Applied Strength of Materials for Engineering Technology




Loading...







BrainHoney – World History Pacing Guide

2021. aug. 19. 2.05: Ancient River Civilizations Module Review ... 3.06: Ancient America Module Exam ... 5.08: Ancient Rome Module Exam.

Module 9.qxd

Water quality for agriculture. FAO Irrigation and Drainage Paper No 29 Rev. 1. Prepared by: Ayers

Tennessee Social Studies Standards

beginnings of ancient civilizations through the fall of the Western Roman Empire 5.08. Describe the challenges of the journey and process for successful ...

Tennessee Social Studies Standards

beginnings of ancient civilizations through the fall of the Western Roman Empire 5.08. Describe the challenges of the journey and process for successful ...

CENTRAL BOARD OF EXCISE & CUSTOMS NEW DELHI

the GSTN is developing back-end modules like assessment audit

The London School of Economics and Political Science Course

8 Undergraduate Programme Regulations module with the permission of the Department Tutor course from outside the Economic History Department.

IFIP TC3 Working Conference “A New Culture of Learning

2015. júl. 1. Learning History: a gamified activity for mobile devices . ... exam is based on the optional module of the basics of programming which ...

Applied Strength of Materials for Engineering Technology

Because the Roman and Greek alphabets contain a finite number of letters symbols are recycled and used exams

40566A: Microsoft Word associate 2019 ebook

Module 3: Working with objects ..... 1 ... Microsoft Office Specialist (MOS) exam objectives. ... They use Roman numerals by default (i ii

The Transition to Computer-Based Assessment

modules. (electronic reading) for future tests. All in all it students taking traditional exams do so without ... New Roman 10pt“.

Applied Strength of Materials for Engineering Technology 155_547233878.pdf I ndiana University - Purdue University Fort WayneO pus: Research & Creativity at IPFWM anufacturing and Construction Engineering $"',-*-&5 "2*152!*(" 1(-,0 $. /1+$,1-% ,2% "12/(,& ,#-,01/2"1(-, ,&(,$$/(,&$"',-*-&5 A pplied Strength of Materials for EngineeringT echnologyB arry DupenI ndiana University - Purdue University Fort Wayne, du penb@ipfw.eduF ollow this and additional works at:'

8.-.20(.%4$#2+"$1(#% ".2!0

 /1-%1'$ ..*($#$"' ,("0-++-,07(

0$#(1(-,' 0!$$,02.$/0$#$#hThi

s Book is brought to you for free and open access by the Department of Manufacturing and Construction Engineering Technology at Opus:

$0$ /"'/$ 1(3(15 11' 0!$$, ""$.1$#%-/(,"*20(-,(, ,2% "12/(,& ,#-,01/2"1(-,,&(,$$/(,&$"',-*-&5 "2*152!*(" 1(-,0!5

, 21'-/(6$# #+(,(01/ 1-/-%.20$0$ /"'/$ 1(3(15 1-/+-/$(,%-/+ 1(-,.*$ 0$"-,1 "1

#+(,*(!(.%4$#2O pus CitationB arry Dupen (2016).App lied Strength of Materials for Engineering Technology. 10 e d. Purdue University.'

8.-.20(.%4$#2+"$1(#% ".2!0 

             &((),-./01

24468:&@0,A(6B0446(C,D08E&1:8&F,I1M:100(:1M,O08E16F6M)C,P1R:&1&,T1:U0(4:@),W,A.(R.0,T1:U0(4:@),_6(@,a&)10

Ubcd,e0U:40R,2.M.4@,fdcgb,OE:4,h6(i,:4,F:80140R,.1R0(,k(0&@:U0,k6ll614,2@@(:m.@:61noE&(02F:i0,pbd, P1@0(1&@:61&F,rkk, sno2,pbdt,o00,8(0&@:U086ll614b6(M,B6(,F:80140,R0@&:F4b c   

A(0B&80bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbu

A.(/640,6B,@E0, 66ibbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbu IR:@6(4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbp k6U0(,AE6@64bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbv O0(l:16F6M)bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbg

-0B:1:@:614bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbw

kE&/@0(,cy,P1@(6R.8@:61,@6,o@(01M@E,6B,D&@0(:&F4bbbbbbbbbbbbbbbbbbbbbbbbbbbcc aE&@,:4,o@(01M@E,6B,D&@0(:&F4zbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcc OE0,_&8@6(nhTh&m0F,D0@E6R,6B,T1:@,k61U0(4:61bbbbbbbbbbbbbbbbbbbbbbbbcf kE&/@0(,fy,o@(044,&1R,o@(&:1bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcttt

96(l&F,o@(044,&1R,o@(&:1bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcttt

o:M1,k61U01@:61bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcw oE0&(,o@(044,&1R,o@(&:1bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbfd kE&/@0(,uy,A6:4461:4,e&@:6,&1R,OE0(l&F,I;/&14:61bbbbbbbbbbbbbbbbbbbbbbfu A6:4461:4,e&@:6bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbfu OE0(l&F,I;/&14:61,&1R,OE0(l&F,o@(044bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbfv kE&/@0(,py,A(044.(0,<0440F4,&1R,o@(044,k61801@(&@:614bbbbbbbbbbbbbbbbf= OE:1na&FF0R,A(044.(0,<0440F4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbf= o@(044,k61801@(&@:61,:1,O014:61bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbud kE&/@0(,vy, 6F@0R,&1R,a0FR0R,>6:1@4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbuu 6F@0R,hTh&/,>6:1@4,hTh6&R0R,:1,O014:61bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbuu a0FR0R,hTh&/,>6:1@4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbu= kE&/@0(,gy,A(6/0(@:04,6B,2(0&4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbpc -:l014:614,&1R,2(0&bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbpc k01@(6:R,&1R,k01@(6:R&F,2;04bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbpc D6l01@,6B,P10(@:&,6B,&,e08@&1MF0bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbpc k6l/6.1R, 0&l4,oE&(:1M,&,k01@(6:R&F,2;:4bbbbbbbbbbbbbbbbbbbbbbbbbpf ?6FF6h, 0&l4,oE&(:1M,&,k01@(6:R&F,2;:4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbpu OE0,O(&14B0(,_6(l.F&bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbpp k6l/6.1R, 0&l4,a:@E,-:BB0(01@,90.@(&F,2;04bbbbbbbbbbbbbbbbbbbbbpv ?6FF6h, 0&l4,a:@E,-:BB0(01@,90.@(&F,2;04bbbbbbbbbbbbbbbbbbbbbbbbbbbp= D6l01@,6B,P10(@:&,&m6.@,@E0,)n),90.@(&F,2;:4bbbbbbbbbbbbbbbbbbbbbbbbvc oE6(@8.@4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbvp e&R:.4,6B,@)(&@:61bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbvp A6F&(,D6l01@,6B,P10(@:&bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbvp kE&/@0(,ttty,O6(4:61,:1,e6.1R,oE&B@4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbvv oE0&(,o@(044,:1,&,e6.1R,oE&B@bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbvv

21MF0,6B,Oh:4@,:1,&,e6.1R,oE&B@bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbvttt

o@(044,k61801@(&@:61,:1,O6(4:61bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbv= kE&/@0(,=y, 0&l,e0&8@:614C,oE0&(,-:&M(&l4C,&1R,D6l01@, -:&M(&l4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbgd hTh6&R4,61, 0&l4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbgd e0&8@:614,B6(,o:l/F)no.//6(@0R,o:l/F0, 0&l4bbbbbbbbbbbbbbbbbbbbbgc e0&8@:614,B6(,AU0(E&1M:1M,&1R,k&1@:F0U0(, 0&l4bbbbbbbbbbbbbbbbbbgp oE0&(,-:&M(&l4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbgg D6l01@,-:&M(&l4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbtttf kE&/@0(,wy,o@(04404,:1, 0&l4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=f 01R:1M,o@(044,:1, 0&l4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=f

01R:1M,o@(044,:1,a:R0n_F&1M0,o@00F, 0&l4bbbbbbbbbbbbbbbbbbbbbbbbbb=poE0&(,o@(044,:1, 0&l4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=ttt

2FF6h&mF0,hTh6&Rbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbwf

kE&/@0(,cdy, 0&l,-0BF08@:61bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbwp e&R:.4,6B,k.(U&@.(0bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbwp OE0,_6(l.F&,D0@E6R,B6(,o:l/F0,k&404bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbwv _6(l.F&,D0@E6R,?:1@4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbw= OE0,_6(l.F&,D0@E6R,B6(,k6l/F0;,k&404y,o./0(/64:@:61bbbbbbbw= <:4.&F:B:1M,@E0,-0BF08@:61,k.(U0bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcdd kE&/@0(,ccy, 0&l,-04:M1bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcdf a:R0n_F&1M0,o@00F, 0&l,-04:M1,:1,o:;,I&4),o@0/4bbbbbbbbbbbbbbcdf O:lm0(, 0&l,-04:M1,:1,o:;,I&4),o@0/4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcd=

2FF,A@E0(, 0&l4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccd

kE&/@0(,cfy,k6lm:10R,o@(04404bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccf O014:61,C, 01R:1Mbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccf 01R:1M,:1,Oh6,-:(08@:614bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccf I8801@(:8,hTh6&R:1Mbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccp kE&/@0(,cuy,o@&@:8&FF),P1R0@0(l:1&@0, 0&l4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcc= -0B:1:1M,-0@0(l:1&@0,&1R,P1R0@0(l:1&@0, 0&l4bbbbbbbbbbbbbbbbbbcc= D0@E6R,6B,o./0(/64:@:61bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcc= kE&/@0(,cpy, .8iF:1M,6B,k6F.l14bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcfp O)/04,6B,k6F.l14bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcfp PR0&F,oF01R0(,k6F.l14bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcfp o@(.8@.(&F,o@00F,k6F.l14bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcfg o@00F,D&8E:10,A&(@4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcfttt kE&/@0(,cvy,<:4.&F:B:1M,o@(044,&1R,o@(&:1bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcud D0&4.(:1M,o@(044bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcud o@(044,&@,@E0, &40,6B,&,oE6(@, F68ibbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcud D6E(:4,k:(8F0bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcuc :mF:6M(&/E)bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcp= O0;@m66i4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcp= A@E0(,e0&R:1M,D&@0(:&Fbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcp=

2//01R:;,2y,T1:@4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcpw

oP,o)4@0l,6B,T1:@4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcpw To,k.4@6l&(),o)4@0l,6B,T1:@4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcpw

2//01R:;, y,D&@0(:&F4,A(6/0(@:04bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcvd

D0@&F4C,k618(0@0C,D,o@610bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcvd

2//01R:;,ky,A(6/0(@:04,6B,2(0&4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcvp

k01@0(,6B,@(&U:@)C,2(0&C,D6l01@,6B,P10(@:&C,&1R,e&R:.4,6B, @)(&@:61bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcvp

2//01R:;,-y,A(6/0(@:04,6B,o@00F, 0&l4,&1R,A:/04bbbbbbbbbbbbbbbbbbbbbbcvttt

anm0&l4bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcvttt o@00F,A:/04bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcgc k6//0(,O.m:1Mbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcgf

2//01R:;,Iy,D08E&1:8&F,&1R,-:l014:61&F,A(6/0(@:04,6B,a66Rbcgu

D08E&1:8&F,A(6/0(@:04,6B,2:(n-(:0R, 6&(R4,&1R,O:lm0(bbbbbbcgu o6B@h66R,hTh.lm0(,&1R,O:lm0(,o:B04bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcgp

2//01R:;,_y, 0&l,IE.&@:614bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcgg

P1R0;bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbctttc

P1R0;bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbctttc

f

A(0B&80

      

cbw,l:FF:61,m&8E0F6(4,R0M(004,&(0,&h&(R0R,&11.&FF),:1,@E0,Tobc,2m6.@,wf,@E6.4&1R,&(0,I1M:100(:1M,R0M(004C,&1R,&m6.@,cttt,

@E6.4&1R,&(0,I1M:100(:1M,O08E16F6M),R0M(004,&1R,O08E1:8:&1,R0M(004b,OE0,1.lm0(,6B,D08E&1:8&FC,k:U:FC,&1R,k614@(.8@:61,

I1M:100(:1M,O08E16F6M),M(&R.&@04,:4,61F),&m6.@,f,@E6.4&1R,/0(,)0&(C,46,@E0,l&(i0@,B6(,&FM0m(&nm&40R,

  ,

@0;@m66i4,B6(,I1M:100(:1M,O08E16F6M),:4,&,4l&FF,B(&8@:61,6B,@E0,l&(i0@,B6(,8&F8.F.4nm&40R,I1M:100(:1M,@0;@m66i4b

o:180,P,&@@01R0R,86FF0M0,:1,@E0,cw=d4C,@0;@m66i,/(:804,E&U0,(:401,&m6.@,@h:80,&4,B&4@,&4,:1BF&@:61b,OE0,:1@0(10@,R:R,16@,0;:4@,

m&8i,@E01C,46,&FF,@0;@m66i4,h0(0,/(:1@0Rb,96h,h0,E&U0,&16@E0(,6/@:61y,F6hn864@,6(,B(00,61F:10,0nm66i4,hE:8E,&(0,(0U:40R,

l6(0,B(0E.01@F),@E&1,/(:1@0R,m66i4b,aE:F0,@(&R:@:61&F,@0;@m66i4,&(0,(0U:40R,0U0(),p,@6,cd,)0&(4,m&40R,61,:1/.@,B(6l,0;/0(@4,

:1,@E0,@6/:8C,@E:4,0nm66i,:4,(0U:40R,0U0(),40l04@0(,m&40R,61,:1/.@,B(6l,0;/0(@4,:1,F0&(1:1My,@E0,4@.R01@4b

o@.R01@4,86l/F&:1,@E&@,@E0,0;/F&1&@:614,:1,l&1),I1M:100(:1M,O08E16F6M),@0;@m66i4,&(0,@66,@E06(0@:8&FC,@66,h6(R)C,&1R,@66,

R:BB:8.F@,@6,.1R0(4@&1Rb,OE0),&F46,86l/F&:1,&m6.@,@E0,F&8i,6B,86l/F0@0,.1:@,861U0(4:614,:1,0;&l/F0,/(6mF0l4C,&1R,

:18614:4@01@,.40,6B,4)lm6F4,m0@h001,(0F&@0R,86.(404b,_6(,0;&l/F0C,46l0,&.@E6(4,.40,C,C,&1R,,B6(,16(l&F,4@(044C,4E0&(,

4@(044C,&1R,4@(&:1C,:14@0&R,6B,@E0,4@&1R&(R,@(00i,4)lm6F4,FC,GC,&1R,Hb,OE:4,.40,6B,hTh&@:1,8E&(&8@0(4,h:@E,l.F@:/F0,4.m48(:/@4,

861B.404,4@.R01@4,m08&.40,@E0,@(00i,4)lm6F4,&(0,.40R,:1,6@E0(,@0;@m66i4C,&1R,m08&.40,8&/:@&F,,:4,.40R,B6(,408@:61,l6R.F.4,

F&@0(,:1,@E0,86.(40b,o@.R01@4,E&U0,@(6.mF0,R:4@:1M.:4E:1M,m0@h001,,&1R,,61,@E0,8E&Fim6&(R,&1R,:1,@E0:(,16@04b

