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An Integrated Multi-Scaling Strategy based on a Particle Swarm Algorithm for Inverse Scattering Problems

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(1)UNIVERSITY OF TRENTO DEPARTMENT OF INFORMATION AND COMMUNICATION TECHNOLOGY 38050 Povo – Trento (Italy), Via Sommarive 14 http://www.dit.unitn.it. AN INTEGRATED MULTI-SCALING STRATEGY BASED ON A PARTICLE SWARM ALGORITHM FOR INVERSE SCATTERING PROBLEMS Massimo Donelli, Gabriele Franceschini, Anna Martini, and Andrea Massa October 2004 Technical Report DIT-04-081.

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(47) hQGMLd@BCF@¿n]@)CFL!hQGMLd@BCFpdNcDCRLdƒŠ> x­>AEHCFPR‡KGAxg>€ududcDGCFE>€nDN^@BGMPF~n]CFGALd@pdNQu7NQLdpOCFLdƒlGMLk>wug>Ac]>€EN,n]NQc h>APRPFNp¸Z]VT©A«¯†¡AZI§ H²¡A¬­§T´5¢#¹O¡AZB¡AX|V,¬zV,Z,—

(48) egGMclLdGMCR@DN,Tx{cDNNkpg>€n]>OSrn]iON>AududcBGOCRE|>5n]N9@BGMPF~n]CFGALd@KhGMLˆ MNQcBƒMN n]G‚nDidNH>AhnD~g>AP@BGMPF~OnDCFGM2L iONQLßn]idNcDNƒM~dPF>AcDC >€nDCFGMLžug>Ac]>€EN,n]NQcŠnDNQLdpO@

(49) nD<G QNQcBGdJ— Kn]idN+c CR@DNASGMLON h>ALfGAbOn*>ACRL >ALfGMuOnDCFE>AP^>AududcBGOCRE|>5n]CFGAL¸GAxn]iONN,O>AhnH@BGMPF~OnDCFGMLsx{GMc>ÔLdGALB NQcDGë €>APR~dN‚GAxn]iON cDNƒM~dP‹>€cD'C Q>€n]CRGMLsug>Ac]>€EN,n]NQc—¸ idN3h*idGACFhQNG€xwnDidN €>APF~dN|GAxn]idNëZ]VT©A«ª¯†¡AZ,I§ H²¡A¬­§T´5¢ ug>€c]>AEHNnDNQckCR@> hQcB~dhQCF>AP>ALdpžLdGMLTn]cDC† ªC‹>APudcDGMbOPFNQE#7— K+~OnSt~dLOPF'C €N&PRCFLdNQ>Ac CFLˆ ANQcD@BN&@Bh>€nBn]NcDCFLOƒ|udcBGMbdPFNE@ x{GMLc idCRh*i. +NPFPАzpdN, MNQPRGMu7NQp

(50) E|>5n]idNE|>€nDCFhQ>AP€EHNnDidGªpd@>ALdp!N HhQCRNQLˆn)Lv~dENcDCRh>APˆ>€PFƒMGMcBCRnDidE@r>AcDN_>€PFcDNQ>ApO‡

(51) > €>ACRP† >AbdPRNASn]idNH@DhCFNLvnDC ghHPFC†n]Nc]>€nD~dcDNpdGªNQ@!LdGAn!udcBG² CRpdN>ALˆ‡ß@DCFEHudPRNcD~dPRNx{GAc

(52) nDidNHGMuOn]CRE|>€Ph*idGMCRhQNHGAx n]idN

(53) cBNQƒM~dPF>AcDC >€nDCFGMLhQGªN HhQCRNQLˆMn idNQLžLdGMLdPRCFLdNQ>AcudcBGMbdPRNQEH@>AcDNpdNQ>APRLn C†n]i  ŽÇ• o— j pdIC NrNcDNQLˆn>€ududcDGM>Ah*ifn]GëcDN@BnDGMcDON `NQPRP†zu7GM@BCRn]CRGMLsCF@9nDGë@D~dC†n*>AbdP†‡¸pON gLdN‚nDidNpdCRENLd@DCRGML GAxn]iON ~dCL vLdG LH@Dug>AhN bˆ‡9x{~dPRPR‡!N,udPRGMCRnDCFLdƒ>€PFPvn]idN> €>ACFPF>AbdPRN`CRLOx{GMcDE>€nDCFGML!GMLkn]iON @DhQNLg>AcBCFG~dLdpONQcn]N@BnQ— <GhGMEHNkn]G3O> +NPFPАzu7GM@DNpëudcDGMbOPFNQE#SrnDidNpdNQ@BhQcBCFuOnDCFGMLëGAx^n]iON~dCL vLdG LW@Bh>€nBn]NcDNQc

(54) CR@@D~dudu7GM@BNQp .

