Etude de l’évolution de la courbe de transition de la ténacité en fonction de la température et du défaut géométrique dans le cas d’un acier moulé

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1 372,73* / 76 +'=2'416, =5+16-:7* 4* 23'/7-, 213 81 .-44731,-'6 /7 =1,53-17 4*8'68 76'7 76* +'=(-61-4'6/*4,3'-4='/*4585=*6,1-3*4/5+3-,4+- /*44'74 E ' H+'6,31-6,* /* ,31+,-'61228-:75* 2*32*6/-+781-3*=*6, 17 2816/* 81 .-4473*I EF H+-44-'6/1648* 2816/* 81 .-4473* *, 1228-:75* 2*32*6/-+781-3*=*6, 17 .3'6, /* 81 .-4473*I H+-44-'6/1648* 2816/* 81 .-4473* *, 1228-:75* 213188@8*=*6, 17 .3'6, /* 81 .-4473*I / 5 " 1 =5+16-:7* /* 81 372,73* *4, 81 4+-*6+* /* 8 5,7/* /7 +'=2'3,*=*6, / 76* 4,37+,73* 1;*+ 4*4/5.17,4F G 88* 2*3=*, / 5,7/-*3 8 5;'87,-'6 /1648* ,*=24/* 81 .-4473* *, 4'6-6,*31+,-'61;*+ 8* =-8-*7 +'6,-67 *4, 81 4+-*6+* :7- 2*3=*, /* =*,,3* *6 3*81,-'676.1+,*73 +131+,53-416, 81 45;53-,5/* 81 4-,71,-'6'(,*67* 213 1228-+1,-'6/ 76* +0139* 473 76* 2-@+* .-44735* * .1+,*73 4'(,-*6, 213 +'64-/531,-'6/*4+'6,31-6,*4*, /*4 /5.'3=1,-'6417 ;'-4-619* /7 .3'6, /* 81 .-4473* 2'73 8*4,3'-4='/*4+-,54+- /*4474 8 *4, B 4-9618*3 :7* 8* ='/* / '7;*3,73* /* 81 .-4473* *4, 8* 2874/169*3*7> 2'73 76* 4,37+,73* *, + *4, +* :7- )74,-.-* 8 -6,53A, 213,-+78-*3 :7- 87- 1 5,5122'3,5/16481 8-,,531,73*

'

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' $ ! 6 =-8-*7 .-44735 2*7, A,3* 3*2354*6,5< 4+05=1,-:7*=*6,< +'==* 473 8* 4+05=1 47-;16,

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θ `'6* / 581('31,-'6 `'6* 4-6978-@3* `'6* *>,53-*73* > >

( F GF G 66598-9* 81 C'6* / 581('31,-'6*, '6+'64-/@3* 8* +'=2'3,*=*6, =5+16-:7* /7 4'8-/* 5814,-:7* 8-651-3* 1 +131+,53-41,-'6 /* 8 -6,*64-,5 /* 81 4-697813-,5 /7 +01=24/*4+'6,31-6,*4B 81 2'-6,* /* 81 .-4473* 2*3=*, 81 /5,*3=-61,-'6+'=28@,* /*4+01=24/* +'6,31-6,*4'7 /* /5.'3=1,-'64/16481 4,37+,73* .-44735*< +'64-/535* +'==* 5814,-:7* *, 8 -6;*34* *4, 1744- ;31-16481 C'6* /* 4-697813-,5/*4+'6,31-6,*4< +*4/*36-@3*44'6, /* 81 .'3=* ?

( ) ( )

" G D D= _π θ +" σ 1;*+ ?

( )

θ D " ? .'6+,-'6/* 8 1698* 2'81-3* 213 3122'3, B 8 *>,35=-,5/* 81 .-4473*< -/*6,-:7* :7*8:7* 4'-*6, 81 .-4473*< 81 2-@+* *, 8* +0139*=*6, S

( )

" ? *4, 5+3-, 2'73 3122*8*3 :7 -8 *>-4,* / 17,3*4,*3=*4:7- ,*6/*6, ;*34" 1;*+ 3 S G ? .1+,*73 / -6,*64-,5/*4+'6,31-6,*4< :7- .->* 8* 6-;*17 /* 81 4-697813-,5 * .1+,*73 / -6,*64-,5/* +'6,31-6,*42'73 8*4=-8-*7> .-44735428164F!G*6='/* *4, /'665213 8 *>23*44-'647-;16,* ?

(

)

G 8-= D " π σ → = 164 81 +14 / 76* 281:7* /* ,3@49316/*4/-=*64-'64+'6,*616, 76* .-4473* /* 8'697*73 1 *, 4'7=-4* B 76* +'6,31-6,* 0'='9@6* σ ? G ₌σ π * 47++@4/* 81 =5+16-:7* /* 81 372,73* 23';-*6, /7 .1-, :7* 8*4+'6/-,-'64/* 8 *>,35=-,5 /* 81 .-4473* /52*6/*6, /* +* 4*78 *, 76-:7* 2131=@,3* *4 .'3=781-3*4 1 > E / *2/ "

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      ≥ , G *, <       ≥ , G 3 1;*+ *81 8-=-,* 5814,-:7* /7 =1,53-17 +'64-/535 164 8* +14 /* 8 523'7;*,,* 213 *>*=28*< .-973* +- /*44'74< 81 +'6,31-6,* 6'=-618* +3-,-:7* B 81 372,73* *4, ?

(

H

)

3 / − = σ *, 8* .1+,*73 +3-,-:7* / -6,*64-,5/* +'6,31-6,*4*4, ?

( )

H " G =σ π σ 'D"σ

( )

