Kinetic Theory and Bose-Einstein Condensation Colm Connaughton

!"# $%&"'
*( ),+.- (/),0101243658789:)80;=<?>,@BADC&),-E@F2G3
H4IKJML:NMIPOQL:RSNMTz m|UKT{}`_VwWKX~s€YZR\[^{|]_]_TT}`FH#OQIPWvOaL:RbY^oOaRaL:[cB]dUTew|UK‚T&ƒ:~KfMg„†hj…eikLPVjflTI:NumnRbY L:NZz oTkUKI:TMfpT&‡‰`qˆP]sƒrdw8tuŠ NuN‹R\I:Tu]vFNZiŒwxT IYZY^Lyi^RQteI:]
*ŽKs8‘Ž
’.œc“"¬† d”M–l•d›l–l–p¦d—'™M–l˜ d™M­®”M–pš^›pžŸœ*¤†“q˜œ*­'žŸ–pšc–p—k—š^ _¢¯—k—¡žŸ”M–l›l•_ dœ*”kœ°™k¢:—M›p¤Ÿœ?—M”k£dœ^›b­˜y¤¥—œcž§¢¯6¦†1¤œy˜¨v¨†–l“_›l¤±œ^”M–l–p“Kš?”kœ^”M™Œ•_˜:œcš^¢:”M™M–l¤“dª‰–l“©¦²¢Pžd—kœc¢:—k“_š^™M—y–l³B¦d´–l“dœ¡ªD–l”M›l•_›l _œ—k”M“_™Œ¢:˜“Ÿ”kœ «
•_—M–l¢s”.µ¤šy˜±˜“/—M–l¦²­'œ}£džd›pœœ^™M¨†–l¶¥–l“_œcœ^ž*”M–p¯aš*™k¢:œc­¹¬K q”M˜•_”Mœ–p¢:—M“§£q˜¯\”M¢:–b™n˜›l”M›l¤•_œ•_¢:”M–l­­¢:œª¥œ^œ^“_¶¥œc¢:¢:›l d _”M—}–p¢:º“·™k¢P¢—k¯¸—M«¼”M»•_œ*–l”Œ˜:—Mœ^£F¶vœc—kš^¨†”M–l™Œ– ˜œc›¬†£q q˜˜™M”M”M–p–p¢:š^“G›pœ/³v½xždœ^•d“Ÿ–p—«
¨v¨v–l–l“_“_œ^œ^”M”M–p–pš?šx”Mœc•_¬†œc q¢:˜™M”M¤¡–p¢:–l“§“°”M˜•_ªPœx™kœc›pœc¢:—¡“dªj1–l”M˜y•¶¥œ^”M›p•_œ^œ“dªP _”M—M•? q˜›l–l›­'¾1–l”¢:j›l”M¿c•_­?œ^™k˜œx“d”M“Ÿ•_«¼œjÀ¢v¢:šc™kš^žŸ d•_£qœ^˜–l­Á”M–p¢:œc“'¬K“K q d˜­¡”M–p¢:¦F“œ^™k¢—1¯x˜¬†™kœj q˜œuÃv“K£²”M dœc­ šu«
”kždœcœcž'—kš^”k™M¢&–l¦²¦Fœcœjž ³›b˜½x™Mª¥•_œPœc³K—k½xœ*•_–l“_œ¸š^—M›l”Œ _˜žd”Mœ/–p¢:“q¦²˜¢:™M”M¤•·—k”M¢:•_›l dœ^™M”M­–p¢:¢†“_žŸ—¤v¢“q¯F˜”M­'•_œ–pš‰ºœc™k¬K¢P d—k—‹–l›l«¼–l»¦d–l™M”Œ–l˜: dœ^­Ä¶Ÿ—M¨v—M£F–l–dœc¨†š^–l”M“_™Œ˜Dœ^”M–p˜š}“_œcžÂ¬K qÅ_˜“d”M–l–p”k¢:œ*“*Æ_˜ Ÿ™kà œ
Ç}—M”Œ¢:˜›l”k­œc—x¢:˜ª¥“_¢:™kž¢y¶K˜™kȟœ}ɲœu˜Ãv¨†£²•qœc˜š^™k”k¢sœc¶*ž—M”k£²¢&œcš^¦²”Mœj™Œ˜Ÿ™k³¥œ^›p½xœ^¶:•_˜œc“†—kœ¸”›b–l˜“”M”k”Mœ^•_™6œ|—M”M£²™Œ˜œcš^“_”M—M™Œ¯a˜&œ^™1˜¢™kœj¯²£q–l“K˜”M™M™M”M–l–p“_š^—k›pœc–pšy—1˜”k›l¢n›l¤›p¢y“_Ê¢:“_­œc¬K¢: d­–l›lœ^–l¦d“K™M”Œ–l˜n d­–l“
”M”M•_–p¢:œe“_—¸–l“d¢–l”M¯–b˜˜e›—k—M¢:”Œ›l˜ dª¥”Mœ'–p¢:“€¢¯6¢”M¯8•_”Mœ'•_šcœ¢:¨v“_–lžd“_œ^œ^“_”M–p—Zš˜”Mœc–p¬K¢: q“˜”M£d–p™k¢:¢†“Ëšcœc¦F—kœ^—sªP³F–l½x“d“d•d–l–p“d—ª'–p—j–l–l›l”M›l•‰ _—k–l”M“d™Œ–l˜”M”k–bœc˜žD›4šc¦K¢:¤±“_žŸ—Œ–l¢:”M­–p¢:œe“_—jšc¢:¯\˜­'™1£d¯a d™k¢:”Œ˜­ «
j”Mœc•d¬†•d–p d—¸–p–lšŒ›l—k•·–l–l¦d“d™M™kªP–lœc d d—M­€ d›b˜›l™M”k³_–l—e½x”¼¤€–l•_“©œ&˜:—x˜±—k¢:–l“_—M›l–l dš^“d”M–lªP£d–p¢: d–pœ^“‰›b“K˜ª¥™M”–lœ^”¼šc“_¤·¢:œ^“_™Œ˜žd˜”e”kœ^œc“_¿y—œ^—Œ™k˜˜¡¢±”kœÆ_­ Ÿ¯\¢:Ã*¢:™M­­?¢¯#œ^˜“†£q”M”M–p˜ d¢:™M“G­Á”M–p³dš^´›pjœc–l—xœ”M•d¯a”M™k–l•_¢:“œ^­Ì“€Å_“d›b£d˜–l™k™M”kœcª¥œ—kœœ^”M“†–l”k­”|¢'œP—k—M¢:³8­?­´˜œ›lœ*› “K­–l d“K¢:­”k­œ^œ^™M™Mœ^£d–p“K™kšy”Œœ^˜˜ ” ›
™k”kœc¢—M d¢: d›l”k™}—x¢:¢:™M“/–lªP”M–l•_“qœ˜›4£Fœu¢PÃv—k£²”‹«¼œc—Mš^–l”Œ“d˜ªP”M d–p¢:›b˜“_™M—¸–l”¼1¤*œ&žŸžd¤†¢'“q˜“_­'¢:–p”|šc—¸¢:¦_˜—Œ“_œ^ž*™M¶¥”Mœ•_”Mœ•_˜œ&£dÇ|£d™k¢:¢¥›l­˜:šk¢:•‰ª¥”k¢:¢e™k¢sœc¶K¬K«Î dɲ–l˜›l–l¨v¦d•q™M˜–l d™k¢y­€¶Ï³q—MÍ1£²¢:œc“†š^”M”M™Œ™M˜ d™M­ ¤
žŸ¢¯ d™M”M–l•_“dœ€ª°šc”M•_¢:“dœ}“_£Fœcœ^š^™M”M–p–p¢v¢:ž“Т¦²¯8œ^šc”¼¢:1“_œcždœ^œ^“Г_—Œ”M˜•_”kœ±œºªP™k™k¢y¢Pj—k—‹”M«¼•G»³Ÿ–l’¼”Œ“*˜:œ^”M¶Ÿ•_—Mœ¨v–lš^–}›p¢P˜—M“_–l“džÑª'¾x—kœc¢:š^›l”M”M¿c–p¢:­?“_˜—1“d“Ÿœ«¼À}˜:¢:žd™kžŸžŸ™k•_œcœ^—k–l—1­Ò”M•_¨vœ|–l“_–p—Œœ^—M”M _–pšœ
œ–lc“¬† q­˜¢:”M–p­¢:“_œ^“K—y³²”M d´­µœ?—M˜£q™M˜:ªPšc _œPœ°Õ¥­?”M•q˜˜”k”šŒ•d”M–l•_“dœ'ªe”.–l“*¢€˜“?œc¬†–l q“K˜”kœ^”M™M–p¢:­“_œc—žŸ•q–b˜˜y”k¶¥œœ™ŒžŸ˜“d–ÔÓ²ª¥œ^œP™M³†–l“d´ªËœj™k­?œ^ªP˜–l­¨¥œœc—&—k¢:¢­¯jœ¸˜—M£d d£dªP›l–pª¥šyœc˜—M¦d”M–l–p›l¢:–l“_”.¤ —
¢¯#•_¢yÖ”M•d–p—|­?˜”kšk•d–l“dª*šy˜“€¦Fœ­¢vždœ^›pœcž‰–l“‰£d™Œ˜:š^”M–pšcœP³
×°TuXØ6L:N‹U:YcÙ"ǖl“_œ^”M–pš”M•_œc¢:™M¤FÕq¾1¢P—Œœu«¼Ú–l“_—M”kœ^–l“Ëšc¢:“_ždœ^“_—Œ˜”M–p¢:“
Û 1Í1h ¢:o™MI:™kœcRSf4—M£²I¥¢:U¥“_UPžŸNMTZ–l“dYZYcª*TZYy˜Ùx dÜP”M•_ÝK¢:ޙß_à†ÞPá_â8ã‹ä:åqâ8ã¼æKçÏèQÍ1¢:›l­éÍ1¢:“d“q˜ dªP•†”k¢:“BêuÕqádÝßqäKë:ìŸà†ÞPá_â8ã‹ä:åqâ8ã¼æKç
èîí¥¶ œc—}»,¢:­œy˜ Bêu³
ïð^ñ.òFðMólôFõös÷_øù'óQõMõÎñcú±õÎûnüýpö^ñsþóañkðÿkóañkôcñ
ô
! "#%$&'(*),+.-/'102-3546'2780(-/ 5944:;('=<>?7A@/7;(BCD:E)
F ;GIHKJLGM#NO78;P02-34@3'!#Q7R$& 'PSBT78'UT0(;U0(S'(7=C'(-3B @/VO7;102-34@/XWD:O7T0(:
'P027802N'P:4LV0(O7800(Y#Z;274*02-3 [HKJ1\H];(=7-3'&^O-_02Y-3`02Y0(;P=96a9O7!-/4b@/-3=-_0cG
Hed
fgGhHi\ jk^O-_02lm,n02E47'(i#I7`:-_#Z ;(oBT7'G0(EO7;102-/4@/'Y4 6'Pi-/
02K'(-3B @/%O78;P02-34@3Q'10L780(pO7cq9-/BUr;(`! !T02:Clts.;(6-/4*026 F aS$I '(p76n+.-/9)
'P0(-/i-3VucvTw8xOy{z|G_u}~€G 02-/' ! =7'‚B ;2780(6!-/T02'(>-3D0(;P'P0‚-3E02O78'P0
6476Y#Z @3@/<>-/BQ0(Y*ƒ90('P-3q N„ƒ|;(-/!T027@…;P B ;P'('I<>-/4L[O78' F [=76b-/
4 6'P-/B†7802 !-/4B 7'('&'(-34‡02‡-/-302-/7@„ƒ;P-/!T02'I-/Vuv vTˆ|y_u8GЉ8~€l|‹|py_uŒ~t#Z ;
7E;(q9-3<%l
&0( ;P0(-/4c78@|6'(4;(-/|02-/†#$+MŽR;(@/-/'-302;E9-30(-/4‚02 ;PaG80('(),4c78@/@/6
$& @_02r=79)’‘b;(6-/“D-/02-34&W9:7802-3 E ; †0(>”N;( 'P'1),s‚-/7802*q9'(D-/-|WD:O780(-/ hG7
WD:O780(-/ [#Z ;0(N02-3=„),'(74N66O7T0•7!@/-_02:6b#02%46'2780(l
K$& @30(r=7|),‘b ;P6-/—–€$M),‘Y˜&D-/02-34NWD:O780(-/ …G
™Oš…›œ
›£¤£Z¤¥¦¤§p¨©š¤c¥(š¤§ª’«9¬i𛣒­ª1«9¬Eš…¤£’­®¯š…›£’š¤£ª’«9¬iš¤c¥P­ª’«9¬iš¤§L­,°
™OŸž¡ M¢
¶
¶
¶
¶
±|ª².³¬µ´³®¯´h¶‚®¯´h·*­±ª¹¸ ³ ¬»º ³ ®¼º ¶ ®¼º · ­½T´³,½T´h¶„½T´h·
–’u˜
<78'6;(-3q6 F aK‘b;(6-/¾y¿uÀ8~D#Z ;Á02M02-3=‚q @/:|02-/K#02M'(4*02;278@|6'(-_0,a G š…¤ G
#7%'P027802-3'P0(-/4c78@/@3aK ! B :'‚'P F @3b8#h-/T0(;278402-3BQW9:7T02:ÂO78;P02-34@3'‚'(9 78#Ã02;M0(•6q @/ =D0#WD:O7T02:Ä'10L780(-/'102-/47@t=4LO7-34'I-/i02bc7;P@3aE0,<IT02-302
4D0(:;Paltm,V0(Q7 F qQWD:O7802-3 ¢
«
›£¤£¤c¥Å¤§
ž
ÆSÇ
¶
·KÈ8ÉËÊ ›£,Ì9¤£ É ¬
É©Ê ¤£¦Ì9›£ É
¶2Í
–€w ˜
<>;P Ê -3'!0('P4c780P02;P-/B¡@/B02…G Æ
-3'!0(S7;P0(-/4@3C=7'P'U76 Ç -3'`s.@Î74LÏ{'
4 'P0L78D0lIm,Ð02-3'U7;102-34@/ F @/6|#74X0,a9C;(;('PT02'X7Ñq 402;U-/ ½ ),6-3='(-3 O7@
'(O784lÒAK'(O7@3@0,a9-34c7@3@3aX:'P ´ 02U;(;('PT0K7U6:!paXq87;(-/7 F @3Q<>-34L-/'b-/T02„)
B ;27026=q ;76 ² 02K;(;('PT0 b<>-34L`-/'M0l|b6-/'102;P- F :0(-/ !6-3'P02;P- F :|02-/
-/';(=7@/-3'(6['P:4LC0(O7800(%O7;P0(-/4@/Y6'(-_0,aX-/'B -_q F a
Hi\ j
«
ž
½T´³9š…¤£„Ô
ÇDÓ –zT˜
Õ V0(%02;O76…G02K”N;( 'P'1)’s.-_0L7*q|'PD-/-‚–€”Y),sI˜&WD:O7802-3 hG
™×
Ö Ç
™ 
ž
®
Ç
¶
Ø ÆÐÙ
¶
×»¬
¶
× Ý
j ªZÚ­’ÛѬµÜ É × É E
w
–ZxD˜
^O;('10Q6;P-3q 6¡-3n02i'(-¿ƒ902-/'iy_uw|G3uc‰~€G-/'%7[=7ÑWD:O780(-/ n#Z ;Y0(i'(O784*)Å02-3=E6„)
6D07=@/-30(:6#02b4 6'(78028lb @3-/7;‚-/T02;274*02-3 i49!4-3T0cG Ü G
-/'
Ü
ž
Ç
Æ
¶
Ê
Ô
–€ˆ ˜
b;( ± -/'02…40(-3q 'P4c780P02;(-/BY@/B02K#O02&0,<&) F |6aK02D0(-Î7@D-3p02&'1)¦<&7cq 7;Pcƒ-3U702-/hl.-/'U7;Pcƒ-3U702-/hG.-/;(T0`-/¼02n”Y),s WD:O780(-/ hGM-/'!q87@/-36
;(q9-/66µ02O780 Ê -3'E†:4L¼'(=7@/@3;Q02O7¯0(V7q;(7B X6-/'10L74 F 0,<I»7802='G
02O70p-3'%0(S'(7aÑ0(UBT78'K-3'Q6-/@/:|02lj ªZÚ­ ;(;('(T0('p02!*ƒ90(;(7@I0(T02-/7@)b0(
02;(7`-/!02•4c7'PY#;Pc7@*ƒ|;(-3=D0('lO ;7U*ƒ902'(-_q N;(*q9-/<?8#02b;( @3•#h0(
”Y),sÂWD:O780(-/ "-3»02C02 ;PaÐ#K$+MŽ '(µy Œ~€l&m,50(n7 F 'P4Ñ#Q7"*ƒ90(;(7@
802T0(-Î7@€G&<&A7;( 4'(-36;P-/BÐ7Ð'PO7802-/7@/@_a» =B :'VBT7'C76 02A”%;P '('’)
s.-30L78q9'(D-/-WD:O7802-3 F 4 !'0(% @3-/7;>‹|4L;P|6-/B ;WD:O780(-/ …l
Y :|02@/-3‡#02-3'7;102-34@/‡-/'I7'&#Z@/@/<>'l9m,['P4*02-/XwQ<IY6;P-3qN7pD-/*02-34b02 ;1a
#Z ;02”Y),sSWD:O702-/Q<>-34Lp6'(4;(- F '02‚02-3=‚*q @3:02-3 K8#02&7cq ;27B&'(4*02;(7@
O7;102-/4@/K6'P-30,al…ÒAp;(#Z;•02`0(†;P'(:@302-3B`D-/02-34†WD:O702-/hGWD:O7802-3 ¼–xu˜*G7'
02Q”
|s¼9-30(-/4YWD:O7802-3 `02i6-3'P0(-/B :-/'(U-30#Z;P k0(%$
|‘ W9:7802-3 hl-/'D-/„)
02-34YWD:O780(-/ X-3=@3-/'M0(O780 ×
!c7-3B†-_06'P4;P- F '02N;PB -3=‡<>;P% @3a
ž
'(;P0.<&7q'I7;(&;(@3q87T0cl8m¦0‚-/'0('278=D-30(-/4W9:7802-3 i7'02780.:'P6i#Z ;.7Y@/B
02-3=Q02[6'(4;P- F †02p'P0L702-/'102-34'Y#M |02-/47@Á02:; F :@/48Gh'(E#Z ;Y*ƒ7!@3`y{v8~ÅGh76
02;‚Ta9'(-/47@O'Pa9'102!'MB q ;P6 F a†02>@/-3c7;.‹|4L;(96-3B ;‚W9:7802-3 hlO @3@/8)
<>-/BY0(-/'.6;(-_q87802-3 hG<&‡766;('P'.02>-/'P'(:8#'10L780(-/ 7;Pap'( @3:02-3 '0(N02D-/02-34
WD:O780(-/ n-3n'(402-3 zl…Ò¡EO7;102-/4:@Î78;(@3aX=O7'(-3'(†0(E |)¦WD:-3@/- F ;(-/: 'P0L702-/)
O7;1a»'10L780('U<>-34L"4c7;P;PaO:|ƒ|'[8#%;(Ba5765O78;P02-34@3'=0(;(:B 5! !T02:
'(O784l&n'(4*02;27µ7'P'(94-/780265<>-30250('Pn |)¦WD:-3@/- F ;(-/:e'P027802-3 O7;1a»'10L780('
7;(K4c7@3@/6b @3=B ;(qT)h7897;(q –Y)˜>'P40(;27la7;(p7n7O78@/ B :K#.0(
