3D modelling of electromagnetic fields in local
hyperthermia
Nicolas Siauve, Laurent Nicolas, Christian Vollaire, Christian Marchal
To cite this version:
Nicolas Siauve, Laurent Nicolas, Christian Vollaire, Christian Marchal. 3D modelling of electromagnetic fields in local hyperthermia. European Physical Journal: Applied Physics, EDP
Sciences, 2003, 21 (3), pp.243-250. .
HAL Id: hal-00140439
https://hal.archives-ouvertes.fr/hal-00140439
Submitted on 18 Apr 2007
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of scientific research documents, whether they are published 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.
! "#$%
&(')
*+,&*$
-/.1024365,718:9<;>=.?-@2BA?C,DB3,E9F;G. H(C,DBDI3624JK8:9L;,36MONG.?PQ3?JKARO3:DIS
9 GT*UVT%=W; XP#YZG%-(Y(0\[>]]1[; T^A6C,DI8_G*86MO`BJL3:DI8NO8=aC,Mb;>c^d*ef1g;,f1h+e?gbe%TiAj5kDIDla
A686N8?mk;>n+JK36M1A68
SoX(M24`qpNr sa,t186JL`qRk8JKu
2I8:;G*86M,`IJK8v(DI86m,2qE%H(35`IJK2wM1;[,x1[beeVH36M1NC,85,71JK8DI8:E-@36M1Aa1;>n+JK36M1A68
8:yFu/3 2wDKz6M12IA6C,DI3,E. E{2w3?5|718:}~86863O. 8?A:yqD4a1C,M+. <J
€‚ƒI„…†?ƒw‡‰ˆ R12ŠE‹t36t18J#NO8:EKA6JL2lŒ18:E#3g Ž<2IM24`q886DI86u/8MO`/<C,JKu
51Dw3?`B2IC,M‘5’EK8?N<C,J“JL3 N2IC <JK86”>5k86M1Aa‘R|a>tb86JL`BR18JKu
2I3
t1JKC6Œ1DI86u•E.T^N–8~<2IM12l`q8—86DI86u/86MO`<ER13718˜Œ18:86M‘A6C 5t1DB8?N™_24`qR36M‰3ŒbEKC,JqŒ12IM1–Œ1C 5kM1N36Jqa‘A6C,M1N24`q2IC,Mb.Y8:EL51Dw`<Eš3 JK8
t1JK8:EK8?M,`q86N2wM›`q86J<u$C _Eœtk8 A624<2IA/3ŒbEC,JLtO`q2BC M“JL3?`Š8>. ˆ Rk8a3:JK8
A C,u
tk3?JK86Nž`qC•86m>tk86JK2Iu/8?M,`q36DuŸ863|Eœ5JK86u/8MO`<EVtk8JL<C,JKu/86N
C,Mž3tR136M,`qC,u R3712IM–/86”>5k2l713 DB8MO`+86DI86Aj`ŠJKC,u
3 –,M18`q2BAtJKC t186JF`Š2I8:Ei`BC
RO5ku
36M
`q2qEEœ5k8:Ej. ˆ R12qE^A6C,u\tk36JL2qEKC,MELRkC ™@E^3¡–C,C,N
3 –,JK8686uŸ86M,`¢Œ18`I™@8686M£Œ1C `qR¤MO5u/8?J<2IA63 D¢36M1N£86m>tk86JL2Iu/8MO`B3 DJ<8:Eœ5kD4`<E.!02wu
51Dw3?`B2IC,MbE 36JK8¥36DqE{C£3:A6RO2I87186N¤C,M3
R18`q8JKC,–8?Mk8?C 5’E*tkR3?M`qC,už. ˆ R18@uŸC,N86Do2qE^`IRk8MŸ5’E{86N•C,Mž3(JK863 D+–,8?C,u/8`qJqaA6C,u/2IM1–
<JKC,u¦A6C,u
tO5`q8JK2w§ 86N/`qC,u/C,–OJ<3?tR,a
E{A63 M’Ej.
¨©ª(«’¬•]O­b. ®O]b. Ž_R n+24M24`q8:yF86DI86u/8MO`“36MNU3:DI8JL¯2wMuŸ8`BR1C,NkEQ°x±e . ­]1. ²<Œ T^DB8?A`qJKC,u/3:–,M18`I2IA™(37³8tkJKC t13:–O36`I2IC,M+´
JL3 N2IC ™_3718VtkJKC tk3 –3?`B2IC,M¡°\µ>®b. [>]b. Y^JoTiDI86A`IJK2IA<2I86DIN1E
¶·,¸^¹6º»¼½¾O¹6¿L»¸
=CA63 D^R,a,t186JL`BR186JLu/2w3ž2qE5bEK86Nš3|EÀ3:NÁK5|713?M`^`IRk8JL36t,a“2IM#C,M1A6C,DIC,–a
`BJK863?`BuŸ86M,`K.:ÂF`bA636M(Œ18^5bE8?N@3 DBC,M18C,Jo`qC,–8`qR186Jo™(2w`IR
A6R186u/C `BR18JK3?t|a
C,J^J<3 N2IC `BR18JK3?t|a
`qC
2IM1A6JK863,EK8`BR18624J^8<L86A`<E(ÃKe6;l­OÄ. ˆ Rk8tO5JLtkCE{8@C,
Y3:NO2BC LJK86”,5186M1A62I8:E•ÅŠY^n+Æ
R,a,t186JL`qRk8JLu/2w3š2qE
`qC#R18636`@ÅFx­kyŠxxkÇG^Æ(3
DIC,A63:DI2qEK8?N A636M1A68?JKC 5’EÈ`I51u/C 5Jș_24`IRkC 5O`ÉC67³86J<R1863?`B24M1– `BR8
EL51J<JKC 5M1N24M–˜M1C,JLu
3:DV`q2ŠEEL518,. ˆ R18“8Fœ86Aj`Š2l7³8`q86u
t186JK3`I5JK8J<3?Mk–,8
C,
DBC,A?3:D(R,a>tk86JL`IRk8JKu
2I3“2qE¡7186JqaEKu/3 DIDq.^v`(`q8u
tk8?J<3?`I5JK8:E
DIC ™@8:J
`BR136M!x,­kÇG^;V`BR18JK8‹2qEŸM1CÊ8?qK86A`K.v`@`q86u
t186JL36`I5JK8:EŸR12B–,R18J
`IRk3?M
xx1ÇGV;1M1C:JKu
3 DA686DIDqE36JKC 51M1N/`IRk8À`I5u/C 5kJ3?JK8@N3?u/36–8?N‹ÃIg,ĝ. ˆ RO2BE
86DI8713?`Š2IC,M/C>+`q86u\tk86JK3?`I5JK82qE%C6ŒO`q3:2IM186N(ŒažEL5|Œ1uŸ2w`I`q2wM1–
DIC,A63 DwDla
`qR8
tk3?`B2I86M>`‰`qC£3JL3:NO2IC <JK86”,5186M1Aa86DI8 A`qJKC,u/3:–,M18`I2IA¥<2I86DINË5’E{2wMO–
86m,`q86JLM136D3?tt1Dw2IA63?`ŠC JE. ˆ R18“ELt13:A?8/Œ18`q™(8686M~`BR18žtk3?`B2I8MO`36M1Nš`BR8
36tOtkD42BA?36`qC,J2qE<2IDBDI86N(ŒOa
3tkCAj¯k8`+C>™_3?`q86J;OA63 DwDI86N(Œ1C,D45’E;O2IM/C JKN86J
`qC37bC,2IN/3 Mž86mA68 EEK2l7³8(Rk8?36`q2wMO–/3?`b`BR18@EL¯12wMžDI87186DL. ˆ R18(C t186JK3`q2wMO–
<JK86”>5k86M1Aa#C,`ŠR18ž36t,t1DI2BA?3`qC,JE713?JK2B8 E(3 A6A6C,JKN24M1–Dlaš`qC`qR18•NO8t`IR
™_R186JK8›`qRk8›`I5u/C 5kJ
`qC˜JK8?3:AR2qE/DIC,A63?`q86Nb. ˆ ™(C~Yin‰Åe?g1.l[,f—3:MON
­®³.Še­\P‹s(§ Æ36JK85bEK86N
KC,J^R18636`N8?8t’yLEK863?`q86N
`I5kuŸC 5JE^DIC,A636`q86NŸ36`
h,]¡u/u¢Œ186DIC,™`qR18(EL¯2wMžEL5JL<3 A68
ÃBg>ÄK.
v(DIDÌ`BR18¥EL5kA?A68:EEC ‰`qR12qE‘`q86ARM12I”,5k8$D42B8 E 2BMÍ`BR18$–C,C,N
œC,A?3:DI2I§:3j`Š2IC,MC #`qR18¢R1863`<;\™_R12IAR2ŠE—3 A`I53 DwDlaJK86DI3?`Š8?N‰`qC‘`BR8
86DI86A`qJKC,u/3 –,M18`q2BA <2I86DINk;Î24M’E{2IN8 `BR18 A?3:M1A686JKC 5bEÏ`B51u/C 5J.
nb5kJF`BR186JLu/C,JK8:;o24`^2ŠEJK8?”,5k24JK86Nž`qC371C,2IN›`ŠR18/C6718?JKRk8?36`I2wM1–2wM#A6DICEK8
C,JK–36MbE(Ã4x,ĝ.|ÂF`+2qE%`IRk8JK8LC,JK8(8:EE86MO`q2w3 D1`qC¡¯MkC ™™(24`ŠRŸ3:A6Aj5kJK3 Aa
`qR8
86DI86A`qJKC,u/3 –,M18`q2BA¡<2I86DIN1EN2qEF`BJK2lŒO5`q2IC M+. ˆ R18
3ŒbE{C,JLt`B2IC,MšC *8?Mk8?JK–:a
2wM#3/u/8?N2l51u$2ŠEJK8jtJK8:EK86MO`q86NžŒ,a`qR180,t186A624<2IA/vŒbEC,JLtO`Š2IC MšY*3?`B8
ÅK0OvY*ÆK;\™_R12IA6R2qE#`IR18u/362wM8?DB8?u/86M,`“24M‰`IR18¢N2qEœ`BJL2 ŒO5O`q2BC,MC 
`q86u
tk8?J<3?`I5JK8@ÃB[>ÄK.