_H *4, 762131=@,3* 95'=5,3-:7* /5+3-, /16481 6'3=* F!G 1 T & / #2 . ' >

( 16476,31;1-8 35+*6,< &'++1++-6- *, 17,3*4F G'6, ='6,35:7* /1648* +14/7 ;*33* H372,73* .319-8*I< '6 2*7, 5;-,*3 81 235.-44731,-'6 213 .1,-97* 213 8 7,-8-41,-'6 /*4 523'7;*,,*4/* ,E2* .8*>-'6,3'-42'-6,4*6,1-885*4*6$ B /*431E'64/* "< µ= 4164:7* +*81 1..*+,* 8* 35478,1, '(,*67 *6,*3=* /* G * ,31;1-8 /* +0*;-33-1 *, 17,3*4F G1 2'3,5473 8 -6.87*6+* /* 81 =-+3'4,37+,73* 473 81 372,73* .319-8* /*41+-*34+'6,*616, /*4=-+3'.-4473*4 67,-8-416, /*4523'7;*,,*4/* .8*>-'6:71,3* 2'-6,4< +*417,*734+'6+87*6, :7* 2'73 1=58-'3*3 81 ,561+-,5/* 8 1+-*3< -8 .17, E 5;-,*3 81 2354*6+* /* 213,-+78*4.319-8*493'44-@3*4 * .1+,*73 +3-,-:7* / -6,*64-,5/* +'6,31-6,* G /52*6/ /* 81 ,*=2531,73* *, /* 81 ;-,*44* /* 4'88-+-,1,-'6 1 .-973* +- /*44'74='6,3* 76*>*=28* /* 8 5;'87,-'6/* G *6 .'6+,-'6/* 81 ,*=2531,73* 2'73 8 1+-*3 (144* ,*=2531,73*< +*, 1+-*3 *4, .319-8* *, G 1 76* ;18*73 .1-(8* S +*,,* ;18*73 179=*6,* 1;*+ 81 ,*=2531,73* *, 8 1+-*3 /*;-*6, /* 2874*62874,*61+* ;*+ 8 179=*6,1,-'6/* 81 ;-,*44* /* 4'88-+-,1,-'6< 81 ,561+-,55;'87* ='-64312-/*=*6, *6.'6+,-'6/* 81 ,*=2531,73* 6* 5;'87,-'6/* 81 ,561+-,5*6.'6+,-'6 /* 81 ,*=2531,73* *, /* 81 ;-,*44* /* /5.'3=1,-'64*=(81(8* B +*88* +- 1 5,5'(,*67* 213 136-*3 F"G2'73 8 1+-*3 $ ,*=2531,73* +'64,16,*< 8* .1+,*73 / -6,*64-,5/* +'6,31-6,*4+3-,-:7* G /-=-67* :716/ 81 ;-,*44* /* 4'88-+-,1,-'6 179=*6,* '==* 8* ='6,3* 81 .-973* 47-;16,*< *6 .'6+,-'6 /* 81 ;-,*44* /* +0139*=*6,< '6 2*7, '(,*6-3 4'-, 76 .1+,*73 / -6,*64-,5 /* +'6,31-6,*4 +3-,-:7* 4,1,-:7* G < 4'-, 76 .1+,*73 / -6,*64-,5 /* +'6,31-6,*4 +3-,-:7* /E61=-:7* G −! " " " " "" "" " "" HY I

G

H 1 =%I " K≈ − − ε ε_K≈ _" − / % ' " . G " A' " 4 (#

(* 561+-,5 / 2 ! "" " . G G

' '

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$

5

5

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      −       =     "" < : , G , G 'D_ _ , G

*4, *>23-=5*6H==I< #$*6H\I *, **6H %==PI

G

G

" " " " " H 1 =% 4 I

(# *,,* +'33581,-'6/* +131+,@3* *=2-3-:7* 1 5,55,1(8-* B 213,-3 /*435478,1,4/ *441-4 3518-454 473 '6C* 6716+*4 / 1+-*34 B 017,* 354-4,16+* 1E16, /*4 +131+,53-4,-:7*4 =5+16-:7*4+'=23-4*4/1648*4/'=1-6*447-;16,4? 8-=-,* / 5814,-+-,5? " a H %==PI a "< ,561+-,5? aG H 1 = % I a "< 56*39-* /* 372,73* ? a#$ H\I a 16481 213,-* (144* *, ='6,16,* /*4+'73(*4/* ,3164-,-'6< 81 372,73* /* ,E2* .319-8* B (144* ,*=2531,73* 5;'87* /* =16-@3* 287417 ='-64312-/*< 4*8'68*46716+*4/ 1+-*34< ;*3476* 372,73* /* ,E2* /7+,-8* B 017,* ,*=2531,73* +* +0169*=*6, / 142*+, /7 ='/* /* 372,73* +'33*42'6/ 76* 585;1,-'6 /* 81 ,561+-,5:7- 4* =16-.*4,* 8'34/*4*441-4473 523'7;*,,*4 *6,1-885*4 874-*734 =5,0'/*4 4'7;*6, /* +131+,@3* *=2-3-:7* '6, 5,5 23'2'45*4/16481 8-,,531,73* /1648* (7, / 5;187*3 G B 213,-3 /*435478,1,4/ *441-4/* 354-8-*6+* 0132E $ /1648* /'=1-6* /* ,3164-,-'6 1 287213, 41228-:7*6, 17> 1+-*34/* +'64,37+,-'6=5,188-:7* B (144* *, ='E*66* 354-4,16+* '73 8*41+-*34B ='E*66* 354-4,16+* 2'73 12213*-84/* 23*44-'6< &134'= *, '8. F G'6, =-4*65;-/*6+* 76* 3*81,-'6*6,3* G *, 81 354-8-*6+* #$/16481 213,-* (144* /*4+'73(*4/* ,3164-,-'6 *,,* 3*81,-'645+3-, +'==* 47-, ? < " G: G = 1;*+ ? G *>23-=5*6H %==I *, #$*6H\'78*4I 1 +'=2131-4'6/*435478,1,4/ *441-4/* 354-8-*6+* #$ *, 81 ,561+-,5G *..*+,754 473 8*4=A=*4=1,53-17>< / 76* 213, *6 .8*>-'6 8*6,* H*441- 4,1,-:7*I< / 17,3* 213, *6 .8*>-'6 213 +0'+ H*441- /E61=-:7*I '6, 2*3=-, B &134'= F G/* .1-3* 8*4'(4*3;1,-'64 47-;16,*4?
8 -6.87*6+* /* 81 ;-,*44* /* 4'88-+-,1,-'623';':7* 8* =A=* /5+1819* /*4+'73(*4/* ,3164-,-'6/* 81 ,561+-,5G :7* +*87- /*4+'73(*4/* ,3164-,-'6/* 81 354-8-*6+* #$473 8 5+0*88* /*4,*=2531,73*4S
81 ;18*73 /7 /5+1819* ∆ HY I *4,.'6+,-'6/* 81 8-=-,* / 5814,-+-,5 */7 =1,53-17 S
81 +'33581,-'6*6,3* G *, 8 56*39-* /* 372,73* #$ =*4735* *6.8*>-'68*6,* H*441-4 4,1,-:7*4I< '(5-, B 81 8'- 47-;16,* ?