b @3=B ;(qT) Õ F :9q†'(40(;(:¾#hDa96;P|6|a|7=-34‡0(:; F :@/4‡<>-/4L=-/'M;('P|)
'(- F @/>#Z ;M;(Ba!02;(7'( ;10-/!#7;‚#Z;( ÂW9:-/@/- F ;(-3:O:-/6'l Õ #O78;P02-34:@/7;‚-/T02;('P0
-/n02U”•)’s 9-30(-/4†0( ;1an-/'N0(i-/Tq ;('(!4c78'(4c786=<>-34L¡-3'N;('( '(- F @/E#Z ;Y0(
02;(7'P#Z;=8#NO7;102-/4@/'i#Z;P -3B ¼0(A@3< = !T027 ;PWD:-/;P6¼#Z ;U$&+IŽk0(¡944:;
-/n7='Pa9'P0( <>-34Ln-/'b-/-_02-Î78@/@3a`7c<7caS#Z;P 02;(!|6|a|7=-34KWD:-/@3- F ;P-/:VlOm,n'(4*)
02-3 Cx!<&p@/9 [780b'( !%02-/!%66T0N'P @/:0(-/ 'b#02QD-/*02-/4%02 ;1a lb'(-3B
'(@3#Î),'P-/!-/@/7;(-_0,a!7;(B :=D0('‡76V9:=;(-/47@h'P-/†:@/7802-3 'M<&Q'(< 0(O780>02Q-3Tq ;P'(
4c7'P4c76S4c78ÐB ;(7802C7n^O-30(O:|ƒÐ#bO7;P0(-/4@/'E0( 0(Cr;P¡! !T02: 'P0L702
'P027;P0(-/BV#Z;( 7V4 T02-3D: :'KO7;P0(-/4@/i6-/'102;P- F :0(-/ Ñ<>-30(-/Ñ^O-_02!02-/!l-/'Q4c7
F p'(¡-3'(=†'P'P!7'Y4;(;('( 6-3B`02`0(E 'P0%#‚4 6'2702-/ ;( ;l
m,`'(40(-/ Xˆ%<&Y;('PT0>'(=‡;(@/-3=-3O7;PapD:=;(-34c7@4 !:027802-3 'M#Á7p'1a9'P02
#MD-/*02-/4KWD:O780(-/ 'Y<>-/4Ln6'(4;(- F †02†'P0P)  q @/:0(-/ hl…‹|:;P;(-3'(-3B @3aX<IE6
0='(S02!•) 'P4c7@3-/B¡-/µ02C'P0P)  ;(B -/! F :0U;2780(;=7A;278-/6Ð7;PT74L
02V7X'(40(;(:]q;1aÑ4@/'(E02[02;(!96a9O7!-/4†W9:-/@/- F ;(-3:Vlm,Ñ02iD:@_02-/=780(
'(402-3 =<Ib766;P'('M02‡'(: F 02@3bWD:'P02-3 !#…0(b4 40(-/ F *0,<&`02b$‚)’‘ 76
”Y),sAD-/*02-34>0(;(-/'l Ò¡•78;(B :>02780‚02b$M)’‘"D-/02-3402 ;Pai'P :@36 F b;P@3q87T0
z
#Z ;&@/7;(Bb! !T0L7†786U02%”Y),s¯WD:O780(-/ `;P@3q87T0&#Z ;M02•@/<?==D027Q<>;(
4 6'(7802-3 »944:;('lIC0,<IR'(:@/6ÐU780(4L»-3Ð'P =V-/T0(;(!6-Î780(V;(7B V#
'(47@/'lDÒA•7;(B :b02780&0(-/'MU7024L-3Bp'P :@36 F •;(7@/-3'(6 F a=0(-/9-3BQ#02 •)
'(4*02;(:k#…02•$M)’‘?WD:O780(-/ !<>-30(U-30(' :|ƒ=#O7;102-34@/'M7'7Q'( :;P4Y8#O7;102-/4@/'
#Z ;‚02Y”Y),sRWD:O780(-/ hlDÒ¡• :0(@/-3>'( !Y7;PB :!T02'M#Á<"0(-/'M=-3B T0 F •74L-/„)
q87 F @/%-3C;(740(-/4 F aC766-3B=7='(:;(4K02;( 0(!0(E”•)’s»WD:O7802-3 C<>-/4LS!96@3'
02=4*0†#0(U7;P0(-/4@3=47'(476!#Z;( @Î78;(B ;Q! !T0L7|lhÒA=4@/'(=<>-_02¡'( !
4 !!T02'N7 F :|0•02E:O7'1<&;(6¡WD:'P02-3 'Y<>-34L<&†#Z@7;(†-3= ;10L7T0‡02X7
#Z:@/@3;:6;P'P0276-3B=8#0(%;(@/7802-3 'P-/ F 0,<ID-/*02-34Y02 ;(-3'‡76V$+MŽ•l
C€T€Dt
Å![KZ "!hZ
#%$'&
(")+*-,'.0/21435,6)+387%9;:<=>,@?/6,A143B12CEDGFAH
I0N:'N4
'P-/6;Y< 0(†'PO7802-/7@/@_aX:-_#Z ;(o4c7'P†<>;P†02p*ƒ902;(O7@0(T02-/7@ÅG
j ªZÚÁ­ G-3'>7 F '(T0cltp”Y),s¼W9:7802-3 hG
™×
Ö Ç
™
Ç
®
ž
¶
¶
×»¬¯Ü É × É †
× Ý
¶
Ø ÆÐÙ
–ÀT˜
#Z @/@3<>'&#Z;( k02Yq87;P-Î780(-/ O78@;P-/4-/@3
±KJ
™×
Ö Ç
™ ¼ž
±×
Ý
–€Œ ˜
<>;PQ0(•7!-/@_02 -Î7hG
J
ž
½ ÚML Ç
Ø Æ
¶
É
Ù
Ü
¶
× É ¬
Ø
É × É NO
Ý
–‰T˜
=7'(:;('E0(`02027@&;PBa¯#‡02[4 6'(78028lMm,¼766-30(-/ A0(Ñ4 'P;1q|-3BG
WD:O780(-/ ¡–ÀT˜7@/'Pi4 'P;1q '‡02N0(0L7@…O7;P0(-/4@/YD: F ;G
H
#%$P#
ž
½ Ú
¶
É× É Ô
J
–vT˜
Q-)+R+9)+37S<;1437%93:)+/T9U:14.0V%/W,A143:
%02;(-_q9-Î7@'( @3:02-3 [#–€ÀT˜4 ;(;P'( 6'>0(U7E'PO7802-/7@/@_a!:-3#Z;(
×iªZÚ.Ý(P­
ž
É ×YX É2Z
Ì[]\
^`_ acb;_
¥Adfecg
Ý
4 6'2702G
x
–1uc}T˜
G
R-/'78S7; F
É ×YX É -/'>78C78; F -_02;278;Pa=4 6'(7802K7!@/-_02:6•76
<>;P
-30(;27;1aUO7'(8l
‡02;. F q9-/ :'.0,a9b#'(@/:0(-/ '.8#.–ÀT˜7;(0(<7cq „),O784L0&'( @3:02-3 '0(%0(
« 4 ;(;P'P 6-/B=02
@/-3c7;P-/'P6VWD:O780(-/ hl'(E'( :@/6 F p;(@3q87T0‡<> Ü
02%6-3@/:0(G<Ic789@_a[-/T0(;278402-3Bi;(B -/!
l'(K7;P F '10‡*ƒ|;('('P602;( :BX0(-3;
O :;(-3;&0(;27'P#Z ;P
«
×iªZÚ.Ý(P­
ªØ ­ ¥ ž
¤ª ­
e d
Ì ¹¤
Z
½T´Ô
–1uu˜
<>;P ½ -/'0(%9: F ;>#'PO780(-Î7@h6-/!'P-/ '76
¤
Ç
ž
º
Ø Æ
¶
Ô
–1uw ˜
ÒA‡0(‡#Z;P –’uw ˜02O70&@3-/7;<7cq' =7p$I '(„)’+.-/'102-/!4 6'(7802•7;(‡-/B@3a
6-/'P;('P-3q 8lm,p0(I<Ic789@_ap-3T02;(740(-/B‡;(B -/!G0('P&<7cq'‚76K02-/;-/T02;274*02-/'
@Î7ca†7i-/! ;10L7T0O7;P0-/E026|a|7=-34'<>-34LE<>-/@/@ F „ƒ7=-36i-3E= ;P6*0L7-3@
-/[02-/'>7;102-/4@/8l
#%$
14V =>,A9=U:T?)%<;97%9;:<=>,@?/6,A143
‹|-/4b<IY78;(‡6c7@3-/B%<>-30(=<&7cq 'G-30M-3'I4 T
q -/T00(K<I (; i-3 O :;P-/;‚'PO748l9Ò¡
76 |002N#Z @3@/<>-/Bp0L702-/`#Z ;02O :P; -/;&02;(7'P#Z;( O
78-/;
•¤ªZP­
×iªZÚ.Ý(P­
«
×iªZÚ.Ý(P­
ªØ ­ ¥ «
ªØ ­ ¥ ž
Z
½ Ú
Ì ¹¤
¹¤
½T´Ô
•¤ªZP­ Z
ž
–1uczT˜
m,!O :;(-/;&02;(7'1#Z ;(!6[q87;(-/7 F @3'G|02b7=-3@30( -Î78U-/'
J
žA ¬
76
«
¤ •¤
¤ ½T´
–1uxD˜
•¤•¤ £ ¤ ¥ Ü
Ø ªØ ­ Ó ­ ¤ § ±|ª´=¬¼´³®¯´h¶‚®¯´h·*­½T´½T´³,½D´…¶„½D´…·
•7!-/@_02 …Ï 'IWD:O780(-/ 'G–ÅŒ ˜„GB -_q ™ •›
™
¬
Ö
› b›
ž
®
ÖÜ
ªØ ­ Ó ¤£ • ¤¥•¤§L±|ª²¬E´³®K´h¶T®p´…·*­½D´³1½T´h¶L½T´h·cÝ
ˆ
–1uˆ ˜
<>-30(g7µ4 ;P;('( 6-3BÐ4 !@/„ƒ?4 P:BT780(6gWD:O7802-3 ?#Z ;
;[027802-3 O7@
› l O
;(7'( '‡-_0>-/'„ƒ6-/T0>02i<I ;(`-3[02%-/T0(;278402-3 [;(;('(D027802-3 C
7 6 0(-/B†0(
q87;(-/7 F @/'G
›ªZP­
d
b›ªZP­ Z Ô
ž
–1ucÀT˜
›ªZP­
QWD:O780(-/ X#=802-/U#Z ;
™ ›
™
Ö Ü
®
ž
Z £ ¥ § d
¶
ªØ ­ Ó -3'
¤£ ¤c¥ ¤§±„£ (¥1§t½T´³¶,·Ô
–1uŒ ˜
;(<&>O7cqb-3D0(;(96:46E02#Z@/@/<>-3BY027802-3 †<>-34Li<I>'(O78@/@4 T02-/D:0(Q:'(
b
02;P :B :002K78;P02-34@3•02!4 !O74*02-_#Ãa=0(N#Z ;(†:@Î7
£ ¥ §
ž
±„£ P¥1§
ž
½T´³¶,·
›b¬
¤ £ ®
¤ ¥ ®
±|ª²¬i´³®p´h¶T®K´h·*­*Ý
¤ § Ý
½T´³1½T´h¶„½T´h·Ô
ž
m,% ;(6;h02‡7cq -36%6 -/B>7>;102:; F 780(-/ N„ƒ7'(-3 %-/Y0(‚6-/!'P-/ 7@87;27!0(;G
¶
Ü G|<INO7cq %-/T02;P|6:46`02Y#Z ;PU78@6-3='(-3 @3'('IO7;(7=*02;G G F a`=7D-/Bp0(
•› lE'P027802=D0•02O780 -/'Y'PU7@3@Á-/'b0(†'10L780(!T0Y02780
;(@Î74!T0 b› d
02[ @/-3c78;K4 T02;(- F :0(-/ A0(02U;(Ba¯-3'p'PU7@3@M<>-_02¯;P'(4*0E020(`@/-3c78;
8l
#%$
:;:935/W,6)+.@: 12C)E:/ )+/6,P:/6,A<)+.7%9;:<=,@?/6,A143
‹|-/4.02‚#Z:@3@ '( @3:02-3 N#–1uŒ ˜…4 T0L7-3'7‡@30#;(6:6O78D0-/|#Z ;(=7802-3 N7 F :00(
O7'P'b76X#7'P0‡ 'P4-3@/@Î702-/'&#7@3= '10@/-3c78;<7cq 'G-30>-3'= ;PN'('(- F @/N02!@/9 
#Z ;7†'10L780(-/'P0(-/47@6'(4;(-302-3 [#Á02N'1a9'P02Cl”N-3qX7†;(76 k'P F @/N#Á-3-30(-Î7@
4 6-30(-/ '†#Z;†02 •¤ Ï{'G.4c78¼<IC4 !:02[0(X;( F 7 F -/@3-30,a¡6-/'102;P- F :0(-/ A# b¤
780‡@Î780(;02-3=
' O ;>'(-3=@/-/4-30,aG|<IK'PO7@/@Á78'('(:=%02O70b0(K-3-30(-Î7@6-/'102;P- F :0(-/ [-3'
”Q78:'('P-Î7S7@30( :B X-_#<IK<I;(K<>-/@/@3-/B†0(=6`7 F -30‡=;(%<& ;PtG0(-/'‡7'P'(:!02-3 4 :@/6 F X<&76"4 'P-/6;27 F @_a lÒ¡S78;(X-/T02;('P026»-3¼0( F 7q9-3 :;i#•0(
==D0('# •¤ <>-34LV<I%6^Op7'#Z @3@/<>'
N
ª².³„Ý2²¶%2²·cÝ2²
(' ª².³*Ý2²¶cÝ2²·)2²
ݴ$#
"!•› £ b› ¥ › § ›%& #
! •
›£ b ›¥•›§ › & ›, ¶ª².³2²¶*­ "! •›£
N
N
Ý2²+*cÝ2² ' ­
­
›%-.#
76Ñ'(X …l…ÒAi;P=7;(X02O70N02i966n==D0('%7;(Er;P F 47:'PGÁ-/n…40cGh<I
7cq ;(7B Cq;`O7'('lMÒAS7;(VO7;102-/4:@Î78;(@3aA-/T02;('P0265-/¼02C'(4 6"! !T0cG
À
¶ ª².³„Ý2²¶*­ 
G '(-34K-30b-/'b'(-/!@_a[;(@Î780(6S0(=02 O :;(-3;02;(7'1#Z ;(
6-/'102;P- F :0(-/ [8
#0(%4 6'(78028l
#.0(pO78;P02-34@3
m¦0>-/'>7E'(-3=@/Y=780(0(;&0(i6;P-3q N0(%WD:O780(-/ '>#!02-3 `#Z ;&0(%==D0('#Z;( –1uŒ˜*lÒ¡>'(O7@3@6i02^O;P'P0‚0,<&lD$IaE-/T0(B ;(7802-3B•02'(‡WD:O702-/'.<&> F 027-/†0(
#Z @/@3<>-/Bp#Z;(=7@…„ƒ;('P'(-3 '>#Z ;02%! !T02'l
Ö Ü
¶ª².³ 2²¶„­ªÃP­
d
¶
ªØ ­ Ó ž
¥ § ¥ £
Z
X
N
› £ ¤ £ ¤ ¥ ¤ § ª O­½
± ¥ £ ¥ ¥ ½T´³¶,·cÔ
¶
®
Ö Ü
d
ªØ ­ Ó X
£ £ ¥ §
Z
N
¤c¥ ¤§ ›¥ ¤£ ª O­½
±c£ L£ (¥ P§t½T´³¶,·cÔ
›£ ›¥ ›§ › & ê P­
d
N ¶
ÖÜ ªØ ­ Ó ¶
ÖÜ ¬
X
ªØ ­ Ó ¶
ÖÜ ®
X
®
ªØ ­ Ó ÖÜ ¶
ªØ ­ Ó X
X
–1uc‰T˜
ž
¥ § § £
Z
' › £ › ¥ ¤ £ ›%& ¤ ¥ ¤ § ª O­½
' ݣ
›¥ ¤£ ›§ ¤c¥
¤§ ª O­½
' ›¥ ¤¥ ¤§ ¤£ ›§ › & ª O­½
d ±*§L£ P¥1§t½D´³¶,·Ô
¥ § & £
Z
d ±
& L£ P¥1§t½D´³¶,·Ô
£ £ ¥ §
Z
d ±£ L£ P¥1§t½D´³¶,·Ô
Z
¥ £ ¥ §
' › £ ¤ ¥ ¤ § ¤ £ › § ›%& ª O­½
± ¥ £ ¥ § ½D´³¶,·Ô
–1ucvT˜
‘b0(Y02O7002'(%*ƒ|;P'P'(-/'#Z ;( 7[:4@/ 'P6V-/;27;P4LDaU#WD:O780(-/ '<>-302`0(
*ƒ|;P'('P-/ V#Z ;c784LC! !T0>-/Tq @3q9-/B†0(%==D0>8#„ƒ90b;(6;‡:hl
Œ
#%$
9=>,'R4)+/6,A143B12C"/594,'3 9/W,A< 9V)+/6,A143 C>=;14* 7K3)+*-,A<)+. 9V)+/6,A143
ÒAQ'(7@/@@3| !#Z ;‡7C7'Pa9!020(-/4%*ƒ|O78'(-3 S ;>74LS! !T0b7'•7i<I;‡'(;(-3'
¶
-/ G
¤ £ ¤
ž
X
¶
¶
¤ £
¤ Ý
–Åw8}T˜
š lÒAQ7;PQ7;P0(-/4:@Î7;P@3a!-/T02;('P026S-3
#Z ;c784L
¶ª².³ 2²¶„­
ž
¶
X
¶
ªZ²‚³*Ý(²¶„­¬
¶
¶
¶ª².³ 2²¶„­ ª².³„Ý2²¶*­¬
N ¶ N ªZ²‚³*Ý(²¶„­¬?ÔcÔcÔ
–Åw9u˜
ÒA%;PWD:-/;PN02O7800(-/''P;P-/' F Q7'Pa9!020(-/48G=7-3B†02O70
«
X
¥ ¶
¤£ ¤
®
X
¶
"!
