii edl Ii acth

01 bemuaas cm aicouboiq boo-chaibeiznclth 18i81ana cdi iIqmia oT

lud iiieinob baa nicio1 diod to nieio1 Ha 43dselnob Ha teduie ,IaQiJnebi cci

cdl diwnllaib oJ I baa a ihqhiiequa cdl *ni8U .alaoo Ia3iincbi itliw

te3ulxnq boo-ciaibcunehth 1athqi £ 1boog eiaibeunctth ciii lo noitanilacb

3 baa % aiaoo Iathwn ww3ni 1nieio Ii in = i baa aiiaeinob Ii ii = I cicdw

baa Cl achinuoo oh boos chaibemichni cdt 1 "i baa x aciiibnaup ni1qqu8 in beeoxe ud1izn ° neil 1(m = ii .e.i) ngieio1 ai I unit II .1evil3eqaci 1

auilT .if = 111 aiicv-eiv baa (i ol 1 vihnuo3 moil ahaoo hoqanint lb eauaed

d nevi ai hiloiq 8'i unit 1alclwn iliad at aelaa lb lnuoa gniiid

(0) .miI = I iol "x[ - ('X'X)'4J + Wx -a+('X10X)°4] = I unit ibac 1icliem ibae oh i3cqaci ulhiw roiv&ded lomuo3 gthmuaaA

seihitnaup cvilcqaci cdl b(a1 iftotq eimix&n 01 'x baa x acililaaup cdl alca

cdl ml x baa inx (0€) mcnl 1eoneH .nsvii u annlt tedho cdl d beilqqua

:anoihibnoo telno iat11 cdl 1aiiaa innit laoiinebi

baz, 0 = bi + % - '4x + Q4X + a4 = —

(IE) .0 = - 1'4x + °4x + '4 = —

Page 25: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

.s.i :boftaiMa ed 03 bemuaaa oela sta anoiiibno3 isbio bno3es sliT

(g.E) 0 <fi) - 's& 0> 1Lic 0> :w '4"x + 10X + + °4 = baa i + + = 1T sisilw

:'at1oiiibno3 3ilidaIa sdl saoqmi sw noi3ibba ni .'1U = ,i baa c I ioI

(SE) 0< —'HiuO > A0> A + + 4 + — 'Abn&11tQX + 1114!X + 4(1+)

— 1'A siszlw

.iCI = ji baa Li ioI

boo* sialbeanelni eif3 lo 3i3naup sdi ,(IE) moil neea sd na ibod no iaeIle all lo 3nuooa 3niial boaiunslsb al i3nuoo sno 'na ,oI beniisob

sia boo3 slalbeuneith sift iol al3tham 3113 d3uodlla auilT .r baa °i a&thq 3113

aaoledhevsn su vodi ieThb nao baa 'i asthiq sill lath snea eth ni beJnemsa

ibum wod ol aa &znlt boo3-olaibeansith sill 10 anoiai3eb slil dguo'uli bsbsnno3

d bnuol ai beilqqua asiiiinaup sib no 'a biadua sib 10 belIe edT .Iqqua 03

ChXIlM = aX = y () 3niau neil ,&nzft 4 sill ioI (U) 3rnlailneleThb 11a3ol

niaido 03 = = 1Y baa

t*w 0 <H\A- = = b\byb (IC) .WH\AUM = babVXb = bab\Yb

boos olaibeanolni sill lo on aeauao aawla ba ni ssasioth na awoth (SE) nA

thoqxs boo3-1anlt 3ilaemob sxzsd baa 3e'ham 3ilasmob ciii 03 beilqqua 3d 01

neil i ann d318) 0 > A 111111 ahoqxo boo3-lanfl ff315101 oalA .eth Mum

.0 < 'A 118th baa ('1 piwoo 101 beaiiasb lix tuqluo all asub51

edt mdi ai siam 03 lnioq lath sill 1aia(Iana 518118w sill ol 3niznuT

lo 3310113 edI iol (21) noiiibnoa tetno lath sill (81) noil3niit siallew 3Iiasmob

auovq sift moil be3nwl3nu sia tol (0) nozaaqxs Iltisvo sib baa

moit lboiib awollol E noiliaoqoi11 1noilaoqoiq Izxlns3 iuo s3n2 .aia1ana

+ '4x + 14 — stsifw .r(I-"4) + fr = A taut sloM ' a'4 = siedW . (1-"M) + jT = 'A eouiia A 03 taups IOn a!

