• Aucun résultat trouvé

Compact finite difference schemes for shallow-water ocean model

N/A
N/A
Protected

Academic year: 2023

Partager "Compact finite difference schemes for shallow-water ocean model"

Copied!
70
0
0

Texte intégral

(1)

HAL Id: inria-00071667

https://hal.inria.fr/inria-00071667

Submitted on 23 May 2006

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

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

ocean model

Christine Kazantsev, Eugene Kazantsev, Eric Blayo

To cite this version:

Christine Kazantsev, Eugene Kazantsev, Eric Blayo. Compact finite difference schemes for shallow-

water ocean model. [Research Report] RR-4913, INRIA. 2003. �inria-00071667�

(2)

ISSN 0249-6399 ISRN INRIA/RR--4913--FR+ENG

a p p o r t

d e r e c h e r c h e

THÈME 4

Compact finite difference schemes for shallow-water ocean model.

Christine Kazantsev — Eugène Kazantsev — Eric Blayo

N° 4913

August 2003

(3)
(4)

Unité de recherche INRIA Rhône-Alpes

655, avenue de l’Europe, 38334 Montbonnot Saint Ismier (France)

Téléphone : +33 4 76 61 52 00 — Télécopie +33 4 76 61 52 52

2346587)965;:<=>@?A>B:9$76<1CEDFGH@I1:<=>@?A>B:9$76<1CEDF4658JKL8>AM'N

OP@QRS%TVUXW1YZRV[B\;]$^_Ya`$bS)^`$c@^_YZR.Y;de]$^_Ya`$b

f Sdhg-dh^hQRS6di`$R.cB\aSj-S6d

kl`6meS)^edn_op"kO

q%]6cBc'`$l^ f S%lS6ihP@Sl)ihP@SrbsTAt-u6vUxw[@y$['dh^"z1{1{1vUx|1|c']$y1S6d

}.~)€)1‚Bƒ$€$„n8b^_PBY;dc']6c'Sl$…1†S"^hS6dh^dh`$RSPBYay$P`$l

f

Slb-[BRSleY;i)]6\@deihP@SRS6d`$bd_YZR.cB\aS`-iS6]6bBY;iR`

f

S\;d)‡ˆS"‰Bl)dh^

i`$R.c']6lS%Š;`$[Bl^_P@‹8`$l

f

Sl"]6b

f

d_YZj-^_P@‹8`$l

f

Sl"i`$R.c']1i^%deihP@SRS6d†Ya^_P^_P@SVie\;]1ded_Y;i)]6\dhS6i`$b

f

‹8`$l

f

Sl"iSbB^hSlS

f

deihP@SRS

`$b^_P@Sdhg-dh^hSR`$Š@S6Œ$[']$^_Ya`$b'd

f

S6deieleYZBYZb@y"^_P@SYZb@Sl^_Y;]$‹8y$l)]6Ž1Ya^_g%†]6Ž1S6d)…1]6b

f

^_P@Sb†SŠ;`-ie['d`$b.^_P@Sc'SleŠ;`$leR]6b'iS6d`$Š

^_P@SŠ;`$[Bl^_P@‹8`$l f Sli`$R.c']1i^deihP@SRS`$b.`-iS6]6bBY;i^_g1cBY;i)]6\-cBl`-iS6dedhS6d)…1d_['ihP.]1d[BbB%'`$[Bb f ]6lg%\;]6g1Sl]6b f d_P']6\Z\a`$†‹

†]$^hSlcBPBg-d_Y;i)d)‡‘[BRSleY;i)]6\]6b']6\ag-d_Y;d`$Š^_P@SdeihP@SRS6d)…-]6b f R]6bBg.i`$R.cB[@^e]$^_Ya`$b']6\'lS6d_[B\a^ed]6lS"cBlS6dhSbB^hS f ‡

’“1”'•h–—B1˜$„™p%iS6]6bBY;iR`

f

S\;d)…-d_P']6\Z\a`$†‹8†]$^hSl$…6b-[BRSleY;i)]6\@deihP@SRS6d)…-i`$R.c']1i^deihP@SRS6d)…$b-[BRSleY;i)]6\']6b']6\ag-d_Y;d)…

'`$[Bb

f

]6lgV\;]6g1Sl$…1YZb@Sl^_Y;]$‹8y$l)]6Ž1Ya^_gV†]6Ž1S6d)‡

(5)

Ar„ o]6b'dViS^_l)]6Ž$]6YZ\_…`$b)^_[

f

YaS

f

S6dVdeihPR]1d%b-[BRleY;Œ$[@S6d f

`$l

f

lS\aS)Žd_[Bl

f

S6dR`

f

Q\aS6dVd_YZR.cB\aS6d

f`-i6]6b‡wcBlQ6d]6Ž1`$YZli`$R.c']6l\aS6ddeihPR]1di`$R.c']1i^ed f`$l f lS"Œ$[']$^_lS"S)^d_YZj]6Ž1S6i\aS%deihPR]ie\;]1ded_Y;Œ$[@S%iSbB^_l

f`$l f lS f S[BjVd_[Bl\aSdhg-dh^hQRS f6Œ$[']$^_Ya`$b'd f 6ieleYaŽ$]6bB^\aS6d`$b f S6d f Sy$l)]6Ž1Ya^1…$`$b.d YZbB^lS6dedhScB\Z['d@c']6l^_Y;ie[B\ZYaQlSRSbB^

]6[Bjc'SleŠ;`$leR]6b'iS6d f [ deihPR]i`$R.c']1i^ f`$l f lSŒ$[']$^_lS.d_[Bl f S6d"cBl`-iS6ded_['d`-i6]6bBY;Œ$[@S6d%^_g1cBY;Œ$[@S6d"^hS\;dŒ$[@S\;]

i`$['ihP@S\ZYZR.Ya^hS f S[BbBS)^\;]"cBPBg-d_Y;Œ$[@SYZb f [BYa^hSc']6l\PBg1c'`1^_P@Q6dhS fS6]6[Vc'S[.cBl`$Š;`$b f S1‡o%S6d)^_[ f S6db-[BRleY;Œ$[@S6d

f SiS6ddeihPR]1d]6YZb'd_YŒ$[@S f S%b@`$RVBlS[Bjl6d_[B\a^e]$^ed f Si)]6\;ie[B\dh`$bB^cBl6dhSbB^6d)‡

E—B€6)•eƒ A „X ` f Q\aS6d"`-i6]6bBY;Œ$[@S6d)…'S6]6[ c'S[ cBl`$Š;`$b f S1…'deihPR]1db-[BRleY;Œ$[@S6d)…@deihPR]1d"i`$R.c']1i^ed)…']6b']6\ag-dhS

b-[BRleY;Œ$[@S

f

SdeihPR]1d)…-i`$['ihP@S"\ZYZR.Ya^hS1…-`$b

f

S6d

f

Sy$l)]6Ž1Ya^1‡

(6)

# $

V. )0

o"[BleYZb@y%^_P@S6dhSc']1dh^u%%g1S6]6l)d)…$b-[BRSleY;i)]6\AR` f S\;d`$Š'^_P@S`-iS6]6bBY;i"ieYZl)ie[B\;]$^_Ya`$bVP']6Ž1S'S)SbŽ1SlgRV['ihPVYZR.cBl`$Ž1S f YZb

^hSleR`$ŠAcBPBg-d_Y;i)d)…lS6]6\ZY;d_R `$ŠB^_P@S]6cBcB\ZY;i)]$^_Ya`$b]6b f i`$R.cB[@^e]$^_Ya`$b']6\1^hS6ihPBbBY;Œ$[@S6d)‡‘"S)Ž1Sl^_P@S\aS6ded)…6^_P@S']1d_Y;i'b-[BRSleY;i)d

`$Š^_P@S6dhS%R` f S\;d]6lS]6\ZR`Adh^[Bb'ihP']6b@y1S f d_YZb'iS%^_P@S%'S)y$YZbBbBYZb@y`$Š`-iS6]6bR` f S\Z\ZYZb@yB…1Y_‡S1‡TA{g1S6]6l)d)‡ `Adh^`-iS6]6b

y1Sb@Sl)]6\ieYZl)ie[B\;]$^_Ya`$b.R` f S\;ddh^_YZ\Z\@['dhS"`$bB\ag.d_YZR.cB\aS"dhS6i`$b f ‹8`$l f SliSbB^hSlS f ‰BbBYa^hS f Y'&'SlSb'iS%deihP@SRS6d)‡)("`$†S)Ž1Sl$…

b-[BRSl`$['dR` f SlebdeihP@SRS6dSjAY;dh^†Ya^_PYZbB^hSlS6dh^_YZb@y%cBl`$c'Sl^_YaS6d)‡+*@`$lSjB]6R.cB\aS1…A^_P@S"YZR.cB\ZY;ieYa^deihP@SRS6d']1dhS f `$b

("SleR.Ya^_Y;]6b Š;`$leRV[B\;]1d)…B†PBY;ihP Y;d%]6b `$\f Yf S6]-,'.`$\Z\;]$^/0]6lS['dhS f d_['i)iS6ded_Ša[B\Z\agYZb ]$Sl`$PBg f l` f g1b']6R.Y;icBl`$B\aSRd

,O`$\;dh^_g1AP@‹1$z0,O`$\;dh^_g1AP@‹1$v08…,O`$\;dh^_g1AP@‹1$v6 08‡Ewb f lSY%n‡O`$\;dh^_g1AP f S)Ž1S\a`$c'S f ]6b f ]6b']6\ag-dhS f Ž1Slg S2ieYaSbB^

PBYay$P ]1i)ie[Bl)]1igYZR.cB\ZY;ieYa^"deihP@SRS6d38dhS)S4,O`$\;dh^_g1AP@‹_t$T50]6b f lSŠ;SlSb'iS6dYZb'd_Yf S56e‡%n8b^_P@S‰@S\f `$Š7B[BYf f g1b']6R.Y;i)d)…

^[email protected]\ZY;ieYa^.deihP@SRS6d`$ldh`1‹_i)]6\Z\aS f 8 ! 9 !V'S6i)]6RSc'`$cB[B\;]6lVR`$lSlS6iSbB^_\ag R`Adh^_\ag

^_PBl`$[@y$P ^_P@S†`$le`$Š:S\aS!,;:S\aS08‡%n8b<,O`$\;dh^_g1AP ‡w‡08…@YZAP']$S\w‡'O`$\;dh^_g1AP] f ]6c@^ed"^_P@SVdeihP@SRS6dcBl`$c'`AdhS f

Bg PBY;dŠ8]$^_P@Sl.^h`^[email protected]`$Y;dh^_[BlS.^_l)]6b'd_c'`$l^S6Œ$[']$^_Ya`$b YZb ^_P@S]$^_R`Ad_cBP@SlS1‡ n8b ^_P@S f `$R]6YZb `$Š%`-iS6]6b@`1y$l)]6cBPBg1…

.P-[ ]6b f *']6b=,'.P-[@‹>*']6b 0]6cBcB\ZYaS f ]VŠ8]6R.YZ\ag`$Š^[email protected]@SRS6d)…@i)]6\Z\aS f 8!?@A 8 B !

^h`V^_P@S%d_YZR.cB\aS"dh^e]$^_Ya`$b']6lgWA^h`$R.RS\BR` f S\;d)‡)C\;]6g1`!,;C\;]6g1`50BYZbBŽ1S6dh^_YayA]$^hS6d^_P@S"c'`1^hSbB^_Y;]6\@YZbB^hSlS6dh^`$Šd_['ihP.PBYay$P@Sl

`$l

f

SldeihP@SRS6d%†Ya^_PBYZb ^_P@Sd_c'S6ieYZ‰'ii`$bB^hSj-^V`$Šb-[BRSleY;i)]6\`-iS6]6b R`

f

S\;d)‡o%SleYaŽ1YZb@y y1Sb@SleY;iVSjAcBlS6ded_Ya`$b'd`$Š

f

Y;deielS)^hS

f

Y;d_c'Sl)d_Ya`$b lS\;]$^_Ya`$b'd_PBYZc'd%Š;`$l.YZb@Sl^_Y;]$‹8y$l)]6Ž1Ya^_g]6b

f

q"`Aded_Bg†]6Ž1S6d)…P@SŠ;`$[Bb

f

^_P']$^.^_P@SŠ;`$[Bl^_P@‹8`$l

f

Sl

Š8]6R.YZ\ag.YZR.cBl`$Ž1S6dd_Yay$bBYZ‰'i)]6bB^_\agV^_P@SŒ$[']6\ZYa^_g.`$Š^_P@S]6cBcBl`6jAYZR]$^_Ya`$b`$Š^_P@S

f

Y;d_c'Sl)d_Ya`$bcBl`$c'Sl^_YaS6d)‡

n8b ^_PBY;d%c']6c'Sl$…†S.^hS6dh^Vdh`$RS.`$Š^_P@S6dhSVPBYay$P `$l

f

Slb-[BRSleY;i)]6\deihP@SRS6d%`$b d_YZR.cB\aSV`-iS6]6bBY;iR`

f

S\;d)‡OP@S

]6YZR!`$Š^_PBY;d.†`$le Y;d.^h` i`$bB^_YZb-[@S^_P@Sdh^_[

f

YaS6d.`$Š^_P@Sc'SleŠ;`$leR]6b'iS6dV`$Š^_P@S6dhS deihP@SRS6d.`$br`-iS6]6bBY;i^_g1cBY;i)]6\

cBl`-iS6dedhS6d)…d_['ihP ]1dYZb@Sl^_Y;]$‹8y$l)]6Ž1Ya^_g †]6Ž1S6d)…[BbB '`$[Bb f ]6lg\;]6g1Sl.]6b f d_P']6\Z\a`$†‹8†]$^hSl%cBPBg-d_Y;i)d)‡[email protected]']6c'Sl

