ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
178
Ȼɚɡɢɫɵ ɝɥɚɞɤɢɯ ɥɨɤɚɥɶɧɵɯ ɫɮɟɪɢɱɟɫɤɢɯ ɫɩɥɚɣɧɨɜ.
Ⱦɥɹ ɨɩɢ-
ɫɚɧɢɹ ɝɥɚɞɤɢɯ ɧɚ ɫɮɟɪɟ ɟɞɢɧɢɱɧɨɝɨ ɪɚɞɢɭɫɚ ɥɨɤɚɥɶɧɵɯ ɫɩɥɚɣɧɨɜ
ɫɧɚɱɚɥɚ ɜɜɟɞɟɦ ɢɯ ɧɚ ɩɪɹɦɨɭɝɨɥɶɧɢɤɟ
[ ; ] [
2 ; 2]
,
S S
S
S
u
3
ɝɞɟ
[ ; )
M
S S

ɢ
(
2; 2)
T
S
S

—
ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɭɝɥɵ, ɨɩɪɟɞɟɥɹ-
ɸɳɢɟ ɩɨɥɨɠɟɧɢɟ ɬɨɱɤɢ ɧɚ ɫɮɟɪɟ, ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ ɟɟ ɩɨɥɸɫɨɜ. Ⱦɥɹ ɬɨ-
ɝɨ ɱɬɨɛɵ ɝɥɚɞɤɢɣ ɫɩɥɚɣɧ, ɡɚɞɚɧɧɵɣ ɧɚ ɩɪɹɦɨɭɝɨɥɶɧɢɤɟ ɉ, ɦɨɠɧɨ ɛɵɥɨ
ɛɵ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɫɩɥɚɣɧ ɧɚ ɫɮɟɪɟ, ɨɧ ɞɨɥɠɟɧ ɭɞɨɜɥɟɬɜɨɪɹɬɶ ɫɥɟ-
ɞɭɸɳɢɦ ɝɪɚɧɢɱɧɵɦ ɭɫɥɨɜɢɹɦ. ȼ ɬɨɱɤɚɯ
( ; )
S T
3
ɢ
( ; )
S T
3
ɛɨ-
ɤɨɜɵɯ ɝɪɚɧɢɰ ɡɧɚɱɟɧɢɹ ɫɩɥɚɣɧɚ ɞɨɥɠɧɵ ɫɨɜɩɚɞɚɬɶ. ȼ ɬɨɱɤɚɯ ɜɟɪɯɧɟɣ
(
ɧɢɠɧɟɣ) ɝɪɚɧɢɰɵ ɩɪɹɦɨɭɝɨɥɶɧɢɤɚ
3
ɫɩɥɚɣɧ ɞɨɥɠɟɧ ɩɪɢɧɢɦɚɬɶ ɨɞ-
ɧɨ ɢ ɬɨ ɠɟ ɡɧɚɱɟɧɢɟ ɢ ɢɦɟɬɶ ɧɭɥɟɜɵɟ ɩɪɨɢɡɜɨɞɧɵɟ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ
ɦɟɪɢɞɢɚɧɨɜ ɫɮɟɪɵ ɫ ɧɚɱɚɥɨɦ ɜ ɟɟ ɜɟɪɯɧɟɦ (ɧɢɠɧɟɦ) ɩɨɥɸɫɟ, ɢɧɞɭɰɢ-
ɪɨɜɚɧɧɨɦ ɜɟɪɯɧɟɣ (ɧɢɠɧɟɣ) ɝɪɚɧɢɰɟɣ ɩɪɹɦɨɭɝɨɥɶɧɢɤɚ ɉ. ɋɩɥɚɣɧɵ,
ɡɚɞɚɧɧɵɟ ɧɚ ɩɪɹɦɨɭɝɨɥɶɧɢɤɟ
3
ɢ ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɟ ɬɚɤɢɦ ɝɪɚɧɢɱ-
ɧɵɦ ɭɫɥɨɜɢɹɦ, ɧɚɡɵɜɚɸɬ ɫɮɟɪɢɱɟɫɤɢɦɢ ɫɩɥɚɣɧɚɦɢ.
