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Analysis of Quantum Mechanics and Quantum Field Theory, Exams of Nursing

An in-depth analysis of quantum mechanics and quantum field theory, discussing various concepts such as schrödinger's equation, heisenberg's uncertainty principle, feynman diagrams, and renormalization. It also delves into the standard model of particle physics and the higgs boson. Rich in mathematical equations and provides a comprehensive understanding of these complex topics.

Typology: Exams

2023/2024

Available from 04/19/2024

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Download Analysis of Quantum Mechanics and Quantum Field Theory and more Exams Nursing in PDF only on Docsity! 2 2 $s &o()*+nt w/s 01+0/1+& 23 th+ 4+1$n/t/5 6+nt/5 7+/5th 41o8+(t9 For %&e()*o+( or co--e+)( p/e0(e co+)0c) &(1 Ph$n&' ()* +0- )1 /01 0210 345' ()* +0- 0/ 67) 1/12 894:;' :n<$=>9h>?@4?$AB C&DE:F&' GGG?>9h>?@4?$AB HIIA&EE' Jn:K&AE:FL $< M4>& N$Gn O&>4AF9&nF $< PELPh:4FAL Q R&nF4; S&4;Fh 7/ T4GU:nE V$4IW XY:;I:nB X V$nI&D$EPhW T$YFh H<A:P4W **00 2c3+o4/e56e-e+)( M$K&A 4AF DL Z&E;&L Mh4An$PU? [;;YEFA4F:$nE DL HnFh$nL T9:Fh 4nI \A4&9& HA&nIE&? 2 3 CONTENTS 1# $N&R()*+&$(N 3 1#1 $hat () *+nta- (--n+)). / 1#2 1+nta- h+a-th () +2+3456d48) 59)(n+)) / 1#/#1 $hat can c69n)+--(n; <362(d+ =63 th+ >6*an. 4 1#/#2 $hat () th+ <36c+)) 6= c69n)+--(n;. 4 2# H/01$N2 (&H/R3 4 @+a-th >63A+3) 6=t+n )++ d()t3+))+d >6*+n# Bt () n6t a->a4) +a)4 t6 An6> h6> 469 can h+-< 63 >hat t6 d6# 4 2#1 $h6 can h+-<. 4 2#2 $hat () a h+-<+3. C 2#/#1 D6n=(d+nt(a-(t4 C 2#/#2 End+3)tand(n; 6th+3) F 2#/#/ End+3)tand(n; 4693)+-= F 2#/#4# G*<ath4 H 3# +(*N3/00$N2 35$003 6 /#1 I()t+n(n; )A(--) J /#1#1 Kct(2+ -()t+n(n; J /#2 K)A(n; L9+)t(6n) 1/ /#2#1 M<+n L9+)t(6n) 1/ /#2#2 D-6)+d L9+)t(6n) 1/ /#/ N+=-+ct(6n )A(--) 1C /#/#1# N+=-+ct(n; =++-(n;) 1C /#/#2# N+)tat(n;O3+<h3a)(n; 1H /#/#/ K==(3*at(6n 1P /#/#4 Q9**a3()(n; 2R 4#1 S+=63+ 469 )ta3t 22 4#2 Bn th+ 5+;(nn(n; 22 4#/ D6nta(n*+nt 22 4#4 D69n)+--(n; a) an (nt+32+nt(6n 2/ 4#C T3act(ca- t(<) 2/ 4#F T365-+* *ana;+*+nt 24 2 6 Bn c6nt3a)t t6 *+nta- (--n+))[ *+nta- >+--_5+(n; (n >h+n a <+3)6n () a5-+ t6 3+a-()+ th+(3 6>n a5(-(t(+)[ can c6<+ >(th th+ n63*a- )t3+))+) 6= -(=+[ can >63A <36d9ct(2+-4 and () a5-+ t6 *aA+ a c6nt3(59t(6n t6 th+(3 c6**9n(t4# 1#2 MDE@aF >DaF@> iB DNDKOLPQORB LIBiEDBB 1+nta- h+a-th ca3+ () 6=t+n )++n a) a )<+c(a-()t =(+-d that 6n-4 h(;h-4 t3a(n+d h+a-th >63A+3) can d+a- >(th[ +#;# <)4ch(at3()t) 63 <)4ch(at3(c n93)+)# 1+nta- (--n+))+) a3+ =a3 *63+ c6**6n than 56th h+a-th >63A+3) and c-(+nt) 6=t+n 3+a-()+# T663 *+nta- h+a-th can a==+ct c-(+nt) (n *an4 >a4)# Zhat () >h4 (t () (*<63tant that a-- -+2+-) 6= h+a-th >63A+3) a3+ a5-+ t6 3+c6;n()+ *+nta- (--n+))# =>O QPER@ >DaF@> wPKXDKB aBX aLPI@ >Pw a SFiDE@ iB VDDFiETG T+3ha<) th+ an)>+3 >(-- 3+L9(3+ t66 *9ch t(*+ and +==63t# Bt *a4 5+ +a)(+3 t6 d+a- >(th a <h4)(ca- <365-+*# T+3ha<) th+ L9+)t(6n 3+*(nd) h+a-th >63A+3) a569t th+(3 6>n <+3)6na- ())9+)# Bt () 6=t+n d(==(c9-t =63 h+a-th >63A+3) t6 h+a3 a569t c-(+nt)8 =++-(n;) 5+ca9)+ th+4 *a4 =++- 9na5-+ t6 6==+3 h+-< t6 c-(+nt)# 2 7 1#3 =>a@ iB SPIEBDFFiETG D69n)+--(n; (n26-2+) -()t+n(n;# D69n)+--(n; () a569t )9<<63t(n; th+ >6*an and +*<6>+3(n; h+3 t6 =(nd h+3 6>n )6-9t(6n)# D69n)+--(n; () EP@ a569t ;(2(n; ad2(c+` 1#3#1 =>a@ SaE SPIEBDFFiET UKPNiQD VPK @>D wPCaEG  K )a=+ )<ac+ t6 5+ h+a3d ] th+ >6*an t+--) h+3 >h6-+ )t634  K >a4 t6 9nd+3)tand h+3 6>n d()t3+))  Q6*+6n+ >h6 >(-- -()t+n >(th69t 5-a*(n; 63 j9d;(n;  N+)<+ct  ba-(dat(6n 6= =++-(n;)  Kn 6<<63t9n(t4 t6 +c<-63+ <3act(ca- 6<t(6n) >(th h+3  Kn 6<<63t9n(t4 t6 -66A =63 )6-9t(6n) t6 h+3 <365-+*)  Q9<<63t 1#3#2 =>a@ iB @>D UKPSDBB PV SPIEBDFFiETG  M<+n(n;V +)ta5-()h(n; a 3+-at(6n)h(< O 59(-d(n; t39)t  Gc<-63(n;V ;66d -()t+n(n;  End+3)tand(n;V c-a3(=4(n; O 3+=-+ct(n; O )9**a3()(n; th+ <365-+*)  U+c(d(n; 6n (nt+32+nt(6nV 9nd+3)tand(n; th+ )(t9at(6n that th+ >6*an () (n  Gc<-63(n; th+ <365-+* t6 =(nd )6-9t(6n)  @+-<(n; th+ >6*an t6 <-an h+3 6>n )6-9t(6n)  16n(t63(n; and *ac(*()(n; 3+)(-(+nc+ 2# H/01$N2 (&H/R3 @+a-th >63A+3) 6=t+n )++ d()t3+))+d >6*+n# Bt () n6t a->a4) +a)4 t6 An6> h6> 469 can h+-< 63 >hat t6 d6# 2 8 2#1 =>P SaE >DFUG Kn456d4 can h+-<` Zh+ +c+3c()+) (n th() *an9a- h+-< 469 9nd+3)tand h6> 5+)t t6 5+ a h+-<+3# d69 d6 n6t n++d t6 5+ a t3a(n+d )6c(a- >63A+3 63 <)4ch6-6;()t t6 ha2+ c69n)+--(n; )A(--)# D69n)+--(n; )A(--) can h+-< +2+346n+ t6 taA+ 5+tt+3 ca3+ 6= th+ >6*+n that th+4 )++# 2 11  Z34 t6 ;(2+ 4693)+-= t(*+ ] +2+34 da4 ] t6 th(nA a569t h6> 469 =++- and >h4#  $h+n >63A(n; ] t34 t6 *6n(t63 >hat 469 =++-[ and a)A >h+3+ th+ =++-(n;) c6*+ =36*#  Z34 t6 n6t(c+ >h+n 469 =++- 2+34 )t36n; =++-(n;) a569t )6*+th(n;#  Z34 t6 th(nA a569t )6*+ 6= 4693 )t36n;+)t =++-(n;)[ and )++ (= th+4 -(nA t6 an4 6= 4693 6>n +c<+3(+nc+)#  Z3+at 4693 6>n =++-(n;) >(th th+ )a*+ c6*<a))(6n and 3+)<+ct 469 >69-d ;(2+ t6 6th+3)# >T/ #&p*t<i9# i9 t/ 9## 2it< t<# #6#9 /5 *$/t<#8@ t/ <#*8 2it< t<# #*89 /5 *$/t<#8 *$( t/ 5##: 2it< t<# <#*8t /5 *$/t<#8.B C$/$6&/79 2 12 2#3#4# /CUa@>O Zh+ t+3*) +*<ath4 and )4*<ath4 a3+ 56th a569t =++-(n; =63 )6*+56d4 +-)+8) )(t9at(6n[ 59t th+4 6=t+n ;+t c6n=9)+d# =>a@ iB DCUa@>OG  T9tt(n; 4693)+-= (n )6*+6n+ +-)+8) )h6+)#  N+)<+ct=9--4 (*a;(n(n; >hat )6*+6n+ +-)+8) -(=+ () -(A+#  Gnt+3(n; (nt6 th+ <3(2at+ >63-d 6= an6th+3 <+3)6n[ >(th69t *aA(n; j9d;+*+nt)#  G*<ath4 () )h6>(n; that 469 9nd+3)tand th+ <+3)6n8) +c<+3(+nc+)[ 5+ha2(693 and =++-(n;)# HPw QP OPI B>Pw DCUa@>OG Bt () ha3d+)t t6 +*<ath()+ >(th th6)+ >h6 a3+ d(==+3+nt =36* 9)# Bn 63d+3 t6 +*<ath()+ >(th an6th+3[ 469 n++d t6 5+V  Op#$%&i$(#(V 469 *9)t )+t a)(d+[ =63 th+ *6*+nt[ 4693 6>n 5+-(+=)[ 2a-9+) and att(t9d+) (n 63d+3 t6 c6n)(d+3 th6)+ 6= th+ 6th+3 <+3)6n#  )&*+i$*tiv#V (*a;(n+ th+ 6th+3 <+3)6n8) 5acA;369nd[ th69;ht) and =++-(n;)#  C/&&itt#(0 >ant t6 9nd+3)tand an6th+3 <+3)6n#  1$/2i$+ *$( *44#pti$+ /5 6/789#:50 An6>(n; 4693)+-= and acc+<t(n; >h6 469 a3+ h+-<) t6 d+2+-6< +*<ath4 =63 6th+3)# )iVVDKDESD LD@wDDE DCUa@>O aEQ BOCUa@>O M=t+n >+ h+a3 th+ >63d) +*<ath4 and )4*<ath4 t6;+th+3# $hat () th+ d(==+3+nc+ 5+t>++n +*<ath4 and )4*<ath4.  ;&p*t<60 <9tt(n; 4693)+-= (n an6th+38) )h6+) and t34(n; t6 )++ th+ >63-d th69;h th+(3 +4+)# Zh() d6+) n6t *+an that 469 2 13 =++- +cact-4 >hat th+4 a3+ =++-(n; 63 that 469 ha2+ 5++n th369;h +2+34th(n; th+4 ha2+ 5++n th369;h#  =6&p*t<6V =++-(n; >hat an6th+3 <+3)6n () ;6(n; th369;h# h63 (n)tanc+[ =++-(n; th+ )adn+)) a =a*(-4 () =++-(n; =36* th+ -6)) 6= th+(3 ch(-d# K h+-<+3 n++d) t6 =++- +*<ath4[ 5+ca9)+ 469 cann6t <6))(5-4 +c<+3(+nc+ +2+34th(n; that <+6<-+ ;6 th369;h# d69 9)+ 4693 +c<+3(+nc+)[ and 4693 att+nt(6n t6 9nd+3)tand th+ 6th+3 <+3)6n8) )(t9at(6n# ACTIVE LISTENING 2 16 =>O B>PIFQ wD IBD aS@iND PK DCUa@>iS FiB@DEiETG  G*<ath(c -()t+n(n; +nc693a;+) th+ >6*an t6 ta-A *63+ a569t h+3 ())9+)# Zh() a--6>) 469 a) a h+-<+3 t6 ;a(n a 5+tt+3 9nd+3)tand(n; 6= th+ d(==(c9-t(+) and h+3 2(+> 6= th+ >63-d#  Bt -+a2+) th+ >6*an >(th th+ 9nd+3)tand(n; that )h+ ha) 5++n h+a3d# j9)t th+ +c<+3(+nc+ 6= 5+(n; h+a3d can 5+ h+a-(n;#  Kct(2+ -()t+n(n; h+-<) +)ta5-()h a 3+-at(6n)h(< 5+t>++n c-(+nt and h+-<+3# /CUa@>iS PK aS@iND FiB@DEiET iENPFNDBZ  Ta3t(c(<at(n; (n th+ >63-d 6= th+ 6th+3 <+3)6n and 5+(n; a <a3t 6= >hat that <+3)6n () +c<+3(+nc(n;# o @+a3(n; >63d) 59t a-)6 -()t+n(n; t6 h6> th+ >63d) a3+ 5+(n; )a(d# o $hat t6n+ 6= 26(c+ () 5+(n; 9)+d. o $hat >63d) a3+ 5+(n; 9)+d t6 d+)c3(5+ th+ +c<+3(+nc+. o $hat 56d4 -an;9a;+ () th+ <+3)6n d()<-a4(n;. o $hat )h6>) 6n th+(3 =ac+. o $hat d6 th+(3 hand *62+*+nt) )h6>. 2 17 o U6 th+ >63d) =-6> 63 a3+ th+3+ -6t) 6= h+)(tat(6n).  