AN EБPLICIT TOWER OF FUNCTION FIELDS OVER CUBIC

Transcrição

AN EБPLICIT TOWER OF FUNCTION FIELDS OVER CUBIC
VW e_Ny]yq q!Gei !3 3=W]qy!W 3yeN*7 !zei ]= y] 3yWyqe
3yeN*7 VW* yW€:7 N!Gei !=W*
F=7]eNyW!
d
eeiiVd ViWVN*! pVi]yVd <eWWyWp 7qy]<qeW!q<1
ytR$ZB I‚ s‚8?s${s _Z„s ‚ V}j${sIsTy_V
eR„sIs *Bts ]sRB„$ts dd(
11;E(Tn1( i$B I‚ Fst‚$„B iF
„s9$j
1
=t$%‚„R$[s *Z$RAZ„TeRR‚t
3 E sY‚8s$, ;xdd eRR‚t
p‚„8stk
7Z88s„kU 3B„ s PZt{$Bt h‚jI Bb$f B%‚„ s ht$‚ h‚jI BP {s„I$tsj$k f I‚tB‚ Ak /wB D
w„‚R} ] wB DD Y‚ ‚tZR w„‚R} Y‚ tZ8A‚„ BP „s$Btsj }js{‚RD BP Bb$f yt Y$R }s}‚„ b‚
}„‚R‚t st ‚-}j${$ Bb‚„ BP PZt{$Bt h‚jIR Bd t B1 t Bn t 333 B%‚„ $f PB„ f ) R n RZ{Y Ys
j$8„ ] wB„ Db/wB„ D w 1wR 1 b dDbwR L 1D
+! yt„CIZ{'Ct
N‚ Bb$f A‚ st sj‚A„s${ PZt{$Bt h‚jI BP Bt‚ %s„$sAj‚ bYBR‚ PZjj {BtRst h‚jI $R Y‚ ht$‚
h‚jI BP {s„I$tsj$k f k G‚$j:R Y‚B„‚8 Y‚ tZ8A‚„ ] ) ] wB D BP }js{‚R BP I‚„‚‚ Bt‚ BP
S
Bb$f $R ABZtI‚I Ak ] › f L d L 1/ f bY‚„‚ / ) /wB D I‚tB‚R Y‚ ‚tZR BP B qY$R Z}}‚„
S
ABZtI $R RYs„} $t Y‚ R‚tR‚ Ys Y‚„‚ s„‚ ‚-s8}j‚R BP PZt{$Bt h‚jIR b$Y ] ) f L d L 1/ f
w$P f $R s RJZs„‚D <Bb‚%‚„ $P Y‚ ‚tZR BP B $R js„‚ b$Y „‚R}‚{ B Y‚ R$9‚ BP Y‚ {BtRst
h‚jI G‚$j:R ABZtI {st A‚ $8}„B%‚I {BtR$I‚„sAjk qY$R bsR h„R BAR‚„%‚I Ak yYs„s R‚‚ >ddH
7‚$t ]f w/D U) 8s-I] wB DJ bY‚„‚ B „ZtR B%‚„ sjj PZt{$Bt h‚jIR B%‚„ $f b$Y /wB D ) /
B
stI \wfD U) j$8 RZ}/ ]f w/Db/ b‚ Ys%‚ Y‚ *„$tP‚jITzjsIZ ABZtI wR‚‚ >nHD
S
\wfD › f b d3
w(3dD
yP f ) R 1 $R s RJZs„‚ Y‚t $t‚JZsj$k w(dD $R $t Ps{ st ‚JZsj$k yt B„I‚„ B RYBb Y$R
Bt‚ }„BIZ{‚R s R‚JZ‚t{‚ BP PZt{$Bt h‚jIR wBz Dzd B%‚„ $R1 RZ{Y Ys /wBz D stI
qY‚ h„R stI R‚{BtI sZYB„R b‚„‚ }s„$sjjk RZ}}B„‚I Ak ]W_JT_i!We ' EE1;(M\dETn w „s9$jD stI
Y$R bB„, bsR sjRB }s„$sjjk RZ}}B„‚I Ak 7sAst{$ =t$%‚„R$k wqZ„,‚kD
d
1
F=7]eNyW!
eeiiV ViWVN*! pVi]yV <eWWyWp 7qy]<qeW!q<
j$8z ] wBz Db/wBz D ) R b d yYs„s >ddH stI qRPsR8st zjsIZ stI $t, >dMH b‚„‚ Y‚ h„R
B }„B%‚ Y$R Ak RYBb$t Ys {‚„s$t 8BIZjs„ {Z„%‚R Ys%‚ RZ^{$‚tjk 8stk „s$Btsj }B$tR
B%‚„ $R1 ps„{$s stI 7${Y‚tBY >EH wR‚‚ sjRB >xHD s%‚ st ‚-}j${$ stI 8B„‚ ‚j‚8‚ts„k
{BtR„Z{$Bt BP RZ{Y s R‚JZ‚t{‚ Ak $t„BIZ{$t s Bb‚„ BP PZt{$Bt h‚jIR Bd t B1 t Bn t 333
B%‚„ $R1 sR PBjjBbRU N‚ Bd ) $R1 w?d D A‚ Y‚ „s$Btsj PZt{$Bt h‚jI stI PB„ sjj 7 w d j‚
B7Ld ) B7 w?7Ld D b$Y
L ?7Ld b ?R7 ) (3
?R7Ld c ?Rd
7
w(31D
yt Y‚ Bb‚„ $%‚t Ak eJ w(1D Y‚ ‚tZR BP Y‚ h‚jI Bz $R /wBz D { R zd wR LdD stI Y‚ tZ8T
A‚„ BP „s$Btsj }js{‚R B%‚„ $R1 $R ] wBz D { R zd wR 1 b dD Y‚t{‚ j$8z ] wBz Db/wBz D ) R b d
wPB„ bB R‚JZ‚t{‚R \z stI 4z Y‚ tBs$Bt \z { 4z 8‚stR Ys j$8z \z b4z ) dD !Y‚„
‚-}j${$ Bb‚„R B%‚„ $R1 ss$t$t Y‚ *„$tP‚jITzjsIZ ABZtI b‚„‚ PBZtI RZAR‚JZ‚tjk wR‚‚
>1H >;H >H >MH >H >d1H stI >dHD
yt {sR‚ f $R tB s RJZs„‚ Y‚ R$Zs$Bt $R I$&‚„‚t y R‚‚8R Ys $t Y$R {sR‚ 8BIZjs„ {Z„%‚R
IB tB Ys%‚ ‚tBZY „s$Btsj }B$tR B%‚„ $f $t B„I‚„ B }„BIZ{‚ s R‚JZ‚t{‚ BP PZt{$Bt h‚jIR
B%‚„ $f b$Y j$8z ] wBz Db/wBz D k ( =R$t {jsRRh‚jI Y‚B„k w$t }s„${Zjs„ Y‚ pBjBIT
7asPs„‚%${ Y‚B„‚8D 7‚„„‚ wR‚‚ >d;H stI >dxHD }„B%‚I Y‚ ‚-$R‚t{‚ BP Bb‚„R wBz Dzd B%‚„ $f
RZ{Y Ys j$8z ] wBz Db/wBz D w  c jB f wb$Y s {BtRst  k ( $tI‚}‚tI‚t BP fD Y‚t{‚
\wfD w  c jB f k ( PB„ sjj f3
w(3nD
qY‚ ‚-s{ %sjZ‚ BP \wfD YBb‚%‚„ $R tB ,tBbt $P f $R s tBtTRJZs„‚ pBBI jBb‚„ ABZtIR PB„
\wfD b‚„‚ BAs$t‚I Y„BZY „‚ht‚8‚tR BP 7‚„„‚:R {jsRRh‚jI Bb‚„ 8‚YBI wR‚‚ >dH >dnH stI
>dHD
yt Y‚ {sR‚ f ) €n w€ s }„$8‚ tZ8A‚„D Y‚ A‚R ,tBbt jBb‚„ ABZtI $R
\w€n D w
1w€1 b dD
3
€L1
w(3;D
qY$R bsR RYBbt Ak $t, >1(H ZR$t I‚‚t‚„s$BtR BP 7Y$8Z„s 8BIZjs„ RZ„Ps{‚R qY‚ 8‚YBI
BP {jsRRh‚jI Bb‚„R stI $t,:R s}}„Bs{Y IB tB j‚sI B st ‚-}j${$ I‚R{„$}$Bt BP Y‚ {B„„‚T
R}BtI$t PZt{$Bt h‚jIR VR s 8sY‚8s${sj {Ysjj‚t‚ stI sjRB PB„ %s„$BZR s}}j${s$BtR ‚
$t {BI$t Y‚B„k stI {„k}B„s}Yk wR‚‚ >dnH stI >dEHD $ $R Y‚„‚PB„‚ I‚R$„sAj‚ B {BtR„Z{
R‚JZ‚t{‚R BP PZt{$Bt h‚jIR wBz Dzd B%‚„ $f ‚-}j${$jk RZ{Y Ys j$8z ] wBz Db/wBz D $R }BRT
$$%‚ wB„ ‚%‚t A‚‚„ s js„‚ tZ8A‚„D
WB ‚-}j${$ R‚JZ‚t{‚R b$Y s }BR$$%‚ j$8$ s„‚ ,tBbt bY‚t f $R s }„$8‚ tZ8A‚„ 3B„
f ) €0 b$Y 0 k d Y‚ Bb‚„ Bd t B1 t Bn t 333 B%‚„ $f I‚ht‚I „‚{Z„R$%‚jk Ak Bd ) $f w?d D
V q!Gei !3 3=W]qy!W 3yeN*7 !zei ]= y] 3yeN*7
n
stI B7Ld ) B7 w?7Ld D b$Y Y‚ „‚js$Bt
E
?E
7Ld L w?7 L dD b d ) (,
bY‚„‚ E ) wf b dDbw€ b dD,
w(3xD
}„B%$I‚R st ‚-s8}j‚ b$Y j$8z ] wBz Db/wBz D w 1bwf b 1D k ( R‚‚ >H <Bb‚%‚„ PB„ f k ;
Y‚ tZ8A‚„ 1bwf b 1D $R Ps„ P„B8 Y‚ *„$tP‚jITzjsIZ ABZtI w(dD
i‚{‚tjk %st I‚„ p‚‚„ stI %st I‚„ zjZ >d(H PBZtI st ‚-}j${$ Bb‚„ B%‚„ Y‚ h‚jI
b$Y M ‚j‚8‚tR b$Y s XBBI" j$8$ qY$R Bb‚„ $R $%‚t „‚{Z„R$%‚jk Ak Bd ) $M w?d D stI
B7Ld ) B7 w?7Ld D bY‚„‚
?17Ld L ?7Ld ) ?7 L d L db?7 3
w(3ED
3B„ Y$R Bb‚„ B%‚„ Y‚ ht$‚ h‚jI $M Y‚ j$8$ $R j$8z ] wBz Db/wBz D ) nb1 bY${Y $R ‚JZsj
B 1w€1 b dDbw€ L 1D PB„ € ) 1 Y‚t{‚ $ ss$tR $t,:R jBb‚„ ABZtI w(;D
y $R Y‚ s$8 BP Y$R }s}‚„ B }„‚R‚t s t‚b ‚-}j${$ Bb‚„ ) BP PZt{$Bt h‚jIR B%‚„ $f
b$Y f ) R n PB„ stk }„$8‚ }Bb‚„ R qY‚ Bb‚„ ) $R I‚ht‚I „‚{Z„R$%‚jk Ak Bd ) $f w?d D stI
PB„ 7 w d B7Ld ) B7 w?7Ld D bY‚„‚ Y‚ PZt{$Bt ?7Ld Rs$Rh‚R Y‚ PBjjBb$t ‚JZs$Bt B%‚„ Y‚
PZt{$Bt h‚jI B7 U
?R7 L ?7 b d
d b ?7Ld
)
3
w(3D
?R7Ld
?7
qY‚ 8s$t „‚RZj $R wR‚‚ qY8nnD
s$t qY‚B„‚8 N‚ f ) R n stI j‚ Y‚ Bb‚„ ) U) wBd t B1 t Bn t 333D BP PZt{$Bt h‚jIR
B7 b$f A‚ I‚ht‚I sR $t w(D qY‚t
j$8 ] wBz Db/wBz D w
z
1wR 1 b dD
3
RL1
qY‚ ‚-s{ %sjZ‚ BP Y‚ ‚tZR /wB„ D $R $%‚t $t qY81 yt Y‚ R}‚{$sj {sR‚ BP s }„$8‚ tZ8A‚„
€ ) R Y$R s$t qY‚B„‚8 }„B%$I‚R s t‚b stI 8B„‚ ‚j‚8‚ts„k }„BBP BP $t,:R jBb‚„ ABZtI
w(;D PB„ \w€n D yt i‚8s„, n b‚ }B$t BZ Ys Y‚ s$t qY‚B„‚8 j‚sIR B st $8}„B%‚8‚t
Bt Y‚ p$jA‚„Tzs„RYs8B% ABZtI sABZ Y‚ sRk8}B${ A‚Ys%$BZ„ BP Y‚ }s„s8‚‚„R BP j$t‚s„
{BI‚R B%‚„ $Rn PB„ sjj }„$8‚ }Bb‚„R R w 
qY‚ Bb‚„ $t >1H stI Y‚ %st I‚„ p‚‚„T%st I‚„ zjZ Bb‚„ >d(H }„B%$I‚I Y‚ $tR}$„s$Bt
PB„ eJZs$Bt w(D yt Ps{ Y‚ Bb‚„ $t >d(H $R s R}‚{$sj {sR‚ BP Y‚ Bb‚„ $t w(DU Y‚ RZAT
R$Z$Bt ?7 db?7 PB„ sjj 7 „stRPB„8R eJw(D $tB eJw(ED $P R ) 1 Z Bt‚ RYBZjI tB‚
Ys Y‚ {sR‚R R ) 1 stI R k 1 I$&‚„ {BtR$I‚„sAjk yt Y‚ h„R {sR‚ wY‚ %st I‚„ p‚‚„T%st
I‚„ zjZ Bb‚„D sjj ‚-‚tR$BtR B7Ld bB7 s„‚ V„$tT7{Y„‚$‚„ ‚-‚tR$BtR BP I‚„‚‚ 1 3B„ R k 1
Y‚ ‚-‚tR$BtR B7Ld bB7 s„‚ BP I‚„‚‚ R AZ Y‚k s„‚ tB ‚%‚t psjB$R qY$R Ps{ 8s,‚R Y‚
;
F=7]eNyW!
eeiiV ViWVN*! pVi]yV <eWWyWp 7qy]<qeW!q<
‚tZR {sj{Zjs$Bt 8B„‚ I$^{Zj
qY‚ }s}‚„ $R B„st$9‚I sR PBjjBbRU yt 7‚{$Bt d b‚ h- tBs$BtR stI }Z B‚Y‚„ RB8‚
„‚RZjR P„B8 Y‚ Y‚B„k BP sj‚A„s${ PZt{$Bt h‚jIR bY${Y b$jj A‚ ZR‚I js‚„ yt 7‚{$Bt 1
b‚ RZIk Y‚ „s8$h‚I }js{‚R $t Y‚ ‚-‚tR$BtR B„ bBd BP Y‚ Bb‚„ $%‚t Ak eJw(D stI
b‚ I‚‚„8$t‚ Y‚ ‚tZR BP B„ PB„ sjj „ w d wR‚‚ qY81D y Z„tR BZ Ys b$jI stI wPB„
R k 1D sjRB s8‚ „s8$h{s$Bt B{{Z„ stI Ys RB8‚ BP Y‚ b$jIjk „s8$h‚I }js{‚R Ys%‚ s
RZ„}„$R$t „s8$h{s$Bt A‚Ys%$BZ„ wR‚‚ _„B}1D qY‚ stsjkR$R BP Y‚R‚ }js{‚R $R {„Z{$sj PB„
Y‚ ‚tZR {sj{Zjs$Bt G‚ }BR}Bt‚ Y$R stsjkR$R B 7‚{$Bt ; sR $ $R %‚„k ‚{Yt${sj yt
7‚{$Bt n b‚ $t%‚R$s‚ „s$Btsj }js{‚R B%‚„ $Rn BP Y‚ PZt{$Bt h‚jIR B„ BP Y‚ Bb‚„ $%‚t
Ak eJw(D yt }s„${Zjs„ b‚ RYBb Ys RB8‚ „s$Btsj }js{‚R BP Y‚ h‚jI Bd R}j$ {B8}j‚‚jk
$t sjj ‚-‚tR$BtR B„ bBd wR‚‚ qY8n1D yt {Bt`Zt{$Bt b$Y Y‚ ‚tZR BP B„ Y$R Ps{ k$‚jIR
Y‚ s$t qY‚B„‚8 yt 7‚{$Bt x b‚ }„‚R‚t s %s„$s$Bt % BP Y‚ Bb‚„ ) sAB%‚ Ys%$t
Y‚ Rs8‚ j$8$ B%‚„ $Rn qY‚ t‚b P‚sZ„‚ BP Y‚ Bb‚„ % $R Ys $ sj‚„ts‚R €Z88‚„ stI
V„$tT7{Y„‚$‚„ ‚-‚tR$BtR
d `„‚j'9'ts„'‚R
!Z„ ‚t‚„sj „‚P‚„‚t{‚ PB„ Y‚ Y‚B„k BP sj‚A„s${ PZt{$Bt h‚jIR $R Y‚ ABB, >dEH 7}‚{$h{sjjk
b‚ b$jj ZR‚ Y‚ PBjjBb$t tBs$BtRU
$f
ƒf
$