['dhS f ^[email protected]@`1^e]$^_Ya`$b'd%YZbB^_l` f ['iS f YZbD,;C\;]6g1`50]6b f Y;d`$lyA]6bBY/)S f ]1dŠ;`$\Z\a`$†"d)‡n8b c']6l^z-…†Sdh^_[ f g ^[email protected]@Sl^_Y;]$‹

y$l)]6Ž1Ya^_g.†]6Ž1S dS6Œ$[']$^_Ya`$b‡ˆS"cBlS6dhSbB^^_P@S"R` f S\_…-^_P@S f Y;deielS)^_Y;dhS f S6Œ$[']$^_Ya`$b'd]6b f b-[BRSleY;i)]6\BlS6d_[B\a^edŠ;`$l^_PBlS)S

d_c']1iS f Y;deielS)^_Y;de]$^_Ya`$b'dYZb ^_PBY;d%d_YZR.cB\aSVi)]1dhSV`$І]6Ž1ScBl`$c']$yA]$^_Ya`$b‡%n8b ^_P@SV^_PBYZl f c']6l^)…'†S.i`$b'd_Yf Sl^_P@SV[BbB

R` f S\`$Š'`$[Bb f ]6lg.\;]6g1Sl$‡CgRS6]6b'd`$Š^_P@Sb-[BRSleY;i)]6\]6b']6\ag-d_Y;d)…B†SVi)]6b cBl`$Ž1S^_P']$^%^_P@SR]6YZb ^hSleR&`$Š^_P@S

Slel`$lY;d f [@S%^h`V^_P@S f SleYaŽ$]$^_YaŽ1S%`$Š^_P@S"Ša[Bb'i^_Ya`$b ]$^^_P@S"'`$[Bb f ]6lg.]6b f ^h`V^_P@S`$l f Sl`$Š^_P@SdeihP@SRS1‡‘[BRSleY;i)]6\

SjAc'SleYZRSbB^ed]6lS]6\;dh`%cBlS6dhSbB^hS f ‡'n8b^_P@SŠ;`$[Bl^_PVc']6l^)…1†Sdh^_[ f gV]%d_P']6\Z\a`$†‹8†]$^hSlR` f S\_‡)*YZl)dh^`$Š]6\Z\_…1†ScBl`$Ž1S

^_P@S4EFVWA‹_dh^e]6BYZ\ZYa^_g.`$Š^_P@SVS6Œ$[']$^_Ya`$b `$Ši`$bB^_YZb-[BYa^_g.†Ya^_P i`$R.c']1i^%deihP@SRS6d`$b^_P@SViS\Z\a‹_iSbB^hSlS f RS6d_P‡%OP@Sb

†ScBlS6dhSbB^b-[BRSleY;i)]6\lS6d_[B\a^ed"`$Š^[email protected]_P']6\Z\a`$†‹8†]$^hSlR` f S\Š;`$l^[email protected]^hSlS f dhS6i`$b f `$l f SldeihP@SRS6d"]6b f Š;`$l

^_P@S%Š;`$[Bl^_P`$l

f

Sl"i`$R.c']1i^"deihP@SRS6d)‡OP@S"\;]1dh^c']6l^Y;d

f

S)Ž1`1^hS

f

^h`.^_P@Si`$b'ie\Z['d_Ya`$b‡

G $

)%+ H%I.J *I"0

p[BlV]6YZR&P@SlSY;d%^h`^hS6dh^^_P@S]1i)ie[Bl)]1ig`$Š^_P@Si`$R.c']1i^deihP@SRS6d)‡VO`^_PBY;d%Sb f …'†S['dhS.]^hS6dh^h‹_i)]1dhSV†Ya^_P ]6b

SjB]1i^†]6Ž1S"dh`$\Z[@^_Ya`$b‡n8bBYa^_Y;]6\ f ]$^e]V]6b f '`$[Bb f ]6lgŽ$]6\Z[@S6d]6lS^e]6ASbS6Œ$[']6\'^h`V^_P@S"SjB]1i^Ž$]6\Z[@S6d`$Š^_P@S%†]6Ž1S1…1YZb

d_['ihP].†]6g^_P']$^"^_P@SSlel`$l)d]6lS`$bB\ag f [@S^h`^_P@S^_le[Bb'i)]$^_Ya`$b ^hSleRd)‡K*@`$l f S)^e]6YZ\;d`$b ^_P@SŠ;`$\Z\a`$†[email protected]Œ$[']$^_Ya`$b'd

]6b

f

b@`1^e]$^_Ya`$b'd)…BdhS)S,;C\;]6g1`0]6b

f

lSŠ;SlSb'iS6dYZb'd_Y

f

S1‡

LKM8N OQPRTSVUXWR)YM

n8b@Sl^_Y;]$‹8y$l)]6Ž1Ya^_gV†]6Ž1S6d`$b ]6bAZB‹;cB\;]6b@S]6lS f S6deieleYZ'S f Bg.^_P@S%\ZYZb@S6]6leY/)S f d_P']6\Z\a`$†‹8†]$^hSlS6Œ$[']$^_Ya`$b'd3;S1‡yB‡K,'EYZ\Z\'0[68\

]^

]_-`

ZabcAd ]@e

]@f g h i

] b

]_

c=Za

^

cAd ]@e

]j

g h i

]@e

]_

c=k=l ]^

]@f c ] b

]jKm g h n

†P@SlSZaY;d^_P@S!.`$leYa`$\ZY;dc']6l)]6RS)^hSl38]1ded_[BRS f i`$b'dh^e]6bB^6]6b f dY;d^_P@Sy$l)]6Ž1Ya^_g]1i)iS\aSl)]$^_Ya`$b…kY;d^_P@SRS6]6b

f Sc@^_P‡OP@S"[BbBAb@`$†b'd]6lS ^ i

b.^_P@S%P@`$leY/)`$bB^e]6\i`$R.c'`$b']6bB^ed`$Š^_P@S%Ž1S\a`-ieYa^_g1…@]6b f-e ^_P@S f Sc@^_P‡

ˆSihP@`A`AdhS]1d]6bYZbBYa^_Y;]6\

f

]$^e]V]cB\;]6b@S%†]6Ž1SYZb

^

… b]6b f-e

…-y$YaŽ1SblS6d_c'S6i^_YaŽ1S\ag.Bg

^ l_

gDh i

f i j m gpoqrst

l>u

f

c=v j m

c=w

qtx>y l>u

f

c=v j m i

b@l

_

gDh i

f ij m gpozrst

l>u

f

c=v j m

c=w

ztx>y l>u

f

c=v j m i

e l_

gDh i f i j m

gDo{rst

l>u f c=vj m c=w

{tx>y

l>u f c=vj m n

(7)

*@`$\Z\a`$†YZb@y!,;C\;]6g1`508…-†S%YZbB^_l`

f

['iS"^_P@Si`$b'dh^e]6bB^ed

g

dk=l>u

cQv

m c<Z

a i

g

dk9v

c=Z

a i

g

dkAu

c<Z

a i

g

dkAu v

w q

w z

w { g

k=l>u w

q

cQv[w

z m

oq g `

Za

w q c

Za

w z

oz g `

Za

w q c

Za

w z

o{ g `

k9v

Za w q c

kAu

Za w z

OP@SSjB]1i^"dh`$\Z[@^_Ya`$b'd`$Š^_PBY;dcBl`$B\aSR ]6lS

^ l_ i f i j m gDoqrst

l>u

f

c=v j ` _ m

c=w

qtx>y l>u

f

c=v

j ` _ m i

b@l

_ i f i j m gpozrst

l>u

f

c=v j ` _ m

c=w

ztx>y l>u

f

c=v

j ` _ m i

e l_ i f i j m gpo{rst

l>u f c=vj ` _ m c=w

{tx>y

l>u f cQvj ` _ m i

LKML R R)W R! "$#%U'&$@M

n8b^_PBY;ddhS6i^_Ya`$b…1†S f Y;deielS)^_Y/)SYZbd_c']1iS^_P@SS6Œ$[']$^_Ya`$b'd`$b]wl)]61]6†]. y$leYf …6YZb.^_P@S"deŒ$[']6lS f `$R]6YZb4,{-…Zu0j@,{-…Zu0>\

]^

]_ ` Za(al[b

m

cAd(

q

) le m g h i

] b

]_

c<Za(al

^ m

cAd*(

z

+ le m g h i

]@e

]_

c=k-,.(

{

) l^ m c/(

{

+

l[b

m10

g h n

†P@SlS

(al^ m f Sb@`1^hS6d^_P@S%YZbB^hSlec'`$\;]$^_Ya`$bdeihP@SRS"y$YaŽ1YZb@yV^_P@SŽ$]6\Z[@S`$Š ^ YZb]bA‹;c'`$YZbB^)…-]6b f dhg1R.RS)^_leY;i)]6\Z\agVŠ;`$l$(al[b

m …

( q

) le m f Sb@`1^hS6d^_P@S]6cBcBl`6jAYZR]$^_Ya`$b`$Š ] ) e YZb ] ^ ‹;c'`$YZbB^)‡

ˆS f S‰Bb@SBg.^_P@Sde]6RS%†]6g2(

{

) l^ m …3(

z

+ le m …3(

{

+

l[b

m

‡‘"`1^hS^_P']$^`$c'Sl)]$^h`$l)d'(

q

) le m ]6b f ( {

) l^ m

]6lS"Yf SbB^_Y;i)]6\_…

]1dŠ;`$l4(

z

+ le m ]6b

f ( {

+

l[b

m ‡

ˆ Ya^_P ^_PBY;d

f

Y;deielS)^_Y;de]$^_Ya`$b…A†S%`$@^e]6YZb^_P@S%Š;`$\Z\a`$†YZb@y

f

Y;d_c'Sl)d_Ya`$b.lS\;]$^_Ya`$b'd_PBYZcQ3,;C\;]6g1`0[68\

5

Za36

g87

a

l>u

i vm

`/9 ,7 q

)

l>u

i vm c 7 z

+

l>u

iv m 0

†P@SlS4(;:1<=?>?@

)A!BC+ED1F

g87 l>u

i v m

<=?>?@

)A!BC+ED … 9

gHGEI JK

L n

W1YZb'iS.^_P@S`$c'Sl)]$^h`$l)dM(al^ m …( q

) le m

S)^ei]6lS.Ž1Slg †S\Z\cBlS)S6dhSbB^hS f ]6b f dh^_[ f YaS f YZbp3,;C\;]6g1`0[6e…†S]6lS.Ž1Slg

BleYaSŠ`$b^_PBY;d"d_[B-meS6i^)‡

LKMON P"SVR3#YRQRR3SVR!&'@M

ˆSi`$b'd_Yf Slb@`$† f Y'&'SlSbB^ f Y;deielS)^_Y;de]$^_Ya`$b'dŠ;`$l"^_P@S`$c'Sl)]$^h`$l)d$S+a]6b f S3TVU

\

W

^_P@S%['d_[']6\dhS6i`$b

f

`$l

f

Sl"iSbB^hSl%deihP@SRSB3YXzAW6e…

Sa Z =A TVU

g[Z

\

lZ

=

c=Z

=A T m i

S3TVU

Z]

=A TVU

g Z =A T ` Z =

^ i

(8)

W

^_P@S%Š;`$[Bl^_P@‹8`$l

f

Sli`$R.c']1i^[email protected]…

Sa

Z Z

= TVU

c<Z

=A TVU

c Z Z =A U g \

l>Z

=

c<Z

=A T m i

S3TVU

Z

\\

Z]

= TVU

c<Z]

=A TVU

c Z

\\

]Z =A

U

g[Z

\

ZZ

Z =A T ` Z =

^ i

W

^_P@Sd_YZj-^_P@‹8`$l f Sli`$R.c']1i^"deihP@SRS3.|AW6e‡

Sa

Z h Z

= TVU

c<Z

=A TVU

c

Z h Z =A U g

l>Z

=

c<Z

=A T m c Z

\ h l>Z

=

T

c<Z

=A m i

S3TVU

\ Z]

= TVU

c<Z]

=A TVU

c

\ ]Z =A

U g

\

Z =A T ` Z =

^ c Z

\

Z =A ` Z

=

T

^ i

o"Y'&'SlSbB^^_YZRSdeihP@SRS6d]6lS]6\;dh`V^hS6dh^hS f \

W

dhS6i`$b

f

‹8`$l

f

Slq[Bb@y1S)‹>F%[@^h^e]deihP@SRS1…

W

Š;`$[Bl^_P@‹8`$l

f

Slq[Bb@y1S)‹>F%[@^h^e]deihP@SRS1‡

[email protected]\ZY;ieYa^MX[B\aSlVdeihP@SRS†]1d]6\;dh`^hS6dh^hS f …B[@^^_P@S.^_YZRS f Y;deielS)^_Y;de]$^_Ya`$b Slel`$l)d%]6lScBlS f `$R.YZb']6bB^Š;`$l\a`$b@y

^_YZRS%YZbB^hS)y$l)]$^_Ya`$bdh`V†S f `b@`1^cBlS6dhSbB^^_P@S6dhS"lS6d_[B\a^ed)‡

ˆS%lS6i)]6\Z\'^_P']$^YZb^_PBY;dc']6l^)…-^_P@S"cBl`$B\aSRY;d].d_YZR.cB\aS†]6Ž1S)‹;cBl`$c']$yA]$^_Ya`$b`$b@S1…A^_P@S%YZbBYa^_Y;]6\ f ]$^e]Y;d^e]6ASb^h`V'S

