ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
128
ɝɞɟ
q
i
—
ɨɛɨɛɳɟɧɧɵɟ ɤɨɨɪɞɢɧɚɬɵ, ɢɡɦɟɧɹɸɳɢɟɫɹ ɩɪɢ ɩɟɪɟɯɨɞɟ ɨɬ
ɨɫɧɨɜɧɨɝɨ ɪɚɜɧɨɜɟɫɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɤ ɫɦɟɠɧɨɦɭ.
Ɏɭɧɤɰɢɹ
L
ɢ ɟɟ ɩɪɨɢɡɜɨɞɧɵɟ
i
L
q
w
w
ɪɚɜɧɵ ɧɭɥɸ ɥɢɲɶ ɩɪɢ
q
i
= 0.
Ɍɨɝɞɚ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɬɟɨɪɟɦɨɣ Ʌɟɠɺɧ-Ⱦɢɪɢɯɥɟ: «ȿɫɥɢ ɜ ɧɟɤɨɬɨɪɨɦ
(
ɨɫɧɨɜɧɨɦ) ɫɨɫɬɨɹɧɢɢ ɤɨɧɫɟɪɜɚɬɢɜɧɨɣ ɫɢɫɬɟɦɵ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪ-
ɝɢɹ ɦɢɧɢɦɚɥɶɧɚ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɡɧɚɱɟɧɢɹɦ ɷɧɟɪɝɢɢ ɜɫɟɯ ɫɦɟɠɧɵɯ
(
ɨɬɤɥɨɧɟɧɧɵɯ) ɫɨɫɬɨɹɧɢɣ ɫɢɫɬɟɦɵ, ɬɨ ɨɫɧɨɜɧɨɟ ɫɨɫɬɨɹɧɢɟ ɹɜɥɹɟɬɫɹ
ɩɨɥɨɠɟɧɢɟɦ ɭɫɬɨɣɱɢɜɨɝɨ ɪɚɜɧɨɜɟɫɢɹ», ɢ ɨɛɪɚɳɟɧɢɟɦ Ʌɹɩɭɧɨɜɚ ɷɬɨɣ
ɬɟɨɪɟɦɵ: «ȿɫɥɢ ɜ ɨɫɧɨɜɧɨɦ ɩɨɥɨɠɟɧɢɢ ɪɚɜɧɨɜɟɫɢɹ ɩɨɬɟɧɰɢɚɥɶɧɚɹ
ɷɧɟɪɝɢɹ ɧɟ ɹɜɥɹɟɬɫɹ ɦɢɧɢɦɚɥɶɧɨɣ, ɚ ɨɬɫɭɬɫɬɜɢɟ ɦɢɧɢɦɭɦɚ ɨɩɪɟɞɟɥɹ-
ɟɬɫɹ ɱɥɟɧɚɦɢ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ ɜ ɪɚɡɥɨɠɟɧɢɢ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ,
ɬɨ ɩɨɥɨɠɟɧɢɟ ɛɭɞɟɬ ɧɟɭɫɬɨɣɱɢɜɨ». ɂɡ ɭɫɥɨɜɢɹ ɪɚɜɧɨɜɟɫɢɹ ɨɫɧɨɜɧɨɝɨ
ɫɨɫɬɨɹɧɢɹ ɫɥɟɞɭɟɬ, ɫɨɝɥɚɫɧɨ ɷɬɢɦ ɬɟɨɪɟɦɚɦ, ɱɬɨ
0.
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Ȼɭɞɟɦ ɢɡɦɟɧɹɬɶ ɧɚɝɪɭɡɤɭ, ɩɪɢɥɨɠɟɧɧɭɸ ɤ ɫɢɫɬɟɦɟ, ɩɨɥɚɝɚɹ
0
0
;
,
P P kx Q Q lx
ɝɞɟ
k
,
l —
ɧɚɩɪɚɜɥɹɸɳɢɟ ɤɨɫɢɧɭɫɵ ɥɭɱɚ
A
n
(
ɫɦ. ɪɢɫɭɧɨɤ).
Ɍɨɝɞɚ ɜ ɧɨɜɨɦ ɫɨɫɬɨɹɧɢɢ, ɜ ɤɨɬɨɪɨɟ ɩɟɪɟɲɥɚ ɫɢɫɬɟɦɚ, ɩɨɥɧɚɹ
ɷɧɟɪɝɢɹ
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) .
2
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Ɉɛɨɡɧɚɱɢɜ
,
i
i
i
k l r
E
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ɛɭɞɟɦ ɢɦɟɬɶ
2
1
1 (
) ;
2
n
i
i
i
i
L
S r x q
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2
2
.
i
i
i
L S r x
q
w
w
Ɂɧɚɤ
r
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ɨɩɪɟɞɟɥɹɟɬɫɹ ɡɧɚɤɨɦ ɩɚɪɚɦɟɬɪɨɜ
k
ɢ
l
.
ɉɪɢ
r
> 0 ɞɥɹ ɧɟɤɨ-
ɬɨɪɨɝɨ ɡɧɚɱɟɧɢɹ
x
ɩɨɥɭɱɢɦ
2
2
0 ( 1, 2, ..., ).
i
i
i
L S r x
i
n
q
w
w
(1)
ɍɫɥɨɜɢɟ (1) ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɩɨɬɟɪɟ ɭɫɬɨɣɱɢɜɨɫɬɢ ɫɢɫɬɟɦɵ ɜ
ɫɦɵɫɥɟ Ʌɟɠɺɧ-Ⱦɢɪɢɯɥɟ ɢ Ʌɹɩɭɧɨɜɚ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɨɩɪɟɞɟɥɢɬɫɹ
ɩɚɪɚ ɤɪɢɬɢɱɟɫɤɢɯ ɡɧɚɱɟɧɢɣ
P
2
ɢ
Q
2
,
ɩɪɢ ɤɨɬɨɪɵɯ ɜɵɩɨɥɧɹɟɬɫɹ ɭɫɥɨ-