"Ia 4 x + 4 x +

Page 26: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

.Iobom bthniqxo audI 03 abnsixe t noiiiaoqoiI ail3 noi3aiIqrni sill aad audi (QI)

boog-el8ibennelth 3laeInob bna ti*i3to1 iilod sia 5i3111 113111W 10 sa sill gnbtal

ol i am flew am 'i iniwolia hilt awollol 31 a1ao3 lm3ilflsbi ifiiw aieouboiq

sill lo qidrioiiwo nieio1 sill m samel3nl am 1auonsobns bsninnslsb

atioqxe boo-1an1I siibiadua 03 eviJnsni sill asoobsi ilaubth booibennslth .bimdzja sill moil honed bluow aieoisbmq boog-simibeimsith Ii 1no baa 11

aug aieoubmq boog-ehaibeiinoith 113111w iebzw anoihibno3 ciii isvswoH

— c ni asgnaIl3 88113w am 't ni aognad3 no bnsqcb won biadua 3111 mml

aloft .s.i :ieimm 3118310Db 511188113w am ngwtol sill ni bsznas a3ilozq no bum

mil = 31 tol 1(0.A)

.[(bmbVhtb)six + sb\b)10x](1-4) + Wi = bab\b

ngwtoI sill ned) (1 mill sno naill 3101081 310111 .3.1) 1 <UM 11 woda (?.) &A

na e31ain oh abnel aid) afl&1 't II .bab\b tot tehlam ni aegnsd3 baa isthain

Ii eneH .meth 't Ii I8ISV 53iV baa 31 annfl sill tdl ehdahflotq amsl ha in 388313rn

sill glIflebiatIOO 10113111 (i1 = 3111 .5.1) 3118sin0b $188111111 boog-ehazbeiznsirn sill

na lnuoa olni siah 01 been bluow plnuoo 3IlasmOb 3111 i1oq gnifludm-lnet

am flew am ngietoI gnF1qqua ni enensqxe bluow ii aunll iBdi aeaoI to aniag

.8133Ub0tq boog-Imall 3ilaSmob

all anfi Ii 'abVb tot aishiam lsiiam 3daemob sill Ino 3aai3no3 a sill 81 ((VI) moit) 113111w = 'abV'rb aeilqmi (?.) 588381111 a! .Ioqonoin £

ax Ioqonorn sill Ii isvoeioM .auonogoxe'i 1111w benialdo am noiaasiqxs 51088

:iznol sill oh asoubsi E) bum (21) gnlau (nsdl ,(il = 3111 si) oxiasmob

() .ab\bYb)\(amb\bwb)bn

ab.nehxsaudT .0 < mb\brb1i1nobna1isviiaoqai (ôE)moi1 nssa sd nao mA

sill ievswoH .auonsgobitc i 1111w ammo Iinsnog stom mliii ol (ii)4 nou1iaoqoi

baa (I) moi .i ni aegnado d b&ooTta sim 0 < "mb\rb doudw iebnu anolhibnoo

nialdo ew (V)

(V() ab\'ibX'i6\w6) + (ab\cb)(+ = bab\hrb

nmo 31 0 < 'q\("q+ q)bn = ah....b baa (8) ) (I) molt etsdw

Page 27: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

3&fIi IIWOIIE

(8E) —

.0 < nt(3- bj)b i Ii bviiiaoq i ikikdw isnei IIIIOiJIbb& na awl 'ab\rb 1) ibiw (Vs) gnnaqmoO

aJ3e1 bill lo noilavneb bib tiupei ailuaei ieithuq .a1l1 i Ii evilan him auth

baGi - him 'i no biadua eztJ lo ((VI .A) eea) d ,mvi q1 belle na awl bidua hoqie iiaeinob edT

(QE) .uH\{EU4ux + 4X]ii'q) + + 1n\'qJ}"1 = = 4 him "q+n\(I+1n)"q = — riwlw

etnas eill evad 4 him 4 neib (U&na al q\"q ladJ gniaoqqu8 .(II.A) moil

.awollol 8 noiliaoqoL ."q aa nia .% Wzo%

.0 = 0 = .0 <h,k\ a 0 � \-\ — Um 'i"q w 0 > "q'

neib llama q\"qitliw 0 > quI (ii) .aeifainav (Qt) nedi 0 = "qIl (1)

audi (QE) moi1 .i(i = j1i sol 0 > 14 baa 0 > 4 (M.A) him (Q) inrnl

C139 .0 < 6 ml 0 < babb aeilqmi

biadua edt lo alaeTte eiailew cdl sol anoila3ilqmi au mail haqA

3v113a cdl lath awoda ii eauaoed *niiaeielni oala al 8 noiliaoqmc ,M& beaau3aib)

