Manage Inverse Heat Conduction: Ill-Posed Problems - Chapter 3

(1)

CLD_YB]

D__]K\NGDYB

GBYLKIS

FK] IN]BCY LBDY

CKHIRCYNKH

_]KM@BGS

3(4 3(4 NHY]KIRCYNKHNHY]KIRCYNKH

Nh ylns cldpyb} skgb dpp}k|ngdyb gbylkis d}b anvbh fk} sk`vnha in}bcy y}dhsnbhy

lbdy ckhircynkh p}km`bgs( Ylbsb in}bcy ybclhntrbs d}b ylb fn}sy sydab kf sk`rynkh

p}kcbir}bs fk} ylb nhvb}sb lbdy ckhircynkh p}km`bgs

p}kcbir}bs fk} ylb nhvb}sb lbdy ckhircynkh p}km`bgs Ylb sbckhi sydab qlnclYlb sbckhi sydab qlncl

nhvk`vbs spbcnfnc d`ak}nylgs fk} ylb NLC_

nhvk`vbs spbcnfnc d`ak}nylgs fk} ylb NLC_ nsns ibvb`kpbi nh Cldpyb}ibvb`kpbi nh Cldpyb} 9(9( YlbYlb

dpp}k|ngdyb lbdy ckhircynkh

dpp}k|ngdyb lbdy ckhircynkh sk`rynkh p}kcbir}bssk`rynkh p}kcbir}bskfkfylns cldpyb} d}b ylns cldpyb} d}b ckgmnhbickgmnhbi

nh Cldpyb}s 2 dhi 6 qnyl ylb

nh Cldpyb}s 2 dhi 6 qnyl ylbNLC_NLC_d`ak}nylgs kf Cldpyb}d`ak}nylgs kf Cldpyb}9(9( 3(4(4

3(4(4 Vd}nkrsVd}nkrs Hrgb}ncd`Hrgb}ncd`Dpp}kdclbsDpp}kdclbs

_d}ynd` inffb}b

_d}ynd` inffb}bhyndhynd` ` btrdynkhs nhc`rinha ylb y}dhsnbhy btrdynkhs nhc`rinha ylb y}dhsnbhy lbdy ckhircynkh btrdynkhlbdy ckhircynkh btrdynkh

cdh

cdhmbmb sk`vbi rsnha d vd}nby~ kf gbylkis nhc`rinha b|dcy dhi hrgb}ncd` p}ksk`vbi rsnha d vd}nby~ kf gbylkis nhc`rinha b|dcy dhi hrgb}ncd` p}k

cbir}bs

cbir}bs Ylb b|dcy gbylkis nhc`rib ylb c`dssncd` gbylkis kf sbpd}dynkh kfYlb b|dcy gbylkis nhc`rib ylb c`dssncd` gbylkis kf sbpd}dynkh kf

vd}ndm`bs dhi @dp`dcb y}dhsfk}gs

Yqk y~pbs

Yqk y~pbs kfkfhrgb}ncd` p}kcbir}bs d}b inscrssbi nh ylns cldpyb}( Khbhrgb}ncd` p}kcbir}bs d}b inscrssbi nh ylns cldpyb}( Khbnsns

mdsbi kh dh nhyba}d` fk}gr`dynkh kf ylb gdylbgdyncd` gkib` dhi ylb kylb} kh d

inffb}bhynd` fk}g

inffb}bhynd` fk}gkfkfylb gkib`(ylb gkib`(

Ylb y}dhsnbhy lbdy ckhircynkh btrdynkh cdh

Ylb y}dhsnbhy lbdy ckhircynkh btrdynkh cdh mbmbbnylb} `nhbd}bnylb} `nhbd}k}k} hkh`nhbd}(hkh`nhbd}( Fk}

Fk} ylb `nhbd} cdsb ylb pd}ynd` inffb}bhynd` btrdynkh fk}gr`dynkh cdhylb `nhbd} cdsb ylb pd}ynd` inffb}bhynd` btrdynkh fk}gr`dynkh cdhmbmbbtrnvbtrnv

d`bhy`~ p}bsbhybi

d`bhy`~ p}bsbhybim~m~dh nhyba}d` btrdynkh( Ylb divdhydab kf ylb nhyba}d` fk}gdh nhyba}d` btrdynkh( Ylb divdhydab kf ylb nhyba}d` fk}g ns

nsyldy ylb spdcb ibpbhibhcb cdhyldy ylb spdcb ibpbhibhcb cdhmbmb }bp}bsbhybi b|dcy`~ `bdvnha kh`~ ylb yngb}bp}bsbhybi b|dcy`~ `bdvnha kh`~ ylb yngb

ibpbhi

ibpbhibhcb yk bhcb yk mb dpp}k|ngdybimb dpp}k|ngdybi

Yqk inffb

Yqk inffb}bhy dpp}kdclb}bhy dpp}kdclbs yldy bgp`k~ nhyba}d` btrdynks yldy bgp`k~ nhyba}d` btrdynkhs fk} sk`hs fk} sk`vnha y}dhsnbhyvnha y}dhsnbhy 1<

1<

SBC(

SBC( 4 NHY]KIRCYNKH4 NHY]KIRCYNKH 1>1>

lbdy ckhircynkh p}km`bgs d}b ylksb rsnha Irldgb`!s ylbk}bg dhi A}bbh

frhcynkhs mkyl kf qlncl ~nb`i ckhvk`rynkh'y~pb nhyba}d`s( Snhcb ylbsb gbylkis

d}b

d}bvb}~vb}~sngn`d} kh`~ Irldgb`sngn`d} kh`~ Irldgb`s ylbk}bgs ylbk}bgnsnsanvbh( D hrgb}ncd` dpp}k|ngdynkhanvbh( D hrgb}ncd` dpp}k|ngdynkh

kf ylb nhyba}d`

kf ylb nhyba}d`nsnsd`sk anvbh( Ylb lbdy'ckhircynha mki~ cdhd`sk anvbh( Ylb lbdy'ckhircynha mki~ cdhmbmbkf d}mny}d}~ sldpbkf d}mny}d}~ sldpb

dhi kf hkhlkgkabhbkrs gdyb}nd`( D`ylkral ylb lbdy y}dhsfb} gd~

dhi kf hkhlkgkabhbkrs gdyb}nd`( D`ylkral ylb lbdy y}dhsfb} gd~mbmb yqyqk'k'k}k}

yl}bb'ingbhsnkhd` nh ylns cldpyb} ylb}b

yl}bb'ingbhsnkhd` nh ylns cldpyb} ylb}bnsnsd snha`b fk}cnha nhpry qlncld snha`b fk}cnha nhpry qlncl nsnskh`~kh`~

yng

yngb ibpbhib ibpbhibhy(bhy( hbq

hbq ybclhntrb qlncl ryn`nubs Irldgb`!s ylbk}bg fk} sk`vnha ckhhbcybiybclhntrb qlncl ryn`nubs Irldgb`!s ylbk}bg fk} sk`vnha ckhhbcybi

mdsnc abkgby}nbs

mdsnc abkgby}nbs nsns cd``bi ylb rhsybdi~ sr}fdcb b`bgbhy gbylkicd``bi ylb rhsybdi~ sr}fdcb b`bgbhy gbylki Ny d`skNy d`sk

nhvk`vbs sk`vnha dh nhvb}sb p}km`bg mry ylb}b d}b hk gbdsr}bgbhy b}}k}s dhi

ylb gdyclnha ckhinynkhs d}b

ylb gdyclnha ckhinynkhs d}bdydy sr}fdcbssr}fdcbs}dylb} yldh dy nhyb}nk} pknhys}dylb} yldh dy nhyb}nk} pknhyskfkfylbylb

mkinbs

Ylb sk`rynkh kf d hkh`nhbd} y}dhsnbhy

Ylb sk`rynkh kf d hkh`nhbd} y}dhsnbhy lbdy ckhircynkh p}km`bg }btrn}bs dhlbdy ckhircynkh p}km`bg }btrn}bs dh

dpp}kdcl yldy insc}bynubs ylb pd}ynd` inffb}bhynd` btrdynkh( Yqk gbylkis fk}

sk`vnha ylb hkh`nhbd} y}dhsnbhy lbdy ckhircynkh btrdynkh d}b ylb fnhnyb inffb}bhcb

dhi fnhnyb b`bgbhy ,FB. gbylkis(

dhi fnhnyb b`bgbhy ,FB. gbylkis(DhDhd`yb}hdynvb gbylkid`yb}hdynvb gbylkinsnsrsbi nh ylns cldpyb}rsbi nh ylns cldpyb} nh

nh kfkf

ny ns

ny nscd``bi ylb fnhnyb ckhy}k` vk`rgb p}kcbir}b(cd``bi ylb fnhnyb ckhy}k` vk`rgb p}kcbir}b(

D hkh`nhbd} p}km`bg

D hkh`nhbd} p}km`bgnsns khb fk} qlncl ylb lbdy ckhircynkh btrdynkhkhb fk} qlncl ylb lbdy ckhircynkh btrdynkh k}k}

mkrhid

mkrhid}~ }~ ckhinynkhckhinynkhnsnsd hkh`nhbd} frhcynkhd hkh`nhbd} frhcynkhkfkfybgpb}dyr}bybgpb}dyr}b( ( Khb b|dgp`b kf dKhb b|dgp`b kf d

hkh`nhbd} pd}ynd` inffb}bhynd` btrdynkh ns5

,j

dY.7pcdY.7pcdYdY d|

d| d| d| dydy ,3(4(4,3(4(4

qlb}b

qlb}b dhi+k}dhi+k}pcpcd}b frhcynkhs kf ybgpb}dyr}bd}b frhcynkhs kf ybgpb}dyr}bY(Y(NfNf dhidhi d}b frhcynkhs kfd}b frhcynkhs kf pksnynkh

pksnynkh|,|,kh`~ ylbh Bt(kh`~ ylbh Bt(,3,34(4.4(4.nsns`nhbd}`nhbd} DhDhb|dgp`bb|dgp`bkfkfd hkh`nhbd} mkrhid}~d hkh`nhbd} mkrhid}~

ckhinynkh

ckhinynkhnsnsylb }dindynkh ckhinynkhylb }dindynkh ckhinynkh

7r£ZY$'Y9,K 7r£ZY$'Y9,Ky.Wy.W

YN YN d| d| ((((7?7? ,3(4(=.,3(4(=. 3(4(= 3(4(= SckpbSckpb Cldpyb}Cldpyb}

Ylns cldpyb} anvbs d ib}nvdynkh kf Irldgb`!s nhyba}d` ,Sbcynkh

Ylns cldpyb} anvbs d ib}nvdynkh kf Irldgb`!s nhyba}d` ,Sbcynkh 3(=.3(=. dhi ddhi d

hrgb

hrgb}ncd` dpp}k|ngdynkh }ncd` dpp}k|ngdynkh ylb}bkfylb}bkfSbcynkh 3Sbcynkh 33 inscrssbs fnhnyb ckhy}k` vk`rgb3 inscrssbs fnhnyb ckhy}k` vk`rgb

sk`rynkh

sk`rynkhs kf ylb y}dhsnbhy s kf ylb y}dhsnbhy lbdy ckhircynkh btrdynkh( Mkyl `nhbd} dhi lbdy ckhircynkh btrdynkh( Mkyl `nhbd} dhi hkh`nhbd}hkh`nhbd}

cdsbs d}b nhc`ribi(

Sbcynkh

Sbcynkh 3(3(23(3(2 ibgkhsy}dybs yldy ylb `nhbd} fnhnyb ckhy}k` vk`rgb dpp}kdclibgkhsy}dybs yldy ylb `nhbd} fnhnyb ckhy}k` vk`rgb dpp}kdcl

cdh ~nb`i b|p}bssnkhs yldy d}b dhd`kakrs yk ylksb kmydnhbi f}kg ylb Irldgb`!s

ylbk}bg gbylki( Ylns

ylbk}bg gbylki( Ylnsnsnsngpk}ydhy mbcdrsb ylb sdgb `nhbd}ngpk}ydhy mbcdrsb ylb sdgb `nhbd}NLC_NLC_d`ak}nylgsd`ak}nylgs

cdh

cdh mbmb bgp`k~bi rsnha gdh~ inffb}bhy gbylkis kf dpp}k|ngdynha ylb lbdybgp`k~bi rsnha gdh~ inffb}bhy gbylkis kf dpp}k|ngdynha ylb lbdy

ckhircynkh btrdynkh dhi mkrhid}~ ckhinynkhs

ckhircynkh btrdynkh dhi mkrhid}~ ckhinynkhs srcl gbylkis nhc`rib dsrcl gbylkis nhc`rib d

hrgb}ncd` fk}g

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<?

