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ȼɵɱɢɫɥɢɬɟɫɬɟɩɟɧɶɝɢɞɪɨɥɢɡɚɚɰɟɬɚɬɚɤɚɥɢɹɜɆɪɚɫɬɜɨɪɟɢS+
ɪɚɫɬɜɨɪɚ
Ɋɟɲɟɧɢɟ
ɍɪɚɜɧɟɧɢɟɪɟɚɤɰɢɢɝɢɞɪɨɥɢɡɚ
&+
&22í+2l&+&22+2+í
Ⱦɥɹɜɵɱɢɫɥɟɧɢɹɫɬɟɩɟɧɢ ɝɢɞɪɨɥɢɡɚ ɧɚɣɞɟɦɩɪɟɠɞɟɜɫɟɝɨɤɨɧɫɬɚɧɬɭ ɝɢɞ
ɪɨɥɢɡɚȾɥɹ ɷɬɨɝɨɜɨɫɩɨɥɶɡɭɟɦɫɹ ɡɧɚɱɟɧɢɟɦɤɨɧɫɬɚɧɬɵ ɞɢɫɫɨɰɢɚɰɢɢɭɤɫɭɫɧɨɣ
ɤɢɫɥɨɬɵɩɪɢɜɟɞɟɧɧɵɦɜɉɪɢɥɨɠɟɧɢɢÂ
.
.
Ƚ
.
+2
Ⱦ
í
Ɍɟɩɟɪɶɧɚɣɞɟɦɫɬɟɩɟɧɶɝɢɞɪɨɥɢɡɚ
.
ȕ
Ƚ
ɋ
Ɇ
ȾɥɹɜɵɱɢɫɥɟɧɢɹS+ ɫɥɟɞɭɟɬ ɩɪɢɧɹɬɶɜɨɜɧɢɦɚɧɢɟ ɱɬɨɜɪɟɡɭɥɶɬɚɬɟɝɢɞ
ɪɨɥɢɡɚɤɚɠɞɨɝɨɚɧɢɨɧɚ&+
ɧɚɹɤɨɧɰɟɧɬɪɚɰɢɹɝɢɞɪɨɥɢɡɭɸɳɢɯɫɹɢɨɧɨɜɋ
ɧɚEɬɨɩɪɢɝɢɞɪɨɥɢɡɟɨɛɪɚɡɨɜɚɥɨɫɶE
&
2+
ɋɥɟɞɨɜɚɬɟɥɶɧɨS2+ ±OJ
Ɉɬɫɸɞɚ
S+ S. S2+
&22íɨɛɪɚɡɭɟɬɫɹɨɞɢɧɝɢɞɪɨɤɫɢɞɢɨɧȿɫɥɢɢɫɯɨɞ
ɦɨɥɶɥɚɫɬɟɩɟɧɶɝɢɞɪɨɥɢɡɚɪɚɜ
0
Â&
ɦɨɥɶɥɢɨɧɨɜ2+íɌɚɤɢɦɨɛɪɚɡɨɦ
0
EÂ&0 Âí Âíɦɨɥɶɥ
&
±OJÂ ±±
2+
+2
±
Ɂɚɞɚɱɢ
ɇɚɩɢɲɢɬɟɜɢɨɧɧɨɦɨɥɟɤɭɥɹɪɧɨɣɮɨɪɦɟɭɪɚɜɧɟɧɢɹɪɟɚɤɰɢɣɩɪɢɜɨ
ɞɹɳɢɯɤɨɛɪɚɡɨɜɚɧɢɸɦɚɥɨɪɚɫɬɜɨɪɢɦɵɯ ɨɫɚɞɤɨɜɢɥɢɝɚɡɨɜɚɧɢɬɪɚɬɫɜɢɧɰɚɢ
ɢɨɞɢɞɤɚɥɢɹɛ ɯɥɨɪɢɞ ɧɢɤɟɥɹɢ ɫɟɪɨɜɨɞɨɪɨɞɧɚɹ ɤɢɫɥɨɬɚɜ
ɤɚɪɛɨɧɚɬɤɚɥɢɹ ɢ