B, o, I333
/wB D
YwB D
w? ) D
8h
] wB D
T
T
T
T
T
T
T
Y‚ ht$‚ h‚jI BP {s„I$tsj$k f
st sj‚A„s${ {jBRZ„‚ BP $f ƒ f D
stk h‚jI w$t 8BR {sR‚R  ) $f B„ $
sj‚A„s${ PZt{$Bt h‚jIR BP Bt‚ %s„$sAj‚ B%‚„ 
Y‚ ‚tZR BP Bb
Y‚ R‚ BP }js{‚R BP Bb
Y‚ }js{‚ BP Y‚ „s$Btsj PZt{$Bt h‚jI w?D bY${Y $R s 9‚„B BP
? b wPB„ D „‚R} Y‚ }Bj‚ BP ? wPB„ ) D
T Y‚ tB„8sj$9‚I I$R{„‚‚ %sjZs$Bt BP Bb sRRB{$s‚I b$Y Y‚
}js{‚ h YwB D
T Y‚ tZ8A‚„ BP „s$Btsj }js{‚R w) }js{‚R BP I‚„‚‚ Bt‚D BP Bb
$t {sR‚  ) $f N‚ obB A‚ s ht$‚ R‚}s„sAj‚ ‚-‚tR$Bt BP PZt{$Bt h‚jIR B%‚„  j‚ h YwB D stI j‚
< YwoD A‚ s }js{‚ jk$t B%‚„ h qY‚t b‚ b„$‚ <Mh B„ h ) <MB stI b‚ I‚tB‚
w<Mh D
Qw<Mh D
T Y‚ „s8$h{s$Bt $tI‚- BP <Mh T Y‚ I$&‚„‚t ‚-}Bt‚t BP <Mh V q!Gei !3 3=W]qy!W 3yeN*7 !zei ]= y] 3yeN*7
x
V Bb‚„ BP PZt{$Bt h‚jIR B%‚„ s h‚jI  $R st $tht$‚ R‚JZ‚t{‚ ) ) wB7 D7d BP PZt{$Bt
h‚jIR B7 b b$Y Y‚ PBjjBb$t }„B}‚„$‚RU
$D Bd B1 Bn 333
$$D sjj ‚-‚tR$BtR B7Ld bB7 s„‚ R‚}s„sAj‚
$$$D /wB7 D k d PB„ RB8‚ 7
y PBjjBbR P„B8 Y‚ <Z„b$9 ‚tZR PB„8Zjs Ys /wBz D PB„ z G‚ tB‚ Ys 
RYBZjI A‚ Y‚ PZjj {BtRst h‚jI BP B7 PB„ sjj 7 $‚ Y‚ h‚jI  RYBZjI A‚ sj‚A„s${sjjk {jBR‚I
$t B7 PB„ sjj 7
3B„ Y‚ {Bt%‚t$‚t{‚ BP Y‚ „‚sI‚„ b‚ „‚{sjj s P‚b „‚RZjR sABZ „s8$h{s$Bt $t ‚-‚tR$BtR
BP PZt{$Bt h‚jIR
N‚88s dd N‚ o ) B wrD A‚ s ht$‚ R‚}s„sAj‚ ‚-‚tR$Bt BP sj‚A„s${ PZt{$Bt h‚jIR B%‚„
 stI j‚ wx D B >x H A‚ Y‚ $„„‚IZ{$Aj‚ 8Bt${ }BjktB8$sj BP Y‚ PZt{$Bt r B%‚„ Y‚ h‚jI
B N‚ h YwB D A‚ s }js{‚ BP Bb
$D 7Z}}BR‚ Ys r $R $t‚„sj s h w$‚ 8h wD w ( PB„ sjj {B‚^{$‚tR  BP wx DD stI Ys
8< wI wrDD ) ( PB„ sjj < YwoD b$Y <Mh qY‚t Y‚ }js{‚ h $R Zt„s8$h‚I $t obB $$D yP <Mh $R Bsjjk „s8$h‚I w$‚ w<Mh D ) >o U B HD stI $P r $R s }„$8‚ ‚j‚8‚t s Y‚
}js{‚ < Y‚t
Qw<Mh D ) 8< wI wrDD3
_„BBP >dEH ]Yyyyx
VtBY‚„ „‚RZj bY${Y b$jj A‚ ZR‚I P„‚JZ‚tjk $t 7‚{$BtR 1 stI ; $R s R}‚{$sj {sR‚ BP
VAYkst,s„:R j‚88s w}jZR Y‚ „stR$$%$k BP I$&‚„‚t ‚-}Bt‚tRD
N‚88s d1 N‚ obB A‚ s R‚}s„sAj‚ ‚-‚tR$Bt BP PZt{$Bt h‚jIR B%‚„  stI j‚ Bd , B1 A‚
$t‚„8‚I$s‚ h‚jIR B | B7 | o RZ{Y Ys o ) Bd c B1 $R Y‚ {B8}BR$‚ h‚jI BP Bd stI B1 N‚
< YwoD stI I‚tB‚ h U) <MB stI h7 U) <MB7 PB„ 7 ) d, 1 7Z}}BR‚ Ys Y‚ „s8$h{s$Bt
$tI${‚R 7 ) wh7 Mh D wPB„ 7 ) d, 1D s„‚ „‚js$%‚jk }„$8‚ stI Ys d $R „‚js$%‚jk }„$8‚ B Y‚
{Ys„s{‚„$R${ BP  qY‚t
$D w<Mh1 D ) d stI w<Mhd D ) 1 $$D Qw<Mhd D ) d c Qwh1 Mh D b wd b dDw1 b dD
yt }s„${Zjs„ Qw<Mhd D ) Qwh1 Mh D $P d ) d
_„BBP 3„B8 VAYkst,s„:R j‚88s wR‚‚ >dEH ]YyyyMD $ PBjjBbR $88‚I$s‚jk Ys b‚ Ys%‚
w<Mhd D ) 1 stI w<Mh1 D ) d stI Y‚t{‚ <Mh1 $R s8‚ k Y‚ „stR$$%$k BP I$&‚„‚t
E
F=7]eNyW!
eeiiV ViWVN*! pVi]yV <eWWyWp 7qy]<qeW!q<
‚-}Bt‚tR wR‚‚ >dEH ]Yyyy;D b‚ BAs$t
Qw<Mh D ) Qw<Mhd D L w<Mhd D c Qwhd Mh D ) Qw<Mhd D L 1 wd b dD,
stI sjRB
Qw<Mh D ) Qw<Mh1 D L w<Mh1 D c Qwh1 Mh D ) wd b dD L d c Qwh1 Mh D3
<‚t{‚
Qw<Mhd D ) d c Qwh1 Mh D L wd b dD b 1 wd b dD3
VR b‚ }B$t‚I BZ $t Y‚ $t„BIZ{$Bt b‚ bst B $t%‚R$s‚ Y‚ Bb‚„ BP PZt{$Bt h‚jIR
ƒ f bY‚„‚ B7Ld ) B7 w?7Ld D b$Y
Bd t B1 t Bn t 333 B%‚„  ) $f wf ) R n D „‚R} B%‚„  ) $
Y‚ „‚js$Bt
d b ?7Ld
?R7 L ?7 b d
)
, PB„ sjj 7 w d3
?R7Ld
?7
G‚ }Z B‚Y‚„ RB8‚ }„B}‚„$‚R BP Y‚ {B„„‚R}BtI$t XAsR${ PZt{$Bt h‚jI"U
ƒ f stI {BtR$I‚„ Y‚ PZt{$Bt h‚jI B ) w?, rD b$Y I‚ht$t
_„B}BR$$Bt dn N‚  ) $
‚JZs$Bt
dbr
?R L ? b d
)
3
wd3dD
rR
?
qY‚t Y‚ PBjjBb$t YBjIRU
$D >B U w?DH ) >B U wrDH ) R
$$D qY‚ }js{‚ w? ) (D BP w?Db $R Bsjjk „s8$h‚I $t Bbw?D $‚ Y‚„‚ $R ‚-s{jk Bt‚
}js{‚ h( YwB D b$Y h( Mw? ) (D G‚ Ys%‚ wh( Mw? ) (DD ) R stI Qwh( Mw? ) (DD ) R
$$$D qY‚ }js{‚ w? ) D $R Bsjjk „s8$h‚I $t Y‚ ‚-‚tR$Bt Bbw?D $‚ Y‚„‚ $R ‚-s{jk
Bt‚ }js{‚ h YwB D b$Y h Mw? ) D G‚ Ys%‚ Ys wh Mw? ) DD ) R stI Ys
Qwh Mw? ) DD ) 1R b 1
$%D N‚ p U) I  R L ) dJ qY‚t PB„ p Y‚ }js{‚ w? ) D BP w?D YsR
‚-s{jk bB }js{‚R h stI < YwB D sAB%‚ $ G‚ Ys%‚ Ys wh Mw? ) DD ) d stI
Ys w< Mw? ) DD ) R b d
%D Vjj BY‚„ }js{‚R BP w?D s„‚ Zt„s8$h‚I $t Bbw?D
%$D 3B„ stk p Y‚„‚ $R s Zt$JZ‚ }js{‚ C YwB D sAB%‚ Y‚ }js{‚ wr ) D BP wrD
stI Y$R }js{‚ $R s {B88Bt 9‚„B BP ? b d stI r b %$$D qY‚ }„$t{$}sj I$%$RB„R $t Y‚ PZt{$Bt h‚jI B BP Y‚ PZt{$BtR ?, ? b d, ? b stI BP
r, r b d, r b wPB„ pD s„‚ sR PBjjBbRU
w?D ) Rh( b Rh w? b dD )
V q!Gei !3 3=W]qy!W 3yeN*7 !zei ]= y] 3yeN*7
;p