SjB]1i^)…']6b f ^_P@S%'`$[Bb f ]6lgVŽ$]6\Z[@S6d"]6lS%^e]6ASb^h`V'S^_P@SŽ$]6\Z[@S6d`$Š^_P@SSjB]1i^"dh`$\Z[@^_Ya`$b'd`$Š^_P@SS6Œ$[']$^_Ya`$b'd)‡

n8b^_P@S%Š;`$\Z\a`$†YZb@yB…A†S%YZb f Y;i)]$^hS"Š;`$l%]6\Z\i)]1dhS6d

W

^[email protected] ^_YZRS1…

W

^_P@S%lS\;]$^_YaŽ1S%Slel`$lYZb

`$b

e

\Slel

g e

) ` e

q

e

)

…-†P@SlS

g l m

^ f^j

…

W

^_P@S%lS\;]$^_YaŽ1S%Slel`$lYZb`$b e \Slel

g

e

) ` e

q

e

)

g

)+ "!#%$'&(*),+.-

`0/132 -4(*),+.-5

)+6 "!#%$'&6(*),+.-5

‡

]6b

f

cB\a`1^^_P@Sdh`$\Z[@^_Ya`$b'd†Ya^_P ^_P@S

f

Y'&'SlSbB^deihP@SRS6d)‡

n8b ]6\Z\i)]1dhS6d)…-†S^h`A`$

W

7u6{8…A\57%z8… w

qBg

w

zg

Z

W k g Za

g d g \ n:9

38i`$lelS6d_c'`$b f YZb@yV^h` f YZRSb'd_Ya`$b']6\Ž$]6\Z[@S6d"`$Š j a

g;9hhh u=<

i

Za

g Z h

?>

id g Z h i

k g

hhh

< i g \ nZ h TVT

n

6e…@]6b f ^_P@S^_YZRSdh^hScA@

g Z h

3;†P@Sb f Y'&'SlSbB^)…A^_P@SSjB]1i^Ž$]6\Z[@S%Y;dy$YaŽ1Sb)6

ˆS`$@^e]6YZb@S f

gCBh n

Z

\ ]6b f

Za-g

\

n;h9

(9)

v-ujBv-u q[Bb@y1SF%[@^h^e].z q[Bb@y1S)‹>F%[@^h^e]T

OYZRS.k z-‡t$T |-‡|1{

S6z Slel

v-‡z% v-‡TAz

Slel

TB‡t1| %-‡z%

OYZRS.k |-‡v1{ u6v-‡z$T

iT Slel

{-‡z {-‡TBu

Slel

{-‡;%$T {-‡;%1|

OYZRS.k |-‡v1{ u6v-‡TAz

i)| Slel

|-‡t1t X‹_{1z {-‡Zu1u

Slel

{-‡Zu6v {-‡Zu6z

|-ujB|-u q[Bb@y1SF%[@^h^e].z q[Bb@y1S)‹>F%[@^h^e]T

OYZRS.k u6z-‡z z1A‡v1

S6z Slel

{-‡t1 {-‡t1

Slel

{-‡1v {-‡1$t

OYZRS.k z%-‡1t %$TB‡1$v

iT Slel

t-‡|1z X‹_{1z v-‡|% X‹_{1z

Slel

-‡;%1MX‹_{1z |-‡|1z X‹_{1z

OYZRS.k z1|-‡;%1t %$TB‡|1z

i)| Slel

u1‡v1{ u1‡{1v X‹_{1z

Slel

u1‡$T u1‡| X‹_{1z

t-ujBt-u q[Bb@y1SF%[@^h^e].z @ g 9 n

Z h

?> q[Bb@y1S)‹>F%[@^h^e]T

OYZRS.k |1{-‡|1|43;TA{1{1{Ya^6 1$|-‡Zu

S6z Slel

{-‡T% {-‡T 1

Slel

u1‡{1t u1‡Zu6z

OYZRS.k u6z1A‡t%43;TA{1{1{Ya^6 u)T%-‡{%

iT Slel

z-‡1${ X‹_{1z |-‡v% X‹_{1v

Slel

%-‡v-u4X‹_{1z u1‡Zu6v X‹_{1z

OYZRS.k u6v-u1‡Zu6v 3;TA{1{1{Ya^6 u)TA|-‡z1|

i)| Slel

v-‡z$TX‹_{1z u1‡v1X‹_{1v

Slel

|-‡TBuX‹_{1z z-‡|-uX‹_{1v

(10)

*@`$l"zV†]6Ž1S6d\

^ g ^ T c ^

…)3alS6d_c‡+b@…

e

6e…B†Ya^_P

^ T l_ i f ij m gpo T

x l>u

T f

cQv

T j ` T _ m ^ l_ i f ij m gpo

x

l>u

f c=v

j ` _ m

]6b f l>u T g Z h 8 i vT g \ 8 m

l>u

g \ 8 i v g Z h 8 m

v-ujBv-u q[Bb@y1SF%[@^h^e].z q[Bb@y1S)‹>F%[@^h^e]T

OYZRS.k v-‡v1z 1A‡z1

S6z Slel

v-‡v% v-‡;%-u

Slel

%-‡{1v %-‡Zu51

OYZRS.k |-‡;%1v u6v-‡1z

iT Slel

{-‡v-u {-‡T1TAz

Slel

{-‡v1t {-‡|1

OYZRS.k |-‡|1v u6v-‡t1z

i)| Slel

-‡TAz X‹_{1z {-‡Zu6v%

Slel

{-‡Zu6{-u {-‡Zu51$v

|-ujB|-u q[Bb@y1SF%[@^h^e].z q[Bb@y1S)‹>F%[@^h^e]T

OYZRS.k u6z-‡ z-‡1$v

S6z Slel

{-‡t$T {-‡t1v

Slel

u1‡|1 u1‡|1

OYZRS.k z1|-‡z %1|-‡v%

iT Slel

t-‡;%% X‹_{1z v-‡|1| X‹_{1z

Slel

{-‡Zu6z TB‡TA| X‹_{1z

OYZRS.k z1A‡TAv %%-‡;%

i)| Slel

{-‡;% u1‡{% X‹_{1z

Slel

{-‡1 u1‡|1{ X‹_{1z

t-ujBt-u q[Bb@y1SF%[@^h^e].z @ g 9 n

Z h

?> q[Bb@y1S)‹>F%[@^h^e]T

OYZRS.k 3;TA{1{1{Ya^6 1 -‡T1T

S6z Slel

[Bb'dh^e]6B\aS {-‡T%

Slel

{-‡1z

OYZRS.k 3;TA{1{1{Ya^6 u)T 1A‡;%1|

iT Slel

[Bb'dh^e]6B\aS |-‡z1v X‹_{1v

Slel

t-‡|1z X‹_{1v

OYZRS.k 3;TA{1{1{Ya^6 u)TAt-‡;%%

i)| Slel

[Bb'dh^e]6B\aS u1‡v1v X‹_{1v

Slel

u1‡|1v X‹_{1v

(11)

Precision

e2 c4 c6 Precision L2

resolution x 10 -3 0.00

0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00 3.20 3.40 3.60

10.00 15.00 20.00 25.00 30.00

"!#$ %&(') &+*,-.&

/

&* 101 2 34%)& ') 15 ')

Cost

e2 c4 c6 Cost

resolution x 10 -3 10.00

20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00 110.00 120.00 130.00 140.00 150.00

10.00 15.00 20.00 25.00 30.00

678.9. "!#$ %&:') &+*,.-.&

/

&

* 101 2 34%)& ') 15 ')

Precision-Cost

e2 c4 c6 Precision L2

1e-03 Cost 2 5 1e-02 2 5 1e-01 2 5 1e+00 2 5

20.00 40.00 60.00 80.00 100.00 120.00 140.00

4;+ 9.<!#. %&$') &+*,+-.& / &=* 01 2

34%$& ') 15 ')

Integral evolution

square e2 square c4 square c6

int e2 int c4 int c6 Integral x 103

TimeStep x 10 3 -0.10

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10

0.00 2.00 4.00 6.00 8.00 10.00

?> @<A B!

+C)DE#FGHGIJ KHK+I

%*

+C)DE#FGHGIJLKHK+I

!#$ %&(& ') -.& / &"* $01 2

34%$& ') 15 ') )%*$ %+M.NO$P"NQ$PSRTUV

Integral evolution

int e2 square e2

int c4 square c4

int c6 square c6 Integral x 103

TimeStep x 10 3 -0.20

-0.10 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90

0.00 0.50 1.00 1.50 2.00

W>78 @<A X!

+C)DE#FGHGIJ KHK+I

%*

C$DE#FGHGIJLKHK+I

!#$ %&(& ') -.& / &:* $01 2

34%)& ') 15 ') )%*$ 6YMNO)PZNQ$P[RT\V

(12)

!"t

Integral evolution

int e2 square e2

int c4 square c4

int c6 square c6 Integral x 10 3

3 TimeStep x 10 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00

0.00 0.50 1.00 1.50 2.00

/@<A 6!

C$DE#FGHGIJ KHK+I %*

+C)DE#FGHGIJLKHK+I !#8 %&=& ') .-.&

/&*

01 2 34%)& ') 15 ') )%*$ NO$PZNQ)PSRTV+

+ %<*%%)!#1N55%< ')

=%4;+,+-.&$ .& ') $% ,

&5* 801 2 34%& ') 1 ') ,&> 78 :%4;+,-.&:9

/& ') 6% ,

%*/&5* 801 2 34%)& ') 15 ') ,&>

(13)

=%4;+,+-.&$ .& ') $% ,

%*

/

&5* 801 2 34%& ') 1 ') ,&

78 :%4;+,-.&:9

/

& ') 6% ,

%*

/

&5* 801 2 34%)& ') 15 ') ,&

=%4;+,+-.&$ .& ') $% ,

%*

/

&5* 801 2 34%& ') 1 ') ,&

78 :%4;+,-.&:9 / & ') 6% ,

%*

/

&5* 801 2 34%)& ') 15 ') ,&

(%4;+,-.&(9 $& ') 4(% ,

%* / &5* 801 2 34%& ') 1 ') ,&>

78 :%4;+,-.&:9 $& ') 6% ,

%* / &5* 801 2 34%)& ') 15 ') ,&

(14)

6 + "%4;+,-.&Z9 5& ') )"% ,%*

/

&

* 801 2 34%)& ') . ') ,&

LKM QU'&$Y"$U'& U2 P$/R4#%@M

OP@S6dhS"b-[BRSleY;i)]6\BlS6d_[B\a^ed f SR`$b'dh^_l)]$^hS"^_P@S%S2ieYaSb'ig.`$Ši`$R.c']1i^deihP@SRS6dŠ;`$l"^_PBY;dd_YZR.cB\aS"†]6Ž1ScBl`$c']$yA]$^_Ya`$b

cBl`$B\aSR ‡.TdeihP@SRS6d\aS6] f YZb f S)S f ^h`d_YZR.YZ\;]6llS6d_[B\a^ed^_P']6b XzdeihP@SRS6dŠ;`$l].^_g1cBY;i)]6\Z\ag^_PBlS)S)‹8^_YZRS6d"i`A]6l)dhSl

lS6dh`$\Z[@^_Ya`$b‡XŽ1Sb YZŠ^_P@S!.|.deihP@SRS6d"]6lS%b@`1^R`$lS%SjAc'Sb'd_YaŽ1S^_P']6b=.TdeihP@SRS6d]6b

f

y$YaŽ1S6d'S)^h^hSl%lS6d_[B\a^edYZb

^_P@S%cBlS6dhSbB^i)]1dhS1…-^_P@S)g]6lSYZbŠ8]1i^R`$lSYZb'dh^e]6B\aS]6b ff

Y'2ie[B\a^^h`V^_[Bb@S"YZbcBl)]1i^_Y;i)]6\]6cBcB\ZY;i)]$^_Ya`$b'd)‡WA`V†S%†YZ\Z\

`$bB\ag.Š;`-ie['dYZb^_P@S%Š;`$\Z\a`$†YZb@y`$b^_P@ST1^_P `$l

f

Sl"i`$R.c']1i^deihP@SRS6d)‡

.( # %JX()J0

n8b^_PBY;ddhS6i^_Ya`$b…-†S%^hS6dh^deihP@SRS"`$b^_P@S%[BbBVR` f S\'`$Š'`$[Bb f ]6lg\;]6g1Sl$‡ˆS"cBlS6dhSbB^YZb^_P@S"‰Bl)dh^d_[B'dhS6i^_Ya`$b

]d_YZR.cB\aS]6b']6\ag-d_Y;d)‡*YZl)dh^"`$Š]6\Z\_…'†SVd_P@`$† ^_P']$^"Š;`$l%[BbBlS6dh`$\aŽ1S f '`$[Bb f ]6lg.\;]6g1Sl$…@].PBYay$P `$l f SldeihP@SRS%Y;d\aS6ded

d_[BYa^e]6B\aS"^_P']6b ]\a`$† `$l f Sl`$b@S1‡ `$lS)`$Ž1Sl$… f [@S%^h`'`$[Bb f ]6lg.i`$b f Ya^_Ya`$b…A^_P@S%`$l f Sl`$Š^_P@SdeihP@SRSY;d f Y'&'SlSbB^

YZb'd_Yf S%^_P@S f `$R]6YZb…B]6b f `$b ^_P@S'`$[Bb f ]6lg1‡o"[@S^h`Vb@`$b@‹;\a`-i)]6\b']$^_[BlS%`$Ši`$R.c']1i^"deihP@SRS6d)…-^_P@SSlel`$l"`$b ^_P@S

