!" # $ !" % !& '( ) * +-,/...
23 downloads
588 Views
799KB Size
Report
This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!
Report copyright / DMCA form
!" # $ !" % !& '( ) * +-,/.10324* 56087:9* 2 ,/03?A@CBCDFEHGI5IJK 5I?ML:* .NB1?M0PO6D>QSR TU7V WXW Y D-Z:Z WC[:[ E\GI5IJ]D_^a`8* J>* 5 bI[1&DN%B\:-3 L 2BD8Z&%-38 BD-3W]">I5 ^&HE%BD8\_#B%`a:-.! 2"K83I3W]BD8X_#B=!"S215B+,"% (:8"%$C-5">-3(::-3BD&H b,=&DN%BTBDcdI3&H2 ">- M` &%-38E> N%BD-e_\B'_\&%-aUf" L3L "% 22I3- 2 BD !"\Nd) 2 =:-a!BM ^-3&H2 ">-3&%(RW]">-5$@BM 2BD-3W]BD g&%-38 I3-3:N%BM 2 2 BD DQ *h&%_i&%(: 2"eN%BM 2UVE% &H!BM$jI3( !"Z;=13 : !!BM OkBD-3-5BM,g !l#&%-38[69-385BM ^ 9mZBD(::-Z$@"% 215B'15BD( L * 2BDW]BD:N%BD8n$@ 2">_o215BD_o,h13:( BO,T :2:-5E L &H 22 +"%$ 213: =213BD 2: MQ mV"% BM"YN%BM D`%*C213&%-549215B L BM" L (:B&H215Bp_\&H213BD_\&H2:WM&%(a83B L &H 22_#BD-.:-SqbI3-38 $@"% L 2"YNK:83:-3Er 2I3W^1s&rE%"d"K8[&%-38s:-3 L : :-5E#BD-.Nd: 2">-3_#BD-.MQ'tp L BDWM:&%()( U%`u*h& L J L 2BDWM)&H!B/">I5 !BDW] 2BM2&H BD &%-380 !Ud 2!BD_v&%83_/:-3: !! ^&H!"% ',g15"V&%(:,&YUd E> N%Bf&% wJ 2: 22&%-3W]BS,g15BD-e-5BMBD83BD8RQ *=213&%-54e_xUe&Y,BD !">_\Bx$j&%_\:( U%Qy">I &H 2Bx&%(:,&YUd h( "YNK:-5E5`3BD-W]">I5 &HE>:-5Er&%-38 2I LL "% 2 N%B%Qy">IV !BMg&%-nB]zK&%_ L ( BSA.Uf215B',=&DUU%">IZ(: N%BS&%-38e*=&%83_\ BSU%">IRQ 6gAC"{N%Bx&%(:(|`K*213&%-54r}aBD 2I3 =,g13"\13&% +W]">_ L ( BM!BD(:Ur! &%- !$P"% ^_#BD8e_xU(: $@B9215B (:&% !$@BM,~U%BD&H ^ MQ[y">I7&H 2B_xU0ACBD !$@ BD-8RQZ*x,&%-.X!" $@"% 2BMN%BM #ACB:-GU%">I3 L 2BD 2BD-3W]B'&%-38n !BM N%B'U%">IR
Q 15B;+ &%_\ &% 2 2& J!h">(:_ tc.I&H2 ">- Q'QSQ'Q'QSQ'QxQ'QSQ'Q'QSQ'QxQ'Q " Q$# O% I52():-5B9"%$ 15BD 2: Q'QSQ'Q'Q'QSQxQ'QSQ'Q'QSQ'QxQ'QSQ'Q'QSQ'QxQ'Q & ' ()d# Q *,+-/*w-a.0 0! 2"K138324I3W]2*,:+">-V-6Q'57QS.0Qx8Q' 97QS ;Q': Q'Q'QSQxQ'QSQ'Q'QSQ'QxQ'QSQ'Q'QSQ'QxQ'Q < = #dd# Q$Q$#? [@>h"%BD2&&HH4e2 3">-"% _Q'I3Q'(:Q'&H2QS:">Qx- Q'QSQSQ'Q'Q'Q'Q'Q'QSQSQxQxQ'Q'QSQSQ'Q'Q'Q'QSQSQ'Q'QxQxQ'Q'QSQSQ'Q'Q'Q'QSQSQ'Q'QxQxQ'Q'QQ BA= d# QC" ;=(:&% 2ED WM&H2 ">-"%$ &DN%BD(:)-5EFF #dQ$& Gd# Q$ K& ".Q "%$"%I$ _\ ".15"%BM"%21 2BDI_H">(:#dI5Q 2 ">Q'-3Q' 9Q'Q'@ QSQS&DQxQxN%BDQ'Q' QSQSQ'Q'Q'Q'Q'Q'QSQSQSQ'Q'Q'QxQxQxQ'Q'Q'QSQSQSQ'Q'Q'Q'Q'Q'QSQSQSQ'Q'Q'QxQxQxQ'Q'Q'QQQJ#%"= d# Q$K& Q$# I ">()I52 ">-3 ,g 21 I :-5E>I3()&H 2 BD Q'QSQ'QxQ'QSQ'Q'QSQ'QxQ'QJ#K #dd# Q$Q$&KK& Q$QC"? IOQ ">()()I3I5:2-5 EX">-321 5BR"%$MF@ LN&d&YN%Q BD"P O "%QSE%QxBM21Q'5BMQS Q'Q'Q'QSQSQ'Q'QxQxQ'Q'QSQSQ'Q'Q'Q'QSQSQ'Q'QxQxQ'Q'QJQJ#? = d# Q$K OS B L BD-385BD-3W]BS">- L &H &%_#BM!BM QxQ'QSQ'Q'QSQ'QxQ'QSQ'Q'QSQ'QxQ'QJ?UT #dd# QVQ$=T @Ftz &DN%(:BD)(:WMBD -5E%21"% _Q'I(:QS&% TQx$@Q'"% XQSG Q'BDQ'&H4%Q'">QS-3 rQxQ'Q'QSQSQ'Q'Q'Q'QSQSQ'Q'QxQxQ'Q'QSQSQ'Q'Q'Q'QSQSQ'Q'QxQxQ'Q'QWQW"",& L Y Z[d? Q -\] 9*w-a^! 92_"K83Z`I3-/W]*P2ab:">-V Q': QSQxQ'QSQ'Q'Q'QSQxQ'QSQ'Q'QSQ'QxQ'QSQ'Q'QSQ'QxQ'QW "\cT ?dd? Q$Q$#? dI 2&&HH A:&H)(:2 :">U -3&%Q'(bQ';=Q'13&HQS ^&%QxW]Q'!BMQS Q'lD&HQ'2 Q'">-[QSQxQxQ'Q'QSQSQ'Q'Q'Q'QSQSQ'Q'QxQxQ'Q'QSQSQ'Q'Q'Q'QSQSQ'Q'QxQxQ'Q'QWQW",",== d? QC" G BD(::_\:-&H 2U\qBD_\_/&% 7Q'Q'Q'QSQxQ'QSQ'Q'QSQ'QxQ'QSQ'Q'QSQ'QxQ'QJ& A ?dQ$& Gd? Q$ K& ".Q "%$"%t$ zd !B15DBM-3"% 2 ">BD_H-e!"?dfQ efQ'giQ'ih Q'QSQSQxQxQ'Q'QSQSQ'Q'Q'Q'QSQSQ'Q'QxQxQ'Q'QSQSQ'Q'Q'Q'QSQSQ'Q'QxQxQ'Q'QJQJKKUKT d? Q$K G "."%$"%$ 15BM"% 2BD_Hd? Q$\? Q'Q'Q'QSQxQ'QSQ'Q'QSQ'QxQ'QSQ'Q'QSQ'QxQ'QJK= #
?dQVT ;">_\_\BD-a2 g">-i@[BD(:( J!G"> !BD83-3BD 2 Q'QSQ'Q'QSQ'QxQ'QSQ'Q'QSQ'QxQ'Q "55Q b*w-a! 2"K()83I3*,W]+2:-/">.0-V 0 ;Q'1 QS24Qx*\Q'+7QS-/Q': Q'Q'QSQxQ'QSQ'Q'QSQ'QxQ'QSQ'Q'QSQ'QxQ'Q 5" Q Q 13BS"% 2!BM,BMEHJ 85B d :BD TtpcdI3&H2 ">- QxQ'QSQ'Q'QSQ'QxQ'Q "5"5Q$Q$#? G; ">".-3"%-3$BD"%W]2$ "> -n15BMk"%BM 2BD,_ BMBD"5-Q xQ'8 Q'd Q'&%QS-8ZQxQ';=&%QS_\Q'&%Q' 2 QS& J!Q'g"Qx>(:Q'_ QSQ'Q'Q'Q'QSQSQ'Q'QxQxQ'Q'QQ
TA c7T TT]# T]K
?
W !"$#%#&('*),+.-/! 02143 65879+.:
15B;+&%_\&% 2 2& J!h">(:_oBDcdI3&H2 ">L Q O ;=@;A-3&%( L " L &HE>&H2 ">- "%$',=&H!BM e,&YN%BD e:--KJ 83:_#BD- 2 ">-3&%(dNH&H J &HA( BD D`d&%-38 efgih ACBD:-5E& L &H &%_#BM!BM + 2BD(:&H!BD8f!"X215BOW] 2:WM&%( 213&%()( "Y, ,&H!BM L BMBD8 WCK& `L# XZY Q#tpcdI3&H2 ">- L Q TO ,&% RD !O"%A32&%:-5BD8[WC?G& Yp&% '&%-F&HA !! ^&%W]SA J 9&%_\:( !">-3)&%-FBDcdI3&H2 ">- ,g 210:- D -3:!BD( U _/&%-aUGW]">- !BM 2NH&H2 ">- (:&D,g X&%-380,=&% 2I5Au !BDc.I3BD-a2( U085BM N%BD8 $@ 2">_ L 1.Ud :WM&%( L :-WM L ( BD \WC&ZY Q 3"% r&[83) 2WMI3 2 2:">-G"%$ 215B L 1.Ud :WM&%( 2BD( BMNH&%-3W]B"%$ L Q xO )-G215BnW]">-.!B]zK\"%$g,=&H!BM \,=&DN%BD \,Be 2BM$@BM !"]W " ` ",G# Y QptpcdI3&H2 ">-6L Q O &H : !BD g&%(: !"\&% T&\_\"d85BD(C$@"% g-5">-(::-5BD&H +,=&DN%BD 9:W]UK(::-385 ^:WM&%(a& z5:&%(:( U !Ud_/_#BM! :W=1.U L BM 2BD(:&% 22:Wp "d83 D`%,g 21 ;LSO^NTQ O 2B L 2BD !BD-.2:-5E 215BS &%8:&%(R !! 2BM2W^1n 2BD(:&H2:N%B'!"/& L BD !! 2BD 2 !BD8e 22&H!B\WC#U_T Y Q tpcdI3&H2 ">- L Q RO 13&% L (:BD-a U'"%$u !! ^I3W]2I5 2B2 BD8X:-.!"9 MQ* ) b&9 2B]J B]z L 2BD 2 ">"%$R215B9E%BM"d83BD 2:WH`3"Y, :-\213BhE% 2">I L "%$W]">_ L 2BD 2 2 Au( Bg83baCBM">_#"% L 13: 2_\ "%$215B WM WM(:BcWC&L" Y `Id2I3 !O(: 4%B215BXtpI3(:BM 9BDcdI3&H2 ">-s: O&%- B]z 2BD 2 2:">-V"%$215BXE%BM"d85BD :W `3"{, :-_#"% L L 13: 2_\ \"%$'215B !"% I3 eWCZ# Y Q D3BD13 p) p215E%BhBM">q_#BD&%BM !! 6^:9WSW]:-.2 !B">M-f L G 2BM 2&)-3H2WM ">-e( Bf(:BDW &%XZ83Yh g!"&\ !2&& HL!Bh 2"d"%"%$R$212133Bh&H !+BUKD !cd!BDI3_~&H2 :"> - ! L &%-Q !$PO"% 2 ^&H_#2)BD w8 J L !"n&%-5"%215BM '-3BD&H 2A.U !2&H!B#215 2">I3E>1[&fI-3:cdI5BD( Un85BM!BM _/:-5BD8i`3"Y, 21&H'_\:-KJ :_\:lMBD #215BVBD-3BM 2E%U%Q 3"% e&G()&H 2E%BZWM(:&% /"%$':- 2:&%(+83&H2&K`TBDcdI3&H2 ">- L Q XO : "
&
&%-7:- Du-3 !B]J 83:_\BD-3 2 ">-3&%(pW]">_ L ( BM!BD( U :-.!BME% &HA( Bi9&%_\:( !">-:&%- !Ud 2!BD_ gA.U _#BD&%-3 x"%$+&%-G: !"> L BDW]! ^&%( L 2"%A(:BD_ ">-5B/WM&%- W]">-aN%BM 2215B/BDcdI3&H2 ">-G:-a!"Z&%:- Du-3 !BX !BDc.I3BD-3W]B#"%$+(::-5BD&H S"% 8:-3&H 2UV8ba BM BD-a2:&%( BDcdI3&H2 ">- S,g13:W^1[WM&%-FACB ! NK:&%(:(:Us)-a!BME% &H!BD8 Lj$@"% #215B L BM "K83:W\WM&% 2Bn !BMB@W BA ` ##ZY `p&%-38 $@"% \&% L BDW]2 "%$g213B8 2BDW] :-.N%BM !B 2WM&H!!BM :-3EF !BM@ B W "3` ?K` # ` #KK`",#d`^",KGY O2Q0mZ"% 2BM"YN%BM D` 215B9;+&%_\&% 2 2& !J h">(:_ BDc.I3&H2:">-/WM&%-\ACBT BDWM&% !:-.!" 9&%_\:(:!">-3:&%-X$@"% _ :-\ ," 83b aCBM 2BD-.+AI5TW]">_ L &H2 A( BS,=&DUK MQ 13: =A !J 9&%_\:(:!">-3:&%- !! I3W]2I3 2BSE> N%BD T ^: !B !"Z&%- :- Du-3 !B\-dI3_xACBM "%$TW]">-3 !BM 2NH&H2 ">- (:&D,gc WC&K` Kd` X_Y QnuI5 2215BM _\"% 2B%` 215B 2_#"d"%21e !">(::2&H 2U/,=&DN%BD g"%)$ L Q Op&H B' !">(: !">-3 WC#K3/` ",#GY Q 15Bx;=&%_\&% 2& !J g">()_ BDcdI3&H2 ">- _#"d83BD(: S,=&DN%BA3 2BD&H4K:-52 E WC&5^` KK` =K` % ` "3` K5` Td` #=K^` &?5^` &KK` K#ZY &%-38e&%83_/ 2 +,=&DN%B 2">(:I52 ">-3 =21&HTB]zK) !T:-385BB Du-3 !BD( U\:-2)_#B WC=K` % ` &d` KZY Q qBMTI +&%(: !" L ">:-.">I5+21&Hg&% 2 !"KWM:&H!BD8e!" L Q O215BM 2B': +&X,g13">( BS13 BM &H W^1aU "%$ :-a!BME% ^&HA( BSBDcdI3&H2 ">-34 WC?UTK7` &&ZY Q
3K58-/7: ,+2 #%7/#
%9$ L &H 22:WMI3(:&H X:-.!BM 2BD !X&%_#">-5Es215Be !">(:I32 ">-3 !" !">(:I32 ">-3
L Q O'&H 2B! &DN%BD(:)-5EZ,=&DN%B ;LSO?NTQ O J LSO\> Q O N gih$N $@"% 2">_#BZ$jI3-3W]2:">- g`h h+Q 15BD !Bs&H 2B ,&YN%BD e213&He_#"YN%Bs,g:215">I5 W 1&%-5E%B"%$ 13& L B',g 21ZW]">-3 !2&%-.9 L BMBD8! {Q+*w-Z213: +215BD : T,B&H BW]">-3W]BM -3BD8 ,g 21V83baCBM 2BD-a9&% L BDW]2 g"%$p! &DN%BD(:)-5E/,=&DN%B# !">(:I32 ">-3 +"%$213BX;=&%_\&% 2& J!g">()_ BDcdI3&H2 ">-RQ @["%$B*! - 2&Y15;=N%"YBD13, (:&:-5L 21Ef!B3M&H,= M`&D#ON%)21BD-G5 OBh&%,g,83 8321BD &H:24# 2">:! -3-F E>&Y!"I3N%sBD(:&H(: 2: -5_# 2Ex:"dBD,"% D21g&Y0N%BD 2BD ">&H"%(:4%I5$R">2-3BD ">cd D-3I3`C D&HWM`b2I 21 ">5-_BM"> -3L Bf MQ `u&H 2 2O 2IB&H3 & _ Bh_WM">(:I3&%-3 2(: M2 ` E2I3D &%3BD-3858R8 B Q L L L W]">_ L "> 2 !BO,=&DN%BD MQ* -@WCG& Y =,&% T-3"%!BD8213&H L Q pO &%83_/ 2 L BD&H4%BD8n! &DN%BD(:)-5E ,=&DN%BD L L BD&H4%">-3 BO'Jx !BMB6L" 8O&%-38 L"#POx"%$h E>I3 2B Q Q?* #,=&% \ 2I3A !BDcdI5BD-a2(:U "%A !BM N%BD8r213 2">I5E>1 L 13&% !B]J L (:&%-5Bh&%-&%( Ud : `|L 2BMB WC& Y O 21&H=&%() !"#WMI3 L BD8/,=&DN%BD B]z5: !\J %L $]#O &%-38 %L &;O "%$S E>I5 2B Q Q('9 2:-3EG&0-&H2I5 &%(T,BD&H4?$@"% _ "%$S215B ;=&%_\&% 2& J!g">()_ BDcdI3&H2 ">-R` ,BpBD !2&HA(:: 1SB]zK&%W]2(:UO)-S,g13&H 2BD-3 !B215BD 2B L BD&H4%BD8 &%-38FWMI L BD8s,&YN%BD &H B/ !">(:I52:">-3 MQ#*w-[$@&%W]M`,B/WM(:&% 2 2:$PUs&%(:(! &YN%BD(::-5Ee,=&DN%B !">(:I32 ">-3 "%$R213: ,BD&H4#$@"% _I3(:&H2 ">-#"%$ L Q 2O Q* 2I5 ^-3 ">I5213&H215BM 2BhB]zK) !2 & L (:BM215"% &e"%$+-5BM, L BDWMI3():&H ' !">(:I52:">-3 S"%A32&%:-3BD8[A.U[W]">_A:-3)-5EnWMI3 L x&%-38 L BD&H4d O:-.!"! &DN%BD():-5E,&YN%BD OJ *L )bTO "%$p E>I3 2B Q Q6h-3"%215BM '-5BM, &%-38s:-.!BM !J BD !2:-3E/WM(:&% 2 h"%$,&YN%BD 9J,g1:W 1e,BXWM&%(:( !2I_ ">-3 +ACBDWM&%I3 !B"%$215BD h 13& BSJ L
