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Published by milogiya, 2020-01-08 11:46:10

G:\МОЎ Ð�ÐžÐ€Ð¢Ð¤ÐŁÐłÐ¬\МОП Ð�Ð£Ð‚ÐłÐŸÐıВЦПП\

A ( x ), (y )
0 0 0
B ( x ) x ( (x )), ( (x y )) , (y ) y ( (x )), ( (y y ))
0 0 0 0 0 0

a 1 0 , a 2 ( x 0 ), (y 0 )
b ( x ), (y ) , b x ( (x )), ( (x y )), ( (y y ))
1 0 0 2 0 0 0

A a 0 , ,...,a 1 a n

a 0 a 1 ... a n




a 0 a 1 ... a n
a 0 a 1 ... a n











 1 ( ) 1( (х  х  0 ) х ( (х  0 )) х ( ( (х х  0 ))))


 1 ( ) 1( (х  х  0 ) х 2 ( 0 ) х 3 ( 0 ))







 *
 ( )х  х (( ) х ( ) х 2 ( )))
1 0 0 0





1
Х

Х Х Х
 0 Х Х
 0 Х Х
 0 Х
 0 Х
 0  0

 
 




   


   

    












 
 

 




  





 0
 ( )x x (  x ( ))
1 0 0

 2
 ( ) x x (  x ( ))  x ( (x  x ( )))
3 0 0 0 0






1( )х 1( х х (1 х (1 ...(1))..)

2 ( )х 1( (х А 0 ) ( х А 1 ( х А 2 ...( А n ))..)

Х Х
1 Х
А 0 Х
1 Х
А 1 Х
1
А 2


  0
 1 ( )х  2 ( )х  x ( A  ( x A  A 1 ) x A ( 0  A  A 2 ) ...
0
0
1

Х


А 0 Х


А 0 А 1 Х

А 0 А 1 А 2 … .




























( ) ( ( (х ) ( у )))
1 0 0 0 0
( ) ( ( (х ) ( у )))
2 1 1 1 1
( ) ( ( (х ) ( у )))
3 2 2 2 2


 





n
0
G(x)=a x +a x + a x + a x + ...+a x =  a x n
2
3
n
1
1
0
n
n
3
2
i=0












   

n n ( n 1)...( n m 1)
m m ( n 1) ... 1

n
m
n
m

n n
1, n
0 1







k
y x r r k y x r k , k 0,r, r - целое число 0



у 1 ;
х


(1 x) r r k x k , к 0,r , r - целое число 0, или х 1









0 1 2 3 4 5 6
0 1 2 3 4 5 6
1 2 3 4 5 6 7
0 1 2 3 4 5 6

2 3 4 5 6 7 8
0 1 2 3 4 5 6
3 4 5 6 7 8 9
0 1 2 3 4 5 6

4 5 6 7 8 9 10
0 1 2 3 4 5 6
5 6 7 8 9 10 11
0 1 2 3 4 5 6

6 7 8 9 10 11 12
0 1 2 3 4 5 6

1 1 1 1 1 1 ...
1 2 3 4 5 6 ...
1 3 6 10 15 21 ...

1 4 10 20 35 56 ...
1 5 15 351 70 126 ...
1 6 21 56 126 252 ...
... ... ... ... ... ... ...

n ( n 1) , n 1, 2 , 3, ...
2

n ( n  1)( n  2 ) , n  1, 2 , 3, ...
6

( n n  1)
n  (k  2) , n  1, 2, 3, ...
2

















(1 ) x n r n x r n ( n 1)...( n r 1) x r
r 0 r 0 ! r
( n r 1)...( n 1) n x r n r 1 x r
! r r
r 0 r 0

n n r 1
r r


n
)
)
P ( x  ( 1  x  ...  x m  1 n    m x r
r
n n 1 n 1 ... n 1
r r r 1 r m 1
m m m m



