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894/A1/)9)=5)5;)949<9;2) #$ ∈ )C1);5</1)=5)5;54P6

%54A1<9/)X/4381438)/041=/A191)9)3);32><) P6O"9 )#:29)=4/8)=>) 6PO #"9 ⊆ )(/=>#"9 =PO )/25;=1E)081;)B9?1;1A19E)9)9:29)3)/041=/A19)/)451)")09)<54A1<9/)#)O:/5)9)9:29

5;)%0,6>+9,)6P6(/=>) /" ⊆ ) /25;=1) :9) ;329/@>) =5) PO"9 ) <54A1<9/) 949<9;29438) B9) ?38</PO!9 ) =5) 6"! ∈ ) *1=1) /<) ;32/2) =5) PO!9 ) 949<9;254) =/89) =389:05;B9) 949<9;25451/! ∈ ) 081;) /041=/A1/) 96) *=9:2) 949<9;2) :9) </1) ;5<9C29) C1) ,6'&,3%') 451) !) 081;) 96PO"9 ):9);5<9C29)1</G1;9/)081;)9)/)<54A1<11)"6*28/G9<) /29;A1/) /:508/) B1:21;=A191) =/89) :9) ?/=9) F;289) :1<U3454) 9) O?5;=A19E

/041=/A19P)C1);32/A1/) PEO!9 )=/89)89089@1;2>)X/43/89/)?5;=A191))9))F;)05;=254)!6

M^

(9)/42?94E)9:29)9X1B9;2)=>95∈ P PEO #" × )1/8) 6PO #!9 ∈

YfQ#_D*c+#6)_94/A1/) B1/G3;/4>)δ) ) F;28J3)<54A1<9)/) 89089@1;2>) 3) ?5;=A19) 09=/89)3);5<1<)?5;=A19),8%3*,-.)OB9?1;12>)09)/P6)(/=>) ^PO $/9 = ):05;9<)=>)?5;=A1/)9)9:29)3)?5;=A19)->3)*'3*.)09)/6

Y)?5;=A19) H/9 →I )=3;:1B98/2>)=/)3)894/A19)F;289)/)C1)H)/89)3)1;X98:>) E!−9=/89)9:29)3)894/A19)F;289) POH9 )C1)/)B9?1;12>)081;

6EE ! 9$!9!$ ∈⇔∈ −

(/=>) <54A1<9/) #) 9:29) 3) 0/829) /) 451) PPEOOPO /9#/9 ⊆ ) /25;=1) <54A1<9/KPOIN #!9! ∈ ) :9) ;5<9C29) ,6'&,3%'5 +%-,0+>-.) 081;) 9) /)<54A1<11)#) C1) :9) ;329/@>

P6O! #9 −

YU:98X><)=>)894/A1/) !−9 );5)9:29E)F;)G9;98/4E)3)/041=/A196) !−9 9:29)3)/041=/A19;5</1)B/=>):9)X981?1=>)1<041=/A1/

6C1POEPO M!M!MM!! $$!!$!9$!9 ≠⇒≠==

[5;=A1/) O/041=/A1/P) 9) 09;285) =/89) !−9 ) 9:29) 232) 3) ?5;=A19) :9) ;5<9C29) 923-1,%I,23,7>-.) :/5) ,3=%-1,%6) Y) ?5;=A19) O/041=/A19P) =/89) 9:29) F;) /=94/C1) 21<0) 1;]9=A19) C1901<38?1:<) :9) ;5<9C29)I,=%-1,%) O:/5) /041=/A19) U1]9=21X>P6)(/=>) H/9 →I ) 9:29) 3

U1]9=A19)/25;=1)C1) /H9 →− I! )9:29)B9)/:9<9;9/)3)U1]9=A196[19) /=5<) 9) 3) /041=/A19) /)<54A1<11)/) F;)<54A1<9/)H) C1)&) 3) /041=/A19) /) 451)H) F;

<54A1<9/)A6) &32><) =5) 9& ) ) /041=/A1/) =/89) ?/=9) :>J1) =389:05;B>) 381=>851) 949<9;2E/! ∈ )949<9;254) PPOO !9& )B1;)A6)(/=>)9)C1)&):5;2)U1]9=A11E)/25;=1) 9& ) )9:29)3)U1]9=A19

6PO !!! −−− = &99& ))

(/=>)9)9:29)3)/041=/A19)/25;=1) !−99 ) )9:29)3)/041=/A19)C1)/;5<9)/041=/A1/)1B9;J

21=>)/)<54A1<11)H)F;)9/)F;:>C1E)F;)21<0)=9) 99 )!− )9:29)3)894/A19)F;)/6)(/=>)F;:>)9)9:29

U15;1X3=>) /25;=1) !−99 ) ) =Z2) C1) 99 )!− ) :5;2) /041=/A11) 1B9;21=9E) 081</) /) <54A1<11PEO/9 )/)B35/)/)<54A1<11)/6*<1;21<)/1=1)C1)58<>23/8949)08308192>A1)G9;98/49)/49)?5;=A11438I

!°6) PROPO #9"9#" ⊂⇒⊂M°6) RPO ∅≠⇔∅≠ "9"

L°6) PROPOPO #9"9#"9 ¿¿ =g°6) PROPOPO #9"9#"9 ¡¡ ="°6) PROPO !! #9"9#" −− ⊂⇒⊂W°6) PROPOPO !!! #9"9#"9 −−− = ¿¿\°6) PROPOPO !!! #9"9#"9 −−− = ¡¡a°6) P6OPO !! "9"9 −− = !!

M!

YfQ#_D*c+#6)79;285)/041=/A11) :9)</1)52141@9/@>)C1)/429)B9;5<181) C1) ;32/A11E) F;/?/8/) =9438) B/29) /1=16) (9) 9H9<045E) /041=/A1149) <54A1<11)N*) /) ;5<989438) ;/258/49F;28J3)<54A1<9)H) :9);5<9:=) D,+2+,) =5) X/4381) F;5 H6) Q9) ?343:9C29) ;32/A1/) PO3!3→:/5E)</1)?89=X9;2E) *N∈33! KN )O:/5)F;=>E)</1):1<045E) KP6N 3!

!6g6"?/(90--":.2%-9.0--<"'4,3-(-)&

[19) R→/9 I )3)/041=/A19)/)5;91)<54A1<1)/)F;)<54A1<9/)R)/);5<989438)89/49C1)?19) 6/" ⊂

Q9):05;9)=>)/041=/A1/) 9)9:29)6,3>+'*.) :/5)6.+&,3,*.5 ,39%+,>+)09)<54A1<9/)"B/=>)<54A1<9/)X/4381438) R⊂PO"9 )9:29)3)<54A1<9)<1;38/2>6)%/8G1;9/)1;?9813/8>

PO1;? "9 ) /) <54A1<11) PO"9 ) :9) ;5<9C29) 6'+&,3%'5 ,39%+,>'+.5 /) /041=/A1915 95 09

<54A1<9/5")C1):9);329/@>) P6O1;? !9"! ∈

)*C/B/8

P6O1;?PO1;? "9!9"!

=∈

&5<>854) PO1;? !96"! ∈

= )9:29)=/8/=2981@/2)B9)58<>23/8949)B35>)08308192>A1I

!°6) PEO!96 < )09;285)381=9) R"! ∈M°6)B/=>) Eα<6 )9H1:2>) "! ∈ )/:2?94)=/) 6PO α<!9Q9):05;9)=>)/041=/A1/)9)9:29)6'=>+'*.):/5)6.+&,3,*.5)20%+,>+)09)<54A1<9/)"

B/=>) 1</G1;9/) PO"9 ) 9:29) 3)<54A1<9)</]38/2>6)%/8G1;9/) :509813/8>) PO:50 "9 ) /<54A1<11) PO"9 ):9);5<9C29)6'+&,3%'5)20%+,>'+.5/)/041=/A19159509)<54A1<9/5")C1):9

;329/@>) P6O:50 !9"! ∈

*C/B/8P6O:50PO:50 "9!9

"!=

∈

&5<>854) PO:50 !9@"! ∈

= )9:29)=/8/=2981@/2)B9)58<>23/8949)B35>)08308192>A1I

!°6) EPO @!9 £ )09;285)381=9) R"! ∈M°6)B/=>) E@<α )9H1:2>) "! ∈ )/:2?94)=/) P6O!9<α(/=>)/041=/A1/)9)9:29)<1;38/2>)O</]38/2>P)09)B3<9;154):>5)B9)B9?1;1A19)/E):9

:05;9E)</1):1<045E)=>)9)9:29)<1;38/2>)O</]38/2>PE)?>8>)/)</1):09=1?1=/)<54A1<9/)09=/89) /89) /=9/:2>) 08308192/29E) 1/8) ;5<>854) PO1;? !9

/! ∈) PPO:50O !9

/! ∈) :9) ;5<9C29)6'+F

&,3%'5,39%+,>'+.)O6'+&,3%'5)20%+,>'+.P)/)?5;=A191596Q9):05;9)=>)/041=/A1/)9)9:29)6.+&,3,*.50%562(1,6%'5"E)B/=>)9:29)C1)<1;38/2>)C1

</]38/2>)09)"E)/B1=>)B/=>)<54A1<9/)X/4381438) PO"9 )9:29)<>8G1;12>6*89)43=)1;9G/412/29/

P6O:50PO1;? !9!9"!"! ∈∈

<

MM

.949)B35>)</8G1;1):5;2)9G/49)B/=>)C1);5</1)B/=>)/041=/A1/)9)9:29)=3;:2/;2>)09)"6(/=>) /041=/A1/) 9) 9:29)<>8G1;12>) 09)/) :9) :05;9E) </1) :1<045E) =>) 9) 9:29)6.+F

&,3,*.E)?>8>)/42>):09=1?1=/A196YU:98X><)=>)B/=>)/)9:29)3)<54A1<9)B9);5<989)89/49)C1)B/=>) 9)9:29)<1;38/2>E

/25;=1)G8/?1=54)451)9):9)/?4>)F;)F;289G1<9):125/2)B9/:508/)B890291) 66$ = )(/=>)/041=/A1/9)9:29)</]38/2>E)G8/?1=54)451)9)9:29):125/2)F;)F;289G1<9):5U)B89/02/) 6@$ = )(/=>)9)9:29<>8G1;12>)G8/?1=54):>5):9)/?4>)F;)F;289G1<9)=5081;:)F;289)B8902949) 6$ = )C1) 6@$ =

7_Y7Y,+c+#6)"0(,-'1,'5 R→/9 I 5%)*%56.+&,3,*.G58'-.5D,5326',58'-.5%!,)*.235326.+5 ^>J 5')*9%(5K3-L*5 J!9 <PO 50%3*+25>+,-%5 6/! ∈

?%6>3)*+'1,%6) *X9<E) F;28J/B9X>8E) KEIPONPO /!!9/9 ∈= ) 1/8) <54A1<9/) PO/99:29) <>8G1;12>) B/=>) C1) ;5</1) B/=>) 9H1:2>) 5;) ;5<>8) ^>J ) /:2?94) =/) 09;285) 381=9

PEO/9$ ∈ ) :>) /1U>) 43=) 1;9G/412/29/) 6J$ < ) (/8) PO!9$ = ) C1) B9=1E) 09;285) 381=9E/! ∈ )/X9<) EPO J!9 < )=99/)=9)289U51/)B9<3;:28/26(1;) /=9/:2>) 08308192/29) 89@542>) =>) /041=/A1/) 9) 9:29)<>8G1;12>) B/=>) C1) ;5</1

B/=>)<3B5454):>5) 9 )9:29)3)/041=/A19)<>8G1;12>6#h#%7$#6)!6)[19) 6=3:PO !!9 = )*=9/:2>)?5;=A19)9:29)B9?1;12>)09)R)C1)9:29)<>8J

G1;12>)O09)RPE)B93/89=9) 6!=3: <! )*X9<

!=3:1;? −=∈

!! R

6!=3::50 =∈

!! R

M6) [19) EdgPO M!!9 −= ) B9?1;12>) 09)

−=

L

MEL

M" ) C1) <>8G1;12>) 09) /=9:2

1;298X/46)%/8G1;149)451)9):5;2

6Mdg:50

^dg1;?

M

M

=−=

=−=

∈

∈

!@

!6

"!

"!

Q9)X981?1=>)1<9B1/2)=>)B/=>) R→/9 I )C1) R→/& I ):5;2)/041=/A11)<>8G1;129E/25;=1)/041=/A1149) &99&9 i1POE R∈αα+ ):5;2)B9)/:9<9;9/)<>8G1;1296

*041=/A1/)9)9:29)<1;38/2>)B/=>)C1);5</1)B/=>) 9− )9:29)</]38/2>6)*X9<

PP6OO:50PO1;? !9!9/!/!

−−=∈∈

*041=/A1/)9)9:29)</]38/2>)B/=>)C1);5</1)B/=>) 9− )9:29)<1;38/2>)C1)/X9<

PP6OO1;?PO:50 !9!9/!/!

−−=∈∈

(/=>) 9) 9:29) 3) /041=/A19) /) 5;91) <54A1<1)/) F;) R ) 9H1:2>) OF;) PR ) 949<9;2949

PO1;? !9/! ∈

)C1) PO:50 !9/! ∈

)B9?1;129)4/)?94)=/)F;)=/@54)/041=/A11438)=5)X/4381)F;)R)O5;B9);5

9H1:2>)F;232B9/5;/)/=9:29)949<9;29P6

ML

#49<9;254) R∈6 ):9);5<9C29)6'+&,3%'5,39%+,>'+.)/)/041=/A191)9)09)<54A1<9//)OC1):9);329/@>) PPO1;? !96

/! ∈= )B/=>) PO!96 £ )09;285)381=9) /! ∈ )C1)B/=>)09;285

381=9) 6>α )9H1:2>) /! ∈ )/:2?94)F;=Z2) 6PO α<!96 <

V;) <3B) /;/43G) 949<9;254) R∈@ ) :9) ;5<9C29) 6'+&,3%'5 )20%+,>'+.) /

/041=/A191) 9) 09)<54A1<9/)/) OC1) :9) ;329/@>) PPO:50 !9@/! ∈

= ) B/=>) @!9 £PO ) 09;285

381=9) /! ∈ )C1)B/=>)09;285)381=9) E@<α )9H1:2>) /! ∈ )/:2?94)F;=Z2) 6PO @!9 <<α*041=/A1/) 9) :9) ;5<9C29) 6.+&,3,*.5 ,39%+,>+) O89:09=21X) :5098138P) B/=>

∞−>∈

PO1;? !9/!

)O89:09=21X) P6PO:50 ∞<∈

!9/!

*041=/A1149)<>8G1;129)1;?98138)C1):5098138):9);5<9:=)6.+&,3,*%6)(/=>

∞−=∈

PO1;? !9/!

)C1) ∞=∈

PO:50 !9/!

