Position resolution of the ATLAS electromagnetic endcap calorimeter
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(44) X V 9 ? J b P C \ rQdb \49 QSQ]R`_aCw; C ZW\ R`r? . . . pRmQGR`{b =P ZCC h Z F ra5 9 5(R`Rm{aemR`{bQ6J raCk;KB ro9 6|BUBUB = P ZS9 Z ? Ck? ?BDCkCemQ ra ;5 ZW9 9 ? B 9[P Z RTbS?RmBU{ = Z]e 99[bSZ R`rJ Q CkB9 9 Q 6 9 B ;xP=(9? ? BDbS?R`Ckre ?|F ra;(HKR`bSO Q \4C o9 QSCQ ZFR E\ Z]Ck9 ?<? bSBQGP C Rmo?BU{ eT=Z]9 J bSC R`Jr R`{a{Q \49 Q]Qw5CkRm?{5Cke`r hah GCU 9 bja b P Z r={ P J RZ CkBDb QdC 9[Z B P CkQ F *. . . ( . . . . . . 9 ?<bSR`; C ZW\ `R r? 9 RZ Ck?C Z {aCUbSRmB 9 emem6"rQSQSRm5(e`C F H 9 B P ra;b P CkQdCzB P 9 ? ?CkeTQ e`C 9 _aCkQ J R VC Z Ck?<b QSR`{? 9 bS= Z CRm? b P C l 8 l n J CUbdCkBDbdr Z F .
(45) .
(46) . l 8 l nRTQ 9 {aCk?C Z]9 e((= Z rQdC J CUbdCkBDbdr Z 5CkRT?{5(= Rme`btbdrC o(e`rR`b b P Cw;x= eTe< P 6oQSRmBUQrabdCk?<bSR 9 e ra; b P C F @A?|r Z J C Z bdr J RTQSBDr _aC Z b P C Rm{a{Qi 9[Z bSRmBUe`C 9 ? J QdC 9[Z B P ; r Z ?CU P 67QSRTBUQUX Rmb \ = Qdb Z CkBDr Z J b P C Ck? C Z {a6aX \ r \ Ck? bS= \ 9 ? J R J Ck? bSR`;x6zb P Cwbc67CNra; 9[Z bSRmBUe`CkQb P 9 b 9[Z C Z r J = BDC J RT?b P CNBDrememRTQSR`r? Q F l J CU_oRmBDC"B 9 eTe`C J 9 QdCke`CkBDbSQ|CU_aCk?<bSQ|b P 9 b P 9 _aC R`{a{Q emRg C 9 bdb Z R`5(=bdCkQzr Z QSRm{? 9 bS= Z CkQ F l ? 9 e`{ar Z Rmb P \ \ = Qdb b P Ck?"QdCke`CkBDb b P C 9[Z bSRmBUemCkQ ; Z r \ b P CkQdCCU_aCk? bSQ}b P 9 b 9[Z CNemRg Ckem6zbdr P 9 _aCBDr \ CN; Z r \ 9 R`{a{Q 9 ? J b P Ck? B 9 emBU= e 9 bdCb P C \49 QSQNra;:b P C Rm{a{Q B 9 ? J R J 9 bdC F @A?r Z J C Z bdr4B 9 emBU= e 9 bdCb P C \49 QSQUXb P C \ r \ Ck? bS= \ 9 ? J Ck?C Z {a6"ra;:b P C 9[Z bSRmBUe`CkQ ; Z r \ b P C J CkB 9 6 \ = QdbN5C g ?r N? F sr? QSR J C Z9 QSR \ (emCbcsr5r J 6 J CkB 9 6 B P 9 ? ?Cke
(47) 39 Q 9 ? C 9a\ (e`C M QdCUCq({= Z C4h F V F 8 P C \49 QSQwra;b P C R`{a{QRmQ Z CkBDr? Qdb Z = BDbdC J 576 . . - . . . . . . (. . . γ x. H. x x. γ. pB P R`{9[=Z {aZ CC J h F 9[Z p bSRmCUBU67e`Ca? X \J 9r ? \ JRT? R 99 {bdCZ]J9a\ 5<6ra;tb P b PCC bdra R`{av<{= Qw9[5ZSg rX QdrRT?? bJ P CkC B 9 n6oY Rm?F {4RT? bdr b}r P rabdr? Q F 6,B 9 ?15C 9 ? 6 (. . < <. M. &. V. ;. . . ;. . < < ; <. . DB rQ ; < M h Fh V P C Z C RmQsb P C \49 QSQsra;:b P C R`{a{QkX 9 ? J M! h#"]V 9[Z Cb P CCk?C Z {a6 9 ? J b P C \ r \ Ck?<bS= \ ra;C 9 B P P rabdr? Z r J = BDC J X 9 ? J ; < RmQ b P C 9 ?{e`C5CUb}CUCk? b P rQdCb}r" P rabdr? Q F l QNRm? J RmB 9 bdC J Rm? q {= Z C|h F 7Xob P C \ rQdb}emR g Cke`6 J CkB 9 64ra;ib P C R`{a{QsRmQKRm?<bdr
(48) 9 ? J { 9 ={aCG5rQSr? QKr Z P C 9 _<6v7= 9[ZSg Q P RTB P NRTeme 9 C 9[Z Rm? b P C J CUbdCkBDbdr Z9 Q ACUbSQra; \49 ?<6 emR`{ P bdC Z\49 Q]Q 9[Z bSRTBUe`CkQNQS=(B P 9 Q(R`r?(Q F p r Z *. . M. &. . V. < <. . ; <. . &. .