A(6B0446(4,86l/F&:1,@E&@,@66,l&1),4@.R01@4,86/),&14h0(4,B(6l,61F:10,46F.@:61,l&1.&F4,6(,B(&@0(1:@),E6l0h6(i,B:F04,:14@0&R

6B,F0&(1:1M,@6,46FU0,/(6mF0l4,B(6l,48(&@8EC,@E01,@E040,4@.R01@4,B&:F,0;&l4b,A(6m&mF),cdI,6B,@E0,F0&(1:1M,:1,

 

,688.(4,:1,8F&44C,&1R,wdI,688.(4,&4,4@.R01@4,46FU0,/(6mF0l4b,-0F:m0(&@0F)C,@E0,/(6mF0l,40@,B6(,@E:4,m66i,:4,16@,

&U&:F&mF0,61F:10C,&1R,:4,8E&1M0R,0U0(),40l04@0(b

P,@0&8E,

  ,@6,D08E&1:8&F,&1R,k614@(.8@:61,I1M:100(:1M,O08E16F6M),4@.R01@4b,OE040,4@.R01@4,@0FF,l0,@E0)

h&1@,E0F/,h:@E,&FM0m(&,4i:FF4C,.1:@,861U0(4:614C,&1R,/(6mF0ln46FU:1M,&//(6&8E04b,OE0,/(6mF0l,40@,@E&@,&886l/&1:04,@E:4,

m66i,861@&:14,/(6mF0l4,(0E.:(:1M,&1,&FM0m(&:8,&14h0(,&4,h0FF,&4,@(&R:@:61&F,/(6mF0l4,(0E.:(:1M,&,1.l0(:8&F,&14h0(b,OE0,

         ,:4,0l/E&4:B0R,B(6l,@E0,B:(4@,8E&/@0(C,&1R,:4,.40R,:1, ,0;&l/F0,/(6mF0l4b o.ll&(:B:1MC,@E0,M6&F4,6B,@E:4,m66i,&(0y •_(00,R:4@(:m.@:61,6U0(,@E0,:1@0(10@ •_(0E.01@,(0U:4:614,m&40R,61,4@.R01@,:1/.@ •k618:40,0;/F&1&@:614 •I;&l/F04,h:@E,86l/F0@0,.1:@,861U0(4:614 •o@&1R&(R,@(00i,4)lm6F4,B6(,4@(044,&1R,4@(&:1 •A(6mF0l4,(0E.:(:1M,&FM0m(&:8,&14h0(4,&4,h0FF,&4,/(6mF0l4,(0E.:(:1M,1.l0(:8&F,&14h0(4 •A(6mF0l4,(0E.:(:1M,&14h0(4,:1,401@01804,@6,4E6h,(0&461:1M,&1R,.1R0(4@&1R:1M,6B,@E0,@6/:84

OE:4,0nm66i,:4,(0U:40R,61,&1,61M6:1M,m&4:4b,AF0&40,401R,4.MM04@:614,B6(,:l/(6U0l01@,@6,l0,&@,R./01mJ:/Bhb0R.b

&((),-./01

P1R:&1&,T1:U0(4:@),W,A.(R.0,T1:U0(4:@),_6(@,a&)10

_6(@,a&)10C,P1R:&1&

2.M.4@C,fdcg

c-&@&,B(6l,fdcunfdcpb,k.((01@,1.lm0(4,&(0,:1,@E0,-:M04@,6B,IR.8&@:61&F,o@&@:4@:84C,/.mF:4E0R,m),@E0,9&@:61&F,k01@0(,B6(,IR.8&@:61&F,

o@&@:4@:84C,Tbob,-0/&(@l01@,6B,IR.8&@:61C,&@,1804b0RbM6Ub u

A(0B&80

  OE040,PA_a,4@.R01@4,0R:@0R,@E0,@0;@,&1R,861@(:m.@0R,@6,:l/(6U:1M,@E:4,m66iy >&86m,2:14h6(@E

2&(61,2F0;&1R0(

@06(M0,2FFh0:1

D&@@E0h,2lm0(M

>&(0R,2(8E0(

D&(i,2(8E0(

D&(i,2(l4@(61M

>.4@:1,2(16FR o@.&(@,24/) k&F0m,2U0(:FF

2F0;, &0(

O(01@61, &(10@@

e)&1, &.MEl&1 >&86m, 0&(R

90:F, 0&.8E6@

D:@8E0FF, 0FF&l

2&(61, 01R0(

Il:F), 01R:;

D&U0(:8i, :(8E

K0U:1, F&8i

>6E1, F&1i014E:/ k6116(, F0i0 >&461, 6m&)

O)F0(, 6F:1M0(

-&1:0F, 610 k()4@&F, 6)R <&F0(:0, (&@@01

2&(61, ()&1@

(&R), ()&1@ @(0M6(), .11

9:8E6F&4, .(8E0FF

>.4@:1, )0(F0) F&i0,k&:1 -&11),k&FR0(61 (6R),k&FF&ME&1

I4/0(&1B&,k&4@:FF6

e:8E&(R,kE&Rh:8i

O)F0(,kE&lm0(4

(:&1,kE&10) >&86m,kF&401

L&8E&(),kF0U01M0(

e)&1,kF:1M01/00F

D:@8E0FF,k6l/&(0@

T(:0F,k61@(0(&4

>6(R&1,k66i hTh6M&1,k6.1@0(l&1 o@0/E01,k6; -:FF61,k(&:M kE&R,k(64m) -&1:0F,k.ll:1M4O&)F0(,k.ll:1M4 (:&1,-&F0) kE(:4@6/E0(,-&U:4

A&@(:8i,-&U:4

e644,-:FF:61 >64E.&,-.1F&/ >&(0R,IFF:6@@ o@0/E01,I1MF&1R k&l0(61,I)l&1 >&86m,_&Fi >64E.&,_&(F00 kE(:4@6/E0(,_&.(6@0

O)F0(,_&)F6(

2.4@:1,_0&(16h

01M&l:1,_:08E@0(

2F0;&1R0(,_:4E0(

>6E1,_:4E0(

D:4&0F,_F6(04

kE&(F04,_6(0l&1 ()80,_6((04@0( k&lR01,_6; -6l:1:8i,_(&186

D:8E&0F,_(:RRF0

9&@E&1,_()0

>&86m,@&0(@0 (0@@,@&M161 >640/E,@&FFl0)0(

D&@@E0h,@&lmF0

k&(F,@&((:1M0( oE&10,@:RR014

21R(0h,@6(R61

2Fl&(:6,@(0010

D:8E&0F,@(04F0)

e)&1,@.:BB hTh.8&4,?&E1 -&U:R,?&F/:1 kE&(F04,?&104

2R&l,?&1B6(R

kE(:4@:&1,?&(l0)0( (:&1,?&(/0( >&l04,?&((:4 oi)F0(,?&)04

D&@@E0h,?&.@0(

2F0;&1R0(,?0:10

k6R),?0/F0( k&l0(61,?0((:1M 01,?:16(&

K&F0m,?0((:8i

o/0180(,?:FF0

O)F0(,?:16(&_(&1i,?6BBl&1

>&l04,?6//04 (&RF0),?6(1 -0(:8i,?64@0@F0( >640B,PB0( o.M:1R&,>&:4&n2(R

2(:&1&,>&(U:4

-&1:0F,>6E14 >&461,>6)10( hTh.8&4,K&:40( >6E1,K0010

2R&l,K0FF:1M

2R&l,K0110R)

>640/E,K01@ ?&11&E,K:1:1ME&l

9&@0,K:/B0(

A&@(:8i,K:(i

21R(0h,K:@(.4E

e&8E&0F,KF6/B014@0:1 >60F,K.lB0( (&1R01,hTh&M&44:0

K)F0,hTh&M0l&11

-6.M,hTh&lm0(@ (&1R61,hTh&10 >.4@:1,hTh&1@B

O&)F6(,hTh&1@B

A&@(:8i,hTh&(6)

<01.4,hTh00 kE(:4@6/E0(,hTh00i -&1:0F,hTh0h:4 >61&@E&1,hTh0h:4

A&(i,hTh:8iF:@0(

I(:8,hTh:F04

>640/E,hTh6(@:0

21R(0h,hTh6.MEm6(6.ME

>61&E,D&8i

K)F0,D&8i0

k.FF&1,D&M1.461 hTh:1R&,D&1R.i&

2.4@:1,D&11

-&F@61,D&11 -&U:R,D&(82.(0F0 hTh.8&4,D&(@:1 o@0(F:1M,D&(@:1

2F0;,D&461

hTh&,K0:4E&,D&461 >&461,D&)04 >&86m,D&B.(0i >60F,D8 &:12R&l,D8k&(@)

O6(:,D8@&:(i

D:8E&0F,D8hTh:1R01

e:F0),D8D.((&) >&l04,D8<:8i0(

21M0F&,D01R6B&

>0RR,D:11:8E

K&:@F:1,D66(0

-0(0i,D6((0&F0 o01&:R,D(BFM&i

O(&U:4,D.FF01R6(0

F&i0,9:86F

K)F0,96FF

D:8E&0F,9.4m&.l

D:@8E0FF,AF10)

>6(R&1,Ah014 >&461,A&80 e)&1,A0&(80 >&86m,A01F&1R

9:8E6F&4,A01(6R

hTh.:4,A0(0&

O&R,AB0BB0(i6(1

>6E1,AE&l kF&)@61,AE:F:/4 >6E1,A6M.0 @&m0,A6h0FF (&;@61,A6h0(4

9&@E&1,A(&@@

O(0),A(6/0(

-&i6@&,e&44l&1 >.4@:1,e0040 >&l04,e0:@B

D&@@E0h,e0M&i

>&l04,e014m0(M0( oE&h1,e0.:FF0 -&1:0F,e0)16FR4 -&1:0F,e:0l&1 kE&(F04,e:10E&(@ >&461,e:1M0( -0(0i,e:/F0)

D&@@E0h,e60FF

>011:B0(,e6)0( k6116(,e.m) (&1R61,e.R0

2.4@:1,e.l40)

:FF:0,o&&FB(&1i

L&8E&(),o&)F6(

>6E1,o8E&B0(

L&8i6(),o8E&0B0(e:F0),o8E.0@@0

L0i0,o8E.F@B

>.4@:1,o0FB e)&1,o0FF0(4

AE:F:/,oE00@4

9&@E&1,oE010l&1

K0:@E,oE0/E0(R

o86@@,oE:BBF0@@ (&R,oE&l6

D&@@E0h,oE:li6

K0110@E,oE6(@

O(01@61,oE(68i

@06(M0,o:RR614

O(&U:4,o:1MF0@&()

I(:8,oE6(@01

oE&10,oF610 >&86m,ol&(i0(

IFF01,ol:@E

D&@@E0h,o6l0(F6@@

>64E.&,o6(M0

D&@@E0h,o@0:10(

>&461,o@(6F0 >61&4,o.4&(&m&

O(6),o.@@0(B:0FR

e6m0(@,oh&1461 kE(:4@6/E0(,oh)M&(@

K)F0,O0h

L&8E,OE6(1

9&@E&1:0F,O:ll614

>&461,O6110( kE&1RF0(,O(&80) k6R),O.(10( >&l04,T/@61 >&461,<&8E61

OE&R:.4,<040)

-&i6@&,<6M0F o86@@,<6(1R(&1 kE&(F04,a&R4h6(@E >&),a0E(F0

O(&U:4,a0:M6FR

o&l,a0:440( (68i,a04@0(M&&(R @(&1@,a:F461

K0110@E,a:1

o86@@,a6FB0

D:8E&0F,a66R868i

hTh)1R4&),a(:ME@

D&@@E0h,s6.1M

O&1M,LE61M

2RR:@:61&F,0R:@:1M,4.MM04@:614,h0(0,/(6U:R0R,m),90:F,A0@(6BBC,<:4:@:1M,244:4@&1@,A(6B0446(,&@,A.(R.0,T1:U0(4:@),o6.@E,

01RN,,P4(&(,2El&R,6B,-&ll&lC,o&.R:,2(&m:&N,&1R,-(b,A&(U:B,@E&U&l:,6B,?&(F:1M01C,O0;&4b p

A(0B&80

  

k6U0(,/E6@64,m),@E0,&.@E6(b,@06R04:8,M(001E6.404,&@,OE0,IR01,A(6M08@C, 6R0FU&C,I1MF&1R,rfdddtN,m&(1,80:F:1M,&@,o6l0(40@,

e.(&F,hTh:B0,D.40.lC,@F&4@61m.()C,I1MF&1R,rcp@E,801@.()tN,:1@0(:6(,6B,&,@6.(:4@,i:64i,10&(,oE.&l:4EC, (:@:4E,k6F.lm:&N,=,

l:F0,F61M,k61B0R0(&@:61, (:RM0,m0@h001,90h, (.14h:8i,&1R,A(:180,IRh&(R,P4F&1R,rcwwttttN,:1@0(:6(,6B,_:@8E:4,86U0(0R,

m(:RM0C,-0FE:C,90h,s6(i,rc=tttdtN,D01&:,4.4/01:61,m(:RM0C,D01&:, (:RM0C,a&F04,rc=fgtb                !"!#!$ v

O0(l:16F6M)

         

08&.40,@E0,e6l&1,&1R,@(00i,&F/E&m0@4,861@&:1,&,B:1:@0,1.lm0(,6B,F0@@0(4C,4)lm6F4,&(0,(08)8F0R,&1R,.40R,B6(,l6(0,@E&1,610

@0(lb,kE08i,@E0,861@0;@,6B,@E0,0E.&@:61,@6,B:M.(0,6.@,hE&@,@E0,.1:@,l0&14,:1,@E&@,0E.&@:61b

A@E0(,48:0180,&1R,01M:100(:1M,R:48:/F:104,.40,R:BB0(01@,4)lm6F4,B6(,86ll61,@0(l4b,_6(,0;&l/F0C,%,:4,.40R,B6(,/6:1@,F6&R,

E0(0N,:1,AE)4:84,8F&4404C,,:4,86ll61F),.40R,B6(,/6:1@,F6&Rb,o6l0,6FR0(,   ,@0;@4,.40,O,B6(,A6:4461:4,(&@:6C B6(,4@(044C,&1R,,B6(,4@(&:1N,@E0,B6(l.F&4,&(0,@E0,4&l0C,m.@,@E0,F&m0F4,R:BB0(b     

αOE0(l&F,0;/&14:61,860BB:8:01@P_ncPkncγoE0&(,4@(&:1⋯⋯γo/08:B:8,h0:ME@,FmbQ:1buC,FmbQB@bu9Qlu