(55) n]GsbNPFGMLOƒsnDG¸>PgLdCRnDN3pdCFEHNQLd@BCFGMLd>AP@Dud>AhQN€S" idCFh*i pdCFEHNQLd@BCFGML CR@@BE|>APRPFNc9n]ig>€L n]iONžN@D@DNLˆn]C‹>€P pdCFEHNQLO@DCFGAL?GAx_pg>5n*>O—!Œ~Oh*iW>‚pOCFEHNQLd@BCFGMLäS7b7NQh>€~d@DNGAx¾nDidN>ALd>APR‡vn]CRh>AP)Lg>€nD~dcDN9GAx¾n]idN9@Dh>5nDn]NcDCRLdƒ GMu7NQc]>5n]GMcS5CR@=> vLdG -L &ª~d>ALˆn]CRnz‡

(56) @BCFLdhN_CRnpdNuNLdpd@)GML!nDidN^N,ªn]NLd@DCRGML&G€xOn]iON^CRLˆ MNQ@¿n]CRƒˆ>€n]CRGML

(57) pdGME>ACFL cDN@Du7NQhnnDGsnDidON > ANQPFNLdƒAnDi  Ž²%š w>ALdp GML n]iON#h*id>Ac]>Ah,n]NcDCF@¿n]CRhQ@GAxln]idNEk~OPRn]CА– ªCFN >A)h &v~dCR@DCRnDCFGML @B‡ª@BnDNQE  ŽÇœ o— „lLOx{GAcBn]~OLg>€n]NPR‡ASn]idNh*idGACFhQNG€xK>ÔE>5CFE9~dE Lv~dE9bNcGAxwcDNnDcDCRN €>AbdPRN|~dCL vLdG Ld@H)N &v~g>€P+n]Gën]iON NQ@B@DNQLˆnDC‹>AP7pdCFEHNQLO@DCFGALGAxn]idNl@DhQ>€nDnDNQcDNp‚pg>€n]>&pdGªNQ@`LdGAn`~d@D~d>APFP†‡kx{~dP dPFPdn]iONKhQcBCRnDNQcDCRGMLHƒMCR ANQL|CRL  Ž²%“  x{GMc>k@B~dCRn]>AbdPRNKcDNudcDN@DNLvn]>€n]CRGMQL ­CRL|n]NcDEH@GAx)@Dug>5n]C‹>€PcBNQ@DGAPF~OnDCFGML ¾x{GMc+b7GAnDi‚n]idNpdCRNQPRNQhnDcDCRhKudcB>G gPFN GAx n]iON‚@DhQ>€nDnDNQcDNc>ALdp nDidN‚CRLdpd~dhNQpfNQPRNQh,n]cDCRh gNPFpä—?yzLfGMcDpdNc9n]G?GÇ ANQcBhQGMEHN@D~dh*i >?EHCF@BE|>5n]h*i CFLdƒOSd A>€cDCFGA~d@@Bn]cD>€n]NƒMCFN@lbd>A@DNp?GML?>Ek~dP†n]CАzcDN@DGMPR~On]CRGML|Nug>ALd@BCFGMLÔG€x0n]iON&~d#L ªLO G LO@Šig> MN&bNNQL udcDGAuGM@BNQpä—  iONQ@DNžEN,n]idGªpd@HpdN dLdN?pdCR@DhcDNnD'C Q>€n]CRGML @Bh*idNQEHNQ@|>ALdp hQGMcBcDNQ@BuGALdpdCFLOƒ¸bg>A@BCF@x{~dLdh n]CRGMLd@ln]>ACFPRGMcDNpžnDG‚cDNudcDN@DNQLˆn

(58) n]iONk A>€cDCFN,nz‡#GAx^PFNQLOƒAn]iÔ@Bh>APRNQ@ŠCRLÔn]idN9CFLˆ MN@Bn]CRƒˆ>€nDCFGMLžpdGME>ACFL RgLdNc @DhQ>APFN@¾LdN>Ac<n]idN pdCR@DhGMLˆn]CFLv~dC†n]CRNQ@¾>ALOpEGMcBN@Dud>€n]CF>APFP†‡&pOC N~d@DNpHG² ANQcn]iON @DEHGGAnDiN,ug>ALO@DNQ@^GAxtn]iON @DhQ>€nDnDNQcDNclGAclCRL#nDidN&Nªn]NQcBLg>AP)idGMEHGMƒMNLdNQGM~O@lbg>€*h ªƒAcDGM~dLOp ,— <>> vCFLdƒ>ApO €>ALˆn]>AƒMN!GAx@B~dh*ißJ> vCRLdp GAx`N,ug>ALd@BCFGMLrS<C†n

(59) CF@u7GM@D@BCFbdPRNnDG3pdCF@¿n]cDCRbd~OnDNHCRLs>#LdGALz~dLOCRx{GMcBS E +>²‡ënDidN~dCL vLdG Ld@&CFLd@BCFpdNn]iON @DhQ>€nDnDNQcDCRLdƒpdGME>ACRLä—< iOCF@¾CF@nDidN hQGAEEHGMLc]>5n]CFGALg>APªGAxnDidN Ek~dP†n]CАzcDN@DGMPR~On]CRGML–bg>A@DNpk>AuOudcDGˆ>€h*idNQ@—  idN>¡ @F¹7Z§T´5Z§rE9~dPRnDC†zcBNQ@BGMPF~OnDCFGML

