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ɧɟɧɬɨɜ. ɉɨɷɬɨɦɭ ɫɤɨɪɨɫɬɶ ɜ ɤɚɠɞɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɞɨɥɠɧɚ ɛɵɬɶ ɜɵɱɢɫ-
ɥɟɧɚ ɤɚɤ ɪɚɡɧɨɫɬɶ
1
i
i
C
Q
{ vv
v
j
ɫɤɨɪɨɫɬɟɣ ɩɪɹɦɨɝɨ ɢ ɨɛɪɚɬɧɨɝɨ ɩɪɟɜɪɚɳɟɧɢɣ. ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɪɚɡɞɟ-
ɥɢɬɶ ɞɜɚ ɷɬɢɯ ɜɫɬɪɟɱɧɵɯ ɩɨɬɨɤɚ ɧɟɜɨɡɦɨɠɧɨ, ɨɞɧɚɤɨ ɞɥɹ v
+
ɢ v
–
ɦɨɠɧɨ ɡɚ-
ɩɢɫɚɬɶ ɭɪɚɜɧɟɧɢɹ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ:
11
() () ()
j
i
mn
i
ij
CC
Q
Q
W W Wvk k . (I.17)
ɗɬɨ ɭɪɚɜɧɟɧɢɟ ɫɨ ɜɫɟɣ ɨɩɪɟɞɟɥɟɧɧɨɫɬɶɸ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɟɫɥɢ ɤɨɧɫɬɚɧɬɚ
ɫɤɨɪɨɫɬɢ ɨɛɪɚɬɧɨɣ ɪɟɚɤɰɢɢ k
–
z 0, ɬɨ ɜɫɬɪɟɱɧɨɟ ɩɪɟɜɪɚɳɟɧɢɟ ɞɨɥɠɧɨ ɫɭ-
ɳɟɫɬɜɨɜɚɬɶ. Ɉɧɨ ɦɨɠɟɬ ɩɪɨɢɫɯɨɞɢɬɶ ɜ ɤɪɚɣɧɟ ɧɟɡɧɚɱɢɬɟɥɶɧɨɣ ɫɬɟɩɟɧɢ ɢɥɢ
ɧɚɨɛɨɪɨɬ – ɛɵɬɶ ɜɟɫɶɦɚ ɫɭɳɟɫɬɜɟɧɧɵɦ. ɗɬɨ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɨɥɶɤɨ ɫɨɨɬɧɨ-
ɲɟɧɢɟɦ ɤɨɧɫɬɚɧɬ. ȿɫɥɢ k
–
" k
+
, ɬɨ ɝɨɜɨɪɹɬ, ɱɬɨ ɪɟɚɤɰɢɹ ɹɜɥɹɟɬɫɹ ɩɪɚɤɬɢ-
ɱɟɫɤɢ ɧɟɨɛɪɚɬɢɦɨɣ. Ɉɬɦɟɬɢɦ, ɱɬɨ ɤɨɧɫɬɚɧɬɵ k
+
ɢ k
–
ɯɚɪɚɤɬɟɪɢɡɭɸɬ ɜ ɤɢ-
ɧɟɬɢɱɟɫɤɨɦ ɨɬɧɨɲɟɧɢɢ ɪɚɡɧɵɟ ɩɪɨɰɟɫɫɵ ɢ ɩɨɷɬɨɦɭ ɧɟɡɚɜɢɫɢɦɵ.
ɍɪɚɜɧɟɧɢɟ (I.17) ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɤɢɧɟɬɢɱɟɫɤɨɟ
ɭɪɚɜɧɟɧɢɟ, ɩɨɞɨɛɧɨɟ ɬɟɦ, ɤɚɤɢɟ ɦɵ ɪɟɲɚɥɢ ɜ ɩɩ. 5, 6. ɉɨɥɭɱɢɦ ɟɝɨ ɪɟɲɟ-
ɧɢɟ ɞɥɹ ɫɚɦɨɣ ɩɪɨɫɬɨɣ ɪɟɚɤɰɢɢ, ɢɞɭɳɟɣ ɩɨ ɩɟɪɜɨɦɭ ɩɨɪɹɞɤɭ ɜ ɨɛɨɢɯ ɧɚ-
ɩɪɚɜɥɟɧɢɹɯ:
A
ĺ
ĸ
B.