n
r m


1 1 n n , r 0,n
r 2

1 1 1 n n r 3 , r 0,n



G 1 ( )  g ,..., g   g
1 i i
i







G 2 ( )  G 1 1 ( ),...,G 1 j ( )   g ji
j i








2
G 3 ( )  G 1 ( ),...,G k 2 ( )    g kji
k j i

а 0 а 1 а 2 ... а i 1
W эв i 1 0 1 2 i
i а а а ... а







 a a a 2 ...a i  1 a i  1
1
0
W  i  1  
э в  i a a a 2 ...a i a i
1
0









m   1,  1 
s



m s   1 ,  1 



m  i   1,  1 
i
m   i
i

m  i
i
m s   1,  1 

S ( )n


S ( n )  S 1 ( n ) , S 2 ( n ) ,. . . , S n ( n )  l 1 ( n ) , l 2 ( n ) ,. . . , l n ( n )


l ( )n , j=1,2,...,n
j




S ( )n   m  S ( )n 
s m s
m   1
s
m   1
s

m   2   1, 1 
s


S ( )n   m  S ( )n 
i m i
m   i
i
m   i
i
m   2i  , i  
i
i








( m  m )  S ( )n  ( 1, 1 ,       )
, i
i
s i

W ( )n   m  S ( )n   m  S ( )n 
э в s i




S ( 4 )  l 1 ( 4 ) ,l 2 ( 4 ) ,l 3 ( 4 ) ,l 4 ( 4 ) ,  1, 3 , 5 , 7



S (4)  (1), (1, 3), (1, 3, 5), (1, 3, 5, 7) 

m   2
s
W s ( 4 )   m  S ( 4 )  
s
  (1, 1), (1, 1; 3, 3), (1, 1;3, 3; 5, 5 ), (1, 1;3, 3; 5, 5; 7 , 7 )          
   2   2, 6   2 , 6,1 0   2 , 6 ,1 0 ,1 4   
,
,
,
   2   8   1 8   3 2  
,
,
,
m   2
i
W i ( 4 )   m  S ( 4 )  
i
 i  (1, 1), (1, 1;3, 3), (1, 1;3, 3;5, 5), (1, 1;3, 3; 5,5;7 , 7 )          
   2   2, 6   2, 6,1 0   2, 6,1 0,1 4   
,
,
i
,
   2   8  , 1 8 ,   3 2  
,
i
( 4 )
W э в   m s  S ( 4 )   m i  S ( 4 )  
   2 , 2   8 , 8   1 8 ,1 8   3 2 , 3 2  
,
,
,
m s






















K
С J P k log P k JH
k 1



J m
C H i P j lo g P ,
j
i 1 j 1

d H k 1 lo g e 0
d J J 2 J

а ) б ) с)

C
d p
C 0


 






































  С /С с







1-й уровень
2 уровень

3 уровень
4 уровень

... P 0 (x )
2
-1
3
P 0(x)= (1 + x ) = 1-x+ x -x +
3
G 0 (x ) G 0 (x )= 1- 2 x+ 2x 2 - 2x +
P 1(x )
3
2
2
3
-2
P 1 (x )= (1 + x ) = 1 -2 x+ 3x -4 x + ... G 1 (x ) G 1 (x )= 1 - 3 x + 5 x - 7x +
P 2 (x )
3
2
-3
P 2 (x )= (1 + x ) = 1 -3 x+ 6x -1 0 x + ... G 2 (x )
3
2
G 2 (x )= 1 - 4 x+ 9 x -1 6x +
P 3(x )
-4
3
2
P 3 (x )= (1 + x ) = 1 -5 x+ 14 x -3 0 x + ... G 3 (x )
2
3
G 3 (x )= 1 -5 x+ 1 4x -3 0 x +
… … … … … … … ..

