AL_4i?tL?@* 5i4w@}h@?}@? V*@tL 54*@ L?t Lu i +i*@ t U L_*@ L?@* W?t @M* ) w i} i c B33L c ih h@?_ c, 5L??i?_hU!ih 2 cl*@_ 2 c,#**l? 5LUh e wwc 2 W,c W+W wlhh@?i N?iht ) Oi?h L?U@h i vw 6h@?Ui e 6 V@hi??itc "imiuc @?@_@ a@?@h) 2c bbh Mt h@u ti4*@}h@?}@? L_4i?tL?@* u** hi*@ t U V*@tL UL_i ulh 4* UL4T ih i?hl?4i? @t _ii*ltti_ L t _) i @UUi*ih@ i_ T@h U*i _)?@4Ut? T@ti tt@ui?_ui_ M) i hi*@ t U 4L_*@ L?@*?t @M* )? @ t hl?}?l?*?i@h hi}4i i? L? @t uluti_ L? t @UUh@U)c t @M* )c @?_ 4T*i4i? @ L? u@u* it L? T@h@**i* UL4T ihtc iui?u) ThLTih it Lu i 4L_i* U @**Lt @ ih) }LL ituht L? Lu T@h U*i @UUi*ih@ L? 4iU@?t4? T@ti tt@ui V*@tL t4*@ L?t tl i LUUh?} Lu ULihi? Lh i t hu hit _i L i?l?*?i@h t@ h@ L? 4iU@?t4 Lu i +i*@ t U L_*@ L?@* W?t @M* ) W? hl_u L?G Qhzo ghyhorsshg kljk0lqwhqvlw odvhuv kdyh eurxjkw qhz dwwhqwlrq ri wkh hog ri hohfwurpdjqhwlf zdyh sursdjdwlrq lq sodvpdv lq wkh qrqolqhdu uhjlph zkhuh wkh hohfwurq txlyhu yhorflw dssurdfkhv wkh oljkw yhorflw 1 Dv wkhvh kljk0lqwhqvlw odvhu kdyh yhu vkruw sxovhv +ohvv wkdq wkh slfrvhfrqg,/ wkh lrq prwlrq fdq eh qhjohfwhg/ vr wkdw zh kdyh wr frqvlghu hohfwurq sdudphwulf lqvwdelolw 1 Dw prghudwh lqwhqvlwlhv/ wkhvh lqvwdelolwlhv duh fohduo lghqwlhg dv wkh Vwlpxodwhg Udpdq Vfdwwhulqj +VUV,/ wkh Uhodwlylvwlf Prgxodwlrqdo Lqvwdelolw +UPL,/ wkh Uhodwlylvwlf Ilodphqwdwlrq Lqvwdelolw +UIL, dqg lq sduwlfxodu Wzr0sodvprq Gh0 fd +WSG,1 Wklv odvw lqvwdelolw qrupdoo rffxuv dw wkh txduwhu fulwlfdo ghqvlw q @ q f @7 1 Uhfhqwo d vwxg ri wkh ixoo uhodwlylvwlf 5G fdvh kdv ehhq lq0 yhvwljdwhg e Txhvqho hw do ^4> 5` e vroylqj wkh glvshuvlrq uhodwlrq ri hohfwurq 4
sdudphwulf lqvwdelolw ri d flufxoduo srodul}hg zdyh lq d frog sodvpd dw dq odvhu lqwhqvlw dqg sodvpd ghqvlw 1 Wkh dxwkruv duh lghqwlhg glhuhqwv uhjlphv dqg lq sduwlfxodu wkh h{lvwhqfh rq xqvwdeoh prghv dw kljk ydoxh ri n B +wkh zdyh yhfwru frpsrqhqw shushqglfxodu wr wkh lqflghqw sxps zdyh qxpehu n r,1 Lq wkh uhodwlylvwlf uhjlph wkh xqvwdeoh zdyhqxpehu duhd pd h{whqg wr kljk ydoxhv ri n B zlwk kljk jurzwk udwhv1 Dw xowud0kljk uhjlphv/ wkh WSG dqg UPL whqg wr phujh1 Wkh fhqwudo jrdo ri wklv sdshu lv wr lqyhvwljdwh wkh qrqolqhdu uhjlph ri wkh UPL dw xowud0kljk lqwhqvlw xvlqj vhpl0odjudqjldq Yodvry vlpxodwlrqv1 2 @tu i^@ L?t @?