C b Rh w? b D ) h L wR b dD< b Rh wrD ) h( L wR b dDh b #;p <# wr b dD ) ;p h b #;p <# wr b D ) RC b #;p <# _„BBP G‚ Btjk RYBb Y‚ sRR‚„$BtR {Bt{‚„t$t Y‚ I$&‚„‚t ‚-}Bt‚tR $t $‚8R $$D stI $$$D
stI b‚ j‚s%‚ Y‚ „‚R B Y‚ „‚sI‚„
$$D N‚ h( YwB D A‚ s 9‚„B BP ? $t B qY‚t $ PBjjBbR P„B8 eJwddD Ys 8h( w?D ) R stI
8h( wrD ) d $‚ Y‚ PZt{$Bt r $R s }„$8‚ ‚j‚8‚t s h( qY‚ 8$t$8sj }BjktB8$sj BP r B%‚„
w?D $R
?
?
cx b R
wx D ) x R L R
? L?bd
? L?bd
R
I
stI Y‚t{‚ Qwh( Mw?( ) (DD ) 8h( w wrDD ) 8h( w?bw? L ? b dDD ) R Ak N‚88s dd
$$$D WBb b‚ {BtR$I‚„ s }Bj‚ h BP ? $t B Vs$t P„B8 eJwddD b‚ BAs$t Ys 8h w?D ) bR
stI 8h wrD ) R b d RB Y‚ PZt{$Bt 0 U) w?rDd $R s }„$8‚ ‚j‚8‚t PB„ h yR $„„‚IZ{$Aj‚
}BjktB8$sj B%‚„ w?D $R
d
?R L ? b d
,
c x Rd b
?
?RLd
w+ I w0DD ) 8h w?d c 0R1 D ) R L wR b 1D ) 1R b 1
+ wx D ) x R b
stI Y‚t{‚ Qwh Mw? ) DD ) 8h
VR st ‚sRk {BtR‚JZ‚t{‚ b‚ BAs$t P„B8 _„B}dn Ys wPB„ R k 1D ABY ‚-‚tR$BtR Bbw?D
stI BbwrD s„‚ tBtTpsjB$R qY$R PBjjBbR P„B8 Y‚ „s8$h{s$Bt A‚Ys%$BZ„ BP Y‚ }js{‚R
w? ) D $t Bbw?D „‚R} Y‚ }js{‚ wr ) (D $t BbwrD
1 is9'P'{s'Ct stI ‚tZR
3$„R b‚ $t„BIZ{‚ RB8‚ sII$$Btsj tBs$Bt w%sj$I Y„BZYBZ Y$R R‚{$BtD
ƒ R $R st sj‚A„s${ {jBRZ„‚ BP $R stI p ) I  R L ) dJ3
)$
) ) wBd , B1 , Bn , 333D $R Y‚ R‚JZ‚t{‚ BP PZt{$Bt h‚jIR B%‚„  bY‚„‚ Bd ) w?d D $R Y‚
„s$Btsj PZt{$Bt h‚jI stI PB„ sjj 7 w d B7Ld ) B7 w?7Ld D b$Y
d b ?7Ld
?R7 L ?7 b d
)
3
?R7Ld
?7
3B„ s }js{‚ < YwB„ D b‚ R‚
<i U) <MBi PB„ i ) d, 3 3 3 , „
w13dD
M
F=7]eNyW!
eeiiV ViWVN*! pVi]yV <eWWyWp 7qy]<qeW!q<
stI b‚ b„$‚ PB„  > IJ
?i ) s < $P
<Mw?i ) D3
N‚88s 1d 3B„ sjj „ w d Y‚ PBjjBb$t YBjIRU
$D >B„ U Bd H ) R „d $$D qY‚ }js{‚ w?d ) (D BP Bd b YsR s Zt$JZ‚ ‚-‚tR$Bt < YwB„ D qY$R }js{‚ < $R sjRB s
9‚„B BP Y‚ PZt{$Bt ?„ stI b‚ Ys%‚ w<Mw?d ) (DD ) R „d stI w<Mw?„ ) (DD ) d
_„BBP 7$t{‚ eJw1dD $R st ‚JZs$Bt BP I‚„‚‚ R $t Y‚ %s„$sAj‚ ?7Ld $ $R {j‚s„ Ys >BiLd U
Bi H › R PB„ sjj i w d stI Y‚„‚PB„‚ >B„ U Bd H › R „d WBb j‚ < YwB„ D A‚ s 9‚„B BP ?d $t B„ y $R RZ^{$‚t B RYBb Ys < $R s 9‚„B BP ?„ stI Ys w<Mw?d ) (DD ) R „d stI w<Mw?„ ) (DD ) d qY‚ {sR‚ „ ) d $R „$%$sj stI
b‚ sRRZ8‚ Ys BZ„ sRR‚„$Bt $R „Z‚ PB„ RB8‚ „ G‚ {YBBR‚ s }js{‚ <I YwB„Ld D b$Y
<I M< stI R‚ <d U) <I Mw?„ ,?„Ld D k _„B}dn b‚ {Bt{jZI‚ Ys <d $R s 9‚„B BP ?„Ld b$Y
w<d Mw?„ ) (DD ) R stI w<d Mw?„Ld ) (DD ) d y PBjjBbR Ys w<I Mw?„Ld ) (DD ) d stI
w<I M<D ) w<d Mw?„ ) (DD ) R Ak VAYkst,s„:R j‚88s <‚t{‚ w<I Mw?d ) (DD ) R „d c R )
R„ G‚ b$jj RYBb js‚„ wR‚‚ qY81D Ys /wBn D k d stI Y‚„‚PB„‚ b‚ Ys%‚U
]B„Bjjs„k 11 qY‚ R‚JZ‚t{‚ ) ) wB7 D7d bY${Y $R I‚ht‚I „‚{Z„R$%‚jk Ak eJw1dD $R s Bb‚„
BP PZt{$Bt h‚jIR B%‚„  stI PB„ sjj i w d b‚ Ys%‚ >BiLd U Bi H ) R
qY‚ 8s$t Bsj $t Y$R R‚{$Bt $R B I‚‚„8$t‚ Y‚ ‚tZR /wB„ D PB„ sjj „ w d Y‚t{‚ b‚
8ZR RZIk Y‚ „s8$h{s$Bt A‚Ys%$BZ„ BP }js{‚R $t Y‚ Bb‚„ ) !Z„ t‚- j‚88s PBjjBbR
$88‚I$s‚jk P„B8 _„B}dn %$$D
N‚88s 1n N‚ „ w 1 stI {BtR$I‚„ s }js{‚ < YwB„ D
$D 3B„ d › i c „ Y‚ PBjjBb$t YBjIR s Y‚ }js{‚ <U
T $P ?i ) ( B„ ?i ) Y‚t ?iLd ) (
T $P ?i ) PB„ RB8‚ p Y‚t ‚$Y‚„ ?iLd ) B„ ?iLd ) d
T $P ?i ) d Y‚t ?iLd ) PB„ RB8‚ p
$$D 3B„ 1 › i › „ b‚ Ys%‚ s Y‚ }js{‚ <U
T $P ?i ) ( Y‚t ‚$Y‚„ ?id ) ( B„ ?id ) T $P ?i ) d B„ ?i ) Y‚t ?id ) PB„ RB8‚ p
T $P ?i ) b$Y p Y‚t ?id ) d
WBb b‚ stsjk9‚ Y‚ }js{‚R < YwB„ D BP Y‚ PZt{$Bt h‚jI B„ bY${Y s„‚ „s8$h‚I $t Y‚
‚-‚tR$Bt B„ bBd V q!Gei !3 3=W]qy!W 3yeN*7 !zei ]= y] 3yeN*7
_„B}BR$$Bt 1; N‚ „ w 1 stI j‚ < YwB„ D A‚ s }js{‚ bY${Y $R „s8$h‚I $t Y‚ ‚-‚tR$Bt
B„ bBd qY‚t < $R BP Bt‚ BP Y‚ PBjjBb$t k}‚RU
qk}‚ dU ?d ) ( s <
qk}‚ 1U ?d ) s <
qk}‚ nU ?X ) s < PB„ RB8‚ X b$Y d c X › „
_„BBP i‚{sjj Ys <i I‚tB‚R Y‚ „‚R„${$Bt BP Y‚ }js{‚ < B Y‚ h‚jI Bi t B„ PB„ d › i › „
7$t{‚ <M<d $R „s8$h‚I Y‚„‚ $R RB8‚ i › „bd RZ{Y Ys <iLd M<i $R „s8$h‚I <‚t{‚ Y‚ }js{‚
< „s8$h‚R $t Y‚ ‚-‚tR$Bt w?i , ?iLd Dbw?i D Ak VAYkst,s„:R j‚88s wR„${jk R}‚s,$t Y‚
„‚R„${$Bt BP < B w?i , ?iLd D „s8$h‚R B%‚„ w?i DD y PBjjBbR P„B8 _„B}dn Ys ?iLd ) (
B„ ?iLd ) s < WBb b‚ s}}jk N‚88s 1n $$D B BAs$t BZ„ sRR‚„$Bt
qY‚ „s8$h{s$Bt A‚Ys%$BZ„ BP ‚s{Y BP Y‚R‚ n k}‚R BP }js{‚R BP B„ $R JZ$‚ I$&‚„‚t P„B8
‚s{Y BY‚„ b‚ b$jj I$R{ZRR $ $t Y‚ RZAR‚JZ‚t }„B}BR$$BtR
_„B}BR$$Bt 1x wqk}‚ dD qY‚„‚ $R ‚-s{jk Bt‚ }js{‚ < YwB„ D bY${Y $R s 9‚„B BP ?d stI
Y‚ PBjjBb$t YBjIRU
$D w<i M<id D ) R w<i Mw?i ) (DD ) d stI Qw<i M<id D ) R PB„ 1 › i › „
$$D Qw<M<d D ) RwR „d b dDbwR b dD
_„BBP G‚ Ys%‚ sj„‚sIk RYBbt $t N‚88s 1d Ys ?d YsR s Zt$JZ‚ 9‚„B < $t B„ stI Ys < $R
s R$8}j‚ 9‚„B BP ?„ y „‚8s$tR B I‚‚„8$t‚ Y‚ I$&‚„‚t ‚-}Bt‚tR BP <i M<id stI BP <M<d G‚ R‚ hi U) <Mw?id ,?i D stI Y‚t Qwhi Mw?id ) (DD ) R Ak _„B}dn $$D 7$t{‚ <id $R s R$8}j‚
9‚„B BP ?id Ak $‚8 $D $ PBjjBbR P„B8 N‚88s d1 Ys Qw<i M<id D ) Qwhi Mw?id ) (DD ) R
y‚8 $$D PBjjBbR Ak $tIZ{$Bt P„B8 $‚8 $D ZR$t Y‚ „stR$$%$k BP I$&‚„‚t ‚-}Bt‚tR wR‚‚
>dEH ]Yyyy;D
_„B}BR$$Bt 1E wqk}‚ 1D qY‚„‚ $R ‚-s{jk Bt‚ }js{‚ < YwB„ D bY${Y $R s }Bj‚ BP ?d qY$R
}js{‚ $R s {B88Bt 9‚„B BP ?1 , 3 3 3 , ?„ stI b‚ Ys%‚
$D w<i M<id D ) R w<i Mw?i ) (DD ) R b d stI Qw<i M<id D ) 1R b 1 PB„ ‚s{Y $tI‚- i b$Y
1 › i › „
$$D Qw<M<d D ) 1wR „d b dD
_„BBP $D N‚ < YwB„ D A‚ s }Bj‚ BP ?d y PBjjBbR P„B8 N‚88s 1n $D Ys < $R s 9‚„B
BP ?1 , 3 3 3 , ?„ stI b‚ }„B%‚ Y‚ „‚8s$t$t sRR‚„$BtR Ak $tIZ{$Bt B%‚„ i qY‚ {sR‚ i ) 1
PBjjBbR P„B8 _„B}dn WBb j‚ 1 › i › „ bd k $tIZ{$Bt Yk}BY‚R$R Y‚ }js{‚ <i $R s 9‚„B
BP ?i b$Y w<i Mw?i ) (DD ) R b d N‚ hiLd ) <Mw?i ,?iLd D Vs$t Ak _„B}dn b‚ Ys%‚ Ys
whiLd Mw?i ) (DD ) R whiLd Mw?iLd ) (DD ) d stI QwhiLd Mw?i ) (DD ) R k VAYkst,s„:R
j‚88s b‚ {Bt{jZI‚ Ys w<iLd M<i D ) R stI w<iLd Mw?iLd ) (DD ) R b d stI Ak N‚88s d1
d(
F=7]eNyW!
eeiiV ViWVN*! pVi]yV <eWWyWp 7qy]<qeW!q<
b‚ BAs$t
Qw<iLd M<i D ) wR b dD c R b wR b 1DwR b dD ) 1R b 13
$$D 3BjjBbR ‚sR$jk P„B8 $‚8 $D Ak $tIZ{$Bt B%‚„ „
qY‚ „s8$h{s$Bt A‚Ys%$BZ„ BP }js{‚R < BP qk}‚ n wR‚‚ _„B}1;D $R 8Z{Y 8B„‚ {B8}j${s‚I
qY‚R‚ }js{‚R s„‚ {Ys„s{‚„$9‚I Ak Y‚ {BtI$$Bt ?X ) s < PB„ RB8‚ X b$Y d c X › „ G‚
8ZR I$R$tZ$RY Y‚ {sR‚R X s d 8BI 1 stI X s ( 8BI 1
_„B}BR$$Bt 1 wqk}‚ n stI X BIID N‚ d c X › „ stI X s d 8BI 1 stI j‚ Y‚ }js{‚
< YwB„ D A‚ s }Bj‚ BP Y‚ PZt{$Bt ?X qY‚t b‚ Ys%‚U
$D qY‚ }js{‚ <X $R „s8$h‚I $t BX bw?X D b$Y „s8$h{s$Bt $tI‚w<X Mw?X ) DD ) R wXdDb1 3
$$D qY‚ „‚R„${$Bt <i BP Y‚ }js{‚ < Rs$Rh‚R
T
d
$P 1 › i › X b d,
€
€
€
€
€
z R b d $P i ) X,
w<i M<id D )
R
$P X c i c 1X stI i s ( 8BI 1,
€
€
€
d
$P X c i c 1X stI i s d 8BI 1,
€
€
Z
R
$P i w 1X3
yt sjj {sR‚R bY‚„‚ w<i M<id D ) R Y‚ I$&‚„‚t ‚-}Bt‚t $R
Qw<i M<id D ) 1R b 13
$$$D qY‚ I$&‚„‚t ‚-}Bt‚t BP <M<d $R
T
€
€
R w1„nXLnDb1 b 1
€
€
€
€
€
€
€
z
Qw<M<d D )
R w„XLnDb1 b 1
€
€
€
€
€
€
€
€
€
Z R w„XL1Db1 b 1
$%D N‚ \„,X
$P X ›
$P
„Ld
,
1
„Ld
c X › „ stI „ s ( 8BI 1,
1
„Ld
c X › „ stI „ s d 8BI 13
1
U) 'I< YwB„ D < $R s }Bj‚ BP ?X J qY‚t
T
„Ld
€
Xd
€
$P
X
›
,
R
€
€
1
€
€
€
€
€
z
„Ld
\„,X )
R w„1Db1 $P
c X › „ stI „ s ( 8BI 1,
€
1
€
€
€
€
€
€
€
„Ld
€
Z R w„dDb1 $P
c X › „ stI „ s d 8BI 13
1
$P
V q!Gei !3 3=W]qy!W 3yeN*7 !zei ]= y] 3yeN*7
dd
_„BBP qY‚ }„BBP BP $‚8R $D stI $$D $R Ys„I stI $ $R Y‚ {Bt‚t BP 7‚{$Bt ;
$$$D 3$„R b‚ {BtR$I‚„ Y‚ {sR‚ X › „Ld
$‚ Y‚ {sR‚ „ w 1X b d k $‚8 $$D stI Y‚
1
„stR$$%$k BP I$&‚„‚t ‚-}Bt‚tR Y‚ I$&‚„‚t ‚-}Bt‚t BP <1Xd M<d $R
wXnDb1
Qw<1Xd M<d D ) R
wXdDb1
3
c wR b 1D L w
R 7 D c w1R b 1D ) R wXLdDb1 b 13
7)(
Vs$t P„B8 $$D stI Y‚ „stR$$%$k b‚ BAs$t
Qw<„ M<d D ) R
„w1XdD
„1X
3
c Qw<1Xd M<d D L w
R 7 D c w1R b 1D
7)(
) R „w1XdDLwXLdDb1 b 1 ) R w1„nXLnDb1 b 13
yt {sR‚
„Ld
1
c X › „ stI „ s ( 8BI 1 b‚ BAs$t $t s R$8$js„ 8stt‚„ Ys
w„XdDb1
Qw<„ M<d D ) R
w„XLdDb1
c wR b 1D L w
3
R 7 D c w1R b 1D ) R w„XLnDb1 b 13
7)(
yt {sR‚
„Ld
1
c X › „ stI „ s d 8BI 1 b‚ Ys%‚
w„X1Db1
Qw<„ M<d D ) R
w„XDb1
c wR b 1D L w
3
R 7 D c w1R b 1D ) R w„XL1Db1 b 13
7)(
$%D k $‚8R $D stI $$D sjj }Bj‚R < YwB„ D BP Y‚ PZt{$Bt ?X Ys%‚ Y‚ Rs8‚ }Bj‚ B„I‚„
ts8‚jk
T
„Ld
€
„X
€
R
$P
X
›
,
€
€
1
€
€
€
€
€
z
„Ld
w<Mw?X ) DD )
R „b1
$P
c X › „ stI „ s ( 8BI 1,
€
1
€
€
€
€
€
€
€
„Ld
€
Z R w„dDb1 $P
c X › „ stI „ s d 8BI 13
1
7$t{‚ R „d ) >B„ U w?X DH ) \„,X c w<Mw?X ) DD b‚ BAs$t Y‚ I‚R$„‚I „‚RZj
_„B}BR$$Bt 1M wqk}‚ n stI X ‚%‚tD N‚ d c X › „ stI X s ( 8BI 1 stI j‚ Y‚ }js{‚
< YwB„ D A‚ s }Bj‚ BP Y‚ PZt{$Bt ?X qY‚t b‚ Ys%‚U
$D qY‚ }js{‚ <X YsR „s8$h{s$Bt $tI‚- w<X Mw?X ) DD ) R wX1Db1 $t Y‚ ‚-‚tR$Bt
BX bw?X D
d1
F=7]eNyW!
eeiiV ViWVN*! pVi]yV <eWWyWp 7qy]<qeW!q<
$$D qY‚ „‚R„${$Bt <i BP Y‚ }js{‚ <
T
d
€
€
€
€
€
z Rbd
w<i M<id D )
R
€
€
€
d
€
€
Z
R
Rs$Rh‚R
$P
$P
$P
$P
$P
1 › i › X b d,
i ) X,
X c i › 1X b 1 stI i s d 8BI 1,
X c i › 1X b 1 stI i s ( 8BI 1,
i w 1X b d3
yt sjj {sR‚R bY‚„‚ w<i M<id D ) R Y‚ I$&‚„‚t ‚-}Bt‚t $R
Qw<i M<id D ) 1R b 13
$$$D qY‚ I$&‚„‚t ‚-}Bt‚t BP <M<d $R
T
€
€
R w1„nXL;Db1 b 1
€
€
€
€
€
€
€
z
Qw<M<d D )
R w„XL1Db1 b 1
€
€
€
€
€
€
€
€
€
Z R w„XLnDb1 b 1
$P X ›
„L1
,
1
$P
„L1
c X › „ stI „ s ( 8BI 1,
1
$P
„L1
c X › „ stI „ s d 8BI 13
1
$%D N‚ \„,X ) 'I< YwB„ D < $R s }Bj‚ BP ?X J qY‚t
T
„L1
€
€
R Xd
$P X ›
,
€
€
1
€
€
€
€
€
z
„L1
\„,X )
R „b1
c X › „ stI „ s ( 8BI 1,
$P
€
1
€
€
€
€
€
€
€
„L1
€
Z R w„dDb1
$P
c X › „ stI „ s d 8BI 13
1
_„BBP 3$„R b‚ sRRZ8‚ Ys X w ; qY‚t b‚ ,tBb Y‚ „s8$h{s$Bt A‚Ys%$BZ„ BP Y‚ }js{‚
< $t Y‚ h‚jI w?1 , 3 3 3 , ?X , 3 3 3 , ?„ D P„B8 _„B}1 B„‚B%‚„ Y‚ }js{‚ <1 $R Zt„s8$h‚I
$t Y‚ ‚-‚tR$BtR w?d , ?1 Dbw?d D stI w?d , ?1 Dbw?1 D Ak _„B}dn Vjj sRR‚„$BtR BP Y‚
$‚8R $D $$D stI $$$D $t _„B}1M PBjjBb tBb Ak VAYkst,s„:R j‚88s yt Y‚ {sR‚ X ) 1 b‚
s}}jk _„B}1E $tR‚sI BP _„B}1 B Y‚ h‚jI w?1 , 3 3 3 , ?„ D y‚8 $%D $R }„B%‚I R$8$js„jk sR
$t _„B}1