<? CLD_(3CLD_(3 GBYLKKS FK] GBYLKKS FK] IN]BCY LBIN]BCY LBDY CKHIRCYNKH DY CKHIRCYNKH _]KM@BG_]KM@BG

3(=

3(= IRLDGB@!S YLBK]BGIRLDGB@!S YLBK]BG

3(=(4

Ib}nvdynkhIb}nvdynkh kfkf Irldgb`!s Ylbk}bgIrldgb`!s Ylbk}bg

Irldgb`!s ylbk}bg cdh mb

Irldgb`!s ylbk}bg cdh mb ckhsnib}ckhsnib}bi ykbi ykmbmbd }bsr`y kf ylb p}nhcnp`b kf srpb}d }bsr`y kf ylb p}nhcnp`b kf srpb}

pksnynkh dhi ylrs ny

pksnynkh dhi ylrs nynsns kh`~ vd`ni fk} `nhbd} cdsbs( Ylb}b d}b sbvb}d` qd~s kfkh`~ vd`ni fk} `nhbd} cdsbs( Ylb}b d}b sbvb}d` qd~s kf

ib}nvnha ny khb k

ib}nvnha ny khb kf qlncf qlncl rsbs l rsbs @dp`dcb y}dhsfk}gs( @dp`dcb y}dhsfk}gs( Sbb Kunsnj ,]bfb}bSbb Kunsnj ,]bfb}bhcbhcb66p( 4>1.p( 4>1.

dhi

dhi @rnjkv ,]bfb}bh@rnjkv ,]bfb}bhcbcb11 399.(399.(Dhkylb} ib}nvdynkh rsbs ylb ckhcbpyDhkylb} ib}nvdynkh rsbs ylb ckhcbpykfkfsrpb}srpb}

pksnynkh: yldy

pksnynkh: yldynsnsylb gbylki rsbiylb gbylki rsbinhnh D}pdcn ,]bfb}bhcbD}pdcn ,]bfb}bhcb<< p(p( 3?1.3?1. dhi G~b}sdhi G~b}s

,]bfb}bhcb

,]bfb}bhcb>>p(p( 422.(422.(Ylb fk``kqnha ib}nvdynkh bgp`k~s ylb p}nhcnp`b kf srpb}Ylb fk``kqnha ib}nvdynkh bgp`k~s ylb p}nhcnp`b kf srpb}

pksnynkh dhi ny d`sk p}kircbs d ckhvbhnbhy hrgb}ncd` dpp}k|ngdynkh(

Irldgb`!s ylbk}bg bgp`k~s d -mrn`inha m`kcj- sk`rynkh qlncl

Irldgb`!s ylbk}bg bgp`k~s d -mrn`inha m`kcj- sk`rynkh qlncl rsbi qnylrsbi qnyl

ylb sr_b}pksnynkh p}nhcnp`b yk kmydnh ylb ybgpb}dyr}b

ylb sr_b}pksnynkh p}nhcnp`b yk kmydnh ylb ybgpb}dyr}bdydydh~ pknhy dhi yngb(dh~ pknhy dhi yngb(

Khb srcl sk`rynkh

Khb srcl sk`rynkhnsns0+E,}0+E,}y.y.qlnclqlnclnsnsfk} ylb ybgpb}dyr}b }nsb dy d pknhy } nh dfk} ylb ybgpb}dyr}b }nsb dy d pknhy } nh d

lbdy'ckhircynha mki~ irb yk ylb lbdy

lbdy'ckhircynha mki~ irb yk ylb lbdyf`r|f`r| K K y0Ky0K t,y.7

t,y.7 44 y8Ky8K ,3(=(4.,3(=(4.

Ylns

Ylnsnsnsskgbyngbs cd``bi d rhny sybp lbdyskgbyngbs cd``bi d rhny sybp lbdyf`r|f`r|k}k}bvbh d ckhsydhy rhny lbdybvbh d ckhsydhy rhny lbdyf`r|(f`r|(

Ylb ylb}gd` p}kpb}ynbs kf ylb mki~ d}b nhibpbhibhy kf ybgpb}dyr}b mry

Ylb ylb}gd` p}kpb}ynbs kf ylb mki~ d}b nhibpbhibhy kf ybgpb}dyr}b mry cdhcdhmbmb

frhcynkhs kf pksnynkh dhi ylb ybgpb}dyr}b insy}nmrynkh hbbi hky mb khb

ingbhsnkhd`(

ingbhsnkhd`( Fk}Fk} ylb ib}nvdynkh lb}bnh ylb kh`~ }btrn}bgbhyylb ib}nvdynkh lb}bnh ylb kh`~ }btrn}bgbhy nsnsyldy ylb p}byldy ylb p}b

sc}nmbi sr}fdcb lbdy

sc}nmbi sr}fdcb lbdyf`r| nsf`r| nsanvbhanvbhm~m~ylb p}kircyylb p}kircy t,s

t,sy.y. ,y.a,s.,y.a,s.

qlb}b

qlb}b nsnsd ckk}inhdyb gbdsr}bi d`kha ylb sr}fdcb( Fk} ckhvbhnbhcb ylb lbdyd ckk}inhdyb gbdsr}bi d`kha ylb sr}fdcb( Fk} ckhvbhnbhcb ylb lbdy f`r| ns

f`r| nsq}nyybh ds d frhcynkhq}nyybh ds d frhcynkhkfkfyngb kh`~(yngb kh`~(

Ylb sr}fdcb lbdy

Ylb sr}fdcb lbdyf`r|f`r| nsnsdpp}k|ngdybi nh ylb gdhhb} slkqh nh Fnar}bdpp}k|ngdybi nh ylb gdhhb} slkqh nh Fnar}b 3(4(3(4(

Ylb l

Ylb lbdy f`r|bsbdy f`r|bsdydyyngbsyngbs

t,y. t,y.

x x ' ( ( ( 9

x x ' ( ( ( 9 ' 5 ! ' ' ' ' ' ' 5 ! ' ' ' ' ' ! ' ' ' ' 5 ' ! ' ' ' ' 5 ' ! ' [ x £ ' ( ' ! ' [ x £ ' ( ' 4 4  FNAR]BFNAR]B3(4 3(4 Dpp}k|ngdyb Dpp}k|ngdyb }bp}bsbhydynkh}bp}bsbhydynkh

D`

D` D=D= DG[4DG[4 kfkft,y.t,y.m~m~ sybps nhsybps nhlbdylbdyLr|Lr|

SBC

SBC 3(=3(= IRLDGB@!SIRLDGB@!SYLBK]BGYLBK]BG

d}b rsbi yk }bp}bsbhy ylb lbdy f`r|bs mbyqbbh yngbs

d}b rsbi yk }bp}bsbhy ylb lbdy f`r|bs mbyqbbh yngbskfkf }bspbcynvb`~}bspbcynvb`~

KyKDy

KyKDy DNDN yKDu,±±±,yKDu,±±±, DG'NDG'N ykyk

!G

Ylb ck}}bspkhinha lbdy f`r|bs d}b ibhkybi

Ylb ck}}bspkhinha lbdy f`r|bs d}b ibhkybit`t` tutu(((( tGtG k}k} nhnhabhb}d`abhb}d`

<4 <4

,3(=(=. ,3(=(=.

Ylb nhnynd` ybgpb}dyr}b insy}nmrynkh

Ylb nhnynd` ybgpb}dyr}b insy}nmrynkhnhnh ylb mki~ylb mki~ nsns ylb ckhsydhy vd`rb kfylb ckhsydhy vd`rb kfYk(Yk(

Ylbh rsnha ylb p}nhcnp`b

Ylbh rsnha ylb p}nhcnp`bkfkf srpb}pksnynkh ylb ybgpb}dyr}bsrpb}pksnynkh ylb ybgpb}dyr}bdydy `kcdynkh } dy`kcdynkh } dy

yngb

yngb nsns ckgpksbickgpksbi kfkfckhy}nmrynkhs irb yk ylb lbdyckhy}nmrynkhs irb yk ylb lbdy f`r|f`r| ckgpkhbhys t`ckgpkhbhys t`

yl}kral

yl}kraltGtGnhc`rsnvb5nhc`rsnvb5

Y,}

Y,} .7.7 *t`Zcp,}*t`Zcp,}yGyG'Dk.'0+E,}'Dk.'0+E,}yGyG'DN.W'DN.W

*tuZ0+E,}

*tuZ0+E,}yG'Di'cp,}yG'Di'cp,} yG'DU.WyG'DU.W *tGZ0+E,}

*tGZ0+E,}yGyG'DG''DG'i'0+E,}i'0+E,}yGyG'DG.W'DG.W

qlb}b

qlb}b0+E,}0+E,}yGyG'DG.'DG. 0+E,}0+E,}?.7?(?.7?(

Rsnha btrd` yngb sybps dhi yngbs

Rsnha btrd` yngb sybps dhi yngbskfkf De7n(54D

De7n(54D :7?,4,:7?,4,((((

~nb`is5

e'

e'DnDn e(54D'e(54D'n(54D7,en(54D7,e :.(54D7De'n:.(54D7De'n

Ylbh Bt(

Ylbh Bt(,3(=(3.,3(=(3.cdh mb q}nyybh dscdh mb q}nyybh ds

,3(=(3. ,3(=(3. ,3(=(9. ,3(=(9. ,3 ,3 2.2. ,3(=(6. ,3(=(6. Fk} ylb `ngnynha cdsb

Fk} ylb `ngnynha cdsbkfkf(54D'*K(54D'*Kdhi fk} ddhi fk} dfn|bifn|bi yngbyngbyGyG yyBtBt ,3(=(6.,3(=(6. mbckgbsmbckgbs

ylb nhyba}d` ylb nhyba}d` ,3(=(1. ,3(=(1. F}kg ylb }b`dynkh F}kg ylb }b`dynkh d0+E,}

d0+E,} D.D. d0+E,}d0+E,}4'4'D.D. dD

dD dydy ,3(=(<.,3(=(<.

Irldgb`!s ylbk}bg ,skgbyngbs cd``bi Irldgb`!s nhyba}d`. mbckgbs

Y,}

Y,}4.7Yk*4.7Yk* t,D.t,D.d 0 + E , } x 5 ' D . d 0 + E , } x 5 ' D . iDiD ,3(=(>.,3(=(>.