ɯɥɨɪɨɜɨɞɨɪɨɞɧɚɹɤɢɫɥɨɬɚɝɫɭɥɶɮɚɬɦɟɞɢɢɝɢɞɪɨɤɫɢɞɧɚɬɪɢɹɞɛɪɨɦɢɞɚɥɸ
ɦɢɧɢɹɢɧɢɬɪɚɬɫɟɪɟɛɪɚ
ɁɚɩɢɲɢɬɟɜɵɪɚɠɟɧɢɟɉɊɞɥɹɨɛɪɚɡɭɸɳɢɯɫɹɨɫɚɞɤɨɜ
ɇɚɩɢɲɢɬɟɜɢɨɧɧɨɦɨɥɟɤɭɥɹɪɧɨɣɮɨɪɦɟɭɪɚɜɧɟɧɢɹɪɟɚɤɰɢɣɩɪɢɜɨ
ɞɹɳɢɯɤɨɛɪɚɡɨɜɚɧɢɸɦɚɥɨɞɢɫɫɨɰɢɢɪɨɜɚɧɧɵɯɫɨɟɞɢɧɟɧɢɣɚɫɭɥɶɮɢɞɧɚɬɪɢɹɢ
ɫɟɪɧɚɹɤɢɫɥɨɬɚɛɫɭɥɶɮɢɞɠɟɥɟɡɚ,,ɢɯɥɨɪɨɜɨɞɨɪɨɞɧɚɹɤɢɫɥɨɬɚɜ
ɚɰɟɬɚɬɤɚ
ɥɢɹɢɚɡɨɬɧɚɹɤɢɫɥɨɬɚɝɯɥɨɪɢɞɚɦɦɨɧɢɹɢɝɢɞɪɨɤɫɢɞɤɚɥɶɰɢɹ
ɁɚɩɢɲɢɬɟɜɵɪɚɠɟɧɢɟɄ
Ɂɚɤɨɧɱɢɬɟɦɨɥɟɤɭɥɹɪɧɵɟɢɧɚɩɢɲɢɬɟɢɨɧɧɵɟɭɪɚɜɧɟɧɢɹ
6+&O
ɚ1D
ɞɥɹɦɚɥɨɞɢɫɫɨɰɢɢɪɨɜɚɧɧɵɯɫɨɟɞɢɧɟɧɢɣ
ɞ
ɛ3E12
ɜ6Q2+
ɝ6Q2+
Ɂɚɤɨɧɱɢɬɟɦɨɥɟɤɭɥɹɪɧɵɟɢɧɚɩɢɲɢɬɟɢɨɧɧɵɟɭɪɚɜɧɟɧɢɹ
ɚ%D2+
ɛ1D+62
ɜ$O2+
ɝ$O2+
Ɂɚɤɨɧɱɢɬɟɦɨɥɟɤɭɥɹɪɧɵɟɢɧɚɩɢɲɢɬɟɢɨɧɧɵɟɭɪɚɜɧɟɧɢɹ
ɚ&D&2
ɛ1D
ɜ=Q2+
ɝ=Q2+
1D,
+62
.2+
+&O
1D2+
+12
.2+
+&O
6)H62
+&O
1D2+
ɋɨɫɬɚɜɶɬɟ ɜɦɨɥɟɤɭɥɹɪɧɨɣ ɮɨɪɦɟɭɪɚɜɧɟɧɢɹ ɪɟɚɤɰɢɣɤɨɬɨɪɵɟ ɜɵ
ɪɚɠɚɸɬɫɹɫɥɟɞɭɸɳɢɦɢɢɨɧɧɨɦɨɥɟɤɭɥɹɪɧɵɦɢɭɪɚɜɧɟɧɢɹɦɢ
í
12
+ +12
2+í &X2+p
&X
3E
,í 3E,p
Ʉ ɢɨɧɧɵɦɭɪɚɜɧɟɧɢɹɦɩɨɞɛɟɪɢɬɟɩɨɞɜɚɦɨɥɟɤɭɥɹɪɧɵɯɭɪɚɜɧɟɧɢɹ
í
6
ɚ+J