(I.18)
ɍɪɚɜɧɟɧɢɟ (I.17) ɩɪɢɨɛɪɟɬɚɟɬ ɜɢɞ:
A
AB
CC
kkC
)
ɢɥɢ, ɩɨɫɥɟ ɩɨɞɫɬɚɧɨɜɤɢ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɨɣ ɫɜɹɡɢ ɦɟɠɞɭ C
A
ɢ C
B
,
00
() (
A
AA
CCC
kk k
B
C .
ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɟɝɨ ɜ ɤɨɧɟɱɧɨɦ ɫɱɟɬɟ ɞɚɟɬ ɤɢɧɟɬɢɱɟɫɤɢɣ ɡɚɤɨɧ
00 00
(
AB AB
A
CC CC
Ce
)
kk
kk kk
kk
W
(I.19)
ɞɥɹ ɤɨɧɰɟɧɬɪɚɰɢɢ
A, ɢ
00 00
()
AB AB
B
CC CC
Ce
W
kk
kk kk
kk
ɞɥɹ ɤɨɧɰɟɧɬɪɚɰɢɢ
B.
ɗɬɨɬ ɜɵɜɨɞ ɢɧɬɟɪɟɫɟɧ ɬɟɦ, ɱɬɨ ɩɪɢ
W ĺ f ɨɛɟ ɮɭɧɤɰɢɢ C
A
(W) ɢ C
B
(W)
ɢɦɟɸɬ ɤɨɧɟɱɧɵɟ ɩɪɟɞɟɥɵ:
00
lim [ ]
AB
A
CC
CA
Wf
{
kk
k
'
,
00
lim [ ]
AB
B
CC
CB
Wf
{
kk
k
'
,
21
ɤɨɬɨɪɵɟ ɦɵ ɛɭɞɟɦ ɨɛɨɡɧɚɱɚɬɶ ɫɩɟɰɢɚɥɶɧɵɦɢ ɫɢɦɜɨɥɚɦɢ [A], [B]. Ɍɚɤɢɦ
ɨɛɪɚɡɨɦ, ɜ ɫɢɫɬɟɦɟ ɫ ɨɛɪɚɬɢɦɨɣ ɪɟɚɤɰɢɟɣ ɜɫɟɝɞɚ ɨɫɬɚɸɬɫɹ ɨɩɪɟɞɟɥɟɧɧɵɟ
ɤɨɥɢɱɟɫɬɜɚ ɢ ɢɫɯɨɞɧɨɝɨ ɜɟɳɟɫɬɜɚ, ɢ ɩɪɨɞɭɤɬɚ.
10. ɏɢɦɢɱɟɫɤɨɟ ɪɚɜɧɨɜɟɫɢɟ
Ɂɚɞɚɱɚ, ɪɟɲɟɧɧɚɹ ɜ ɩɪɟɞɵɞɭɳɟɦ ɩɭɧɤɬɟ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɫɢɫɬɟɦɚ ɫ ɨɛ-
ɪɚɬɢɦɨɣ ɪɟɚɤɰɢɟɣ ɩɪɢɯɨɞɢɬ ɜ ɫɨɫɬɨɹɧɢɟ, ɜ ɤɨɬɨɪɨɦ ɨɛɳɚɹ ɫɤɨɪɨɫɬɶ ɪɟɚɤ-
ɰɢɢ
v = 0 ɩɪɢ ɨɬɥɢɱɧɵɯ ɨɬ ɧɭɥɹ ɫɤɨɪɨɫɬɹɯ ɩɪɹɦɨɝɨ ɢ ɨɛɪɚɬɧɨɝɨ ɩɪɟɜɪɚɳɟ-
ɧɢɣ. ȼ ɫɚɦɨɦ ɞɟɥɟ, ɤɨɥɶ ɫɤɨɪɨ ɧɢ ɨɞɧɨ ɢɡ ɜɟɳɟɫɬɜ ɧɟ ɢɫɱɟɡɚɟɬ,
lim [ ]
A
Wf
vk
'
ɢ . ȼ ɬɨ ɠɟ ɫɚɦɨɟ ɜɪɟɦɹ, ɤɚɤ ɫɥɟɞɭɟɬ ɢɡ ɪɟ-
ɲɟɧɢɹ (I.19),
li .