(49)
(50) . b P C \ r Z C{aCk?C Z]9 eL? 5r J 6"q(? 9 eQdb 9 bdCaX2Ckv<= 9 bSRmr?,h F hzB 9 ?15C Z C Z R`bdbdCk? 9 Q . <. &. < . . . <. M h F V. P C Z C Z = ?(Q}; Z r \ hbdr? F 8 P C Z CU; r Z CaX l 8 l nRmQ J CkQSR`{?C J bdr| Z r _oR J C 9 {ar<r J Ck?C Z {a6 Z CkQSrem=bSR`r? 9 ? J 9 {ar<r J \ C 9 QS= Z C \ Ck? bra; b P C 9 ?{e`C| P RmB P Rm? bS= Z ? Z Ckv<=(R Z CkQ {ar7r J rQSR`bSRmr? Z CkQdreT=bSR`r? 9 ? J b P C 9 QSQS= \ bSR`r? b P 9 bwb P C P rabdr? QwBDr \ C; Z r \ b P Cr Z Rm{Rm? F l QwB 9 ? 5CQdCUCk?; Z r \ Ckv7= 9 bSR`r?,h F h[X(5rab P 9[Z C? CUC J C J Rm?r Z J C Z bdrB 9 emBU= e 9 bdCb P C \49 QSQNra;:b P C Rm{a{Qw Z CkBURmQSCke`6 F l 8 l n 9 BUBDr \ (emRmQ P CkQwb P RmQ 5761= QSRm?{ QdCU_aC ZW9 eLQS=5 J CUbdCkBDbdr Z QN P RmB P B 9 ? 5C{ Z r=C J Rm?<bdr b P Z CUC \9 Rm?Qd67QSbdC \ Q b P 9 b QS= ZSZ r= ? J b P CwBDrememRTQSR`r?|r Z R`{Rm?Rm?e 9 6aC Z Q F 8 P CwRm?(?C Z J CUbdCkBDbdr Z}\ C 9 QS= Z CkQ b P C J R Z CkBDbSR`r? QUX \ r \ Ck?<bS= \ X 9 ? J QSR`{?(Q"ra; Cke`CkBDb Z RTB 9 eme`6 B P 9[Z {aC J 9[Z bSRmBUe`CkQ Z r J = BDC J Rm? C 9 B P Z rabdr? Z rabdr? BDrememRmQ]R`r? F 8 P C|B 9 e`r Z R \ CUb Z 6 Qd6oQdbdC \ \ C 9 QS= Z CkQb P C|Ck?C Z {a6 9 ? J b P C|rQSRmbSR`r? ;xr Z B P 9[Z {aC J 9 ? J ? Ck=b Z]9 eo 9[Z bSRTBUe`CkQ F l Q Q P 9 eme75C QSCUCk?Rm?B P 9 bdC Z 7X<b P Cw; ZW9 BDbSR`r? 9 eoCk?C Z {a6 Z CkQdreT=bSR`r? ra;Gb P C B 9 e`r Z R \ CUb Z 6 R \ Z r _aCkQ 9 Q b P C Rm?(BUR J Ck?<b 9[Z bSRmBUe`CCk?C Z {a6 Rm? B Z C 9 QdCkQ F yR VC Z Ck? b4b6<CkQ ra; 9[Z bSRTBUe`CkQ:emC 9 _aC B P 9[Z]9 BDbdC Z RmQdbSRTBsQ]R`{? 9 emQ:Rm?zb P CsB 9 e`r Z R \ CUbdC Z 9 ? J P Ck? BDCsb P CwB 9 e`r Z R \ CUb Z 6Qd6oQdbdC \ B 9 ? Z r _7R J C| 9[Z bSRmBUe`CR J Ck?<bSR`q(B 9 bSR`r? 9 QsCkeme F pRm? 9 eme`6aXb P C \ =r? QdCkBDb Z r \ CUbdC Z RmQG;xr Z R J Ck? bSRmq(B 9 bSR`r? 9 ? J \ C 9 QS= Z C \ Ck? b:ra; b P C \ r \ Ck?<bS= \ ra; \ =r?(Q:QdCkBUR`q2B 9 eme`6 F @btRTQLr?|b P C}r= bSQSR J C ra;(b P C J CUbdCkBDbdr Z 5CkB 9 = QdC P Rm{ P Ck?C Z {a6 \ =r?(QwNRmeme2{aCk?C Z]9 eTe`6Ck?CUb Z]9 bdCzb P CB 9 e`r Z R \ CUbdC Z Q F pR`{= Z C4h F 4Q P r Qwb P C {aCUr \ CUb Z RTB 9 ee 9 6ar=b ra;Lb P CGQS= 5BDr \ r? Ck? bSQ}ra;Lb P C l 8 l n J CUbdCkBDbdr Z F p Z r \ b P CBDrememRmQSRmr?BDCk?<bdC Z bdr b P C C obdC Z R`r Z ra;b P C J CUbdCkBDbdr Z1Z CkQdCkBDbSR`_aCke`6aXwb P C Rm? ?C Z J CUbdCkBDbdr Z M 6aCkeme`r GVWXwb P C B 9 emr Z R \ CUb Z 6 Qd6oQdbdC \ M { Z CUCk? 9 ? J r ZW9 ?{aC V 9 ? J b P C \ = r? QdCkBDb Z r \ CUbdC Z M 52em=C V 9[Z C|BUe`C 9[Z em61_7RmQ]R`5(e`C FN~ ?C|Ck? J ra;b P C ; r Z 9[Z J Z CU{R`r? M Ck? J B 9 V ra;b P C B 9 e`r Z R \ CUb Z 6Qd6oQdbdC \ RmQ J RTQd(e 9 6aC J Rm? \ r Z C J CUb 9 RmeRm? q {= Z C'h F F 8 P C Cke`CkBDb Z r \9 {?CUbSRmB B 9 e`r Z R \ CUbdC Z Rm? b P C Ck? J B 9 Z CU{R`r?ra;b P C J CUbdCkBDbdr Z RmQb P C . . . . . . .
