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li.oc.sndevil.rawrednu//:ptth tcejorProirraWrednU -1-

. ptth//:rawrednu.sndevil.oc.li . , , , ,

, . .

ronevEihcaZmoc.socyl@roneve-z:liamElagtahab~/li.ca.uat.www//:ptth:egaPemoH

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li.oc.sndevil.rawrednu//:ptth tcejorProirraWrednU -2-

(- ' : ; " ) . 1

. F a ii . + + + + =x a x a x a a x pnn ... ) (2 1 02 F : .= + + + =x x x0 ... 0 0 0 ) (02 : . = x) (0ged . =a n x pn0 | xam ) ( ged} { / : .= c0 ged c0 = + + + =c x x c x p... 0 0 ) (2 :

. 2

gniR R ". "" " R : , ) ( 1: )R r q p, , ,

1 )= p p1( 2 (. )= + = + + + = + + + = +p p p r q p r q p p q q p0 ) ( , 0 0 , ) ( ) ( , .+ = +rp qp r q p) (: ( 5. )=pq qp( 4. )=rq p r qp) ( ) (( 3(. )1

.x F] [ " " " " F : . x x xn ,..., , ,12} { : .+ =q p qpged ged ) (ged( 2. ) +q p q pged, ged xam ) (ged} {( 1: )x F x q x p] [ ) ( ,) ( : ". " . qp0 q p0 , 0 :

.=r q p0 =rp qp : . =r q = r q0 p0 = =r q p rp qp0 ) ( : (.=x x q x p) (1 ) ( ) (, )= qp1 x F q] [ p : . = =c x p p0 ) ( 0 ged , ( ) : .= =p qp qged ) (ged 0 ged < =p qp qged ) (ged 0 . p0 :

, . 3

. : x F r] [ : , x F g f] [ , :

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li.oc.sndevil.rawrednu//:ptth tcejorProirraWrednU -3-

.0 g f f g : x F h h hk] [ ,..., ,2 1 , f g f g f gk | , ... , | , |2 1 :

1|k

i ii

f h g= .

.p g| p f| f g| : .g f| f g| g f , x F g f] [ , : . c =g c f g f : 1 x f0 ) ( = x f0 ) ( . x F f] [ :

. f ( = af1 ged: ) g f ( 2". )f " f ( 1 ):

.g=f , , ) p . x F q q] [ ,2 1 : (.= p0 ged ) ( q p q p| |2 1

. 4

" F F . + + + =x a x a a x pnn ... ) (1 0 F :... ) (1 0

n .p = x p) ( + + + = a a a pn

.= c c F) ( ., . = F0 ) (0., : .= q p qp) ( ) ( ) () (( 2. )+ = + q p q p) ( ) ( ) () (( 1. ) : .= p0 ) ( x F x p] [ ) ( F : x) ( p . x p) ( :

.= p x p x0 ) ( ) ( | ) (: . p . + =x r x s x x p) ( ) ( ) ( ) ( r,s , . p ) ( : ) (. p x| ) ( = r0 + = = r s p) ( ) ( 0: ,

. = p0 ) ( =x s x x p) ( ) ( ) ( , p x| ) ( .+ = p x s x x p) ( ) ( ) ( ) (: x F x p F] [ ) ( , :

. 5

. f f,1 0 :

f0 (. ) dcg f1 . f1 ) , . f2

. f3 f2( - dcg 0

. .=f f fk ) , (dcg1 0,

. fk f1 f0 ( 1): . =f f fk) , (dcg1 0 :dcg

.= +f f h f hk 1 1 0 0 x F h h] [ ,1 0 ( 3. )f f f fk k| |1 0 ( 2)

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li.oc.sndevil.rawrednu//:ptth tcejorProirraWrednU -4-

f . f f,1 0 :dcg f0 ( 2. )f f f f| |1 0: , f f,1 0 f ( 1: )

.=f f f) , (dcg1 0 . = +f f h f hk 1 1 0 0 x F h h] [ ,1 0 ( 3. )f f1 . 3 , :

x F f] [ ' : . 3-1 . f f' | 2 , , f f| ' 1 . 3-1

. =f f'

: . f f,1 0 : .= +f h f h1 1 1 0 0 x F h h] [ ,1 0 ( 3. )= f f1 ) , (dcg1 0( 2. ) f1 f0' ( 1)

dcg , )1 2( : x F h h] [ ,1 0 )3 1(. )2 3(. 1

. . 1 f1 f0 . = +f h f h1 1 1 0 0 . 6

: . p1 ged x F p] [ : . p < p p pged ged, ged 12 1 =p p p2 1 - ( 1) . p , . - ( 2)

. elbicuderri - p - p = p3 ged = p2 ged ( 2. )- = p1 ged ( 1 ):