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

6

4

4

)

7

$ #

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$

%

$

1 =5+16-:7* /* 81 372,73* 5814,-:7* 8-651-3* 4722'4* :7* 81 /5.'3=1,-'62814,-:7* 1;16, 81 372,73* *4, 6598-9*1(8* 213 3122'3, B 81 8'697*73 /* 81 .-4473* *, 17> /-=*64-'64 /* 81 4,37+,73* ,*88* :7* 8 521-44*73 /* 8 5+016,-88'6 *,,* 0E2',0@4* 8-=-,* 8*4 2'44-(-8-,54/ 1228-+1,-'6/* +*,,* ,05'3-* /* 372,73* 213,-+78-@3*=*6, 8'34:7 -8 419-, /* =1,53-17> B 9316/* /7+,-8-,5 87;-619* F G1 +'64-/53581 =5+16-:7* 5814,'2814,-:7* /*4372,73*4+'==* 765,1, 8-=-,* 4-,75*6,3* /*7> 5,1,48-=-,*4(-*6,E254? 8* /'=1-6* /*4372,73*45814,-:7*4*, 8* /'=1-6* /* 81 37-6* 2814,-:7* 8 1 5918*=*6, +81445 8*4 +3-,@3*4 /* 372,73* 4*8'6 8 1223'+0* 1/'2,5* ? 1223'+0* 8'+18* '7 1223'+0* 98'(18* *4 +3-,@3*4 2*7;*6, A,3* *>23-=54*6,*3=*4/* +'6,31-6,*4< /* /5.'3=1,-'64'7 56*395,-:7*4

)

7#

!

! / / #$

8 E 1 /* +*81 2874/* "" 164< 8 *>253-*6+* /* 5'613/ /* $-6+-< :7- 1('7,-, B 81 +'6+874-'6:7* 81 354-4,16+* B 81 ,31+,-'6/ 76.-8 / 1+-*3 *4, / 17,16, 2874.1-(8* :7* 8* .-8 *4, 8'69< -8874,3* +81-3*=*6, 81 61,73* 4,1,-4,-:7* /* 81 /-4,3-(7,-'6 /*4/5.17,417 4*-6 / 76* 4,37+,73*

( 1 354-4,16+* B 81 372,73* σ, 6*4, 21476* 23'23-5,523'23* /7 =1,53-17 4*78*=*6,< =1-4*88* /52*6/ /* 81 ,561+-,5*, /* 81 ,1-88* /7 /5.17, +3-,-:7* B 8 '3-9-6* /* 81 372,73* / , . I * ='/@8* 23'(1(-8-4,* /53-;5/* 81 ,05'3-* /7 8-*68* 2874.319-8* *4, /5;*8'225213 T*-(788 F G*, *4, /5+3-, 213 87;-619* F G *,,* ,05'3-* *4, (145* 473 8*4 /*7> +'64-/531,-'6447-;16,*4? 81 23'(1(-8-,5/* ,3'7;*3 76 /5.17, /* 45;53-,5/'665/16476 ;'87=* 13(-,31-3* /7 =1,53-17 *4, 81 =A=* 213,'7,< +* :7- 3*;-*6, -=28-+-,*=*6, B 4722'4*3 :7* 8* =1,53-17 *4, 4,1,-4,-:7*=*6, 0'='9@6*< 81 372,73* /7 /5.17, 8* 2874+3-,-:7* +'6/7-, B 81 372,73* ,',18* 1 .-973* +- /*44'74-8874,3* 81 /-42*34-'6/*4+'6,31-6,*4/* ,31+,-'6B 372,73* /164 8* +14 / 76 =5,18 *, / 76 +531=-:7* +01:7* ;18*73 /* 81 +'6,31-6,* /* ,31+,-'6 76-.'3=* σ< '62*7, 144'+-*3 76* .35:7*6+* /* 372,73* '7 23'(1(-8-,5 / & ! A =5,18 +531=-:7* +'6,31-6,* B 81 372,73* H 1I '=(3* /* 2-@+*4 3'=27*4

( !""#!"#$% & #'% *40E2',0@4*4/5,1-885*4/* +*,,* ,05'3-* 4'6, ? 8* =1,53-17 *4, 144-=-85B 76* +01N6* /* 6=1-88'64< 81 +'6,31-6,* /* 372,73* *4, +*88* /7 =1-88'68* 2874.1-(8*< 81 +'6,31-6,* /* ,31+,-'6σ 1228-:75* *4, 76-.'3=* *, +'64,16,*< 8*4 354-4,16+*4 B 81 372,73* /*4 =1-88'64 4'6, /*4 ;13-1(8*4 1851,'-3*4 -6/52*6/16,*4< 81 2'2781,-'6/*4354-4,16+*4B 81 372,73* /*4=1-88'64*4, 0'='9@6* *4σ, /*4/-..53*6,4=1-88'6447-;*6, 81 =A=* 8'- /* 23'(1(-8-,5?

( )

σ ₌

(

σ _< σ

)

, / 3 31,-:7*=*6,< '623*6/ 76=1-88'6+'==* 5,16, 76585=*6, /* ;'87=* $ ' ( ' '##") !%(*# +%,- # , 1 23'(1(-8-,5/* 473;-* /* 8 585=*6, /* ;'87=* $ 4'7476* +'6,31-6,* σ *4, ?

( )

σ _{= :}

(

σ_,>σ

)

+ :< 2'73 /*7> =1-88'64H0E2',0@4* I ?

(

_{: :<K}σ

) ( ) ( )

_{+ :<}σ _{+ :<K}σ + + = / 'D? +

( )

:<σ /* 81 .'3=* ? *>2

(

−:φ

( )

σ

)

0E4-:7*=*6,< 4- σ 179=*6,* 18'34 81 23'(1(-8-,5 /* 473;-* /-=-67* 23'2'3,-'66*88*=*6, B $ +13 4- $ 179=*6,* 18'34 8* 6'=(3* /* /5.17,4 179=*6,* H0E2',0@4* I . #/,#0#. "#, !1 ( - "( ! & #'% * ='/78* /* T*-(788 L = M< :7- *4, 76 6'=(3* 4164/-=*64-'64< +131+,53-4* 81 /-42*34-'6 /*4+'6,31-6,*4 1 .-973* 47-;16,* ='6,3* 8 5;'87,-'6 /* 81 23'(1(-8-,5 /* 372,73* *6.'6+,-'6/* 81 +'6,31-6,* /* 372,73* 1 ;18*73 /* = /*;-*6, -6.-6-* 4- ,'7,*48*4 523'7;*,,*4+144*6, B 81 =A=* ;18*73 /* σ, S 81 /5+3'-4416+* /* = 3*.8@,* 81 /-42*34-'6 -=2'3,16,* /*4+'6,31-6,*417>:7*88*48*4523'7;*,,*4+144*6, 1648* +14213,-+78-*3 /*41+-*34< 8*4;18*734/* = 4'6, 231,-:7*=*6, +'=23-4*4 *6,3* " *, ""

& / ! " 0 H 1 +'6,31-6,* *6/*44'74/* 81:7*88* 81 23'(1(-8-,5/* 372,73* *4, 6788* *4, 122*85* L +'6,31-6,* 4*7-8 M*, *88* *4, 6',5* σ * .1+,*73 / 5+0*88* σ"< :7- /52*6/ /* =< /'66* 76* -/5* 473 81 2'4-,-'6 /* 81 +'73(* 213 3122'3, B 8 1>* /*423'(1(-8-,54 ( ' '##") (%1"%( +%,- # , 1 23'(1(-8-,5/* 372,73* /* 8 585=*6, /* ;'87=* $ 4'7476* +'6,31-6,* σ *4, ?

