Detecting Multiple Change-Points in the Mean of Gaussian Process by Model Selection

(1)

HAL Id: inria-00071847

https://hal.inria.fr/inria-00071847

Submitted on 23 May 2006

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Detecting Multiple Change-Points in the Mean of Gaussian Process by Model Selection

Emilie Lebarbier

To cite this version:

Emilie Lebarbier. Detecting Multiple Change-Points in the Mean of Gaussian Process by Model

Selection. RR-4740, INRIA. 2003. �inria-00071847�

(2)

ISRN INRIA/RR--4740--FR+ENG

a p p o r t

d e r e c h e r c h e

THÈME 4

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Detecting Multiple Change-Points in the Mean of Gaussian Process by Model Selection

Emilie Lebarbier

N° 4740

Février 2003

(3)

(4)

Unité de recherche INRIA Rhône-Alpes

+ &,&, -.!0/1#2 &&43657#28:92;< #

=?>A@CBD@CEFEHGJILKMG<@CENKPO

QSR"T-U6V?W%XZY\[]U^"_a`cbd[feHgV-bhejikbd[fU6[alm`nbm[]ejg

o V?lqpklqbmTrUsVMlteHUsiu_fV-v\VMl

w;xmejyzVb{qY"|

}h`niui~eHxqb o V?xdVrtR"VrxdtRuVgLW\cWHX<-\xd[fVrx|nHjX7|cW6iu`nHVrl

P1r-c"nH QSR"[al%iu`niLV-x o Vr`j_]l%[bdRbmRuVi"xdej"_]V-Uej o VbmVMtbd[fg"bmR"VtRu`jg"jV-CiLej[]gNbdl?[]g

U6Vr`jgej1`2lm[]jgu`j_tejxdxd^"ikbmV o \p`ng` o"o [bd[fHV?`j^uldlq[a`ngg"eH[]lmVj ;QSR"VgN^uULV-xen;tRu`jg"jVMl

`ng o bmRuV-[]xi~eNlq[fbm[]ejgulS`jxmV¡^"g"¢\g"ecg JuxmeHU'`g"eHgu`jlmp\U6ikbmejbm[atiLej[]gNbSej,\[fVr?£k V¡i"xdejiLeHlmV

bmeVrlqbm[]U2`cbmVbmR"VrU¤[bdR`PU6V-bmR"e

o

u`HlqV

o

ejg`i~Vrgu`n_][]¥-V

o

_fVM`jlqbq¦lm§N^u`jxmVMltxd[bdV-xd[feHg ¨t

teHx

o

[fg"bdebdR"V2xdVrlm^"_bl?enS©[fxdj2`ng o«ª

`jldlm`jxqbM£¬ VPtR"e\eNlqV%bmR"V2iLV-g~`n_fbzp®^"gutbm[]ejglm^utR

bmR~`cbbmR"V¯xmVMlq^"_fbm[]g"%Vrlqbm[]U6`nbmeHxU6[fgu[fU6[]¥-VrlbmRuV¡§N^u`

o

xd`nbm[atxd[]lm¢° <QSR"[ali~Vrgu`n_fbzp

o

V-iLV-g

o

leHg

^"g"¢\g"ecgt-ejgulqbd`jgHbl`ng o V?i"xdejiLeHlmV?`2t-`n_][]"xd`nbm[]ejg_fVM` o []g"6bde`ng`n^"bmejU2`nbm[atUsV-bmR"e o

QSR"V?iLV-xm®ejxdU2`ngut-VrlenbmR"V?U6VbdR"e o `nxdV¡`HlmlmVrldlmV o bdR"xdej^"HRlm[fU%^"_a`cbm[]ejgVvkiLV-xd[fU6VrgHbl- ;¨g

`niui"_f[at-`nbm[]ejgbme6xdVr`n_ o `cbd`s[allqRuecg

±²N³°´mµ¶ c·H¹¸ VbdVrtbd[feHgen<tR~`ng"HVºi~eH[fgNbdlr»\w1V-gu`j_f[]¥-V o t-ejgNbmx`jlqbr» ª e o Vr_lqVr_fVMtbd[feHg

¼½~¾¿ÁÀÁ¿ÁÂÃÄ\ÂzÅcÆÇÈÅÉ¿ÁÂzÇºÊ<¿ÁËÉÇÈ¿ÌÆÀÁÍnÂzÎmÃÏfÇqÃ¡Ð,ÑM¿ÁÎÇÈÂqÎDÂqÆÇDÒºÑPÑcÆÎ ÅnÂqÂzË6ÇÈÂqÆÀÁ¿ÁÓzÂqÔ6Õ,ÑÉÂzËP½ÃÄ\ÂzÅcÆÇDÅM¿ÁÂqÇÕÆÎ Õ,¿ÖDÑ

ÄkÆÅn×ÇDÆdÖC×¿ÁÇÈÂ ÔMÂJ¾hÆdÖCÑÉØz¾hÆdÖD¿ÁÙrÚMÂqÎÛLÜËÉ¿ÝÂzÇÈÎC¿ÖDØ;ÞuÆÇÈ¿ÁÎ,ß<àºÃ

(5)

/<#2&,&&'&&, (?/ #28 8&-; -# 8

#28

V¯i~`ni"[]V-x bmx`n[fbmV o î"xdeju_fTrUsV o V o bdVrtbd[feHg o V¡xd^"ikbmûxmVMl o `jgul_]Ù6ecpjV-gug"V

o^"g lm[]jgu`j_H`j^uldlq[]V-g VPg"eHU"xdV o Vxd^"ikbm^uxmVMlVbs_fVr^"xl_]ekt-`n_][alm`nbm[]ejgullmejgNb6lq^"iui~eNlqMl

[]guteHg"g\ûl- ¸^"g i~eH[fgNb o V\^"Vg"ejgk¦`jlmp\U6ikbmejbm[a§HûVj£g"eHûliuxmeHi~eNlqeHgul o V_fVMlVMlzbd[fU6V-x

_`n[o V o^"g"V«U6bdR"e o V~`jlm-Vlm^"x^"g t-xm[fbmTrxmV o VrlU6ej[]g o xdVrlt-`jxmxdrl2iL-g~`n_][]lmrlr g

`niui"_f[a§Nû`ngNbP_]VrlxmMlq^"_fbd`nbdl o V© []xdj`ng o:ª `jldlm`jxqbM£ g"eHûltRuej[alq[almlmejg~l%ûg"V®ejg~tbm[]ejg o V

iL-gu`j_f[fbmbmV-_]_]V§N^"V_ VMlzbd[fU2`nbmV-^uxiL-gu`j_f[alqtejxdxdVrlmi~eHg o `ngNbPxdr`j_f[alqV_]Vxd[alm§N^"V§N^u` o xd`nbm[at

U6[fgu[fU2`n_C VbmbmViL-g~`n_][bd o ri~Vrg o$o V«t-ejgulqbd`jgHbdVrl[fgut-ejg"g\^"VMlV-bg"eH^uli"xmeHi~eNlqeHgul o V

_]Vrltr`n_][fuxmVrxPùg oej"bmV-gu[fxPûg"V`n^"bmejU2`nbm[a§HûVUs-bmR"e o VH hg"V-bm^ o V o Vlm[fU%^"_a`cbm[]ejg~l

VrlqbU6V-g"rV6i~eH^"x-c`j_f^"Vrx_]`iLV-xm®ejxdU2`ngut-V o V2_a`U6bmRue o Vj£<Vb?^"g"VP`ji"i"_][]tr`cbm[]ejg lm^"x o Vrl

o eHg"g"-VMlSxmrV-_]_fVMlSVrlqbxmM`n_][]lmj

¶ r ´ "! ¸ -bmVrtbm[]ejg o V?xd^"ikbd^"xmVMl¡»# ejgNbmx`jlqbmV¡iL-gu`j_f[alq2»uYk-_]Vrtbd[feHg o VUse o Tr_fVMl

(6)

) *

%,/1#28;< #

QSR"V®eH_f_]ec[fgustRu`jg"jV-CiLej[]gNbdl[]gbdR"V?U6Vr`jgU6e o V-_,[]lt-ejgulm[o V-xdV o$+

,-/.102(3-546879- :;.=<>!?@?!?>BA CED

DGF

R"VrxmV

3-H.

-

I

`ng o bdR"VVrxmxdejxl

279-J4

`nxdVlm^"i"iLeHlmV o bdeLV¥rV-xdenºU6Vr`ng,£[o V-gNbd[]tr`n_]_fp o [alz

bmxd[]"^kbmV o ^"g"eHulmV-xdÉ`j"_]V`n^uldlq[a`ng2[]g o Vri~Vrg o `jgHbxd`jg o eHU c`nxd[a`n"_]VrlJejtejU6U6ejg2c`jxm[a`ngut-V

K$L

QSR"V®^ugutbd[feHg

0

bdeLVxmVMtecjVrxmV o []l6`jldlm^"U6V o bdeLVi"[fVMtVr[]lmVt-ejgulqbd`jgNbr QSR\^ul-£

bmRuV-xdV2Vvk[]lqbdl%lqeHU6V2[fgulqbd`jgNbdlNMO

.QPSR MT

RU?@?!?;R M!V

.W<

lm^utR«bmR~`cbbdR"V2®^"gutbm[]ejg

0

[alteHgulqbd`ngNbLVbzV-Vrgbzelq^utrtVMlmlm[fHVtRu`jg"jV-CiLej[]gNbdl[]gulzb`ngNbdlr {¦gejbmR"Vrxejx o l-£bmRuV-xdV

Vvk[alzbl`6lqVM§H^uV-gut-V

2X0

T

>@?!?!?!>0 V 4

lq^utRbmR~`cbr£"®ejxh`ng\pZYZ[

< £

0\.

V

]

^`_

T 0 ^

<%acbJd

[fbmRfe

^

.hg

M

^i T > M ^ g£

CED | F

QSR"[alU6e

o

V-_ U6Vr`ng~l?bmR~`cbkjml

<

tRu`ngujVrl`9n°VrtbbmR"VPU6VM`ngen

2(,-54

`cbslqeHUsV^"g"¢\g"ecg

[]gulzb`ngNbdl

2:

^

>@<po Y o

jql

<G4

[bdR

:^

.srA M ^ g

R"VrxmV6bdR"V2g\^"ULV-xenhtRu`ngujVºiLej[]gHbl

C

jtl

<GF

[allm^"i"iLeHlmV o bdeALV^"g"¢\g"ecg, QSR"Vi"xdeju_fVrU[al2bde o V-bmVMtb`jg o _]e\tr`cbdVbmRuV

tRu`jg"jV-CiLej[]gNbdl[fg~lzb`ngNbdlSej

,

`jg o bme2Vrlqbm[]U2`cbdV¯bdR"VSyz^"U6iulej<U6VM`ng

QSR"VtR~`ng"HV o VbdVrtbd[feHgi"xdej"_]V-U)Ru`jl~VrV-gAlqbm^ o [fV o ®ejx%UseHxmV6bdRu`ng ®ej^"xmbmVrV-gpjVM`nxl

[]gU6`jg\p®x`nU6V-ejxd¢kl- pu¯guVt-`jg«xdV®Vrx?bmebmR"VPLe\ej¢kl?ej©S`HlmlmV-\[]_f_]V2`ng o8v [f¢\[f®ejxdecxw|9yC£

©xme o lm¢\p«`jg oA¸ `nxd¢\R"ecklq¢\pzw{yC£ `jxm_alzbdV-[]g£ ªf| _]_]V-x2`ng o Y\[fVrjU%^"g o w}GyS®ejx6`t-ejU6i"_]VbdV

"[]"_][feHjx`ni"R\pj

{¦gbdR"V%tr`jlmVen;U%^"_bd[fiu_fVstRu`ng"HVrlr£"bdR"Vi"xdeju_fVrU [alhU6eHxmV[]gNbmxd[]tr`cbdV%`ng o ®V-`niui"xmeN`jtR"VMl

`nxdV o V o [at-`nbmV o bme¯bmR"[al1i"xdej"_]V-U <¨hU6ejg"¯bmRuV-U©S`ÉpjVMlq[a`ng?bdVrtR"gu[]§N^"VMl~w

D

yº£j`jg o iLV-gu`j_f[]¥-V o

txd[fbmV-xd[a`w

D

yC£w

D

{Gyº£wGy tr`ng ~V o []lqbm[]g"H^"[]lmR"V o QSR"[al?¢\[fg o entxd[bdV-xd[feHg[al?g"ec t_a`jldlq[at-`j_