L
K
: "%A32&%)-5BD8#AdUX)-3 !BM 22:-3E9:-.!BM 2NH&%(: ,g13BM 2BZBDc.I&%(: &'W]">-3 22&%-a&H215BgW] 2BD 22 "%$ 2I3 2&HA(:BOWMI L BD8,&YN%BD TJ 2BMB LOp"%$ E>I5 B Q Q * -s15B';=13_\& &H!B!BMM ^ :&%?X( L, 2BBD 2 !BD2I-a3!B83DUf8n21)3-VB ;=13BM& L "K!B83M:` W #\:BD +&H4%W]">BD8V-a2&! % )&Y-5N%BDBD8V(:::-5@- E/W ",XG&YY N%Q BD MMQ @[B D ! L L L 215"{, 213&H'213B L BM ^ "d8:W L BD&H4%">-3 x&H 2B/ !">(:I32 ">-3 9"%$+&N &H )&H2 ">-3&%( L "%A( BD_eQ 21515B B L BD1.&HUd4%"> :-WM g&%(WM&%)-a- !BMAC BxL 2WMBM(:2&&%H 22 2 ">D3-0BD8n"%&%$g 9213_\: :-3NH:_/&H &:&H"%2 $">W]-3">&%-(= !W^! 13&%&H: -5&%BDW]8V!BMBD -5 lDBM&H 22E%:U%">Qg-76 : 2212&3%-K&HJ L 83&H 8 L :-3WM L ( Bh:- L 1aUK 2:WM +&% 2 2BM 22 T213&Hh !2&H!BD g"%$ ( "{,BD !hBD-5BM 2E%U&H 2Bx !2&HAu( B%Q mZ"% 2BM"YN%BM D` -.I_#BM :WM&%(C 2:_I3(:&H2:">-3 I5E%E%BD !+213&H+215B' lMBD +&%-38N%BD( "KWM 2 BD ="%$ 215B L BD&H4%">-3 +85"X-5"%+W 13&%-3E%B'&% +& BD 2I3( "%$bW]">(:(): 2 ">-f !"X213&H=215BD !B L &H!!BM - &H 2BB]z L BDW]!BD8s!"fACB !2&HAu( B%QO3"% O215B L BD&H4%">- h!"ACB L 1aUK 2:WM&%(:(:Uf"%Au !BM 2NH&HA( B : p-5BDW]BD 2&H 2U\213&H215BD = 213& L Bh 2BD_\&%:-3 & L3L 2"YzK)_\&H!BD( U#215BO 2&%_#BO&% 2:_#B BMN%">( N%BD MQ 15BM 2BM$@"% 2BS215B' 22&HA:(: U/"%$ 215B L BD&H4%">-3 h: ="%$ E% 2BD&Hg:-.!BM 2BD !MQ 6 2_\&%(:(uW 13&%-3E%B9:-\215Bh 21& L Bg"%$& L BD&H4%">-fWM&%-/UK BD(:8\&%-3"%215BM ">-3Bg,g 21r& 83b aCBM 2BD-.h L BMBD8RQ 15B& L3L 2" L ^:&H!B-5"%2:">-V"%$p 22&HA:(: Un: h215BM 2BM$@"% 2B21&Hh"%$ "% 2A:2&%(5 !2&HA:(:: %U gb& L BM "K83:W,=&DN%B9,g 21#&%-/)-3 2:&%( L 2" Du( B+WM( "> !BT!"& L BD&H4%"> 2BD_\&%)-3 XWM( "> !Be!"F !">_#Be! ^&%-3 2(:&H!B"%$O X$P"% \&%(:(+()&H!BM #2:_#BD MQ 13&H#: M`p215B 213& L BX"%$=215B\,=&DN%Br 2BD_\&%:-3 S& LL 2"Dz5:_\&H!BD(:UZ215Br 2&%_#B\$@"% x&%(:( 2:_\BD MQ\* ': 4K-5"Y,g - WC#&ZY21&H L BD&H4%BD8G! ^&DN%BD(::-3EV,=&DN%B !">(:I52 ">- S"%$ L Q Og,h13:W 1GN &%-: 21 &HO:- D-3: U&H 2B 22&HA( B%Q @[B#W]">-3 2)85BM g215B L BM "K83:WSWM&% !B#&%-38Z 215"Y, !2&HAu:(: U "%$215B L BM "K83:W L BD&H4%">-3 MQ * -715BS;= 213BD& I3!B( M2 +:"s-V,;=Br1&2I5L ^!BM-F` !"?#sWM21&%5-VBA 2BO_#$@"d">"%I321-3G8e! : @- &YN%W BD"\(:TG:-5YE &%-3,=8 &DN%W ",BD=Z MY Q Q @[BBD !2&HA(): 21 L &\W]"% 2 BD L ">-385BD-3W]B'ACBM ,BMBD-Z 2_#"d"%21n! &YN%BD(::-5E\,=&DN%BX !">(:I32 ">-3 +"%M$ L Q O&%-38 ! &YN%BD(::-5E#,=&DN%BD h"%$ 215B S"% 2!BM,BMEHJ 85B d ^ BD L '8 d OpBDcdI3&H2 ">LN#dQ O ;=6KG;=;=BHEM;ABDBDB4J A N O gih$NHQ6R A -5">15-3BO():,-5BDBD(:&H( J 4K -5U#"Y&%,h-3- 8ex838: d BMBD cd I3">&H-X2 J">13-f&%J =21&H5!B'! &%:W]_ !BDL 8n( BDBD 2B-3"%D cd_#I3&H">2I3 "> =-&H!BD!B_D-.AC2"d ">85-eUK:"Y-5N%EBM gAC"%21521 B L U%BD&H T&%-8f1&% + !BM 2N%BD8e&% +215BS_#"K85BD( BDcdI3&H2 ">-$@"% +215BS85BMN%BD( " L _#BD-.+"%$b 2">(: J !">-I3E>1 & W]">-3-5BDW]2 ">- ACBM ,BMBD- 215BZ: 2"> L BDW]! &%( L 2"%Au( BD_\ =&% 2 !"KWM:&H!BD8e!" L Q Op&%-38 LN#dQ O2`3,B'W]">-3 !! IW]T&#-3&H2I5 &%(R_\& LL :-5E 2&H4K:-5Ex 2_\"."%21r! &DN%BD():-5E',=&DN%BD ="%$C215BS;=&%_\&% 2 2& !J h">(:_ BDc.I&H2 ">-r)-a!"'! ^&DN.J BD(::-3E,=&DN%BD h"%$215B '8 d BDcdI3&H2 ">-RQ 15B'_\&H!BM ^:&%(:-V;=1& L !BM "/: =213BxW]">-a!BD-.g"%$$ WC& A Y Q
T
(a) - Smooth periodic
(b) - Smooth with decay
(c) - Periodic peakon
(d) - Peakon with decay
(e) - Periodic cuspon
(f) - Cuspon with decay
2
(g) - Composite waves (a < c + 4ck)
(g) - Composite waves (a > c 2 + 4ck)
2
(h) - Stumpons (a = c + 4ck)
9176; -)- 79 829 %'#&% "!$#&%'#)("*+ , - /. 10'23 / L54bO >L O
$M
$
. =:.5 8+ 3 5 7/+H:
*w-n213: hW 13& L !BM 9,BX85BM!BM _\:-3Bx&%(:(b! &DN%BD(:)-5E/,=&DN%B# !">(:I32 ">-3 M` |Q B%Qg !">(:I32 ">-3 "%$215B'$@"% _
; LSO?NTQ O J LSO\> Q O N gih$N $@"% g !">_#B'$jI3-3W]2:">- @g,h h+`"%$ 215B;=&%_/&% 2 2& J!h">(:_ BDcdI3&H2 ">L Q O ;=@;A-3 M`,B,g:(:( 2BMB213&HO215BM B&H 2BX&f_I3(:2 2I385B "%$! &YN%BD(::-5Ef,=&DN%BD O,g 21 2:-3E>I3(:&H 2:BD Dg L BD&H4%">-3 D`CWMI L ">-3 M`u 22I3_ L ">-3 M` &%-38
]W ">_ L "> 2 !BS,=&DN%BD DQ * - I BDW]2 ">-3 #dQ$#O&%-38 #dQ$?K`>,B+:-.! 2"d8I3W]B 2">_#BT-5"%2&H2 ">-#&%-38X85BM ^ N%B+&h,BD&H4 $@"% _I(:&H2 ">-r"%$b215Bx;=&%_/&% 2 2& J!h">(:_ BDc.I&H2 ">-RQ*w- I BDW]2 ">- #dQC"#,BS !2&H!Bx">I5 _\&%:-x215BM"% 2BD_ g &9WM(:&% 2 2E DuWM&H2 ">-x"%$215B! ^&DN%BD(::-3Eh,=&DN%B+ !">(:I32 ">-3 "%$BDc.I3&H2:">L Q O2Q 15B L 2"d"%$h: XW]">-.2&%:-5BD8?)- I BDW]2 ">- #dQ$&KQG*w- I BDW]2 ">- #dQ$Ks,Be 215"{, 213&H215Bp! ^&DN%BD(::-3Eh,=&DN%BD 85B L BD-38W]">-a2)-.I5">I 2( UO">-&%()(.:-.N%">( N%BD8 L &H &%_#BM!BM ^ MQ :-3&%(:(:U%`=)- I BDW]2 ">-f #dVQ TG&%-3
8 #d$Q =K`T,B 85BM!BM ^_\:-5Bn213BZ,=&DN%BD( BD-3E%21 "%$S215B ! &YN%BD(::-5E#,=&DN%BD 9&%-38n85BM ^ N%BSB]z L (::WM =$@"% _I(:&% =$P"% g215B L BD&H4%BD8n !">(:I32 ">-3 MQ
.
,+5%65 7/+H:
q BM h7ACB&%-X" L BD-# !BMMQ@[BT85BD-3"%!B%`>$P"% )-a!BME%BM N `>AdU "! #/L O 215BF L &%W]BF"%$&%()(O$@I3-W]2 ">-3 & g$ # L O/,g 21 83) !! AI32 ">-3&%(g83BM NH&H2 N%BD
=
X
B &Jg $ # L Ox$P"% J N N Q7* $ J #d`=,Be,g !B L6O:-3 !!BD&%8 "%$ ! L6O2Q 15B h)( ACBM 2 L &%W]BD 7L6Op&H BSBD-385"Y,BD8e,g:21r213B':-3-5BM L 2"K8KJ I3W]2 &%N ) J $ L B &;O LSO ObL B )bO LSO O # O @[:- BxG ( BMQ*&% ( ) ' LL 6 O Op83ACBDBS-5"%215!BDB = 21L 5&%B`W]B'9"%: !( #"$ AC 2BM_# 2 "d"%21&%eW]B9$jI3"%-3$W]&%2 (:">( -3&n = 2,hI3W^ 211/e21W]">&H_ /.L &%& W]9 g2 I L3 L L"% 2O L $@"% g&%(:(C!BD+- !, T$) jI3-3W]2:">-3 . g0% ) ' L O2Q I5 2213BM _#"% 2B%`,Be( BM21439L O'A Bf215Bn L &%W]Bf"%$983: !! ^ AI52 ">- S">- G`|Q B%Q (::-3BD&H xW]">-a2)-.I5">I '$jI3-3W]2 ">-3&%() S">-5% ) ' L6 O2Q6% L6 OS85BD-5"%!BD 215Br &%W]B/"%$ 2:_\BD W]">-.2:-dI5">I3 2( U[83Ca BM 2BD-.2:&HA(:B#$@I3-W]2 ">-3 '">- G QV* $Wg71203 LL6 O2`,B 7
,T :!B ^B#$@"% g 2 T8: !! AuI52 ">-3&%(u85BM NH&H2 N%B'85BBD-3BD8A.U
^B N98:(J > N98 B/N 8 g0% ) ' L6O N ,g15BM B ; N ; =: +215B L &% :-5EXACBM ,BMBD- &LON O D HJIK KQP $@"% T&%-aU Z&%-8e&%-aU83: d!">:-.W]">()( BDW]2 ">-"%$b 2BME>_#BD-a2 LON I NRL I O N LON NRL Op:C ,g15"> !B'(:BD-5E%213 T 2&H2) !$PU LML >SN O F !JI P 6 $@I3-W]2 ">- & : T&HA !">()I5!BD( UrW]">-.2:-dI5">I3 +">- v $ &%-38">-3( U $&_g I ! I L O2Q *w-?213: /WM&% !BZ213BZWM(:&% 2 :WM&%(g85BM ^ N &H2:N%BV"%$ & B]z5: !2 r&Hf&%(:_\"> !/BMN%BM 2U +T, ) L ">:-. O g &%-38BDcdI3&%(: T215Bx83: 2! AI52:">-3&%(85BM ^ N &H2:N%BS"%$& L|W]$ QHWC?#ZY O2Q @[@[BB/( 2BM&Y/UUZ[213AC&HB'&qeBMA W]">BD 2-aE>2I5:-dB'I5_#">I3BD O&% 2$jI5I3 -3BSW]2">:-">- h=4KI3 T 9&H$@ 2IB'-3WMW]&%2 (:">( BD- 8 ?. : W OV& 2 &%0 )8V !"e,13 &Y"%N% B\. & 6 W* V?2 / . Q &HfO[ $
BA
: 2_#"d"%21n( "KWM&%(:( Ur">-eAC"%21n 2:83BD ="%$ O &%-38 (:)_ B ?B L]\bO J >n():_ B ?B L]\bO J`_(a Y9Z Y9^ @[B'* $ ,g )(:(C: \WM&%"%(:(RA3,=2&%&D:N%-5BDBD h8 ,gA. U721e:-3WMI3 2BM 2L 2 :-5* E[?2 /&%. - 60 )-a !BM 2NH&% (T"%: -?* ,g?2 /13.: W^1 Q : \W]">-3 22&%-a&H &sWMI3 L `213BD-0,Be 2&DU0213&H 1&% #& M?7 . QF* - "%215BM #,"% 83 D`215BM 2Be: &%:-.!BM 2NH&%( W 4=N Yb">-n,g13:W^1 : +W]">-3 !2&%-.h&%-38 G) T 2_#"d"%21n( "KWM&%(:( Ur!"\215Bx( BM$@ "%$ 4f&%-8!"\215B' :E>1a+"%$ AI5 ()B :_ B LSO O J >n()B :_ B LSO O J`_(a Z ^ @F&D* N%$ BDF h:,g 21215VBO ! 22I133&_ L B9 ="%,h$b:&(:(u,A &YBSN% B%BM`3$P,BM 2B9 BD,h8e:(:!"(/WM&%&%() ( &% M-.?U 7 . "> : -. p,Q h15BM 2B F13&% =&X( "KWM&%( L L _\& z5:_I3_ & * - , Q+6 L ">:-a+,h15BM 2B 1&% g&/(:"dWM&%(_/:-3:_I3_ ,g:()(uACBxWM&%()( BD8 & - ?& Q @[B9 2&DU#21&Hs: & 0 6*6 @ :$u215BM Bg: &'W]">- !2&%-a N gih 2I3W^1e213&H]>SN g I L0h O Q
.
+ ? ! 3 -/65 7/+H: 3"% 9&#! &DN%BD():-5E#,=&DN%BK;;LSO?NTQ O J LSO\> Q OpBDcdI3&H2 ">- L Q pO 2&H4%BD g215B'$@"% _ LN?dQ O > ?BHE ^BDBDBFE ? ^BHE #Ue ^BKJ # ^B ^BDBE ^BDBDB
6h$P!BM g)-a!BME% &H2:">-n,B'E%BM LN?d$Q #/O > cE BDB E #? E #Ue @J BDB E # B E 4# N $@"% g !">_#BxW]">- !2&%-a 4fg h+Q`@[Bx_\&YUf BM,T !BS213) +&% LN?d$Q ?/O B E ? E L0"\e > # 8O @J L i> 8O BDB E 4 3"% LN?d$Q ?/OO!" _/&H4%B 2BD-3 !Br: 2I rW]BD 21&H Wg +-I , ) L0h O Q @[Be_\&H4%Bf215B $@">(:( "Y,h:-5E#85BB D-3:2 ">-RQ
- 7 ^ 8 9? 7 & ' 0 ? ) * ' ! g% )( +TI , ) L00h O + ]= ? -5 ) ) ) ) %
!
