-
1 demahoM iluoatsuoM rf.tfi.shtambara//:ptth
: -
b a `* b ] a b r 0 + =r qb a ` ] r q;) (
- ]* c b a *
= = = a a a c b a c b a a b b a) ( ) ( = = c bc ac b a
= = = a a a cb ca c b a a b b a) ( = a b a a b
= = ba b a b a1 = b r b a b a r a b `* b a *
m b a = m b a ]* b a - * -
= b a ]* b a + = vb ua ] v u
- = b a = m b a ]* b a
= ba m -
n2 `n n p2 n p n
- - * p pn......p2 p1 - *
= p p n i p p p pi n;....;2 ;1 ...... 2 1} {
- - 1 1 n
p p p nkk ...... 2 12 1 1 pn......p2 p1 =
= 1 n ......2
= p p p bkk ...... 2 12 1 = p p p akk ...... 2 12 1 ]* b a
pn......p2 p1
= p p pkk ...... 2 12 1 b a * k;....;2;1} { i = i i i; fni)
(
= p p p mkk ...... 2 12 1 b a * k;....;2;1} { i = i i i; pus)
(
-
2 demahoM iluoatsuoM rf.tfi.shtambara//:ptth
n -I -1
` n ] b a b a n n b a] [ n b a
] ]= nk b a k b a n n b a b a;2] [ ) ( "n " - 2
" n " ] n a a a] [ - " n " ] n a b n b a b a;] [ ] [ ) ( -" n "
] n c a n c b te n b a b a) ( ) ( ;] [ ] [ ] [ ) ( -
" n "
-
` n ] b a n b a n b a] [
n r 02 n r 01 + =r qn b2 2 + =r qn a1 1 ` n ] b a
= q q n b a2 1) ( =r r2 1 n b a n b a] [
= kn b a ] k n b a] [ r r2 1 n = n q q k r r2 1 2 1) (
n r r2 1 n r 02 n r 01 =r r2 1 = r r0 2 1
n -3 ] ]
` ] ` ] + = n r te r qn a r q n a0 ; ;) ( ) ( - * ` ` ] n r te n
r a r n a1 ;.....;1;0 ;} { ] [ ) ( - r ] n r x x/} {] [ -
r n ] "n " r r
n r x r x] [ - ] r a n r a/ 1 ;....;1;0} { ] n r a n r a/ 1
;....;1;0] [ } { - * =r r' n r' 0 n r 0 =r r' - * (n r ) ` ] r x n
r n x/ 1 ;..;1;0 ;} { ) ( - *
] =n1 .... 2 1 0) ( ] ]n n1 ;.....;1;0} {
] ]n
] ] + = =k k x x1 2 / 1} {) ( ] =2 0 ] ]= 21;0} { * ] ] + = =k k
x x1 7 / 1} {) ( ] =7 0 ] ]= 76;5;4 ;3 ;2 ;1;0} { * ] ] + = =k k x
x3 7 / 3} {) ( ] ] + = =k k x x2 7 / 2} {) (
-
3 demahoM iluoatsuoM rf.tfi.shtambara//:ptth
] ] + = =k k x x6 7 / 6} {) (................. 7 4 235] [ =4 235
] ]7
7 6 63] [ = 6 63 " n " -4
- ` n ] t z y x