C

bdR"VuxlzbSVv"`nU6i"_]VrlS`jxmVbmR"V ª `j_f_]echl ; [bdR"[fgbmRuV¯®x`nU6Vr eHxm¢6en,bmR"VxdV-jxdVrldlm[feHgfw|jGyC£

bmRuVhhe wD

yL`ng o bmR"Vhke wÁ|j|y°txd[bdV-xd[]`[fbmRu[fg6bdR"V®x`nU6V-ejxd¢en¬U2`cvk[]U^"U _][f¢HV-_][fR"e\e o

Vrlqbm[]U2`cbd[feHg

F

`ng

o

Ru`jl6LV-Vrg:lqbm^

o

[fV

o

\pU2`ng\pA`j^kbmR"eHxdl%[]gAbdR"Viu`nxmbm[at^"_a`nx6i"xdeju_fVrU en

o

V-bmVrtbm[]g"6tRu`ng"HVºi~eH[fgNbl;[]gPbmRuV¡U6VM`ng£klmV-Vh®eHx V-v"`nU6i"_]Vh`jewÁ|nGyº£

ª

[a`ne ! %

wÁ|

D

y`jg

o

U6ejxdV xdVrt-V-gNbm_]p

`ÉN[]V-_]_]V V-b

ª

ej^"_][fguVrlw

D

@yº <QSRuV-[]xJi"^"xdi~eNlqV[]l<bdeVrlqbm[]U6`nbmVteHgulm[]lqbmVrgHbd_fp`j_f_

bmRuVtRu`ngujVºiLej[]gHbl- {¦gbmR"VrejxdpPbdRu`cbxdVr§N^"[]xdVrlSbdR"V?®^"gutbm[]ejg

0

bmePLV[]gbmR"V%tej_]_]Vrtbd[feHgen

U6e o V-_alteHgulq[o VrxmV o ®ejx ubqbm[]g"2`ng o []gi"xd`Htbd[]t-VbdR"V?i~Vrgu`n_fbzpPU%^ulzbLVtR"eHlmV-g`jtrtejx o []g"

bmei"x`jtbm[at-`j_Nt-ejgulm[o V-x`cbm[]ejg~l- eHgNbmx`nxdp¯bde¡bmR"[al1i~eH[fgNbJenL\[fVr?£c VteHgulm[o Vrx[]g%bmR"[alJiu`ji~Vrx

`¡g"ejg~`jlmpNU6ikbdenbd[]tS`niui"xmeN`jtR QSR"Vi"xdej"_]V-U[al;lmV-Vrgs`HlJ`iu`nxmbm[at^"_a`nx1i"xdeju_fVrUen#"vkV oso V

lm[fHg%`n^uldlm[]`jgxmVrjxdVrldlq[]ejg?RuV-xdV;bmRuVxdV-HxmVMlmlm[]ejg¡®^"gutbm[]ejg

0

bmeLVSVrlqbm[]U2`cbmV o [al<i"[fVMtVr[]lmV

teHgulqbd`ngNbM VsteHgulq[o VrxbmR"V%g"ejguiu`nx`nU6Vbdxm[atU6e o V-_1lqVr_fVMtbd[feHgi~eH[fgNbej;\[fVr o V-HV-_]ejiLV o

\p©[fxdj`ng oª `Hlmld`nxmbwyC JQSR"Vr[fxh`j[fU'[alSbde6tRueNeNlqV

0

U6[]g"[fU6[]¥-[]g"P`6§N^u` o x`cbd[]t¯xd[]lm¢°£N\p

^ulm[fguP`jl®V-0i"xd[]ejx[]gk®ejxdU2`cbm[]ejg`jlhi~eNlmlm[fu_fVH£"xd`nbmR"VrxSbmRu`jgbme o V-bmV-xdU6[fguVbmR"V?bdxm^uV®^"gut

bm[]ejg

0

JQSR"[]lS[alS`%lm[fbm^u`nbm[]ejgRuV-xdV¯[fbU6`Ép2LVi"xdV®V-x`nu_fVbme6[fHg"ejxdV¯lmejU6VtRu`ngujVºiLej[]gHbl

teHxmxdVrlmiLejg o []g"bde«lmU2`n_]_<yz^"U6iul6enU6VM`ng x Ru[f_]V`ni"i"_]p\[fgubmRuV-[]x2xmVMlq^"_fbdlr£;VH[fHV[]g

w;xdejiLeHlm[bd[feHg|k

D

bdR"ViLV-gu`j_bzps®^"g~tbm[]ejg[fg\Hej_]jV o []g2bmRu[]lS`niui"xmeN`jtR2`ng o `ngP^ui"i~Vrx Lej^ug o

en<bmRuV§N^u` o x`cbm[at¡xm[alm¢2®ejxSbdR"VteHxmxdVrlmi~eHg o []g"iLV-g~`n_][f¥rV o Vrlqbm[]U2`cbmeHxr

QSR"VhiLV-g~`n_fbzp®^"gutbm[]ejg o Vri~Vrg o lejgsbz et-ejgulqbd`jgNbdl1R"eNlqVeHikbm[]U2`n_"c`n_]^"VMl;`nxdVg"enb`Ht-t-Vrlq

lm[f"_]VbmRuV-ejxdVbd[]tr`n_]_fpH£u`ng

o

ejgbmR"Vg"ej[alqV?c`jxm[a`ngut-V

K$L

R"[atR[]l^ug"¢\g"ecg[fgi"x`jtbm[atVH ~«V

i"xdejiLeHlmV%`Pbz ejºlqbmVrii"xde\t-V

o

^uxmVbmeVrlqbm[]U6`nbmV%bmR"VsiLV-gu`j_bzpH []xlzbM£°bmR"Vsg"ej[almVc`nxd[]`jgutV%[]l

lm^"i"iLeHlmV

o

bdeh~V ¢\g"ecg`ng

o

bmR"V É`j_f^uVrlenkbmRuV;bzeteHgulzb`ngNbdl`nxdV;t-`j_f[]"x`cbmV

o

\p`

o

`ni"bm[]g"

bmRuV%lm[fU%^"_]`nbm[]ejgi"xdektV o ^"xdVi"xdejiLeHlmV o \p©[]xmH`ng o }ej¥rV-g"R"eH_]tw

y1[]gbmR"V o V-g~lq[fbzpVMlzbd[

U2`cbd[feHg®x`nU6V-ejxd¢sNpR"[]lqbmeHjx`nU2l [fgU6e o V-_lmV-_]Vrtbd[feHg`ji"i"xdeH`jtRlzbd^ o []V o Np `jlqbmV-_]_a`ng

wÌyº ;QSR"V-g£"bmR"V?g"eH[]lmVc`nxd[]`jgutV¡[]llqVrV-g`jl`si~Vrgu`n_fbzpt-ejgulqbd`jgNb`jg o [bh[alVrlqbm[]U2`cbdV o [bdR

`2U6VbdR"e o u`HlqV o ejgR"Vr^"xd[]lqbm[at`ng o bmR"VrejxdVbd[]tr`n_,[o VM`jlhiuxmeHi~eNlqV o \p©[fxdj`jg oª `Hlmld`nxmb

wWyº ¯QSR"[alU6V-bmR"e o [al o Vbd`j[f_]_]V o []gbmRu[]l¡iu`ji~Vrxr ¨trteHx o []g"2bdelmejU6V o [%Pt^"_fbm[]Vrl¡ekt-t-^"xdV o

(7)

ejglm[fU%^"_]`nbmV oo

`cbd`s[fbmRbmRu[]lU6V-bmR"e

o

£u`6lmi~VMt[~tt-`j_f[]"x`cbm[]ejg[alSi"xmeHi~eNlqV o

{¦g g\^"U6V-xd[]tr`n_;V-v\iLV-xd[]UsVrgNbdlr£,ej^uxt-`n_][]"xd`nbmV

o

U6V-bmR"e

o

[]l%teHUsi~`nxdV

o

bmebmRuV

/ª

`n_]_]echl

wÁ|nGy;`ng

o

bdR"VHke

txd[bdV-xd[]`u£¬lqVrV6YktR\S`nxd¥wÁ|j|yº£¬®ejx¡R"[atR`Hlqp\U6ikbmejbm[atiuxmeHi~Vrxqbd[fVMlRu`ÉHV

LV-V-g«Vb`n"_][alqR"V o %QSRuV-gbz eenbmRuV-xl¡lm[]U^"_a`cbd[feHgullzbd^ o []Vrl?`nxdViLV-xm®ejxdU6V o bme`jldlqVMlmlbmRuV

U6VbdR"e o RuV-gbmR"V?U6e o Vr_,`jldlq^uUsi"bm[]ejgulS`nxdVg"enbhc`j_f[o J{¦gbmR"V uxlqbhejg"VH£\bmR"V®^"g~tbm[]ejg

0

[al1g"enb`¡i"[]Vrt-V-[alqVteHgulqbd`ngNb1®^"gutbm[]ejg2`ng o []gsbmR"VhlmVrt-ejg o ejg"VbdR"Vg"ej[almV[alJg"ejb`n^uldlq[a`ng,

QSR"Viu`ji~VrxP[alPejxdH`jg"[]¥-V o `jl6®eH_f_]echlr ${¦g$Y\VMtbm[]ejg |«bdR"VVrlqbm[]U2`cbd[feHg i"xmekt-V o ^"xdV[]l

o VMlmt-xm[]~V o `jg o bdR"VS®ejxdU en~bmR"VSiLV-gu`j_bzp®^"gutbd[feHgs`jg o `ngs^"i"iLV-xJLej^"g o en~bmR"V§N^u` o xd`nbm[at

xd[]lm¢®ejxPbmR"Vt-ejxdxmVMlqiLejg o [fg"«iLV-gu`j_f[]¥-V o VMlzbd[fU2`nbmejxP`jxmVH[fHV-g R"Vrg bmR"Vc`jxm[a`ngut-Ven

bmRuVPg"ej[almVs[al?¢\g"ecg£,bmR"VPbz eiLV-gu`j_bzp«teHgulzb`ngNbdl?`jxmV2tr`n_][f"x`cbdV o [fg `eHikbm[]U2`n_;S`Ép[]g

Y\VMtbm[]ejgu 6QSRuV-g«bmR"V2RuV-^"xd[]lqbm[at6U6VbdR"e o bdeVrlqbm[]U6`nbmV6bdR"V2g"ej[almVsc`jxm[a`ngut-V%[al?i"xdVrlmV-gNbdV o

`ng o `tr`n_][f"x`cbd[feHgPen¬bdR"[al U6V-bmR"e o [al i"xmeHi~eNlqV o [fgY\Vrtbm[]ejgWu JY\Vrtbm[]ejg

lqRuechl o [%nLVrxmVrgNb

lm[fU%^"_]`nbm[]ejgullzbd^ o []Vrlbme`HlmlmVrldl1bmRuViLV-xm®ejxdU6`jgutVej¬ej^"xt-`n_][]"xd`nbmV o U6V-bmR"e o J<[fg~`n_]_fpsbmRuV

U6VbdR"e o [al¡`ji"i"_][fV o bme o V-bmVrtbtR~`ng"HVºi~eH[fgNbdl[fgbmR"VsU6ejgNbmRu_fpg\^"ULV-x¡enbmVrlqbdl{ []g

"x`ng~tVejglqVrjVrxd`j_LpHVr`jxdlr <¨ lmR"eHxqb o [almt-^uldlq[]ejgV-g o lbmR"V?iu`ji~Vrxr

&¬ ? # /1#28/<

{¦gsbmR"[allmVrtbm[]ejg£nbmR"VhVMlzbd[fU2`nbm[]ejg6i"xde\t-V o ^uxmVS[alJi"xdVrlmV-gNbmV o QSR"Vi"xm[]gut-[fi"_]V[al1bmR"VS®eH_f_]ec[]g"

ejguV + ¨teH_f_]Vrtbm[]ejgenJ_]Vr`Hlzbmºld§N^u`nxdVrlSVMlzbd[fU2`cbdejxl[al o VMlq[]jg"V o `ng o bdR"VLVrlqb¡`Ht-teHx o [fg"sbde

`si~Vrgu`n_][]¥-V o _]Vr`Hlzbmºld§N^u`nxdVrltxd[bdV-xd[feHg[altR"eNlqVrg ;QSR"V¡®ejxdU ej,bmRuVi~Vrgu`n_fbzp2®^"g~tbm[]ejg`jg o

`sg"ejg~`jlmpNU6ikbdenbd[]t¡xd[]lm¢PLej^"g o ®eHxSbmR"Vt-ejxdxmVMlqiLejg o [fg"%i~Vrgu`n_][]¥-V o VMlzbd[fU2`cbdejx`nxdVj[]jVrg

"!$#%&(') *+!,#-/.0!,(12*3.4%657#589.:;<%=

V-b?>

I

~VsbdR"V2lqV-bej `n_]_<bmR"V6iu`jxqbd[bd[feHgul¡ejgbmR"V6jxd[oA@

3 T

>B3

L

>!?!?@?>53

ICB

%QSR"V-xdV%[al¡bmRuV

g"VrV o bme6\[]lm[fb`n_]_¬iu`nxmbm[fbm[]ejgul`HlSi~eNlmlm[]"_fVlm[]gutVg"e6i"xd[feHx[fg"®ejxdU6`nbm[]ejgejgbmR"V?_]ekt-`nbm[]ejgen

bmRuV%tRu`jg"jV-CiLej[]gNbdl[]gulqbd`ngNbl[al¯`Éc`j[f_a`n"_]Vj «V%t-ejgulm[o V-xbmR"V6teH_f_]Vrtbm[]ejg @ D E

>FHG

> I B

R"VrxmV®ejxJ`¡j[]jVrg%i~`nxmbm[fbm[]ejg

F

en o [fU6V-g~lq[]ejgJI E £

FW.