ƒ R I‚ht‚I Ak eJw1dD qY‚t
qY‚B„‚8 1 N‚ ) ) wBd , B1 , Bn , 333D A‚ Y‚ Bb‚„ B%‚„  ) $
Y‚ ‚tZR /wB„ D Rs$Rh‚R
/wB„ D
RL1
j$8
)
3
„
„
R
1wR b dD
B„‚ }„‚{$R‚jk b‚ Ys%‚U
V q!Gei !3 3=W]qy!W 3yeN*7 !zei ]= y] 3yeN*7
dn
$D 3B„ „ s ( 8BI ;
/wB„ D )
d
„
wR „Ld L 1R „ b 1R w„L1Db1 b 1R „b1 L RD b c R w„1Db1 c wR L dD3
1wR b dD
;
$$D 3B„ „ s 1 8BI ;
/wB„ D )
d
„ b 1 w„1Db1
wR „Ld L 1R „ b ;R w„L1Db1 L RD b
cR
c wR L dD3
1wR b dD
;
$$$D 3B„ „ s d 8BI 1
/wB„ D )
d
„ b d w„dDb1
wR „Ld L 1R „ b R w„LnDb1 b nR w„LdDb1 L RD b
cR
3
1wR b dD
1
_„BBP G‚ b$jj Btjk {BtR$I‚„ Y‚ {sR‚ „ s ( 8BI ; Y‚ BY‚„ {sR‚R s„‚ R$8$js„ stI b‚ j‚s%‚
Y‚8 B Y‚ „‚sI‚„
3B„ 1 › X › „ b‚ {YBBR‚ s }js{‚ <wXD YwB„ D bY${Y $R s }Bj‚ BP ?X stI b‚ I‚tB‚ Ak
wXD
QX U) Qw<wXD M<d D
wXD
Y‚ I$&‚„‚t ‚-}Bt‚t BP <wXD B%‚„ <d U) <wXD MBd VR $t _„B}1 stI 1M b‚ j‚ \„,X I‚tB‚
Y‚ tZ8A‚„ BP }Bj‚R BP ?X $t B„ V}}jk$t _„B}1; 1x stI 1E b‚ R‚‚ Ys Y‚ I‚„‚‚ BP
Y‚ I$&‚„‚t BP Y‚ ‚-‚tR$Bt B„ bBd $R
„
3
R„ b R
„d
I‚ *$& wB„ bBd D )
L 1wR
b dD L
QX c \„,X 3
Rbd
X)1
V{{B„I$t B _„B}1 stI 1M b‚ R}j$ Y‚ RZ8
;„wiD U)
3
QX c \„,X
QX c \„,X $tB PBZ„ }$‚{‚R sR PBjjBbRU
PB„ i ) d, 1, n stI ;,
X;-i
bY‚„‚ Y‚ R‚ -i $R I‚ht‚I sR
-d U) IX L X s d 8BI 1 stI n › X › w„ L dDb1J,
-1 U) IX L X s d 8BI 1 stI w„ L dDb1 c X › „J,
-n U) IX L X s ( 8BI 1 stI 1 › X › w„ L 1Db1J,
-; U) IX L X s ( 8BI 1 stI w„ L 1Db1 c X › „J3
w131D
d;
F=7]eNyW!
eeiiV ViWVN*! pVi]yV <eWWyWp 7qy]<qeW!q<
7$t{‚ „ s ( 8BI ; b‚ Ys%‚ Ys
-d ) IX L X ) d L 17 PB„ RB8‚ 7 b$Y d › 7 c „b;J,
-1 ) IX L X ) w„ L ;7 b 1Db1 PB„ RB8‚ 7 b$Y d › 7 › „b;J,
-n ) IX L X ) 17 PB„ RB8‚ 7 b$Y d › 7 › „b;J,
-; ) IX L X ) w„ L ;7Db1 PB„ RB8‚ 7 b$Y d › 7 › „b;J3
3„B8 _„B}1 stI 1M b‚ Ys%‚
wdD
w„;Db;
w1D
„b;
w„b;DL17
wnD
„b;
„L1n7
w;D
„b;
w„b;DLd7
;„ )
;„ )
;„ )
;„ )
7)d
7)d wR
7)d wR
7)d wR
wR „n7 b 1D c R 17 )
d
1R 1
wR „ b R wn„L;Db; D b 1
wR w„;Db1 b dD,
Rbd
R bd
b 1D c R w„1Db1 )
d
„
wR wn„L;Db; b R w„L1Db1 D b c R w„1Db1 ,
Rbd
1
d
1R
wR „Ld b R wn„L;Db; D b 1
wR „b1 b dD,
Rbd
R bd
b 1D c R 17d )
b 1D c R „b1 )
d
„
wR wn„L;Db; b R w„L1Db1 D b c R „b1 3
Rbd
1
WBb $ PBjjBbR P„B8 eJw11D Ys
I‚ *$& wB„ bBd D ) 1wR „d b dD L
) 1wR „d b dD L
b
) 1wR „d b dD L
R„ b R
wdD
w1D
wnD
w;D
L ;„ L ;„ L ;„ L ;„
Rbd
d
wR „Ld L 1R „ b 1R w„L1Db1 b RD
Rbd
1R
„
wR L dDwR w„1Db1 b dD b c R w„1Db1 c wR L dD
bd
1
R1
d
„
wR „Ld L 1R „ b 1R w„L1Db1 b 1R „b1 L RD b c R w„1Db1 c wR L dD3
Rbd
1
qY‚ <Z„b$9 ‚tZR PB„8Zjs $%‚R
1/wB„ D b 1 ) b1R „d L I‚ *$& wB„ bBd D,
stI Y‚t{‚
1/wB„ D )
d
„
wR „Ld L 1R „ b 1R w„L1Db1 b 1R „b1 L RD b c R w„1Db1 c wR L dD3
Rbd
1
V q!Gei !3 3=W]qy!W 3yeN*7 !zei ]= y] 3yeN*7
dx
n is'Ctsj }js{‚R stI Y‚ j'9' CP Y‚ Cc‚„
yt Y$R R‚{$Bt b‚ RZIk Y‚ Bb‚„ ) sR s Bb‚„ BP PZt{$Bt h‚jIR B%‚„ Y‚ ht$‚ h‚jI $f
BP {s„I$tsj$k f ) R n 7B b‚ Ys%‚ Y‚ PBjjBb$t R$Zs$BtU
) ) wBd , B1 , Bn , 333D $R Y‚ Bb‚„ BP PZt{$Bt h‚jIR B%‚„ $f b$Y f ) R n bY‚„‚
Bd ) $f w?d D $R Y‚ „s$Btsj PZt{$Bt h‚jI stI B7Ld ) B7 w?7Ld D b$Y
?R7 L ?7 b d
d b ?7Ld
)
3
?R7Ld
?7
wn3dD
WB‚ Ys >B7Ld U B7 H ) R stI Ys $f $R Y‚ PZjj {BtRst h‚jI BP B7 PB„ sjj 7 w d wsR PBjjBbR
P„B8 ]B„11D B„‚B%‚„ R$t{‚ Y‚ ‚tZR BP s PZt{$Bt h‚jI B%‚„ $f IB‚R tB {Yst‚ $t Y‚
ƒ f Y‚ PB„8ZjsR PB„ Y‚ ‚tZR /wB„ D $%‚t $t qY81 sjRB
{BtRst h‚jI ‚-‚tR$Bt b$Y  ) $
YBjI PB„ Y‚ Bb‚„ ) {BtR$I‚„‚I B%‚„ $f !Z„ 8s$t Bsj Y‚„‚ $R B RYBb Ys {‚„s$t „s$Btsj
}js{‚R BP Bd ) $f w?d D R}j$ {B8}j‚‚jk $t Y‚ Bb‚„ ) $‚ Y‚k R}j$ {B8}j‚‚jk $t B„ bBd PB„
sjj „ w d qY$R b$jj }„B%$I‚ 8stk „s$Btsj }js{‚R BP B„ b$f stI $t {Bt`Zt{$Bt b$Y qY81
Y$R b$jj }„B%‚ BZ„ 8s$t „‚RZj bY${Y $R qY8nn
3B„ sAA„‚%$s$Bt b‚ $t„BIZ{‚ Y‚ „s$Btsj PZt{$BtR
ywx D U)
xR L x b d
dbx
stI
Kwx
D
U)
3
xR
x
G‚ {BtR$I‚„ Y‚ R‚R
ƒ f RLd ) b dJ stI U) I $
ƒ f ywD CJ3
C U) I $
wn31D
_„B}BR$$Bt nd $D G‚ Ys%‚ t $f stI ' ) RwR L dD
ƒ f stI sjj Y‚R‚
$$D N‚ qY‚t Y‚ ‚JZs$Bt ywD ) KwD YsR ‚-s{jk R „BBR $t $
„BBR A‚jBt B Y‚ R‚ G‚ }BR}Bt‚ Y‚ }„BBP BP _„B}nd B Y‚ ‚tI BP Y$R R‚{$Bt stI b‚ I„sb h„R RB8‚
{BtR‚JZ‚t{‚R BP $
qY‚B„‚8 n1 N‚ ) ) wBd , B1 , Bn , 333D A‚ Y‚ Bb‚„ BP PZt{$Bt h‚jIR B%‚„ $f b$Y f ) R n
bY${Y $R I‚ht‚I „‚{Z„R$%‚jk Ak eJwndD stI j‚ qY‚t Y‚ }js{‚ w?d ) D R}j$R
{B8}j‚‚jk $t sjj ‚-‚tR$BtR B„ bBd qY‚„‚PB„‚ Y‚ tZ8A‚„ BP „s$Btsj }js{‚R BP B„ b$f Rs$Rh‚R
] wB„ D w >B„ U Bd H c ' ) R „ wR L dD3
_„BBP G‚ {js$8 YsU
]js$8 $DU qY‚ }js{‚ w?d ) D YsR ‚-s{jk R „d I$R$t{ ‚-‚tR$BtR < YwB„ D
dE
F=7]eNyW!
eeiiV ViWVN*! pVi]yV <eWWyWp 7qy]<qeW!q<
]js$8 $$DU 3B„ stk RZ{Y }js{‚ < Y‚„‚ $R RB8‚ I RZ{Y Ys < $R s 9‚„B BP Y‚ PZt{$Bt
?„ b I y $R {j‚s„ Ys Y‚ sRR‚„$BtR BP qY8n1 PBjjBb P„B8 ]js$8 $D G‚ }„B%‚ ABY {js$8R Ak
$tIZ{$Bt Bt „ qY‚ {sR‚ „ ) d $R „$%$sj stI b‚ sRRZ8‚ Ys ]js$8 $D stI ]js$8 $$D s„‚
ABY „Z‚ PB„ RB8‚ „ w d N‚ < YwB„ D A‚ Bt‚ BP Y‚ }js{‚R jk$t sAB%‚ w?d ) D Y‚t
Ak $tIZ{$Bt Y‚ }js{‚ < $R s 9‚„B BP ?„ b I b$Y I qY‚ PZt{$Bt ?„Ld Rs$Rh‚R Y‚
‚JZs$Bt yw?„Ld D ) Kw?„ D qB stk RBjZ$Bt BP Y‚ ‚JZs$Bt ywD ) Kw I D {B„„‚R}BtIR s
}js{‚ <I YwB„Ld D b$Y <I M< RZ{Y Ys <I $R s 9‚„B BP ?„Ld b k _„B}nd Y‚ ‚JZs$Bt
ywD ) Kw I D YsR ‚-s{jk R I$R$t{ „BBR stI Y‚t{‚ Y‚ {js$8R $D stI $$D sjRB YBjI PB„
„ L d
3B„ stk Bb‚„ 7 ) wxd , x1 , xn , 333D BP PZt{$Bt h‚jIR B%‚„ s ht$‚ h‚jI Y‚ j$8$
w7 D U) j$8
„
] wx„ D
/wx„ D
‚-$RR R‚‚ >H Vt $88‚I$s‚ {BtR‚JZ‚t{‚ BP qY81 stI qY8n1 $R tBbU
qY‚B„‚8 nn N‚ ) ) wBd , B1 , Bn , 333D A‚ Y‚ Bb‚„ BP PZt{$Bt h‚jIR B%‚„ $f wb$Y f ) R n D
bY${Y $R I‚ht‚I „‚{Z„R$%‚jk Ak eJwndD qY‚t $R j$8$ Rs$Rh‚R
w)D ) j$8
„
1wR 1 b dD
] wB„ D
w
3
/wB„ D
RL1
3B„ Y‚ „‚sj tZ8A‚„ \wR n D wR‚‚ I‚ht$$Bt $t Y‚ $t„BIZ{$BtD b‚ BAs$tU
]B„Bjjs„k n; wp‚t‚„sj$9s$Bt BP $t,:R jBb‚„ ABZtID 3B„ stk }„$8‚ }Bb‚„ R b‚ Ys%‚
\wR n D w
1wR 1 b dD
3
RL1
WBb b‚ }„B%‚ _„B}nd 3B„ Y$R b‚ t‚‚I Y‚ PBjjBb$t bB j‚88sRU
N‚88s nx N‚ Y‚ R‚R C stI A‚ sR I‚ht‚I $t wn1D qY‚tU
$D 'C ) R L d stI ' ) RwR L dD
$$D yP C Y‚t R
1 LRLd
) bd yt }s„${Zjs„ Y‚ R‚ C $R {Bts$t‚I $t $f $$$D qY‚ R‚ $R {Bts$t‚I $t $f ƒ f BP Y‚
_„BBP $D k I‚ht$$Bt Y‚ R‚ C {BtR$RR BP Y‚ 9‚„BR $t Y‚ sj‚A„s${ {jBRZ„‚ $
}BjktB8$sj W wx D ) x RLd b x L d 7$t{‚ W wx D $R {j‚s„jk R‚}s„sAj‚ b‚ ‚ Ys 'C ) R L d
7$8$js„jk Y‚ R‚ {BtR$RR BP Y‚ 9‚„BR BP _ wx D U) x R L d x b d PB„ sjj ‚j‚8‚tR C
qY‚R‚ }BjktB8$sjR s„‚ {j‚s„jk R‚}s„sAj‚ Y‚t{‚ ' ) RwR L dD
$$D yP RLd ) b d Y‚t R
1 LR
) R b d Zj$}jk$t Y‚ jsR ‚JZsj$k Ak b‚ Y‚t ‚ Ys
V q!Gei !3 3=W]qy!W 3yeN*7 !zei ]= y] 3yeN*7
d
1
R LRLd ) RLd b ) bd WB‚ Ys R 1 L R L d $R Y‚ tB„8 ‚-}Bt‚t $t $f b$R stI Y‚t{‚ Y‚
R‚ C $R {Bts$t‚I $t $f $$$D N‚ qY‚t ywD ) PB„ RB8‚ C $‚ b‚ Ys%‚ d b ) R =R$t $‚8 $$D $
Y‚t PBjjBbR Ys
R
n
1
n
1
1
) b R LRLd c R ) b RLd w R DR ) b RLd wd b DR ) b RLd L RLd c R
) b RLd L c w R DR ) b RLd L wd b DR ) b RLd L b R
) b RLd L b wd b D ) wb RLd L b dD L ) ,
1
stI Y‚t{‚ Y‚ R‚ $R {Bts$t‚I $t $f N‚88s nE yP Y‚t KwD C
_„BBP N‚ qY‚t Y‚„‚ $R RB8‚ C b$Y R ) d b 3 <‚t{‚
KwD )
R L b d
R b R
)
) Rd wd b D )U #,
stI b‚ Ys%‚ B RYBb Ys # C G‚ Ys%‚
1
w# RLd b # L dD ) wwd b DRLd c R d b wd b D Rd L dD
1
) wd b b R L RLd D R b wd b D R L 1
) b RLd c R b wd b D R L ) bw R DR b wd b Dwd b D L ) bwd b DR b d L L ) R b d L ) (3
<‚t{‚ # RLd ) # b d stI # C
WBb b‚ Z„t B Y‚ }„BBP BP _„B}nd
_„BBP BP _„B}BR$$Bt nd $D qY$R $‚8 bsR sj„‚sIk RYBbt $t N‚88s nx
ƒ f KwD CJ 7$t{‚ I‚wKD ) R Y‚ {s„I$tsj$k BP Y‚ R‚ Rs$Rh‚R
$$D N‚ U) I $
' › R c 'C ) RwR L dD k N‚88s nE b‚ ,tBb Ys t stI R$t{‚ ' ) RwR L dD Ak
N‚88s nx b‚ {Bt{jZI‚ Ys ) qY$R {B8}j‚‚R Y‚ }„BBP BP _„B}nd
qY‚ PBjjBb$t „‚8s„, bsR }B$t‚I BZ B ZR Ak ] _ $tU
i‚8s„, n w{P >1(HD y $R b‚jjT,tBbt Ys BBI jBb‚„ ABZtIR PB„ Y‚ JZst$k \wfD
}„B%$I‚ jBb‚„ ABZtIR PB„ Y‚ PZt{$Bt f w&D bY${Y }jskR s }„B8$t‚t „Bj‚ $t {BI$t Y‚B„k
3B„ Y‚ I‚ht$$Bt BP f w&D b‚ „‚P‚„ B >dnH 7‚{E1 B„ >dEH ]Yzyy1 qY‚ p$jA‚„Tzs„RYs8B%
ABZtI Rs‚R Ys
f w&D w d b If w&D PB„ sjj & >d, wf b dDbfH,
wn3nD
dM
F=7]eNyW!
eeiiV ViWVN*! pVi]yV <eWWyWp 7qy]<qeW!q<
bY‚„‚ If w&D I‚tB‚R Y‚ fTs„k ‚t„B}k PZt{$Bt qY‚ PBjjBb$t ABZtI bY${Y $R AsR‚I Bt
sj‚A„s${T‚B8‚„${ {BI‚R bsR h„R }„B%‚I Ak qRPsR8st zjsIZ stI $t, wR‚‚ >dMHD
f w&D w d b & b \d PB„ stk \ b b$Y ( c \ › \wfD3
wn3;D
3B„ f ) R n b‚ {st {YBBR‚ \ ) 1wR 1 b dDbwR L 1D Ak ]B„n; stI ‚%sjZs$t Y‚ ABZtIR wnnD
stI wn;D sAB%‚ s &( U) wf b dDbw1f b dD b‚ htI ‚sR$jk Ys
d b &( b
RL1
k d b IRn w&( D PB„ sjj R w 3
1wR 1 b dD
qY‚„‚PB„‚ Y‚ qRPsR8stTzjsIZT$t, ABZtI $8}„B%‚R Bt Y‚ p$jA‚„Tzs„RYs8B% ABZtI $t s
tBtT‚8}k B}‚t $t‚„%sj {Bts$t$t &( PB„ sjj f ) R n b$Y R w 
; is9'P'‚I }js{‚R CP k}‚ n
yt Y$R R‚{$Bt b‚ b$jj }„B%‚ Y‚ $‚8R $D stI $$D BP _„B}BR$$Bt 1 stI YZR {B8}j‚‚ Y‚
‚tZR {sj{Zjs$BtR wR‚‚ qY81D PB„ Y‚ Bb‚„ ) ) wB7 D7d $%‚t Ak eJw(D i‚{sjj Ys
Y‚ ‚-‚tR$BtR B7Ld bB7 s„‚ $%‚t Ak B7Ld ) B7 w?7Ld D bY‚„‚
d b ?7Ld
?R7 L ?7 b d
)
3
?R7Ld
?7
qY$R 8‚stR Ys ?7Ld $R s „BB BP Y‚ }BjktB8$sj
?R7 L ?7 b d
c x R L x b d B7 >x H,
?7
stI Y‚t{‚ b‚ s„‚ j‚I B RZIk }BjktB8$sjR BP Y‚ PB„8 yx R L Kx L  b$Y {B‚^{$‚tR y, K, 
$t s PZt{$Bt h‚jI B N‚88s ;d N‚ obI A‚ s R‚}s„sAj‚ ‚-‚tR$Bt BP PZt{$Bt h‚jIR B%‚„ s h‚jI  BP {Ys„s{T
‚„$R${ € k ( VRRZ8‚ Ys >o U IH ) E s ( 8BI € stI j‚ o A‚ RZ{Y Ys o ) Iw D
7Z}}BR‚ Ys Rs$Rh‚R st ‚JZs$Bt
y
E
LK L)(
b$Y y, K,  I stI j‚ h YwID A‚ s }js{‚ BP I RZ{Y Ys 8h wyD ) 8h wKD ) ( qY‚t Y‚
PBjjBb$t YBjIRU
$D yP 8h wD w ( Y‚t h $R Zt„s8$h‚I $t obI
$$D yP 8h wD ) bd Y‚t h $R Bsjjk „s8$h‚I $t obI stI Y‚ PZt{$Bt d $R s }„$8‚
‚j‚8‚t PB„ Y‚ }js{‚ < YwoD bY${Y j$‚R B%‚„ h B„‚B%‚„ Y‚ I$&‚„‚t ‚-}Bt‚t BP
<Mh $R ‚JZsj B Qw<Mh D ) 1E b 1
V q!Gei !3 3=W]qy!W 3yeN*7 !zei ]= y] 3yeN*7
_„BBP
d
k sRRZ8}$Bt Y‚ }BjktB8$sj
y