(60) >€ududcDGM>Ah*i  Ž²%™ oSAG CFLOƒln]Gk>¡ @F¹7Z§T´5Z,§rhQGMLd@BCFpdNc]>€nDCFGMLO@)GAL9n]idN^E>€n]i NQE>€n]CRh>AP Ld>€n]~dcBN?GAxnDidN?uOcDGMbdPRNQE >ALdp GAxn]idNžCFLˆn]cBCFLd@BCFh3x{N>€nD~dcDN@|NOiOCFbdC†n]NQp bv‡ n]iON?hQPF>A@D@|GAx cDN,n]cDCRN €>AbdPRNx{~dLdhnDCFGMLO@QS¾>A@B@DGªhQCF>€n]N@9ug>Ac¿nkGAx+n]idNHn]GAn]>AP`Lv~dE9bNc9GAx ~OCL vLdG Ld@kn]Gë>žhQGˆ>AcB@DNcDNQuª cDN@DNQLˆn]>€n]CRGMLëGAx¾n]iOTN idGMPRNkpdGME>ACFLr—=žGMcBNQG² MNcQSCRnlhQGALdhQNLvnDc]>€nDNQ@n]iONkcDNE|>ACRLdCFLOƒ|GMLdN@ŠCFLžn]idGM@BN ug>Ac¿n]@^GAxän]iONKcDNƒMCFGAL~dLOpdNQc^n]NQ@¿.n idNcDN>!bN,nDnDNQc+cBNQ@BGMPF~OnDCFGMLHh>€L|b7NŠ>Ah*idCRN ANQpä—`=?>€nDidNQE>€nDCFh>€PFPR‡AS n]idN

(61) >€cDCF@BCFLdƒuOcDGMbdPRNQE CF@ @DGAPR MNp#nDidcDGA~dƒMin]idN

(62) EHCFLdCREC >€nDCFGMUL ­GALdPR‡|GMLdhQVN +GAx0>HhGM@Bn x{~dLOhn]CRGML3cDN P‹>€nDNQp|nDG9n]iONŠ@DhQ>€nDnDNQcDCRLdƒkN &ª~d>€n]CRGMLd.@ idNcDNCFLn]idNK~dCL vLdG Ld@w>AcDNlcDNudcDN@DNQLˆnDNQ<p CRn]i‚nDidN>¡ @F¹7Z§T´5Z§ Ek~dP†n]C†–cDN@DGMPR~On]CRGMLNug>ALd@BCFGML#bˆ‡3hQGMLd@BCFpdNcDCRLdƒ>H@B~dCRn]>AbdPR9N > ANQPFN,nlnDc]>ALO@Bx{GMcBE|>€nDCFGMLr— j @BCFEHCFPF>AcEk~dP†n]C†–cDN@DGMPR~On]CRGMLë>AuduOcDGˆ>Ah*irSbg>A@BNQpfGML¸>ÔIŠ>A~db7NQh*iOCFNQ-@ > MNPFN,nN,ug>ALO@DCFGALäSCF@!~d@BNQp CFL  ›€” _n]G#N>A@BCFP†‡ëE|>€Lg>AƒMNpdIC NrNcDNQLˆ-n vCFLdpWGAxudcBCFGMc

(63) @¿n*>€nDCF@BnDCFhQ>APEHGpdNPF@

(64) GMLßn]idN@DhNQLg>AcBCFG#~dLdpdNc n]N@B9n iONQLßPFCRLdN>AchGMLdpdC†n]CFGALd@liOGMPFpä—lyzLë@D~dh*iß>h>A@BNASäcBNQƒM~dPF>AcDC >€nDCFGML3CR@Š>AhhQGMEHudPFCR@DidNpžnDidcDGM~OƒMi >HE9~dPRnDC†z@Bh>APRNŠudcBCFGMc @¿n]Gªh*ig>A@BnDCFh!EGªpdNP>ALdpÔ>@Bn]>€n]CR@BnDCFhŠn]GªGM$P {bg>A@DNpÔGML3n]idN!~d@BN9GAx<n]idN!cDNP‹>€nDCR MN •.

(65) NQcBcDGMc3hQG² €>AcBC‹>ALdhNßE|>€nDcDCН:|CR@#>ApdGMuOnDNQp(n]G pdNgLONWn]iONs@Bug>AhN,– €>Ac¿‡ªCFLdƒ GMuOn]CRE|>€PK@DhQ>APFNßx{GMcn]iON cDNhQGMLd@¿n]cB~dhnDCFGML䗾 iON

(66) >AcDCR@DCFLOƒkCFLˆ MNcD@BN@Dh>5nDn]NcDCRLdƒudcDGAbdPFNE CR@+n]idNL3cDNQhQ>A@Bn nDG9n]iONECRLdCFEHC'Q>€n]CRGML GAx^>Bn `G€–nDNQcBE@ŠhGM@BnKx{~dLdhnDCFGML?NQLOx{GMcBhQCRLdWƒ gpdNPFC†nz‡#nDG‚@DhQ>€nDnDNQcBCFLdƒ‚pd>€n*>‚>€LdpÔn]idN9E|>€nDh*idCFLOƒ CRnDi n]idN