I()t+n(n; t6 >hat () EP@ 5+(n; )a(d[ 63 -()t+n(n; t6 th+ )(-+nc+)#  Bn c69n)+--(n;[ ca3(n; 63 +*<ath(c -()t+n(n; () an +c<+3(+nc+ >h+3+ 4693 >h6-+ 5+(n; 5+c6*+) t9n+d (nt6 th+ >63-d and +c<+3(+nc+ 6= an6th+3 <+3)6n#  K c6*5(nat(6n 6= +*<ath4 and -()t+n(n; () a 5a)(c 3+L9(3+*+nt =63 a-- c69n)+--(n; 5+ha2(693 and (n i@BDFV () 6=t+n 2+34 th+3a<+9t(c =63 th+ c-(+nt#  Zh+3+ () h+a-(n; <6>+3 (n 5+(n; -()t+n+d t6[ and (n 5+(n; a5-+ t6 ta-A and 5+ h+a3d 54 an6th+3# 2 18 =>a@ TD@B iE @>D waO PV aS@iND PK DCUa@>iS FiB@DEiETG  S+(n; )+-+ct(2+V n6t -()t+n(n; t6 th+ =9-- *+))a;+ 6= >hat () 5+(n; )a(d[ 59t Wh+a3(n;X 6n-4 >hat 469 >ant t6 h+a3#  S+(n; d()t3act+dV a<<+a3(n; t6 -()t+n >h+n 3+a--4 4693 *(nd () a *(--(6n A(-6*+t3+) a>a4 and 469 ha2+ n6t act9a--4 h+a3d a >63d that ha) 5++n )a(d#  T+3)6na- 2a-9+) k>hat >+ 5+-(+2+ t6 5+ (*<63tantlV +ach 6= 9) ha) d(==+3+nt 2a-9+)#  $hat () ha<<+n(n; (n 4693 6>n -(=+V th() *a4 chan;+ 4693 <+3)<+ct(2+ a569t >hat th+ >6*an () ;6(n; th369;h#  T3+<a3(n; a 3+)<6n)+V (= 469 a3+ <3+<a3(n; >hat 469 >(-- )a4 n+ct[ 469 cann6t 5+ -()t+n(n; t6 th+ >6*an#  h++-(n; th3+at+n+d 54 >hat th+ >6*an () )a4(n;#  D9-t93+V )6*+t(*+) th+ >6*an8) c9-t93+ () d(==+3+nt t6 693)#  Ian;9a;+V *an4 t(*+) >+ a3+ n6t )<+aA(n; (n 693 6>n -an;9a;+ and th+3+ can 5+ c6**9n(cat(6n d(==(c9-t(+) >(th th()# 3#1#2 _DKLaF FiB@DEiET :/n/51& v%8A1& 8%4p#n4%V Zh+)+ a3+ 2+35a- 3+)<6n)+) )h6>(n; that 469 a3+ -()t+n(n;# b+35a- 3+)<6n)+) (nc-9d+V W***m***[X W9h_h9h[X 63 W4+)#X Zh+)+ *(n(*a- 3+)<6n)+) )h6> th+ >6*an that 469 a3+ -()t+n(n; t6 h+3[ and +nc693a;+) h+3 t6 c6nt(n9+ ta-A(n;# 3#1#3 NPE\NDKLaF FiB@DEiET Zh+ QMIGNh *+th6d () a 9)+=9- >a4 t6 W-()t+nX >(th69t )<+aA(n;# 3 3`IaKDFO =ac+ <+3)6n _ n6t t93n+d t6 th+ )(d+# ( 9)+ (UDE <6)t93+ >(th69t c36))+d a3*) and -+;)# 0 0DaE )-(;ht-4 t6>a3d th+ <+3)6n 3ath+3 than )(tt(n; 5acA (n th+ cha(3# / 9)+ /OD c6ntact (n)t+ad 6= )ta3(n; 6== (nt6 d++< )<ac+# R RDFa^[ A++< (t nat93a- (n)t+ad 6= )(tt(n; -(A+ a 56a3d# 9 -66A 9KiDEQFO and >+-c6*(n; 3ath+3 than n+9t3a- 63 2 21 B#* 18% &/40%n/n3 0# 5% Ch%nD d69 c6*+ L9(+t-4 (nt6 *4 <3(2at+ >63-d and -+t *+ 5+o d69 3+a--4 t34 t6 9nd+3)tand *+ +2+n (= B8* n6t *aA(n; *9ch )+n)+o d69 ;3a)< *4 <6(nt 6= 2(+> +2+n >h+n (t8) a;a(n)t 4693 6>n )(nc+3+ c6n2(ct(6n)o d69 3+a-()+ that th+ h693 B t66A =36* 469 ha) -+=t 469 a 5(t t(3+d and d3a(n+do d69 a--6> *+ th+ d(;n(t4 6= *aA(n; *4 6>n d+c()(6n) +2+n th69;h 469 th(nA th+4 *(;ht 5+ >36n;o d69 d6 n6t taA+ *4 <365-+* =36* *+[ 59t a--6> *+ t6 d+a- >(th (t (n *4 6>n >a4o d69 h6-d 5acA 4693 d+)(3+ t6 ;(2+ *+ ;66d ad2(c+o d69 d6 n6t 6==+3 *+ 3+-(;(69) )6-ac+ >h+n 469 )+n)+ B a* n6t 3+ad4 =63 (to d69 ;(2+ *+ +n69;h 366* t6 d()c62+3 =63 *4)+-= >hat () 3+a--4 ;6(n; 6n# C$/$6&/ 79 2 22 The table below gives examples of good listening and unhelpful listening. 0iB@DEiET NP@ FiB@DEiET S+ a>a3+ 6= 4693 6>n =++-(n;) and th+ >a4 that 469 a3+ 3+)<6nd(n; Za-A(n; a569t 4693)+-= 63 4693 6>n +c<+3(+nc+) Z34 t6 =(nd a <3(2at+[ L9(+t <-ac+ =63 c69n)+--(n; O )9<<63t S+(n; 62+3_)4*<ath+t(c Za-A(n; >(th 6th+3 <+6<-+[ an)>+3(n; th+ <h6n+ Q(t )t(-- and -66A (nt+3+)t+d h++-(n; )6334 =63 th+ <+3)6n[ and th+n t34(n; t6 ;(2+ h6<+ 63 <-at(t9d+) kc-(ché)l 162(n; a369nd[ )tand(n; 9< $a(t =63 th+ <+3)6n t6 )<+aA a=t+3 469 ha2+ ;(2+n a )h63t (nt36d9ct(6n T36*()(n; t6 d6 +2+34th(n; Y(2+ th+ <+3)6n an 6<<63t9n(t4 t6 t+-- h+3 )t634 (n h+3 6>n >a4 S3+aA(n; c6n=(d+nt(a-(t4 U6n8t (nt+339<t th+ <+3)6n >h(-+ )h+ () ta-A(n; Bnt+339<t(n; th+ <+3)6n Qh6> th369;h 4693 W56d4 -an;9a;+X that 469 a3+ -()t+n(n; I66A(n; (33(tat+d 63 563+d[ 4a>n(n; h++- 3+-ac+d >(th a<<36<3(at+ )(-+nc+) D6nc+nt3at(n; 6n-4 6n th+ =act) and a)A(n; -6t) 6= L9+)t(6n)# I+t th+ <+3)6n An6> that 469 a3+ >(--(n; t6 -()t+n =93th+3 1(n(*()(n; th+ <365-+* kW(t c69-d 5+ >63)+`Xl K)A a =+> L9+)t(6n) ] a)A L9+)t(6n) 6n-4 >h+n 469 n++d *63+ (n=63*at(6n t6 9nd+3)tand th+ )(t9at(6n T3+ach(n; 63 j9d;(n; Y(2(n; (na<<36<3(at+ ad2(c+ >(th >h(ch th+ >6*an d6+)n8t a;3++ 1aA+ )93+ that th+ >a4 469 9nd+3)tand th+ )(t9at(6n () c633+ct f6t 5+-(+2(n; >hat th+ <+3)6n () )a4(n; h++-(n; 9nc6*=63ta5-+ >(th )6*+6n+ +-)+8) =++-(n;) M2+3 )4*<ath+t(c 2 23 N+=-+ct 5acA t6 th+ <+3)6n (n >63d) >hat th+4 a3+ =++-(n; and )a4(n; h++-(n; )6334 =63 th+ <+3)6n and th+n t34(n; t6 ;(2+ =a-)+ h6<+# 8S@iNi@OZ E81>0/4/n3 (/ff%8%n0 2/n(4 #f F*%40/#n4 f+ct t(*+ 469 ;+t a chanc+ t6 chat >(th a =3(+nd 63 c6--+a;9+[ t34 t6 <3act(c+ a)A(n; L9+)t(6n)# K)A an PUDE DEQDQ `IDB@iPE -(A+[ W@6> d6 469 =++- a569t >hat ha) ha<<+n+d >(th(n th+ <a)t =+> da4).X d69 >ant th+* t6 5+ a5-+ t6 ;6 6n at )6*+ -+n;th# K=t+3 a =+> *(n9t+)[ 469 can t34 t6 c6n)t3a(n 63 3+d(3+ct c6n2+3)at(6n 54 a)A(n; a SFPBDQ `IDB@iPE )9ch a) WU6+) th() *aA+ 469 =++- ;66d 63 5ad.X d69 a3+ -66A(n; =63 an +(th+3O63 an)>+3# &>iEX aLPI@ @>D QiVVDKDE@ XiEQB PV aEBwDKB @>a@ aKD TiNDE w>DE OPI aBX PUDE PK SFPBDQ `IDB@iPEB# HPw QP OPI @>iEX @>D QiVVDKDE@ XiEQB PV `IDB@iPEB CaXD @>D BUDaXDK VDDFG 2 26 Zh+ =6--6>(n; act(2(t4 ;+t) 469 t6 <3act(c+ 6<+n and c-6)+d L9+)t(6n)# E)+ 4693 -()t+n(n; )A(--) and 3+*+*5+3 t6 9)+ 4693 56d4 -an;9a;+ a) >+--` $CUPK@aE@ UPiE@B aLPI@ FiB@DEiETZ Bt () 2a-9a5-+ =63 a >6*an t6 5+ a5-+ t6 ta-A and 5+ h+a3d#  Za-A(n; a569t (*<63tant th(n;) can 5+ 2+34 ha3d#  $6*+n n++d t6 5+ a5-+ t6 )<+aA (n a )a=+ <-ac+[ (n th+(3 6>n >63d)#  $h+n -()t+n(n;[ t34 n6t t6 (nt+339<t#  D6nc+nt3at+ 6n >hat () 5+(n; )a(d[ n6t >hat 469 n++d t6 )a4 63 d6#  I()t+n t6 th+ >63d) )a(d[ >hat h+3 56d4 t+--) 469[ and >hat )h+ () EP@ )a4(n;# GH15p&%I G/&*$V WB8* th+ 6n-4 6n+ >63A(n; (n *4 =a*(-4# 14 *6th+3[ *4 )()t+3 and h+3 t>6 ch(-d3+n )ta4 >(th *+ and *4 th3++ A(d)# B can8t a==63d th+ )ch66- =++) =63 *4 6>n ch(-d3+n a-3+ad4[ )6 B d6n8t An6> >hat B8* ;6(n; t6 d6 n6> B8* <3+;nant a;a(nX C/7$9#::/80 Wd69 )69nd >633(+d and 62+3>h+-*+d#X 2 27 3#3 RDVFDS@iPE BXiFFB N+=-+ct(n; act) -(A+ a *(3363o (t ;(2+) 5acA t6 th+ >6*an >hat )h+ ha) j9)t c6**9n(cat+d t6 9)# Bt -+t) th+ >6*an An6> >hat 469 9nd+3)tand a569t >hat )h+ ha) )ha3+d and c6**9n(cat+) +*<ath4# $CUPK@aESD PV KDVFDS@iET  N+-at(6n)h(< 59(-d(n;V 3+=-+ct(n; () 2a-9a5-+ (n 59(-d(n; a 3+-at(6n)h(< >(th th+ >6*an 54 c6**9n(cat(n; t39)t[ acc+<tanc+ and 9nd+3)tand(n;#  D-a3(=(cat(6nV 3+=-+ct(n; () h+-<=9- =63 >6*+n t6 5+ a5-+ t6 c-a3(=4 =63 th+*)+-2+) th+(3 <365-+*) and =++-(n;)#  Bn=63*at(6nV 3+=-+ct(n; h+-<) th+ c69n)+--63 ;+t (n=63*at(6n a569t th+ >6*an and h6> )h+ 2(+>) h+3 )(t9at(6n#  b+3(=(cat(6nV 3+=-+ct(n; h+-<) th+ c69n)+--63 t6 ch+cA h+3 <+3c+<t(6n 6= >hat th+ >6*an c6**9n(cat+)# Zh+3+ a3+ =693 d(==+3+nt 3+=-+ct(n; )A(--)# Zh+)+ a3+ )A(--) that can 5+ 9)+d at an4 )ta;+ (n th+ c69n)+--(n; )+))(6n[ 59t a3+ 3+a--4 (*<63tant =63 59(-d(n; t39)t and +c<-63(n; th+ <365-+*#  N+=-+ct(n; =++-(n;)  N+)tat(n;O3+=3a*(n;  K==(3*at(6n  Q9**a3()(n; 3#3#1# RDVFDS@iET VDDFiETB N+=-+ct >hat th+ c-(+nt () =++-(n;# h6c9) 6n =++-(n;)[ fMZ th+ d+ta(-) 6= >hat () )a(d# 2 28 &iUB VPK KDVFDS@iET VDDFiETBZ  I()t+n =63 and 3+=-+ct 56th 2+35a- and n6n_2+35a- c6**9n(cat(6n 6= =++-(n;)#  N+ad 56d4 -an;9a;+ and 3+=-+ct >hat 469 )++ (= =++-(n;) a3+ n6t +c<3+))+d 2+35a--4# H# WB -6)t *4 =(3)t 5a54# Qh+ >a) 563n t66 +a3-4 and )h+ d(d n6t 53+ath+# B A++< th(nA(n; a569t h+3 n6> that B a* <3+;nant a;a(n# Qh+ >69-d ha2+ 5++n 2 4+a3) 6-d# X kL8i#5 H :/99 H 9*( H 2/886 5/8 t<# $#2 E*E6l J# WQ(nc+ B ca*+ (n =63 *4 @Bb t+)t -a)t >++A B ha2+ n6t 5++n a5-+ t6 )-++< >a(t(n; =63 *4 t+)t 3+)9-t)#X kC$Mi/79lWB had an a563t(6n -a)t 4+a3# Q(nc+ th+n B can8t )t6< th(nA(n; a569t (t[ and >6nd+3(n; (= B d(d th+ >36n; th(n;# B ha2+ 536A+n 9< >(th *4 564=3(+nd# Q6*+t(*+) B th(nA B a* 5+(n; <9n()h+d#X kL7i:tl P# WB ha2+ 5++n 9n+*<-64+d =63 2 4+a3)# B d6 n6t An6> >hat t6 d6 a569t *6n+4# 14 A(d) and B ha2+ 5++n )ta4(n; >(th *4 )()t+38) =a*(-4 59t 4+)t+3da4 h+3 h9)5and )a(d that >+ ha2+ t6 -+a2+ 5+ca9)+ th+4 d6 n6t ha2+ *6n+4 +(th+3#X kD#9p#8*t# H 2/88i#(l GH15p&%I G/&*$V WB8* )6 an;34 >(th *4 h9)5and# B j9)t >ant t6 A(-- h(*o h+ *aA+) *+ )6 *ad#X C/7$9#::/8V WBt )69nd) -(A+ 4693 (33(tat(6n and =39)t3at(6n >(th 4693 h9)5and ha) (nc3+a)+d and () 3+ach(n; a c-(*ac#X 2 31 3#3#2# RDB@a@iETaKDU>KaBiET