( )

:<σ = :

(

σ,<σ

)

= − +

( )

:<σ = −*>2

(

−:φ

( )

σ

)

41+016, :7* :

(

σ,<σ

)

=/:

( )

σ *4, 81 ;18*73 /* 81 .'6+,-'6 /* 35213,-,-'6 *6 σ / 'D

( )

σ φ *4+'6/-,-'64-=2'45*4B φ

( )

σ 4'6, ? 2'4-,-;*< 6'6/5+3'-4416,*< 416678* 2'73 76* +'6,31-6,* 4*7-8 σ7<

( )

σ φ W       − " σ σ σ

( )

σ ₌" : / 4-σ<σ

( )

_             − − − = : : / " *>2 σ σ σ σ _4-σ_>σ 1;*+ = 8* ='/78* /* T*-(788 *, σ"8* .1+,*73 / 5+0*88* = W b = W " = W ,

σ

"< "<" <"

( ' '##") (%1"%( +%, 1#. 1 23'(1(-8-,5/* 372,73* B 81 +'6,31-6,* σ / 76* 2-@+* /* ;'87=* $ *6,31+,-'6273* Hσ7W "I *4, ?

( )

              − − = =/_: : " *>2 σ σ σ /164 8* +14 / 76* +'6,31-6,* 1228-:75* 6'6 76-.'3=*< '6 23*6/ *6 +'=2,* 41 ;13-1,-'647-;16, 8 585=*6, /* ;'87=* +'64-/535?

( )

              − − =

∫

: / : : *>2 " σ σ σ 4'-, 213 +'=2131-4'61;*+ 8* ='/@8* 235+5/*6, ?

( )

              − − = : : / " =1> *>2 σ σ σ 'D$ *4, 8* ;'87=* *..*+,-. S 8* ;'87=* :7* /*;31-, 1;'-3 76* 523'7;*,,* /* ,31+,-'6 2'73 1;'-3 81 =A=* 23'(1(-8-,5/* 372,73* 0 ,0 % ,. %* %- ! %!. ,"( #," 1 23'(1(-8-,5 /* ,3'7;*3 /*4 /5.17,4 /164 76 ;'87=* 2874 9316/ /*;-*6, 2874 -=2'3,16,*< / 'D/-=-67,-'6/* σ '64-/53'64/*7> 5+016,-88'64/* ;'87=* $ *, $ 4'7=-4< 3*42*+,-;*=*6,< 17> +'6,31-6,*4σ *, σ S -84173'6, 81 =A=* 23'(1(-8-,5/* 372,73* H,31+,-'6273*I 4- ?               − − : " *>2 _σσ W               − − : " *>2 _σσ / 'D? : : _      = σ σ σ %σ $ %$ = W = W = W = W ! = W " = W = W < < ! < <" <" <" <" <""" < < " < ! < < < " < < < ! < < < < ! <! ! < ! < < < < ! < "

5+016,-88'6 8* 2874;'87=-6*7> /*;31 A,3* 4'7=-4B 76* +'6,31-6,* -6.53-*73* B +*88* 1228-:75* B 8 5+016,-88'628742*,-, / ,0 % ,. %"21 ! #.#""#, 1 +'645:7*6+* /-3*+,* /* 8 *..*, /7 ;'87=* 4'74 +'6,31-6,* *4, :7* 2'73 76 5+016,-88'6/* ;'87=* $ 4'7=-4B 76* +'6,31-6,* /* ,31+,-'6σ,'7 /* .8*>-'6σ.< -8 E 1731 =A=* 23'(1(-8-,5/* 372,73* 4- ? " : : _      = σ σ 3 ,"( %."#, . ,"( #," & #'% 1 +'6,31-6,* /* T*-(788 σH< *4, 76 ,*3=* -6;*6,5213 8* 93'72* &*3*=-6 F!G< 2'73 9565318-4*3 8* +'6+*2, /* 81 372,73* 23'(1(-8-4,* *, 8*44722'3,4/* /5;*8'22*=*6, /*423'+5/73*4:7- 76-.-*6, 8*4=*473*4/* 81 ,561+-,5B ,31;*34/-..53*6,*4+'6.-9731,-'64 /* 81 .-4473* *, /7 ='/* /* +0139*=*6, * ,31;1-8 /* &*3*=-6 F!G2*3=*, / 5,1(8-3 76 3122'3, *6,3* 8* =-+3'359-=* /* 372,73* *, 81 .-4473* =1+3'4+'2-:7* H,*8 :7* 8 -6,59318* \I *6-6,3'/7-416, 81 +'6,31-6,* /* T*-(788 σH +'==* 2131=@,3* /* 81 372,73* 23'(1(-8-4,* * 2'-6, +85 /* 8K1223'+0* &*3*=-6*4, :7* σH 47-, 8*4/*7> 2131=@,3*4/* /-4,3-(7,-'6/* T*-(788 F G? 8* ='/78* /* T*-(788< =< *, 8* 2131=@,3* /* 8K5+0*88*< σ" 1648K1223'+0* 8'+18* /* 81 372,73* 213 +8-;19*< 81 /-4,3-(7,-'6/* 81 23'(1(-8-,5 2'73 81 +'6,31-6,* /* 372,73* /K764'8-/* .-4473547-, 8*4/*7> 2131=@,3*4/* 81 /-4,3-(7,-'6 T*-(788 F!G<

( )

_             − − =               − − =

∫

H : H : : / " " " *>2 *>2 _σσ σ_σ σ 'D? $ ? 8* ;'87=* /* 81 C'6* /7 23'+*4474/* 81 372,73*< $'? 76;'87=* /* 35.53*6+* *, σ _{? 81 +'6,31-6,* 23-6+-218* =1>-=18* B 8K-6,53-*73 /* 81 C'6* /7 23'+*4474/* 81} 372,73* /5.-6-* 213 σ ≥λσ" 1;*+ λ≈ F"G *8'6&*3*=-6F!G<81 +'6,31-6,* /* T*-(788 *4, /5.-6-* +'==* 47-, ?