/041=/A1/)9):9);5<9C29)3%6.+&,3,*.6YfQ#_D*c+#6)(/=>)/041=/A1/)9);5)/89)X/4381)89/49)C1)1/)X/4381)F;28J5;):0/A15)=5M³3 )B1<9;:15;1E);5)</1)/5):9;:);3A15;149)B9)/041=/A19)<1;38/2>):/5)</]38/2>)C1

;1=1) ;3A15;149) B9) </8G1;9) 1;?9813/8>) :/5) :509813/8>) OB93/89=9) F;28J5;) /:9<9;9/:0/A15);5):9)B9?1;9C29)3)894/A19)B9)38B1;9P6

!6"6"@2.0-/")+2+%+3-9

[19)/)3)<54A1<9);9X1B>)C1)f)3)<54A1<9)B9)0>8A1)/49)451)/E)=/89)/89)58<>23/J8949)08308192>A1I

!°6)B/=>) :,," ∈KN )9:29)3)?/<1419)3/89=/89) O;9X1B>P)B9)<54A1<1)/0/8A1;Z;B) 451

fE)/25;=1) R":,

,"∈

∈ f

M°6)B/=>) 3""" EEE M! ! )/0/8A1;)451)fE)/25;=1)#3

,,"

!=∈ f;

L°6) f∈/ )C1) 6f∈∅(/=>):9)B>)<54A1<9/ f)=5)08308192>A149)B9)</1):5:):9):05;9)=>)09)<54A1<9/)/):J/

B/2)3)*>0>(>&,%)τ)O:/5):J/)B9?1;12)3))*+2-*2+.5*>0>(>&,-.P6).5)/429)=5X1;29E)3)230343G19/:508/)<54A1<11);9X1B9)/)9:29E)081;)B9?1;1A19E)3)?/<1419)f)=5)08308192>A149)!°)j)L°6

%54A1<9/)/)09;285)=/89):J/)B/2)3)230343G19)τ)O09;285)=/89):J/)B9?1;12)3):285=J258>)230343G1=>P):9);5<9C29))0'1,25*>0>(>&,-6)#49<9;2949)5;51):0/A15)230343G1=):9;5<9:=)023-*%6)%54A1<149)/0/8A1;Z;B)451)f):9);5<9:=)62(1,6,58%)-C,)%6)/)9:29)3<54A1<9)B9:=b1:>)C1)B9)/:9<9;9/)<54A1<9/)X1B>)9:29)3)<54A1<9)B9:=b1:>6

V;28J3)<54A1<9) :9) 032) 1;283B5=9) B1X98:9) 230343G116) .9/)</1) :1<04>) 9:29) 23J0343G1/)?38</2>)B1;)<54A1<9/)/)F;:>C1)C1)B1;)<54A1<9/)X1B>6

k;) /42) 9H9<045) B9) 230343G19) F4) =3;:212519) ?/<141/) 2525838) 0>8A1438) 451) /6*=9/:2>)230343G19):9);5<9C29)230343G19)8,)-+%*.6

Mg

(#[+&+c+#6)M5 0'+*%5 #5 '5 232,5 )0'1,25 *>0>(>&,-5 )%5 326%D*%5 62(1,6%5 K3-C,).G8'-.562(1,6%'5 #" != 5%)*%5>562(1,6%58%)-C,).6

V;28J5;):0/A15)230343G1=)h)<54A1<149)F;=b1:9)/5)58<>23/8949)08308192>A1I!°6)B/=>) :,,# ∈KN )9:29)3)?/<1419)3/89=/89)O;9X1B>P)B9)<54A1<1)F;=b1:9E)/25;=1

#:,,#

∈)9:29)3)<54A1<9)F;=b1:>R

M°6) B/=>) 3### EEE M! ! ) :5;2) <54A1<1) F;=b1:9E) /25;=1) "3

,,#

!=) 9:29) 3) <54A1<9

F;=b1:>RL°6)<54A1<149 ∅ )C1)/):5;2)<54A1<1)F;=b1:96(9<3;:28><)08308192>A149)!°)j)L°)/49)<54A1<1438)F;=b1:96!°6) [19) ,# ) 3) <54A1<9) F;=b1:>6) *25;=1E) F;) U/@/) B9?1;1A191) B/29) </1) :5:E

<54A1<9/) ,, #" != )9:29)3)<54A1<9)B9:=b1:>)C1)B9)/:9<9;9/) ":,

,"∈

)9:29)B9:=b1:>6

(1;)9G/412/29/

" "#:, :,

,,:,

, "##∈ ∈∈

==

!!

89@542>)=>)<54A1<9/)#:,

,#∈

)9:29)F;=b1:>6

M°6)Q9):2/U149C29)F;)<3B)/;/43GE)?343:1;B)9G/412/29/

6! !!

# #"3

,

3

,,,

3

,, "##

= ====

!!

L°6)*=9/:2>)08308192/29)89@542>)B1;)9G/412>A149) 6E // =∅∅= !!

(1;) =949) B9) </1) :5:) 89@542>) =>) B/=>) F;28J3) <54A1<9) /) :J/5) B9?1;12) S:5UJ

<54A1<149) F;=b1:9T) /25;=1) /) 9:29) 5;) :0/A15) 230343G1=6) V;28J/B9X>8E) 3) <54A1<9

/" ⊂ )X/)?1E)081;)B9?1;1A19E)3)<54A1<9)B9:=b1:>)B/=>) "! )9:29)F;=b1:>6

V;) 49G>258>) =5) 08308192/29/) L°) /) <54A1<1438) F;=b1:9) ?/=9<) 3U:98X/A1/) =>:0/A154)230343G1=)/)C1)<54A1<9/)∅ ):5;2E)F;)/=94/C1)21<0E)<54A1<1)F;=b1:9)C1)<54A1<1B9:=b1:96) V;28J5;) :0/A15) F;@9:28/2) =5) 230343G1/) B1:=892>E) 381=9) <54A1<9) 9:29) F;

/=94/C1)21<0)C1)B9:=b1:>)C1)F;=b1:>6

A&9-(4).)&."/(/-"2/(9)6)[19) ^! )5;)05;=2)3/89=/89)/4):0/A15451)230343G1=)/6

781;) 8%9,3,1,%E) >+,-%5 62(1,6%) E/B ⊂ ) 0%3*+25 -'+%5 %!,)*.5 >5 62(1,6%5 8%)-C,).5 !B

')*9%(5-.5 E!^ BB! ⊂∈ 5%)*%57%-,3.*'*%5'5023-*2(2,5 6^!

V;)0/821=54/8E)381=9) 1;298X/4)B9:=b1:) PEO I' )=/89)=3;A1;9)05;=254)!)9:29)3)X9J

=1;>2/29)/)451)!6

!"

#$%&'()*++,-.,-#/012- 3210456762! "- 7- 8480- 98416- :# - ;2- 92- ;/27967- /27<5-R1=4>042-=-3210456762-?0@26/015- ABC :: ε+ε− ## -7-<80- ,:# -)010- B:>ε -7/D06/7/B-?8E010246

;2- @01,- F46/G7;235/B- E02- ,ABC: "$%# ⊂∈ - %5- <85@- ,:ABC@04 :: >−−=ε #$%#

)68410- BABCABC :: "$%## ⊂⊂ε+ε− -;210- ABC :: ε+ε− ## -2?62-=-3210456762-7-<80- :#041<8?5-H4-",

!,-"&'()*+*,(-&- <80- ∞ - I0- ,∞− - J02- ;210- @8<>0@27- ,R - K/04- .&/()(,(&B- 01('&23-,(2&! .&! )32&1&! 1&%-&! '%1&! '0),()&! 3)! ()+&14%-! .&5'6(5! 7(! )&2*18()(+! ABBC ∞%01('%1&!%1!/(! BR∈% !&5+&!0!4&'()*+%+&!%!-3(! ,∞

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=;@=; ZZ εδ<−εδ<− 44$$ +<8+$901+ -=@; ε<α−4$#

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@=; ε>$# +&$:+7(43&2&$+7$+ =;$# +<8+$%$:2&48+907&48'82&&++ =@; ε∞− +0<'0+07D&9$)04'8+7*-=; ε<$# +F+3538('(,+"+<0+6(:1*)0$E8+$<'60)F

/*472&$+ RR →⊂ "!# F +$:0+)&1&'$+ ∞+ + ?4+%*47'*)+ @Z$ +3$78+5&+4*1$&+3$78

%04':*+(:&70+ Z>ε +7(:0<%*430+ @Z=; >εδ +$<'60)+?47U'+(:&7$:0+$:+6&+ @@Z !$$$ ∈≠ +7*

=;Z εδ<− $$ +<8+$901+ -=; ε>$#

/*472&$+ RR →⊂ "!# F + $:0+ )&1&'$+ ∞− + ?4+ %*47'*)+ @Z$ + 3$78+ %04':*+ (:&70

Z>ε + 7(:0<%*430+ @Z=; >εδ + $<'60)+ ?47U'+ (:&7$:0+ $:+ 6&+ @@Z !$$$ ∈≠ + 7*

=;Z εδ<− $$ +<8+$901+ -=; ε<$#,°-+f($'0+%:(%:&0'82&)0+ )&1&'0)(:+30+ 6*472&&+ :0$)0+30+(+ <&4B*:8+9$:&$C&)8+ :0$)8

<0+%8<':0$E8+ 5&+ %04':*+ 6*472&&)0+ :0$)0+30+1$&+1*)'0+9$:&$C&)0+ :0$)0-+A0+ $<01040$@%:(%:&0'82&)0+)&1&'0)(:+30+6*472&&+:0$)0@+7$:0+4*+&1%)&78+:0)$2&$+30+(:3&40+5&+%:(3*<*)<0+%8<':0$E8+5&+%04':*+6*472&&)0+907'(:&$)0-

L5$3$:@+ 3$78+ #+ 0<'0+ (+ #%"&'()* 0)&23+(,-.+ 306&4&'8+ %0+1*)2&10$+ @"! R⊂ + 7*

9$)(:&+ ?4+ @;R + &$:+ Z$ + 0<'0+ *4+ %*47'+ 30+ $7*1*)$:0+ %04':*+ 1*)2&10$+ !@+ )&1&'$

6*472&0&*#++?4+%*47'*)* Z$ +<0+306&405'0+$<'60)F

K07'(:*)+#∈ ;R +0<'0+-(;(2,*#%"&'()(*0)&23+(,-)*#++?4+%*47'*)+ @Z$ +3$78+%04':*

(:&70+907&48'$'0+C+$+ )*&+#+ ;?4+ =;R +0Q&<'8+(+907&48'$'0+D+$+ )*&+ Z$ + ;?4+ ="R +$<'60)

?47U'+(:&7$:0+$:+6&+ @!D$ ¡∈ +7*+ @Z$$ ≠ +<8+$901+ -=; C$# ∈F+35+38('(,+"+3&4+7$E*)+6*472&&)(:+:0$)0+309&40+$7*1F/*472&$+ ;"!# RR →⊂F + $:0+ )&1&'$+ #+ ?4+ %*47'*)+ Z$ + 3$78+ 5&+ 4*1$&+ 3$78

%04':*+(:&70+ Z>ε +0Q&<'8+*4+4*18:+ @Z=; >εδ +$<'60)+?47U'+(:&7$:0+$:+6&+ Z$$ ≠ +3&4+!@

&40B$)&'$'0$+ =;Z εδ<− $$ +&1%)&78+ -=; ε<− #$#

G,&.*)$(:2.*-(;(2,*%")(*#%"&'((*0)&23+(,-)*B"2+<%"*5%"&2=*),*):2)*%"(&.?K07'(:*)+ #∈ ;R + 0<'0+ )&1&'$+ 6*472&0&+ #+ ?4+ %*47'*)+ Z$ + 3$78+ 5&+ 4*1$&+ 3$78

-Z=;)&1Z

=−→

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!g

F+3538('(,+ *:18'($:0+ :03*70+ <'*3&*)+ )&1&'0)(:+ 6*472&0&+ 907'(:&$)0+ )$+ 70)+ $))&1&'0)(:+7(1%(404'0)(:+<$)0+:0$)0-

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===→→

→→

,-+/&0+ Z@=@;@=@; " >∈= $4$$4$# 4 R +5&+ -Z@=@; " >∈ ,1, R

=-@;)&1=@;)&1 1,#,$4$# 14

14,$

14,$

===→→

→→

;1$,'$#',4,*4( +#$%&''/12( 2*4/*( )*( 342'47'/5( 3*%,12'4/5-+ /&0+ 6*472&$RR →⊂ "!# F +5&+*4+%*47'+ -Z !$ ∈

A>/N_NMN>-+H%"&'(,*#*):2)*&3"2("%.*B"*5%"&2%-+ Z$ +/,&.*5)"2+%*3+(&)*0)&(".2,2)

C+,*-%(+ =; Z$# +)$(:2.*3*0)&(".2,2)*D*,*-%(* Z$ +,:2#)-*B"&E2@+3+(&,+)*,+*#(+ !D$ ¡∈:.*,0);+ -=; C$# ∈

R$&+1042&(481+$)'0+3(*8+/)#("('((*$)0+7(4'&4*&'82&&@+07D&9$)04'0+7*+$70$<'$-OJGOGdNMNL+ .-+ /*472&$+ #+ 0<'0+ &3"2("%.* B"* 5%"&2%-* @Z$ + 3$78+ 5&+ 4*1$&+ 3$78@

%04':*+(:&70++5&:+ @@ST !$$ """ ∈∈ *N7(490:B04'+78':0+ @Z$ +$901

=-;=;)&1 Z$#$# ""

=∞→

OJGOGdNMNL+ "-+ /*472&$+ #+ 0<'0+ &3"2("%.* B"* 5%"&2%-+ @Z$ + 3$78+ 5&+ 4*1$&+ 3$78@%04':*+ (:&70+ 4*18:+ @Z>ε + 0Q&<'8+ *4+ 4*18:+ @Z=; >εδ + $<'60)+ ?47U'@+ (:&7$:0+ $:+ 6&

=;@ Z εδ<−∈ $$!$ +&1%)&78+ -=;=; Z ε<− $#$#

A$78+ Z$ + 0<'0+ %*47'+ 30+ $7*1*)$:0+ %04':*+1*)2&10$+"! R⊂ + <0+ %($'0+ 3$+ (

306&4&2&0+$+7(4'&4*&'82&&+7*+$b*'(:*)+)&1&'0&-A>/N_NMN>-+ /*472&$+ #+ 0<'0+ &3"2("%.* ?4+ %*47'*)+ Z$ + 3$78+ 5&+ 4*1$&+ 3$78

=@;=;)&1 ZZ

$#$#$$

=→

+$3&78+3$78+5&+4*1$&+3$78F

-Z=;=;)&1 ZZ

=−→

$#$#$$

!^

A$78+ 6*472&$+ #+ 0<'0+ 7(4'&4*8+ ?4+ 6&07$:0+ %*47'+ 3&4+ !@+ <0+ <%*40+ 78+ #+ 0<'07(4'&4*8+%0+;%-'(;),*!-

GHI>JKLMNN-+.-+ A$78+ %*401+ ?4+ 09&30428+ 7((:3(4$'0)0+ ZZ"

Z. @@@ "$$$ ! + $)0

%*47'*)*&+ @Z !$ ∈ + $'*47&+ 6*472&$+ #* 0<'0+ 7(4'&4*8+ ?4+ !$$$$ " ∈= =@@@; ZZ"

Z.Z !

3$78+ 5&+ 4*1$&+ 3$78@+ %04':*+ (:&70+ 4*18:+ :0$)+ @Z>ε + 0Q&<'8+ *4+ 4*18:Z=; >εδ + $<'60)+ ?47U'+ (:&7$:0+ $:+ 6&+ %*47'*)+ !$$$$ " ∈= =@@; ". ! + 7*

@Z$$ ≠ + &40B$)&'82&)0+ =;@=@;=@; ZZ""

Z.. εδ<−εδ<−εδ<− "" $$$$$$ ! + &1%)&78

-=@@@;=@@@; ZZ"

Z.". ε<− "" $$$#$$$# !!