Ʉ ɢɨɧɧɵɦɭɪɚɜɧɟɧɢɹɦɩɨɞɛɟɪɢɬɟɩɨɞɜɚɦɨɥɟɤɭɥɹɪɧɵɯɭɪɚɜɧɟɧɢɹ
6L2
ɚ&D
Ʉ ɢɨɧɧɵɦɭɪɚɜɧɟɧɢɹɦɩɨɞɛɟɪɢɬɟɩɨɞɜɚɦɨɥɟɤɭɥɹɪɧɵɯɭɪɚɜɧɟɧɢɹ
í
ɚ12
+
Ʉɚɤɢɟ ɢɡ ɩɟɪɟɱɢɫɥɟɧɧɵɯ ɧɢɠɟ ɫɨɥɟɣ ɩɨɞɜɟɪɝɚɸɬɫɹ ɝɢɞɪɨɥɢɡɭ
1D&1 .12
+J6ɛ&2
í
&D6L2ɛ$O2+
1212
.2&O 1D12 1+&+&22 &D&O 1D&O2 .+&22 .%U" Ⱦɥɹ
í
+
&2
+2
2+í >$O2+@í
+2ɛ$J%Uí $J%U
ɤɚɠɞɨɣ ɢɡ ɝɢɞɪɨɥɢɡɭɸɳɢɯɫɹ ɫɨɥɟɣ ɧɚɩɢɲɢɬɟ ɭɪɚɜɧɟɧɢɟ ɝɢɞɪɨɥɢɡɚ ɜ ɢɨɧɧɨ
ɦɨɥɟɤɭɥɹɪɧɨɣɮɨɪɦɟɢɭɤɚɠɢɬɟɪɟɚɤɰɢɸɟɟɜɨɞɧɨɝɨɪɚɫɬɜɨɪɚ
ɍɤɚɠɢɬɟɤɚɤɢɟɢɡɩɟɪɟɱɢɫɥɟɧɧɵɯɧɢɠɟɫɨɥɟɣɩɨɞɜɟɪɝɚɸɬɫɹɝɢɞɪɨ
ɥɢɡɭɚ=Q%U
.6)H620J62ɛ.12.&21D32&X&OȾɥɹɤɚɠ
ɞɨɣ ɢɡ ɝɢɞɪɨɥɢɡɭɸɳɢɯɫɹ ɫɨɥɟɣ ɧɚɩɢɲɢɬɟ ɜ ɦɨɥɟɤɭɥɹɪɧɨɣ ɢ ɢɨɧɧɨ
ɦɨɥɟɤɭɥɹɪɧɨɣ ɮɨɪɦɟ ɭɪɚɜɧɟɧɢɹ ɝɢɞɪɨɥɢɡɚ ɩɨ ɤɚɠɞɨɣ ɫɬɭɩɟɧɢ ɭɤɚɠɢɬɟ ɪɟɚɤ
ɰɢɸɜɨɞɧɨɝɨɪɚɫɬɜɨɪɚɫɨɥɢ
ɇɚɩɢɲɢɬɟ ɦɨɥɟɤɭɥɹɪɧɵɟ ɢ ɢɨɧɧɵɟ ɭɪɚɜɧɟɧɢɹ ɝɢɞɪɨɥɢɡɚɛɪɨɦɢɞɚ
ɰɢɧɤɚɢɤɚɪɛɨɧɚɬɚɥɢɬɢɹɄɚɤɦɨɠɧɨɭɫɢɥɢɬɶɨɫɥɚɛɢɬɶɝɢɞɪɨɥɢɡɷɬɢɯɫɨɥɟɣ"
ȼɵɱɢɫɥɢɬɟ ɤɨɧɫɬɚɧɬɭ ɝɢɞɪɨɥɢɡɚɯɥɨɪɢɞɚɚɦɦɨɧɢɹɨɩɪɟɞɟɥɢɬɟɫɬɟ
ɩɟɧɶɝɢɞɪɨɥɢɡɚɷɬɨɣɫɨɥɢɜɆɪɚɫɬɜɨɪɟɢS+ɪɚɫɬɜɨɪɚ
ɉɪɢ ιɋ ɢɨɧɧɨɟ ɩɪɨɢɡɜɟɞɟɧɢɟ ɜɨɞɵ
.