(67) @¿n*>€nDCF@BnDCFhQ>APrudcBCFGMc+EGªpdNQPx{GMcn]idN

(68) hGMLˆn]c]>€@BnSgcBNQ@BuNhn]C† MNPR‡M— j pdIC NrNcDNLvn>AududcBGˆ>Ah*i‚bd>A@DNpGML>9@¿n]NQuªX CF@BNŠcDN gLdNENLvnudcDGªhQNpd~dcDNlCF@`pdN ANQPFGAuNpbv‡|Ÿ —d=#CFPFPRNQc CFL  ›Ž x{GAc >LdGMLdPRCFLdNQ>Ac@DhQ>€nDnDNQcBCFLdƒEHGpONQPT—0j @D)N &v~dNLdhQN&GAx)pdC NNQcBNQLˆn9>¡ @F¹7Z§T´5Z,§_iˆ‡ªuG€n]idN@DCF@ nDNQ@BnD@ ­Co— N€—RSg>hGMPFPRNQhnDCFGML|GAx>€LdGME>APR‡hQGMYL gƒM~dcD>€n]CRGMLd*@ >€cDNNQEHudPRGLJANQ<p gcD@¿nn]GPFGªh>APR'C NŠ>ALdGAE|>APRGM~d@`bN ig> ªCFGMcB@ CFL3P‹>AcBƒMN>AcBN>A@w>ALOp#nDidNQL3n]GcDN gLdN

(69) n]idN@DN

(70) CFLOCRn]CF>AP7NQ@BnDCFE>€n]N@n]GHbN,nDnDNQc h*ig>AcD>AhnDNQcB'C QN

(71) n]iON >AhnD~g>AP^@BnDcD~dh,n]~dcBNQ@Q—߁ idN|udcDGMu7GM@BNQpf@Bn]>AbdPRN|hQGM>AcD@BN,–nDG€X dLdN‚PFGªh>€PF'C Q>€n]CRGMLëEHNn]iOGp pON gLdN@>?pdN hQGMEHu7GM@DC†n]CFGAL&udcBGhNQpd~OcD,N o>€bdPFN^n]ZG GGME GML@¿n]cDGALdƒ@DhQ>€nDnDNQcDNcD@¾b7Nx{GMcBNcDN gLdCRLdƒŠGAnDidNQc@¿n]cB~dhnD~dcDN*@ >ALdp#>udcD~OLdCFLdƒ@¿n]NQu#n]GcDNEG² AN!~OLdcDNPFC‹>€bdPFNŠhQ>ALdpdCRpg>€nDN

(72) >ALdGME>APFCRNQ@+x{cBGME x{~OcBn]iONQcudcDGªhQN@D@BCFLdƒd— yzLžnDidN&x{cD>AEN +GA[c 3GAxw¡ˆ£ˆ¡,¹7¬­R§ \AV&Ek~dPRnDC†–cDNQ@BGMPF~n]CFGAL>AududcBGˆ>Ah*idN@QSä}>AGMcD@BCV,¬ ¡A¯†¤ludcDGAuGM@BNQpÔCRL  ›M›  >AL3CRnDNQc]>5n]CR ANŠn]Nh*idLd'C &v~d]N idNcDN

(73) n]idN

(74) pdCR@BnDcDCFbO~On]CRGML‚GAx)n]idN

(75) ~d#L ªLO G LO@KCF@!>¡ @F¹g´²¥,¬zV,Z§T´5Z§^pONn]NcDEHCFLdNp GMLWnDidN|bd>A@DCR@9GAxnDidN|uOcDN ªCRGM~d@9NuNcDCFNLdhQN|>Ab7GM~On!n]idNuGM@B@DCRbdPFNHGMb BNhn]@&n]G?b7N|cBNQhGMLd@BnDcD~dh,n]NpäS bd~Onl> MGMCRpdCFLOƒ|>ALˆ‡W>¡ @F¹7Z§T´5Z§+>€@D@D~OEuOnDCFGML#GML3n]idN!u7GM@DC†n]CFGALž>€M@ `NQPRP)>A@lGAL#nDid-N vCRLdpžG€x~dCL vLdG L @DhQ>€nDnDNQcDNcD@—  idNÔ>AuOudcDGˆ>€h*i n*%> ANQ@|>ApO €>ALˆn*>€ƒMNžG€x>WhGMLd@¿n*>ALˆnEk~dPRnDC†–@Dh>€PFCFLOƒÔudCFNhQNX CF@BNžuO~dPF@BN cDNudcDN@DNQLˆn]>€n]CRGMLH>AbdPFNnDG