7 + "
%
-,BD&H 34f*P$@"% a _ ' &%0 tc.I3&H2:">- L Q hO ) O"%$P!BD- |L !BMB\$@"% xB]z5&%_ L ( B WC# Y hO ,T :!!BD-F:LNd? QC" O ;A B O I ; E # ; B E #UeI; B J A "%$M15LNBXd? QC 2"PBD=O &% 2:"> +-F213,&HB#h212&5H4%BxB_" LN?dBMQ$ ?/&HOh!"%&% xL 85BB>D-3 2 :O "> -ZI "%:$ T,BD&%BD !&HUe4 !"! f^&D83N%BBBDD(::-5-3BSEe,g,15&YBDN%-]BD ;LS:-O^ !NT!BQ DO=&%:8 B L BL M "K83:W"% 1&% p85BDWM&YU\&H:- Du-3 U%`aAI5 LN?dQ$? O: pW]">-.N%BD-3 BD-.p$@"% &x,g:85BM pWM()&% 2 "%$5! &YN%BD(::-5E9,&YN%BD MQ3"% L BM "K83:W ! &YN%BD(::-5E9,=&DN%BD &%-38! &DN%BD():-5Eg,=&DN%BD ,g 21 85BDWM&YU&Hh:- D -3: U%`K215B' ,"/83BBD -3 2 ">- W]">)-3WM:85B%Q * -85BMBD8R`. I L3L "> !B;LSO^NTQ O J LSO.> Q O : L BM "K83:W"% 13&% p85BDWM&YU\&H)- D-3 U &%-38e 2&H2) 3D BD LNd? QC"b2O Q 15BD?> E # E L > B O I E # B E #UIe ; B J A :- 1 3 L0h O 6 83: !! :AI52 ">-13&% lMBM 2"x83BM NH&H2 N%BT $u&%-8#">-3( U $u ) &SW]">-3 !2&%-.`L|W]$ Q$W " A Y 2O Q 15BM BM$P"% 2BS213BM 2BSB]zK) !2 T&%- 4fgih I3W 1e21&H > E # E L > B O I E # B E #UIe ;J 4 )- 1 3 L0h O 6 L3L ( UK:-5EFL > B bO !"AC"%21/ 2)85BD E> N%BD [LNd? Q$?/2O Q;">-.N%BM !BD(:U%`d $ s 2">( N%BD `LNd? Q$? 2O ` 215BD-e! ^&%WM:-5E#215BD !B !!B L +A&%W 4.,=&H 83 gUd:BD(:83 LNd? QC"P2O Q
"
. -9$#%#%7 65 7/+H: + 8H -7/:
. #
%OI5I [L0D3h O2 2`Oh"%21$F5BML "% Q BD_ O2Q?WM* (:\&% 22I 25 D3 -BD h X&%">()I5(b#AC">213I3&H-M`85=BD$P8V"% r! ^&&DN%D5BD(:zK:-3BD8 Ef,=e &DgN%BD h+`9 LS21O 3Be> ! Q&DO2N%` BD (:)-5g E
,=&D+-, N%) BD x&H B L &H &%_#BM! ^ lMBD8sA.U 215BD '_/& zK:_I3_e`b_\:-3:_I3_e`C&%-38F L BMBD8Q"% 83b aCBM 2BD-.TNH&%(:I5BD h"%$215BD !B L &H &%_#BM!BM D`C8ba BM BD-aT U L BD 9"%$,=&DN%BD S&H : 2B'J+ !BMB E>I5 2B Q Q
( - -/)b - ' 0 ! # %'e #)( g h ' 0 / J . > #U) e\> > *+ %/ , 5@0 ! =+ ?0 0 5L 4PO !#" 7 . ) +5 05*(%$'& (' ) - ' " +7 . , 0 * - ' LSO > Q O P ! # P %'#)( P J _\:-IB*)(+ LSOO 0 J _/& zIB*)(+ SL OO
#
L O #! " 7 LSO > Q 0O 6 *6 @,! ( # %'$'#)( J J :-5$ *B ()(' + LSO O ' +J 7 _\ && z B* ) -+ )LS OO ' P P
0 +. 5 A@ O _(a % L" 8O ! - ) +5 '05* . WV LS O ( > $'& Q O ! # %'#)( J ( ' J _\ :-I' B*)( + . )LS +O5 O 0 5*0 . WV& J 0 P P _/& zIB*)(+ SL OO L"# O ! 6 W V SL O > Q O 0 6*6 ! @,# ( %'#)$'( J J :-5$J B*)( + ' SL O O ' ' J . 6_\ WV& 6z 0 B* ) -+ )SL OO ' P
0 +. 5 A@ O _(a % %L $]O ! ) +5 05* * ?2 /. ( $'& ' ) - ' . , 0 * * ? . 0 - ' LSO > Q O P "! #&P %#( P "J _\:- B*)(+ LSOO 0 KJ _/& zIB*)(+ SL OO L%&;O ! ?2 / . SL O > Q O 0 6 *6"! @,#( %'#)$'( J "J :-3$ B*)(+ )SL -O O '' K J * ?_\ . & z 0 B* ) -+ )SL OO ' P P
0 +. 5 A@ O _(a % L54 3 O !# -" 7 ' . ) +5 0 5*LS(%O $'> & Q OR ! #R %'#) ( R (' J ) - _\': - B* ") + +7 LSO O . 0 , 0J * _/& zIB*)(+ SL OO L [3 O !#" 7 SL O > Q O0 6 *6 ! @,( #&%$'#( J R J _\R :- (B*' )( + SL OO ' +7J 2 &I - )SL OO ' L B*) +
0 +. 5 A@ O _(a % "L 39O ! ) +5 05* . WV ( $'& R R J (' ' . ) +5 05* . WV& 0 - ' LSO > Q O ! # %'#)( J _\:- B*) + LSOO 0 J _/& z B*)(+ SL OO "L # 3 O ! 6 WV 0 6*6 @,( $' J R J ' ' . 6 WV60 - ) SL O > Q O ! # %'#)( J :-5$ B*) + SL O O ' J _\& z B*) + SL OO '
0 +. 5 A@ O _(a % %L $ 3 O ! ) +5 05* * ?2 /. ( $'& R R R ' ) - ' . , 0 * * ? . 0 - ' LSO > Q O "! #&%#( KJ _\:-IB*) + LSOO 0 J _/& zIB*)(+ SL OO
?
L%& 3 O ! 2? / . SL O > Q O 0 6 "!*6 @,#&( %#$'( J 4R J _\R :- B*)(+ )LS -O O'' * J ? 2. I 0 - )LS OO ' L B*) +
0 +. 5 A@ O _(a % *L )bO ! 7 . , 3 ( @ 0 gWh 0 4 R > ) ' ? 5 L05" Q O 4 J > ,> L E O L" $> #Ue > > O N 0, * +]=+ . L eN 4O . 1 *+) ) N )
0"7 ) ' ' 0 -6* 5 L NV> O )6 >?2 8%'# %
@ L*+ e ,N - /.N 81O 0g '2 * ?2 /. . WV *6*6 0 / R "L O > %L &;O 0) -""L 3 O > P %L & 3 O % *6 ? / >= " ?7 =+ " "* ?2 /. 0 . WV *6 , - /. 0 / . L eN N 8O =, / 7 . ) ' 7 B@ =+ ) 1 0
& )' * - , / ) ,79 *6 7 . , )+ *L )7O B? - #&%#&% $' =+ B? 7 ?2 U L I "L 8O O J A ' ) ' - ) - ! #&%#(% L O . !#" ' M? 7 .L e N( N 8 O JW4 L"J ZN 8 O 4 E 0 "\L e e N N 8O JW . L" Z3NV> > ! #U%'#)eb( O % *+ /' . )
@
+* , - /. 10 / ) *6 / 7 ) + " % 2 #&%#&%
? >= A@
U L I L 8O O6R L O >?
A
?
=
=
=@
* 2 /. % , *6 7 . + / 1 0
) * 2 . &*) 0 % ' - ) - ! #&%#( - '" * ) .1 - ) 0
@
?
?
"
&%W]" BrE%"%BM$ e&&H &%E%_#BM">BM_#!BMBM ^! ::WM-.&%!"(SVI 2-3I385ABM ! BM !2 2&S%-J983BD:&%-5W E[1 "% 2$ I5Au !15BMBMxW"%] 2"%BD 2_ 2BD d# Q ">-,83B[:-5Ee83 !"NK :85&VBV83215 $PB J L L L $@BM 2BD-ae,=&DN%BG U L B%Q qBM6L eN N 8O g h A B[W]"d"% 83:-&H!BD e:- h &%-8 ( BM J > #U]e > > sQ 15BZ215 2BMB L (:&%-5BD J >` J >`h&%-38 ( J 83 NK:85B h :-a!"/BD E>1ah"dW]2&%-.2 9,g 21ZW]"% -5BM h&H LT>`e&NV>`e&NV>[ebO2QM@[B
( BM !0&%-8" ACBS ,"/"%$215BD !B'" L BD-n I5A !BM2 Dg
J N J R R R N ,g15BM Br,B,T !B P P P n:-3 2!BD&%80"%$ ,L eN N 8O g h g >QF>h"%!B\P 213&H P [J P : S !UK_\_#BM! ^:WX&H 2">I3-38s 2 SW]"% -3BMP P P #
$
%
%
(
)
&
'
L,gT>` 21e&/NV>`213e& NV8r>[W]eb".O2"%Qx ^mV83:"%-3 &HBM!B"YN% gBM D:`b $P&"% O! BD:&%&%W -51 E>(: BT`RJ21 !5BMB#BhW] 2 ">E> I3 wJ 2 !B BD#dW]2Q ">Qp-s* -r"%$$@&%&%W](:M`( L ">:-.2 9:- R >`e r&%-8 >[e >Q 15B\WM&% 2BD 5L 4bgO 2BD L BDW]2 N%BD(:U 5L 4 3 hO :- 13BM"% 2BD_ d# Q "KWMWMI5 TB]z5&%W]2( U,gP 15BD-6L eN N 8O)g 0 2BD L BDW]2 N%BD( U L eN N 8O g Q SOBD-5"%!Bx215Bx215 2BMBS ,"HJ 83:_\BD-3 2 ">-3&%( 2:85BD ="%$ FAdU !
"
" !
I J J N iJ ( J N J J N ,g15BM B n: 215B+AC">I3-83&H 2US"%$ Q qBM I iJ J ( J @[B 13&YN%B L BD&H4%">-3 O$@"% FL eN N 8Og:- 7&%-8Z,=&DN%BD ',g 21 85BDWM&DUs $ L eN N O g pQF%S-s215B\(::-5B 7215B\ !">(:I32 ">-3 O&H 2B L BD&H4%BD8[,g 21s85BDWM&YU%Q >g"%!B/213&H $@"%I J >[eu` 85BME%BD-5I BM ^&H!BD 9)-a!"f& L ">:-.MQ 15BM 2BM$@"% 2B%` $ J >`eu` 215BM 2B&H 2B
-5" L BD&H4%BD8n"% h 2_#"d"%21e! &DN%BD():-5E\,=&DN%BD gJ">-3( UWMI3 L ">-3 =B]z5: !MQ -O 3>*P a LT>' O 'O: p>h&"%2! : W]&YBxN%21BD(::&H-5hE ,$ &Y N%LSBOOO"%$ ) gL &#Q ! O &Y,gN% BD21(:f:-5euEr`d, 2BD&Y N%BBD"%W]2$M N%L BD(:Q U O2 {`u`K21 25B BD-V(:&%&%W]()BD !8" L L Adi U >`eu`5 BD L BDW]2 N%BD( e U > Q* - L &H 22:WMI3(:&H Y`d213B' 2B L (:&%W]BD_\BD-a2 L0"5$Q #/O L LSOO N ZN eN N ebO LT> LT>OO NV> ZNV> eNV> NV>`ebO N ! &%-3 2$P"% _/ 215B= !2&H!BD_#BD-.2 L54bO_> L%&;OC"%$ 13BM"% 2BD4 _ #dQ W]"% 2BD L ">-383:-3ET!" >`eu` :-.!"n215B/ 22&H!BD_#BD-a2 fL543 O > L%& 3 OhW]"% 2 2BD L ">-83:-5Ef!" euQr* -[213B/E%BM">_#BM! )WM&%( :-.!BM L 2BM2&H2:">-0213Bf B L (:&%W]BD_#BD-.2 iL0"5$Q #/O'&%_#">I3-.X!"F_\& L3L :-3E &%-38 W]"% 2 2BD L ">-83:-5ES!" eu`5:-.!" &%-38 W]"% 2 2BD L ">-83:-5E'!" >`euQ 13BM 2BM$P"% Bh,B _\&YU%`3$P"% h 2:_ L ():WM U%`5&% 2 I3_#B >`euQ " "KW]2&%"[-a2 E%9BMBD">-3_\WMBM( ">! 2 BD:WM8V&%(:Ad( U U21855BDB 2W]21 3:A 2BMBfB ,g15()&%BM-5 BfBD 213 BJWMI L >">`-3 "dWMJ WMI5 Y >`` ,&%Bn-38 (:"."% 4 J &H# 215 >B Q L qBMg ,"\"%$ 215BD !B'ACB J$ N J$ R R R >hqBM"%!B9 21&HJ [ J P J P >&%Q -3 P8 15 sB &H 2BMB9 8"K:83 d!:W=">:WM-aI3p, g"> 21-/ W]"d">WM_/WMI3_# ">,g-f13A BD-">IL -3 e83N&H 2U N O pg Q L L &%-38eI ,B'13&YN%BxWMI3 L ">-3 =,g:21f83BDWM&DUe $b&%-8e">-3( Uf $ L eN N 8O)g I I pQ
&
M
{m=z}
{m=c}
ns spo Cu
Co mp os ite wa ve s
yeca hd wit
∂ 1Σ + Peakon with decay - ∂12Γ+ {M=c}
-Π (a) Stu mp + on sΠ( c+ Periodic cuspons 4c 2 k) Σ+ +
{m=M}
Periodic peakons - ∂2 Γ+
(-k,c)
h wit th oo Sm
(c,c) a>
Smooth periodic
2
c+
Γ+
2
c+ k 4c
2
k
-3 13B]BMzK"%) 2 !BD+"_ >-e#dQ 215BxW]"% 2I5 2 2BD$j &%L W]">B-38ZL"!" (21E 5B"\e 8I5O2 2Q $j&%W]BD @ B13&YN%B > ,> L L E O L" $> #Ue > > O [ J "? L > $> ? #Ue 8O E L ,> $> ? #Ue O# E L > " O > L" $> ? #UebO hBD-3W]B%`3$@"% 5D zKBD8 ZN &e N&%-38 4cR > ) 215Bx 2BMT"%$)L eN JO &H2: !$@Ud:-3E 4 J > ,> L E O "L $> #U e > > O : &%-XBD(:(: L !B)-213B L eN 4|O J L ()&%-5B=,g 21XW]BD-a!BM ) N ) &%-38X_\&_d!"% p& z5: :-215B'8 2BDW]2 ">- L NV> 2O Q "> 2 "Z!BT !,=BMB\&DN%,gB%13`K,&HS4B9K_/:-3&H84% hBh"%215$=Bh,=$P&D">N%()( Bf"Y,g !BM)E>-5_#ESBD"%-.A2 !'BM 221NH3&H&H2xW ">M-3&% D-GQ*wAC-\BFNKd! ">BM:,-3(:U/215BxWM&% 2B R >`ue Q QptN%BM UfBD()(: L !BO&% 2 !"KWM:&H!BD8V!"/&%- 4 2I3W^1e213&H > "L $> ? #UebO # e >3e 4 E "\e P P P :-.!BM !BDW]2 &%-380W]">-a2&%:- xB]z5&%W]2( U[">-5B L ">)-a':-GBD&%W 10"%$+215Br 2BM2 &%-38 I pQ 15B L &H 2p"%$R213BgBD(:(: L !BT:- [: p& !! :W]2(:UX83BDW] 2BD&% 2:-5E$@I-3W]2 ">WMI5 2N%B:-'215B`L eN 4O|J L ()&%-5B%Q 15BBD(:() L !B85"dBD -5"%:-.!BM !BDW]b&%-.US"%215BM b"%$5215B !BM2 +_#BD-.2 ">-5BD8:- 13BM"% 2BD_ Q 1dI3 215BSW]">_ L "> 2 !BO,&YN%BD TW]"% 2 2BD L ">-83:-5E
#
T
!"F215BD 2BVBD(:(: L !BD X_\&DU?W]">-.2&%:- ,&YN%BZ !BME>_#BD-.2 r$P 2">_ L" 8O NL%$]O N=&%-38 L%&;Ox"%$ 15#dBMQ "% BD* _$ 4 Q J E "\e `g215B BD(:(: !BnE%"dBD 215 2">I5E>1-Q ?&H 2d2 Qxt"%$ N%BM213 UVBTBDBD(:(:(:(: L ! !BBx),h- 21 &4e%-3R8 PE &H"\ 2e Bh !! : -.:!BW]M2( !UBD85W]2 BDOW] 2ACBD"%&%21 2)-5E' ?&$jI3-3%W]-28 ">-# WMI5Q N%BD15 MB Q L L tp&%W^1F 2I3W^1 BD(:(: L 2B&%(: !"nW]">-.2&%:-3 O ">-3B L ">)-aO:- BD&%W 1["%$215B\ !BM2 I 2 !B/,&YN%BD W]"% 2BD L ">-383:-3Ef!" 4MR E"\e /WM&%W]">I -.2& %:-e,=&DN%BX !BME>_#BD-.2 T$@ 2">_ L%$]O NL%&;O NL%$ 3 O N&%-38 L%& 3 Op"%$ 15BM"% BD_ Q -BDcdI3 3&%(*P!" a 21'5BD Y >h15BD"% !BE>T1.21MQ3V&H6h&%() !(:"n( L "%BDA&H !4%BM"> -3N% DBr`a21WM3I3&H L ">21-35 MBr`>N&%&%-(:8#I3B\ !2I"%3$+_ 21L 5">B -3 &H13 &Y&%N%_#BgBM !BL MBM BD8e L :-BDcdI3&H2 ">6 - L Q O L (:&YUd g-5"\ 2 E>-3 DWM&%-a+ ">( B%`5B]zKW]B L h&ZaCBDW]2:-5E\215BW]">-3 !2&%-. !"n,g1:W 1F 2">(:I52 ">-3 x85BDWM&DUF&Hx)- D-3 U%Q\*w-385BMBD8R` 6$ ;;LSO?NTQ O9 !">(:N%BD L Q O9&%-38 LSO^NTQ O J;LSO\>SN^Q/NTQ O E NG$P"% 9 !">_#B'W]">-3 22&%-a&N3g h`b215BD- 2&H2: D3BD
N O BKJ # B BDBFE BDBDBIN O g h6NHQ6R A hBD-3W]B ef: T WM&%( BD8e">I5TAdU( BM!2:-5E NeJ ue Q
"
* ^.9-_' 9 *7 b *\+7-/: @[B',h:(:(C !BMB':- I BDW]2:">- #dVQ T213&HT213BSBD( J :( L !BD 2BM$@BM 2 2BD8r!")- LjE O"%$ 15BM"% BD_ #dQ 13&DN%BO215B9$@">(:( "Y,h:-5E L " L BM U%g"% BD&%W 1BD(:() L !B215BM B: b&hW]">- !2&%-a Ne 2IW 1213&Hb $ iR Nf215BD-215BM 2B=: &9WMI3 L ">,g 21 L BM "K8 nW]"% 2 2BD L ">-83:-5E'!"\& L ">:-.">-f215BOBD(:(: L !B%Q mV"% 2BM"{N%BM D`3$@"% =215B BD(:(: L !BD +,g:21 4 E " eu`R,BX13&YN%BN J A Q 15BM 2BM$@"% 2B%` W]">_ L "> !B,=&DN%BD W]"% 2 2BD L ">-83:-5E\!"fBD(:(: L !BD T,h 21 4 E " eZWM&%-sW]">-a2&%)-s,&YN%BX 2BME>_#BD-a2 "%$ &H 2A ! &H ^:( U/ 2_/&%(:(R( BD-5E%21RQ qBM% h ACB&%-.UWM(:"> !BD8 2BMMQ 15BD-R`% $ 4 E " eu`>,B=WM&%-X&%( ,=&DUK W]">-KJ !! IW]p&xW]">_ L "> 2:!BT,&YN%B9 I3W 1/213&H % J I L" O2Q*w-385BMBD8`a215BgW]">_ L ( BD_#BD-. "%$ % W]">-3 2: !2 ="%$&#W]">I3-.2&HA( B'-dI3_xACBM ="%$" L BD-:-.!BM 2NH&%(: H' JI )Q %O-fBD&%W 1 :-.!BM 2NH&%( ,BX85BB D-5B !"fA B215BWMI L ">-V"%$ L BM "K8 iJ `C,g15BM 2B 85BD-5"%!BD g215Bx( BD-3E%21e"%$ Q QO()I3:-5EX215BD !Bx,&YN%B !BME>_\BD-a2 h!"%K E%BM21K 5BM 9Ud BD()83K +& K W]">_ L "> 2 !BS,=&DN%B,g 21 % J I L" O2Q
=
ϕ ϕ=c
x
1
0
917;- ' ' - ) ) ) - J ' / ) /%
-
?