(51) .
(52) . ATLAS. Detector. pe`CkR`?{{a= b Z P C,X(haF \ GRm? CUr P \ kC RmCU{ b PZ Rmb B 99 e? J e 9 6a}rCk= R`{ bP raQ ;G baP aC 4lbdr8 ? Q Fl n J CUbdCkBDbdr Z F 8 P C J CUbdCkBDbdr Z RmQ 9 5r=b \ Rm? ;xr7BU= Q|ra; b P RTQb P CkQSRTQ 9 ? J RmQ Rm?,; Z r?<bzra; M BUe`rQSC Z bdr b P CBDrememRmQ]R`r?,BDCk?<bdC Z Vzb P C P 9 J Z r? RmB Ck? J B 9 B 9 e`r Z R \ CUbdC Z Q F l 8 l n NRmeme5CB 9 9 52e`Cra; J RTQSBDr _aC Z RT?{ b P C R`{a{Q|5rQdr?,r _aC Z b P C \49 Q]Q Z]9 ?{aC"ra; [ GCU bdr hUaa GCU M QdCUC q({= Z Ch F P RTB P Q P r NQ1b P C b P CUr Z CUbSRTB 9 eme`6 Z CU;xC ZSZ C J Z]9 ?{aC ra;hUa GCUbdr"[a CU j xVWX 9 e`b P r={ P HKO 9 e Z C 9 J 6 C oBUem= J C J R`{a{Q \49 QSQ 5CkRm?{5Cke`r hah GCU 9 b ja BDr? q J Ck? BDCemCU_aCke F 8 P C q({= Z C4Q P r NQb P C4QSUR TUC4ra; b P C4QSRm{? 9 e J R`_oR J C J 576 b P C4C ZSZ r Z r?3b P C 5 9 B g { Z r=(? J \ C 9 QS= Z C \ Ck? bUX 9 v7= 9 ?<bSR`bc6 B 9 eme`C J
(53) F l Q]R`{? 9 etQSR`{? R`q2B 9 ? BDC|ra; 7X R F C F b P C Q]R`{? 9 eoRmQ GbSR \ CkQ 5(R`{a{aC Z b P 9 ? b P C = ? BDC Z b 9 Rm?<bc6 r?b P Cw5 9 B g { Z r= ? J X RTQ BDr? QSR J C Z C J 9 QdremR J. (+(. . . . . . . . . ( .
(54)
(55) . pR`{= Z C4h F =b 9 9 61_7R`CU0ra;r?CzCk? J B 9 B Z 6arQSb 9 b F 9 ? J Z CkemR 9 5(e`CB Z R`bdC Z R 9 ;xr Z b P C J RmQSBDr _aC Z 6 ra; 9 ?CU 9[Z bSRmBUe`Cr Z P Ck?r \ Ck?r? F 8 P Cq {= Z CQ P r NQ b P C QSR`{? 9 e}QSR`{? R`q2B 9 ? BDC4;xr Z _ 9[Z R`r= Q R`{a{Q QSR`{? 9 bS= Z CkQ 9 Q 9 ;x= ?(BDbSR`r? ra;wb P C R`{a{Q \49 QSQ F 8 P C 5 9 B g { Z r=(? J RmQG; Z r \ rab P C Zg ?r N? Z roBDCkQSQdCkQGb P 9 b Z r J = BDC QSR \ RTe 9[Z QSRm{? 9 bS= Z CkQG5(=b= QS= 9 eme`6 J r ?rab;xr Z]\ 9 C 9[g 9 b 9 9[Z bSRmBU= e 9[Z RT? _ 9[Z R 9 ?<b \49 QSQ F~ b P C Z QSr= Z BDCkQra;s5 9 B g { Z r= ? J BDr \ C4; Z r \ X ;xr Z C 9a\ (e`CaX \ RmQ]R J Ck?<bSR`q(B 9 bSR`r? ra; 9[Z bSRmBUemCkQ 9 ? J ; Z r \ q(? RmbdC \ C 9 QS= Z C \ Ck?<b Z CkQSrem=bSR`r? F. . . . . .