+ +n t y z x] [ n t z] [ n y x] [ n t y z x] [ n t z] [ n y x]
[
" n " - + = +r r r r' ' r r x x' ' + +r r x x' ' r x' ' r x -
*
= r r r r' ' ` ` ] n b a n b a n p b ap p ; ;* 2] [ ] [ ) ( ) (
- *
= = 2 21 4 3 , = = + + + +0 01 4 3 2 1 0 , = = +2 7 4 3 ] ]5
*
= + x2 5 ] ]7 x
] ]4 -1 31 +3 207 07 -2 ` n n n n0 1 4] [ ) ( -1 `* n + n n2 5
32 3 1 2 71 -2 4 + + +n n n n4 3 2 1 ` n -3
-II -1
]* b a = b a1 b a
tuozeB - 2 ]* b a
]= + vb ua v u1 / ;2 ) ( = b a1 ]= + vb ua v u1 / ;2 ) ( ]* b a
:
= b a1 = D Db a1;1} { 1 b a tuozeB ]* b a
]= + = vb ua v u b a1 / ; 12 ) ( -3
b a d ]* b a d b ab a1
d d = =
-
4 demahoM iluoatsuoM rf.tfi.shtambara//:ptth
]* q p = b a ]* b a = = = q b p a q p; ; 1
emrohT ed SSUAG -4 -
]* c b a b c = c a1 ba c
= c a1 ba c ]* c b a ]= = + ck ba vc ua k v u; 1 / ; ;) (
+ = + = + = + = =vb uk c vcb uck vcb uab vc ua b b b1) ( ) ( b
c
- - a
]* c b a = c ba c b te c a te b a1
3 2 6 x
= b a1
= 42 4 6 6 2 4 63 -b
`* n ]* c b a
] [ ] [1
n ca ban c b
n a=
] [) (
nk ca ba k n ca ba
c b a n
=
]
n c b] [ c b n) ( = n a1
-5
1 1 ]* c b a - *1
b acb a
c a = = =
= = b a b an1 1 `* n ]* b a - * = = b a b an m1 1 `* m n ]* b a
- *
]* b a
] ]+ = vb ua x v u x;2 ) ( = b a1
= +y x49 3 71
1 = + y x0 02 3 2 71) ( ) ( = +y x49 3 71 = + 49 02 3 2 71
-
5 demahoM iluoatsuoM rf.tfi.shtambara//:ptth
= y x02 3 2 71) ( ) ( ]= k x k3 2 x2 3) ( = 1 3 71 x2 71 3)
(
]+ = k x k2 3 ]+ = k y k02 71 ]= + + y k k49 3 2 3 71) ( ] + +
=k k k S/ 02 71 ;2 3} {) ( 2
] [] [] [] [ ) (
3 49 71 49 3 713 49 71
3 1 2
3 1
3 1
y x y xx
x
x
x
= = +
] = k x k1 3 = x3 1] [ = 1 3 1 ]+ = k y k73 71
] + =k k k S/ 73 71;1 3} {) (
u3 u2 u1 u0 = q u1 0 `* u0 q = +u u u44 20 3 12 q
= +ba b a1 ) ( = +b b a1 ) ( = b a1 2
3 22 3n
n n+
+ +
2 3
TAMREF - 6
p
p k1 1 k Cpk p -1 ` + + n n p np p1 1) ( ) ( -2 ` p n n np] [ /
-3
= n p1 ` p n np1 1] [ / = a p1 ] p a ap1 1] [ ] p a a ap] [
-4
Cpk p -1
) ( ) ( ) () ( 1 ...... 2 1 !!