7 6 ) 7
5
'
I,BE%:BM-3W]! BT &%&Y-.N%BDU\(::W]-5">E+I3,=-.2&&DHN%ABD( bBg,g-d I321_ON%ACBMBM 2 US"% !$ ! ,=^&%&D-5N%E%BOB !BM 2E>"_#DuBD( BD-. M2 Q3WM"%&% b-\B]ACzKB &%_d!">:-5( BBD8#,!"B% 2E%15BM"Y21, 5BM: Y- ` L L E>I5 2B)d# Q$g# 15"{,0!"OW]">-3 !! ^I3W]b&9W]">_ L "> 2 !B,=&DN%Bn 2I3W 1x213&H O g SL OO J : &';=&%-.!"% !BMMQ g> "%!B%`d15"Y,BMN%BM D`a21&H $ 4cR E " Bue `a215BD-X215B+W]">-3 !! IW]!BD8 ,=&DN%BX: g&/! &DN%BD(:)-5E/,=&DN%BX"%$BDcdI3&H2 ">- L Q O $&%-38V">-3( Ue $ U L % O J A Q 15B !2&%-38&H 8Z;=&%-.!"% h !BMh13&% TqBMACBD !E>I3Bx_#BD&% 2I5 B A `AI5+213BM 2Bx&H 2B;+&%-a!"% 9(: 4%B !BM2 h"%$ A "%21VlMBM 2"r&%-8V !! )W]2( U L "> 2 N%B'_#BD&% 2I3 2B |L !BMBcWC&U_T Y 2O Q+*w- L &H 22)WMI3(:&H D` ,BrW]">I3(:8013&DN%B U L % O4R A BMN%BD- :-[213BrWM&% !Bf,g15BD- % 13&% xBD_ L UF:-a!BM ^ "% DQ 3"% 4 J AE " Xe &%(:(d">I5 W]">-3 !! ^I3W]!BD8\W]">_ L "> 2 !B+,=&DN%BD &H 2B+! &YN%BD(::-5ES,=&DN%BD "%$ L Q 2O Q - 3*Pa ' E ; ;^@ -\Bx 2BD !*,! + :-\W]:g">I5 15 !BDBM( "%N% 2BDBD T_ !"\d# Q AC">85I3BD-3&%85(: RBD">8e-3 !(:">Uh(),gI52: 21">O-3A =">ACIB]-3J 85BD8 ! &YN%BD(::-5E#,=&DN%BD 9"%$ L Q 2O Q [ WM&%I3 !Bh215BMU/&H 2B L 1.Ud 2)WM&%(:( UX_#"% 2Bh&%WMW]B L 2&HA( BO&%-38/ACBDWM&%I3 2Bg215B9WM(:&% 2 2EDuWM&H2 ">: gBD&% 2 BM O!"f83BD 2W] ACB%Q h"Y,BMN%BM D`$@">(:( "Y,h:-5E#215B L 2"KW]BD83I5 2BxA BD(:"Y, h: hBD&% !U !"/WM(:&% 2 $@Ur&%(: !"#213B'I3-aAC">I3-85BD8/! ^&DN%BD(::-3E\,&YN%BD MQ [ @ BxE> N%Bx !">_#BxB]zK&%_ L ( BD "%$ I3-aAC">I3-85BD8f! &DN%BD(:)-5E#,&YN%BD O:- E>I5 2B #dQ$?dQ
"
"
.
8+f+@+ + - * ' 0 ^ L O =+ 2 g +TI , L0h O ' , ) LN&dQ O L OhBDBKJ
8 (! . . @ 7 5 B E ; L O
*6 *)/ %
1 3 L0h
O
?
6 7
X
(i)
(ii)
(iii)
(iv)
917;- ' EY =6 ?0 0
- ' , -
7 + 7
)
LN&dQ$#/O
?
5 %
g0%L0h O e # - )% 3 2">_ LN&dQ Op,Bx !BMB'21&H L O BDB g $ +TI , L0h O2Q`hBD-3W]B L O B g -+ I , ! I L0h O ) !"#213&H L OhB\: +&HA 2">(:I5!BD( UW]">-a2)-.I5">I T&%-38 ) 0g % I L0h O >h"%!B'213&H g0%FL0h)O 7 +TI , ) L0h 2O QhmZ"% 2BM"{N%BM D` L OhBDB J L L OhB/OhB4J e# L OhB B J e# L hO B L hO BHE L hO BDB J eL! e > #\O B E e# L hO BDB '9 2:-5EiLNd& Q O ,BxW]">-3WM()I385BS213&H LN&dQ$?/O L OhBDB4J eL!e > #? O B E e# ;L O
3"% Re
J ?X215B' ^ E>1a+13&%-8n 2:85BO"%$MLN&dQ$?/O) +:- $ -+I , ) L0h O2Q`@[Bx85BD83IW]BS213&H
g0% I L0h O
#A
>hB]zdT,Bx-5"%2)W]BS213&H LN&dQ$? O:_ L (::BD LNd& QC" O L O BDB J "e L!e > ?# O L O B E e# ;L O N e " I :-W]B R0g % I L0h OO =$P">(:(:"Y,g +21&H LNd& Q$&/O 0g % L0h O N e " g> "{, (:BM e d= Q [ @ B13&YN%B ^L O)gE% L0h O9A.U LN&dQ$& O2Q+mZ"% 2BM"YN%BM Y`C :-3W]B N 6g % ]L0h 2O `,B'E%BM B J " L ]OhB e > " L ]OhBF0g % I L0h O @[BxW]">-3WM()I385BS$@ 2">_ LNd& Q$?/pO 21&H 0g % L0h O N e = tzK!BD-383:-3E213BD !Bx&H 2E>I3_\BD-a2 g!"/13 E>15BM +NH&%(:I5BD T"%$ e L 2"YN%BD LNd& Q$#/2O Q - * ' ' & g,h h =+ >= ) ? )A@ *+ ? ?2 ?* 5 % ) &ZBfJ A % % & I L" 8O @ gih % O : O&eWM( "> 2BD8[ !BMMQ 15B/;=&%-.!"% !J - )% I )-3W]B &G: SW]">-.2:-dI5">I3 M` % J & I "L 8g kBD-383 z5 !">-/215BM"% 2BD_~$P ">_ !" L ">( "%E%U_L| !BMBO$P"% B]zK&%_ L ( B WC?=ZY O &DUK =213&H213BM 2B : '& L BM 2$PBDW] !BM &%-380&VW]">I3-.2&HA( Bf !BM 2IW 1F21&H4% J QnqBM O g #Q 15BD-R`&% i: #& L BM 2$@BDW]# !BMM`p213BM 2Bn&H 2B L ">:-.2 O g #` ` 2I3W^1G21&H O O7&% 2 a Q 15BM 2BM$@"% 2B%` 2)-3W]B &LSO O4J /$P"% #&%(:(:!`,B !BMB'21&Hg $&s) +83baCBM 2BD-a2)&HA( BS&HFO`215BD- & B SL OO J A Q I :-3W]B &s: +&HAu !">(:I5!BD( U W]">-.2:-.I3">I3 M`& : x83baCBM 2BD-a2)&HA( B#&Hx&%(:_#"> 2'BMN%BM 2U L ">:-a')-#Q 1: S 215"{,g 213&H &ZB LSOO J A &KQ B%Q">-#Q 13Bh !BM : W]">I3-.2&HA( BO&%-3815BD-3W]B9"%$_#BD&% 2I3 2B lMBM 2"5Q [ @ BW]">-3WM(:I383BS213&H&ZB SL OO J A &KQ B%Q">-6%#Q
"
&
"
- gi h % * ' Y
#
&
g +T , !) I L0h O %
&
BDB J A
% % &
I L" 8O
@
)
- )% 6h \)-0213B L 2"d"%$g"%$SqBD_\_/&6#dQ$# ,BVWM&%-?,T !B % J & I L" O&% \& I3-3:">-s"%$=& L BM $PBDW]' !BM &%-380&nW]">I3-.2&HA( B/ !BM QfqBMKO g #Q I )-3W]B : & L BM $PBDW]X !BMM`215BM B&H B L ">:-.2 O g #` `p I3W 1 213&H O O7&% a Q & g +T , !) I L0h O % I L0h O 2" & : S83baCBM 2BD-.2:&HA( BX&Hx&%(:( L ">:-.2 MQ @[B 13&YN%B &LSO O J T$@"% &%(:( !Q 13BM 2BM$P"% B&ZB LSOO J A Q @[BS85BD8I3W]Bh21&H &ZBfJ A ">#QgmZ"% 2BM"{N%BM D` & B g +-I , ! I L0h OO !"& B : h&%-Z&HAu !">(:I5!BD( UeW]">-.2:-dI5">I3 h$@I3-W]2 ">-RQ I:_ :-W](:B BD &ZBDBf& J B IA L A &KO2Q B%`Qpq">BD0- _\) %_\& &%-3#d8n$Q #rW] ">15_ "Y,g(: OBM!B21D T&H215&ZB BDB J "."%A$ Q &KQ B%QS">- #QSk=I5h21": L L L TBDWM&%(:X( SOBB D-3 2 ">- #dQ "%$S&[! &YN%BD(::-5EF,=&DN%Bs !">(:I32 ">8- gV6 $jI3-3W]2 ">- Hg +-I , ) L0h OO: +&#! &YN%BD(::-5E#,=&DN%B"%)$ L Q O,g 21e L BMBD8 O $215BSBDcdI3&H2 ">LN&d$Q K/O B E ? E L0"\e > # 8O @J L i> 8O BDB E 4 :- 1 3 L0h O N 15">(:8 #$P"% !">_#B 4 gWh+Q mZ"% 2BM"{N%BM D`g,BV 2BDWM&%()(T213&HU 85BD-5"%!BD f !2&%-38&H 8 qBMACBD !E>I3B'_#BD&% 2I5 2B%Q
- * ' E
eig h @ ?
g6 +TI , ) L0h O
% * ' " ! # %'#)( " /. 6 0 0" ) 6 , / )7 ) 2 0
' ' 10 *) )603 ) % h B% J * !' JI ' g %('fL O ) ' LSOO J X ) O_g H' JI ' LSOO J O_g0% 4fgih ? * 2 LN! &d ( QV T/OJ 6L & *O ) ' O_ g ' , g h ? *) @ 2 )0+. ' N
!,#,( - 0' ) ,. ' ,
* 2 &
)
0 %
?
!, 8)(
B
LN&dQ$= O ! ' (
L O J L" P> U# e $> > O E 4 E '$ U L % O R A ' 4 J E " e %
##
L i> O g +T , !) I L0h O % - )% 69 2 2I3_#B g I L0h OO: +&#! &YN%BD(::-5E\,=&DN%B"%$ML Q Op,g:21n L BMBD8 Q 6 L3L ( UK:-5E/qBD_\_\& d# Q ,g +T21, ) J > x&%-38 ;L OPJJ? 6E L0"\e > # 8O > 4 215"{,g +213&H L i> 8O g % L0h O $P"% e # @["%$9Bh215W]">BV- !WMBM(:I385 B+ 21I 3"L &H 82O Q I: )-3 2W]_#B "d"%21#: #B]W]z5">W]-aB L2)-.I5L ">">I 2 M ` A( Ux &HI "L 8L O ">):-a #2 &G)WM-X( ">21 !5BDBT8?AC !">BMI3MQ-383&H@[ UB ( BM%J I L" 8O2Q tN%BM 2U[" L BD-G 2BM: &ZW]">I-a2&HA(:BrI3-3:">-["%$T83: d!">:-.'" L BDh:-. >!B %M 2" NHJ &%(: 2 M"{Q N% H' JIBfgBDL -3 W]Q WBr[@ #\21B5OBM,85 2BDBBf83( &HIBM 2W]BrB%`583A.) UACdw">B'W])">-a">-3O"-3 !Bx! L "%IBD$W]-G2125 :">BD-.-R !!BB`3M 221" NH3&%&HBD(: -VL :-. !B` M 2NHpO &%:(: T MQ ` 2&HI 2I3::-3 W W]3D1GB BD218R73Q &H: L L 2_#"d"%21/)- `a,Bh83BD83I3W]BT213&H[L Nd& Q$K O 15">(:83 L ">:-. ,h: !BT:- Q 15BM 2BM$@"% 2B%`a,B _\&YU_I3( 2 L ( U#AdU B !"\E%BM B E ? ^BHE L0"\ e > # 8O ^B J L i> 8O BDB ^BHE 4 ^B N O g >h"Y, )-a!BME% &H2:">-eE> N%BD B "L $> O J "L $> #U e > O E 4 E N O_g N $@"% 9 !">_\BXW]">- !2&%-aO"%$p)-a!BME% &H2:">- Q OS :Nd:8:-5E#AdU > ,B"%A2&%:-3LNd& QVT 2O Q 013&%&H-386 L '&HO2gQ 21313B : D -3 2:!B"{'N%BDBD -38L] L O">"%:-.$ 2 L +"% $ #\O2 Q $@">(:( "{,g T$@ 2">_ 215BxW]">-.2:-.I Ue"%$ !"#21315&HBT( BML $@1 W3&%?\-3pO 8#$P"> 2)()85( "YB=,gL "% D$^Q LNd& Q$K O : :- $ +-I , ) L0h ^O Q gBD-3W]B L i> 8O BDB g $ +-I , ) L0h O "n 15"Y, L]O OT"%$[! I L W#\O2`( BMSI3 S&% 2I3_#B4U L % O.R A Q I :-3W]B gS +TI , ) L0h O &%-38 L > 8O g +T, ) L0hM2O `u,B+85BD83IW]B+$P 2">_ qBD_\_\& d# Q$9# 2BD L BDW]2 N%BD(:UqBD_/_\& d# Q$X? 213&H LNd& Q X/O ^B4J A &%-38 L i> O BDB SL O O J A &KQ B%Q">-6% *w-rNK BM, "%$215BO$@&%W]g213&H L > 8O g +T , !) I L 2O `3,B' !BMBS213&H LNd& Q$K/pO 15">()83 =&KQ B%Q ">-i+h ` Q B%Q B E ? E L0"\ e > # 8O @J L i> 8O BDB E 4 &KQ B%Qp">- h *w- L &H 22:WMI3()&H D`K213: +BDcdI3&H2 ">-n13">(:83 +&KQ B%Q">- %X`3 !"#213&HM`uA.U LNd& Q X/2O `3,Bx13&YN%B LNd& Q BA O ? E L0"\ e > # 8O J 4 &KQ B%Qp">-0%
!, (
#?