(56) "!$#%!$ '&. 8 P C l 8 l n&BDr7r Z J Rm? 9 bdC Qd6oQdbdC \ RmQ 9 Qd P C Z RTB 9 eNre 9[Z BDr<r Z J Rm? 9 bdC Qd6oQdbdC \ P C Z C rQSR`bSR`_aC J RZ CkBDbSR`r?.emR`C r?.b P C 5C 9a\ 9 RmQ 9 ? J ; r ZW\ 9'Z R`{ P b P 9 ? J C J BDr7r Z J RT? 9 bdC Qd67QSbdC \ NR`b P 9 RmQ rRm?<bSRm?{ bdr 9[Z J Q b P CBDCk? bdC Z ra;tb P C Z Rm?{X RmQ b P Cre 9[Z 9 ?{e`C \ C 9 QS= Z C J ; Z r \ b P C5C 9a\ . . . - .
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(58) . pR`bSR`Q {\4= Z 9 C QSQh F F nR`no{?R`{9 ? eL9 QSe(Rm{QSR`? {R`? q(R`B q29 B ? 9 BD? C|BDCNRmQ raJ ;CUb q2P ?C C J Rm9{aQG{Q}b P5CzrQdC ro?"CkRm?4BDbd_ C 9[J Z R`?7r= =(\ Q 5J CkC BZ 9 ra6; B QSP R`{9 ? ?(9 ?eCkCUemQ _aCk9 ? Q bS9 Q ;xJ =(R`? _7BDR J bSR`C rJ ?45<ra6 ; bRmQwP C= QSQSC v7J = 9[bdZr C J Z CUr<bdraC bZ]\ra; Rmb?P CCsb C P oCQSCkRmBD{bd? C 9 J e?<QS=R`{\ ? 5Rmq(C B Z 9 ra? ;2BD5CaX9 B g P { CkZ ?r= ? J CU_aCk?<RmQ bSQ e`CkM QSR Q F C b F P 9 ? a4 VF FO rRmQSQdr?Qdb 9 bSRmQSbSRmBUQ 9 RmQ 9 ? J &RmQ b P C 9 TkR \ =b P 9 e 9 ?{emC F @A? Z]9 BDbSRmBDCaXsb P Cre 9[Z49 ?{e`C1RmQC o Z CkQ]QdC J Rm? bdC Z]\ Q ra; (QdCk= J r Z]9 (R J R`bc6 ? P RTB P QSR \ 2emR`q CkQwb P C4B 9 emBU= e 9 bSR`r? ra;sB Z rQSQQdCkBDbSR`r? 9 ? J rab P C Z ra5(QdC Z _ 9 5(e`CkQG;xr Z b P C B 9 QdC P Ck? b P C P 9[Z J Q]B 9 bdbdC Z BDCk? b Z C ra; \49 QSQ \ r _aCkQRm? b P C e 9 5 ; Z]9a\ C F 8 P CkQdC BDr7r Z J RT? 9 bdCkQ NRmeTe 5C= QSC J bdr Z Cke 9 bdCb P CGr Z R`Ck?<b 9 bSR`r?ra;Lb P C l 8 l n"B 9 e`r Z R \ CUbdC Zw\ r J = e`CkQ}bdrb P CGBDr7r Z J RT? 9 bdCkQ = QdC J Rm?b P C5C 9a\ bdCkQdb F . . . . . . . . . . U \LOo]T b h}fOPko]PWV X PSU o]\c{ORO\no h U
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(61) Z0 * ,/40 , 04
(62) 3* Z0 ,. P 9[Z {aC J 9[Z bSRmBUe`CkQ 9 ? J P rabdr? Q1Rm?<bdC Z]9 BDb1NRmb P \9 bdbdC Z b P Z r= { P b P C Cke`CkBDb Z r \49 {?CUbSRTB M>H Y V ;xr Z BDC F 8 P C Z CU; r Z CaX2; r Z b P C|(= Z rQdCra; b P RTQNQdbS= J 6aX(b P C Rm? bdC ZW9 BDbSR`r? Qra; Cke`CkBDb Z r? QUX2rQSR`b Z r? Q 9 ? J P rabdr?(Q 9[Z Cra;t Z R \9[Z 6"Rm?<bdC Z CkQdb F l eme<B P 9[Z {aC J 9[Z bSRmBUe`CkQe`rQdCsCk?C Z {a6 Rm? \49 bdbdC Z _oR 9 R`r? UR T 9 bSR`r? 9 ? J C BUR`b 9 bSR`r?ra;(b P C 9 bdr \ Q Rm? b P C \ C J Rm= \ F H e`CkBDb Z r? Q 9 ? J rQSR`b Z r? Q 9 emQdr Z]9 J R 9 bdC Ck?C Z {a6 9 Q P rabdr?(Q P Ck? J CkBDCke`C ZW9 bdC J 5CkB 9 = QdC ra;|RT? bdC Z]9 BDbSRmr? QNR`b P b P C \ C J RT= \ F OKP rabdr?(Q1Rm? bdC ZW9 BDb1NR`b P \49 bdbdC Z b P Z r= { P i: 9 RZ Z r J = BDbSR`r?LX( P rabdr7Cke`CkBDb Z RTBWC VCkBDb 9 ? J QSB 9 bdbdC Z Rm?{ Z roBDCkQSQdCkQGQS= B P 9 Qsr \ bdr? QSB 9 bdbdC Z RT?{ F .