c x L I>x H
K
y
B%‚„ Y‚ h‚jI I
wx D ) x E L
$R Y‚ 8$t$8sj }BjktB8$sj BP
$D yt Y$R {sR‚ 8h wKbyD ) ( stI 8h wbyD w ( Y‚t{‚ $R $t‚„sj B%‚„ Y‚ %sjZs$Bt „$t BP
h stI PB„ sjj < YwoD b$Y <Mh b‚ Ys%‚ 8< w I w DD ) 8< wKbyD ) ( y PBjjBbR Ak N‚88s
dd $D Ys Y‚ }js{‚ h $R Zt„s8$h‚I $t obI
$$D N‚ < A‚ s }js{‚ BP o jk$t B%‚„ h qY‚t 8< wyD ) 8< wKD ) ( stI 8< wD ) b
b$Y ) w<Mh D 3„B8 Y‚ ‚JZs$Bt y E L K L  ) ( b‚ {Bt{jZI‚ Ys 8< w D c (
Y‚t{‚ 8< wy E D ) E c 8< w D c 8< w D ) 8< wK D qY‚t E c 8< w D ) 8< wD ) b 7$t{‚
› >o U IH ) E Y$R $8}j$‚R Ys ) E stI 8< w D ) bd stI RB Y‚ PZt{$Bt d $R s
}„$8‚ ‚j‚8‚t PB„ < qY‚ 8$t$8sj }BjktB8$sj BP d B%‚„ I $R
'wx D ) x E L
K
y
c x Ed L