_ i?4ihu@* UL_i Ohw xv frqvlghu d flufxoduo srodul}hg hohfwurpdjqhwlf zdyh sursdjdwlqj lq wkh {0gluhfwlrq1 Wkh sodvpd lv prghohg e dq lqqlwh krprjhqhrxv v vwhp lq erwk { dqg gluhfwlrqv1 Wkh hofwurq glvwulexwlrq ixqfwlrq I +{> > s> w, reh v wkh qrupdol}hg uhodwlylvwlf Yodvry htxdwlrq= CI Cw. s 3 CI C u. H. E s 3 CI C s @ 3 +4, zkhuh u @+{> > 3, dqg s @+s { >s >s }, zlwk wkh Oruhqw} idfwru jlyhq e 3 5 @4.s 5 1 E frqvlghulqj wkh iroorzlqj fodvv ri h{dfw vroxwlrq ri +4,/ Ht1 +4, fdq eh zulwwhq lq wkh irup= Ci Cw. s { Ci C{. s Ci C.. H. S }E { s { E } H {. s E } S } E Ci Cs { Ci Cs @ 3 +5, zlwk d qhz h{suhvvlrq ri wkh Oruhqw} idfwru jlyhq e 5 @4.s 5 {.s 5.S}+{> 5 > w, /dqgs } yhulhv wkh _xlg_ htxdwlrq CS} @ H Cw } 1 Wkh hohfwurpdjqhwlf hog H> E duh frpsxwhg xvlqj wkh Pd{zhoo htxdwlrqv1 Wkh vhpl0odjudqjldq Yodvry frgh kdv ehhq dgdswhg wr rswlpdoo xvh wkh sduwlfxodu sdudooho dufklwhfwxuh ri wkh Fud W6H1 Iru h{dpsoh lq wkh rqh0glphqvlrqdo fdvh ghvfulehg e wkh vlp0 solhg Yodvry htxdwlrq= Ci Ci Ci Cw.y C{.JCs { @ 3 dqg zkhuh wkh ixqfwlrq y dqg J duh ghqhg e y +{> s { >w,@s { @ / 5 @4.s 5 {.d 5 +{> w, zkhuh d ghqrwhv wkh qrupdol}hg dpsolwxgh ri wkh srwhqwldo yhfwru dqg J +{> s { >w,@h { 4 C 5 C{ d 5 / wkh zhoo0nqrzq iudfwlrqdo vwhs ru _vsolwwlqj vfkhph_ xvhg wr lqwhjudwh wkh glvwul0 exwlrq ixqfwlrq i +{> s { >w, lv vwudljkwiruzdug +lq zklfk zh vkliw wkh glvwulexwlrq ixqfwlrq dowhuqdwlyho lq wkh {0gluhfwlrq ohdglqj wr wkh pdwkhpdwlfdo h{suhvvlrq= i +{> s {,@i+{ { >s { >w q, zlwk { @wy { { @5>s { >w q.4@5 +6, dqg wkhq lq wkh prphqwxp s { 0vsdfh zlwk wkh fruuhvsrqglqj h{suhvvlrq= i +{> s { >w q.4,@i +{> s { s{, zlwk s{ @wj {> s { s{ @5>w q.4@5 +7, 5
Hdfk vkliw lv hdvlo sdudoohol}hg e mxvw dvvljqlqj d iudfwlrq ri wkh glvwulexwlrq ixqfwlrq wr hdfk qrgh1 Wkhq d wudqvsrvlwlrq ri wkh glvwulexwlrq ixqfwlrq lv uhtxluhg wr shuirup wkh sdudoohol}hg vkliw lq wkh vhfrqg gluhfwlrq1 Wkh phwkrg fdq eh gluhfwo jhqhudol}hg wr kljkhu glphqvlrqv ri wkh glvwulexwlrq ixqfwlrq1 4ihU@*t +it* t Zh frqvlghu khuh d flufxoduo srodul}hg hohfwurpdjqhwlf sxps zdyh ri iuhtxhqf $ r @ s 5$ s dqg ri zdyhqxpehu n r f@$ s @4=557 +wkh fruuhvsrqglqj ydoxh lv 31;99 lq $ r f 4 xqlwv,1 Wkh txlyhu prphqwxp lv s rvf @pf @ s 6/ +zlwk wkhvh ghqlwlrqv wkh ydoxh ri s rvf @ s 5 fruuhvsrqgv wr dq lqwhqvlw ri 8 43 4; Zfp 5 iru d 4139 p zdyhohqjwk,1 Wkh qrupdol}hg Oruhqw} idfwru lv wkhq jlyhq lq wkh fdvh ri d flufxodu srodul}dwlrq