ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
175
ɫɬɟɦɭ ɤɨɨɪɞɢɧɚɬ, ɟɫɥɢ ɢɡɜɟɫɬɟɧ ɰɟɧɬɪ ɡɜɟɡɞɧɨɣ ɨɛɥɚɫɬɢ, ɨɝɪɚɧɢɱɟɧ-
ɧɨɣ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɩɨɜɟɪɯɧɨɫɬɶɸ. ɇɨ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɬɚɤɨɣ
ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ ɜɨɡɧɢɤɚɸɬ ɩɪɨɛɥɟɦɵ «ɩɟɪɢɨɞɢɱɟɫɤɨɣ» ɫɤɥɟɣɤɢ
ɩɨɜɟɪɯɧɨɫɬɢ ɢ ɟɟ ɨɩɢɫɚɧɢɹ ɜ «ɩɨɥɸɫɚɯ» [4].
ȼ ɧɚɫɬɨɹɳɟɣ ɪɚɛɨɬɟ ɩɪɟɞɥɚɝɚɸɬɫɹ ɦɟɬɨɞɵ ɚɩɩɪɨɤɫɢɦɚɰɢɢ ɝɥɚɞ-
ɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɨɝɪɚɧɢɱɢɜɚɸɳɟɣ ɡɜɟɡɞɧɭɸ ɨɛɥɚɫɬɶ ɟɜɤɥɢɞɨɜɚ ɩɪɨ-
ɫɬɪɚɧɫɬɜɚ, ɫ ɩɨɦɨɳɶɸ ɫɮɟɪɢɱɟɫɤɢɯ ɫɩɥɚɣɧɨɜ, ɹɜɥɹɸɳɢɯɫɹ ɝɥɚɞɤɢɦɢ
ɮɭɧɤɰɢɹɦɢ ɧɚ ɫɮɟɪɟ ɟɞɢɧɢɱɧɨɝɨ ɪɚɞɢɭɫɚ. ȼ ɷɬɢɯ ɦɟɬɨɞɚɯ ɜɵɛɨɪ ɷɤɫ-
ɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɬɨɱɟɤ ɩɨɜɟɪɯɧɨɫɬɢ, ɡɚɞɚɧɧɵɯ ɫ ɧɟɤɨɬɨɪɨɣ ɩɨɝɪɟɲ-
ɧɨɫɬɶɸ, ɫɥɭɱɚɟɧ, ɱɬɨ ɧɟ ɩɨɡɜɨɥɹɟɬ ɨɪɢɟɧɬɢɪɨɜɚɬɶɫɹ ɧɚ ɤɚɤɢɟ-ɥɢɛɨ
ɫɟɬɤɢ ɩɨɜɟɪɯɧɨɫɬɢ. ɉɨɷɬɨɦɭ ɜ ɪɚɛɨɬɟ ɪɚɫɫɦɚɬɪɢɜɚɸɬɫɹ ɩɫɟɜɞɨɫɟɬɤɢ,
ɩɨɡɜɨɥɹɸɳɢɟ ɜɨɫɫɬɚɧɨɜɢɬɶ ɥɨɤɚɥɶɧɵɟ ɫɟɬɤɢ ɞɥɹ ɧɨɫɢɬɟɥɟɣ ɛɚɡɢɫɧɵɯ
ɫɮɟɪɢɱɟɫɤɢɯ ɫɩɥɚɣɧɨɜ. ɗɮɮɟɤɬɢɜɧɨɫɬɶ ɩɪɟɞɥɨɠɟɧɧɨɝɨ ɩɨɞɯɨɞɚ ɩɨ-
ɤɚɡɚɧɚ ɧɚ ɚɩɩɪɨɤɫɢɦɚɰɢɹɯ ɫɮɟɪɢɱɟɫɤɢɦɢ ɫɩɥɚɣɧɚɦɢ ɞɨɫɬɚɬɨɱɧɨ
ɫɥɨɠɧɵɯ ɝɥɚɞɤɢɯ ɩɨɜɟɪɯɧɨɫɬɟɣ, ɨɝɪɚɧɢɱɢɜɚɸɳɢɯ ɡɜɟɡɞɧɵɟ ɨɛɥɚɫɬɢ
ɟɜɤɥɢɞɨɜɚ ɩɪɨɫɬɪɚɧɫɬɜɚ.
Ȼɚɡɢɫɵ ɥɨɤɚɥɶɧɵɯ ɫɩɥɚɣɧɨɜ ɞɥɹ ɝɥɚɞɤɢɯ ɧɚ ɨɬɪɟɡɤɟ ɮɭɧɤ-
ɰɢɣ.
ȼ ɧɚɫɬɨɹɳɟɣ ɪɚɛɨɬɟ ɱɢɫɥɟɧɧɨɟ ɨɩɢɫɚɧɢɟ ɝɥɚɞɤɢɯ ɧɚ ɫɮɟɪɟ
ɮɭɧɤɰɢɣ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɥɨɤɚɥɶɧɵɯ ɫɩɥɚɣɧɨɜ, ɫɬɪɭɤɬɭɪɚ
ɤɨɬɨɪɵɯ ɭɱɢɬɵɜɚɟɬ ɬɨɩɨɥɨɝɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɫɮɟɪɵ. Ⱦɥɹ ɜɜɟɞɟɧɢɹ
ɬɚɤɢɯ ɞɜɭɦɟɪɧɵɯ ɫɩɥɚɣɧɨɜ ɢɫɩɨɥɶɡɭɸɬɫɹ ɨɞɧɨɦɟɪɧɵɟ ɥɨɤɚɥɶɧɵɟ
ɫɩɥɚɣɧɵ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɟ ɫɩɟɰɢɚɥɶɧɵɦ ɝɪɚɧɢɱɧɵɦ ɭɫɥɨɜɢɹɦ ɜ
ɤɨɧɰɚɯ ɡɚɞɚɧɧɨɝɨ ɨɬɪɟɡɤɚ.
ɉɭɫɬɶ ɧɚ ɨɬɪɟɡɤɟ
[ ; ]
a b
ɡɚɞɚɧɵ ɫɟɬɤɚ
Ⱥ
ɢ ɟɟ ɪɚɫɲɢɪɟɧɢɟ ɞɨ ɫɟɬɤɢ
0
A
ɡɚ ɷɬɨɬ ɨɬɪɟɡɨɤ, ɞɥɹ ɤɨɬɨɪɵɯ
0 1
0
3 2 1 0 1
1
2
3
(
, , ...,
);
( ,
,
, , , ...,
,
,
,
),
N
N N N N
A a
b
A
W W
W
W
W
W
W W
W
W
W
W
­
°
® °¯
(1)
ɝɞɟ
3
2
1 0 1
1
2
3
...
.
N N N
N
W
W
W
W
W
W
W
W
W
Ⱦɥɹ ɜɜɟɞɟɧɢɹ ɧɟɨɛɯɨɞɢɦɵɯ ɥɨɤɚɥɶɧɵɯ ɫɩɥɚɣɧɨɜ ɧɚ ɨɬɪɟɡɤɟ
[0;1]
ɨɩɪɟɞɟɥɹɟɬɫɹ ɮɭɧɤɰɢɹ
Q
D
ɜɢɞɚ
3
3
3
3
3
3
, 0
;
(
)
2 (1 ) ( )
,
1 ;
1 2
(
1) (
) , 1
1,
1 2
t
t
t
Q t
t
t
t
t
t
t
­
°
d
°
°°
d
®
°
°
°
d d
°¯
D
D
D
D
D
D
D
D
D
D
D
D
(2)