@ e ^ B

^_

TLKNMNMNMKO4P £ D E [al<bmR"V_][]g"Vr`jx

lm^"ulmiu`jt-V¡ej,bdR"V®^"gutbm[]ejgulRu[]tR`nxdV¡i"[fVMtVr[]lmV?tejg~lzb`ngNbejgbmR"V?iu`jxqbd[bd[feHg

F £

D E . Q<R

. O P

]

^_

T R ^ <abJd >2 R ^ 4

^`_

TSKNMNMNMNKO P

GUT

O

PWV

¸ V-g"ejbm[]g" D

.YX E6Z\[]

D E £~VteHgulm[o VrxbmRuV_]Vr`jlqbq¦ld§H^~`nxdVrlht-xm[fbmVrxm[]ejg£ o V ~g"V o ®eHx¯`jgNp

R G D £ ^ I 2R 4 . <

A I

]-_ T r,-

l R

2(3-E4gL .Y_,

l R _ LI >

R"VrxmV

_9?`_

I o

Vrg"enbdVrlbmR"Vsg"ejxdU2`n_][f¥rV

o

^ut_][

o

Vr`ngg"ejxdU¤ejg

T I ?¨¯lmlmekt[a`cbmV

o

bmebmRuVst-ej_f

_]Vrtbd[feHg

@aD E

>F G > I B

£ Vt-ejgulqbmxd^utbbdR"V teH_f_]Vrtbm[]ejg en%_]Vr`Hlzbmºld§N^u`nxdVrlVrlqbm[]U2`cbdejxl

@2b

0 E

>FcG

>

I"B

R"V-xdV¡®ejx

FcG

> I +

b

0 E . d\ef+gJhji

k

Zml

P ^ I 2R 4;.

O4P

]

^`_

T4n , ^ <acb d>

R"VrxmV

n

, ^

[]lbmRuVV-U6i"[]xd[]tr`n_,U6VM`ngej

,

eHgbmR"V%[fgNbdV-xdÉ`j_ e ^ £ (

n

, ^ . T

I

d=o -d

-_ -(dLprqs

T

,-

£

[fbmR

A ^

[al,bmR"Vg\^"ULV-xen

3 -

LV-_]ejguj[]g"hbdebmR"V[]gHbdV-xdc`n_ e ^

`ng o _fV-bxdVrtr`n_]_nbmR~`cb

: ^ . rA M ^ g

(8)

QSR"VPVMlzbd[fU2`nbm[]ejg i"xdej"_]V-U)en

0

xmV

o

^utVMlbmetR"e\eHlmV6bmR"V~VMlzbi~`nxmbm[fbm[]ejg£1lm`Ép

b

F

`jg

o

bd`j¢jV

b

0

E ejgulm[

o

V-xd[fgubdR"VS_feNlml<®^"g~tbm[]ejg,£nR"[atR%[alJ`jldlqekt-[]`nbmV

o

bme¡bmRuVVrU6i"[fxd[at-`n_kt-ejgNbmx`jlqb

®^"gutbm[]ejg

^ I

®eHxh`ng\p

R G D

NpPbmR"V?xdV-_a`cbd[feHg

2X0 >R 4 . r

^ I 2R 4 l ^ I

20G4g#.Y_!0

l R _ LI > C

|" F

`ng o bd`j¢\[fg"bmR"Vs_]eHldlU6Vr`jgej;bmR"Vs_]Vr`jlqbq¦ld§H^~`nxdVrlVMlzbd[fU2`cbdejx b

0 E £¬_]Vr` o lhbde[fbdl§N^u` o xd`nbm[at

xd[]lm¢PR"[atR[al o VMteHUsiLeHlmV o `jl®eH_f_]echl +

_!0

l b

0 E _ L

I .Y_!0

l n

0 E _ LI 6 I E

A K L £ C

|" W F

R"VrxmV

n

0 E

[albmR"V?eHxqbdR"ejHejgu`j_~i"xdenyzVMtbd[feHgej

0

eHg D E +

n0 E . d\ef+g hi

k

Zml P

20 > R 4;.

O4P

]

^`_

T <

A ^ -d

]

-_ -(dLprqs

T

02(3-E4 <%acbJd ?

{¦gsbmR"[al

o

VMtejU6iLeHlm[bd[feHg

C

|k W F

£cbmR"VSbdV-xdU

_!0 l n

0 E _ LI

[al;`¡"[a`jl<bdV-xdUU6Vr`jlm^"xd[fgubdR"Vh§N^u`n_][bzp

enu`ji"i"xdeÉvk[fU2`cbd[feHgen

0

Np D E £cR"V-xdVr`Hl°bmRuV;bmVrxmU O P

I

K$L

[]l<`c`nxd[]`jgutV;bmV-xdU0xmVri"xdVrlmV-gNbm[]g"

bmRuV?Vrlqbm[]U6`nbm[]ejgV-xdxmeHxS[fg D E

QSR"V?[o Vr`j_¬iu`nxmbm[fbm[]ejg,£"lm`Ép

n

FS20G4

[alU6[fg"[]U6[f¥r[fgu6bmR"V?xd[]lm¢

C

|k W F ecjVrx>

I £

I

2X0 > D

4~. hi

E6Z\[]

_!0

l b

0 E _ L

I

? C

|"

F

hg"®ejxmbm^"gu`nbmVr_fpH£

n

FS20G4

[alh^"g"¢\g"ecglm[fg~tV[fb o Vri~Vrg o lheHgbmR"V^ug"¢\g"ecg®^"gutbm[]ejg

0

QSRuV

i"^"xdiLeHlmV?en<bmR"ViuxmeHi~eNlqV o VMlzbd[fU2`cbd[feHgi"xmekt-V o ^"xdV[]lbmePi"xdec\[o V` o `cbd`no xm[]jVrgtxd[fbmV-xd[]ejg

lmV-_]Vrtbd[fgu¡`jgVrlqbm[]U2`cbdejx

0

Ru`É\[]g"¯`¯xm[alm¢`jl1t_]eHlmV`Hl,iLeHldlm[f"_]Vbme¯bmR"VSxd[]lm¢?en b

0 E

£cgu`nU6Vr_fp

lm^utRbdRu`cb

r 2X0 >

04g o I

20 > D

4`> C

|" { F

®ejxh`sg"eHg"g"VrH`cbd[fHV¡t-ejgulqbd`jgNb

=81$ *r 5 *+!$#-/. ! 1

¡[]jV-g lmejU6Vi~Vrgu`n_fbzp ®^ugutbd[feHg"!$#

A I 2uFf4&%

>

I(' T s

£ bmRuVi~Vrgu`n_][]¥-V o _]Vr`Hlzbmºld§\`nxdVrl

Vrlqbm[]U2`cbdejx[al o V uguV o \p +

0\.

b

0 E > C

|" Á

F

R"VrxmV b

F

U6[]g"[fU6[]¥-VMlbmR"V?iLV-gu`j_f[]¥-V o _fVM`jlqbq¦lm§N^u`jxmVMl t-xm[fbmVrxm[]ejgecjV-x > I o V ~g"V o \p +

)+*-, :I 2uFf4;.

^ I 2 b

0 E 46

!$#

A I

2uFf4`? C

|" F

QSR"V%i"xmeH"_]V-U¤[]lbmetR"e\eHlmV`Pt-ejg\jVrg"[fVrgNbi~Vrgu`n_fbzp®^"gutbm[]ejgRu[]tRlmV-_]Vrtbdl.

0

_fVM` o []g"2bde

`ng[]g"Vr§N^u`j_f[fbzp2enbmR"V¡bzp\i~V

C

|k { F «V?[f_]_lmV-V¯bmRu`nbbmR"V?tR"eH[]t-V¯ej,bmRu[]lSiLV-gu`j_bzpP®^"gutbd[feHg

o Vri~Vrg o leHgbdR"V?xm[atR"g"VMlmlSej,bdR"VteH_f_]Vrtbm[]ejgeni~`nxmbm[fbm[]ejgul > I

QSR"VJ®eH_f_]ec[]g"hi"xdejiLeHlm[bd[feHgj[]jVrlbmR"V®ejxdU ejkbmR"V i~Vrgu`n_fbzp¯®^"gutbd[feHg`ng o `xd[]lm¢¯Lej^ug o

en<bmRuV`Hlmlmekt[a`cbdV o i~Vrgu`n_][f¥rV o Vrlqbm[]U2`cbmeHxr

/ ¶10 ¶ 32®32¶547698;:58=<

B ?> c'A@~CB9'XED9 &'9`J9 (

) T

) L

+F&'xNG

B 9 AH c JI; 'Gk B`X(

FcG

> I KH

!$#

A I 2uFf4~.

I E

A K

LML ) T

aON+f L A

I EQP 6R)

L P > C

|" } F

(9)

!1 B ?> c`( !

S&`J9

2;) T > ) L 4

!

2;)

T

>?)

L 4 F&' 9H `c Gf

B 9 'Z `

9J

0

;I~ '

!9XcI

r

2X0>

0@4Jg o

2;)

T > ) L 4 hi

E6Z\[ ] _@0 l n

0 E _ LI 6

!$#

A I 2uFf4

6

2J)

T

>?)

L 4 K$L

A C

|k

D F

/ ¶¶ 8QSR"V6i"xmeH"_]V-Ut-`jgLV6V-ULV ouo V o []gHbdebdR"VP`n^uldlm[]`jgi"xdektVrldl¯®xd`jU6V-ejxd¢`jg o

VP^ulmV`xdVrlm^"_fben©[]xmHP`ng oª `Hlmld`nxmbw9yº <[fxlzb% VxmVMt-`n_]_JbdR"VPbdR"V-eHxmVrU H[f\[]g"bmRuV

jVrg"V-x`n_,®ejxdU¤en;bdR"V%iLV-g~`n_fbzp®^"gutbd[feHg`jg o `Pxd[alq¢Lej^"g o en;bdR"V6`jldlqekt[a`cbdV o iLV-gu`j_f[]¥-V o

Vrlqbm[]U2`cbdejxM

²\¶ ² 698698 `

9'm` ) ! @"! E B

E6Z\[] ' G HG @~ G

(

X9XED9 ?B ' #1F ' '

!9XcEGH9 Z k&'9 9X(9

# . ]

$

E6Z\[%

O P'& O)(

#

i+*

P O P R 6-,

F !&'9`( k B 9 AH G F&!X(9 +F&'

!$#

A;2uFf4 [zj

K L I E

A

2E<6/. 0

!E

4 L

Gmk9

FcG

> I

j21

< C

|k

DDGF

H&mSB JB9 9 MB ! p 'X 9J

0 > c` G`9 B ' HZc F 43KF \B !