lim [ ]B
Wf
vk
'
m0
A
C
Wf
'
ȼ ɨɛɳɟɦ ɜɢɞɟ ɞɥɹ ɨɛɪɚɬɢɦɨɣ ɪɟɚɤɰɢɢ
m-ɝɨ ɩɨɪɹɞɤɚ ɜ ɩɪɹɦɨɦ ɧɚɩɪɚɜ-
ɥɟɧɢɢ ɢ
n-ɝɨ – ɜ ɨɛɪɚɬɧɨɦ ɫɭɳɟɫɬɜɭɟɬ ɫɨɫɬɨɹɧɢɟ, ɩɪɢ ɤɨɬɨɪɨɦ
v = 0, v
+
, v
–
z 0. (I.20)
ɗɬɨ ɫɨɫɬɨɹɧɢɟ ɧɚɡɵɜɚɟɬɫɹ
ɞɢɧɚɦɢɱɟɫɤɢɦ ɯɢɦɢɱɟɫɤɢɦ ɪɚɜɧɨɜɟɫɢɟɦ, ɚɭɫɥɨ-
ɜɢɟ (I.20) –
ɤɢɧɟɬɢɱɟɫɤɢɦ ɭɫɥɨɜɢɟɦ ɯɢɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ. ɋɥɨɜɨ «ɞɢ-
ɧɚɦɢɱɟɫɤɨɟ» ɨɡɧɚɱɚɟɬ, ɱɬɨ ɜ ɫɨɫɬɨɹɧɢɢ ɪɚɜɧɨɜɟɫɢɹ ɜɫɟɝɞɚ, ɢ ɫ ɪɚɜɧɵɦɢ
ɫɤɨɪɨɫɬɹɦɢ, ɫɭɳɟɫɬɜɭɸɬ ɜɫɬɪɟɱɧɵɟ ɩɨɬɨɤɢ: ɩɪɹɦɨɣ «
» ɢ ɨɛɪɚɬɧɵɣ «–».
Ʉɨɧɰɟɧɬɪɚɰɢɢ ɜɟɳɟɫɬɜ, ɭɫɬɚɧɨɜɢɜɲɢɟɫɹ ɜ ɯɢɦɢɱɟɫɤɨɦ ɪɚɜɧɨɜɟɫɢɢ, ɧɚɡɵ-
ɜɚɸɬɫɹ
ɪɚɜɧɨɜɟɫɧɵɦɢ ɤɨɧɰɟɧɬɪɚɰɢɹɦɢ ɢ ɨɛɨɡɧɚɱɚɸɬɫɹ [A
i
], [BB
j
].
ɉɪɢɦɟɧɢɦ ɡɚɤɨɧ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ ɞɥɹ ɫɨɫɬɨɹɧɢɹ ɯɢɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨ-
ɜɟɫɢɹ. ɉɨɫɤɨɥɶɤɭ ɜɟɳɟɫɬɜɚ ɫɨɞɟɪɠɚɬɫɹ ɜ ɫɜɨɢɯ ɪɚɜɧɨɜɟɫɧɵɯ ɤɨɧɰɟɧɬɪɚɰɢ-
ɹɯ, ɫɨɝɥɚɫɧɨ ɭɫɥɨɜɢɸ (I.20)
11
[] [ ] 0
j
i
mn
ij
ij
AB
Q
Q
kk . (I.21)
Ɉɛɚ ɱɥɟɧɚ ɫɥɟɜɚ, ɜ ɨɬɥɢɱɢɟ ɨɬ (I.17), ɧɟ ɡɚɜɢɫɹɬ ɨɬ ɜɪɟɦɟɧɢ, ɢ ɨɛɚ ɱɥɟɧɚ (ɟɫɥɢ