Btrdynkh

Btrdynkh,3(=(>. ns,3(=(>. ns d lbdyd lbdyf`r|f`r| fk}gfk}gkfkfIrldgb`!s ylbk}bg: nyIrldgb`!s ylbk}bg: nynsnsd ckhvk`rynkhd ckhvk`rynkh

mbcdrsb ylb}b

mbcdrsb ylb}bnsnsd p}kircyd p}kircy kfkfyqk frhcynkhs khb kfyqk frhcynkhs khb kf dhi ylb kylb}dhi ylb kylb}kfkfy'D:y'D:

yldy

yldynsnsylb}bylb}bnsnsfk`inhafk`inhak}k}ckhvk`rynhackhvk`rynhakfkfkhb frhcynkh qnyl }bspbcy yk ylb kylb}(khb frhcynkh qnyl }bspbcy yk ylb kylb}(

Fk} d ybgpb}dyr}b'mdsbi fk}g kf Irldgb`!s ylbk}bg

Fk} d ybgpb}dyr}b'mdsbi fk}g kf Irldgb`!s ylbk}bg sbbsbb Bt(Bt( ,=(9(4.,=(9(4. dhidhi

]bfb}bhcbs 6

(3)

<=

<= CLD_(3 CLD_(3 GBYLKIGBYLKIS S FK] FK] IN]BCY IN]BCY LBDY LBDY CKHIRCYNKH _]KM@BGSCKHIRCYNKH _]KM@BGS

3(=(=

Hrgb}ncd`Hrgb}ncd`Dpp}k|ngdynkhDpp}k|ngdynkh Irldgb`!sIrldgb`!sYlbk}bgYlbk}bg D hrgb}ncd` d

D hrgb}ncd` dpp}k|ngpp}k|ngdynkh dynkh fk} Bt( ,3(fk} Bt( ,3(=(=(>.>.nsnskmydnhkmydnhbi f}kg Bt( ,3(bi f}kg Bt( ,3(=(=(6.( Hkyb y6.( Hkyb yldyldy 0p,}

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abhbkrs DhDh b|dgp`bb|dgp`bnsnsylb p}km`bg fk} d lk``kq c~`nhib}ylb p}km`bg fk} d lk``kq c~`nhib}

,}

KY.7_CKY.7_CdYdY a,}a,}y.y. d 0 } 0 md 0 } 0 m

d} k}

d} k} dydy

7t,y.

7t,y. rhjhkqh lbdyrhjhkqh lbdyf`r|f`r|

YN

d} d}

7lZY,my.'Y 7lZY,my.'Y((,y.W,y.W

YN

d} d} }7m}7m Y,} Y,}?.?. F,}.F,}. ,3 ,3 =3.=3. ,3(=(=9d. ,3(=(=9d. ,3(= ,3(==9m.=9m. ,3 ,3=(=2.=(=2. Ylb

Ylb bN8,}bN8,}y.y. p}km`bgp}km`bg nsns ylb sk`rynkh kf ylb p}km`bg kfylb sk`rynkh kf ylb p}km`bg kf dY+dtcdY+dtcqlb}bqlb}b t,y.7tc!t,y.7tc! Sbb Sbcynkh

Sbb Sbcynkh4(6(4(6(YlbYlbbN8,}bN8,}y.y.p}km`bgp}km`bgnsns

,}

db`ºdb`º pcpcdb`8db`8 ,3,3 =6.=6. d} k} d} k} dydy [ j [ jdb`8db`8 7 7 4 4 ,3(=(=1d.,3(=(=1d. k} k} }7}7

x x @ m 

7lb`8,m7lb`8,my.y. ,3(=(=1m.,3(=(=1m. cf8,} cf8,}?. 7 ??. 7 ? ,3,3=(=<.=(=<. Hkyb yldy ylb kh`~ hkhlkgkabhbkrs yb}g

Hkyb yldy ylb kh`~ hkhlkgkabhbkrs yb}gnsnsdy ylb lbdybi sr}fdcbdy ylb lbdybi sr}fdcb }7}7 YlbYlb b`8n

b`8n vd`rbvd`rb nsns ylb sk`rynkh kf Bts( ,3(=(=6.ylb sk`rynkh kf Bts( ,3(=(=6. ,3(=(=<. fk} ylb sbhsk} `kcdynkh dhi,3(=(=<. fk} ylb sbhsk} `kcdynkh dhi yngb

yngbynyn

Ylb s~gmk`

Ylb s~gmk` yGN,yGN, 7k7k }bp}bsbhys ylb cd`cr`dybi ybgpb}dyr}b fk} ylb gkib`}bp}bsbhys ylb cd`cr`dybi ybgpb}dyr}b fk} ylb gkib` dy yngb

dy yngbyGyGfk} ylb bsyngdybi lbdyfk} ylb bsyngdybi lbdyf`r|f`r| ckgpkhbhysckgpkhbhyst`t` t=t=±±±±±!±!tG'NtG'N mrymrytGtG nsns

sby btrd` yk ub}k(

sby btrd` yk ub}k( FkFk b|dgp`b fk} ylb gkib` anvbh m~ Btsb|dgp`b fk} ylb gkib` anvbh m~ Bts ,3(=(=3.',3(=(=2.,3(=(=3.',3(=(=2. jhkqh

jhkqh vd`rbvd`rb kfkfa,} y.a,} y.d}b rsbi nh Bt(d}b rsbi nh Bt( ,3(=,3(==3.=3.jhkqh vd`rbs kfjhkqh vd`rbs kfY(,y.Y(,y.d}b rsbid}b rsbi nh Bt( ,3(=

nh Bt( ,3(==9m=9m. dhi ylb jhk. dhi ylb jhkqh nhnynd` ybgpb}dyr}b insy}nmrynkhqh nhnynd` ybgpb}dyr}b insy}nmrynkhF,}.F,}.nsnsrsbi: ylbrsbi: ylb ybgpb}dyr}b dy ylb sbhsk} `kcdynkh

ybgpb}dyr}b dy ylb sbhsk} `kcdynkhnsnscd`cr`dybicd`cr`dybidydyyngbyngbyGyGqnyl ylbsb ckhinynkhsqnyl ylbsb ckhinynkhs dhi qnyl ylb lbdy f`r|

dhi qnyl ylb lbdy f`r|t,y.t,y.btrd` ykbtrd` yk fk} ?fk} ? N`yN`yt=t=fk}fk}N`N` ykyk=4`y=4`y(((( tGtG fk}

fk} dhidhi 7?7? fk}fk} 0yG!0yG! Ylb ybgpb}dyr}bYlb ybgpb}dyr}b

G*

i

(((( 7?7?nsnssngn`d}`~ fkrhisngn`d}`~ fkrhidydyylb sbhsk} `kcdynkhylb sbhsk} `kcdynkhdhidhidydy qnyl ylbqnyl ylb jhkqh

jhkqh tntn vd`rbs fk}vd`rbs fk} n7n7 (((( , G ' `, G ' ` dhi d`skdhi d`sk tG7tG*N7K(tG7tG*N7K( Fk}Fk} ylb cdsbylb cdsb a,} y.

a,} y. nh Bt(nh Bt(,3,3=(=3.=(=3.Y(,y.Y(,y. YkYknh Btnh Bt ,3(=(=9m. dhi,3(=(=9m. dhiY,}Y,}?.?. YkYknh Btnh Bt,3(=(=2.,3(=(=2. ylb

ylby`t7ky`t7kvbcyk} ns sngp`~ anvbh m~vbcyk} ns sngp`~ anvbh m~

G'N G'N tn``b`8G tn``b`8G n*n* YkYk n7 n7 G'N G'N Y`t Y`t k7k7 ``b`8G'n*4``b`8G'n*4 YkYk n7 n7 ,3(=(=>.,3(=(=>. G' G' tn``b`8G'n*}'N*Y tn``b`8G'n*}'N*Y n7 n7 SBC(3(3 INFFB]BHCB

SBC(3(3 INFFB]BHCBGBYLKISGBYLKIS <1<1

Ny

Ny nsns dpp}kp}ndyb yk ckgpd}b Bts(dpp}kp}ndyb yk ckgpd}b Bts( ,3,3 41.41.dhidhi ,3(=,3(=4>.(4>.( D`ylkral ylb s~gD`ylkral ylb s~g mk`nsg rsbi nh ylbsb yqk btrdynkhs

mk`nsg rsbi nh ylbsb yqk btrdynkhsnsnsvb}~ sngn`d} ylb yqk btrdynkhs d}b }bd``~vb}~ sngn`d} ylb yqk btrdynkhs d}b }bd``~ trnyb inffb}bhy( Btrdynkh

trnyb inffb}bhy( Btrdynkh ,3,3 41. ns41. nsinsp`d~bi gk}b c`bd}`~insp`d~bi gk}b c`bd}`~ m~m~ BtBt ,3,34(46.4(46.fk}fk} qlncl

qlncl ybgpb}dyr}bs d}b anvbh syd}ynha dy yngbybgpb}dyr}bs d}b anvbh syd}ynha dy yngb dhi ckhynhrnha rp yk yngbdhi ckhynhrnha rp yk yngb

yG

yG*('4!*('4! Gk}bkvb} ylb}bGk}bkvb} ylb}bnsns kh`~ khb lbdy nhprykh`~ khb lbdy nhpryykyk ylb mki~: hdgb`~ ylb rhylb mki~: hdgb`~ ylb rh jhkqh sr}fdcb lbdy f`r| dhi d`sk ylb nhnynd` ybgpb}dyr}b

jhkqh sr}fdcb lbdy f`r| dhi d`sk ylb nhnynd` ybgpb}dyr}bnsnsylb rhnfk}g vd`rb kfylb rhnfk}g vd`rb kf Yk

Yk BtrdynkhBtrdynkh,3,3=(4>.=(4>.nsnsgrcl gk}b abhb}d` dhi cdh nhc`rib ylb ckhinynkhs fk}grcl gk}b abhb}d` dhi cdh nhc`rib ylb ckhinynkhs fk} Bt

Bt ,3(=(46.,3(=(46.k}k} Bt( ,3(=(41Bt( ,3(=(41..

x 4 2 ! 

sbJnn`asbJnn`a444444

5:´q`d

4'f`5

*k*k BtrdynkhBtrdynkh ,3(=(4>.

,3(=(4>. cdh d`sk ckvb} ylb cdsb kf dh d}mny}d}~ ybgpb}dyr}b insy}nmrynkh dycdh d`sk ckvb} ylb cdsb kf dh d}mny}d}~ ybgpb}dyr}b insy}nmrynkh dy yngb

yngb dhidhid jhkqh lbdy f`r| dyd jhkqh lbdy f`r| dy|7|7 ZkZk kylb} kylb} hkhlkgkabhbhkhlkgkabhbkrs ckhinynkhskrs ckhinynkhs ds

dsslkqh nh Btsslkqh nh Bts ,3(=,3(==3.=3.dhidhi,3,3 =9.W(=9.W(

3(3

INFFB]BHCBINFFB]BHCB GBYLKISGBYLKIS Irldgb`!s ylbk}bg

Irldgb`!s ylbk}bgnsnsd pkqb}fr` ybclhntrb fk} sk`vnha d qnib vd}nby~ kf `nhbd}d pkqb}fr` ybclhntrb fk} sk`vnha d qnib vd}nby~ kf `nhbd} lbdy ckhircynkh p}km`bgs( Rhfk}yrhdyb`~ gdh~

lbdy ckhircynkh p}km`bgs( Rhfk}yrhdyb`~ gdh~ snyrdynkhs b|nsy nh qlnsnyrdynkhs b|nsy nh qlncl bnylb}cl bnylb} ,N.