ˆ R18~0vYÐN2qEL`IJK2lŒO5`B2IC,M—™(24`BR24M˜`IR18t3?`B2I86M,`(2qE/–OC67186JKM186N#Œa
`BR18/24M`q8JK3 A`B2IC,M#C `qR18/2wJLJ<3 N2436`q86Nš86DI86A`qJL2BA\<2I86DIN“36M1N`IR18
tk3`q2I8M,`
`q2ŠEEL518:E. ˆ R2qE¦2wM>`q86J<3 A`q2IC:MÑ2ŠEÒJ<3?`BR18JÐA?C,u
tkDI86mN,518¥`qCÍ`BR8
2wMORkC,uŸC,–86M186C 5bEN2I86DI86A`qJK2IA tJKC tk8?Jq`q2I8:EC `qR18:EK8 `I2qEEL518:E.šv_E
A6C,MbEK86”>5k86M1A68 ;oN8`q86JKu/24M3?`B2IC,M“C ^`qR18
86mA624`q3?`Š2IC M“36u\tkDw24`I5kNO8:E36MON
tkRO3|E{8:E%KC,J^C t`q2Iu/3:D’`B51u/C 5JR1863?`B24M1–/C,M/`IR18Œ13|E{2ŠE*C,2IMO`B512l`q2IC:Mž2BE
3N24qL2BAj5kD4`2qEEœ5k8ž3:M1N#A636MOMkC `^Œ18NC,M18ÓEC,DI86Dwa#ŒOa˜2IMO`B524`q2IC:M!ÃwfOÄK.
nb51Jq`IRk8?J<u/C,JK8À`BR18ž0vYÔNO2qEL`BJK2lŒO5O`B2IC,M2qEN24q<2IA51Dw`wauŸ863|Eœ5kJK3Œ1DI824M
`BR18¡tk3?`q2I8MO`^N,5JL2wM1–•R,a>tk86JL`IR186J<uŸ2w3
`IJK8636`Iu/8MO`_Ã4®ÄK.1n+C,JV`BR18:E{8¡`q™@C
JK863,EKC,MbEK;,24`b2qEo`IRk8M
M186A68:EEK3 Jqa¡`qC@u/C,NO86D1`BRO2qE0OvYÊN2qEL`IJ<2lŒO5O`Š2IC,M³.
ˆ CN8j`Š8?JKu24M18˜M,51u/8JK2BA?36DID aÌ`qR18˜86DI86A`qJK2IA#<2I86DIN¢NO2qEF`BJK2lŒO5`q2IC:M
KC,J/R,a,t186JL`BR186JLu/2w3štJKC6Œ1DI86u•E;^`qR18tJK24M1A624t3:D(u/8j`BR1C,NkE\5’E{86NÊ3 JL8
`BR18›n+2wM124`q8Ž@24q<86JK8?MkA?8 ˆ 24u/8Ž@C,uŸ3:24M¢ÅInbŽ ˆ Ž@Æ(`q86A6ROM2I”,518“36MON
`BR18Vn+2IM24`q8T^DI8uŸ86M,`±ÅŠnbT^Æu/8`BR1C,N1. ˆ R18n³Ž ˆ Ž¢`q86A?RM2I”>5k83:D4DBC ™E
`qC
u/C,N86DI2I§ 8R18`q8JKC,–86M186C 5bE^86DI86A`qJKC,u/3 –,M18`q2IAtJKC6Œ1DB8?u•;O36M1N2Õ`+2BE
EK2Iu
t1DI8Ö`qC×2Iu
tDI86u/8MO`<.ÐÂF`¥Rk3,EË36DwJK8?3:N a،b8?86M5bEK86NÙœCOJ
R,a,t186JL`BR186JLu/243•A63 DIA5kDI3`q2IC MZÃIµ;4h,Ä<;36M1N“2Õ`*RO3|EVŒ18:8?MQE{R1C ™_Mš`qC•Œ³8
™@86DID/EL512w`q86NÌ<C,Jž`BR18˜NO8:EK2I–OMÔC žMk8j™ÚRa>tk8?JL`BR18JKu2I3˜3?tt1Dw2IA63?`qC,J
ÃKe]k;LeeÄ.,s(C,™@87186J;124`±NO8636DqE%™(24`ŠRžA5,Œ12BA(8?DB8?u/86MO`<E%™_R12IA6Rž36JK8MkC `
JK8636DIDla¦36tOtkJKC tkJL2I3`q8`qCu/C,N8?DB2I§ 8‰™(24`qRÐ3 A6A5kJK3 AaÒ`qRk8‘A5kJq718 N
2wMO`q8JL<3 A68:E#EL51A6R‰3,E`IR1CEK8—KC 5kM1N2wMR,51u3?M¢Œ1C,N2I8:E—ÃKe­Ä.(Û(M
36M1C `qR18JR136MONk;>`BR18n1T˜u/8`IRkC,N
R13,E3?DŠE{C¡tkJKC67186N/24`<E^A63?t3Œ12BDI24`wa/C>
u/C,NO86DIDB24M1–@R18`q8JKC,–86M186C 5bEiEœ`qJL5kA`I5JK8:Ej.:n³5kJF`BR18JKu/C:JK8 ;24`+3?DBDIC ™@E`<C
R3?MkNODI8™(2w`IRÜ24J<JK8?–,5DI36J˜EL`IJL5kA`I5JK8:Eš`IRJKC 51–,R‰`IRk8Ì5`I2BD42I§636`q2IC MC 
`q8`qJ<3?Rk8?N,JK36D86DI86u/8MO`<E. ˆ RO36`2qE*`BR18(JK863,EKC,Mž™(R|aә_8¡Rk3718@A?RkCE8 M
`BR18ŸnbTÔuŸ8`BR1C,Nb.‘0C,u/8ŸnbTÔu/8j`BR1C,NkEÀRk3718ž3:D4JK8636N:ašŒ18:8?M#5’E{86N
KC,JuŸ2BAJKC ™(37³8R18636`q24Mk–#u/C,NO86DIDI2wM1–1.ÂqMÃœe?g,Ä(3š­,Ž¥u/C,N8?D™(3|E
EL`I51N2I86Nž<C,JR,a,t186JL`qRk8JKu
2I3,.bÂqM—ÃœejxÄ3•g|ŽÝA?3|E{8RO3|E^Œ18 86M#EKC,Dl7b8 N
KC,J`IR18u/2IAJKC ™(36718(Rk8?36`q2wMO–/C 3@DICEE<aŸN2I86DI8 A`qJK2BA@EœtR18JK8>.ÂqM
`IR2BE
tk3?tk8?Jœ;š`IR18nbTÞuŸ8`BR1C,Nß2ŠEà36tOtDB2I86N`qC¥3JK863 Dw2qEL`q2IAÐA?DB24M2IA636D
tkJKC6Œ1DI86u›.
Û5kJu/3?2wM“C6ŒÁ86Aj`Š2l7³82qEV`qCžN87186DqC t“3/u/8j`BR1C,Nk;1Œ13,EK86NC,M›`BR18
g Ž¤MO5u/8?J<2IA63 D@u/C,NO86DIDI2wM1–¢C •8?DB8 A`qJKC,u/3 –,M18`B2IA#t1Rk8M1C,u/8M13Ê24M
`BR18
RO5u/36M/Œ1C,N,a1;o2BMšC,JKN86J*`ŠCžC t`q2Iu/24§:8¡`BR18¡`BJK8?36`Iu/86M,`^C N8 8t+y
EK8?36`q86N—A63 MkA?86JKC 5’E\`I5ku/C 5JEj. ˆ RO2ŠE\tk3?tk8J/2qE\`BR18L2BJEœ`EL`q8tC /3
A6C,u
t1DI8`q8QEœ`I5kN,ab. ˆ R18“n³TœC,JKu
5DI3`q2IC,M¢NO87186DIC tk8?NKC,JÓEœ5kA6R!3
t51Jqt1CEK8ž2qE(L2BJEœ`tJK8:E{86M,`q86N³. ˆ R18•8?m,tk8?JK2wu/8MO`B3 D^tJKC,A686N>5kJK8Ÿ5’E{86N
KC,J‹713 DI2BNO3`q2IC:M¦2ŠE~`IR18M¦N8:E{A6JK2lŒ186Nb.•G*C,u
t5O`Š8?N$0vYá2qE~`qR186M
A6C,u
t13:JK8?N@`qC¡u/863,EL5kJK8?N@JK8:Eœ5kD4`<E.|ÂFM
`BR18DB3,EL`EK86A`q2IC,M
`IRk8u/C,NO86Db2BE
5’E{86N×C,MÉJK8?3:D$–8?C,u/8`qJqaEL`q86u/uŸ2wM–Î<JKC,u
ˆ C,u/C,–OJK36tR,a/ÅLG ˆ ÆEKA?36MbE.
G^C,u
t5O`q8JK24§:8?N
¿<¸V¿q¹
1¸^¹»º!½o¹j¿L»¸
ˆ R18i7186Aj`ŠC,J™_37b886”>5k3?`Š2IC M
2ŠE™(JK2l`I`q8M24M¡`Š8JKu‰C 86DI86A`qJK2IAV<2I86DIN+z
ÅeÆ
∇×
∇ × − ε = − ωµ
µ
Ê24`IR q` R18˜A6C,MbEL`I36MO`\C Ÿ`ŠR18#tJKC t13:–,3?`q2IC:MC /`qR18
86DI86A`qJKC,u/3 –,M18`q2BAÀ<2I86DIN•3?MkNž²(Åqv!qu#"<Æ%`IRk8¡N86MbEL24`waC,%`qRk8¡86DI86A`qJK2wA
A5kJLJK8MO`<.
2ŠEÝ`BR18$t186JKu/863Œ12IDw24`wa¤3 M1N
2qE `BR18¥A?C,u
tkDI8 m
tk86JKu
24`w`q2l7124µ`wa
$ N8<2IM186N(Œa
2IMO`BJKC,N>5kA624M1–(`BR18A?C,εMk$ N>5kA`q2l7124`wa σ ÃKe6[,Äz
=ω µ ε
. % ' .0/ *21 − 3 ε ( )+*-, & ε %
σ
ε 4 5+687 =
ÅF­Æ
ε =ε ε = ε
™_24`qR
ÅLg,Æ
ω
cia¦36tOtkDwaO2IMk– `IR18àU3 DI8JL¯2wM™(862I–RO`q86NJK8:E{2IN 5k3 Du/8`BR1C,N1;Ÿ`BR8
œC,DIDIC,™(2IM1–@86m>tJK8:EE{2BC,MŸ2ŠEC6ŒO`q3:24Mk8?N+z
9 ? F ∇ × E ∇ × J − A G H ε ; J CDB <>=
ÊR186JK8K: £2ŠE±`BR18Vµ™_; 862I–,RO`1q5kM1A`q2IC M+.
@ G 9 ? I B <>=
= − ωµ
:
ÅFxÆ
cia—5bEK2IM1–˜`IRk8ž7186A`qC,JK2I3:D2IN8MO`q2l`waÅ<[>Æ3 M1N˜`IR18˜0,`qC ¯k8 E
`IRk8?C,JK86u
ÅqfOÆ.
L N − ∇M
[ R Z
[S R Z
P
>
U
T
X ∇ × µ W ∇ × \ =V × µ W
M
∇×∇×
L
= ∇×
OM
∇×
L
ÅL[,Æ
\ Y >P Q
ÅFfÆ
×∇×
∇×
ˆ R18`I2BuŸ8R36JLu/C,MO2BAVnbTš<C,JKu
5kD436`I2IC,M2qE±`BR18M/C6ŒO`q3:24Mk8?N\Ŋ®Æz
]− ∇ ` × p ∇ × t m ^_ − ] `ed q r ε t m ^_ + ] c × o `
k
k
l
j f ig h
µ
n
l
m
]
>
^
_
`
s
a
= − ωµ q
∇×
tvu m ^b
Åq®,Æ
Γ
v(D4`BR1C 5k–,RÒ`BR18!<JK86”,518MkAa2qE—DBC>™ FÅ ­®b.qe­ P#s(§:ÆK;Ÿ™_8A63 MM1C `
2I–,MkC,JK8À`BR18@NO2qELtkD43:A?86u/86MO`A5JLJK8M`3 A66A C,JKNO2wM1–
`qC
`qR18(t186J<uŸ2w`4`q2 7124`wa
713:D4518:E%C,o`BR18RO5u/36M¡`B2qEEL5k8 E.