ɇɨɫɢɬɟɥɢ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɞɚɥɟɟ ɥɨɤɚɥɶɧɵɯ ɫɩɥɚɣɧɨɜ ɨɩɪɟɞɟ-
ɥɹɸɬɫɹ ɩɨɞɪɚɡɞɟɥɟɧɢɟɦ
3
ɧɚ ɛɨɥɟɟ ɦɟɥɤɢɟ ɩɪɹɦɨɭɝɨɥɶɧɢɤɢ, ɜɟɪɲɢ-
ɧɵ ɤɨɬɨɪɵɯ ɧɟɥɶɡɹ ɡɚɞɚɬɶ ɧɟɤɨɬɨɪɨɣ ɞɜɭɦɟɪɧɨɣ ɫɟɬɤɨɣ ɧɚ ɩɪɹɦɨ-
ɭɝɨɥɶɧɢɤɟ ɉ. Ɍɚɤɨɟ ɩɨɞɪɚɡɞɟɥɟɧɢɟ ɧɚɡɵɜɚɟɬɫɹ ɭɤɥɚɞɤɨɣ ɩɪɹɦɨɭɝɨɥɶ-
ɧɢɤɚ ɉ. Ɉɧɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦ ɧɚɛɨɪɨɦ ɬɨɱɟɤ-ɭɡɥɨɜ
ɩɪɹɦɨɭɝɨɥɶɧɢɤɚ (ɜɟɪɲɢɧɚɦɢ ɩɪɹɦɨɭɝɨɥɶɧɢɤɨɜ ɭɤɥɚɞɤɢ). ɗɬɨɬ ɧɚɛɨɪ
ɭɡɥɨɜ ɞɥɹ ɧɨɫɢɬɟɥɹ ɤɚɠɞɨɝɨ ɛɚɡɢɫɧɨɝɨ ɥɨɤɚɥɶɧɨɝɨ (ɫɮɟɪɢɱɟɫɤɨɝɨ)
ɫɩɥɚɣɧɚ ɢɧɞɭɰɢɪɭɟɬ ɫɜɨɸ ɥɨɤɚɥɶɧɭɸ ɫɟɬɤɭ; ɞɚɥɟɟ ɨɧ ɧɚɡɵɜɚɟɬɫɹ
ɩɫɟɜɞɨɫɟɬɤɨɣ, ɩɨɫɤɨɥɶɤɭ ɬɚɤɨɣ ɧɚɛɨɪ ɫɨɞɟɪɠɢɬ ɧɟ ɜɫɟ ɭɡɥɵ ɷɬɢɯ ɥɨ-
ɤɚɥɶɧɵɯ ɫɟɬɨɤ, ɧɨ ɩɨɡɜɨɥɹɟɬ ɢɯ ɜɨɫɫɬɚɧɨɜɢɬɶ ɢɡ ɭɡɥɨɜ ɭɤɚɡɚɧɧɨɣ
ɩɫɟɜɞɨɫɟɬɤɢ.
ɇɚ ɩɪɹɦɨɭɝɨɥɶɧɢɤɚ
3
ɬɚɤɚɹ ɩɫɟɜɞɨɫɟɬɤɚ ɢɦɟɟɬ ɜɢɞ
^
`
( ,
) : 0
1, 0
,
i
i
k
C
i N
k n
W
W
d d
d d
(11)
ɝɞɟ
1
0 1
1
(
, , ...,
)
N
A
S W W
W
—
ɱɚɫɬɶ ɫɟɬɤɢ
0 1
1
(
, ,...,
,
N
A
S W W
W
),
N
W
S
ɜɜɟɞɟɧɧɨɣ ɜ (1) ɜɦɟɫɬɟ ɫ ɫɟɬɤɨɣ
0
,
A
ɭɞɨɜɥɟɬɜɨɪɹɸɳɟɣ
ɭɫɥɨɜɢɹɦ (3).
Ʉɪɨɦɟ ɬɨɝɨ, ɟɫɥɢ
0
1,
i N
d d
ɬɨ
0 1
(
2 , , ...,
2)
i
i
i
i
n
A
S
W W
W
S
—
ɫɟɬɤɚ, ɚɧɚɥɨɝɢɱɧɚɹ ɫɟɬɤɟ
Ⱥ
ɢɡ (1) ɫ ɪɚɫɲɢɪɟɧɢɟɦ
0
i
A
3 2 1 0 1
1 2 3
,
,
, , , ..., ,
,
,
i
i
i
i
i
i
i
i
i
n n n n
W
W
W
W W
W W
W
W
ɜɧɟ ɨɬɪɟɡɤɚ
[
2; 2],
S
S
ɤɨɬɨɪɨɟ ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɭɫɥɨɜɢɹɦ
1
1
1 1
0
,
,
2
2
i
i
i
i
i
i
n
n
n
W
W
W
W
W
W
ɚɧɚ-
ɥɨɝɢɱɧɵɦ ɜɜɟɞɟɧɧɵɦ ɜ (6).