,N. ylns ybclhntrb mbckgbs crgmb}skgbylns ybclhntrb mbckgbs crgmb}skgbk}k} ,=.,=. nyny nsns hky dpp`ncdm`bhky dpp`ncdm`b Ylb gksyYlb gksy sbvb}b `ngnydynkh ns fk} hkh`nhbd} p}km`bgs srcl ds fk} mkinbs qnyl ybgpb}dyr}b sbvb}b `ngnydynkh ns fk} hkh`nhbd} p}km`bgs srcl ds fk} mkinbs qnyl ybgpb}dyr}b ibpbhibhy ylb}gd` p}kpb}ynbs( Nh gdh~ l

ibpbhibhy ylb}gd` p}kpb}ynbs( Nh gdh~ lbdy y}dhsfb} p}km`bgs ylb ybgpb}dyr}bbdy y}dhsfb} p}km`bgs ylb ybgpb}dyr}b cldh

cldhab kf d mki~ b|pksbi yk ab kf d mki~ b|pksbi yk d lbdyd lbdyf`r|f`r| nsnssrffncnbhy`~ `d}ab yldy ylb cldhabs nhsrffncnbhy`~ `d}ab yldy ylb cldhabs nh ylb}gd` p}kpb}ynbs d}b dpp}bcndm`b( Fk}yrhdyb`~

ylb}gd` p}kpb}ynbs d}b dpp}bcndm`b( Fk}yrhdyb`~ hrgb}ncd` gbylkis cdh mbhrgb}ncd` gbylkis cdh mb rsbi

rsbi yk ckhvb}y ylb hkh`nhbd} pd}ynd` inffb}bhynd` btrdynkh kf lbdy ckhircynkhyk ckhvb}y ylb hkh`nhbd} pd}ynd` inffb}bhynd` btrdynkh kf lbdy ckhircynkh nhyk d s~syb

nhyk d s~sybg kf `nhbd} d`abm}dnc btrdynkhg kf `nhbd} d`abm}dnc btrdynkhs nhvk`vnha ylb ybgpb}dyr}s nhvk`vnha ylb ybgpb}dyr} dydyinsc}bybinsc}byb `kcdynkhs(

`kcdynkhs(

3(3(4

FnhnybFnhnyb Ckhy}k`Ckhy}k` Vk`rgbVk`rgb _}kcbir}b_}kcbir}bfkfk CkhsydhyCkhsydhy

_}kpb}y~

_}kpb}y~_`dhd}_`dhd} Abkgby}nbsAbkgby}nbs

Gdh~ gbylkis b|nsy fk} insc}bynunha pd}ynd` inffb}bhynd` btrdynkhs

Gdh~ gbylkis b|nsy fk} insc}bynunha pd}ynd` inffb}bhynd` btrdynkhs YqkYqkpkpr`d}pkpr`d} khbs d}b

khbs d}b,4.,4.fnhnyb inffb}bhcbsfnhnyb inffb}bhcbs dhidhi ,=.,=. fnhnyb b`bgbhysfnhnyb b`bgbhys DhDh d`yb}hdynvb dpp}kdcld`yb}hdynvb dpp}kdcl nh

nhqlncl ckhsb}vdynkhqlncl ckhsb}vdynkhkfkfbhb}a~bhb}a~nsnsdpp`nbi in}bcdpp`nbi in}bcy`~ yk ckhy}ky`~ yk ckhy}k` vk`rgbs` vk`rgbsnsnsdikpybidikpybi lb}b( Ylb fnhnyb ckhy}k` vk`rgb ,FCV. p}kcbir}b rsbs d ckhy}k` vk`rgb

lb}b( Ylb fnhnyb ckhy}k` vk`rgb ,FCV. p}kcbir}b rsbs d ckhy}k` vk`rgb kfkf

d}mny}d}~ dhi fnhnyb snub ds nh Fnar}b

d}mny}d}~ dhi fnhnyb snub ds nh Fnar}b 3(=3(= dhi ylb nhyba}d` fk}g kf ylb bhb}a~dhi ylb nhyba}d` fk}g kf ylb bhb}a~ btrdynkh ns dpp`nbi yk ylns ckhy}k` vk`rgb

btrdynkh ns dpp`nbi yk ylns ckhy}k` vk`rgb Ckhsb}vdynkh kCkhsb}vdynkh kf bf bhb}a~ fk} d sydynkhhb}a~ fk} d sydynkh d}~ sk`ni }btrn}bs yldy ylb srg

d}~ sk`ni }btrn}bs yldy ylb srgkfylbkfylb}dyb kf lbdy f`k}dyb kf lbdy f`kq dc}kss ylb q dc}kss ylb ckhy}k` ckhy}k` vk`rgbvk`rgb mkrhid}~ dhi ylb yngb }dyb kf cldhab

mkrhid}~ dhi ylb yngb }dyb kf cldhabkfkfbhb}a~ qnylnh ylb ckhy}k` vk`rgbbhb}a~ qnylnh ylb ckhy}k` vk`rgbnsns btrd` yk ylb }dyb

btrd` yk ylb }dyb dydy qlncl bhb}a~qlncl bhb}a~ nsnsp}kircbi qnylnh ylb ckhy}k` vk`rgbp}kircbi qnylnh ylb ckhy}k` vk`rgb NhNh btrdynkh fk}g ylb ckhsb}vdynkh

btrdynkh fk}g ylb ckhsb}vdynkhkfkfbhb}a~ cdh mb q}nyybh dsbhb}a~ cdh mb q}nyybh ds

ff

t(iD*

f}

ff

pbi'^pbi'^

ff

b!-i'^b!-i'^ ,3(3(4.,3(3(4.

'} '}

qlb}b

qlb}b dhi '^d}b ylb c`ksbi sr}fdcb d}bd dhi vk`rgb }bspbcynvb`~dhi '^d}b ylb c`ksbi sr}fdcb d}bd dhi vk`rgb }bspbcynvb`~kfkf lb ckhy}k`lb ckhy}k` vk`rgb

(6)

<<

<< CLD_(3 CLD_(3 GBYLKISGBYLKISFK] IN]BCY LBDY CKHIRCYNKH _]KM@BGSFK] IN]BCY LBDY CKHIRCYNKH _]KM@BGS ]bankh

]bankhkfkf nhyb}bsy nhyb}bsy

FNAR]B

FNAR]B3(=3(= Y~pncd` fnhnyb ckhy}k` vk`rgbY~pncd` fnhnyb ckhy}k` vk`rgb spbcnfnc bhb}a~ ,bhb}a~ pb} rhny gdss. dhi

spbcnfnc bhb}a~ ,bhb}a~ pb} rhny gdss. dhibgbgnsnsylb bhb}a~ p}kircynkh }dyb pb}ylb bhb}a~ p}kircynkh }dyb pb} rhny vk`rgb( Nh ylb ckhy}k` vk`rgb slkqh nh Fnar}b

rhny vk`rgb( Nh ylb ckhy}k` vk`rgb slkqh nh Fnar}b 3(=3(=d pd}yd pd}ykfkfylb ckhy}k`ylb ckhy}k` vk`rgb mkrhid}~ cknhcnibs qnyl ylb mkrhid}~

vk`rgb mkrhid}~ cknhcnibs qnyl ylb mkrhid}~kfkfylb mki~ylb mki~dhidhi ylb }bgdnhnhaylb }bgdnhnha ckhy}k` vk`rgb mkrhid}~

ckhy}k` vk`rgb mkrhid}~ nsns ckgp`byb`~ qnylnh ylb mki~ckgp`byb`~ qnylnh ylb mki~ Ckhsbtrbhy`~ ylbCkhsbtrbhy`~ ylb sr}fdcb nhyba}d`

sr}fdcb nhyba}d`kfylbkfylblbdy f`rlbdy f`r| | cdh nhvk`vb mkyl lbcdh nhvk`vb mkyl lbdy f`rdy f`r| f}kg b|yb}hd` | f}kg b|yb}hd` skr}cbsskr}cbs ,mkrhid}~ ckhinynkh

,mkrhid}~ ckhinynkhs. dhi s. dhi lbdy ckhircybilbdy ckhircybiykyk ylb anvbh ckhy}k` vk`rgb f}kgylb anvbh ckhy}k` vk`rgb f}kg d`` hbnalmk}nha ckhy}k

d`` hbnalmk}nha ckhy}k` vk`rgbs(` vk`rgbs(

Nh

Nhnys p}bsbhy fk}g Bt(nys p}bsbhy fk}g Bt(,3(3(4.,3(3(4.ns ykk abhb}d` yk ibgkhsy}dyb ylb ibydn`sns ykk abhb}d` yk ibgkhsy}dyb ylb ibydn`skfkfylbylb FCV p}kcbir}b( @by rs }bsy}ncy

FCV p}kcbir}b( @by rs }bsy}ncykr}kr}dyybhynkh yk khb'ingbhsnkhd`dyybhynkh yk khb'ingbhsnkhd` p`dhd}p`dhd}p}kmp}km `bgs dhi invnib ylb mki~

`bgs dhi invnib ylb mki~ kfkfnhyb}bsynhyb}bsy nhyknhyk nhc}bgbhysnhc}bgbhyskfkfbtrd` snub ,cd``bi b`btrd` snub ,cd``bi b` bgbhys. ds slkqh nh Fnar}b

bgbhys. ds slkqh nh Fnar}b3(3(3(3( Bdcl b`bgbhy lds nys kqh ylb}gd` p}kpb}ynbsBdcl b`bgbhy lds nys kqh ylb}gd` p}kpb}ynbs

dhi

dhi dh b`bgbhy mkrhid}~ cdh d`sk ck}}bspkhidh b`bgbhy mkrhid}~ cdh d`sk ck}}bspkhiykyk d gdyb}nd` nhyb}fdcb( Ylbd gdyb}nd` nhyb}fdcb( Ylb ckhy}k` vk`rgb mkrhid}nbs

ckhy}k` vk`rgb mkrhid}nbsd}d} clksbhclksbhykyk`nb`nbdydyylb gnip`dhbylb gnip`dhbkfkfbdcl b`bgbhy:bdcl b`bgbhy: ylns sb`bcynkh

ylns sb`bcynkhkfkfckhy}k` vk`rgb mkrhid}~ ns skgbqldy d}mny}d}~(ckhy}k` vk`rgb mkrhid}~ ns skgbqldy d}mny}d}~(YlbYlb clkncbclkncb fk} ckhy}k` vk`rgb mkrhid}nbs pb}gnys yqk inffb}bhy gdyb}nd`s

fk} ckhy}k` vk`rgb mkrhid}nbs pb}gnys yqk inffb}bhy gdyb}nd`s ykyk mb p}bsbhymb p}bsbhy qnylnh d snha`b ckhy}k` vk`rgb( Bdcl b`bgbhy ckhydnhs yqk hkibs

qnylnh d snha`b ckhy}k` vk`rgb( Bdcl b`bgbhy ckhydnhs yqk hkibs khkh dydybdclbdcl

mkrhid}~

mkrhid}~kfkfylb b`bgbhy qlncl d}b ylb b`bgbhy qlncl d}b nibhynfnnibhynfnbibim~m~d ,d , nh Fnar}bnh Fnar}b3(3(3(3( Fn}sy ylb abhb}d` ckhsb}vdynkh

Fn}sy ylb abhb}d` ckhsb}vdynkhkfkfbhb}a~ Bt(bhb}a~ Bt(,3(3(4.,3(3(4.nsnsdpp`nbidpp`nbiykykylb ckhy}k`ylb ckhy}k` vk`rgb sr}}krhinha hkib 4: Fnar}b

vk`rgb sr}}krhinha hkib 4: Fnar}b 3(9?3(9? p}kvnibs dh b|pdhibi vnbqp}kvnibs dh b|pdhibi vnbq kfkfylnsylns ckhy}k` vk`rgb(

ckhy}k` vk`rgb(YlbYlb}bsr`y}bsr`ynsns

dYN

d| D|`=D|`= iyiy

Ek

,3(3(=.,3(3(=.

qlb}b ylb bhb}a~ ckhybhy

qlb}b ylb bhb}a~ ckhybhynsnsanvbh m~anvbh m~b7cYb7cYdhidhib-!7K(b-!7K(FkFk ylb d}mny}d}~ ylb d}mny}d}~ nhyb}nk}nhyb}nk} hkib

hkib dhi ylb dhi ylb mdcjfmdcjfdcb dcb hkibhkib ,sbb Fnar}b,sbb Fnar}b 9m9mdhidhicc}bspbcy}bspbcynvb`~nvb`~. . dpp`ncdynkhdpp`ncdynkh

kf

kfylb ckhsb}vdynkhylb ckhsb}vdynkhkfkfbhb}a~ btrdynkh bhb}a~ btrdynkh ~nb`i~nb`i

dYN dYN

d| \E*\E*D|+=D|+= d|d| |}|}D|+=D|+= iyiy |}|}D|+=D|+= ,3(3(3.,3(3(3.

dYN i

dYN i f\Hf\H tH,y.*j

tH,y.*j *'i'*'i' pcYi|7KpcYi|7K

\H'D|+=

\H'D|+= ! | H ' D | + =! | H ' D | + = ,3(3,3(39.9.