! !k kp p
C k p p p p C kpk p k
= + =
= k p1 ! p k! p k C kpk ! p Cpk p
-
6 demahoM iluoatsuoM rf.tfi.shtambara//:ptth
` + + n n p np p1 1) ( ) ( -2 ) (
01
pi i p
ni
n C n=
1 ) ( = +1
1 1p
i i p pn
in C n n
= + + = +
1 ) ( ) ( 1
1 1p
i i p pn
in C n n
= = + +
p p i 1 Cpi p 1
1
pi in
in C
=
` + + n n p np p1 1) ( ) ( ` p n n np] [ -3
p o op] [ = n0 + +p n np1 1] [ ) ( p n np] [
+ + p n n p n np p1 1] [ ] [ + +p n np p1 1] [ ) ( ` + + n n p
np p1 1) ( ) (
+ +p n np1 1] [ ) ( ` p n n np] [
= n p1 ` p n np1 1] [ / p np1 1] [ = n p1 p n np] [
] [ ] [ 1
n ca ban c b
n a=
= a p1 ] p a ap1 1] [ ] p a a ap] [ -4 ]a
`a ; a0 a0
a a2 2 = a a a a1 2) ( = p2 p ; p2
p a ap] [ p a ap] [ ) ( p a ap] [ ) ( ] p a a ap] [
p ap1 1] [ = a p1 p a ap] [
p ] p a a ap] [
p
= a p1 ] p a ap1 1] [
-
7 demahoM iluoatsuoM rf.tfi.shtambara//:ptth
- 7
]* an......a3 a2 a1 1
]* an......a3 a2 a1
]* an......a3 a2 a1 1 ]* un......u3 u2 u1
11
n
iia u
= =
]= + c yb xa y x;2 ) ( -
= +y x9 46 5701 ]2 46 5701
15 61 46 570131 1 15 4621 3 31 151 1 21 310 1 21 21
+ =+ =+ =+ =+ =
= 1 46 5701 = +y x9 46 5701 ]2 y x;) (
= =a b5701 46
) () () (
) () () ( ) (
61 1561 31
61 3 61 21
61 3 61 61 1
48 5 1
b ab a b
b a b b a
b a b b a b a b
b a
= = =
=+ =
+ =46 657 5701 54 9 + =b a657 54 9 = + +y x0 )657 (46 )54 (5701
= +y x9 46 5701 657;54) (
+ x54 46) ( = 1 46 5701 + x54 5701 46) ( ]+ = k y k657 5701 ] =
k x k54 46 ]= + k x k46 54
= +y x9 46 5701 = + =k x k y54 46 ; 657 5701 ] + =k k k S/ 657
5701;54 46} {) (
b0 a0 ]= + c yb xa y x E;2 ) ( ) (
]= = = b a b b te a a b a1 ' ' ' ' / ' ;'2* ) ( = b a =c c' = +c
y b x a' ' ' c *
= +c y b x a' ' ' = +c v b u a' ' '0 0 ]2* v u;0 0) ( =b a' '
1
-
8 demahoM iluoatsuoM rf.tfi.shtambara//:ptth
= +c yb xa0 0 y x;0 0) ( ]2 = +c yb xa * c = + c y b x a) ' ' (0
0
= b a ]2 b a;) (
c ]2 = +c yb xa = +c yb xa
= +c y b x a' ' ' c = +c v c b u c a' ' ' ' '0 0 = +y b x a1 ' '
v u;0 0) ( =b a' ' 1 = v c y b u c x a) ' (' ) ' ('0 0 = + v c y b
u c x a0 ) ' (' ) ' ('0 0
y v c a' '0) ( =b a' ' 1 y v c b a' ' '0) ( + =u c bk x' '0 ]k +
=v c k a y' '0
= +c y b x a' ' ' + +v c k a u c bk' ' ; ' '0 0) ( ] + +k v c k
a u c bk/ ' ' ; ' '0 0} {) (
= y x1 3 7 ]2
2 1 3 7 a ` a 53 a
-III -1
` + m n m m n mn1 1 1 ;2) ( ) ( -1 ; ` ` ; ` p m n p m mn 1 -2 `
` ; ` + b n b k n b bk k ! 11 -3
` + m n m m n mn1 1 1 ;2) ( ) ( -1 ) ( ) ( ) ( ) () ( ` n m;2 )
(
2 01 1 1 1 1 1
i i ni i nn i n in n
i im C m n m C m m
= =
= = + + = = + =
+ m n mn1 1) ( m0 1 ; ` ` ; ` p m n p m mn 1 -2
; m1 `m + m n mn1 1) ( n
`p ;p mn ; +p m n1 1) ( ; p m n1 1) ( ` n
` ` ; ` + b n b k n b bk k ! 11 -3 ] =+ b n k Ank /1} {
An ; ; ` ` ; ` +n b b k n b bnk kn n 11( 2) 0 0 kn0 An ` An
+ b n bk kn n1 ; bkn1 2 0 n2 ;n bkn0
0 kn0 1 0 kn1
; + n bkn1 )1 (0 0
An kn0 A kn n1 = n1
0 + b b11 0 0) ( = kn0
-
9 demahoM iluoatsuoM rf.tfi.shtambara//:ptth
-2
9 8 7 6 5 4 3 2 1 0 . 01 1 0 . 2 9 8 7 6 5 4 3 2 1 0 . 21
11 01 11 01 7 6 5 4 3 2 1 0 . 8
; b1) ( . b -3 1 -
; b1) ( b b qk 0 b rkk 0 + =r q b nk k k ` qk rk k n
; b1) ( ` n b;2 ) (
= n0 ` + b n b kk k !1 `n*
` qk b rkk 0 + =r q b nk k k bk n b qk 0 + b nk1 + =+ b r q b nk
kk k1 + b b qkk k1 b qk
b qk 0 b qk 0 b rkk 0 + =r q b nk k k 1 -
) b qk 01 b rkk 011 + = r q b rk k kk1 1 1 rk k
(b rk r1 rk1
2 2 12 k
r q b rk k k
b qk 02 b rkk 022 + = . . .