( : H : :"       =

∫

σ σ

) '

$

/ # "

#

"

"

5,7/* /* 799-*3- *, 17,3*4F G2'3,* 473 81 ,3164.*31(-8-,5/* 81 ,561+-,5B 81 372,73* 5814,'2814,-:7* *6 7,-8-416, 8K1223'+0* /* 81 +'6,31-6,* /* T*-(788 * =1,53-17 5814,'2814,-:7* *=28'E5/1648*41618E4*4/* +*417,*734'(5-, B 81 8'- /* 8 5+3'7-4419* 47-;16,* ? " " σ σ ε ε = < ε≤ε"       = " " σ σ ε ε < ε >ε" 'Dσ" *, ε" 4'6,< 3*42*+,-;*=*6,< 81 +'6,31-6,* *, 81 /5.'3=1,-'6/* 35.53*6+*< *, 6*4, 8* +'*..-+-*6, / 5+3'7-4419*

23'7;*,,* _{& H==I T H==I 1 H==I 1%T H==I H==I}

H&I _{" ""} H&I _{" " ""} H&I _{" "" " " ""} 5 ' " $ ! B C 1 .-973* -8874,3* 81 23'+5/73* /* +'33*+,-'6 *41618E4*417> 585=*6,4.-6-4 .'736-44*6, 8* 3122'3, *6,3* 81 +'6,31-6,* T*-(788 HσHI *, 8* +0139*=*6, 1228-:75* H\I 2'73 76* ;18*73 425+-.-5* /7 ='/78* /* T*-(788< = ? =188 +18* -*8/-69 *4+'73(*4/* 81 .-973* 4'6, +'64,37-,*42'73 = .->*< H8* ;'87=* 6'3=18-416, 2'73 81 +'6,31-6,* T*-(788< $'< *4, 144-965B 81 ;18*73 /* == 213 +'6;*6,-'6I H σ J 1 ++K J 1 5+K J 1 H< σ = ? +'64,16,* H W"I H&I / 2 ) 0 . J5+K
J++K -L . ' ++K ? . ' + ;3<;5+K<

*4 ;18*734 /* 81 ,561+-,5 4'6, 4'7;*6, 6'3=18-45*4 213 (σ" 2'73 .'736-3 76 *64*=(8* /* +'73(*4 H\ %(σ" *6 .'6+,-'6 /* \ %(σ"I 1228-+1(8* 2'73 ,'7,*4 8*4 523'7;*,,*4 1;*+ 1%TW"< < T W&< W T *4 214 47-;16,4 /5+3-;*6, 8* 2816 /* +18-(319* 23'2'45 213 799-*3- F G:7-4-=28-.-* 859@3*=*6, 81 =5,0'/'8'9-* /5+3-,* 213 1'< 799-*3- *, '//4 F G
*4,*C/*7> *64*=(8*4 / 523'7;*,,*4 1;*+ 8*4 +'6.-9731,-'64 /* 81 .-4473* /-..53*6,*4 H *, 4I/164 81 359-'6 /* 81 ,3164-,-'6 /7+,-8* % .319-8* *, 23'/7-3* /*7> /-4,3-(7,-'64 /* 81 ,561+-,5 B 81 372,73* 7+76 /5+0-3*=*6, /7+,-8* 6* /*;31-, A,3* /5;*8'225 1;16, 81 372,73* 213 +8-;19* /164 8K76 '7 8K17,3* *64*=(8*4 / *441-4 *441- 473 523'7;*,,* 23'.'6/5=*6, *6,1-885* 4*31 +'64-/535 +'==* 81 +'6.-9731,-'6 '73 81 +'6.-9731,-'6 4< /*4 523'7;*,,*4 B /-=*64-'64 4*=(81(8*4 =1-4 1;*+ 8*4 *6,1-88*4 2*7 23'.'6/*4< + B /< 1%T W"<  1-3* 76* 1618E4* /5,1-885* 213 81 =5,0'/* /*4 585=*6,4 .-6-4 2'73 8*4 95'=5,3-*4 /*4 523'7;*,,*4 7,-8-45*4 /164 8*4 *441-4  ;18*73 /* = +'64,16,*< +18+78*C81 +'6,31-6,* σH *6 .'6+,-'6 /* 8 5;'87,-'6 /* \ 2'73 8*4 +'6.-9731,-'64 *, 4 2'73 +'64,37-3* 8* ='/@8* :7- 2*7, 5;187*3 81 ,561+-,5 12213*6,* 17> /*7> +'6.-9731,-'64  18+78*3 8K*33*73 /* ,561+-,5 ?

( )

4 ₄ 4 J J J , " " < " − = - H=I≠"< 3525,*C8*4 214 *, 2'73 /*4 ;18*734 /* = 472285=*6,1-3*4  18+78*3 H=I*6 .'6+,-'6 /* = * ='/78* /* T*-(788 5,18'665 /'66* H=IW" 1;*+ 76* 2*,-,* ,'85316+*  18+78*C 81 ;18*73 σ 23@4 1;'-3 /5,*3=-65 81 ;18*73 /* =< σ *4, .1+-8*=*6, '(,*67* B 213,-3 /* σH *6 .'6+,-'6 /* 8 5;'87,-'6 /* \ 2'73 81 ;18*73 = 5,18'665* - ($% 123@4 87;-619* F G< 8 1223'+0* 23'(1(-8-4,* /* 81 372,73* ,*88* :7 *88* 1 5,5 7,-8-45* 213 &*3=-6* F!G2354*6,* 76 +*3,1-6 6'=(3* /* /-..-+78,54 /'6, ? • 8* ;'87=* *..*+,-. $ *4, /5.-6-, 213 0E2',0@4* +'==* +*87- /* 81 C'6* 2814,-:7* (-*6 :7* 81 +'6,31-6,* 4*7-8 / *6/'==19*=*6, 4'-, 4'7;*6, 47253-*73* B 81 8-=-,* / 5814,-+-,5 S

* • 81 /5.-6-,-'6 /* 81 +'6,31-6,* /* T*-(788 +'6/7-, 17 .1-, :7* 8* 23'/7-,

( )