'`$[Bb f ]6lgVcBl`$c']$yA]$^hS6dYZb'd_Yf S"^_P@S f `$R]6YZb‡

NKM8N OQPR "$& UXWR)YM

OP@SV[BbBR` f S\Y;d%].R` f S\`$Š^_P@S†S6dh^hSleb '`$[Bb f ]6lg.\;]6g1Sl$…@`$@^e]6YZb@S f Bg^_P@S\a`-i)]6\S6Œ$[BYZ\ZYZBleYZ[BR 'S)^_†S)Sb

^_P@S S&'S6i^"]6b f ^_P@S%\;]$^hSl)]6\ f Y;ded_YZc']$^_Ya`$b‡OP@S%S6Œ$[']$^_Ya`$bY;d

^ b@lf m

^ f

` Z

b@l

f m

gph f

h

f lh m

gph

3ab@`d_\ZYZc'`$[Bb f ]6lgi`$b f Ya^_Ya`$b)6

f lc

m

gDh

3a‰BbBYa^hS%†Yf ^_P `$Š^_P@S%'`$[Bb f ]6lg\;]6g1Sl6

3hu56

†P@SlS^_P@SVc']6l)]6RS)^hSl

g TVU

Y;d] ihP']6l)]1i^hSleY;dh^_Y;i\aSb@y1^_P…

^_P@SŽ1Y;dei`Ad_Ya^_g]6b f ^_P@Sy$l)] f YaSbB^%`$Š"^_P@S

.`$leYa`$\ZY;dc']6l)]6RS)^hSl$‡OP@Sdh`$\Z[@^_Ya`$b`$Š^_PBY;dS6Œ$[']$^_Ya`$bY;dy$YaŽ1SbBg.^_P@S%Š;`$\Z\a`$†YZb@ySjAcBlS6ded_Ya`$b+\

b@l f m

g

<

K!#"%$'&)(

f

\

38z6

†PBY;ihP Y;dcB\a`1^h^hS f `$b ‰@y$[BlSu1uŠ;`$l.^_g1cBY;i)]6\"`-iS6]6bBY;iŽ$]6\Z[@S6d`$Š%^_P@Sc']6l)]6RS)^hSl)d\

g Z

hh

< t T … g \

n+*

Z h TVT

<0 T t T

]6b f ^_P@Sb g Z

AR ‡OP@Si`$b'dh^e]6bB^

i)]6b'SSjAcBlS6dedhS f YZb^hSleRd`$Š^_P@S%R]6jAYZRV[BRŽ$]6\Z[@S`$Š

^_P@SŽ1S\a`-ieYa^_g ,.-0/1

g , \ 8

( pg

(

\ <

32

U

54

dh`

b@lf m g \

<62

U

54

(

,.-0/1

<

K!

"%$'&)(

f

\

38v6

OP@S†Yf ^_P`$Š^_P@S"'`$[Bb f ]6lgV\;]6g1SlY;d`$Š`$l f Sl

\ 8 87

‡

(15)

0 50 100 150 200 250 300 -0.5

0 0.5 1 1.5 2

8 <!& 1A +$=& 5Y*%4% .!#

%+ %4A% 8!& %%') P R +'=,%Y%.+'=,

*% 15'$M

NKML P"SVR3#YMR!"YO@M

ˆS%i`$b'd_Yf Sl^_P@S f `$R]6YZb

h i

8…1†Ya^_P

g ( 8

3aY_‡S1‡v"c'SleYa` f d`$Š^_P@SSjB]1i^dh`$\Z[@^_Ya`$b)6e‡ˆS f S‰Bb@S]%lS)y$[B\;]6l

RS6d_P `$b

h i

8…†Ya^_P d_c']1iS.dh^hSc ^ g 7 y \ f = g x^ 3

xgVh innniy

6e‡OP@S[BbBAb@`$†b'd"†YZ\Z\'S!b

=

…)b]

=

S)^b

>VD

= …

†PBY;ihP]6lS"^_P@S]6cBcBl`6jAYZR]$^_Ya`$b'd`$Š+b@… b]@]6b f b3>VD ]$^^_P@S"b@` f S6d`$Š^_P@S"RS6d_P‡OP@S"S6Œ$[']$^_Ya`$b'd^h`'S f Y;deielS)^_Y;dhS f

]6lS\

b3>VD lf m g ^

b][lf m

^ f

b][lf m g ^ b@lf m

^ f

^ b@l f m

^ f

` Z

b@l

f m g h

3;T 6

†Ya^_P ^_P@S%'`$[Bb

f

]6lg.i`$b

f

Ya^_Ya`$b'd\

b@l

h m gph

b@l

m

gDh

b ]lh m g ,.-0/1

< 2 U

54 b ]l

m

gph

€6‚˜‚-1˜ ƒ1“@€6“16ƒ“ “A

OP@SS6Œ$[']$^_Ya`$b'd3;T 6i)]6b'S f Y;deielS)^_Y;dhS f ]1dŠ;`$\Z\a`$†"d

b >VD

= g

b]

=A T ` \ b]

=

c=b]

=

T

^ l

xg

Z

nnn8y-`

Z m

b]

= g b =A T ` b

=

T

\ ^ l

xg

Z

nnny-`

Z m

b >VD

= ` Z

b = g h l

xgphKnnn8y m

3>%6

†Ya^_P ^_P@S%'`$[Bb f ]6leYaS6di`$b f Ya^_Ya`$b'd

b5a

gph b

gDh b ]

a g ,.-0/1

< 2 U

54 b ]

gDh

OP@S6dhS%S6Œ$[']$^_Ya`$b'dlS6d_[B\a^YZb^_P@Sdhg-dh^hSRA\

` l Z c \ ^

mb T ` \ b c=b

gT`

\ ^ b ]

a

` b

=

c \ b

= T ` \ ^

b = ` \ b =A T c=b

=A

gph xg

\

innniy-`

\

` b c \ b cDl

Z ` \ ^ mb T

gph

38|6

OP@S%[BbBAb@`$†b'db]

=

S)^Xb

>VD

=

]6lSi`$R.cB[@^hS f \;]$^hSl"†Ya^_P^_P@SS6Œ$[']$^_Ya`$b<3>%6e‡ˆSi)]6b ]6\;dh`.i`$R.cB[@^hSb! -‡

(16)

—‚Bƒ$€B€ —B1˜“16ƒ“ “A

OP@SS6Œ$[']$^_Ya`$b'd3;T 6]6lS f Y;deielS)^_Y;dhS f b@`$† ]1dŠ;`$\Z\a`$†"d

Z

Z h b >VD

=

T

c=b

>VD

= c Z

Z h b >VD

=A T g 9 ^ l[b ]

=A T ` \ b ]

=

cQb ]

=

T m l

xg

Z

nnn8y-`

Z m

316

Z

b ]

=

T

c=b ]

= c Z

b ]=A T g ^

l[b

=A T ` b

=

T m l

xg

Z

nnn8y-`

Z m 36

b >VD

= ` Z

b = g h l

xgphKnnn8y m

38t6

†Ya^_P ^_P@Sde]6RS"'`$[Bb

f

]6leYaS6di`$b

f

Ya^_Ya`$b'd)‡ˆSi)]6blS)†leYa^hS%^_P@Sdhg-dh^hSR YZb^_P@S%Š;`$\Z\a`$†YZb@yŠ;`$leR …A†Ya^_P

rg

>

]6b

f

r ]

g \

b T c \ r ]b ]

T c Z

Z h b

`Qr ]b ]

g r ]b]a

b ]T

`Qr b c Z

b ]

g ` Z

b ]

a

Z

Z h b

=

T

`Qr ]b ]

=

T

c=b

= c \ r ]b ]

= c Z

Z h b =A T

`Ar

]b ]=A T g h xg

\

innniy-`

Z

r b

= T c Z

b ]

=

T c b ]=

`Qr

b =A T c Z b ]=A T g h xg

\

innniy-`

Z

Z

Z h b

`Qr ]b ]

c=b T c \ r ]b ]

T g h

r b c Z

b ] c b ]

T g h

3hu6{6

OP@S"[BbBAb@`$†b'db

>VD

=

]6lSi`$R.cB[@^hS f \;]$^hSl"†Ya^_P^_P@S"lS\;]$^_Ya`$b'd_PBYZcA316e‡ˆSi`$R.cB[@^hSb! Bg]VdeihP@SRS%d_YZR.YZ\;]6l^h`

36e‡

“1;ƒ1‚ 1“Aa€6

OP@SV^_†`RS)^_P@`

f

dcBlS)Ž1Ya`$['d_\agcBlS6dhSbB^hS

f

†SlS['dhS

f

^h` dh`$\aŽ1S^[email protected]Œ$[']$^_Ya`$bD3;T 6e…†Ya^_P

f

Y'&'SlSbB^RS6d_P d_Y/)S

^ ‡

ˆSVi`$R.cB[@^hS"YZb S6]1ihP i)]1dhS^_P@SSlel`$lYZbb@`$leR

`$bAb@…b]]6b f b! V†Ya^_P ^_P@SSjB]1i^%dh`$\Z[@^_Ya`$b‡‘"`1^hS^_P']$^Ž$]6\Z[@S

`$Š"^_P@SSjB]1i^Vdh`$\Z[@^_Ya`$b `$b ,]6lS!b

) l

m g h

]6b f b]

) l

m g b]

a l ` \ 8 ( m

†PBY;ihP Y;dV]6cBcBl`6jAYZR]$^hS\ag

b]

) l

m b]

a * Z h TVT

n * Z h T

‡OP@S"lS6d_[B\a^ed]6lS"cBlS6dhSbB^hS f YZb^_P@S%Š;`$\Z\a`$†YZb@yV]6lel)]6g.]6b f `$b^_P@S%‰@y$[BlS

u6z-‡

Xz .T

e

3aAR96 b /

`

b

1

b]

/

` b]

1

b!

/

`

b!

1 b /

`

b

1

b]

/

` b]

1

b!

/

`

b!

1

* Z h * Z

h * Z h

TVT

* Z h * Z

h * Z h

TVT

16TB‡{1{1v z15% |1|-‡T t1t-‡ v1t1 z11A‡v v%-‡v$T

%1z-‡%1t t1v v-u6v-‡| u1u6|-‡v u6t1t T -‡ 1 -‡Zu%

v1A‡{1{-u v1|-u v1z1{-‡;% |$TB‡z |1t-‡ |1{-‡z z-u1‡z$T

z$TB‡|1|1 z1|1t u-‡T 1 -‡;% z1|-‡z u51A‡z -‡TAt

u-‡;%1{-u u%1t u1u1u1‡| T -‡;% -‡| %-‡|1v v-‡{

u6z-‡v1v$T 1Au1‡t %-u1‡T z-u1‡Zu u1‡11 u1‡Zu6| {-‡|

t-‡z%1{ TA{-‡1 z1t-‡v u1u1‡ {-‡;% {-‡v {-‡TBu

1A‡TA{1{ z%-‡;% u-‡T 1A‡;% {-‡z% {-‡Zu6| {-‡|1{

|-‡Zu6|1 u51A‡t u6z-‡t %-‡v {-‡Zu)T {-‡{ {-‡t-u

TB‡|1z% u6{-‡{ 1A‡z v-‡Zu {-‡{ {-‡{1v u1‡1$v

v-‡1${1{ |-‡;% TB‡1 z-‡T {-‡{1 {-‡{1z z-‡1{

(17)

$;+.@8,%*!# 5!<& 4') &=

NKMON P"SVR3#Y 8&$#Y*=U2 PRPR)SVR!@M

ˆS%lS6i)]6\Z\^_P@Sdhg-dh^hSR `$b ]‰BbBYa^hS f `$R]6YZb

h i

'†Ya^_P'`$[Bb f ]6lg.i`$b f Ya^_Ya`$b'd)…1b']6RS\ag

] b

]@f

` Z

b g h

†Ya^_P ^_P@S%'`$[Bb f ]6lg.i`$b f Ya^_Ya`$b'd\

b@l

h m gph b@l

m gDh

b ]lh m g ,.-0/1

< 2 U 4 b ] l

m gph

:S)^['dYZbB^_l` f ['iS

g

) … ^ l_ m g b@lf m

…

g

‡ˆS`$@^e]6YZb+\

] ^

] ` ^ g h

†Ya^_P ^_P@S%'`$[Bb f ]6lg.i`$b f Ya^_Ya`$b'd\

^ lh m

gDh

^

l

m

gDh

^ ]lh m

g -0/1

<

^ ]

l

m

gph n

:S)^

y

'S^_P@Sde]6RS.YZbB^hS)y1Sl]1dcBlS)Ž1Ya`$['d_\ag1‡ˆSYZbB^_l`

f

['iS

e

g g

‡ ˆSi`$b'd_Y

f

SlV^_P@S

f

Y;deielS)^_Y;dhS

f

S6Œ$[']$^_Ya`$b'd"cBlS6dhSbB^hS

f

cBlS)Ž1Ya`$['d_\ag1‡ˆ P']$^hS)Ž1Sl^_P@SVb-[BRSleY;i)]6\deihP@SRS6d3YXz`$l!.T 6e…'^_P@S)gi)]6b'SlS)†leYa^h^hSbYZb