Zh() () )a4(n; >hat 469 9nd+3)tand th+ >6*an t6 5+ c6**9n(cat(n;# S4 d6(n; th() 469 a3+ -+tt(n; h+3 An6> that 469 9nd+3)tand and[ (= 469 d6n8t[ a3+ >(--(n; t6 5+ c633+ct+d# &iUB VPK KDB@a@iETZ  E)+ 4693 6>n >63d) t6 +c<-a(n 4693 9nd+3)tand(n; 6= >hat th+ >6*an () )a4(n;#  E)+ )-(;ht-4 d(==+3+nt >63d) that ha2+ th+ )a*+ *+an(n;o d6 n6t j9)t 3+<+at >hat )h+ )a(d#  N+<h3a)+ 56th c6nt+nt and =++-(n;)#  D6n2+4 +*<ath4[ acc+<tanc+ and ;+n9(n+n+))#  S+ t+ntat(2+ and 3+)<+ct=9-[ (#+# WB h+a3 469 )a4(n;m[X 63 WBt )69nd) -(A+mX 8S@iNi@OZ E81>0/4/n3 J%4010/n3LJ%ph814/n3 HPw wPIFQ OPI KDBUPEQ @P @>D VPFFPwiET B@a@DCDE@B LO KDB@a@iET PK KDU>KaBiETG *BD OPIK KDVFDS@iET BXiFFB# 1# W$ B@aK@DQ BDDiET @>iB TIO# =D BUDE@ `Ii@D a Li@ PV @iCD @PTD@>DK aEQ $ KDaFFO FiXD >iC# =D wDKD KDaFFO SaKDVIF aEQ >aQ UKP@DS@DQ BD^# 8V@DK aLPI@ @wP CPE@>BJ CO LPOVKiDEQ BaiQ >D QPDB EP@ waE@ @P IBD a SPEQPC# HD BaiQ @>a@ iV $ @KIB@ >iC $ B>PIFQ EP@ aBX >iC @P IBD a SPEQPC# NPw $ aC UKDTEaE@# $ QP EP@ XEPw w>a@ @P QP#b )t 9/7$(9 *9 t</7+< 6/7 2#8# *9F#( t/ &*F# * (i55i47:t (#4i9i/$ t<*t 6/7 2#8# $/t 4/&5/8t*E:# i$ &*Fi$+@ *$( $/2 6/7 *8# 7$978# /5 </2 t/ (#*: 2it< t<# 4/$9#N7#$4#. 2# cSKOiETd e0aB@ EiT>@ CO >IBLaEQ SaCD >PCD KDaFFO Fa@D# HD waB QKIEX aTaiE# =D B@aK@DQ aKTIiETJ LI@ i@ iB EP IBD# $ aC BP aETKO a@ >iC# HD wiFF EDNDK S>aETD#b O/7 9##& t/ E# 5##:i$+ 5879t8*t#( E6 6/78 <79E*$(P9 (8i$Fi$+@ 2<i4< /5t#$ :#*(9 t/ *8+7&#$t9. O/7P8# *:9/ 7$978# /5 </2 t/ (#*: 2it< t<i9 p8/E:#&@ 2<i4< :#*v#9 6/7 5##:i$+ <#:p:#99@ 9*( *$( </p#:#99. 2 32 Qta3t a 3+)tat(n; )tat+*+nt >(th <h3a)+) -(A+V i$hat B^* 9nd+3)tand(n; () ###i iBn 6th+3 >63d)###i iQ6 5a)(ca--4 >hat 469^3+ )a4(n; ()###i iU6 469 *+an###.i iBt )69nd) a) (=###i iB^* n6t )93+ that B^* 9nd+3)tand(n; 469 c633+ct-4[ 59t###i id69 )69nd####i iB ;ath+3###i Zh+ act(2(t4 5+-6> h+-<) t6 <3act()+ 3+)tat(n;# E)+ 4693 6>n >63d) t6 )h6> that 469 9nd+3)tand >hat th+ >6*an () )a4(n; t6 469# 2 33 3# WMO CP@>DK iB TD@@iET BiSX# 3>D iB aFPED iE >DK NiFFaTD aEQ PEFO >aB PED PV CO LKP@>DKRB S>iFQKDE B@aOiET wi@> >DK# HI@J $ aC EP@ BIKD @>a@ @>D LPO iB KDaFFO @aXiET TPPQ SaKD PV >DK# $ aC BP wPKKiDQ LDSaIBD @>DO aKD VaK VKPC @>D >PBUi@aF aEQ >D wiFF EP@ XEPw w>a@ @P QP iV B>D TD@B BiSXDK#b )t 9/7$(9 :iF# 6/7P8# i$48#(iE:6 *$Mi/79 *t t<# &/&#$t@ 2/886i$+ *E/7t 6/78 &/t<#8P9 <#*:t<. O/7 *:9/ 9##& t/ E# 4/$4#8$#( t<*t t<# E/6 9t*6i$+ 2it< <#8 2i:: E# 7$*E:# t/ ://F *5t#8 <#8 i5 $#4#99*86. 4# W0a@DFO CO ViKB@\LPKE TiKF >aB LDDE @DaBDQ a FP@ a@ BS>PPF# &>DO SaFF >DK EaCDB aEQ BaO @>a@ B>D iB ITFO# 0aB@ EiT>@ B>D waB SKOiET aTaiE# $ TD@ BP aETKO a@ @>PBD SKIDF XiQB aEQ waE@ BP LaQFO @P B@PU @>iB#b )t 9##&9 t<*t 6/7 *8# 2/88i#( *E/7t 6/78 (*7+<t#8@ 2</ i9 E#i$+ E7::i#( *t 94<//:@ *$( t<*t it :#*v#9 6/7 2it< 5##:i$+9 /5 *$+#8 *$( 5879t8*ti/$. )t *:9/ 9/7$(9 :iF# 6/7 <*v# * 9t8/$+ (#9i8# t/ p8/t#4t <#8@ E7t *8# 7$978# </2 t/ (/ t<i9. 7# WMO >IBLaEQ UaBBDQ awaO FaB@ CPE@># HD waB BiSX VPK BPCD @iCD LI@ >D KDVIBDQ @P LD @aXDE @P @>D >PBUi@aF# NPw $ >aND ]IB@ VPIEQ PI@ $ aC H$_f# 3PJ EPw $ VDDF BP SPEVIBDQ# $ KDaFiBD CO >IBLaEQ >aQ 8$)3 aEQ >D QiQER@ @DFF CDJ aEQ $ CIB@ >aND TP@ H$_ VKPC 2 36 Zh+ =6--6>(n; act(2(t4 <9t) t6;+th+3 a-- th+ )A(--) 469 ha2+ -+a3nt )6 =a3[ and h+-<) 469 t6 <3act()+# Bt () n6t a->a4) +a)4 t6 d6 (t 3(;ht` I+a3n =36* th+ *()taA+) that a3+ *ad+# Zh+ *63+ 469 <3act()+[ th+ +a)(+3 (t () t6 9)+ th+ n+> )A(--)# 8S@iNi@OZ E*00/n3 0h% 42/&&4 0#3%0h%8 $h+n 469 n+ct ha2+ a chanc+ t6 chat t6 a =3(+nd 63 c6--+a;9+[ t34 t6 9)+ aS@iND FiB@DEiETJ KDVFDS@iET VDDFiETBJ KDB@a@iETJ BICCaKiBiET aEQ aVViKCa@iPE Y+t 3+ad4 t6 -()t+n act(2+-4# Zh(nA a569t 4693 +nc693a;(n; 56d4 -an;9a;+# Zh(nA a569t n6n_2+35a- +nc693a;+3)# E)+ 6<+n_+nd+d L9+)t(6n) -(A+[ W@6> a3+ th(n;) ;6(n; =63 469 t6da4.X d69 >ant th+ )<+aA+3 t6 ;6 6n at )6*+ -+n;th# Zh(nA a569t >hat th+ )<+aA+3 () )a4(n; and 3+=-+ct (t# &>iEX aLPI@ @>D BUDaXDK 1# U6 469 th(nA that th+ )<+aA+3 =+-t th+4 >+3+ 5+(n; h+a3d >(th +*<ath4. 