>V>ROWX-+/*472&$+#+3$'8+%:&4

""

"" =$:77(<;=@;

4$

4$4$#

++=

306&4&'8+%0+1*)2&10$=SZ@ZT;hS.F=@T; """ £4$J4$! +∈=

0<'0+7(4'&4*8+%0+!-"-+A06&4&2&$+ 7(4'&4*&'82&&+ 6*472&&)(:+ :0$)0+ 30+ 9$:&$C&)8+ 907'(:&$)8+ ;30+ "

9$:&$C&)0+:0$)0=+<0+0Q'&430+5&+%04':*+6*472&&)0+907'(:&$)0-/&0+ 6*472&$+ ;"!# RR →⊂F + 5&+ *4+ %*47'+ -Z !$ ∈ + A06&4&2&$+ 3$'8+ %:&4

%:(%(E&2&$+"+%04':*+6*472&$+ RR →⊂ "!# F +<0+6(:1*)0$E8+$<'60)F

/*472&$+907'(:&$)8+ ;"!# RR →⊂F +0<'0+7(4'&4*8+?4+%*47'*)+ @Z !$ ∈ +3$78+5&4*1$&+ 3$78@+ %04':*+ (:&70+ 4*18:+ @Z>ε + 0Q&<'8+ *4+ 4*18:+ Z=; >εδ + $<'60)+ ?47U'@

(:&7$:0+$:+6&+ =@;@ Z εδ<−∈ $$!$ +&1%)&78+ -=;=; Z ε<− $#$#

<21-2'*,5&'(4/*(+#$%&''/12(2*4/*(%1$,'$#*-+O:(%:&0'82&)0+6*472&&)(:+:0$)0+30+(<&4B*:8+ 9$:&$C&)8+ :0$)8+ :81U4+ 9$)$C&)0+ 5&+ %04':*+ 6*472&&)0+ :0$)0+ 30+ 1$&+ 1*)'09$:&$C&)0-+/&0+6*472&$+ RR →⊂ "!# F +5&+ -Z !$ ∈

.-+A$78+6*472&$+#+0<'0+7(4'&4*8+?4+%*47'*)+ !$ ∈Z +;<$*+%0+1*)2&10$+!=+$'*47&# +0<'0+7(4'&4*8+?4+%*47'*)+ Z$ +;:0<%07'&9+%0+1*)2&10$+!=-

"-+A$78+6*472&$+#+0<'0+7(4'&4*8+?4+ Z$ +5&+ @Z=; Z ≠$# +0Q&<'8+(+907&48'$'0+D+$+)*&

Z$ +%0+7$:0+6*472&$+#+0<'0+3&60:&'8+30+E0:(-,-+A$78+6*472&$+#+0<'0+7(4'&4*8+?4+%*47'*)+ @Z$ +0Q&<'8+(+907&48'$'0+D+$+)*&+ Z$

%0+7$:0+6*472&$+#+0<'0+18:B&4&'8-!-+A$78+ RR →⊂ "!# F + 5&+ RR →⊂ "!7 F + <*4'+ 6*472&&+ 7(4'&4*0+ ?4

%*47'*)+ Z$ +;<$*+%0+1*)2&10$+!=+&$:+α+0<'0+*4+4*18:+:0$)+$'*47&+6*472&&)0+ 7# + +5&#α +<*4'+7(4'&4*0+?4+%*47'*)+ Z$ +;:0<%07'&9+%0+1*)2&10$+!=-]-+/&0+1*)2&1&)0+ "! R⊂ +5&+ -R⊂> +A$78+6*472&$+ >!# →F +0<'0+7(4'&4*8+?4

%*47'*)+ @Z !$ ∈ + &$:+ 6*472&$+ R→>7 F + 0<'0+ 7(4'&4*8+ ?4+ %*47'*)+ + @=; ZZ >$74 ∈=$'*47&+ 6*472&$+ 7(1%*<8+ R→!#7 F" + 0<'0+ 7(4'&4*8+ ?4+ %*47'*)+ -Z !$ ∈ + A$78+ #0<'0+ 7(4'&4*8+%0+1*)2&10$+!+ 5&+7+ 0<'0+ 7(4'&4*8+%0+1*)2&10$+>+ $'*47&+ #7 " + 0<'07(4'&4*8+%0+1*)2&10$+!-

!Y

,-,-+=*2'34,*(-42&'4/*

I8+7(4<&30:81@+%04':*+<&1%)&6&7$:0$+0Q%*40:&&@+6*472&$+ -F " RR →⊂!# +/&0=@; ZZ 4$ +*4+%*47'+&4'0:&(:+$)+1*)2&1&&+ "R⊂! +5&+ =@; 4$ +*4+%*47'+($:07$:0+3&4+!-A>/N_NMN>-+H%"&'(,* #* ,+)* B"* 5%"&2%-* =@; ZZ 4$ +/)+(0,2.* 5,+'(,-.* B"* +,53+2* &%

0,+(,1(-,*$=*/,&.*-(;(2,

Z

ZZZ =@;=@;)&1

Z $$

4$#4$#$$ −

−→

)$(:2.* I(* ):2)* #("(2.-+ K(;(2,* B":.I(* :)* "%;)I2)* /)+(0,2,* 5,+'(,-.* B"* +,53+2* &%0,+(,1(-,* $* ,* #%"&'()(* #* B"* 5%"&2%-+ =@; ZZ 4$ + I(* :)* "32),8.+ =@; ZZ 4$#$′ + :,%

$

4$#

∂∂ =@; ZZ +:,%*B"&.+ =-@; ZZ 4$#G$ +L5$3$:@

-=@;=@;

)&1=@;Z

ZZZZZ

Z $$

4$#4$#4$#

$$$ −

−=′→

P4+1(3+$<01848'(:@+ <%*401+78+ #%"&'(,* #* ,+)* B"*5%"&2%-+ =@@; ZZ 4$ +/)+(0,2.5,+'(,-.*B"*+,53+2*&%*0,+(,1(-.*4@+/,&.*-(;(2,

Z

ZZZ =@;=@;)&1

Z 44

4$#4$#44 −

−→

)$(:2.* I(* ):2)* #("(2.-+ K(;(2,* B":.I(* :)* "%;)I2)* /)+(0,2,* 5,+'(,-.* B"* +,53+2* &%0,+(,1(-,* 4* ,* #%"&'()(* #* B"* 5%"&2%-+ =@; ZZ 4$ + I(* :)* "32),8.+ =@; ZZ 4$#4′ + :,%

4

4$#

∂∂ =@; ZZ *:,%*B"&.+ =-@; ZZ 4$#G4 +L5$3$:@

-=@;=@;

)&1=@;Z

ZZZZZ

Z 44

4$#4$#4$#

444 −

−=′→

A>/N_NMN>-+ /*472&$+ #+ $:0+ /)+(0,2.* 5,+'(,-.+ ?4+ :$%(:'+ 7*+ $+ ;:0<%07'&9+ 4=+ 5)* 3:%1;%-'(;)* @!L ⊂ + 3$78+ #+ $:0+ 30:&9$'8+ %$:2&$)8+ ?4+ :$%(:'+ 7*+ $+ ;:0<%07'&9+ 4=+ ?46&07$:0+ %*47'+ -=@; L4$ ∈ + A$78+ 6*472&$+ #+ $:0+ 30:&9$'8+ %$:2&$)8+ ?4+ :$%(:'+ 7*+ $

;:0<%07'&9+ 7*+4=+ %0+1*)2&10$+L+ $'*47&+ 6*472&$+ $# ′ ;:0<%07'&9+ =4# ′ + 306&4&'8+ %0+L+ <04*105'0+/)+(0,2,*5,+'(,-.*,*#%"&'()(*#*B"*+,53+2*&%*$*;:0<%07'&9+B"*+,53+2+7*+4=+5&+<0

4('0$E8+ $# ′ +<$*+ $#

∂∂+<$*+?478+ #G$ +

+:0<%07'&9 4# ′ ++<$*+ 4#

∂∂+ -?478<$*

#G4

O:$7'&7@+ 30:&9$'$+ %$:2&$)8+ $# ′ + <0+ 7$)7*)0$E8+ 7(4<&30:U43+ ?4+ =@; 4$# + %0+ 47(4<'$4'+5&+30:&9U43+%0+ #+ +7$+(+6*472&0+30+(+<&4B*:8+9$:&$C&)8@+$-+A0:&9$'$+%$:2&$)8

4# ′ +<0+7$)7*)0$E8+7(4<&30:U43+?4+ =@; 4$# +%0+$+7(4<'$4'+5&+30:&9U43+%0+#+7$+(+6*472&030+(+<&4B*:8+9$:&$C&)8@+4-

>V>ROW>-+.-++/&0+6*472&&)0+#=*7*306&4&'0+%0+ "R +%:&4F

-=@;@=@; $44$74$4$# =+=

]Z

L901-=@;@=@;@.=@;@.=@; $4$744$74$#4$# 4$4$ =′=′=′=′

"-+/&0+6*472&$+#+306&4&'8+%0+ "R +%:&4

-$:7'B=;=@; ""

4

$4$4$# +=

L901

44

$$

4$

44$

4

$$4$#$ +=

+++=′ $:7'B"=;$:7'B"=@;

""""

-$:7'B"=;$:7'B"=@;""

"" $4

$4

4$

$4$

4

$44$#4 −=

++−=′

,-+/&0+6*472&$+#+306&4&'8+%0+<01&%)$4*)+30<7D&<+ Z>$ +%:&4

-=@; ", 4$4$4$# −=L901

."",=@; −−=′ 4$ 4$4$4$#

-)4"=@; , $$4$4$# 44 −=′

53$6*-%(-*'(8%9$%,9#("#,2$*(+*,)&''-#($#%-#(.#(.3*1(/%$'%0'-#($#%-#4/&0+6*472&$+ RR →⊂ "F !# +5&+ =@; ZZ 4$ +*4+%*47'+ &4'0:&(:+1*)2&1&&+!-+I8+$)0B01

*4+ %*47'+ $:C&':$:+ =@; 4$ + 3&4':a(+ 907&48'$'0+ C+ $+ )*&+ =@; ZZ 4$ + 5&@+ (3$'8+ $)0<@+ <8

1042&401+6&Q+%*47'*)+ =@; 4$ -+I8+%:0<*%*401+78+0Q&<'8+30:&9$'0)0+%$:2&$)0+ $# ′ +5&+ 4# ′

%0+907&48'$'0$+C+$+)*&+ =@; ZZ 4$ +5&+<8+7(4<&30:81+0B$)&'$'0$

=@;=@;=@;=@;=@;=@; ZZZZZZ 4$#4$#4$#4$#4$#4$# −+−=− ;.=

/&0+ C4% ∈=@; + 5&+ C0$ ∈=@; Z + 3(*8+ %*47'0+ $:C&':$:0+ 3&4+ 907&48'$'0$+ C+ $

%*47'*)*&+ =-@; ZZ 4$ +I8+4('81

=-@;=;=c@;=; Z 0$#04%#% =ψ=ϕ ;"=

A0($:070+30:&9$'0)0+%$:2&$)0+ $# ′ +5&+ 4# ′ +0Q&<'8+%0+907&48'$'0$+C@+6*472&&)0+ϕ+5&+ψ+<*4'30:&9$C&)0+5&+$901

=-@;=;=c@;=; Z 0$#04%#% 4$ ′=ψ′′=ϕ′ ;,=

L%)&7U43+ '0(:01$+7:05'0:&)(:+ 6&4&'0+ 6*472&&)(:+ϕ+ 5&+ψ@+ 303*701+78+ 0Q&<'8+ *4%*47'+ =@; Z $$∈ξ +5&+*4+%*47'+ =@; Z 44∈η +$<'60)+?47U'

==;;=;=;=c=;;=;=; ZZZZ 4444$$$$ 4$ −ηψ′=ψ−ψ−ξϕ′=ϕ−ϕ

$3&78@+*'&)&EU43+;"=+5&+;,=@

==;@;=@;=@; ZZ $$4#4$#4$# $ −ξ′=−5&

=-=;@;=@;=@; ZZZZZ 44$#4$#4$# 4 −η′=−

].

>B$)&'$'0$+;.=+309&40

=-=;@;==;@;=@;=@; ZZZZZ 44$#$$4#4$#4$# 4$ −η′+−ξ′=−

L70$<'8+ :0)$2&0+ <0+ 4*105'0+ #3+;%-,* -%(* K,7+,"7)* 5)"2+%* #%"&'((-)* +),-)* /)/3%.*0,+(,1(-)*+),-)-

L<$3$:@+ /,&.* /)+(0,2)-)* 5,+'(,-)+ $# ′ + I(+ 4# ′ + ,-)* #%"&'()(+ RR →⊂ "F !#

)$(:2.*5)*3* 0)&(".2,2)*C* ,* 5%"&2%-%(+ =@; ZZ 4$ + ("2)+(3+* -%(+!@+,2%"&(* 5)"2+%* 3+(&)

5%"&2* C4$ ∈=@; +)$(:2.*%"*"%;.++ξ+&%5+(":* B"2+)+ Z$ +I(*$* I(*%"*"%;.+*η* &%5+(":B"2+)* Z4 *I(*4*,:2#)-*B"&E2**,+)*-3&*#3+;%-,*-%(*K,7+,"7)?

X'&)&EU43+6(:1*)$+)*&+W$B:$4B0+301(4<':81f>GJ>RL-+G,&.*#%"&'(,*#**,+)*/)+(0,2)*5,+'(,-)*;.+7("(2)*B"2+<3*0)&(".2,2)*C

,*-%(* =@@; ZZ 4$ *("2)+(3+*-%(*!@*,2%"&(*#*):2)*&3"2("%.*B"*5%"&2%-* =-@; ZZ 4$

GMN6AOPJLQRM?+ /*472&&)0+ $# ′ + 5&+ 4# ′ + 6&&43+ 18:B&4&'0+ %0+ C@+ 0Q&<'8+ *4+ 4*18:@Z>K +$<'60)+?47U'

@=@;@=@; K4$#K4$# 4$ ££ ′′

%04':*+(:&70+ -=@; C4$ ∈A&4+6(:1*)$+)*&+W$B:$4B0+:0E*)'8

-=;

=@;=;=@;=@;=@;

ZZ

ZZZZ

44$$K

44$#$$4#4$#4$# 4$

−+−

−⋅η′+−⋅ξ′−

£

££

A$:

Z==;)&1 ZZ

Z

Z

=−+−→→

44$$44$$

5&+307&=@;=@;)&1 ZZ

Z

Z

4$#4$#44$$

=→→

$3&78+6*472&$+#+0<'0+7(4'&4*8+?4+%*47'*)+ =-@; ZZ 4$

=*2'34,*/*(-42&'4/*(4/*(#$*'( +#$%&''( 2*4/*()*(!( 342'47'/*( 2*4/*-+ /&0+ $7*16*472&$+ =,;F > RR "!# " →⊂ +5&+ =@@@; ZZ

"Z.Z "$$$$ != +*4+%*47'+&4'0:&(:+1*)2&1&&+!-

A>/N_NMN>-+ H%"&'(,* #* ,+)* /)+(0,2.* 5,+'(,-.* B"* 5%"&2%-* Z$ * B"* +,53+2* &%

0,+(,1(-,* S$ */,&.

Z

ZZ"

Z.

ZZ.

Z.

Z"

Z. =@@@;=@@@@@@@;

)&1SS

""SSS

$$ $$

$$$#$$$$$$#

S −−+−

→

!!!

)$(:2.* I(* ):2)* #("(2.-+ K(;(2,* B":.I(* :)* "%;)I2)* /)+(0,2,* 5,+'(,-.* ,* #%"&'()(* #* B"

+,53+2* &%* S$ * I(* :)* "32),8.* =@@@; ZZ"

Z. "$ $$$#

S!′ * :,%*

S

"

$

$$$#

∂∂ =@@@; ZZ

"Z. !

* :,%* B"&.

=-@@; ZZ. "$ $$#G

S!