na aehlnuoo diod ni boo* eiaibearieini cdi lo aiczlqqua etnas cdl lo lncmev!ovni

cIqmaxe io9: .biadzja lioqxe na ol 'ilo noiiaei cdl b$1u1d3 (Ilnaaiuinia

a ibiw ibae nakeso1 eno him 3ilaemob CilO annft owl esa cicib mdi caoqqu biadua lloqxe 3ilaetnob cdl 0 = "q ibiw nedT .sbnuo3 nwo siedi ni Ioqononi

cdt sol bnatneb ni8tol gth3nbei flit ol wqluo boog-lanft fl3iclol eaua bluow

trOqXb 3iiaeinOb eu eaeupeanoo & aA .9i eoubei bluow d3idw boos elaiboirneini jq mail laadno3 '[ .ahoqxc *niaiai ni evil3eTle met ed bluow '(biadua

ai 9: ilnuoo in bIoa boo-e1&ibetinemni cdl 1 (ii1naup cdl neifl 0 = "qli (i)8

Page 28: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

.3n*1no3 amami i JadJ bub31 (Lnei3fflu8

awode(8!.A) — noobeedio3bqa91diiW (04) + A(bfl\CI))uM =

A-'A II .(t.€.A) moft -' — ô iol ô'1q - 1n\(! +'n)'q = A-A r13dw

oio eih aJathmob A 330M3 iib 3di Ii .e.i) 0 > bna 0 > (04) mml 0 > b\qb nodJ Iu1ii8du8 3iVii8 3uqiuo lanil bna

noiJoub3l bn * n3h3qx3 IIau3* bi8du8 31b nivioz b ann?t iaifi n1woi1a

e) ailqm1 (0t) n1ft uenil *1 bnanisb Ii mIu3iIzaq a! .3803 I3niam in

taili ((Qt .A)

(fl) .0 < (1+"M)\! = = b*b\OibiO> (1+V'M- = lull m8nqiUE lou 81 Ii UIU1 81 bfl&fl3b ni1w befl&13nU 81 ni2 (44) 8e8) 1*uoneoxe Ie* 'i iiliw beniuldo e*oulJ ol Iaoiinebi sia (fl) anozaa-zqxs

.(1+LtM = "9bnuO = ñliw fl338 3*d 81 flO &,oneobge "i thvut 10 leTte llaisvo cuT

bnu (E) gthau (QI) mozI :nnol *niwolloI ciii rn biadu8 larnilqo cdi niaaciqxc

thaldo ew () () b\bYb)\{ab\ib)S6\br6)bn + 0 + bf]by) =

81 () lath aluevet (!) iftiw (4) 10 nothsqrno3 A .() d 118V13 81 0 etcufw

cn12 .bBb\ib *thvlovth intel lanoijibbu flu aud lud (!) 01 miol th ialimia

0 < bubVtib li b eeiaz 01 *nibnei eviiiuoq ul rn-id uhdi (8) motI 0 < ti6\Lr6

o = bubVib Ii eIqmla (hu1u31huq 81 eunooiuo edT .0> bV'b Ii evila*sn bnu

bab\\b gthulea 3813 8111311! ((1)8 noi3iaoqoi ces) bnumcb tuerni duiw uiuoo aa

> bV1Xb acilqmi d3udw (Q) baa (U) moiI 0 > A ncull 0 = "q 1! (It) mofi 0

'q darn 01 8808 abninuoo 88013* (1lfl13ft1f1g1a icThb 83803 lantgt*rn 1! ' cdl cla!oiv ion been eldT .0 < A-'A eldisaoq 81 Ii cviiucn baa eia1

al 6'q + b11\(l +'n)q = A - A bebivoiq (tt) unoiiibnoo v1i1ida38

.eVilaen (I1fls13fflU8

Page 29: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

evad ow en9H .(1) 03 oubo'i ()) )ad3 nwoda ed fl&3 31 (1) $n180 baa 0 = ni out nisnenoo a3hiao woiveiq edt us Iadt nolia3ilqmi oldaiwnoi iedlai edt

"q jol noi$iaoqoi (iii)1 noi1iaoqoiT thbubni iaethl al bnameb nedw lo .1suneobuio tea si i nedw lqqa oats (ii) baa (1) ahaq V noi1iaoqm baa 0 =

bool-stgib9IIn9tni edt biswot itoI 2itaemo(I 2

ahoqmi ot beilqqa 1 IThat a lo ataelle edt flffl03flO3 flO 3308 aIdt ioq

edt 1 noii3ubmq 3liaemob 01 biadua a baa J3ubolq elaibennotth cdi lo m lebom out ol *thznutei d aia'tana alit 1ilqrnia ow t3uboiq otaibeaneith