δkE&1M0,:1,R:l014:61,rF01M@EC,R:&l0@0(C,0@8bt:1bll

ΔkE&1M0⋯⋯

Δ 0&l,R0BF08@:61,:1bll

εo@(&:1⋯⋯

η&

>6:1@,0BB:8:018)II

νA6:4461:4,(&@:6,⋯⋯

ρ-014:@)4F.MQB@buiMQlu

σ96(l&F,r/0(/01R:8.F&(t,4@(044/4:C,i4:DA&

τoE0&(,r/&(&FF0Ft,4@(044,/4:C,i4:DA&

θ21MF0,6B,@h:4@r(&R:&14tr(&R:&14t

' 2(0&:1bfllfC,lf O0(l,:1,@E0,@010(&F,oE0&(,_6(l.F&:1bfllfC,lf  &40,R:l014:61,6B,&,(08@&1MF0:1bll O6(4:61,/(6mF0ly,R:4@&180,B(6l,801@(6:R,@6,6.@0(,4.(B&80 0&l,/(6mF0ly,R:4@&180,B(6l,10.@(&F,&;:4,@6,6.@0(,4.(B&80:1bll -:&l0@0(:1bll O(&14B0(,R:4@&180:1bll  ' P14:R0,&1R,6.@4:R0,R:&l0@0(4,6B,&,/:/0:1bll (?6F0,R:&l0@0(:1bll I8801@(:8:@):1bll )s6.1M:4,l6R.F.4,r&bib&b,l6R.F.4,6B,0F&4@:8:@)t/4:C,i4:DA& _bob_&8@6(,6B,4&B0@)⋯⋯ *oE0&(,l6R.F.4,r&bib&b,l6R.F.4,6B,(:M:R:@)t/4:C,i4:DA& ?0:ME@,R:l014:61,6B,&,(08@&1MF0:1bll _:FF0@,h0FR,@E(6&@:1bll +D6l01@,6B,:10(@:&:1bpllp ,A6F&(,l6l01@,6B,:10(@:&:1bpllp -o@(044,861801@(&@:61,B&8@6(⋯⋯ -IBB08@:U0,F01M@E,B&8@6(,r:1,86F.l1,&1&F)4:4t⋯⋯ _:FF0@,h0FR,F0M:1bll hTh01M@E,r6B,&,@014:61,l0lm0(,6(,&,m0<B@bl O6@&F,h0FR,F01M@E:1b8l D6l01@Fmb⋅B@bC,i:/⋅B@bi9⋅l g

O0(l:16F6M)

  !      9.lm0(,6B,4E0&(,/F&104⋯⋯ .9.lm0(,6B,m6F@4⋯⋯ .9.lm0(,6B,E6F04,:1,@E0,B(&8@.(0,/F&10⋯⋯ _F.:R,/(044.(0/4:C,i4:iA& %A6:1@,F6&RFmbC,i:/i9%I.F0(,8(:@:8&F,m.8iF:1M,F6&RFmbC,i:/i9 %* 6F@,F6&R,W,M(644,@014:F0,B&:F.(0,6B,@E0,/F&@0FmbC,i:/i9 %. 6F@,F6&R,W,10@,@014:F0,B&:F.(0,6B,@E0,/F&@0FmbC,i:/i9 %% 6F@,F6&R,W,m0&(:1M,B&:F.(0,6B,@E0,/F&@0FmbC,i:/i9 % 6F@,F6&R,W,m6F@,4E0&(,B&:F.(0FmbC,i:/i9 %a0FR,F6&R,rF&//0R,/F&@04,F6&R0R,:1,@014:61tFmbC,i:/i9 /O0(l,:1,@E0,@010(&F,oE0&(,_6(l.F&:1bullu e&R:.4,r6B,&,E6F0C,B:FF0@C,6(,M(66U0t:1bll *e&R:.4,6B,M)(&@:61:1bll

0e0&8@:61,B6(80FmbC,i:/i9

0e&R:.4,6B,8.(U&@.(0:1bC,B@bllC,l

o08@:61,l6R.F.4:1bullu OE:8i1044:1bll O6(E.0Fmb⋅B@bC,i:/⋅B@bi9⋅l O0l/0(&@.(0P_Pk

1oE0&(,F6&RFmbC,i:/i9

-:4@(:m.@0R,F6&R,rh0:ME@,/0(,.1:@,F01M@EtFmbQB@bC,i:/QB@bi9Ql

2a0:ME@FmbC,i:/i9

;C,)C,B2;04,:1,@E(00nR:l014:61&F,4/&80y,;,:4,E6(:B61@&FC,),:4,U0(@:8&FC &1R,B,:4,:1@6,@E0,/&M0b⋯⋯

3-:4@&180,&F61M,@E0,;n&;:4:1bC,B@bllC,l

4-:4@&180,&F61M,@E0,)n&;:4C,4.8E,&4,@E0,R:4@&180,B(6l,@E0,

10.@(&F,&;:4,:1,m0&l,/(6mF0l4:1bC,B@bllC,l

4-:4@&180,B(6l,@E0,(0B0(0180,&;:4,@6,@E0,;n;,&;:4,6B,&,

86l/64:@0,4E&/0,Rl6l01@,6B,:10(@:&,/(6mF0l4S:1bll

4O0(l,:1,@E0,@010(&F,oE0&(,_6(l.F&:1bll

5-:4@&180,&F61M,@E0,Bn&;:4:1bC,B@bllC,l

6AF&4@:8,408@:61,l6R.F.4:1bullu

ttt

O0(l:16F6M)

      " #  $  " #  $

2α2F/E&Νν9.

β 0@&ΞξT:

Γγ@&ll&A

οAl:8(61

Δ

δ-0F@&ΠπA:

I

εI/4:F61AρeE6

L

ζL0@&Σσo:Ml&

?ηI@&O

τO&.

Θ

θOE0@&sυT/4:F61

P

ιP6@&ΦϕAE:

KκK&//&T

χkE:

ΛλhTh&lmR&

ΨψA4:

D

μD.ΩωAl0M&

= -0B:1:@:614 !  

2FF6h&mF0,r4@(044C,F6&RC,0@8btbbbbbbbbbbbbbbA0(l:@@0R,B6(,4&B0,R04:M1b,

01R:1M,l6l01@C, bbbbbbbbbbbbbbbbbbbbbbbbD6l01@,:1,&,m0&l,@E&@,:4,F6&R0R,:1,m01R:1M,h:@E,@(&14U0(40,F6&R4b

01R:1M,4@(044C,σbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb2,16(l&F,4@(044,&F61M,@E0,F01M@E,6B,&,m0&l,@E&@,R0U0F6/4,R.0,@6,@(&14U0(40,F6&R:1Mb

.8iF:1Mbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbk6FF&/40,6B,&,F61MC,@E:1,l0lm0(,.1R0(,F61M:@.R:1&F,86l/(044:U0,F6&R:1MC,&@,&,F6&R,

l.8E,F6h0(,@E&1,@E0,F6&R,@E&@,8&.404,):0FR:1M,:1,@014:61b

-014:@)C,ρbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbD&44,R014:@),:4,@E0,l&44,6B,&1,6mM08@,6(,BF.:R,R:U:R0R,m),:@4,U6F.l0b,o00,

  ,01@(),B6(,h0:ME@,R014:@)b

-:4@(:m.@0R,F6&RC,bbbbbbbbbbbbbbbbbbbbbbbbbbb_6(80,&8@:1M,6U0(,&,F01M@E,r4.8E,&4,@E0,h0:ME@,6B,&,m0<,6(,&(0&,r4.8E,&4,&,416h,F6&R

61,&,(66Btb,k6l/&(0,

 b

I8801@(:8:@)C,

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb-:4@&180,m0@h001,@E0,10.@(&F,&;:4,6B,&,/&(@,&1R,@E0,F68&@:61,6B,&1,&//F:0R,/6:1@,F6&Rb

IBB08@:U0,F01M@E,6B,&,86F.l1bbbbbbbbbbbbbbA6(@:61,6B,@E0,F01M@E,6B,&,86F.l1,@E&@,m6h4,F:i0,&,B.FF),/:110R,86F.l1b

IF&4@:8,R0B6(l&@:61bbbbbbbbbbbbbbbbbbbbbbbbbbbbbO0l/6(&(),R0B6(l&@:61N,(0F0&40,@E0,F6&R,&1R,@E0,/&(@,(0@.(14,@6,:@4,6(:M:1&F,4E&/0b,

k6l/&(0,   7  b

IF&4@:8,l6R.F.4C,)bbbbbbbbbbbbbbbbbbbbbbbbbbb2,l0&4.(0,6B,@E0,4@:BB1044,6B,&,l&@0(:&F,r@E0,(04:4@&180,@6,0F&4@:8&FF),R0B6(l:1M,.1R0(,

&,M:U01,F6&Rbt,OE0,4F6/0,6B,@E0,F:10&(,0F&4@:8,/6(@:61,6B,@E0,4@(044n4@(&:1,8.(U0b,2F46,

8&FF0R,8 7 ,6(,7 

   4b

I.F0(,8(:@:8&F,m.8iF:1M,F6&RC,%bbbbbbbOE0,F6&R,&@,hE:8E,&1,:R0&F,I.F0(,86F.l1,h:FF,B&:FC,&44.l:1M,/0(B08@,l&@0(:&F,&1R,

/0(B08@F),&F:M10R,F6&R:1Mb

_&8@6(,6B,o&B0@)C,_bobbbbbbbbbbbbbbbbbbbbbbbbbbbOE0,l&@0(:&F:4,4@(01M@E,r@)/:8&FF),):0FR,4@(01M@Et,R:U:R0R,m),@E0,&8@.&F,4@(044,:1,@E0,

/&(@b,2F46,8&FF0R,UB&8@6(,6B,:M16(&180V,m08&.40,:@,:18F.R04,.1i16h14,4.8E,&4, l&@0(:&F4,R0B08@4C,:l/(6/0(,:14@&FF&@:61C,&m.40,m),@E0,6/0(&@6(C,F&8i,6B,l&:1@01&180C,

86((64:61,6(,(6@C,@0l/0(&@.(0,U&(:&@:614C,0@8b

_:FF0@,h0FRbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb2,h0FR,h:@E,&,@(:&1M.F&(,8(644,408@:61,.40R,B6(,M6:1:1M,F&//0R,/F&@04b,T1F:i0,46FR0(:1M

6(,m(&B:1MC,h0FR:1M,:1U6FU04,l0F@:1M,@E0,m&40,l0@&F,&4,h0FF,&4,@E0,M6:1:1M,l&@0(:&Fb

_(&8@.(0,/F&10bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbP1,&,m6F@0R,M6:1@,@E&@,B&:F4C,B(&8@.(0,688.(4,@E(6.ME,@E0,m6F@,E6F04,6(,@E(6.ME,&,/F&@0,

&h&),B(6l,@E0,m6F@,E6F04bbb@E0,4:@0,6B,B(&8@.(0,:4,8&FF0R,@E0,B(&8@.(0,/F&10b

@010(&F,4E0&(,B6(l.F&bbbbbbbbbbbbbbbbbbbbbbbbIE.&@:61,B6(,B:1R:1M,@E0,4E0&(,4@(044,h:@E:1,&,m0&l,6B,&1),4E&/0b

>6:1@,0BB:8:018)bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbOE0,0BB:8:018),6B,&,m6F@0R,6(,h0FR0R,M6:1@,:4,@E0,F6h04@,&FF6h&mF0,F6&R,R:U:R0R,m),@E0,

&FF6h&mF0,F6&R,6B,@E0,h0&i0(,6B,@E0,@h6,/F&@04,46l0,R:4@&180,B(6l,@E0,M6:1@b

hTh61M:@.R:1&F,R:(08@:61bbbbbbbbbbbbbbbbbbbbbbbb2F61M,@E0,F01M@E,6B,&,/&(@C,4.8E,&4,&,m0&l,6(,4E&B@b,k6l/&(0, 

 b

hTh61M:@.R:1&F,r&;:&Ft,4@(044C,σbbbbbbbbbbb96(l&F,4@(044,@E&@,R0U0F6/4,:1,&,@014:F0,6(,86l/(044:U0,l0lm0(,R.0,@6,&;:&F,F6&R:1Mb

D6R.F.4,6B,0F&4@:8:@)C,)bbbbbbbbbbbbbbbbbbbo00,  7 b

D6l01@C, bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbD6(0,&88.(&@0F),8&FF0R,&,B6(80,l6l01@C,@E0,/(6R.8@,6B,&,F01M@E,&1R,&,@(&14U0(40F),

&//F:0R,B6(80b,T40R,:1,m0&l,/(6mF0l4b,OE0(0,&(0,6@E0(,@)/04,6B,l6l01@,r4.8E,&4,&(0&, l6l01@y,@E0,/(6R.8@,6B,&,F01M@E,&1R,&1,&(0&tb

D6l01@,6B,:10(@:&C,+bbbbbbbbbbbbbbbbbbbbbbbbbD6(0,&88.(&@0F),8&FF0R,U40861R,l6l01@,6B,&(0&Vb,-:U:R0,&,4E&/0,:1@6,,@:1),&(0&4, C,

0&8E,&@,&,R:4@&180,4B(6l,@E0,;n;,801@(6:R&F,&;:4C,&1R,4.l,@E0,&(0&4,&1R,R:4@&1804,&4

+3=∑c  4 fb,OE0,F&(M0(,@E0,l6l01@,6B,:10(@:&C,@E0,M(0&@0(,@E0,m01R:1M,F6&R,&,m0&l,

8&1,4.//6(@C,&1R,@E0,F044,m01R:1M,R0BF08@:61,h:FF,688.(b

96(l&FbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbA0(/01R:8.F&(C,:1,@E0,l&@E0l&@:8&F,40140b

96(l&F,4@(044C,σbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb_6(80,R:U:R0R,m),&(0&C,hE01,@E0,B6(80,&8@4,/0(/01R:8.F&(,@6,@E0,&(0&b,O014:F0,&1R,

86l/(044:U0,4@(04404,&(0,16(l&F,4@(04404b

AF&4@:8,R0B6(l&@:61bbbbbbbbbbbbbbbbbbbbbbbbbbbbbA0(l&101@,R0B6(l&@:61N,(0F0&40,@E0,F6&R,&1R,@E0,/&(@,(0l&:14,R:4@6(@0Rb,k6l/&(0,

   7  b

AF&4@:8,408@:61,l6R.F.4C,6bbbbbbbbbbbbbbbbo.l,6B,@E0,B:(4@,l6l01@4,6B,&(0&4,&m6U0,&1R,m0F6h,@E0,10.@(&F,&;:4,6B,&,4@00F,m0&lb,

T40R,B6(,8&F8.F&@:1M,m01R:1M,4@(04404,:1,4@(.8@.(&F,4@00F,m0&l4b A6:1@,F6&RC,%bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb_6(80,&8@:1M,&@,&,4:1MF0,/6:1@b,k6l/&(0,   b

A6:4461:4,(&@:6C,νbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb2,l08E&1:8&F,/(6/0(@),6B,01M:100(:1M,l&@0(:&F4,0E.&F,@6,@E0,10M&@:U0,6B,@E0,@(&14U0(40

4@(&:1,R:U:R0R,m),F61M:@.R:1&F,4@(&:1b,2,l0&4.(0,6B,E6h,l.8E,&,@014:F0,l0lm0(,h:FF,

@E:1,R.(:1M,0F&4@:8,R0B6(l&@:61b w -0B:1:@:614

A6F&(,l6l01@,6B,:10(@:&C,,bbbbbbbbbbbbbbbbD6(0,&88.(&@0F),8&FF0R,U/6F&(,40861R,l6l01@,6B,&(0&Vb,-:U:R0,&,4E&/0,:1@6,,@:1),

&(0&4, C,0&8E,&@,&,R:4@&180,B(6l,@E0,801@(6:RC,&1R,4.l,@E0,&(0&4,&1R,R:4@&1804,&4 ,=∑c  fb,OE0,F&(M0(,@E0,/6F&(,l6l01@,6B,:10(@:&C,@E0,M(0&@0(,@E0,@6(E.0,&,4E&B@,8&1