(76) pdN>AYP CRn]iH>APRPOu7GM@D@BCFbdPRNEk~dP†n]CАzcDN@DGMPR~On]CRGML9hGMEkbdCRLg>€nDCFGMLd"@ ­~dLOPF'C €"N > ANQPFN,n N,ug>ALO@DCFGAL ‚>ALdp(CRnCR@3>ACFEHNQpJ>5n3pdNnDNQcDEHCFLOCFLd^ƒ gcB@BnDPR‡ nDidNëcDNƒMCFGMLO@¿zG€x‹zCFLˆnDNQcDN@BAn `_wGAyz*@ W idNQcBN n]idN@Bh>€nBn]NcDNQcB@H>AcDN‚PRGhQ>€n]Np >ALdp @D~OhQhQN@D@BCR MNPR‡ >€nkcDNnDcDCRN ªCFLdUƒ &ª~d>ALˆn]CRn]>€n]C† MNCRLOx{GMcDE>€nDCFGMLä—? idN cDNhQGMLd@¿n]cB~dhnDCFGMLsudcDGªhQN@D@&CF@

(77) pdN ANQPRGMuNpf>A@&>#@B)N &v~dNLdhQN‚G€xCFLOhQcDNQ>A@DCRLdƒMP†D‡ /BgLONQ1c 0cDNQuOcDNQ@BNQLˆn*>5n]CFGALd@. idCFPRN9>5nKn]iONk@]>AEHN&nDCFEHN&cBNn]>ACFLdCRLdƒnDidNkCRLOx{GMcDE>€nDCFGML#>Ah*idCRN ANQpëCFL?EG² ªCFLdƒHx{cDGME6>|hGˆ>AcB@DN9nDG> gLdN

(78) @DhQ>APFN€— alG `N MNcQSg~dLOPF'C €NKn]iONŠPFCRLdN>Ac^h>€@DNASOCFLLdGMLOPFCFLON>Ac^CFLˆ MNcD@BNudcDGMbOPFNQEH@QSªn]idNKhQGMLdpOCRn]CRGML‚GAx)>kLv~dE9bNc GAx¾CRLdpdNQu7NQLOpdNQLˆnpg>5n*>|N &ª~d>AP0GMcw@DE>APRPFNQc nDig>AL?nDidNkLv~dEkb7NQclGAx¾cDN,n]cBCFN €>AbOPFN!~dCL vLdG Ld@E>²‡#LdG€n @D#~ HhNn]G#cDNQ>Ah*if>3cDNPFC‹>€bdPFNCRLv ANQcB@DCFGAL¸b7NQh>€~d@DNGAx+nDidNHx­>€PF@DN@BGMPF~OnDCFGMLO@!uOcDGMbdPRNQE#—}+NcBn*>€CFLdP†‡MS)> Ek~dP†n]C†–cDN@DGMPR~On]CRGMLl@¿n]cD>€n]NƒA‡hQGALd@DCRpdNQcD>AbdPR‡KPFCREC†n]b@ c CRnDi

(79) cDNQ@BuNhnn]G@¿n*>ALdpd>AcDp

(80) pdN,n]NQcBECRLdCF@¿n]CRhEN,n]i GpO*@ Kn]idNGªhQh~dcDcBNQLdhNGAx+PFGªh>AP0ECRLdCFE>CRLsnDidNH>AcDCR@DCFLOƒhQGM@¿n&x{~dLOhn]CRGMLßbˆ‡ßcDNQpO~dhQCRLdƒ#nDidNH@DN>€cDh*i @Dug>€hQNA(— K`~OnSvn]idNcDNlCF@_LdG9ƒA~g>Ac]>€LvnDNQNlGAx> MGACFpdCRLdƒ&PRGhQ>APgEHCFLdCRE|!> C†n]idGA~On>!udcDGAuNc`CRLdCRnDC‹>APR'C >5n]CFGAL š.

(81) c idNL. dp N,n]NQcBECRLdCF@¿n]CRh#GAuOn]CRECQNQcB@H>AcDNž~d@DNp,— }+GMLd@BN)&v~dNQLˆnDPR‡MSwCRnCF@HLdNNQpdNp n]G¸CRLˆn]NQƒAc]>€nDNžn]iON Ek~dP†n]C†–cDN@DGMPR~On]CRGMLk@BnDc]>€nDNQƒA‡U­>ACFEHNQp>€n`udcDN, MNQLˆnDCFLdƒ9nDidNKCRPFPАzu7GM@DC†n]CFGALdCFLdƒwGAxänDidNKCRLˆ MNQcB@DNl@Dh>5nDn]NcDCRLdƒ udcDGAbdPFNOE 7 C†n]iÔ>@D~OCRn*>€bdPFN