.fleVi i8U0fI0$0X8 81 1 113111W

biadua Isupena 1111w benldmoo ai d1 taut ciaun oiinioqtaifl edT

m baa dado = du etha nedJ 3- = a .0.1 1boog aiaibeuncith edt lo ahoqmi 01

10 alevel edt grnrnmieieb (0!) anoilibnoo tehio taift ciii 0 = b8 Ia " + = as molt benialdo ed bluow tadt eaoult ot 1aiinebi cia in baa 11 annñ 10 tuJqluo

edt *niskpi eoni .'t- = = level emsa edt is lea enola biadua hoqxe IaIeve!odJ1a"t- = 'anoitathdmiloqftd1iwbiaduahoqxo

aieoubrnq boo*-lsnht lo alevel tuqluo baa 81803 lanigiam cult no 330113

.awollol Q noiiiaoqoi

1oo% MnitiUt jXoq tu oamc . O1ZOi 03 Sth Z0'fl% U* "i- = %'% . g 11Ui% 31'% 1I Th%IUe (iuck

.zflo 00%4a103 1%U% aiI 1fl U t3 W1jH tab .noliiaoqmq aidt molt etaibeunmi 81 1sll(no3 niwollo1 CdT

.1

03 oq an 1%toqmt 7.1 t'oo% ictiu it 1i cn zwI ianz it n tt too %na 03 SVU% toqm an

03 tSiiz aott n iaob ü oo iM \ ian n boos %na1s 01 (b%l% oçm an ban boos snic1rn

Page 30: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

8 no 33e115 emaa sib aasf 1- = 8 lo noilanidmoo (3zIoq sñi i1uoib1A

smaa sib Ii isa snoI biadua hoqxs iii am suMew 3ilasmob baa lfio-iq 3uq1uo

.biadua hoqxs am imun ol am oe da baa 'i ethdmoo 01 I&nilqo o*' mlii Isvs1

.awollol 01 noiiiaoqoi aoi3ioq Iainiiqo hthoj sill I emaiqsi i baa a niJlsJ \, *o .0 <* bu 0 <' ou% .I zcoi

'-nIg ib baI -c* tsiOt 01

ib IOi hMot %(0qm - <% uusi t't4 aonnisno o%io t 1%U%

1svi1sqmsi sia l baa m lo asulav lamiiqo IithoL sill (Q.A) moi1 :QQ] (Us) .Y\[3-',-1rx-Y1 = i baa = I&dI smaa sib o* miii sasH .(8.A) mcnl 0 <Y\(dx+mx) - = dw

U3Q.*ml=dm

3iloq lmrniiqo sib ladi awoda 01 noiIiaoqoz lgaithqwa loT4

lo noil3uboIq 3iiaeInob no (xml iswol io) bimdum isiliil a asvlovth noiianidmo3

*nitutrrleith anoilibao3 sill olm 2d*imnI .a3Ioqmi no nmdi boo* eI&iboitnslth sill

hoqxs sib 03 a baa i *thialsi d bsni&ido ml msi3iloq lniol sill lo mnim sift

(.A) (0 = "6 si) a1ao laiInsbi svad m baa if snnfl niaoqque . biadum

ladi lqmi (.A) baa

(44) .,'Y"x+xyn - - = ""3 tiui Y"T4\("'x +"xrn - = aabsmubam0 = "6uisH .""l- < < daib(44i)moitawollo1nsdJJI

aovlovni noiiaaidmo3 (3iIoq Iamiiqo sib nsib ,ois.t sd 01 mnsqqad ,3zloq slom a ai Ii isvswoH ."I IliiaI sviiiaoq 1isiiim a baa "'ia ibiadua sviliaoq lj3nim a sd bluoth ahoqni Jail lqtni bluow ibudw 0 > ""'I Jail sldimmoq miii ,sviliaoq

nisio1 01 alItoiq fluda lI3eiib noilomoiq Jioqmi d3um Ii nev3 .bsibimdu

sill Ii nia limo Inuoo oiimenob sib maslsdhsvsa ,misouboiq boo-s3aibszmstth

ol ma om misouboiq boo-laiift 3lIaemob lo alaoo Lanigiam sib aooub5i oi!oq

rsif bsinseeiq bimdaa tioqmi am tol sviiom siT .aJioqxs boo-lanñ slomrnq

£ d bsouboiq ahoqmi *nlibimdum tol svilom sib nioiI llainernabmñ a-isIIib

Page 31: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

behoqmi sift saa nsdi iii .Q8Q1) isnsq2 bus ibna-i8 in loqonoin nisio1

isvosioM .shoqxs no 3o11s on bad bus boos noilqmuanoo losiib a aaw boog

-isvo sd bluow ethq 3oqmi sail nsdw anollaulia in 1no tol b31153 85W biadua £ 3daeinob 03 n1s edi ci biadua sill lo inuoma sill iwft siom d gthllit bsffida