]"

/*472&$+ RR →⊂ "!# F +$:0+"+30:&9$'0+%$:2&$)0+?4+%*47'*)+ -=@@@; ZZ"

Z. !$$$ " ∈!

>V>ROW>-+.-+A$78+ #+ 0<'0+(+ 6*472&0+ :0$)8+30+ ':0&+ 9$:&$C&)0+ :0$)0+ 306&4&'8+ %0+ (1*)2&10+ ,R⊂! + 5&+ 3$78+ ;,@* 1@* &T+ 0<'0+ *4+ %*47'+ &4'0:&(:+ 1*)2&1&&+ !@+ 70)0+ ':0&30:&9$'0+$)0+)*&+#+<*4'F

,$

&1,#&1$#&1,#G

$

&1,#&1,#

,$$$ −

−==∂

∂=′→

=@@;=@@;)&1=@@;

=@@;=@@;

14

&1,#&4,#&1,#G

4

&1,#&1,#

1444 −

−==∂

∂=′→

=@@;=@@;)&1=@@;

=@@;=@@;

&8

&1,#81,#&1,#G

8

&1,#&1,#

&888 −

−==∂

∂=′→

=@@;=@@;)&1=@@;

=@@;=@@;

%04':*+(:&70+ -=@@; !84$ ∈"-+A0:&9$'0)0+%$:2&$)0+$)0+6*472&0&+ RR →,F# +306&4&'8+30

"""=@@; 84$84$# ++=<*4'

"""""""""cc

84$

8#

84$

4#

84$

$# 84$

++=′

++=′

++=′

7*+ =-Z@Z@Z;=@@; ≠84$A0($:070+ 30:&9$'0)0+ %$:2&$)0+ $)0+ 6*472&0&+ =";F >RR "!# " →⊂ + <*4'+ 7D&$:

30:&9$'0)0+ 6*472&&)(:+%$:2&$)0+$)0+ )*&+ #+ ;7$:0+ <*4'+ 6*472&&+ :0$)0+30+(+ <&4B*:8+9$:&$C&)8:0$)8=@+:0E*)'8+78+(%0:$2&&)0+$)B0C:&70+0607'*$'0+$<*%:$+6*472&&)(:+:0$)0+30+"+9$:&$C&)0:0$)0+7$:0+$*+30:&9$'0+%$:2&$)0+7(43*7+'('+)$+6*472&&+7$:0+$*+30:&9$'0+%$:2&$)0-+J0B*)&)030+30:&9$:0+$+<*10&@+3&60:0420&@+%:(3*<*)*&@+7U'*)*&+6*472&&)(:+30+"+9$:&$C&)0+:0$)0+7$:0$*+30:&9$'0+%$:2&$)0+<*4'+$70)0$5&+7$+5&+%04':*+6*472&&)0+:0$)0+30+(+9$:&$C&)8+:0$)8-

f($'0+%:(%:&0'82&)0+:0)$'&90+)$+30:&9$'0)0+%$:2&$)0+$)0+6*472&&)(:+:0$)0+30+3(*89$:&$C&)0+:0$)0+:81U4+$3098:$'0+5&+%04':*+30:&9$'0)0+%$:2&$)0+$)0+6*472&&)(:+:0$)0+301$&+1*)'0+9$:&$C&)0-

=*2'34,*/*( -42&'4/*( 4/*( #$*'( +#$%&''( 3*%,12'4/*-+ /&0+ ;"!# RR →⊂F + (

6*472&0+ 907'(:&$)8+ $)0+ 78:0&+ 7(1%(404'0+ :0$)0+ ;### @@@ ". ! + $*+ 30:&9$'0

%$:2&$)0+ ?4+ :$%(:'+ 7*+ ==@@@;;@@@ ".". !$$$$$$$ "" ∈= !! + ?4':a*4+ %*47'

@@@; Z"

Z.Z !$$$ = + -N4'=@ Z !$" ∈!

H%"&'(,* #* ,+)* /)+(0,2.* 5,+'(,-.* B"* +,53+2* &%* S$ * B"* 5%"&2%-* Z$ * /,&.* 23,2)

&3;53")"2)-)*+),-)* ;### @@@ ". ! *,%*/)+(0,2.*5,+'(,-.*B"*+,53+2*&%* S$ *B"*5%"&2%-

Z$ ?*G)+(0,2,*5,+'(,-.*S$

$#

∂∂ =; Z * ):2)* 0)&23+%-*/("* ;R * &,+)*,+)*/+)52* &3;53")"2)

/)+(0,2)-)*5,+'(,-)*B"*+,53+2*&%* S$ *,-)*#%"&'((-3+* -@@@ ". ;### ! +A07&

-=;

@@=;

@=;=; ZZ"Z.Z ;

S

;

SSS $

$#

$

$#

$

$#

$

$#R∈

∂

∂∂

∂∂

∂=∂

∂!

],

f($'0+%:(%:&0'82&)0+ :0)$'&90+ )$+ 30:&9$'0)0+ %$:2&$)0+ $)0+ 6*472&&)(:+ :0$)0+ 30+1$&1*)'0+ 9$:&$C&)0+ :81U4+ $3098:$'0+ 5&+ %04':*+ 30:&9$'0)0+ %$:2&$)0+ $)0+ 6*472&&)(:907'(:&$)0-

>V>ROWX-+/*472&$+ ,,F RR →# +306&4&'8+%:&4

++++++=

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@Z=@;=@;)&1 ZZ

Z

Z

=ϕ=ϕ→→

4$4$44$$

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-=;=;=@;=;=;=@;=@; "Z

"ZZZZZ 44$$4$44$$4$#4$# −+−ϕ+−β+−α=−

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899999 !!""!"!"!"!"## −+−=−==

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45765656576576 9999 #!"!!""!"$!"$ ϕ+−β+−α=−@2+>$%&

49576>.+,

9

9

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A$31'$0$

7565675656 89

899

89

899 !!""!!!!"""" −+−−−+−− <<

1().30)+%$=1.+&;<+.$)) 4B576>

7B576>

99 <<!"

!!

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"" −−

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89

899999 56565765656576576 !!""!"!!""!"$!"$ −+−ϕ+−β+−α=−

.(;,)) 79!! = )3?<+%$,

457656576576 999999 ""!"""!"$!"$ −ϕ+−α=−

A$)1+0+7)-'+%)J,-;'<+'$1)0() 799 ≠− "" )'$K(.&;

4576576576

9

99

9

999

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576576576

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999

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49576576.+,

576.+,576.+,

999

9

99

9

99

9

99

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ϕ

→

→→

!"!"

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!N

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457656576576 999999 !!!"!!!"$!"$ −ϕ+−β=−

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576576576

.+, 999

999

9

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%.;<+/01&,-.4)U+$)$=1.+&1&$1

#!"!!""!"$!"$ 5765656576576 9999 ϕ+−β+−α=−

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[ ] 9576576.+, 99

9

9

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9

9

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7

0$$1)0$)1'1&;)0;)/(%0<+1)$)$*&$)03%&+%(;)J%)-(%0&(.) 5476 99 !"

:DPQ@:FPGR4)%&'()$*+',-&)$)./0.)#-$.1.+,-&2-3()5.);*3,-;.&)6)&0*+'-).&)./0.'<+0-+*()5.)64

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DVQ@CWHGFF4)B°4)U+$) /(%0<+1) 5X6Y >RR +6$ + →⊂ ) I+) 57776 998

9B9 +"""" !=

(%)-(%0&)+%&$'+3')1.),(.<+,++)64

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U(%0<+1)$)$*&$)>+/$'$%<+1?+.;)J%)-(%0&(.) 5776 99B9 +""" != )>10;)$S+*&;)%(,$'$.$

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89B +""" ! )1>+0;

795777657776.+, 998

9B8B

9

988

9BB

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→

→→ ++

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#""""""""$"""$ +

+

----++ 57776565777657776

B8B

9998

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=ϕ+−α=− !!!

(%>$

456B

89∑=

−=+

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7F%&576 99 6!" ∈ )>10;)&31&$)03,-3%$%&$.$) ;$$$ 777 8B ! )*(%&)>+/$'$%<+1?+.$)J%)10$*&

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;-#!"!!""!"$!"$ ----- 7787B75765656576576 9999 !=ϕ+−β+−α=− 7

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J%)-'3-3K+<+1)B7)'$K(.&;

)!

!"$

"

!"$ --

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∂=β

∂∂

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7576 9999 7

1>+0;

7576576

77576

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"

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∂=

∂∂

∂∂=αα=α !!

4576576

77576

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!

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∂=

∂

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!"

#$!$!"#$%&%'(#)*)!+'%#!$+',(##!-%!!!.)&#)/#*%!&%)*%

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3,4:,;&'<*'82*(=2;' >5? @@ #$ ',*=./,)/'02;3,0,,'!$'AB,+=&'-.(,'.C4;,=4=.4

5>5?>>?5?>>?5?>5?>5? @@@@@@@@ %#$###$"$$#$"#$"#$" #$ ϕ+−′+−′=−2*-.

$>?>?5@>5?>5?;,0 7@

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@

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>5? @@ #$ 'E,'+.'*)=.4H&' >$5?- @@ #$" 'GE4-4/

>$>?5?>>?5?>5I5?- @@@@@@@@ ###$"$$#$"#$#$" #$ −′+−′=D.)4/.(.

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?>@?@ = $#$& = ) I+3*+',) 92+'2,2/) .-/) J+..2() 2D/598) -3) 6-349) ?((@ = $$∈ξ ) &%48

$$ <= )@5%-) ?((@ =$$∈ξ )&%48) $$ >= ?)%59*2.)<34K9) >=?@ =ξ′& )F%'

α−−−=

=α−−−+−

−−

−′′′−+′′−−′′−+′−′=′

−+

−+−

B?B@

B?B@?@B

L

?@?@A

?@

?@?@A

?@?@

?AB@

?@

?@AL?@

?@AB

?@AB

?@?@?@

%!!

%!!

!!

'$%'#!

'$

'$%'#!

'$'#

!

'$

'#'$

'#'$

'#'$

'#'#'&

!

!

$/

>=?@?@A?@

?@ B?B@ =αξ−−ξξ−=ξ′ −+ %!!

$%#!

$&

F2)%/4/)+G:/32,

>?@A?@ ?B@

B

ξξ−=α ++−

!%!

#%!

$

J27-.98

>?@A

?@?@?@ ?B@

B= ξξ−−= +

+−!

%!%

! #%!

$$$$(

M-K3&) (B+= !% )+G:/32,

>?@?AB@

?@?@ ?B@

B= ξ

+−= +

+!

!

! #!

$$$(

C-G)%42%598)*+',8() !( )52)3-,2$92))*+',-.-,/.01&)1!&*>

F2+%'242) ξ )2592)4-6'/35)<39'2) =$ )$/)$()2D/598)-3)3-,8') B= <θ< )%59*2.)<34K9

?>@ == $$$ −θ+=ξ ) F%48) 3+98,) (=$$2 −= ) %9-34/) ?(B=@= <θ<θ+=ξ 2$ ) /%'*+',-.%).-/)0%1.+')&2)+'&/3-.)!()4+'256-3789+%'2)*-34:/2/)'2%.2)&2)+)H%'/%G/.8)#()<36-349-.) (=$ )52)54'/2

?(@?AB@

?@A

?@AB

?@?@ =?B@

B

=?@

=== 2$#!

2$#

!

2$#

2$#2$# !

!!

!θ+

++++′+=+ +

+!

-3&2)'259-.) !( )2592)54'/5)<3)*+',%).-/)M%E'%3E2>

!N

O3)6%'9/4-.%'()&%48) "∈= )$/)&%48).-8,) (== =$ )*+',-.%).-/)0%1.+')4-)'259-..-/)M%E'%3E2)&2H/32

?B=@?(@?AB@

?=@A

?=@AB

?=@?@ ?B@B

?@ <θ<θ+

+++′+= ++

$#!

$#

!

$#

$#$# !

!!

!

!

C-G)%42%598)*+',8()*+',-.%).-/)0%1.+')@<3)6-349-.)=()4-)'259-.).-/)M%E'%3E2?)52),%/3-,2$92)#3)4,-1.-,/.516.01,)/!>

!"#$%#%#&'()*%#%+) ?>(@ 7$(! )P/2)&/3)3+-) RR →⊂ L; "# )$/)6-349-.)/392Q

'/+') >?(@ == "7$ ∈ ) C8) 6'25-6-32,) 48) *-34:/%) #) *+'*. 8/#*)*!9/1:/-;. 8*) n +1 ) 3)/<!')=3. >*6/!;'1'*) ?) 1. @,!6',-,/) ?(@ == 7$ ) A/. +;. -,;4) ?(@ BB 7$ ) 1):/')1). <!. >*6/=!;'1'*1)?>

C8) 4+35/&2'8,) *-34://.2) R→RB(=S;$ ) $/) (RB(=S; R→7 ) &2*/3/92) 6239'-+'/42) RB(=S∈' )6'/3)'2.%://.2

'$$$'$ ?@?@ =B= −+=

'777'7 ?@?@ =B= −+=

$/)*-34:/%)4+,6-58)&)&2*/3/98)6239'-) RB(=S∈' )6'/3)2E%./9%92%

?>?@(?@@??@?(@@?@ =B==B= '777'$$$#'7'$#'& −+−+==

TG52'H8,)48)*-34:/%)4+,6-58)&)2592)&/*2'23:/%G/.8)&2) B+! )+'/)62)S=()BR)$/

>B((L(B??(@?(@@?@&?@&?@& +=

∂∂+

∂∂= !%'7'$#'7

7'$

$'&

%

% !

F%') '77'7'$$'$ &?@?@&(&?@?@& =B=B −=−= )$/)&24/

>&??@?(@@?@?@?@& =B=B%

%

% ''7'$#777

$$$

'&

−

∂∂+−

∂∂=

#$%&%'

??(@?(@@?@?@&?@&

=B=B '7'$#777

$$$'

'&%

%

%

−

∂∂+−

∂∂=

/%'

>B((B?((@?@?@?=@&

===B=B +=

−

∂∂+−

∂∂=

∂!%7$#77

7$$

$'

&%

%

%

!

U2) &2) %.98) 6%'92() &2+%'242) *-34:/%) &) 2592) &2'/H%G/.8) &2) B+! ) +'/) 62) S=() BR(6-92,)54'/2)*+',-.%).-/)V%4)M%-'/3)&2)+'&/3-.)!()4+'256-3789+%'2)*-34:/2/)&)@&2)+H%'/%G/.8?>)#H2,

?>B=@?(@?AB@

?=@A

?=@AL

?=@AB

?=@?@ ?B@B

?@L

<θ<θ+

+++′′+′+= ++

'&!

'&

!

'&

'&'

&'& !!

!!

!

!W

TG52'H8,) 48) ?(@??=@?(=@@?=@ == 7$#7$#& == ) /%') == ??B@?(B@@?B@ 7$#&

?>(@ BB 7$#=F/3)*+',-.%).-/)V%4)M%-'/3)'27-.98

?>@?AB@

B?=@

AB

?=@ALB

?=@ABB

?=@?B@ ?B@?@ θ+

+++′′+′+= +!! &!

&!

&&&& !

F24/

??>@?(@@?@?@?AB@

B

?(@?@?@A

B

?(@?@?@ABB

?(@?B@?(@

B

=B=B

===B=B

===B=B==BB

θθ

−

∂∂+−

∂∂

++

+

−

∂∂+−

∂∂+

+

−

∂∂+−

∂∂+==

+

7$#777

$$$!

7$#777

$$$!

7$#777

$$$

7$#&7$#

!

!

!

!

F%48)3+98,) ?@?(@ θ=ηθ=ξ 7$ )$/):/32,)52%,%)48)6-349-.) ?(@ BB 7$ )%)*+59)%.25

%'G/9'%') <3) H24/389%92%) ?. %) 6-349-.-/. ?(@ == 7$ ) '27-.98) 48) 6239'-) +'/42) 6-349

?7$ ∈?(@ ) 2D/598) -3) 6-349) ?(@ ηξ ) @62) 52E,239-.) 42) -32$92) ?(@ == 7$ ) 4-) ??(@ 7$

%59*2.)<34K9

?>(@?@?@?AB@

B

?(@?@?@A

B

?(@?@?@ABB

?(@?(@

B

==

====

======

ηξ

−∂∂+−

∂∂

++

+

−

∂∂+−

∂∂+

+

−

∂∂+−

∂∂+=

+

#777

$$$!

7$#777

$$$!

7$#777

$$$

7$#7$#

!