stI Ak N‚88s dd $$D b‚ BAs$t
Qw<Mh D ) 8< w'I w d DD ) 8< wwKbD c w d DE1 D
) 8< wKD b 8< wD L wE b 1D ) 1E b 13
ƒ R $R st sj‚A„s${
3„B8 Y‚„‚ Bt b‚ sRRZ8‚ sjj tBs$BtR P„B8 7‚{$Bt 1 yt }s„${Zjs„  ) $
{jBRZ„‚ BP $R stI Y‚ Bb‚„ ) ) wBd , B1 , Bn , 333D B%‚„  $R „‚{Z„R$%‚jk I‚ht‚I Ak Bd ) w?d D
stI PB„ 7 w d B7Ld ) B7 w?7Ld D b$Y
?R7 L ?7 b d
d b ?7Ld
)
3
?R7Ld
?7
w(3D
G‚ t‚‚I B $t%‚R$s‚ Y‚ „s8$h{s$Bt A‚Ys%$BZ„ BP }js{‚R BP Xqk}‚ n PB„ X BII" qY$R
8‚stR wR‚‚ _„B}1;D Ys b‚ {BtR$I‚„ s }js{‚ < YwB„ D bY${Y $R s }Bj‚ BP Y‚ PZt{$Bt ?X
PB„ RB8‚ BII X In, 3 3 3 , „J 7$t{‚ b‚ b$jj I‚R{„$A‚ Y‚ „s8$h{s$Bt A‚Ys%$BZ„ BP RZ{Y }js{‚R
$t sjj ‚-‚tR$BtR Bz bBd b‚ {st sRRZ8‚ Ys „ w 1X RB b‚ Ys%‚
X ) 10 L d b$Y 0 w d, stI „ w ;0 L 13
7$t{‚ ?X ) s < $ PBjjBbR P„B8
T
(
€
€
€
z ?i )
€
d
€
€
Z
#7
N‚88s 1n Ys Y‚ PBjjBb$t YBjIR s Y‚ }js{‚ <U
PB„
PB„
PB„
PB„
i
i
i
i
w 10 L 1,
) 10 L d,
) 10 L d b 17, d › 7 › 0,
) 10 L 1 b 17, d › 7 › 0,
w;3dD
1(
F=7]eNyW!
eeiiV ViWVN*! pVi]yV <eWWyWp 7qy]<qeW!q<
b$Y {‚„s$t ‚j‚8‚tR #7 p ) I  R L ) dJ, PB„ 7 ) d, 3 3 3 , 0
N‚ obB A‚ st ‚-‚tR$Bt BP PZt{$Bt h‚jIR RZ{Y Ys B t o t B„ G‚ Rsk Ys Y‚ }js{‚
< YsR „s8$h{s$Bt $tI‚- $t obB $P Y‚ }js{‚ <Mo YwoD YsR „s8$h{s$Bt $tI‚- B%‚„
Y‚ }js{‚ <MB 3„B8 _„B}BR$$Bt dn b‚ {st „‚sI B& Y‚ „s8$h{s$Bt $tI‚- BP < $t RB8‚
RZA‚-‚tR$BtR BP B„ U
T
d
€
€
€
€
€
R
€
€
€
€
€
z Rbd
)
d
€
€
€
R
€
€
€
€
€
Rbd
€
€
Z
d
$t
$t
$t
$t
$t
$t
$t
w?7 , ?7Ld Dbw?7Ld D
w?7 , ?7Ld Dbw?7 D
w?7 , ?7Ld Dbw?7Ld D
w?7 , ?7Ld Dbw?7Ld D
w?7 , ?7Ld Dbw?7Ld D
w?7 , ?7Ld Dbw?7 D
w?7 , ?7Ld Dbw?7 D
PB„
PB„
PB„
PB„
PB„
PB„
PB„
7 w 10 L 1,
7 w 10 L d,
7 ) 10 L d,
7 ) 1, ;, 3 3 3 , 10,
7 ) d, n, 3 3 3 , 10 b d,
7 ) 10,
d › 7 › 10 b d3
w;31D
3B„ 0 ) 1 Y$R }s‚„t $R RYBbt $t 3$Z„‚ dU
x1 = 1
1
x2 = 2
1
q
1
q-
q
x4 = 1
x3 = 1
1
q
x5 =
q-1
1
K(x 5 ,x 6 )
1
K(x 3 ,x 4 )
K(x 7 ,x 8 )
q
x6 = 0
1
q
x7 = 0
1
q
x8 = 0
1
q
x9 = 0
1
x10 = 0
Figure 1 (for t = 2)
k VAYkst,s„:R j‚88s wR‚‚ N‚88s d1D b‚ {Bt{jZI‚ P„B8 w;1D Ys Y‚ „s8$h{s$Bt
$tI‚- BP Y‚ }js{‚ < Rs$Rh‚R sjRB
T
€
z
d
$t Bi bBid PB„ i ) 1, 3 3 3 , 10,
)
R b d $t Bi bBid PB„ i ) 10 L d,
€
Z R0
$t B10Ld bw?10Ld D3
qY$R }„B%‚R Y‚ $‚8 $D stI }s„ BP Y‚ $‚8 $$D $t _„B}1 =tPB„Zts‚jk VAYkst,s„:R
j‚88s IB‚R tB s}}jk PB„ i w X L d ) 10 L 1 R‚‚ 3$ 1
V q!Gei !3 3=W]qy!W 3yeN*7 !zei ]= y] 3yeN*7
1d
?
K(xs-1 ,xs ,x
s+1)
K(xs-2,xs-1,xs )
q-1
q
1
q
K(xs-1 ,xs )
q
1
K(xs-2 )
xs-2 = 1
q-1
q
1
K(xs-1)
K(xs)
xs-1 =
xs =
q-1
q
K(xs+1)
xs = 0
+1
Figure 2
y b$jj A‚ {Bt%‚t$‚t B {Yst‚ Y‚ ‚t‚„sB„R ?7 BP Y‚ h‚jIR w?7 D Rj$Yjk s{{B„I$t B
Y‚ }js{‚ < G‚ R‚
l
?10Ld7 b d
PB„ d › 7 › 10, 7 s ( 8BI 1,
…7 U)
?10Ld7 b #w7LdDb1 PB„ d › 7 › 10, 7 s d 8BI 1,
V U) ?d
10Ld
.7 U) ?10LdL7 PB„ sjj 7 w d3
y $R Y‚t BA%$BZR Ak w;dD Ys Y‚ }js{‚ < $R s {B88Bt 9‚„B BP Y‚ PZt{$BtR …d , 3 3 3 , …10 V, .d , .1 , 333 G‚ {st „‚b„$‚ eJw(D $t ‚„8R BP Y‚ PZt{$BtR …7 , V, .7 sR PBjjBbRU
R
b…7Ld
…7R L …7
)
R
…7R L #w7LdDb1
…7Ld L d
PB„ 7 s d 8BI 1,
R
…7Ld
L …7Ld
b…7
)
PB„ 7 s ( 8BI 1,
R
…7 L d
…7Ld L #w7L1Db1
w;nD
w;;D
…dR b #d
bd)
,
…d L #d
w;xD
.d b d
V R b V Rd b d
)
,
.dR
V Rd
w;ED
R
V bV
Rd
11
F=7]eNyW!
eeiiV ViWVN*! pVi]yV <eWWyWp 7qy]<qeW!q<
d b .7Ld
.7R L .7 b d
)
PB„ 7 w d3
R
.7Ld
.7
w;D
qY‚ PBjjBb$t RZAh‚jIR BP B„ b$jj }jsk s {„Z{$sj „Bj‚ PB„ Y‚ I‚‚„8$ts$Bt BP Y‚ „s8$h{s$Bt
A‚Ys%$BZ„ BP Y‚ }js{‚ < G‚ R‚ PB„ d › i › 7 › 0 wR‚‚ 3$ nDU
I7,i U) w…d , …1 , 3 3 3 , …17 , V, .d , 3 3 3 , .1i1 D,
o7,i U) I7,i w.1id D
Ui U) oi,i w.1i D3
B„‚B%‚„ b‚ R‚
h7,i U) <MI7,i stI <7,i U) <Mo7,i 3
qY‚ t‚- Y‚B„‚8 $R Y‚ ,‚k „‚RZj j‚sI$t B Y‚ ‚tZR PB„8ZjsR $t qY81 qY‚ sRR‚„T
$BtR BP qY8;1 {B„„‚R}BtI B Y‚ ‚t{$„{j‚I „s8$h{s$Bt $tI${‚R $t 3$n
L 3 = F 13
1
E 3,3
q
q
H3,3
E 3,2
q
H3,2
L2
1
E 3,1
E2,2
q
q
H3,1
q
q
H 2,2
q
q
E 2,1
q
H 2,1
q
L1
1
q
q
E1,1
q
q
H1,1
q
q
q
1
1
1
q
1
1 1
q
q q-1
1
x6 = 1
x7 =
q-1 q
1 q
1 q
1
x8 = 0
x9 = 0
x10 = 0
x11 = 0
q
1
q
1
F1
x1 = 1
x2 = 3
x3 = 1
x4 = 2 x5 = 1
Figure 3 (for t=3)
x12 = 0
x13 = 0
V q!Gei !3 3=W]qy!W 3yeN*7 !zei ]= y] 3yeN*7
1n
qY‚B„‚8 ;1 N‚ d › i › 7 › 0 qY‚t Y‚ }js{‚ < $R Bsjjk „s8$h‚I $t Y‚ ‚-‚tR$Bt
o7,i bI7,i stI $ $R Zt„s8$h‚I $t Y‚ ‚-‚tR$Bt Ui boi,i B„‚B%‚„ Y‚ I$&‚„‚t ‚-}Bt‚t BP
<7,i Mh7,i $R
Qw<7,i Mh7,i D ) 1R b 13
VR s {BtR‚JZ‚t{‚ BP qY8;1 b‚ Ys%‚ Y‚t
]B„Bjjs„k ;n qY‚ „‚R„${$Bt <i ) <MBi BP Y‚ }js{‚ < Rs$Rh‚R
$D w<i M<id D ) d $P 10 L d c i c ;0 L 1 stI i s d 8BI 1
$$D w<i M<id D ) R stI Qw<i M<id D ) 1R b 1 $P 10 L d c i c ;0 L 1 stI i s ( 8BI 1
$$$D w<i M<id D ) R stI Qw<i M<id D ) 1R b 1 $P i w ;0 L 1
WB‚ Ys ]B„;n $t{jZI‚R sjj Y‚ 8$RR$t sRR‚„$BtR BP _„B}1 stI Y‚t{‚ {B8}j‚‚R Y‚
}„BBP BP Y‚ s$t qY‚B„‚8
_„BBP BP ]B„;n $D 3$„R b‚ {BtR$I‚„ Y‚ {sR‚ i ) ;0 L d qY‚t Bi ) U0 stI Bid ) o0,0 stI < $R Zt„s8$h‚I $t U0 bo0,0 Ak qY8;1
W‚- j‚ 10 L d c i c ;0 L d stI i s d 8BI 1 qY‚t Bi ) I0,>Ld stI Bid ) o0,> PB„ RB8‚ >
b$Y d › > › 0 b d wR‚‚ 3$nD !AR‚„%‚ Ys I0,>Ld u o0,> u o>,> stI I0,>Ld u U> u o>,> stI Ys I0,>Ld $R Y‚ {B8}BR$‚ h‚jI BP o0,> stI U> k qY8;1 Y‚ }js{‚ < $R Zt„s8$T
h‚I $t Y‚ ‚-‚tR$Bt U> bo>,> stI Y‚„‚PB„‚ < $R Zt„s8$h‚I $t Y‚ ‚-‚tR$Bt I0,>Ld bo0,> Ak
N‚88s d1
$$D WBb j‚ 10 L d c i c ;0 L 1 stI i s ( 8BI 1 qY‚t Y‚„‚ $R RB8‚ > b$Y d › > › 0
RZ{Y Ys Bi ) o0,> stI Bid ) I0,> stI sjj sRR‚„$BtR BP $‚8 $$D PBjjBb $88‚I$s‚jk P„B8
qY8;1
$$$D 3B„ ibd w ;0Ld Y‚ „s8$h{s$Bt $tI‚- BP < $t Y‚ ‚-‚tR$Bt Bid bw?id D $R ) Rbd
Ak qY8;1 wR‚‚ 3$nD qY‚ }js{‚ < $R Bsjjk „s8$h‚I $t Y‚ ‚-‚tR$Bt w?id , ?i Dbw?id D
b$Y I$&‚„‚t ‚-}Bt‚t Q ) R wR‚‚ _„B}dn $$DD =R$t N‚88s d1 b‚ {Bt{jZI‚ Ys
w<i M<id D ) R stI 8B„‚B%‚„ Qw<i M<id D ) wR b dD c R b wR b 1DwR b dD ) 1R b 1
y „‚8s$tR B }„B%‚ qY8;1 qY$R }„BBP b$jj A‚ I$%$I‚I $tB bB }„B}BR$$BtR bY${Y „‚s
Y‚ {sR‚R i ) d stI i k d „‚R}‚{$%‚jk yt ABY {sR‚R Y‚ 8s$t $I‚s $R B s}}jk N‚88s
;d =tPB„Zts‚jk Y‚ XBA%$BZR" ‚t‚„sB„ BP Y‚ {B„„‚R}BtI$t h‚jI ‚-‚tR$Bt o7,i bI7,i
w„‚R} Ui boi,i D IB‚R tB 8‚‚ Y‚ sRRZ8}$BtR BP N‚88s ;d qY‚„‚PB„‚ b‚ 8ZR h„R }‚„T
PB„8 X}Bj‚ B„I‚„ „‚IZ{$BtR" stsjBBZR B <sRR‚:R }Bj‚ B„I‚„ „‚IZ{$BtR PB„ V„$tT7{Y„‚$‚„
1;
F=7]eNyW!
eeiiV ViWVN*! pVi]yV <eWWyWp 7qy]<qeW!q<
‚JZs$BtR wR‚‚ >dEH ]YyyyD
qY‚ PBjjBb$t tBs$Bt b$jj A‚ %‚„k ZR‚PZj 3B„ s PZt{$Bt h‚jI Bb s }js{‚ h YwB D
‚j‚8‚tR Fd , F1 B stI st $t‚‚„ z b‚ b„$‚
Fd ) F1 L 2wzD s h,
$P 8h wFd b F1 D w z
yt }s„${Zjs„ b‚ b„$‚ F ) 2w(D s h 8‚st$t Ys F $R YBjB8B„}Y${ s Y‚ }js{‚ h i‚{sjj
Ys h7,i w„‚R} <7,i D I‚tB‚R Y‚ „‚R„${$Bt BP Y‚ }js{‚ < YwB„ D B Y‚ h‚jI I7,i w„‚R}
o7,i D PB„ d › i › 7 › 0
3$Z„‚ ; A‚jBb Y‚j}R B ZtI‚„RstI Y‚ Rs‚8‚tR $t _„B};; stI ;x
f3
1
3,3
Q3,3
q
q
P3,3
Q3,2
3,2
q
f2
P3,2
1
3,1 = 3 Q
3,1
q
2,2
q
P3,1
3
Q2,2
q
q
P2,2
q
2
q
2
f1
1
P 2,1
q
q
Q2,1
q
q
1 Q1,1
q
q
1 P1,1
q
q
q
1
1
1
q
1
1 1
q
q q-1
1
x6 = 1
x7 =
q-1 q
1 q
1 q
1
x8 = 0
x9 = 0
x10 = 0
x11 = 0
q
1
q
1
F1
x1 = 1
x2 = 3
x3 = 1
x4 = 2 x5 = 1
Figure 4 (for t=3)
x12 = 0
x13 = 0
V q!Gei !3 3=W]qy!W 3yeN*7 !zei ]= y] 3yeN*7
1x
_„B}BR$$Bt ;; wqY‚ {sR‚ i ) dD 3B„ d › 7 › 0 b‚ {BtR$I‚„ Y‚ PZt{$BtR
+7 U) V d c 7>)d …1> I7,d stI
7
U) V d .d L
7
>
>)d wbdD \> #> +>
o7,d b$Y \> U)
>
E)d
R
#E
3
qY‚t Y‚ PBjjBb$t YBjIRU
$D 8h7,d wV D ) R 7 l
8h7,d w…> D )
R w17>LdDb1 c wR b dD PB„ d › > › 17, > s d 8BI 1,
R w17>Db1 c wR b dD
PB„ d › > › 17, > s ( 8BI 1,
8h7,d w+7 D ) bd $‚ Y‚ PZt{$Bt +7d $R s jB{sj }s„s8‚‚„ s Y‚ }js{‚ h7,d $$D o7,d ) I7,d w 7 D stI Y‚ 8$t$8sj }BjktB8$sj BP
wx D ) x R b
7
B%‚„ I7,d YsR Y‚ PB„8
…d L #d
c x L wbdD7Ld \7 +7 b _,
…dR b #d
PB„ RB8‚ PZt{$Bt _ I7,d bY${Y $R YBjB8B„}Y${ s Y‚ }js{‚ h7,d $$$D qY‚ }js{‚ h7,d $R Bsjjk „s8$h‚I $t Y‚ ‚-‚tR$Bt o7,d bI7,d stI Y‚ PZt{$Bt
jB{sj }s„s8‚‚„ s <7,d qY‚ I$&‚„‚t ‚-}Bt‚t BP <7,d $R
Qw<7,d Mh7,d D ) 1R b 13
$%D 3B„ 1 › 7 › 0 Bt‚ YsR
+7d ) \Rd
c +7R b +7 L 2w(D s h7,d 3
7
%D 3B„ 1 › 7 › 0 Bt‚ YsR
7d
%$D N‚ Wd U) .1 c
R
d
L d c
d
) #7R c
7
b #7 c
R
7
L 2w(D s <7,d 3
Ud b$Y d ) #dRd qY‚t Ud ) od,d wWd D stI
w.dR L .d b dD c WdR L w.d c
RwRdD
D
d
c Wd L _d ) (,
PB„ RB8‚ _d od,d bY${Y $R YBjB8B„}Y${ s Y‚ }js{‚ <d,d %$$D qY‚ }js{‚ < $R Zt„s8$h‚I $t Y‚ ‚-‚tR$Bt Ud bod,d _„BBP qY‚ $‚8 $D PBjjBbR ‚sR$jk P„B8 w;1D stI VAYkst,s„:R N‚88s {P 3$n
G‚ b$jj h„R }„B%‚ $$D stI $$$D $t Y‚ {sR‚ 7 ) d eJw;ED {st A‚ b„$‚t sR
w WR
.d
.d b d
)
R
V
V wV b V Rd b dD
d
7
$R s
1E
F=7]eNyW!
stI Ak eJw;xD Y$R $%‚R
w
eeiiV ViWVN*! pVi]yV <eWWyWp 7qy]<qeW!q<
.d
V
WR
b
…d L #d .d …d L #d d
c
L R
c ) (3
…dR b #d V
…d b #d V
w;3MD
!AR‚„%‚ Ys od,d ) Id,d wjD b$Y j ) .d bV stI Ys eJw;MD $R st ‚JZs$Bt PB„ j B%‚„
Id,d BP Y‚ PB„8 yjR L Kj L  ) ( sR $t N‚88s ;d b$Y 8hd,d wyD ) 8hd,d wKD ) ( <Bb‚%‚„
N‚88s ;d {sttB A‚ s}}j$‚I I$„‚{jk R$t{‚ 8hd,d wD ) bR G‚ Y‚t „‚}js{‚ Y‚ ‚t‚„s$t
‚j‚8‚t .d bV BP Y‚ h‚jI ‚-‚tR$Bt od,d bId,d Ak Y‚ ‚j‚8‚t
.d
b \d #d +d 3
V
$R s 9‚„B BP Y‚ }BjktB8$sj
d
y PBjjBbR P„B8 eJw;MD Ys
d
)
wx D ) x R b
b$Y
/d ) \Rd #dR +dR b \d #d +d c
…d L #d
c x L /d
…dR b #d
w;3D
…d L #d
…d L #d d
L R
c Id,d 3
R
…d b #d …d b #d V
WB‚ Ys #d $R1 R$t{‚ #dR L #d ) d qY‚„‚PB„‚ b‚ Ys%‚ \d ) #dR $R1 stI \Rd #dR ) #dRd =R$t +d ) …1 bV stI eJw;nD b‚ BAs$t
/d ) #dRd c +dR b
d
)
V
…d L #d
+d
…d L #d d
c Rd L R
c
R
…d b #d #d
…d b #d V
w
W
…1R
…d L #d …1
…d L #d
Rd
#d c Rd b R
c
L
3
V
…d b #d #dRd …dR b #d
3„B8 eJw;nD stI w;xD b‚ Ys%‚
…1R wd b V D
wd b V Dw…1 L dD
…1R
)
)
Rd
Rd
R
V
V
bV
w…d L #d DRd
stI Y‚t{‚
/d
d
)
V
d
)
V
w
#dRd wd b V D
…d L #d …1
…d L #d
c w…1 L dD b R
c Rd L R
Rd
w…d L #d D
…d b #d #d
…d b #d
W
w
W
…1
wd L 2wRDD c w…1 L dD L wd L 2wRDD c Rd b d L 2wRD
#d
w
W
d
…1
)
…1 L Rd L 2wRD
V
#d
)
w;3d(D
…1 d
c
L 2w(D ) \d +d L 2w(D s Y‚ }js{‚ hd,d 3
V #dR
w;3ddD
V q!Gei !3 3=W]qy!W 3yeN*7 !zei ]= y] 3yeN*7
1
G‚ Ys%‚ ZR‚I Y‚„‚ Ys 8hd,d wV D ) R stI 8hd,d w…d D w R qYZR b‚ Ys%‚ }„B%‚I $$D $t Y‚ {sR‚
7 ) d qY‚ sRR‚„$BtR BP $$$D wPB„ 7 ) dD PBjjBb tBb $88‚I$s‚jk P„B8 N‚88s ;d wBAR‚„%‚
Ys Y‚ }js{‚ hd,d $R s 9‚„B BP …d stI 8hd,d w+d D ) bd Ak $D RB N‚88s ;d s}}j$‚RD
WBb b‚ RYBb Y‚ $‚8 %$D
k eJw;D b‚ Ys%‚
w.dR L .d b dD c .1R L .d c .1 b .d ) (,
Y‚t{‚
RwRdD
D
d
w.dR L .d b dD c WdR L w.d
R1
d
c Wd b w
R 1 RLd
D
d
L d
c .d L Rd
R
d
K d ) (,
L_
K d od,d bY${Y $R YBjB8B„}Y${ s Y‚ }js{‚ <d,d 7B b‚ Ys%‚ B }„B%‚
b$Y RB8‚ PZt{$Bt _
Ys Y‚ PZt{$Bt
w
R1
d
R 1 RLd
D
d
L d
c .d b Rd
R
d
w;3d1D
$R YBjB8B„}Y${ s <d,d y PBjjBbR P„B8 w;D stI w;ddD Ys
+d ) b#dR w
stI Y‚t{‚
.d bV
R
d
L
dD
L 2w(D s <d,d ,
)
d
L \d #d +d )
)
d
b #d w
)
b#d Rd
R
d
) b#d
R
d
d
L
dD
L 2w(D
w;3dnD
L wd b #d D
L #dR
eJw;xD stI w;ED $%‚
V
.dR
c
) w…d L #d D c
R
V
.d b d
w
bd
#d
L #d #dR +d
d
d
L 2w(D
L 2w(D s <d,d 3
W
L 2wR 1 wR b dDD s <d,d ,
stI Y‚„‚PB„‚
.dR
.d
d
)b
L L 2wR 1 wR b 1DD s <d,d 3
R
V
V
V
G‚ {Bt{jZI‚ P„B8 w;dnD stI w;d;D Ys
d
) b#dR c
V
Y‚t{‚
V ) b#dR c
stI
.d )
R1
d
R 1
d
.d
c V ) w#dRd DR c
V
R 1 Ld
d
c wd b
c wd L
R 1 LR
d
b
L 2wR 1 DD,
R 1 Ld
d
L 2wR 1 DD
R 1 Ld
d
L 2wR 1 D s <d,d 3
w;3d;D
1M
F=7]eNyW!
eeiiV ViWVN*! pVi]yV <eWWyWp 7qy]<qeW!q<
7$t{‚ d ) #dRd b‚ BAs$t
w
R1
d
L d
R 1 RLd
D
d
c .d b Rd
R
d
) 2w(D s <d,d 3
qY$R {B8}j‚‚R Y‚ }„BBP BP Y‚ $‚8 %$D {P w;d1D qY‚ sRR‚„$Bt $t %$$D PBjjBbR tBb P„B8
%$D stI N‚88s ;d
!Z„ t‚- s$8 $R B }„B%‚ Y‚ $‚8R $%D stI %D BP _„B};; $t Y‚ {sR‚ 7 ) 1
BP Y‚ PZt{$Bt +i b‚ Ys%‚ +1 ) …; c +d stI Y‚t{‚
+d ) +1R c
k I‚ht$$Bt
d
3
c …;
+1Rd
3„B8 eJw;nD w;;D stI w;xD b‚ BAs$t
V Rd …1
w…n L #1 DRd c w…d L #d DRd c wd L …1 DRd
d
)
c
)
R
R
…1 …;
wd b V Dwd L …; D
+1Rd c …;
) w#d #1 DRd c wd b …; D L 2wRD
) \Rd
c wd b …; D L 2wRD s h1,d 3
1
G‚ Ys%‚ ZR‚I sAB%‚ Ys h1,d $R s 9‚„B BP …d , …1 , …n stI V BP B„I‚„ w R stI $ $R s 9‚„B BP
…; BP B„I‚„ wR b dD 7$t{‚ Y‚ PZt{$Bt +1d $R s }„$8‚ ‚j‚8‚t s h1,d $ PBjjBbR Ys
+d ) +1R c \Rd
c wd b …; D L 2w(D
1
) \Rd
c +1R b +1 \Rd
c +1Rd c …; L 2w(D
1
1
c +1R b +1 L 2w(D s h1,d 3
) \Rd
1
qY$R $R Y‚ sRR‚„$Bt $t $%D PB„ 7 ) 1
k w;D stI w;ddD
R
d
RB
R
d
b
b
…d L #d
c
…dR b #d
…d L #d
c
…dR b #d
d
L
…d L #d
cw
…dR b #d
d
d
L \d +d ) 2w(D s hd,d ,
d
R
c w\Rd
1 +1 b +1 D ) 2w(D s h1,d 3
#dR
qY‚„‚PB„‚
w
d
L \1 #1 +1 DR b