D9 N~!9XcI

r 20 >

04g o 2j 4 hji

E8Z\[ ] r 20 > n

0 E 46

!5#

A;2uFf4g 6 2j 4 #A K L

«V¡guV-V

o

bme2tR"e\eNlqV`6tejg\HV-g"[]V-gNbÈ`nU6[f_]pPejV-[]jRNbdl

@5! E B E8Z\[ ]

;Q`j¢\[fg"

! E

`HlS`

®^"gutbm[]ejgen<bmRuV

o

[fU6Vrgulq[]ejg,£

! E . ! 2I E

4;.

! O P _]Vr`

o

lbme

# . ]

E6Z\[

#

i+*

P O P . I

]

O _ T # i O

*76

8

*"9

@ F G > I > I E . I B

o I

]

O _ T # i O * 6 L A I P

o I

]

O _ T # i O

*:6<;

# A

I>=

O

o I

]

O _ T # i O 2

*76 i T i?@ A

]

6 4

ejg~lqVM§H^uV-gNbm_]pj£"[fJ Vb`n¢HV ! O

.>06 aON+fCB

I

OED bmRuV-gF#

R <

`ng o bdR"[]l_fVM` o lbmeP`6iLV-gu`j_bzp

®^"gutbm[]ejg2ejLbdR"V®eHxmU

C

|" } F

1QSR"V-g2VhjV-b;w;xdejiLeHlm[bd[feHg2|"

D o V o ^ut-V o ®xdejU QSR"V-eHxmVrU |" |"

G

² "5H :58QSR"ViLV-gu`j_bzp o V-iLV-g o l¡eHgbmR"Vsiu`jxqbd[bd[feHg

F

eHg"_]p\[a`P[fbdl o []U6V-gulm[feHg I E

QSR"V%È`jtbmejx

aN\f

; I

O P =

`niui~VM`nxd[fg"[fgbmR"[al¡i~Vrgu`n_fbzpxmVMlq^u_blh®xdejU¤bdR"Vst-ejU6i"_]Vvk[fbzpej;bmRuV

teHgulm[o VrxmV o teH_f_]Vrtbm[]ejg ejhiu`nxmbm[fbm[]ejgul > I £ ( bmRuVg\^"U%~Vrx%ejhiu`nxmbm[fbm[]ejgulRu`É\[fgubmRuV

ld`nU6V o []UsVrgulm[feHg«[]g bmRu[]lt-ej_]_fVMtbd[feHg

C

R"V-xdV

L A l <

I l < P

®ejx%`"vkV o o []UsVrgulm[feHg3I

F

QSR"[]l

(10)

È`jtbmeHx t-`jg2~V¯xmVrH`jx o V o

`jllm^"xdi"xd[]lm[fgu

+

®eHx[]gulqbd`ng~tVj£N[fb

o

e\Vrl g"ejb `ni"iLVr`jx[]g2bmRuViLV-gu`j_bzp

enbdR"V

/ª

`j_f_]echl

lt-xm[fbmVrxm[]ejg wÁ|n9yC ©[fxdj`jg o ª

`Hlmld`nxmbw9ylqR"ec bdRu`cbsbmR"[albmV-xdU[]l

g"VMtVrldld`nxdp2[fgbmRuV?xm[alq¢2H[fHV-g\p

C

|"

D F

®xmeHU `sU6[fg"[]U2`cvi~eH[fgNbhen<\[fVr?

² "5H 698 v enbmV¯bmR~`cbbmR"VteHgulq[o VrxmV o teH_f_]Vrtbm[]ejg2eniu`nxmbm[fbm[]ejgulr£ > I £ o V-iLV-g o leHgPbmRuV

lm[f¥rV¡ejbdR"Vld`nU6i"_]V

A

teHgHbdxd`jxmp6bdesbmR"V ! ª `j_f_]echl w|jGy,eHxh¨h{ RuV-^"xd[]lqbm[at-lw

D

yº

² "5H 8¨t-teHx o [fg"bme%bmR"V[]g"Vr§N^u`j_f[fbzp

C

|"

D F

£HbdR"Vxm[alm¢sej,bdR"Vi~Vrgu`n_][f¥rV o Vrlqbm[]U6`nbmeHx

[alS~eH^"g o V o \p

r

20 >

04Jgo

aN\f 2A4 I

2X0>

D 4 C

|k

D | F

QSRu`nbhUsVM`ngulbmRu`nbr£u[]gbmVrxmU2lejJxm[alq¢°£

0

[]l`jlHeNe o `jlbmR"V?LVrlqben1bdR"V b

0 E [fbmR`sÈ`jtbmeHx

aN\f;A

{¦g2bdR"V¡bmR"VrejxdVbm[at-`j_~`ji"i"xdeH`jtR,£jbdR"V¯iLV-g~`n_fbzp%®^ugutbd[feHg[al o V-iLV-g o []g"sejg`¢\g"ecgPc`nxd[f

`ng~tV

K$L

ec VrjVrx2[fg iuxd`Htbm[at-`j_[fU6i"_]V-U6VrgHb`cbd[feHg bmR"VÉ`jxm[a`ng~tVU^~lzbLVVMlzbd[fU2`cbdV o

ª eHxmVrecjV-xSbdR"Vsi~Vrgu`n_fbzp®^"gutbd[feHg o Vri~Vrg o l¡ejgbzet-ejgulqbd`jgNbdl

)

T`jg o ) L

R"[]tRejikbd[fU2`n_

c`n_]^"Vrl`nxdVh^"gu¢Nguecg JQ,e o Vr`n_L[fbmRLenbdRi"xdeju_fVrU6lr£N VhiuxmektVrV o []g2bze%lqbmVriul- J<[]xdlqb []g

Y\VMtbm[]ejg«"£LbmRuVsc`jxm[a`ngut-VenbmR"Vsg"ej[almV

K$L

[]llm^"i"iLeHlmV o bme~Vs¢\g"ecg`ng o `tr`n_][fuxd`nbm[]ejg

enbmR"V?eHikbm[]U2`n_°c`n_]^"VrlSej

)

T¯`jg o ) L

®xmeHU `U6e o Vr_lqVr_fVMtbm[]ejgiLej[]gHbej\[fVr$[alSi"xdejiLeHlmV o

\p`6lq[]U^u_]`nbm[]ejgi"xmekt-V o ^"xdVj JQSR"Vrg[]gY\Vrtbm[]ejgWu£k[fbmR

)

T¡`jg o ) L

"vkV o bmesbmR"V?iuxmVrN[]ej^~l

c`n_]^"Vrlr£

K$L

[al?Vrlqbm[]U2`cbdV o Np`RuV-^"xd[]lqbm[atsU6VbmRue o `jg o `tr`n_][f"x`cbd[feHgej bdR"[]lU6V-bmR"e o []l

i"xdejiLeHlmV o

# #*

<

8

0

()«~5Z*c;< #

{¦g bmR"[allqVMtbm[]ejg,£

K$L

[allm^"i"iLeHlmV o bme:~V ¢\g"ecg '©V-®ejxdV o VMlmt-xm[]"[]g" bdR"Vlq[]U^u_]`nbm[]ejg

i"xdektV o ^"xmVSbde%`ji"i"xdeÉv\[]U2`cbdVSbmR"VheHikbm[]U2`n_Lc`n_]^"Vrlen

) T

`jg o ) L

£HV o V ug"V¡`ngP`niui"xmeHi"xd[]`nbmV

xdV®V-xdV-g~tVej<§N^u`j_f[fbzp6en,bdR"V¡i~Vrgu`n_][f¥rV o Vrlqbm[]U2`cbmeHxlm[]gutV¯bmR"V?t-_]`Hlmlm[]tr`n_Lejg"V¡j[]jVrgP\p

C

|"

F

`niui~VM`nxlbde2~V?^ug"xmVr_f[a`nu_fV[]geH^"x®xd`jU6V-ejxd¢L

8.0! #* ! = ( 5 1$9'L91 %8C ('8.4#!

}VMt-`n_]_LbmRu`nb bdR"V?`n[]U4[]l bde%i"xdec\[o V¯`%i~Vrgu`n_fbzp6®^"gutbm[]ejglq^utRbmRu`nb bdR"Vxm[alm¢sejbmRuVt-ejxdxmV-

lmi~eHg o []g"hVrlqbm[]U2`cbdejxM£Éld`ÉpC

02J)

T

>?)

L 4

£c[]l`jl<t_]eHlmV;`jli~eNlmlm[]"_fV;bmehbdR"VU6[]g"[]U^"U0ejguV I

20 > D 4

C

|"

F

<{ºbJ[]lbmRuV-gsgu`cbd^"xd`j_Nbme¡V-c`n_]^u`cbdVbdR"VSi~Vrxq®eHxmU2`jgutVen

02J)

T

>?)

L 4

\pbmRuVU6VM`jlm^"xmVrU6V-gNb

enbmR"Vs®ej_]_]ec[fg"x`cbm[]e

r_@0

l

0 2J) T > ) L

4 _ LI g

I

20 > D 4

HV2`jxmV%_fe\ej¢\[]g"®ejx¡bmR"V6c`n_]^"VMl

en

)

T?`ng o ) L

bdRu`cb¡Us[]g"[]U6[f¥rVrlbmR"[alxd[alq¢xd`nbm[]e2^"g"[f®ejxdU6_fp®ejx¡`n_]_®^"g~tbm[]ejg

0

`jg

o

ld`nU6i"_]V

lm[f¥rV

A

¨t-t-ejx

o

[fgubde

C

|"

D | F

£,bmR"[al?x`cbd[fe[al?~eH^"g o V o

\p`§N^u`ngNbm[fbzp

o

V-iLV-g

o

[]g"eHg

A

ejg~lqVM§H^uV-gNbm_]p2bmRuV?i~Vrgu`n_fbzpt-`jgguenbhLVt-`n_][]"xd`nbmV o [fbmRxmVMlqiLVrtbbme

A

«V¡R~`ÉjV?tR"eHlmV-g`6g"V- xmV-®V-xdV-gut-Ven<§N^u`j_f[fbzp2bde2~VbdR"V®ej_]_fec[]g"sejg"V +

I K 2X0 > D

4~. hji

O _

TSKNMNMNMKI r_@0 l b

0 O _ LI g> C

"

D F

R"VrxmV b

0 O [albmRuV?~VMlzbh_]Vr`Hlzbmºld§N^u`nxdVrl Vrlqbm[]U2`cbmeHxen o [fU6Vrgulq[]ejgUI +

b

0 O . d\ef+gJhji

$ k Zml

6 _

P

]

P 6 l P ( ^ I 2R

4;. dme f\gJhji

$

E6Z\[ ] K%E %_ O ( ^ I 2 b 0 E 4

(11)

lm[fgut-VPbdR"ViLV-gu`j_bzp«®^"g~tbm[]ejg

o

V-iLV-g

o

leHgbmRuViu`jxqbd[bd[feHg ejg"_]p«N[a`[fbdl

o

[]U6V-gulm[feHg QSRuV

_]Vr`jlqbq¦ld§H^~`nxdVrl%Vrlqbm[]U6`nbmeHxdl

@2b

0 O > I

.t<>@?!?!?!>5A

B

`nxdVtejU6i"^"bmV

o

^ulm[]g"`

o

p\gu`nU6[atiuxmej

jx`nU6U6[]g"?[bdR`t-ejU6i"^kb`cbm[]ejgugu`n_LtejU6i"_]Vvk[fbzp%ej¬ejx

o

V-x;ej

2(A L 4hC

VhxdV®V-xbmR"V¯xmVM`

o

Vrx

®ejxSU6ejxdV o Vb`n[]_]lS`nLej^"bbdR"[al`j_fHejxd[bdR"U bme%bmRuV¡Le\ej¢2ej?`Ép wD W9y

F

;QSR"Vugu`j_°Vrlqbm[]U6`nbmeHx

[al

0\.

b

0 O

R"VrxmV

b

I U6[fg"[]U6[f¥rVrlbdR"V?i~Vrgu`n_][]¥-V o t-xm[fbmVrxm[]ejg

C

|k F

QSR"ViLV-xm®ejxdU2`ngut-V ej~bdR"Vi~Vrgu`n_][]¥-V o _]Vr`jlqbq¦ld§H^~`nxdVrl<Vrlqbm[]U2`cbmeHx1[]l1bdR"V-g6U6Vr`Hlq^uxmV o [fbmRsbmRuV

xd[]lm¢Px`cbm[]e

I

2X0>?)