k
+
ɢ k
–
ɤɨɧɟɱɧɵ) ɧɟ ɪɚɜɧɵ ɧɭɥɸ. ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɭɪɚɜɧɟɧɢɟ (I.21) ɢɦɟɥɨ
ɛɵ ɬɪɢɜɢɚɥɶɧɨɟ ɪɟɲɟɧɢɟ: [
A
i
] = 0 ɢ [BB
j
] = 0 ɨɞɧɨɜɪɟɦɟɧɧɨ. Ɍɟɦ ɫɚɦɵɦ, ɫɨ-
ɫɬɨɹɧɢɟ ɪɚɜɧɨɜɟɫɢɹ ɦɨɠɧɨ ɨɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶ ɬɚɤ, ɱɬɨ ɜ ɧɟɦ ɨɞɧɨɜɪɟɦɟɧɧɨ
ɩɪɢɫɭɬɫɬɜɭɸɬ, ɜ ɤɨɧɟɱɧɵɯ ɤɨɧɰɟɧɬɪɚɰɢɹɯ ɜɫɟ ɭɱɚɫɬɧɢɤɢ ɪɟ-
ɚɤɰɢɢ. ɇɚɛɥɸɞɚɬɟɥɶ, ɢɡɦɟɪɹɸɳɢɣ ɜ ɪɚɡɧɵɟ ɦɨɦɟɧɬɵ ɜɪɟɦɟɧɢ ɢɯ ɤɨɧɰɟɧɬɪɚ-
ɰɢɢ, ɧɟ ɨɛɧɚɪɭɠɢɬ ɧɢɤɚɤɢɯ ɢɡɦɟɧɟɧɢɣ ɢ ɭɫɬɚɧɨɜɢɬ, ɱɬɨ
ɫɨɫɭɳɟɫɬɜɭɸɬ
0
i
C
.
ɍɪɚɜɧɟɧɢɟ (I.21) ɩɨɥɟɡɧɨ ɩɪɟɨɛɪɚɡɨɜɚɬɶ ɬɚɤ, ɱɬɨɛɵ ɤɨɧɰɟɧɬɪɚɰɢɢ ɤɨɦ-
ɩɨɧɟɧɬɨɜ ɨɫɬɚɜɚɥɢɫɶ ɜ ɨɞɧɨɣ ɱɚɫɬɢ:
1
1
[]
.
[]
j
i
n
j
j
m
i
i
B
K
A
Q
Q
{
k
k
(I.22)
22
ɧɟɧɬɨɜ. ɉɨɷɬɨɦɭ ɫɤɨɪɨɫɬɶ ɜ ɤɚɠɞɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɞɨɥɠɧɚ ɛɵɬɶ ɜɵɱɢɫ- ɤɨɬɨɪɵɟ ɦɵ ɛɭɞɟɦ ɨɛɨɡɧɚɱɚɬɶ ɫɩɟɰɢɚɥɶɧɵɦɢ ɫɢɦɜɨɥɚɦɢ [A], [B]. Ɍɚɤɢɦ
ɥɟɧɚ ɤɚɤ ɪɚɡɧɨɫɬɶ ɨɛɪɚɡɨɦ, ɜ ɫɢɫɬɟɦɟ ɫ ɨɛɪɚɬɢɦɨɣ ɪɟɚɤɰɢɟɣ ɜɫɟɝɞɚ ɨɫɬɚɸɬɫɹ ɨɩɪɟɞɟɥɟɧɧɵɟ
1 ɤɨɥɢɱɟɫɬɜɚ ɢ ɢɫɯɨɞɧɨɝɨ ɜɟɳɟɫɬɜɚ, ɢ ɩɪɨɞɭɤɬɚ.