L \1 #1 +1 D L
…d L #d
d
c \1 #1 +1 b R c +1 ) 2w(D
R
…d b #d
#d
V q!Gei !3 3=W]qy!W 3yeN*7 !zei ]= y] 3yeN*7
stI Ak Y‚ I‚ht$$Bt BP Y‚ PZt{$Bt
R
1
b
1
1
…d L #d
c
…dR b #d
1
b \1 +1 ) 2w(D s h1,d 3
w;3dxD
k N‚88s ;d Y‚ }js{‚ h1,d $R Bsjjk „s8$h‚I $t Y‚ ‚-‚tR$Bt o1,d bI1,d stI Y‚ PZt{$Bt
$R s }„$8‚ ‚j‚8‚t BP Y‚ }js{‚ <1,d ) <Mo1,d B„‚B%‚„ b‚ {Bt{jZI‚ P„B8 w;dxD Ys
d
1
R
1
7$t{‚
1
)
d
L
1
b \1 +1 ) 2w(D s <1,d 3
L \1 #1 +1 Y$R $8}j$‚R
)
d
1
b #1 \1 +1 )
) b#1
R
1
L #1R
1
1
b #1 w
R
1
L
1D
L 2w(D
L 2w(D s Y‚ }js{‚ <1,d 3
<‚„‚Ak b‚ Ys%‚ }„B%‚I Y‚ $‚8 %D $t Y‚ {sR‚ 7 ) 1 WB‚ Ys b‚ Ys%‚ sjRB }„B%‚I Y‚
$‚8R $$D stI $$$D BP _„B};; $t Y‚ {sR‚ 7 ) 1 Ak w;dxD
WBb b‚ }„B{‚‚I Ak $tIZ{$Bt N‚ 1 › 7 c 0 stI RZ}}BR‚ Ys Y‚ sRR‚„$BtR $$D T %D BP
_„B};; YBjI PB„ 1 › > › 7 G‚ bst B RYBb Ys Y‚k YBjI sjRB PB„ > ) 7 Ld k $tIZ{$Bt
Yk}BY‚R$R b‚ Ys%‚
+7 ) …17 c +7d ) …17 c \Rd
c +7R L 2w(D s h7,d
7
stI Y‚t{‚
c
+7 ) \Rd
7
…17
R
c +7Ld
L 2w(D s h7Ld,d 3
R
…1w7LdD
k eJw;nD stI w;;D Y‚ PBjjBb$t $I‚t$k YBjIRU
R
…17
w…17
L dDw…17Ld L #7Ld DR
)
3
R
…1w7LdD
w…17Ld L #7Ld Dw…1w7LdD L dD
7B
w;3dED
…17
Rd
) #7Ld
c wd b …1w7LdD D L 2wRD s h7Ld,d
R
…1w7LdD
stI {BtR‚JZ‚tjk
Rd
R
+7 ) \Rd
c #7Ld
c wd b …1w7LdD D+7Ld
L 2w(D
7
)
\Rd
7Ld
c
R
+7Ld
b
\Rd
7Ld
c
Rd
w…1w7LdD +7Ld
D
w;3dD
c +7Ld L 2w(D s h7Ld,d 3
WBb b‚ BAR‚„%‚ Ys
Rd
…1w7LdD c +7Ld
) \dR
7Ld L 2wdD s h7Ld,d ,
bY${Y PBjjBbR ‚sR$jk Ak $tIZ{$Bt wZR$t w;d(D stI w;dEDD stI Y‚t{‚ w;dD k$‚jIR
R
+7 ) \Rd
7Ld c +7Ld b +7Ld L 2w(D s h7Ld,d 3
w;3dMD
n(
F=7]eNyW!
eeiiV ViWVN*! pVi]yV <eWWyWp 7qy]<qeW!q<
qY$R $R sRR‚„$Bt $%D BP _„B};;
qY‚ $tIZ{$Bt Yk}BY‚R$R PB„ $‚8 $$D RskR Ys
R
7
b
…d L #d
c
…dR b #d
7
L wbdD7Ld \7 +7 ) 2w(D s h7,d 3
k w;dMD b‚ BAs$t Y‚t
R
7
b
…d L #d
c
…dR b #d
7
R
L wbdD7Ld \7 w\Rd
7Ld c +7Ld b +7Ld D ) 2w(D s h7Ld,d 3
qY‚„‚PB„‚
w
WR
w
d Rd
…d L #d
7Ld
\7 c w
D +7Ld b R
c
7 L wbdD
#7Ld
…d b #d
7
7Ld
L wbdD
\7 c w
d
#7Ld
W
Rd
D
c +7Ld
d Rd
…d L #d
c wbdD7Ld \7 c w
D
c +7Ld L wbdD7 \7 +7Ld ) 2w(D s h7Ld,d 3
R
…d b #d
#7Ld
qY$R $8}j$‚R Ys
L
w
7
L wbdD7Ld \7Ld #7Ld +7Ld DR b
…d L #d
cw
…dR b #d
7
L wbdD7Ld \7Ld #7Ld +7Ld D
LwbdD7L1 \7Ld +7Ld ) 2w(D s h7Ld,d
$‚
…d L #d
c 7Ld L wbdD7L1 \7Ld +7Ld ) _I
w;3dD
R
…d b #d
b$Y _I I7Ld,d YBjB8B„}Y${ s h7Ld,d qY$R $R sRR‚„$Bt $$D PB„ > ) 7 L d stI tBb Y‚ $‚8
$$$D PBjjBbR P„B8 N‚88s ;d 3$tsjjk P„B8 Y‚ I‚ht$$Bt BP i R
7Ld
b
7Ld
)
7
L wbdD7Ld \7Ld #7Ld +7Ld
stI Y‚t $ PBjjBbR P„B8 w;dD Ys
7
)
7Ld
L wbdD7L1 #7Ld \7Ld +7Ld
w
)
7Ld
b #7Ld
) b#7Ld
R
7Ld
R
7Ld
R
L #7Ld
…d L #d
b R
c
…d b #d
7Ld
W
7Ld
L 2w(D
L 2w(D s <7Ld,d 3
qY$R ht$RY‚R Y‚ }„BBP BP _„B};;
yt Y‚ PBjjBb$t }„B}BR$$Bt b‚ b$jj $t%‚R$s‚ Y‚ {sR‚ i w 1 G‚ ,‚‚} sjj tBs$BtR sR
sAB%‚ yt }s„${Zjs„ b‚ Ys%‚ s }js{‚ < YwB„ D BP qk}‚ n stI {BtR$I‚„ Y‚ h‚jIR I7,i , o7,i
stI Ui stI Y‚ }js{‚R <7,i stI h7,i PB„ d › i › 7 › 0 VR A‚PB„‚ b‚ R‚ d ) #dRd V q!Gei !3 3=W]qy!W 3yeN*7 !zei ]= y] 3yeN*7
nd
_„B}BR$$Bt ;x wqY‚ {sR‚ i w 1D *‚ht‚ 7,d U) 7 o7,d sR $t _„B};; stI PB„
1 › i › 7 › 0 I‚ht‚ Y‚ PZt{$Bt 7,i o7,i Ak
T
R
R
€
$P 7 ) i,
z .1i7 c id,id L d c #1 c i,id
7,i U)
€
Z R
R
7d,i L w#7iLd c #7iL1 b#d D c 7,id $P 7 k i3
qY‚t Y‚ PBjjBb$t YBjIR PB„ 1 › i › 7 › 0U
$D 8h7,i wV D ) R id c R 7 8h7,i w.> D ) R id c R 7> c wR b dD
l
8h7,i w…> D )
PB„ d › > › 1wi b dD
R id c R w17>LdDb1 c wR b dD PB„ d › > › 17, > s d 8BI 1,
PB„ d › > › 17, > s ( 8BI 13
R id c R w17>Db1 c wR b dD
$$D o7,i ) I7,i w7,i D stI Y‚ PZt{$Bt 7,i Rs$Rh‚R st ‚JZs$Bt BP Y‚ PB„8
R
#7iL1
L .1i1 b dD c
L w.1i1 c
c 7,i L
c i1
c 7,id ) _,
d
#d
b$Y RB8‚ PZt{$Bt _ I7,i bY${Y $R YBjB8B„}Y${ s h7,i R
w.1i1
R
7,i
Rd
id,id
D
d
$$$D qY‚ }js{‚ <7,i $R Bsjjk „s8$h‚I B%‚„ h7,i Y‚ PZt{$Bt 7,i
$R s jB{sj }s„s8‚‚„ s <7,i stI Y‚ I$&‚„‚t ‚-}Bt‚t $R
Qw<7,i Mh7,i D ) 1R b 13
$%D yP 7 L d › 0 Y‚t Y‚„‚ ‚-$RR s PZt{$Bt _ o7Ld,i bY${Y $R YBjB8B„}Y${ s Y‚ }js{‚
<7Ld,i RZ{Y Ys
#7iL1 R
R
7,i ) #7iL1
c 7Ld,i b id c 7Ld,i
L _3
d
R
%D N‚ Wi U) .1i c i,i
L id c i,i Ui qY‚t Ui ) oi,i wWi D stI Y‚ PZt{$Bt Wi Rs$Rh‚R st
‚JZs$Bt BP Y‚ PB„8
RwRdD
R
w.1id
L .1id b dD c WiR L w.1id c i,i
D c Wi b _ ) (,
b$Y RB8‚ PZt{$Bt _ oi,i bY${Y $R YBjB8B„}Y${ s Y‚ }js{‚ <i,i %$D qY‚ }js{‚ <i,i $R Zt„s8$h‚I $t Y‚ ‚-‚tR$Bt Ui boi,i _„BBP G‚ h„R {BtR$I‚„ Y‚ {sR‚ i ) 1 y‚8 $D PBjjBbR Y‚t wPB„ sjj 1 › 7 › 0D $88‚I$s‚jk
P„B8 _„B};; stI VAYkst,s„:R N‚88s R‚‚ 3$n G‚ }„B%‚ Y‚ „‚8s$t$t sRR‚„$BtR wPB„
i ) 1D Ak $tIZ{$Bt B%‚„ 7 k _„B};; %$D Y‚ PZt{$Bt Wd ) .1 Rd L d d $R YBjB8B„}Y${
s Y‚ }js{‚ h1,1 $‚
.1 Rd ) bd d L 2w(D s h1,1 3
n1
F=7]eNyW!
eeiiV ViWVN*! pVi]yV <eWWyWp 7qy]<qeW!q<
eJw;D PB„ 7 ) 1 $%‚R
w.1R L .1 b dD c .nR L .1 .n b .1 ) (3
R
d
G‚ 8Zj$}jk Y$R ‚JZs$Bt Ak
stI BAs$t
w.1R L .1 b dD c w.n
R
dD
Rd
d
L .1
c w.n
dD
R
d
b .1
) (,
Y‚t{‚
w.1R L .1 b dD c w.n
R
dD
Rd
d
L .1
c w.n
dD
L d
d
) 2w(D s h1,1 3
!AR‚„%$t Ys Y‚ }js{‚ <1,d j$‚R A‚jBb h1,1 stI ZR$t _„B};; %D b‚ ‚
w.1R L .1 b dD c w.n
7$t{‚ w.1R L .1 D c
R
1
R
dD
Rd
d
L .1
c w.n
dD
R
1
b d #1
L d #1R
1
) 2w(D s h1,1 3
$R YBjB8B„}Y${ s h1,1 $ PBjjBbR Ys
w.1R L .1 b dD c w.n
b .1
Rd
d
d
L Rd #1R
c Rd #1R
1
1D
R
L .1
L d #1R
1
Rd
d
c w.n
d
L Rd #1R
1D
) 2w(D s h1,1 3
7$t{‚ w.1 Rd
L d D c d $R YBjB8B„}Y${ s Y‚ }js{‚ h1,1 stI R$t{‚ 8h1,1 w d D ) bR b‚ Ys%‚
d
Rd
.1 d ) bd L 2wRD s h1,1 stI Y‚t{‚
R
L .1
w.1R L .1 b dD c 1,1
Rd
d
c 1,1 L
#1R
c
#d
1
) 2w(D s h1,1 3
w;31(D
7$t{‚ 8h1,1 w 1 D ) bd $ tBb PBjjBbR P„B8 N‚88s ;d Ys Y‚ }js{‚ h1,1 $R Bsjjk „s8$h‚I
d
$t Y‚ ‚-‚tR$Bt o1,1 bI1,1 Ys Y‚ PZt{$Bt 1,1
$R s }„$8‚ ‚j‚8‚t s Y‚ }js{‚ <1,1 stI
Ys Qw<1,1 Mh1,1 D ) 1R b 1 B„‚B%‚„ b‚ BAs$t P„B8 w;1(D Ys
#1R
1
R
) #d 1,1
L #d d 1,1 L 2w(D s <1,1 3
w;31dD
G‚ ,tBb P„B8 _„B};;%D Ys
d
) #1R
1
b w#1R
R
1D
L 2w(D s <1,1 ,
w;311D
Y‚t{‚ w;1dD k$‚jIR
1
d
1
1
R
R
dR
) b#dR c 1,1
L #dR c 1,1 L 2w(D ) b#dR c 1,1
wd b 1,1
L 2wR 1 DD
stI Y‚„‚PB„‚
w
WR
d
dR 1
R 1
)b
c 1,1
c wd L 1,1
L 2wR 1 DD s <1,1 3
#d
3„B8 Y‚ I‚ht$$Bt BP Y‚ PZt{$Bt 1,1 stI w;1dD b‚ Ys%‚
d
d
.n
d
R
) #dR 1,1 b Rd #d 1,1
L 2w(D s <1,1 ,
stI Y‚t
.n ) w.n
d
dD d
wR 1 RD
) Rd
c 1,1
d
wR 1 dD
b 1,1
L 2wR 1 D s <1,1 3
w;31nD
V q!Gei !3 3=W]qy!W 3yeN*7 !zei ]= y] 3yeN*7
nn
eJw;D $%‚R PB„ 7 ) n
RwRdD
R R
w.nR L .n b dDw.; 1,1
D L w.n 1,1
1
R
R
Dw.; 1,1
D b .n 1,1
) (3
R
7$t{‚ w.nR L .n D c 1,1
$R YBjB8B„}Y${ s <1,1 Y$R $8}j$‚R
RwRdD
R
w.nR L .n b dDw.; 1,1
L 1d c 1,1 DR L w.n 1,1
R
Dw.; 1,1
L 1d c 1,1 D
1
w;1;D
1
R
R RLd
R
1
L 1R
L 1,1
D ) 2w(D s <1,1 3
d c 1,1 b .n wd c 1,1
k w;1nD b‚ Ys%‚
1
wR 1 RD
1
R RLd
R
.n c w1d c 1,1
L 1,1
D ) wRd
c 1,1
d
wR 1 dD
b 1,1
1
1
R RLd
R
L 2wR 1 DD c w1d c 1,1
L 1,1
D
R
c 1,1
L 2w(D ) w1d c 1,1 DR L 2w(D s <1,1 3
) Rd
d
7B w;1;D $%‚R st ‚JZs$Bt PB„ Y‚ PZt{$Bt W1 B%‚„ o1,1 sR PBjjBbRU
RwRdD
w.nR L .n b dD c W1R L w1,1
.n D c W1 b _d ) (,
b$Y _d o1,1 YBjB8B„}Y${ s <1,1 qY$R $R sRR‚„$Bt %D wPB„ i ) 1D stI $‚8 %$D PBjjBbR
P„B8 %D stI N‚88s ;d qY‚ $tIZ{$Bt Yk}BY‚R$R B%‚„ 7 wPB„ i ) 1D ‚jjR ZR Ys
R
L .1
w.1R L .1 b dD c 7,1
b$Y _ I7,1 YBjB8B„}Y${ s h7,1 7
R
) #7Ld
c
Rd
d
c 7,1 L
#7R
c
#d
7
)_
k _„B};; %D b‚ Ys%‚
7Ld
b #7Ld c
R
7Ld
L 2w(D s h7Ld,1 ,
Y‚„‚PB„‚
R
w.1R L .1 b dD c 7,1
L .1
VR w.1R L .1 D c
Rd
d
c 7,1 L
#7R R
w#
#d 7Ld
7Ld
b #7Ld
R
7Ld D
) 2w(D s h7Ld,1 3
R
7Ld
$R YBjB8B„}Y${ s h7Ld,1 $ PBjjBbR Ys
w
WR
w
W
#7 R
#7 R
R
Rd
w.1 L .1 b dD c 7,1 L R #7Ld 7Ld L .1 d c 7,1 L R #7Ld 7Ld
#d
#d
R
#7 R
#7 R
b .1 Rd
#
7Ld ) 2w(D s h7Ld,1 3
R #7Ld 7Ld L
d
#d
#d 7Ld
=R$t Bt{‚ ss$t Ys .1
i ) 1 $‚
w.1R
L .1 b dD c
Rd
d
R
7Ld,1
L
) bd L 2wdD s h1,1 b‚ {Bt{jZI‚ Y‚ }„BBP BP $‚8 $$D PB„
.1 Rd
d
R
#7Ld
c 7Ld,1 L
c
#d
7Ld
) 2w(D s h7Ld,1 3
w;31xD
n;
F=7]eNyW!
eeiiV ViWVN*! pVi]yV <eWWyWp 7qy]<qeW!q<
7$t{‚ h7Ld,1 $R s R$8}j‚ }Bj‚ BP Y‚ PZt{$Bt 7Ld b‚ s}}jk N‚88s ;d B eJw;1xD stI Y$R
ht$RY‚R Y‚ }„BBP BP $‚8 $$$D PB„ i ) 1 y „‚8s$tR B }„B%‚ Y‚ $‚8 $%D 3„B8 eJw;1xD $
PBjjBbR Ys
R
#7Ld
R
7Ld,1 L d c 7Ld,1 b
c 7Ld ) 2w(D s <7Ld,1 3
w;31ED
#d
=R$t Y‚ I‚ht$$Bt BP Y‚ PZt{$Bt 7Ld,1 eJw;1ED k$‚jIR sRR‚„$Bt $%D BP _„B};x PB„ i ) 1
$‚
#7 R
7,1 ) #7R c 7Ld,1 b c 7Ld,1
L 2w(D s <7Ld,1 3
d
qY‚ }„BBP BP _„B};x $t Y‚ {sR‚ i ) 1 $R YZR ht$RY‚I
7Z}}BR‚ tBb Ys sjj Rs‚8‚tR BP _„B};x YBjI PB„ RB8‚ i b$Y 1 › i c 0 G‚ bst B
RYBb Ys Y‚k sjRB YBjI PB„ i L d
VRR‚„$Bt $D wPB„ i L dD PBjjBbR P„B8 Y‚ $tIZ{$Bt Yk}BY‚R$R w$‚ P„B8 $‚8R $$$D stI %$D
R
L id c i,i
PB„ iD y sjRB PBjjBbR P„B8 Y‚ $tIZ{$Bt Yk}BY‚R$R Ys Y‚ PZt{$Bt Wi ) .1i c i,i
$R YBjB8B„}Y${ s Y‚ }js{‚ h7,iLd PB„ 7 w i L d stI Ys
R
7,i ) #7iL1
c 7Ld,i b
#7iL1 R
c 7Ld,i L 2w(D s h7Ld,iLd 3
id
d
qY$R 8‚stR Ys PB„ 7 w i b‚ Ys%‚
R
) b id c i,i L _
.1i c i,i
stI
w;31D
#7iL1 R
I
w;31MD
id c 7Ld,i L _
d
YBjB8B„}Y${ s h7Ld,iLd 3„B8 eJw;D b$Y 7 ) 1i stI eJw;1D b‚
R
7,i ) #7iL1
c 7Ld,i b
b$Y _, _I I7Ld,iLd
htI
R
Rd
w.1i
L .1i b dD c w.1iLd c i,i DR L .1i c i,i
c w.1iLd c i,i D L i7 c i,i ) 2w(D s hiLd,iLd 3
WBb eJw;1MD PB„ 7 ) i $8}j$‚R
R
Rd
w.1i
L .1i b dD c w.1iLd c i,i DR L .1i i,i
c w.1iLd c i,i D
R
L id c #1R c iLd,i b d #1 c iLd,i
) 2w(D s hiLd,iLd 3
!AR‚„%$t Ys Y‚ }js{‚ hiLd,iLd $R s R$8}j‚ }Bj‚ BP Y‚ PZt{$Bt iLd,i Ys Y‚ PZt{$Bt
R
R
Rd
w.1i
L .1i D c iLd,i
$R YBjB8B„}Y${ stI Ys .1i c i,i
) b id L 2wdD s Y‚ }js{‚ hiLd,iLd b‚
BAs$t
R
Rd
w.1i
L .1i b dD c w.1iLd c i,i L Rd c #1R c iLd,i DR L .1i c i,i
c w.1iLd c i,i L Rd c #1R c iLd,i D
Lid c #1R c iLd,i L id c Rd c #1R c iLd,i ) 2w(D s hiLd,iLd 3
V q!Gei !3 3=W]qy!W 3yeN*7 !zei ]= y] 3yeN*7
nx
qYZR s Y‚ }js{‚ hiLd, iLd b‚ Ys%‚
R
w.1i
L .1i b dD c
R
iLd,iLd
L w.1i c
Rd
i,i
D
#1R id
c iLd,iLd L
c  c iLd,i ) 2w(D3
#d d
w;31D
k $tIZ{$Bt B%‚„ 7 b‚ RYBb Y‚t Ys
R
w.1i
L .1i b dD c
R
7,iLd
L w.1i c
Rd
i,i
D
R
#7iLd
K
c 7,iLd L
c id
c 7,i ) _
d
#d
w;3n(D
K I7,iLd YBjB8B„}Y${ s h7,iLd PB„ i L d › 7 › 0 yt Ps{ w;1D $%‚R w;n(D PB„
b$Y _
7 ) i L d VRRZ8$t w;n(D PB„ 7 stI ZR$t w;1MD b‚ BAs$t
R
R
Rd
L .1i b dD c 7,iLd
L w.1i i,i
D c 7,iLd
w.1i
w
W
R
#7iLd
#7iL1 R
id
R
L
c d
#7iL1 c 7Ld,i b id c 7Ld,i ) _I
#d
d
w;ndD
b$Y _I I7Ld,iLd YBjB8B„}Y${ s h7Ld,iLd 7$t{‚ h7Ld,iLd $R s R$8}j‚ }Bj‚ BP 7Ld,i R$t{‚ Y‚
R
R
Rd
PZt{$Bt w.1i
L .1i D c 7Ld,i
$R YBjB8B„}Y${ stI R$t{‚ .1i c i,i
) bid L 2wdD s h7Ld,iLd b‚
BAs$t P„B8 w;ndD stI Y‚ I‚ht$$Bt BP Y‚ PZt{$Bt 7Ld,iLd Ys
R
w.1i
L .1i b dD c
R
7Ld,iLd
L
Rd
w.1i i,i
D
c 7Ld,iLd L
R
#w7LdDiLd
#d
c id
c 7Ld,i ) 2w(D
d
s h7Ld,iLd G‚ Ys%‚ YZR }„B%‚I w;n(D PB„ sjj 7 b$Y i L d › 7 › 0 stI Y‚t{‚ _„B};x $$D
YBjIR PB„ i L d y $R Y‚t {j‚s„ Ys sjRB Y‚ sRR‚„$Bt $$$D YBjIR PB„ i L d Ak N‚88s ;d
W‚- b‚ }„B%‚ $‚8 $%D PB„ i L d k _„B};x $$$D stI BAR‚„%$t Ys 7Ld,i YsR s R$8}j‚
}Bj‚ s h7Ld,iLd b‚ R‚‚ Ys Y‚ PZt{$Bt
R
7Ld,iLd
L
id
R
#7iL1
c 7Ld,iLd b
c id
c 7Ld,i
d
#d
w;3n1D
$R YBjB8B„}Y${ s <7Ld,iLd WB‚ Ys w;n1D $t {sR‚ i L d ) 1 $R `ZR w;1ED 7B sR $t {sR‚
i L d ) 1 b‚ BAs$t sRR‚„$Bt $%D P„B8 w;n1D stI P„B8 Y‚ I‚ht$$Bt BP Y‚ PZt{$Bt 7L1,iLd $‚ b‚ Ys%‚
#7iL1 R
R
7Ld,iLd ) #7iL1
c 7L1,iLd b
c 7L1,iLd L _,
id
b$Y _ YBjB8B„}Y${ s Y‚ }js{‚ <7L1,iLd d
yt B„I‚„ B R$8}j$Pk tBs$Bt b‚ R‚ 7 U) 7,7 3„B8 _„B};x $$$D $ PBjjBbR Ys iLd
)
d
iLd,iLd $R s jB{sj }s„s8‚‚„ s Y‚ }js{‚ <iLd,iLd stI Ak w;n1D b‚ Ys%‚
R
iLd
L
id
#1R id
c iLd b
c  c iLd,i ) 2w(D s <iLd,iLd 3
#d d
w;3nnD
nE
F=7]eNyW!
eeiiV ViWVN*! pVi]yV <eWWyWp 7qy]<qeW!q<
WB‚ Ys w;nnD $t {sR‚ i L d ) 1 $R `ZR w;1dD
i ) i,i ) #1R c iLd,i b
k _„B};x $%D b‚ ,tBb Ys
#1
R
id c iLd,i L 2w(D s <iLd, iLd 3
d
<‚t{‚ $ PBjjBbR P„B8 w;nnD Ys
1
R
L #dR c iLd L 2w(D
i ) b#dR c iLd
1
1
R
dR
) b#dR c iLd
c wd b iLd
L 2wR 1 DD s <iLd,iLd
stI {BtR‚JZ‚tjk
id ) b
d
dR 1
R 1
1
R c iLd c wd L iLd L 2wR DD s <iLd,iLd 3
#d
7$t{‚ .1iLd c i ) iLd b Rd c #1R c iLd,i b‚ BAs$t P„B8 w;nnD Ys
w
W
#d
#dR
R
R
R
.1iLd c i ) iLd b d c #1
c iLd L R c iLd L 2w(D s <iLd,iLd
#1
#1R id
d
stI Y‚t{‚ b‚ Ys%‚ st ‚JZs$Bt BP Y‚ PB„8
.1iLd c i ) #dR c iLd b Rd c
#d
R
id c iLd L _,
d
b$Y _ YBjB8B„}Y${ s <iLd,iLd G‚ 8Zj$}jk Y$R ‚JZs$Bt Ak id stI b‚ BAs$t
w
W
Rd RR1
dR 1
dR 1
1
.1iLd ) b iLd b i c iLd L 2wR D c wd L iLd
L 2wR 1 DD
d
1