2# $hat d(d th+ )<+aA+3 =++- >h+n th+4 -+=t th+ )+))(6n. &>iEX aLPI@ FiB@DEiET 1# @6> d(d 469 =++- (n)(d+ 4693)+-= >h+n 469 >+3+ -()t+n(n;. 2# U(d 469 =++- 469 >+3+ W6n th+ )a*+ <a;+X a) th+ )<+aA+3. B= n6t[ >h4 n6t. /# @6> acc93at+-4 d6 469 th(nA 469 >+3+ a5-+ t6 )9**a3(g+ th+ 2 37 )<+aA+3) (n=63*at(6n. 1Rn. PRn. $h4. 4# $+3+ 469 a5-+ t6 3+=-+ct 5acA th+ <+3)6n8) =++-(n;). U6n8t >6334 (= 469 a3+ n6t c6*<-+t+-4 acc93at+# Zhat () >h4 th+ -()t+n+3 W<-a4) (t 5acAX t6 th+ )<+aA+3 9)(n; a t+ntat(2+ t6n+# RDCDCLDKJ @>D UDKBPE CaO VPKTD@ w>a@ OPI BaiQJ LI@ wiFF EDNDK VPKTD@ h#C OPI CaQD @>DC f%%&h 4#3 +PE@aiECDE@ $h+n =++-(n;) a3+ <a(n=9- and 62+3>h+-*(n;[ th+ >6*an *a4 n++d )6*+6n+ t6 h+-< h+3 t6 h6-d and 9nd+3)tand th6)+ =++-(n;)# Zh() () ca--+d [SPE@aiECDE@R# Zh(nA 6= a j9;[ >h+n th+3+ () t66 *9ch >at+3 (n (t[ (t 62+3=-6>)[ and an6th+3 c6nta(n+3 *a4 5+ n++d+d t6 h6-d th+ >at+3 9nt(- )6*+ 6= th+ >at+3 (n th+ =(3)t j9; ha) 5++n 9)+d 9<# h++-(n;) can 5+ -(A+ th()# Q6*+6n+ +-)+ *(;ht n++d t6 h6-d th+ <a(n=9- =++-(n;) 9nt(- th+ <+3)6n () 3+ad4 t6 d+a- >(th th+*# 2 38 4# 811R(8+H/3 &( +(*N3/00$N2 Zh+ ;9(d+-(n+) 5+-6> 6==+3 ;+n+3a- a<<36ach+) =63 c69n)+--(n; <3+;nant >6*+n and *6th+3)# 4#1 HDVPKD OPI B@aK@ S+=63+ *++t(n; a *6th+3 =63 th+ =(3)t t(*+[ (t () h+-<=9- t6 ch+cA an4 (n=63*at(6n that ca*+ >(th th+ 3+=+33a-[ +#;# an4 )c3++n(n; =63*)[ 5acA;369nd h()t634[ -+tt+3) =36* 6th+3 h+a-th >63A+3)# Bt >69-d 5+ 5+)t t6 <-an t6 )++ th+ *6th+3 4 t6 F t(*+)[ 59t th+3+ () a->a4) a chanc+ 469 >(-- 6n-4 )++ h+3 6nc+[ a) )h+ *a4 n6t c6*+ 5acA[ 63 469 *a4 n6t ha2+ *63+ t(*+# 4#2 $E @>D LDTiEEiET  Bt () (*<63tant t6 c3+at+ a BaVD aEQ BIUUPK@iND DENiKPECDE@ =63 th+ *6th+3)# N+a))93+ h+3 that (t () a ;66d (d+a t6 ;+t an 6<<63t9n(t4 t6 ta-A 5+=63+ th+ 5a54 () 563n )6 that )h+ =++-) *63+ <3+<a3+d >h+n th+ 5a54 c6*+)#  $63A 69t >(th h+3 >h4 )h+ () >(th 469 t6da4 and >hat )h+ +c<+ct) =36* ta-A(n; >(th 469#  I()t+n ca3+=9--4 and d6n8t (nt+3<3+t 63 ana-4)+# Zh() c3+at+) a )a=+ )<ac+ =63 h+3 t6 26(c+ th+ c6*<-+c(t4 6= h+3 =++-(n;) a369nd <3+;nanc4 and ch(-d5(3th# Qh+ can th+n +2+n 3+ach h+3 6>n )6-9t(6n)[ 56th +*6t(6na--4 and <3act(ca--4#  Zh+ *6th+3 >(-- h6<+=9--4 d+)c3(5+ h+3 -(=+ a) )h+ 9nd+3)tand) (t# Z3+ad ;+nt-4# d69 *a4 th3+at+n 4693 3+-at(6n)h(< >(th h+3 (= 469 t3+at h+3 )t634 a) a c6--+ct(6n 6= )4*<t6*)[ ha5(t) 63 <365-+*)#  I66A =63 +ca*<-+) 6= <3+2(69) h+a-th4 c6<(n; and <365-+*_)6-2(n; a5(-(t(+)#  K) a c69n)+--63[ 469 *a4 act a) a 53(d;+ 5+t>++n c3()() and c6<(n;#  16th+3) n++d t6 An6> that th+4 a3+ >63th4 6= )+n)(t(2+ and 3+-(a5-+ ca3+# 8S@iNi@OZ Mn(%8401n(/n3 p8#A&%54 Z34 t6 th(nA 6= a *6th+3 (n 4693 c6**9n(t4 that ha) a <365-+*# Mn+ <365-+* 6=t+n ha) *an4 <a3t) t6 (t# Z34 t6 53+aA (t d6>n (nt6 )*a--+3 <a3t) that t6;+th+3 *aA+ 9< th+ >h6-+ <365-+*# &>iEX aLPI@ @>D UKPLFDC iE @>D VPFFPwiET waOBZ $hat *aA+) (t d(==(c9-t =63 th+ >6*an a) an (nd(2(d9a-. $hat h+-<) h+3 t6 c6<+ >(th h+3 <365-+*. $hat a569t h+3 =a*(-4 *aA+) th() <365-+* 5+tt+3 63 >63)+. $hat a569t h+3 c6**9n(t4 *aA+) th() <365-+* 5+tt+3 63 >63)+. $hat a3+ th+ d(==+3+nt <a3t) t6 h+3 <365-+*. 2 41 4#; 1KPLFDC CaEaTDCDE@ 1ana;(n; <365-+*) () 6n-4 <6))(5-+ (= th+ c69n)+--63 and >6*an ha2+ -6t) 6= t(*+ t6;+th+3# Zh() can8t 5+ d6n+ (n 6n+ )+))(6n# Bn 63d+3 t6 h+-< th+ >6*an c6<+ >(th h+3 <365-+*)[ (t () (*<63tant t6 9nd+3)tand h6> +ach <+3)6n =(t) (nt6 th+ +n2(36n*+nt a369nd th+*# Zh() *6th+3 *a4 5+ <a3t 6= a =a*(-4[ a c6**9n(t4 and a )6c(+t4 that c69-d h+-< h+3# Mn th+ 6th+3 hand[ th6)+ a369nd h+3 c69-d 5+ <a3t 6= th+ <365-+*# Zh+3+ a3+ )+2+3a- <6))(5-+ )t+<) t6 *ana;(n; <365-+*)V  End+3)tand(n; th+ <365-+*  I66A(n; at 6<t(6n)  Q+tt(n; ;6a-)  U+2+-6<(n; a <-an 6= act(6n  16n(t63(n; and +2a-9at(6n 4#;#1# *EQDKB@aEQiET @>D UKPLFDC Zh+3+ *a4 5+ *an4 )6-9t(6n) t6 a <365-+*[ 59t (n 63d+3 t6 9nd+3)tand >hat >(-- >63A 5+)t =63 th+ >6*an[ a-- th+ <a3t) 6= th+ <365-+* *9)t 