ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
181
Ɇɟɬɨɞɵ ɩɨɫɬɪɨɟɧɢɹ ɚɩɩɪɨɤɫɢɦɚɰɢɢ ɩɨɜɟɪɯɧɨɫɬɢ ɫɮɟɪɢɱɟ-
ɫɤɢɦ ɫɩɥɚɣɧɨɦ.
ȼ ɜɵɛɪɚɧɧɨɣ ɫɮɟɪɢɱɟɫɤɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ
( , , )
R
T M
ɟɜɤɥɢɞɨɜɚ ɩɪɨɫɬɪɚɧɫɬɜɚ ɝɥɚɞɤɚɹ ɩɨɜɟɪɯɧɨɫɬɶ, ɨɝɪɚɧɢɱɢɜɚ-
ɸɳɚɹ ɡɜɟɡɞɧɭɸ ɨɛɥɚɫɬɶ ɬɪɟɯɦɟɪɧɨɝɨ ɟɜɤɥɢɞɨɜɚ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɡɚɞɚɧɚ
ɭɪɚɜɧɟɧɢɟɦ
( , ),
R f
T M
S T S
d d
ɢ
2
2 ,
S
S
M
d d
(18)
ɝɞɟ ( , ) 0
f
T M
!
—
ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɝɥɚɞɤɚɹ ɮɭɧɤɰɢɹ ɫɜɨɢɯ ɩɟɪɟɦɟɧ-
ɧɵɯ (ɭɝɥɨɜ) ɧɚ ɩɪɹɦɨɭɝɨɥɶɧɢɤɟ
[ ; ] [
2; 2]
Ȇ.
S S
S
S
u
ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɞɚɧɧɵɟ ɞɥɹ ɷɬɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɩɪɟɞɫɬɚɜɥɟɧɵ
ɜ ɫɥɟɞɭɸɳɟɦ ɜɢɞɟ. Ɂɚɞɚɧɵ ɟɟ ɜɧɭɬɪɟɧɧɢɣ «ɰɟɧɬɪ», ɪɚɫɩɨɥɨɠɟɧɧɵɣ ɜ
ɧɚɱɚɥɟ ɤɨɨɪɞɢɧɚɬ, ɢ ɬɨɱɤɢ ɩɨɜɟɪɯɧɨɫɬɢ
1
1 1
1 1 1
(
)
(
)
,
,
, ,
, ...,
,
, ,
m m m m m m
P f
P f
T M
H T M
T M
H
T M
(19)
ɝɞɟ
1
,
H
…,
m
H
—
ɧɟɡɚɜɢɫɢɦɵɟ ɫɥɭɱɚɣɧɵɟ ɜɟɥɢɱɢɧɵ (ɩɨɝɪɟɲɧɨɫɬɢ),
ɪɚɫɩɪɟɞɟɥɟɧɧɵɟ ɩɨ ɧɨɪɦɚɥɶɧɨɦɭ ɡɚɤɨɧɭ ɫ ɧɭɥɟɜɵɦ ɦɚɬɟɦɚɬɢɱɟɫɤɢɦ
ɨɠɢɞɚɧɢɟɦ ɢ ɨɞɢɧɚɤɨɜɨɣ ɞɢɫɩɟɪɫɢɟɣ.
Ⱦɚɥɟɟ ɞɥɹ ɬɨɱɟɤ
1
,
P
…,
m
P
ɢɡ (17) ɩɪɢɧɹɬɵ ɨɛɨɡɧɚɱɟɧɢɹ
1
1 1
1
(
)
(
)
.
,
, ...,
,
m
m m m
R f
R f
T M
H
T M
H
(20)
ɑɢɫɥɨ
R
ɜɢɞɚ
1
1
m
j
j
R
R
m
¦
(21)
ɧɚɡɵɜɚɟɬɫɹ ɫɪɟɞɧɟɜɵɛɨɪɨɱɧɵɦ ɪɚɞɢɭɫɨɦ ɬɨɱɟɤ (19) ɞɥɹ ɩɨɜɟɪɯɧɨ-
ɫɬɢ (18).
Ʉɚɤ ɛɵɥɨ ɨɩɢɫɚɧɨ, ɧɚ ɩɪɹɦɨɭɝɨɥɶɧɢɤɟ ɉ ɫɨɡɞɚɸɬɫɹ ɩɫɟɜɞɨɫɟɬɤɚ
ɜɢɞɚ (10)
^
`
( , ) : 0
1, 0
i
k
i
C
i N
k n
W W
d d
d d
(22)
ɢ ɛɚɡɢɫ ɥɨɤɚɥɶɧɵɯ ɫɩɥɚɣɧɨɜ
1
,
S
<
2
,
S
<
i
k
S
1
1, 3
1 ,
i N
k n
d d
d d
,
n
S
x
1
,
n
S
x
ɨɩɪɟɞɟɥɟɧɧɵɣ ɜ (12).
Ɋɚɧɟɟ ɨɩɪɟɞɟɥɹɥɨɫɶ, ɤɚɤɢɦ ɨɛɪɚɡɨɦ ɩɫɟɜɞɨɫɟɬɤɚ (22) ɢɧɞɭɰɢɪɭɟɬ
ɧɚ ɩɪɹɦɨɭɝɨɥɶɧɢɤɟ ɉ ɭɤɥɚɞɤɭ, ɹɜɥɹɸɳɭɸɫɹ ɟɝɨ ɩɨɞɪɚɡɞɟɥɟɧɢɟɦ ɧɚ
ɛɨɥɟɟ ɦɟɥɤɢɟ ɩɪɹɦɨɭɝɨɥɶɧɢɤɢ. Ɂɞɟɫɶ ɫɟɬɤɚ (22) ɜɵɛɢɪɚɟɬɫɹ ɬɚɤɢɦ
ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɜ ɤɚɠɞɵɣ ɩɪɹɦɨɭɝɨɥɶɧɢɤ ɷɬɨɣ ɭɤɥɚɞɤɢ ɩɨɩɚɥɨ ɨɞɢ-