!

!

!

F2)%/4/)&2&-42,

?(@?@?@?AB@

B?(@

B

== ηξ

−

∂∂+−

∂∂

+=

+

#777

$$$!

7$(!

!

$/>=?(@./,

=

=

=→→

7$(!77$$

#,)&2,+359'%9) &24/) 48()816;. #,!69/1) RR →⊂ L; "# ) *+'*. 8/#*)*!9/1:/-;8*. B+! )3)/.<!')=3.>*6/!;'1'*.?.1.@,!6',-,/. "7$ ∈?(@ == )1',!6/B.@*!'),.3)/6*.@,!6'

?7$ ∈?(@ )*$/+';.,!.@,!6'. ?∈ηξ ?(@ )@@*.+*&4*!',-.61)*.,!*A'*.@,!6'*-*. ?(@ == 7$A/) ??(@ 7$ )1+'#*-.<!6C'

?>(@?@?@?AB@

B?(@

B

== ηξ

−

∂∂+−

∂∂

+=

+

#777

$$$!

7$(!

!

!"

#$%&'()*++,-.,-!"#$% &'(#)*"% RR →⊂ /0 +& -",-%.-,*/"0-%1",)*"2-%.-%3,.*4

('2%(%#3(0*('-%5(0,43%/-#*($0"0-%6%"%1'(#0'2'*% 1+23415 "" +78 ∈ -,-90'2%&3,:'2-*%2'*

;"723,%.-%3,.*('2%(<%#3,-91'(=$03",-%&'(#)*-*%&%%5(%1'(#0'2% 4115 "" 78 -9-%13"0-%1'(-9'>%&3,:"

4154156

.415 78.78(

78? (( ϕ=

'(.-% &'(#)*"- RR →⊂ϕ /0 + - -90-% #3(0*('$% @*% ('2$% 5(% 1'(#0'2% 415 "" 78 <% *",

,4545415 /"

/" 778878. −+−=

72-89:3;<=>9:1-."#$%&'(#)*"- RR →⊂ /0 +& -",-%.-,*/"0-%1",)*"2-%.-%3,.*('2

.3*% #3(0*('-% 5(0,43% /-#*($0"0-% 6% "% 1'(#0'2'*% 4115 "" 78 - "0'(#*% 1-(0,'% 3,*#-678 ∈415 -",-%23#%&3,:'2"

?,454@5415/.

45415

4455415

/45415

/.

45415

45415

415415

/"

/"

/"/

""/

""""

//

"/""

/

"""

"""

""

778878

777

78&7788

78

78&88

8

78&

777

78&88

8

78&78&78&

−+−ϕ+

+

−

∂∂+−−

∂∂∂+−

∂∂+

+−∂

∂+−∂

∂+=

/,-AB:C=>9->=;-D9E>B:-F93G-9;<;-8H23:=-I=2<J;;>H-:H9>H-FH-FB=G-K9:;9L;>H-:H9>H5M;- N2-89:3;<=>9:-8H23:=- I=2<J;;>H- :H9>H-FH-B-K9:;9L;>G- :H9>G4- OH-8B93H- O<:;H- N2-CBF9OHCG2G3B:-M;-8H23:=-I=2<J;;>H-:H9>H-O9=-KH<3B:;9>H-FH- 4P5 ≥(( -K9:;9L;>H-:H9>H,-QH9OHCH2H9-3HB:HCH>H-8:HRH2393H-C9;-O=O-:GCS2-9FHKG:93H-M;-8H23:=-I=2<J;;>H-FH-C9;C=>3H-K9:;9L;>H,

P,!,!"#$%&'&(&!)*+,-..(/%!%&0(&!1&! 4/5 >(( !20%.03.(&!%&0(&

A;H- RR →⊂ /0 +& -B-I=2<J;H-:H9>G-FH-FB=G-K9:;9L;>H-:H9>H-81%71-FHI;2;3G-8H

C=>J;CH9- /R⊂+ -M;- 415 "" 78 -=2-8=2<3-9>-C=>J;C;;-+,

Q&A+T+*+&,- A'(#0'2- +78 ∈415 "" - -90-% 1'(#0% .-% :"8*:% 23#"2% 5,-2"0*/4% "2&'(#)*-*% &<% ."#$% -8*90$% 3% /-#*($0"0-% 6% "% "#-90'*% 1'(#0<% "90&-2% 5(#B0% 1-(0,'% 3,*#-

4,154151415 "" 78&78&+678 <¡∈ -A'(#0'2% +78 ∈415 "" - -90-% 1'(#0% .-% :*(*:23#"2% C,-2"0*/D% "2% &'(#)*-*% &<% ."#$% -8*90$% 3% /-#*($0"0-% 6% "% 9"<% "90&-2% 5(#B0<% 1-(0,'3,*#-% 4,154151415 "" 78&78&+678 >¡∈

U=2<3H>H-FH-C9V;C->B<9>-M;-FH-C;2;C->B<9>-OH-2=CHO<-1'(#0-%.-%-80,-:%23#"2C,-2"0*/D-9>H-I=2<J;H;-&,

!.

Q9<G- 415 "" 78 - HO3H- =2- 8=2<3- FH- C9V;C- >B<9>- 5C;2;C- >B<9>4- 9>- I=2<J;H;- &1

93=2<;- 415 "" 78& - OH-2=CHM3H-:"8*:%23#"2- 5:*(*:%23#"24%9>- I=2<J;H;,-W9V;CH>H-M;C;2;CH>H->B<9>H-5:H>93;KH4-OH-2=CHO<--80,-:-%23#"2-%5,-2"0*/-4-9>H-I=2<J;H;-&,

A;H- 415 "" 78 -=2-8=2<3-FH-HV3:HC-5>B<9>4-9>-I=2<J;H;-&1-;23H:;B:-C=>J;C;;-+,-%G

8:HO=8=2HC-<G-I=2<J;9-&-9:H-FH:;K93H-89:J;9>H- 8& ′ -M;- 7& ′ -N2-8=2<3=>- 4,15 "" 78 -)3=2<;1

I=2<J;9-89:J;9>G- 10"

RR →⊂ϕ 7+ -FHI;2;3G-8H-C=>J;CH9

X41510Y ""+7888+7 ∈∈= R

HO3H- FH:;K9L;>G- N2- 8=2<3=>- ,"8 - )KHC- 41545 "78&8 =ϕ - M;- 4,1545 """ 78&8 8′=ϕ′QHB9:H<H- "8 -HO3H-=2-8=2<3-;23H:;B:-C=>J;C;;-+-M;-=2-8=2<3-FH-HV3:HC-9>-I=2<J;H;-ϕ1N2-L9R9- 3HB:HCH;- >=;-AH:C931-FH:;K939- ϕ′ -9- I=2<J;H;-ϕ- OH-92=>H9RG- N2-8=2<3=>- 1"8

9F;<G- ,"45 " =ϕ′ 8 -'HR=>3G- ,"415 "" =′ 78&8ZB2O;FH:S2F-98B;-I=2<J;9-89:J;9>G- 10

"RR →⊂ψ 8+ -FHI;2;3G-8H-C=>J;CH9

X41510Y ""+7877+8 ∈∈= R

OH-9:93G-<G- ,"415 "" =′ 78&7)M9F9:1-9:H->B<-1,313=*)*"0!"#$% &'(#)*"% &% ",-% .-,*/"0-% 1",)*"2-% 5(0,4'(% 1'(#0% .-% -80,-:- 4115 "" 78

*(0-,*3,%:'2)*:**%+<%.-,*/"0-2-%1",)*"2-% 8& ′ -M;- 7& ′ -9-%"('2-"=$%5(%"#-90%1'(#0<-9F;<G

,"4151"415 """" =′=′ 78&78& 78

#$%&'()*++,-.,-U:B8BR;J;9-FHCB2O3:93G-9;<;-HO3H-9FHKG:93G-M;-F9<G- 415 "" 78 -2=HO3H-8=2<3- ;23H:;B:-C=>J;C;;-+1-F9:-+-<B2J;2H-FB=G-OH[CH23H1-=2=>-89:9>H>-<=-9V9#81- ;9:- <H>G>9>3- <=- 9V9- #71- <9:H- OH- ;23H:OH<3H9RG- N2- 415 "" 78 - 9O3IH>- <9- 8=2<3=>

415 "" 78 -OG-2=-OH-9I>H->9-2;<;-=29-F;2-HV3:HC;3GJ;>H-<H>B:-FB=G-OH[CH23H,

/,- A;H- 415 "" 78 - =2- 8=2<3- ;23H:;B:-C=>J;C;;-+,- Q9<G- 415 "" 78 - HO3H- =2- 8=2<3FH- HV3:HC- 9>- I=2<J;H;- &- M;- F9<G- &- HO3H- F;IH:H2J;9L;>G- N2- 9<HO3- 8=2<31- 93=2<;

1"415F "" =78& -<HH9-<H-:HR=>3G-;CHF;93-F;2-H[9>;393H9

778&878&78& 78 F415F415415F """""" ′+′==2FH

,"4151"415 """" =′=′ 78&78& 78

P,-E(%1'(#0% 415 "" 78 - *(0-,*3,%:'2)*:**%+<% 1-(0,'% #",-% 1"415F "" =78& - O9=1

<HH9-<H- HO3H- 9<H>9M;- >=<:=1- 8H23:=- <9:H- "4151"415 """" =′=′ 78&78& 78 - 9-%(':-@0-

1'(#0% 90")*3(",% "2% &'(#)*-*% &F- )M9F9:1- F9<G- 415 "" 78 - HO3H- =2- 8=2<3- O39J;B29:- 9>

I=2<J;H;- &1- I=2<J;9- &- HO3H-F;IH:H2J;9L;>G- N2- 415 "" 78 - M;- 9:H- FH:;K93H- 89:J;9>H- 2=>H- N29<HO3-8=2<3,

!/

Q;2-1,313=*)*"-FHCB2O3:93G-C9;-O=O-:HR=>3G-<G-3,*#-%1'(#0%.-%-80,-:%523#"24.*(%*(0-,*3,'2%:'2)*:**%+<%5(%#",-%&'(#)*"%&%-90-%.*&-,-()*">*2$<%-90-%1'(#0%90")*3(","2% &'(#)*-*% &F% G8*90$% 5(9$% 1'(#0-% 90")*3(",-% "2-% &'(#)*-*% &% #",-% ('% 9'(0% 1'(#0-% .--80,-:-5>B<9>41-9M9-<=C-:HR=>3G-M;-F;2-=:CG3B9:H>H-HVHC8>H,

&\&WU]&,-.°,-A;H-I=2<J;9-&-FHI;2;3G-8H- /R -8:;2-H[9>;393H9

//415 7878& −=

M;-8=2<3=>- ,4"1"5 /R∈ -Z9><=>GC- 78 && ′′ 1 -M;- df .

1"F^F/F/F1/1/ =−=−=′=′ &7788&7&8& 78 --N2-5"1-"4

M;,"4"1"51"4"1"5 =′=′ 78 &&

A=2<J;9- &- 9:H-FH:;K93H-89:J;9>H- <B23;2=H- N2- 5"1- "41- FH<;- HO3H- F;IH:H2J;9L;>G- N29<HO3-8=2<3,-)M9F9:-8=2<3=>-5"1-"4-HO3H-8=2<3-O39J;B29:-9>-I=2<J;H;,-%G-<H:<H3GC-F9<G9<HO39-HO3H-8=2<3-FH-HV3:HC,

UH23:=-B:;<H-8=2<3- 4"158 -9KHC- 4,"1"5"4"15 / &88& >>= -UH23:=-B:;<H-8=2<3

411"5 7 -9KHC- 4,"1"5"41"5 / &77& <<−= -QH<;- 4"1"5415 &78& − -2=-8GO3:H9RG-9<H_

>9M;- OHC2- 8H23:=- B:;<H- 1415 /R∈78 - 9F;<G- I=2<J;9- &- 2=- 9:H- N2- 8=2<3=>- 5"1- "4- 2;<;C;2;C-5>B<9>41-2;<;-C9V;C-5>B<9>4,

/°,-A;H-I=2<J;9-&--FHI;2;3G-8H- /R -8:;2

,/415 // 87878& +−=

)KHC- 778878&7&8& 78 F/F4//5415F1/1// −+=−=′+=′ - M;- "F =& - 8H23:=

,"1. =−= 78 -U=2<3=>-5`.1-"4-2=-HO3H-8=2<3-FH-HV3:HC1-FHB9:H<H

//// 4.5./4"1.5415 78878&78& −+=++−=−− -M;- "4.5 // >−+ 78

F9<G- "4.51. // <−+>+ 7878 -F9<G- ,. 78 <+a,-Q;2-BLOH:K9J;;>H-/-M;-P-:HR=>3G-<G1-F9<G-+-HO3H-B-C=>J;CH-FHO<b;OG-M;-F9<G

I=2<J;9-&-HO3H-F;IH:H2J;9L;>G-8H-C=>J;CH9-+1-3B93H-OB>=J;;>H-O;O3HC=>=;

"415"415 =′=′ 78&78& 78

O=23- O39J;B29:H,- U=2<3H>H- FH- HV3:HC- >B<9>- 5I;;2F- 8=2<3H- O39J;B29:H4- OH- 9I>G- 8:;23:HOB>=J;;>H-9<HO3=;-O;O3HC1-F9:-2=-03"0--OB>=J;;>H-O;O3HC=>=;-FH-C9;-O=O-O=23-8=2<3H-FHHV3:HC,

UH23:=-9-;FH23;I;<9-8:;23:H-8=2<3H>H-O39J;B29:H-'(-2--8=2<3H-FH-HV3:HC1-3:HL=;HOG-=3;>;RGC-FH:;K93H>H-89:J;9>H-FH-B:F;2=>-FB;-9>H-I=2<J;H;-&,

A;H-FH<;- 415 "" 78 -=2-1'(#0%90")*3(",-9>-I=2<J;H;- ,0 / RR →⊂+& -%G-8:HO=_8=2HC-<G-I=2<J;9-&%",-%.-,*/"0-%1",)*"2-%.-%3,.*('2%.3*%#3(0*('--N23:_B-KH<;2G393H-69-8=2<3=>=;- 4,15 "" 78

!P

Z=C-- 415 "" 78 - -HO3H--=2--8=2<3- -O39J;B29:1- - ,"4151"415 """" =′=′ 78&78& 78

QHB9:H<H-I=2<J;9-&-9:H-FH:;K93H-89:J;9>H-FH-B:F;2=>-FB;-<B23;2=H-8H-KH<;2G393H9-6-9>=;- 4115 "" 78 - 8=3HC- O<:;H- IB:C=>9- >=;- D9E>B:- FH- B:F;2=>- FB;1- <B:HO8=2RG3B9:H

I=2<J;H;-&1-N2-8=2<3=>- 4,15 "" 78 -UH23:=-B:;<H- 678 ∈415 -9KHC

415415/

.?44515

4454515/44515@/

.

4451544515415415

//"""/

""""/

"""/

""""""""

78.787778&

778878&8878&

7778&8878&78&78&

7

878

78

ϕ+−′′+

+−−′′+−′′+

+−′+−′+=

=2FH- "415415>;C ""

"

"

=ϕ=ϕ→→

78787788

-M;- ,4545415 /"

/" 778878. −+−=

%G- 2B3GC- 4,1541154115 """""" // 78&#78&>78&" 7788′′=′′=′′= - AB:C=>9- >=;

D9E>B:-OH-C9;-O<:;H

415415/

.

?454455/45@/

.415415

/

/"""

/"""

78.78

77#7788>88"78&78&

ϕ+

+−+−−+−=−

FHB9:H<H,"415^"415 """" =′=′ 78&78& 78

UH23:=- 441554115415 "" 6787878 ∈≠ - 9KHC- "415 ≠78. - FH<;- 8=3HC- 2B39

,415

4151415

415 ""

78.

