ó . ( ). :
;
;
;
;
;
.
, f (x) :
W = W (x, f (x)). f (x) , f* (x) .. f (x), f* (x) , W.
:
xi = ci , i = 1,, m;
f (x) = cj , j = 1,, l;
xi min £ xi £ xi max , i = 1,, k;
fj (x) £ cj, j = 1,, n.
, .
:
.
:
.
, , , , . , .
. , .
:
, (2.14)
xi , a ij , cj ³ 0 .
a ij, j , .
.
, , , , ..
|
|
, , . , m = 1 x 1 > 0, x 2 > 0,, xk > 0 (2.4) .
(2.4) :
.
,
. (2.15)
W, x 1, x 2,, x k :
(2.5)
Y (X 1, X 2,, Xk) = C + a1 x 1 + a2 x 2 + +ak x k.
.
3
1. ?
2. ?
3. ?
4. .
5. ?
6. .
7. ?
8. ?
9. .
10. ?
11. ?
12. .
13. .
14. ( )?
2.4.3.
4
(. 2.8). .
(, ) (, ) , D, x 2 + y 2 £ R 2.
.
, D, .
, (0, ), , D.
.
, . , 1 ( 1). , .
a Ð 10 1, E 1 C 1 + C 1 F 1 = 2 R tga;
E 1 F 1 arc E 1 F 1 = 2 R a.
tga > a a Î .
, , 1, E 1 F 1 F 1 B, , 1 .
, .
2, E 2 F 2, F 2 B, Ð 0 2 = Ð 0 F 2 = b.
S. :
. (2.16)
, (2.16')
a 10 0 Y.
(2.16') , 1 D, .
|
|
b0, S . S (b) :
. (2.17)
:
P = 4; R = 1.
.
p R (2.6),
.
,
.
b .
.
, b, b0, S . , cosb = 1/2.
b = p/3.
, , (2.16). b = b0, S (b) .
S (b)
.
b0 = p/3,
.
. , , . , , . , . S (b) b:
.
, b = p/3 S (b) , . , S (b) (. 2.9) , (2.16') (2.16) . b0 = p/3, b, . . , AE 1 GF 1 B S (p/3) = 4,511.
, (2.6) p R , , . , S (b) .
(2.6)
.
, :
.
2 R ( , , R > 0, , . . ),
.
( sin(b) > 0) ,
.
cos2(b) , .. , , .. .
0 ³ 4 pR 4 R 2 p ³ R.
p R (. . 2.5).
, ( (2.6)) , b = p/2 a . , p R:
( /2, 0); 1( R sin(a), R cos(a)); F 1(R sin(a), R cos(a)); B (p /2, 0),
a = .
4
1. ?
2. b ?
3. S b ?
2.5.
5
() (), , (, , ).
n - :
1-
|
|
, .
, , :
x 1(0) = C 1, x 2(0) = C 2,, xn (0) = Cn.
, , . , . . . . , , .
m, n (. 2.10).
, , f (t). f (t) , , . .
, :
. (2.18)
:
x (0) = x 0; . (2.19)
(2.18) (2.19) .