. . . . . .
b q 01 b r 01 + =r qb r1 1 2 =r q1 0 =q r10 1
0
k ii
ii
b q n=
= =
k;....;2;1} { i b qi 0 2
; b1) ( b k n
0
k ii
ii
b q n=
= b qi 0 =
; n0 ; qk0 k;....;2;1} { i
0
k ii
ii
b q n=
= n k;....;2;1} { i b qi 0 =
b
-
01 demahoM iluoatsuoM rf.tfi.shtambara//:ptth
=q q q nb k k...........0 1) ( b n b
+ + + =3 01 0 01 7 01 2 30722 3 3072 * 51 8 *
0001 8 + + + =0 2 0 2 0 2 1 82 3 1111 51 + + + =1 2 1 2 1 2 1
512 3
* =71 518) ( + =7 8 1 51 =302 1318) ( + + =3 8 0 8 2 1312
- ` ; ` b b n; 1
0 1 0
1 2 1 1
1
2 1
; 0; 0
. .; 0
.....k k k k
q
r qb n b rr qb q b r
r qb q b rq q q n
+
+ = + =
+ =
=r qk k k ` =q q A.... ;2 1} {
0 1 0
1 2 1 1
1 1 1
; 0; 0
. .k k k k; 0
k k
r qb n b rr qb q b r
r qb q b rr q
+ = + =
+ = =
bi i 0 1
21 2 1
11
. .i i ii i i
r qb n
rb q b qb
+ +r b q b q b
+ =+ =
+ =
1 11 1
. .k k k
k k kk kk k
r b q b q b
r b q b
+ = =
0
0k i
ii i
ir b n b r
=
= k i;....;2;1} { =
=r r r r nk k......0 1 1 rk0
b n r k ii ) 0(
-
11 demahoM iluoatsuoM rf.tfi.shtambara//:ptth
=r r r r nb k k......0 1 1) (
4523
=27 1 452321) (=6626 45238) (
-3
=c c c yb m m......0 1) ( =a a a xb n n.....0 1) ( y x ;x y ;n
m
=c c c yb n n......0 1) ( =a a a xb n n.....0 1) ( y x
ci ai y x = = = + +a c a c a c te c an n n n i i i i.......1 1 1
1
-5 b x b
= yyyyyy xxx xxx b
-6 =a a a a xn n.....0 1 1 x
-
http://arabmaths.ift.fr Moustaouli Mohamed 12
[ ][ ][ ] { }
1 0
0 1
1 0
0 4 4
0 5 0 5
0 5 00;25;50;75
x a a
x a ou a
x a a
= =
[ ] [ ][ ] [ ][ ] ( ) [ ]
0
0
0
0 3 0 3
0 9 0 9
0 11 1 0 11
i n
iii n
iii n i
ii
x a
x a
x a
=
==
==
=