Уровни Подоболочки P i (x) Оболочки G i (x)
иерархии
0 <1,1,1,1,…> <1,2,2,2,…>
1 <1,2,3,4,…> <1,3,5,7,…>
2 <1,3,6,10,…> <1,4,9,16,…>
3 <1,4,10,20,…> <1,5,14,30,…>
4 <…………….> <……………>







































  ( 1 x )( 1 y )( 1 z )( )   x ( ) y  ( x ( )) z  ( x ( ) y  ( x ( )))
n





  ( 1 x  y  ) z



n
 n  ( 1 x  y  z ) ( )




  ( 1 A  A  ...  A n )
2












 




















 















  
  







  

  






   
  







  

  





































   


  






m n (n ,i) m n (n ,i)
r (m , )n l - p
n 1 i 1 n 1 i 1

r ( m , )n n


m n ( n ,i)
r ( m , )n l
n 1 i 1

m n k m n k
r ( m , , ,...)n k ...l ( n , , ,...)k s ...p ( n , , ,...)k s
n 1 k 1 s 1 n 1 k 1 s 1



































 m   2  1, 1 
s





n
m
S m ( m , n , k ,. . . )   m s    k . . .l ( n , k , s , . . . )
s
n  1 k  1 s  1
l ( , , ,...)n k s

 m   2i   1, 1 
i
i
n
m
S m ( m i , n , k ,. . . )   m i    k . . .l ( n , k , s , . . . )
n  1 k  1 s  1


( )m
( )m
S ( , , ,...)m n k  S m s , S m i 



S ( , , ,...)m n k  S m ( )m s ,S ( )m i m 

S ( , , ,...)m n k


S ( )m
s m


( m , ,n k ,...) m n k
S m   m s    ...l ( n , , ,...)k s
s
n  1 k  1 s  1
S ( )m
i m
n
k
m
S ( m , , ,...)n k   m i    ...l ( , , ,...)n k s
m i
n  1 k  1 s  1



 m   2  1, 1 
s

 m   2i i  1, 1 
i


l ( , , ,...)n k s






























f
...A  ...A n 1  A n ...
f
i


 



















 
 




 



 

А x   x

 





( А I )x 0




(а 11 ) 1 x а 12 2 x ... а 1n x n 0
а 1 x (а ) 2 x ... а x n 0
21 22 nn
.....
а n1 1 x а n 2 2 x ... (а nn )x n 0

det(A i I) 0






det( A I) q 0 q 1 ... q n n


q 0 q 1 ... q n n 0






( A i I)x 0









A x i x i , i 1,n,


AV V



x 1 1 ... x 1 n 1 0 ... 0
V ( ,...,x 1 x n ) ... ... ... 0 2 ... 0
0 0 ... 0
x 1 n ... x n n 0 0 ... n






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





  





  

  



   1,05 10  34 Дж с
 2 / me 2

10  10



 










e i b x i b e i b x
x







e i x i e i x
x

e ibx  e ibx 1



e ibx e ( i 1 b b 2 ... b n ) x

















         
 






      
             
    

      
    


  
de x e x
dx



_
de A x _ x
A e
dx





   е iB x  С










   е iBx е iCx ...е iZx  С


...
Y  A ((e iBx ) e iCx ) ) e iZx  C




е ix(B C ... Z)

iA e iA x C

d Y Y A T
d x


x x
iA T x iA T x
iAe x 0 e x 0 e iA T ( x x 0 )
1

T
e iA x
1

dY 1 d (e iA x ) iA e iA x
T
T
T
dx 1 dx
d Y Y A T
d x

T
T iA x
iA e T e iA x iA T
d Y T
Y A
d x





   

       


x
e [ i 1 ,x 2 ,..., n x ] [e i 1 x ,e i 2 x ,e i 3 x ,...,e i n x ]

Y 1 [e i 1 x ,e i 2 x ,e i 3 x ,...,e i n x ]





Y 1 [e i 1 x ,e i 2 x ,e i 3 x ,...,e i n x ]





),
A T J ( ), J ( ), J ( 3 ... J ( )
1 h 1 2 h 2 3 h n h n

i
1
J ( ) i
1 i h i ... ... ... ...
1 i



 





     






     

       

