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9∣(cdull)f
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9 llf∣A&lf
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9∣(cdull)f
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Δ=δ
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0E.&@:61bδ=%⋅
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=π pf
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2=ρπf
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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&(,
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M66R,m61Rz
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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
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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,
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8
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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
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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,
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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
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δ=%
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8E&1M0,:1,F01M@E,6B,@E0,(6Rb
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F6&R,6B,pdd,Fmbz,e0/6(@,@E0,&14h0(,:1,:18E04b
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B@b=dbdug:1b
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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
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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,
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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
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l0@&Fy,=πb oE0&(,4@(044
τ=%
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π=gi9
π⋅p8l⋅ull∣DA&lf
cdui9∣cdd8l l∣cdull
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γ=δ
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b ff kE&/@0(,uy,A6:4461:4,e&@:6,&1R,OE0(l&F,I;/&14:61 .& / 0 1 / 0
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: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,
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ε =δ
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δ=εb
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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
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ν=-ε
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/.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,ε33
=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
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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