v{ Ci v v
Qi
10. ɏɢɦɢɱɟɫɤɨɟ ɪɚɜɧɨɜɟɫɢɟ
ɫɤɨɪɨɫɬɟɣ ɩɪɹɦɨɝɨ ɢ ɨɛɪɚɬɧɨɝɨ ɩɪɟɜɪɚɳɟɧɢɣ. ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɪɚɡɞɟ-
ɥɢɬɶ ɞɜɚ ɷɬɢɯ ɜɫɬɪɟɱɧɵɯ ɩɨɬɨɤɚ ɧɟɜɨɡɦɨɠɧɨ, ɨɞɧɚɤɨ ɞɥɹ v+ ɢ v– ɦɨɠɧɨ ɡɚ- Ɂɚɞɚɱɚ, ɪɟɲɟɧɧɚɹ ɜ ɩɪɟɞɵɞɭɳɟɦ ɩɭɧɤɬɟ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɫɢɫɬɟɦɚ ɫ ɨɛ-
ɩɢɫɚɬɶ ɭɪɚɜɧɟɧɢɹ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ: ɪɚɬɢɦɨɣ ɪɟɚɤɰɢɟɣ ɩɪɢɯɨɞɢɬ ɜ ɫɨɫɬɨɹɧɢɟ, ɜ ɤɨɬɨɪɨɦ ɨɛɳɚɹ ɫɤɨɪɨɫɬɶ ɪɟɚɤ-
m n
v(W) k CiQi (W) k C j j (W) .
Q
(I.17) ɰɢɢ v = 0 ɩɪɢ ɨɬɥɢɱɧɵɯ ɨɬ ɧɭɥɹ ɫɤɨɪɨɫɬɹɯ ɩɪɹɦɨɝɨ ɢ ɨɛɪɚɬɧɨɝɨ ɩɪɟɜɪɚɳɟ-
i 1 j 1 ɧɢɣ. ȼ ɫɚɦɨɦ ɞɟɥɟ, ɤɨɥɶ ɫɤɨɪɨ ɧɢ ɨɞɧɨ ɢɡ ɜɟɳɟɫɬɜ ɧɟ ɢɫɱɟɡɚɟɬ,
ɗɬɨ ɭɪɚɜɧɟɧɢɟ ɫɨ ɜɫɟɣ ɨɩɪɟɞɟɥɟɧɧɨɫɬɶɸ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɟɫɥɢ ɤɨɧɫɬɚɧɬɚ lim v k [ A] ɢ lim v k [ B ] . ȼ ɬɨ ɠɟ ɫɚɦɨɟ ɜɪɟɦɹ, ɤɚɤ ɫɥɟɞɭɟɬ ɢɡ ɪɟ-
W'f W'f
ɫɤɨɪɨɫɬɢ ɨɛɪɚɬɧɨɣ ɪɟɚɤɰɢɢ k– z 0, ɬɨ ɜɫɬɪɟɱɧɨɟ ɩɪɟɜɪɚɳɟɧɢɟ ɞɨɥɠɧɨ ɫɭ-
ɳɟɫɬɜɨɜɚɬɶ. Ɉɧɨ ɦɨɠɟɬ ɩɪɨɢɫɯɨɞɢɬɶ ɜ ɤɪɚɣɧɟ ɧɟɡɧɚɱɢɬɟɥɶɧɨɣ ɫɬɟɩɟɧɢ ɢɥɢ ɲɟɧɢɹ (I.19), lim C A 0.
W'f
ɧɚɨɛɨɪɨɬ – ɛɵɬɶ ɜɟɫɶɦɚ ɫɭɳɟɫɬɜɟɧɧɵɦ. ɗɬɨ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɨɥɶɤɨ ɫɨɨɬɧɨ- ȼ ɨɛɳɟɦ ɜɢɞɟ ɞɥɹ ɨɛɪɚɬɢɦɨɣ ɪɟɚɤɰɢɢ m-ɝɨ ɩɨɪɹɞɤɚ ɜ ɩɪɹɦɨɦ ɧɚɩɪɚɜ-
ɲɟɧɢɟɦ ɤɨɧɫɬɚɧɬ. ȿɫɥɢ k– " k+, ɬɨ ɝɨɜɨɪɹɬ, ɱɬɨ ɪɟɚɤɰɢɹ ɹɜɥɹɟɬɫɹ ɩɪɚɤɬɢ- ɥɟɧɢɢ ɢ n-ɝɨ – ɜ ɨɛɪɚɬɧɨɦ ɫɭɳɟɫɬɜɭɟɬ ɫɨɫɬɨɹɧɢɟ, ɩɪɢ ɤɨɬɨɪɨɦ