(63) hah 8 P C;xreme`r NRm?{ QdCkBDbSR`r? Q J CkQSB Z R`5Czb P CkQdC4Rm?<bdC Z]9 BDbSR`r? Q F pRZ QdbUXb P C4Rm?<bdC Z]9 BDbSR`r?(Qra;KCke`CkBDb Z r?(Q 9 ? J rQSR`b Z r?(Q NR`b P \49 bdbdC ZG9 ? J Xb P Ck?Xb P CzRm?<bdC Z]9 BDbSR`r? Qwra; P rabdr? QwNR`b P \9 bdbdC Z9[Z C J RmQSBU= QSQSC JF } k
(64) O m ] } O . . $ . GCk?C ZW9 eme`6aX 9 bdr \ Q 9 ? J \ re`CkBU=(e`CkQ 9[Z C CkemCkBDb Z RmB 9 eme`6?Ck= b Z]9 e; F r sCU_aC Z XR`;b P C Z C RmQ"QS= BUR`Ck?<b Ck?C Z {a6 9 _ 9 Rme 9 5(e`CaX 9 bdr \ Qr Z\ re`CkBU= e`CkQ B 9 ? e`rQdCCkemCkBDb Z r? Q 9 ? J 9 BUv7= R Z C 9 ?CUb Cke`CkBDb Z RTB 9 eLB P 9[Z {aC F 8 P RTQi Z r7BDCkQSQRmQ g ?r N? 9 Q R`r?(RUT 9 bSR`r? F @; b P C 9 bdr \ RTQiC BUR`bdC J bdr 9 P R`{ P C Z Ck?C Z {a6|5(=b 9 ?CkemCkBDb Z r? RmQ ? rabKemR`5C Z]9 bdC J Xab P C Z roBDCkQSQ RmQKB 9 eme`C J C BUR`b 9 bSR`r? F P 9[Z {aC J 9[Z bSRTBUe`CkQ 9 ? J P rabdr? Q b Z]9 _aC Z QSRm? { 9 \ C J RT= \ \49 6b Z]9 ?(Qd; C Z Ck?C Z {a64bdrb P CGBDr?(QdbSR`bS=Ck?<b 9 bdr \ Q _7R 9 R`r? R T 9 bSR`r?r Z C BUR`b 9 bSR`r? Z CkQ]= e`bSRm?{ Rm? b P C e`rQSQGra;sCk?C Z {a6 ra;Kb P C Rm? BUR J Ck? bG 9[Z bSRTBUe`C 9 ? J b P C{aCk?C Z]9 bSR`r?X:Rm? b P C4B 9 QdC ra;}R`r?(UR T 9 bSR`r?X ra;:Rmr?" 9 RZ Q M rQ]R`bSR`_aCR`r? 9 ? J Cke`CkBDb Z r?2V F 8 P CG?7= \ 5C Z ra;tQS= B P 9 R Z QK Z r J = BDC J RTQ} Z rar Z bSR`r? 9 e bdr4b P CzCk?C Z {a6e`rQdb 576"b P CRm? BUR J Ck?<b 9[Z bSRmBUemC F 8 P CCk?C Z {a6,e`rQSQz_7R 9 R`r? R T 9 bSR`r? 9 ? J C oBURmb 9 bSR`r?'RTQ 9[Z]9a\ CUb Z UR TUC J 576 b P C E CUb P C E emr7B P hU iCkv7= 9 bSR`r? < !< #" < <%&$ ' h < ( h em? , M "h < ' <' ) < V +* ' < .%- / M Fh V P C Z 1C 0#042 3 RmQ|b P C \ C 9 ? Ck?C Z {a6 J CUrQ]R`bSR`r?,C Z = ? R`bz 9 b P e`Ck?{ab P.M R F C F RmQ|RT? \49 Q]QzC Z = ? R`b 9[Z C 9 VWX 9 ? 5J 9[Z C b P C \9 QSQ 9 ? J BUe 9 QSQSRmB 9 e Z]9 J Rm= Qra;b P C Cke`CkBDb Z r?LX 9 ? J ' 9[Z C b P C B P 9[Z {aC M Rm? = ? RmbSQwra; h [a B3hU :3;6 V 9 ? J b P C|_aCke`r7BURmbc6 M ' 87 " Vwra; b P C 9[Z bSRmBUe`CaX RmQ l _ara{ 9 J Z r IQ ?7= \ 5C Z X $ 9 ? J & 9[Z C"b P C 9 bdr \ RmB 9 ? J b P C \49 QSQ?7= \ 5C Z Qzra; b P C 9 bdr \ Qra; b P C \ C J RT= \ X , RmQ b P C \ C 9 ?&R`r? UR T 9 bSR`r?rabdCk?<bSR 9 eN P RmB P RmQ 9 Z r R \49 bdCke`60hU $ CU 9X ) +* RmQb P C \49 R \ = \ g Rm?CUbSRmBCk?C Z {a6 b ZW9 ? Qd;xC Z]9 5(e`Cbdr 9 ; Z CUCzCke`CkBDb Z r? RT? 9 QSRm?{emCBDreTemRmQSR`r? 9 ? J - RmQwb P C J Ck?(QSR`bc6 WC VCkBDb. . . . . . . &. &. . (. . . &. .. . I ][ \mR_LONa`\|b3T e\clk\cjcV bKTR]UdPSUs\+:]h jcVKlWX \4;Lih}l VKT^VK[O\R_LON^`\cb3T}ef]bKT VKT ROU v ][ PSUdPSUsLOU LOh lSlWX bK\ce \cb bK\no VKT h UsPSTROP=<nhAVKPSTRp\R]\cbKq X lSTU Udh Rio-VK[OPSUsjTR_yH\cR_VKPST R rsPSlSl`\Ze TlSlSTAr\nopPSR VK[OPSU3VK[O\cU PkUu.