^_P@S%Š;`$leRA\

^ >VD

g w ^ ] c

^ ] g w ^

^ >VD

g ^

:S)^['d f Sb@`1^hS%Bg ^ ^_P@SSjB]1i^"dh`$\Z[@^_Ya`$b`$Š^_P@SdeihP@SRS1‡n_^Ž1SleYZ‰@S6d)…-]$^`$l f Sl"!`$l$#YZb e \

^ >VD

g w

^ ]

c T c r

e&%

^ >% AVD

3hu1u56

^ ] g

w'

^ c r T e)(

^ >(A T D

3hu6z6

^

>

VD

g ^ 3hu6v6

†P@SlS*

=

Y;d.] Ž1S6i^h`$l†Ya^_P ^_P@SYa‹8^_P

f SleYaŽ$]$^_YaŽ1S`$Š+^

]$^.^_P@S'`$[Bb

f

]6leYaS6d)‡q"SR]6le ^_P']$^

r T ]6b

f r

i)]6b 'S

R]$^_leY;iS6d]1dŠ;`$l%i`$R.c']1i^"deihP@SRS6d)…$Š;`$l%SjB]6R.cB\aS1‡

,

$1—B.‚‚ a”;

ˆS

f

Sb@`1^hSBg <93alS6d_c‡2<]6"^_P@S

f

Y'&'SlSb'iS'S)^_†S)Sb ^[email protected]]1i^dh`$\Z[@^_Ya`$b ]6b

f

^_P@S]6cBcBl`6jAYZR]$^_YaŽ1S`$b@S1…3alS6d_c‡

'S)^_†S)Sb ^_P@SYZl

f

SleYaŽ$]$^_YaŽ1S6d6e‡ˆS%P']6Ž1SM<

g

^ ` ^

…B]6b

f

<]

g

^

] ` ^

];‡*@`$l$<]6b

f

<]'†S%`$@^e]6YZb^_P@Sdhg-dh^hSRA\

^ >

VD

`

^

>

VD

g w < ] c r e %)^ >% AVD

< ] g w <Xc

r T e ( ^ >(A TD

l[b

>VD

^ >VD

<

(18)

dh`\

< g w < ] c r e %^ >% AVD

< ] g w <Kc

r T e)( ^ >(A T D

]6b

f < g w

l[w <Xc

r T e)( ^

>

(A

T Dm c r e %^ >% AVD

^_P@Sb

< g w w <Kc

r T e)( w

^ >(A

T D c r e %^ >% AVD

:S)^['dlSR]6leV^_P']$^w

l

^ >(D

m ] g

^

>(AVD

` (A

T

`-r

e %

^

>% A (AVD ]1i)i`$l

f

YZb@y^h`V^_P@S%O]6g1\a`$lSjAc']6b'd_Ya`$b`$l^h`V^_P@S

‰Bl)dh^S6Œ$[']$^_Ya`$b`$ŠX3hu1u56e‡ˆSi`$b'dhS6Œ$[@SbB^_\ag.`$@^e]6YZb+\

< g w w <Kc

r T e (

^

>(AVD

`Qr T e (

(A T c r

e&% ^ >% AVD

]6b f d_YZb'iS+^ g

^ …AYa^Š;`$\Z\a`$†"d

l ^ ` w w m < g r T e ( ^

>

(D

`Qr T e (

(A T c r

e&% ^

>% D 3hu)T 6

“Aa€

o"[@S%^h`V^_P@S] f YZRSb'd_Ya`$b']6\ZY;de]6^_Ya`$b…6Š;`$l"]RS6d_Pd_Y/)S ^ …A†S%`$@^e]6YZb^_P']$^ e g

-‡*@`$l[BbBlS6dh`$\aŽ1S f '`$[Bb f ]6lg\;]6g1Sl$…

e

Z

]6b f ^_P@Sb…'d_YZb'iS^_P@SSlel`$lY;d%]c'`$†Sl"`$Š e …@]6b ]1i)ie[Bl)]$^hSdeihP@SRS%`$ŠPBYay$P `$l f SlYZb e †YZ\Z\y$YaŽ1SV]V†`$l)dhS

dh`$\Z[@^_Ya`$b^_P']$^"]\a`$†r`$l f Sl`$b@S1‡

“Aa€

q"SR]6le^_P']$^

(A

T

Y;d%].Ž1S6i^h`$l%YZb

T

{ K

^e]6[email protected]^h`]1i)i`$[BbB^^_P@S f SleYaŽ$]$^_YaŽ1S`$Š^_P@SŠa[Bb'i^_Ya`$b]$^%^_P@S'`$[Bb f ]6lg1‡

n8ŠYa^Y;db@`1^S6Œ$[']6\^h`!/)Sl`B…-^_PBY;d^hSleR Y;d`$Š`$l f Sl # ` \

…B†PBY;ihPY;d\aS6ded^_P']6b^_P@S`1^_P@Sl"^hSleRd)‡

,

)€ ‚-€;— — ^ ]‚˜ — ^ > D

‚˜ —"€“—B —

o T

>

‚˜

o T Ta

:S)^['d]6cBcB\ag.^_P@S%cBlS)Ž1Ya`$['dlS6d_[B\a^^h`2XzV]6b f .TdeihP@SRS6d)‡

ˆS%YZbB^_l` f ['iS"^_P@S%Š;`$\Z\a`$†YZb@y43ab@‹eu563ab@‹eu56^_leYf Y;]$y1`$b']6\@R]$^_leY;iS6d\

g h Z h h h

` Z h Z h h

h ` Z h Z

h

‡‡‡ ‡‡‡ ‡‡‡ ‡‡‡ ‡ ‡ ‡ ‡‡‡

h ` Z h Z h

h h ` Z h Z

h h h ` Z h

g ` \ Z h h h

Z ` \ Z h h

h Z ` \ Z

h

‡‡‡ ‡‡‡ ‡‡‡ ‡‡‡ ‡ ‡ ‡ ‡‡‡

h

Z ` \ Z h

h h Z ` \ Z

h h h Z ` \

o > g Z Z 7 h h h

Z 7 Z Z 7 h h

h Z 7 Z Z 7

h

‡‡‡ ‡‡‡ ‡‡‡ ‡‡‡ ‡ ‡ ‡ ‡‡‡

h

Z 7 Z Z 7 h

h h Z 7 Z Z 7

h h h Z 7 Z

o Ta g Z Z 7 Z h h h h

Z 7 Z h Z Z 7 Z h h h

h Z 7 Z h Z Z 7 Z h h

‡‡‡ ‡‡‡ ‡‡‡ ‡‡‡ ‡ ‡‡ ‡‡‡

h

Z 7 Z h Z Z 7 Z h h

h h Z 7 Z h Z Z 7 Z h

h h h Z 7 Z h Z

ˆSAb@`$† ^_P@SSjB]1i^dh`$\Z[@^_Ya`$bV`$Š'^_P@S[BbBcBl`$B\aSREŠ;`$l g

c ‡ˆSd_[BcBc'`AdhS^_P']$^ Y;dd_[2ieYaSbB^_\ag%\;]6ly1S

]6b f ^_P']$^^_PBY;d%SjB]1i^Vdh`$\Z[@^_Ya`$b Š;`$l[Bb-'`$[Bb f S f f `$R]6YZb i)]6b'Si`$b'd_Yf SlS f ]1d%^_P@Sdh`$\Z[@^_Ya`$b Š;`$lV^_P@S'`$[Bb f S f

`$b@S1‡n8bŠ8]1i^)…-Ya^Ž1SleYZ‰@S6d^_P@S"cBl`$B\aSR †Ya^_P ^ ]l

m

g …

b@`$bS6Œ$[']6\^h`!/)Sl`B[@^Ž1Slgd_R]6\Z\_‡

ˆS%lS6i)]6\Z\^_P']$^^_P@Sdh`$\Z[@^_Ya`$bY;d

^ l f m g < K

tx>y ( f

(19)

†Ya^_P

g

4

)

‡:S)^['di`$R.cB[@^hS+^ ]@S)^ ^ ]]‡

^ ] g

< K

\

`tx>y ( f

\ c (

rst ( f

\ i

^ ]] g

`

<

K

\

tx>y ( f

\ c (

rst ( f

\ i

ˆS"i`$R.cB[@^hS^_P@S

b@`$leR`$Š'^_P@S6dhSdh`$\Z[@^_Ya`$b'd]6b

f

^_P@S b@`$leR`$b

h i

A†Ya^_P ]"RV[B\a^_YZcB\aS`$Š'^_P@Sc'SleYa`

f

`$Š^_P@Sdh`$\Z[@^_Ya`$b‡

^ >T D g

lZ ` < m i

^ > D g

\ lZ ` < m n

^

>T D g (

\ i

^ > D g (

\ n

ˆS%lS6i)]6\Z\^_P']$^^_P@S%SYay1SbBŽ$]6\Z[@S6d`$Š

]6lS

9 @ gT`

"%$'&

: @ 2

F

‡ˆS^_P@Sb`$@^e]6YZb

n

:S)^

o

f Sb@`1^hS.^_P@S.^_leYf Y;]$y1`$b']6\R]$^_leYZj †Ya^_P Ž$]6\Z[@S

Z

`$b ^_P@S f Y;]$y1`$b']6\]6b f T

`$b ^_P@SV\a`$†SlV]6b f [BcBc'Sl

d_[B@‹ f Y;]$y1`$b']6\;d)‡'ˆS%]6lSYZbB^hSlS6dh^hS f BgV^_P@Si)]1dhS

‡W1YZb'iS

o`

l c \ m ^ g

…-^_P@S"SYay1SbBŽ1S6i^h`$l)d`$Š

]6lS]6\;dh`VSYay1SbBŽ1S6i^h`$l)d`$Š

o

i`$lelS6d_c'`$b f YZb@y^h`.^_P@SSYay1SbBŽ$]6\Z[@S6d

9 @ g Z c \

rst u=8

y i

]6b f ^_PBY;d)…AŠ;`$lu

Z

iiy-`

Z

‡n_^Š;`$\Z\a`$†"d^_P']$^^_P@SSYay1SbBŽ$]6\Z[@S6d`$Š

o

i)]6b'S%'`$[Bb f S f Bg

Z ` \

9

=

9 )

Z c \

n

OP@SbŠ;`$l

g

]6b f g Z h \ o >

\ i o T

>

\

o Ta

9 i o T

Ta

9 n

€6‚˜‚-1˜ 6“Aƒ1—˜ —B1˜“1ƒ1“@€6“11“A˜r6ƒ“ “

ˆS%lS)†leYa^hS%^_P@S f Y;deielS)^_Y;dhS f S6Œ$[']$^_Ya`$b'd3>%6YZb ]R]$^_leY;ieY;]6\@Š;`$leRA\

^ >

VD

g Z

e ^ ] c

^ ] g Z

\ e ^

^ >VD

g ^

†Ya^_P

g T

{ K ^ ]a

hh‡‡‡

hh

(20)

OP@S%SjB]1i^%dh`$\Z[@^_Ya`$b

^

Ž1SleYZ‰@S6d)…-†Ya^_P^_P@SdhS6i`$b

f

`$l

f

SlYZb

e

^ >VD

g Z

e

^ ]

c

` e

Z \

^ > D

^

] g Z

\ e ^ ` e ^ >

VD

^ >VD

g

^

ˆS]6cBcB\ag.^_P@S%lS6d_[B\a^`$Š^_P@S%cBlS)Ž1Ya`$['ddhS6i^_Ya`$b†Ya^_P+\

! g # g \

w g Z

e

w g Z

\ e

T g

(A

T g g

)a

gph d_YZb'iS

^ a 7E{

r T g ` Z

r g ` Z

Z \

]6b f `$@^e]6YZb… f Sb@`1^_YZb@yV^_P@S%Slel`$lBg < \

^ ` Z

\ e < g ` e

^ > D ` e

Z \

^ > D

Y_‡S1‡

^ ` Z

\ e < g ` e

^ > D

3hu%6

O]6AYZb@yV^_P@S%b@`$leR …A†S"P']6Ž1S

< e

: ^ ` T

{ 2F

T *

^ > D i

—‚Bƒ$€6ƒ“ “— B€ —B1˜“1

ˆS%lS6i)]6\Z\^_P@S

f

Y;deielS)^_Y;dhS

f

S6Œ$[']$^_Ya`$b'd3168‹838t6YZbR]$^_leY;ieY;]6\@Š;`$leRA\

^ >VD

g 9 e o T

T a ^ ] c o T Ta

T

^ ] g

e o T

> ^

^ >VD

g ^

†Ya^_P

T g

{ K ^ ]

a

hh‡‡‡

hh

:S)^ ^ 'S%^_P@SSjB]1i^%dh`$\Z[@^_Ya`$b…-]1d'SŠ;`$lS1‡n_^Ž1SleYZ‰@S6d)…A†Ya^_P ^_P@S%T1^_P `$l f SlYZb e \

o Ta^

>

VD

g 9 e ^ ] c c e >

9 n:9

^ > D

o >

^ ] g

e

^ c e >

9

^ > D

^ >VD

^

(21)

ˆS]6cBcB\ag.^_P@S%lS6d_[B\a^3hu)T 6`$Š^_P@S%‰Bl)dh^dhS6i^_Ya`$b†Ya^_P+\

! g # g

w g 9 e o T

Ta

w g

e o T

>

T g o T

Ta

(A

T g

gDo T

T

a

r T g Z

9 o T

>

r g

9 n:9 o T

Ta

YZb

l ^ ` w w m < g r T e)( ^ >(D

`Ar T e)(

(A

T c r e %^ >% D

o%Sb@`1^_YZb@yV^_P@SSlel`$lBg < >

…-†S`$@^e]6YZb+\

^ `

Z h e o T T a o T

> < > g e >

9 o T

> ^ >> D ` e >

9 o T

> c

9 n:9 o T

Ta e >

^

>> Dn

]6b f … f [@S%^h`.^_P@S%Š8]1i^^_P']$^ ^ >> D g

^ ]