4.//6(@C,&1R,@E0,F044,&1M.F&(,@h:4@,h:FF,m0,/(6R.80Rb

A(044.(0,r6B,&,BF.:RtC,bbbbbbbbbbbbbbbbbbbbb_F.:R,0E.:U&F01@,6B,16(l&F,4@(044b,2,/(044.(:B0R,M&4,/(6R.804,&,.1:B6(l,/(044.(0,

/0(/01R:8.F&(,@6,@E0,h&FF4,6B,@E0,/(044.(0,U0440Fb,2,/(044.(:B0R,F:E.:R,/(6R.804,&, .1:B6(l,/(044.(0,:1,&,4l&FF,/(044.(0,U0440FN,@E0,/(044.(0,:4,161.1:B6(l,:1,&,@&FF,U0440F R.0,@6,M(&U:@),rF6h0(,/(044.(0,&@,@E0,@6/C,E:ME0(,&@,@E0,m6@@6ltb

e&R:.4,6B,8.(U&@.(0C,0bbbbbbbbbbbbbbbbbbbbbPB,&,m0&l,40Ml01@,:4,m01@,h:@E,&,8614@&1@,m01R:1M,l6l01@C,@E0,40Ml01@,m086l04,&,

8:(8.F&(,&(8,h:@E,&,(&R:.4,6B,8.(U&@.(0C,0b

e&R:.4,6B,M)(&@:61C,*bbbbbbbbbbbbbbbbbbbbbbk61801@(&@0,&1,&(0&,&@,&,R:4@&180,,B(6l,@E0,;n;,10.@(&F,&;:4b,PB,@E0,l6l01@,6B,:10(@:&,

6B,@E0,6(:M:1&F,&(0&,:4,@E0,4&l0,&4,B6(,@E0,861801@(&@0R,&(0&C,@E01,*3,:4,@E0,(&R:.4,6B,

M)(&@:61,&m6.@,@E0,;n;,&;:4b,OE0,F&(M0(,@E0,(&R:.4,6B,M)(&@:61C,@E0,l6(0,(04:4@&1@,&,

86F.l1,:4,@6,m.8iF:1Mb,k&F8.F&@0,

*=√+/b e0&8@:61,l6l01@C, ,6(, 9bbbbbbbbD6l01@,&@,(0&8@:61,/6:1@,2,6(, ,hE:8E,4.//6(@4,&,@(&14U0(40F),F6&R0R,8&1@:F0U0(, m0&lb e0&8@:61,B6(80C,

0,6(,09bbbbbbbbbbbbbbbb_6(804,&@,(0&8@:61,/6:1@4,2,6(, ,hE:8E,4.//6(@,&,@(&14U0(40F),F6&R0R,m0&lb

o08@:61,l6R.F.4C,bbbbbbbbbbbbbbbbbbbbbbbbbbbD6l01@,6B,:10(@:&,R:U:R0R,m),@E0,R:4@&180,B(6l,@E0,10.@(&F,&;:4,@6,@E0,4.(B&80b,OE0,

F&(M0(,@E0,408@:61,l6R.F.4C,@E0,l6(0,(04:4@&1@,&,m0&l,:4,@6,m01R:1Mb oE0&(,l6R.F.4C,

*bbbbbbbbbbbbbbbbbbbbbbbbbbbbbOE0,4F6/0,6B,@E0,F:10&(,0F&4@:8,/6(@:61,6B,@E0,4E0&(,4@(044,W,4E0&(,4@(&:1,8.(U0b

oE0&(,F6&RC,1bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbO(&14U0(40,F6&R,61,&,m0&lb

oE0&(,/F&10bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbP1,&,m6F@0R,M6:1@,h:@E,@h6,/F&@04,/.FF:1M,:1,6//64:@0,R:(08@:614C,@E0,4E0&(,/F&10,:4,@E0,

@(&14U0(40,/F&10,h:@E:1,&,m6F@,@E&@,F:04,&@,@E0,:1@0(B&80,6B,@E0,@h6,/F&@04b oE0&(,4@(&:1C, γbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbboE0&(,R0BF08@:61,R:U:R0R,m),6(:M:1&F,.1:@,F01M@E

oE0&(,4@(044C,τbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb_6(80,R:U:R0R,&(0&C,hE01,@E0,B6(80,&8@4,/&(&FF0F,@6,@E0,&(0&b

o/08:B:8,h0:ME@C,γbbbbbbbbbbbbbbbbbbbbbbbbbbbbo/08:B:8,h0:ME@C,&bib&b,h0:ME@,R014:@)C,:4,@E0,h0:ME@,6B,&1,6mM08@,6(,BF.:R,R:U:R0R,m),:@4

U6F.l0b,OE0,4)lm6FC,F6h0(,8&40,M&ll&C,:4,&F46,.40R,B6(,4E0&(,4@(&:1b,P1,@E:4,@0;@C, /F&:1,M&ll&,l0&14,4E0&(,4@(&:1C,hE:F0,m6FR,M&ll&,l0&14,4/08:B:8,h0:ME@b,o00,  4,01@(),B6(,l&44,R014:@)b

o@(&:1,r16(l&FtC,εbbbbbbbbbbbbbbbbbbbbbbbbbbbbbkE&1M0,:1,F01M@E,6B,&,l&@0(:&F,.1R0(,16(l&F,F6&R,R:U:R0R,m),:1:@:&F,F01M@Eb

o@(044bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbo00, 7 ' ' '   '    b

o@(044,861801@(&@:61bbbbbbbbbbbbbbbbbbbbbbbbbbbb2,F68&FF),E:ME,4@(044,R.0,@6,&,4E&(/,R:4861@:1.:@),:1,4E&/0C,4.8E,&4,&,E6F0,6(,16@8E,

h:@E,&,4l&FF,(&R:.4b,aE:F0,@E0,6U0(&FF,4@(044,:1,@E0,/&(@,l&),m0,&@,&,4&B0,F0U0FC,@E0,

4@(044,&@,@E0,R:4861@:1.:@),8&1,0;800R,):0FR,6(,.F@:l&@0,4@(01M@EC,8&.4:1M,B&:F.(0b

O014:F0,4@(01M@EC,

σbbbbbbbbbbbbbbbbbbbbbbbD&;:l.l,4@(044,61,@E0,4@(044n4@(&:1,R:&M(&lb, 0)61R,@E:4,/6:1@C,@E0,l&@0(:&F,108i4,

&1R,4661,m(0&i4b

OE0(l&F,0;/&14:61,860BB:8:01@C,αbbbbD&@0(:&F4,/(6/0(@),@E&@,R0@0(l:104,E6h,l.8E,&,l&@0(:&F,0;/&1R4,6(,861@(&8@4,h:@E,

8E&1M:1M,@0l/0(&@.(0b

O6(E.0C,bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbe6@&@:61&F,l6l01@,&//F:0R,@6,&,4E&B@b,T1:@4,6B,l6l01@,&1R,@6(E.0,&(0,@E0,4&l0,rB6(80

W,R:4@&180tb

O6(4:61bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbOh:4@:1M,6B,&,4E&B@,R.0,@6,&1,&//F:0R,@6(E.0b

O6(4:61&F,4@(044C,τbbbbbbbbbbbbbbbbbbbbbbbbbbbb2,4E0&(,4@(044,@E&@,R0U0F6/4,:1,&,4E&B@,R.0,@6,@6(4:61&F,F6&R:1Mb

O(&14B0(,R:4@&180C,bbbbbbbbbbbbbbbbbbbbbbbbbbO0(l,.40R,:1,8&F8.F&@:1M,l6l01@,6B,:10(@:&,6B,&,86l/6.1R,4E&/0b

O(&14U0(40,R:(08@:61bbbbbbbbbbbbbbbbbbbbbbbbbbbA0(/01R:8.F&(,r8(644h:40t,@6,@E0,F01M@E,6B,&,F61M,/&(@C,4.8E,&4,&,m0&l,6(,4E&B@b,

k6l/&(0,      b TF@:l&@0,@014:F0,4@(01M@EC,σbbbbbbbbbo00, b s:0FR,4@(01M@EC,

σ8bbbbbbbbbbbbbbbbbbbbbbbbbbbb 0F6h,@E0,):0FR,4@(01M@EC,&,l&@0(:&F,R0B6(l4,0F&4@:8&FF)N,&m6U0,:@C,@E0,l&@0(:&F,R0B6(l4

/F&4@:8&FF),r.1R0(M604,/0(l&101@,R0B6(l&@:61tb s6.1M:4,l6R.F.4C,)bbbbbbbbbbbbbbbbbbbbbbbbbo00,  7 b cd kE&/@0(,cy,P1@(6R.8@:61,@6,o@(01M@E,6B,D&@0(:&F4    %&         '  (      '  )   ,:4,@E0,4@.R),6B,B6(804, &8@:1M,:1,0E.:F:m(:.l,61,(:M:R, m6R:04b,U 6R:04V,&(0,46F:R,6mM08@4C

F:i0,4@00F,8&mF04C,M0&(,@00@EC,

@:lm0(,m0&l4C,&1R,&;F0,4E&B@4,r16,

F:E.:R4,6(,M&404tN,U(:M:RV,l0&14,

@E0,m6R:04,R6,16@,4@(0@8EC,m01RC,6( @h:4@N,&1R,U0E.:F:m(:.lV,l0&14, @E0,(:M:R,m6R:04,&(0,16@, &880F0(&@:1Mb,D64@,/(6mF0l4,:1,&, o@&@:84,@0;@m66i,&F46,&44.l0,@E0, (:M:R,m6R:04,&(0,4@&@:61&()b,OE040, &44.l/@:614,R6,16@,l&@8E,(0&F:@), /0(B08@F)C,m.@,@E0),l&i0,@E0,l&@E, l.8E,0&4:0(b,OE:4,l6R0F,:4,8F640,

016.ME,@6,(0&F:@),@6,m0,.40B.F,B6(,

l&1),/(&8@:8&F,/(6mF0l4b

P1,

  C,h0,i00/, @E0,&44.l/@:614,6B,m6R:04,:1,

0E.:F:m(:.lC,m.@,h0,R(6/,@E0,

U(:M:RV,&44.l/@:61b,e0&F,8&mF04,

4@(0@8E,.1R0(,@014:61C,(0&F,BF66(,

M6:4@4,m01R,hE01,)6.,h&Fi,&8(644,

&,h66R,BF66(C,&1R,(0&F,&;F0,4E&B@4, @h:4@,.1R0(,@6(4:61&F,F6&Rb    ,:4,&,R:BB:8.F@

86.(40,m08&.40,@E0,@6/:84,&(0,

8.l.F&@:U0,&1R,E:MEF),

:1@0(861108@0Rb,PB,)6.,l:44,&1,

0&(F),@6/:8C,)6.,h:FF,16@,

.1R0(4@&1R,F&@0(,@6/:84b,OE:4,@&mF0,

F:4@4,

  ,@6/:84C, &1R,:1R:8&@04,hE:8E,8E&/@0(4,.40,

0&8E,@6/:8bkE&/@0(,1.lm0(

cfupvgttt=wcdcccfcucpcv

2FM0m(&,D,46l0,@(:M616l0@()XXXXXXXXXXXXXXX

_&8@6(nF&m0F,l0@E6R,6B,.1:@,861U0(4:61XXXXXXXXXXXXXXX

96(l&F,4@(044XXXXXXXXXX

96(l&F,4@(&:1XXX

s:0FR,4@(01M@EXXXXX

O014:F0,4@(01M@EXXX

oE0&(,4@(044XXXXXX oE0&(,4@(&:1XX s6.1M:4,l6R.F.4XXXXXX

2;:&F,R0BF08@:61XX

A6:4461:4,(&@:6X

O(&14U0(40,4@(&:1X

O(&14U0(40,R0BF08@:61XXXX

o@(&:1,R.0,@6,l.F@:&;:&F,F6&R4X

OE0(l&F,0;/&14:61X

OE0(l&F,4@(044X

A(044.(0,U0440F4XX

o@(044,861801@(&@:61XX >6:1@,0BB:8:018)XX 6F@0R,M6:1@4X a0FR0R,M6:1@4X

D6l01@,6B,:10(@:&,6B,&,4:l/F0,4E&/0XXXXXXX

D6l01@,6B,:10(@:&,6B,&,86l/6.1R,4E&/0XX

A6F&(,l6l01@,6B,:10(@:&XX

e&R:.4,6B,M)(&@:61XX

O6(E.0XX

oE0&(,l6R.F.4X 0&l,(0&8@:614XXXXX oE0&(,R:&M(&l4XXXXX

D6l01@,R:&M(&l4XXXXX

-0BF08@:61,R:&M(&l4X o08@:61,l6R.F.4XXXX

AF&4@:8,408@:61,l6R.F.4XXX

P1@0(/6F&@:61,Q,o:l:F&(,@(:&1MF04XXXXX

k6lm:10R,4@(04404X

I8801@(:8,F6&R:1MX

o@&@:8&FF),:1R0@0(l:1&@0,m0&l4X k6F.l1,m.8iF:1MX

D6E(:4,8:(8F0X

PB,)6.,h&1@,@6,m0,4.88044B.F,:1,&,

  ,86.(40C,)6.,100R,@E0,B6FF6h:1My

•*     b,o6FU0,0U0(),/(6mF0l,l0@E6R:8&FF)b,D&i0,)6.(,4@0/nm)n4@0/,46F.@:61,0&4),B6(,@E0,(0&R0(,r@E0,M(&R0(t,

@6,.1R0(4@&1RC,h:@E,@E0,B:1&F,46F.@:61,&@,@E0,m6@@6lb •*,o6FU0,0U0(),/(6mF0l,&FM0m(&:8&FF),m0B6(0,:1@(6R.8:1M,1.lm0(4,&1R,.1:@4b •     b,T40,@E0,         C,@E0,4@&1R&(R,:1,I1M:100(:1M,&1R,kE0l:4@()b,OE0,

861U01@:61,:1,AE)4:84,:4,@6,861U0(@,0U0()@E:1M,:1@6,oP,.1:@4C,/F.M,1.lm0(4,:1@6,@E0,0E.&@:61C,&1R,E6/0,@E0,.1:@4,86l0,6.@

AKb,P1,01M:100(:1M,&1R,8E0l:4@()C,h0,:1@(6R.80,@E0,&8@.&F,.1:@4,:1@6,@E0,0E.&@:61C,&1R,&RR,@E0,.1:@,861U0(4:614,&@,@E0,

01R,6B,@E0,0E.&@:61b,OE0,(0&461,:4,@E&@,(0&F,6mM08@4,&(0,R:l014:610R,:1,l6(0,@E&1,610,.1:@b,_6(,0;&l/F0C,:1,@E0,TbobC,4@00F

m0&l,F01M@E4,&(0,:1,B00@C,R0/@E4,&(0,:1,:18E04N,:1,k&1&R&C,4@00F,m0&l,F01M@E4,&(0,:1,l0@0(4C,R0/@E4,&(0,:1,l:FF:l0@0(4b,

s6.,l:ME@,m0,&mF0,@6,861U0(@,:18E04,@6,B00@,:1,)6.(,E0&RC,m.@,:@,:4,0&4),@6,l&i0,l:4@&i04,hE01,@E0,.1:@,:4,0;/6101@:&F,

r861U0(@:1M,:1bu,@6,B@bu,6(,llp,@6,lptC,46,.40,@E0,     ,&1R,&U6:R,4:l/F0,l:4@&i04b cc kE&/@0(,cy,P1@(6R.8@:61,@6,o@(01M@E,6B,D&@0(:&F4 •   (   b,PB,)6.,86/),46l0610,0F40Y4,E6l0h6(i,46F.@:614,:14@0&R,6B,h6(i:1M,@E0l,6.@C,)6.,h:FF,B&:F,@E0,