ÂLMßC,J<NO86J`qC¦`q36¯182wMO`qC 3 A6A6C 51MO`Ê`IRk8 ™(3718 tkJKC tk3 –3?`q2IC:M
`BROJKC 5k–R\`BR18nbTÊNOC,u/362wM1;O`BR18nbT~<C,JKu
5DI3`q2IC:Mž2qE^A6C 5t1DI86N
™(2w`qR/3
<2IJEL`‰C,JLN86J‰7186Aj`ŠC,J TM1–,”>5k2qEL`!PQ3LÁNO3vŒbE{C,JqŒ12IM–£cC 51MkNO36Jqa
G^C,M1N2Õ`Š2IC,MbE—ÅqvcG^ƐÃKefĝ. ˆ R18¢86m>`Š8JLM136D/Œ1C 5kM1N3?JqaÜ2qEQ`BR18MÜ3
tk36JK3?DBDI86DI8t124tk86NŒ1C,mk;¡DIC,A63?`q86NA6DICEK8~`ŠCÌ`qRk8—N8712BA?8,.(ÛM1Dla!<2IJEL`
C,JKN86J7186Aj`ŠC,J#vcGß2qEš5’E{86N¢Œ186A?365bEK8—`qR18—nbT$<C,JKu
5kD436`I2IC,M‰2BE
Œ13|E{86NÖC,ML2BJEœ`ÜC,JKN8?J`q8`BJL36R186N,JK36D‘86DI86u/86MO`<E.—Ž(5k8`ŠCË`qR8
86DI86A`qJKC,u/3 –,M18`q2BA@Eœ¯k24M•NO8t,`BR
713:D4518:E^2wMŸ`BR18RO5ku
36MŸ`B2qEEœ5k8:E^3?`o`BR8
A6C,MbEK2IN8?JK86N
<JK86”>5k86M1Aa1;³C,MkDlaŸ3@u/2IM12wu
3 Dbt136Jq`C `qR18<2I86DIN•A6C,uŸ8|E
C 5`LJKC,u¥`qR18Œ1C,N,a³. ˆ R18ÓEœt51JK2BC 5bE(JK8LDB8?A`q2BC,MbE¡C,M#`qR18•8?m,`q86JLM36D
ŒbC 51MkNO36Jqa
JK86u
3 2wM¡`BR18M•ELu/3 DwD136M1N
NC(M1C `bR37183(–,JK8?36`b2wMO<D45186M1A8
C,M˜`IR18ž<2I86DINkE
24M’EL2INO8ž`BR18•R>5ku
36M#Œ1C,N,ab. ˆ R18ž<2IJEF`(C,J<NO86J718?A`<CJ
TM1–”>52ŠEœ`“P˜3LÁN3‘A636M3 A`I5k36DIDla‰Œb82IN8?M`q24<2I86N `qC‘`ŠR18 024D 718?Jy
PxwkDIDI8JA6C,M1N,24`q2BC Mz
‚
ƒ  z|{+} † ƒ … €~  „ ƒ y
—2w`IRˆ‰¦‡ `qRk8*`Š3?M–8?×M,`q∇2w3 ×D186DI86≅A`qJ<2IAV<2I86DINb. =
Å<µ>Æ
ˆ Rk8ŸN2qEKA6JK8j`B2I§63?`B2IC,M“2qE(C6ŒO`q3 2wM186NžŒa›5’EK2IM1–“A?DB3,EE{2IA636D%-@p6Np?DB8?A
68 NO–8 86DI86u/86MO`<E Üej®,Ĝ;#EL2wM1A68‘`BR18a$86MbEL5JK8‘`BR18 A6C,MO`Š24M,512l`wa¥C>
`q36M1–8MO`B2I36DË<2I86DIN A C,u
t1C,Mk8?M`<E 3:AJKCEE 2IM`q8JL<3 A68׌18`q™(8:8 M
N24qK86JK86M>`ÓuŸ86N243ÜÃKe6µ,Ä{. ˆ 8`IJ<3?Rk8?N,JK36D•8?DB8?u/86M,`<E#3?JK8—5’EK8?NÜEK2IM1A8
`BR18až<24`iC,MšA6C,u
t1DB8?m–86C,u/8j`ŠJK2I8:E(Eœ5kA6R3,E*`BR18@RO5u/36M/Œ1C,NO2I8:E(COJ
A6C,u
t1DI86m
36tOtkDw2IA63?`qC:JEj.
ˆ Rk8Ÿu3?`BJL2Im2qE@ELt3?JEK8/36M1N“EFau/uŸ8`qJ<2IA,.oÂqM“C,JKNO8JV`qC“EKC,Dl718/24`<;
36M2Õ`Š8?J<3?`B2l718“uŸ8`qRkC,N~2ŠE\5’E{86N+z^A?C,MÁ{5k–O36`q8“–,JL3 N,2B8?M,`EKC,Dl7186J\™_24`qR
EK87186JK3 D(tJK86A?C,MkNO2l`q2IC:M124Mk–~`q86A6ROM2I”,518:E. ˆ R12ŠEŸ3 Dw–C,JK2Õ`BR1u¤2qEŸu/C,JL8
3 N:7136MO`q36–8?C 5’Ež`qR136M!N2wJK8?A`/u/8`BR1C,NÌ<C,J/ŒbC `qR‰G%dbXß`q2BuŸ8:E36MON
u/86uŸC,Jqa
CA6A5Otk3?`q2BC,M¡JK863,EKC,MbEÃ<e6h>Ä.
ˆ Rk8$0OvY q2 EDI2IM,¯186N$`qC¦`ŠR1886DI86Aj`ŠJL2IA <2I86DIN¥36M1N$`qC¦`BR18
A6C,M1N,51A`q2l712w`wa
3 M1(
N `BR18NO86MbEL24`Õa
C>+`q2qEEœ5k8:E^ÅLh,Ɲ.
’2“K”
=
‘ ŠŒ‹ Ž-
σ
Å0•I¯1–,Æ
Å<h>Æ
—Rk8?JK8T—–˜š™2qE%`qR18(u/C,N>5kDI8(ρ C `qRk8(A?C,u
tkDI86m/8?DB8?A`qJK2BAL2B8?DBN1; σ `BRO8
86DI86A`qJK2IA63 DA6C,M1N 51A`q2 7124`wa“Å{0›qu/Æ36M1N ρ `BR18
u/3|EEN8MbEK24`wa“ÅŠ¯k–›quœFÆ
™(2w`qR¡JK8:ELt186A`b`qC(`IR18N,24qK86JK86M>`’uŸ86N2I3,.
•žxŸ+ ¡¢KŸ+£¤¡¥§¦¥+¨!£©ª«§¬®­¯¥§¢ª ˆ 1R 8@A63 DIA5kDI3`q2IC,MA6C,NO8@R13|E%Œ18686M/713 DI2IN,36`q86NžC,M•3/EFabEL`q86uÐC>iNO8:8?t
R,a,t186JL`BR186JLu/243_Ŋ`I5u/C 5kJE%EK24`I536`q86N¡3`*e]]¡u/u5MON86Jo`IRk8(EL¯24M1ÆK.
°±0²´³µ›¶¸·º¹¼»¾½¿·€ÀÁÀÄÆÅ·¼Ç»šÈ€·
ˆ 1R 2qENO8712IA68(2qE^u/3 N8(C 3ÀtR36MO`qC,uÜ3?MkN
36M
3?tt1Dw2IA63?`ŠC J;>™_R12IAR/2BE
3 A`I5k36DIDla3#™(3718?–,5k2INO8QŊn+2I–b.ejÆK. ˆ Rk8š<2I86DIN2qEŸ–8M186J<3?`q86N˜Œ,a!3
N24t1C,DB8¡3:M>`q8MOM13\ÅF[/u
u/Æ^DIC,A63?`Š8?N•24Mž`BR18@3tOtkD42BA?36`qC,JK;bC t186JK3`q2wMO–•3`
­®³.Šej­ÖP#s(§ Ŋn+2I–1.Ðe . 3 ÆK. ˆ R18͙_37186–,512IN8¤2qE <2IDIDB8?N ™_24`qR
A6C,M1N,51A`q2wM1–¡™_3?`q86J. ˆ R18VtR136M,`qC,u 2ŠE%u/3 N8C 3713?`+2IM
tDI86m2I–D43|EKE
A6C,MO`q3:24M24Mk– t1C,D aO3 A6JK2IDB3?u/2wNO8 –O86D Ŋn+2I–b. e . A6Æ ™_R1CE{8
86DI86A`qJKC,u/3 –,M18`q2IA#tJKC tk86JL`q2I8:E›36JK8ÊA?DBCE{8˜`qCÌ`ŠRO36`žC •`IRk8—u
5bEKA6D48
`q2qEEL518,.
Õ2Ö2Ì8×ÙؾÚDÛ
ê|ëìîíÔۗÛïξØÓð¾í§ñ2ò Ì-פÎ
Õ2ÖÔÌ-×ÙؾÚDÛ
óÆÎñ8ØÓÖ´Ýã+Û—Û ô ÚDÛ§ñ2ÌðõÑÓì¾ÚDקñÔò Ì8×2Î8ì
ÜÝÙÞ éß
çç
÷›Ýã+Û§Û
äåæ
Õ¤ÖÔÌ8×8ؾÚDÛ
çç
ËeÌÍÎÏ-ÐÑÓÒÔÎ
èæø
á2âDã+Û§Û
ùÚ-ñ§ÍÔÑÓÎú
ÜÝ8Þ Ì8ß
ɧ»iʛ±+²±kU8?C,u/8`qJqa
ÜÝÙÞC,öÔoß `qRk886m>tk8JK2wu/8?M,`q36D1N8712IA68>.
æèæ
çç
¸à ×ÙؾÎ0×2×ÔÌ
ËeÌÍÎÏ-ÐÑÓÒÔÎ
TiDI86A`IJKC,u/3 –,Mk8j`B2IAtJKC t186JL`q2I8:E%C +`qR18NO24q<86JK86MO`bu/86NO2w3(36JK8–,2l7186M/24M
ˆ 3Œ1DI8\e?.
™(3:JLJK36M,`q86Nž`IR18A?C,M|718?JK–86M1A68
C,^`qR18
2w`q8JL36`q2l718
3:DI–C JK24`BROuÐ5bEK86Nž`IC
EKC,Dl7³8`qR18u/3`IJK2wm/Eqa1EL`q86u›.