T

>?)

L

4.

_!0

l(

02;)

T

>?)

L

4a_ LI

I K

20 > D 4 ? C

"

D W F

QSR"[alxd`nbm[]elmV-VrU6l¯bdeLV6U6ejxdVs`ji"i"xdeji"xd[]`nbmVslq[]gutVs[fb[alVvkiLVrtbmV o bmeLVsLej^ug o V o []g o V

iLV-g o VrgNbm_]pejg

0

`jg o A

;QSR"[]lh[]lbdxm^"V`HlSlqe\ejg`jl

r_!0 l b

0 O _ LI g . hi

$

E8Z\[ ] K%E%

_ O ( @ _@0

l 0 E _ LI 6

!$#

A I 2uFf4

B >

"^kb VRu`ÉjVg"e?iuxme\en°®eHx;bmR~`cbH^"VrldlJR"[atR2Ru`jl~VrV-gt-ejg ~xmU6V o \p6lq[]U^"_a`cbd[feHgulJ[]g2bmRuV

g"V-vNblm^"ulmVrtbm[]ejg

#- 8. !,#% 61$ C 5 81$

«Vtejg~lq[o V-x`2t-ej_]_fVMtbm[]ejgen1c`n_]^"VrlSej

A o V-g"ejbmV o \p . @

0P> P>!<PP>P P> PP>

<@P PP> P PP

B

`ng o `tej_]_]Vrtbd[feHgej i"[]Vrt-V-[alqV2t-ejgulqbd`jgHb®^"g~tbm[]ejg~l o V-g"ejbmV o \p `jg o

x`ng o eHU6_fpPlm[fU%^"_a`cbmV o [fgbmRuV¯®eH_f_]ec[]g"6`ÉpH «Vlm[fU%^"_]`nbmV

bmR"V2g\^"U%~Vrx?enSi"[fVMtVMl

A0

#

. 6 <

R"VrxmV

®ej_]_fechl?`w1ej[almlmejg o [alzbdxm[]"^kbd[feHg

[bdRi~`nx`nU6VbdV-x

Vr`jtRtRu`ng"HVºi~eH[fgNb¡[fgulqbd`jgNbM

^ £ Y

.U<>@?!?!?!>5A0

#Hl

<

®ej_]_]echl¡`jg g"[®eHxmU o []lqbmxd[f

"^kbm[]ejgejg

gP>@<g

Vr`jtRU6Vr`ng

0 ^ £ Y

.=<>!?@?!?>BA0

#6®eH_f_]echl`6lzb`ng

o

`jx

o

[f¥rV

o

`j^uldlq[a`ng

o

[alzbdxm[]"^kbd[feHg

«V"v

K$L . <

`ng o bmRuVU2`cvk[]U2`n_ o [fU6Vrgulq[]ejg enbdR"Viu`nxmbm[fbm[]ejg I E

. P

lq[]gut-V[]g

i"x`jtbm[atV[fb [alg"enbg"Vrt-Vrldlm`jxmp%bmesteHUsiu^kbmVbmR"V¡iu`nxmbm[fbm[]ejg~lRu`É\[]g"`bme\e_a`nxdjV o [fU6V-g~lq[]ejg

«VlmVr`jxdtR®eHxsbmR"Vc`n_]^"Vrl

) T `jg o ) L

iLV-xm®ejxdU6[fg" `jl%V-_]_h`jl%i~eNlmlm[fu_fV®ejx2`j_f_bmRuV

®^"gutbm[]ejgulhejg J{ºbh_]Vr` o ltR"e\eHlm[fg"

) T `jg o ) L

Us[]g"[]U6[f¥r[fg"

I

2;) T > ) L

4;. "!

Z$#

I

20 > ) T > ) L

4`? C

"

D F

"eHx,`ng\p

A

£É`jg\p

0

`jg o lmV-jVrxd`j_cc`n_]^"Vrl¬ej

) T `ng o ) L £

_!0

l

02;) T > ) L

4 _ LI

`ng o I K 20 >D 4

`nxdV2V-c`j_f^u`nbmV o NpbmRuVPV-U6i"[]xm[at-`j_U6Vr`jgul?eHkbd`j[fg"V o ecjVrx

0$ P

lm[]U^"_a`cbd[feHgul- QSR"Vlq^"iuxmV-

U^uU

C

u

DGF

[albmR"Vrg t-`n_at^u_]`nbmV«®ejx

A

[]g%0 QSR"[]l_fVM` o lbde ` _a`nxdjVlmVbejsc`n_]^"VMl

@ I

2;)

T

>?)

L

4> ) T > ) L 1

P>5A G B

lm^"U6U6`jxm[]¥-V o []g <[fH^"xdV

<

Np:bdR"V®^ugutbd[feHgul

) T '

I

2;) T > ) L 4

®ejxSbdR"xmVrVÉ`j_f^uVrlej

) L .1P

£ £"&"

V-b

)('

T

2(A/> ) L 4

LVbdR"V¡Us[]g"[]U6[f¥rV-xSen)

I

2;)

T

>?)

L 4

;QSR"V[o Vr`%[al;bde o VMt_a`nxdV¯`HleHikbm[]U2`n_LÉ`j_f^uV

enJbdR"V6tejg~lzb`ngNb

) L

£°ld`Ép

)'

L

£LbdR"VeHg"VR"[atRU2`n¢HVrl

)'

T

2(A/>) L 4

lqbd`j"_]V[fbmRxdVrlmi~VMtb¯bme

A

QSR"V?eHikbm[]U2`n_¬c`n_]^"Ven

)

T¯[]_f_LV

)'

T . )'

T

2A/>)('

L 4

®eHxh`ng\p

A

Y\eHUsV?t-ejU6U6V-gNbdl`jxmV[]geHx

o

V-x

+

(12)

0 1 2 3 4 5 6 0

0.5 1 1.5 2 2.5 3

n=20 n=50 n=100 n=300 n=500 n=1000 n=5000

0 1 2 3 4 5 6

0 0.5 1 1.5 2 2.5 3

0 1 2 3 4 5 6

0 0.5 1 1.5 2 2.5 3

<[fH^"xdV

D

+

¿ÁËÖCÑMÂÀÁÂ¦ÏfÖ<×ËÖCÑMÂ ÖD×Í

¿ÁËÖDÑÉÂÇÈ¿Ñ-Ö1×ËÖCÑÉÂÖC×Í <ÆËÉÔ

!" #

Ï]×ÇÂqÆÒºÑ%$uÃ

R)'

T

2(A/>BP4

o VrtxdVr`HlqVMl[bdR

A

R)'

T

2(A/>

& 4

bdV-g o lSbme6[]gutxdVr`HlqV[fbmR

A

®ejx

) L []g

r?

&

>'&9g

£

)'

T

2A/>) L 4

lmV-V-U2lbdesLVlqbd`nu_fV`jxmeH^"g o 0

®eHxh`ng\p

A

Q<`n"_]V

<

lm^"U6U2`nxd[f¥rVrlSg\^"U6V-xd[at-`n_¬c`j_f^"VMlSen o [n°V-xdV-gNbhxd[]lm¢Px`cbd[feNl- 1"eHxVr`jtR

A

£k[fbhj[]jVrl

I

2J)'

T

2A4`>?)'

L

2A454

R"V-xdV

2J)'

T

2A4`>?)'

L

2A454

`nxdVbdR"VAU6[]g"[fU6[]¥-Vrxdlen I

2;) T > ) L 4

`jg

o

I

20> 4

bmR"V;`ÉHV-x`njV<en I

2;)'

T

2A/>'0G4`> )('

L

2(A/>0G454 ecHV-x

0?G

o V-g"ejbmV o \p)( I

R"V-xdV

2;)('

T

2(A/>0G4`>?)'

L

2(A/>0G454

`nxdVbdR"VSUs[]g"[]U6[f¥rV-xl1en I

20 >?)

T

>?)

L 4

`jg o bdR"V`ÉjVrxd`jjV;ej I

20 > 0> 4 ecHV-x

0 o V-guenbmV o

Np*( L K+

I

QSR"Vxd[]lm¢x`cbd[feNl<`ji"iLVr`nx1bde?~Vht-_feNlqVH uejx;V-vk`jU6i"_fVH£cbmRuV o [n°V-xdV-g~tVLVbzV-V-g I 20> 4

`jg o

I

2;)'

T

2A4> )'

L

2A4B4

®ejxh`j_f_

A

[alS_fecV-xbmR~`ng

P?<0

QSR\^ulr£k[blmV-VrU6lbde6~V?xdVr`HlqeHg"gu`nu_fV¯bme2tR"e\eHlmV

2J)

'T

>?)

'L

4~. 20> 4`?

}VrU6`jxm¢ bdRu`cb6bdR"V o [%nLVrxmVrgHb2xd[]lm¢x`cbm[]eHl6`jxmVlqU2`j_f_]V-xsbmR~`ng

0

`jg o bmV-g o lsbme

<

[bdR

A

QSR"[al;xdVrlm^"_fbteHg uxdU2l1bmR"V¡lzb`cbdV-U6V-gNb;bdRu`cb bmR"V¯xm[alq¢sx`cbm[]e I

20 >) T > ) L 4

H[fHV-g6\p

C

"

D W F []l

Lej^"g o V o []g o Vri~Vrg o V-gNbd_fpen

A

`jg o lqePbmRu`nb¯ej^ux¯tR"e\eHlmV-gxdV®VrxmVrgutV?ej§H^~`n_][bzpj[]jVrg\p

C

u

D F

`niui~VM`nxlbde2~V` o Vr§N^u`nbmV¡[fgeH^"xS®xd`jU6V-ejxd¢L

(13)

D

¼ $ ¼ $

$

Ã

Ã'

Ã

$

Ã'

Ã!`

Ã

$

Ã Ã

Ã

$

Ã Ã

Ã

$

Ã

$

Ã

Ã`

$

Ã

Ã'

Q`j"_]V

D +

½uÎDÖD¿Á¾hÆdÖC¿Á×Ë×Ï"ÔÉ¿jÂzÇDÂzËÖ1ÇÈ¿ÁÎÇDÆdÖC¿Á×Î,Ï]×ÇÂqÆÒºÑ)$uÃ

&¬ ? # #*A)«~5 #&%

Y\[]gutVbdR"VteHgulqbd`ngNb

) T `jg o ) L

`nxdVguec o V-bmV-xdU6[fguV o £Sejgu_fpbdR"Vg"eH[]lmVÉ`jxm[a`ng~tV

K$L []l

^"g"¢\g"ecg, ¨4U6V-bmR"e o u`HlqV o ejg«bmR"VrejxdVbd[]tr`n_`jg o R"V-^uxm[alzbd[]trl?[o Vr`Hl?i"xdejiLeHlmV o [fg ©[]xmH

`ng o«ª

`jldlm`jxqbwWy[alteHgulq[

o

VrxmV

o

2{ºb[al?V-U6i"_]ecpjV

o

[]g

Vbd^"Vfw

D

}9y®ejxbmRuV`

o

yz^~lzbdUsVrgNben

`xdV-jxdVrldlm[feHg®^"g~tbm[]ejg[]g bmRuV eÉvU6e

o

V-_C {¦gAY\^"ulmVrtbm[]ejgWu

D

bmRuVPjVrg"V-x`n_JU6VbdR"e

o

[]l

i"xdVrlmV-gNbmV o `jg o [blht-`j_f[]"x`cbm[]ejg[]lhi"xmeHi~eNlqV o []gY\^"ulmVrtbm[]ejgWu Á|k

!= = -/ ! = 5

ejg~lq[o V-xSbdR"VjVrg"V-x`n_¬iLV-gu`j_bzpP®^"gutbd[feHg

!$#

A#"

KI 2I

4;.%$'&

I 2I 4

®ejx`j_f_9I [

<> C

Wu

D { F

R"VrxmV

& I

[]l`6lm^"[fbd`nu_fV?iLV-gu`j_f[]¥-[]g"s®^"gutbm[]ejg ;QSRuV`jldlqekt[a`cbdV o i~Vrgu`n_][f¥rV o txd[fbmV-xd[]ejg[al

)+*-,X: " KI 2I 4~.