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(67) P C Z C RTQ B 9 eme`C J b P C # M Rm? \9 QSQ C Z = ? R`b 9[Z C 9 V 9 ? J RmQ J CUq2?C J 9 Q b P C J RTQdb 9 ? BDC r _aC Z P RmB P 9 ?0RT? BUR J Ck?<bCke`CkBDb Z r?0Ck?C Z {a6 RmQ Z C J = BDC J 576 9 ; 9 BDbdr Z ra;"h M R F C F F V J =C bdr 5 Z C \ QSQdb Z]9 P eT= ?{ Z]9 J R 9 bSR`r? r? e`6 M QdCUCGCkv7= 9 bSR`r? F {R`_aCk? e 9 bdC Z Rm?4b P RmQ B P 9 bdC Z ; r Z 9 ;xr Z]\ = e 9 ;xr Z b P 9 b J CUCk? J Q r?1b P C Z raC Z bSR`CkQ ra;b P C \ C J Rm= \ V F . . . . &. . .. *+. . . . O 9 RZ Z r J = BDbSR`r?RmQ b P C ; r ZW\49 bSR`r?ra; 9 ? Cke`CkBDb Z r? 9 ? J 9 rQSR`b Z r? ; Z r \ 9 P rabdr? b Z]9 _aCkeTRm?{ b P Z r= { P \49 bdbdC Z F 8 P CwCke`CkBDb Z r? 9 ? J b P CrQSR`b Z r? e`rQSC Ck?C Z {a6 _oR 9 R`r? R T 9 bSR`r? F 8 P C rQSR`b Z r?4B 9 ? 9 emQdr 9 ? ? R P RTe 9 bdCR`b P 9 ? Cke`CkBDb Z r? Rm?b P C \ C J Rm= \ Rm?<bdr4b}r"r ZN\ r Z C P rabdr? Q FKO 9 RZ Z r J = BDbSR`r? RmQz5<6 ; 9[Z b P C" Z Rm? BURm 9 et Z roBDCkQSQzRm?3 P RmB P,P R`{ P Ck?C Z {a6 P rabdr?(Q 9[Z C 9 5(Qdr Z 5C J Rm? \49 bdbdC Z M QdCUC . \|bKN-h R e T bd`]bK\nh _PkR]qab hoPkh}VKPSTR.
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(69) O m ] } O . *. . pe`C R`9 {J= F Z C F h s8RmQw;xr P Z Cb B P Z CzrQS Q P QSraCkbdBDr7bSCkR`re`Ck? BDQ b Z raRm;tB CWPVraCkbdBDrbU?X Ck? C Z {a6e`rRTQwQSQ ; r \ Z Ckb B P P C 9 ? u RT9Q \67emQCkR`9{ QP 9 QSB ;>9 = bd? bdBDC bSZ R`RTr?? {X ra;tCk? C Z {a6RmRm? Q ;xRmQr Z ;xr b Z P Cb P C r \ 9 RZ bdr ? Z r Q]J B = 9 BDbdbSbdR`C rZ ? Rm?J{=X Cbdr4 b RmP Q C;xr CkZ e`Ckb BDP b C|Z r ? 9 q RZ Cke JLZ F r J =(BDbSR`r? J =Cbdr"b P Cz?7= BUe`C 9[Z q(Cke J 9 ? J " . %"
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(95) oh RmQ {R`_aCk? 576 b P C ?7= BUe`C 9[Z Rm?<bdC Z]9 BDbSR`r?.e`Ck?{ab P X X J CUq(?C J 9 Qb P C \ C 9 ?0e`Ck?{ab P ra; \ C J Rm= \ b Z]9 _aC Z QdC J 5<6b P C P 9 J Z r? 5CU;xr Z C RT? bdC Z]9 BDbSRT?{,NR`b P 9 ?7= BUe`Ck= Q ra;b P C \ C J RT= \ F 8 P C ?<=(BUe`C 9[Z Rm?<bdC Z]9 BDbSR`r? e`Ck?{ab P Q; r Z O 5LX = 9 ? J l Z|9[Z C h F j B \ M [ VWXwhk F B \ M hU V 9 ? J F ja B \ M V hU F 8 P C Z CU; r Z CaX b P C1e`r?