(82) ƒMPRGMbg>APGMun]CFEH'C Q>€n]CRGML‚udcBGhNQpd~OcDNk>€bdPFNn]GHx­>AhQN

(83) n]iON&udcBGMbdPRNQE GAxx­>€PF@DN @DGMPR~On]CRGMLd@bˆ‡kn]>> vCFLdƒ

(84) CRLvnDG

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(117) ƒMPFGAbg>APrEHCFLOCFEk~dE GAx<n]idNŠx{GAPFPFG CRLdƒkhQGA@Bnx{~dLdh,n]CFGAUL ä • Ö – ä]{zå (} ‡æDèXç é ê*ë ŒÜì íè î'ïBð§ð ’cñ»ŒÜì ŒÙò è èóˆô 𠒟’ õ ö+÷Œ×ì ðùè ø`ð ’ ëú º æ ¿ õ èXç ýXé ÷¡ñ ê*ëŒ ò è í'î’ ïBõ ð§ö[ð ÷ È ëŒ ú ì è ’ Œ ’ ì ñ è æ èXç é ê*ë ûÙü î Œ ì è ûÝü ’ ð ðÝøŸð ëú æ èXç é ê ë ûÙü î ë ú. Tœ>. idNQcBNn]idN¾nB `G n]NQcBE@CRLJTœ 7NQLOx{GMcBhQNÉgpONQPFC†nz‡lnDG n]idN¾pg>5n*>CFLŠnDidN¾GMbd@BNQc¿ A>5n]CFGALpdGME>ACFL6`u `v žc  w¡w+{R©:þ$ÿ è ƒª%þ(ÿ è }S {c©:þ(ÿ è ƒ:ª%þ(ÿ è }6¶ µ · l>ALOpÔCFL#n]idN&CFLˆ MN@Bn]CRƒˆ>€nDCFGML#pdGME>ACFL Ÿu ¥§v ¦ ž {c© ¦ ƒdª ¦ ,} S‹{R© ¦ ƒ:ª ¦ } ¶^· ScBNQ@Du7NQh n]C† MNQP†‡dg å ‚¿V‰ {c© ¦ ƒdª ¦ }ƒu wyv xzw {c© ¦ ƒ:ª ¦ } :ÑD ƒV„I„I„ƒ*Ð :~€>ƒV„„I„Iƒ8† È ‚¿%å “T ƒV„I„„Iƒ 2ÇÐ ßt† È — „l@B~g>APFP†‡MS^n]idN#~dLCv LdG L udcBG>g PFN#GAxŠnDidN#GMbB NQh,n|x{~dLOhn]CRGML CR@GAbOn*>ACRLdNQp >A@Hn]idN#@DGMPR~On]CRGML GAxŠn]iON x{GMPFPRG CFLdƒ&LdGMLdPRCFLdNQ>AcPFNQ>A@Bn@+v& ~g>AcDN!udcBGMbdPFNE . . . . . .   . å x 8w ¹ÅG| Ê ŸÑ yä *å • *– o“. idNQcBN Gå • *– « ˁ ƒV„I„„Iƒ CR@K>H@DNª& ~ONQLdhNGAxn]cBC‹>AP@BGMPF~n]CFGALd@- « b7NQCRLdƒnDidN9C†n]Nc]>€nDCFGML3Lv~dEkb7NQc4 CRnDNQc]>5n]CR ANQP†‡¸~du7pg>€nDNQp ­bd~On>API >‡ª@hQGMLO@DCFpONQcDCRLdƒW>AL ~OLdC'v& ~dN3cDNudcDN@DNLvn]>€n]CRGML x{GAckn]idN3~dLCvLdG L udcDG%gPFN‚pO~dcDCRLdƒÔn]idNEHCFLOCFEHC' >5n]CFGALsuOcDGªhQNQ@B@*kbˆ‡f~d@BCFLdƒßEHCFLdCREC >€nDCFGMLën]Nh*idLdC&ª~ONQ@@D~dh*i >A@kn]iON hQGML B~dƒˆ>€nDN,zƒAc]>ApdCRNQLˆn EHNnDidGp  ›Mœ GAc @Bn]Gªh*ig>A@¿n]CRh!EHNnDidGªpdGMPFGAƒMCFN@  ›A™%o S  ‘M” T — „lLOx{GAcBn]~OLg>€n]NPR‡ASn]G >€h*idCFN, MNß>¸@B~dCRn]>AbdPFN#@Dud>€n]CF>APcDNQ@BGMPF~n]CFGAL CFL n]idN?CFLˆ MN@Bn]CRƒˆ>€nDCFGML pdGME>ACFLäS"Ð @DidGA~dPFp#bN

(118) MNcB‡#P‹>€cDƒMN

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(120) G² MNc]>APRPCFLˆ MN@BnDCFƒˆ>€nDCFGMLpOGME|>€CFL‚x{GMc>-’/ bd>AcDN80 cDNhQGMLO@Bn]cB~dhnDCFGML:,—

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(122) ge Gh~d@DCRLdƒ‚GMLÔnDidNkpdCRENLd@DCRGMLÔGAx¾nDidN~dLCvLdG Ld@

(123) @Dud>AhQNj{LdNQƒMPRNQh,n]CFLOƒ,B~d@Bn

(124) LOG nDidNLdGMLdPRCFLdNQ>AcDC†nz‡ udcDGAbdPFNEOSC†nŠ@DiOGM~dPFpëb7Nku7GMCFLˆnDNQpÔGM~nŠn]ig>5nSrx{GMcK>‚@DhQ>€nDnDNQcDNcGAx_PFCREC†n]Npž@Bug>€n]CF>AP)N,ªn]NLd@DCRGMLäSän]iON @DhQ>€nDnDNQcDNUp gNPFpd@l>AcDN