dR
) b iLd
L
Rd
id
w;3n;D
1
RR
c iLd
L 2wR 1 D s <iLd,iLd 3
G‚ Ys%‚ P„B8 eJw;D PB„ 7 ) 1i L d Ys
1
RwRdD
R
R
R
R
w.1iLd
L .1iLd b dD c w.1iL1 c iLd
DR L w.1iLd c iLd D c w.1iL1 c iLd
D b .1iLd c iLd
) (3
VR A‚PB„‚ w{P w;1;DD Y$R $8}j$‚R Ys
RwRdD
R
R
R
w.1iLd
L .1iLd b dD c w.1iL1 c iLd
L iLd
c iLd DR L w.1iLd c iLd D c w.1iL1 c iLd
L iLd
c iLd D
d
d
wiLdDR
L d
1
1
R
R RLd
R
c iLd
b .1iLd c wiLd
c iLd
L iLd
D ) 2w(D s <iLd,iLd 3
d
3„B8 w;n;D b‚ Y‚t ‚
1
1
R RLd
R
.1iLd c wiLd
c iLd
L iLd
D
d
w
W
Rd RR1
dR 1
R 1 RLd
R1
1
) b iLd b i c iLd L 2wR D c wiLd
c iLd
L iLd
D
d
d
R R
) di c iLd
L 2w(D s <iLd,iLd 3
d
V q!Gei !3 3=W]qy!W 3yeN*7 !zei ]= y] 3yeN*7
n
R
7$t{‚ WiLd ) .1iL1 c iLd
L iLd
c iLd b‚ Ys%‚ YZR PBZtI st ‚JZs$Bt
d
RwRdD
R
R
w.1iLd
L .1iLd b dD c WiLd
L wiLd
c .1iLd D c WiLd ) _
b$Y s PZt{$Bt _ oiLd,iLd bY${Y $R YBjB8B„}Y${ s Y‚ }js{‚ <iLd,iLd qY$R }„B%‚R sRR‚„$Bt
%D PB„ i L d stI sR A‚PB„‚ sRR‚„$Bt %$D PBjjBbR P„B8 %D stI P„B8 N‚88s ;d qY‚ }„BBP BP
_„B}BR$$Bt ;x stI Y‚„‚PB„‚ BP Y‚ s$t qY‚B„‚8 $R ht$RY‚I
x s/'t Y‚ Cc‚„ sjC'R
G‚ {BtR$I‚„ ss$t Y‚ Bb‚„ ) ) wBd , B1 , Bn , 3 3 3 D B%‚„ Y‚ h‚jI $f wb$Y f ) R n D bY${Y $R
I‚ht‚I „‚{Z„R$%‚jk Ak Bd ) $f w?d D stI BzLd ) Bz w?zLd D bY‚„‚ ?zLd Rs$Rh‚R Y‚ ‚JZs$Bt
d b ?zLd
?Rz L ?z b d
)
,
?RzLd
?z
PB„ sjj z w d3
wxdD
VR b‚ }B$t‚I BZ A‚PB„‚ sjj ‚-‚tR$BtR BzLd bBz $t Y$R Bb‚„ ) s„‚ BP I‚„‚‚ R stI Y‚k
s„‚ tBtTpsjB$R $t Y‚ {sR‚ R k 1 yt Y$R R‚{$Bt b‚ RYBb Ys b‚ {st ‚tjs„‚ ) B s Bb‚„
% B%‚„ $f Ys%$t Y‚ Rs8‚ j$8$ sR ) stI b$Y Y‚ sII$$Btsj }„B}‚„k Ys sjj R‚}R $t Y‚
Bb‚„ % s„‚ psjB$R ‚-‚tR$BtR
G‚ I‚ht‚ Y‚ Bb‚„ % B%‚„ Y‚ h‚jI $f ) $Rn $tIZ{$%‚jk sR PBjjBbRU
% ) wtd , Id , t1 , I1 , 3 3 3 , ti , Ii , 3 3 3 D,
td ) $f w?d D
$R Y‚ „s$Btsj PZt{$Bt h‚jI,
Id ) td wFd D
b$Y
tzLd ) Iz w?zLd D
IzLd ) tzLd wFzLd D
FdRd L w?Rd L ?d b dDb?d ) (,
b$Y
b$Y
wx1D
w?zLd Fz DR b w?zLd Fz D L Fz ) (,
Rd
FzLd
L w?RzLd L ?zLd b dDb?zLd ) (,
PB„ sjj z w d qY‚ 8s$t „‚RZj BP Y$R R‚{$Bt $R
qY‚B„‚8 xd qY‚ Bb‚„ % ) wtd , Id , t1 , I1 , 3 3 3 D B%‚„ Y‚ h‚jI $f ) $Rn sR I‚ht‚I $t
wx1D YsR Y‚ PBjjBb$t }„B}‚„$‚RU
w$D 3B„ sjj z w d Y‚ ‚-‚tR$BtR Iz btz stI tzLd bIz s„‚ psjB$R qY‚ ‚-‚tR$Bt Iz btz $R
s €Z88‚„ ‚-‚tR$Bt BP I‚„‚‚ >Iz U tz H ) R b d stI tzLd bIz $R st V„$tT7{Y„‚$‚„
‚-‚tR$Bt BP I‚„‚‚ >tzLd U Iz H ) R
w$$D qY‚ j$8$ w%D Rs$Rh‚R w%D w 1wR 1 b dDbwR L 1D
i‚8s„, x1 y PBjjBbR $88‚I$s‚jk P„B8 wx1D Ys Y‚ ‚j‚8‚tR ?z tz Rs$RPk Y‚
‚JZs$Bt
wd b ?zLd Db?RzLd ) w?Rz L ?z b dDb?z ,
PB„ sjj
<‚t{‚ Y‚ Bb‚„ ) $%‚t Ak wxdD $R s RZABb‚„ BP Y‚ Bb‚„ %
z w d3
nM
F=7]eNyW!
eeiiV ViWVN*! pVi]yV <eWWyWp 7qy]<qeW!q<
3B„ Y‚ }„BBP BP qY8 xd b‚ t‚‚I st stsjBZ‚ BP Y‚ <Z„b$9 ‚tZR PB„8Zjs PB„ Bb‚„R BP
PZt{$Bt h‚jIR R‚‚ >H 3B„ Y‚ {Bt%‚t$‚t{‚ BP Y‚ „‚sI‚„ b‚ „‚{sjj Y$R „‚RZj Y‚„‚ ]BtR$I‚„
s Bb‚„ / ) wUd , U1 , Un , 3 3 3 D BP PZt{$Bt h‚jIR B%‚„ $f bY‚„‚ UzLd bUz $R R‚}s„sAj‚ BP I‚„‚‚
>UzLd , Uz H k d PB„ sjj z w d G‚ I‚ht‚ Y‚ „‚js$%‚ ‚tZR w/bUd D sR
w/bUd D U) j$8 /wUz Db>Uz U Ud H3
z
B„‚B%‚„ b‚ I‚ht‚ Y‚ „s8$h{s$Bt jB{ZR BP /bUd sR
~ w/bUd D U) Ih YwUd D h $R „s8$h‚I $t Uz bUd PB„ RB8‚ z w 1J3
yP ~ w/bUd D $R ht$‚ b‚ I‚ht‚ Y‚ I$%$RB„R
3
\z w/bUd D U)
<,
PB„ sjj
z w 13
<;YwUz D
<Ud ;~ wRbUd D
y $R ‚sRk B R‚‚ Ys Y‚ j$8$
w/bUd D U) j$8 I‚ \z w/bUd Db>Uz U Ud H
z
‚-$RR WBb b‚ {st Rs‚ Y‚ <Z„b$9 ‚tZR PB„8Zjs PB„ Bb‚„R BP PZt{$Bt h‚jIR
_„B}BR$$Bt xn wR‚‚ >H qY8 nED 7Z}}BR‚ Ys / ) wUd , U1 , Un , 3 3 3 D $R s Bb‚„ BP
PZt{$Bt h‚jIR B%‚„ $f N‚ Ud bUd A‚ s ht$‚ R‚}s„sAj‚ ‚-‚tR$Bt RZ{Y Ys Ud stI Uz s„‚
j$t‚s„jk I$R`B$t B%‚„ Ud stI RZ{Y Ys $f $R sj‚A„s${sjjk {jBR‚I $t Uz U) Ud c Uz PB„ sjj
z w d *‚tB‚ Ak / U) wUd , U1 , Un , 3 3 3 D Y‚ {B8}BR$‚ Bb‚„ BP / stI Ud VRRZ8‚ Ys Y‚
PBjjBb$t {BtI$$BtR YBjIU
w$D qY‚ „s8$h{s$Bt jB{ZR ~ w/bUd D $R ht$‚ stI w/bUd D ) (
w$$D Vjj }js{‚R h ~ w/bUd D s„‚ s8‚ $t Y‚ ‚-‚tR$Bt Ud bUd qY‚t b‚ Ys%‚
1/wUd D b 1w/ bUd D b 1 ) >Ud U Ud H c w1/wUd D b 1w/bUd D b 1D L &,
b$Y
&)
3
Qw< M < ? Ud D c I‚ <3
<;YwUd D
<Ud ;~ wRbUd D
]B„Bjjs„k x; yt sII$$Bt B Y‚ sRRZ8}$BtR w$D stI w$$D $t _„B} xn b‚ sRRZ8‚U
w$$$D Vjj }js{‚R h YwUd D bY${Y s„‚ „s8$h‚I $t Y‚ ‚-‚tR$Bt Ud bUd A‚jBt B Y‚ „s8$h{sT
$Bt jB{ZR ~ w/bUd D
qY‚t b‚ Ys%‚ w/ bUd D ) >Ud U Ud H c w/bUd D
V q!Gei !3 3=W]qy!W 3yeN*7 !zei ]= y] 3yeN*7
n
_„BBP 3„B8 sRRZ8}$Bt w$$$D $ PBjjBbR Ys Y‚ tZ8A‚„ & $t _„B} xn $R ‚JZsj B Y‚ I$&‚„‚t
I‚„‚‚ BP Y‚ ‚-‚tR$Bt Ud bUd stI Y‚t{‚ 1/wUd D b 1 ) >Ud U Ud Hw1/wUd D b 1D L & WBb Y‚
sRR‚„$Bt BP ]B„ x; PBjjBbR $88‚I$s‚jk P„B8 _„B} xn
_„BBP BP qY8 xd VR $t 7‚{Bt n j‚ ZR I‚tB‚ Kwx D U) wx R L x b dDbx G‚ Rs„ b$Y
Y‚ Bb‚„ ) ) wBd , B1 , Bn , 3 3 3 D bY${Y $R „‚{Z„R$%‚jk I‚ht‚I Ak wxdD $‚ Ak Y‚ ‚JZs$Bt
wd b ?zLd Db?RzLd ) Kw?z D stI b‚ {BtR$I‚„ Y‚ {B8}BR$‚ Bb‚„ ( ) wod , o1 , on , 3 3 3 D BP Y‚
Bb‚„ ) b$Y Y‚ PZt{$Bt h‚jI od U) Bd wFd D bY‚„‚ FdRd L Kw?d D ) ( WB‚ Ys oz ) Bz wFd D
stI $t }s„${Zjs„ o1 ) B1 wFd D ) od w?1 Fd D b$Y Y‚ PBjjBb$t „‚js$Bt
w?1 Fd DR b w?1 Fd D L Fd ) Fd w?R1 FdRd b ?1 L dD
) Fd wb?R1 c Kw?d D b ?1 L dD ) Fd ww?1 b dD b ?1 L dD ) (3
wxnD
k _„B} 1; stI N‚88s 1n Y‚ „s8$h{s$Bt jB{ZR BP )bBd $R
~ w)bBd D ) Iw?d ) D ) (, d, B„ R L ) dJ3
7B ~ w)bBd D $R ht$‚ stI $ PBjjBbR P„B8 _„B} 1x 1E 1 stI 1M Ys w)bBd D ) (
qY‚„‚PB„‚ {BtI$$Bt w$D BP _„B} xn $R Rs$Rh‚I qY‚ {BtI$$Bt w$$D BP _„B} xn YBjIR
„$%$sjjk R$t{‚ od bBd $R psjB$R BP I‚„‚‚ R b d k Y‚ Y‚B„k BP €Z88‚„ ‚-‚t$BtR BP
PZt{$Bt h‚jIR wR‚‚ >dEH _„B} yyynD Btjk Y‚ 9‚„B‚R stI Y‚ }Bj‚R BP Y‚ PZt{$Bt Kw?d D )
w?Rd L ?d b dDb?d 8sk „s8$Pk $t Y‚ ‚-‚tR$Bt od bBd stI Y‚t{‚ sjRB Y‚ {BtI$$Bt w$$$D $t
]B„ x; YBjIR qY‚„‚PB„‚ b‚ BAs$t w(bod D ) wR b dD c w)bBd D P„B8 ]B„ x; !AR‚„%$t
Ys w(bo1 D ) R c w(bod D stI Ys w)bBd D ) RwR L 1Db1wR b dD Ak qY8 1 $ PBjjBbR
w(bo1 D ) R 1 wR L 1Db13
wx;D
W‚- b‚ RYBb Ys RZ^{$‚tjk 8stk „s$Btsj }js{‚R BP o1 R}j$ {B8}j‚‚jk B%‚„ $Rn $t Y‚
Bb‚„ (bo1 N‚
U) I $f KwDRLd ) KwD b dJ,
stI
wBd D U) Iw?d ) D J t YwBd D3
G‚ ,tBb P„B8 _„B} nd stI qY8 n1 Ys ' ) RwR L dD stI Ys sjj }js{‚R h wBd D
R}j$ {B8}j‚‚jk $t Y‚ Bb‚„ )bBd G‚ bst B RYBb Ys Y‚ }js{‚R h ) w?d ) D wBd D sjRB R}j$ {B8}j‚‚jk $t Y‚
‚-‚tR$Bt od bBd yt Ps{ R$t{‚ od ) Bd wFd D stI FdRd ) bKw?d D b‚ Ys%‚ B RYBb Ys Y‚
‚j‚8‚t bKwD $R s wR b dDTY }Bb‚„ $t Y‚ ht$‚ h‚jI $f stI Y$R sRR‚„$Bt $R ‚JZ$%sj‚t B
1
RYBb Ys wbKwDDR LRLd ) d G‚ Ys%‚ Ak N‚88s nx
wbKwDDR
1 LRLd
) bKwDR
1 LRLd
) bwbdD ) d
;(
F=7]eNyW!
eeiiV ViWVN*! pVi]yV <eWWyWp 7qy]<qeW!q<
stI Y$R }„B%‚R BZ„ {js$8 7$t{‚ oz ) od c Bz $ PBjjBbR tBb Ys Y‚ }js{‚R h wBd D s„‚
sjRB {B8}j‚‚jk R}j$$t $t Y‚ ‚-‚tR$BtR oz bBd PB„ sjj z w d 7‚$t
wo1 D U) Ih Ywo1 D h ? Bd wBd DJ
b‚ Ys%‚ RYBbtU
wdD Vjj }js{‚R h wo1 D s„‚ $f T„s$Btsj stI Y‚k R}j$ {B8}j‚‚jk $t Y‚ Bb‚„ (bo1 w1D 'wo1 D ) >o1 U Bd H c 'wBd D ) R 1 wR 1 b dD
wnD qY‚ }js{‚R h wo1 D s„‚ ‚-s{jk Y‚ 9‚„B‚R $t Y‚ PZt{$Bt h‚jI o1 BP Y‚ PZt{$BtR
?1 b b$Y 3„B8 wdD stI w1D $ PBjjBbR Ys Y‚ tZ8A‚„ BP $f T„s$Btsj }js{‚R BP oz Rs$Rh‚R Y‚
$t‚JZsj$k ] woz D w >oz U o1 H c R 1 wR 1 b dD stI Y‚t eJwx;D k$‚jIR
w(D w
'wo1 D
R 1 wR 1 b dD
1wR 1 b dD
) 1
)
3
w(bo1 D
R wR L 1Db1
RL1
yt Y‚ Bb‚„ (bo1 Y‚ ‚-‚tR$BtR ozLd boz s„‚ tBtTpsjB$R PB„ sjj z w 1 w$t Y‚ {sR‚ R ) 1D
stI b‚ {BtR$I‚„ Y‚„‚PB„‚ Y‚ {B8}BR$‚ Bb‚„ / ) wU1 , Un , U; , 3 3 3 D BP Y‚ Bb‚„ ( b$Y Y‚
PZt{$Bt h‚jI U1 U) o1 wF1 D bY‚„‚ F1Rd L Kw?1 D ) ( VR A‚PB„‚ b‚ R‚‚ Ys Un ) U1 w?n F1 D b$Y
w?n F1 DR b w?n F1 D L F1 ) ( RB Un bU1 $R st V„$tT7{Y„‚$‚„ ‚-‚tR$Bt BP I‚„‚‚ R qY‚ „‚js$%‚
‚tZR BP /bUn $R
w/bUn D ) RwR b dD c w(bo1 D,
stI Y‚ R‚
wUn D U) Ih YwUn D Y ? o1 wo1 DJ
YsR {s„I$tsj$k RwR b dD c 'wo1 D Vjj }js{‚R h wUn D R}j$ {B8}j‚‚jk $t Y‚ Bb‚„ /bUn stI b‚ BAs$t Ys Y‚ j$8$ BP Y‚ Bb‚„ / Rs$Rh‚R w/D w 1wR 1 b dDbwR L 1D ]Bt$tZ$t
Y$R }„B{‚RR b‚ tBb I‚ht‚ Y‚ Bb‚„ 0 ) w-n , -; , -x , 3 3 3 D sR Y‚ {B8}BR$‚ BP Y‚ Bb‚„
/bUn b$Y Y‚ PZt{$Bt h‚jI -n ) Un wFn D bY‚„‚ FnRd L Kw?n D ) ( ‚{
7‚$t td U) Bd Id U) od t1 U) o1 I1 U) U1 tn U) Un In U) -n ‚{ b‚ R‚‚ Ys
Y‚ Bb‚„ % ) wtd , Id , t1 , I1 , 3 3 3 , D $R I‚ht‚I sR $t wx1D 7$t{‚ Y‚ j$8$ BP sjj YB„$9Btsj
Bb‚„R $t 3$ x A‚jBb $R A$‚„ Yst B„ ‚JZsj B 1wR 1 b dDbwR L 1D $ PBjjBbR Ys sjRB Y‚
j$8$ BP % Rs$Rh‚R w%D w 1wR 1 b dDbwR L 1D stI Y$R }„B%‚R qY8 xd
V q!Gei !3 3=W]qy!W 3yeN*7 !zei ]= y] 3yeN*7
;d
qY‚ PBjjBb$t }${Z„‚ RZ88s„$9‚R Y‚ {BtR„Z{$Bt sAB%‚ j‚sI$t B s Bb‚„ b$Y sj‚„tsT
$t €Z88‚„ stI V„$tT7{Y„‚$‚„ ‚-‚tR$BtR wY‚ ABjITPs{‚ %‚„${sj ‚-‚tR$BtR s„‚ €Z88‚„
‚-‚tR$BtR BP I‚„‚‚ R b d stI Y‚ ABjITPs{‚ YB„$9Btsj ‚-‚tR$BtR s„‚ V„$tT7{Y„‚$‚„ ‚-‚tT
R$BtR BP I‚„‚‚ RD
N5
M3
M4
M5
L2
L3
L4
L5
...
M:
L:
...
N4
N:
...
E:
E1
E2
E3
E4
E5
...
F:
F1
F2
F3
F4
F5
...
Figure 5
i‚P‚„‚t{‚R
>dH
>1H
>nH
Vtj‚R stI ] s$„‚ V tB‚ Bt s8‚jk „s8$h‚I Bb‚„R BP jBAsj PZt{$Bt h‚jIR 3$t$‚ 3$‚jIR V}}j
M w1((1D 1(u1dx
F ‚9‚„„s stI V ps„{$s V Bb‚„ b$Y tBtTpsjB$R R‚}R bY${Y ss$tR Y‚ *„$tP‚jITzjsIZ ABZtI B
s}}‚s„ $t F WZ8A‚„ qY‚B„k
zp *„$tP‚jI stI 7p zjsIZ qY‚ tZ8A‚„ BP }B$tR BP st sj‚A„s${ {Z„%‚ 3Zt,R$Btsj Vtsj $
_„$jB9Y‚t d wdMnD EMuE >3Zt{ Vtsj V}}j d wdMnD xnux;H
;1
>;H
>xH
>EH
>H
>MH
>H
>d(H
>ddH
>d1H
>dnH
>d;H
>dxH
>dEH
>dH
>dMH
>dH
>1(H
F=7]eNyW!
eeiiV ViWVN*! pVi]yV <eWWyWp 7qy]<qeW!q<
W* ej,$‚R e-}j${$ 8BIZjs„ Bb‚„R $tU _„B{‚‚I$tR BP Y‚ qY$„kT3$PY >dH VttZsj Vjj‚„Bt
]BtP‚„‚t{‚ Bt ]B88Zt${s$Bt ]Bt„Bj stI ]B8}Z$t wq sRs„ stI V zs„Ik ‚IRD =t$% BP
yjj$tB$R s =„AstsT]Ys8}s$t wdMD 1nun1
W* ej,$‚R e-}j${$ Bb‚„R BP *„$tP‚jI 8BIZjs„ {Z„%‚R $tU eZ„B}‚st ]Bt„‚RR BP sY‚8sT
${R w s„{‚jBts 1(((D zBj yy w] ]sRs{ZA‚„s ‚ sjj ‚IRD $„,YsZR‚„ sR‚j w1((dD dMudM
s„$%U8sYWq\(((xd;( w1(((D
V ps„{$s stI < 7${Y‚tBY V Bb‚„ BP V„$tT7{Y„‚$‚„ ‚-‚tR$BtR BP PZt{$Bt h‚jIR ss$t$t Y‚
*„$tP‚jITzjsIZ ABZtI yt%‚t sY d1d wdxD 1ddu111
V ps„{$s stI < 7${Y‚tBY !t Y‚ sRk8}B${ A‚Ys%$B„ BP RB8‚ Bb‚„R BP PZt{$Bt h‚jIR B%‚„ ht$‚
h‚jIR F WZ8A‚„ qY‚B„k Ed wdED 1;Mu1n
V ps„{$s stI < 7${Y‚tBY !t s8‚ Bb‚„R B%‚„ ht$‚ h‚jIR F i‚$t‚ Vt‚b sY xx w1((nD
xnuM(
V ps„{$s < 7${Y‚tBY stI qYB8sR !t Bb‚„R stI {B8}BR$s BP Bb‚„R BP PZt{$Bt h‚jIR B%‚„
ht$‚ h‚jIR 3$t$‚ 3$‚jIR V}}j n wdD 1xu1;
p %st I‚„ p‚‚„ stI %st I‚„ zjZ Vt sRk8}B${sjjk BBI Bb‚„ BP {Z„%‚R B%‚„ Y‚ h‚jI b$Y
‚$Y ‚j‚8‚tR Zjj NBtIBt sY 7B{ n; w1((1D 1dun((
O yYs„s 7B8‚ „‚8s„,R Bt Y‚ tZ8A‚„ BP „s$Btsj }B$tR BP sj‚A„s${ {Z„%‚R B%‚„ ht$‚ h‚jIR F3s{
7{$ =t$% qB,kB 1M wdMdD 1du1;
GT]G N$ < sYs„s` stI < 7${Y‚tBY W‚b B}$8sj Bb‚„R B%‚„ ht$‚ h‚jIR $tU VjB„$Y8${
WZ8A‚„ qY‚B„k >7kIt‚k 1((1H w] 3$‚,‚„ stI * €BY‚j ‚IRD n1unM
< W$‚I‚„„‚$‚„ stI ] $t is$Btsj }B$tR Bt {Z„%‚R B%‚„ ht$‚ h‚jIRU Y‚B„k stI s}}j${s$BtR
]s8A„$I‚ =t$% _„‚RR ]s8A„$I‚ 1((d
FT_ 7‚„„‚ 7Z„ j‚ tB8A„‚ I‚R }B$tR „s$Btt‚jR I:Zt‚ {BZ„A‚ sj?‚A„$JZ‚ RZ„ Zt {B„}R ht$ ]i V{sI
7{$ _s„$R 1E wdMnD nu;(1 ) eZ%„‚R >d1MH
FT_ 7‚„„‚ is$Btsj }B$tR Bt {Z„%‚R B%‚„ ht$‚ h‚jIR Zt}ZAj$RY‚I j‚{Z„‚ tB‚R Ak 3+ pBZ%|‚s
<s„%s„I =t$%‚„R$k wdMxD
< 7${Y‚tBY Vj‚A„s${ 3Zt{$Bt 3$‚jIR stI ]BI‚R 7}„$t‚„ z‚„js ‚„j$t dn
V q‚8,$t‚ <$jA‚„ {jsRR h‚jI Bb‚„R BP PZt{$Bt h‚jIR B%‚„ ht$‚ h‚jIR stI jBb‚„ ABZtIR PB„ \wRD
F WZ8A‚„ qY‚B„k M w1((dD dMu1d(
V qRPsR8st 7p zjsIZ stI q $t, BIZjs„ ]Z„%‚R 7Y$8Z„s ]Z„%‚R stI pB}}s ]BI‚R A‚‚„
Yst Y‚ zs„RYs8B%Tp$jA‚„ ABZtI sY Ws{Y„ d( wdM1D 1du1M
F GZjPst‚ sY8‚ q[
Z„8‚ sj‚A„s$R{Y‚„ 3Zt,$Bt‚t,[
B„}‚„ _Y* Y‚R$R weRR‚t 1((nD
qY $t, *‚‚t‚„s$Bt BP 7Y$8Z„s RZ„Ps{‚R stI s }„BAj‚8 $t {BI$t Y‚B„k $tU 3ZtIs8‚tsjR BP
]B8}Zs$Bt qY‚B„k >]BAZRH wN ZIs{Y ‚ID 7}„$t‚„Tz‚„js W‚b OB„, dMx x(nuxdd

Documentos relacionados

Bitzer | Bock

Bitzer | Bock Volumétrico (m³/h)

Leia mais

Snorkel Ford Ranger 07 Desde 1/07 Ref. SFR07 Preço 180,00euros

Snorkel Ford Ranger 07 Desde 1/07 Ref. SFR07 Preço 180,00euros Snorkel Land Rover Defender TD5 Desde 1999 Ref. SLDF Preço 180,00euros c/iva

Leia mais

Table4-Conserved in All Ecoli

Table4-Conserved in All Ecoli 1761493_s_at 1761494_s_at 1761499_s_at 1761502_s_at 1761505_s_at 1761513_s_at 1761516_s_at 1761522_s_at 1761524_s_at 1761526_s_at 1761528_s_at 1761540_s_at 1761541_s_at 1761543_s_at 1761544_s_at 1...

Leia mais