ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
39
0
0
0
1
1
(
) (
)
(
) (
)
(
) ,
( )
( )
l
l
l
x f
x dx
x P x
P x dx
P
P
W
W
W
W
W
W
W
§
·
¨
¸
¨
¸
©
¹
³
³
ɨɬɤɭɞɚ
0
0
1
(
)
1
(
) (
)
(
)
(
) .
( )
( )
( )
l
l
P l
x f
x dx
l
P x dx
P
P
P
W
W
W
W
W
W
W
W
W
³
³
ɉɨɞɫɬɚɜɢɜ ɧɚɣɞɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɜ ɜɵɪɚɠɟɧɢɟ (6), ɩɨɥɭɱɢɦ ɢɫɤɨ-
ɦɭɸ ɮɨɪɦɭɥɭ (3).
ɋɜɨɣɫɬɜɚ ɩɨɤɚɡɚɬɟɥɹ
( )
l
ȡ lj .
Ɏɨɪɦɭɥɚ (3) ɩɨɡɜɨɥɹɟɬ ɭɫɬɚɧɨɜɢɬɶ
ɫɥɟɞɭɸɳɢɟ ɫɜɨɣɫɬɜɚ ɩɨɤɚɡɚɬɟɥɹ (2).
1.
ɂɦɟɟɬ ɦɟɫɬɨ ɨɰɟɧɤɚ
( )
,
l
l
W
U W
W
d
ɩɪɢɱɟɦ ɨɰɟɧɤɚ ɫɩɪɚɜɚ ɞɨɫɬɢɠɢɦɚ ɬɨɝɞɚ ɢ ɬɨɥɶɤɨ ɬɨɝɞɚ, ɤɨɝɞɚ
(
)
( ).
P l
P
W
W
2.
ɋɩɪɚɜɟɞɥɢɜɨ ɫɥɟɞɭɸɳɟɟ ɫɨɨɬɧɨɲɟɧɢɟ:
0
lim ( ) ,
l
l
r
W
U W
of
o
ɝɞɟ
0
( )
l
r P t dt
³
—
ɫɪɟɞɧɹɹ ɧɚɪɚɛɨɬɤɚ ɞɨ ɨɬɤɚɡɚ.
3.
ɂɦɟɟɬ ɦɟɫɬɨ ɮɨɪɦɭɥɚ
( )
(
) ( ) ( )
,
( )
l
l
P l
P
U W
W
O W
U W
W
W
W
w
w
(7)
ɝɞɟ ( )
O W
—
ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɨɬɤɚɡɨɜ,
( )
( )
.
( )
P
P
W
O W
W
c
(8)
ɉɟɪɜɵɟ ɞɜɚ ɫɜɨɣɫɬɜɚ ɨɱɟɜɢɞɧɵ, ɩɨɷɬɨɦɭ ɞɨɤɚɠɟɦ ɬɪɟɬɶɟ ɫɜɨɣɫɬɜɨ.
Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɜɡɹɜ ɱɚɫɬɧɭɸ ɩɪɨɢɡɜɨɞɧɭɸ ɩɨ ɩɟɪɟɦɟɧɧɨɣ
W
ɨɬ
ɩɪɚɜɨɣ ɱɚɫɬɢ (3), ɢɦɟɟɦ
2
( )
1 1
( ) (
) ( )
( )
( ) ,
( )
l
l
P P l P P P t dt
P
W
W
U W
W
W
W
W
W
W
§
·
w
c
¨
¸
¨
¸
w
©
¹
³
ɨɬɤɭɞɚ ɫ ɭɱɟɬɨɦ ɜɵɪɚɠɟɧɢɹ (8) ɩɨɥɭɱɢɦ ɮɨɪɦɭɥɭ (7).