Ylns ckhy}k` vk`rgb dpp}kdcl nhsr}bs yldy ylb lbdy ckhircybi

Ylns ckhy}k` vk`rgb dpp}kdcl nhsr}bs yldy ylb lbdy ckhircybi krykry kfkfkhbkhb

ckhy}k` vk`rgb

ckhy}k` vk`rgb nsns ckhircybi nhyk ylb diedcbhy ckhy}k` vk`rgbckhircybi nhyk ylb diedcbhy ckhy}k` vk`rgb Nh k}ib}Nh k}ib} ykyk bvd`rdyb ylb nhyba}d`s dhi ib}nvdynvbs nh Bts(

bvd`rdyb ylb nhyba}d`s dhi ib}nvdynvbs nh Bts( ,3(3(=.,3(3(=. ,3(3(9.,3(3(9.dhidhi ckhvb}y ylbgckhvb}y ylbg

| |pksnynkh[pksnynkh[

x x e 

} } ' '} } ' '

' '

N N N N B`bgbhy mkrhid}~ B`bgbhy mkrhid}~ , 7 x x ! 5 ! ! , 7 x x ! 5 ! ! 5 5 ! ! ! ! : ' 7 5 5 ! ! ! ! : ' 7 ' 5 5 E ! '' 5 5 E ! ' Ckhy}k`Ckhy}k` , vk`rgb , vk`rgb t,y.

t,y. B`bgbhyB`bgbhy mkrhid}~mkrhid}~

Hkib5 Hkib5HkibHkib N N = = x x ' x ' x x ' x ' x ' x ' x ' x x x x x  x x ' x ' x x ' x ' x ' x ' x ' x x x x x  ! 7 ' 7 ' 7 7 ! 7 ' 7 ' 7 7 ' 7 ' 7 x ' ' 7 ' 7 x ' 7 ' ' 5 5 5 7 ' ' 5 5 5 ' x ' x  t x y .  t x y . 

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H'H' FNAR]B

FNAR]B3(33(3 Khb'ingbhsnkhd` gkib` fk} p`dhd} Khb'ingbhsnkhd` gkib` fk} p`dhd} abkgby}abkgby}~ slkqnha b`bgbhy dhi ckhy}k` ~ slkqnha b`bgbhy dhi ckhy}k` vk`rgbvk`rgb mkrhid}nbs( mkrhid}nbs( ' ' ' , ' ' ' , 4 4 t , y . * t , y . *

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y}k` vk`rgbs ,d.,d. Ckhy}k` vk`rgb sr}}krhinhaCkhy}k` vk`rgb sr}}krhinha sr}fdcb hkib N :

sr}fdcb hkib N :,m.(,m.(ckhy}k` vk`rgb sr}}krhinhackhy}k` vk`rgb sr}}krhinha d}mny}d}~ nhyb}nk} hkib

d}mny}d}~ nhyb}nk} hkibe:e: ,c.(,c.( ckhy}k` vk`rgbckhy}k` vk`rgb sr}}krhinha

(7)

>?

>? CLD_(3CLD_(3 GBYLKISGBYLKISFK] IN]BCYFK] IN]BCYLBDYLBDYCKHIRCYNKHCKHIRCYNKH_]KM@BGS_]KM@BGS

nhyk rsbf

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dmkry ylb ybgpb}dyr}b p}kfn`b qnylnh bdcl b`bgbhy( Gdh~ dssrgpynkhs cdh mb

gdib ckhcb}hnha ylb b`bgbhy ybgpb}dyr}b p}kfn`b: lkqbvb} ylb gk}b pl~sncs

b|b}cnsbi ylb mbyyb}(

b|b}cnsbi ylb mbyyb}( DsDsdh b|dgp`b fk} d sybdi~'sydyb p`dhd} abkgby}~ qnyldh b|dgp`b fk} d sybdi~'sydyb p`dhd} abkgby}~ qnyl

spbc

spbcnfnbnfnbi ybgpb}dyr}bs i ybgpb}dyr}bs ds mkrhid}~ ckhinynkhs ds mkrhid}~ ckhinynkhs dhi ckhsydhydhi ckhsydhy j,j,ylb ybgpb}dyr}bylb ybgpb}dyr}b

p}kfn`b

p}kfn`bnsns`nhbd} qnyl pksnynkh( Ylrs fk} ylb y}dhsnbhy cdsb d `nhbd} ybgpb}dyr}b`nhbd} qnyl pksnynkh( Ylrs fk} ylb y}dhsnbhy cdsb d `nhbd} ybgpb}dyr}b

p}kfn`b

p}kfn`bnsnsdssrgbidssrgbifk}fk}ylb b`bgbhy(ylb b`bgbhy( FkFk dh b`bgbhy mkrhibidh b`bgbhy mkrhibi m~m~ \e\e x \ x \ e , x \ x \ e , 

ylb dssrgbi ybgpb}dyr}b

ylb dssrgbi ybgpb}dyr}b p}kfn`bp}kfn`bnsns Y,

Y, ,|'\e.,|'\e. Y(Y(E E ,|'|e[i,|'|e[i \ e ' `\ e ' `x \ x \ e x \ x \ e 

, \ e ' `

, \ e ' ` \e.\e. ,\e',\e'\e[\e[ ,3(3(2.,3(3(2. qlb}b

qlb}b 4e4e Y,|e.Y,|e. nsns d hkib pknhy ,k} hkid`. ybgpb}dyr}bd hkib pknhy ,k} hkid`. ybgpb}dyr}b BtrdynkhBtrdynkh ,3(3(2.,3(3(2. nsns

q}nyybh nh ylb fk}g kf d @da}dhandh nhyb}pk`dynkh pk`~hkgnd`( Ylb `kcd` lbdy

f`r| ns

f`r| nsibyb}gnhbi m~ inffb}bhyndynha Bt(ibyb}gnhbi m~ inffb}bhyndynha Bt( ,3(3(2.,3(3(2.dhi rsnha Fkr}nb}!s `dqdhi rsnha Fkr}nb}!s `dq jd jd ,4e'4e',4e'4e' t,|.7' t,|.7' ' : ' 7 ' j' : ' 7 ' j \e[`0\0\e\e[`0\0\e ,3(3(6.,3(3(6. ,N\ ,N\ \e'\e'`\e'\e'`

Ylb `nhbd} b`bgbhy ybgpb}dyr}b p}kfn`b p}kircbs d ckhsydhy lbdy

Ylb `nhbd} b`bgbhy ybgpb}dyr}b p}kfn`b p}kircbs d ckhsydhy lbdy f`r|f`r| qnylnhqnylnh

b`bgbhys: lkqbvb} ylb lbdy

b`bgbhys: lkqbvb} ylb lbdyf`r|f`r| cldhabs f}kg b`bgbhy yk b`bgbhy(cldhabs f}kg b`bgbhy yk b`bgbhy(

Dssrg

Dssrgnha yldy nha yldy ylb vk`rgby}nc lbdy cdpdcny~ylb vk`rgby}nc lbdy cdpdcny~,pc.,pc.nsnsd ckhsydhyd ckhsydhyfk}fk}bdcl b`bgbhybdcl b`bgbhy

d hrgb}ncd` b|p}bssnkh fk} ylb bhb}a~ syk}dab yb}g }btrn}bs ylb bvd`rdynkh kf

nhyba}d`s kf ylb fk}g

nhyba}d`s kf ylb fk}g Y,|.i|Y,|.i| NyNynsnsckhvbhckhvbhnbhy ynbhy yk pb}fk}g k pb}fk}g ylbsb nhyba}d`s kvb}ylbsb nhyba}d`s kvb}

pk}ynkhs kf b`bgbhys dhi ylbh dii ylb dpp}kp}ndyb ckhy}nmrynkh yk ylb ckhy}k`

vk`rgb bhb}a~ md`dhcb( Ylb yqk nhyba}d`s yldy kccr} d}b bvd`rdybi rsnha Bt(

vk`rgb bhb}a~ md`dhcb( Ylb yqk nhyba}d`s yldy kccr} d}b bvd`rdybi rsnha Bt( ,3(3(2. ,3(3(2.yk kmydnhyk kmydnh ,3(3(1. ,3(3(1. ,3(3(<. ,3(3(<. Hkyb yldy Bts(

Hkyb yldy Bts( ,3(3(1.,3(3(1. dhidhi ,3(3(<.,3(3(<. d}b p}kpk}ynkhd` yk ylb dvb}dab b`bgbhyd}b p}kpk}ynkhd` yk ylb dvb}dab b`bgbhy

ybgpb}dyr}b kvb}

ybgpb}dyr}b kvb}ld`fld`fkf ylb b`bgbhy(kf ylb b`bgbhy(

F}kg ylb fk}baknha `nhbd} b`bgbhy ybgpb}dyr}b p}kfn`bs ylb fnhnyb ckhy}k`

vk`rgb bhb}a~ md`dhcb fk} hkibs

vk`rgb bhb}a~ md`dhcb fk} hkibs 44 dhidhiH,H,d}bd}b ,Y

,Y'Y'Y D|D|

D|

D| 't,y.*pc't,y.*pc

=-iy

,n,n nYnY .7.7 ,3(3(>.,3(3(>. j,4e'4e*i

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D| D|

D| D| pcpc iyiy

D| D| *p

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,YH'4'Y D|D|

tH,y.'j

tH,y.'j D|D| *_C*_C ,9,9 H' `*nH' `*n H.7?H.7? ,3,33(44.3(44.

SBC(

SBC( 3(3 3(3 INFFB]INFFB]BHCBBHCBGBYLKISGBYLKIS >4>4 Ylbsb yl}bb btrdynkhs }bp}bsbhy d s~sybg kf

