, . ,
:
:
, xi () :
:
D = D() , Q , .
, D = D() , (, ), | |.
:
1. , =
2. .
3. ,
4. : .
:
,
:
| |. . | |> 1, 1% 1%, , 1% 1%, . , | | ≤ 1, .
.
, R(Q) R(Q) = QP(Q), P(Q) . R'(Q) .
.
, (| | ≤ 1), ; (| |> 1), , , . : .
:
S = S(P) , Q , . S = S(P) , ,
,
|
|
|
|
.4
, (≤1).
. 5 R(Q) RP(Q) Q, .
|
|
. 5.
Q; R , R .
, , =1 Q = (Q). Q=4,517, P(Q)=1,37.
1. = (Q).
2. .
3. .
4. .
5. .
6. .
7. , |ED| = 1. . , .
8. Q, |ED| = 1.
9. .
, -
.
- .
.
6
( ..)
, . , , , , , . .
.. - (Input-output analysis I/O analysis), , . , , .
n (). , .
, - , . , . .
, . .
|
|
- 0 , , , .
1
( - ) ( ) | ( , (+), (-)) | ||||||||
. | j | .. | n | ||||||
11 | 12 | . | 1j | . | 1n | y1 | q1 | ||
21 | 22 | . | 2j | . | 2n | y2 | q2 | ||
.... | .... | .... | .... | .... | .... | .... | .... | .... | |
i | i1 | i2 | . | ij | . | in | yi | qi | |
.... | .... | .... | .... | .... | .... | .... | .... | .... | |
n | n1 | n2 | . | nj | . | nn | yn | qn | |
( , , , ) | g1 | g2 | .... | gj | .... | gn | - | D | |
| q1 | q2 | .... | qj | .... | qn | D | V |
(output) . ij i, j (i, j = 1,2,) . yi i- , , , . qi ( ) i- . :
= + ,
(1)
(input), , . :
= +
(2)
, i () 1,2,...,n. , , , , .
, :
= ,
= .
:
(3)
(4)
(3) (4) . (, ) , . .
1 . . αij 1 qj ( j ), yi qi , aij =αij /qj , i,j = 1,2,,n, i - , j;
yi / qi , i = 1,2,,n, i , .
aij ,i = 1,2,,n, , j j : , aij. , aij .
|
|
=[ aij ], aij , , . , , .
,
2
1947 . | 1958 . | |
0,2149 | 0,1569 | |
0,4769 | 0,4969 | |
0,1328 | 0,0881 |
2 , , , , .
. :
[T0, T], >T0. [T0, T] () .
, , i- xi xiaij , j=1,2,,n, .
, - . , .
i- xi, i=1,2,,n, . X = [ , ,., ]T - . , i .
. (5)
, (5) xi ,
y i- .
AX = X - Y,
(E A) X = Y, (6)
Y - , E .
B = (E-A)-1 . (6) A X, Y . : X , Y , A.
Y X, (6), .
-:
(6) :
X = (E A)-1 Y = B∙Y,
B = (E A)-1 - . C , . bij : bij i j.
, , ; , .
|
|
1. .
2. .