ˆ R18¡86m,t186JK2Iu/8M`I3:D^0OvY¢N2qEL`qJL2 ŒO5O`q2BC,M24MbEL2BNO8(`IRk8ÀtkR136M>`ŠC,u¦2qE
:C ŒO`q3 2wM186N/Œa›3:Mš2wMNO2wJK86Aj`iu/8`IR1C,Nb.bÂI`RO3|E^Œ1868?M‹EKR1C ™(M`IRk3j`F;³2wM3
<2IJEL`•3?ttJKC,mO2wu/3j`Š2IC Mb;(`IR18¢0vYßN2qEL`qJK2lŒO5`I2BC,M‘u3a¢Œ³8ÊNO2IJK86A`qDwa
JK86Dw3?`q86Nž`qC/`qR18¡`q86u
tk8?J<3?`I5JK8NO2qEL`BJL2lŒO5`q2IC,MÊÃ4­],ĝ. ˆ R18@`q86u\tk8JK3`I5J<8
2wMÌ`BR18tR136M>`ŠC,uË2qEŸ`BR18Mu/863,EL5JK86N—™(24`BR—`I™_8?D 718~C t`q2IA63:DÀ<2lŒ18:J
`q86u
tk8?J<3?`I5JK8N8`q86Aj`ŠC,JEÃ4­±ejÄK.
ˆ 3Œ1DB8­ ELRkC ™@Eš`qR18ÊM>5ku@Œ18?J‹C “24`q8JK3`q2IC,M’Eš36MON`BR18G%dbX
`q2Iu/8:Ež5bEK86NÌ`qC¢EC,D4718#`qRk8~u/36`IJK2wmE<a1EL`q86uљ(2w`qR!`BR18˜A?C,MÁ{5k–O36`I8
–JL3 N2I8M,` ™_JK24`w`q86Mљ(2w`IRÞN,24qL86JK86MO`ÜtJK8?A6C,M1N2l`q2IC,M24M1–áuŸ8`BR1C,N+z
N2I3 –C M136Dq;0:aOu/u/8j`ŠJK2IA‘0,5kA6A?8:EEK2l718Û7186J#Y86DI3:mO36`I2BC,MÐÅ{0b0ÛYÆ
36M1N 24M1A6C,u
tkDI8`q8 G%RkC,DI8:Eœ¯ab.ØG^C,u
tO5`q3`q2IC,MbE R3718 Œ18:8 M
tk8?JL<C,JKu/86N—C,M3šsd‰EL`q36`q2IC M²[,]O]]ÅIdov JL2qEL¯¢µ[>]]~tJKC,A68:EECOJ
™(2w`qR eÖUCÎC £YvPQƝ.ÜÂF`¥2qE¤EKR1C ™(MÎ`ŠRO36`$`IRk8 0b0ÛY
tkJK8?A6C,M1N2l`q2IC,M24M1–@DI863 NkEo`qCÀ`BR18DIC ™_8?JiG%dbX`q2Iu/8:Ej.
°± e³Äî· È¼ÁÙ¹ ›½ ÂʛÀ|·¼ÁÙ»¾È›ÀÆÅ È ›½¶ ÁÀÁ8» ÀÆÂ>Ä|È +›¹ Â>È2ÁÙ·€¹» Á8»šÈ
ˆ 1R 8(–86C,u/8j`ŠJqaž2qE^u/8 EKR186NŸ™_24`BRžx]\`ŠC/[>]/M1C,N8:E%t186J^™(3718?DB8?Mk–>`qR
Ãw­O­Ä.+0>5kA6R3¡`BRO2wMu/8 EKRN8?M’EL24`wa2qEJK86”>52wJK86N24Mž`BR18¡tR36M>`ŠC,u$24M
C,JKN86J\`ŠC—86MbEL5JK8š`IRk8#A6C,M,7186JK–O86M1A68#C 
`ŠR18˜EKC,Dl7³86J/`qC—3˜A6C,JLJK86A`
EKC,D45`q2IC,Mo. ˆ Rk8žu/8:ELR~2ŠE¡u/3 N8žC Óe]Ox±ejfk[›`q8`BJK36R186N,JL3 D86DI86u/86M>`ŠE
36M1N­]kgOg ®MkC,NO8:E;¡DI863 N,2wM1–!`qCÝe6g>]­Ofkµ!N86–,JK8?8:EšC,<JK868?NkC,u›.
TiDI86A`IJKC,u/3 –,Mk8j`B2IA
tJKC tk8?JL`Š2I8:EÀ36MNuŸ8:EKR#N8MbEK2Õ`q2B8 E(36JK8
tJK8 EK86M>`Š8?N
2wM ˆ 3Œ1DI8\e?.
 |ľ· ±,-(5u@Œ186J%C ±24`q8JK36`I2IC,M’E36M1NG%d³X`Š24u/8:Ej.
°±î° ›½¶ ÁÀÁ8» ÀÆÂ>Äƹ2· |ÄîÁ
6
7
98:
;
<
ô Õ ¾Ø Ñ ÛÎ|ܾì¾ß
Ý8â á
Ýã
Ý8â
÷2÷2÷ Ôá
Õ2ð Î8é8ÚD×2ÒÃÑ ØîÑÓÚ8×Ñ ×Ï
ÆÐ2Û§öÎiðÚ ›Ñ ؾÎ0ð ÌiØîÑÓÚD×ì
óÆÑ Ì8ÏÃÚD×2Ì8ò
Ý ›Ý
÷ 2ã›Ý
ôô Ö¤ÚDòÓÎ8ì Ôí§Ü¾ÒÃÑ ðiÎ8é Ø›Ñ Ò2Î×ÙØîÑ ÑÓéÌiؚÑÓÚ-×Ôß
Ö¤ÚDòÓÎ8ì Ôí§Ü +ÌÐ ìiì›Ì8òÓÏ2Ú-ð Ñ ØîÖÔۏß
Ý áá§áDã â
J
LK
M
;ONP N
Õ2ÖÔÌ-×ÙؾÚDÛ
â ÞÓÝ
ÕÎ0ð Û Ñ Ø ØîÑ ÍÔÑ Ø íÜÓðiÎÌ8ò¤ñÔÌð Ø ε ß
ÕÎ0ð Û Ñ Ø ØîÑ ÍÔÑ Ø íÜšÑ ۏÌ8Ï2Ñ ×2Ìð¾í§ñÔÌð Ø ε ß Ô÷›Ý8Þ
Ý
ôÕÎ0ÚÃð ×2Û Ò8ÎÐ Ì-é¾öÔØîÑ Ñ ÍÔò Ñ Ñ Ø Øîí í Ü Óۏß
¤
ã
Þ ¤á
Ýã2÷2ã
óÆÎ×2ìiÑ Øîí ρ Ü Ï σÓÛ šß
ã¤Þ ¤â2á
ËeÌÍÎòÓÎi×ÏØîÖ λ Üîۏß
›ò Î8é¾Øîð ÚDۏÌDÏ8×Î Ø¾Ñ é+ì Ñ ×Ò2ÎñÙØîÖ δ šÜ Ûß ã¤áÃ÷Þ Ý÷
´Î8ìõ֏ÒÔÎ×2ìiÑ Øîí Üî×ÔÚ2Ò2Î8ì λß
YZ [\
] ^_[ `
ËeÌiØîÎið
¤Þ á
Ý8Þ ÷
Ý
ãÞ ã2ã
ÝãÔã2ã
Ý8Þ ÷2ã
¤Þ á
á
;V
Q
O_R
V
_
2 < dc
V
e
O
X
g
RO
Q
aSb
ÕòÓÎ Ñ ÏÃò ÌÃìiì
¤Þ á
ã
Ý
ã
Ý÷2ã2ã
¤Þ ãÔã
á 2ã
O
N
LQ
R
f
Q
STS U
K
R
XW
OOR
OR
; V DR
DV
PQOV
n+2I–,5JK8­1. 3(ELR1C ™E`BR18_g|ŽÜ0vY—N,2ŠEœ`BJK2lŒO5`I2IC,M/C:M¡`IRk8VR3 DwC o`ŠR18
tkRO36MO`qC,u‰36MN¡<2I–>5JK8­b. Œ
JK8tJK8:EK8?M`<E±`BR2qEV0vYÊNO2qEL`BJL2lŒO5`q2IC,M
C,M
`BR18mÛ(§VtkD436M18,.
ɧ»iʛ± ›±b0OvYÊN2qEL`IJ<2lŒO5O`Š2IC,M
C,M¡`BR18VtR36M>`ŠC,uÅF­1. 36Æo36M1N@C,M¡`BR18mÛ§
tkDI36M18(ÅI­b. Œ1Æ.
=
 ¸Ä ·²±³TiDI86A`IJKC,u/3 –,Mk8`q2IA(tJKC t186JL`q2B8 E36M1N/uŸ8:EKRNO8MbE{2w`waC ^`qR8
LQP DR
OVPNONV
ONPV
ñ2ò Ì×Î
N24qK86JK86M>`’uŸ86N2I3,.
ˆ R18713 Dw518:EVC `qR18(™(37³86DI86M1–,`BR 36M1N
`IRk8¡86DI86A`qJKC,u/36–,M18`q2IAEœ¯k24M
N8tO`qR δ 2wM¡DBCEELa
u/86N2I3(36JK8V–2l7186λM(Œa/Åe]OÆ36MN/ÅeOeÆ^Üe?[,ÄK.
λ=
"
&
!
ω µ / µ ε / 0413 ε π
(
+
&
'
+ )
)
σ
,
,-.
*
ωε / 0213 ε % +
#
Åe]OÆ
í ìší2ۗÛïξØÓð¾í§ñÔò Ì8×Î
#
$ δ=
"
(
ω µ / µ ε / 0413 ε &
!
&
'
+
,
,-.
σ
+ )
)
ωε / 0213 ε
*
% −
#
ÅeeÆ
ã
#
$ ˆ R18/vcG2qE¡EK8`3?`V[>]“u
u¥C `qR18/NO8712qA68,. ˆ R18/36M>`q86MMO3•24M
`BR18
™(367186–,512IN8/2qE(uŸC,Nk8?DBDI86NžŒa#3A51J<JK8?M,`N86MbE{2l`waš<2Im86N#C,M#3 M
86N–O8,.+Û(MODla`qR18
R3 DwC `qRk8Ÿ–86C,u/8j`ŠJqaš2qE(NO8:EKA6JK2lŒ186N1;N>5k8¡`qCž`BR8
W QELaOu/u/8`qJqa¡tkDI36M18Ŋn+2I–1.+e?. Œ1Ɲ.
doJK86DI2wu/24M36JqaMO51u/8J<2IA63 D@86m>tk8JK2I8MkA?8:EžR13718˜EKR1C ™(M`IR3?`(`BR18
u/8:E{RN8MbEK2l`wažR13|E*`qC@Œ18@8?”,5k3 Do`qC/­]žM1C,N8:E*tk8?J^™_37186DI86M1–,`IRž<CJ
N2I86DI86A`qJL2IAßtJKC6Œ1DB8?u.n+C,J$N,2I86DI86A`qJL2BA£u
3?`q8JK243:DqEҙ(2w`IRÞDICEEK8:E
ÅqA?C,u
tkDI86mž713:D45k8ŸC `qRk8\tk86JLu/2l`I`I2 7124`waOƜ;±`BR18/u/8:E{R“NO8MbE{2w`wašR3,E`IC
Œ183Œ³C 5`x]M1C,N8:E‹tk86Jš™(37186DI86M1–>`BRb. ˆ Rk8 EK8u/8:ELR N8MbEK2Õ`q2B86E
Ü ¤Þ Ì8ß
í
ãÞ ã2ã›ÝË Ï
5
Ü ¤Þ öÔß
°±
›½¿¶+¹¼» ›À
È ½¿¶ Á-ºÁÙ» À+Â›Ä ¹¼· |ÄîÁ
½ ·ºÂ ƹ·€½· ÀÁ ›À  ½ Ê>· À —¶ ÆÂ>ÀÁ ›½
>
8:
E;
?<
F
A@
G H
B
I
;
<
e»îÁ
C
D
n+2I–,5JK8•gšEKR1C ™@E`qR18M1C,JLu/3 Dw2I§:8?N˜0vY‰N2qEœ`BJL2 ŒO5O`q2BC,Mš2wMš`BR18@aOÛ@§
ELau/uŸ8`qJqa£t1DB3 M18,.˜no2w–,5JK8xáEKR1C ™@EÒ`ŠR18¥M1C JKu
3:D42B§ 86NÑ0vY
N2qEL`IJK2lŒO5`B2IC,M/3?`*ej]u
uNO8t,`BR/24M
`BR18tRO36MO`ŠC,u 2wM\`BR18mOÛa
t1DB3 M18 .