Ylbsb yl}bb btrdynkhs }bp}bsbhy d s~sybg kf fn}sy'k}ib} fn}sy'k}ib} k}inhd}~ inffb}bhyndk}inhd}~ inffb}bhynd

btrdynkhs

btrdynkhsnhnhyngb(yngb(M~M~dssrgnha dh b`bgbhy ybgpb}dyr}b p}kfn`b dhi nhyba}dynhadssrgnha dh b`bgbhy ybgpb}dyr}b p}kfn`b dhi nhyba}dynha

kry ylb spdynd` ibpbhibhcb ylb

kry ylb spdynd` ibpbhibhcb ylb p}kcbir}b ~nb`is d s~sybg kf k}inhd}~p}kcbir}b ~nb`is d s~sybg kf k}inhd}~

inffb}bhynd` btrdynkhs ,ds kppksbi yk d snha`b pd}ynd` inffb}bhynd` btrdynkh.(

Hkyb yldy bdcl kf ylb bhb}a~ syk}dab yb}gs

Hkyb yldy bdcl kf ylb bhb}a~ syk}dab yb}gs nhnh Bts(Bts(,3(3(>.,3(3(>. ,3(3(44.,3(3(44. ckhydnhs dckhydnhs d

ckhy}nmrynkh f}kg d hkib krysnib ylb ckhy}k` vk`rgb: ylns kccr}s mbcdrsb ylb

`nhbd} b`bgbhy ybgpb}dyr}b p}kfn`b ibpbhis kh yqk hkid` ybgpb}dyr}bs khb

kf qlncl `nbs krysnib ylb ckhy}k` vk`rgb kf nhyb}bsy( Ylb fk}baknha }bsr`ys d}b

skgbyngbs }bfb}}bi yk ds insy}nmrybi cdpdcnydhcb bffbcys mbcdrsb ylb ylb}gd`

cdpdcnydhcb kf d ckhy}k` vk`rgb gd~ mb insy}nmrybi kvb} ds gdh~ ds yl}bb hkibs(

Ylb fnhnyb inffb}bhcb gbylki

Ylb fnhnyb inffb}bhcb gbylki nsnsdhkylb}dhkylb}ybclhntrbybclhntrbfk}fk} d}}nvnha dy d s~sybgd}}nvnha dy d s~sybg

kf k}inhd}~ inffb}bhynd` btrdynkhs }bp}bsbhynha lbdy ckhircynkh qnylnh d sk`ni(

Ylns p}kcbir}b

Ylns p}kcbir}b nsns d`sk cd``bi `rgpbi cdpdcnydhcb mbcdrsb d`` kf ylb ckhy}k`d`sk cd``bi `rgpbi cdpdcnydhcb mbcdrsb d`` kf ylb ckhy}k`

vk`rgb ylb}gd` cdpdcnydhcb

vk`rgb ylb}gd` cdpdcnydhcb nsns`rgpbi dy ylb cbhyb} hkib pknhy fk} d`` nhyb}nk}`rgpbi dy ylb cbhyb} hkib pknhy fk} d`` nhyb}nk}

ckhy}k` vk`rgbs( Ylns

ckhy}k` vk`rgbs( Ylns nsns dcckgp`nslbidcckgp`nslbi m~m~ }bp`dcnha}bp`dcnha

,n

4e4e 4e.4e.m~m~ 4e4edhidhi ,n4e*n4e*i

,n4e*n4e*iqnylqnyl 4e4enh Bt(nh Bt( ,3(3(4?.:,3(3(4?.:fk} sr}fdcb ckhy}k` vk`rgbsfk} sr}fdcb ckhy}k` vk`rgbs ,n,n

mbckgbs

mbckgbs YNYN dhidhi ,n,n mbckgbsmbckgbs YH!YH! Diinynkhd` ibydn`s kh inffb}bhcbDiinynkhd` ibydn`s kh inffb}bhcb

gbylkis d}b dvdn`dm`b nh G~b}s> Sgnyl

gbylkis d}b dvdn`dm`b nh G~b}s> Sgnyl _dydhjd}=4 Dhib}skh by_dydhjd}=4 Dhib}skh by d`(==d`(==dhidhi Slnl_

Slnl_

Dhkylb} gbylki fk} ylb hrgb}ncd` sk`rynkh kf lbdy ckhircynkh p}km`bgs

Dhkylb} gbylki fk} ylb hrgb}ncd` sk`rynkh kf lbdy ckhircynkh p}km`bgs nsns

ylb fnhnyb b`bgbhy ,FB. gbylki(

ylb fnhnyb b`bgbhy ,FB. gbylki(N4N4 4949 _{Gdh~ gbylkis cdh mb rsbi yk ibvb`kp}_{Gdh~ gbylkis cdh mb rsbi yk ibvb`kp} fnhnyb

fnhnybb`bgbhy y~pb s~sybgs kf inffbb`bgbhy y~pb s~sybgs kf inffb}bhynd` btrdynkhs( Ylb Ad`b}jnh'y~pb }bhynd` btrdynkhs( Ylb Ad`b}jnh'y~pb gbylkigbylki

kf qbnalybi }bsnird`s

kf qbnalybi }bsnird`s nsnskhb kf ylb sngp`b} dpp}kdclbs dhi }btrn}bs yldy ylbkhb kf ylb sngp`b} dpp}kdclbs dhi }btrn}bs yldy ylb

nhyba}d` qbnalybi dvb}dab kf ylb pd}ynd` inffb}bhynd` btrdynkh mb ub}k kvb} skgb

ikgdnh( ikgdnh(FkFk b|dgp`bb|dgp`bfk}fk}d s`dmd s`dm

,dY

Y.

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spbcnfnbi( Ylb}b

spbcnfnbi( Ylb}bnsnsdh nhfnhnyb hrgmb} kf pkssnm`b qbnalynha frhcynkhs: ylb y}ncjdh nhfnhnyb hrgmb} kf pkssnm`b qbnalynha frhcynkhs: ylb y}ncj ns

nsyk clkksb d qbnalynha frhcynkh yldyyk clkksb d qbnalynha frhcynkh yldy anvbsanvbsakki }bsr`ysakki }bsr`ys D pkpr`d} D pkpr`d} qbnalqbnalynhaynha

frhcynkh

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\ e * ` ' \ \ e * ` ' \ \ e * ` \ e * ` ? ? d`` kylb}d`` kylb} ,3(3(43.,3(3(43.

Hkyb ylb sngn`d}ny~ mbyqbbh ylb qbnalynha frhcynkh

Hkyb ylb sngn`d}ny~ mbyqbbh ylb qbnalynha frhcynkh Qe,|.Qe,|.dhi ylb @da}dhandhdhi ylb @da}dhandh

nhyb}pk`dynkh pk`~hkgnd` nh Bt

nhyb}pk`dynkh pk`~hkgnd` nh Bt ,3,33(2.3(2. dhi yldy ylb qbnalynha frhcynkhdhi yldy ylb qbnalynha frhcynkh nsns

inffb}bhy fk} bdcl hkib

(8)

>=

>= CLD_(3 GBYLKKSCLD_(3 GBYLKKSFK]FK] IN]BCY LBDYIN]BCY LBDYCKHIRChKHCKHIRChKH_]KM@BGS_]KM@BGS

q,|. q,|.

FNAR]B 3(2

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}bsnird`s( pk}ynkh

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Ylb

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yk

yk ylb cbhyb} ybgpb}dyr}bylb cbhyb} ybgpb}dyr}b 4.4. YlbYlb FBFB btrdynkhs fk}btrdynkhs fk}ylbylbsr}fdcb hkibs d}bsr}fdcb hkibs d}b

,Y

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clksbhykykmbmbylbylbIn}dc ib`yd frhcynkhIn}dc ib`yd frhcynkh

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SBC(

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3(3[=

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lbdy f`r|mkrhid}~mkrhid}~ckhickhinynkh nynkh qds ckhsnib}bi( D lbdy f`rqds ckhsnib}bi( D lbdy f`r| anvbh m~ d ckhvbcynvb| anvbh m~ d ckhvbcynvb lbdy y}dhsfb}

lbdy y}dhsfb} ckbffncnbckbffncnbhyhydhidhid ybgpb}dyr}b inffb}bhcb i}nvnha pkybhynd` ns d`sk dd ybgpb}dyr}b inffb}bhcb i}nvnha pkybhynd` ns d`sk d ckggkh

ckggkh mkrhid}~mkrhid}~ckhinynkh(ckhinynkh(FkFk ylnsylns`dyyb} cdsb`dyyb} cdsbylbylb bhb}a~ md`dhcbbhb}a~ md`dhcbkhkh ylbylb ckhy}k` vk`rgb

ckhy}k` vk`rgbsr}}krhinha hkibsr}}krhinha hkib cdhcdhmb kmydnhbi in}bcy`~ f}kg Bt(mb kmydnhbi in}bcy`~ f}kg Bt(,3(3(4>.(,3(3(4>.(

,\

i ,_Y

i ,_Y*4!Y*4!Y.7.7 , Y  ' Y, Y  ' Y. * ' ' , Y -   ' Y  .. * ' ' , Y -   ' Y  . ,3(3(=3.,3(3(=3. D|

D| pcD|pcD|

Hkyb

Hkybyldyyldyckhvbcynvbckhvbcynvbmkrhid}~mkrhid}~ckhinynkhs ckhinynkhs nhvk`vnhvk`vb ylb b ylb sr}fdsr}fdcb ybgpb}dyr}bcb ybgpb}dyr}b

Ylb

YlbFCVFCVdpp}kdcl cdhdpp}kdcl cdhmb }bdin`~ b|ybhibi yk b`bgbhysmb }bdin`~ b|ybhibi yk b`bgbhyskfkfhkhrhnfk}g snubhkhrhnfk}g snub dhi inffb}nha gdyb}nd` p}kpb}ynbs: srcl d ckhy}k` vk`rgb ns slkqh nh Fnar}b

dhi inffb}nha gdyb}nd` p}kpb}ynbs: srcl d ckhy}k` vk`rgb ns slkqh nh Fnar}b3(6(3(6(

Gdyb}nd` Gdyb}nd` nhyb}fdcb nhyb}fdcb N! N! ,b* ,b*4.4. e* e* FNAR]B 3(6

(9)

>9

>9 CLD_(3CLD_(3 GBYLKIS FK] IN]BCY LBDY CKHIRCYNKH _]KM@BGSGBYLKIS FK] IN]BCY LBDY CKHIRCYNKH _]KM@BGS Ylb yqk diedcbhy b`bgbhys

Ylb yqk diedcbhy b`bgbhys d}b(d}b( ibhkybiibhkybi,b.,b.dhidhi,b*,b*4.4.qnyl bdcl ldvnha nys kqhqnyl bdcl ldvnha nys kqh ybgpb}dyr}b ibpbhibhy p}kpb}ynbs

ybgpb}dyr}b ibpbhibhy p}kpb}ynbs ,pc.`b.,pc.`b.dhidhi `b`b.(.(Dpp`~nha dh bhb}a~ md`dhcbDpp`~nha dh bhb}a~ md`dhcb `b

`b 4.'4.*44.'4.*4 [j[j`b`b _{4 . ' N ' 4 . * , p c . b , \}_{4 . ' N ' 4 . * , p c . b , \ } \ e [ N . x , 4 ! 4 . [ 4 }_{} \ e [ N . x , 4 ! 4 . [ 4 }*+44..*+44.. \ e * ` ' |

\ e * ` ' | \e'\e[4\e'\e[4 iyiy

pc.`b*

pc.`b*N.,\e*N.,\e* ' \ e .' \ e . ,+44.*4!4.*,+44.*4!4.*

i7K

,3(3(=9.,3(3(=9. Ylb b`bgbhy ylb}gd` ckhircynvny~ ns bvd`rdybi

Ylb b`bgbhy ylb}gd` ckhircynvny~ ns bvd`rdybidydyylb gni'p`dhb ylb gni'p`dhb kf bdcl b`bgbhy:kf bdcl b`bgbhy: fk} d `nhbd} b`bgbhy ybgpb}dyr}b p}kfn`b ylb dpp}kp}ndyb ybgpb}dyr}b fk} fk} d `nhbd} b`bgbhy ybgpb}dyr}b p}kfn`b ylb dpp}kp}ndyb ybgpb}dyr}b fk} b`'b`' bgbhy

bgbhy ,b.,b.nsns `b`b_{.7,4.[4 *4..+=( Ylb}b d}b sbvb}d` clkncbs fk} ylb dpp}kp}ndyb}_{.7,4.[4 *4..+=( Ylb}b d}b sbvb}d` clkncbs fk} ylb dpp}kp}ndyb} ybgpb}dyr}b

ybgpb}dyr}bdydy qlnclqlnclykyk bvd`rdyb ylb vk`rgby}nc lbdy cdpdcny~( Ylb sngp`bsybvd`rdyb ylb vk`rgby}nc lbdy cdpdcny~( Ylb sngp`bsy p}kcbir}b

p}kcbir}b nsns yk rsb ylb dvb}dab b`bgbhy ybgpb}dyr}b yk bvd`rdybyk rsb ylb dvb}dab b`bgbhy ybgpb}dyr}b yk bvd`rdyb ,pc.`b.,pc.`b.dhidhi dssnah ylns vd`rb yk mkyl ld`vbs

dssnah ylns vd`rb yk mkyl ld`vbs kfkfylb b`bgbhy( D s`naly`~ gk}b ckgp`ncdybiylb b`bgbhy( D s`naly`~ gk}b ckgp`ncdybi dpp}kdcl

dpp}kdcl nsns yk ckgpyk ckgp ryb ylb dvb}dab ybgpb}dyr}b kryb ylb dvb}dab ybgpb}dyr}b k f bdf bdcl ld`f kf dh b`bgbhy dhicl ld`f kf dh b`bgbhy dhi bvd`rdyb ylb vk`rgby}nc lbdy cdpdcny~

bvd`rdyb ylb vk`rgby}nc lbdy cdpdcny~ dydy ylns ybgpb}dyr}b(ylns ybgpb}dyr}b( Fk}Fk} b|dgp`b ylbb|dgp`b ylb }naly ld`f

}naly ld`fkfkfb`bgbhyb`bgbhy ,b.,b.ckhy}nmrybsckhy}nmrybsykykckhy}k` vk`rgb dhi ylb dvbckhy}k` vk`rgb dhi ylb dvb}dab y}dab ybgpb}bgpb} dyr}b

dyr}b kf ylns ld`f kf b`bgbhykf ylns ld`f kf b`bgbhy,b.,b.nsns f x . 

f x . 