I 215:-"{W],gB rU 21L 3% &Hr&FO R %(:(gA ! &% &D-3N%8 BD() :-5E , &Y">N%-SBD %X"%`C$S,21B#5BsW]">;=-3&%WM(:_/I385&% 2B 2&213J!h"&H >(:4 _ J BDc. I3 &HE 2:">" - !B ? 2&H2) D3BD L O > L W?\O2Q @[B#,g:(:( L L3L 215"{, 213&H ) +&#! &DN%BD():-5E#,=&DN%B"%$)L Q O2Q qBM % &%-8 ` `ACB/&% :-L O2QnqBM 4sACB/&% :-L W#\O2Qi@[B -5"%2:W]BS21&Hg83baCBM 2BD-.2:&H2 ">-"%$MLNd& QVT\pO UK BD(:83 LNd& Q % O B E ? E L0"\ e > # 8O @J L i> 8O BDB E 4 ">- !' JI * $ U L % O J A `3215BD-6LNd& Q % pO 2&DUK T21&H LNd& Q # O B E ? E L0"\ e >3# O J L i> 8O BDB E 4 &KQ B%Q">-ih I&X:! - W]&YB N%BD(:L :i-5E\> ,= 8&DO N%BBD !B ">g(:I52$ :">+TI , -) L0"%h $ =O L A.U Q L2O Q W?\2O `LNd& Q # O :_ L () BD LNd& Q$K/O !"213&H [: * g 2BD_\&%:-3 =!"r 215"Y, 213&H LN&dQ # O15">(:83 +&%(: 2"\:-215BxWM&% !Bx,g15BD-GU L % O6R A Q I85BDI 83LIL W]">Bh 2B $@ 2">U _ L % qcO BD_\R _/A &Q d# I Q$# :- 2W]BDB! BDW]g2:N% BD( +-U/I , ) qL0h BD_/O _\&%-3&F8 d# Q$L ? [21>3&H 8RLO N d& Q g X/O 15">+T , (:!)83I ML0hQ O3`S ">,_ B L]O OT"%$ L W#\OT,BX1&DN%B 4 J L E " euQ 15BM 2BM$@"% 2B%` 2:-3W]B ">- %X`R,B
E%BM LN&dQ ? O B E ? E L0"\e >3# O J L i> 8O BDB E 4 &KQ B%Q">-0% !">"%(:E%I3BM221 ">5-BM V"%)$,gL :214Q OpLN&d&%Q-3%8eO/21521B3: 2"dE>:"%N%$bBD: 6 TW]LN&d">Q_ # O2( QBM!B%hBQ D-3W]B : e& ! &YN%BD(::-5E7,=&DN%" B L L L"%$ @[ WqBDB\_\?\O,g_\W]:">()& (b-#d 2 213CQ:"5 !"Y2 `3, 213B]21zK:3 +&%&HW],hS2(::21(:U\(5"%B\$R 2 2"Y21BMN%59"BBg%21,=$5&DBSACN%">21BDI35 +-3BM 2"%852& 2HBDBD8Z!B_nD8f$jQI3)-3-\W]221 5">B -3 O 15 2&HBM2"%) 2 !BD$PUK_ :-5#dE Q L Q*w -\NK O BM,> I&#W]">I I3L3-.L 2&H">A !B( BS -dI3 2&H_x2AC: BMD3 =BDR "%$ L 2L_# "d"%21O?> ,L &YN% WB !?\BMO2E>Q _# BD15-.BD2 -RT`K !AdB U &HL &H!B D8eO2Ad` UfG&XW]WM">( -"> 2 !:BD !8V2 = !BM"%$ %XQkU L W#\OpBD&%W 1 2I3W^1e,=&DN%B 2BME>_#BD-a9 !">( N%BD L LN&dQ " O B J L O $P"% O g N L O J L" $> #Ue P> > O E 4 \E N &Hg&%-.fU Du-3 !BOBD-38 L ">:-.="%$ N $@"% g !">_#Bx)-a!BM 2NH&%( ~&%-38nW]">-3 !2&%-.2 4&N Q
#"
I\`C&%I -3L38 L ">83 !baCBxBM, 2BDBX-.W]gN">HI3&%(:8_(:I5BDD h-38 "%$ &%4n(:(&% 2-3">8 (:I52 Q ">-3 15BD7-R"%` $ ,LNBX&dQWM&%"b- Odw$@">"%: S- 83 !b">aC(:BMI3 22BD -.">h-3 g:-.83!BBBMD 2NH-5&%BD(:8 ">-n:-.!BM 2NH&%(: =,g15"> 2BOI-3 ">-e: h >%o$P"% g 2">_#B'WM( "> !BD8n 2BM % "%$ _#BD&% 2I5 2BSlMBM "5Q * : BD&% !U\!"X !BMB9213&H213Bh$jI3-3W]2 ">-`.85BBD-3BD8\">-fh=` 21&H,B9E%BMM`d,h:(:(3 2&H2) !$PU L uO &%-38 L W#\O $K&%-38S">-3(:U9 $K&%(:(%,=&DN%B= !BME>_#BD-.2 2&H2: !$@U LNd& Q "bO ,g 21'215B 2&%_#B 4uQmZ"% 2BM"{N%BM D`. $,B%`%$@"% 4 J IE "\e `a&%(:( "{,5U L % (O R A `>21: L 2"dW]BD8I5 2B ,g:()( E> N%B/I3 &%(:($jI3-3W]2 ">- ' 2&H2: !$@UK:-5E6L O9&%-8 L W#\O2Q @[Br,h:(:( 215"{, 213&HX215BD !B$jI3-3W]2 ">- xACBD( ">-5EZ!" +TI , ) L0h 2O `g21&H213BMU0 2&H2: 2$PU L ?\2O `&%-38 213&Hh215BMUe&H 2BxB]z5&%W]2( Ue215B,&YN%BD 9 22&H!BD8Z:- 15BM"% 2BD_ d# Q Q 13: +,h:(:( L 2"{N%B 15* BM-"% "%BD _H83BM #dQ!"'Q 22I385U LNd& Q "PRO ,B 3D ! W]">-3 2:83BM bE%BD-5BM ^&%(KBDc.I3&H2:">-3 "%$215B=$@"% _ LNd& Q & O B J L O N ,g15BM B gUh h : T&# &H2:">-3&%(R$jI3-3W]2 ">-RQ[ @ B,g:(:( B]z L ( "% 2BS215Bc.I3&%() 2&H2 N%B ACBD13&DNK "% "%$ !">(:I52:">-3 !" LNd& Q & O -5BD&H L ">)-a2 ,g15BM 2B 1&% &lMBM 2"X"% & L ">( B%Q 6 ( UK:-5E213: =!"\213B :- LN&dQ$= O2`5,g:(:( E> N%BxI +215B' !">(:I32 ">-3 ="%$MLN&dQ "PO2Q
L3L
@[qBMB D3 !hB]z L (:"% 2Bx215BXcdI3&%(: 2&H2 N%BACBD13&DNK "% 9"%$ 2_#"d"%21 2">(:I52 ">-3 g!" LN&dQ & O2Q J B*:-5)(+$ SL O/O N J 2B*I )(L+ SL O O * $ @g,h h : p&AC">I3-385BD8r 2_#"d"%21r !">()I52 ">-\"%$ LNd& Q & 2O `K,BO13&DN%B ^B A &% A&% -.QS UZmV:"%-. !BBMM "Y 2NHN%&%&%BM-3( D8Z` ,g&% 13 BML 2B O L A HO $P"%QMR &hB A DQ -3W] B 1. I3LNd& 9Q $& O ^ 2B &%13-3"Y8,gA g &H213:S h&H! 2">! _# :W]BL 2( Un ">O:_#-.J M`">-3 7"%!"L > ,g-3)(::(WXO AC:J - B L !! )W]2( UF85BDW] 2BD&% 2)-5EZI3-.2:( E%BM2 #WM(:"> !Br!"s215P B-5B]zKlMBM " "%$ #Q_OS BD-5"%2)-5E 213: TlMBM 2"% s`u,BX13&YN%B sQ @ 13&Hh,g:(:(R13& LL BD-V!"/215B !">(:I52:">-n,g15BD-Z & L3L ">&%W 15BD OS B L BD-83:-5Ef">-[,g15BM213BM S215B\lMBM 2"n: S83">I5A( BX"% x 2)_ L ( B%` 13&% T&/83baCBM 2BD-a=ACBD13&YNd "% YQ [ @ BxB]z L ( "% 2BS215BS ,"fWM&% !BD g)-2I5 -RQ Qp69 2 2I3_#B L O=13&% T&\ :_ L ( B9lMBM 2"/&H i !"\213&H 3 L O(R A Q 15BD B JWL i> O 3 L O E FL L e> O O &%
@[B'E%BM
O J ! L i> O 3 L O E" L L i> O O # #
I :-W]B !
&%-38
#&
L i> O 3 L O E F L L i> O O J i > L ! 3 L O E" L i> O O N ! 3 L O E FL L > O O J ! 3 L O E" L i> O N
,B'E%BM
# #
*w-a!BME% &H2:">-nE> N%BD
O J LL > OI O ! L i> O 3 L O E F
>@OcJ ! # 3 L O ! L i> O%E FL L e> O O N ,g15BM B 2&H2) D3BD L O J sQ 13BM 2BM$P"% B L >@O O J 3 "L O L e> O E" L i> O '9 2:-5EX213&H E FL i> O J " E L i> O2`3,B'"%A32&%:L > O O J 3 "L O L i> O E FL L i> O O 13) BDcdI3&H2 ">-V 215"Y,h T213&H L L >@O O O J L L i> O O2Q @[B'E%BM LN&dQ K O LSO O J E " LSO > O 3 L O%"E L LSO > O O &% O N ,g15BM B L O J s Q3@[Be,&%-.#!"FW]">-a2)-.I5Be213B 2">(:I52 ">- ACBMU%">-38 `|Q B%Q ,B,=&%-.S!"n85BBD-5B LSO Og$@"% fO2R Q >h"%!B#213&H L I5!2:-3E LSO OJ v $@"% '&%(:( OR ,">I3(:8FUd BD()8G&V 2">(:I52 ">-G"%$ LN&dQ & O2Q h"Y,BMN%BM D`213) ' !">(:I52:">-G: -5"%
2_#"d"%21 !"Z,B E>-5"% 2Bf x$@"% 213Bf_#">_\BD-aMQ >g"%2)W]Bf:- !!BD&%8G21&H215Bf">-3( U ,=&DU\!"E%BM& 2_#"d"%21r 2">(:I52 ">-r: 213&H 2I5 ^-3 p:_/_#BD83:&H!BD( UA&%W 4/I L &HE>&%)&H O J Q[*w-G21: XWM&% !B LN&dQ K OO,g:(:(pA BfNH&%(::8F$@"% #&%(:(6O7WM( "> !B!" Q[3 ">_ LN&dLSQ OO& OTJ , B\L &%(:> !"LS"%O\A> 2BM 2N%O O2B\Q 213&H ,g:()(ACB# !UK_\_#BM! :W,g:21s 2BD L BDW]O!" `b|Q B%Q
#K
#A `3,dQbB'* "%$ A3 2&L% :- O :-3 2!BD&%8'13&% &T83">I5A( B lMBM 2"g&H s`{ !"g213&H 3 L O J A ` 3 L O(R B J4L i> O 3 L 8O E" FL L i> O O 4 kUf&/ 2:_\:()&H =W]">_ L I52&H2 ">-n&% g215BS">-5B'21&Hg( BD&%8e!" LNd& Q K O2`3,B'E%BM LNd& Q T/O SL O O > NB]z L TL >O ! 3 L O O &% O aN $@"% g !">_#BxW]">- !2&%-a NQ 1.I3 B]z L ">-5BD-.2:&%(:( Uf&% O a Q * -nNd BM, "%$b213) +83: 2WMI3 2 ">-f,BWM&%-V85 &Y, 215BS$@">(:( "{,g:-5E#W]">-3WM(:I 2 ">-3 MQ Q @ 15BD-5BMN%BM 13&% x ,"[ 2)_ L ( B#lMBM 2"> I N &%-8 L O R A $P"% I `215BM B\B]zK) !2 '& L BM "K83:W !">(:I32 ">- I5Au( BglMBM 2" I `3&X 2:_ L (:BglMBM 2" `3&%-38 L 6O R A $@"% I `215BD- 215BM B#B]zK: 22 S&f 2">(:I52 ">- ,g 21 J I ` J &%-38 P I &%P HO _ a Q6h()(C215BD !Bx !">()I52 ">-3 +&H 2BI3-3:cdI5BOI L !"\! &%- 2(:&H2 ">-RQ d? QV* $ 13&% &Z 2:_ L ( B\lMBM 2"s&H I &%-38 L O R A $P"% I p` 215BD- -5" AC">I3-385BD8 !">()I52 ">- 0B]z5: !2 +$@"% 2R Q
I
P
* $R,BOBD-3(:&H E%Bh215BOWM(:&% 2 "%$ !">(:I52 ">- "%$ LN&dQ & O ,BO&H 2BS( "."%4K:-5E&H=!"X)-3WM(:I385B &%(:( Jg I L0h O `g_\"% 2B L "> 2 A:(::2 BD O&H : !B%Q * DU X-5"%X&%-.Ud_#"% Bf-5BDW]BD 2&H :( U ! I5B213&H +T, ) &%-38 &H 2B=lMBM 2"> "%$ L O2QmZ"% 2BM"YN%BM Y`a215BACBD13&DNK "% "%$ VWM&%ACB\_#"% 2B/W]">_ L ( B]zCQ I I LL "> 2B : ':-3W] BD&% 2:-5Ee&%WMW]"% 83)-5En!"3LN&dQ & O2Q 15BM 2B &H 2B'-5"{, 215 BMB L "> 2 A:() 2 BDD g #d?dQQQ n 2W] 2II3">83-.885285:BDBD-.-3-3I3( ( BDUOU/ TW 2!"1!"/&%L-5:-E% TW]BD&% 2 -3BD83&%8e ! 2B' BDBDW]&%_\2WM:W]&%">"%:--3 83&% +-3)W]-58X">E#-3 !!" 22&2&H% LN-a2 &dbM`Q E%">& )O2-5` EOA&%W2485"Y,g-&%WMW]"% 83)-5E !" LN&dQ & O2Q * -VWM&% !B ,BSE%BMh 2_\"."%21n 2">(:I52 ">-3 =&% gA BM$@"% 2B%Q3 ">_ LN&dQ & O,Bx !BMBx213&H WM&% !B #rWM&%-Z">-( Ue"dWMWMI3 O&H L ">:-.2 g,h15BM 2B L O$J A [Q @[B#&%(: 2"r"%A 2BM 2N%BX213&H &/ I38385BD-e !!" L "%$ L 2"K83I3W]BD g& d2I3_ L :- ?BDBKQ TBME>&H ^83:-5E/WM&% 2B ?d` ,B-5"%!B 213&H' $215B/W^13&%-5E%B\"%$=83 2BDW]2:">-s"dWMWMI5 ^ '&Hx& L ">:-.9,h15BM 2B J X A ` ^B,g:(:( 13&YN%B'& d2I3_ L 2)-3W]B ^B J X A 2I8385BD-3( HU d2I3_ L !" >^BKQ 13: : =15"{, L BD&H4%">- &H : 2B%Q
#UT
|Q B%15Q B/()&% !xWL M&%O= !13Br&%, gB/&\W] 2">:_ - 2:85( BhBM xlMBM) '"521Q369&H'" 2 2%I3$_# BS21& L&HL 2">&%W : +1:85-5BDEnW] 2&VBD&% ::_ -5LE\( !"B {L,">&H( B#8Z"%& $ L "L >:-.@J ',g15BM 2B ~13&% g& L ">( B%Q 13BD-n215BM 2B: g&r 2_#"d"%21n$jI3-3W]2 ">- L O 85BBD-3BD8e:-e&\-5BD E>1.AC"% 15"d"d8f"%$ J ` 2I3W^1e213&H "L 6 O R A N L O J L" 8?O E FL i> 8O ! L O J L O i> ZN 13) )_ L (: BD D`d:-NK BM, "%$ LNd& Q & 2O `213&H LNd& Q = O ##*O J ! L O J L" 8O i> E FL L i> 8O O
*w-a!BME% &H2:">-nE> N%BD
O > O " J # ? L" O L i> 8O E" FL L > 8O O N ,g15BM BfO " : T 2IW 1e213&H LSO " O J Q hBD-3W]B LN&dQ$# A O LSO\>@O " O J # ? L" O L i> 8O E FL i> 8O I :-W]B L E" FL i > 8O O J "E FL i> 8O2`u,B'E%BM LN&dQ$# O LSO >@O " O J # L? " 8O L i > 8O E" L L i> 8O O 13) BDcdI3&H2 ">-V 215"Y,h T213&H L L i > 8O O J FL LSO\>@O " O O2Q @[Bx&H 2 :N%B'&H LN&dQ$## O LSO O > J N O\>@O " "E L LSO > O " O O &% O O " N ,g15BM B NiW J L ) O Q K K 6h g$P"% ?KB `3,B'E%BM ^B J ! L O J L O i > J L L" 8O8E FL i > 8O O ! N LSO\>@O O "E L LSO > O O O " "
LN&dQ X O
%9A 2BM 2Nd)-5E21&H N SL O\>@O " O E" FL LSO\>@O " O O J N LSO\>@O " O I E F LSO\>@O " O N
#=
,B'"%A32&%:-
^BKJ "L 8O N)LSO >@O O I E" L LSO > O O O " " '9 2:-5EX213&H B I B J E" L LSO >@O " O O2`5,B85BD83I3W]B I ^BKJ L" 8O N LSO\>@O " O I E" L LSO >@O " O I O I :-W]B ) I J N`,B Du-38f213&H LN&dQ$#? O B LSO O J > N KN O O > > O " O K " I I "E E" F L LSO\L LSO>@>@O " O O "I O I O O &% &% O O KO " O N " N K K
*w- L &H 22:WMI3()&H D`K,g15BD-5BMN%BM 13&% T& L ">( B%`K215B !">(:I52 ">
1&% T&\WMI3 L Q
* $b,B'& L3L ( Ur215Bx&HAC"YN%B83: 2WMI 2 2 ">-r!"\215B L H& 22:WMI3(:&H TWM&% 2B L" $> #Ue > O E 4 cE LN&d$Q #"PO B J L O J N 6> ,BhWM&%-fWM(:&% 2 2 $@UX&%(:(3AC">I3-383BD8# !">(:I52 ">- "%$ LN&dQ "PO2Q 13B L 2"d"%$R: A&% 2)WM&%(:( UX&%:-3 L BDW]2:">-V"%$&%(:( L "> 2 2 A(:Bx83: !! ^ AI52 ">- T"%$p213B#lMBM 2"> '&%-38 L ">( BD O"%$ L| 2BMB E>I5 2B #dCQ "/$P"% T213Bx83: !! ^ AI52 ">- $@"% T,g13:W^1e215BM 2B'&H B'AC">I3-385BD8 !">(:I32 ">-3 O2Q IW]"dB /:-3WMW] BBD-. 2 M `%L" . 1> 3&%#U e BD:> 215 BM O?">E -54Bp]"% E 215 2BM: SB 2&BD&%213(%lM BM8Z 2">"% W]85">BMI3 -.L !BD">8x( UK,h-5"> 21_\')_&%(I3,g( 2:21s():WM 2 BD&%U%(Q %:O x-5">B -3D( Us-83"> =-5B/213 &HBDT&%(215lMBMBM 2B'"5QZ&H 2* Bx-3-583"#BMBDAC8R">`bI3W]-3">83-3BD :8f85BM 2"> :(:-3I5Ee2 ">21-35 =Bf"%8$ b a LN&dBM Q BD"P-aOxW,gM&%15 2BDBD-5 MBM`N%">BM-5 TL Br213 2BMBM 2BDB 213&HS $">-3(:Ue">-5BXlMBM 2"e: g BD&%(|`C215BM 2B#: 9-5"r,=&DUZ!"E%BM'&rAC">I3-85BD8V !">()I52 ">,g13)W 1F: 2_#"d"%21F$@"% J X {Q @[B&% 2 2I3_\B\215BM 2BM$@"% 2B/21&Hx215BM 2Bf&H 2B/213 2BMB 2BD&%(RlMBM "> MQ SOBD-5"%!Bx213BD !B'Ad%U eN `&%-38 ` !"#213&H LN&d$Q #& O L" $>3#Ue > O E 4 E JWL > O L e> O L i> O
z
m
M
c
z=m
(a) - Smooth periodic
z
m
m c
M
(e) - Periodic cuspons
917;- ' ? A? M= ? N eN N V ?