T
Y 1 e iA x [e J 1 h ( )x ,e J 1 h 2 ( )x ,...,e J hr ( )x ]
2
1
r
[ ,A A 2 ,..., A r ] m [A m 1, A m 2,..., A m r ]
1
e [ i J 1 h ( 1 ),...,J h r ( r )]x [e J 1 h ( 1 )x ,e J 1 h 2 ( 2 )x ,...,e J hr ( r )x ]


)
Y 1 [e 1 h J ( 1 )x ,e 1 h J 2 ( 2 )x ,...,e J hr ( r x ]










F  e 1 e 1

F  e 2 1 e 2 e
F  n e 1 e 2 e ... n e 1 n e


1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
n J ( ) ... ... ... ... ... ... ...
0 0 0 0 0 1
0 0 0 0 0 0








d 0 0 0 0 0 0
dx
d ''
0 0 0 0 0 0
dx
d '''
0 0 0 0 0 0
F n dx
... ... ... ... ... ... ...
d n 1
0 0 0 0 0 0
dx
d n
0 0 0 0 0 0
dx

J ( ) 0 0 0 0 0 0
1
0 J 2 ( ) 0 0 0 0 0
0 0 J ( ) 0 0 0 0
( )n
n J ( ) ... ... 3 ... ... ... ... ...
0 0 0 0 0 J n 1 ( ) 0
0 0 0 0 0 0 J n ( )




F 1 0 0 0 0 0 0
0 F 2 0 0 0 0 0
0 0 F 3 0 0 0 0
( )n
F n ... ... ... ... ... ... ...
0 0 0 0 0 F 0
n 1
0 0 0 0 0 0 F n



S n ( )n ( ) F n ( )n J n ( )n [ (1) S (1) , (2) S (2) ,..., ( )n S ( )n ]

( )i [ 1 , 2 , 3 ,..., i ] S n ( )i A 1 A 2 A 3 ... A 1 i i n
J n ( )n ( )


( )n
S n ( )n ( ) F J ( )n ( ) ( )n S ( )n
S n ( )n [ A A 2 A 1 , A 3 A 2 A 1 ,..., A 3 A 2 A 1 , A 2 A 1 , A 1 ]
,
1









i
1
i 2
2
( )n 3
n 3 i
... ... ... ... ...
i n
n


1 0 0 0 0
d
0 (1 ) 0 0 0
dx
Y n ( )n 0 0 (1 d )
dx
... ... ... ... ...
d
0 0 0 0 (1 )
dx




S T n ( )n Y n ( )n  S n ( )n




















1 0 0 0
1 0
0 0 0
1 1
S n (1) 1 0 0
0 0 1 1 0 0
1 1 1
... ... ... ...

1 0 0 0
1 0
0 0 0
3 1
S (2) 1 0 0
n
0 0 3 1 0 0
5 3 1
... ... ... ...


1 0 0 0
1 0
0 0 0
4 1
S n (3) 1 0 0

0 0 4 1 0 0
9 4 1
... ... ... ...




























3 3
4 4
e iAx (iAx A x 2 2  iA x  A x  ...)

3
T
T
T
e iA x (iA x A T 2 x 2 iA x 3 A T 4 x 4 ...)



Уровни Подоболочки P i (x) Оболочки G i (x)
иерархии
0 <2,2,2,2,…> <2,4,4,4,…>
1 <2,4,6,8,…> <2,6,10,14,…>
2 <2,6,12,20,…> <2,8,18,32,…>
3 <2,8,20,40,…> <2,10,28,60,…>
4 <…………….> <……………>























i= -1






i  1, i  , i i  1, i  , i i  1, ...
3
4
2
0
1
 1, , 1,i   
i




 e i x   i x
 x i e

e iB x e  iB x  1









е
е iх -iх






















ix
ix
e i x2  e e  e ix (cos x  i sin )x
e i xB  e ix 1 b  ... ix b n




 X i



e Ax e  Ax


A
x
Ax
e  e  Ax  e  (e e  x ) e A 1 
e A

e x






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