+2
í
ɋɱɢɬɚɹ ɱɬɨ
ɤɨɧɫɬɚɧɬɚɞɢɫɫɨɰɢɚɰɢɢɯɥɨɪɧɨɜɚɬɢɫɬɨɣɤɢɫɥɨɬɵɧɟɢɡɦɟɧɹɟɬɫɹɫɬɟɦɩɟɪɚɬɭɪɨɣ
ɨɩɪɟɞɟɥɢɬɟS+ɧɪɚɫɬɜɨɪɚ.2&Oɩɪɢɢɩɪɢ
ɉɨɱɟɦɭ ɪɚɫɬɜɨɪ1D+&2
ɢɦɟɟɬɫɥɚɛɨɳɟɥɨɱɧɭɸɚ ɪɚɫɬɜɨɪ1D+62±
ιɋ
ɫɥɚɛɨɤɢɫɥɭɸɪɟɚɤɰɢɸ"
ɉɪɢɫɥɢɜɚɧɢɢɜɨɞɧɵɯɪɚɫɬɜɨɪɨɜ&U12
ɢ1D6ɨɛɪɚɡɭɟɬɫɹɨɫɚɞɨɤ
ɝɢɞɪɨɤɫɢɞɚ ɯɪɨɦɚ ,,, ɢ ɜɵɞɟɥɹɟɬɫɹ ɝɚɡ ɋɨɫɬɚɜɶɬɟ ɦɨɥɟɤɭɥɹɪɧɨɟɢɢɨɧɧɨ
ɦɨɥɟɤɭɥɹɪɧɨɟɭɪɚɜɧɟɧɢɹɩɪɨɢɫɯɨɞɹɳɟɣɪɟɚɤɰɢɢ
ɂɧɞɢɤɚɬɨɪ ɦɟɬɢɥɨɜɵɣɨɪɚɧɠɟɜɵɣ ɢɡɦɟɧɹɟɬ ɨɤɪɚɫɤɭɨɬ ɤɪɚɫɧɨɣ ɞɨ
ɠɟɥɬɨɣɜɢɧɬɟɪɜɚɥɟS+ ɨɬ ɞɨɄɚɤɨɜɚɛɭɞɟɬɨɤɪɚɫɤɚɆɜɨɞɧɨɝɨ ɪɚɫ
ɬɜɨɪɚ ɚɰɟɬɚɬɚ ɚɦɦɨɧɢɹ &+
&221+ ɫɨɞɟɪɠɚɳɟɝɨ ɦɟɬɢɥɨɜɵɣ ɨɪɚɧɠɟɜɵɣ ɢɧ
ɞɢɤɚɬɨɪɚɤɪɚɫɧɚɹɛɨɪɚɧɠɟɜɚɹɜɠɟɥɬɚɹ"
ɇɚɩɢɲɢɬɟ ɜ ɦɨɥɟɤɭɥɹɪɧɨɣ ɢɦɨɥɟɤɭɥɹɪɧɨɢɨɧɧɨɣ ɮɨɪɦɚɯ ɭɪɚɜɧɟ
ɧɢɹɪɟɚɤɰɢɢɜɡɚɢɦɨɞɟɣɫɬɜɢɹɫɥɟɞɭɸɳɢɯɜɟɳɟɫɬɜɚɧɢɬɪɚɬɚɫɟɪɟɛɪɚɢɯɥɨɪɢɞɚ
ɠɟɥɟɡɚ ,, ɛ ɤɚɪɛɨɧɚɬɚ ɤɚɥɶɰɢɹ ɢ ɯɥɨɪɨɜɨɞɨɪɨɞɧɨɣ ɤɢɫɥɨɬɵ ɜ ɝɢɞɪɨɤɫɢɞɚ
ɛɚɪɢɹɢɚɡɨɬɧɨɣɤɢɫɥɨɬɵ
ɁɚɩɢɲɢɬɟɜɵɪɚɠɟɧɢɟɉɊɨɫɚɞɤɚ.