0;&l4C,&1R,)6.,h:FF,E&U0,@6,(0/0&@,@E0,86.(40b,OE0,61F),h&),@6,F0&(1,@E:4,l&@0(:&F,:4,m),/(&8@:8:1Mb,_6(,0U0(),E6.(,6B,

8F&44,@:l0C,0;/08@,@6,4/01R,&@,F0&4@,@E(00,E6.(4,R6:1M,E6l0h6(ib,2,M66R,04@:l&@0,:4,cdI,6B,@E0,F0&(1:1M,688.(4,:1,@E0,

8F&44(66lN,wdI,6B,@E0,F0&(1:1M,688.(4,hE:F0,)6.,&(0,46FU:1M,@E0,/(6mF0l4b,o@&(@,@E0,E6l0h6(i,@E0,4&l0,R&),&4,8F&44,

rhE:F0,)6.(,l0l6(),:4,B(04EtC,h6(i,h:@E,6@E0(,4@.R01@4,:1,4@.R),M(6./4C,M6,@6,@E0,/(6B0446(Y4,6BB:80,E6.(4,:B,)6.,R6,16@,

.1R0(4@&1R,46l0@E:1MC,&1R,@.(1,:1,0U0(),E6l0h6(i,&44:M1l01@,61,@:l0b

• b,P@,86l04,:1,F:ME@,M(001,6(,F:ME@,)0FF6hC,h:@E,&,M(:R,/(:1@0R,61,@E0,m&8ib,a(:@0,61,@E0,B(61@,61F)N,@E0,

/(:1@0R,M(:R,61,@E0,m&8i,4:R0,E0F/4,)6.,&F:M1,M(&/E:84,&1R,@0;@b,a:@E,I1M:100(:1M,A&/0(C,)6.,8&1,4i0@8E,m0&l,/(6mF0l4,

@6,48&F0b,OE0,M(&/E:8&F,(04.F@,h:FF,@0FF,)6.,:B,@E0,8&F8.F&@0R,1.lm0(4,&(0,:1,@E0,m&FF/&(ib   

,:4,610,6B,@E0,l64@,.40B.F,86.(404,:1,&1,I1M:100(:1M,O08E16F6M),0R.8&@:61b,P@,:4,@E0,B6.1R&@:61,B6(,

&RU&180R,o@(.8@.(04,86.(404,:1,k614@(.8@:61,I1M:100(:1M,O08E16F6M)C,&1R,@E0,B6.1R&@:61,B6(,D&8E:10,IF0l01@4,:1,

D08E&1:8&F,I1M:100(:1M,O08E16F6M)b

  + ," '          

P1,I1M:100(:1M,R:48:/F:104C,h0,.40,@E0,@E(00n4@0/,_&8@6(nhTh&m0F,D0@E6R,6B,T1:@,k61U0(4:61,@6,46FU0,&FM0m(&:8,/(6mF0l4,h:@E,

l:;0R,.1:@4b,   %,a(:@0,@E0,&FM0m(&:8,0E.&@:61,46,@E0,R04:(0R,E.&1@:@),:4,61,@E0,F0B@,6B, @E0,0E.&F4,4:M1C,&1R,&1,&FM0m(&:8,0;/(044:61,:4,61,@E0,(:ME@,6B,@E0,0E.&F4,4:M1b   -,-(&h,&,E6(:B61@&F,F:10,61,@E0,/&M0C,&1R,01@0(,1.lm0(4,&1R,.1:@4, &m6U0,&1R,m0F6h,@E0,F:10,&886(R:1M,@6,@E0,&FM0m(&:8,0;/(044:61b   .,-(&h,&,U0(@:8&F,F:10,@6,4E6h,@E0,40/&(&@:61,m0@h001,0&8E,.1:@,

861U0(4:61C,&1R,01@0(,&FF,.1:@,861U0(4:614,108044&(),@6,46FU0,@E0,/(6mF0lb,PB,

@E0,.1:@,:4,(&:40R,@6,&,/6h0(C,@E01,@E0,861U0(4:61,B&8@6(,and,.1:@,l.4@,m0, (&:40R,@6,@E&@,/6h0(b,k614:R0(,l0l6(:B:1M,@E0,l64@,86ll61,861U0(4:61, B&8@6(4C,F:i0,@E0,6104,&@,@E0,(:ME@b,o00,Appendix A,B6(,l6(0,.1:@,861U0(4:614 &1R,l0@(:8,/(0B:;04C,&1R,Appendix B,B6(,l&@0(:&F4,/(6/0(@:04,4.8E,&4, @E0(l&F,0;/&14:61,860BB:8:01@,&1R,s6.1M:4,l6R.F.4b,O&mF0, c,M:U04,@E040, /(6/0(@:04,:1,Tbob,k.4@6l&(),.1:@4C,hE:F0,O&mF0, f,M:U04,@E0l,:1,obPb,.1:@4b OE0,.1:@4,:1,@E0,B:1&F,&14h0(,must,&//0&(,:1,@E0,0E.&@:61C,and,&FF,6@E0(,.1:@4 l.4@,8&180FbcB@b=cf:1b cl=cdd8l=cdull ci:/=cduFmb cA&=c9/lf c9=ciM⋅l/4fD0@(:8,/(0B:;04 l:FF:n(l)=cd-u

801@:n(8)=cd-f

i:F6n(i)=cdu

D0M&n(D)=cdg

@:M&n(@)=cdw !"

OE0,&(0&,6B,&,(08@&1MF0,:4,

=⋅b,@:U01,&,m&40,==u:1b,&1R,&,E0:ME@,=pvB@bC,8&F8.F&@0,@E0,&(0&,:1

4E.&(0,B00@b

  %,OE0,&FM0m(&:8,0E.&@:61,R604,16@,100R,@6,m0,l&1:/.F&@0Rb   -,-(&h,&,E6(:B61@&F,F:10b,I1@0(,=u,:1b,&1R,pv,B@b,:1,@E0,

1.l0(&@6(b

=⋅==u:1b⋅pvB@b  .,a0,h&1@,@6,0F:l:1&@0,:18E04,@6,6m@&:1,&,B:1&F,(04.F@,:1

4E.&(0,B00@b,OE0(0B6(0C,/.@,cf,:18E04,:1,@E0,R016l:1&@6(,6B,

@E0,.1:@,861U0(4:61C,&1R,c,B@b,:1,@E0,1.l0(&@6(b=⋅==u:1b⋅pvB@b ∣B@b cf:1b=uccbfvB@bf cf kE&/@0(,cy,P1@(6R.8@:61,@6,o@(01M@E,6B,D&@0(:&F4  !# o@(044,:4,B6(80,R:U:R0R,m),&(0&b,PB,@E0,4@(044,:4,c,9QllfC,hE&@,:4,@E0,4@(044,:1,DA&z   %,OE0(0,:4,16,&FM0m(&,@6,46FU0,E0(0,m08&.40,h0,&(0,861U0(@:1M,610,.1:@,@6,&16@E0(b   -,-(&h,&,E6(:B61@&F,F:10b,I1@0(,c,9,:1,@E0,1.l0(&@6(C, &1R,llf,:1,@E0,R016l:1&@6(b,c9 llf   .,2,/&48&F,:4,R0B:10R,&4,A&Z9QlfC,46,01@0(,A&,:1,@E0,

1.l0(&@6(b,P14@0&R,6B,h(:@:1M,:1,9Qlf,@E0,R016l:1&@6(C,/.@,

9,:1,@E0,R016l:1&@6(,&1R,lf,:1,@E0,1.l0(&@6(bc9

llf∣A&lf

996h,01@0(,@E0,.1:@,861U0(4:614,@6,0F:l:1&@0,@E0,@h6,&(0&,

@0(l4y,lf,&1R,llfb,OE0(0,&(0,cdu,ll,:1,&,l0@0(C,46,.40, /&(01@E0404,@6,4E.&(0,@E0,1.lm0(,&1R,@E0,.1:@b c9 llf∣A&lf

9∣(cdull)f

lf_:1&FF)C,cDA&ZcdgA&b,A.@,DA&,:1,@E0,1.l0(&@6(,&1R,cdg,A&, :1,@E0,R016l:1&@6(b,PB,)6.,h(:@0,@E0,0E.&@:61,h:@E6.@,,

1.lm0(4C,:@,F66i4,F:i0,

9 llf∣A&lf

9∣llf

lf∣DA&

A&b,k(644,6.@

R./F:8&@0,@0(l4C,&1R,&FF,@0(l4,8&180F,0;80/@,B6(,DA&b,PB,)6., h(:@0,@E0,0E.&@:61,h:@E6.@,.1:@4C,:@,F66i4,F:i0, c ∣(cdu)f ∣cdgbc9 llf ∣A&lf

9∣(cdull)f

lf∣DA& cdgA& 9 llf∣A&lf

9∣(ll)f

lf∣DA& A&o6FU:1M,@E0,0E.&@:61,h:@E,1.lm0(4,&1R,.1:@4C,h0,M0@ c9/llf=cDA&b,OE:4,:4,&,.40B.F,861U0(4:61,B&8@6(,:1,oP,    ,/(6mF0l4bc9 llf∣A&lf

9∣(cdull)f

lf∣DA& cdgA&=cDA& !$ -0BF08@:61,R.0,@6,@E0(l&F,0;/&14:61,:4δ=α⋅⋅Δb,OE0,.//0(n8&40,@(00i,F0@@0(, R0F@&,l0&14,U8E&1M0VC,46,Δ,l0&14,U8E&1M0,:1,@0l/0(&@.(0bV,@:U01,&,R0BF08@:61 δ=dbdg:1bC,&,F01M@E,==B@bC,&1R,&,@E0(l&F,0;/&14:61,860BB:8:01@ α=v×cd-g:1b/:1bP_C,8&F8.F&@0,@E0,8E&1M0,:1,@0l/0(&@.(0,:1,R0M(004,_&E(01E0:@b   %,e0h(:@0,@E0,0E.&@:61,&FM0m(&:8&FF),@6,46FU0,B6(,[bδ=α⋅⋅Δ,\,

Δ=δ

α  -,-(&h,&,E6(:B61@&F,F:10b,I1@0(,dbdg,:1b,:1,@E0,

1.l0(&@6(b,o:180,@E0,.1:@4,B6(,],&(0,&,B(&8@:61C,01@0(

v×cdg:1b,:1,@E0,R016l:1&@6(,&1R,:1bP_,:1,@E0,1.l0(&@6(b,

I1@0(,=,B@b,:1,@E0,R016l:1&@6(b

Δ=dbdg:1b:1bP_

v×cd-g:1b=B@b  .,k61U0(@,B00@,@6,cf,:18E04,46,@E0,F01M@E,.1:@4,@6,

8&180FC,&1R,@E0,(04.F@,:4,:1,P_bΔ=dbdg:1bP_

v×cd-g=B@b ∣B@ cf:1b=cfv:_ cu# ^ $ kE&/@0(,cy,P1@(6R.8@:61,@6,o@(01M@E,6B,D&@0(:&F4  !% o@(044,:4,B6(80,R:U:R0R,m),&(0&yσ=% b,@:U01,&,B6(80,%,Z,tttddd,Fmb,&8@:1M,61,&1,&(0&,,Z,u,B@bfC,8&F8.F&@0,@E0,4@(044,:1,.1:@4,

6B,/6.1R4,/0(,4E.&(0,:18E,r/4:tb

  %,OE0,0E.&@:61,R604,16@,100R,@6,m0,l&1:/.F&@0Rb   -,-(&h,&,E6(:B61@&F,F:10b,I1@0(,tttddd,Fmb,:1,@E0,

1.l0(&@6(C,&1R,u,B@bf,:1,@E0,R016l:1&@6(b

σ=%

=tttdddFmb uB@bf  .,OE0,4@(044,:4,:1,.1:@4,6B,/6.1R4,/0(,4E.&(0,B66@b,OE0(0 &(0,cf,:18E04,:1,&,B66@C,m.@,h0,100R,@6,861U0(@,4E.&(0,B00@C,

46,4E.&(0,@E0,1.lm0(,&1R,@E0,.1:@y,(cf:1b)fb,oE.&(0,B00@,

8&180FC,&1R,@E0,&14h0(,:4,:1,/6.1R4,/0(,4E.&(0,:18EC,&F46,

h(:@@01,/4:b

σ=%

=tttdddFmb uB@bf∣B@bf (cf:1b)f=cgbfFmb :1bf=cgbf/4: !&

2,@014:F0,m&(,4@(0@8E04,&1,&l6.1@,δ=%⋅

⋅),hE0(0,%,:4,@E0,&//F:0R,F6&RC,,:4,@E0,F01M@E,6B,@E0,m&(C,,:4

@E0,8(644n408@:61&F,&(0&C,&1R,),:4,s6.1MY4,D6R.F.4b,OE0,m&(,E&4,&,8:(8.F&(,8(644,408@:61b,@:U01,&,F6&R,6B

ud,i9C,&,F01M@E,6B,=d,8lC,&,R:&l0@0(,6B,g,llC,&1R,&,s6.1MY4,D6R.F.4,6B,fdttt,@A&C,8&F8.F&@0,@E0

R0BF08@:61,:1,llb

  %,P1,l&@E,8F&44C,@E0,&(0&,6B,&,8:(8F0,:4,M:U01,m) =πfb,P1,(0&F,F:B0C,h0,l0&4.(0,R:&l0@0(,.4:1M,8&F:/0(4N,:@ :4,l.8E,0&4:0(,@6,l0&4.(0,&,R:&l0@0(,@E&1,&,(&R:.4,61,l64@,

6mM08@4b,k61U0(@,(&R:.4,@6,R:&l0@0(C,&1R,@E0,&(0&,0E.&@:61,

m086l04,l6(0,.40B.Fb,OE:4,:4,&,M66R,0E.&@:61,@6,l0l6(:B0b=πf=π( f) f =πf p=π pfk6lm:10,@E0,@h6,0E.&@:614,@6,6m@&:1,&,4:1MF0,&FM0m(&:8,

0E.&@:61bδ=%⋅

⋅)=p%

πf)

  -,-(&h,&,E6(:B61@&F,F:10,&1R,01@0(,@E0,1.lm0(4,&1R, .1:@4bδ=p⋅udi9⋅=d8l

π(gll)ffdttt@A&

  .,OE0,oP,.1:@,6B,4@(044,6(,/(044.(0,:4,@E0,/&48&FC,hE0(0 A&=9 lfC,46,@A&=cdw9 lfb,o:180,ci9=cdu9C,h0,8&1, h(:@0,@A&=cdgi9 lfb,OE(00,861U0(4:61,B&8@6(4,&(0,100R0Ry,

610,@6,8&180F,@A&,&1R,i9N,&,40861R,@6,8&180F,llf,&1R,lfN,

&1R,&,@E:(R,@6,/.@,@E0,B:1&F,&14h0(,:1,llb

δ=p⋅udi9⋅=d8l

π(gll)ffdttt@A&∣@A&lf

cdgi9∣(cdull)f lf∣cdll 8l =pbcllcp% % kE&/@0(,cy,P1@(6R.8@:61,@6,o@(01M@E,6B,D&@0(:&F4  !'