7778/

78.

8878'

−=

−= -QH-9;<;1-8H23:=-B:;<H-8=2<3- 4115415 "" 7878 ≠

BLJ;2HC- ;FH23;393H9- 1.415415 // ≡+ 78/78' - <9:H- 9:93G- <G- B:;<H- 8BR;J;H- 9:- B<=89

8=2<3=>- 415 78 -N2-KH<;2G393H9-6-9-8=2<3=>=;- 415 "" 78 -8=2<3=>- 415 /' -FHO<:;H-=2-<H:<<=-<H23:=>-N2-B:;[;2H-FH-:9RG-.,-)M9F9:

4,15?415415415415/415@/

.

415415

///

""

78.7878#/78/78>'78"'

78&78&

ϕ+++=

=−

%HC2=>- F;IH:H2JH;- 415415 "" 78&78& − - HO3H- 9<H>9M;- <=- OHC2=>- HV8:HO;H;- F;289:923HRH-F;2-CHCL:=>-F:H83-9>-9<HO3H;-H[9>;3GJ;,

%G- 8:HO=8=2HC- <G- ,"/>− >"# - 72- 9<HO3- <9R- 3:;2BC=>- #>" +α+α // - 9:H

:GFG<;2;- <BC8>HVH1- 9F;<G- 2=- OH- 92=>H9RG- 8H23:=- 2;<;- B- K9>B9:H- 5:H9>G4- 9- >=;- α,QHB9:H<H- .415415 // =+ 78/78' -:HR=>3G-<G-M;

415415415/415 // 78#/78/78>'78"' ++

!a

2=-OH-92=>H9RG-N2-2;<;-=2-8=2<3- 441541155 78/78' -M;-9:H-9<H>9M;-OHC2-<=-",-W9;

C=>31--F;2-<B2F;J;9-<G- 1"415>;C

"

"

=ϕ→→

787788

-FHF=<HC-<G-HV;O3G-=2-F;O<-<;:<=>9:-6-<=

<H23:=>-N2- 415 "" 78 -M;-:9R9-O=I;<;H23-FH-C;<G1-9O3IH>-N2<S31-8H23:=-B:;<H- 1415 678 ∈

4,15415415/415415 // 78#/78/78>'78"'78 ++<ϕ

QH<;-N2-KH<;2G393H9-6-HV8:HO;9

415415415415/415 // 7878#/78/78>'78"' ϕ+++

9:H-9<H>9M;-OHC2-<=- 4115415415/415 // 78#/78/78>'78"' ++ -9F;<G-9:H-9<H>9M;-OHC2<=-",

)M9F9:1-N2-;8B3HR9- "/>− >"# -5O9=- 4"4?15@415415 /"""""" // >′′−′′′′ 78&78&78& 7878

F9<G- ">" -93=2<;- "415415 "" >− 78&78& -M;-FH<;- 415 "" 78 -HO3H-=2-8=2<3-FH-C;2;C

>B<9>^-F9<G- 1"<" -93=2<;- "415415 "" <− 78&78& -M;-FH<;- 415 "" 78 -HO3H-=2-8=2<3-FHC9V;C->B<9>,

%G-<B2O;FH:GC-9<=C-<9R=>-<S2F- 1"/<− >"# -9F;<G

,"4?15@415415 /"""""" // <′′−′′′′ 78&78&78& 7878

D:;2BC=>- #>" +α+α // - 9:H- :GFG<;2;- :H9>H- M;- F;O3;2<3H1- FH<;- 9:H- =2- 92=C;3OHC2-8H23:=-K9>B:;-9>H->=;-α-<=8:;2OH-N23:H-:GFG<;2;-M;-OHC2-<B23:9:-8H23:=-K9>B:;9>H->=;-α%-N2-9I9:9-:GFG<;2;>B:,-'HR=>3G-<G

415415

415/

415

415 /

/

78/#78/

78'>

78/

78'"

++

;9- 93S3- K9>B:;- O3:;<3- 2H[93;KH- <S3- M;- K9>B:;- O3:;<3- 8BR;3;KH,- U:;2- =:C9:H1- N2- B:;<HKH<;2G393H-9-8=2<3=>=;- 415 "" 78 -F;IH:H2J9- 415415 "" 78&78& − - ;9-K9>B:;-2H[93;KH-M;K9>B:;-8BR;3;KH1-FH<;- 415 "" 78 -2=-HO3H-=2-8=2<3-FH-HV3:HC,

)C-FHCB2O3:93-FH<;- 0-3,-:"- N2-L9R9-<G:H;9- :H<=2B9M3HC-8=2<3H-FH- HV3:HC5>B<9>4-8:;23:H-8=2<3H>H-O39J;B29:H,

D&#'&Wc,-!"#$% 415 "" 78 --90-%'(%1'(#0%90")*3(",%"2%&'(#)*-*%&%@*%."#$%&'(#)*"%&",-%.-,*/"0-%1",)*"2-%.-%3,.*('2%.3*%#3(0*('-%5(0,43%/-#*($0"0-%"%1'(#0'2'*- 415 "" 78"0'(#*0

),-!"#$- 4151"4?15@415415 ""/

"""""" // 7878&78&78& 7878>′′−′′′′ - -90-% '(% 1'(#0

.-%-80,-:%23#"2%"2%&'(#)*-*%&%@*%"(':-H

415 "" 78 --90-%'(%1'(#0%.-%:*(*:%23#"21-F9<G- ^"415 ""/ >′′ 78&8

415 "" 78 --90-%'(%1'(#0%.-%:"8*:%23#"21-F9<G- ,"415 ""/ <′′ 78&8

!d

$,-!"#$- 4151"4?15@415415 ""/

"""""" // 7878&78&78& 7878 <′′−′′′′ -('%-90-%'(%1'(#0

.-%-80,-:%"2%&'(#)*-*%&F&\&WU]e,-A;H

,4151P415 /PP R∈++= 78877878&

)I>GC-8=2<3H>H-O39J;B29:H,-UH23:=-9<H9O39-:HRB>KGC-O;O3HC=>

=+=′=+=′

,"PP415

"PP415/

/

8778&

7878&

7

8

#LJ;2HC- OB>=J;;>H- 5"1- "4- M;- 5`.1- `.4,- Z9><=>GC- 9<=C- FH:;K93H>H- 89:J;9>H- FHB:F;2=>-FB;

,f415^P415^f415 // 778&78&878& 7788 =′′=′′=′′

QH-9;<;"4"1"5^P4"1"5^"4"1"5 // ==′′=′′

7788 &&&

M;,f4.1.5^P4.1.5^f4.1.5 // −=−−′′=−−′′−=−−′′

7788 &&&

)KHC1"g4?"1"5@4"1"54"1"5 /

// <−=′′−′′′′ 7878 &&&

FH<;-5"1-"4-2=-HO3H-8=2<3-FH-HV3:HC,-)8B;

------------------------ 1"/[email protected] /// >=−=−−′′−−−′′−−′′ 7878 &&&

FH<;- 5`.1- `.4- HO3H- 8=2<3- FH- HV3:HC,- QHB9:H<H- 1"f4.1.5/ >−=−−′′8& - :HR=>3G- <G

5`.1-`.4-HO3H-8=2<3-FH-C9V;C,

#$%&'()*+&,-Q9<G- "4?15@415415 /"""""" // =′′−′′′′ 78&78&78& 7878 - 2=- 8=3HC- 9I;:_

C9-<G-8=2<3=>- 415 "" 78 -HO3H-8=2<3-FH-HV3:HC-9>-I=2<J;H;-&,-72-=2H>H-<9R=:;- 415 "" 78HO3H-8=2<3-FH-HV3:HC1-N2-9>3H-<9R=:;-2=-HO3H,-72-9<H9O3G-O;3=9J;H-HO3H-;2F;<93-9-OH-I9<H=2-O3=F;=-F;:H<3-9>-OHC2=>=;-F;IH:H2JH;- 4,15415 "" 78&78& −

&\&WU]e,-A;H-I=2<J;9-&-FHI;2;3G-N2-B:;<H-8=2<3-- /415 R∈78 -8:;2-:H>9J;9

,415 a/ 7878& +=)KHC

Pa415^/415 778&878& 78 =′=′

M;- "1" =′=′ 78 && - N2- 8=2<3=>- 5"1- "4,- QH<;- 5"1- "4- HO3H- 8=2<3- O39J;B29:- 9>- I=2<J;H;

<B2O;FH:93H,-)8B;1./415^"4151/415 /

// 778&78&78& 7788 =′′=′′=′′

1"4?"1"5@4"1"54"1"5 /// =′′−′′′′ 7878 &&&

FH<;-2=-8=3HC-9I;:C9-2;C;<-FHO8:H-8=2<3=>-5"1-"4,

!f

%G-BLOH:KGC-N2OG-<G- "4"1"5 =& -M;- 1"415 >78& -8H23:=- 41"1"5415 ≠78 -9F;<G"4"1"5415 >− &78& -M;-FH<;-5"1-"4-HO3H-=2-8=2<3-FH-C;2;C-9>-I=2<J;H;,

"#$%&'&! (/,0(&! 4&+$%*! )*+,-..(&! %&0(&! 1&- 4P5 >(( - 20%.03.(&! %&0(&,- A;H

RR →⊂ (+& 0 -B-I=2<J;H-:H9>G-FH- 4P5 >(( -K9:;9L;>H-:H9>H-FHI;2;3G-8H- (+ R⊂ -M;

41115 ""/

"." (8888 != -=2-8=2<3-9>-C=>J;C;;-+,

Q&A+T+*+&,-A'(#0'2% +8888 ( ∈= 41115 ""/

"." ! - -90-% '(% 1'(#0% .-% :"8*:% 23#"2

C,-91-#0*/%.-%:*(*:%23#"2D%"2%&'(#)*-*%&<%."#$%-8*90$%3%/-#*($0"0-%6%"%"#-90'*%1'(#0<"90&-2%5(#B0<%1-(0,'%3,*#-% +68888 ( ¡∈= 41115 /. ! -9$%"/-:

4111541115 ""/

"./. (( 888&888& !! <

,-91-#0*/4,111541115 ""

/"./. (( 888&888& !! >

Q9<G- 41115 ""/

"." (8888 != - HO3H- =2- 8=2<3- FH-C9V;C- >B<9>- 5:HO8H<3;K-C;2;C

>B<9>4- 9>- I=2<J;H;1- 93=2<;- 41115 ""/

". (888& ! - OH- 2=CHM3H- :"8*:% 23#"2- 5:HO8H<3;K

:*(*:% 23#"24- 9>- I=2<J;H;- &,- Q9<G- 41115 ""/

"." (8888 != - HO3H- =2- 8=2<3- O39J;B29:

F;2- ;23H:;B:=>- C=>J;C;;- +1- 93=2<;- 1"4111545 ""/

"." =′=′ (88 888&8&

**! ,11/1. (* !=

A'(#0'2- +8 ∈" - -90-% '(% 1'(#0% 90")*3(",% "2% &'(#)*-*- &1- ."#$% &'(#)*"% &% -90-

.*&-,-()*">*2$%5(- "8 -@*%."#$- ,"45F " =8&

U=2<3H>H- O39J;B29:H- 9>H- I=2<J;H;- 10 RR →⊂ (+& - =2FH- +- HO3H- B- C=>J;CHFHO<b;OG1-OH-FH3H:C;2G-:HRB>KS2F-O;O3HC=>-FH-H<=9J;;

=′

=′

=′

,"41115

,

"41115

"41115

/.

/.

/.

/

.

(8

(8

(8

888&

888&

888&

(!

!!!!!!!!!

!

!

%H- FHCB2O3:H9RG1- N2- 9<H>9M;- CBF- <9- 8H23:=- I=2<J;;>H- FH- FB=G- K9:;9L;>H1=:CG3B9:H9- 0-3,-:$- <9:H- 2H- 8H:C;3H- OG- ;FH23;I;<GC- 8=2<3H- FH- HV3:HC- 8:;23:H8=2<3H>H-O39J;B29:H-9>H-I=2<J;H;-FH-C9;-C=>3H-K9:;9L;>H,

D&#'&Wc,- A;H- 41115 ""/

"." (8888 != - =2- 8=2<3- O39J;B29:- 9>- I=2<J;H;- ⊂+& 0

,RR →⊂ ( -%G-8:HO=8=2HC-<G-I=2<J;9-&-9:H-FH:;K93H-FH-B:F;2=>-FB;-<B23;2=H-N23:_BKH<;2G393H-B9:H<9:H-9-8=2<3=>=;- ,41115 ""

/"." +8888 ( ∈= !

),-Q9<G- ∑=

′′(

I*I*(88 ''888&

I*.1

""/

". 141115 ! -=2FH- 1

"

.

88' ***

−= 145 /"

.

/*

(

** 88. ∑

=−= 2

=-OH-92=>H9RG1-93=2<;- "8 --HO3H-=2-8=2<3-FH-HV3:HC-9>-I=2<J;H;-&-M;-92=CH0

41115 ""/

"." (8888 != -HO3H-=2-8=2<3-FH-C;2;C->B<9>-F9<G- ^"45

.1"∑

=>′′

(

I*I*88 ''8&

I*

!!

41115 ""/

"." (8888 != -HO3H-=2-8=2<3-FH-C9V;C->B<9>-F9<G- ,"45

.1"∑

=<′′

(

I*I*88 ''8&

I*

$,- Q9<G- ∑=

′′(

I*I*(8 ''888&

I8*.1

""/

". 41115

1! - ;9- N2- B:;<H- KH<;2G393H- 9- 8=2<3=>=;

41115 ""/

"." (8888 != -93S3-K9>B:;-8BR;3;KH-<S3-M;-K9>B:;-2H[93;KH1-8=2<3=>- "8 -2=-HO3H

8=2<3-FH-HV3:HC,

P,h,!5&$/10!,&(/%!'0.!'.,.!46$%0$&

%G- 8:HO=8=2HC- <G- O=23- <=2BO<=3H- K9>B:;>H- I=2<J;H;- 458&7 = - N2- 92=C;3H

8=2<3H- 9>H- FBCH2;=>=;- FH- FHI;2;J;H1- 9F;<G- O=23- <=2BO<=3H- 8H:H<b;>H- FH- K9>B:;

111/1.4154115141154115 //.. (*8&7787878 **(( !! == -IG:G-9-I;-<=2BO<=3G-I=2<J;9

&,- e:CG:;C- OG- 98:BV;CGC- 458& - 59F;<G- OG- HV8:;CGC- >H[G3=:9- F;23:H- K9:;9L;>H>H

8-M;-74-8:;23:_B-I=2<J;H-8B>;2BC;9>G- 458A: -FH-[:9F=>- ,(: <

A;H- ,11/1.145 (*78A **: !== -&:B:;>H-<9:H-OH-I9<-F9<G-OH-N2>B<=;HO<-K9>B:;>H

45 *8& -8:;2- 45 *: 8A -O=23- ,11/1.41545 (*8A8&77- *:**** !=−=−=Q9<G-OH-;9-F:H83-#,*0-,*'%.-%:*(*:*=",-%"%-,3,**%.-%"1,38*:",--O=C9-3=3=:B:

9L93H:;>B:- ∑=

(

*** --

.

11 - BLOH:KGC- <G- 9<H9O39- <B2F=<H- >9- B- 9>H[H:H- [:HM;3G- 9- I=2<J;H;

1:A -FHB9:H<H- (--- 111 /. ! -8B3-9KH9-OHC2H-F;IH:;3H-M;-FH<;-O=C9->B:-9>[HL:;<G-2=

HV8:;CG- <B:H<3- H:B9:H9- 3B39>G,- W9;- ;2F;<93- 9:- I;- OG- OH- <B2O;FH:H- ,.