ɫɥɚɛɨɝɨɷɥɟɤɬɪɨɥɢɬɚ
Ⱦ
.
+2
ɞɥɹ
ɩɪɨɞɭɤɬɨɜɪɟɚɤɰɢɢɜɡɚɢɦɨɞɟɣɫɬɜɢɹɫɥɟɞɭɸɳɢɯɜɟɳɟɫɬɜɚɫɭɥɶɮɚɬɚɫɬɪɨɧɰɢɹɢ
ɯɥɨɪɢɞɚɛɚɪɢɹɛɯɥɨɪɢɞɚɚɦɦɨɧɢɹɢɝɢɞɪɨɤɫɢɞɤɚɥɶɰɢɹɜɭɤɫɭɫɧɨɣɤɢɫɥɨɬɵ
ɢɝɢɞɪɨɤɫɢɞɚɛɚɪɢɹ
ɋɨɫɬɚɜɶɬɟ ɩɨ ɞɜɚ ɦɨɥɟɤɭɥɹɪɧɵɯ ɭɪɚɜɧɟɧɢɹ ɪɟɚɤɰɢɣ ɤ ɤɚɠɞɨɦɭ ɢɡ
.
ɦɨɥɟɤɭɥɹɪɧɨɢɨɧɧɵɯɭɪɚɜɧɟɧɢɣ
ɚ&D
ɛ&2
2+í +2
ɜ+
ɋɦɟɲɢɜɚɸɬ ɩɨɩɚɪɧɨ ɪɚɫɬɜɨɪɵ ɚ &X12
ɜ.12ɢ1D&Oɝ$J12ɢ.&Oɞ&D2+ɢ+&Oȼɤɚɤɢɯɢɡɩɪɢɜɟ
.
62
í
&2
í
&D&2p
+ &2n+2
ɢ1D62 ɛ %D&Oɢ
ɞɟɧɧɵɯɫɥɭɱɚɟɜɪɟɚɤɰɢɢ ɩɪɚɤɬɢɱɟɫɤɢɢɞɭɬɞɨɤɨɧɰɚ"ɋɨɫɬɚɜɶɬɟɞɥɹɷɬɢɯɭɪɚɜ
ɧɟɧɢɣɦɨɥɟɤɭɥɹɪɧɵɟɢɦɨɥɟɤɭɥɹɪɧɨɢɨɧɧɵɟɭɪɚɜɧɟɧɢɹ
Ɇɨɠɧɨ ɥɢɩɪɢɝɨɬɨɜɢɬɶɪɚɫɬɜɨɪ ɫɨɞɟɪɠɚɳɢɣ ɨɞɧɨɜɪɟɦɟɧɧɨɫɥɟɞɭ
ɸɳɢɟɩɚɪɵɜɟɳɟɫɬɜ
ɚ=Q2+
ɛ%D2+
ɜ)H2+
.2+
+&O
1D2+
ɉɪɟɞɫɬɚɜɶɬɟɜɨɡɦɨɠɧɵɟɪɟɚɤɰɢɢɜɦɨɥɟɤɭɥɹɪɧɨɦɢɦɨɥɟɤɭɥɹɪɧɨɢɨɧɧɨɦ
ɜɢɞɟ
ɋɨɫɬɚɜɶɬɟ ɩɨ ɞɜɚɦɨɥɟɤɭɥɹɪɧɵɯ ɭɪɚɜɧɟɧɢɹ ɤ ɤɚɠɞɨɦɭ ɢɡ ɦɨɥɟɤɭ
ɥɹɪɧɨɢɨɧɧɵɯɭɪɚɜɧɟɧɢɣ
ɚ$X2+
ɛ)H2+
ɜ%H2+
2+í >$X2+@í
+ )H+2
+ >%H+2@+
ɉɪɟɞɫɬɚɜɶɬɟ ɜ ɦɨɥɟɤɭɥɹɪɧɨɦɢ ɦɨɥɟɤɭɥɹɪɧɨɢɨɧɧɨɦ ɜɢɞɟ ɪɟɚɤɰɢɢ
ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɟɠɞɭ ɚ ɝɢɞɪɨɤɫɢɞɨɦ ɯɪɨɦɚ ,,, ɢ ɫɟɪɧɨɣ ɤɢɫɥɨɬɨɣ ɛ ɦɟ
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ɝɢɞɪɨɤɫɢɞɨɦɫɬɪɨɧɰɢɹ
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í
ɇƝlɋíɇɈ
ɉɪɢɜɟɞɢɬɟɭɪɚɜɧɟɧɢɟɡɚɜɢɫɢɦɨɫɬɢɩɨɬɟɧɰɢɚɥɚɷɬɨɣɪɟɚɤɰɢɢɨɬɪɇɢɪɚɫ
ɫɱɢɬɚɣɬɟɟɝɨɡɧɚɱɟɧɢɟɩɪɢɪɇ Ɍ .ɢɚɤɬɢɜɧɨɫɬɹɯɢɨɧɨɜɋ
ɪɚɜɧɵɯɟɫɥɢ
ɇɚɩɢɲɢɬɟɭɪɚɜɧɟɧɢɟɇɟɪɧɫɬɚɞɥɹɪɟɚɤɰɢɢ
(
&O2 &O
ȼ
í
+Ɲl+12+2.
12
ɉɪɢɜɟɞɢɬɟ ɭɪɚɜɧɟɧɢɟ ɡɚɜɢɫɢɦɨɫɬɢ ɩɨɬɟɧɰɢɚɥɚ ɷɬɨɣ ɪɟɚɤɰɢɢ ɨɬ ɪɇ ɪɚɫ
ɬɜɨɪɚɢɪɚɫɫɱɢɬɚɣɬɟɟɝɨɡɧɚɱɟɧɢɟɩɪɢɪɇ
í
ɢɦɨɥɟɤɭɥ+12ɪɚɜɧɵɯ( %
12
Ɋɚɫɫɱɢɬɚɣɬɟ ɪɚɜɧɨɜɟɫɧɵɣ ɩɨɬɟɧɰɢɚɥ ɷɥɟɤɬɪɨɞɚ ɧɚ ɤɨɬɨɪɨɦ ɩɪɨɬɟ
Ɍ .ɢɚɤɬɢɜɧɨɫɬɹɯɢɨɧɨɜ
ɤɚɟɬɪɟɚɤɰɢɹ
í
ɇƝlɋíɇɈ.
ɋɈ
ɋɬɚɧɞɚɪɬɧɵɣ ɩɨɬɟɧɰɢɚɥ ɷɥɟɤɬɪɨɞɚ ɪɚɜɟɧ ȼ ɚɤɬɢɜɧɨɫɬɢ ɢɨɧɨɜ
í
ɋɈ
ɢɋíɪɚɜɧɵɪɇ Ɍ .
Ɉɩɪɟɞɟɥɢɬɟ ɪɚɜɧɨɜɟɫɧɵɣ ɩɨɬɟɧɰɢɚɥ ɷɥɟɤɬɪɨɞɚ ɧɚ ɤɨɬɨɪɨɦ ɩɪɨɬɟ
ɤɚɟɬɪɟɚɤɰɢɹ
í
+Ɲl0Q+2.