6 6:_" σ _{W +'64,16,* 1 +'6,31-6,* *..*+,-;* /52*6/ /7 ;'87=* /* 35.53*6+*} +0'-4- 6 +*81 +*,,* 1223'+0* 6 *4, 214 ;53-,1(8*=*6, 8'+18* +13 8*4 /*7> 2131=@,3*4 +'6,31-6,* *..*+,-;* *, ;'87=* *..*+,-. 6* 4'6, 214 -6/52*6/16,4 13 ,31642'4-,-'6< +*,,* 1223'+0* *4, 1618'97* 17 .1-, :7 *6 =5+16-:7* 8-651-3* /* 81 372,73* 8* 23'/7-, /* 81 +'6,31-6,* +3-,-:7* 213 81 31+-6* +1335 /* 81 /-4,16+* *4, 76* +'64,16,* S • 8* ;'87=* 13(-,31-3* $' *4, +0'-4- *6 .'6+,-'6 /* 81 95'=5,3-* *, /* 81 :718-,5 /*4 =1-88*4 /* 81 =5,0'/* /*4 585=*6,4 .-6-4 8 *6 35478,* 4'7;*6, 76 +0'-> /* ;18*73 /* $' +'6/7-416, B /*4 ;18*734 /* 81 +'6,31-6,* /* T*-(788 2*7 3518-4,* H47253-*73* B 81 +'6,31-6,* =1>-=18*I< • 81 /-42*34-'6 179=*6,* *, =R /-=-67* 8'34:7* 8* 31E'6 / *6,1-88* 179=*6,*< /'6+ 6 *4, 214 -6,3-64@:7* /7 =1,53-17

) )

*

$ "

*

##

) ) !! # $ #* * ## 1 2354*6+* / 76 /5.17, /164 76* 4,37+,73* 4* 35;@8* =5+16-:7*=*6, (*17+'72 2874 931;* :7* 81 4-=28* +'645:7*6+* / 76* 35/7+,-'6 / 76* 4*+,-'6 4722'3,16, 8 *..'3, ,3164=-4 F G *, *..*, 19931;16, *4, +'731==*6, /54-965 +'==* 8 *..*, / *6,1-88* 1 6'+-;-,5 /*4 *6,1-88*4 /52*6/< *6 2874 /* 8*734 /-=*64-'64< /*4 2131=@,3*4 95'=5,3-:7*4 ,*84 :7* 8* 31E'6 / *6,1-88* ρ *, 4'6 1698* ψ *4 ;18*734 /* +*4 /*7> 2131=@,3*4 2*3=*,,*6, /* /5.-6-3 8* ,E2* /7 /5.17, 6 *..*,< 2'73 76* .-4473*ρW" *, ψW" S 2'73 76* *6,1-88* -6.-6-=*6, 1-97VρW" *, ψ≠" S *, 2'73 76* 4-=28* *6,1-88* '6 1 ?ρ≠" *, ψ≠_" ψ ρ 1 / (2 0 "

# *..*, / *6,1-88* 2*7, A,3* 1-45=*6, =-4 *6 5;-/*6+* 473 76 /-1931==* +'6,31-6,* 98'(18* +3-,-:7* *6 .'6+,-'6 /* 81 ,1-88* /7 /5.17, 6'3=18-45 122*85 /-1931==* /* *//*34'6 * /-1931==* *4, 3*2354*6,5 473 81 .-973* 47-;16,* 2'73 8* +14 / 76* 4-=28* 281:7* 4'7=-4* B 76 +0139*=*6, 76-.'3=* *, +'=2'3,16, 76* *6,1-88* +*6,318* /* 8'697*73 1 * 3*2'3, /* 8 *..'3, ,3164=-4 473 8* 8-91=*6, -=28-:7* :7* /164 8*4 +'6/-,-'64 +3-,-:7*4< 81 +'6,31-6,* 6'=-618* +3-,-:7* 4'-, 5918* B 81 354-4,16+* 78,-=* /7 =1,53-17 8 *6 35478,* 76* /-=-67,-'6 8-651-3* /* 81 +'6,31-6,* 98'(18* +3-,-:7* 4*8'6 81 3*81,-'6 ?       − = σ T 1 = + 9 6 2354*6+* / 76* *6,1-88*< 81 +'6,31-6,* 98'(18* +3-,-:7* 5;'87* 4*8'6 76* 3*81,-'6 8-651-3* *, B 76* ;18*73 -6.53-*73* B +*88* '(,*67* 4*8'6 8 5:71,-'6 +- /*4474 *>+*2,5 2'73 8*4 ,3@4 2*,-,4 *, 8*4 ,3@4 9316/4 /5.17,4 1 /-..53*6+* /* ;18*73 *6,3* 8*4 /*7> +'6,31-6,*4 98'(18*4 +3-,-:7*4 1-64- '(,*67*4 +131+,53-4* 8 *..*, / *6,1-88* 6 =5+16-:7* 8-651-3* /* 81 372,73* H372,73* B +131+,@3* .319-8*I*, /164 8* +14 / 76* .-4473*< 8* 23'/7-, /* 81 +'6,31-6,* 98'(18* +3-,-:7* 213 81 31+-6* +1335* /* 81 23'.'6/*73 L1 M*4, +'64,16, F G? + 9 1 =+4, σ /164 8* +14 / 76* *6,1-88*< 'D 81 6'+-;-,5 *4, ='-6/3* :7* +*88* / 76* .-4473*< +*,,* 5:71,-'6 /*;-*6, ? 1%T + 9 σ + 9 1 =+4, σ _H.-4473*I + 91 =+4, σ α H*6,1-88*I = + ₌ σ , = + J % = σ / 2 ! / ' 0