OE0,h0:ME@,6B,&,46F:R,6mM08@,:4,@E0,4/08:B:8,h0:ME@,6B,@E0,l&@0(:&F,@:l04,@E0,U6F.l0,6B,@E0,6mM08@y,2=γ1b,OE0,U6F.l0,6B

&,(6RC,/:/0C,6(,m&(,:4,@E0,8(644n408@:61&F,&(0&,@:l04,@E0,F01M@Ey,

1=b,k&F8.F&@0,@E0,h0:ME@,6B,&,f,:18E,R:&l0@0(C,u,B66@,

F61M,m&(,6B,4@00Fb,_(6l,2//01R:;, C,@E0,4/08:B:8,h0:ME@,6B,4@00F,:4,dbf=p,FmbQ:1bu,

  %,k6lm:10,@E0,@h6,0E.&@:614,@6,46FU0,B6(,h0:ME@y,2=γb,o:180,@E0,(6R,:4,(6.1RC,@E0,8(644n408@:61&F,&(0&,:4

=π pf

C,@E0(0B6(0,2=γπf

p   -,-(&h,&,E6(:B61@&F,F:10,&1R,01@0(,@E0,1.lm0(4,&1R, .1:@4b2=γπf p=dbf=pFmb :1buπ(f:1b)fuB@b p   .,OE0,61F),.1:@,861U0(4:61,:4,B00@,@6,:18E04b2=γπf p=dbf=pFmb :1buπ(f:1b)fuB@b p ∣cf:1b

B@b=ufbcFmb

 !(

k&F8.F&@0,@E0,h0:ME@,6B,&,v,8l,R:&l0@0(C,f,l0@0(,F61M,m&(,6B,4@00Fb,_(6l,2//01R:;, C,@E0,R014:@),6B,4@00F,:4,tttb=v,MQ8lu,

  %,T40,2=γπf p,B(6l,I;&l/F0,_gb,o/08:B:8,h0:ME@,:4,R014:@),@:l04,M(&U:@)y,γ=ρC,46,

2=ρπf

pb   -,-(&h,&,E6(:B61@&F,F:10,&1R,01@0(,@E0,1.lm0(4,&1R, .1:@4b2=ρπf p=tttb=vM

8luwb=cl

4fπ(v8l)ffl

p   .,OE0,oP,.1:@,6B,h0:ME@,:4,@E0,10h@61y,

9=iM,l

4fb

96@:80,@E0,.1:@,UMV,B6(,M(&l4,&1R,@E0,@0(l,UV,B6(,

M(&U:@)b,P1,48:0180,&1R,01M:100(:1MC,h0,@01R,@6,.40,(6l&1 @)/0,B6(,.1:@4C,&1R,   4,B6(,U&(:&mF04b,216@E0(,

0;&l/F0,:4,&,mF68i,4F:R:1M,61,&1,:18F:10R,/F&10C,hE0(0,U9V

4@&1R4,B6(,10h@614,&1R,U.V,4@&1R4,B6(,16(l&F,B6(80b2=tttb=vM

8luwb=cl

4fπ(v8l)ffl

p∣iM cduM∣cdd8l l∣9,,4f iM,l=udf9  !)

2,vd,ll,@E:8i,h66R,m6&(R,:4,/F&10R,@6,&,@E:8i1044,6B,u=,llb,k&F8.F&@0,E6h,l.8E,l&@0(:&F,h&4,(0l6U0RC,:1,/0(801@b

k&F8.F&@0,@E0,/0(801@,8E&1M0,m),4.m@(&8@:1M,@E0,:1:@:&F,U&F.0,B(6l,@E0,B:1&F,U&F.0C,@E01,R:U:R:1M,m),@E0,:1:@:&F,U&F.0b,OE:4,

l0@E6R,h6(i4,hE0@E0(,)6.,&(0,8&F8.F&@:1M,@E:8i1044,8E&1M0C,h0:ME@,8E&1M0C,/(:80,8E&1M0C,6(,&1),6@E0(,i:1R,6B,8E&1M0b,

OE0,h6(R,U/0(801@V,l0&14,U/0(,E.1R(0RVC,46,&,(04.F@,6B,dbug,:4,ugIb  -  =u=ll-vdll vdll=-dbfp,6(,-fpI,OE0,l:1.4,4:M1,l0&14,@E0,U&F.0,R08(0&40Rb cv kE&/@0(,cy,P1@(6R.8@:61,@6,o@(01M@E,6B,D&@0(:&F4  !* Oh6,/:0804,6B,8&(m61,B:m0(,86l/64:@0,&(0,MF.0R,@6M0@E0(,&4,&,F&/,M6:1@b,oE0&(,4@(044,:4,τ=% b,PB,@E0,MF.0,E&4,&,4E0&(,

4@(01M@E,6B,cbf,i4:,&1R,@E0,M6:1@,:4,F6&R0R,h:@E,&,4E0&(,F6&R,%=ctttddFmbC,E6h,l.8E,MF.0R,4.(B&80,&(0&,:4,(0E.:(0R,B6(,&,

M66R,m61Rz

o6FU0,&FM0m(&:8&FF)C,&1R,4/F:@,i4:,:1@6,i:/4 :1bfb,,o.(B&80,&(0&,=%

τ=ctttddFmb:1bf

cbfi:/4 ∣i:/ cdddFmb=cbpf:1bf cg kE&/@0(,fy,o@(044,&1R,o@(&:1    -&      $       OE0,h6(R4,U4@(044V,&1R,U4@(&:1V,&(0,.40R,:1@0(8E&1M0&mF),:1,/6/.F&(,8.F@.(0,:1,& /4)8E6F6M:8&F,40140y,UPYl,B00F:1M,4@(0440RV,6(,UPYl,.1R0(,&,F6@,6B,4@(&:1bV,P1,01M:100(:1MC @E040,h6(R4,E&U0,4/08:B:8C,@08E1:8&F,l0&1:1M4b,PB,)6.,@:0,&,4@00F,h:(0,@6,&,E66i,:1,@E0

80:F:1M,&1R,E&1M,&,h0:ME@,61,@E0,F6h0(,01RC,@E0,h:(0,h:FF,4@(0@8Eb,-:U:R0,@E0,8E&1M0,:1

F01M@E,m),@E0,6(:M:1&F,F01M@EC,&1R,)6.,E&U0,@E0,4@(&:1,:1,@E0,h:(0b,-:U:R0,@E0,h0:ME@ E&1M:1M,B(6l,@E0,h:(0,m),@E0,h:(0Y4,8(644,408@:61&F,&(0&C,&1R,)6.,E&U0,@E0,@014:F0,4@(044 :1,@E0,h:(0b,o@(044,&1R,4@(&:1,&(0,(&@:64b OE0,4)lm6F,B6(,@014:F0,4@(044,:4,FC,@E0,F6h0(,8&40,@(00i,F0@@0(,4:Ml&b,PB,@E0,h0:ME@,:4,fv Fmb,&1R,@E0,8(644n408@:61&F,&(0&,6B,@E0,h:(0,:4,dbddf,:1bfC,@E01,@E0,4@(044,:1,@E0,h:(0,:4

σ=2

=fvFmb dbddf:1bf=cfCtttddFmb :1bf=cfCtttdd/4:b

OE0,4)lm6F,B6(,4@(&:1,:4,HC,@E0,F6h0(,8&40,@(00i,F0@@0(,0/4:F61b,PB,@E0,6(:M:1&F,F01M@E,6B,@E0,h:(0,=pd:1b,&1R,@E0,8E&1M0,:1

F01M@E,Δ=dbdcttt:1b,r&F46,h(:@@01,δ=dbdcttt:1btC,@E01,4@(&:1,ε=Δ =δ =dbdcttt:1b pd:1b=dbdddpfvb,OE:4,:4,&,4l&FF,1.lm0(C,

46,46l0@:l04,@E0,4@(&:1,1.lm0(,:4,l.F@:/F:0R,m),cdd,&1R,&1R,(0/6(@0R,&4,&,/0(801@y,

dbdddpfv=dbdpfvIb,s6.,l&),&F46,

400,4@(&:1,(0/6(@0R,:1,l:8(64@(&:1y,dbdddpfv×cdg=pfvl:8(64@(&:1b,o@(&:1,:4,.4.&FF),(0/6(@0R,&4,&,/0(801@,B6(,E:MEF),0F&4@:8

l&@0(:&F4,F:i0,(.mm0(b  !"

2,g,:18E,F61M,86//0(,h:(0,:4,4@(0@8E0R,@6,&,@6@&F,F01M@E,6B,gbdv,:18E04b,aE&@,:4,@E0,4@(&:1z

   ,OE0,8E&1M0,:1,&1)@E:1M,:4,@E0,B:1&F,R:l014:61,l:1.4,@E0,:1:@:&F,R:l014:61b,?0(0C,@E0,8E&1M0,:1,F01M@E,:4,@E0,B:1&F,

F01M@E,l:1.4,@E0,:1:@:&F,F01M@Ey,Δ=

- =gbdv:1b-gbd:1b=dbdv:1bb,o@(&:1,:4,ε=Δ =dbdv:1b gbd:1b=dbdd=ub,

PB,h0,E&1M,&,m.8i0@,B(6l,@E0,h:(0,&1R,M(&R.&FF),B:FF,@E0,m.8i0@,h:@E,h&@0(C,@E0,h0:ME@,h:FF,M(&R.&FF),:18(0&40,&F61M,h:@E,@E0

4@(044,&1R,@E0,4@(&:1,:1,@E0,h:(0C,.1@:F,B:1&FF),@E0,h:(0,m(0&i4b,a0,8&1,/F6@,@E0,4@(044,U4b,4@(&:1,61,&1,;n),48&@@0(,M(&/EC,&1R,

@E0,(04.F@,h:FF,F66i,F:i0,@E:4y

OE:4,M(&/E,4E6h4,@E0,4@(044n4@(&:1,m0E&U:6(,6B,&,F6hn8&(m61,4@00Fb,o@(044,:4,:1,.1:@4,6B,i4:C,6(,i:/4,/0(,4E.&(0,:18EC,hE0(0

ci:/=cduFmb,rc,i:F6/6.1Rtb,OE0,/6:1@4,@6,@E0,F0B@,6B,@E0,(0R,R&4E0R,F:10,&(0,46,8F640,@6M0@E0(,@E&@,@E0),4l0&(,:1@6,&,F:10b,

OE:4,4@(&:ME@,/&(@,6B,@E0,4@(044n4@(&:1,8.(U0,:4,@E0,0F&4@:8,/6(@:61,6B,@E0,8.(U0b,PB,)6.,B:FF,@E0,m.8i0@,h:@E,61F),016.ME,h&@0(,@6

cttt [,6(^ a dbdddbdfdbdpdbdgdbd=dbcddbcfdbcpdbcgdbc=dbfddcdfdudpdvdgdtttd o@(&:1o@(044 ri4:t kE&/@0(,fy,o@(044,&1R,o@(&:1

4@(0@8E,@E0,h:(0,:1,@E0,0F&4@:8,B610C,@E01,@E0,h:(0,h:FF,(0@.(1,@6,:@4,6(:M:1&F,F01M@E,hE01,)6.,0l/@),@E0,m.8i0@b

a0,8&1,8E&1M0,@E0,(&1M0,6B,@E0,4@(&:1,&;:4,B(6l,dbdndbf,@6,dbdddndbddfC,@6,4E6h,@E0,0F&4@:8,R&@&,61F)y

OE:4,M(&/E,4E6h4,@E0,F0B@l64@,cI,6B,@E0,/(0U:6.4,M(&/Eb,OE0,R&4E0R,(0R,F:10,:4,:1,@E0,4&l0,/64:@:61,61,m6@E,M(&/E4b,96h,

@E0,:1R:U:R.&F,R&@&,/6:1@4,&(0,U:4:mF0C,&1R,@E0,8.(U0,:4,&Fl64@,/0(B08@F),4@(&:ME@,./,@6,&,4@(&:1,6B,&m6.@,dbddc=b,OE0,4@(&:ME@,

F:10,E&4,&,4F6/0C,8&FF0R,s6.1MY4,D6R.F.4Cf,6(,IF&4@:8,D6R.F.4C,)b,OE0,4F6/0,6B,&,4@(&:ME@,F:10,:4,@E0,(:40,6U0(,(.1C,46,h:@E:1,

@E:4,0F&4@:8,B610C,)=σ εb,o:180,4@(&:1,:4,.1:@F044C,s6.1MY4,l6R.F.4,E&4,@E0,4&l0,.1:@4,&4,4@(044b,s6.1MY4,l6R.F.4,:4,&, l08E&1:8&F,/(6/0(@),6B,@E0,l&@0(:&F,m0:1M,@04@0Ry, ud×cdg/4:6(,fdttt,@A&,B6(,4@00F4C,cd×cdg/4:,6(,tttd,@A&,B6(,&F.l:1.l, &FF6)4b,o00,Appendix B,B6(,l&@0(:&F4,/(6/0(@:04,6B,6@E0(,l&@0(:&F4b  !# aE&@,@014:F0,4@(044,:4,(0E.:(0R,@6,/(6R.80,&,4@(&:1,6B,=Wcdnv,:1,&F.l:1.lz,e0/6(@,@E0,&14h0(,:1,DA&b    ,2F.l:1.l,E&4,&,s6.1MY4,l6R.F.4,6B,),Z,tttd,@A&b,e0h(:@0, )=σεC,46FU:1M,B6(,4@(044y

σ=)ε==×cd-v⋅tttd@A&

∣cduDA& @A&=vbgDA& OE:4,8&(@661,6B,&,4@(044n4@(&:1,8.(U0,:FF.4@(&@04,@E0,  ,&1R   ,B6104b,PB,)6.,E&1M,&,F:ME@,h0:ME@,@6,@E0,h:(0,E&1M:1M, B(6l,@E0,80:F:1MC,@E0,h:(0,4@(0@8E04,0F&4@:8&FF)N,(0l6U0,@E0, h0:ME@,&1R,@E0,h:(0,(0@.(14,@6,:@4,6(:M:1&F,F01M@Eb,2//F),&, E0&U:0(,h0:ME@,@6,@E0,h:(0C,&1R,@E0,h:(0,h:FF,4@(0@8E,m0)61R, @E0,0F&4@:8,F:l:@,&1R,m0M:14,@6,/F&4@:8&FF)u,R0B6(lC,hE:8E, l0&14,:@,4@(0@8E04,/0(l&101@F)b,e0l6U0,@E0,h0:ME@,&1R,@E0, h:(0,h:FF,m0,&,F:@@F0,F61M0(,r&1R,&,F:@@F0,4i:11:0(t,@E&1,:@,h&4,

6(:M:1&FF)b,?&1M,&,4.BB:8:01@F),E0&U),h0:ME@C,&1R,@E0,h:(0,

h:FF,m(0&ib Oh6,4@(044,U&F.04,&(0,:l/6(@&1@,:1,01M:100(:1M,R04:M1b,OE0 ):0FR,4@(01M@EC,FsoC,:4,@E0,F:l:@,6B,0F&4@:8,R0B6(l&@:61N,m0)61R @E:4,/6:1@C,@E0,l&@0(:&F,U):0FR4CV,6(,/0(l&101@F),R0B6(l4b