{R`bS= J Rm? 9 e J CU b P ra; 9 P 9 J Z r?(RmBQ P r sC Z RmQ \ = B P M 9 ? r Z J C Z ra; \49 {? R`bS= J C V e 9[Z {aC Z b P 9 ? b P 9 bra; 9 ? H Y Q P r sC Z F 8 P RTQ 9 emQdr P re J Q b Z =C|; r Z b P C e 9 bdC Z]9 eiQd Z C 9 JF Y =r? QNRT? bdC Z]9 BDbNR`b P b P C \ C J Rm= \ _aC Z 6 J R VC Z Ck?<bSe`6 BDr \ 9[Z C J bdr"Cke`CkBDb Z r? Q 9 ? J 2R`r? Q F 8 P CwB Z RmbSRmB 9 e7Ck?C Z {a6aX Xra; \ =r? Q RmQ 9 5r=b aaabSR \ CkQte 9[Z {aC Z b P 9 ?b P 9 b ra;2Cke`CkBDb Z r? Q QSRT? BDC RmQ Z rar Z bSRmr? 9 e bdrb P CQSv7= 9[Z CGra;ib P C 9[Z bSRmBUe`C \9 QSQ F Ck? BDCaXb P C Z R \9[Z 6Ck?C Z {a6"emrQSQ \ CkB P 9 ?(RmQ \ ;xr Z}\ =r? QKRTQ R`r? UR T 9 bSRmr?4=4bdr|_aC Z 6 P R`{ P Ck? C Z {R`CkQ F 8 P CwCk? C Z {a64e`rQSQK_7R 9 Rmr? UR T 9 bSR`r?4RTQKQ \49 eTe M h Y CU { :3;B \ < hahxVWXiQSr P R`{ P Ck?C Z {a6 \ =r?(Qb Z]9 _aCke \9 ? 6 bSR \ CkQ;>= Z b P C Z Rm? b P C \ C J Rm= \ b P 9 ? Cke`CkBDb Z r?(Q 9 ? J (Rmr? Q ra;b P CQ 9a\ CCk? C Z {a6 F } k
(96) O m ] } O . . . +*. . . *. 5. . . . . (. . . Y. ( * }, 8&* 40 . l B 9 e`r Z R \ CUbdC Z RmQ 9 ? Rm? QSb Z = \ Ck?<bN= QdC J bdr \ C 9 QS= Z C|b P C Ck?C Z {a6 ra; b P C|Q P r }C Z9 ? J b P = QUXra; b P C Rm? BUR J Ck? b 9[Z bSRmBUe`C F 9 e`r Z R \ CUbdC Z Q 9 eTQdr rNVC Z b P C 9 5(RmemRmbc6 bdr J CUbdCkBDb 9 ? J \ C 9 QS= Z C4b P CCk?C Z {a6 ra; ?Ck=b ZW9 eL 9[Z bSRTBUe`CkQUX(= ?(emRg C \49 {?CUbSRTBzQdCkBDb Z r \ CUbdC Z Qb P 9 b= QdCzbdCkB P ? RTv<=CkQGRm?1 P RmB P 9[Z bSRmBUemC \ r \ Ck?<bS= \ RTQ \ C 9 QS= Z C J 576 b P C 9a\ r=(? b 9 9[Z bSRTBUe`CRmQ J C CkBDbdC J RT? 9 \9 {?CUbSRmB4q(Cke J 9 ? J'P Ck? BDC 9[Z C4r?(e`6 =(QdCU;x=(e; r Z B P 9[Z {aC J 9[Z bSRmBUemCkQ F Y r Z CUr _aC Z Xb P C; Z]9 BDbSRmr? 9 e Ck?C Z {a6 Z CkQSrem=bSR`r? Z r _oR J C J 576 B 9 e`r Z R \ CUbdC Z QR \ Z r _aCkQGNR`b P Rm?(B Z C 9 QSRm?{"Ck?C Z {a6aXiRT? BDr?<b Z]9 QdbR`b P \49 {?CUbSRmB QdCkBDb Z r \ CUbdC Z Q P C Z C b P C Z CkQdrem=bSRmr? J CU{ Z]9 J CkQNRmb P Rm? B Z C 9 QSRT?{"Ck? C Z {a6 F 8 P C Z CU;xr Z CaXLB 9 e`r Z R \ CUbdC Z Q 9[Z C b P C J C bdCkBDbSR`r? J CU_7RTBDCkQwra; B P rRmBDC 9 Qw 9[Z bSRmBUemCBDrememR J C Z Q 9 B P R`CU_aC P R`{ P C Z Ck?C Z {R`CkQ F . .