.biadua lo Jaoo sill bsbesxs atstnuanoo

lo 515115w 3ziasmob no 3eits sill s.1ana 01 svj3Inlan ai 31 11ath1

sill n1ioneU .sno1a boog-olsibeansith sill 03 biadua noilauboiq 3Iiasmob £

isill awoila (4€.A) d (3iloq sloa a as beau biadua audI 10 sulav lamllqo

() • ________ +

[1_LI +

(dth\m)]dX = (dth\dXj)) dg (4ab\4Xb)

iii) amisi bnooes bias lath sill biadua ltoqxs sill tol (0) ol 1auo*olsnA

sail bus 'bells 1V3" sill Inseeiqsi 1svibsqast () lo (a3said staups

sbaiI lo ai3 (svilagsn) silT .biadua noilaubotq sill 10 '33s11s sbai3 lo srinsI

n1ans boo* sisibernislni sill lo sathq sill in noibub51 sill 01 ais1si sisal 'belle

neilw ahoqmi Ic level navk* a wI luqiuo 3i)asinob lo noianaqxs isvo sill inoil

lo intel biidi silT is3uboiq boog-elaibeinielni 3llasmOb eno usd3 siom al etedi

.isimm boog-lanfl sill ni benias aIftoiq 3iiaemob lo belle sill absflsi () ((?.A) sea) 03 asoubex (?i') = du — u gfljfl5j

(at) Y''\[(+ f)bY + UdX = .awollol 11 nouiiaoqot (11) mail 0 <

03*1 %% dI t $10 0'1Y

u 0 < — x nsil .,0 <+ t 'j .oq, io i tou ii o *%l% ,0 = + 1' . %o(W)nfl 4 o tilut nmi$co s#$

.0 <'t Unljt ii 0 <

ml ai snola lThsl lamilqo sill ,0 = a ilhiw (.A) bias (d&.A) mail ,oaIA gniaizi ni I 10 130115 edT .(3b\nXb)\[(mlb\alb)(+ 1)'Y - X + (lbV'iib)'1nJ- =

mls3lflao>rnisldiaaoqaililud,o <Jsm03abnslsunsvsi11halbus .0 <+1li11ilo1gthaua,°iaeaiai

Page 32: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

bqib wow 8nthuwiuS 19 fIG COUPIRIpIt tC9Jf f19f N4ICU fIG

BLJ1UJGU1 nuqcuiiiuiut pG fl9C °L CXbOLj 8np€iqIc oi iwc-pqput bmbo

iUqGCq MG!CGU8 fIG q0wC21fC !UCCUf AC to 8np8lqll'G G1b0149 jp18 b.oA1q V UCIft

IUCqI8TG ooq LLOUJ LOLMU IHqIGL f 7811 (CdflWJI) GWC!G1Jt) qowcpc bwqnco

J7oq9 mIqcL pLo,q couqlpou8 i.npu on biojg oAcL-9pqpug) tp bnwpw °L fIG

8M 1 cumGqIc-ooq bwqnc !Aonjq iu tiom 8ncp, 8np81q) (!pcp111 Cou2tqGUut fIG 2flp21q 10 u!J-8ooq crbOLj8 V 1118111 LG8flJI I $0

Rooq 8WG ww po couiqcLq

GboL$ put bx.oqncpou 8np8IqA uq wiboq wu wbbpGq pc !u101.wCq1C-

VIIGUII0U 18 EIACU to fIG GC18 °L V 8bCCIIJC 9np8qA 1bbJGq to utj-koq

cpwuG8 ! 1p btcc uq dn8ut!O qumuqq o fiG UUi1GG ooq Lt!CflVL

bou$!wj1X gJLqiGL epiq to mtc-ooq bioqncou fIUJutJI cucJOwon8

jpi occnLa GCVU8G fIG bw Riucq p? qowcc u-ooq bwqnc vwLCUtO $0 pW!1J LW8 anbb1Thi* Vu wreuI1oqt ooq 10 tpc qowpc Qcouow?