. F p p2 ged ( 3. )F . p1 ged x F p] [ :- I

(.) c - q qk ,...,1 =q q c pk ...1 . - 1 . :

- , , - n p . n 1-n p p,2 1 < p p pged ged, ged 12 1 =p p p2 1

. =+q q q q c c pk t t... ... ) (1 1 2 1 = =+q q c p q q c pk t t... , ...1 2 2 1 1 1 - : p x F p] [ :

(. , )g p| f p| gf p| , x F g f] [ , . f pi | k i 1 f f pk ... |1 p : .- p , p p0 : =q q p2 1 p1 ged, p :

q p|1 ( )q q p|2 1. . p q qged , ged2 1 =p qged ged1 . p q| 1 q p|1 ... q p|2

. - p, , . , , = q1 ged2 x f0 ) ( : II = =c c k k' , ' q q p pk k,..., , ,...,' 1 1 F c c' , =q q c fk ... '' 1 =p p c fk ...1

.= = q p k ii i . ,...,1 : . q q p pk k,..., ,...,1 1

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li.oc.sndevil.rawrednu//:ptth tcejorProirraWrednU -5-

f qi|, . f , =c c'. " : pj0 . p qj i| k j 1 , qi p p qk j... |1

( ) . =p qj i , qi - )=k k' -p -q

. (. " , ) x F x p] [ ) ( 0 :- III

.- p p (. p1 ged , . - p ) ((. II ) ) ( :

, f p| . g p| f p| gf p| ,x F g f] [ , p q - p p q , =p f q) , (dcg . g p| f p|

f p| =p q (. =qq p' ) q , . = p f1 ) , (dcg . = =p f q) , (dcg 1 q

p p| = +g p g h gf h) ( ) (2 1 g . = +p h f h1 2 1 x F h h] [ ,2 1 . p . g p| , = +g p g h gf h p) ( ) ( |2 1 gf p|

. x F x f] [ ) ( 0 (:III II, I )

( , ) - p pk ,...,1 F c =x p x p c x fk) ( ... ) ( ) (1 , . " .

". " " - f " , . 7

. =p pj i , 6 : . + 1 , ,

, ) - p pk ,...,1 F c =x p x p c x fmR Rm ) ( ... ) ( ) (11) ( ) (: .f " . R m ii1 . 1 (

, f g f g : . R ii i 0 . = p p c gkk ... '11: . f g

i ig f ) , (dcg} , {nim) ( ) ( , x F x g x f] [ ) ( ,) ( :i

R Ri

g f pp g f

. =

. g f : .f h hl| ...1 hi f h f hl| .... | 1 :

. 7

f x| ) ( . F x F x f] [ ) ( 0 : x . f - x .1 . = x . f x fR| ) ( + xR| ) (1 R : . 1 :

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li.oc.sndevil.rawrednu//:ptth tcejorProirraWrednU -6-

: ,=n f ged , n x f) (( ) :11

k t t... ) ( ... ) ( ) (1 1RR R R

F t ,...,1 =++ q q x x c x fk t t . 1 - +q qk t,...,1 F

( 1 ):1

gedt

ii

R f n=

. n n ( 2. ) = = x x c x fk RRk ) ( ... ) ( ) (11 : . F k ,...,1 : , f :

1

gedk

iif R

= .=

: f ) (. ) ( :1

i ) ( ) ( ) (k

Ri

i x x q x f

= , =

1 1 1

i iged ) (ged ) ( gedk k k

R Ri i i

i i i f R x x

= = = . = q0 ged = = =

: f ( ) f : (. n f , )=n f ged = x x x x fn) (...) () ( ) (2 1

. : . 8

1 z p) ( : , ^ : .

. ^ z p z) ( . p1 ged + + + =z a z a z pnn ... 1 ) (1 : + + + =z a z a z pn kn k... 1 ) ( , ak , . = p1 )0( :

k1 ^ ak

< =t p p) ( 1 )0( < tk0 1 . = . = z0 , . < = + =+ Mt t tM t t pk k k1 ) 1( 1 1 ) (1

^ z p z) ( . + + + =z a z a a z pnn ... ) (1 0 :1 . p = z0 = a0 0 = z0

. ( a01 )p a0 0 : ^ z p z) ( . p ged 1 ^ z p) ( : + z z z0 " :2

.p z0 z0

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li.oc.sndevil.rawrednu//:ptth tcejorProirraWrednU -7-

. p ged 1 + + + =z a z a a z pnn ... ) (1 0 : z zz a z pa an nnn ... ) (0 1 z0

zn n1 } { , . + + + = =

= zn n1 } { . ^ = z p z) ( fni . = z p nn) ( mil = z nn mil - - , . = z p nn) ( mil

} {k nk1

z . = z z knk mil0 , ^ =

^ z0, 2 z0 = = z p z p nn) ( ) ( mil0 . .