OE0,.F@:l&@0,@014:F0,4@(01M@EC,FTOo,r&F46,8&FF0R,@014:F0,4@(01M@EC,FOot,:4,@E0,E:ME04@,4@(044,U&F.0,61,@E0,4@(044n4@(&:1,8.(U0b,OE0

(./@.(0,4@(01M@E,:4,@E0,4@(044,&@,B:1&F,B(&8@.(0N,@E:4,U&F.0,:4,16@,/&(@:8.F&(F),.40B.FC,m08&.40,6180,@E0,@014:F0,4@(01M@E,:4,

f9&l0R,B6(,OE6l&4,s6.1MC,&1,I1MF:4E,/E)4:84,/(6B0446(C,hE6,R0B:10R,:@,:1,c=dtttb u?0(0C,@E0,h6(R, 

,:4,.40R,:1,:@4,cttt@E,801@.(),40140,U8&/&mF0,6B,m0:1M,R0B6(l0RV,(&@E0(,@E&1,@E0,fd@E,801@.(),R0B:1:@:61,U/6F)l0(bV

c=dbdddddbdddfdbdddpdbdddgdbddd=dbddcddbddcfdbddcpdbddcgdbddc=dbddfddcdfdudpdvdgdtttd o@(&:1o@(044 ri4:t    5  o@(044C,F o@(&:1C,H)   8 0  

8 

')  5    5  kE&/@0(,fy,o@(044,&1R,o@(&:1

0;800R0RC,@E0,l0@&F,h:FF,m(0&i,4661,&B@0(b,s6.1MY4,l6R.F.4C,)C,:4,@E0,4F6/0,6B,@E0,4@(044n4@(&:1,8.(U0,m0B6(0,@E0,@04@,

4/08:l01,4@&(@4,@6,):0FRb,OE0,4@(&:1,hE01,@E0,@04@,4/08:l01,m(0&i4,:4,&F46,8&FF0R,@E0,0F61M&@:61b

D&1),l&1.B&8@.(:1M,6/0(&@:614,61,l0@&F4,&(0,/0(B6(l0R,&@,4@(044,F0U0F4,m0@h001,@E0,):0FR,4@(01M@E,&1R,@E0,@014:F0,4@(01M@Eb,

01R:1M,&,4@00F,h:(0,:1@6,&,/&/0(8F:/C,R00/nR(&h:1M,4E00@,l0@&F,@6,l&i0,&1,&F.l:1.l,8&1C,6(,(6FF:1M,4@00F,:1@6,h:R0nBF&1M0,

4@(.8@.(&F,m0&l4,&(0,@E(00,/(6804404,@E&@,/0(l&101@F),R0B6(l,@E0,l0@&FC,46,σso<σ2//F:0Rb,-.(:1M,0&8E,B6(l:1M,6/0(&@:61C,

@E0,l0@&F,l.4@,16@,m0,4@(0440R,m0)61R,:@4,@014:F0,4@(01M@EC,6@E0(h:40,:@,h6.FR,m(0&iC,46,σso<σ2//F:0R<σTOob,D&1.B&8@.(0(4,

100R,@6,i16h,@E0,U&F.04,6B,):0FR,&1R,@014:F0,4@(01M@E,:1,6(R0(,@6,4@&),h:@E:1,@E040,F:l:@4b

2B@0(,@E0),&(0,46FR,6(,:14@&FF0RC,l64@,l&1.B&8@.(0R,/(6R.8@4,&1R,8:U:F,01M:100(:1M,4@(.8@.(04,&(0,.40R,m0F6h,@E0,):0FR,

4@(01M@EC,:1,@E0,0F&4@:8,B610bp,P1,@E:4,

  ,86.(40C,&Fl64@,&FF,6B,@E0,/(6mF0l4,&(0,0F&4@:8C,46,@E0(0,:4,&,F:10&(, (0F&@:614E:/,m0@h001,4@(044,&1R,4@(&:1b O&i0,&1,&F.l:1.l,(6R,6B,F01M@E,C,8(644n408@:61&F,&(0&,C,&1R,/.FF,61,:@,h:@E,&,F6&R,%b OE0,(6R,h:FF,F01M@E01,&1,&l6.1@,^b,a0,8&1,8&F8.F&@0,^,:1,@E(00,40/&(&@0,0E.&@:614C,6(, h0,8&1,.40,&FM0m(&,@6,B:1R,&,4:l/F0,0E.&@:61,@6,8&F8.F&@0,^,R:(08@F)b,s6.1MY4,l6R.F.4, :4,R0B:10R,&4)=σ

εb,o.m4@:@.@0,@E0,R0B:1:@:61,6B,4@(044Cσ=%

C,&1R,)=σ

ε=%

⋅εb, o.m4@:@.@0,@E0,R0B:1:@:61,6B,4@(&:1C,

ε=δ

C,&1R,)=% ⋅ε=% δb,e0h(:@0,@E:4,0E.&@:61, @6,46FU0,B6(,R0BF08@:61y,

δ=%

)b,96h,h0,E&U0,&,R:(08@,0E.&@:61,B6(,8&F8.F&@:1M,@E0,

8E&1M0,:1,F01M@E,6B,@E0,(6Rb

 !$

2,g,B66@,F61M,&F.l:1.l,(6R,E&4,&,8(644n408@:61&F,&(0&,6B,dbd=,:1bfb,?6h,l.8E,R604,@E0,(6R,4@(0@8E,.1R0(,&1,&;:&F,@014:F0,

F6&R,6B,pdd,Fmbz,e0/6(@,@E0,&14h0(,:1,:18E04b

   ,2F.l:1.l,E&4,&,s6.1MY4,l6R.F.4,6B, )=cd×cdg/4:b -0BF08@:61,δ=% )=pddFmbgB@b dbd=:1bf:1bf cd×cdgFmb ∣cf:1b

B@b=dbdug:1b

$ ,s6.1M:4,l6R.F.4,:4,:1,.1:@4,6B,/4:C,m.@,hE01,)6.,h(:@0,:@,:1,&1,0E.&@:61C,4/F:@,./,@E0,Fmb,&1R,@E0,:1bf,m0@h001,

1.l0(&@6(,&1R,R016l:1&@6(,@6,&U6:R,.1:@,861B.4:61b

    

2,F6&R,@E&@,/.FF4,:4,8&FF0R,&,

,F6&Rb,PB,@E0,F6&R,/.4E04C,h0,8&FF,:@,&, 7 ,F6&Rb,OE0,0E.&@:614,&(0,@E0,4&l0y,

86l/(044:U0,4@(044,

σ=%/C,86l/(044:U0,4@(&:1,ε=δ/C,&1R,86l/(044:U0,R0BF08@:61δ=%/)b,a0,100R,&,h&),@6,

R:BB0(01@:&@0,m0@h001,86l/(044:61,&1R,@014:61C,46,h0,.40,&,4:M1,861U01@:61b,O014:F0,F6&R4,&1R,4@(04404,&(0,/64:@:U0N,

86l/(044:U0,F6&R4,&1R,4@(04404,&(0,10M&@:U0b,P18(0&404,:1,F01M@E,&(0,/64:@:U0N,R08(0&404,:1,F01M@E,&(0,10M&@:U0b

pA10,0;80/@:61,:4,@E0,8(.l/F0,B6104,:1,&,8&(b,-.(:1M,&1,&.@6,&88:R01@C,@E0,E66R,&1R,6@E0(,4E00@,l0@&F,86l/6101@4,):0FRC,/(0U01@:1M,

R&l&M0,@6,@E0,R(:U0(,&1R,/&4401M0(4b,216@E0(,0;80/@:61,:4,&,4E0&(,/:1,:1,&,416h,mF6h0(b,PB,&,8E.1i,6B,:80,M&l4,@E0,mF&R04C,@E0,4E0&(,

/:1,0;800R4,:@4,.F@:l&@0,4@(01M@E,&1R,m(0&i4C,/(6@08@:1M,@E0,R(:U0@(&:1,m),h6(i:1M,&4,&,l08E&1:8&F,B.40b

cw% % ;< kE&/@0(,fy,o@(044,&1R,o@(&:1  !%

2,tttd,i9,86l/(044:U0,F6&R,:4,&//F:0R,@6,&,v,8l,R:&l0@0(C,u,8l,@&FFC,4@00F,8)F:1R0(b,k&F8.F&@0,4@(044C,4@(&:1C,&1R

R0BF08@:61b

   ,OE0,F6&R,:4,Wtttd,i9C,46,@E0,4@(044,:4,bσ=% =pA

πf=p(-tttdi9)

π(v8l)f∣DA&lf

cdui9∣(cdd8l)f lf=-uvbgDA&, OE0,10M&@:U0,4:M1,@0FF4,.4,@E0,4@(044,:4,86l/(044:U0b,s6.1M:4,l6R.F.4, )=σεb,e0h(:@0,@E0,0E.&@:61,@6,46FU0,

B6(,4@(&:1y,

ε=σ

)=-uvbgDA& fdttt@A&∣@A& cduDA&=-dbdddctttfo@(&:1,:4,R0B:10R,&4,

ε=δ

b,e0h(:@0,@6,46FU0,B6(,R0BF08@:61y,δ=ε=-dbdddctttf⋅u8l ∣cdll

8l=-dbddvfllb,OE0,

10M&@:U0,4:M14,@0FF,.4,@E&@,@E0,8)F:1R0(,:4,4E(:1i:1M,&F61M,@E0,R:(08@:61,6B,@E0,F6&Rb

       OE0,4@(044,:1,@E0,/(0U:6.4,0;&l/F04,:4,8&FF0R,U16(l&F,4@(044V,m08&.40,@E0,4@(044,&8@4,61,&1,&(0&,

@E&@,:4,16(l&FC,6(,/0(/01R:8.F&(C,@6,@E0,R:(08@:61,6B,@E0,&//F:0R,F6&Rb,Pl&M:10,&,@&FF,4@&8i,6B,86:14

MF.0R,@6M0@E0(,61,@E0:(,B&804b,PB,)6.,/.FF,61,@E0,01R4,6B,@E0,4@&8iC,@E0,MF.0,h:FF,0;/0(:0180,&,

4@(044,@E&@,:4,16(l&F,r/0(/01R:8.F&(t,@6,@E0,B&80,6B,0&8E,86:1b,PB,@E0,MF.0,:4,@E:8i,&1R,@&8i)C,

l&)m0,:@,h:FF,@01R,@6,4@(0@8EC,&1R,)6.,8&1,400,@E0,86:14,M(&R.&FF),/.FF,&/&(@,&F61M,@E0,R:(08@:61,6B @E0,&//F:0R,F6&Rb,PB,@E0,F6&R,:4,cdd,Fmb,&1R,@E0,B&80,&(0&,6B,0&8E,86:1,:4,c,:1bfC,@E01,@E0,16(l&F,

4@(044,:4,cdd,/4:b

90;@C,:l&M:10,@&i:1M,@h6,86:14,@E&@,&(0,MF.0R,@6M0@E0(,61,@E0:(,B&804C,&1R,@(),@6,4F:R0,@E0l,&/&(@b

96h,@E0,4@(044,:4,&8@:1M,/&(&FF0F,@6,@E0,MF.0,:14@0&R,6B,/0(/01R:8.F&(,@6,:@b,OE:4,4@(044,:4,8&FF0R,

 C,4)lm6F:B0R,m),@E0,F6h0(,8&40,@(00i,F0@@0(,@&.C,Gb,OE0,.1:@4,&(0,@E0,4&l0,&4,B6(,

16(l&F,4@(044,m08&.40,4E0&(,4@(044,:4,&F46,B6(80,R:U:R0R,m),&(0&b,PB,@E0,F6&R,:4,fv,Fmb,&1R,@E0,B&80,

&(0&,6B,0&8E,86:1,:4,c,:1bfC,@E01,@E0,4E0&(,4@(044,:4,fv,/4:b oE00@,l0@&F,M6:1@4,&(0,6B@01,l&1.B&8@.(0R,@E:4,h&)C,h:@E,&RE04:U0,m61R:1M, @h6,F&//0R,4E00@4,@6,B6(l,&,F&/,M6:1@b,OE0,F6&R,:4,/&(&FF0F,@6,@E0,&(0&,.1R0(,

4@(044,r@E0,&RE04:U0,:1,@E0,4E0&(,/F&10,m0@h001,@E0,@h6,F&//0R,/&10F4tb,>6:1@4,

8&1,m0,R04:M10R,@6,/.@,@E0,&RE04:U0,:1,0:@E0(,@014:61,6(,:1,4E0&(N,@)/:8&FF)C,

@E0,4E0&(,4@(01M@E,6B,&1,&RE04:U0,:4,16@,@E0,4&l0,&4,@E0,4@(01M@E,:1,@014:61b

_6(,0;&l/F0C,8)&16&8()F&@0,&RE04:U0,rU4./0(MF.0Vt,:4,4@(61M0(,:1,@014:61,@E&1,:1,4E0&(b,21,&RE04:U0,F&/,M6:1@,h:FF,B&:F,hE01,

@E0,4E0&(,4@(01M@E,6B,@E0,&RE04:U0,:4,0;800R0Rb PB,@E0,4E00@,l0@&F,:4,E0FR,@6M0@E0(,h:@E,(:U0@4,:14@0&R,6B,MF.0C,@E01

0&8E,(:U0@,:4,F6&R0R,:1,4E0&(,&8(644,:@4,8(644n408@:61b,OE0,4E0&(,

/F&10,/&4404,@E(6.ME,@E0,(:U0@,hE0(0,@E0,@h6,4E00@4,l00@b,P1,&, m6F@0R,M6:1@C,.40,&,m6F@,h:@E,&,4l66@E,4E&1i,:14@0&R,6B,&,m6F@,@E&@, :4,@E(0&R0R,&F61M,:@4,01@:(0,F01M@Eb,OE:4,h&)C,@E0,4E0&(,/F&10,8&1, /&44,@E(6.ME,@E0,4l66@E,4E&1iC,hE:8E,E&4,&,F&(M0(,8(644n

408@:61&F,&(0&,@E&1,@E0,(66@,6B,&,@E(0&RC,&1R,@E0(0B6(0,8&1,E&1RF0,&,E:ME0(,&//F:0R,F6&Rb,hTh&@0(,:1,@E0,m66iC,h0,h:FF,400,@E&@,

@E0,@E(0&R,(66@,&F46,&8@4,&4,&,4@(044,861801@(&@:61,4:@0,W,)0@,&16@E0(,(0&461,B6(,i00/:1M,@E(0&R4,6.@,6B,4E0&(,/F&104b

fd% % % %% % %% %%4E0&( /F&10 kE&/@0(,fy,o@(044,&1R,o@(&:1

A10,h&),@6,/(6R.80,E6F04,:1,4E00@,l0@&F,:4,m),/.18E:1M,@E0l,6.@,h:@E,&,/.18E,&1R,R:0,40@b,OE0,/.18E,4E0&(4,@E0,4E00@,

l0@&FC,46,h0,8&1,.40,4E0&(,4@(044,8&F8.F&@:614,@6,B:M.(0,6.@,@E0,4@(044,:1,@E0,4E00@,l0@&FC,τ=% b,?0(0C,%,:4,@E0,B6(80,6B,@E0,