^ I 2 b

0 O 4#6

!$#

A " KI 2I

4? C

Wu

D F

QSR"VPiuxm[]gut[]i"_]VPenSbdR"Vu`Hlq[at6R"Vr^"xm[alqbm[at6®ejxstR"e\eHlm[fg"

$

[al?bdR"V2®eH_f_]ec[fguejg"V + ®eHx_a`nxdjV

I£

^ I 2 b

0 O 4

[al6_][fg"VM`nx6[fbmR:xmVMlqiLVrtb%bde

& I 2I 4

`ng o bdR"VVrlqbm[]U6`nbmV o lm_feHi~V[al l $ 0 {¦g

Y\^"~lqVMtbm[]ejg W~

D D

£°bmR"[al?R"Vr^"xm[alqbm[at6[]llm¢jV-bdtR"V o `jg o i~Vrxq®eHxmU6V o []gYk^"ulmVrtbd[feHg Wu

D

Á|k 6{¦g

bmRu[]l?lm^"ulmVrtbm[]ejg£ o [%Pt^"_fbm[]Vrlen;bdR"[]lRuV-^"xd[]lqbm[at6`nxdV o VMlmt-xm[]LV o %{¦g Y\^uulqVMtbd[feHgW~

D u£°`jg

Vv\bdV-gulm[feHgej<[fbhi"xdejiLeHlmV o Np© []xdj?`ng oª `Hlmld`nxmb[ali"xdVrlmV-gNbdV o

( 8;:58;: C ² 1"32È ² 2Èr 2È

{ o VrgHbd[®p\[]g"

C

W~

D F

[bdRbmR"V ;6ª `n_]_fechlStxd[fbmV-xd[]ejgw|jGyC£kRu[]tRRu`HlbmR"V®eHxmU

)+*-, :2

I 4 . ^ I 2 b

0 O

4#609r_ b

0 O l n

0 O _ LI

gX> C

Wu

D F

_]Vr`

o

lbme

r_ b

0 O l n

0 O _ LI g .*)+&

I

[fbmR

$. 0,)

ª

ejxdV-ecHV-xM£HVRu`ÉjV

r^ I 2 b 0 O 4 l ^ I

2X04Jg . r^ I 2 n

0 O 4 l ^ I

20G4g6= r^ I 2 b

0 O 4 l ^ I 2 n 0 O 4g

. r^ I 2 n

0 O 4 l ^ I 20G4g l

)+&

I 2I 4`?

©plm[fU%^"_]`nbm[]ejg£

9r

^ I 2 n

0 O 4 l ^ I 20G4g

[al?ejbmRuV2ejx o V-x¡en

r_ n

0 O l 0 _ LI g

®xdejU¹`t-V-xmbd`n[]g

I R"VrgbdR"VPteHgulq[o VrxmV o iu`jxqbd[bd[feHg[alR"[]jRk o []UsVrgulm[feHgu`n_C£¬ejg"V2tr`ngt-ejgulm[o V-x¡bmR~`cb?bmRuV

"[a`jlbmVrxmU£

r_ n

0 O l 0r_ LI g

£¯[]lt-_feNlqVbmeA¥rV-xdeu {º

^ I 2 b

0 O 4

[]lteHgutVrgNbmV-xdV o `jxmeH^"g o [fbdl

VvkiLVrtbd`cbd[feHg£kbdR"V-g

^ I 2 b

0 O 4

[alejbdR"Vejx o Vrxenl

)-&

I 2I 4

`jg o bmR"Vlm_]ejiLV?en

^ I 2 b

0 O 4

[bdR

(14)

D D

xdVrlmi~VMtbbme

& I 2I 4

£"ld`Épfl

b

)

£k[al`ngVrlqbm[]U6`nbmeHxej~l

)

;[]gu`j_f_]p2bmRuV¡iLV-g~`n_][f¥rV

o

VMlzbd[fU2`nbmejx

0

[al

b

0 O

R"VrxmV

b

I U6[fg"[]U6[f¥rVrlSbdR"Vtxd[fbmV-xd[]ejg

)K*3, :L KI C W~

D F

² "5H

(

8h RuV-gsbmR"Vt-ej_]_fVMtbm[]ejgsen°iu`jxqbd[bd[feHgul4>

I

Ru`Hl1ejg"VSiu`jxqbd[bd[feHg%iLV-x o [fU6V-g~lq[]ejg£

bmRuV-g

r^ I 2 n 0 O 4 l ^ I

20G4g

[]lSVM§N^u`n_°bde

_ n

0 O l 0 _ LI

( 8;:586 00 !;2Djk32 ¶54

QSR"VR"Vr^"xd[]lqbm[at[]l2`ji"i"_][fV o ejg:bmR"xdV-Viu`jxqbd[]t-^"_a`nx2xdVr`n_][]¥r`cbd[feHgulr£ tR"eNlqVrgAbde lmR"ec É`jxm[]ej^~l

lm[bd^u`cbd[feHgul-£k[fbmR

). K L >

`ng o & I 2I

4;.

IA ;

aON+f

; A

I = 6 0?

=

®ejxh`j_f_9I [

<?

«V[]_]_SlmV-VbmR~`cb6bmR"[al6R"Vr^"xm[alqbm[at[alsVr`jlmp«bme `ni"iu_fp `Hlslme\ejg:`jl

^ I 2 b

0 O 4

[als_f[]g"VM`nx6[bdR

xdVrlmi~VMtbSbme

& I 2I 4

ejg~lq[o V-xJ`®^"gutbm[]ejg i"_]enbqbdV o [fg2<[]j^"xdVS|

2 4 «VhlqV-b

K$L . <

QSR"xdV-VSxdVr`j_f[]¥r`nbm[]ejgulr£

g"ejbmV o

,$2 8 4 £

,$24

`ng o

,$2;)@4

£`nxdVlq[]U^"_a`cbdV o ®xdejU bdR"VbmRuxmVrV®eH_f_]ec[]g"t-`jlmVrl2`jg o `nxdV

i"_]enbmbmV

o

[]g[]j^uxmV

0 +

12 8 4

+;o

[%2t-^"_fb

o

VbdVrtbd[feHg`ng

o

lqU2`j_f_

A + 0\.

`ng

o A . &P

»

124

+;o [%Pt^"_fb o V-bmVrtbm[]ejg`ng o _a`nxdjV

A + 0 .

`jg o A . PP

»

12;)!4

+ VM`jlmp o VbdVrtbd[feHg`ng o lqU2`j_f_

A +

0\.

P`ng o A . & P

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−5 0 5

(g)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−5 0 5

y(a)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−5 0 5

y(b)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−5 0 5

(3 g)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−5 0 5

y(c)

[]j^uxmV| +

Ð,ÑMÂ1ÖCÑÉÇÈÂzÂ;ÇDÂqÆÀÁ¿ÁÓqÆdÖC¿Á×ËMÎ1ÆËÉÔÖCÑÉÂJÏfÚÉËÉÒ¦ÖD¿Á×ËÉÎ,ÏfÇÈ×¾AÖDÑÉÂÆÇÈÂ;ÎC¿Á¾ ÚÉÀÌÆdÖCÂzÔNÃ

QSR"VS`jldlqekt-[]`nbmV o Hxd`ji"Rej

2& I 2I 4`>

^ I 2 b

0 O 454

`nxdV;i"_]enbmbmV o [fgs<[fH^"xmV" 1"eHx_a`nxdjV;g,£

^ I 2 b

0 O 4

[alh_][fg"VM`nx[fbmRxdVrlmiLVrtbbde2bmRuV?®^"gutbm[]ejg

& I 2I 4

[]g_]`jxmHV o [fU6V-g~lq[]ejgul

C

lmV-V<[]j^"xdV

f24BF

£

`ng o bdR"V2tR"ej[atVsen;bdR"V6i~eH[fgNbl¡bmeVrlqbm[]U2`cbmV%bmRuVsxdV-HxmVMlmlm[]ejgt-eNV!Pt[]V-gNb¡[alg"ejb?lmV-g~lq[fbm[]jVH

AxC

lmV-V¯[]j^uxmV

2

8

45F

®ejx R"[atR

^ I 2 b

0 O 4

Ru`Hlx`cbdR"V-x`

_]ejH`jxm[fbmRuUs[athLV-R~`ÉN[]ejx[fbmRxmVMlqiLVrtb bde

& I 2I 4

;QSRN^~l-£\bdR"VVrlqbm[]U6`nbm[]ejgen,bdR"VxmVrjxdVrldlq[]ejg

te\V!2t-[fVrgNb[]lR"[]jR"_]p o V-iLV-g o [fg"enJbmRuV%tR"eNlqVrg[]gNbmVrxmc`n_C R"VrgbmR"V%tRu`ng"HVºi~eH[fgNblh`nxdV

(15)

D

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0 0.5 1 1.5 2 2.5 3 3.5 4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0 0.2 0.4 0.6 0.8 1 1.2 1.4

[]j^uxmV?

+

ÇCÆÍÉÑ¡×Ï

'

LÏf×Ç

Ïf×Ç¬ÖCÑMÂ1ÖCÑÉÇÈÂzÂ ÇÈÂqÆÀÁ¿ÁÓqÆdÖC¿Á×ËÉÎqÃ

jVrxmp lmRu`nxdi

C

lmV-V<[fH^"xmV

2;)@45F

£;bmR"Vjx`ni"R lmR"echl%`U2`nxd¢jV o V-_]~ec ®eHx o []U6V-gulm[feHg

}VrU6`jxm¢bmRu`nb ! l ) R

*

#hUsV-bmR"e o l C

lmV-VS®ejxVv"`nU6i"_]Vw

D

9yº£w

D

|yº f ]

F

tr`ng6~Vh`ji"i"_][fV o [fg6bdR"[]l

iu`jxqbd[]t-^"_]`jxteHg uH^"xd`nbm[]ejg[fbmR"eH^kb`jg\p o [%Pt^"_fbzpj ¡¨U6ejxdVteHU6i"_fV-bmVslq[]U^"_a`cbd[feHglzbd^ o p

o eHg"V[]gw

D

Gy¬[al lmR"ec[]g"bdR"V¡[fg~^"V-gut-VejbmR"VtR"eNlqVrg o [fU6Vrgulq[]ejg~lbdeVMlzbd[fU2`cbdVhbdR"V¡lm_]ejiLV

iu`jxqbd[]t-^"_]`jxmp6®eHxhlqU2`j_f_

A

QSR"V§N^"VMlzbd[feHg:[al6bdR"V-g R"ec bme tR"e\eNlqVbmRuV

o

[]UsVrgulm[feHg:[]gNbmVrxmc`n_SbdejV-b`ng R"ejguVrlqb

Vrlqbm[]U2`cbdV¡ejbdR"V?xdV-jxdVrldlm[feHglq_]ejiLVj

(

8;:58 ² !² n324 ² ·2 ² 4 32¶54 c 4~² ! ² % ¶ 0 0 !³ ² ² 2Èr 2D

¨hgsVv\bdV-gulm[feHgen~bmR"VR"Vr^"xm[alqbm[at o VrjVr_feHi~V o £c\p© []xdj `jg osª `jldlm`jxqbwWy\[al1teHgulq[o VrxmV o R"VrxmVH

QSR"VrplmR"ec0[fg8w9y<bmR~`cb¯`6bde\elqU2`j_f_i~Vrgu`n_fbzpÉ`j_f^uV_fVM` o lhbmelmV-_]Vrtb¯`2R"[]jR"o []U6V-gulm[]ejgu`j_

iu`jxqbd[bd[feHg

Cj R <

®ejx

C

|k

DDGF5F

SQSRuViLV-gu`j_bzp[bdR j 1 <

t_]eHlmV?bme

<

[]l¯t-`n_]_]V o U6[fgu[fU2`n_

iLV-gu`j_bzpH {ºb¡[]l¯`jldlqekt-[]`nbmV o bmePbmR"V%i~Vrgu`n_fbzp

)+&

I 2I 4

`jg o _fVM` o lbme`2xdVr`HlqeHg"gu`j"_fV o []U6V-gk

lm[feHg QSR"Vr[fxJ[o VM`[albme?teHgulq[o Vrx o [%n°V-xdV-gNbJÉ`j_f^uVrl<en

)

®xmeHU

P

[]g!5#

A KI C Wu

D { F

`jg o lmV-_]Vrtb

bmRuV`jldlqekt-[]`nbmV oo []U6V-gulm[feHg£uld`Ép

b

I 2) 4

£uU6[]g"[fU6[]¥-[]g"

)+*-, : KI 2I 4NC

Wu

D F

QSRu[]liuxmektV o ^"xdV

_]Vr` o lbme2` ug"[fbmV?[]gutxdVr`Hlq[]g"6lqVM§N^"V-gut-Ven,bdV-U6iLV-x`cbm^uxmVMl

) T .1P

1 ) L 1

?!?!?