-@C,JKu/36DI2w§ 86N 0OvY 2qE$C ŒO`Š3 2wM186NˌaÖA C,u
t13:JL2qEKC,Mљ_24`BR `BR8
u/3 m,2Bu\5u¢713:D4518C o`qRk8À0vYÊ2wM¡`IRk8VtR3?M`qC,uÜÅe­OÆK.
= ::69@B8 A 598
?9698
=>57696788
<7698
;9678
ܚ÷Þ Ì8ß
:@BA 598 :698
?9698
36M1N tRO36MO`qC,u/ÆK. ˆ R18Ö8?DB8?A`qJKC,u3 –,M18`q2IAtJKC tk86JF`q2I8:E£C ¥`qR12BE
N24qK86JK86M>`bu/86N2I336JK8–O2 718?M24M¡`BR18 ˆ 3Œ1DB8(gžÃw­gO;l­Ox,Ä.
Åe­Æ
:@BA 598
?7698
C: 698
:C@>A 598
?7698
=B5969678 8
<9698
;9678
ܚ÷Þ ö2ß
Ü á2Þ Ì8ß
'ÚD×ÔÎ
à¸ñÃñò ÑÓéÌiØîÚDð >ù ÐÔۏÚ-Ð2ð
'ò Ú2ÚÃÒ
Õ2ÖÔÌ-×ÙؾÚDÛ
ܾá2Þ öÔß
ɧ»iʛ±§°±G*C,u
tk36JL2qEKC,MšC A63 DBAj5kDI36`q86N#0OvYÔN2qEœ`ŠJK2lŒO5O`B2IC,M‹ÅLg1. 3 Æ36MON
`q86u
tk8?J<3?`I5JK8u/863,EL5JK86uŸ8M>`<EiÅLgO. Œ1Æ24M¡`BR18aOÛ(§@E<aOu/u/8j`ŠJqa¡t1DI36M18,.
Ü Þ Ì8ß
XQ
1 -230
. /,ç-
)*
)*
ç
+,
Ü ¤Þ öÔß
Ôã4
Ôã4
2ã4
áDã4
ɧ»iʛ± ±“G^C,u
t136J<2qE{C,M
ç
+,
ÕÎ0ð¾ÛïÑ Ø ØîÑ ÍÔÑ Ø íÜÓðiÎÌ8ò2ñÔÌðÓØ ε Æ
ÕÎ0ð¾ÛïÑ Ø ØîÑ ÍÔÑ Ø íÜšÑ ۏÌ8Ï2Ñ ×ÔÌð¾í§ñÔÌðÓØ ε ß
ôÕÎ0ÚDð¾×ÔÛïÒ8ÎЀÌ8é öÔØîÑ Ñ ÍÔò Ñ Ñ ØÓØîí í Ü Óۏß
ó+Î×ÔìiÑ Øîí ρ Ü ¤Ï σÓÛ šß
ËeÌÍÎòÓÎi×ÏØîÖ λ Üîۏß
›ò Î8é Øîð¾ÚÃۏÌDÏ8×Î¾Ø¾Ñ é+ì ¤Ñ ×Ò2ÎñÙØîÖ δ Üîۏß
!Î8ì¾ÖÒ2Î×ÔìiÑ Øîí Üî×2ÚÔÒ2Î8ì λß
YZ [\
N
] ^_[ `
aSb
C —A63:DIA51DI36`q86N0vYÖN2qEL`qJK2lŒO5`I2BC,M¥ÅFx1. 36Æ
36M1N(`q86u
t18JK3`I5JK8u/863,EL5JK86uŸ8MO`<EÅFxb. Œ1Æ+24M¡`BR18mOÛa¡tkDI36M18,.
4 < dc
>
c C `ŠR¦M,51u/8JK2BA?36D“36M1N¦86m,t18JK24u/86M>`Š3?D“JK8:Eœ5kD4`<E—36JK8‰2wM¦–C,C,N
3:–,JK8?86u/86M>`œ.—0DI2w–,RO`¢NO2wF<86JK86M1A68:E‘u/3a¥Œb8$86m>tkDI3 2wM186N$Œaß`qR8
tkJK8:E{86M1A68C #`ŠR18]b.lµ‰uŸuØN243:uŸ8`q8J—A63?`BR18`q8JE~5’E{86N <C,J~`BR8
`q86u
tk8?J<3?`I5JK8ÔuŸ863|Eœ5JK8u/86M,`<Ej. ˆ Rk8 EK8A63?`BR18`q86JE—36JK8!<2IDIDI86NC 5`
™_24`qR˜3 2wJ. ˆ R18a˜3 JK83 A`I53:D4D a~M1C `_u/C,NO86DI2I§:86N#MO5kuŸ8JK2IA63?DBDla³. ˆ R8
86m,t186JK2wuŸ86M,`q36D1u/8`IR1C,NC,DIC,–,a/ÅI`q86u
t186JK3?`B5JK8Vu/863,EL5JK86u/8MO`b2wMbEL`q863?N
C,/L2B8?DBNuŸ863|Eœ5kJK86uŸ8MO`qÆ
u/3a3:DqE{CRk3718˜EC,u/8#2Bu\tk3 A`C,MÌ`BR8
JK8:EL51D4`FE.
8
=
+,
Ü á2Þ éß
6
V
°±! Â€Ä¾È |ÄõºÁÙ·›Å#"$% Å» Áù» Á8» ›À »¾À  ¸·Á·›¹ ʛ·€ÀŒ·
¶ ÆÂ>ÀÁ ½
)*
ç
 |ľ· °›±³TiDI86Aj`BJKC,u/3 –,M18`q2IA(tJKC t186JL`q2I8:E3?MkNŸu/8:EKRNO8M’E{24`Õa›C i`qRO8
N24qK86JK86M>`bu/86N2I3
Q
Q
1 -230
. /,çç
D,
)*
1 -230
. ,/ç-
ɧ»iʛ±&!±G^36DIA51DB3j`Š8?N¤0vY×N2qEL`qJL2lŒO5`q2IC,M£2wM£3ÐR1C,u/C,–O86M186C 5’E
tkRO36MO`qC,uÞÅ<[O. 3 ƞ36MN!2wM¢3~Rk8j`Š8?JKC,–86M186C 5bEžtkRO36MO`qC,uÞÅ<[O. A6Ɵ™_24`qR
EK87186JK3 D,Œ12BC,DIC,–O2BA?3:DbuŸ86N243_ÅL[1. Œ1Æ.
1 -230
. /,çÝã4
2ã4
1 -230
. ,/çç
D,
)*
AA
v@E^3 M•86mO36u
t1DB8 ;Onb2B–>5JK8@[/EKR1C ™@E%`qR18(3Œ12IDI24`ÕažC>`ŠR18KC,JKu
5DI3`q2IC,M
`qCR136M1N,DI8™(2w`qREK8718?JK3:D1Œ12IC,DBC,–O2IA63:Dou/86NO2I3Å4Œ1C,Mk8 ;,Œ1DICC,Nk;k`B51u/C 5kJ
e
g
Õ2ÖÔÌ-×ÙؾÚDÛ
â ¤Þ Ý
2÷ºÝ8Þ
Ý
ãÞ ¤á
ÝãÔ÷2ã
ãÞ âÔá
ãÞÓÝ÷
áD÷
L
V
Q
Q
VOQ
V
_
ù›Ð2ۏÚ-ÐÔð('ÚÃ×2Î
2ã
Þ ÷
áD÷›Ý Ý ¤Þ
Ý
Ý
ãÞ â
ãÞ ã2÷
Ý2Ý
Ý8â Ýã
ãÞ
Þ 2÷
ãÞÓÝ2Ý ãÞ
¤á
V
'ò Ú2ÚDÒ
Ý2Ý8â
2÷2ã
Ý
Ý8ÞÓÝ
Ýã Ôã
ãÞ áD÷
ãÞÓÝã2ã
›Ý
R
;N
N
;R_R
R
VOQO
;Q
QON
OV
N
OQ
VOR
O
Q
Â<Mš`BR12qE
EL`45kN:a1;^EK3 u/8ž–86C,u/8j`ŠJqa#3 M1N#u/8:ELR˜NO86MbEL2w`waQ<C,JŒ³C `ŠR
1R C,u/C,–8?Mk8?C 5’E3?MkNR18`q8JKC,–8?Mk8?C 5’E“Eœ`qJq51A`I5JK8:E36JK8Q5’EK8?Nb.ÛMkDla
`BR18 tkJKC tk8?JL`B2I8:EÑC,¤`qR18ØuŸ86N2I3×36JK8ØuŸC,N24<2I86Nb.¦n+C,J`qRO8
R1C,u/C,–8?Mk8?C 5’EQtkR136M,`qC,u•;`BR18¢24MkA?Dw5bEK2IC M’E~36JK8Ì<2IDBDI86N‘™(2w`qR‘`BRO8
EK3 u/8VtJKC tk86JF`q2I8:E`BR3?M@`IR18^tR136M,`qC,u.
ˆ Rk8
NO2wF<86JK86M1A68(Œ18`q™@8?86M“R1C,u/C,–O86M186C 5’E36M1NžR18`q8JKC,–O86M186C 5’E
tkRO36MO`qC,u A?C,u/8:EÑ<JKC,u `qR18 713 D45k8:E C>`ŠR18Îtk3?JK36u/8`q8JœE
ÅFA6C,M1N,5kAj`Š2l7124`wak;itk86JKu/2Õ`I`B2l7124`Õa~3:M1N˜NO8M’E{24`ÕaOƝ. ˆ R18N86MbEL24`wa˜R13|E\36M
2Iu
tkC,JF`q36M,`1t136Jq`oC:M¡`BR18¡0vYÊNO2ŠEœ`BJL2lŒO5`q2IC,Mb.