(125) bg>€LdpzPRCFEHCRnDNQp‚x{~dLdh,n]CRGMLd@l>ALdpžnDidN!pdCFEHNQLd@BCFGML3GAx0n]idN!hQGMcBcDN@Du7GMLdpdCRLdJƒ dLdCRnDN pdCFEHNQLO@DCFGALg>AP@Dug>€hQNßpdNQu7NQLOpd@3GML n]idNë@Bh>€nBn]NcDNQc3NnDNQLd@BCFGML  Ž²%š o—q iONQcDN,x{GMcDN€SKGMLOPR‡ > PFCFEHCRnDNQp Lv~dEkb7NQcGAx^CFLOpdNQu7NQLdpONQLˆn!pg>€n*>‚CR@>Ah,n]~g>APRPR‡ž> €>ACFPF>AbdPFN9>ALdpäSä>A@

(126) >hQGMLd@B)N &v~dNLdhQN€S0~dLdPRNQ@B@@DGMEHN3>¡ @ ¹7Z§T´5Z,§KCFLOx{GMcBE|>5n]CFGALsCR@9> €>ACRP‹>AbdPRNGMc9@BGMEJN vCFLdp¸GAxcDNƒM~dP‹>€cD'C Q>€n]CRGMLßCF@&N,udPFGACRn]NpäS0GALdPR‡Wj> dLdCRnDN Lv~dEkb7NQc_GAxä~OCL vLdG Ld@+hQ>AL|b7Nw>AhnD~g>APFP†‡kcBNn]cBCFN, MNQpr—^}+GMLd@DN &v~dNQLˆn]P†‡MS~dLg> MGMCRpg>AbdPRNcDNQ@¿n]cBCFhnDCFGMLO@¾GML n]idN!>Ah*iOCFN €>AbOPFNŠcBNQ@DGAPF~OnDCFGML#>AcBNNQLOx{GMcBhQNpä— ŠL nDidN#GAn]idNcig>ALdpäS`pd~dNn]Gßn]iON#cB)N &v~dCRcDNQp ­CRL uOcDCFLOhQCFuOPFN>ALOp x{GMc>ß@DCRLdƒMPRN,z@¿n]Nu cBNQhGMLd@BnDcD~dh n]CRGMLßudcDGªhQN@D*@ pdCR@DhQcBNnD'C >5n]CFGALäSCRn

(127) CF@!>APREGA@BnCREu7GM@D@BCFbdPRN9n]G#@]>5n]CF@¿x¨‡Ôn]iON@B#~ HhQCFNLˆnkhQGALdpdCRnDCFGMLÔnDG ig> MNLdG|PFGªh>AP)ECRLdCFE>GAn]iONQcKnDig>ALÔn]iONƒMPFGMbd>APGMLdN  ›A%“ o—!=žGMcBNQG² MNcQS>‚LdGAnŠ@D~dC†n*>AbdPRN&h*iOGMCFhNGAx n]idN~d#L ªLO G LO5@ ­Co— N€—RS>€LWNOhNQ@B@DCR ANQP†‡WPF>AcDƒANpdCFEHNQLd@BCFGMLëG€x`nDidN~dCL vLdG Ld@9@Bug>AhN|>A]@ `NQPRP_>A@!>AL CFLg>€ududcDGAudcDCF>€n]NcDNQuOcDNQ@BNQLˆn*>5n]CFGAL GAxnDidN3~dCL vLdG Ld@HCFLfn]NcDEH@GAxwbg>A@DCR@kx{~dLdh,n]CFGALd*@ 9hGM~dPFp CREudP†‡ CFPRP†zhGMLdpdC†n]CRGMLdCFLOƒbN@DCFpONQ@l>AL3CFLdhcDN>€@DNQp#@DNLd@DC†n]C† C†nz‡‚n]Gx­>APR@DN@BGMPF~OnDCFGMLO@Q— }+GMLd@B)N &v~dNQLˆnDPR‡MS5n]GwhQGMEHNn]GwL> +NPFPАzu7GM@DNp i `NQPFPАzhGMLdpdC†n]CFGALdNQpludcDGMbOPFNQE;>ALdp

(128) n]GƒM~g>AcD>ALˆn]NN_nDig>€nn]iON @DGMPR~On]CRGML

(129) PFCRNQ@CFL

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(131) n]idN^LdGMLdPRCFLdNQ>AcäLg>5n]~dcBN`GAxn]idN¾x{~dLOhn]CRGMLg>AdP o œ ,S5>hQ~d@¿n]GMEH'C NQp!ƒMPFGAbg>APMGMun]CFEH'C NQc @DidGA~dPFpsbNH~d@BNQpä—3yzLWx­>€hnS)~dLdPR'C €NHnDidNPRCFLdNQ>Ach>€@DNAS0>žLv~dEkb7NQc!GAx+CFLdpdNuNLdpdNLvn9pg>€n]>ž)N &v~g>€P_nDG n]idN

(132) Lv~dEkb7NQcwGAx0~dCL vLdG Ld@KE>‡3LdGAnw@DY~ hN&nDG|>Ah*iOCFN AN9>€LÔ>AhhQ~dcD>€n]N!CFLˆ MNcD@BCFGML#bNh>A~O@DN9G€x0n]iON x­>APF@BN@DGMPR~On]CRGMLudcDGMbOPFNQE  ›A“ T—_}+GALd@DN &ª~ONQLˆn]P†‡MSg>AL|>AududcBGˆ>Ah*ibg>A@DNp|GML|>&LdN ‚­cBNQPF>€n]C† MNQP†‡MSMx{GMc_n]iON cDNEGAnDN@DNLd@DCRLdƒdS >ALOp N@Du7NQhQCF>APFP†‡ CRL nDidN3x{c]>AEHN `GM[c ¸GAxKEHCFhcDG +>² ANžCRE|>€ƒMCFLdGƒ HX«ª¯µ¬o§ ¹7¯FV @¿¡²©ªV,¢g¬ n]Nh*idLd'C &v~dN

(133) CR@>ApdGMuOnDNQp TŒNhnQ—`; — ŽMŽ.