wut LLW owiu fO qomG8tC bwqnc °L' u'iooq wvA o VOLAG to pjj

Ji8 b8bcti. mvjc bows spvr opidic piqc bo,!c! viwcq Vt Vpuput

qowpc uJ-ooq bwqncqowtc Mq(laC pocow j 94uut0u1 8117CC (pG onpq? vjo opij bwio

tpc couqwou mlqci. MpIcp V 8np9qA 10 iui I •wtG4ooq bwqnc1ou Lv!9G8

/A7fl7 bcqoct couibcppou w 1uiGuuCqv1Q4ooq 8IIbbI) H0MC I 7 + > 0 $pGU

c1a =Ui+ JE11q > Ø9t fiG cxbo14 9npeJq? a to p boVIpAG in fIG pw CtG

wdniwwGul — u+ I--U,> 0 ' tpw ,uvjokng to sp wdniwuju

OWG8PC MGJG tpionji btot-9piijut in fIG uuCfiVrG-*ooq uJVIfGr JJIG

Sooq 81 no GGC1 on uj-ooq bio ( Iobopou , ciliA VCC18

ooq (0 fIG OWG8flC COIWIA IL I + = Ø 8111CC fIG bcc °L $G U(GUIJQqV1G

UUVI bwqnc; Vuq fIG OfICL '4tP LGVbQCI to L0LC111 QZbOL4CI2 o qic IUICUIIGfIVIG

bwUf-BpWlut VWG2 1UA0JAG OUG Mifi LGObGC( 10 tpG Lowik bLoqnc o fIG

j,tobooipou H CVII G nuqG1rooq jtow fIG LVCI rptt 8I.G o

Page 33: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

1o io*1 1&noIlibba na n1vas1 ,i38smob 1(l5uIq 81 1(1l8ubth boo*-slrnbsisnelth

lo snrz sill saaotath n s&I l3ubmq slJubsunslni Sill Ia noilLIsqfno3 loinuoD

313830101) aeasn1 bluow 83ioqxs boo*-lanñ lo noiI&ibi8du8 113111W 01

nove svthaoq sd lil*im bi8duB gnflld8-Jne1 Ilmuiqo sill 1J111J3iJ18q ni .suIlsw

bsnlaldo 3188110831 111am iuo IiUOI131A .8lnsmelqmoo 3*318118318 aboo* lanit Ii 81111 thxi1sr no boo*-o1&ibsane3th sill iol shq fl*iSlOI uonsoxs na 1131w

no bluow 8lInaei sill lo laom laill 1*ththpu8 isdiai bnlI sw noiiqmu8aa

.auons*obns i 11111w Isbom 18131139 31001 £111 13'F0

SW l3ubo1q ei*ibemislth sill ol beilqqa 1lQe1ib esi3iloq 01 3sq8s1 1111W

bi8dua hoqmi na bna biadiJ8 noii3ubmq 311830101)110 noiiathdmoo alaili woila

i3libmq-Iaflht ol beilqqa biadii8 Iiwpe 11801 lnslavwps 81 Inuoma sinsa sill lo

lainilqo 3111 131)110 boniaido ed 1113 siiHSW 3138&flob isdgid isvswoH .aJioqxs

131)110 naill 3*818 1)00*-slalbomloJnx 311318 bedqqa asi3iIoq owl 311310 noil&rndmo3

.3(1013 bi8d01 hoqxs lamilqo 3113

boa boog sl&lbsunslth sill lull noilqmuaa sill xalsl 03 sldIa8oq all! 11th sill iliioil31A .boo hnIt sill niubmq in noihoqmq bsxft in bsau 318 10(181

.*nlnoilnsin ilhow ai *nlwollol sill isqaq alill 10 sqoa sill bnosd al aia'18na

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llOqxs ugh nsdT .(snolu 'todal d 83803181113180131183811031131w be3ubrnq boos

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jpi — > ww (1!!) VJob iom (ve) (y) uq (v)= < 0 1u; qxp\qlm = 0wp,E,i)\kn' (v8)= -U\b > Ø qX\q2, = (v)

nJU x1 = J41Z tOL Jc=pw wuq u(b+xb) =

1p\Iq = {J + Uw9En\XD]\kn IJq qxw\qq = -[j -Up9En\ ]i (vu)Hug k' — 14+ IE lAG OpW1U (j) o pc rGzr:

flH!I C1WGL I1jG l HOfAC (vt) iuq (va) uq uoiu En • XD'\ 9 —

u+zt)q + = qru, - (va)+ n(b+z,bjqz1 = - - (4)

q'u'uq O4 W° 1JLt OIqCL couqou (j MG opium:

EaGc O ; ; 00 Onfbnt: jru (PCMpGICJ1 — UL+jQE > oqk — M+!-E > otow(

= b4 < 0 "'% = (Uq\U)(UçQ)\b%4 (v)IAGU pA

o HO iucz.Gc iii — ou uvJ-8ooq onbn (HpoMu w () ot n' ICu) 'e

2o,A!u (vi) uq (v) niu ni uq nut i%b = -b (P0 ouocrb+A1b)q) + [(uL+j)bt+J.(bjqA = 0 (v)

[(Uq+J)b+AqbjqAq + ub+Aqb)qA = -qb (vi)(JIG rjr OUJCL COUIfIOUH ( MC

E1L O - - on }jimj-(ooq onibol: JV (PC (0(11 qILJpLIpvI OJ

F C04LVWfJJAE 2LVflC EhEC12 Oh aq . VL4I) p 014 OfLLIfLL

vnDGiJqx

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Miff iq w qomu8 wrcupouj dzoc'wourH m MP!CP Wn(ntJ

wopAroq ro n Lcur-HpijpuR boJ!c!ce pnr 010 P0 ! 4P'T BOCP

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tiu 0 < = dth\arj < u9tMT = b\ayj (QA) .0 > "9'Vn = )b\axb

ia aboo Iaai11 :0 < q iwo znTAwr . = ? ni 3b = I io 0 > 'q\(q+ 'an = 3o-'n Th aJn3m5Iqmoo

= 9 nia baa 0 <9 + 0 < aeilqmi (LV) n = M *nimuaaa

ThO < nth3do3w,3ho

(OLA) .0 < E"n(!-'n-!] + 3b0j0 + = 3h0bfl + (1+dn en3H .0> -'n iot 0> aeilqmi (01.A) baa 0 � dn(1bn).! nii3 � bnU

= b mJieZ .1 = bfl iiupei 3w 313 alfl3In3Iqfflo3 3ita1t ñi ni 0 < ioI

Th 0 < Iadi (OLA) moit svad w 1 (11 .A)0 < q\(q+ 'qS) + 'q(q+ 'q)"n(I +d) = ao- + (1 +'n)(-n) baa °X = ('qY *tiiiaitn11ib ffa)oT :i ur'1 iaiasio' uoooa1ta .€

Iaitiaq evad ('XIX)14 = baa (XX)'4 = o, (8) gaiau baa 'X = (S1t)'Y

:aevilavh3b

(! A) o > 'n\'q — = 0 > b\bc = =

= a4 1q'+'q = = a4

iadi (1.A) molt woIIo1 aaiil iI.(%q)\bn yby_1iyby = I iol

(U .A) qô - = - a94 boa bn\tq = a4 - aU4 n\'q = - nialdo ew (E1.A) moiI koaLA .(-'( • ô ioI

(M.A) - = U4 boa 1nV'q + 4 = ."q' + bn\(!+n)q = a4 boa "q + n\(1+'n)"q = 4

(E) anothbnoo 3ihdaIa 3d3 baa (H .A) ,(U .A) moit noi3ibba a! (t.A) — o1 q-1n\'q(!+'M) =

— A baa 0 > li4tX+U4X+I4(M) = 11A 3131fW

SQ = j,i boa j I oI (bth\aTh)14 + (bV'Xb)4 = 'abV'ib eth2 :bab\J baa thV'ibIo noiiwin9U

3ad3 (€1 .A) gaiau awollol 31 €) thau "H\[A4 - A4]"M = (ô1 .A) - A(nVci)}14 = babVlib

Page 36: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

nimldo 3W (ôI .A) in (I .A) mOft 'qö + aR4 = O4 bna (1 .A) gniau n3H :lx3J 3th lo (QE)

(VI .A) .H\{[j'4°X + 4X](n\'q) + q6[ + 'n\'ciJ} = - 4O1t,,I = (b8bVIXb)c104 + UTh)0U = bab\cb ath8 halimi

:3x33 311J 10 (04) nido ew ((1€) mail)

(81.A) .(A-A)°4 + A(bn\q)}h1M = = UH bna n\(I+n)'q(1+"M) = 1+"M) = 1A 113113 0 = "q II

i1qmi (81 .A) 0€ mail) 11b11\(I +M)r(qf(I +4) tsu 0> (1 +MM)V'T4- = b8b\b

(21 .A) .0 < (I +'St)\I = I + b\b = = [b\ 4+(\I4J(1-4) bna (if) (0€) mo1 €1 (?.E) in 88 1r aIItoiq no b8 10133113 edi 1M\(bab\qb)(1hiT4)