^ `

Z h e o T Ta o T

> < > g e >

9 o T

>

^ ] ` e >

9 o T

> c

9 n:9 o T

Ta e >

^ ]n

3hu6|6

†Ya^_P

gDo T

T a

gpo T

Ta

]6b f

g { K ^ > D

a

hh‡‡‡

hh

g 9 e ^ > D

a Z

hh‡‡‡

hh

g 9 e ^ > D a T

dh`\

^ `

Z h e o T T a o T

> < > g e >

9 o T

> ^ ] c

9 n:9 o T

Ta e >

^ ] ` e

9 n:9

^ > D

a o T

> o T T a T

n8ІS"'`$[Bb

f

^_P@S%b@`$leR `$Š

o T T a

]6b f o T

>

Bg^_P@S"cBlS)Ž1Ya`$['d_\ag.`$@^e]6YZb@S

f

S6dh^_YZR]$^hS1…B†S"P']6Ž1S

< >

: ^ `

Ta { o T Ta o T

>

2F

T 5 e

9

^ > D

a c

ZZ e >

n:9 ^] 6

WA`V^_P@SSlel`$lY;d`$Š`$l f Sl e YZŠ ^ > D

a

gph

‡

— “@€6

W

OPBY;dlS6d_[B\a^Y;dYZb f Sc'Sb f SbB^`$Š^_P@S"Š8]1i^^_P']$^^_P@S%deihP@SRSY;di`$R.c']1i^\Ya^Y;d`$bB\ag f [@S"^h`^_P@S%`$l f Sl`$Š^_P@S

deihP@SRS1‡‘"S)Ž1Sl^_P@S\aS6ded)…1YZŠ^_P@S%deihP@SRSY;db@`1^i`$R.c']1i^)…A^_P@S%Slel`$l\ZYaS6db@S6]6l^_P@S"'`$[Bb f ]6lg`$Š^_P@S f `$R]6YZb

]6b f `$bB\ag^_P@SlS1‡B*@`$li`$R.c']1i^deihP@SRS1…'^_P@ScBl` f ['i^Bg^_P@SVR]$^_leY;iS6d

o T

>

]6b f o T

T a

cBl`$c']$yA]$^hS6d"^_PBY;d

Slel`$l`$bB^h`V^_P@S†P@`$\aS f `$R]6YZb‡

W

OP@Sb@`$leR&`$Š^_P@SR]$^_leY;iS6d

: ^ ` T

{ F T

]6b f : ^ `

Ta { o T Ta o T

> F T

]6lS'`$[Bb f S f

YZb f Sc'Sb f SbB^_\agV`$Š e \^_PBY;dY;d^_P@Sie\;]1ded_Y;i)]6\dh^e]6BYZ\ZYa^_gVlS6d_[B\a^Š;`$l"^_P@SdeihP@SRS6d[Bb f Sl"i`$b'd_Yf Sl)]$^_Ya`$b‡

(22)

NKM QU'&$Y"$U'& U2 P$/R4#%@M

OPBY;ddhS6i^_Ya`$b cBl`$Ž1S6d"^_P']$^%Š;`$l[BbBlS6dh`$\aŽ1S f '`$[Bb f ]6lg\;]6g1Sl$…]\a`$†‹8`$l f SldeihP@SRSV†YZ\Z\'SV'S)^h^hSlV^_P']6b ]PBYay$P

`$l f Sl%`$b@S1‡*@`$l]VlS6dh`$\aŽ1S f '`$[Bb f ]6lg.\;]6g1Sl$…@^_P@SSlel`$l"Y;dc'Sb']6\ZY/)S f Bg].^hSleR f Sc'Sb f YZb@y.`$b^_P@S f SleYaŽ$]$^_YaŽ1S

`$Š^_P@SVdh`$\Z[@^_Ya`$b]$^"^_P@S'`$[Bb f ]6lg1‡‘[BRSleY;i)]6\Z\ag1…B^_PBY;d^hSleR f `AS6db@`1^"†SYay$PB^P@S6]6Ž1YZ\ag]6b f PBYay$P@‹8`$l f Sl"deihP@SRS

y$YaŽ1S6d'S)^h^hSldh`$\Z[@^_Ya`$b^_P']6b\a`$†‹8`$l f Sl`$b@S1‡

. ()()"*,+-*% !.(10

OP@Sd_P']6\Z\a`$†‹8†]$^hSl"R` f S\Y;d]d_YZR.cB\aSR` f S\Š;`$l7B[BYf R`1^_Ya`$b‡.OP@S.Ž$]6leY;]6B\aS6d]6lSV^_P@SVP@`$leY/)`$bB^e]6\Ž1S\a`-ieYa^_g

^ i b ]6b f ^[email protected]].\aS)Ž1S\P@SYay$PB^ e ‡VOP@SVS6Œ$[']$^_Ya`$b'd"^e]6ASYZbB^h`]1i)i`$[BbB^%^_P@S4.`$leYa`$\ZY;d^hSleR …'^_P@S f Y;ded_YZc']$^_Ya`$b]6b f

^_P@SV†YZb f Š;`$l)ieYZb@yB‡OP@S)glScBlS6dhSbB^^_P@SVS6Œ$[']$^_Ya`$b'd"`$ŠR`1^_Ya`$b ]6b f ^_P@SR]1ded%i`$b'dhSlŽ$]$^_Ya`$b‡%ˆS‰Bl)dh^cBlS6dhSbB^

^_P@SS6Œ$[']$^_Ya`$b'd)…]6b f YZb ]dhS6i`$b f c']6l^dh^_[ f g ^_P@S9EFVWA‹_dh^e]6BYZ\ZYa^_g`$Š^[email protected]]1dedi`$b'dhSlŽ$]$^_Ya`$b S6Œ$[']$^_Ya`$b `$b ]6b

.‹8y$leY

f

†P@Sb

f

Y;deielS)^_Y;dhS

f

Bgi`$R.c']1i^deihP@SRS6d)‡ˆS^_P@SbcBlS6dhSbB^

f

Y'&'SlSbB^b-[BRSleY;i)]6\@lS6d_[B\a^ed`$@^e]6YZb@S

f

†Ya^_P

i`$R.c']1i^"deihP@SRS6d]6b

f

['d_[']6\iSbB^hSlS

f

deihP@SRS6d)‡ˆSi`$R.cB\aS)^hS%^_PBY;dc']6l^Bg]Vi`$b'ie\Z['d_Ya`$b‡

XM8N "$#%U'&$@M

OP@SS6Œ$[']$^_Ya`$b'di)]6b'S†leYa^h^hSbYZb f Y'&'SlSbB^S6Œ$[BYaŽ$]6\aSbB^†]6g-d\

]^

]_ `

l>Z!c m bc

] w

]@f g

@>)D

a e `

^ c ^ 3hu516

] b

]_

cDl>Z!c m^ c ] w

]j

g

@>

+ED

a e

` bc

Bb 3hu6

]@e

]_

c ] l e^

m

]@f

c ] le b m

]j g h

3hu6t6

†Ya^_P

Z g

ZaKc +j

38z1{6

g ] b

]@f ` ]^

]j

38z-u56

w g d ]e c Z\ :^ cQb

F 38z1z6

†PBY;ihP i)]6b'S%lS)†leYa^h^hSb ]1d\

]^

]_ ` Zbc

^

]^

]@f c=b

]^

]j c ]

l'd]

e m

]@f g

@>)D

a e `

^ c ^

38z1v6

] b

]_

c<Z ^ c ^ ] b

]@f cQb

] b

]j

c ] l'd]e m

]j

g

@>+ED

a e

` bc

Bb 38z$T 6

]@e

]_

c ] l e^

m

]@f

c ] le b m

]j g h

38z%6

`$l

]^

]_ ` Zbc=b

]^

]j

c ] w q

]@f g

@>

)D

a e `

^ c ^

38z1|6

] b

]_

c<Z ^ c ^ ] b

]@f c ] w z

]j g

@>+ED

a e `

bc

Bb 38z16

]@e

]_

c ] l e^

m

]@f

c ] l e b m

]j g h

38z6

†Ya^_P

Z g

ZaXc +j

38z1t6

w q g d ]e c Z

\ :^ F 38v1{6

w z g d ]e c Z

\

:>b

F 38v-u56

OP@S%^_PBlS)S%Š;`$leRV[B\;]$^_Ya`$b'd]6lS%^_P@S)`$lS)^_Y;i)]6\Z\ag.S6Œ$[BYaŽ$]6\aSbB^)‡‘[BRSleY;i)]6\Z\ag1…A^_P@S)g]6lS%S6Œ$[BYaŽ$]6\aSbB^†P@Sb['d_YZb@y^_P@S

iSbB^hSlVdhS6i`$b f `$l f SldeihP@SRS43aYa^%Y;d%S6]1dhg^h`cBl`$Ž1S56e…@B[@^"b@`1^%†Ya^_P i`$R.c']1i^deihP@SRS6d)‡*@`$l^[email protected]`$b f `$l f Sl

d_c']1iSdeihP@SRS1…-†S"['dhS%^_P@S%‰Bl)dh^Š;`$leRV[B\;]$^_Ya`$b…A]6b f Š;`$l"^_P@Si`$R.c']1i^Š;`$[Bl^_P`$l f Sl"deihP@SRS1…A^_P@S%\;]1dh^`$b@S1‡

(23)

XML '# 4YO U PR U'&$ R%#%R W$RR!&$R U RR3#% U O P USHR4#

PR)SVRpU'&[R)YYR!&' RR)W SVR! PM

1“A6“@€6‚-€;— —€“ “1;ƒ1‚ 6ƒ“ “

ˆSdh^_[ f g.^_P@S%Š;`$\Z\a`$†YZb@yS6Œ$[']$^_Ya`$b+\

]@e

]_

c ^ x b@le^

m gph

ˆS †`$le `$br^_P@Swl)]61]6†]<.‹8y$leY

f

…]6b

f

†S†]6bB^.^h` ‰Bb

f ] i`$R.c']1i^deihP@SRS†PBY;ihP cBlS6dhSlŽ1S6dV^_P@SR]1ded

i`$b'dhSlŽ$]$^_Ya`$b\;]6†‡+*@`$l%d_YZR.cB\ZY;ieYa^_g1…A†Si`$b'd_Y

f

Sl^_P@S`$b@S)‹

f

YZRSb'd_Ya`$b']6\-cBl`$B\aSR `$bB\ag1‡

]@e

]_

c ] le^

m

]@f

gDh YZb=l

h i

Z m n

38v1z6

o"[@S^h`.^_P@S"YZR.c'SleRS6]6BYZ\ZYa^_g'`$[Bb f ]6lg.i`$b f Ya^_Ya`$b'd)…A†S%P']6Ž1S ^ lh m g ^ l Z m

gph

‡

:S)^['d f Sb@`1^hS^_P@S"c'`$YZbB^edYZb^_P@S%Š;`$\Z\a`$†YZb@y†]6g@\

^_P@S ^ ‹;c'`$YZbB^edQ38]6b f S)Ž1SlgrŽ$]6\Z[@S ^e]6ASbYZb^_P@S6dhSc'`$YZbB^ed6†YZ\Z\'S f Sb@`1^hS f Bgr^_P@SYZb f Sj

x8i

Y_‡S1‡ ^ l h m g

^ a

innni

^ =

innni

^

g ^ l Z m gph i

^_P@S e ‹;c'`$YZbB^ed38]6b f S)Ž1SlgŽ$]6\Z[@S%^e]6ASbYZb^_P@S6dhS"c'`$YZbB^ed6†YZ\Z\''S f Sb@`1^hS f Bg.^_P@S%YZb f Sj

x c Z 7 \

‡OP@Sy$leYf dh^hSc

†YZ\Z\''S

f

Sb@`1^hS

f

Bg f

‡OP@S%RS)^_P@`

f

cBl`$c'`AdhS

f

YZbQ,;C\aS6ih-‹>C`$[

f

l)]0@Y;d['dhS

f

^h`VYZbB^hS)y$l)]$^hS%^_P@SS6Œ$[']$^_Ya`$b+\

]@e

]_

c ] 5 e ) ^ 6

]@f gph

38v1v6

†P@SlS e ) f

Sb@`1^hS6d^_P@S%YZbB^hSlec'`$\;]$^_Ya`$b`$Š

e

]$^^_P@S

^

‹;c'`$YZbB^ed)‡n8b ^_P@SŠ;`$\Z\a`$†YZb@yB…1Š;`$ld_YZR.cB\ZY;ieYa^_g1…-†S

f

Sb@`1^hS%Bg

e

^_P@S%[BbBAb@`$†b 5 e ) ^ 6

‡ˆS"['dhS%]Vi`$R.c']1i^deihP@SRS`$ŠT1‹8^_P`$l f Sl^h` f Y;deielS)^_Y/)S%^_P@Sd_c']1iS f SleYaŽ$]$^_YaŽ1S%`$c'Sl)]$^h`$l$‡

ˆS f Sb@`1^hS%BgVcBleYZRS"^_P@Sd_c']1iS f SleYaŽ$]$^_YaŽ1S6d)‡+*@`$l"^_P@S"YZbBb@Slc'`$YZbB^ed)…A^_P@SS6Œ$[']$^_Ya`$bY;d

e ]