1 ) V >

`ng o ` ugu[bdV o Vrt-xmVM`jlm[fg"6lmVr§N^"V-g~tVen o [fU6Vrgulq[]ejg~l`jldlqekt[a`cbdV o bme6bmRuVbmV-U6iLV-x`cbd^"xmVMl

I T . A 1 I L 1

?!?@?

1 I V . <>

R"VrxmV¡®ejx

,/. 0>!?!?@?>

j

) . gJhji

!#"

O$

prq

^ I 2 b

0 ! 4 l ^ I 2 b 0 O $

prq

4

& I 2I i T 4 l & I

2&% 4 . ^ I 2 b

0 O $4 l ^ I 2 b 0 O $

prq

4

& I 2I i T 4 l & I 2I 4 ?

QSR"Vi~`jldlm`jjV¡bme2bdR"VU6[]g"[fU2`j_iLV-gu`j_bzp[alhVvkiLVrtbmV o bdePLVU2`nxd¢jV o \p`Plq^ o"o V-gÈ`j_f_

en¬bdR"V o [fU6Vrgulq[]ejg~lejbmR"V`jldlme\t-[]`nbmV o iu`nxmbm[fbm[]ejgulr£Ni"R"V-guejU6V-gPeHulmV-xdjV o []giuxd`Htbm[atVH <QSRuV

(16)

D

U6VbdR"e

o

t-ejgulm[]lqbdlenLlqVr_fVMtbm[]ejgbmR"VSc`n_]^"V

b

)

en

2) 4 T

V$`jldlqekt[a`cbdV

o

bdebdR"VR"[fHR"VrlqbLyz^"U6i

en

o

[]U6V-gulm[feHgulSej~lqVrxmHV

o

[]g

2I X4

T

V6

!= .:#81$. !$#<% (' !8 - 9!8 5

hVrxmVh`jxmVSi"xdVrlmV-gNbdV o lqeHUsV[]U6i~eHxqb`ngNbJi"x`jtbd[]tr`n_ki"xdeju_fVrU6l;ejg%bmR"VhVMlzbd[fU2`nbm[]ejg6en

)

R"[atR

t-`jgRu`ÉHVst-ejgulmVr§N^"VrgutVsejgbmR"V6iLV-xm®ejxdU2`ngut-V%ej;bmR"V ~gu`n_1Vrlqbm[]U2`cbdejxM %¨ t-`j_f[]"x`cbm[]ejgen

bmRuV?UsV-bmR"e o £uR"[]tR[alSVvkiLVrtbdV o bme6iLV-xm®ejxdU'V-_]_[fgU6eHlqblq[fbm^~`cbm[]ejg~l-£k[alSi"xdejiLeHlmV o

D

{º,bmRuV¯U2`cvk[]U2`n_Nyz^"U6ien o []U6V-gulm[]ejgenbdR"V?lqVM§H^uV-gut-V

2I 4 _

TSKNMNMNMKV []lS`nbqbd`j[fguV o \p

lqVrjV-x`n_Lc`n_]^"VrlSej

2) 4

_

TSKNMNMNMNKV£uR"[]tReHg"V[]lbde2~VtR"eNlqVrg

|" ¸ e\VrlPbmR"VU2`cvk[fU2`j_ o []U6V-gulm[feHg enbmRuVteHgulm[o VrxmV o iu`nxmbm[fbm[]ejgul I E `9n°VrtbbmRuV

tR"ej[atV¡en

)

¨hU6eHg"lqVrjV-x`n_Jc`j_f^"VMl?en

)

xdVr`HtR"[]g"bdR"VPU2`cvk[]U2`n_°yz^"U6i£1V o Vrt-[o V6bdeteHgulq[o Vrx

bmRuVlqU2`j_f_]Vrlqb;ejg"Vhlm[]gutV[fb[al;`jldlqekt-[]`nbmV o bmebdR"V uxlqb`n"xd^"ikb tR~`ng"HVej o [fU6V-g~lq[]ejgulr 1QSR"[]l

tR"eH[]t-V`ji"iLVr`nxl bme6LV?xmVM`jlmejgu`j"_fV¯®xdejU lm[fU%^"_a`cbm[]ejgg"ejbhxmVri~eHxqbdV o RuV-xdVj

{¦gsi"xd`Htbd[]t-Vj£nlmejU6V u[f o []U6V-gulm[feHgyz^uUsi~lJ`nxdV eHulqVrxmHV o ®ejx<bme\e?lqU2`j_f_\c`n_]^"Vrl1ej

)

`jg o

`i~`nxmbm[fbm[]ejgPej¬bme\e%Ru[fHRk o [fU6V-g~lq[]ejgPtr`ngPLV¡lmV-_]VrtbmV o JQSR"[]l[al;bdR"Vlq[fbm^u`nbm[]ejgP[]gtr`jlmV

C` F +

[]g[]j^uxmV

28 4

£ubdR"Vc`n_]^"VMl 8 T`ng o 8 L

`jxmVbdR"Vc`n_]^"Vrlhen

)

xdVrlmi~VMtbd[fHV-_]p`jldlme\t-[]`nbmV o bde

bmRuVbz e"[]jHVrlqb°yz^"U6iul- 1{º9I E

.%P

£cbdR"V-g b

)S.

8 TS`ng o b I . <(

£HR"[]_fV[f9I E

. 0$

£

bmRuV-g b

) . 8 L

`ng o b

I .

?Q,e`ngulmV-xhbdR"V6lqVMtejg o §H^uVrlqbm[]ejg£ I E tr`ngi"_a`Ép`Pxdej_]V[]g

bmRuV6lmV-_]Vrtbm[]ejg«en bmR"V2iLV-gu`j_f[]¥-V o VMlzbd[fU2`nbmejxM {¦g i"x`jtbm[atVH£°bmR"V2^ulmV-x[]_f_JR~`ÉjV%bmetR"e\eHlmV

`n^"bmejU2`nbm[atU6VbdR"e

o

¨ ^"g"[]jV-xld`n_<É`j_f^uVenI E

[al¯guenbxmVr_fVrÉ`jgNb¡lm[fgut-V%[fb

o

V-iLV-g

o

l¯eHg

bmRuVi"xdej"_]V-U «Vi"xdejiLeHlmVbmePVr_f[]U6[fgu`nbmV?bdR"VRu[fHRk

o

[fU6V-g~lq[]ejg"g~`n_iu`jxqbd[bd[feHgul\p®ejxt[]g"

)

bde~V2"[]jHV-xbdRu`ng `g"enbdV o bmRuxmVMlqR"eH_o ) -

j Y\[]gutV2[]g«bmR"[al®x`nU6V-ejxd¢

)1. K$L

£,V

i"^kb

) . K$L $

2QSR"Vrg«[fblm^PtVrl¯bdetR"e\eHlmV

$ -

6`jg o iu^kb

)-

. K$L $ -

c PY\[fg~tV6bmRuV

c`nxd[]`jgutV

K$L

[]l^"g"¢\g"ecg£H[b[]l lq^uulzbd[bd^u`cbdVh\p%eHg"Vhej°[fbdlVrlqbm[]U2`cbmeHxdlr JY\[fg~tVbdR"Vhg\^"ULV-x

entRu`jg"jV-CiLej[]gNbdl2`Hl2 Vr_f_¡`jl6bdR"V-[]x_]ekt-`nbm[]ejgulP`jxmV^ug"¢\g"ecg£bmR"Vt_a`jldlq[at-`j_hxmVrjxdVrldlq[]ejg

Vrlqbm[]U2`cbdejxSt-`ngug"enbS~V¡^ulmV o ~u¯g"Vt-`jg ug o []gPbmRuV¡_][fbmV-x`cbd^"xdV¯lmV-jVrxd`j_uHeNe o VMlzbd[fU2`nbmejxl en

bmRuVsc`jxm[a`ngut-V

Cw DG

yº£ ] f ]

F

k«V o VMt[o V6R"V-xdVbdebd`n¢HVbdR"V6Vrlqbm[]U2`cbmeHxi"xmeHi~eNlqV o []g ¯`n_]_

9 w

DD

yR"[]tRt-`jgLV§N^"[at¢N_]pt-ejU6i"^kbdV o$+

b

K L .=2A

l ( 4 i T I i

]

^`_

T

]! _ O 9 ! , ! s ^ L > C

Wu

D } F

lm^utRbdRu`cb

o

! _ O 9 ! . P

`jg o o ! _ O 9 L

! . <

2uej_]_fec[]g"W`n_]_ ! 9 £V2tR"eHlmV ( .

`ng o bdR"V`jldlqekt-[]`nbmV o lmVr§N^"V-g~tV[]l

249

! 4! _ O KNMNMNMNK

.=2(P?%< 0>BP?0 &

P>BP? & 0>

l

P?

& &

04`?

¶

2È

²¶:

² ² ¶

!D·

$ -

8«V2i"xdejiLeHlmVbmetR"e\eNlqV%bmR"VsbdR"xmVMlqRuR"ej_

o $ -

®xdejU

` g\^"_]_¡RNp\iLenbdR"Vrlm[]lbmVMlzb O

%

g"e:tRu`ngujVºiLej[]gHb[]li"xdVrlmV-gNb

`jH`j[fgulqbPbdR"V«`j_bdV-xdgu`cbdV

R\p\i~ejbmR"VMlq[al T

%

bmR"VrxmV6V-v\[alqbdl?`cb_]Vr`Hlzb`tRu`jg"jV-CiLej[]gNb

Vb

$

LV6bmR"V ~xdlqb?É`j_f^uV

en<bmRuVlqVM§H^uV-gut-V

2$ 4 _

TSKNMNMNMNKV ®ejxhRu[]tRbmR"Viu`nxmbm[fbm[]ejgen o []UsVrgulm[feHg

<

[alhlmV-_]VrtbdV o ;QSRuV

bmVMlzbh[al

O

% $ -

[

$

`nN`n[]gulzb T

%,$ -

R $?

(17)

D

0 2 4 6 8 10 12

0 5 10 15 20 25 30 35 40

0 0.5 1 1.5 2 2.5

0 5 10 15 20 25 30 35 40

0 1 2 3 4 5 6 7 8 9

0 5 10 15 20 25 30 35 40

q q

<[]j^"xdVW +

ÚÉËÉÒ¦ÖD¿Á×Ë

Ïf×ÇÖDÑÉÂJÖDÑÉÇDÂzÂ;ÇÈÂmÆÀÁ¿ÁÓqÆdÖD¿Á×ËÉÎmÃ

V-b6~VbdR"V?_]V-jVr_¬enbmR"VbdVrlqbr£

$ -

.

T

i 2$4>

R"VrxmV

T

i 2$94

[alSbmR"V§N^u`jgNbm[]_fV?ej<eHx

o

Vrx

<

lPen

$

{ºbh[alVrlqbm[]U2`cbdV

o

`jl[fbdlhV-U6i"[]xm[at-`j_

jVrxdlm[]ejg?ej"bd`n[]g"V

o

ejg

0P PP

lm[fU%^"_a`cbm[]ejg~l- ,QSRu[]l<i"xdektV

o

^"xmV []l<iLV-xm®ejxdU6V

o

<P

bm[]U6Vrl<®eHxVM`jtR

A

`ng o bmR"VbmR"xdVrlmR"ej_o

$-

2(A4

[alhbdR"V%`ÉHV-x`nHV¯ejJbmR"V%xmVMlq^"_fbm[]g"

<P

c`n_]^"Vrlr VsteHgulq[o Vrx

bze?É`j_f^uVrl;ej`jtrtejx o []g"¡bme

AR 0PP

`jg o A [

0P P

lq[]gutVhbmR"VhLV-R~`ÉN[]ejxJej°bmR"V®^"gutbd[feHg

) ' b

I lmR"echl`6tVrxqb`n[]glqbd`j"[f_][fbzp2®ejx_a`nxdjV

A

;QSR"V?xdVrlm^"_bl`nxdV¯H[fHV-g[fgQ<`n"_]V

0

$

MÃ

MÃ MÃ

!