/.18E,&1R,,:4,@E0,4E0&(0R,&(0&,r@E0,/0(:l0@0(,6B,@E0,4E&/0,@E&@,:4,/.18E0R,@:l04,@E0,@E:8i1044,6B,@E0,4E00@,l0@&F,tb

 !&

2,u,ll,@E:8i,&F.l:1.l,4E00@,:4,8.@,h:@E,&,p,8l,R:&l0@0(,(6.1R,

/.18Eb,PB,@E0,/.18E,0;0(@4,&,B6(80,6B,g,i9C,hE&@,:4,@E0,4E0&(,4@(044,:1, @E0,4E00@z,e0/6(@,@E0,&14h0(,:1,DA&b    ,OE0,/.18E,h:FF,8(0&@0,&,(6.1R,4F.MC,hE0(0,@E0,8.@,0RM0,:4, &(6.1R,@E0,8:(8.lB0(0180,6B,@E0,4F.Mb,OE:1i,6B,@E0,8.@,0RM0,&4,@E0,h&FF,

6B,&,8)F:1R0(,h:@E,&,E0:ME@,6B,u,ll,&1R,&,R:&l0@0(,6B,p,8lb,OE0,&(0&,

0E.&F4,@E0,8:(8.lB0(0180,6B,@E0,8:(8F0,@:l04,@E0,@E:8i1044,6B,@E0,4E00@,

l0@&Fy,=πb oE0&(,4@(044

τ=%

=%

π=gi9

π⋅p8l⋅ull∣DA&lf

cdui9∣cdd8l l∣cdull

l=cvbwDA&2,/(68044,01M:100(,:1,&,4@&l/:1M,/F&1@,h:FF,(0h(:@0,@E:4,0E.&@:61,@6,46FU0,B6(,%,:1,6(R0(,@6,B:1R,6.@,hE0@E0(,&,/(044,:4,

8&/&mF0,6B,/.18E:1M,6.@,mF&1i4,6B,&,M:U01,4:B0,:1,&,4E00@,l0@&F,6B,i16h1,4E0&(,4@(01M@Eb

oE0&(,4@(044,861@(6F4,@E0,R04:M1,6B,@6(4:61,l0lm0(4b,OE:1i,6B,&, (6.1R,4E&B@,&4,&,40(:04,6B,R:4i4,MF.0R,@6M0@E0(,61,@E0:(,B&804b,PB, )6.,@h:4@,@E0,4E&B@,h:@E,&,@6(E.0,C,@E0,MF.0,h:FF,m0,F6&R0R,:1,

4E0&(,m08&.40,@E0,F6&R,:4,/&(&FF0F,@6,@E0,B&80,6B,0&8E,R:4ib

k614:R0(,&,(08@&1M.F&(,mF68i,F6&R0R,:1,4E0&(b,OE0,mF68i,h:FF,R:4@6(@,&4,&, /&(&FF0F6M(&lC,46,@E0,@6/,0RM0,l6U04,&1,&l6.1@,^b,-:U:R0,@E0,R:4@6(@:61,m) F01M@E,,/0(/01R:8.F&(,@6,@E0,R:4@6(@:61C,&1R,)6.,E&U0,@E0,4E0&(,4@(&:1C

γ=δ

b,hTh:i0,16(l&F,4@(&:1C,4E0&(,4@(&:1,:4,.1:@F044b,k614:R0(,@E0,&1MF0, B6(l0R,m0@h001,@E0,:1:@:&F,&1R,F6&R0R,/64:@:614,6B,@E0,mF68ib,_(6l, @(:M616l0@()C,h0,i16h,@E&@, @&1ϕ=δ bOE0,&l6.1@,6B,4@(&:1,:1,@E0,8&(@661 :4,0;&MM0(&@0Rb,_6(,l0@&F4C,8618(0@0C,,h66RC,&1R,l64@,/6F)l0(4C,&1MF0, ϕ,:4,46,4l&FF,@E&@,@&1ϕ≈ϕ,:B,h0,l0&4.(0,@E0,&1MF0 :1,(&R:&14C,@E0(0B6(0,ϕ≈γ=δ b fc%^ ϕ/.18E%  4F.M  kE&/@0(,fy,o@(044,&1R,o@(&:1 +,  

96(l&F,4@(044,:1,&,@014:F0,6(,86l/(044:U0,l0lm0(,:4,@E0,F6&R,R:U:R0R,m),@E0,8(644n408@:61&F,&(0&y,σ=%

96(l&F,4@(&:1,:4,@E0,8E&1M0,:1,F01M@E,/&(&FF0F,@6,@E0,F6&R,R:U:R0R,m),:1:@:&F,F01M@Ey,ε=Δ =δ 

s6.1M:4,l6R.F.4,:4,@E0,(&@:6,6B,4@(044,6U0(,4@(&:1,h:@E:1,@E0,0F&4@:8,B610,6B,@E0,4@(044n4@(&:1,R:&M(&ly,)=σε

OE0,8E&1M0,:1,F01M@E,6B,&,@014:F0,6(,86l/(044:U0,l0lm0(,:4,R0(:U0R,B(6l,@E0,@E(00,/(0U:6.4,0E.&@:614y,δ=%

) oE0&(,4@(044,:4,@E0,F6&R,R:U:R0R,m),@E0,&(0&,/&(&FF0F,@6,@E0,F6&Ry,τ=% 

oE0&(,4@(&:1,:4,@E0,R0B6(l&@:61,/&(&FF0F,@6,@E0,F6&R,R:U:R0R,m),:1:@:&F,F01M@E,/0(/01R:8.F&(,@6,@E0,F6&Ry,γ=δ

b ff kE&/@0(,uy,A6:4461:4,e&@:6,&1R,OE0(l&F,I;/&14:61    .&   / 0     1     / 0 

o@(0@8E,&,@E:8i,(.mm0(,m&1RC,&1R,)6.,16@:80,@E0,l&@0(:&F,M0@4,@E:110(,&4,:@,M0@4,F61M0(b,OE:4,0BB08@,

688.(4,:1,l0@&F4C,/F&4@:84C,8618(0@0C,&1R,l&1),6@E0(,l&@0(:&F4b,a0,8&1,/(0R:8@,E6h,l.8E,@E0,

@E:8i1044,8E&1M04,h:@E,&,l&@0(:&F4,/(6/0(@),8&FF0R,A6:4461Y4,(&@:6Cv,hE:8E,(0F&@04,@E0,4@(&:1,&F61M,@E0,

@014:F0,&;:4,h:@E,@E0,4@(&:1,:1,@E0,@(&14U0(40,r8(644h:40t,R:(08@:61b,OE0,4)lm6F,B6(,A6:4461Y4,(&@:6,:4,`C

@E0,F6h0(,8&40,@(00i,F0@@0(,1.C,hE:8E,F66i4,4:l:F&(,@6,@E0,F6h0(,8&40,e6l&1,F0@@0(,Ub,A6:4461Y4,(&@:6,

:4,ν=-ε 

ε C,hE0(0,ε ,:4,@E0,4@(&:1,:1,@E0,@(&14U0(40,r8(644h:40t,R:(08@:61C,&1R,ε ,:4,

@E0,4@(&:1,&F61M,@E0,F61M:@.R:1&F,&;:4,r&F46,8&FF0R,ε 3 tb,OE0,4:M1,861U01@:61,B6(,4@(&:1,:4,/64:@:U0,B6(

0;/&14:61C,10M&@:U0,B6(,4E(:1i&M0b,A6:4461Y4,(&@:6,:4,dbfv,B6(,4@00FC,dbuu,B6(,&F.l:1.lC,&1R,dbcd,@6,

dbfd,B6(,8618(0@0b,a0,8&1,8&F8.F&@0,@E0,8E&1M0,:1,F01M@E,6B,&,(6R,m),@&i:1M,@E0,R0B:1:@:61,6B,4@(&:1C

ε =δ 

C,&1R,(0h(:@:1M,:@,&4,δ =ε b,P1,@E0,4&l0,h&)C,h0,8&1,8&F8.F&@0,@E0,8E&1M0,:1, R:&l0@0(,m),4.m4@:@.@:1M,ε ,B6(,ε 3 C,&1R,R:&l0@0(,,B6(,F01M@E,y,

δ =ε b

 !"

21,&F.l:1.l,(6R,E&4,&,8(644n408@:61&F,&(0&,6B,dbcwguv,:1bfb,21,&;:&F,@014:F0,F6&R,6B,gddd,

Fmb,8&.404,@E0,(6R,@6,4@(0@8E,&F61M,:@4,F01M@EC,&1R,4E(:1i,&8(644,:@4,R:&l0@0(b,aE&@,:4,@E0, R:&l0@0(,m0B6(0,&1R,&B@0(,F6&R:1Mz,e0/6(@,@E0,&14h0(,:1,:18E04b    ,OE0,(6R,E&4,&,8:(8.F&(,8(644,408@:61C,46,@E0,8(644n408@:61&F,&(0&,m0B6(0,@E0,(6R,:4,

F6&R0R,:4,

=π pfb,e0h(:@0,@6,46FU0,B6(,@E0,:1:@:&F,R:&l0@0(C = √pπ=√p⋅dbcwguv:1bf π=dbvdddd:1bb,aE01,@E0,(6R,:4,F6&R0RC,@E0,&;:&F,4@(&:1,:4

ε =σ

)=% )=gdddFmb dbcwguv:1bf:1bf cd×cdgFmb=dbddudgb

A6:4461Y4,(&@:6,

ν=-ε 

ε C,46,ε =-ν⋅ε =-dbuu⋅dbddudg=-dbddcdc

OE0,8E&1M0,:1,R:&l0@0(,:4,

δ =ε ⋅=-dbddcdc×dbvdddd:1b=-dbdddvdp:1bOE0,B:1&F,R:&l0@0(, = +δ =dbvdddd:1b-dbdddvdp:1b=dbpwwv:1b P1,&,8:U:F,01M:100(:1M,4@(.8@.(0C,&,R:l014:61&F,8E&1M0,6B,E&FB,&,@E6.4&1R@E,6B, &1,:18E,:4,:14:M1:B:8&1@C,m.@,:1,&,l&8E:10,:@,86.FR,&BB08@,/0(B6(l&180b, Pl&M:10,&,l&8E:10,/&(@,@E&@,4F:R04,:1,&,4F6@y,:B,@E0,/&(@,:4,F6&R0R,&;:&FF),:1,

86l/(044:61C,A6:4461Y4,0BB08@,86.FR,8E&1M0,&,/&(@,@E&@,4F:R04,r4F:/,B:@t,:1@6,&,

/&(@,@E&@,4@:8i4,r/(044,B:@tb s6.,8&1,B00F,@E0,0BB08@,6B,A6:4461:4,(&@:6,hE01,)6.,:140(@,&,(.mm0(,4@6//0(,6(, &,86(i,:1,&,m6@@F0b,OE0,A6:4461:4,(&@:6,6B,(.mm0(,:4,&m6.@,dbvC,hE:F0,86(i,:4, &m6.@,dbdb,PB,)6.,@(),@6,/.4E,&,(.mm0(,4@6//0(,:1@6,@E0,108i,6B,&,m6@@F0C,@E0, l&@0(:&F,&m6U0,@E0,108i,h:FF,4E6(@01,&1R,@E:8i01C,l&i:1M,:@,R:BB:8.F@,@6,:140(@, :1@6,@E0,m6@@F0b,OE0,E&(R0(,)6.,/.4EC,@E0,l6(0,@E0,4@6//0(,h:FF,0;/&1R,:1,@E0, @(&14U0(40,R:(08@:61C,&1R,@E:4,0;/&14:61,:4,&m6.@,vdI,6B,@E0,86l/(044:61,:1 v9&l0R,B6(,o:la61,A6:4461C,&,_(018E,l&@E0l&@:8:&1,&1R,/E)4:8:4@b fu% = 3  = 

86(i(.mm0(%%

4E(:1i40;/&1R4%

%0   7         3    kE&/@0(,uy,A6:4461:4,e&@:6,&1R,OE0(l&F,I;/&14:61

@E0,&;:&F,R:(08@:61b,9&@.(&F,86(i,:4,l&R0,B(6l,@E0,m&(i,6B,@E0,86(i,6&i,@(00C,&1R,R604,16@,0;/&1R,@(&14U0(40F),hE01,)6.,

/.4E,61,:@b,OE0,61F),(04:4@&180,86l04,B(6l,86l/(044:1M,@E0,86(i,:1,@E0,m6@@F0,108iC,&1R,B(:8@:61b k614:R0(,&,mF68i,@E&@,:4,/.FF0R,:1,@h6,R:(08@:614,m),B6(804,%3,&1R,%4b,OE0,4@(&:1,:1,@E0

3,R:(08@:61,R.0,@6,@E0,&;:&F,4@(044,B(6l,%3,:4,ε3 3

=σ3 )b,PB,%3,:4,/64:@:U0,r@014:61tC, @E01,@E0,4@(&:1,:4,&F46,/64:@:U0bbb@E0,m&(,:4,4@(0@8E:1M,&F61M,@E0,3,&;:4,R.0,@6,@E0,&8@:61,

6B,%3b,?6h0U0(C,@014:F0,F6&R,%4,:4,&8@:1M,@6,4E(:1i,@E0,m&(,:1,@E0,3,R:(08@:61N,@E0,4@(&:1,

R.0,@6,@E:4,@(&14U0(40,F6&R,:4,ε3 =-νσ4 )b,2RR,@E040,@h6,4@(&:14,@6,B:1R,@E0, @6@&F,4@(&:1,:1,@E0,3,R:(08@:61C,

ε3=σ3

)-νσ4 )=c )(σ3-νσ4)b o:l:F&(F)C,@E0,@6@&F,4@(&:1,:1,@E0,4,R:(08@:61,:4,

ε4=σ4

)-νσ3 )=c )(σ4-νσ3)b

e0&F,mF68i4C,6B,86.(40C,&(0,@E(00nR:l014:61&Fb,PB,@E0,mF68i,:4,F6&R0R,:1,&FF,@E(00,R:(08@:614C,8&F8.F&@0,@E0,4@(&:1,:1,@E0,3C,4C,&1R

5,R:(08@:614,&4,ε3=c

)(σ3-νσ4-νσ5)C,ε4=c )(σ4-νσ3-νσ5)C,&1R,ε5=c )(σ5-νσ3-νσ4)b  !# k&F8.F&@0,@E0,4@(&:14,:1,@E0,3C,4C,&1R,5,R:(08@:614,B6(,@E:4,4@00F,mF68ib    ,_:(4@C,8&F8.F&@0,@E0,16(l&F,4@(044,:1,@E0,3C,4C,&1R,5,R:(08@:614,&4,@E0, B6(80,R:U:R0R,m),@E0,/0(/01R:8.F&(,4.(B&80,@E&@,:@,&8@4,61b OE0,4@(044,:1,@E0,3,R:(08@:61,&8@4,61,@E0,(:ME@,B&80,6B,@E0,mF68iC,46,@E0,16(l&F,

4@(044,:4,σ3=ui9

f8l×p8l ∣DA&lf cdui9∣(cdd8l)f lf=ubtttvDA&b,OE0,4@(044,:1,@E0

4,R:(08@:61,&8@4,61,
Politique de confidentialité -Privacy policy