ôà|ÚÃö×2ì¾Ú8ÒÃð¾Ñ Øîö2ÑÓÑ Ú8פ×Ï ì'|ܾà Ú-ÐÔ' ×ô ÒDß Ìð ÑÓÎ8ì
ˆ C¢EC,Dl7b8#`qR12qEu
3?`BJL2BmEqabEœ`Š8?u`qRk8~A6C,MÁK5k–O36`q8˜–OJ<3 N2I8M,`•E{C,D 7³8:J
™_24`qR$0b0ÛY£tJK8?A6C,M1N24`q2BC M12wM1–‰2qE#3 DqEKC5bEK86N³. ˆ R18M,51u@Œ186J˜C 
24`Š8?J<3?`B2IC,MbE36M1NÀ`BR18_GidbX`q2wu/8:E%36JK8VtJK8:E{86MO`Š8?N@2wM¡`IRk8 ˆ 3Œ1DB8xb.›˜8
A63 MÐEK868Ì`BR18ʌ13 M18q5kD24MO<D45k86M1A68!C “`qR18tkJK8 EK86M1A68!C,QE{87³86JK36D
u/86NO2B3 ;³™_R12IAR“N8?A6JK863,EK8¡`BR18
8L<2IA62I86M1AašC,^`qR18\E{C,Dw7186JV™_R12IDI8¡`BR8
N86–OJK868:E%C <JK868?NC,u 2ŠE`IRk8EK3 u/8 .
 ¸Ä · ±>-(5u@Œ186J%C ±24`q8JK36`I2BC,MbE36M1NG%dbX`q24u/8:E
:>
+ÐÔÛ§öÎ0ðÚ
Ñ ØšÎ0ð ÌiØ¾Ñ ÚDפì
›Ý|â€Ý
⠛Ý
8ØÓðîÐéiØÓÐ2ð θÚ
ØÓÖÎñDÖÔÌ8×8ؾÚDÛ
ÆÆÚDξؾۏÎiðiÚ2ÚDÏ2ÏÔÎiÎ××Î8ÎÚ8Ú8ЀРì ì
S
J
K
£¡0 ¡€Ÿ+£¡¥§¦ ¥+¨£©ª
¥§
Ÿ§¦«­ª ©Kª
LK
Q
V
Q R
ô Õ #ùÑ ÛÎ8ì
ܚìiÎ8éÚDפÒ2ì¾ß
Ý÷2ã â
Ý â2â8÷
TM
PV DQ
à|×8ؾÎi×2×2Ì
;QON
§¬ ­¯¥§¢ª ¥§¦ªŸ§ ©­Ÿ—¦
ˆ 1R 8/A63 DBAj5kDI36`I2IC,M‹A?C,N8ž2ŠE_5’E{86Nš`ŠCšu/C,N8?DB2I§ 8
`qR18/N2qEL`IJK2lŒO5`q2IC:M#C,
86DI86A`qJK2IAš<2I86DIN2BM!3˜R,51u
36Mʌ1C,N,a!™(Rk8?M¢2IDIDw5uŸ2wM3?`q86N˜Œa!3#Yn
EKC 51JKA68,. ˆ R18ÓE{C 5kJKA68ž2qE@3NO24tkC,DI8•3?M`q8MM13žq5M1A`q2IC Mk24M1–“3?`­,®b.qe­
P#s_§O. ˆ R18¡86m,`q86JLM136DbŒ1C 5kM1N3?Jqa•2qEV3¡tk36JK36DIDI86DI8t12wt186N
Œ1C,mk;³DBC,A?36`q8 N
A6DICE8`qC(`IR18iŒ1C,N,a/Ŋn+2I–b.,f1. Œ1Ɲ.
Ü Þ öÔß
XV
ɧ»iʛ±›±kU8?C,u/8`qJqa
C,o`qRk8Vu/C,N86D³N8712IA68(Åqf³. Œ1ÆA6C,uŸ2BM1–À<JKC,uÜG
EKA?3:MbE^ÅIfb. 3 Ɲ.
ˆ
±0² · ›½¿·¼Á-¹
>
A
ˆ 1R 8uŸ8:EKR
2qE%C6ŒO`Š3 2wM186N¡<JKC,u[h
G ˆ EKA63?M’E;,3 DwDIC ™(2BM1–¡`qC(`q3¯1824M`IC
3 A6A6C 5kMO``IRk8¡JK8636DE{R3?tk8@C %`qRk8Àtk3?`q2B8MO`iŊn+2I–1.kf1. 3:ÆK.1ÂF`2ŠEVC6ŒO`q3:24M186N
5’E{2wM1– `BR18v(u
2wJK3t3 A¯13:–O8ÝÃ4­k[>ÄK./ÂF`“2wM1A6D45kNO8:Eggoe6µ+eÌM1C,N8:E;
e6µ>­f1[,](`q8`IJ<3?Rk8?N,JK36Db86DI86u/8MO`<E36M1N¡­­+efO]f¡N86–,JK868 EC>+LJK8686NC,u›.
± ï¹ ›¶|·›¹2Á8»š· ½¿·›Å»iÂ
> FA@
ˆ R12qE^–86C,uŸ8`qJqa/2IM1A6D45kN8 E@e­/NO24<<8?JK86MO`±u/8?N,2B3>. ˆ R18tkJKC tk8?Jq`q2I8:E^C>
`BR18:E{8`q2qEEœ5k8:Ež3 JK8“–O2 718?M2wM ˆ 3Œ1DI8‹[QœC,J\`ŠR18›<JK86”,5186M1Aa­O®b.Šej­
P#s_§/Ã4­kgO;l­Oxĝ. ˆ R18u
3:24M
<3 A`qC,JRk3712wM1–
2wMO<D4518M1A68(C,M\`BR18i713 D45k8:E
C,`qR18•A6C,M1N>5kA`I2 7124`wa#3 MkN›`BR18Ÿtk8J<uŸ2l`I`q2 7124`wa#C,`qR18
`q2ŠEEL518:E¡2ŠE_`BRO8
™(36`q86JšA6C,MO`Š8MO`“Ãw­OfÄK. ˆ R18JK8jœC,JK8:;À`I2ŠEEL518:EšA63:MŒ18—N2l712IN86N24M`IC
`BR1CE{8™_24`qR@R12I–,R¡™_3?`q86JA6C,MO`q8MO`q;kEœ5kAR/3,E%8a8 ;u\5’EKA?DB8 ;kEœ¯k24M’;>Dw2l718 J
36M1N¡¯k2IN,M18a1;3 M1N(`IRkCE{8™_24`qR/DIC ™¢™(3?`Š8?JA6C,MO`q86M,`<;1EL51AR/3|E<3?`+36MON
ŒbC,M18,.
 |ľ· !±^TiDI86Aj`BJKC,u/3 –,M18`B2IAt1JKC tk86JL`I2I8:E/C>
`ŠR18šN24qK86JK86M,`@uŸ86N243
KC,J`BR18^LJK86”,5186M1Aa
­®³.Še­ÀP#s_§O.
Ü Þ Ì8ß
V
6
±î°
>
98
Á8»¾½¿·
ã
Ý8á ÓÛ
=
40478
0,1%
3685
8,2%
9,1%
5160
69,9%
12,7%
28297
100%
3311
Other
Nodes to
edges
3D
assemblage
ɧ»iʛ±€±,Y8t13:JF`q2w`I2IC,MC G%dbX`q2Iu/8:Ej.
± %· |ÄîÁ
2D
assemblage
25
Solving
45000
40000
35000
30000
25000
20000
15000
10000
5000
0
Total
CPU times (s)
ˆ 1R 8(tJKC6Œ1DI86uÐ2qEEKC,Dw718?N•2IMx]Ox,®kµžEK86A?C,MkN1EÅFf­1µ,®ž2l`q86JL36`I2IC,M’E{Æ^C,M
3žsd²/[,]O]]˜EL`I36`I2BC,M³. ˆ Rk8Ÿu/CEL`8?m,tk8?M’EL2l718žC tb86JK36`I2IC,M‹24M˜G%dbX
`q2BuŸ82qEo`BR18uŸ3`BJK2ImE{C,Dl712BM1–
ÅIn+2I–1. ®Æ.
ɧ»iʛ±±kG*36DIA5kDI3`q86N¡86DI86A`qJK2IA^<2I86DIN@NO2ŠEœ`qJK2 ŒO5O`B2IC,M
C,M¡`BR18ŒbC,M18C>+`qRO8
RO5u/36M(Œ1C,N,ab.
n+2I–,5JK8Üej]ÜEKR1C ™@E#`qR18JK8:Eœ5kD4`<E#2wM‘`q8JLu C,˜0Ov(Y£N2qEL`qJK2lŒO5`q2IC,M
™(2w`qR12wMÀ`BR18RO5u/36M(Œ1C,N,a/C,M¡`IRk8^Œ1C,M183?MkN¡C,M¡`BR18^`I5u/C 5kJ.
Differents phases
> >
;
<
ˆ 1R 8ÜA63 DIA5kDI3?`B2IC,M¥A6C,NO8Ü3 DIDIC,™@E!`qC C ŒO`q3:2IM$`IRk8 86DI86A`qJL2IA‰<2I86DFN
N2qEL`IJK2lŒO5`B2IC,M—2wM#`IR18N24q<86JK8?M`(C,JK–,36MbE
u/C,NO86DI2I§:86N1.n+C,J
86m3 u¡tkDw8
`BR18L2B–>5kJK8#µÊE{RkC ™@EŸ`qR18“A63 DIA5kDI3`q86N—86DI86A`qJK2IA<2I86DIN—N2qEL`qJL2lŒO5`q2IC,M
ÅquŸC,N,5kDI8:E{ÆC,M!`BR18Ê8?m,`q86JL2BC,J#EL5JL<3 A68Åqu\5’EKA?DB8—36MON¢L36`qƞC •`qR8
tk3?`B2I86M>`œ. ˆ R18
L2B–>5JK8•h“ELR1C ™@E`qR12qE<2I86DIN“NO2qEL`BJL2lŒO5`q2IC,M™(24`BR12wM›`BR8
RO5u/36M(Œ1C,N,a
C,M
`BR18^Œ1C,Mk8>.