c
M
(b) - Smooth with decay
M=c
z=m
M=c
(c) - Periodic peakons
z
#LX
(d) - Peakons with decay
c
z=m
M
(f) - Cuspons with decay
L PLO$> O L ;O
%& 6 7 8%# 5 *+ + , . 0' / 54 0 . 0
, / !&%# (% - +. 0 0' , , 5 0 2 .1 0 ,* 6 0 0 % 5* & ' '0 *+ , /%
B? 5= ?
@
(1)
ϕ=c
(2)
(4)
ϕ=c
?A
(5)
(3)
(6)
(7)
9 17; - ,' ' !/8 ( ' 0! ( )' -!),( ' M @6.,0 ! -+:=( 6 B ?2 100 0 1 ) 0 ? 5 2 / ! &%# & ( % ' ) + 2 & % , ' ! #,(" 03! ( 0 0 ' ) + & ? /
'
?
=
)' . , 0 0 *6 , / !-( )
@
, %
;">_ L &H :-5EX215B'W]"dB /WM BD-.2 T"%$ H`5,Bx"%A32&%:LN&d$Q #K O J $>6#Ue > > @[B83BD83I3W]B'213&H9 #2_#"% "d"% 21 L BM "K83: WO !">()I52 QZ">-36o =B]ACz5">: !I3T-!"85BD8FLN&d !Q ">"P(:I3O2 $">- &%- 8n,g">-3 21( U $ P &%P O P _(a P `dB]zK) !2 P$@"% J P P Q6 !">(:I52:">- s,h 21 &%f O _(a `RB]z5: !2 S,h15BD- P J P QX* -3 L BDW]2:">-Z"%$215B\83Ca BM 2BD-. WM&% !BD = 215"{,g 213&H=215BD !BO&H 2BO&%(:P (u _#".P "%21fAC">I3-383BD8\ !">(:I52:">-3 p"%$ LN&dQ "PO2Q >h"%!B 213&H=215BD !B' 2">(:I52 ">-3 -5BMN%BM T!">IW 1215BS(::-3B J Q hBD-3W]BS215BS:-.!BM 2NH&%( :LWMN&d&%Q-n"P-5O BMN%_BMI h !ACABSCE>BT(:21I55BDBh8,g!"%15E%">BM( 21BT5 BMBD 9&%(,g(: :21-3eB%Qb&%*w-5- "%21L 3&HBM g2:,=WMI3&DN%(:&HB% DQ `a215BD !Bh _#"."%21f !">(:I32 ">-3 > g"{ O, &Hg&,BZFDu2I5-3 !B-7S!"BD0-38K21J5BZ">:WM-.&%=" !B %$ "%/$S)QAC">QOI3(:-3I85:-5BDEX87 2,">"/(:I5"%2$ ">21-35 \BD !!"B'!"%LN&dE%QBM21"P3OBM h$P"%,g f)(:,g( 13E>) W N%1 B L : 2B/!"s&Z-5">-5J 2_#"d"%210,=&DN%B%Q[qBMXI x2&H4%B ,"sB]zK&%_ L ( BD !"s 2BMBf15"{, 215B !">(:I32 ">-3 "%M$ LN&dQ "POWM&%-eACBS$@">I3-38RQ
?
Q f" !BMB13"Y, L BM :"d83)W L BD&H4%">-3 h&H : !Bx,B( BM J Q+* -e21: WM&% !B L O=) h&rc.I3&%83 &H2:W L ">( UK-5">_\)&%(R,g 21Z&/ 2:_ L P ( B'lMBM 2P "&H s` L JO6J L" 8OfR A `&%-38 L OfR A $P"% Q\qBM ACB\&e !">(:I52 ">-[)-Z21: :-.!BM 2NH&%(|QX* $ h"%!BT213&H WM&%-r-5"% !!" L "% 2I5 -XA&%W 4X&%-.Ud,g15BM 2B+ACBDWM&%I3 !Bg213&H,">I(:8 E> N%BS ) !Bh!"\&# :-5E>I3(:&H ^ U\"%$ 0&Hg& L ">)-a=,g15BM B J X {Q h"Y,BMN%BM D`u,g15BD- :-3W] BD&% !BD =&%-38f 2BD&%W 15BD T215B L ">)-a J h:WM&%-e_\&H4%B'&X 2I8385BD-\2I3 -&H21: L ">:-.=&%-8n !"#E> N%B' ^: !BS!"/& L BD&H4 Q # L d Q O 1"&% h !BM&\Bh8315">"{I5,?A21( BS5BglMBMWM 2I" L &H">-3 J ,g s21#`u83&\BDWM 2&D)_ U\&H( B : 2B%`.">( ( BMB'&H J `u &%-38 L OP R Q A >g$@"{"%, {Qf* $ ) '&n !">(:I32 ">-F:-s213) ':-.L !BM 2NL &%(p ',g:()(1&DP N%B/B]P z L ">-5BD-.2:&%( 85BDWMP &YU[!" P &H:- D-3: UVAdUs215B/&HAC"YN%B83: WMI3 2 2 ">-Q\6=215B L ">)-aS,g13BM 2B 2BD&%W^15BD X215B L ">(:B%`213BM 2Br,h:(:(ACBf& WMI L Q 13: WMI3 L : &%()( "Y,BD8 2:-3W]Br215B 2:-3E>I3(:&H U/:- 0213&Hh L 2"K83I3W]BD =ACBD( ">-5E> =!"/215Bx !BMeJ Q L" 8 OE>* I5-> 2 BL L%&;BD#dW]Og$Q 2&\&% O2">-3Q -\8 21515L" BD"{39 !,gO B'> &H21 L%3Bx& &H3 &%OT(:21(C"%5$ACBg"> 83I315C -3a BM85"%BMBD 2 28BDBD-._ !">L #d()I5">Q 2 2 ` 2"> L -3Au(: =:I3(: "% h2$ 21BDLN5 &dB\&HQ 2 !"PBT">O2(:21QI332"> "> !B-3 L BD ! BD-a!B fD8rL| 2BM:- B - 3*Pa ' *w- 15BM"% 2BD4_ #dQ 215B 2">(:I52 ">-3 b&H 2B+85BB D-5BD8">-215B,h15">( B 2BD&%( (::-3B%Q hBM 2Bx,Bx 2BD 2! :W]T215B !">(:I52:">-e!"/215B:-.!BM 2N &%(ACBM ,BMBD-V ,"W] 2BD !2 9:215B#WM&% !B\"%$ L BM "K83:Wx,&YN%BD M`b&%-38s!"V215B L &H 2'( BM$@O"% ' E>1.O"%$215B#W] 2BD 2x:215BxWM&% 2B'"%$85BDWM&DUK:-5E\,=&DN%BD DQ 15B':-.!BM 2N &%( : g&%WMW]"% 83:-5E>(:Uf85BB Du-5BD8!"/ACB & D-3:!BS"% g13&%( $PJ :- D- !B9)-a!BM 2NH&%(|Q "
*w-x213) b !BDW]2:">-X,B+85BM!BM _/:-5Bp,h13:W 1 !">(:I32 ">-3 b"%$LN&dQ "POR213&H13&YN%B213B= &%_#B 4u`3 !"\213&HT213BMUfWM&%-VA BSE>()I5BD8!"%E%BM215BM O:-a!"\&\$@I3-W]2 ">-e 2&H2: !$@UK:-5EiL W?\O2Q 215BXW]15".B B 4/r:WM- BD-aLN&d2 QO"P"%O$ W]?"% 2) 23- BD LNL &d">$Q #-& 83O2:Q -5ETBD!"XWM&%&(:(:) !-5">E/(:I32123 ">&H- p `3J : F$@">> I3-3#U8re A.> Uf :85BD> -.2 s $PUK`C:,-5EB "%A32&%:LN&d$Q #UT/O 4 J > > L E O J > > L E O L" $>6#Ue > > O 69 =,B'4K-5"{, $P 2">_ I BDW]2 ">- #dCQ "3` LN&d$Q #UT Op85BD 2W] ACBD =&%-eBD(:() L !BO:-f215B L eN JO|J L (:&%-3B%Q 15BM BM$P"% 2B%`a,B+"%A32&%)-#&%(:(dA ">I-385BD8$@I3-W]2 ">-3 2&H2: !$@UK:-5E L O&%-38 L 2&%_# WBS#\BDOO()(:A. UF !B%E>Q ()I3:-5E5` :-G&%()( L "> 2 2:A( B\,=&DUK M` !">(:I32 ">-3 W]"% 2 2BD L ">-383)-5Ee!"s215B L
?#
>,Bg !BM"%B!B9$P 21">3_ &Hp LN2&d">Q$#(:I5"b2O 21">3-3&H p WM &%$ -\ ">-3N ( UAC&HB 2Bd!">,:-5"OBD8# !">&H(:I52L ">">-:-. 2 "%$,gLN&d13Q$BM# 2"bBO eW]"%J 2 2BD Q* ">--8583BM:BD-58RE ` L !"/83Ca BM 2BD-. U M`3215BD- ?B#,h:I (:(C13&DN%B&.d2I3_ L &HT215B L ">)-a+,g13BM 2B I &%-38! &H 2B dw">:-3BD8RQ I :-3W]Bg&%()(! &YN%BD(::-5E,&YN%BD +13&DN%BO!"ACBh 2_#"d"%21r,g15BD-5BMN%BM J X ` ,=&DN%BD 9WM&%-eACBSE>(:I5BD8e!"%E%BM215BM h">-3( U&H L ">:-.2 =,g15BM 2B J Q I 2BD_J:-3d# QW]Bg`.212155BgB ,= 2&D"dN%"%BD$ =,g&H :():(a :AC-5B)ESD Ad-3U: 2E>13()BDI38x:-5">E'-3&HW] 2B+Bh,B]B zK&%W] 22("{:N%U\B+212153Bg&H">-321BD5 pBD ! !B+2&H,=!BD&D8N%BD: p- AC BD( 15">BM-5"HE J L L !" +-I , ) L0h OO&%-38e 2&H2: 2$PU L W?\O2Q -dI3_x15ACBVBM "%I5$A3,=2( &DB N%BTL "> !BM:-.E>/1_\5BD-aBM 22 BZ,h: # 21213&H&H f&AF ! ,=&H &D)N%( USB 2 _\&%WM&%(:(d- I3B%-a`%2&BMHN%AuBD( - B 215">I5E>1 =&Hp&%(:(KBD-38 L ">:-.2 "%$ 215Bg:-.!BM 2NH&%(: M`> : -3"%BMN%BD-/WM( BD&H p213&H : =W]">-.2:-.I3">I3 MQ 13) _/&H4%BD +215B L 2"d"%$"%$b215B'-5B]zKT( BD_\_\& &H213BM T:-a! ^:WM&H!B%Q - * ' @ =6 B?210 0 ?* ) ' ' @ L O 0 L W#\O =+ / +-I , L0h O 10 ' L W?\O % ) kBM$P"% 2Bf,B L 2"{N%BrqBD_/_\&_d# Q$n & ,Bf13&DN%Br!"VBD !2&HA(): 21F !">_\Br-5"%2&H2 ">-Qf6 $jI3-3W]2 ">- &]g +h ` J W 4=N Y +h `: T 2&%)8!"\ACBS"%$ =+ ?0 0" , & $ 2I L &L Q O > &L Q I O a
"
HJI K
KQP
,g15BM B+215Bg 2I L 2BD_I_ : 2&H4%BD-r"YN%BM =&%(:( &%-38#"YN%BM =&%(:(3W^15">:W]BD p"%$#VQ 9 2I3W^1 213&H
JQ " Q I ; ; ; Q J L POR83BD-5"%!B=215B+ !BM "%P $3$@I-3P W]2 ">-3 P &ig h 4
@[">- B+Q( BM L0h Of83BD-5"%!BD #215BV &%W]Be"%$O$@I3-W]2 ">-3 & "%g $uh AC"> I3-385h BD8x 2NI3&HW 1?)&H2123 ">&HL +T, ) & g FL PO'$P"% \&%(:(+W]">_ L &%W]\:-.!BM 2N &%() h+Q 6 $jI3-3W]2 ">- & g h 85BBD -3BD8n">-s !">_#BX !BM h : 9&%- ?* $ &0_\& L 9 !BM2 9"%$p_#BD&% 2I3 2B A !"n !BM2 S"%$_#BD&% 2I5 B A `|Q B%Q U L%&L O OFJ A ,g15BD-3BMN%BM : S& 2I3A !BMO"%$ ,g 21GU L O J A Q @2 ">-3 DBSQ ,g:(:(u-5BMBD8f215B9$P">(:(:"Y,g:-3Ex ,"# 2BD 2I( 2 p">-&HA 2">(:I5!BD( U/W]">-.2:-dI5">I3 $jI3-3W J [ - * ' &ig h ' J W 4&N Y h ' =, "*6 ' ? ?2 ?* 5 =6 B?210 0 +5 5 % ) &
>=) ? @ *+ ? ?2
0 @ &
?* 5 %
??
I BMB'$@"% TB]z5&%_ L ( B WC&Z= Yb"% KWC?=GY Q - * ' 9c $' & g h ' J W 4&N Y h ' ' *6 ? ?2 10 &
>=) ? @ *+ ? ?2 ' ) & ' >= ) A? )A@ *6 ? ?2 % K K - )% I ! &% E>1.!$@"% 2,&H ^8nI3 2:-3E213Bx85BBD-3:2 ">-f"%$&HA 2">(:I5!B'W]">-.2:-.I U%Q L q BM -gI pO &% M --3D386 !L T 7 157 "Y#\, 2O Q821%q&%&HBM 69 2 2 :I +&%_#-&%-_8B F>T% J :$jAC +I3B'&-3&%W]AC2 g"> ">:I3- --3QL83qBD8/ BM $jI32O-3Q W]AC2B' ">&\-f !,gBM1T":%W $ 1_# 2&HBD2&%: 2 I3D3 2BDB A Q 13BD L O J L % O H' #" L O O% -sBD&%W^1G:-.!BM 2NH&%( `I3-385BD8 NH&H :&H2 ">-RQ3 2">_ 215B &% !UK_ L !"%2:W$@"% _I(:&% LNd& Q$## =O &%-38 LNd& Q$#? =O ,B:-3$PBM 9213&H E g I L O $@"% O&%(:( !Q 15BM BM$P"% 2B%`uqBD_\_\&f#dQ$K\ 213"Y,g h213&H : g&%- >gJ $@I3-W]2 ">-n">-VBD&%W 1 $@"% Q gBD-3W]B%` I3 2:-3E21&H L % O J >` U L L O O J U L ?O E ' U L L O O J A H#" 13q) BM L 2"Y N%BD g' 213&HACB'&\: 2 +I5&%Au-_ !BDT> c.I3J $jBDI3-3-3W]W]BS2 2">I3-W Q1n213&H - )%
"
"
JI
'
aN JI K QK P
,g15BM B 85BD-3"%!BD T215B'( BD-3E%21e"%$b213B':-a!BM N &%( Q @[Bx,h:(:( 215"Y, 213&H : ="%$ AC">K I3-385K BD8fNH&H :&H2 ">-">-VBD&%W 1ZW]">_ L &%W]h I5A:-.!BM 2NH&%( LN&d$Q #= O % ' JI N $@"% g&%-aUe 2IW 1n !BDcdI5BD-3W]B Q 1: =,g:(:(C 213"Y, 213&H g +-, ) L0h O2Q 3"% Z :_ L (:)WM U7,BF85BD-5"%!B[215BF 2BDc.I5BD-W]
B ' AdU ' `S&%-38 ,B &% 2 2I_#B O:- $P"% h&%(:( 5Qp* -NK BM, "%M$ LN&dVQ T\Op,B'JI"%A 2BM 2N%B'213 &HJI
LN&dQ$#LX O
P
$ ) $> K K J # ! L" $> #Ue > ?O E 4 E # K K
?"