e r 5 @4.s 5 rvf 1 Wkh udwlr ri wkh ghqvlw ri wkh fulwlfdo ghqvlw lv wkhq q@q fulw @3=8 / l1h1 q@ r q fulw @3=581 Zh fkrrvh d sodvpd er{ ri ohqjwk O { @ O { @5@n r / ohdglqj wr ydoxhv ri wkh ixqgdphqwdo zdyh qxpehuv ri fn { @$ r @3=;99 dqg fn @$ r @3=;99 iru wkh wudqvyhuvh gluhfwlrq1 Iru wkhvh sdudphwhuv/ wkh jurzwk udwh ri wkh uhodwlylvwlf Prgxodwlrqdo Lqvwdelolw uhdfkhv wk @$ r 3=69 iru +n { f@$ r >n f@$ r, @ +41:63/ 31, iru wkh sxps orqjlwxglqdo prgh dqg wk @$ r 3=57 iru +n { f@$ r >n f@$ r, @+5193/ 31;99,/ wkh fruuhvsrqglqj qxphulfdo ydoxhv/ rewdlqhg gluhfwo e wkh frgh duh qxp @$ r 3=68 lq wkh uvw fdvh iru n { f@$ r @5n { @4=:55> n f@$ r @ 3/ dqg lq wkh vhfrqg fdvh/ qxp @$ r 3=568 iru n { f@$ r @6n { @5=8<; dqg n f@$ r @n @3=;991 Wkh prvw vwulnlqj dgydqwdjh ri wkh vhpl0odjudqjldq Yodvry frgh lv wkh yhu qh uhvroxwlrq rewdlqhg lq skdvh vsdfh/ fdsdeoh ri uhvroylqj wkh qhvw phfkdqlvp ri wkh sduwlfoh dffhohudwlrq1 Ilj1 4 h{klelwv fohduo wkh prgxodwlrq ri wkh zkroh glvwulexwlrq ixqfwlrq iroorzhg e wudsslqj dqg irupdwlrq ri frkhuhqw Vwuxfwxuhv lq wkh { s { uhgxfhg skdvhv vsdfh fruuhvsrqglqj wr wkh vdwxudwlrq ri wkh UPL1 Wkh fxuyhv duh vkrzq dw uhvshfwlyh wlphv w$ s @43=8> 45=8> 46=8> 48= e L?U*tL? Lq rughu wr lqyhvwljdwh wkh wudqvyhuvh jhrphwulfdo hhfwv rq wkh Uhodwlylvwlf Prg0 xodwlrqdo Lqvwdelolw / qxphulfdo vlpxodwlrqv xvlqj d vhpl0odjudqjldq Yodvry frgh kdyh ehhq fduulhg rxw rq d sdudooho frpsxwhu lq d xowud0lqwhqvh hohfwurpdjqhwlf uhjlph1 Wkh qxphulfdo uhvxowv vkrz fohduo wkh irupdwlrq ri frkhuhqw vwuxfwxuhv lq skdvhv vsdfh dv d uhvxow ri wkh vdwxudwlrq ri wkh UPL lqvwdelolw 1 D U!?L*i_}4i? tg Wkh dxwkruv duh lqghewhg wr wkh L1G1U1LV1 frpsxwdwlrqdo Fhqwhu iru wlph door0 fdwlrq rq wkh Fud W6H dqg wkh Fud F<; frpsxwhuv1 6
S +iuihi?uig ^4` E1 Txhvqho/ S1 Prud/ M1 F1 Dgdp/ D1 Khurq/ J1 Odydo/ Sk v1 Sodvpdv 7 +<,/ 668;0669; Vhswhpehu 4<<:1 ^5` E1 Txhvqho/ S1 Prud/ M1 F1 Dgdp/ D1 Khurq/ V1 Jxhulq/ J1 Odydo/ Sk vlfdo Uhylhz Ohwwhuv/ Yro :;/ Q 44/ 546505468/ Pdufk 4<<:1 Ilj14 Skdvh vsdfh uhsuhvhqwdwlrq {0s { ri wkh glvwulexwlrq ixqfwlrq1 7
Sulqflsdo*v dxwkru= Dodlq JKL]]R dguhvv= Oderudwrluh gh Sk vltxh ghv Plolhx{ Lrqlvhv Xqlyhuvlwh khqul0srlqfduh Qdqf 0L ES 56< 87839 Ydqgrhxyuh ohv Qdqf Fhgh{ Iudqfh Skrqh= 66 36 ;6 <4 5: 74 Id{= 66 36 ;6 5: 67 <; hpdlo= jkl}}rcospl1x0qdqf 1iu 8