(0.A) uW[(8bViib)x + + wx = bV'wb

:U1 TILMAT (MA 'E Y(1128UZ MOITDUUO$i .1MrNO HT .1

10 133113 3113 (V.A) bn& (01) nl8u (2) moiq :81floR no 1 bn8 lo €bo11

€1 311oiq €d unit no

(I.A) ,('+ 1)dx = {[(a8bV'xb)(1-4n) + (4abVXb)]'+ 1}ax = a8b\",th

= jbV'b taut gallon o€IA +mfl — tol U\Uy) — 3-1311w

mi1 = 1 tot 0 < 't\("q'x+ ''n = oan bna [(b\dxb)(uhh1b\OXb)]cx

3V811 3W (I1) moit

(.A) .0 < g 3*d)dX1fl11 = d novig ii in unit ugietol a lo iIIotq edt no 'J bna a8 lo 81331133113 haIimi2

(E.A) .+ 1r- = ts 0 > = taut b€(OX)q = °i bna (V) moil 8wofloI Ii llath1

(.A) 1bbX+ 1)- = tb\b bna (a8b\b)(+ 1)- = 4abVrb

.(Q.A) mail 0 <U4m = JItth\(LJ () > Y4\d11 = (iL\a)th) = dab\.xb iol

bnaa8 (8I)dnevigaa'Wn10 = '€gthh1eZ :96Wno'Ibnaa8loabella 31311W 0 = m,b\UWb () = dgj\U(fj 1ai1aa 3

Page 37: dH inq - nber.org · rpef (JJGLG ew couqiqoue nuqoi. lItp!cp VflCJI V enpeiqA wipr ectnvjjA EJAG piqq (P BLVIJqGL euq 2bGUCGL (ma) woqi o vscJc-rivq bojicA pee to em UJVLJCGT epew

(aS.A) 'i*u = d\awb (d.A) .(ib\dXbyfa(b\_xbynl + mX + (3b\'-Eb1n+ (b\b)'n = emod (da?.A) anoi8aeiqxe 1(1.A) bna (.A) (I.A) (8.A) (V.A) moL tx mtmfl)(i5,+l) + ud + 3)bY}(1&9\d) = 1b\uWb

H1bdnx + (+ j)by)9\1II) = (ô.A) {\mj + *\(u thiifl)(m,+d) + X +

JadI awollol Ii t'n - = l3dn *niau (à.A) ino1 % (U3nIm)(m3 + ) - + ( + 1)by] =

(A) (U3dfl)(ml+*d) - [UD4X - u4(mX+dX) + (\+ 1)byJ = ilqmi noiaqxe owl &b 3nimznu ibidw

(8.A) .0 < (mx+dx)c = = U$ n-1 + ('3-mn) — thau bna (.A) olin 1acf (8S.A) nu3uiil2due

:3x3 if3 lo (U') nthldo ndI w ,.,,''f\1 = bna U3 +dn+mn

(.A) .Y\[(M3o1rx. by1 = _ by\[u3nuJm + 'x + YJ- = (1) .A) moi1 :3 bnai bi1oq fliiot iIl bni nw38 qidnoila6$I

O)(\mX = "O bna

(0€.A) YtM\[0bY - °xv'a'x'x + 'x)] - =

- !)] - Q j by = ax b = - I = ,\{[&fZmfl+ bym 'x\'a) +mXdX} = ObYthlildo w () mml U.\[(Ua..I)nhi.

i1qmi 1(O.A) gm2u I13iLiW

(IE.A) .,lYIM4[dnmx9C - ÔZnIIidII + dXIXJ(x\M3) - (mX+hIX)mfl} - = 03 visx.ubei (I.A) [&x + &1xJ"n'n = [dnmxmX - ôJIxmnn + xrnl,q

(SE.A) .Y\['X\"3'n - IJ("x+'xrn - = iadl 8woIIoI Ii (8.A) mo'ft bY\(mx+dx) - - = l niu (t.A) moit o1A

(€C.A) byUM\[UX\u3ômfl + I1(x+mxyhn - = in 0 = 3 ni33s :snolA booa sMibsnnsknl sift 03 bidu nob3uboldI A

d nvi* k (I.A) lo nois-iqx iiñ eift *thau bna (a.A)

(1t.A) (d\bTb)bfl + ____ + ]'q')C = (dab\dTh) d0 (dabVtXb)

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MGLG — u+ i-=E> O•

= [xu + Ag(!+)]\'LAq (v7)= Ex - A(i +k3)(dllp)1\(dlXptqp)

w (vtY MG Of1U

MJICJ7i () o *PG r nrnR (vY (v4Y q'\q = -'4\k iiq b% =

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