3 2">_ I I5A !BDW]2 ">-F#dQ$&KQ$?9,B=4d-3"Y,7213&H215B L ">( UK-5">_\:&%( L O J L" =>F#Ue > O/E 4 6E 13&% b215 2BMBlMBM 2"> N N{&%-8 Q mV"% 2BM"{N%BM D` &%-38 L" 8O A $P"% =&%(:( 5Q 15B9 85BM NH&H2 N%B9"%$ ) :-85B L BD-3 85BD-."% $ PX&%-38r215B $j&%W]T213&H &%( ,&YUd h13&% T213 2BMB'lMBM 2"> h 215"Y,h T213&HT213B U T$@"% _ &\A ">I-385BD8 !BMMQ hBD-3W]B%`3,Bx13&YN%Bx215B'I-3 $@"% _ BD !2:_\&H!B LN&d$Q ? A O A L O L" $> O N _N hBM 2B'&%-38e:-f215B' !BDcdI5BD( L|:-385B L BD-385BD-.p"%$ O85BD-5"%!BD T&E%BD-5BM )WSW]">-3 !2&%-. 213&Hg_/&DUeW 13&%-3E%B',g 213)-f&/W]">_ L I52&H2 ">-Q ;">_A:-3:-3fE LN&d$Q #LX O&%-36 8 LN&d$Q ? A O,B'E%BM $ ) P> K K 6>
LN&dQ$? O
_L $> O N
# "
15BS!"%2&%(N &H ^:&H2 ">-"%$0">- /) +AC">I3-385BD8&HAC"YN%B'AdU # ' "L $> B*_\)) - LSO O O J # ' L" $> O JI JI '9 2:-5EiLNd& Q$? O ,B uD -38 # ' "L $> O # ' a JI JI K K P 153BM 2 ">BM_$P"% 2LNB &dQ$? ) =O ,"%$BAC&%">(: !I3"9- !85BMBDB8f21N &H&H )e&H2) ">-W]">">-.- 2:-.QI3"> I31. I"> - 33Qg * -85BM+-BD, 8R) L0` h 215O Q BW]">-.2:-dIKJ U\: 4K-5"Y,h-/&H=&%(:( L ">:-.2 B]z5W]B L 215"> !Bg,h15BM 2B SL O O J Q* $8O " gih ) p 2I3W^1 213&H SL O , O J `K,B'83: !2:-3E>I3: 21# ,"\WM&% 2BD MQ* $215BM 2BS: =&X13&%( $" L BD-:-.!BM 2NH&%( L]\&N O Yd I3W 1213&H L]\=N O Y I L" 8O JO `H215BD- O ) 215B E>1.BD-385J L ">)-ab"%$3&%:-.!BM 2" NH&%( Q I :-3W]B " +&H)D-3:!B+BD-3" 8KJ L ">:-.2 " "%$R215B U M`d,B985BD83I3W]Bg213&H (::_ B Z B SL OO J 4J SL O " 2O Q 15BX"%215BM 'WM&% !B#: O $BMN%BM UZ13&%( $p" L BD-s:-.!BM 2NH&%( LE>]\& N%N BDO T" Y &%` -n\ BD !2:O _\" `u&H!BW]'">-a">2&-n%:21-5 gBS&%N -n&H ^::-P&HD2-3 "> -!BS"% 2$I5GAu !">BM-n+"%&%$-aU I L" 8 O2Q]L * \&-eN O 21Y :Q + WM&%1 !:B + 2LN&d15Q$"{? ,g O P 213&H ) T( BM$@TW]">-a2:-dI5">I3 h&HFO " Q I :_\:()&H ( U#,B L 2"{N% Bx E>1.TW]" ">-.2:-.I U%Q [ @B E%BMg21&H : gW]">-a2:-dI5">I3 g">- r$@"% gBMN%BM 2U 2&H2: 2$PUK:-5E LN&dQ$#= O2Q 15BM 2BM$@"% 2B : +W]">-.2:-dI5">I3 +">-i+h Q
?&
I:_ :(:-3 BDW] SB#Ad,UFBrq BD15_\"Y,_/BD& 8F#d21Q$3KZ&H213 &H : ' &%)-3 >T&HAJ $j 2I3">-3(:I5W]!B2D ">( UF-FW]"%">$-.AC2:">-dI3I5-">85I3BD M8sQ N &H15 ^:BM&H 22BM $@">"%-R 2Bf`21215:B L 83: 2! AI52:">-3&%(T85BM :N &H2 N%Bs"%$ ) f)- $ +TI , ) L0h 2O ` : 83baCBM 2BD-a2)&HA( Bs:- 215B WM(:&% 2 :WM&%(u 2BD-3 !BO&H=&%()_#"> !=&%(:( L ">:-.2 M`K&%-38r215BO ,"X83BM NH&H2 N%BD =W]">:-3WM:85B%Q " 215"{, 213&H g_ LNd& QVT\pO 213&H [ $ B # O J # $ ) ! L O # N P> '9 2:-5EiLNd& Q$? A O ,B'E%BM $ B # O ! $> $ ) P> # _"L $> O N hBD-3W]B%`:-NK BM, "%$ LNd& Q$? pO ,B'"%A32&%)
$
@[BxW]">-3WM()I385BS213&H $ LNd& Q$?# O ,g15BD-3BMN%BM ' JI &KQ B%Q">-s;9Q d1 I3
B *O
#
B O
#
K K N
'
aN JI K KP
K K P a Q I :-3W]B '">- %#`qBD_\_/& #dQ$#/Ud BD()83 ^B J A $ B # O J A
*w-eW]">_xA)-3&H2 ">-e,g:21 LN&dQ$?# Op213) =E> N%BD 3g +-I , ) L0h O2Q ACBS&\15 2BgI5()A&% 2 !BD c.!I5!BBD-L W]:B' 2!"I3W L1n 221"{3N%&HBg213 &H' L > 8O g a Q+-*w , -!) I L0Ndh BMO , q %" BM$)M`dLN&d&%QV T &HOAC,"YBxN%B%1` &DN% B JI
K KP
LN&dQ$?? O L e> 8O B J L O P> (N O g N @[&KQ B%BOQ 4d">-3-4"Y%#, Qb213&H 2K ">_ ^B LN&dg Q$?$? OC+T , K ,) L0B=h :OT-5$@&%BM-3 8 213^&HBKJ L HA > &K 8Q B%O Q^B">-: %X 2Q _#hB"dD"%-321W]BF">L-\&%> -.Ux 8O:-.^!BBKM 2J NH&%A (
K
K
?K
` &%-L i8 > K L @ 8O > ^B 8O W]">B -3K 2 : !2 AT"%&H$9&%,-."rU 1.DI3-_ !BL ' +BD&%-3-38 8nL ">: +:-. 2T"Ud%_\$ _\ BM ! Q9 :6hWOW],g2I3 21&%()( U% BD`u ">L -ZBDW]BDT&%W !"1 215 B'_\K )8 L ">:-a"%K $ Q @[Bh,h:(:(5 215"{, 213&H L > O ^B : LN&d"%Q$$R? ACO">I3,-3B'83"%BDA8X2&N%&H:- )&H2 ">-R`.W]">-.2:-dI5">I3 &%-38 &%- >gJ $@I-3W]2 ">-RQ '9 2:-5EiK LN&dQ$? A O&%-386 K LN&dQ$?"PO B* ) I L L LSOO > 8O ^BPLSOO J B* 2) I L ! L OTB* 2)I L $> K K
$> ! $> L [> 8O ^B ">- & W]">_ L &%W]e 2I5AK )-a!BK M 2NH&%(+"%$
hBD-3W]BZ213BZ!"%2&%(9NH&H :&H2 ">- "%$ % ' JI ) =A ">I-385BD8fA.U
K
!
K
" ' *B 2)I L L LSO O > 8O ^BPLSOO ' a K JI K K P JI K L i13) 9> 815O "Y^,gB ':21 T3W]&H">-.2L :2-dI5> ">I3 8 MO Q ^B g +T, ) L0h O2Qn3 2">_ LN&dQ$?"POg,B\&%(: !"n !BMB/213&H K %$ _#BD&% 2I3 2KB A Q 13BD q M B v C A ' B \ & ! M B T" K K L i> 8O ^B L O J L i> 8O ^B L % O H' JI L i> O ^B L O O% -fK BD&%W 1V:-a!BM K N &%( ` K L >! 8O ^B K : = 2_#"d"%21e&%-3821K 5BS&% !UK_ L !"K %2:W9$@"% _I(:&% L Nd& 15Q$#BM# BM=O $P"%&% 2-3B%8 `qLNd& BDQ$_\#? _\O & 15#d"YQ$,K KZ 21153"Y&H,g L e213K >&H 8O L ^MB > ) g 8O &H AB !">():I5 !BD&%( - Ue>TW]">J -a$jI32-3)-.W]I52"> ">I-0 g">">-- QQ K K mZ"% 2BM"YN%BM D` :-3W]B L e> 8O ^B : hW]">-.2:-dK I5">I3 9&%-38 K L > O ^B A &H`Du-3 !B BD-38 L ">:-.2 f"%$213BGK :-.!BM 2N &%() K `9,BG:-3$PBM 213&H K L > O ^B K J A &%- 215B AC">I3-383&H U\"%$b213B' !BM H' JI Qpk=I5T215BSAC">I3-83&H 2K U\"%$ &\ !BMT:K TBDc.I3&%(C!"/215B AC">I3-383&H U#"%$b 2 +W]">_ L ( BD_#BDK -.MQK gBD-3W]B L > 8O ?B J A ">-215BOA ">I-383&H 2U#"%$ %XQ 6=)-a!BM :"% L ">:-a2 "%$ %X`>,Bg"%AdNd:">I3K 2( UX13&DN%B L K > O B J A Q 15BM 2BM$@"% 2B L i> 8O ^B A ">-0%#Q @[B'E%BM
K
K
K
K
U L i> 8O B L O J U L A O8E ' U L i> 8O B L O J A HJI K K K K 1 3) 15"Y,g T213&H L e> 8O ^B : T&%- >TJ $jI3-3W]2 ">-Q @[B/-5"{, & L3L ( UZK qBD_\_\& #dKQ$Ke!"eE%BM'213&H L 2> 8O ^B : S&HA 2">(:I5!BD( U W]">-KJ 2:-dI5">I3 MQ* $p,B/WM&%-F 215"{, 213&H L > O ^Bn: SK W]">-.2:-dI5">I3K M`bqBD_\_\& #dQVT,g:(:( 215"{, 213&H L i> O ^B\: g&HA !">(:I5!BD(:UrW]">-.2:-.I3">I3 MQ
?UT
IW]">-.2::-3-.W]IB UGL &H> 8">O :-.B 2 : :-7 2_\%X".QF"%21k=I5#,g13 $FBD-5O BMN%g`BM %#O `,J X Be13 `O&YN% B6:L f LSBDO-5O6">I5> E>1 8O ?!"7BPLSO 215O "{J, L215 Bx> W]"> 8-.O 2^:-dB I3SL OUfO L J"%$ A LQ e > 15BM O BM^$P"%B 2B%Q)`5@[W]">B-.W]2:">-d-I3WM (:I3Ur85"%BS$)21L3 &H > L 8eO ?> B# 8&HO O^B/e:$@ T">(:&H( "{Au,g !"> =(:I5$@ 2!B">D_( U K K W]">-.2:-.I3">I3 MQ &%-38e15WMB(:&%$j I3 2-3:WMW]&%2(:">85- BM ^L PN K &H>2 :N%O BD T) W]&H">A:-3 !K ">WM:()83I5BO!BD&%( UO-8eW]">,-a2B:-d13I5&D">N%I3B DQ;hBD-3W]B 2 83: !! :AI52 ">-3&%( L i> O B J # L i> 8O ^B I :-I W]! I B L \> 8O ^B) &HA 2">(:I5!BD( U\W]">-.2:-dI5">I3 M!`KI 213: :_ L (: BD 213&H L > 8O B g +-, ) L0h O ;">-3 !BDcdI5BD-.2( U L M> 8O 3g +-, ) L0h rO &%-387,BV13&YN%B D -3: 15BD8 215B 2"d"%$"%$qBD_\_\& #dQ$&dQ
L
"
.
