8
П.В. Храпов
Ⱦɨɤɚɡɚɬɟɥɶɫɬɜɨ
. Ɂɚɩɢɲɟɦ ɜɟɪɨɹɬɧɨɫɬɶ
H
(
S
l
,
h
l
,
p
) ɜ ɫɥɟɞɭɸɳɟɦ
ɜɢɞɟ:
( , , ) exp{ ( , , )}.
l
l
l
l
H S h p
g S h p
ɉɭɫɬɶ
g
(
S
l
,
h
l
,
p
) <
N
. Ɍɨɝɞɚ ɭɜɟɥɢɱɢɜɚɟɦ
S
l
ɧɚ ɟɞɢɧɢɰɭ. əɫɧɨ, ɱɬɨ ɩɪɢ
ɷɬɨɦ
g
ɜɨɡɪɚɫɬɚɟɬ ɧɟ ɛɨɥɟɟ ɱɟɦ ɧɚ
( ) ,
l
h
l
h Cp
ɝɞɟ
C
— ɧɟɤɨɬɨɪɚɹ
ɚɛɫɨɥɸɬɧɚɹ ɤɨɧɫɬɚɧɬɚ. ɍɜɟɥɢɱɢɜɚɟɦ
S
l
ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ
g
ɧɟ ɫɬɚɧɟɬ
ɛɨɥɶɲɟ
N
. Ɂɚɬɟɦ ɭɜɟɥɢɱɢɜɚɟɦ
h
ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ
g
ɧɟ ɫɬɚɧɟɬ ɦɟɧɶɲɟ
N
, ɢ ɬ. ɞ. əɫɧɨ, ɱɬɨ ɬɟɩɟɪɶ ɢɡ ɷɬɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɨɛɴɟɦɨɜ
ɦɨɠɧɨ ɜɵɛɪɚɬɶ ɩɨɞɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɭɸ ɥɟɦɦɟ.
Ʌɟɦɦɚ ɞɨɤɚɡɚɧɚ.
Ɋɚɫɫɦɨɬɪɢɦ ɬɟɩɟɪɶ ɞɥɹ ɥɸɛɨɝɨ k = 1, 2, … ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ
ɨɛɴɟɦɨɜ
2
,
k
m i
/
/ ]
ɩɪɢ
,
m
of
,
,
,
k
k
m i
m j
/ /
,
1,..., ,
i j
k
ɬɚɤɭɸ, ɱɬɨ
Ȝ
,
{ȗ 0}
,
k
k
m i
m
P
e
of
o
ɝɞɟ
,
ȗ
k
m i
— ɫɥɭɱɚɣɧɚɹ ɜɟɥɢɱɢɧɚ, ɪɚɜɧɚɹ ɱɢɫ-
ɥɭ ɤɨɧɬɭɪɨɜ ɩɪɨɬɟɤɚɧɢɹ ɜ
,
,
k
m i
/
1,..., ;
i
k
2
]
— ɜɟɪɯɧɹɹ ɩɨɥɭɩɥɨɫ-
ɤɨɫɬɶ ɪɟɲɟɬɤɢ. ɗɬɨ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨɟ ɫɥɟɞɫɬɜɢɟ ɢɡ ɥɟɦɦɵ.
ȼɵɛɟɪɟɦ ɨɬɫɸɞɚ ɩɨɞɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɨɛɴɟɦɨɜ
,
,
j
j
k
m i
/
1, 2,...;
1,..., ,
j
j
i
k
ɬɚɤɭɸ, ɱɬɨ
( )
0,
m j
j
h
j m
j
k h Cp
of
o
ɝɞɟ
j
m
h
— ɜɵ-
ɫɨɬɚ ɨɛɴɟɦɚ
,
.
j
j
k
m i
/
Ɂɧɚɱɟɧɢɹ
j
m
h
ɜɵɛɢɪɚɟɦ ɫɬɪɨɝɨ ɦɨɧɨɬɨɧɧɨ ɜɨɡɪɚɫ-
ɬɚɸɳɢɟ,
k
j
ɛɟɪɟɦ ɦɨɧɨɬɨɧɧɨ (ɧɟ ɨɛɹɡɚɬɟɥɶɧɨ ɫɬɪɨɝɨ) ɜɨɡɪɚɫɬɚɸɳɢɦ.
ȼɵɛɨɪ ɤɨɧɫɬɚɧɬɵ
C
ɫɬɚɧɟɬ ɹɫɟɧ ɢɡ ɞɚɥɶɧɟɣɲɢɯ ɪɚɫɫɭɠɞɟɧɢɣ. Ʌɟɝɤɨ
ɜɢɞɟɬɶ, ɱɬɨ ɩɨɫɥɟ ɩɟɪɟɧɭɦɟɪɚɰɢɢ (
j
ĺ
n
) ɩɨɥɭɱɚɟɦ ɩɨɫɥɟɞɨɜɚ-
ɬɟɥɶɧɨɫɬɶ ɨɛɴɟɦɨɜ
/
n,i
,
n
= 1, 2, …,
i
= 1, …,
k
(
n
), ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɯ
ɩɭɧɤɬɭ ɚ).
ɉɭɧɤɬ ɛ) ɫɥɟɞɭɟɬ ɢɡ ɬɨɝɨ, ɱɬɨ
,1
,
{ȗ (ȗ ... ȗ )
n
n
n k
P
z
0} ( )( ) .
n
h
n
h k n Cp
z d
Ⱦɨɤɚɠɟɦ ɩɭɧɤɬ ɛ):
,
,
,
ȗ
,
n i
n i
R
*
* */
F
¦
1,..., ( ),
i
k n
ɝɞɟ
F
*
— ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɚɹ ɮɭɧɤɰɢɹ ɤɨɧɬɭɪɚ
*
. əɫɧɨ, ɱɬɨ
,
,
,
,
{ȗ 1}
(
, ),
n i
n i
n n
n i
R
P
p q H
p
* w*
* */
/ *
¦
ɝɞɟ
,
(
, )
n i
H
p
/ *
— ɜɟɪɨ-
ɹɬɧɨɫɬɶ ɧɟɩɪɨɬɟɤɚɧɢɹ ɜ ɨɛɴɟɦɟ
,
n i
/ *
(ɬ. ɟ. ɜ
,
n i
/ *
ɨɬɫɭɬɫɬɜɭɸɬ
ɤɨɧɬɭɪɵ
,
,
n i
R
/
c*
*
— ɡɚɦɵɤɚɧɢɟ ɜ
,
.
n i
/
ȼ ɬɨ ɠɟ ɜɪɟɦɹ
,
,
,
ȗ
.
n i
n i
R
M
p q
* w*
* */
¦
ɇɨ
,
,
( , )
(
, ) ( , ),
n i
n i
H p H
p H p
/ d / * *
ɬɚɤ ɤɚɤ