% + 91 =+4, σ α 1;*+α 76* +'64,16,* -6.53-*73* '7 5918* B "< * :7- 2*3=*, /* /5/7-3* :7 B 23'.'6/*73 +'64,16,* L1 M< 81 +'6,31-6,* 98'(18* +3-,-:7* *4, 2874 -=2'3,16,* /164 8* +14 / 76* *6,1-88* :7* +*87- / 76* .-4473* *, *..*, / *6,1-88* *4, *6 .1-, 81 ,31/7+,-'6 /* 81 61,73* /7 23'+*4474 / 581('31,-'6 /* 81 372,73* 164 8* +14 / 76* *6,1-88*< 81 372,73* 65+*44-,* 20E4-:7*=*6, 76 +*3,1-6 ;'87=* / 581('31,-'6 87;-619* 1 ='6,35 +'==*6, 81 /-4,3-(7,-'6 /*4 +'6,31-6,*4 /164 8* ;'87=* / 581('31,-'6 /*4 23'+*4474 /* 372,73* B 213,-3 / *6,1-88* 2*7, A,3* /5+3-, B 213,-3 /7 +'6+*2, /* .1+,*73 / -6,*64-,5 /* +'6,31-6,*4 / *6,1-88* '6+*3616, 81 /-4,3-(7,-'6 /*4 +'6,31-6,*4 *6 .'6/ / *6,1-88*< *, 2'73 76* 523'7;*,,* /* ,E2* .8*>-'6 ,3'-4 2'-6,4< 87;-619* F G1 5,1(8- 8 18873* 9565318* /* 81 /-4,3-(7,-'6 /*4 +'6,31-6,*4 6'3=18*4 17 2816 / *6,1-88* 473 81 .-973* +- /*44'74 *4 /-4,3-(7,-'64 '6, 5,5 +18+785*4 213 81 =5,0'/* /*4 585=*6,4 .-6-4 2'73 /-..53*6,4 31E'64 / *6,1-88* / *2 " . " " " ' B %C 1 3*2354*6,1,-'6 93120-:7* *4, .1-,* *6 2131=@,3*4 6'6 /-=*64-'66*84 ? +'6,31-6,* 6'3=18-45* /-;-45* 213 81 +'6,31-6,* 6'=-618* *6 .'6+,-'6 /*< 81 /-4,16+* 6'3=18-45* 213 81 23'.'6/*73 / *6,1-88* L1 M *,,* /-4,3-(7,-'6 2*7, A,3* +131+,53-45* 213 /*7> 585=*6,4 ? 81 +'6,31-6,* =1>-=18* *6 .'6/ / *6,1-88* σ_=1> *, 81 .'6+,-'6 /* /-4,3-(7,-'6

) ) 7 $ # & ! # $ "! - $ ##" $ 164 81 8-,,531,73*< 2874-*734 +3-,@3*4 4'6, 23'2'454 S -84 4'6, 9565318*=*6, (1454 473 8*4 +'6,31-6,*4 '7 473 8 56*39-* =1-4 313*=*6, 473 8*4 /5.'3=1,-'64 1 /-4,3-(7,-'6 /*4 /5.'3=1,-'64 23@4 /7 .'6/ / *6,1-88* ='6,3* 76* 24*7/' 4-697813-,5 /*4 +'6,31-6,*4 F!G :7- 2*7, A,3* /5+3-,* 213 8* .1+,*73 / -6,*64-,5 /*4 /5.'3=1,-'64 :7- *4, /* 81 .'3=* ?

( )

KK -) . > α − = ε 69', *, 87;-619* F!G'6, /5.-6- 81 ,561+-,5 +'==* 5,16, 8* 23'/7-, ?

( )

KK KK = + =1> α ε *, -84 8 '6, +'=2135* B +*88* /5.-6-* 213 *, # F G? ρ ε+ 8 1 ,561+-,5 /5.-6-* 213

( )

K K KK = + =1> α ε _{/5+3'N, 1;*+ 8* 31E'6 / *6,1-88*} 1618E4* /* 16/188 *, *3J8* *4, (145* 473 81 3*81,-'6 /* *7(*3 ?

( )

J, =JσJε 'D? J_, *4, 8* .1+,*73 /* +'6+*6,31,-'6 /* +'6,31-6,*4 5814,-:7*4< σ J *4, 8* .1+,*73 /* +'6+*6,31,-'6 /*4 +'6,31-6,*4 5814,'2814,-:7*4< *, ε J *4, 8* .1+,*73 /* +'6+*6,31,-'6 /* /5.'3=1,-'64 5814,'2814,-:7*4 '73 76* *6,1-88* *88-2,-:7* /164 76* 281:7* .-6-* 4'88-+-,5* *6 ,31+,-'6< 8* .1+,*73 /* +'6+*6,31,-'6 /*4 +'6,31-6,*4 5814,-:7*4 *4, /'665 213 81 3*81,-'6 47-;16,* ?

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1 T 1 J_, = + ρ σ 'DL1 M*4, 81 23'.'6/*73 /* 8 *6,1-88* *,ρ *4, 8* 31E'6 *6 .'6/ /* +*88* +-< σ

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1 T *4, 8* .1+,*73 /* +'33*+,-'6 95'=5,3-:7* 13 8 1228-+1,-'6 /* 81 3*81,-'6 /* *7(*3< '6 ,3'7;* ? 9 8 9 8 , J                 ε ε         σ σ = 'Dε₉ *, ε₈ 4'6, 3*42*+,-;*=*6, 81 /5.'3=1,-'6 98'(18* *, 81 /5.'3=1,-'6 8'+18* S σ₉ *, σ₈ 4'6, 81 +'6,31-6,* 98'(18* *, 81 +'6,31-6,* 8'+18*

722'4'64 :7* 8'-6 /* 8 *6,1-88* 8* +'=2'3,*=*6, 3*4,* 5814,-:7*< '6 1 ? 9 9 σ = ε 1;*+ 8* ='/78* /* '769 7 6-;*17 8'+18< '6 ,3'7;* ? 8 8 8 σ = ε D ₈ *4, 8* ='/78* 8'+18 /* /5.'3=1,-'6 6 2*7, 4722'4*3 :7 B 81 372,73* 8* +3-,@3* 8'+18 *4, /'665* 213 ? + 8 8 =ε ε _S + 9 9 =σ σ

( )

+ 9 8 8 ρ = 1 T 1 ε ε σ 1 :716,-,5 ε₈ ρ *4, +'64-/535* +'==* 76 2131=@,3* /* ,561+-,5 * +3-,@3* 98'(18 /* /5.'3=1,-'6 ε *4, /'665 213 81 3*81,-'6 /* 81 =5+16-:7* 8-651-3* /* 81 372,73* ?

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1 T 1 * % #c_{+ E} + 9 _π ε = ε σ 'Dε_E *4, 81 /5.'3=1,-'6 *6 ,31+,-'6 *, c + # *4, 81 ,561+-,5 12213*6,*

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+ 9 8 c + + 8 * * % # ε π = ρ ε       = * #c₊ c 'D *4, 76 2131=@,3* .'6+,-'6 /* 81 ,*=2531,73* *, 8 521-44*73 69', *, 87;-619* F!G< '6, 23'2'45 8* +3-,@3* 8'+18 /* /5.'3=1,-'6 / *6,1-88* * +3-,@3* *4, (145 473 81 /-4,3-(7,-'6 35*88* /*4 /5.'3=1,-'64 *6 .'6/ / *6,1-88*< 213,-+78-@3*=*6, /164 81 359-'6 /* 81 24*7/' 4-697813-,5 /* 81 /5.'3=1,-'6< /5+3-,* 8* .1+,*73 / -6,*64-,5 /* /5.'3=1,-'6 / *6,1-88* * .1+,*73 +3-,-:7* / -6,*64-,5 /* /5.'3=1,-'6 / *6,1-88* *4, 235+-45=*6, /5.-6- +'==* ,561+-,5 '6 5;'87,-'6 *6 .'6+,-'6 /7 31E'6 / *6,1-88* 1 5,5 *>1=-65* 213 +*4 17,*734 5;'87,-'6 /* +*,,* ,561+-,5 =13:7* 76* ,3164-,-'6 *6 .'6+,-'6 /7 31E'6 *6 .'6/ / *6,1-88*