ã
ÝÙáDã2ã ÓÛ
B
ã
ãÞ ã›ÝË Ï
ˆ 5kuŸC 5J
ɧ»iʛ±+²
±1G%3:DIA51Dw3?`Š8?N•0OvYÊN2qEF`BJK2lŒO5O`Š2IC M/C M@Œ1C,M1836MON(`I5kuŸC 5J.
n+2I–,5JK8ee¡ELR1C ™ÀE*`qRk8
EK24u
5kD436`q86Nž86DI86A`IJK2BAÀ<2I86DIN•N,2qEœ`BJK2lŒO5`I2BC,MC Mž3
EK8?A`q2BC,M‰ÅF§ g,]¢A?uƟ<C,JN,24qK86JK86M>`\A?C,ML2B–>5JK3`q2IC:MbEC žJK3:N,2I3`q2IC,M
Ü σÓۏß
2ã¤Þ ã ÷2÷ÞÓÝ ãÞ ãá
ÌiØ
Ý2Ý÷Þ ã 2ã Þ ãÞ ›Ý
KФì0éòÓÎ
Þ ÷ Ý Þ ›Ý ãÞ ã2÷
'ÚD×ÔÎ
Ý8â Þ ›Ý Þ ã¤Þ
|ÑÓÒD×ÔÎí
Ý8â2â2Þ 2÷Þ á ã¤Þ Ô÷â
Dñ2òÓÎ8Î×
Ý2Ý Þ áD÷Þ á ã¤Þ ÷¤â
›Ñ ͤÎ0ð
â2âÔÞ â â2Þ ã¤Þ ÷ á
à+Ú8ð ØîÌ
Ý2Ý8â2Þ ã 2÷2ãÞÓÝ Ý8ÞÓÝã
+ÎÑ ×ì
2ã Þ á Þ ÝÙÞ
Ó×8ؾÎ8ìÓØšÑ ×Î
'ò Ì8Ò2ÒDÎð 2÷2›ã¤Ý8Þ ãÞ áDÝ8÷›âD÷Ý8ÞÞ ã ã¤ã¤ÞÞ âÃã2ã
ù›Ð2ۏÚ-ÐÔð
Ý8Þ ã
ã
ã
à|Ñ ð
Î
8
Ì
2
ò
2
ñ
Ì
ð
›
Ø
Ú
Ó
Ø
Ö
Î
ñ
0
Î
¾
ð

Û
Ñ
Ó
Ø
î
Ø
Ñ
Ô
Í
Ñ
î
Ø
í
ε Î8îé ÛØ ðiÌDÚDÏÃÛÑ ×ÔÌ8ÌÏÃðî×2í§ÎiؚñÔÑÓÌé¸ðÓ؛ì Ú Ñ ¤×ØîÖ2ÒDÎÎñÙñØîÖÎið¾ÛïÑ Ø ØšÑ Í2Ñ Øîí
ε
›
Ó
ò
δ
εY Z [ \
ε] ^O[ `
σ
Ü Ûλ ß ÜÓۏδ ß
Þ ã ãÞ á2âDã
ãÞ âÃã ãÞÓÝ
Þ 2÷ ãÞ 2ã
ãÞ Ôã ãÞÓÝ8áDã
ãÞ ›Ý÷ ãÞÓÝ8áDã
ãÞ â ãÞÓÝ
ãÞ âD÷Ô÷ ãÞÓÝ8â2â
ãÞ áD÷ ãÞÓÝã2ã
ãÞ á Ý ãÞ ãâ2â
ãÞ â ãÞ ÷›Ý
ãÞ
ãÞÓÝ2Ý
Ý2ÝÙô Þ ã
y
ÚÃ×2Ò8Ð é¾ØîÑ ÍÔÑ Øîí
λ
aS_
;N
Q OQ
g
R
ɧ»iʛ±±@G%3 DIA5kD436`q86N86DI86Aj`ŠJL2IAš<2I86DINN2qEL`IJK2 ŒO5O`q2BC M¢C,MÌ`BR18#u
5’E{A6Dw8
36M1N(`IRk8V<3?`bC +`qR18R,51u
36M(Œ1C,N|a³.
;N
LR
N
OQ
V
V
N
Q ;Q
V_OQ
QO
V
S
;N
N
R
N
_R
V
V
Q_ROV
R R
O
NORON
Q
] ^_[ `
e
U
_Q
_ROV
LK
LK
X
;NOV
Q
V
YZ [ \
VOR
VO
L
OQ
;QO
N
V ;
VOQ_
;Q
_V
ËeÌÍÎòÓÎ×ÔÏ8Ø Ö
ÅIno2B–³._ee?. 3 Ɲ. ˆ R18žt136`I2B8MO`(2ŠE\86m,t1CEK86N#`qC#3 MÊ86DI86Aj`ŠJK2IAž<2I86DIN#™(24`qR
,C M1D a#C,M18ŸY^nÌE{C 5kJKA68•ÅFno2B–³.*eOe . Œ#3?MkN›n+2I–b.ee?. A?Æ36M1N›`BR18M“™(24`qR
`I™_C
Y^n‹EC 5kJKA?8:EŊn+2I–b.+ee?. NÆK.Š`±2qE%A6DI8636JKDla•E{R1C ™_MŸ`BRO36`b`IR185’EK8(C 
`I™_C/3 MO`q8MOM3,E^A6R136MO–8:E^DI36JK–O86Dla
`qR18(N2qEL`IJK2lŒO5`q2IC:MžC i86DI86Aj`ŠJK2IA<2I86DFN
2wM¡`BR18m1y<E{86A`q2IC,Mo.0C; ŒaŸC t`q2Iu/2w§ 2wMO–(`IRk8VDBC,A?36`q2IC,M
36M1N(`BR18E{C 5kJKA68
713:D4518:E¡C,`ŠR18ž3:M>`q86MMO3|E;C M18•A?3:M˜8?3|E{2wDla#2Iu/3:–O2wM18Ÿ`ŠC›œC,Aj5³EÀ`qR8
J<3 N2436`I2IC,MC,M¡`IRk8*`B51u/C 5J.
ɧ»iʛ±²²±
G^36DIA51DB3j`Š8?NÔ8?DB8?A`qJ<2IA~<2I86DINÔNO2qEL`BJL2lŒO5`q2IC,MC,MÔ3¢E{86A`q2IC,M
ÅF§ g,]‰A?u/ƙ(24`BR C,Mk83 M,`q86MOM3ÅeOe?. ŒyÊeOe . A?Ɠ3 MkNà™_24`qR‰`I™(C
36MO`q8MM13|E%ÅeOe?. NOÆK.
¥§¦ €¡¥§¦#Ÿ§¦¢ªª£¤¡
ïª
v
v
gOyqNO2wu/86MbEL2IC,M136D u/C,N86D֌13,EK8?N C,M `IRk8ÏnbT u/8j`BR1C,N
2Iu
tDI86u/86M>`q86N—™_24`qR¢8?N–8#86DI86uŸ86M,`<EžR3,E
Œ18686M!N87³86DIC tk86N³. ˆ RO8
MO5u/8JK2IA63:DJK8 EL5kDÕ`<E˜R13718ZŒ18 86M¦A6C,u
tk3 JK86N ™(24`BRÐ8?m,tk8?J<2Iu/8M,`q36D
u/863,EL5JK8?u/86M,`<EŸ36MNELR1C ™¥3‹–OCC,N—3:–,JK8?86u/86MO`<. ˆ Rk8šN8718?DBC tb8 N
u/C,NO86D@2qEž3Œ1DB8š`qC—Rk3?MNDI8š™(2w`IRR18`q8JKC,–O86M186C 5’EEœ`qJL5kA`I5JK8:Ež36MON
™(2w`qR¡JK863:DORO5u/36M
C,JK–,36MbEu/8 EKR18:E3,EE{86u@Œ1DI86N¡<JKC,uG ˆ E{A636MbE.
×8ؾÎi×2×ÔÌ
B
v
v
×ÙؾÎ0×2×Ô̏Ý
×ÙؾÎ0×2×ÔÌ|÷
ˆ Rk8L2BM136DoC6ŒÁ86A`q2l7b8(2qE%`qR18(u/C,N8?DBDI24Mk–ŸC iEK87b86JK3 Db3?ttDI2IA63`qC,JE
q51MkAj`Š2IC,MO2wM1–ÖEK2wu\5kDl`q36M186C 5bEKDla1;`qCC:ŒO`q3 2IM¤`IR18 Œ18:Eœ`‰tbCEE{2 Œ1DF8
KC,A63:DI2I§ 3`q2BC,M‘C •`qR18ÊR1863?`•24M`BR18—N8:E{2BJK8?NÔ3?JK863‰Ãw­O®ÄK. ˆ R18~nbT
KC,JKu
5DI3`q2BC,M—™(2IDID`BR18M˜Œ18“A C 5tkDI86N~`qCÊ3#–O86M18`q2BAšC t`q2Iu/2w§ 3`q2IC,M
3 DB–OC,J<24`IRuž. ˆ R12qE™_2IDwD³36DIDBC ™`qC¡C t`q2Iu/2w§ 8iŒ1C `qR
`IR18DIC,A636`q2IC,M
C +`qRO8
ôà¸ÚDö×Ôì¾Ú8ÒDð¾Ñ ؚöÔÑÓÑ Ú-××Ï ì'|ܾà Ú8Ð2' ×ô ÒÃß Ìð¾ÑÓÎ8ì
ã
Ý2Ý8Þ Ì
áDã ÓÛ
ÕÌiØîÑÓÎi×ÃØ
à¸×ÙؾÎ0×2×Ô̏Ý
=
à¸ñÃñò ÑÓéÌiØîÚDð Ý
3?ttkD42IA636`qC,JEÀ36MN›`BR18@713 Dw518:E¡C,`qR18/A51J<JK8?M,`EKC 51JKA68:E@ÅF3 u
tkDI2l`I51N,8
36M1N¡tR3,EK86Æ24M
C,JKN8Jo`qC@2Iu¡tJKC6718`qR18NO2qEL`BJL2lŒO5`q2IC,M
C +`q86u
t186JK3`I5JL8
2wM!`IRk8~§:C,M18#tJKC,A68 EE86Nb.v(M1C `BR18J3|Eœtk86A`/C /`qR18ÊEœ`B51N,a¢2qEž`qRO8
u/C,NO86DIDB24M1–“C (C `ŠR186J`wa>tk8:E¡C>_EC 5kJKA68:Ej.+v@E¡86mO3:u
t1DI8:;o`IRk8\<2I–,5JL8
e­ELR1C ™E#`qR18u/8:E{RÜC #3:M R,a,t186JL`BR186uŸ2w3N8712IA68 E#™(24`ŠR `I™(C
3?ttkD42IA636`qC,JE. ˆ R18‹A?C 5tkDI24Mk–˜Œ18j`B™@8?86M`IRk8š™(3718?–,5k2INO8:Ež3:M1N~`BRO8
tk3?`B2I86M>`b2ŠE3:A?R2I87186N(ŒaŸ3Œ1C,D45’E^ÅqM1C `bJK8tJK8:E{86M,`q86N
C,M¡`BR18^L2B–>5JK86Ɲ.
Ý2Ý8Þ ö
à¸×ÙؾÎ0×Ô×2Ì
ɧ»iʛ±+² ±>P˜C,N86DIDI2wM1–@C o`I™@C@3?tt1Dw2IA63?`ŠC,JE36M1N(`IRk8*tk3`q2I8M`L.
Ý2Ý8Þ é
à¸×ÙؾÎ0×2×ÔÌ
à¸ñÃñò ÑÓéÌiØîÚDð
T
à¸×ÙؾÎ0×2×ÔÌ|÷
n+2I–,5JK8 e6g E{RkC ™@EÎ`qR18 JK8 EL5kDÕ`<E×C6ŒO`q3:24Mk8?N ™_24`IR `BR18
A6C,MO<2I–,51JK3`q2IC:M¥24M1AD451N2wMO–`IRk8‘`I™_Cҙ_36718?–,5k2INO8:E!C t’8?JK36`I2wM1–Ð3`
­®³.Šej­/P#s(§|;’`BR18(Œ1C,D45’E36M1NŸ`BR18¡tk3`q2I8M`L. ˆ R18/EKC 51JKA68:E(ÅFu/C,N,51DI8jE
36M1N¡tR3,EK8:E{Æ36JK8M1C `+C tO`B2Iu
2B§ 86N1; `BR18JK82ŠEoM1CÀtRk3,EK8(ELR124q`kŒ18`I™(8:8 M
`BR18!`I™_CEC 5kJKA68 E—36M1N‰`IRk8?2wJ˜3 u
tDI2l`I5kNO8:E—36JK8Ì`BR18‰EK36u/8>. ˆ RO8
JK8:EL51D4`FE›36JK8~tJK8:EK86M>`q86N2wM!`q8JKuÑC Óu/3 –,M12l`I5kNO8ÊC ž`qR18Ê86DI86Aj`BJK2wA
<2I86DINb.