= TVU

c \\ e ]=A TVU

c e ]=A U g

\

f le =A T ` e =m

38v$T 6

pb ^_P@S'`$[Bb

f

]6lg1…B†Sb@S)S

f

]deihP@SRS†PBY;ihPSb'd_[BlS6d‰Bl)dh^"`$b^_P@S\aSŠ;^%P']6b

f

d_Y

f

SV].^_leY

f

Y;]$y1`$b']6\R]$^_leYZj ]6b

f

]6\;dh`^_P@SR]1ded"i`$b'dhSlŽ$]$^_Ya`$b…BY_‡S1‡ @le ]m g;

T

a e ]lf m

^ f

g e l Z m ` e lh m

‡:S)^"['d%i`$b'd_Yf Sl%^_†`deihP@SRS6dŠ;`$l^_P@S

'`$[Bb f ]6lg@\^_P@S%‰Bl)dh^`$l f Sl`$Š]1i)ie[Bl)]1ig.`$b@S

\ e ]

TVU

c e ] U g >

) le T ` e a m n

e ] U c

\ e ]

TVU

g >

) le T `

e

m n

38v%6

†P@SlS e lZ m ` e lh m g

@le ]m g le ]m

cl e ] m

†Ya^_P

le ]m g f

= T

= a e ]=A

TVU

i

]6b

f

^_P@S^_PBYZl

f

`$l

f

Sl`$Š]1i)ie[Bl)]1ig.`$b@S

e ]

TVU

` e ] U g T

) l ` e c \ e T ` e a m n

` e ] U c e ] TVU

g T

) l ` e

c \ e

T ` e

m n

38v1|6

†P@SlS

e lZ m ` e lh m g

@l

e ]m g > le ]m

cl e ]> m

†Ya^_P

> le ]m g f

= T

= a e ]=A

TVU

c Z

\ l\ e ]

TVU

` e ] U c e ] U c \ e ] TVU

` e ] U c e ] U m n

W1YZb'iS^_P@Sdhg-dh^hSR Y;ddh`$\aŽ1S f YZbŠ8]1i^'b@`1^'Š;`$l e B[@^@Š;`$l e^ …6†SP']6Ž1S1… f [@S^h`"^[email protected]'SleRS6]6BYZ\ZYa^_g1…eP@`$R`1y1Sb@S)`$['d

o"YZleY;ihPB\aS)^KC`$[Bb f ]6lg4.`$b f Ya^_Ya`$b'd)‡

(24)

’ •e)€6‚-~ a€e”

:S)^['d%b@`$†,dh^_[ f g ^_P@Sdh^e]6BYZ\ZYa^_g `$Š^_P@S`$c'Sl)]$^h`$l$…'['d_YZb@y^_P@SVRS)^_P@` f cBl`$c'`AdhS f BgQE['dh^e]6Š8dedh`$b…)F%lSY;ded]6b f

W1[Bb f dh^_l$R YZbT,'EFVW0 f Sb@`1^hS f BgDEFVWA‹hWA^e]6BYZ\ZYa^_g1…Š;`$\Z\a`$†YZb@y^_P@SRS)^_P@` f `$Š\ZYZb@S dh^_[ f YaS f YZbT,ZWA^_leYZ-†Sl f ]0

,'.]6lec'SbB^hSl‹E"`1^h^_\ZYaS@‹_w']6le']6b@S\;08‡

““‚-€;—

OP@SVS6Œ$[']$^_Ya`$bY;d38v1z6e…^_P@SVb-[BRSleY;i)]6\deihP@SRSY;dB38v1v6‡VO`dh^_[ f g^[email protected]^e]6BYZ\ZYa^_g`$Š^_P@SdeihP@SRS1…@†S.i`$b'd_Yf Sl

^_P']$^ ^ Y;d].i`$b'dh^e]6bB^)‡

W1YZb'iS ^ i)]6b'S%c'`Ad_Ya^_YaŽ1S%`$lb@S)yA]$^_YaŽ1S1…-†S%†YZ\Z\dh^_[ f g.^_P@Sdh^e]6BYZ\ZYa^_gV`$Š^_P@S^_†`VS6Œ$[']$^_Ya`$b'd\

]@e

]_

c ] 5 e ) 6

]@f g h

YZb<l

h i

Z m i

38v16

]@e

]_ ` ] 5 e ) 6

]@f g h

YZb<l

h i

Z m

38v6

†Ya^_P o"YZleY;ihPB\aS)^P@`$R`1y1Sb@S)`$['d'`$[Bb f ]6lg.i`$b f Ya^_Ya`$b'd)‡

ˆS f Sb@`1^hSBg@a^_P@SYZbB^hSlec'`$\;]$^_Ya`$b`$c'Sl)]$^h`$l$…BY_‡S1‡ e ) g

@a e ‡VWA`B…'^_P@ScBl`$B\aSR i)]6b 'SlS f ['iS f ^h`^_P@S

['d_[']6\EFVWA‹_dh^e]6BYZ\ZYa^_gŠ;`$l"^_†`VS6Œ$[']$^_Ya`$b'd\

]@e

]_

c ] l@a e m

]@f

g h

YZb=l

h i

Z m

]@e

]_ ` ] l@a e m

]@f g h

YZb=l

h i

Z m

†Ya^_P o"YZleY;ihPB\aS)^P@`$R`1y1Sb@S)`$['d'`$[Bb

f

]6lg.i`$b

f

Ya^_Ya`$b'd)‡

’ •e)€6‚-~ a€e”

ˆSlS6i)]6\Z\-^_P@SR]6YZbV^_P@S)`$lSRdi`$b'iSlebBYZb@y^_PBY;dd_[B-meS6i^,'.]6lec'SbB^hSl‹E"`1^h^_\ZYaS@‹_w']6le']6bBS\;08‡.`$b'd_Y

f

Sl^_P@Sn8bBYa^_Y;]6\

C`$[Bb

f

]6lg ]6\Z[@S%kl`$B\aSR 3;nC "kX6

] ,

]_

g , i

f)

h

, l_

i8h m g h

, l

h i

f m g , a

38v1t6

†S%P']6Ž1S\

“A—B1“

) E Y B'

B' @> !!58[[>B8"D> #

? '1$4[ 4BA@?E &%'B' [>98" [[ 4@B !-'9" 9>?E 4

l` i c

m

[+ !(K[ X&) *#3 '@+@?E X'>?E +[B[ +X(KB @B '"

)*%K[ >? '1!([ #B!@?E '? Q>4[ BB>A([83 K@?E "

“A—B1“

-,

K .) *#3 '@)@?E [)'XB[ X?5X[ &%+@ 8E' [

8>!>? '19(-[ ./V021 '4[=3 >D45'["5)'4[ '4>+9[ ![

Y #' 85

[ B#' B 85@> *"

“A—B1“ 76 BB '-> > $1'8*#"8&9*%B-B' 4@ 45B>D'>?E B=3 :#

'C- B-<;+ "3 #O$ >>;+#O!4![-[K'M ' 8 Y !>?E '$->->!#B -[ B'*#

>'>:%[ >> Y !' !@ 45B> '>?E BQ[ ! %X5 '"3-5B[ >? '14=3

([ $;+#OV![9 858B[ ([ B' >C>@"

:S)^['db@`$†

f

S‰Bb@S^_P@SSYay1Sb'dh`$\Z[@^_Ya`$bV`$Š@^_P@SnC "k ,'.]6lec'SbB^hSl‹E"`1^h^_\ZYaS@‹_w']6le']6b@S\;0@,;F%lSY;ded0@,ZWA^_leYZ-†Sl

f

]08‡

>“"? a€;—

A@

A3 >.[ /V021 [@9?4() >B(C"D*!4'->? >

, lf

i8t

m

+ ->'K9E

F " t ,

g5 , i

f)

hG

H " , l

h i8t m gphG

C"I <l

t m hG

J "K+I <l

t m h i

, l f

i8t m

'?" 95 f<L

%

M

"KI <l

t m gDh i

, lf

i8t

m

gN

$

<OP a9Q

, lf

i8t c m

%K+

, lf

i8t c m

>'KR

F

!B

J

!<[

t

3 '

? !"

(25)

E‚ 1“Aa€

:S)^['di`$b'd_Y

f

Sl"^_P@S"RS)^_P@`

f

‹8`$Š;‹;\ZYZb@S6d^_P@S)`$lgVŠ;`$l%`$[BlS6Œ$[']$^_Ya`$b'd)‡:S)^['dYZbB^_l`

f

['iS%dh`$RS"b@`1^e]$^_Ya`$b'd\

k TVU

Y;d^_P@S‘"‹8Ž1S6i^h`$l

f

S‰Bb@S

f

Bg!k TVU

g le TVU

i e U innni

e U i e

TVU

m

…

k T

Y;d^_P@S!3;‘u568‹8Ž1S6i^h`$l

f

S‰Bb@S

f

Bg!k

T g le a i e T

innni e

T i e

m

…B†S"lS6i)]6\Z\^_P']$^

e a g e

gDh

‡

o )

Y;d^_P@S%R]$^_leYZji`$lelS6d_c'`$b f YZb@y^h`^_P@S%b-[BRSleY;i)]6\deihP@SRS"Š;`$l%^_P@Sd_c']1iS f SleYaŽ$]$^_YaŽ1S1‡W1YZb'iS†S%['dhSi`$R.c']1i^

deihP@SRS1…

o ) g

T

…-†P@SlS

Y;d^_P@S%^_leYf Y;]$y1`$b']6\BR]$^_leYZj f S‰Bb@S f `$b^_P@S"\aSŠ;^P']6b f d_Yf S%`$Š^_P@S"lS\;]$^_Ya`$b'd_PBYZc'd

38v$T 6]6b f 38v%6`$l38v1|6e…@]6b f

Y;d^_P@S%R]$^_leYZj f S‰Bb@S f ^_P@S"Bg.leYay$PB^h‹;P']6b f ‹_d8Yf S`$Š^_P@S6dhS%lS\;]$^_Ya`$b'd_PBYZc'd)‡

:S)^['di`$b'd_Yf Sl‰Bl)dh^^_P@S%cBl`$B\aSR 38v16e‡OP@S f Y;deielS)^hS"Š;`$leR `$Š^_PBY;dS6Œ$[']$^_Ya`$b†YZ\Z\'S\

^ k TVU

^_

c o )

@ak TVU

gph i

3;TA{6

W1YZb'iS%†S"['dhSi`$R.c']1i^deihP@SRS6d`$Š|$‹8^_P`$l f SlŠ;`$l"^_P@S"YZbB^hSlec'`$\;]$^_Ya`$b…A†S%†YZ\Z\d_[BcBc'`AdhS"^_P']$^^_P@S"YZbB^hSlec'`$\;]$^_Ya`$b

`$c'Sl)]$^h`$l$@a%Y;dSjB]1i^)…-Y_‡S1‡@ak TVU

g k T ‡

“A—B1“ ) $/V021T[@A?4[ !() > J !R[-B(3 @" X?" E9 8>:%

[ (C M !4.(C(!-5?" E4 ![<@a4[ B45 > '>= >*%X'>?E "

%d_YZb@y^_P@S%^_P@S)`$lSRdTB‡Zu%]6b

f

TB‡z-…1Ya^Y;dd_[2ieYaSbB^^h`cBl`$Ž1S^_P']$^^_P@SlSY;db@`VSYay1Sb'dh`$\Z[@^_Ya`$b.Š;`$l^_P@ScBlS)Ž1Ya`$['d

S6Œ$[']$^_Ya`$b‡:S)^['d\a`A`$Š;`$l"SYay1Sb'dh`$\Z[@^_Ya`$b‡ˆSd_[BcBc'`AdhS"^_P']$^†S"P']6Ž1S]Vdh`$\Z[@^_Ya`$b^h`\

t k TVU

g `o

)

@ak TVU

gT`o

) k T 3;TBu56

.`$b'd_Yf SleYZb@yV]YZbBb@Sl\ZYZb@S1…A†S%P']6Ž1S

`t f le

= TVU

c

\\

e =A TVU

c e = A

U m g

\

le =A T ` e =m n

OP@Sdh`$\Z[@^_Ya`$bY;d`$Š^_P@S%Š;`$leRA\ e = g r a j

=h‡n8bB^_l` f ['ieYZb@y^_PBY;d)…-†S"P']6Ž1S1…-†Ya^_P

gDt f …

`

Klj

=

T c \\ j =A T c j =

A

m g

\ lj =A ` j = m n

ˆSd_YZR.cB\ZYZŠ;gVBg j

=

T

^h`.`$@^e]6YZb+\

`

Kl

Z c \\ j c j > m g

\ lj ` j m i

Y_‡S1‡

j > c \

j c \\ j `

\

j

c

gph n

3;TAz6

OPBY;dS6Œ$[']$^_Ya`$b ] f

R.Ya^edŠ;`$[Bldh`$\Z[@^_Ya`$b'd)…B]6b

f

]6\Z\^[email protected]`$\Z[@^_Ya`$b'dŠ;`$l

e

]6lS`$@^e]6YZb@S

f

Bg.\ZYZb@S6]6li`$RVBYZb']$^_Ya`$b'd

`$Š^_P@S6dhSŠ;`$[Bldh`$\Z[@^_Ya`$b'd)‡%n_^Y;d"`$BŽ1Ya`$['d^_P']$^"YZŠ j Y;d%]dh`$\Z[@^_Ya`$b…@^_P@Sb T