5+ 9nd+3)t66d# Q6*+ ())9+) *a4 5+ h(dd+n# I+a3n(n; <6(nt)V 2 42  Gach <a3t 6= th+ <365-+* h+-<) t6 59(-d a >h6-+ <(ct93+ 6= >hat () >36n;#  Q*a--+3 <a3t) d6 n6t )++* L9(t+ )6 9n*ana;+a5-+# Bt *a4 5+ +a)(+3 t6 tacA-+ 6n+ <a3t 6= th+ <365-+* at a t(*+  Zh+ >6*an *9)t 5+ +*<6>+3+d t6 )6-2+ h+3 6>n <365-+*) ] n6t t6-d >hat t6 d6# 2 43 4#;#2 0PPXiET a@ PU@iPEB Zh+ c69n)+--63 h+-<) th+ >6*an t6 -()t th+ <a3t) 6= th+ <365-+*[ and <3(63(t(g+ >hat n++d) t6 5+ d+a-t >(th =(3)t# Zh+n th+ c69n)+--63 and >6*an can d()c9)) h6> th+ <365-+* c69-d 5+ *ana;+d# Zh+ c69n)+--63 and >6*an ta-A a569t d(==+3+nt >a4) 6= <9tt(n; )6-9t(6n) (nt6 act(6n# Gach 6<t(6n >(-- ha2+ ad2anta;+) and d()ad2anta;+)# Bn a))+))(n; 6<t(6n)[ (t () (*<63tant t6 <6)(t(2+-4 3+(n=63c+ c6<(n; 5+ha2(693) that th+ >6*an )h6>)# N+)(-(+nc+ () a t+3* 9)+d t6 d+)c3(5+ th+ <6)(t(2+ a5(-(t4 t6 c6<+ >(th )t3+)) and d(==(c9-t(+)# h63 +ca*<-+[ +2+n th69;h (t *a4 =++- d(==(c9-t =63 a >6*an t6 ;+t 69t 6= 5+d[ )h+ ha) c6*+ t6 an a<<6(nt*+nt# Zh() <6)(t(2+ 5+ha2(693 n++d) t6 5+ 3+c6;n()+d# T362(d(n; th+ >6*an >(th )A(--) t6 c6<+ >(th th+ <365-+* >(-- h+-< h+3 t6 =++- )t36n;+3 and *63+ a5-+ t6 d+a- >(th >hat )h+ n++d) t6 d6 ] th+)+ c6<(n; )A(--) h+-< h+3 t6 =++- *63+ (n c6nt36- 6= h+3 )(t9at(6n# 4#;#3 3D@@iET TPaFB Zh+ c69n)+--63 h+-<) th+ >6*an t6 d+c(d+ 6n )(*<-+ ;6a-) that *a4 5+ )9cc+))=9--4 ach(+2+d# Q*a--+3 ;6a-) *a4 -+ad[ 62+3 t(*+[ t6 3+ach(n; -a3;+3 ;6a-)# 4#;#4 )DNDFPUiET a UFaE PV aS@iPE Zh+ >6*an n++d) t6 d+c(d+ >hat >(-- >63A 5+)t =63 h+3 ] and th+ c69n)+--63 h+-<) t6 d3a> 9< a <-an 6= act(6n# Zh+ >6*an )h69-d =++- +*<6>+3+d that th+ act(6n) )h+ ch66)+) >(-- h+-< h+3 t6 3+ach h+3 ;6a-)# 2 46 h6> )h+ =++-)# B =++- t+33(5-+# B An6> h6> 469 =++-# =++-(n;)# 1KDNDE@ LIKEPI@ Zh() () a )t3+))=9- and +*6t(6na- j65# Qta== >h6 <362(d+ c69n)+--(n; n++d t6 \d+_53(+=8 and )ha3+ th+ -6ad# d69 >(-- n6t 5+ a5-+ t6 A++< -()t+n(n; and h+-<(n; 6th+3 <+6<-+ (= 469 a3+ n6t ca3+d =63 4693)+-=` 2 47 7# +8R$N2 9(R &H/ +(*N3/00(R Mn+ 6= th+ 5(;;+)t <365-+*) =63 <+6<-+ >63A(n; (n th+ h+-<(n; 63 ca3(n; <36=+))(6n) () [LIKEPI@R# Zh() can ha<<+n >h+n 469 ;(2+ t66 *9ch 6= 4693)+-= t6 4693 >63A[ 59t d6 n6t An6> h6> t6 taA+ ca3+ 6= 4693 6>n n++d)# B= 469 d6n8t taA+ ca3+ 6= 4693)+-=[ 469 can )ta3t t6 =++-V  Gcha9)t+d  IacA(n; (n *6t(2at(6n  I6)) 6= j65 )at()=act(6n  N+)+nt*+nt 6= th+ >63A that 469 ha2+ t6 d6 O <+6<-+ that 469 >63A >(th  B)6-at(6n =36* c6--+a;9+)  Q(cA $63A(n; >(th >6*+n >h6 a3+ t3a9*at(g+d can 5+ <a3t(c9-a3-4 )t3+))=9-#  Z3a9*a d()63;an()+) ] (t *a4 *aA+ >6*+n =++- *9dd-+d and (nt+3=+3+) (n th+(3 9)9a- >a4) 6= c6<(n;#  Z3a9*a (nt+3=+3+) >(th 3+-at(6n)h(<) and t39)t ] th() *a4 *aA+ (t =++- that (t () ha3d t6 h+-< >6*+n# U6n8t 5-a*+ 4693)+-=#  Z3a9*a *aA+) 469 =++- +cha9)t+d and 62+3>h+-*+d# B= 469 can 3+c6;n()+ th()[ th+n 469 can taA+ )t+<) t6 -66A a=t+3 4693)+-=#  Z34 n6t t6 taA+ 6n t66 *9ch# B= 469 a3+ 62+3>h+-*+d[ 469 >(-- n6t 5+ a5-+ t6 ca3+ =63 4693)+-= 63 th+ >6*+n (n 4693 ca3+#  I66A =63 )(;n) 6= 593n69t ] (n 4693)+-= and 4693 c6--+a;9+) ] th+n 469 can act 5+=63+ (t () t66 -at+# Z34 t6 ;+t 4693 h+a-th =ac(-(t4 63 63;an()at(6n t6 th(nA a569t taA(n; ca3+ 6= th+ )ta==# Zh+ =6--6>(n; <6(nt) *a4 5+ h+-<=9- t6 469V  N+c6;n()+ th+ )t3+))=9- nat93+ 6= 4693 >63A ] >hat a3+ th+ <a3t(c9-a3 )t3+))+) that 469 and 4693 c6--+a;9+) ha2+ t6 d+a- >(th.  