c : : +.:
8! 5% 8#
@[ &%_#BXBM 215!BM"Y ^, e-5"{N, 21N Z&HN h&%-32158_Beu! Q &YN%BD(::-5Er,&YN%BD S85B L BD-38VW]">-.2:-dI5">I3 2( U">-Z215B L & J ( ) --/ b -- *6 ' , - ' /. ) 0L N N '2N e O ': ! 1#&%0 #( L e *6N*6 N0 ZNeb O' / =+ L54P O ? >_*) L%&; O 2 & 6 -)7 8%'# % ' J N I# N 0 =, , - ) , - , & 0 2 @ ' *) ,
O@J A %%$' L N N N e O L eN N ZN ebO ' ) ' I L0h O % $+ . 5* ? ' 2 ? +7 *+ ) 2*, &
*6 7 . &* ) %
+T, )
-ACB# 3"%$+*P83baaCBM' 2BD -3W]Sh> "%U !BBD21 M`&HB%gQ E5215QrB,,Bf&YW]N%">BDI3 (:8[ 13` &YPN%R B A BM&% -3 "K8 83:7W:WM- I3 15">BM-3"% S BDW]_ ">-.N%#dBMQ$#r 2E>WM:-3&%-E L L L !"Z& L BD&H4%">-0,g 21G85BDWM&DU%Q_%9$+W]">I5 ^ !B 13BM"% 2BD_ #e13">(:83 '&%(: 2"n$P"% ,=&DN%BD X:5L 4 3 O > %L & 3 O "%$ 15BM"% BD_H#dQ Q &%-38 L eN N ZN ebO/ACB !BDc.I3BD-3W]BD &% - )% qBM L N N N e 2O ` :-G215Br !2&H!BD_\BD-a#"%$ 13BM"% 2BD_ d# Q$d# QsqBM &%-38 ACB/213BrW]"% 2 2BD L ">-83:-5E ! &YN%BD(::-5E#,=&DN%BD g,g 21W] 2BD !2 h&H+lMBM 2"5QpqBM 2BD L BDW]2:N%BD( UVACBO215B L BM "K83 "%$ 2BD L BDW]2:N%BD( UpQ [ @ B,g:(:(73D 2 L 2"YN%Bx213&H $ L Bf> ^B O # O A &% aN LNdK Q O
"
?=
$@"% g&%-aUeW]">_ L &%W]g 2I5A 2BMC h+Q 3 2">_ LN&dQVT/O|J LN&dQ$= O,B' !BMBx213&H `
R A `&%-8! &H 2BSE> N%BD-Z:_ O E Y " LNKdQ$#/O O\J O > Y Y ^^B B R AA N " Y P ,g15BM B SL O " O J " Q * - L &H 22:WMI(:&H r,Bs_\&DU W 15"d"> !B O " J A " J _\& z B*) + LSO O J _\)- ( N >Q @[BE%BM #\ N NL KdQ$?/O OcJ > $ N O A ! L]\bO #
L (:)WM 2( UXA.U
&%-38 N%BD-nAdU LNKdCQ " O
6>S\ ! ! L > \bO L]\ > O L]\ > O #\ &%-38 J $>3#Ue > ,> &% TACBM$@"% 2B%QM>g"%!B213&Hg,B&%(:(:"Y, J a Q*w-e$j&%W] 213: +1& L3L BD-3 =$P"% h&%(:(C,&YN%BD g,h 21e85BDWM&DU%Q 3 2">_ LNKdQC"bO&%-38#qBMACBD !E%BDI?U S9">_/:-3&H!BD8r;">-.N%BM 2E%BD-3W]B 15BM"% 2BD_ ,BT:-5$@BM 213&HS215B L BM :"d8 : S&eW]">-.2:-.I3">I3 O$@I-3W]2 ">-s"%$ L eN N ZN ebO9 2"e213&H cJ # $
! )
\ J #$ L]b\ O #
! )
&% a Q#;">-3 !BDcdI5BD-.2( U%` $ 13&% S&W] 2BD !'&HS215B L ">:-. `R213BD- ,g:(:( W]">-.N%BM 2E%B#!"e& L ">:-. #,g15BM 2B ?13&% O&W] 2BD !MQSmZ"% 2BM"YN%BM Y`b&HO215BXW] 2BD !2 M`R,B 13&YN%B LNKd$Q &/O B %fO I E ]N (R A N O > # N K K K KQP $@"% V !">_#B W]">-3 !2&%-.2 %.N ]N :-383B L BD-85BD-a"%$ !Q * -85BMBD8R`O$P"% L BD&H4d Z&%-38 2_#"d"%21\,=&DN%BD D` LNKd$Q & Ob: "%AdNd:">I3 MQ 3"% =WMI3 L 213Bg&% !UK_ L !"%2:Wg$P"% _I3(:F& LN&d$Q #? O E> N%BD B LSOO J > N O > O " I I E" L LSO >@O " I O I O &% O O " N N O K >@O " K E" FL LSO\>@O " O O &% O KO " N K K ,g15BM B ? N JWL # L" 8O O &%-38 ! L O J P> L O
?LX
@[ BF !a BMBsQ+21* 3- &He&H21 252:B[WMI3W]()"d&HB D/`521WM5 BDB-. 22 BDc.I5N BD -W]W]">B -.N%N BM 2E%XBF: T!"AC">N I3-W]85"%BD 8R 2BD`3 !L "r">21-3383&H:h,-3EGBx!" "%A 2&%&%:- L 215B'I3- $P"% ^_ BD 22:_\&H!B LNdK Q$& pO ">-e215Bx83BM NH &H2 N%BD MQ I :-3W]B C : 9W]">_ &%W]M` 13&% h">-3( Ue& D-3 !Bx-dI3_ACBM g"%$ BD&H4d h"% OWMI3 9:C QfqBM C LACB\215B/ !BM"%A32&%:-5BD8G$P ">_ C A.Us 2BD_\L "YNK:-5EV 2_/&%(:(L" L BDA&%(:() h"%$= &%8:I3 R A &H 2">I3-8F&%-aU L ">:-.9,h15BM 2B 13&% '&eW] BD !'"% '! 2">I3E>1RQ @[ 2I3BhW^1e83BD21383&HI3W]BT:-#NK BM,?"%$ LNdK Q$& O 213&HM`aE>:N%BD-DR A `.215BM Bg&H 2B R A &%-8 R A ` $ B # O DDN R ]N LNdK Q$K/O P &%-380&%(:(pW] 2BD 22 &%-38G! 2">I5E>13 "%$ ` R 0` () B/:- C W Qi[ @ B_\&DUF&%() !" &% 2 2I_#BS213&H $ B # O D LNdK QVT\O P @ B13&YN%B [ $ L Bf> ?B/O #*OcJ Bf> ^B E $ L Bf> ^B O # O LNdK Q$=/O B E E $ L Bf> ^B/O # O I I LL "> 2B,BhW]">I(:8\ 215"{, 213&H B B I3-3 $@"% _\( Ux">- Q 15BD-R`a :-3W]B 13&% MDu-3 !BS_#BD&% 2I5 B%`3215BM 2BS,">I3(:8 B]z5: !g&%- v 2IW 1e213&H $ L Bf> ^B O # O DDN R LNdK Q X/O P ;">_A:-3)-5EfLNdK Q$K 2O `LNdK QVT/2O `&%-8 LNdK Q X 2O `3,B'E%BM LNdK Q BA O B E E $ L Bf> ^B/O # O B& DVN R ]N $@"% g !">_#B 0Q hBD-3W]B LNdK Q$= O ,">I3()8E> N%B B ?B\)- $+T, ) L0h 2O Q I5 2213BM _#"% 2B%`% 2:-W]B215B U &H 2BI3- $P"% ^_\( UgAC">I3-85BD8S$@"% R A `H 15 :-54K:-5E
$b-3BDW]BD 2 2&H 2U%`3,Bx85BD8I3W]BS213 &H LNKdQ % O >
DDN R
A
"A
1dI3 M`5 $,B'WM&%-Z 215"{, 213&H I3-3:$P"% _/( U\">- `3,B',">I(:8"%A32&%:LNdK Q # O $ L > O # O J > E $ L > O # O #BDDN R ]N $@"% ' !">_#B 0Q I )-3W]BC h &%-8 DKR A ,BM 2B\&H 2A ! ^&H 2U%` LNKdQ # Og&%-38 LNKdQ BA O 215"{, 213&H :- N%BD-nA.U $ > \ O L O J > ! L > \PO L]\ > O L]\ > O # \&N ! ) LNdK Q ? O N qBM F R A A B' I3W 1e21&H O;|L _\:- ( N > F,O &%-38 O;L E5F,(O R[O I: r:-85W]BBB D -5 BD 8()-. !N%"/BM 2W]E%">BD-.-3KN%W]BMB 2E%"%BD$ h KI P-3Q $@"% _\( U%`d,Bx 2BDWM&%(:(R213&H !JI LNKdQ T/O B J L O J L > O L > > O L > O
15B'_/& L
L eN N ZN N O L O J L > O L $i> > O L e> O : TI-3 $@"% _\( UfW]">-a2:-dI5">I3 h">-V&%-.UnW]">_ L &%W]S !BMhAC">I3-385BD8e&Y,&YUV$@ 2">_ L ">:-.2 ,g15BM B J Q 15BM 2BM$@"% 2B LNKdQ & O!"%E%BM213BM ,h 21\215B9I3-3 $@"% _ W]">-.N%BM 2E%BD-3W]BO"%$ 0">- W N O Y ` 213"Y,g +21&HT215BM 2Bx) +&% 2I3W 1n213&H LNKdQ = O B > B J L SL O O O > L SL OO O DDN O g W N O YhN R 21513B ) ' BD". !"%2&H$K A"%()$ : 2 15BD15 BM"%21 25K BDB_ I3K d#-3Q$ d# $@"%Q _ W]">-.N%BM 2E%BD-3W]Be"%K $ BZ!" ^BK`p&%-38 W]">_ L (:BM!BD L
"
.
H (-9 :5
*w-n213: 9 !BDW]2 ">-Z,B !2I85Un15"Y, 215B,&YN%BD( BD-5E%21 "%$215B! &DN%BD():-5Ef,&YN%BD S85B]J L BD-383 X">- 215B L &H &%_\BM!BM eN Np&%-38 Q @[BZ85BD W] ACB215BV( BMN%BD(h !BM2 \"%$ ,=&DN%BD ,g 21s215Bf 2&%_#B\,=&DN%BD(:BD-5E%21 L| !BMB/ E>I5 B #dQ$K\OO&%-38G 215"Y, 213&Hx213BM 2B &H 2B L BD&H4%">-3 O&%-38sWMI3 L ">-3 h,g 21V&H A ! &H )( Ue 2_\&%(:(,&YN%BD( BD-5E%21RQ 13: TE>:N%BD I3 =,=&DN%BD h,g 21 L 2" D( BD = 2I3W^1n&% T213B;=&%-.!"% T,&YN%B)- :E>I5 2B #dQ$#dQ LNKd$Q q#/OpBM , B'E%ACBMBrT&Z213,=Bx&D:N%_ BeL W]():"%WM 2 2p$BD@ "%L ">_-3I38(::& -5En!" L54PO6> L%&;O9"%$ 13BM"% 2BD_ #dQ QZ3 ">_ L!T.Q O O >@O " J $ ! L >E\b O L] P\ > > \ O L]\K> O # \
K
K
",#
15B'W^13&%-5E%B'"%$ NH&H :&HA(:BD ! &%-3 2$P"% _/ RL!T.Q pO :-.!"
L!T.Q$#/O
J E L > Oa :- N
O\> O " J # $ !! F>E 2 2):-- QQ # Q/N K K J 6> > &%-38 J , > >
,g15BM B L!T.$Q ?/O 69 2 2I3_#B R >`euQ* $ h `K,B'(:BM ) 83BD-5"%!BS215BSW] 2"> 2 wJ 2BDW]2 ">-"%$ L ">:-.2 :- ,g 21213 ^8eW]"."% 8:-3&H!B Q 15B'_/& L L!T.CQ " O L eN 4O L N O JWL P> > N ,> > O N : +&#Au dwBDW]2:">-A BM ,BMBD-V215Bx !BM2 L!T. $Q &/O R N R A N A N R A N ? E > R A N ) )
I ) I )
A N P P )
J N A N J N J A N I ) ? N J A N J ZN R J A N P R P N J
15B')-aN%BM 2B': =E> N%BD-nAdU L!.T Q$K/O L N O L eN JO ,g15BM 2B L eN 4O J "L $> ? #UebE O E > L > O N L" $> #UebO8?E ]LE > > O E # L" (E ebO 21515B'BS85&%">85_/NH&%&%-.:-2&H,gE%B' 213"%)$-rI,h 2:13-5:E W 1 L L N N O&%O WML&%-e&H NH&%&H_# 2UBM!BM: T T:-)-385B !!BDBD&%-3885"%BD-.$ "L e%$ N O 4&%O2-3`8_) =eu21Q 3&H L L!.T QVT\O 15B L BM "K8f"%$ : =E> N%BD-eAdU # $ ! ) ! L >S\PO ]L $\ > > \ O ]L \ > O #\ J " $ " !! >FE 2 2):-- QQ # QN
",?
{m=c}
p=0
co n
p=∞
p=0
+
t ons p=c ∂2 Γ+
{M=c}
p=
∂ 1Σ
M
B
Σ+
st
∂ 1Γ+
Γ+
m
0
1
{m=z}
p=∞
A
{3A+B-1=0}
0 $9. 17;0- ' 7 0 +e . %3L eN 4OB? L + 2 N O 7 +. ? ) / 0 ,) ? * M /? ) '
) ) , *6 / . ) +5 0&%
""
,g15BM B\_\:- ( N cJ ,E L > Oa 2:- B Q >g"%!B/213&Hx 2:- B J ,g15BD-3BMN%BM `u&%-38 BKJ #\ $ R Q* $ L N OA BD(:">-5E> =!"/&%-.Ur"%$ 215BS !BM2 T)_ - L!PT.Q$& O2`5,B'( BM L N Op85BD-5"%!BO215B L BM "K8r"%$215BSW]"% 2 2BD L ">-83:-5E pQptN%BD-n215">I5E>1 B\13&% T&\W]"% -3BM g&H J `3">-5B !BMBD +213&H : % I &%-38
L N (O R A N L N O A P ;=( BD&H ^( U%` L N O A &% a Q I )-3W]B J A W]"% 2 2BD L ">-383 x!"Z,=&DN%BD ,g 21 83BDWM&DU%`',BF4K-5"Y, 21&H L N O a &% A Q 15BM BM$P"% 2B%`S $ L " N " O J &H= !">_#B L ">:-.XL " N " O2`K215BD-r215BM 2B9: &I3-3)c.I5B J L O &% 2 !"KWM:&H!BD8#!"SBD&%W^1 :-X&S-5BD E>1.AC"% 15"d"d8"%$ " 2I3W^1X213&H L N fL O O J Q mZ"% 2BM"YN%BM D`p215BD !BrWMI3 2N%BD &H Bf85BBDu-5BD8[$@"% &%(:( R I &%-8R` A.U[215Br* _ L (::WM I3-W]2 ">- 15BM"% 2BD_e`H215B+_\& L L O: % I ">-X 2 85">_\&%:-"%$85BBD- 2 ">-RQ I :-W]B ;L N O J " $ ! W]E"> = 2Q :- Q # Q J " $ I E # " ! " I J "(:-L $E E O " K ,Bx85BD83I3W]BS21&H L O 2&H2: DBD
cJ"()- L E
L!T.Q$=/O
@[Bx !">(:N%B'$P"% fL O!"\E%BM
!
L OE O LO
!
L OJ
2 :-1 L " O @[,=&DBVN%BDW] +">-3,gWM:()21I385BBM21 3 "K&H8 \$n@"%W] /"% 2&s BDE> N%">BD--383L BM!" X:"d&8 WM`O OeuW]` 2">215 2 BV:-5 !EBM#"215%B $ L L (::-3B J &H_L N I # O&%-87215BD-?E%">)-5E[G" a !"G:- Du-3 U%Q '9 2:-3E[215B $@"% _I(:&iL!T.Q$K O$P"% h215Bx_\& L L N O L eN JO2`u,BWM&%- W]">_ L I3!Bx215B L ">:-. L " N 8O)g ) W]"% 2 2BD L ">-83:-5E!" L N O JWL N I # O2Q @[BxE%BM
I# > P > # U f e E "J # E I #
",&
\# O J E # 2)-31 L " O2`,B D-38 " J W]"> 1E e # >3e 15">BM-3 83BM$P "%!" 2/B%`=&/:-7WMI521 23N%BBx:L - e N 4 2O|2&J HL 2(:2&%:-5-5BnE/21&H5hBZ:- !D BM-3/":%U%$O`5,=W] 2&D">N% 2BD 2 f)-5,gE 21 L BM&H T "K218 5B W]">"%: -. 2B]J L L ) ) L!T.Q X/O L eN JO JWL W]"> 1 E L e #\O > &e N O)g N &%-38215BD-Z& L3L 2">&%W^13:-5EX215B(::-5B J >Q mV"% BM"YN%BM D`b$P"% 5D zKBD8 215 BXN%BM 22:WM&%( (::-3B ,L N HO g A >`: O_\& L3L BD8 ">-.!"n215B\(::-3B J ) I 215 ">I5E>1 L eN 4HO JH"L ZN 2O Q gBD-3W]B%`b215B#$j&%W] 213&H L N O A `_#BD&%-3 g213&H Z:-W] 2BD&% !BD T&% L eN JO _\"YN%BD g&Y,&YUn$@ 2">_ L"%" ZAN ! 8BMO N%,gB[ 21213:&H- P L N !O &% (:">-5A EF&%&% -aU !! &%:E>A 1aQ /( ):-51Bf: 21_#5 2BD">&%I5-3E> 1 213L" Z&HNe 8O221Q 5B @[BVBM &%:()"d !8" L & L3L ">&%W 15BD lMBM 2"&%(:">-5E'215BhA ">I-383&H 2UX(::-5B J _N R 9"%$ ) Q* - L &H !J 2:WMI3()&H D`%$P"% pBD&%W 1 J X >`e &%-38 _g L A N a2Y215BM 2Bh: &'I3-3)c.I5B L BM "K83:W L BD&H4%BD8 ! &YN%BD(::-5E ,&YN%B"%$T215Bn;=&%_\&% 2 2& J!h">(:_ BDcdI3&H2 ">-0,g 21 L BM "K8 ! &DN%BD(:)-5E ,g 21e BMBD8 Q I :_
L (: $@Ud)-5ESA.UeI3 2BS"%$b215B:85BD-.2 UW]"> 21 L
!
!
.
L
0 -7 7 5 + ?! 3 -9$# V + F+.: #
*w-x213) b !BDW]2:">-,B=85BM N%BB]z L ():WM $@"% _I3(:&% b$P"% 215B L BD&H4%BD8! ^&DN%BD(::-3Eh,=&DN%BD MQ * $ ?: g& L BM "K83:W L BD&H4%">-Z 2">(:I52 ">-V$P 2">_ L" 8O"%$ 15BM"% 2BD_#dQ ` 213BD-! R >`eu` J &%-38 R A Q 1dI3 RL!T.Q$# OE> N%BD LN=dQ O O >@O " J # $ ! W]E">= 2Q :- Q # Q J # (:-L| 2)- E ! E 2:- O K K K ;=15"d"> 2:-3E O " !"f213&H LSO " O6J s`C,BE%BM " J A Q I )-3W]B J( `C,B#13&YN%B 2:- J ) @[B'E%BM
LN=dQ$#/O \O > O " J # (:K K J # (:-
E ) i> E ! L" P> O%E i> ! L" P> O
) E
",K
I :-W]B J ) J ) `5,Bx:-5$@BM +213&H LNd= Q$?/O U# e E #* !$ B B J ]> E ! #Ue4E #* E i>
@[@[BB'"% 2">A3( 2&N%%Bx)- 213) T!"/"%A2&%:-V&%-ZB]z L (::WM +B]z L 2BD 2 ">-e$@"% g215B L BM ^ "d8:W L BD&H4%">- MQ LNd= QC" O SL OO JWL E ebaO W]"> 21 O >@O " >3&e N O >@O " #IN K K K K ,g15BM B cJ " ()- > E #Ue E #Ue#* E E : 215B L BM ^ "d8/"%$F"%A32&%:-5BD8r$P ">_ L!.T Q$= 2O Q F: B]zK!BD-385BD8 L BM "K83:WM&%(:( U!"X215B 2BD&%(():-5B%Q L 6h ) (: !B# M -3 &H>32 N%&e BDN( 8U%pO `=$@,"% BVL WMBD&%&H- 4%">I-3 ! TB Ad eU &%L!-3.T 8Q X 2O 21 O\>@O " >3&e N O >@O " # K K K K * $ : h& L BD&H4%">-n,g:21n85BDWM&DUn&% 9:-6"L #PO "%$ 15BM"% BD_ d# Q `,B1&DN%B J &%-38 J A QXL!.T Q$# O Ud:BD(:83 LNd= Q$K/O O > O " J # $ W] ">:-P =QQ # Q J # (:-|L 2:- O K K K ;=15"d"> 2:-3EHO " &H 215B L BD&H4 `> !"O213&H SL O " O J `%,B+E%BM 2:- " J 2:- BKJ Q mZ"% 2BM"YN%BM D` 2:-3W]B J `3,Bx13&YN%B 2:- J ) 7 15BM 2BM$@"% 2B LNd= QVT\O O > O " J # (:-L
K
8
K
"!#$
)+*-,*/.0.12*3*#4576989:/8;.=?A@CBD6 E
GF
$
IH
%& ('
J "!# K ML
F NPO '
!#"%$'&)(+* ,.-/$'01(2" 3 ;=1 5D.*/?5476 * 1286 *D8 .1 . < ? * :A1 :$ 9 2; 87=@? .12*\; @ A BA C069@ *ED B .8; G F HF 4 $N4 / H / / L F NO LPO =Q? L / H L H ;
I#J IKJ IMI I I I IMI