(97) a 9 e`r Z R \ CUbdC Z Q B 9 ?5C Qdr Z bdC J RT? bdrb}r ;>= ? J 9a\ Ck?<b 9 eBUe 9 QSQSCkQ bdrab 9 e 9 5(QSr Z bSR`r? M>P r \ ra{aC ?CUr= Q V 9 ? J Q 9a\ (emRm?{ M>P CUbdC Z ra{aCk?CUr= Q V F ~ ? em6aX7Q 9a\ (emRm?{ B 9 e`r Z R \ CUb Z 6 NRmeme(5C J RTQSBU= QSQdC J ;x= Z b P C Z 9 Q b P RmQwRmQ b P Cb6<C= QSC J Rm? l 8 l n F n 9a\ 2emRm?{ B 9 e`r Z R \ CUbdC Z Q 9[Z C J CkQSR`{?C J bdrNb 9[g C \49 ?<6Q 9a\ (e`C \ C 9 Q]= Z C \ Ck?<bSQLra;ob P CKQ P r sC Z b P Z r= { P r=bzR`bSQ J CU_aCke`ra \ Ck? b F l Q 9a\ (eTRm?{1B 9 e`r Z R \ CUbdC Z BDr? Q]RmQdbSQra; 9 e`bdC Z ? 9 bdC"e 9 6aC Z Q|ra; J Ck? QdC 9 5(Qdr Z 5C Z}\49 bdC Z R 9 e(bdr|Rm? B Z C 9 QdC b P C Z ra5 9 5(RTemR`bc6|ra;LRm?<bdC Z]9 BDbSR`r? Q 9 ? J \49[g Cb P CB 9 emr Z R \ CUbdC Zs\ r Z C BDr \ 9 BDb 9 ? J 9 BDbSR`_aC \9 bdC Z R 9 e:bdrQ 9a\ (e`C Ck?C Z {a6 emrQSQ F @? b P Cq Z QSbN{aCk?C Z]9 bSRmr? M bdr 5C Z CU;xC ZSZ C J bdr 9 Q4BDr?<_aCk?<bSR`r? 9 e V ra;Q 9a\ (emRm?{ B 9 e`r Z R \ CUbdC Z Q Rm? 9[Z bSRmBUe`C P 67QSRTBUQUXKb P C1r Z R`Ck? b 9 bSRmr?ra;b P CkQdC 9 e`bdC Z ? 9 bdCe 9 6aC Z Qs 9 Q}C Z Ck? J RmBU= e 9[Z bdrb P C J RZ CkBDbSRmr?ra;L 9[Z bSRmBUe`CkQ}bdr5C J CUbdCkBDbdC JFs~ b P C Z r Z R`Ck? b 9 bSR`r? QNb P 9 b Nr VC Z BDr? QSR J C Z]9 5(e`C 9 J _ 9 ?<b 9 {aCkQRm? bdC Z]\ Qwra; J CUbdCkBDbdr Z P C Z]\ R`bSRTBUR`bc6aX Z C 9 J r=bUX { Z]9 ?7= e 9[Z Rmbc6aX CUbSB[X P 9 _aC5CUCk? J CkQ]R`{?C J X Q]= B P 9 Q b P C H Y H R`b P 9 ? 9 BUBDr Z J R`r?{aCUr \ CUb Z 6 F 8 P C H Y H 9 BUBDr Z J Rmr? {aCUr \ CUb Z 6 NRmeme}5C;x= Z b P C Z J RmQSBU= Q]QdC J Rm? P 9 bdC Z F l 52Qdr Z 5C Z Q= QdC J Rm? Q 9a\ (emRm?{ B 9 e`r Z R \ CUbdC Z Q 9[Z C b6<(RTB 9 eme`6 e`C 9 J XiBDra C Z9 ? J RZ r? J CUCk? J RT?{r? b P C J CkQSRZ C J Z]9 J R 9 bSR`r? r Z Rm? bdC Z]9 BDbSR`r?emCk?{ab PF Y CUb 9 e cQSBURm?<bSRmeme 9 bdr Z Q 9 ? J RmB P X \ CUb 9 e cemRmv7= R J 9[Z {ar? Rmr? UR T 9 bSR`r? B P 9a\ 5C Z49 ? J \ CUb 9 e { 9 QSCUr= QG Z rar Z bSR`r? 9 eNR Z CB P 9a\ 5C Z Q 9[Z C|BDr \4\ r?(e`6 =(QdC J b6<CkQ ra; Q 9a\ (emRm?{ B 9 e`r Z R \ C bdC Z Q hk F l Z R`r? R T 9 bSR`r? B 9 e`r Z R \ CUb Z 6NRmeTe5Cb P C ; roBU= Q ra; J CkQSB Z R`(bSR`r? Qwb P 9 b; reTe`r XQSRm?(BDC 9 eme ra;b P CCk? J B 9 B 9 e`r Z R \ CUb Z 6 Rm? l 8 l n \49[g CkQN=(QdCra;b P RmQ bdCkB P ? Rmv7=C F } k
(98) O m ] } O . . . . . *. . . . . . . . . ! "& . l l Z B 9 e`r Z R \ CUbdC Z RmQ \49 J C}= zra; 9 QdC Z R`CkQira; \ CUb 9 e 2e 9 bdCkQ:R \4\ C Z QdC J Rm?emRTv<= R J 9[Z {ar? F @r?(RUT 9 bSR`r? kC e`CkBDb Z r?(Q1 Z r J = BDC J Rm?.b P C l Z { 9 (Q \ r _aC'= ? J C Z b P C3Rm? 2=Ck? BDC ra; 9 ? C 7bdC Z ? 9 eme`6 9 ((emR`C J Cke`CkBDb Z RTB1q Cke JF 8 P C \ rabSR`r?ra;b P C Cke`CkBDb Z r?(QRm? J = BDCkQ4BU= ZSZ Ck? bSQr? b P C (e 9 bdCkQ" P RmB P B 9 ? 5C \ C 9 QS= Z C J = QSRm? { Cke`CkBDb Z r? RmBUQ F pR`{= Z C F Q P r NQ 9 Q g CUbSB P ra;Gb P C1b Z R 9 ?{= e 9[Z 9 _aCU;xr Z]\ ra; 9 ? . . .
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