¤£ ¤
$#
ž
Ý
–Åww ˜
#Z ;I7Ta!^-30( l9ÒAb<?'(: F 'P02-_02:0(b0(•„ƒ7'(-3 hG…–Åw} *˜ GD-/T02Q02b*ƒ|;P'('P-/ 'G
¶
–1u‰ ˜*GÁ–’uvT˜ ÔcÔcÔ Gt
7 6C'P @3qQ-_02;2780(-3q @3aG ;P6; F aX ;P6;>-/ l
Xr;(802Ñ ;(6;G…c74LÑ! =T0N-/'Y4 '10L7T0Q76ÑB -_q F aS-30cÏ{'Y-3-30(-Î7@q87@/:lh$Ma
7'('P:!-/BS”Q78:'('P-Î7¡-/-_02-Î78@46-30(-/ 'Gh<IU4c78R4@3 '(i02!-3;278;(4LTa #! =T0
WD:O780(-/ ' F a*ƒ|;P'P'(-/B[-/B ;Y ;P6;b==D0('N7'•7`'(:o#M;(96:4*02'Y8#‚O7-/;P'
#'P46[ ;(6;M '&:'(-3B†7%Ò?-/4Li64 ! 'P-30(-/ hl-/'&7@/@3<>'‚:'M02†B0&780I0(
;('(:@_02'%<>-302 :0Q;(4 :;P'(i02X02!! ;(i4=@3*ƒ 78'Pa9=|020(-/4E4@3 '(:;(=7;(B :=D0('
yŠw9G3uˆ~;(W9:-/;(6C-3[02%4c78'(%# |)’”Q7:'('(-/7X-/-_02-/7@4 6-_02-3 'l
0 -/B ; ;P6;P'G02Q;102:; F 780(-/ X'(;(-3'>-/4@/:6'"&’'P4:@Î7;'Y02;(!'<>-/4LCB ;(<
‡
7'<&;('#  l t;I„ƒ78=@3GD#Z ;7†B-3q `! =T0cGD<&N!-/B T0IO7cq •0(•#Z @3@/<>-/B
¶
'(4LU702-/4 F O7cq9-/:;>780> ;P6; %
¶
ªZP­
ž)(
¶
ªZP­¬µ+ *
¶
ªÃP­
–Åw8zT˜
¶ ¶ <>;P F 802 ªÃP­ 76 * ªZP­ 7;(-, ª1«­ 7'  d
fglI;('(4n#N0(
¶ (
'(4:@/7;E02;P * ªÃP­ !c78'E02O780E0(X*ƒ|O7'(-/ –€w}T˜K#Z ; ªZP­ -/'E¡@3 B ;
¶
q87@/-36µ#Z;!0(-/!'iB ;(7802;!0(O7 « \ lM-/'!-/' F 4c7:'(70=0(-/'i02-3=8G02V'(4 6
02;( F 4='&#… ;(6;Il|‹|-34><&•7;(‡-/T0(;('P0(6U-3=0(b@3 BN02-3= F O7cq9-/:;
#02%'Pa9'102VGO02-3'-/'>7E;P F @/Cl
m¦0†-3'p<Iq ;G.7C;( F @/Ÿ<>-_02R7V<&@/@M9<>µ'P @/:0(-/ …G9<>¼7'Q02==*0296
#M†:@_02-/@/Q'(4c78@/'lhE'P4:@Î7;•0(;P='N47 F E;P!q 6Ñ-3Ñ7`4 'P-/'102T0N<&7ca F a
7@/@3<>-/B‡02r;P02E ;P6;.'P @/:|02-/K02N66E<Ic7D@3ap †02-3=8lÒA 'P0(:@Î702I0(
‰
*ƒ|-/'1024"&’p:@30(-/@3‚0(-/!*)¦'(4c78@/''LG ¶
76V;(@Î74
X
d
X
ªÃP­
ž
X
ª
¶Ý
N
¶
ž
 G8<>-/4LE<&0270( F -/66T0cG
ÝcÔcÔԊ­
–ÅwxD˜
Õ :;-30(;(7802-3 U;P|46:;(Y<>-/@3@0([B;2780(%766-_02-/O7@O02;(!'&<>-/4L[4 !•#Z;( 6- ;PT02-/7802-3BN02'(‡<&7†02-3=>664'lm,= :;M*ƒ7!@/<Ib<"^O6=02780
¶
780> ;P6; <&%<&:@/6VO7cq ¶
ªZP­
ž
¶
(
ªZP­¬µ *
¶
ªÃP­®R
™ ™
¶
X
Ô
–Åwˆ ˜
¶
ÒAU4c7µ<Ä;(6;†0([;P0(:; F 7802-3 R'(;(-3'pq87@3-/6A#Z ;Q02-3='p@Î78;(B ;K027 « \ F an4L9 '(-3B[02E<Ic7S0(-/!†664U8# ­ 0([[email protected]'(4:@Î78;%0(;P='l
D:'M<I‡7;(;P-3q>780‚02#Z @3@/<>-/BY4 '(-/'1024ai4 6-_02-/EB q ;P-/B%0(>@Î7;PB &0(-/!
F O7cq9-/ :;
™ X
™
¶
ž
*
¶
ªZP­*Ô
–Åw8ÀT˜
Õ #N4 :;('(C-/Ð :;!*ƒ7!@/[<IO7cq C @3aµ;P!q 6»'(4:@Î78;!0(;(!'i<>-/4L"78;(-/'P
¶
7 0N ;P6; l O:;P0(;•'(:4Ln02;(!'•<>-/@3@78;(-/'PE780• ;(6; N <>-/4L<I :@36n-/Tq87@/-36O7802
8
02b*ƒ|O7'(-/=#Z ;‚02-3='M@/7;(B;.02O78 « \ N lb4‡02`†:@_02-3@/'P4c7@3b;P|46:;(
†:'10 F %7@/-/6X ;(6; F aX ;(6;l
m, 0(!;('(T0†7;P0(-/4@3p<IU'(7@/@#Z94:'K Ñ02!'P4 6R ;P6;%! !T0N<>;P!0(
:@_02-/@/•'P4c7@3N4 '(-/'1024aX4 6-_02-/Ua9-/@36'02QD-30(-/4YW9:7802-3 XB q ;P-/Bi0(
†
@/ B!0(-/!N6a9O7!-/4'‡#02Q'(4*02;278@O78;P02-34@3Q6'P-30,a ltm,S0(-/'>47'(Q<&K'(O7@3@h^O6
¶
02O70I0(;PY7;PbK'(4:@/7;I0(;(!'I780&;(6; 786U02‡^O;P'P0& T02;P-3q9-Î7@O4 'P-/'P0(4*a
4 6-30(-/ Ñ7;P-/'P'Q780% ;P6; N lhÒ¡!'PO7@3@0%B V7Tan#Z:;102;Y02O78 0(-/'N'P-/4i0(
7@/B F ;(7†-/Tq @_q 6CWD:-34L9@_a F 4='‡6- !4:@_002i=7O7B 8l
‘b0(N02O7800(Q7'('P:!02-3 X#'10L780(-/'102-/47@… =B -30,aU-/!@/-3'
¶ª².³ 2²¶„­
ž
¶ªZ²‚³(­±|ª².³®R²¶*­„Ô
Æ
–ÅwŒ ˜
;(K<Ip7qp-3D0(;(96:46 šª².³(­ 0(U;P;P'(T0Y02Q'(4*02;(7@7;P0(-/4@3N6'(-30,alÒ¡
b
¶
< „ƒ|O76 ¶ªZ²‚³ (²¶„­ -/R<&;('i# :¯02;(6; N l+.WD:O780(-/ '[–1u‰T˜K76
–1uv ˜I02CB -_q ¶
¶
¶
X
ª².³ 2²¶„­ªÃP­
ª².³ 2²¶„­ªÃP­
ž
¶
X
ª².³„Ý2²¶*­ª ­ gš.ªZ²‚³(­±c£ *¥
ž
ÖÜ
ª Ø ­ Ó ¨ P¥P§ *¥L£,°TªZP­ v
N
X
–Åw8‰T˜
›£ ¤£ ¤¥ ¤§
± ¥ £ ¥ § ½T´³¶,·Ô
ÖÜ
®
ª Ø ­ Ó ¨ c£ „£ (¥1§(°TªZP­ ±c£ „£ (¥1§t½T´³¶,·Ô
N
X
¤c¥ ¤§ ›¥ ¤£
–Åw8vT˜
ªØ
¬
ªØ
¬
ªØ
®
®
ªØ
®
ªØ
¬
®
ªØ
ªØ
ªØ
¶ N ª ².³ 2²¶„­ªÃP­
ž
¶
Ü
¨ c£ P¥P§ & *¥ L£ ,¶
­ Ó X
' ¤£ ¤),
¤.- ¤ & ¤c¥ ¤§ ¶
Ü
¨
c£ L£ P§ & *¥ P¥,
¶
­ Ó X
' ¤c¥ ¤§ ¤ & ¤£ )¤ , $¤ - ¶
Ü
¨
c£ ,- (¥ 1§ & ¶
­ Ó X
' ¤c¥ ¤§ ¤ & ›£ .¤ , .¤ - ¶
Ü
¨
£ £ & ¥ , - ¶
­ Ó X
' ¤c¥ )¤ ,
.¤ - › & ›¥ ¤£ ¶
Ü
¨
£ £ & § , - ¶
­ Ó X
' ¤§ )¤ ,
.¤ - ¤ & ›¥ ¤£ ¶
Ü
¨
¥ , - ¥ £ & ¶
­ Ó X
' ›£ ¤£ ¤ & ¤c¥ .¤ , .¤ - ¶
Ü
¨
1§ , - *¥ L£ & ¶
­ Ó X
' ›£ ¤£ ¤ & ¤§ .¤ , .¤ - ¶
Ü
¨
P¥ P§ & *¥ ,- ¶
­ Ó X
' ›£ .¤ , .¤ - ¤ & ¤¥ ¤§ P¥1§ ¥ „£¦°DªZP­
±*¥L£ P¥P§t±c£ & ,-t½T´³¶,· * '
N
c£ L£ P¥P§P°DªZP­
±c£ L£ P¥P§t±*¥ & ,-t½T´³¶,· * '
£ L£ P¥1§P°9ªÃP­
N
±c£ „£ (¥1§t±$L£ & , -t½T´³¶,· * '
N
£ £ ¥ § °9ªÃP­
±£ L£ P¥1§t±$1§ & ,-t½T´³¶,· * '
N
£ £ ¥ § °9ªÃP­
±c£ „£ (¥1§t±$P¥ & , -t½T´³¶,· * '
N
¥ § ¥ £ °9ªÃP­
±*¥„£ (¥1§t±$1§ & , -t½T´³¶,· * '
N
(¥1§ *¥L£¦°9ªÃP­
±*¥„£ (¥1§t±$P¥ & , -t½T´³¶,· * '
N
(¥1§ *¥L£¦°9ªÃP­
±*¥„£ (¥1§t±$L£ & , -t½T´³¶,· * '
N
u}
–€z}T˜
‘ 0(b0(O780&0(•0(-/!b664N#0(N7 F q •0(;P='IO7' F [@/94c7@3-/'(6=-3T02K0(
b
#Z @/@3<>-/Bp0,<I!-/T02B ;27@3'
d
¨ O°9ªZP­
ž
Z
X
½
–€z|u˜
d
¨†¬ 9° ªZP­
ž
¨ O°9ª t
­
X
Z
½
–€z w ˜
-3; F 7q9-3 :;.#Z ;‚@Î7;PB 02-3='‚<>-3@/@602;(!-/0(b'P4:@Î7;‚02;(!'M7;(-3'(-/BQ-3!0(
*ƒ|O7'(-/hl
X
Q;(c78@/@3a=026-/ :'‡'102S-/X02p77@3a9'(-3'-/'02!'(@/-300( 77;(-3Bi-/[02'(
*ƒ|;P'('P-/ 'N-/T02=;(96:4*02'Y#‚'P4 6n ;P6;Y! !T02'‡-/Tq D-/BU0(E”%7:'P'(-/7-30,a
#M02i-/-302-/7@6-/'102;(- F :0(-/ hltÒ¡!'PO7@3@. @3aSA7-/;P'N#I0(E#Z ;( ! •›£ ›¥$#
ž
š…›£1±|ª².³®A²¶„­ '(-34N7-/;P'#Á02Y#Z ;P b›£ •›¥ ; ! ›£ ›$
¥ # 78;(Nr;( F 4c78:'(
#7q;(7B -/B!q;>#7'P0> 'P4-3@/@Î702-/'l|$&c78;(-/Bi0(-/'-3X=-36`<&N<>;P-302
N
X
ª².³„Ý2²¶%2²·cÝ2²
(' ª².³*Ý2²¶cÝ2²·)2²
N
š›£’š…›¥ª±c£ „§2±*¥ & ¬Ð±c£ & ±*¥ „§L­
­
N
ž
–€zzT˜
š› £ š…› ¥ š› § ª€± £ &(± ¥ , ± § -
Ý2²+*cÝ2² ' ­
ž
¬¡±£ & ±*¥ -2±„§ ,Á¬Ð±c£ ,(±*¥ & ±„§ ¬¡± £ , ± ¥ - ± § &¬Ð± £ - ± *¥ & ± § ,
¬
± £ - ± ¥ , ± § &L­
–€z8xD˜
b p'P: F '102-30(:02-3 Q-/T02K–€z}T˜76p-3T02B;2780(-/B> :0Á0(I7-/;Á6@30L7#Z:4*02-3 '7;(-3'(-3B
#Z;( Ä02'(Q64 ! 'P-30(-/ 'I<&%^O6
¶
ª².³ 2²¶„­ªÃP­
¶
¶ N ª².³ 2²¶„­ªÃP­
ž
Ø Ü
–€z ˆ ˜
¶
¨Ëš…¤£’š…¤¥(š…¤§¬µš…›£’š¤c¥(𤧂®¯š…›£,š…¤£,š…¤§
¶
ªØ ­ Ó ®‡š…›£1𤣒š¤c¥P°Dª
¨ Ý c£ L£ (¥ P§1°9ªZP­¬
¨ Ý® c£ L£ (¥ P§1°9ªZP­P­
e
± › £ ¤ £ Ì9¤ ¥ Ì9¤ § ½T´³¶,·b± £ ¥ Ô
–€zÀT˜
ž
¶
‹ -/4p0(E ;(6; 02;( -3S02E*ƒ|O7'P-/ Ж€w}T˜‡#Z ; ¶ª².³*Ý2²¶„­ªÃP­ -/'•r;P[02;(
|
-/'MQ'(4:@Î78; F O7cq9-/:;&786=0(•†:@302-3@/&'(4c78@/‡4 'P-/'1024a!4 6-30(-/ =7;(-3'(-3BQ780
02-3' ;(6;>-/'0(N02;(-_q9-Î7@ ™ ¶
¶
™
ª².³ 2²¶L­
¶
ž
Ô
–€z Œ ˜
u u
<Iq ;Y02p ;(6; N 0(;(o69'b*ƒ|- F -30Y'P4:@Î7; F O7cq9-/ :;lm¦0Y7;(-3'('b<>Ñ<I
b
0L78N02%@/BE02-/!Y@3-/!-30 ¨ Ý O°9ªZP­
ª ±|ª ­Á¬
«
Ö j
­ 8
L ®
™
Ö
O
™
7'  d
f
Ý
–€z‰T˜
<>;P j ª1Ԋ­ 60(•02NŽ7:4LTa`s‚;P-/4-/O78@M78@/:8l9D:'>70I0(-/'I ;(6;GD02b†:@¿)
02-3@/Y'P4c7@3%;(946:;(Na9-/@/6'>7i 9)¦02;P-3q9-Î78@4 '(-3'P0(4*aX4 6-302-3 ™ ¶
X
ª².³ 2²¶L­
™
Ü
¶
˨ š…¤£,š…¤c¥Pš…¤§¬µš…›£’š¤c¥(𤧂®Rš…›£1š¤£¦š…¤§
¶
ªØ ­ Ó ®‡š…› £ š ¤ £ 𤠥 °±|ª £ £ ¥ § ­P± £ £ ¥ § ½T´³¶,·„± £ ¥
ž
N
™Oš…›£
™
ž
±c£ *¥Ô
–€zvT˜
N
‘ 0(K0(O780Y0(p6@3027=#Z:4*02-/*ƒ|;P'('P-/B['PO780(-Î7@ ! B -_0,aV#78402;('•:0cl
‡„)
b
N  <&`02U0(O780†0(-/'KWD:O780(-/ ¯-3'†74*02:O78@/@3an0(`<I@/@¿),D<>
4c7@3@/-3BV0(O780
ž
N
D-/*02-/4>W9:7802-3 =Bq;P-/B%02b;P@Î7ƒ702-/!8#…02b'P402;(7@tO7;102-/4@/6'(-_0,ai-/=7
'P F @/%#<&7D@3aX-/T0(;278402-3B†<&7q' ™Oš…›£
™
ž
¶
Ü
N
ªš¤£’š¤c¥(𤧬¼š›£’š…¤¥(š…¤§‚®Rš…›£1š¤£,š¤§M®Rš…›£,š…¤£,š…¤c¥2­
¶
ªØ ­ Ó e
±|ª ›£h¬
¤£®
¤®
¤§„­1± ›£ ¤£¦Ì9¤¥PÌ9¤§ ½D´³¶,·Ô
–x }T˜
‘ 0(N02O780>0(K'102;P:40(:;(Q#0(-/'>W9:7802-3 C-3'q ;1aX;(=-3-/'P4T0‡#02K$M)’‘ WD:O7)
b
02-3 –1u˜„lÒA%'PO7@/@ F N;P-/=7;(-3@3a!-/T0(;('P0(6V-/[02%-36c7@3-/'P6['(-_02:O702-/`<>;P%0(
==D0(: 6-/'102;(- F :0(-/ hG š…›£ G-/'†'10L780(-/'P0(-/47@/@_aÑ-/'(802;(-/48lm,¯02-3'E4c7'PG 𛣠-3'E7
#Z:4*02-/Ð# ¸…³
É ².³ É l.Ò¡C47»'P-/!@/-_#ÃaR :;!6-/'(4:'('P-/ F a¼<>;P-30(-/BÑ02VD-/„)
ž
02-34NWD:O780(-/ V-/V;(BaX'PO74K;(7802;02O7V! =T02: 'PO74lOÒA%-3D0(;(96:4%0(
q87;(-/7 F @/
' 7'#Z @3@/<>' «
³
ž
¶
¸ ³ Ý
Ø
«
¶
ž
¶
º ³ Ý
Ø
«
·
ž
Ø
¶
º ¶ Ý
«
N
ž
Ø
¶
º · Ô
‹| !%7@/B F ;(7p027@3@/<>'&02QD-30(-/4NWD:O702-/X0( F %;(„)¦<>;P-30(0(V7'
™Oš€£
™
«
ž
³ N
¨©š £ °
–xu˜
<>;P
N
¨Ëš€£¦°
ž
£Ã¥Î§
& ªZšÃ¥1šÎ§(š & ¬µš€£’šÎ§(š & ®Rš£’šÃ¥1š & ®¯š€£,šÃ¥(š/§L­
±|ª ³ ¬
³®
¶M®
¶*­½
uw
¶2½
·„½
N
Ý
–xTw ˜
76
€£Ã¥ Χ &
ž
N
Ü
¶
¶
ªØ ­ Ó
³ ¶ ·
N
±|ª².³¬¼´³®¯´
®¯´h·„­½ ¶L½ ·„½ N
Ô
–x zT˜
m,»02-/'i#Z ;(†:@Î7G ½ ¶L½ ·„½ ;(;('(D0('U02S-/T0(B ;(7802-3 Ðq;` @Î78;i7B @3'!-/
N
´³1´h¶2´…· '(O784l&‘b0(V0(O780
€£Ã¥ Χ & -/'=7¡ ! B :'!#Z:40(-/ Ð#N6B ;( « \ Ø l
X7B:@Î7;K-/T02B ;2702-/A#0([6@_0L7C#Z:40(-/ ¯47 F U6 [„ƒ@/-/4-30(@3aÑ-/¡0,<&
76S0(;(p6-3='(-3 'ltÒ¡†78;(Q-/T02;('1026n-/C0(K0(;(*)¦6-/!'P-/ 7@4c7'PK<>;(
½
G-30>-3'#Z :6¡y{x~
ž
¶
Ü
£ ¥ § &
N
Ô
³„Ý ¶Ý ·Ý –xxD˜
ªØ ­ '
ž
N
0,<IQ6-/!'P-/ O78@947'(8GT7@3 Bb<>-_02E=7Tap802;.7'(4*02'.#O0(D-/*02-34I02 ;1a
#Z ;02Q @/-3c78;>‹|4L;P|6-3B ;WD:O780(-/ hGO-3'*ƒ|@/7-/6X-/X6027-/@…-/Ñy{v8~Ål
+ W9:7802-3 µ–xu˜>-3'‡0(K<&7cq ED-/02-34KWD:O7802-3 S<I@3@D<>n-/V02Q02 ;PaV#.<&7cq .