ɱɟɫɤɢ ɧɟɨɛɪɚɬɢɦɨɣ. Ɉɬɦɟɬɢɦ, ɱɬɨ ɤɨɧɫɬɚɧɬɵ k+ ɢ k– ɯɚɪɚɤɬɟɪɢɡɭɸɬ ɜ ɤɢ- v = 0, v+, v– z 0. (I.20)
ɧɟɬɢɱɟɫɤɨɦ ɨɬɧɨɲɟɧɢɢ ɪɚɡɧɵɟ ɩɪɨɰɟɫɫɵ ɢ ɩɨɷɬɨɦɭ ɧɟɡɚɜɢɫɢɦɵ. ɗɬɨ ɫɨɫɬɨɹɧɢɟ ɧɚɡɵɜɚɟɬɫɹ ɞɢɧɚɦɢɱɟɫɤɢɦ ɯɢɦɢɱɟɫɤɢɦ ɪɚɜɧɨɜɟɫɢɟɦ, ɚ ɭɫɥɨ-
ɍɪɚɜɧɟɧɢɟ (I.17) ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɤɢɧɟɬɢɱɟɫɤɨɟ ɜɢɟ (I.20) – ɤɢɧɟɬɢɱɟɫɤɢɦ ɭɫɥɨɜɢɟɦ ɯɢɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ. ɋɥɨɜɨ «ɞɢ-
ɭɪɚɜɧɟɧɢɟ, ɩɨɞɨɛɧɨɟ ɬɟɦ, ɤɚɤɢɟ ɦɵ ɪɟɲɚɥɢ ɜ ɩɩ. 5, 6. ɉɨɥɭɱɢɦ ɟɝɨ ɪɟɲɟ- ɧɚɦɢɱɟɫɤɨɟ» ɨɡɧɚɱɚɟɬ, ɱɬɨ ɜ ɫɨɫɬɨɹɧɢɢ ɪɚɜɧɨɜɟɫɢɹ ɜɫɟɝɞɚ, ɢ ɫ ɪɚɜɧɵɦɢ
ɧɢɟ ɞɥɹ ɫɚɦɨɣ ɩɪɨɫɬɨɣ ɪɟɚɤɰɢɢ, ɢɞɭɳɟɣ ɩɨ ɩɟɪɜɨɦɭ ɩɨɪɹɞɤɭ ɜ ɨɛɨɢɯ ɧɚ- ɫɤɨɪɨɫɬɹɦɢ, ɫɭɳɟɫɬɜɭɸɬ ɜɫɬɪɟɱɧɵɟ ɩɨɬɨɤɢ: ɩɪɹɦɨɣ «» ɢ ɨɛɪɚɬɧɵɣ «–».
ɩɪɚɜɥɟɧɢɹɯ: Ʉɨɧɰɟɧɬɪɚɰɢɢ ɜɟɳɟɫɬɜ, ɭɫɬɚɧɨɜɢɜɲɢɟɫɹ ɜ ɯɢɦɢɱɟɫɤɨɦ ɪɚɜɧɨɜɟɫɢɢ, ɧɚɡɵ-
Aĺĸ B. (I.18) ɜɚɸɬɫɹ ɪɚɜɧɨɜɟɫɧɵɦɢ ɤɨɧɰɟɧɬɪɚɰɢɹɦɢ ɢ ɨɛɨɡɧɚɱɚɸɬɫɹ [Ai], [Bj]. B
ɍɪɚɜɧɟɧɢɟ (I.17) ɩɪɢɨɛɪɟɬɚɟɬ ɜɢɞ: ɉɪɢɦɟɧɢɦ ɡɚɤɨɧ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ ɞɥɹ ɫɨɫɬɨɹɧɢɹ ɯɢɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨ-
C A kC A kCB ɜɟɫɢɹ. ɉɨɫɤɨɥɶɤɭ ɜɟɳɟɫɬɜɚ ɫɨɞɟɪɠɚɬɫɹ ɜ ɫɜɨɢɯ ɪɚɜɧɨɜɟɫɧɵɯ ɤɨɧɰɟɧɬɪɚɰɢ-
ɢɥɢ, ɩɨɫɥɟ ɩɨɞɫɬɚɧɨɜɤɢ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɨɣ ɫɜɹɡɢ ɦɟɠɞɭ CA ɢ CB, ɹɯ, ɫɨɝɥɚɫɧɨ ɭɫɥɨɜɢɸ (I.20)
m n
C A (k k )C A k (C A0 CB0 ) .