∑=

(

**- - 72OG1

FHB9:H<H- I=2<J;9- CBF=>- 2=- HO3H- FH:;K9L;>G- N2- B:;[;2H- OH- FH3H:C;2G- :*(*:':'29':-*%1$0,"0-23,%-,3,**

∑ ∑= =

−=(

*

(

***:* 8&8A-

. .

// ,4?545@

QH-9;<;1-:-03."%i#-23,%:"*%:*#*%1$0,"0-j,A;H- 145 ."

::: 8"8""8A +++= ! -=2FH-<BHI;<;H2J;;- :""" 111 ." ! -OH-FH3H:C;2G

F;2-<B2F;J;9-<9-∑=

(

**-

.

/ -OG-I;H-C;2;CG,

%H-<B2O;FH:G-I=2<J;9

,?545@41115.

/."." ∑

=+++−=

(

*

:*:**: 8"8""8&"""J !!

!h

ZB2F;J;;>H-FH-C;2;C-N2-:98B:3-<=-K9:;9L;>H>H- :""" 111 ." ! -O=230

1"11"1"."

=∂∂=

∂∂=

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:"

J

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J

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O9=

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.."

.."

.."

=−+++

=−+++

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!

!

)<HO3-O;O3HC-FH-H<=9J;;-OH-O<:;H-O=L-IB:C9-(3,:"2$-5k9=OO4

=+++

=+++

=+++

∑ ∑ ∑ ∑

∑ ∑ ∑ ∑

∑ ∑ ∑

= = = =

+

= = = =

+

= = =

(

*

(

*

(

*

(

**

:*

:*:

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*

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*

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***

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!

Q9<G- K9>B:;>H- (888 111 /. ! - O=23- F;O3;2<3H- 93=2<;- O;O3HC=>- FH- H<=9J;;- 9:HOB>=J;H-=2;<G1-FH<;-I=2<J;9- :A -HO3H-=2;<-FH3H:C;293G,

#$%&'()*+&,-72->B<=>-I=2<J;H;-8B>;2BC;9>H- :A -OH-8B93H->=9-B-I=2<J;H-K-B9:H<9:H,WH3BF9- FH- 98:BV;C9:H- 9- =2H;- I=2<J;;- 2H<=2BO<=3H- &- 8:;23:_B- I=2<J;H- K- OH

2=CHM3H-"I'90",-1-K-I;;2F-&'(#)*"%.-%"I'90",-,-UH23:=-9-9>H[H-<S3-C9;-<B:H<3-I=2<J;9FH-9l=O39:H-HO3H-2H<HO9:-OG-OH-:H8:HR;23H-N2-8>92-8=2<3H>H- (*78 ** 11/1.4115 != -M;OG-OH-3:9OHRH-8:;23:H-M;-8:;2-=2H>H-F;2-9<HO3H-8=2<3H-B-<=:LG-9O3IH>-N2<S3-H:B:;>H-8BR;_3;KH- M;- 2H[93;KH- OG- OH- <BC8H2OHRH,-U:B<HFH=>- 9<HO391- 2=C;3-"I'90",-% K,"&*#$- 8H:_C;3H-9I>9:H9-0*1'2'*-FH-<=:LG-;2F;<93-8H23:=-9l=O39:H,-72-O<B8=>-"I'90$,**%"("2*0*#--9F93H>B:-HO3H-2H<HO9:-OG-OH-9>H9[G-C9;-C=>3H-<=:LH-M;-98B;-F;23:H-9<HO3H9-OG-OH-:HJ;2G18H23:=-=3;>;R9:H9-CH3BFH;-<H>B:-C9;-C;<;-8G3:93H-5O9=-9-9>3H;-CH3BFH-FH-98:BV;C9:H9-I=2<J;H;-&%41-9<HH9-<G:H;9-N;-<B:HO8=2FH-O=C9-8G3:93H>B:-9L93H:;>B:-C;2;CG,

)U]+Z)*+&,- 'HR=>393=>- =2=;- HV8H:;CH23- HO3H- N2O<:;O- N23:_B- 39LH>G- FH- K9>B:;,11/1.4115 (*78 ** != - %G- OH- HV8:;CH- >H[G3=:9- F;23:H- K9:;9L;>H>H- 8- M;- 7- 8:;23:_B

I=2<J;H- FH- [:9F=>- N23S;- FH- IB:C9- 1>"87 += - K9>B:;>H- "- M;- >- I;;2F- FH3H:C;293H

!g

9O3IH>--N2<S3--9L93H:H9-I9JG--FH-;2IB:C9J;9--I=:2;R93G-FH-CGO=:G3B:;1-9L93H:H-F93G-FH

145 /

.

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∑=

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*** >"87>"J

.

/ ,45415

ZB2F;J;;>H-2H<HO9:H-FH-C;2;C-F9=

1"415

1"415 =

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4C44:) 55

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!

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C(4B(

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(( → ∞→ $ -,2(*$ R/0/R0/072+ R∈∀=∞→

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-7&-)4-'&$'&,81*$0-+&724'-)*/$<#-#$(4C

(4)F

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!!Q

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593;-54387)B<4:-L1-)9)('3*#'(")$')B-31</)25-2;17)B<46284/3-NIK) 5-0) 5-) 3/) ?4;B/3-) ?-) I234) C909;-L1-) 2'3&%("() 9) 23/:417) ;/:7) ?-) I234

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-B;A

;-B;A -

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--- B;AB;A "#""#", −= A/B

7/>*'/6#/$7289'7+$(2./4:&';-#2+./$:1+4-.**$4&5/*$"-$:/$:/.*2+7+$7/$#*5:$#@

!M-

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7289'7-$&'*#+.-$+'&+1-.+03+5('3$:1+7*+*K+ ./--

B/;/A:

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F&3+ B+C+-K+ 8$71+ %)$4$635'*)+ 4*63&+ "-+ 43+ ?$73+ %3+ %32&($8$+ 83+ '&6%+ #+P+B;+ $'*57&O$)($23$+ ?&5$)1+ 34'3+"+A"-;+ #+P+BB.+Q$2&$=&$+ 4*63&+ ?&5$)3+"+ <5+ &5'32O$)*)+ 83+ '&6%+ 83)*5R&63+B+34'3

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B;A8

B;A8-

- #">#

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∫ αα+=#

">"#""-

--- .8B;AB;A A!B

L5+%$2'&7*)$2;+8$71+"-+N+/+*.6.+@&+#+N+/+$5;

∫ αα+=+=+=/

-

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7(54'$5'1.+ D37&;+ <5+ &%('3:$+ ;8

B;A8

8

B;A8.;7' --

- #

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-- .8B;AB;A AZB

!M/

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-

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B.AB;AB;A

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7#

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L5+7(58&=&&)3+&5&=&$)3+8$'3+23:*)'1

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A]B

.BA/B;A-

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#

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L5+%$2'&7*)$2;+8$71+?A#B+N+*+(9=&536

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%2.5&1/1/+ A"B+ 6*+ A/-B+ 4&'#$ &#*1*;+#/$ 3'$ :.+(#*(-$ :/'#.&$ 7/#/.5*'+./+$ 0+12.**>*'+1/$3'$:1+4+5/'#/1/$3'$./?*5$7/$7289'7-$4*5:1-.

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./--

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./--

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∑=

θ='

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θ=θ=θ='

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5';(=;'&7<+ ;-+ '=;@*&;+ 6C+ =;%=;E&9';+ >(@M9>$+ %;+ %;=&($>$+ >;+ '&?%+ %M9C+ )$+ 67$>;9:C7(=;6%*9EC'($=;+7$%&'$)*)*&+67(9'$'<+;F$)*$'C+7*+*9+$9*?&'+%=(7;9'A-

/$7C+67=&;?+5.A+6*@+H(=?$

-% ;;; += 5,A

%*9;?+D9+;F&>;9:C+H$%'*)+7C+,-.)/(4*#,/#*#A%4*-(*+.36)+%*%9#$#)/0*8%4.$''*%-/(%4#;%*%*-%"'/%4(4('*+',".)'3'4*4%*,-%+#)&0*;<+ *"#*+($%/%* ∗θ−θ=/ +>'*-(*"$.-#)/(4*+#,-.)/+<+N+.KK=-+[=(7;9'*)+>;+67(9'+<+%($';+H&+;G$)+6$*+9*+%=(7;9'*)+>;+;?&6&*9;+$%()&:;&+"+N.KK'-

!"#

$%&'()*+%,*%)*,(+ -'+%&'.&/01(,(2+%)+ 345+ 62+')027(2+ !"#$%& '()*#$(+8+9/1%2+ ,*(/2:)*(,(+%,/2+,;/&<102,:=+6%&'()*+/,>1&',*+62+')027(2+!"#$%&"#,-'"*(+8

?@ABCBDB@8+.#$!%($%(&/&!-&$0,-1%-&2#34$25&($0(+5&0$*%('5&2-&!"#$%+6,)+'(%5($0(+5&2-&!"#$%8

E/1'+ ,',*&F12+ %)+ G&HI'G,+ 610;*=+ 71+ G&HI'G,+ %&0;)6=+ G2&62H10+ !"#$%0+!*,6+0+71+!"#$%0+&"#,60!8

44848+!"#$%&'()*+,

?@ABCBDB@8+7("5&2#34$2(&(8-'-$%5&"(6*%(+0+0*&("%0(++3!"#$%(%5+9(&-!%-&"(+"0:+(%5&"(&2#34$25&!*,6+5J+(%0$"*&#6-'()*0$-(&-!%-&K2-&!"#$%&!*,6+0L8

A12+ 9"J+!+ M+ N,*&,/2,+ 6%&'()*)1+ 610;*)8+ ?,%=+ ;/&%2'()*+ ,'),*+ G2+ 6%&'(+ 26(2;+O+PQQ/+ 71+ G,%=+ &;2/,>1)'2,+ 62+ G26.=7&,/=+ %)+ ,%2*,71+ ;/&%2'(+ ,'),*+ G2+ 6%&'(+ ;2G)/,(,+%J+,()'%1J+;&(/1N1(+G2.1'1>121+G2+0,1+6)6J

++++++++

++++++++++++++++

+

?,%=+&;2/,>1)

%J+1,/+ <

$

<

% θ= ∑=P

+71+-

JPQQ << /; = +,N20

U1%1+$

<

% θ= ∑=P

?1'+ 3P5+ /2:)*

?,%=+>1'20+62,0,+%

E/1'+)/0,/2+ 9

62+2<;/10=+-'+,'1J+6

9"@&!+O

++ JPQQ

%;9%/9 ((

⋅=⋅⋅ ++++++++++G,%=+%+62+2<;/10=+-'+,'1R 3!5

++ JPQQ ,

%;9

,

%/9 ,

(,

( ⋅⋅=⋅⋅ +G,%=+%+62+2<;/10=+-'+./,%>1)'1

+++++++++++++++++++++++++++++++++++++++++2F,*2+3,5+G2+,'+3%,58 3S5

'2,+')+62+2.2%()2,:=+%)+,%2*,71+;/&%2'(+,'),*+G2+6%&'(+;2+G)/,(,

'+;2/1&,G,+G2+(10;+ <θ +62+&;2/2,:=+%)+;/&%2'()*+,'),*+G2+6%&'(

<<

$

<

(<<

$

<(!" ;

9/99 θ=θ= ∑∑

== PPJ PQQ

8 3T5

< +26(2+-=6'*,(%&>$&($*?

(=+ J"( 999 −= + 6,)J+ -'+ %,:)*+ 6%&'()*)1+ 610;*)J+ 8J !"( 999 −=

=+ /%99 (!" =J +3;/10,+.&/0)*=+3!55J+&H>1'20

8P /%

99( +

= 3"5

!"J +%,*%)*,(+-'+.)'%>12+G2+N,*&,/2,+.1',*=+,+&;2/,>1)'11+9J+G,%=+%

2+&H>1'2+-'*&%)1'G+9(+G,(=+G2+3"5+-'+3!58+V2:)*(=

8PQQPJ ;%

9;%

/%

9/%9 !" +

=+

= 3W5

!"X

!"9 J + %,*%)*,(+;&(/1N1(+ .&/0)*21+ 3W5+ 62+')027(2+!"#$%& !*,6+0&'()*#$(+8+ Y*+ N&0

'&(,+ 853J'!"9 + Y'+ %&'62%1'>=J+ 8#',0+(& 3"5+ 2-8*$-1%-& "(6*%(+0+& !"#$%(%& 9(& 6-$%'0& !"#$%

!*,6+0&'()*#$(+8Y'+;,/(1%)*,/J+G,%=+9+O+P+)808+71+%+O+P+,'+.&/0)*,+3W5+G2N1'2

8P

53J /

/9 '

!" +=

?@ABCBDB@8+.#$!%($%(

/

/0

+=P

3W′5

!-&$0,-1%-&!"#$%&0$*%('+6,)+0$*%(%-&2-&!"#$%89H62/N=0+%=+ 6%&'()*+)'1(,/+26(2+ 2F,*+%)+N,*&,/2,+,%(),*=+ ,+G&HI':11+ ,'),*2

)'1(,/2+/Z?@ABCBDB@8+ .#$!%($%(+ 0/A −=+= − P5P3 P + !-& $0,-1%-& 8("%#'& 2-& ("%0(+*B('-

!(0&8("%#'&2-&!"#$%8Y'+;/,%(1%=+ P[P −+ /% +71+3W5+62+/2G)%2+*,

JJ 9/%9 !" = 3#5

%+.11'G+-=6'*,(%&>$&($*8+?,%=+ J,

%% ,= +.&*&61'G+3S5+&H>1'20

,

9;%9 ,

!" PQQJ = 8 3#′5

$%&'()*+ 610;*)+ %,*%)*,(+ ;&(/1N1(+ 3#5+ 6,)+ 3#′5+ 3G2%1+ -'+ 1;&(2:,+ P[P −+ /% 5+ 62

')027(2+!"#$%&!*,6+0&"#,-'"*(+8+Y*+'&(=0+ 853J"!"9

?1'+%&'G1>1,+ 53J"!"( 999 −= +71+3#5+/2:)*(=

8QP5JP3 >−−= /%/%99( 3X5

C"-(!%5&8#',0+5&2-8*$-1%-&"(6*%(+0+&!"#$%(%&9(J+ >$&"(B0+&!"#$%0+0*&"#,-'"*(+8?2&,/2%2+/%&\+P+G2G)%20+%=+6%&'()*+610;*)+%&02/%1,*+')+62+,;*1%=+;2'(/)+;2/1&,G20,/1+G2+(10;8

!"#$%&'()*%%+,(%-%#&+ 53J'!"9 +.%+ 53

J"!"9

P5+ J53J53J

"!"

'!" 99 < + %22,+ %2+ ,/,(=+ %=+ 53

J"!"9 + %&'N1'2+ H='%11+ %,/2+ %)0;=/=+ G&%)]

02'(2*2+G2+;*,(=J+;2+%I'G+ 53J'!"9 +%&'N1'2+G2>1'=(&/)*)1+G&%)02'(2*&/+3;&*1>2158

45+?1'+3!5+71+ 3S5+ /2:)*(=+%=+ 53J'!"9 + /2;/2:1'(=+G&HI'G,+610;*=+%&/26;)':=(&,/2

N,*&/11+6%&'(,(2+9(+;2+G)/,(,+G2+(10;+%+G2+*,+6%&'(,/2+71+;I'=+*,+6%,G2'>,+;&*1>21J+%,*]%)*,(=+%)+;/&%2'()*+,'),*+G2+6%&'(+;+O+PQQ/8+?1'+3#5+71+3#′5+/2:)*(=+%= 53

J"!"9 +/2;/2:1'(=

G&HI'G,+ 610;*=+ %&/26;)':=(&,/2+ N,*&/11+ .1',*2+ 3%,;1(,*)*)1+ '&01',*5+ 9J+ (&(+ ;2;2/1&,G,+G2+(10;+%+71+%)+,%2*,71+;/&%2'(+,'),*+G2+6%&'(+;8

!WQ

!5+?1'+3W5+71+3#5+&H>1'20

JP

53J53

J /%

99

"!"'