02:; F :@34l…m,C02-3'•7;102-34@/N<I†'(7@/@Á;(*#Z;‡02іZxu˜>7'b0(E”N;( 'P'1),s‚-_0L7*q9'(D-/-ÁD-/„)
02-34•WD:O702-/U02†6-/'P0(-/B:-/'PU-30M#Z;(¾0(N$&@302rU78|)’‘‡ ;(6-3 D-/*02-/4bWD:O780(-/ …G
–1u˜„l •7cq9-/B='(<>n<“02E”
|s5D-/*02-/4QWD:O702-/S4c78 F K6;P-3q6S#Z;P 7cq ;(7)
B -/Bp'(@/:0(-/ '‚#0(• @/-3c78;&‹94L;(96-/B ;IWD:O780(-/ !#Z ;I0(•4 6'2780(•<&7q*)
#Z:4*02-/hG8<I<Ð0(:;(E:;.780P02T0(-/ †0(N-302''( @3:02-3 'l8Ò¡'(O78@/@|^;('P0‚„ƒ7=-3I0(
02-3=„),-/66T0`'P @/:0(-/ '!<>-34L56'(4;P- F 'P027802-3 O7;1a¼WD:-/@3- F ;P-/:e765|)
WD:-3@/- F ;(-/: ! !T02:
6-/'102;P- F :0(-/ 'l&?<& '(O78@/@Y'102:6a"0(-/!*)¦66T0
'( @3:02-3 'l
"!…
€8
O
C` %!h

|
…|%
…
¦m 0Á-/'Á702;P-3q9-Î78@=780(0(;…0(>q;P-3#ÃaY0(O78002MD-30(-/4.WD:O702-/hGD–x }T˜*G#Z;(=7@/@_a>4 'P;1q '
02N0(0L7@…;(BaV76X0(0L78@hO7;102-/4@/YD: F ;‡B-3q F a
žg ¤š¤.½T´
–xTˆ ˜
76
H
ž
š…¤½D´
–x ÀT˜
(; '(40(-3q@3al•'P0L702-/O7;Pa!'P @/:0(-/ '&7;P•-3D0(-/=7802@3aE@3-/86U<>-_02U0('PY4'(;1)
q87802-3 C@/7c<>'lt;PE7;PKW9:-/@/- F ;(-3: '10L780(-/ 7;PaX'10L780('Gt<>-34LS6'(4;P- F pW9:-/O7;’)
02-_02-/R#b4 'P;1q 6ÐWD:O7T02-_02-/'G.786Ð |),WD:-/@3- F ;P-/: 'P027802-3 O7;1aA'10L780('G<>-/4L
uz
6 'P4;P- F •4'P027T0 O:|ƒ|'&#4'(;Pq 6XW9:7T02-30(-/'&-/!! =
T02:¾'(748l|b0,<&
02;(!|6|a|7=-34WD:-3@/- F ;(-/: 'P @/:0(-/ '.4c7 F ‡'(=#Z;P Z– xu˜.7@/! '10 F ai-3'(4„)
02-3 hl*aV7;(
¶³
ž
š
ž
š
–xTŒ ˜
ÌO³
Ý
–x ‰T˜
¶ 7;PN4 <>;P ³ 76
'10L7T0('lN^O;P'P08#0('P%4 ;P;('P6'02i78[WD:-/6-/'P0(;(-¿)
F :0(-/ X#O7;102-/4@/YD: F ;G02Q'P4 6C0(!7CWD:-/6-3'P0(;(- F :02-3 `#;(Bal
E'102:6|a`02• |)¦WD:-/@3- F ;P-/:Â'P @/:|02-/'&-_0-/'&4 Tq -/T0‡0(†<>;(-_02•0(Y4'(;Pq87)
02-3 X@Î7c<>'>7'>4 T0(-/D:-30,aUWD:O780(-/ '‡-3X;(Ba['PO74 ™ H
™
™
™
ž
™ª 2 H ’ ­
™O
<>;PpH
O:|ƒ|'G
ž
ž
–ň8}T˜
X
½
H T
76
™
ž
®
-/'0(%-/T02B ;2780(6XO7;102-34@/ND: F ; F 0L78-/6X#Z;P š…›M½T²
™
®
ž
–x vT˜
N
N
Ô
–ň9u˜
–xu˜ Gt78;(%c7'P-/@_aU F 0L7-36[#Z;(
¨©š ¿°½
–ňw ˜
–ň8zT˜
¨©š ¿°½
‘b0(•0278002'( :|ƒ|'>7;PY6^6X'(:4LV0(O780
-/' 'P-302-_q ‡#Z ;&O78;P02-34@3' <>-3B
02V02=@/#Ã0Q4 ;(;P'( 6-/BV0278A-/Tq;('P`4c78'(4c786`76 -/'%'(-30(-3q!#Z ;Q;(B8a
O<>-/B[0(`02i;(-3B T0N4;(;('( 6-3B`02V7[6-3;(4*0N4c78'(4c786i-/02!;PBan'P4c7@3lhm¦#
Ì <&>4 '(-36;‚<&;M@/7c<»'P402;(7Q8#0(#Z ;( š
02=6-/!'P-/ O78@77@3a9'(-3'
ž
'(:BB '102'X02O780X0(O:|ƒ|'G
786 7;(n-366T0C# [#Z ;
\ µ76
ž
\ ;P'(4*02-_q @_a l|'PY<I;@/7c<>'7;P‡0( b@/! B ;PqT)h7DO7;(qp'(40(;27
ž
4 ;P;('( 6-3BY02%4'P027T0 O:|ƒ|'‚#O7;102-34@/'.76i;PBaE;('(4*02-3q@_a lO ;.$&+IŽ
-30M-/'.0(b-3Tq ;P'(b4c7'P4c76‡<>-/4L=-/'‚#…O7;P0(-/4:@Î7;.-3T02;P'10&'P-/4b-_0I-3'‚;( 'P- F @3#Z ;
02‡02;(7'P#Z;&#hO7;P0(-/4@/'‚02K@/<?! =T02:Â'10L780('I<>-/4L[4LO7;(740(;P-/'('I0(b^O7@
'P027802%#02%4 6'2780(l
b
@/! B ;PqT)h7DO7;(qV'(4*02;(7X6-/'(4:'('P6¡7 F qi7;(E! ;PK027Ñ6-/!'P-/8)
O7@3@3a 4 '(-/'102D0i<Iq;l.aµ78;(`„ƒ7840i'P027802-3 O
7 ;1a '( @3:02-3 'p8#‡0(`D-/02-34
ucx
P³ |œ^ªP–p¢:“Ë¢¯#–l“K”kœ^ªP™Œ˜”M–p¢:“˯a¢:™j”M•_œ
*¢¯#œc¬† q˜”M–p¢:“§è¥êu³
WD:O780(-/ Ðy w w9G v8~€l-/'N#74*0%4c7 F i6='P0(;2780(6¡76Ñ02iq87@/:E8#I0( b @3=8)
B ;PqU4 'P0L78D0‡4 =:026V:'(-/Bi7X-/B -/:'&02;(7'1#Z ;(=7802-3 U6:N02 h7DO7;Pq
yŠw8}G w9u~€lN6*0L7-3@/'&8# h7897;(qÏ '!0(96X7;(•<I@3@…„ƒ@Î7-36[-3`02N;P#Z;P4'
'(!;PN<&Q'(O78@/@h @3a`B-3q %7 F ;P-/# :|02@/-3l
® ³ $&c78;(-/Bn-/µ=-36R02780 ¶
·¬
G0(X-/T02B ;2780(-/ A;(B-/ R#Z ;†0(
ž
4 @3@/-3'(-/5-/T02B ;278@ÅGN–ZxDw ˜„G-/"02 ª ·NÝ ­ @/7n-/'[0(Ñ'(O766g;PB -3 ?'(<> -/
^OB :;PXu lh!-/67`#&0( h7DO7;Pq02N ;(7'P#Z;(=7802-3 -/'Y0(S78'('(:=i7X<I;%@Î7c<
Ì 6-/'102;P- F :0(-/ …G š
G976=02U02KU7!02‡02>02;(•;(B-/ ' bw|G bzK76 >x
ž
-/T02%02b;PB -3 %u‡-/=7Q'P4c7@3*),-3Tq78;(-Î78D0.<&7ca lDm¦0M<>-/@/@|02 F > '('P- F @302p'P80M0(
4;P-302;(-3 <>;P F aÑ02i-3D0(B ;(76nq87-3'('lhÒ¡!6^Oi*< q87;(-/7 F @3' ª ¶ Ý · Ý ­
N
-/Xc784LC#02Q;PB -3 ' bw|G ‡z
G >x=78'#Z @/@3<>'
Ø bØd «
d
%
d
«
«
ª c
¶ Ý · Ý
ª c
¶ Ý · Ý
N
ª c
¶ Ý · Ý
N
N
L
­ d
L
­ d
L
¶
­ d
³
¶
³ ·
N
³
·
N
³ ·
Ý
¶
³
Ý
³
–ňxD˜
¶ N N O
³ ¶
³
Ý
· · O
Ý
Ý
N O
¶ ¶
³ ¶
Ý
–ňˆ ˜
Ô
–ň8ÀT˜
66-3BE02%;('(:@_02-3BE#Z :;4D0(;(- F :02-3 '0( B 0(;<I% F 0L78-/
·
³
£ ¥ § <>;P `®
ž
q87-/'P'#Z ;
&cª ³ ¶ ·
N
­
Ì
ª ³ ¬
¶ ®
· ®
N
­
Ì
³ ª ³
±|ª ³ ¬
¬
¶ ®
¶
Ì
®
·D®
·
Ì
N
®
­½
Ì
­
N
¶,· Ô
N
\ Ø lm¦0‡-/'-3=!6-Î780(@3a!4@/c78;02O7800(Q4 @3@/-/'P-/ =-/T02B ;278@ÅG
uˆ
¨Ëš° G
ž
ž
ž
«
;(!96a9O7!-/4»WD:-/@3- F ;P-/:
@3:02-3 'G–xTŒ ˜76Á–ZxT‰T˜
«
ž
ž
ž
\ Ø
\
'()
Y)'( @3:02-3 '
–ňŒ ˜
–ň8‰T˜
Õ h
# 4:;('PGD02•)['( @3:02-3 '‚4c70I*ƒ|-/'10I-3=-3'( @/7802-3 hl8 :|ƒ|'
; †:'10
F &'(:'10L7-36 F a†4 :@3-/B•0('1a|'102 02N„ƒ|0(;PO7@'P :;(4'lTm¦0.-/'02 F :6;('1029|6
02O70I0('P•'(:;(4'78;(‡@/94c7@3-/'(6!780&'P: !4-3T02@_a=@/7;(B ;I'PU78@/@O'(47@/'M0(†7@3@/<¼#Z ;
02X„ƒ-3'P0(4C# &’-3;102-/7@I;(7B ' '[<>;(X02V6|a|7=-34'E-3'ET02-3;(@_aR6=-3O78026
F aS02†<7cq „)¦<&7cq U-3T02;(740(-/ 'l…m,Ñ'P:4L¡'P-30(:O7802-3 '‡02 •)A'P @/:|02-/-/'•0(E;(„)
@/*q78D0p !<>-302-/Ñ02`-3;102-/7@.;27B U#;(B -3'l b<Iq ;†02-3'K'P @/:|02-/A†:'10
02Ð=780(4L¼0( 0(XO7;P0(-/4:@Î7;K#Z ;(4-/BÑ76Ð6-3'('P-/O780(-/ ¯;(^O@3'E<>-34LÐ;Pq|-36
02 O:|ƒ|'l†WD:'102-3 Ñ#.<>n0( •)A'P402;P: -3'Y7`:-3q ;('(7@ F P40Gh-/9)
66T0!#‡02[6*0L7-3@/'K#‡'( :;P4'=786µ'(-/9'i70E@Î7;PB [76¼'PU78@/@M'(4c78@/'E-3'E7
T02;P-3q9-Î78@ K#Z;P 02K -/T0b#q9-3< #‚78O7@3a9'P-/'l Õ V02K02;•O786hGt*ƒ|;(-¿)
=T0L7@ F '(;Pq8780(-/ 'I#q87;(-3 :'M<7cq N0(:; F :@/4Y'1a|'102=''P:B B 'P00(O780-3`U78Da
4c7'P'02 •)S'(4*02;P: -/'&= ;P•;P F :'1002O7`0(N=7802U702-/47@t'(-3=@3-3^O47802-3 '
:6;(@_a|-3Bi-30('6;P-3q87802-3 [!-/B T0'P:B B 'P0cl
b@/! B ;Pq†4 '10L7T0G G94c78 F Y4 !