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(135) ~dCL vLdG Ld@Š>AcDN

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(137) >AhQhGM~dLˆn`>ŠbdcDGˆ>€p@Du7NQhnDcD~dE GAxrPRNQLdƒ€n]i@DhQ>APFN@¾c]>ALOƒMCFLdƒlx{cDGME PFG zcBNQ@BGMPF~OnDCFGML!PFN, MNPF@0nDGidCFƒMiªzcDN@DGMPR~On]CRGML!PFN ANQPR@Q—0 iON @D~dEHE|>5n]CFGAL9G² MNc‹K| c]>€LdƒMNQ@<x{cDGMEÏM S  idCRh*i hQGMcBcDN@Du7GMLdpd@ŠnDG|n]idN9P‹>AcBƒMNQ@¿nŠh*ig>AcD>AhnDNQcBCF@BnDCFhkPRNQLdƒ€n]iÔ@Bh>APRNASrnDG 6{zÀ ,} SÍ idCFh*iëhGMcDcBNQ@Du7GMLdpO@Šn]G‚n]iON @DE>APFPRNQ@¿nlbd>A@DCR@¿–x{~OLdhnDCFGMLÔ@B~dudu7GMcBn>€nKnDidN6À –nDiÔ@DhQ>APFCRLdƒ|@¿n]NQur—

(138) etGAcŠ>|ƒMC† MNLëPFN ANQP | S»Ð^{`|>l} CR@ln]iON Lv~dEkb7NQcGAxLdGML–GÇ ANQcBP‹>Audu7NQp!bg>A@BCF@äx{~dLOhn]CRGMLd@hQNLˆn]NQcBNQp&CFLn]idN^>AcBN> n]Gb7N^cBNQudcBNQ@BNQLˆn]Np>€nn]idN(²| –nDi GF. F. H. . . . I. Dc N@DGMPR~On]CRGMLä—) idNQcBNx{GMcBNASMn]iONn]NQcBE@0GAx7@DE>APFPªPFNLdƒAn]i@Bh>APRNh>€LbN hGMLdhQNLˆn]c]>5n]NQp>€nnDidGM@BN cDNQƒACFGMLd@. idNQcBNHnDidNH~dLCvLdG Ld@9uOcDG>gPRN A>€cDCFN@

(139) EGMcBNc]>AudCRpdPR‡A— idNQLäS)n]G3x{~dPFP†‡ÔNOuOPFGMC†nn]idN?¡>@F¹7Z§T´5Z,§T­GAc CRnDNQc]>5n]CR ANQP†‡ƒM>ACFLdNp `CRLOx{GMcDE>€nDCFGMLGMLn]idNpdCRNQPRNQhnDcDCRhŠpdCF@¿n]cBCFbd~OnDCFGML|CFL‚n]iONCFLˆ MN@Bn]CRƒˆ>€nDCFGMLpdGAE|>ACRLäS n]idNx{GMPRPFG CFLOƒk>Apg>€uOn]C† MN

(140) Ek~dP†n]C†–@BnDNQuudcBGhNQ@D@CR@ uNcBx{GMcBENpä  f [¢g§¨¬o§­¡A¯µI§ H²¡A¬­§T´5¢ zÀ! G ŒN,nn]idN¾udcBGMbdPRNQE(~dCL vLdG Ld@n]Gn]iONx{cDNQNz@Bug>AhQN_hGM#L gƒM~Oc]>€nDCFGMJL R‰Š{c©Šƒ[ªC}‹ Y„ >ALO-p u wyv xzw {R©Šƒdª#}‹ KJ. u §¥ v ¦ ž {R©ŠƒªC}+g. KJ -J. ŽÇ›.

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(142) GAxnDidNk@Bh>€n¿ nDNQcDCRLdƒpg>€n]>  Ž²%š Ÿg f U?«¯µ¬­R§ @ t¬zVz¹ `Z]´²±*V*¥*W¥ zÀ! Yƒ „I„„)ƒ x *w ´Q[*¥K\^¥,¬­§¨XH¡A¬­§T´5¢ IKN gLdN

(143) n]idN

(144) Lv~dEkb7NQc •  – SdnDidN

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(158) ƒMPFGMbd>APrEHCFLdCREk~dWE ¾x{GAcn]idN

(159) @D~OhQhQN@D@BCR MN9@Bn]Nuä—  iv~d@QSª>AhhQGMcBpdCFLdƒnDG

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