Qj
k [ Ai ]Qi k [ B j ] 0. (I.21)
i 1 j 1
ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɟɝɨ ɜ ɤɨɧɟɱɧɨɦ ɫɱɟɬɟ ɞɚɟɬ ɤɢɧɟɬɢɱɟɫɤɢɣ ɡɚɤɨɧ
0 0 0 0
Ɉɛɚ ɱɥɟɧɚ ɫɥɟɜɚ, ɜ ɨɬɥɢɱɢɟ ɨɬ (I.17), ɧɟ ɡɚɜɢɫɹɬ ɨɬ ɜɪɟɦɟɧɢ, ɢ ɨɛɚ ɱɥɟɧɚ (ɟɫɥɢ
C A CB C A CB ( k k ) W k+ ɢ k– ɤɨɧɟɱɧɵ) ɧɟ ɪɚɜɧɵ ɧɭɥɸ. ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɭɪɚɜɧɟɧɢɟ (I.21) ɢɦɟɥɨ
CA k k e (I.19)
k k k k ɛɵ ɬɪɢɜɢɚɥɶɧɨɟ ɪɟɲɟɧɢɟ: [Ai] = 0 ɢ [Bj] = 0 ɨɞɧɨɜɪɟɦɟɧɧɨ. Ɍɟɦ ɫɚɦɵɦ, ɫɨ-
B
ɞɥɹ ɤɨɧɰɟɧɬɪɚɰɢɢ A, ɢ ɫɬɨɹɧɢɟ ɪɚɜɧɨɜɟɫɢɹ ɦɨɠɧɨ ɨɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶ ɬɚɤ, ɱɬɨ ɜ ɧɟɦ ɨɞɧɨɜɪɟɦɟɧɧɨ
0 0 0 0 ɩɪɢɫɭɬɫɬɜɭɸɬ, ɫɨɫɭɳɟɫɬɜɭɸɬ ɜ ɤɨɧɟɱɧɵɯ ɤɨɧɰɟɧɬɪɚɰɢɹɯ ɜɫɟ ɭɱɚɫɬɧɢɤɢ ɪɟ-
C A CB C A CB
CB k k e ( k k ) W ɚɤɰɢɢ. ɇɚɛɥɸɞɚɬɟɥɶ, ɢɡɦɟɪɹɸɳɢɣ ɜ ɪɚɡɧɵɟ ɦɨɦɟɧɬɵ ɜɪɟɦɟɧɢ ɢɯ ɤɨɧɰɟɧɬɪɚ-
k k k k ɰɢɢ, ɧɟ ɨɛɧɚɪɭɠɢɬ ɧɢɤɚɤɢɯ ɢɡɦɟɧɟɧɢɣ ɢ ɭɫɬɚɧɨɜɢɬ, ɱɬɨ C i 0 .
ɞɥɹ ɤɨɧɰɟɧɬɪɚɰɢɢ B. ɍɪɚɜɧɟɧɢɟ (I.21) ɩɨɥɟɡɧɨ ɩɪɟɨɛɪɚɡɨɜɚɬɶ ɬɚɤ, ɱɬɨɛɵ ɤɨɧɰɟɧɬɪɚɰɢɢ ɤɨɦ-
ɗɬɨɬ ɜɵɜɨɞ ɢɧɬɟɪɟɫɟɧ ɬɟɦ, ɱɬɨ ɩɪɢ W ĺ f ɨɛɟ ɮɭɧɤɰɢɢ CA(W) ɢ CB(W) ɩɨɧɟɧɬɨɜ ɨɫɬɚɜɚɥɢɫɶ ɜ ɨɞɧɨɣ ɱɚɫɬɢ:
ɢɦɟɸɬ ɤɨɧɟɱɧɵɟ ɩɪɟɞɟɥɵ: n
Qj
0 0 0 0 [Bj ]
C CB
lim C A k A
C CB
{ [ A] , lim CB k A { [ B] , j 1 k
{ K. (I.22)
W'f k k W'f k k m
Qi k
[ Ai ]
i 1
21 22
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