:026[-/U0(;P='I#02O:|ƒ[47;(;P-/6 F a
02•)'P402;P:Vl t
;6027-/@3''(Uy¿uˆ|GŠw w ~€l
|
h
V
ÁZ
K
9 t B
Z
­ G-/'Á#7;Á#Z;( “0(&W9:-/@/- F ;(-3:
‹|: 'P&02I-/-_02-/7@ O7;102-34@/‚6-3'P0(;(- F :02-3 hG š.ª Ý(
ž 4 |^OB :;(7802-3 ¡#Z ;%02U'Pa9'102 <>-/4L¡<& :@/6R@3-/i02C'(`O7;102-/4@/'K6;P A-3T02C0(
r;(n! =T02: 'P027802`-3R ;P6;p0(nB ;2702U0([:-_#Z ;( 46'2780(['( @3:02-3 –1u} ˜*lMS02-3=X66D0X'P @/:|02-/»#=–Zxu˜E6'P4;(- F 'U02;(@Î7ƒ780(-/ Ð;(94'('
<>-/4LK02E|44:;P'lb<&*q ;G 'P-/4I<ID<¼#Z;P “ :;6-/'P4:'P'(-3 †#0(&;(q9-3 :'
'(402-3 hG0(N-/Tq;('P%4c7'P4c76% @3a=O7'^O-_02N47O74-30,a!02!7 F 'P ; F O7;102-34@/'&'Pi0(
'( @3:02-3 V#‚WD:O780(-/ ¯–xu˜<>-/@3@Áq T02:O7@3@3a F ;Pc7VO7;102-/4@/%D: F ;Y4 'P;Pq8780(-/ …l
ÒAÑ60(Ñ0(n02-3=n70[<>-/4L?02-3'`#7-/@3:;(C|44:;P' F a  ln#7-/@3:;(C#K0(
4 '(;1q87802-3 µ@Î7c<Ä4c7 F [-3T02;P;(*026»7'†0(XB ;2702-/¯#b7Ñ |),r;P :|ƒµ#
O7;102-/4@/'`02 l>$&a 6?02-3'[02-/!W9:7802-3 –xu˜U¼@3 B ;[;(q9-/6'V7
ž
7;P ;P-Î780(b6'(4;(-/|02-/`#02YTa9'(-/4''(-34Y-_0I#78-/@/'.0(E744 :T0#Z ;‚02•'(-/B :@Î78;
O780(:;(Q#02Qr;(!=96l IÁ747rQ0b7@€ly¿ucx~ÁO7cq K;( 'P6C7!'1a9'P02—8#D-/02-34
WD:O780(-/ '#Z ;0( 'P01)  q @/:|02-/ F 7'P6i i7i7'2780(r&<>-/4Li'P@/-_02'0(O78;P02-34@3
6-/'102;P- F :0(-/ Ñ-3D0(C'P=90(A76A'(-3B :@/7;NO7;102'lÁÒ¡!4 'P-/6;Q0('PUW9:7802-3 'Q-/
02%„ƒ90b'P4*02-/hl
uÀ
ÒA4 'P-/6;#Z ;<µ026a9O7!-/4';(„)  l I *0.:'.@/9 N#Z ;7Y'(@_#Î),'P-/!-/@Î78;'( @3:02-3 #02N#Z ;P
«
š
ª ­„Ý
ž
–ň8vT˜
<>;PQ0(%'(-3=-3@Î7;P-30,aEq87;(-/7 F @3'G
ž
Ý

ž
76
Gt78;(%6^6C7'
®R„Ô
–€À}T˜
`„ƒ T02'
76!7;P=02 F =60(;(!-/6hl‘b0(=0(O780†-_#02;(U-/'K7SWD:O7'(-¿)
Ì 'P027802-3 O7;1ap<&;.@Î7c<¼6-/'102;(- F :0(-/ p780.@Î78;(B ! !T0L7|G š G80(E02>7'2702r
® –ňv ˜I-/!@/-3'‚02O70
\ lOD:'02N„ƒ T02'‡#Á02N'P-/!-/@Î78;(-30,ap02;278'P#Z ;PU7)
ž
02-3 ¼7;([;P@Î7026¯0( 0(X'(4c78@/-/Bn#b0(X-/B¼! !T02: O7;10i#‡02X'(@/:0(-/ hl
b 5'P: F 'P0(-30(:02-3 »#=–€ˆvT˜!76 –À }T˜E-/T02 02WD:O7802-3 »<IS^O6Ð02O780=<&S4c7
;(=q N0(N02-/!Y664Q#Z;( Ä02%;P F @/ F a[4L9 '(-3B
¬?«
ž
Ø
Ô
–€À|u˜
ÒAQ7;P%@/#Ã0&<>-302V7V-/T0(B ;P8),6- …;(D0(-Î7@WD:O702-/X#Z;02N#Z:4*02-3 £®
½ D³ ½
£
ž
³
Ì ¥£
®
£
¥
§
&
£ ¥
ª
¥ §
&
¬
£ §
&
®
ª ­ £ ¥
&
–€À w ˜
§„­±ª9³h¬D³®8¶M®8¶*­½9³1½8¶„½8·cÝ
<>-30(
£ ¥ § & B-3q F a!WD:O780(-/ –xTz ˜*l Ò¡•†:'10&'P:@3!T0&0(-/'‚W9:7802-3 =<>-_02
7Y'(4 6i;P@Î702-/ F 0,<I
786I-3† ;(6;0(N'( @_q &0(;( F @/Clm,E'( !47'('G
-30%=7'K'P'P!0(S78'('(:=i02O7[email protected]! :T0%#&'( !i4 '(;1q 6RWD:O7T02-_0,a
B ;(<>'.@3-/7;(@_a%-/†02-3=I6:&0(%7Y4 'P0L78D0‚-3:0 O:|ƒl -3'.4c7E'P =*02-3='a9-/@36E7
'(4 6=;(@Î780(-/ F 0,<I
7
6 G <>-/4LU7'‚'(<> F a t7@3q9-/4L!76U‹|O7#7;(
y_uu~ÅG-/!@/-3'>02O70•02E'(@_#Î),'P-/!-/@Î78;'( @3:02-3 *ƒ|- F -30('b0( b @3=B ;(qT)h7897;(q
'(47@/-3Bi780>@Î78;(B N! !T0L7l
m,¡:;%4c7'PG02E0([email protected]: F ;Q8#O7;102-34@/'N4 T027-/6¡-3n02i'(4*02;P: 4c70
-/4;(7'(I@/-/c7;P@3aY-3K0(-/!M'P-/4M<ID<¯027800(M^O7@9'(40(;(: 4D027-/'7>^O-30(
7! :T0N#IO7;102-/4@/'lÒ¡i6X0%D< 8#7TaS02;%;2780(-/ O78@4 'P0(;27-3T0N<>-/4L
02C'Pa9'P0( †:4L5'(7802-3'P#Ãaµ-/Ð ;(6;=0(¡#Z:;P-/'P57A'P4 6";(@Î780(-/ ¼7@_02:B Ð<I
O7cq %=76Y'P =N4 P402:;('#Z ;I02Q7O78@/ B :'&;P F @3k#Z;&02N6-/;(40>47'(476
-/[<&7qQ0(:; F :@/4!y{À8~Ål
‹|-/4i<&!4c70p7O7@_a90(-/47@/@_aC602;(!-/E0(!q87@3:'%#
76E76 4=0(
'(47@/-3BN780‚@/7;(B I==D027G 7Y;(-/;(-ÅG<I‡'P @3q6E02 ;(-3B -/O78@9WD:O7802-3 iD:=;(-34c7@3@3a
uŒ
20
t=41.999
t=41.998
t=41.972
t=40.984
t=9.365
t=0
Best fit
15
log(w)
10
5
0
-5
-15
-10
log(e)
-5
0
q£–p—8˜˜x™Œ˜Å_­“dŸ–lœ^³x”k”kœ1œ^Í1™#šy¢:˜¶P­'£q˜˜:›l£d _š^ dœc–l”¼”Œ—,¤n˜žd”M—M–pœc¤Ÿ¢:—k“E—Mš^”k™Mœ^–l¢¦d­€¯&–l“d³y”Mª½x•_œ€•_¾xœ6¢P–l“K”M—k™Œœu¶¥˜:«¼œ^ښc™kœc—Œ–l“_œ±—#—M—Mšy”k•_œ^˜:¢y–l—k“'jšy˜:“°šcžd¢:˜œË“_™kždœ6–lœ^“ЗM“_“q—Œ”M˜˜•_£_”Mœ±—M–p¢:•_ d“°¢:“Ÿ”k–l¯a—8“¢:¢™k¸žšc¯_œcŸ”Mž •_–l­œ6¨vœ^—k–l“_£F“_—Mœcœ^–pš^”M¢:”M–p“_šË™M d—jœc­ èa¬†À q˜˜”8d”M˜¸–pêu¢:³—Œ“нxœ^™M•d¯\–p¢:œc–p——™
­¢¯|¢:šc­¢:“_œ^“†—kœc”M dš^ d­€”M–l³B¶¥½xœ*•_”Mœ–l­Å_œc”M”k—yœc³,žË½x£F•_¢sœÅ_œ^“q™¸˜›b›1˜y ”M™Œ˜:˜šc”¸œ›b˜–p—¡™Mª¥š^œ›p¢P­—kœ¢:­”k¢€œ^“†”M”Œ•_˜'œ?•qÅ_˜:“d—¸–l”kœuœÃŸ£F”M–l¢:­“_œ^œ“†—M” –l“dPªP³ d›b˜™MŸ–l³”.¤§˜”e¿yœ^™k¢
02i!c7'P:;(N<>O780‡'P4c7@3-/BE-3''(@34*026…l % D:!;P-/47@h4=:|0L780(-/ `8#0(%'( @3:02-3 #WD:O780(-/ ¡–xu˜&-/''P<>S-/[^OB:;(Kwp<>-30(C78C-3-30(-Î7@t46-30(-/ [B-3q F a
š.ª Ý(
ž
­
ž
«
Z
Ì9·
Ô
–€ÀzT˜
m,=@3-/<>-_02!;(4T0I-/Tq 'P0(-/BT780(-/ '.#…^O-30247O74-30,aE'1a9'P02='I-/E<&7qb0(:; F :@/4
y À~‡76»@/'P<>;( y ˆ8~<IV^O6Ð02780i02V;(„)  '(4c78@/-/B -3'E0!02 ‡ @/! B ;PqD)
h7DO7;PqC'(47@/-3BltÒAp=7'(:;Pi7`WD:O7'(-¿),'10L780(-/ O78;PaX<I;N@/7c< 6-/'P0(;(- F : F 0(-/ S780
-/BC! !T0L7E<>-30(C„ƒ T0 « Ô Ø ;(q9-/6-3B!-/66D0bq ;(-3^4c780(-/ V#0(
*ƒ| T0b=7'(:;(6 F a IÁ74c78r%0b7@€ly_ux8~Á-/[0(-3;'(-/p:@Î780(-/ 'l
Y ;c
Z>
Á
R
IÁ74c7rK*0N7@€ly¿ucx~O7cq K;( 'P6n7i'Pa9'P0(o#D-30(-/4QWD:O780(-/ '>#Z ;02K 'P01) 
q @/:0(-/ F 7'(6E E7i78'2780(r&<>-34LE'(@3-302'Á02O7;102-/4@/M6-/'102;P- F :(0 -/ K-/T02•'(!|0(
76V'(-3B :@/7;O7;102'>7'#Z @3@/<>' š.ªZ²IÝ(P­
ž
š X ªZP­±|ª²­¬¼Û•ª²MÝ(P­„Ý
–€À8xD˜
<>;P Û -/'`7 ;(B :@Î78;!#Z:402-3 "780 ²
76 š XªZP­ -/'i027=@/-30(:6X#Y0(
ž '(-3B :@/7;`O7;10X#Q02ÑO7;102-34@/S6-/'102;(- F :0(-/ »<>-/4L?<&Ñ@/9 'P@3aÐ02-3»8#†7'`0(
4 6'(7802¼–Z'(n'(4*02-3 ?À F @/<b˜„lI'(ÑWD:O702-/'`4:@/V02S'(!|0(5O7;10
u‰
#02`O7;102-/4@/!6-/'102;P- F :0(-/ 02S0(`'P-/B :@Î7;QO7;10E7@3@/<>-/BX#Z ;p7R*ƒ|4LO78B [#
U78'(' F 0,<Iµ^O-_02`! !T02: O7;102-34@/'†76µ0([46'2780(l.m¦#‡<&X7'P'(:!
7`-3'(0(;( -34b7;P0(-/4@3b6-/'P0(;(- F :02-3 =<IY47X7cq ;(7B •0(YW9:7802-3 '&8#I784c7rY0>78@
¶
¸ l9Y;('(:@_02-3B
q ;7B @3'786U<>;(-_02‡02k-3=02;(!'&#Á;PBa!q78;(-Î7 F @/'G ž
'Pa9'P0( #WD:O780(-/ '02C;Pc76'
™OÛM³
™ 
½Tš
½ 
X
ž
ž
X
¨©Û‚°9¬¼š
N
·¨ËÛM°
–€À ˆ ˜
X¬µš X·¨©Û‚°
–€ÀÀT˜
X -/'N02 ‡ /@ ! B ;PqD)h7DO7;Pq O:9ƒ¡780%r;(S! !T02: 4=-3B`#Z;( <>;P
³
02%-3Dq;P'(Q4c7'P4c76
/- `02Q4 T02-39: :'‡O7;P0>8#0(%'(40(;(: 786
N
«
¨©Û‚°
ª
³LÝ
¶Ý
·Ý
N
­¨Ëۏ¶LÛ·2Û
ž
®bۂ³1ۏ¶Lۏ·2°±|ª ³Á¬ ¶I® ¶I® ­½ ¶ ½ · ½ N
N
«
¨Ëۏ¶Lۏ·M®¯ÛM³1Û¶I®AÛM³1ۏ·2°±|ª 
³ ® M
¶ ®
³ «
¬
³ ³ «
¬
ž
Ø ¬¼Û‚³1ۏ·LÛ
N
·¨©Û‚°
·¨©Û‚°
³ ž
·*­½
®¯ÛM³1Û¶LÛ
N
¶½
·I®
³P­½
¶½
·
¨Ëۏ¶Lۏ·¬¼Û‚³1ۏ¶M®¯ÛM³’Û·2°±ª ‚
· ®
³®
¶„­½
¶½
·
¶½
·½
N
®¯Û¶2Û·I®¯Û¶LÛ
N
°±|ª M
¶ ®
·M®
N
­½
–€À Œ ˜
·
¨Ëۏ¶Lۏ·M®¯ÛM³1Û¶¬µÛM³’Û·2°±ª ‚
¶ ®
¨©Û·LÛ
N
–€À‰T˜
–€ÀvT˜
N
¨©Û‚° -3'p02U;(B:@Î7;K4 @3@/-3'(-/ 0(;( #
`^O;P'P0†0(;( <>;(-_0(02R'Pa9 F @3-/4c78@/@3an7'
N
·¨ËÛM° -/'&0(N4@/@/-3'(-3 !0(;P
02Q”
|sµD-/*02-/4b02 ;PaG02N'P4 6[02;(k<>;P-30P02X78'
7;(-3'(-3BC#Z;P z)¦<&7cq [-/T0(;278402-3 'UyŠw w~76¯6'P4;(- F 'p02[ @3|47@‚4 :@/-/BS#
02E'P=90(O7;10N#.02E'(40(;(:—02U0(E4 6'(78028l†02;( ·¨©Û‚° 4 :@3'
02b4 6'(7802 F 74Li02%02b'(!|802!O7;P0I#h0(•'P40(;(:VlTÒA•7;(‡6q@3 -/B†7
D:=;(-34c7@496•02p-/T02B ;2780(•02'(NWD:O7802-3 '-3`02-3=><>-30(`02N78-/¾#*ƒ|@3 ;(-3B
02 F O7cq9-/:;E#‡02X'Pa9'102 78#Ã0(;†0(X'(-/B :@Î78;(-30,a 02-3=8G  G6'(4;(- F 6Ð-3µ0(
;(*q9-/ :'X'P40(-/ …lm,?0(-/'['P4*02-/ <IÑ;( ;10V0(Ñ;(@/-3=-3O7;Pa¯^6-/B 'X#p:;
-/Tq 'P0(-/BT780(-/ 'l
ÒAp;P#Z ;P=6S02K#Z @/@3<>-3B!9:=;(-/47@*ƒ|;(-3=D0lÒ¡p029 V7n-3-30(-Î7@6-3'P0(;(-_)
ÌO³ ¶,·
F :0(-/ R#Z ; ÛYª ­ <>-34L F 7q'i@/-3 N 70E@/<Ä;(B -3'i76¼64c7ca9'i*ƒ|8)
T0(-Î7@3@3aÑ#Z ;E-3B ¯;(B -3'l.-/'E;P^O@3`=-3=-34'Q02['('(T02-Î78@#Zc780(:;('!8#‡0(
´”M•_œšcœ°¢:“_˜žd™kœnœ^“_“_—Œ¢:˜””kœœuÃd–p—xš^›lšy _˜žŸ™M–l™M“d–pœcª*ž”M¦†•_¤œ¡”M£²•_¢Pœ}—k—M“_–l¦d¢:“d–l›l›p–l¢†”¼¤‰šy˜”M›²•q–l˜“K””kœ^ ™Œ˜:Xš^”M–p¢:“_—j˜žd“_œcžÏ—Œš^˜™M›l–l›8¦F”Mœc•_ž*œn¦K”M¤™Œ˜ “_
—M¯aœ^™ ˜¢“_¯ž­? ˜:—k—} ”k¢ ³
’.—M“_­?žd˜œc›lœc›Q³qž½x¢:•d d–p™—j–l–p“d—j–l”M–l–b“±˜›B˜“†ªP d™kœc­œ^­œ^™Mœ^–pšy“†˜”|›²j™kœc–l”M—M•€ d›l”k”M—•_œn—k d˜ªP™Mª¥ªPœc d—M­”6œ^”M•q“†”k˜—¸”–l “ËX —Œœc–p—6š^”M£d–p¢:™k¢:“¦qŸ˜¦d³ ›l¤¿yœ^™k¢e¢:™1˜”6›pœy˜:—k”6¶¥œ^™M¤
³
·
uv
·
1e+06
t=0.00
t=0.02
t=0.18
e^-1
10000
mass
100
1
0.01
0.0001
0.0001
0.001
0.01
0.1
1
10
šŒšŒ•q¨†›l˜¤‰™Œ˜:škŸ³š^•q”k˜œ^»8“d™M¢P–pª¥—M—Mœc”M”‹—}–p« š}¢y¢¶¥¯™kœ^œ^”M™}›b•_˜”kœ|Ã_¢?˜£d˜°”M™k–pœu¢:—M«¼“£²—M–lœc¢“dš^¯FªP”M™M˜ d d“e›b˜­–l™M“d–l”¼š^–l¤”M›p–b¢P˜™k—k›dœ^œªP£d”k–l™k­¢ ¢Å_œP›p³vœx½xœu•_škÃv•qœj•d˜–l›p¦d™Œ¢s˜:Ð–l”Mš^–l”k“d­œ^ª™M¢:–p”M­—M•_”M–pœ^œ1še“K”M”M¢™Œ d¯8˜­µ“_”M•_—M–p¦²œ^œ^™Mœ^“K­•q”˜c¢v—Œ¶všyžŸ–p˜¤v¢:›l“q d–l“d™6˜ª_­'¶¥Õ œ^–pšn™M¤œc¬†¬† d dN –Ô–Ô«« Õ
›l–l¦d™M–l d­€³
energy
ÌO³ ,¶ ·
ÌO³
Mass in continuous part
Mass in singular part
Total mass
Total energy
12
10
mass
8
6
4
2
0
0
0.05
0.1
0.15
0.2
_
³
Ï
:
¢
d
“
l
–
k
”
:
¢
M
™
l
–
d
“
¡
ª
c
š
:
¢
_
“
k
—
^
œ
M
™
P
¶
˜
M
”
p
–
:
¢
?