7 ` Z f

`b`b* 4.W* 4.W74Zy,4.'474Zy,4.'4 4..4.. * 4.W* 4.W 7n4.*%4.'4

7n4.*%4.'4 ,3(3(=2.,3(3(=2.

qlb}b ylb srmsc}npy

qlb}b ylb srmsc}npy nhincdybnhincdybs }naly s }naly ld`fld`fkfkfb`bgbhyb`bgbhy,b.(,b.(Sngn`d}`~ fk} ylb `bfySngn`d}`~ fk} ylb `bfy ld`f

ld`fkfkfb`bgbhyb`bgbhy,b,b 4.4.ylb dvb}dab ybgpb}dyr}bylb dvb}dab ybgpb}dyr}b nsns f}

f} N.N.744.*%4.*744.*%4.* ,3(3(=6.,3(3(=6.

Dy ylns pknhy d qk}i kf cdrynkh

Dy ylns pknhy d qk}i kf cdrynkh nsns dpp}kp}dpp}kp} ndyb fk} ylb bvd`rdynkh kf ybgpb}dyr}bndyb fk} ylb bvd`rdynkh kf ybgpb}dyr}b ibpbhibhy ylb}gd` p}kpb}ynbs( Gksy ylb}gd` p}kpb}ynbs d}b jhkqh kh`~ qnylnh ibpbhibhy ylb}gd` p}kpb}ynbs( Gksy ylb}gd` p}kpb}ynbs d}b jhkqh kh`~ qnylnh 2" dy mbsy( Ckhsbtrbhy`~ ny ns hky pd}yncr`d}`~ f}rnyfr` yk ibvb`kp lnal`~ 2" dy mbsy( Ckhsbtrbhy`~ ny ns hky pd}yncr`d}`~ f}rnyfr` yk ibvb`kp lnal`~ skplnsyncdybi ybclhntrbs yk p}bcnsb`~ ldhi`b ybgpb}dyr}b'ibpbhibhy ylb}gd` skplnsyncdybi ybclhntrbs yk p}bcnsb`~ ldhi`b ybgpb}dyr}b'ibpbhibhy ylb}gd` p}kpb}ynbs yldy d}b jhkqh ngp}bcnsb`~( Gdh~ yngbs ylb sngp`bsy dpp}kdcl p}kpb}ynbs yldy d}b jhkqh ngp}bcnsb`~( Gdh~ yngbs ylb sngp`bsy dpp}kdcl nsns gk}b yldh dibtrdyb(

gk}b yldh dibtrdyb(

3(3(3

Hrgb}ncd`Hrgb}ncd` YbclhntrbsYbclhntrbsfkfk Sk`vnhaSk`vnha S~sybgsS~sybgs Fn}sy'K}ib}

Fn}sy'K}ib}K}inhd}~ Inffb}bhynd`K}inhd}~ Inffb}bhynd` BtrdynkhsBtrdynkhs

Nh p}nhcnp`b dh dhd`~yncd` sk`rynkh kf ylb s~sybg kf bhb}a~ md`dhcb Bts( Nh p}nhcnp`b dh dhd`~yncd` sk`rynkh kf ylb s~sybg kf bhb}a~ md`dhcb Bts( ,3(3(4>.,3(3(4>. ,3(3(=4.

,3(3(=4. ns pkssnm`b( Lkqbvb} hrgb}ncd` ybclhntrbs kffb} sk`rynkhsns pkssnm`b( Lkqbvb} hrgb}ncd` ybclhntrbs kffb} sk`rynkhs ykyk gk}bgk}b abhb}d` p}km`bgs dhi cdh mb }bdin`~ b|ybhibi yk ylb ybgpb}dyr}b'ibpbhibhy abhb}d` p}km`bgs dhi cdh mb }bdin`~ b|ybhibi yk ylb ybgpb}dyr}b'ibpbhibhy ylb}gd` p}kpb}ynbs( Hr

ylb}gd` p}kpb}ynbs( Hr gb}krs gb}krs hrgb}ncdhrgb}ncd` ybclhntrbs d}b ` ybclhntrbs d}b dvdn`ddvdn`dm`b(m`b(

Khb kf ylb sngp`b} ybclhntrbs ns ylb Br`b} ,k} fk}qd}i inffb}bhcb FK. Khb kf ylb sngp`b} ybclhntrbs ns ylb Br`b} ,k} fk}qd}i inffb}bhcb FK. gbylki qlncl cdh mb ibvb`kpbi f}kg d Yd~`k} sb}nbs b|pdhsnkh( @by

gbylki qlncl cdh mb ibvb`kpbi f}kg d Yd~`k} sb}nbs b|pdhsnkh( @by r,y.r,y.mb dmb d frhcynkh kf yngb yldy sdynsfnbs ylb fn}sy'k}ib} k}inhd}~ inffb}bhynd` btrdynkh frhcynkh kf yngb yldy sdynsfnbs ylb fn}sy'k}ib} k}inhd}~ inffb}bhynd` btrdynkh

ir ir iy

iy f,rf,ry.y. ,3(3(=1.,3(3(=1.

SBC(

SBC(3(33(3 INFFB]BHCB GBYLKISINFFB]BHCB GBYLKIS B|pdhinha

B|pdhinhaR,`R,` NP`.NP`.nhnh d Yd~`k} sb}nbs dmkry yngbd Yd~`k} sb}nbs dmkry yngb``anvbsanvbs iR,`.

iR,`. r,y*`Py.7R,`.*

r,y*`Py.7R,`.*---iy---iy NP`*NP`*

((((

Nf ylb yb}gs

Nf ylb yb}gs?,`Py?,`Py d}b nahk}bi ylbhd}b nahk}bi ylbhr,yr,y NPy.NPy.nsns anvbhanvbh m~m~ r,y

r,y NPy.NPy.ur,y.*ur,y.*fZr,y.fZr,y.`W`Py`W`Py Nf

Nf r,y(.r,y(.nsns ibhkybi dsibhkybi dsr(r( ylbh Bt( ,3(3(=<. mbckgbsylbh Bt( ,3(3(=<. mbckgbs

R( R( 7r(*7r(* f,r( y(.`Py7r(*f,r( y(.`Py7r(*

x x N ( ` P ` 

,FK.,FK. >6 >6 ,3(3(=<. ,3(3(=<. ,3(3(=>. ,3(3(=>. ,3(3(3?. ,3(3(3?. Ylb d`ak}nylg anvbh

Ylb d`ak}nylg anvbh m~m~ Bt( ,3(3(3?.Bt( ,3(3(3?. nsns slkqhslkqh nhnh Fnar}b 3(1: nyFnar}b 3(1: ny nsns sngp`~ ylbsngp`~ ylb b|y}dpk`dynkh kf ylb s`kpb

b|y}dpk`dynkh kf ylb s`kpbdydypknhy ,rh!pknhy,rh!yh.yh. ykyk,r,r N,N,yh*yh* i(i(DsDs dh b|dgp`b kf ylbdh b|dgp`b kf ylb

Br`b} gbylki ny

Br`b} gbylki ny nsns dpp`nbi yk Bt(dpp`nbi yk Bt( ,3(3(4>.,3(3(4>. qnyl +474+=qnyl +474+=4!7?4!7?,@C.( Snhcb ylb,@C.( Snhcb ylb srmsc}npy

srmsc}npykhkh }bp}bsbhys hkib hrgmb} d srpb}sc}npy}bp}bsbhys hkib hrgmb} d srpb}sc}npy nsns rsbirsbi ykyknhincdyb yngbnhincdyb yngb

h`P`

Ye Ye YeYe =p,Ye=p,Ye

Y n . * x 

pcr| pcr| ,3(3(34.,3(3(34. qlb}b

qlb}b p7d(`Py+`P|p7d(`Py+`P| nsns d Fkr}nb} hrgmb} mdsbid Fkr}nb} hrgmb} mdsbi khkh ylbylb y n g b ' s p d c x y n g b ' s p d c x (a}ni( Ylb(a}ni( Ylb Br`b} gbylki fk} ylb @C fk}gr`dynkh

Br`b} gbylki fk} ylb @C fk}gr`dynkh nsns d`sk jhkqh ds ylb b|p`Ncny gbylkid`sk jhkqh ds ylb b|p`Ncny gbylki snhcb

snhcbYeYe 4 nh Bt(4 nh Bt( ,3(3(34.,3(3(34. cdh mb q}nyybh ds dh cdh mb q}nyybh ds dh b|p`ncb|p`ncny frhcynkh kf jhkqh ny frhcynkh kf jhkqh ybgpb}ybgpb} dyr}bs kh`~ dy yngb

dyr}bs kh`~ dy yngb h:h:dhkylb} hdgbdhkylb} hdgb nsns ylb fk}qd}i inffb}bhcb gbylki mbcdrsbylb fk}qd}i inffb}bhcb gbylki mbcdrsb ylb yngb ib}nvdynvb

ylb yngb ib}nvdynvb nsns }bp`dcbi}bp`dcbi m~m~ d fk}qd}i yngb inffb}bhcb( B|p`ncny }bsr`ys d}bd fk}qd}i yngb inffb}bhcb( B|p`ncny }bsr`ys d}b d`sk kmydnhbi f}kg Bts( ,3(3(=?. dhi ,3(3(=4. fk} ylb @C fk}gr`dynkh(

d`sk kmydnhbi f}kg Bts( ,3(3(=?. dhi ,3(3(=4. fk} ylb @C fk}gr`dynkh( Ds

Dscdh mb sbbh f}kg Fnar}bcdh mb sbbh f}kg Fnar}b 3(13(1 ylb Br`b} gbylki rhib}p}bincys ylb ybgpb}ylb Br`b} gbylki rhib}p}bincys ylb ybgpb} dyr}b nf ylb y}rb sk`rynkh

dyr}b nf ylb y}rb sk`rynkh nsns ckhcdvb rpqd}i( Nh dh ckhcdvb rpqd}i( Nh dh dyybgpy yk dyybgpy yk ngp}kvb sydmn`nngp}kvb sydmn`ny~ dy~ d mdcjqd}i yngb inffb}bhcb ,MK.

mdcjqd}i yngb inffb}bhcb ,MK. nsns kfybh rsbi: dhd`kakrs yk Bt(kfybh rsbi: dhd`kakrs yk Bt( ,3(3(=<.,3(3(=<. ylbylb

r,y. r,y. !+!+ s N K p b R x * `  s N K p b R x * `  B|y}dpk`dynkh kf B|y}dpk`dynkh kf s`kpb s`kpb z,rhyz,rhy FNAR]B

FNAR]B3(13(1 SclbgdyncSclbgdynckfkfylb Br`b} ,fk}qd}i inffb}bhcb. dhi ngp`ncny ,mdcjqd}i inffb}bhcb.ylb Br`b} ,fk}qd}i inffb}bhcb. dhi ngp`ncny ,mdcjqd}i inffb}bhcb. gbylkis(

(10)

>6

>6 CLD_(3CLD_(3 GBYLKISGBYLKISFK] IN]BCY LBDY CKHIRCYNKH _]KM@BGSFK] IN]BCY LBDY CKHIRCYNKH _]KM@BGS

btrdynkh btrdynkhnsns (( (( N`yN`y Rk7Rk*`'rk*`ry*Rk*4 Rk7Rk*`'rk*`ry*Rk*4

=4'±±±

3(3(3=.3(3(3=. Hba`bcynha yb}gs kf

Hba`bcynha yb}gs kf?,``y?,``y ..ylb mdcjqd}i inffb}bhcb nhyba}dyk} anvbsylb mdcjqd}i inffb}bhcb nhyba}dyk} anvbs

,3(3(33. ,3(3(33.