Z34 t6 taA+ )6*+ t(*+ t6 th(nA a569t 4693 6>n n++d) ] n6t j9)t th6)+ 6= 4693 c-(+nt)  @+-< t6 d+2+-6< )4)t+*) 6= )9<<63t k=63*a- and (n=63*a-l =63 4693)+-= and 4693 c6--+a;9+)#  Q<+aA t6 th+ -+ad+3)h(< >(th(n th+ h+a-th =ac(-(t4 63 63;an()at(6n )6 that th+4 can <36t+ct and )9<<63t )ta==# 2 8 2 ;# +(N+0*3$(N Zh+ )A(--) and a<<36ach+) t6 c69n)+--(n; that a3+ 69t-(n+d (n th+ <3+2(69) )+ct(6n) ha2+ 5++n 9)+d t6 h+-< *an4 d()t3+))+d >6*+n# Zh() )t634 () =36* a >6*an >h6 3+c+(2+d c69n)+--(n; =36* th+ T+3(nata- 1+nta- @+a-th T36j+ct# Qh+ )h6>) h6> (*<63tant (t () t6 5+ a5-+ t6 t+-- h+3 )t634 and 5+ -()t+n+d t6 >(th69t 5+(n; j9d;+d# 8 =PCaERB B@PKOZ e3UDaXiET aEQ HDiET HDaKQb LO 2FPKia M Zh(n;) a3+ +a)(+3 =63 >6*+n t6da4[ 5+ca9)+ >+ a3+ (nd+<+nd+nt# M93 *6th+3) >+3+ n6t 3+)<+ct+d# Zh+4 d(dn8t ha2+ th+ 3(;ht) >+ ha2+ n6> and d(dn8t ha2+ th+ )a*+ 6<<63t9n(t(+)# Zh+4 >+3+ -(A+ )-a2+)# Zh+)+ da4) (= th+3+ () a <365-+*[ th+3+ () h+-< a2a(-a5-+[ )6*+th(n; that B >a) =63t9nat+ t6 ha2+ >h+n B d()c62+3+d that B >a) )9==+3(n; =36* <6)tnata- d+<3+))(6n# $h+n B =(3)t 5+ca*+ a *6th+3[ B d(dn8t An6> a569t d+<3+)) (6n# f6> B >69-d -(A+ t6 -+t +2+346n+ An6> a569t th() <365-+* )6 that <+6<-+ can )tand 9< and d6 )6*+th(n; a569t (t# B >a) 563n[ 6n+ 6= t>(n)[ (n th+ Da<+ Z6>n Z4;+35+3; @6)<(ta-# 14 <a3+nt) d(263c+d >h+n B >a) 6n-4 t>6 da4) 6-d# S+ca9)+ *4 *6th+3 >a) a-6n+ )h+ c69-dn8t d6 >hat )h+ >a) )9<<6)+d t6 d6 a) a *6th+3 and B ;3+> 9< >(th h+3 =a*(-4# Zh+3+ >a) 3+a--4 n6 6n+ t6 ta-A t6 63 t6 d()c(<-(n+ 9) and B 5+ca*+ <3+;nant at th+ a;+ 6= 14# B ha2+ )9==+3+d d+<3+))(6n )(nc+ th+n# @a2(n; a 5a54 at )9ch an +a3-4 a;+ >a) 3+a-- 4 ha3d# B had t6 -+a2+ )ch66- and >a) =63c+d t6 >63A a) a d6*+)t(c >63A+3[ >h(ch B c69-dn8t 3+a--4 d6 5+ca9)+ B >a) )6 469n;# B t3(+d 2+34 ha3d[ 59t B j9)t c69-dn8t d6 (t# Q6[ B d+c(d+d t6 ;6 5acA t6 )ch66- >h+n *4 5a54 >a) th3+ + 4+a3) 6-d# B <a))+d *4 )tanda3d n(n+[ <+n9-t(*at+ 4+a3 6= 2 2 8 $h+n 469 a3+ d+<3+))+d th+3+ a3+ )6 *an4 th(n;) that a3+ a==+ct(n; 469# d69 *a4 n6t 5+ a5-+ t6 t+-- +cact-4 >hat (t () that () *aA(n; 469 =++- )6 5ad[ 59t j9)t that 469 can8t ; +t 69t =36* th+ =6; 469 a3+ (n# G2+34th(n; can =++- -(A+ (t () j9)t =a--(n; a<a3t[ that n6th(n; () ha<<+n(n; 3(;ht 63 acc63d(n; t6 <-an)# d69 *a4 n6t An6> t6 taA+ (t )+3(69)- 4 >h+n 469 a3+ =(3)t )9==+3(n; =36* (t[ 59t (t () 2+34 (*<63tant t6 add3+)) (t and t6 =(nd a >a4 69t# Zh+3+ a3+ )6 *an4 >6*+n >h6 a3+ d4(n; (n)(d+ =36* th() th(n;# Zh+4 d6n8t An6> h6> t6 d+a- >(th (t 63 h6> t6 c6<+# G2+34th(n; (n th+(3 -(2+) () t93n(n; 9<)(d+ d6>n# Knd th+4 n++d )6*+6n+ >h6 >(-- 9nd+3)tand and n6t j9d;+ th+*# Zhat () >h4 B ta-A a569t th() d+<3+))(6n >(th +2+346n+# B +2+n ta-A t6 *6th+3) B )+ + 6n th+ 59)# B >ant +2+346n+ t6 An6> a569t th() <365-+*# B >ant th+ *6th+3) t6 -()t+n# B= B c69-d ha2+ *4 >a4[ +ach and +2+34 6n+ 6= th+ h6)<(ta-) >69-d ha2+ th+)+ A(nd) 6= c69n)+-63)[ +)<+c(a--4 th+ ;62+3n*+nt h6)<(ta-) >h(ch a3+ =63 +2+3456d4# Zhat >a4 +2+346n+ (nc-9d(n; a-- 5-acA >6*+n[ >h6 3+a--4 d6n8t An6> an4th(n; a569t th() d+<3+))(6n[ c69-d ;+t h+-<# Ent(- that ha<<+n)[ B h6<+ that a-- th+ *6th+3) 69t th+3+[ >h6 a3+ )9==+3(n; =36* <+3(nata- and <6)tnata- d+<3+)) (6n[ >(-- taA+ ca3+ 6= th+*)+-2+) and =(nd )9<<63t# d69 6n-4 -(2+ 6nc+[ and (t d6+) n6t ha2+ t6 5+ a -(=+ =(--+d >(th d+<3+))(6n` 29 3ICCaKO >iT>FiT>@B Z3+ad ca3+=9--4 ] 3+)<+ct <+6<-+8) =++-(n;) and d6 n6t j9d;+# I()t+n ] t6 >hat () 5+(n; )a(d[ h6> (t () +c<3+))+d and t6 >hat () n6t 5+(n; )a(d a-69d# $6*+n *a4 n6t 3+*+*5+3 >hat 469 )a4[ 59t th+4 >(-- 3+*+*5+3 h6> 469 *aA+ th+* =++-# d69 n++d t6 9nd+3)tand 4693 6>n =++-(n;) t6 9nd+3)tand 6th+3)# Z6 taA+ ca3+ 6= 6th+3)[ 469 n++d t6 -66A a=t+3 4693)+-=# 2 2 30 :# R/9/R/N+/3 Sa)(c_c69n)+--(n;_)A(--)#c6* htt<VOO>>>#5a)(c_c69n)+-(n;_)A(--)#c6*Oa)A(n;_L9+)t(6n)#ht*- C/&&7$it6 R#$t*: S#*:t< T8/j#4t UVWWXYV Z3a(n(n; and 3+)693c+ *an9a- =63 c6**9n(t4 ca3+ ;(2+3)[ U+<a3t*+nt 6= T)4ch6-6;4[ En(2+3)(t4 6= U935an $+)t2(--+ Y(5)6n[ e[ Q>a3tg[ I and Qand+n5+3;h[ N k2RR2l C/7$9#::i$+ *$( C/pi$+[ Mc=63d En(2+3)(t4 T3+))[ Da<+ Z6>n Zi5#Zi$#HC<i:(Zi$# [*&iEi* U\]]XYV D6**9n(t4 D69n)+--63 Z3a(n(n; Z66-A(t[ 16d9-+ 2[ Sa)(c D69n)+--(n; QA(--)[ Ta3t(c(<ant 1an9a- >>>#=h(#63;OfNOD69n)+-(n;Z66-A(t16d9-+2Ta3t(c(<ant@b#<d= T#8i$*t*: R#$t*: S#*:t< T8/j#4t U\]V]YV 1at+3na- 1+nta- @+a-th Q+32(c+) d+2+-6<*+nt ;9(d+-(n+) d69th>63A I(nA) and Bd+a)V Bnt36d9ct(6n t6 c69n)+--(n; )A(--) htt<VOO>>>#469th>63A#c6*Oc69n)O(nd(22#ht*-
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