“
b
›
y
˜
¸

—
\
¯
:
¢
™
M
”
_
•
j
œ
²
£
P
¢
M
—
‹
”
«
^
œ
¥
¶
:
¢
l
›
d
M
”
p
–
:
¢
G
“
†
³
´
¸
œ
k
—
c
œ
x
œ
_
•
s
¢
Ð

M
”
_
•
j
œ
?
­
:
˜
Œ
—
—
”k”M¢•_¢:¯”Œœ&”M˜•_—k›²œ¡¤v­?—M—M”k˜:–lœ^“d—k­ —xªP d˜šc›b“_˜¢:ž*™}­£q”kœc¢:—¸˜”Œ™M”k˜”¢›F¢œ^œc¯“_¬K”Mœ^ d•_™M–lªPœ¡›l–l¤¦d—k™M£F™k–lœ^œc d­?š^­”M˜™M–l d–Ô“/¯#­%¢:šc“_¢:ªP“_œ™k—k¢yx”Œ¸˜˜—“K–l”k”x˜—}”|”M˜°•d”M™k•_—M¢: œ¡ d?ªPœuÃv•_š^–p£²¢:œ^ dœ^“†“_”j”M›l—k”M¤‰œn•d–p›p¢—x¢:¯“dœu”MªÃŸ•_šŒœ¡”M•q–l­—M˜­“dœPª¥¢v³ œP¢:³v”M»•Ë™k£qœc—M˜ d™M”y­?³F˜½x¦d•_›l¤ œ
time
;(„),'P-/B :@Î7;P-30,a[6-3'P0(;(- F :02-3 X'(<>n-/V^OB :;PEwE<>-/4L<IpO7cq†6-/'P4:'P'(6n-/C0(
;(*q9-/ :'I'(402-3 hl O ; š X <Ib0(| i78U-/-302-/7@ &,'(6 '>q87@/:‡<>-34LU<&7'&#…02b ;(6;
Ì *
« «
# #h02 /214/A)+. =7'('I#02b'Pa9'P0(Vl-3'7; F -3027;Pa!78'('(-3B !T0-3'&4'1)
'27;1a F 47:'( F aUWD:O780(-/ –À ÀT˜&7[-3-30(-Î7@3@3aKr;(!7!@/-_02:6‡46'2780(Q;P=7-/'
X -/'i7@3'(nr;(Ñ#Z ;   78'!:;
#br;PA78=@3-30(:6U#Z ;i78@/@I0(-/!`-3#‡02 :|ƒG
'(-3†:@Î702-/'•'P:B B 'P0cl % 0%;P'PT0p<I!7;(E02;1a9-/B`0(C6*02;(!-/i7[4'(-3'P02T0Q<&7ca
#6*02;(!-/-3BN02‡q78@/:>#Z ;.02-3' &,'(6 '2l ‡<Iq;-_0&-3'‚ :;&-/-3 E02O70I0(•6„)
w}
0L7-3@/6U!4LO7-/'(¾<>;( F a`0(YTa9'(-34c7@…'Pa9'P0( 7'('P'02;P :B =02Y'P-/B:@Î7;P-30,a
 -/n ;P6;b02XB ;2702†02-/'Y'P6 -/'• :02'P-/6E8#M0(E'(4 E#‚02ED-/02-34
780 
ž
02 ;PaU#Z ;;(7'( '‡<>-34LV<I%'(O78@/@h6-3'(4:'('‡-/[02Q*ƒ90‡'(4*02-3 hl
‹ !c7;P@3aK;('(:@_02'.#Z;( :;.4 =:0L780(-/ '.7;('P<>=-3E^OB :;P'Mz%76ixl-3B :;P
|
zU-/@3@/:'102;(7802'‡:;b^O;P'P0•U7-3C F '(;Pq87802-3 t02†'(4*02;(:oq;PaCWD:-/4LD@_a F B-/'‡02
;(@Î7ƒ F 784L%0(•7‡'(4*02;(: <>-/4L†-3'Áq;1aK4@/ 'PM0(b0(M0(;P=96a9O7!-/4‚W9:-/@/- F ;(-3:
ÌO³
ÌO³
X
'(4*02;(:CG l8Ò?-_02i7 'P402;P: <ID<
l8;(>-3''(=*q9-/64
ž ÌO³
02!'(:BB '10b0(O780‡02%'(4*02;P: -/'>'(@3-/B T02@_a`'102;‡0(O7 7@_02:B [02-3'>=-3B T0
F S75…40`4 !-/BÑ#Z;( 0(S;P@Î702-3q@_aµ'(=7@/@'P4c7@3-/B¡;27BV<>-34L5<&CO7cq F U7 F @/0(p;('( @_q ‡'(Q#7;l Õ :;‚'(4 6`U%
7 P ;‚ F '(;Pq8780(-/ hGT-3@/@3:'P0(;2780(6E-/i^OB :;(
xG-/'•0(†*ƒ|4LO78B E#‚=7'(' F *0,<&Ñ02p4 T02-3D: :'Y7;P0N8#.02†'P40(;(: 76
02i'P-/B :@Î7;bO7;P0lh-3'N*ƒ|4LO7B=4 '(;Pq'K0(E02027@=7'P'%76Ñ;(BaÑ8#M0(
'Pa9'P0(
78'[4c7 F c78'(-/@_a»4L4L6 #Z;P WD:O7802-3 'іÀTˆ ˜U786 –€À À ˜*l % 0`;('(T0
02CU78-/T02O74S#Y0(C0('P4'(;Pq87802-3 5@/7<>'=-/'!;( F @/U780(-/4X-/Ð :;!496
76i;(WD:-/;P'‚'( !0,<&7D-/BQ76!0(:-/B!–€7'.<&7'‚6 02%;P|6:4^OB:;(>xD˜<>-_02
U78'('0(6-3B•0(N@/c78Q#Z;P “02'1a|'102ClÒ¡7;P4:;(;(T02@3aQ02;1a9-/BY0(Y-/E6<>†0(
;(7'( Ñ#Z ;•0(-/'N'P'P-30(-3q9-30,aS-/Ñ ;(6;Y02X;1#Z ;(—'( !E=;(†;P F :'10K'P-/†:@Î780(-/ '
q ;.@/7;(B;;(7B '.#'(47@/'.76!76E@3 B ;0(-/!'
l •'(-_02026- !4:@302-3'<>-/4L
'P0(-/@/@t;PWD:-/;PY;('( @3:02-3 =<>-_02-3` :;ID:=;(-34c7@'(4L=8G<I F @/-/*q ‡02O780I02•U7-3
#Zc780(:;('>#:;>4 !:027802-3 '7'>6'(4;(- F 6C7 F q Q7;(%WD:-_02%;( F :'P0l
K9Z D %9† à O
KZc C€T 9t |
Vt8
O
[
Õ U802-/4'p7C'P0(;(-39-3BV'(-/!-/@/7;(-_0,a F 0,<I¯02U$
|‘¾WD:O780(-/ ¯786¡0(UD-/02-34
WD:O780(-/ 'M#Z ;‚02•7!@3-302:6#…<&7cq '-/T02;274*02-/BQq9-Î7N02b@/-3c7;.0(;(Â-3!0(
”%;P '('’)’s.-Î78q9'(D-/-‚W9:7802-3 #Z;p7X'P027802-3'P02-34c7@3@3aS ! B :'Q46'2780(l;P*)
#Z ;(V V=7aR@/B-302-3U702@_a¡7'(µ-3#‡02;(C-/'i'(=V4 4*02-/ F 0,<I50(X0,<&
6'P4;P-/0(-/ t$
|‘gq9'•” 9sG0(% -3T0<&Q'(7@/@h4 'P-/6; F @3<%l
&4 40(-/ Q4 !'Á#Z;(g02‚#74*00(O780Á02M944:O7802-3 Q9: F ;('7'('P|4-Î780(6%02
02%@3 B8)Å<7cq Q*ƒ|4-30L702-/C78;(%@Î7;PB l % 0•WD:-/@3- F ;P-/:VG90(Q$& 'PK6-3'P0(;(- F :02-3 [;(„)
¶ ¥
6-/4*02'‡02O780b02-3'•D: F ;•6-3q;(B'Y@3-/ š 70Y'(=7@3@! !T02: ¸ G<>-_02
º
=
7
P
'
.
'
#
(
0
/
6
T
2
0
3
c
4
7
|
@
O
7
P
;
(
0
/
4
/
@
'
G
I
$
3
@
(
0
r
=
7
†
4
'P027T0I76
7 F '( @3:020(E)
Æ
;2780(:;(S–@3'P'Q0(O7Ñ02i02=;(7802:;Pi#&0(;27'P-30(-/ t˜„l O ;%;(B -3'Q027 F @3aS@/'('
º 02O7802p0(;PU78@;PBa G š -/'•p:4L F -/B B;>02O7 « l…;(#Z;(†WD:O7T0(:
O:4*02:O780(-/ 'E-/¯02'(X'P027802'=78;([;(@Î780(-3q@3a¡'(=7@3@ÅG F aR0(`#7!-/@3-Î7;K$& B @/-/: F q
7;(B:=T0I„ƒ90266`0(K|),r;(K==D027 D0(‡W9:7T02:Ä7!@/-_02:6>7'('P|4-Î780(6
¶ Û Û -3'Y#‚ ;P6;N8#‚U7B-30(:6Û ¥
02 š Gh76n-/'Y@/7;(B 8l*)
ž
« -3D0(;(96:4'•B @3-/B - F @/
;(*#Z ;(Q02KW9:7T02:o4 !†:027802-3 V4 6-302-3 ¨ Û Ý Û c°
ž
¶ 4 ;P;(402-3 hGD02p0(•@/7;(Bb ;P6;&#=7B -_02:6‡'102-3U780( Û Û ¥
l-3'
w|u
=7'p0(O780E-3A02`;27B ¸ '(=7@3@ÅG U4c7¯B @/40†0([WD:O7T02: O:4*02:O702-/'
76[4 '(-36;0(O780 Û 76 Û 7;P•02t:;(-3;I0(;27'P#Z ;Pk#7†4@Î7'P'(-34c7@4 !@/„ƒD)
q87@/:6¼^@/6 ×iª ­ l.-/'E#Z:4*02-3 Ð7'E02 F [02V'P @/:|02-/¼8#N7n @3-/7;†^O@/6
WD:O780(-/ …G02O70b-3'02K”N;( 'P'1),s‚-_0L7*q9'(D-/-hWD:O7802-3 hl
-/'‡”
|sµWD:O780(-/ …G|<>V0(N @3-/7;I0(;P -/'&4 'P-/6;(6C78'>7i;102:; F 780(-/ hG
a9-/@36'7><7cq9-30(-/4IWD:O780(-/ p0(O780O7'„ƒ740(@3a%02&'27!I#Z ;P 7'0($
9‘АD-/„)
02-34•WD:O702-/hG9<>[;('P0(;(-/4*026`02p-_02'I4: F -34b0(;(!'78'6-/'P4:'P'(6V-3U'P40(-/ Vw9l|-3'
-/'‡0•'(:;P;(-3'(-/BU'(-348G-3C0(p@3-/!-30#@Î7;PB K944:O780(-/ VD: F ;P'G…p„ƒ4*02'
02O70>7†4@/7'('P-/4c78@^O@/6[WD:O702-/hG@3-/N” |sG7;(cƒ|-/=7802'&<I@/@02Y#Z:@/@…6|a|7=-34c7@
;( F @/Cl ‡<Iq;0(-/'Á-3'00(M4 !@/*02‚'(@/:0(-/ %#|02M;( F @/“#„ƒ|0(6-/B
02b$
|‘"D-/02-34>WD:O780(-/ i02%02#Z:@3@O;27B >#h '('P- F @3<7cq D: F ;('l-3'‚ @3a
'(<>'p0(O780Q02i<&7q`D-/*02-34=W9:7802-3 A786A02U$
9‘ĐD-/02-34=WD:O7802-3 Aq;(@/7
-/C'( !p;(7B Q#.<&7qD: F ;P'G…0(p;(7B Q<>;Pp02p944:O7802-3 SD: F ;('N7;P
q ;Pa @Î7;PB i4 !O7;P6 02SGÁ ;’)b#Z;K7X02;(=7@‚BT7'’)b0(!;27B=#;(B -3'%#7;
'(=7@/@3;&0(O7[02%0(;PU78@h;(Bal
-/'p@/c7cq'E<Iq ;!70(;†6 U78-/A8#‡q;1aR'(=7@3@M<&7cq D: F ;('G<>;(`0(
|44:7802-3 `D: F ;P'7;(•'P02-3@/@Oq ;PaU@Î7;PB G F :0<>;(Y0(Y-3D0(;(740(-/ =;(Ba`76
02QD-/*02-34Q;PBaC7;(Q#02Q'27!Q ;(6;b8#=7B -_02:68l O ;‡7=D: F ;‡6'(-_0,a
š 786n7='P4c780P02;(-/B=@3B0( Ê GO0(p4;( 'P'1),q;•944:;('‡<>q ;Y02%<&7qD: F ;
³ ¦¶
-/'Q#;(6;K# ;K'PU78@/@/;Y02O78 ¸ J
lÁm,¡0(-/'Q;27B =8#q ;Pa '(=7@/@
Ç ª Ê šh­
ž
<7cqD: F ;P'G> n470`B @34*0V7Ta|! ;PS02n-3T02;(740(-/ »;(Bal$&:0G 02=02;†O786hGÁ02=W9:7T02: O:4*02:O780(-/ '†7;P=0280L7@3@3anB @/-3B - F @/E-/ 02U'27!