*& ) ) ' * $ " * ## * +3-,@3* 8'+18 /* 372,73* /5;*8'225 2'73 8*4 +'6+*6,31,-'64 /* +'6,31-6,* 213 8* 1('31,'-3* /* -1(-8-,5 5+16-:7* 4722'4* :7* 81 372,73* 65+*44-,* 76 +*3,1-6 ;'87=* / 581('31,-'6 /7 23'+*4474 /* 372,73* 8 -6,53-*73 /* +* ;'87=*< 4722'45 +E8-6/3-:7* /* /-1=@,3* 5918 B 81 /-4,16+* *..*+,-;* *..< 3@96* 76* +'6,31-6,* ='E*66* 2'6/535* 5918* B 81 +'6,31-6,* *..*+,-;* /* 372,73* *,,* 0E2',0@4* 2*3=*, /* 3*6/3* +'=2,* /* 8 -6.87*6+* /* 8 *..*, / 5+0*88*< /* 81 95'=5,3-* /* 81 4,37+,73* *, /7 ='/* /* +0139*=*6, 473 81 354-4,16+* /* 81 372,73* * +'6+*2, L2'-6, +017/ M+K*4, B /-3* 81 4*78* 23-4* *6 +'=2,* /* 81 +'6,31-6,* =1>-=18* 6* 2*3=*, 214 /* 3*6/3* +'=2,* /* +*4 -6.87*6+*4 F G 1 /-4,16+* *..*+,-;* *, 81 +'6,31-6,* *..*+,-;* 4'6, /*7> 2131=@,3*4 /* +* +3-,@3* 8'+18 /* 372,73* 23@4 1;'-3 /5,*3=-65 81 +'6,31-6,* 6'3=18* 17 2816 /* 8 *6,1-88* *6 .'6+,-'6 /* 81 /-4,16+* B 213,-3 /7 .'6/ /* +*88* +-< 8 -=2'3,16+* /7 931/-*6, /* +'6,31-6,* *6 .'6/ / *6,1-88* 1 5,5 3*=13:75*< *, /164 8* (7, /* /5+3-3* +* 931/-*6, '6 .1-, 122*8 B 76* 3*2354*6,1,-'6 473 76 /-1931==* (-8'913-,0=-:7* H1I H(I / # + . . A .

* 1 /-4,3-(7,-'6 /*4 +'6,31-6,*4 2*7, A,3* /-;-45* *6 ,3'-4 /'=1-6*4 H.-973* H1II? /'=1-6* ? 81 +'6,31-6,* /* ,31+,-'6 *4, 231,-:7*=*6, +'64,16,* *, *88* *4, 5918* B 81 +'6,31-6,* =1>-=18*< /'=1-6* ? 81 ,3164-,-'6 *6,3* 8* /'=1-6* *, 8* /'=1-6* < /'=1-6* ? 81 /-4,3-(7,-'6 /*4 +'6,31-6,*4 *4, 76* .'6+,-'6 27-4416+* /* 81 /-4,16+* > ?

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α σ ≈ $_" − KK 1 /-4,16+* *..*+,-;* *.. +'33*42'6/ B 81 /-4,16+* '(,*67* 213 -6,*34*+,-'6 *6,3* 81 8-96* /7 /'=1-6* *, 81 8-96* /7 /'=1-6* < *, B 8 5,1, +3-,-:7*< '6 1 ?

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α ρ π σ "" KK M G =1> < = 'DGρ *4, 8* .1+,*73 / -6,*64-,5 /* +'6,31-6,* / *6,1-88* *, Gρ 41 ;18*73 +3-,-:7* 1 /-4,16+* *..*+,-;* *4, *6 3*81,-'6 1;*+ 81 ;18*73 =1>-=18* /7 931/-*6, /* 81 +'6,31-6,* 3*81,-. dH.-973* !I? / %2 ! " . ' " " " . B#*C

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6 1 ;7 :7* 81 ,561+-,5 '7 354-4,16+* B 81 372,73* 6 *4, 214 -6,3-64@:7* 17 =1,53-17 =1-4 /52*6/ /* 2874-*734 2131=@,3*4 /'6, 81 95'=5,3-* /* 81 4,37+,73* *,,* ,561+-,5

* /52*6/ 4'-, /* 81 ,3-1>-18-,5 /*4 +'6,31-6,*4 H3122'3, /* 81 +'6,31-6,* ='E*66* 473 81 +'6,31-6,* 5:7-;18*6,*I< 4'-, /7 .1+,*73 / *6,31;* B 81 2814,-+-,5 H3122'3, /* 81 +'6,31-6,* =1>-=18* 473 81 +'6,31-6,* 6'=-618*I 1 ,05'3-* H122*85* =5,0'/* ;'87=5,3-:7*I /5;*8'225* 213 8* 1('31,'-3* /* -1(-8-,5 5+16-:7* 1,,3-(7* +*,,* -6.87*6+* 17 931/-*6, /* +'6,31-6,* 3*81,-. 6 7,-8-416, +*,,* /*36-@3* ,05'3-*< '6 4* 23'2'4* / 5,7/-*3 8* 2056'=@6* *6 *>1=-616, 8 5;'87,-'6 /* 81 +'73(* /* ,3164-,-'6 /* 81 ,561+-,5 / 76 1+-*3 ='785 *6 .'6+,-'6 /* 81 ,*=2531,73* 473 /*4 523'7;*,,*4 /* .8*>-'6 ,3'-4 2'-6,4 +'=2'3,16, /-..53*6,4 ,E2*4 /* /5.17,4 95'=5,3-:7*4 H*6,1-88*4 *6 $< *6,1-88*4 *6 < .-4473*4I*, 473 /*4 523'7;*,,*4 *6,1-885*4 B /-..53*6,4 31E'64 6 +'64-/53*31 1744- /*4 523'7;*,,*4 235.-44735*4 1E16, 81 =A=* 8'697*73 /7 8-91=*6, =1-4 1;*+ /*4 /-=*64-'64 /-..53*6,*4 H8'697*73< 017,*73< 23'.'6/*73 3*81,-;* /* 81 235.-4473*I

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