4
П.В. Храпов
Ȝ
Ȝ
(ȗ )
.
!
l
n n
n
e
P l
l
of
o
Ⱦɨɤɚɡɚɬɟɥɶɫɬɜɨ ɬɟɨɪɟɦɵ 1
. ȼɟɪɨɹɬɧɨɫɬɶ ɧɟɩɪɨɬɟɤɚɧɢɹ
( , , )
H S h p
ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɫɥɟɞɭɸɳɟɦ ɜɢɞɟ [3–5]:
1
2
( , , )
( , , ) ( , , ) ,
H S h p Z S h p Z S h p
(3)
ɝɞɟ
1
( , , )
...
m
j
j
j
Z S h p k k
* *
¦
,
1, 2
j
. (4)
ɋɭɦɦɢɪɨɜɚɧɢɟ ɢɞɟɬ ɩɨ ɜɫɟɦ ɞɨɩɭɫɬɢɦɵɦ ɧɚɛɨɪɚɦ ɤɨɧɬɭɪɨɜ, ɩɪɢ
ɷɬɨɦ
2
;
k p q
* *
*
1
0,
k
*
ɟɫɥɢ
,
R
*
ɢ
1
2
,
k k
* *
ɟɫɥɢ
.
R
*
ɉɪɢ ɢɫɫɥɟɞɨɜɚɧɢɢ ɪɚɜɟɧɫɬɜɚ (4) ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɬɟɨɪɢɟɣ ɤɥɚɫ-
ɬɟɪɧɵɯ ɪɚɡɥɨɠɟɧɢɣ [6, 7]. ɉɨɫɤɨɥɶɤɭ ɷɬɚ ɬɟɨɪɢɹ ɩɨɧɚɞɨɛɢɬɫɹ ɢ ɩɪɢ
ɞɨɤɚɡɚɬɟɥɶɫɬɜɟ ɚɧɚɥɨɝɢɱɧɨɣ ɬɟɨɪɟɦɵ ɞɥɹ ɦɨɞɟɥɢ ɂɡɢɧɝɚ, ɢɡɥɨɠɢɦ
ɧɭɠɧɵɟ ɧɚɦ ɮɚɤɬɵ ɜ ɨɛɳɟɦ ɜɢɞɟ.
ɉɭɫɬɶ
T
— ɫɱɟɬɧɨɟ ɦɧɨɠɟɫɬɜɨ ɫ ɦɟɬɪɢɤɨɣ
U
(
x
,
y
), ɩɪɢɱɟɦ ɞɥɹ
ɧɟɤɨɬɨɪɨɝɨ
d
> 0 ɦɨɳɧɨɫɬɶ
d
-ɨɤɪɟɫɬɧɨɫɬɢ ɥɸɛɨɣ ɬɨɱɤɢ
t
T
ɧɟ
ɩɪɟɜɨɫɯɨɞɢɬ
v
. ɇɚɡɨɜɟɦ ɪɚɡɛɢɟɧɢɟ
J
= {
*
1
, …,
*
k
} ɦɧɨɠɟɫɬɜɚ
/
T
ɞɨɩɭɫɬɢɦɵɦ, ɟɫɥɢ ɞɥɹ ɥɸɛɵɯ ɞɜɭɯ ɪɚɡɥɢɱɧɵɯ ɟɝɨ ɛɥɨɤɨɜ
*
i
,
*
j
ɢɦɟɟɬ
ɦɟɫɬɨ ɧɟɪɚɜɟɧɫɬɜɨ
U
(
*
i
,
*
j
)
d
. ɉɨɫɬɚɜɢɦ ɜ ɫɨɨɬɜɟɬɫɬɜɢɟ ɥɸɛɨɦɭ
ɤɨɧɟɱɧɨɦɭ
A
T
ɬɨɱɤɭ
t
A
A
. ȼɜɟɞɟɦ ɨɪɢɟɧɬɢɪɨɜɚɧɧɵɣ ɝɪɚɮ [7],
ɦɧɨɠɟɫɬɜɨɦ ɜɟɪɲɢɧ ɤɨɬɨɪɨɝɨ ɹɜɥɹɟɬɫɹ ɦɧɨɠɟɫɬɜɨ
F
=
F
(
T
) ɜɫɟɯ
ɤɨɧɟɱɧɵɯ ɩɨɞɦɧɨɠɟɫɬɜ
T
. ɂɡ ɜɟɪɲɢɧɵ
A
F
ɜɵɯɨɞɢɬ ɪɟɛɪɨ ɜ
ɜɟɪɲɢɧɭ
B
F
ɬɨɝɞɚ ɢ ɬɨɥɶɤɨ ɬɨɝɞɚ, ɤɨɝɞɚ
B
=
A
– {
t
A
}. ȼɟɪɲɢɧɚ
B
ɥɟɠɢɬ ɧɢɠɟ ɜɟɪɲɢɧɵ
A
, ɟɫɥɢ ɫɭɳɟɫɬɜɭɟɬ ɩɭɬɶ ɩɨ ɝɪɚɮɭ
F
,
ɧɚɱɢɧɚɸɳɢɣɫɹ ɜ
A
ɢ ɤɨɧɱɚɸɳɢɣɫɹ ɜ
B
. ɋɚɦɨɣ ɧɢɠɧɟɣ ɜɟɪɲɢɧɨɣ
ɞɟɪɟɜɚ
F
ɹɜɥɹɟɬɫɹ
. Ɋɚɫɫɦɨɬɪɢɦ ɭɩɨɪɹɞɨɱɟɧɧɵɟ ɧɚɛɨɪɵ
J
= {
B
1
,
A
1
; … ;
B
i
,
A
i
},
l
=
l
(
J
) 1 ɧɟɩɭɫɬɵɯ ɩɨɞɦɧɨɠɟɫɬɜ, ɭɞɨɜ-
ɥɟɬɜɨɪɹɸɳɢɟ ɫɥɟɞɭɸɳɢɦ ɭɫɥɨɜɢɹɦ.
1. Ⱦɥɹ ɥɸɛɵɯ
i
= 2, …,
l
ɥɢɛɨ
B
i
=
C
i
, ɥɢɛɨ
B
i
ɥɟɠɢɬ ɧɢɠɟ
C
i
, ɪɚɜɧɨɝɨ
1
1
1
1
1
,
,
,
{ :
, ȡ( , ) }.
i
i
i
i
i
i
i
i
i
i
i
B A m C B A A A A t T t A t A d
w w
2.
{ },
i
i
i
B
A B t
1,
i
A
t
1,..., .
i
l
ɉɭɫɬɶ ɞɥɹ ɤɚɠɞɨɝɨ ɧɚɛɨɪɚ ɤɨɧɬɭɪɨɜ
1
(Ȗ)
Ȗ { ,...,
},
l
* *
(Ȗ)
Ȗ
1
.
i
l
i
k
k
*
Ʌɟɦɦɚ 1
. ɉɪɢ ɞɨɫɬɚɬɨɱɧɨ ɦɚɥɵɯ
p
<
p
0