®b.
µ1.
h1.
e]³.
à¸ñÃñò ÑÓéÌiØîÚDð Ý
0O86A`q2IC,M
ee|.
e6g’.
ex³.
e6[’.
ã
Ý ÓÛ
ÜÝ÷¤Þ Ì8ß
ã
=
÷ ÓÛ
=
ÜÝ÷Þ öÔß
ef³.
e®³.
e6µ’.
e6h’.
­]³.
ɧ»iʛ±§²€°±+G%3 DBAj5kDw3?`q86N/86DI86Aj`ŠJL2IA<2I86DIN•C,MŸ`BR18(u
5bEKA6DI8(36M1N
`IR18<36`C,
`BR18Vtk3`q2I8M`+Åe6gO. 36Æ+3?MkN¡C,M
3_E{86A`q2IC,M•Åe6g’. Œ1Ɲ.
ˆ R12qE^A63 DIA5kD436`q2IC M/`qC,C,Dq;13 DBDIC ™(2IMk–\`ŠC
C ŒO`Š3 2wMŸ`BR18(86DI86Aj`ŠJK2IA<2I86DIN1;
0vYNO2ŠEœ`qJK2 ŒO5O`B2IC,M36M1N2wM1A6Dl51N24M–A6C,u
tO5`q86JL2B§ 86NC t`q24u/2w§ 3`q2IC,M
tkJKC,A68?N,5kJK8 ;#™(2IDBD˜Œ18Ò5’E{86N¥KC,J`qR18R,a,t186JL`BR186JLu/2w3¦`IJK863`qu/8M,`
tkDI36MO2wM1–(t186JL<C,JKu/86NÀ™_24`IR
Y^n•tRO3|E{86N
36J<JL3a/E<a1EL`L86u•E.
5
>
F>
>
e­³.
à¸ñÃñò ÑÓéÌiØîÚDð
²?. T%Ti;/². -/.@d1TT%YyqH(v=0 ˆ vY;
d. ²6.(YÂFT ˆ HT=Ž;¡=.
UVYvnbn±;#U¡.lG.žYis(Û(Û-;šÂqMO`<.²6.ŸY3:NO2w3?`Š2IC M¥ÛMkA?C,DBC,–,a
c2IC,DL.:doR|a1E. k;+ej­,]k[
Åe?hhµ>ÆK.
²?. v
.0,s(
v Z;G_. s
.
Ž(XY^-(TW;ŸŽ/. v GisY0 ˆ T%-/0,T-;
ÂFTTT ˆ J<36MbEj.6c2IC,u/86N2IA63 DOTM1–,2wM18686JK24M#
– ° k;Oµ,f±eVÅe?hhbejÆ.
d.lG G%sTYVYiW; P. n Â0 @v-(Ž(T%Y;ÖÂFTT%T ˆ JK36MbE.
P˜2IA6JKC ™(37³8 ˆ R186C,Jqa
3 M1N ˆ 8?A6RMO2B”>5k8:E ;+ef1h,­
Åe?h,h,­Æ.
-/. PZ.Ÿd+Û ˆ sT*G^vY^W;“G_. ²6.
Yv(ÂF= ˆ Û-;›ÂITTTËP ˆˆ yK0
Ž@2I–8 EL`<;+eOe6[+eVÅe?hhOg Æ.
G. T.^Y^TX ˆ TY;v
. ˆ vnb=Û(HT;H@.(0Ov ˆ s(Â<v
0,T%T=v-;
ÂFTTT ˆ JK3?M’E.¡P‹2IA6JKC ™(3718 ˆ R186C,Jqa 3 M1N ˆ 86A?RM2I”>5k8:E ;
goe6g
ÅehOhµ>ÆK.
W/. @v-@v(œ; ˆ . ˆ 0,X @vP˜Û ˆ Û@; ˆ . @v
0,s( —v@;(ÂFTTT
ˆ JK36MbE. P‹3 –,M18`q2IA:§E ° k;+ejff+eÅehh,fOÆK.
Ž/. YÖ=W(-G%s@
; /. ŽØd+vX=0>T-;š²6. 0 ˆ YÛs(ciT^s-;
²C 5kJKM3 D1C G*C,u
t5O`Š3j`Š2IC,MO3:DOdbR,akE{2BA,E ! 1;,­xOfÅe6hOµ[ Ɲ.
v
.%0,T @v ;oH
. -
. @v-(T==Ûd+ÛX(=Û
0k;±=.bd+ÂKG%s(Û-;
v
. Yv T ;>ÂqTT%T ˆ JL36MbE.:P#3:–,M18`q2IA:—E °|²:;oe6µ>fk[@Åe6h,hO[,Ɲ.
G. v
.
cv=v-@0k;
v(N:713 MkA?86N
8?Mk–O2wM18686JL2wM1–
86DI86Aj`ŠJKC,uŸ3:–,M18`q2IA:E(ÅF²C,R
M —2IDI8
a ¥01C,MbE;oÂqM1A,. ;³-@8j™‰W@C,JL¯’;
e?hµh>Ɯ;|tb.+e[,]b.
c(.¡T-U X(Â0 ˆ ;/v
.ÀPQv(²{Ž@v@;
P#36`IRb.G*C,u
t+. «
; °|²:;
fO­kh
Åe6h>®®Æ{.
²?. G.?-(TŽT=T*G^;>-(5u/86J.6P˜3`IRo. °!;Og+e?[@Åe6hµ>]ÆK.
²?. d›. #T%cic;OÂFTTT ˆ JL36MbE.?P˜36–,M18`q2BA E ;+ejxf]
Åe?hh,g>Æ.
0b. ˆ .G%=T*U(U; . v
.6P#XY^dos(W; ¢. ˆ .|²Û(Âq-T01;U¡.6YÂF-(T*;
ˆ . H¡.•03?u
5kDqEL¯2q;ŸÂITTT ˆ JK36MbE.@P˜2IAJKC ™_37b8 ˆ R186C,Jqa 3:M1N
ˆ 86A6RM124”,5k8 E k;oe6h,µ,x/Åe?hh>xÆK.
G.³-@ÂqŽ(T%Y(0 ˆ ;±d’R³. Ž/.³`BR18:EK2qEK;±5Mk2l7186JE{2l`qp
d+3?5kD03Œ13?`B2I86J(N8
ˆ C 5kDIC 5’E{8:;e6hh>®b.
v
.HT%Yv@yIsT^Yi-@v-(Ž(T i;Od+Ro. Ž/.>`BR18:EK2qEK;124MbEL`B24`I5,`M3?`B2IC,M3 D
t1C,Dwa,`q8 A6RM12I”,518N8V=C,JLJK362wM18:;oe6hhOhO.
!. T.:cÛW/0,T;bU¡. -
.,P˜ÂF-(TY^cÛ@; /. Ž/.,dovX=0,T%-;OŽ/. Y(.
=W(-G%s@;OÂqT%TT ˆ JK36MbE. P‹3 –,M18`B2IA:E k;+e?gg,g
Åehhg>ÆK.
0b.UvcYÂFT=i;*Y_. ¢.%=v(X@;G.*UvÀcYÂqT%=i;^doR|a1E.%PÊ86N³.
c2IC,DL. ¸²|;>­­k[beÅehh>fÆK.
0b.UvcYÂFT=i;*Y_. ¢.%=v(X@;G.*UvÀcYÂqT%=i;^doR|a1E.%PÊ86N³.
c2IC,DL. ¸²|;>­­®+eÅehh>fÆK.
ˆ 86u
tkD436`q8(UJL3?tR2IA:EV0C q`q™(3 JK824MkA>. ; ™(™(™
. 3 u/2wJL3712qEj. A6C,u.
G. /. Gis_ÛX@;s.¦cv/0b0>T-;²6.$Û
0,Td±Gis(X ; .
cv= v-@Û@; Y(.×dbT ˆ T%Y_0>T-; P.×P#T= ˆ i; Y(.
G%=T^HT=v-(Ž;>c2IC,86DI86A`qJKC,u/3 –,Mk8j`B2IA:KE ² O;+e6hO[@Åe6h,h>fÆK.
v
.cÛ(v@U(;ÀW/.=T^H(Â<v ˆ v-;¡v
.cÛ(v@U(;¡ÂFTTT ˆ JK36MbE.
c2IC,u/86NO2BA?3:Db8?Mk–,24M18686JL2wM1– k;h>xf
ÅehOhg,Æ{.
­±e|.
­­³.
­kg’.
­x³.
­k[’.
­f³.
E
:5
d
d>E
F5
F
>
>
d5
­®³.
ª¨Ôª Œ ª¦ª
²?.1=v-U(;³c(.1TY^Ž(P˜v-@-;³P.0,TT%cv
0b0k;oÂFTTT ˆ JL36MbE.
c2IC,u/86NO2IA63:D³86M1–,2wM18686JL2wM1– k;oee­h
Åe?hhOh,ÆK.
Û
.40b.
-@ÂFT=0,T%-À;ŸP.
s(ÛY_0>PQv-;ž²?./Û(HTYUv@vY^Ž;
T%5JKC tk863 M
²C 51J<MO3:D1C G^36M1A686§J ° ;+e?[µ ®/ÅF­,]]±ejÆK.
G_. /.ÖG%s_ÛX@;ÑÂqT%TT ˆ JK36MbE.áÂqMbEœ`BJL5u/8MO`B3?`q2BC M 36M1N
P˜863,EL51JK86u/8MO|` ° ,;[>x®
Åe?hhµ>ÆK.
v
. P. ˆ XP‹T%sÀ;ÚP. n.ßÂ0 @v-(Ž(T%Y;£ÂFTTT ˆ JL36MbE.
P˜2IA6JKC ™(37³8 ˆ R186C,Jqa
3 M1N ˆ 86A6RMO2I”,5k8 E ° +eOe­f
Åe?h,µh>Æ.
0b.
Yv ˆ -@v(²KTT^H(v-;
s
.
s_Û(Û=T;
H
.
0v ˆ s_ÂLv
0,TT%=v-;ov
. ˆ 0,T-U;oÂIT%TT ˆ JL36MbE.1P#3:–,M18`I2BA E
1;+ej]±eeVÅe?hh ]OÆ.
²6!. ÊÂFTY(0,P˜v@;_Y_. v
. P.H(v-£P˜v(vY(0,TiHT%T-;²6. Ž. d.
H(v-¢Ž@ÂL² ;OÂqM>`<.,². sa,t186JL`BR186JLu/24#
3 ²k;,®1g@ÅF­]O],­Æ.
e.
>
­b.
g1.
xb.
[1.
fb.
>
5