.^ x ( ) ^ - : . = x x c x fk RRk ) ( ... ) ( ) (11 ^ , . ^ : :

0) (

ni

ii

x a x f=

: =0

) (n

ii

ix a x f

= . =

.= f f) ( ) (( 3. ) = g f g f( 2. )+ = +g f g f( 1 ): . , f ^ f ^ :

( ) . 9

. + + + =x a x a a x fnn ... ) (1 0 (: ) p

q .] p qa an,0 , a p|0 a qn | . f q p _

... 01 0 . =q p x/ :n

na a ap pq q

, + + + = qn

2 2 1... 02 1 0n n n n

p a q p a qp a q an. = p a qp a q a p q ann n n n) ... (2 1 01 2 1 + + + + =

.a p|0 , q p p . a qn | = pq a q a q a pn nn n n) ... (1 01,

, + + + =x x a a x fn ... ) (1 0 : . . a0

. . , ^ . Rx x f] [ ) ( :

(. + =b ib a z0 |) x f) ( :1 . - :2 .=x f x f) ( ) ( , Rx f] [ : . f = ib a f b0 + = ib a :

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li.oc.sndevil.rawrednu//:ptth tcejorProirraWrednU -8-

: f :

1 1ij j) ( ) ( ) ( ) (

t sRR R

j j is j i

x x x x f+ = =

R s ,...,1 = .+ t s,...,1 R ^ + t s,...,1

. + = + + = = x x x x x x xR RRRR eR2 ) ( ) () ( ) ( ) (2 22) ( : R - :

.< ca b0 4 2 + + =c xb xa x p) (2 :

2) ( 04 2 2

4 2 + = + + = x c xb xc b b

4 42 24 2 2

. = + = x xc b b c b b . 2 , R :

( dcg ) . 01

: ) x F] [ I :

. I f p x F f I p] [ , ( + I g f I g I f, . :

x F f fn] [ ,...,1 I p pn ,...,1 : 1

n

i iiI p f

= .

p . x F x p] [ ) ( : . p . =x F p p] [ ) ( p "

.= = =p x F p x F p p) ( ] [ ] [ ) (0 0 p p0 . . : p , , x F I] [ : .p I p, , =x F p I] [

= p0 = I}0{ . , . , :. I ' p I p I}0{ , .

, . I x F f pf] [ | I p . I p =I sp f r I ps f,

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li.oc.sndevil.rawrednu//:ptth tcejorProirraWrednU -9-

q ( 2. ) p( 1: ). = p) (dcg :dcg x F h hn] [ ,...,1 ( 4. ) p ( 3. )p q

1

) (dcgn

i ii

h p=

.= = = I0 ) (dcg }0{ }0{( 5. ) = = . p 3-1 : q p q| : = p) (dcg :

. q qn | , .... , |1: , .=f f f f f f) , (dcg, dcg , , dcg3 2 1 3 2 1) ( ) ( :: x F q] [ . =f f f p) , (dcg, dcg3 2 1) ( :

. f q f q f q f f f q| | | ) , , (dcg |3 2 1 3 2 1 p q f f q f q f q f q f q| ) , (dcg| | | | |3 2 1 3 2 1) ( q , .

. .=f f f f f fn n n)) , (dcg,..., (dcg, dcg ,..., dcg1 2 1 1) ( ) ( : x p) ( J x F] [ : J J . x p) ( . =mcl p) (

h ( 2. ) p( 1: ) =mcl p) ( :mcl . p( 3. )p h 1 01 0 :

1 0

) , () , (dcgf f mclf ff f .=

.=f f mcl f mcl f f f mcl) , ( , , ,3 2 1 3 2 1) ( ) ( =f f mcl f mcl f mcl f f mcln n n) , ( ,..., , ,...,1 2 1 1) () ( ) ( :

h hn ,...,1 ( 2. )= f fn1 ) ,..., (dcg1( 1: ) :

1

1n

i iif h

= .f fn ,...,1 p - ( 3. )=

f fn ,...,1 - p , )2 3(. dcg )1 2( :

1

1n

i iif h

= f fn) ,..., (dcg1 )3 1(. p1| =

. = f fn1 ) ,..., (dcg1 1 f fn ,...,1 . fj fi, j i , f fk ,...,1 : - ( 2. ) f fk ,...,1( 1: ) :

- ( 3. )j i f fk ,...,1 , fj fi, 1 1 1:

1

... ... . ,...,1k

k i i j ij i

+ f f f f f g k i=

.= g gk1 ) ,..., (dcg1( 4. )= = = x F h hk] [ ,...,1 , f fk ,...,1 :

1 1 1) (1 1 1

1 ... ...k k k

k i i i j ii j i i+ f f f f h f h

= = =

. = =