ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
29
ȼɚɠɧɨ ɨɬɦɟɬɢɬɶ ɢɡɜɟɫɬɧɵɣ ɮɚɤɬ, ɱɬɨ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɜɨɡɦɭɳɟɧɢɣ
ɩɨɩɪɚɜɤɚ, ɜɵɱɢɫɥɟɧɧɚɹ ɩɨ ɪɟɤɭɪɪɟɧɬɧɵɦ ɮɨɪɦɭɥɚɦ ɮɢɥɶɬɪɚ Ʉɚɥɦɚ-
ɧɚ, ɫɨɜɩɚɞɚɟɬ ɫ ɩɨɩɪɚɜɤɨɣ, ɩɨɥɭɱɟɧɧɨɣ ɢɡ ɪɟɲɟɧɢɹ ɫɢɫɬɟɦɵ ɧɨɪ-
ɦɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ ɦɟɬɨɞɨɦ ɧɚɢɦɟɧɶɲɢɯ ɤɜɚɞɪɚɬɨɜ.
Ɉɫɧɨɜɧɚɹ ɢɞɟɹ ɩɪɟɞɥɚɝɚɟɦɨɝɨ ɚɥɝɨɪɢɬɦɚ ɫɨɫɬɨɢɬ ɜ ɢɫɩɨɥɶɡɨɜɚ-
ɧɢɢ ɪɟɡɭɥɶɬɚɬɨɜ ɫɝɥɚɠɢɜɚɧɢɹ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɜɨɡɦɨɠɧɵɯ ɦɨɦɟɧɬɨɜ
ɜɨɡɦɭɳɟɧɢɣ.
ɉɭɫɬɶ ɞɜɢɠɟɧɢɟ ɄȺ ɨɩɢɫɵɜɚɟɬɫɹ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɦ ɭɪɚɜɧɟɧɢɟɦ
,
,
d
t
t t
dt
x F x B ȟ
(1)
ɝɞɟ
x
—
ɜɟɤɬɨɪ ɫɨɫɬɨɹɧɢɹ;
,
t
F x
—
ɜɟɤɬɨɪ-ɮɭɧɤɰɢɹ;
t
B
—
ɦɚɬ-
ɪɢɰɚ, ɨɩɢɫɵɜɚɸɳɚɹ ɜɨɡɞɟɣɫɬɜɢɟ ɲɭɦɚ ɧɚ ɫɢɫɬɟɦɭ;
t
ȟ
—
ɛɟɥɵɣ
ɲɭɦ ɫ ɧɭɥɟɜɵɦ ɦɚɬɟɦɚɬɢɱɟɫɤɢɦ ɨɠɢɞɚɧɢɟɦ ɢ ɡɚɞɚɧɧɨɣ ɦɚɬɪɢɰɟɣ ɢɧ-
ɬɟɧɫɢɜɧɨɫɬɢ
t
Q
ɩɨɪɹɞɤɚ 3 × 3.
ɇɚɱɚɥɶɧɵɟ ɭɫɥɨɜɢɹ ɞɥɹ ɫɢɫɬɟɦɵ (1) ɡɚɞɚɸɬɫɹ ɚɩɪɢɨɪɧɵɦ ɜɟɤɬɨ-
ɪɨɦ
0
x
ɢ ɟɝɨ ɤɨɜɚɪɢɚɰɢɨɧɧɨɣ ɦɚɬɪɢɰɟɣ
0
.
P
ȼ ɦɨɦɟɧɬɵ ɜɪɟɦɟɧɢ
1 2
, , ...,
N
t t
t
ɩɪɨɜɨɞɹɬɫɹ ɢɡɦɟɪɟɧɢɹ ɮɭɧɤɰɢɣ
1 2
,
, ...,
,
N
Ȍ Ȍ Ȍ
ɡɧɚɱɟɧɢɟ ɤɨɬɨɪɵɯ ɨɛɨɡɧɚɱɢɦ ɱɟɪɟɡ
ɧɚɛ
i
Ȍ
.
Ⱦɥɹ ɤɚɠɞɨ-
ɝɨ ɦɨɦɟɧɬɚ ɜɪɟɦɟɧɢ
i
t
ɫɩɪɚɜɟɞɥɢɜɨ
ɧɚɛ
,
,
i
i i
i
t
˜
Ȍ
Ȍ x Ș
(2)
ɝɞɟ
i
Ș
—
ɫɥɭɱɚɣɧɵɣ ɜɟɤɬɨɪ, ɢɦɟɸɳɢɣ ɧɭɥɟɜɨɟ ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɠɢ-
ɞɚɧɢɟ ɢ ɤɨɜɚɪɢɚɰɢɨɧɧɭɸ ɦɚɬɪɢɰɭ
.
i
R
ȼ ɥɢɧɟɣɧɨɦ ɫɥɭɱɚɟ (2) ɩɪɢɨɛɪɟɬɚɟɬ ɜɢɞ
,
i
i i
i
i
t
t
z H x Ș
(3)
ɝɞɟ
i
z
—
ɜɟɤɬɨɪ ɩɚɪɚɦɟɬɪɨɜ ɪɚɡɦɟɪɧɨɫɬɢ
r
i
,
ɢɡɦɟɪɹɟɦɵɯ ɜ ɦɨɦɟɧɬ
ɜɪɟɦɟɧɢ
t
i
;
i i
t
H
—
ɦɚɬɪɢɰɚ ɪɚɡɦɟɪɚ
r
i
×
n
.
Ɂɚɩɢɫɶ ɜ ɤɚɱɟɫɬɜɟ ɩɚɪɚɦɟɬɪɚ
˜
x
ɮɭɧɤɰɢɢ
i
Ȍ
ɨɡɧɚɱɚɟɬ, ɱɬɨ
ɮɭɧɤɰɢɹ
i
Ȍ
ɡɚɜɢɫɢɬ ɧɟ ɨɬ ɦɝɧɨɜɟɧɧɨɝɨ ɡɧɚɱɟɧɢɹ ɜɟɤɬɨɪɚ ɫɨɫɬɨɹɧɢɹ,
ɚ ɨɬ ɮɭɧɤɰɢɢ
,
t
x
ɤɨɬɨɪɚɹ ɹɜɥɹɟɬɫɹ ɪɟɲɟɧɢɟɦ ɭɪɚɜɧɟɧɢɹ (1).
Ɋɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ (1) ɧɚ ɢɧɬɟɪɜɚɥɟ
0
,
N
t t
ª
º
¬
¼
ɛɭɞɟɦ ɚɩɩɪɨɤɫɢɦɢ-
ɪɨɜɚɬɶ ɮɭɧɤɰɢɹɦɢ ɜɢɞɚ
( )
( )
( ),
D
P
A
t
t
t
x
x
x