Ylb mdcjqd}i yngb inffb}bhcb nhyba}dyk}

Ylb mdcjqd}i yngb inffb}bhcb nhyba}dyk} nsns d`sk jhkqh ds ylbd`sk jhkqh ds ylb fr``~fr``~ ngp`ncnyngp`ncny

gbylki mbcdrsb ylb }naly'ldhi snib ckhydnhs ylb rhjhkqh

gbylki mbcdrsb ylb }naly'ldhi snib ckhydnhs ylb rhjhkqh N(N( D cbhy}d`D cbhy}d` inffb}bhcb ,CI. yngb ib}nvdynvb

inffb}bhcb ,CI. yngb ib}nvdynvbnsns jhkqh yk mb gk}b dccr}dyb ,rhib} cb}ydnhjhkqh yk mb gk}b dccr}dyb ,rhib} cb}ydnh

ckhinynkh

ckhinynkhs. yldh s. yldh bnylb} ylb bnylb} ylb fk}qdfk}qd}i}ik}k} mdcjqd}i inffb}bhcb dhi cdhmdcjqd}i inffb}bhcb dhi cdhmbmbib}nvbiib}nvbi

f}kg ylb fk``kqnha Yd~`k} sb}nbs b|pdhsnkhs5

f}kg ylb fk``kqnha Yd~`k} sb}nbs b|pdhsnkhs5 N`y

N`y r-r-,N`y.=,N`y.= r K * N + = 7 r k * r x = * = x 

r K * N + = 7 r k * r x = * = x 

=

*

(((

,3(3(39.,3(3(39.  N`y

 N`y R5*R5* ,N`y.=,N`y.= *N+47R

*N+47R *N'R*N'R *4*4 *Y*Y

=

((

,3(3(32.,3(3(32.

Btrdynha ylbsb yqk b|p}bssnkhs dhi sk`vnha fk}

Btrdynha ylbsb yqk b|p}bssnkhs dhi sk`vnha fk} anvbs ylb cbhy}d` anvbs ylb cbhy}d` inffb}inffb}bhcbbhcb

nhyba}dyk}

,3(3(36. ,3(3(36.

qlncl

qlnclnsnsd`sk jhkqh ds ylb C}dhj'Hnck`skh gbylki( vkh ]ksbhmb}ad`sk jhkqh ds ylb C}dhj'Hnck`skh gbylki( vkh ]ksbhmb}a ibsc}nmbsibsc}nmbs

ylb C}dhj'Hnck`skh p}kcbir}b ds srccbssnvb dpp`ncdynkhs kf ylb fk}qd}i dhi

mdcjqd}i nhyba}dyk}s( Ylb fk}qd}i mdcjqd}i dhi cbhy}d` inffb}bhcb nhyb

a}dyk}s cdh d`` mb ckgmnhbi nhyk d abhb}d` nhyba}dyk} ,AN. ds fk``kqs5

a}dyk}s cdh d`` mb ckgmnhbi nhyk d abhb}d` nhyba}dyk} ,AN. ds fk``kqs5 Z K R x * N 

Z K R x * N * , 4 ' ? . r x W ` ` y * , 4 ' ? . r x W ` ` y 

Ylb yl}bb spbcnd` cdsbs d}b5

?7?

?7? fk}qd}i fk}qd}i inffb}binffb}bhcbhcbk}k}Br`b}Br`b} ?7=!

?7=! cbhy}d` cbhy}d` inffb}binffb}bhcbhcbk}k}C}dhj'Hnck`skhC}dhj'Hnck`skh ?7

?744 mdcjqd}i mdcjqd}i inffb}binffb}bhcbhcbk}k}fr``~fr``~ngp`ncnyngp`ncny

3(3(9

Abhb}d`Abhb}d`Fk}gFk}g Inffb}bhcbInffb}bhcbBtrdynkhsBtrdynkhs

fk

LbdyLbdy

Ckhircynkh

Ckhircynkhnhnh _`dhd}_`dhd} Mki~Mki~

,3(3(31. ,3(3(31.

,3(3(3<. ,3(3(3<.

Ylb abhb}d` nhyba}dyk} anvbh

Ylb abhb}d` nhyba}dyk} anvbhm~m~ Bt(Bt(,3(3(31.,3(3(31.fk} fn}sy'k}ib} btrdynkhs ckhvb}ysfk} fn}sy'k}ib} btrdynkhs ckhvb}ys

dh k}inhd}~ inffb}bhynd` btrdynkh nhyk d snha`b inffb}bhcb btrdynkh( Ylb hb|y

sybp

sybpnsns yk ckhvb}y ylb s~sybgyk ckhvb}y ylb s~sybgkfkfk}inhd}~ inffb}bhynd` btrdynkhs Bts(k}inhd}~ inffb}bhynd` btrdynkhs Bts(,3(3(4>.,3(3(4>. ,3(3

,3(3=4.=4. nhyk d s~sybgnhyk d s~sybg kfkf d`abm}dnc inffb}bhcb btrdynkhs( Ylb p}kcbir}b fk}d`abm}dnc inffb}bhcb btrdynkhs( Ylb p}kcbir}b fk}

dpp`~nha ylb AN Bt(

dpp`~nha ylb AN Bt(,3(3,3(331.31.nsnsyk bvd`rdyb ylb inffb}bhynd` btrdynkh dy yngbsyk bvd`rdyb ylb inffb}bhynd` btrdynkh dy yngbs

4 dhi

4 dhihhgr`ynp`~ ylbsb btrdynkhsgr`ynp`~ ylbsb btrdynkhsm~m~ dhidhi,4,4 ?.,?.,}bspbcynvb`~ dhi dii ylb}bspbcynvb`~ dhi dii ylb

yqk btrdynkhs( Rsnha

yqk btrdynkhs( RsnhaBtBt ,3(3(4>.,3(3(4>.ds dh ds dh b|dgp`b anvbb|dgp`b anvb

SBC(

SBC(3(3 3(3 INFFB]BINFFB]BHCB HCB GBYLKIGBYLKI >1>1

d( d( ?*?* ,]Y ,]Y .?*4.?*4 [ , Y k * ` [[ , Y k * ` [Y x * N . * KY x * N . * K iy iy N!N! N`|4N`|4 pc``|pc``| K!

K! ,fE,fE N*~YN*~Y.? 7' <!.? 7' <! ((((d(d(

= , Y x ' Y x . * ? ! 

t5t5

pcr| pcr|

qlb}b

qlb}b<!<! 4 4 dhi dhi ylb srpb}sc}npy h gbdhs bvd`rdybiylb srpb}sc}npy h gbdhs bvd`rdybidydyyngbyngbyk±yk± Diinha ylbDiinha ylb

fk}ba

fk}baknha yqk btknha yqk btrdynkhrdynkhs anvbss anvbs i

i d(d(

,fEY

,fEY *~Y4.?* 4*~Y4.?* 4*<*< 'i ,fEY'i ,fEY *~Y4.?7*~Y4.?7 , Y x * , Y x * 4 4 Y x * Y x * N.N. iy iy r\r\ '' '' _{, Y x }_{, Y x }

Y x . * x 

,Kt-*,Kt-* *<!t-.*<!t-. ,3(3(3>.,3(3(3>. N`| N`| pcr|pcr|

Ylb abhb}d` nhyba}dyk} cdh mb dpp`nbi in}bcy`~ yk ylb `bfy'ldhi snib kfBt(

Ylb abhb}d` nhyba}dyk} cdh mb dpp`nbi in}bcy`~ yk ylb `bfy'ldhi snib kfBt(,3(3(3>.,3(3(3>.

qnyl

qnylylb }bsr`yylb }bsr`y Yfy*

Yfy*4 [4 [ YK.YK. ,Y,Y YK.YK.

fE

fE = =

N`y

N`y N`yN`y

,3(3(9?. ,3(3(9?.

qlb

qlb}b fk} ckhvbhnbhcb y}b fk} ckhvbhnbhcb ylb fk``kqnha ibfnhnynkhlb fk``kqnha ibfnhnynkhnsnsbgp`k~bibgp`k~bi t-*b7

t-*b7KtK*KtK* *K!t-*K!t- ,3(3,3(394.94.

Btrdynkh

Btrdynkh,3(3(9?.,3(3(9?.cdh mb cdh mb sngp`nfnsngp`nfnbi yk bi yk ~nb`i~nb`i

N`y N`y , p K * f E . Y x * N [ , p K ' ~ . Y x * 

, p K * f E . Y x * N [ , p K ' ~ . Y x *  ',pK!',pK!' f E . Y x ' f E . Y x *,pK!*,pK!* ~ . Y x * ~ . Y x  '''-D'''-D_pcr|_pcr|t?*bt?*b ,3(3(9=.,3(3(9=.

Dpp`~nh

Dpp`~nha yla yl ANANyk Bts(yk Bts(,3(3(=?.,3(3(=?.dhidhi,3(3(=4.,3(3(=4.anvbsanvbs

' , p K ' ~ . Y e x 5 

' , p K ' ~ . Y e x 5 *=,pK**=,pK*fE.Y}fE.Y}4[,pK'~.YL54[,pK'~.YL57,p<!7,p<!*~.Ye[4*~.Ye[4 *=,fE

*=,fE'pK!.Ye*,p<!'pK!.Ye*,p<!*~.Ye**~.Ye*N,N, e7=e7=33(((( ,3(3(93.,3(3(93.

N`y N`y

' , p K ' ~ . Y H x 4 4 

' , p K ' ~ . Y H x 4 4 *,pK*fE.YH*N 7,pK!*,pK*fE.YH*N 7,pK!*~.Y*~.Y *,fE*,fE pK!.YH'pK!.YH'' ' : '' ' : '_pcr|_pcr|tH*6tH*6 ,3(3(99. ,3(3(99.

Btrdynkhs

Btrdynkhs,3(3(9=.,3(3(9=. ,3(3,3(399.99. fk}g d `nhbd} s~sybg kf H d`abm}dnc btrdynkhs qnylfk}g d `nhbd} s~sybg kf H d`abm}dnc btrdynkhs qnyl

H rhjhkqhs( Ylbsb d`abm}dnc btrdynkhs ldvb d vb}~ spbcnd` sy}rcyr}b yldy

H rhjhkqhs( Ylbsb d`abm}dnc btrdynkhs ldvb d vb}~ spbcnd` sy}rcyr}b yldy nsns

jhkqh ds y}nindakhd` dhi

jhkqh ds y}nindakhd` dhinsnsmbsy vnsrd`nubimbsy vnsrd`nubim~m~q}nynha ylbg nh gdy}n| fk}g fk}q}nynha ylbg nh gdy}n| fk}g fk}

ckhsydhy ylb}gd`

ckhsydhy ylb}gd` p}kpb}ynbp}kpb}ynbss pK*fE pK*fE ',pK'~.',pK'~. ',pK'~. ',pK'~. =,pK*5_.=,pK*5_. ',pK'~.',pK'~. Y H x P  Y H x P  ',pK'~. ',pK'~. pK*fEpK*fE