6 =7-/…l8;(*#Z ;(0(;(@/q87T0.WD:O7802-3 E-/'.” |sl ‡<Iq;‚02-3'WD:O702-/E'( :@/6
F ‡4=@30(6E02Q-/4@/:6‡'P !‡-3#Z ;PU780(-/ p4 !-/BN#Z;P 02‡'P ;10I<&7cq •7;P0M#
02%'P402;P:VG02% %6'(4;(- F 6 F a`02Q$
9‘ D-30(-/4Y02 ;1a lO-3'‡-3#Z ;PU780(-/ 4 !'>-3V-3`0,<&=6- ;PT0<&7a9' , ˜•;Pi-/'N7[4:@/-3B
F 0,<I 02E'P ;10N<7cq !O7;10%#‚02i'P402;P:Ÿ76Ñ0(
@/ BÑ<&7cq CO7;P0i0(O78¥0=
-3Д |s
B C0(X4: F -34C-3T02;(740(-/ ¯0(;(
7! :T02'E02 4LO¥
7
¶
¶
×É YX É "
× X 02 Ø ª É ×YX É ¬ Ø š ­ G9<>;( š K-/'‚02b6'P-30,a!#
#Z;( 0(•:'(:O7@ Ø 02b ;PU7@tBT78'G9= '102@_a!744 :T026X#Z; F a!02b'( ;10<&7qNO7;10&#0(•'P40(;(:Vl
,', ˜1;([-3'E7S=7'('†„ƒ|4LO7B F 0,<I¼0([4 6'(7802[6'(4;(- F 6 F a¡02U0(;P
;( ;102-3 O7@0( š X 6;(-_q 6=#Z;(Â$
|‘ F a!7'('P:=-3BQ7Q4 ! T0M#h! !T02:
6-/'102;P- F :0(-/ K<>-302!7 •-/;(746@30L7Y7;P0M780Mr;(%! !T02:
ˆ|l
7'‚6'P4;P- F 6!-/i'(402-3 ;( WD:O7802-3 C–€ÀTˆ˜q87;P-/ :'.-/! ;10L7T0‚4 '(WD:4'47 F ‡6;27c<>hl -3;('10.02;(
O
69'p0†'P 02 F U7C '('P- F -3@/-_0,an# ‡ @/! B ;P t)h7DO7;PqS'P @/:0(-/ 'P0  G
*ƒ|40QU7ca F E-3Ñ7[q;1a02;(7'(-3T0%'P0278028lhm,Ñ;(-34-3@/p'(:4L R'( @3:02-3 'N7;P
-/T02;('P02-3B F 47:'PS02*a»B-3q S7¡4 'P027T0 O:|ƒ¼0(<&7;P65r;(R! !T02:Vl‚
̦·
-/Tq ;('P[4c7'P4c76[7'i7S<I;E@/7c< F 7q9-3 :;†@3-/ Û
7'†6'(4;(- F 6¯-/
ž ¨ËÛM° -/UWD:O780(-/ іÀTˆ ˜„l‡<&*q ;
'(402-3 [zG902-3'&474@/'M02•^;('P04 @3@/-/'P-/ E0(;(VG
w w
N
(' :4LA7V4 '10L7T0O:|ƒ 'P @/:0(-/ n4780 F !7V'10276aÑ'(@/:0(-/ n7;%r;(V;(B -3'
<>-30(?7A'(!|802»0(-/!S66T0V49!4-/T0
l&-/'`-3' F 4c7:'(G F a»@/:B B -/B
02-3'†0,a9[# F O7cq9-/ :;E-/R02[4 @3@/-/'P-/ 02;( „ƒ|@/-34-30(@_a <>;P-30P02…G [ F 0L7-3'
d £ 02O780Y-/'Y#M ;P6; ÌO³ ' G…#7; F -3B B ;
7`4 T0(;(- F :02-3 02`0(†02-3=K6;P-3q87802-_q Ì '
c78; >'(=7@3@027[02%*ƒ|4*026 <&;‡@/7c<%l
-/'.@3c76'. 02%@3| %#Z ;802;0,a|># F O7cq9-/ :;.8# ەª ­ #Z;M'PU78@/@Ål % 4*02:O7@3@3aG
<&b*ƒ|40I02O70M0(•'P @/:|02-/i<>-3@/@*q @_q b-/! ><7ca! ;.02‡0(;‚02KWD:-/@3- F ;P-/:Vl
-/'NWD:-/@3- F ;P-/: '(@/:0(-/ F O7cq'Q@/-/8 ەª ­ b c7; %'(=7@3@Ål;P#Z ;Pi<I
02;1aX7X*ƒ|O7'(-/C#02Q'P @/:|02-/[#0(%D-/*02-/4NWD:O7802-3 A–€ÀTˆ ˜I7'
ÛYª ­
ž
X
¬Ð±ÛYª ­
–ÅŒ8}T˜
<>;P ±ەª ­ -/'7p#Z:402-3 [#&02780>-/'I†:4LX'(=7@/@3;M02O7`0(N6 !-/7T04D0(;(-¿)
F :0(-/ b 02 Û -3i0(@/-3=-_0 .'PU7@3@Ål-/'‚;102:; F 7802-3 E'(;(-3'‚-/'4'('(7;Pai02%B *0
X G F 4c7:'( F aS:0(0(-/B!02††q ; •02;(o-/C0(
7W9:7802-3 #‚!02-3 C#Z;
4 @3@/-3'(-/S02;(!'Gh !B02'%r;(G F 4c7:'P=-_0%-/'Y0( F O7cq|-3 :;%#M02iW9:-/@/- F ;(-3:
'( @3:02-3 R70p'PU7@3@‚;(B -3'l‹|-/!@3!'P4c7@3-/BS7;(B:=T02'p'P<k0(O780 F a¡-/'(;102-3B
-/T02%02b4 @/@3-/'(-3 p0(;(„ƒ|@/-34-30(@_ap<>;(-_0(0(!-/!WD:O780(-/ S–€ÀTˆ˜*GT ‡B *02'I7%#Z:402-3 # &02780'(47@/'@/-3
b G902-3' F -3B†;('P0(;(-/4*026`02†02;(!'&@3-/7;I-3U02Y;(@Î780(-3q @3a
³
'(=7@/@ ±Û lT$&7@Î74-/B•02-3'<>-30(E026=-3O7T00(;( E02@3#Ã0.'P-/68G O7!@_a Ó d b
£
YB02'M02O70 ±ÛYª ­ †:'10 F O7cqN@/-/8
; &'(=7@3@Ål O;( Â0(-/'M<&Y6;(-_q •0(Ó c78
š
X ³h¬
X GO@/-/8 Ó d b
-3'
WD:O780(-/ V#=0(-/ `#Z;
X ¶ ³ lOK4 'P0L78D0
ž
Ó
4 !:0(6 F a!;(7802;&4 =@/-/478026i†:@30(-/6-3='(-3 O7@|-/T02B ;278@/'lT•'278=‡-/'.02;P:
#Z ;0(4 'P027T0
02780;P;P'(T02'M70(;4 T02;P- F :|02-/p02•0(&0(-/!I6;(-_q702-3q
X 4 =-3B†#Z;(k02%0(;P
¨Ëۂ° -/[02QD-30(-/4NWD:O702-/hl
#
N
Õ N4 :@/6X4 T0(-/D:%780>-3B ; ;(6;-/ 02EB0>4:@/6XWD:O780(-/ '#Z;02Y0(-/!
6 ;P-3q8780(-3q C#Y0(49!4-/T0('`#Y0( IÁ7:;PT0`„ƒ7'(-3 "# ەª ­ 7; l
ž ÒAi78;(†;P'PT02@_a<&;(D-/BX Ñ78n*ƒ|@/-34-_0•<&7a#M:'(-3BX7@/@02-3'Y-/|#Z ;(=7802-3 X02
B 0b;(740(-/4c78@/@3a`7!D:!;P-/47@/@_a`'(@3q87 F @3N4 :@/6C'(*0Y#9-30(-/4%WD:O702-/'‡#Z;>0(
4 6'(7802Q6'(-_0,aV76[02%'P=902X! !T02: 8;PBa`6-3'P0(;(- F :02-3 hl
b<Iq ;N02-3'•69'b0N602K'P0( ;PalÒ¡†'P0(-/@/@ÁO7cq†02`67@<>-_02V02†WD:'P0(-/ #h0(•4 6'2780( F aU-_02'P@3#’l Ò¡•7qY-/==-36=7p;2780(;M F q9-/ :'&WD:'102-3 9B -3q
-/-_02-/7@4 6-_02-3 'N#Z ;Y02=6'(-_0,a 76 ;(BaÑ'P:4LA0(O780%02iW9:-/@/- F ;(-3:o'P0L702
O7'E7C4 6'(7802X780pr;(! !T02:VGÁ<Ä6|'p02-/'p-3-30(-Î[email protected] 6-_02-3 A*q @_q 02<&7;(6S0(K^O7@ÁWD:-3@/- F ;(-/: 'P027802 pÒ¡p'PO7@/@Á@3-/!-30:;('Pq 'Y02=;2780(;b'(*024LTa
;(U7;PD'& U0(-/'IWD:'102-/hG|0(O780&<I :@36`;(WD:-/;PY7p;(7802;&@3 Bp6-/'(4:'('P-/ X78DaD<&7ca l
0†02[= !T0Q#Z;( D:!;(-34c7@I76µ78O7@3aD0(-/4c78@I'102:6-3'[y¿ucx~& `:6;P'P0276'
<&@/@02O780G-_#02N-3-30(-Î7@O6'(-_0,a`-3'&029†@Î78;(B ‡#Z ;7†B -_q [;(BaGt7p'(!|802`-3-30(-Î7@
4 6-30(-/ V#0(†$
9‘ D-/02-34KWD:O7802-3 F 4 ='b'P-/B:@Î7;>-37!^-30(K02-3=8lO
'( @3:02-3 F @/<>'Y: F 47:'(E-_02'‡q78@/:p780Yr;([;PBa F 4 !'Y-3^O-_02p780N7=<I@3@
%
wz
6^6i^O-_02&0(-/!G  G 66-/BNi0(-/-302-/7@D4 6-30(-/ 'l8-/'.69'.80.=7
<&*q ;Y02O780•'( !0(-/BU@/-3p7U4 6'(7802 ?59= :9 -/'‡#Z ;(!6S780•0(p'P-/B:@Î7;P-30,a
02-3=8lc-/'Á-3'h#Z ;h0,<&b;(7'( 'l -/;P'P0Á700(.02-3=.#902M'P-/B:@Î7;P-30,a‡02M=7'('-3'(-36
02‡'(-3B :@/7;(-_0,a†-3'Mr;PG F 4c7:'P‡0(‡= !T0(: 6-3'P02;P- F :|02-/hGT7@_02 :B i'(-/B :@Î78;
780Er;(Ñ;PBa G.;P=7-/'p-/T02B ;27 F @/l O:;P0(;P=;(G02[4 6'2702GM7'p:'(:O78@/@3a
:6;('1029|6hGD-3=@3-/'-/^-30(‡;(7B ‡4;(;(@Î780(-/ '.-/!'(O74 97@3@O7;102-/4@/'‚0(;PY7;P
-/E02'27! ! B :'MB;( :6!'10L780(lT-3'.-/^-30(;27B K–O78'(˜4 ;(;P@Î702-/
4c70 F :-/@/69),:!-/'10L7T027:'(@_a`780I02•4 @3@Î7'P‡0(-/!lDm¦0470&q F :-3@/6|)¦:
780-3^O-_02M6-/'10L74'-/E7TaQ^O-_02I0(-/!I-3T02;1q87@…y¿uv~Ål8;P#Z ;PG*ƒ|4*02'02780
78#Ã02;E02V-/-_02-/7@ F @3<),:hG0(;PC<>-3@/@ F C'P !02-/BÑ@/-3V7Ñ4 T02-3D: :'=;(94'('
#KB ;(<02 #Q02Ñ;(7B n#Q02 4 ;(;P@/7802-3 '[7'P'(94-/78026 0(Ð7¯!|6:@/:'U#K0(
<7cq#Z:4*02-3 †B ;P<>-3B‡-302'P@_#-/%02I4 :;('P&#02-/!.:T02-3@D-30;(74L'-30('W9:-/@/- F ;(-3:
q87@/:8l
-/';P|4'('4c780 F ‚6'(4;(- F 6 F aQ0(I$
|‘¯D-/*02-/4.0( ;1a F 4c7:'(M-307'('P:!'
02O70V0(n<7cq@/B0( -/'X@/'('[027 0( n#Z ;[<>-/4L?02¡-3D0(;(740(-/ ?;(B8a
F 4 !'E'P-/B -3^O47T0E4 !O7;P6R0(02[D-/02-34U;PBa¯#>02[*ƒ|4-_0L780(-/ 'l-3'
@/76'•pWD:-_02QO7802:;27@3@3a[02U7'('P:!K02780•0(p@3 B=<&7cq †7;P0•#02p'(4*02;P:
-/'6'(4;(- F 6 F a`02p”
|sÐW9:7802-3 hG02780>O7'02 F Q=780(4L6V'( !< <>-30(X0(
$
|‘ÂWD:O702-/¡70%'( ;10Q'(4c78@/'lÁ-/'N-3'Q6 i-/n0,<IC6- …;(D0%<&7ca|'G66-3B
[02Y0(-/!Y780<>-/4LX-30-3'6 lON<&7q%9-30(-/4YWD:O7802-3 X-/'&0(%'27!N7'0(
$
|‘¾WD:O780(-/ ;('P0(;(-/4*026A02V-30('K4: F -/4i02;(!'G02= =;P@/*q87T0K0(S6'(4;P- F !0(
4 @3@Î7'(l;P#Z ;PK-_0-/'>7iB 9|6X7;(cƒ|-/=7802-3 `02E0(%4 @3@Î7'PN;(94'('>02E0L78
7'-/-302-/7@O46-30(-/ U#Á02Q”
|sµWD:O780(-/ X7p#Z:402-3 `02780;(;('(D0('•7844:;2780(@3a
02•'(@_#Î),'P-/!-/@Î78;'( @3:02-3 U8#02YD-30(-/4‡WD:O780(-/ hl|-/'I=7'M02O780-30I†:'P0&O7cq 02•'(40(;27@6-/'102;P- F :0(-/ !D<>X9:=;(-/47@/@_aXy¿ucx~<>-302U;276 ¾O7'P'#Z ;Ic74L
'(4*02;278@M!96l!02-3=E*q @3:02-3 78#Ã02;P<&7;(6'Q'( :@/6 F E<>-_02 :|0K'P-/B:@Î7;P-30,a
–Z#Z ;02b”
|s WD:O7802-3 t˜76!'P :@36E6'P4;P- F b7N'P=902†0(;27'(-30(-/ K#Z;( 7N;(B-/!
<>-30(K^O-_02M;27B I'PO780(-Î7@D4;(@/7802-3 '02•7b;PB -3=‚#OO7'(I4 ;P;(@Î780(-/ 'Á„ƒ|0(6-/B
780E@/7;(B ;†76¼@/7;(B;p6-/'P0274'i7'†0(-/!UB 9'†hl Õ 4`0([O78'([4;(;(@Î780(-/ '
*ƒ9026n780‡6-3'P0274'‡#78;‡@3 B ;02O7X02Q0,a9-34c7@@3B0(C'P4c7@3Q<>;(%02KD-/02-34
;(BaS76C02K-/T02;274*02-/7;Pp#0(†'(7=Q ;P6;b#‚U78B -30(:68Gp47S0L78
02U6'P-30,aR7'('P|4-Î780(6A0(02'([@/BC<&7cq O:4*02:O780(-/ '†7'p0(`6'(-_0,aR#0(
'(-3B :@/7;O7;10•#02Q! =T02: 6-/'P0(;(- F :02-3 hG š X -/X02KD-/02-34%WD:O780(-/ hlt-3'
B -3q'‚7Y<&7ap02NB *0.02>-/-302-/7@D4 6-30(-/ p#Z;02-3' š X -/†0(‡$
|‘»D-30(-/4WD:O702-/'
4 :@/-3B`02i4 6'2780(`7!@3-302:6†76 0(i'(!|0(ÑO7;P0%8#&02!6-/'P0(;(- F :02-3 hl
% 0†02['27!U02-3=8G02[-3-30(-Î7@q87@3:U#Z ;Q02['P=902AO7;P0p#>02-3'†6-3'P02;P- F :|02-/
4c7 F •0L78V7'0(Y'P402;P: #Z :6[-/`0(Y'(@/:0(-/ `8#0(%”
|sµWD:O780(-/ `<>-_02
02V'(@3#Î)¦'(-/!-/@/7;p-3-30(-Î7@M46-30(-/ …l-/'!B -_q '=7 <I@3@6^6 –7@30( :BÐ;(7802;
4 !@3-/4c7026O˜&;(946:;(K#Z ;>6'P4;(- F -/B=02K02;(7'P-302-3 V74;P '('‡02K'(-3B :@/7;(-_0,a`#
02Q$
9‘ 9-30(-/4NW9:7802-3 hl
Ñ$
|‘—9-30(-/4WD:O7802-3 "-/'='(@3#Î),4 T0L7-36…G76"-_0`6'(4;(- F '`0(^OO78@•q8)
@/:0(-/ ¯0(<&7;P6ÐW9:-/@/- F ;(-3:VG F :0i#Z ;i V-/4C8#Y-/|#Z ;(=7802-3 hÁ
G 02Vq;!B -3B
;(94'('I#O78'(•'1a94L;(-/r7802-3 U#02b4 6'(7802‡02;P :B :&
0 7@/@O'PO748l-3'
w8x
-/'N6'(4;(- F 6 F a02U”
|s?WD:O780(-/ …GÁ7'%7@/;Pc76|a*ƒ|@/7-/6hl ‡<&*q ;%02-/'N-/'N0
'(: !4-/T0G F 47:'([” |sGh<>A@/#Ã0Q02V-30('(@3#’Gha9-/@/6'K7C*q ;p6-/BC4c7'P4c76U#
;(Bai0(<&7;P6U02‡'(=7@3@O'(4c78@/'by¿uz8~€l9-/'M-/'M4@/7;(@_aE-/4 !O780(- F @3&<>-30(=02‡^O7@
;(@Î7ƒ780(-/ E02<&7;(6=WD:-3@/- F ;(-/:CG8'(-/4>02‡:@30(-/=7802&;('P:@30I#02-3'M47'(476b'( :@/6
F =7@3@02!U78'('Q4 4T02;(78026R-/Ñ02Ur;(V<7cq D: F ;†O78;P0K#&0(='P40(;(:VG
@/:'%7X -/'Pi780%-/^-30(@3aC'(=7@3@<&7cq @3B802hlÒ¡E*ƒ|40K-/'10276n^O-30(E|44:7)
02-3 nD: F ;('N6-3q ;(B -3B`@3-/ « \ Y#Z ;Y'PU7@3@;PB -/'Gh0N'(=*02-3B`026-/B`02
r;(l‚A;(;('(D0=02-3'i VO7'i02¡766Ð0( 0(S” |s WD:O780(-/ »7 -/'(V7657
6O7!-/B`02;P]'(:;P-/BX02O70p70Q7TanB -3qÑ02-3=†0(i'(40(;(:Ÿ8#I0(i'( @3:02-3 #02-/'W9:7802-3 `=78024L'&02Y YB-3q F a=0(N'( @3:02-3 U8#02YD-30(-/4•WD:O7802-3 c78;!r;P ;PB -/' 02-3'E-/'†0(X:'(:O78@'P02;(7802Ba¯#b-/;’), :0(;†„ƒ|O7'P-/ hG0(
@/7;(BϏ;PB -/'E ;†! !T0L7S8#•7n'P @/:0(-/ A#>02V”•)’s“WD:O702-/¼-3'E74*02:O7@3@3a¡7
'(=7@/@.;PBa»– ;Q! =T02:U˜•<>¯'P¡#Z;( ]0(U -/T0K#&q9-3<¾#0(`$ |‘
D-/*02-/4QWD:O702-/hlt;P#Z ;P†-30‡=7'•'('(K02U:'(p0(K'PU78@/@;(B8a F O7cq9-/:;
#Á7%'( @3:02-3 !#$
9‘?0(p6*02;P=-302‡;P ;P0(-/'M#Á7% -3'(>02;(¾780I'(=7@/@O'P4c7@3
#Z ;02p”
|s¼WD:O780(-/ hl
-/'U-/'U6 F a"766-/B 02R0(є
|sÄWD:O7802-3 "7µ”%7:'P'(-Î785 -3'( …ªZ„Ý ­ 76
7S6O7!-3BC0(;(Vla¡-/T026R02S;(;('PT0i6- …;(T0pTa|'P-/47@&;P|4'P'('l.