!" += 3PQ5

G2+)'G2

J53J

53J

53J /%999 '

!"'!"

"!" ⋅=− 3PQ′5

%22,+ %2+ ,/,(=+ %=+ G,%=+ 6%&'()*+ 610;*)+ /,>1&',*+ 6],/+ ;*,6,+ ;2+ G)/,(,+ %+ %)+ G&HI'G=610;*=+ 71+ %)+ ;/&%2'()*+ ,'),*+ ;+ O+ PQQ/J+ ,()'%1+ G&HI'G,+ %&/26;)':=(&,/2+ ;*,6,]02'()*)1+26(2+2F,*=+%)+G1.2/2'>,+G1'(/2+6%&'()*+610;*)+%&02/%1,*+71+%2*+/,>1&',*8

S5+?1'+3W5J+(/2%I'G+*,+*101(=+;2'(/)+ ∞→% +&H>1'20

8*10 53J 99 '!"

%=

∞→3PP5

E/1'+ )/0,/2J+ G,%=+ ;2/1&,G,+ G2+ (10;+ %+ ;I'=+ *,+ 6%,G2'>=+ 26(2+ .&,/(2+ 0,/2J

99 '!" →53J +71+G2%1+ Q→(9 +3N2:1+71+3"558

/'0)*%%+1#2('+93+ ∗9 +.%+9(A12+9+%,;1(,*)*+'&01',*+%,/2+62+&H>1'2+;/1'+;*,6,/2,+6)021+9Q+;2+G)/,(,+θ+%)

;/&%2'()*+6+O+PQQ*J+-'+/2F10+G2+G&HI'G=+610;*=8+U)+*&%+2F,*1(=>1*2Z

JQ5JP35JP3 QQ θ<θ<θ+=θ+= ∗∗∗ *99*99

G1'+%,/2+/2:)*(=

8P

5P3∗

∗

θ+θ+=

*

*99

Y'*&%)1'G+,%2,6(=+2<;/2612+;2'(/)+9+-'+3"5+71+/26;2%(1N+3X5+&H>1'20

J5P53P3

5P3

/%*

*99( +θ+

θ+=∗

∗3P45

6-$%'0&!"#$%0+&!*,6+0&'()*#$(++71

JP

5P53P3∗

∗

θ+−θ+=

*

/%*99( 3P!5

6-$%'0&!"#$%0+&!*,6+0&"#,-'"*(+8

9^$@V_UDB@8+ ?1'+ 3P45+ G2G)%20+ J∗< 99( + G,%=+ 8P ∗θ+

>*

*/ + Y'+ %,:+ %&'(/,/

8∗99( ³ + U',*&FJ+ G1'+ 3P!5+ /2:)*(=+ ∗< 99( + G,%=+θ+

>*

*/P

+ 71+ ∗99( ³ + -'+ %,:

%&'(/,/8+Y'+;/,%(1%=+26(2+;&61H1*=+&/1%,/2+G1'(/2+,%26(2+61(),>118@`@aEbc8+ A12+ θQ+ 0&02'()*+ -'+ %,/2+ ,+ .&6(+ %)0;=/,(=+ &+ ;&*1>=+ *,+ ;/2>)*

8J)80P4QQQQ =9 + 6%,G2'(=+PQ+ *)'1+0,1+ (I/:1)+ %)+ ;/&%2'()*+ ,'),*+ G2+ PQd8+E/26)]

!WP

;)'I'G+%=+;&626&/)*+;&*1>21+62+;/2:1'(=+*,+6%&'(,/2+%)+!+*)'1+-',1'(2+G2+6%,G2'>=J+6=62+G2(2/01'2Z

,5+N,*&,/2,+'&01',*=+,+;&*1>21+*,+6%,G2'>=+395RH5+N,*&,/2,+.1',*=+*,+6%&'(,/2+3%)/6)*+;&*1>215+3 ∗9 5R%5+ N,*&,/2,+ 6%&'(,(=+ ,+ ;&*1>21+ 39(5J+ ,;*1%I'G+ .12+ 6%&'()*+ 610;*)+ /,>1&',*J+ .12

6%&'()*+ 610;*)+ %&02/%1,*+ %)+ )')*+ G1'+ ;/&%2'(2*2+ ,'),*2+ G2+ 6%&'(+ ;P+ O+ #dR+ ;4+ OO+PQdR+;!+O+P4d8

9#+0)*-?+,5+ 8)80P!QQQP4

PQPJQPP4QQQRPQ =

⋅+=

+= 9

,

%*99 ,

H5+ 8)80P4WQQP4

WPJQPP4QQQ5RP3Q =

⋅+=θ+= ∗∗∗ 9*99

%5+E2'(/)+6%&'(+610;*)+/,>1&',*+62+,;*1%=+3"5R+/2:)*(=

===

=d8P4;2'(/))808!TXJP4"4P

dRPQ;2'(/))808X4"JP4"#4

dR#;2'(/))808QX#JP4WST

;

;

;

9(

E2'(/)+6%&'(+610;*)+%&02/%1,*+ 5RP3 /%99( −= +/2:)*(=

===

=d8P4;2'(/))808P4"PQ

dRPQ;2'(/))808P4"WT

dR#;2'(/))808P4WSQ

;

;

;

9(

9H62/N=0+%=+;2'(/)+ JdJ# (99; <= ∗ +%22,+%2+-'62,0'=+%=+G2>1'=(&/)*+;&*1>21;/1027(2J+ ;/1'+ NI':,/2,+ ,%26(21,J+ &+ 6)0=+ 0,1+ 0,/2+ G2%I(+ N,*&,/2,+ 21+ *,+ G,(,6%&'(=/11J+.,;(+*$(2,*!*3*+8

448!8+!"#$%&"#)*,'

?@ABCBDB@8+7("5&2#34$2(&(8-'-$%5&"(6*%(+0+0*&("%0(++3!"#$%(%5+9(&-!%-&"(+"0:+(%5&"(&2#34$25&"#,60!5J+(%0$"*&#6-'()*0$-(&-!%-&K2-&!"#$%&"#,60!L8

C&(=0+6%&'()*+%&0;)6+%)+ 8J ""9

?2&,/2%2+-'+/2F10+G2+G&HI'G=+%&0;)6=

%( /99 5P3 += 3PS5

6,)

J5P3 %( /99 −+= 3PT5

1,/+ J(" 999 −= +-'+H,:,+G2.1'1>121+G2+0,1+6)6+/2:)*(=

e85P3PfeP5Pf3J%%

("" /9/99 −+−=−+= 3P"5

!"#

$%&'(!()*+),(&%(-%.(*/*,()012.-%+(34(%4.(5.( ,6

"

#

"

! θ= ∑=

(.%2(34(1)2.7%8%(8)(+.-1

"θ (*)(71)2)%9'(&/(127&)4+/:(%4/%:(8)(*&74+( ,,6,6;; #"$% "" == (%+/4&.

<=6>66=6> 6

66,

θ+−=

−θ+= −

==∏∏ ""

#

"""

#

"&'' $($(( >6"=

?4( .17+)9%( &'( 87@A48%( /4.+%2'( %4/%:'( 8)( *&74+( $( )*+)( -.&'( :/'-$!$ ! +≈+ 6=6> (5.(B72-/:):)(>6C=(8)D.4

=>,, 6)*'&'' (

$!

($!$!(( =

+== < >6E=

FG%:.+'H.:)( >6C=( 5.( >6"=( 8)B.4)*&( *'+#!,-. '+/0,*. )&12+#&-,( 1)( &%2)( 3:( 47+'-

<=>,)''( (FG%:.+'H.:)(>6E=(8)B.4)*&(*'+#!,-.'+/0,*.'+/3)'2&-,(47+%+( <=>,

'''(

!"#$%&&'()*+"'(&(,&' ∗( '()'-.)/&%&&#"'$0#&-1+&&'2-.)*3#3&'-.4032I.)J(;( K( D%:7%2)%( .4.H.%:'( >8)( &/-1'2%2)=( %( 17:.H).,( &%2)( )*+)( *&%8)4+'( :%

-7-)4+/:(θL0(M(6;;2( K(127&)4+/:(8)()D%:/%2)(%(17:.H).L

∗θ ( K(-7-)4+/:(34(&%2)(*)(*&74+)%9'(17:.H%,(&/(&748.H.%( <θ<θ∗

N/(:7&()G%:.+'H.:)

,=6>,=6> ;;∗θ∗θ +=+= 2((2(( >6O=

8)(/48)

<=6>=6> !2(2(( +=+= ∗θ−θ∗ ∗ >#;=

P.4A48( *)%-%( 8)( >6Q=( 2)9/:+'( &',( 4#. '+#52122-3. &0-2'6)22. *'+#!,-,2. '+/0,*,4#!)3.'&02!&-,-.*'+#!&!.(&..72.',)*,-.0+-2132. ∗( &,.-+'.)3-&122-3J

,6

6!

& $

2((

++= ∗ >#6=

03#!),.*'+#!,-.'+/0,*.)&12+#&-(5.

,6

=6>

$!

2((

!

& ++= ∗ >##=

03#!),.*'+#!,-.'+/0,*.'+/3)'2&-<$.4(>#6=(2)9/:+'(&'( ∗((& £ (8%&'( ,2$ ³ .%2(8.4(>##=(8)8/&)-(&'( ∗((& £ (8%&'

<6=6>

!

2$

! −+³

$FIRSRPRF<( 8+#*!&#!&(!

2$

! 6=6>;

−+= . ',. 0)+0)23!&!3&. =>=> ;; $($(& ∗= ( *3

#,/37!3.0)&9.&-.0)+'3#!,-,2.53.*'+#!<

FTFUVWX<(Y(17:.H'(%2)(D%:7%2)%( 8)( )-.*./4)( </<-6;Z; =( ( 5.( )*+)( *&%8)4+'1)*+)(Q(%4.(&/(127&)4+/:(%4/%:(0(M(E[<($%&'(*&74+%2)%(17:.H).(*)(B%&)(&/(127&)4+/:8)(6;[(*'(*)(%B:),(%+A+(34(&%9/:(*&74+/:/.(*.-1:/(&A+(5.(34(&):(%:(*&74+/:/.(&7-1/*,&)(*/-'(12.-)5+)(17*)*72/:().J(%=(:%(*&%8)4H'L(@=(&/(87.(%4.(34%.4+)(8)(*&%8)4H'L(&=&/(7(\/-'+%+)(8)(%4(34%.4+)(8)(*&%8)4H'<

(+-,123<(%=( </<-6ZCO!,#E;,E=>66; QZ =+=(@=(!(M(#(%4.L($(M(;,6,

=

=<1)4+2/=6Q><&B>/<-<#;C,6#6Z!

=L1)4+2/=O>&B<>/<-<Z6Z,6Z!OO

=L*%/1)4+2/=6Q>=,C><&B></<-Z,6##ZZ

=>,

=>,

=>,

=>,

)''

'*'

'''

)*'

&

(

(

((

(

&=(#

6=! (%4.L($(M(;,6,

=

=

<1)4+2//<-<,Z#Z,6Z;;E

L1)4+2//<-<,C6C,6!OQE

L1)4+2/<,/<-C,6!OO!

=>,

=>,

=>,

=>,

)''

'*'

'''

)*'

&

(

(

((

(

Y]^F_`NPRF<( N1:.&%2)%( *&74+/:/.( *.-1:/( *%/( %( *&74+/:/.( &7-1/*( 8)1.48),2)B)2.48/a4)(:%(+.-1,(87%2(8)(:/4G.-)%(1)2.7%8).( ∗θ−θ=! (8)(:%(*&74+%2)(:%(*&%8)4H'5.( 4/( 8)1.48)( 8)( )0+2)-.+'H.:)( .4+)2D%:/:/.( b<,c θθ∗ ( U%.( -/:+,( 8)7%2)&)( &%1.+%:/:*&74+%+((&(*)(&%:&/:)%9'(34(B/4&H.)(8)(&%1.+%:/:(47-.4%:(((B7:7*.48(/4%(8.4(B72-/:):)J

7@*)2D'-(&',(8%&'(!

&))%( &)( )01:.&'( 12*&/2+<

FTFUVWX<(Y( 887@A48%(%B)2)4+'(&6;[,(8/1'(Q(%4.(8)%4/-.+)( 2)8/&)2.( 312)9.4+'(1)4+2/(%&e

!"!

=&(

,1)4+2/,\=^>6

L1)4+2/=,6>

L*%/1)4+2/,6

=>,

+a

=>,

=>,

=>,

)''

'*'

'''

)*'

(

($!(

(($!

(

+

−+

(d(6(%4,(%+/4&.

,=6>=6>=6> 6 !$($!($!( −− +<+<−

)B)2.4H%( @'4&.:72( 1)4+2/( *&74+/:( *.-1:/( &7-)2&.%:,( 1)( +)2-)4

%+72.)( </<-6;C; =( ( +2)@/.)( 2%-@/2*%+'( .4+)G2%:( 3-12)/4'( &/%:&/:%+',( 34( 2)G.-(8)(87@A48'(&7-1/*',( &/(127&)4+/:(%4/%:(8)(:%(8%+%(348%+72'2..<(?4(&74+2%&+/:(8)(3-12/-/+(*/4+(12)D'9/+)(5.4( &%9( 8)( 2%-@/2*%2)( 34%.4+)( 8)( *&%8)4H'<( $%&'( 8)@.+72/:( *).+%2)%(8%+72.).(8/1'(Z,Q(%4.(&%2)(%2(+2)@/.(*'(B.)(127&)4+/:(%4/%:

!"Z

8)( ,6;;,=>, $%( ''' = (1)4+2/(&%(8)@.+72/:(*'(1:'+)%*&',(B%H'(8)(D%:7%2)%(8%+72.).(:%(8%+%

*&74+'2..,(7(*/-'J(%=(-%.(-%2)L(@=()G%:'L(&=(-%.(-.&'<(+-,123:( `%:7%2)%( 8%+72.).( :%( *&%8)4H'( >!(M(Q(%4.=( )*+)( ,=6>; !2(( += ( %8.&'

((M(6C6;Q6;( /<-<( `%:7%2)%( 8%+72.).( &/(#

6( %4.( 34%.4+)( 8)( *&%8)4H'( )*+)( >*7:/H.%

2%H.74%:'=( </<-6Q!"!;Q=∗( ($)7%2)&)( ∗= ((& (1)4+2/(12%G/:(127&)4+/:/.(8)(*&74+

,6=6>

; !

2$

! −+= (%8.&'($;(M(;,;O"C6"C(2)9/:+'J

%=( 8%&'( ,;$$ < ( %+/4&.( ∗> ((& ( 5.,( 34( &74*)&.4H',( 8)@.+72/:( 2%-@/2*)%9'( 7*/-'(-%.(-%2)(8)&A+(D%:7%2)%(8%+72.).(:%(8%+%(*&74+'2..(%&)*+).%L

@=(8%&'( ,;$$ = (%+/4&.( L∗= ((&&=(8%&'( ,;$$ > (%+/4&.( <∗< ((&Y]^F_`NPRF<( $%&'( *)( &%:&/:)%9'( *&74+/:( &7-)2&.%:( *.-1:/( &/( 127&)4+/:

%(M(6;;$,(.4)G%:.+'H.:)(.-1:.&%+)(34(%871+%2)%(8)&.9.).(12.D.48(-'2.-)%(127&)4+/:/.%4/%:(8)(*&74+(2'-A4(4)-78.B.&%+),(8%2(12%G/:(8)(*&74+( ;$ (*)(-78.B.&'<(?4+2a%8)D'2,

=6>=6>=6> $!2($!(( !& −+=−= ∗ ( 5.(8.4( &748.H.%( ∗((& £ ( 2)9/:+'(

!

!

2!

2$

=6>

6=6>

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