MÃ MÃ

MÃ` MÃ

MÃ MÃ

Q<`n"_]V| +

½~ÎÈÖC¿Á¾hÆdÖD¿Á×ËÉÎ¬×Ï"

$

Ï]×ÇÂqÆÒºÑ%$ÆËÉÔÖÕ¬×SÔÉ¿jÂzÇÈÂqËÖ<ÖDÂzÎDÖ,ÀÁÂ¦ÝÂzÀÁÎ Ã

{ºbhlqVrV-U2lSbdesLV?xdVr`jlmejgugu`n"_]V¯bme2tR"e\eHlmV

$ -

. #

P?& 0 [f

AR 0PP

P?%$ &

[f

A [ 0PP?

(18)

DG

4 0 0²

¶ 4 · º¶

) 8 {¦gAi"x`jtbm[atVj£[b6Ru`niui~Vrgul%bmRu`nb

) -

[al%bme\e«_]`jxmHV

+

K$L []l

ecjVrxmVMlzbd[fU2`nbmV

o

£cV-[fbmR"Vrx

$-

[]lJbme\e?_]`jxmHVj£n`jg

o

bmR"VU6[]g"[fU2`j_"i~Vrgu`n_fbzp%tr`ng"guenbJ~V

o

VbdVrtbdV o

QSR"[al[albmRuVt-`HlqVen1bdR"VxdVr`n_][]¥r`cbd[feHg

,$2J)!4NC

lmV-V<[]j^"xdV

2;)@45F

o

[fbmR bdR"xdVrlmR"ej_o £ b

) . 8 L

£JbmRuViu`jxqbd[bd[feHg en o [fU6Vrgulq[]ejg

<

[al%lmV-_]VrtbmV o Q,e `ÉjeH[o bdR"[]l

i"xdej"_]V-U£

)

[alLej^"g o V o \p b

K$L

<[fg~`n_]_fpH£;bmRuVtr`n_][fuxd`nbmV o U6VbmRue o t-`jgALVlq^"U6U2`nxd[]¥-V o `jl%®ej_]_]echl + bmR"VteHgulqbd`ngNb

)

[]l

xdVrlqbmxd[]tbmV o bme

r)- > b

K$L g

`ng o

[fgbmR"Vtr`jlmVR"V-xdV¡bmR"VrxmVVvk[alzblh`cb_]Vr`Hlzbh`¯yz^"U6ien o [fU6Vrgulq[]ejg,£

b

). dme f\g d

$ _

TSKNMNMNMNKVO $ q i O $ & O)(

@ I

js

T l I B C

Wu Á|n

F

V-_alqV

b

). ) -

? C

Wu Á|

DGF

0 0 !;2ÈHk 2¶$4 8 V-b^ulteHUsV¡u`Ht¢6bme%bmR"V¡bmRuxmVrV¡xdVr`j_f[]¥r`nbm[]ejgulr 1QSR"V¡tr`n_][fuxd`nbmV o `ng o bmRuV

g"ekt-`j_f[]"x`cbdV o UsV-bmR"e o l%`nxdV2xmVMlqiLVrtbm[]jVr_fp o V-g"ejbmV ox ( `ng o ( uejxt-ejU6iu`nxd[alqeHg£

bmRuVUsV-bmR"e o [fbmR ¢\g"ecg `ng o Vrlqbm[]U2`cbmV o É`jxm[a`ng~tV

C

®eHx2R"[]tR

K$L

[]g:bmR"ViLV-g~`n_fbzp []l

lm^"ulqbm[fbm^kbdV o \p b

K$L C W~

D } FBF

£Mg"enbdV o xdVrlmi~VMtbm[]jVr_fp `ng o £c`nxdV;`niui"_f[]V o ®eHxbdR"VJbmRuxmVrV

xdVr`n_][]¥r`cbd[feHgul o Vrldtxd[]~V o []gAY\^"~lqVMtbm[]ejg W~

D |" P{¦g[]j^uxmV

`jxmV6i"_]enbmbmV o bdR"V2Vrlqbm[]U2`cbdejxl

lmV-_]VrtbdV o Np2VM`jtRUsV-bmR"e o `ng o Q`j"_]V¡%j[]jVMlbdR"V o []UsVrgulm[feHgulenbdR"VrlmV¯VMlzbd[fU2`nbmejxl[bdR

bmRuV-[]x`jldlqekt-[]`nbmV o _feNlml ®^"g~tbm[]ejg

C

|k F

! ! # ! # !

!

! ! !

! ! # # !

Q<`n"_]V? +!

¿Á¾ÂzËÉÎD¿Á×ËÉÎ°ÎDÂqÀÁÂzÒ¦ÖDÂqÔ¡Å hÖDÑÉÂJÒqÆÀÁ¿ÁÅÉÇCÆdÖDÂzÔÆËÉÔÖCÑMÂJËÉ×rÒqÆÀÁ¿ÁÅÉÇDÆdÖDÂqÔ¡¾ÂzÖDÑÉ×-ÔÉÎ ÉÆËÉÔ¯ÖDÑÉÂJ¾Â¦ÖDÑÉ×rÔMÎ

Õ,¿ÖCÑ rËM×mÕ,ËÆËÉÔ ÂqÎÈÖC¿Á¾hÆdÖDÂzÔ ÝÆÇD¿ÌÆËÉÒzÂÕ,¿ÖCÑÖCÑÉÂz¿ÁÇuÀÁ×ÎCÎqÃkÐÑÉÂ¬ÀÌÆÎDÖuÒz×ÀÁÚÉ¾ËÍÉÇD×qÝM¿ÁÔMÂqÎuÖCÑMÂ,ÅnÂzÎDÖ~×ËÉÂ¬¿ÁËÖCÂzÇÈ¾Î

×Ï"ÀÁ×ÎCÎqÃ

"eHxbdR"VrlmV;iu`jxqbd[]t-^"_]`jxxdVr`n_][]¥r`cbd[feHgulr£-bdR"V tr`n_][f"x`cbdV o U6VbdR"e o ejxd¢\l Vr_f_Nlq[]gutV[bJlqVr_fVMtbl

bmRuVUs[]g"[]U2`n_u_]eHldl1Vrlqbm[]U2`cbdejxM "eHx

,$2 8 4

£Nlq[]gut-V 8 T R ) -

R 8 L £ (7lmV-_]VrtbmV o b

0"

£N`ng o ®eHx

,$2;)!4

bdR"V ^ui"i~VrxJ~eH^"g o ®ejx

)

`n_]_fechl,bmRuVU6V-bmR"e o bde?lqVr_fVMtb b

0#

ª ejxdV-ecjVrxr£rbmRu[]l1t-`j_f[]"x`cbdV o

U6VbdR"e o ejxd¢\l~V-bqbdV-x ®ejx

, 28 4

`jg o

,$24

bmR~`ng2bdR"V¯U6V-bmR"e o [fbmR¢\g"ecg`ng o Vrlqbm[]U2`cbmV o

c`nxd[]`jgutVH

$

92 < # &%6«S/< <&

{¦g«bmR"[allmVrtbm[]ejg£<lqeHU6VPlq[]U^"_a`cbd[feHgulVvkiLV-xd[fU6VrgHbl`nxdV6i~Vrxq®eHxmU6V

o

bde`jldlqVMlml¡bdR"V2iLV-xm®ejxm

U2`ngut-VejbmR"Vt-`j_f[]"x`cbdV

o

i"xdejiLeHlmV

o

U6V-bmR"e

o

JQSR"V uxlzbejg"V¡tejU6iu`jxmVMlJbdR"V¯iLV-xm®ejxdU2`ngut-V

en1lqeHU6V¡VMlzbd[fU2`nbmejxlSlqVr_fVMtbdV o NpPbmR"[alU6VbdR"e o bdesbmR"V?eHg"VrlSlmV-_]VrtbdV o \pPenbdR"V-xiLV-gu`j_f[]¥-V o

txd[fbmV-xd[a`lm^utRbdRu`cbbmRuV ª `n_]_fechltxd[bdV-xd[feHg`ng o bdR"VN e txd[fbmV-xd[]ejg 1QSR"V?lqVMteHg o ejguV

i"xdejiLeHlmVrlbdeP`jldlqVMlmlbdR"VLV-Ru`É\[]ejxen1bdR"VU6VbdR"e o R"V-gbmRuV`jldlq^uUsi"bm[]ejgulejbdR"VU6e o V-_

`nxdV6g"enb%É`j_f[o P{¦g bdR"V uxlqbt-`jlmVj£

0

[al?g"ejb`i"[fVMtVr[]lmVPteHgulzb`ngNb®^"gutbm[]ejg `ng o []g bmRuV

lmVrteHg o t-`jlmVj£\bdR"V?g"eH[]lmV[]lSg"ejb¯`n^uldlm[]`jg

(19)

D

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−1 0 1

(s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−5 0 5

(b−1)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−5 0 5

(b−2)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−5 0 5

(a−1)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−5 0 5

(a−2)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−5 0 5

(c)

<[fH^"xdV

+

ÞkÂzËcÆÀÁ¿ÁÓzÂzÔ¡ÂzÎDÖD¿Á¾hÆdÖD×ÇDÎ,ÎCÂzÀÁÂzÒ¦ÖCÂzÔÅ hÖCÑÉÂJÒqÆÀÁ¿ÁÅÉÇDÆdÖDÂqÔ¡¾ÂzÖDÑÉ×-Ô

Â¦Ö

ÆËÉÔÖCÑÉÂ

×ËÉÂzÎ,ÎCÂzÀÁÂzÒzÖDÂzÔ¡Õ,¿ÖCÑ rËM×mÕ,ËÆËÉÔ¯ÂzÎDÖD¿Á¾hÆdÖCÂzÔ¯ÝÆÇD¿ÌÆËMÒqÂ

ÂzÖ Ã

-76. 12#*r% #! :! =91 C1 #! 1 #.

QSR"V?lqbm^ o []V o txd[fbmV-xd[a``nxdV¡i~Vrgu`n_][f¥rV o _fVM`jlqbq¦lm§N^u`jxmVMltxd[fbmV-xd[a`[fbmRbmR"V o [%n°V-xdV-gNb ®eH_f_]ec[]g"

iLV-gu`j_bd[fVMl +

/6ª

`n_]_fechl

!5#

A2

I

4~. 0 K L IA ?

e

!5#

A b 2I

4. K L IA aON+f;A/?

QSR"Vi~Vrgu`n_fbzpeHkbd`j[fg"V o []gej^"x®x`nU6V-ejxd¢2j[]jVrg\p

C

|k } F

[fbmR¢\g"ecgc`jxm[a`ngut-V

!5#

A

2I 4~.

K L IA ; 0 aN\f

; A

I = 6 = ?

QSR"Vi~Vrgu`n_fbzp[fbmRVrlqbm[]U2`cbdV o É`jxm[a`ng~tV

C

H[fHV-gNp

C

Wu

D } F5F

!5#

A 2I 4~.

b

K L IA ; 0 aN\f

; A

I = 6 = ?

QSR"V?t-`n_][]"xd`nbmV o iLV-gu`j_bzp

!5#

A 2I

4~.

b

) IA ; 0 aN\f

; A

I = 6 = ?

R"V-xdV b

)

[]lSeHkbd`j[fguV o NpbmR"Vtr`n_][fuxd`nbmV o U6VbmRue o

«V¡t-ejgulm[o V-x

K$L

. < £ A . & P>PP

`ng o lm[fv o [n°V-xdV-gNb ®^"gutbd[feHgul

0C

g\^"U%~VrxmV o ®xdejU

0 T bde

0 # F

i"_]enbmbmV o []g<[fH^"xdV

&

<wxmektVrV o []g"6`jl [fgY\VMtbm[]ejg"£\®eHxVM`jtR

A

`ng o Vr`HtR2®^"gutbm[]ejg

0 £

bmRuVhxm[alm¢x`cbm[]e I

20 > 0> 4C

"

D W F

[]lJVMlzbd[fU2`nbmV

o

ecHV-x

P P

lq[]U^"_a`cbd[feHgul;`jg

o

bmR"VhiLV-xtVrgNbd`nHV

en°bdR"Vhg\^"ULV-x en°bm[]U6Vrlr£

o

Vrg"enbdV o

! E I

£HbmRu`nb;bmR"V¯tejg~lq[

o

V-xdV

o

t-xm[fbmVrxm[]ejg6_]Vr`

o

[fg"bde?bmRuV