6O7!-/B02;P
–€78666¼02n02V;P-/B T0iO786Ð'P-/6X#Y”
|sM˜p†:'P0 F X#b0([#Z ;(
® Ö Ç ¶ ×iª ÁÝ(P­ G9<>-_02 K;(c78@ '(-_02-_q lDm¦0I;(;('(T0('02b@/ 'P'I#hO7;P0(-/4@/'‚-3=02•@/B
<7cqQ6 U78-/ F a`4 @/@3-/'P-/ '‚<>-30([O7;102-/4@/'&-/`0(Y02;(=7@ F 780(hlm¦#Á02-3'6O7!-3B
02;( <I;P`7@3 G02i6'(-_0,aÑ#&0(i4 6T0L780(=<I :@36 64c7ca¡780N0(=4 '10L7T0
;2780( Ol&m,?02nD-/02-34n-/4*02:;P02-3'U0L78'V-/T0(µ744 :T0C7@/@b@/ 'P'`02;P='[8#Q0(
WD:O780(-/ #Z; š X l;P#Z ;P [O78'%7[<I@3@6*^O6¡„ƒ;('P'(-3 ¡B-3q F a02i$ |‘
WD:O780(-/ …l Õ 4i02-3'Q-3'%6 8GÁ0(!02;%-/4!#&0(=:rr@/GÁO78=@3aS0(! -/'P
02;(VG-3'b7'PaV02U^6hlm¦0Y-/'•7[”%7:'('P-Î7C -3'(p-3C0(-/! F 47:'(p-30b;(;('PT02'Y0(
766-_02-3 p#t;(76 <&7cq '.0(•02&4 6'(78028l t:;P02;(! ;PI<I*ƒ|40.0(-/' -/'P
02;( 02`7q†=4 ;P;(@/7802-3 V-/C0(-/!Gt'(-34K-30b4 4;P'•<&7cq 'Y<>-_02V#Z;(WD:4-3'
†:4LR@/7;(B;N02O78A<>O780p-/'Q6'P4;(- F 6 F a¯”
|sl V ;(q;†-_0Q'( :@/6RO7cq`'(O784
4 ;P;(@Î780(-/ '^0(026V0(!a9-3@/6 F 784LX0( b
Ø Æ ¥ b '(4*02;(:o-3[02N<&7qD: F ;
ž
'(O784l-/'Y4 4;('N0(†'( ;P0N<&7cq iO7;10N#‚02!”
|s?WD:O780(-/ #Z;b<>-34LÑ0(
@3-/7;K0(;Pe-/'†B @3-/B - F @/8l;(*#Z ;(X-_0E-/'†@3aR7U780P02;E# .0,'3 9)+= 7@3B F ;(7
02!^O6S0(p„ƒ@/-/4-30>#Z ;P #02p4;(;(@Î780(-/ '‡8#.02Q -3'(K0(;P 0(O780‡a9-/@36 F 784L
02Q;P'(4;(- F 6 b
Ø Æ ¥ b -3V0(K<&7cq K9: F ;b'PO74K#Z ;>'(@/:0(-/ V#0(p” |s
ž
WD:O780(-/ …l ÒA>;(*#Z;‚02>-3D0(;P'P0(6=;(c786;‚02K7N4 !-/B%: F @/-34c780(-/ E i02-/'02-/48l
K
ÒAQ44@3:6%<>-302C7 F ;(-/*#6-3'(4:'('P-/ C#'P =%#02QU78Da`W9:'P0(-/ 'b<>-34LS;(„)
U78-/Ñ02 F `78'P<I;P6 F #Z ;P`7V#Z:@/@.:6;('10L76-/BS#02U44*02-3 F 0,<I
D-/*02-/4†0(;PaÑ76¡$&+IŽ -/'N F 0L7-36hl -/;P'P02@_a G F 0(n02!$M),‘ WD:O780(-/ Ж1u˜Y76
02E”Y),s?D-30(-/4pWD:O7802-3 µ–Zxu˜b78;(p-3'(=†'P'PE=7S^O@/6;P'P:@30('lh$I02Ñ7;P
w ˆ
F 027-/6 F aE0(;(:47802-3BQ7U„ƒ|O7'P-/ =780M@/<I'P0I T0(;(-3q9-/7@ ;P6;M76=B@/4*02-3B
02E-/B ;N ;(6;•0(;(!'Y<>-34L¡6'(4;(- F O:4*02:O702-/'%7;(-3'(-3BU#Z;(—-3B ;N ;(6;
@3-/7;N-/T0(;278402-3 'lhm¦0Q-/'%0Q4@3c7;Q7[;P-/ ;P-02O780N0('P O:402:7802-3 '%4c7¡7@¿)
<7ca9' F iB @/4026hlÁm,66A-_0N-/'%-3B @_aS@3-/@3aR–'Pi#Z ;N*ƒ7!@/†0(=7;(B :=D0('
-/Ñy¿uˆ~ΘI02O7002N-3B ; ;(6;02;(!'6 F 4 !N;(@/*q78D0‡70q ;1a[@/< ==D027
76¯78;(`„ƒ4*026µ0(!|6-_#Ãa02•)Ð'P402;P: -3A'P =!<7calC#Z:;P0(;†:|)
6;P'P0276`02'(•-/'('P:'I-/'I7Kq ;Pa=4LO7@3@/B -/BQ;P F @/ <>-/4LU-/'M0:-/WD:‡02K0(
O7;102-/4:@Î78;MDa9'P-/4c78@…'(-_02:O702-/U:6;4 '(-36;(7802-3 U;(8lm¦0>78;(-/'P'I-/U=7Ta=7;(7'
#WD:-/@3- F ;P-/:—76 |)¦WD:-3@/- F ;(-/:—'10L780(-/'P0(-/47@!4LO7-/4'%<>;(!=7 ^@/6¡7
-/4*02:;P%;(WD:-3;('‡!96-3^O47802-3 U0(=7844:T0‡#Z; O:40(:O780(-/ 'l
'P46¯-/'P'(:=;(@/7802'K0(C02`'(47@/-3B F 7q9-3 :;p8#02=;(„)  'P @/:0(-/ #0(
D-/*02-/4`0(;Pa l.‹|-/4[02['P4c7@3-/Bn F '(;1q 6»-/'E |)¦0(;(-_q|-/7@M-/R02V'P'PV0(O780i-_0
4 ;P;('( 6'K-_02;%0(C0( •)µ'P4c7@3-/BX ;%02X02=W9:-/@/- F ;(-3: GÁ-30%=78'
'('(‡02%<& 6;‚<>0(;M02;(‡-/'‚'(=>Ta9'(-34c7@ F 7'P-/'.#Z ;.02‡'P4c7@3-/B%„ƒ T0cG
« Ô Ø †m¦0Y-3'• '('P- F @3K02780•0(-/'b*ƒ|T0N-3'•0(-/B`=;(%02O70(p'P @/:|02-/S#
02= @3-/7;%-3B Tq87@/:!;( F @3 –ÀTw ˜%76A4 T0L7-3'p02-3BV6;l t;P 7
Ta9'(-/47@;('P40(-3q Q<Iq ;G-30<I :@36 F %-34Y02iO7cqp7E! ;(N;(7802-3 O7@*ƒ|@/7)
O780(-/ `#Z ;0(Nq87@/:N8#0(%*ƒ|T0cl
%
ÒA†<I :@36 7@/'P`@/-3p0(V:6;P'P0276 = ;P†4@3c7;P@3aX<>O780%7'N02`0(-/'N'1a9'P02
78#Ã02;02'(-/B :@Î78;(-30,a%0(-/!G  l Õ E02 O76hG026;(-_q87802-3 †#7Y!|6-_^O6ED-¿)
0(-/4‡02 ;Pa!<>-/4L=0L78'-3D0(E744 :T0I02Y 'P'(- F -/@/-_0,aE#Á7K:-3#Z;(Â46'2780(G
•›
GÁ!-/B T0%'(6¯'(=!@/-3B T0% ¡0(-/'lU-/4@/:'(-/ 8#>7C|),r;(C=7
ž '(:@/6 F V 'P'(- F @/`-3µ0(V7;PT74Lµ#b'(402-3 »wÑ78@302 :B ¯-_0†<>-/@3@&;('(:@_0i-/¼7
'(-3B -3^4c7T0 P:!C-3V7@/B F ;278-/4N4=@3*ƒ|-30,aU#.7i;P F @/k<>-34L7@3;(76a[4 T0L7-3'
7p@/80&#0(;P='lY;P'P:@30(-/BKWD:O780(-/ '&;('(:=7 F @_a!<I :@36`;('( F @/b02 'PY'(:B8)
B '1026†-/Uy_ucx~786p'102:6-36K9:=;(-/47@/@_aN-/%02&;P'(T0‚7;P0(-/4@/l Õ Q02I02;O76
'(:4LS7p02 ;PaU<& :@/6 F NB0(0(-/BE;(7802;#7;>7c<&7aU#Z;( Ä02%;(7@hTa9'(-34c7@'1a9'P02
<& F B : <>-302¡76¡qA#Z:;102;Q#Z;P 0(U„ƒ;P-/!T0L78@.'(-30(:O780(-/ hl…m¦0p-3'Q4@/7;
02O70-/U7p;(7@Ta|'P-/47@…'1a|'102k<IY4c70B;(<?-/^-30(b4 ;(;P@Î702-/'.<>-302-/`7Q^)
-30(‡0(-/!>7'I0(‡'(-/B :@Î78;M'P @/:|02-/!8#'(402-3 UxK'(:BB '102'lO:;P0(;P=;(‡;(c78@$&+IŽ
*ƒ|;(-3=T02'b7;(%q ;PaV'(O702-Î78@/@3a=-/ ! B :'lts.;( F 7 F @3aX! ;(%-3D0(;P'P0(-/B!-/9)
'(-3B T02'N4:@/6 F †#Z :6 F aS0(;Pa9-/B`02[:6;('10L76¡< '(O702-Î78@4;(;(@Î780(-/ 'YB ;(<
76 < 02=-3 ! B -_0,aS#I02i02;(7Ñ-/ :4'Q02iTa9'(-34'p8#&02!-3Tq ;P'(
4c7'P4c76p !S6'(4;P- F 6C;Pl$&02X02'(K-/'P'(:'•7;PK'P !<>O780b :0('(-36
#02%;(=-_0#'P0276O7;P6CD-30(-/4Y02 ;P-/'l
D| %
Â`²i^³ R\eT^B³iŒ}T^Փ_
ždœ^™k—k¢: “G՟
_Õ ³ n³vڟ“_³ —M•_œ^™yÕ Â³ n³ D˜”M”M•_œ^¸—yÕ_ͳ Ú¸³v´Ê–pœ^­?˜“G՟˜“_ž*Ú¸³e³ŸÍ1¢:™M“_œ^›l›Q³
°³ _³4¾1œ^“d“_œ^¤"˜“_ž¡³ ͳ4À}œ^1œ^›l›Q³ ˜“_žd¢:­ x˜c¶¥œ*š^›p¢P—M d™kœc—y³Ë`BOa]ŸU1RîrKrBfÏIPOSWbÕ
wÀ
dè sê sÈ ŸÕ Ÿ³
F³ Àe³d¾x¢P—kœP³ VWKXYpÕ ŸÕ _³
½³qÍx˜™M›pœ^­?˜“G³ ¸icOQI ÏI¥OSWpÕ PÕ Ÿ³
ͳqÍ1¢:“d“q˜ dªP•†”k¢:“D˜“_ž F³ e³dÀ˜¿s˜™kœ^“d¨¥¢d³£d™kœ^£d™M–l“†”˜™–l¶ £d•†¤v—M–pšc—
_Õ Ÿ³
ͳ_Í1¢:“d“q˜ dªP•†”k¢:“GÕ ¡³ ͳŸÀœ^œ^›l›QÕ_˜“_ží'³v»8¢:­œy˜ G³#À}¢:“Ÿ«¼—k”Œ˜”M–p¢:“q˜™M¤*—M£²œcš^”M™Œ˜e¢¯4›p¢všy˜›
x˜c¶¥œn”M d™M¦d d›pœ^“_šcœP³1VWKXYuRaikInÕ qè u« †ê È ŸÕ Ÿ³
x³ ˜›Ô¯\¢y¶¥¢dÕ F³sº–p¢:™MªP–l“d–QÕ ³ »8³s»–l”Œ˜:œc—k¶†¨v–l–QÕs˜“_ž F³ †”M™M–l“dªK˜™M–Q³K½x•_œc¢:™M¤¢¯d¾x¢P—kœu«¼Ú–l“_—M”kœ^–l“
šc¢:“_ždœ^“_—Z˜”M–p¢:“€–l“€”M™Œ˜£d£²œcž‰ªK˜:—kœc—y³6{¸T ÏLyU†TuNZËVW†XYpÕ ŸÕ Ÿ³
Ç'³ ¾³ ˜c¶v–p—yÕ Â³ « ±œ^1œc—yÕ §³ ¡³ }“_žŸ™kœ^¸—yÕ²À¡³ _³B¶P˜“ ™M d”kœ^“GÕ °³ F³ d™‹¯\œcœPÕ °³ ³
Ç d™M“GÕB˜“_ž/´ ³_ǜ^”M”kœ^™M›pœP³1VWKXY {¸T GH4TcO\O pÕ ŸÕ Ÿ³
F³ ¤K˜:šk•_œ^“d¨¥¢dÕ e³ ͳÀœ^œ^›l›QÕ e³?» _—M•d¨:˜™kœ^¶²Õ‰˜“_
ž
e³ Ú¸³‰É²˜¨v•q˜™k¢y¶²³ }£d”M–pšy˜›
”MÀ d¢:™M“d¦d›l d–l“_›pœ^œy“_˜šc™ œ všŒ&•d´™k¢†œyžŸ˜–l“d¨ ª¥œ^”M™ d™Mœc¦d¬K d q›p˜œ^”M“_–pšc¢:œP“GÕ°³šcV1¢:WK“_XždYZœ^R\“_ikI —Œ˜&”kœcÕ —© ˜“_ ž¹sÈ šc ¢:›l›bŸ˜Õ £_—k–l“d ªÖŸ³ Å_›b˜­œ^“K”k—–l“¹”M•_œ
ږl“_—M”kœ^–l“G³¸`qRSO JkTuN × :f 4V1NMT^]KYZY IKU "!/RîYŒY bÕv£q˜ª¥
œ PÕ _³
²º'³ Ú¸#³ B˜›l¨¥¢y¶v–pšk•¹˜“_ž e³ e³ †•q˜¯\˜™kœ^“d¨¥¢d³ÁÀ¢:“Ÿ«¼—M”Œ˜”M–p¢:“q˜™M¤ 1˜y¶¥œ©”M d™M¦d d›pœ^“_šcœP%
³ $
mnL:_f RTMI:N`Fi^R bÕ sÈŸÕ P³
BÚ|³ »,³Bº™k¢P—k—y³6m]dL L z RSo?TuqOQLPÕ _Õ P³
²Í³ K¢P—k—kœ^™Œ˜“_ž ³Í1¢:­'­¡ d“d–pšy˜”M–p¢:“Ï–l“‰”M•d–p—¸¶¥¢:›l d­œ¡˜“_ž/”M•_œ™kœu¯\œ^™kœ^“_šcœc—¸”M•_œ^™kœ^–l“G³
¡³ 4˜:šy˜¿yœPÕn»8³ ,˜›l›pœ^­?˜“_ž Õ&í'³»,¢:­œy˜ GÕ°˜“_ž F³ |–pšy˜Ÿ³ ¤v“q˜­'–pšy˜›¯\¢:™M­?˜”M–p¢:“
™k­¢œu¯Ë¯\¢:œ^­˜E™kœ^œ^“_¾x“†šc”M¢Pœx d—kœu­Á—M«¼•_Ú¢yžŸ–l¸“_–p—M—#—M”M”k–l™Mœ^“°–l–l¦d“ £q d˜”Mšc™M–p¢:¢:”M–p“G“_š^ždÕ4 dœ^›b¶v˜“_–b™˜Ë—Z˜•_˜‰”k¢sœP·Å_³ “d˜–l”kVšcœ¢:WK“_”MX–lždYZ­R\œ^ik“_œ*I&—Œ—M˜&–l”k“dœxÕ ªPšy d ˜›b “°˜™°¦²« —kœ1¢:š^›l d™kœy”M'˜–p¢:”k “§œcsž¡È(¢¯a ¯¸™k
¢:”MŸ­!•_Õ œ˜|¾1šc¢: ¢:›lP“†”M³ ¿c”M–l­?“K _½x˜¢:“d•d _“Ÿ–p——«
À¢:™kžŸ•_œ^–l­ ¨v–l“_œ^”M–pš&œc¬† q˜”M–p¢:“G³
e³ ͳqÀœ^œ^›l›QÕ F³FÀ˜¿s˜™kœ^“d¨¥¢dÕ²˜“_ž 6³B¾1–l¶¥œ^“G³¸´"˜y¶¥œn”M d™M¦d d›pœ^“_šcœ'˜“_ž±–l“K”kœ^™M­'–l”M”kœ^“_š^¤¥³
V1WKXYZR\ikI)nÕ « sÈ ŸÕ P³
6³ ´ ³dÀ¢:™kžŸ•_œ^–l­€³1V1NMLyi 4{ 4`FLyi 4HGL:BUKL: &Õ ŸÕ Ÿ³
²Í³ q³y»,œ^”M•d–pšŒ¨n˜“_ž e³ †­'–l”M•G³ *|LYyT +ahxRîdY^O¼TuRS z L:BUKTu_Y^IPOaR\L:eRî, RSf ]vO¼T -¸IYyTZYu³¥Í/³ .e³ »,³lÕ
Íx˜­¡¦d™M–pžŸª¥œPÕ Ÿ³
6³ »,³_»–l”Œ˜:œ^¶v—M¨v–l–Q³x`FL VWKXY 0$:,h 1 VxÕ PÕ P³
_í'³6»8¢:­œy˜ G³ G¢:“dª©”kœ^™M­ È©›p¢:“dª©™Œ˜“dª¥œDžŸ¤v“q˜­'–pšc—*¢¯°˜"š^›b˜:—k—k–pšy˜›|Åqœ^›pž ³!VWKXYuRaikI
`²i^NZR rFOQIPÕd½1« PÕ Ÿ³
°³ Ú¸³qɲ˜¨v•q˜™k¢y¶²³j`FL VWKXY 0$:,h 1 VxÕ ŸÕ v³
°³ Ú¸³qɲ˜¨v•q˜™k¢y¶²³j`FL VWKXY 0$:,h 1 VxÕ ŸÕ Ÿ³
°³ Ú¸³±É²˜¨v•q˜™k¢y¶²2Õ e³ F³ ¶¥¢y¶²Õ±˜“_ž º°³ Ú¸3³ B˜›l¨¥¢y¶v–pšk•G³ ×eL:f o4L ¥L:NML `PrdTMiyOaN‹I6L 5
1_]vNcJu]vfpTuBiŒT^³†£d™M–l“dª¥œ^™‹«7œ^™M›b˜ª_ÕB¾xœ^™M›l–l“GÕ Ÿ³
w Œ