ɬɨɥɶɤɨ ɧɚ ɜɟɥɢɱɢɧɭ
n
1
/T
y
&
ɤɚɤ ɜ ɜɵɪɚɠɟɧɢɢ
"+.#&
ɧɨ ɬɚɤɠɟ ɧɚ ɜɟɥɢ
'
ɱɢɧɭ
n
1
/
2
T
y
(
ɗɬɢ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ ɨɛɭɫɥɨɜɥɟɧɵ ɩɪɨ
'
ɫɬɪɚɧɫɬɜɟɧɧɨɣ ɞɢɫɤɪɟɬɢɡɚɰɢɟɣ
"
ɜɞɨɥɶ ɤɨɨɪɞɢɧɚɬɧɨɣ ɨɫɢ
y
0
#&
ɤɨɬɨɪɚɹ ɜ
ɤɚɠɞɨɦ ɩɨɥɭɤɚɞɪɟ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɫ ɩɟɪɢɨɞɨɦ
&
ɪɚɜɧɵɦ
2
T
y
(
ȼ ɬɨ ɠɟ
ɜɪɟɦɹ
&
ɡɚ ɞɜɚ ɩɨɥɭɤɚɞɪɚ ɩɟɪɢɨɞ ɞɢɫɤɪɟɬɢɡɚɰɢɢ ɫɨɫɬɚɜɥɹɟɬ ɡɧɚɱɟɧɢɟ
&
ɪɚɜɧɨɟ
T
y
(
ȼɫɥɟɞɫɬɜɢɟ ɷɬɨɝɨ ɩɪɢ ɱɟɪɟɫɫɬɪɨɱɧɨɦ ɡɚɤɨɧɟ ɫɤɚɧɢɪɨɜɚɧɢɹ
ɦɨɠɧɨ ɨɠɢɞɚɬɶ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɩɨɦɟɯ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɣ ɞɢɫɤɪɟɬɢɡɚ
'
ɰɢɢ
&
ɛ
©i
ɥɶɲɢɯ
&
ɱɟɦ ɩɪɢ ɩɪɨɝɪɟɫɫɢɜɧɨɦ ɡɚɤɨɧɟ
(
Ɉɞɧɚɤɨ ɩɪɢ ɱɟɪɟɫɫɬɪɨɱ
'
ɧɨɦ ɡɚɤɨɧɟ ɩɨɥɭɤɚɞɪɵ ɫɥɟɞɭɸɬ ɫ ɱɚɫɬɨɬɨɣ
&
ɜ ɞɜɚ ɪɚɡɚ ɛ
i
ɥɶɲɟɣ
&
ɱɟɦ
ɩɪɢ ɩɪɨɝɪɟɫɫɢɜɧɨɦ ɡɚɤɨɧɟ
(
ɉɨɷɬɨɦɭ ɢɡ
'
ɡɚ ɢɧɟɪɰɢɨɧɧɨɫɬɢ ɡɪɢɬɟɥɶɧɨɣ
ɫɢɫɬɟɦɵ ɞɟɣɫɬɜɢɟ ɷɬɢɯ ɩɨɦɟɯ ɨɫɥɚɛɥɟɧɨ
(
ɑɬɨɛɵ ɤɨɥɢɱɟɫɬɜɟɧɧɨ ɨɰɟɧɢɬɶ ɨɩɢɫɚɧɧɵɣ ɷɮɮɟɤɬ
&
ɛɵɥɢ ɩɪɢɧɹɬɵ
ɤɨɧɤɪɟɬɧɵɟ ɡɧɚɱɟɧɢɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɢ ɩɚɪɚɦɟɬɪɨɜ ɫɬɪɭɤɬɭɪɧɵɯ ɷɥɟ
'
ɦɟɧɬɨɜ ɦɨɞɟɥɢ Ɉɗɉ
&
ɩɪɟɞɫɬɚɜɥɟɧɧɨɣ ɧɚ ɪɢɫ
( -(
ȼ ɱɚɫɬɧɨɫɬɢ
&
ɜ ɤɚɱɟɫɬɜɟ
ɦɨɞɟɥɢ ɢɫɬɨɱɧɢɤɚ ɫɢɝɧɚɥɚ ɛɵɥɚ ɩɪɢɧɹɬɚ ɦɨɞɟɥɶ ɬɨɱɟɱɧɨɝɨ ɨɛɴɟɤɬɚ
&
ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɫɩɟɤɬɪɚɥɶɧɨɣ ɹɪɤɨɫɬɢ ɤɨɬɨɪɨɝɨ ɢɦɟɟɬ ɜɢɞ
b
L
w
(
x, y, t, w
) = b
J
w
(
w
)
p
(
x, y
)
,
(
,2
)
ɝɞɟ
b
J
w
(
w
)
ɩɪɢɪɚɳɟɧɢɟ ɫɩɟɤɬɪɚɥɶɧɨɣ ɫɢɥɵ ɢɡɥɭɱɟɧɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨ
ɫɢɥɵ ɢɡɥɭɱɟɧɢɹ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨ ɪɚɜɧɨɦɟɪɧɨɝɨ ɮɨɧɚ
(
ɉɨɥɢɯɪɨɦɚɬɢɱɟɫɤɚɹ ɮɭɧɤɰɢɹ ɪɚɫɫɟɹɧɢɹ ɨɩɬɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɚɩ
'
ɩɪɨɤɫɢɦɢɪɨɜɚɧɚ ɞɜɭɦɟɪɧɨɣ ɮɭɧɤɰɢɟɣ Ƚɚɭɫɫɚ ɜɢɞɚ
H
N
(
x
0
, y
0
) =
1
2
{r
2
i
exp
μ
a
x
0
2
+
y
0
2
2
r
2
i
¶
;
(
,3
)
ɡɞɟɫɶ
r
i
ɷɮɮɟɤɬɢɜɧɵɣ ɪɚɞɢɭɫ ɩɹɬɧɚ ɪɚɫɫɟɹɧɢɹ ɨɩɬɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ
&
ɤɨɬɨɪɵɣ ɨɩɪɟɞɟɥɹɥɫɹ ɜ ɞɨɥɹɯ ɩɟɪɢɨɞɚ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɣ ɞɢɫɤɪɟɬɢɡɚ
'
ɰɢɢ
4
r
i
=
T
y
/
4
&
ɩɪɢɱɟɦ
T
y
= 0
,
05
ɦɦ
(
ɉɪɨɫɬɪɚɧɫɬɜɟɧɧɵɣ ɢɦɩɭɥɶɫɧɵɣ ɨɬɤɥɢɤ ɉɂ ɨɩɪɟɞɟɥɹɥɫɹ ɫɥɟɞɭɸ
'
ɳɢɦ ɨɛɪɚɡɨɦ
4
H
ɉɂ
(
x
V
, y
V
) =
1
A
ɉɂ
l_]n
μ
x
0
a
ɉɂ
,
y
0
b
ɉɂ
¶
,
(
-*
)
ɝɞɟ
a
ɉɂ
=
b
ɉɂ
=
T
y
ɪɚɡɦɟɪɵ ɱɭɜɫɬɜɢɬɟɥɶɧɨɝɨ ɷɥɟɦɟɧɬɚ ɉɂ
5
A
ɉɂ
=
=
a
ɉɂ
b
ɉɂ
ɩɥɨɳɚɞɶ ɱɭɜɫɬɜɢɬɟɥɶɧɨɝɨ ɷɥɟɦɟɧɬɚ ɉɂ
(
ɂɦɩɭɥɶɫɧɵɣ ɨɬɤɥɢɤ ȼɄɍ ɚɩɩɪɨɤɫɢɦɢɪɨɜɚɧ ɜɵɪɚɠɟɧɢɟɦ
"++#&
ɜ ɤɨ
'
ɬɨɪɨɦ ɩɚɪɚɦɟɬɪ
r
ȼɄɍ
ɛɵɥ ɩɪɢɧɹɬ ɪɚɜɧɵɦ
T
y
/
3
(
ɉɟɪɢɨɞ ɫɥɟɞɨɜɚɧɢɹ ɤɚɞɪɨɜ ɞɥɹ ɩɪɨɝɪɟɫɫɢɜɧɨɝɨ ɢ ɱɟɪɟɫɫɬɪɨɱɧɨɝɨ ɡɚ
'
ɤɨɧɨɜ ɛɵɥ ɨɞɢɧɚɤɨɜɵɦ
4
T
ɤ
= 0
,
04
ɫ
(
Ⱦɥɹ ɩɪɨɝɪɟɫɫɢɜɧɨɝɨ ɡɚɤɨɧɚ ɛɵ
'
ɥɢ ɩɪɢɧɹɬɵ ɡɧɚɱɟɧɢɹ
s
]
= 0
,
813
&
s
ɤ
= 0
,
92
&
ɚ ɞɥɹ ɱɟɪɟɫɫɬɪɨɱɧɨɝɨ ɡɚ
'
ɤɨɧɚ ɢɫɩɨɥɶɡɨɜɚɧɵ ɡɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ
&
ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɫɬɚɧɞɚɪɬɭ
CMMH *,-0'-3--(
ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ
(
ɇ
(
ɗ
(
Ȼɚɭɦɚɧɚ
(
ɋɟɪ
(
ɉɪɢɛɨɪɨɫɬɪɨɟɧɢɟ
( ,**/(
ʋ
+ +/