+

Y;d%]6\;dh`]dh`$\Z[@^_Ya`$b‡WA`†SP']6Ž1S^_†`

i)]1dhS6d)‡*YZl)dh^)…@]$^"\aS6]1dh^%`$b@S`$Š^_P@SŠ;`$[Bldh`$\Z[@^_Ya`$b'dP']1d%]6'dh`$\Z[@^hSŽ$]6\Z[@SS6Œ$[']6\^h`u1‡n8b^_PBY;d%i)]1dhS1…'^_P@SS6Œ$[']$^_Ya`$b

i)]6b'S"lS)†leYa^h^hSbŠ;`$l"^_PBY;ddh`$\Z[@^_Ya`$b j YZb^_P@S%Š;`$\Z\a`$†YZb@yŠ;`$leR …-†Ya^_P j g l

x m \

Klj > c Z m c

\

lj ` j m c

\\

j

gDh n

Y_‡S1‡

lx \ m l*Kl

lx\ m c l

`Xx

\ m c

\\

m c

\ l l

x m ` l

`Xx mmm gph

dh`

Kl\

rst

l\ m c \\

m g `

\ l\

xtx>y l mm

]6b

f

‰Bb']6\Z\ag

g x `

\

tx>y l m

rst l\ m c

ZZ

^_P@Sb P']1d]lS6]6\'c']6l^S6Œ$[']6\^h`.{-‡

ˆSP']6Ž1S^_P@Sb^h`i`$b'd_Yf Sl]V\ZYa^h^_\aSc'Sl^_[Ble']$^_Ya`$bYZb'd_Yf S%^_P@S[BbBYa^%ieYZl)ie\aS1…@^_P']$^Y;d†SP']6Ž1S^h`i`$b'd_Yf Sl%^_P@S

dhS6i`$b f i)]1dhS1‡

WAS6i`$b f i)]1dhS\d_YZb'iS j ]6b f T

+

]6lSdh`$\Z[@^_Ya`$b'd)…1SjB]1i^_\ag^_†`.dh`$\Z[@^_Ya`$b'd)…-de]6g j T ]6b f4j

…AP']6Ž1S]6'dh`$\Z[@^hS"Ž$]6\Z[@S6d

\aS6ded^_P']6b u]6b f ^_P@SŠ;`$[Bl%dh`$\Z[@^_Ya`$b'di)]6b'S f Sb@`1^hS f Bg j T … j … j g T

+

… j > g T

+ K

‡ˆSAb@`$† ]6\;dh`Šal`$R 3;TAz6

^_P']$^

j T j c j T j c j T j > c j j c j j > c j j > g

\\

(26)

Y_‡S1‡

j T j c Z

j T j ` j T c j

j T j g

\

n

 `$lS)`$Ž1Sl$…-]6\;dh`Šal`$R 3;TAz6e…B†S"P']6Ž1S

j T c j c j c j > g `

\

Y_‡S1‡

j T c j ` j T c j

j T j g `

\

n

:S)^['dYZbB^_l` f ['iS

g j T c j ]6b f-f

g j T j

…-^_P@S6dhS^_†`VS6Œ$[']$^_Ya`$b'dy$YaŽ1S"['d

f c Z

f ` ` \ f

f g

\ ]6b

f ` f g `

\

i

dh`

g f `

\\

f c Z

]6b

f g `

\

f

lf ` Z m n

3;TAv6

W1YZb'iS"]6b.SYay1Sb'dh`$\Z[@^_Ya`$bVY;d'`$[Bb f S f

†P@Sb

x L …1S)Ž1SlgSYay1Sb'dh`$\Z[@^_Ya`$b'd]6lS`$Š'^_P@SŠ;`$leRVb=

g T j

=T c j =

‡

o"[@S^h`V^_P@So"YZleY;ihPB\aS)^'`$[Bb f ]6lgi`$b f Ya^_Ya`$b'd)…b

a

gDh

]6b f T

gT`

‡‘"`$leR.YZb@y^_P@SSYay1Sb'dh`$\Z[@^_Ya`$b…1†S]1ded_[BRS

^_P']$^

T g Z

‡OP@Sb†Si`$b'd_Yf SlXb3>?=

D g j =T ` j =

…-†Ya^_P j T ]6b f4j

dh`$\Z[@^_Ya`$b'd`$ŠX3;TAz6e‡

:S)^['di`$b'd_Yf Slb@`$†^_P@S.‰Bl)dh^%\ZYZb@S`$Š"^_P@ScBl`$B\aSR 3;TBu56†Ya^_P ‰Bl)dh^h‹8`$l f Sl'`$[Bb f ]6lg deihP@SRSA38v%6e‡ˆS

`$@^e]6YZb+\

`

Kl

\ b >T D c=b

>

VD

m g

\ b > D

Y_‡S1‡

`

\

Klj T ` j m `

Klj T ` j

m g

\ lj

T ` j

m

^_P@Sb

`

\ Kl

j T ` j m `

Kl

j T ` j m lj T c j T j c j m g

\ lj T ` j m lj T c j m n

W1YZb'iS

j T g j

YZR.cB\ZYaS6d^_P']$^Xb

gDh

†PBY;ihPY;db@`1^"]6bSYay1Sb'dh`$\Z[@^_Ya`$b…A†Si)]6bd_YZR.cB\ZYZŠ;gBg9l

j T ` j m

‡n_^lS6d_[B\a^ed

`

\ `

Klj

T c j T j c j m `

\

lj T c j m

gph

]6b f ^_P@Sb

`

\

` :8lj T c j m ` j T j F `

\

lj T c j m gph n

n8bB^_l` f ['ieYZb@y

g j T c j ]6b f-f

g j T j

…B†S%`$@^e]6YZb

`

\ ` Kl

` f m `

\

gDh n

]6b

f

y1S)^

Kl

` f c

\

m g `

\

n

3;T1T 6

n8bB^_l` f ['ieYZb@y43;TAv6YZb=3;T1T 6e…-Ya^Š;`$\Z\a`$†"d

`

\ f lf `

\\

f c Z ` f c

\

m g `

\ lf `

\\

f c Z m lf ` Z m i

^_P@Sb

f l` f c \

m g ` lf `

\\ f c Z m

]6b f f c Z

gDh n

WA`

f g ` Z

‡BC[@^d_YZb'iS†SVP']6Ž1SVd_[BcBc'`AdhS

f

^_P']$^

j T

]6b f9j

P']6Ž1S.]6b ]6'dh`$\Z[@^hSŽ$]6\Z[@SV\aS6ded"^_P']6b `$b@S1…'Ya^%Y;d

YZR.c'`Aded_YZB\aS"^_P']$^^_P@S%cBl`

f

['i^Y;dS6Œ$[']6\^h`

` Z

‡WA`V†S"P']6Ž1S"b@`VSYay1Sb'dh`$\Z[@^_Ya`$b…-]6b

f

^_P@SdeihP@SRSY;ddh^e]6B\aS1‡

.`$b'd_Y

f

Slb@`$†r^_P@S%‰Bl)dh^\ZYZb@S%`$Š^_P@S%cBl`$B\aSR 3;TBu56†Ya^_P^_PBYZl

f

‹8`$l

f

Sl'`$[Bb

f

]6lg.deihP@SRSB38v1|6e‡ˆS`$@^e]6YZb

b >> D cKl[b >VD

` b >T Dm ` \ b > D gph

Y_‡S1‡

lj >T ` j > m cKlj=T

`

j=

m ` \ lj T ` j m `

Klj T ` j m gph

^_P@Sb

lj T ` j m : lj T c j m lj T c j m

cKlj T c j T j c j m ` \ lj T c j m `

%F

gph n

(27)

W1YZb'iS

j T g j

YZR.cB\ZYaS6d^_P']$^Xb

gDh

†PBY;ihPY;db@`1^"]6bSYay1Sb'dh`$\Z[@^_Ya`$b…A†Si)]6bd_YZR.cB\ZYZŠ;gBg9l

j T ` j m

‡n_^lS6d_[B\a^ed

lj T c j m lj

T c j

m cKl

j T c j T j c j m ` \ lj T c j m `

gDh

]6b f ^_P@Sb

lj T c j m

:8lj T c j m ` \ j T j ` \ F

cB :8lj T c j m ` j T j ` Z F

gph n

n8b ^hSleR `$Š

g j T c j ]6b f-f

g j T j

…B†S%`$@^e]6YZb

l

` \ f ` \ m cBKl

` f ` Z m gph n

3;T%6

n8bB^_l` f ['ieYZb@y43;TAv6YZb=3;T%6e…-Ya^Š;`$\Z\a`$†"d

l f `

\\

f c Z m lf ` Z m lf `

\\

f c Z ` \ f ` \ m `

\ f lf `

\\

f c Z ` f ` Z m gDh i

^_P@Sb

lf `

\\ f c Z m lf ` Z m lf `

\ f ` Z m `

\ f lf `

\

m gph

]6b f f ` f > c

99h f?

c \\

f c f c Z

gph n

ˆSi`$R.cB[@^hS^_P@Sl`A`1^edb-[BRSleY;i)]6\Z\ag1‡ OPBlS)S]6lSlS6]6\_…^_P@S`1^_P@Sl)d^_†` ]6lSi`$R.cB\aSj-Si`$b$mh[@yA]$^hS f ‡ ˆS

`$@^e]6YZb ]6cBcBl`6jAYZR]$^_YaŽ1S\ag

f T g `h n

Z hB i

f g

\\

n 9 f g

\

n

9 f >

gph n;h 9

`Qxh n

Z

hB i f g f > n

E"S)^h^_YZb@y

Šal`$R 3;TAv6e…@†S`$@^e]6YZb j T ]6b f-j

Bg^_P@SS6Œ$[']$^_Ya`$b j ` j c f

gph

‡n8b]6\Z\i)]1dhS6d)…B]$^\aS6]1dh^`$b@S`$Š

j T `$l j

P']1d]6b ]6'dh`$\Z[@^hS%Ž$]6\Z[@S%y$lS6]$^hSl"^_P']6b u1‡WA`B…-^_P@SlS"Y;db@`VSYay1SbBŽ$]6\Z[@S6d]6b f ^_P@SdeihP@SRS"Y;ddh^e]6B\aS1‡

‘"`1^_Y;iS^_P']$^YZІS%^e]6AS^_P@SS6Œ$[']$^_Ya`$b=38v6e…B^_P@S`$bB\agihP']6b@y1S"Y;d

t L

`t

]6b f ^_P@S%lS6d_[B\a^Y;d^_P@Sde]6RS1‡

OP@SVdeihP@SRS6d"]6lSVdh^e]6B\aSŠ;`$l^_P@S^_†`.cBl`$B\aSRd38v16"]6b f 38v6e…'†Ya^_P'`1^_P '`$[Bb f ]6lgdeihP@SRS6d`$ЉBl)dh^"`$l

^_PBYZl f `$l f Sl$‡

XMON P"SVR3#YMR!"YO@M

> ;6ƒ$1“1€

“A˜

,

‚-€;—

OP@S f Y;deielS)^_Y;dhS f ‰Bl)dh^Š;`$leRV[B\;]$^_Ya`$b`$Š^_P@Sd_P']6\Z\a`$†‹8†]$^hSlS6Œ$[']$^_Ya`$b'dY;d^_P@S%Š;`$\Z\a`$†YZb@y\

]^

]_ `

l>Z!c m + b )+

c ] w

]@f g

@>)D

a e )

`

^ c ^

3;TA|6

] b

]_

c l>Z4c

m ) ^ )+ c ] w ]j

g

@>

+ED

a e +

` bc

Bb 3;T 16

]@e

]_

c ] 5 e ) ^ 6

]@f

c ] 5 e + b 6

]j g h n

3;T 6

†Ya^_P

Z g

ZaXc +j 3;TAt6

g ] b

]@f ` ]^

]j

3>%1{6

w g d ]e c Z\

:l^)

m

cDlb + m F

3>%-u56

OP@S

f

Y;deielS)^_Y;dhS

f

\;]1dh^Š;`$leRV[B\;]$^_Ya`$b`$Š^_P@Sd_P']6\Z\a`$†‹8†]$^hSlS6Œ$[']$^_Ya`$b'dY;d\

]^

]_ ` l>Z

`

]^

]jKm + b

)+

c ] w q

]@f g

@>)D

a e )

`

^ c ^ 3>%1z6

] b

]_

c l>Z4c ] b

]@fXm

)

^)+

c ] w z

]j g

@>+ED

a e +

` bc

Bb 3>%1v6

]@e

c ] 5 e ) ^ 6 c ] 5 e + b 6

3>%$T 6

Références

Documents relatifs

To test whether the vesicular pool of Atat1 promotes the acetyl- ation of -tubulin in MTs, we isolated subcellular fractions from newborn mouse cortices and then assessed

Néanmoins, la dualité des acides (Lewis et Bronsted) est un système dispendieux, dont le recyclage est une opération complexe et par conséquent difficilement applicable à

Cette mutation familiale du gène MME est une substitution d’une base guanine par une base adenine sur le chromosome 3q25.2, ce qui induit un remplacement d’un acide aminé cystéine

En ouvrant cette page avec Netscape composer, vous verrez que le cadre prévu pour accueillir le panoramique a une taille déterminée, choisie par les concepteurs des hyperpaysages

Chaque séance durera deux heures, mais dans la seconde, seule la première heure sera consacrée à l'expérimentation décrite ici ; durant la seconde, les élèves travailleront sur

A time-varying respiratory elastance model is developed with a negative elastic component (E demand ), to describe the driving pressure generated during a patient initiated

The aim of this study was to assess, in three experimental fields representative of the various topoclimatological zones of Luxembourg, the impact of timing of fungicide

Attention to a relation ontology [...] refocuses security discourses to better reflect and appreciate three forms of interconnection that are not sufficiently attended to