0Q2
ɋɬɚɧɞɚɪɬɧɵɣɩɨɬɟɧɰɢɚɥɪɚɜɟɧ ȼɚɤɬɢɜɧɨɫɬɢɢɨɧɨɜ0Q2
ɪɚɜɧɵɪɇ
Ɍ .
Ɋɚɫɫɱɢɬɚɣɬɟ ɪɚɜɧɨɜɟɫɧɵɣ ɩɨɬɟɧɰɢɚɥ ɷɥɟɤɬɪɨɞɚ ɧɚ ɤɨɬɨɪɨɦ ɩɪɨɬɟ
ɤɚɟɬɪɟɚɤɰɢɹ
í
+Ɲl0Q+2
0Q2
ɋɬɚɧɞɚɪɬɧɵɣɩɨɬɟɧɰɢɚɥɪɚɜɟɧȼɚɤɬɢɜɧɨɫɬɢɢɨɧɨɜ0Q2
ɪɚɜɧɵɪɇ Ɍ .
ȼɵɱɢɫɥɢɬɟɪɚɜɧɨɜɟɫɧɵɣɩɨɬɟɧɰɢɚɥɷɥɟɤɬɪɨɞɚɧɚɤɨɬɨɪɨɦɩɪɨɬɟɤɚ
ɟɬɪɟɚɤɰɢɹ
í
ɇƝlɋíɇɈ.
ɋɈ
ɋɬɚɧɞɚɪɬɧɵɣ ɩɨɬɟɧɰɢɚɥ ɷɥɟɤɬɪɨɞɚ ɪɚɜɟɧ ȼ ɚɤɬɢɜɧɨɫɬɢ ɢɨɧɨɜ
í
ɋɈ
ɢɋíɪɚɜɧɵɪɇ Ɍ .
Ɋɚɫɫɱɢɬɚɣɬɟ ɪɚɜɧɨɜɟɫɧɵɣ ɩɨɬɟɧɰɢɚɥ ɷɥɟɤɬɪɨɞɚ ɧɚ ɤɨɬɨɪɨɦ ɩɪɨɬɟ
ɤɚɟɬɪɟɚɤɰɢɹ
í
&U
ɋɬɚɧɞɚɪɬɧɵɣ ɩɨɬɟɧɰɢɚɥ ɷɥɟɤɬɪɨɞɚ ɪɚɜɟɧ ȼ ɚɤɬɢɜɧɨɫɬɢ ɢɨɧɨɜ
í
&U
ɢ&U+ɪɚɜɧɵɪɇ Ɍ .
2
+Ɲl&U+2.
2
í
ɢɋɈ
í
ɢ0Q
í
ɢ0Q+
í
Ɉɩɪɟɞɟɥɢɬɟ ɪɚɜɧɨɜɟɫɧɵɣ ɩɨɬɟɧɰɢɚɥ ɷɥɟɤɬɪɨɞɚ ɧɚ ɤɨɬɨɪɨɦ ɩɪɨɬɟ
ɤɚɟɬɪɟɚɤɰɢɹ
í
&U
ɋɬɚɧɞɚɪɬɧɵɣ ɩɨɬɟɧɰɢɚɥ ɷɥɟɤɬɪɨɞɚ ɪɚɜɟɧ ȼ ɚɤɬɢɜɧɨɫɬɢ ɢɨɧɨɜ
í
&U
ɤɚɟɬɪɟɚɤɰɢɹ
ɢ&U+ɪɚɜɧɵɪɇ Ɍ .
2
Ɋɚɫɫɱɢɬɚɣɬɟ ɪɚɜɧɨɜɟɫɧɵɣ ɩɨɬɟɧɰɢɚɥ ɷɥɟɤɬɪɨɞɚ ɧɚ ɤɨɬɨɪɨɦ ɩɪɨɬɟ
+Ɲl&U+2.
2
ɊEɈɇƝlɊEɇɈ.
ɋɬɚɧɞɚɪɬɧɵɣ ɩɨɬɟɧɰɢɚɥ ɪɚɜɟɧ ȼ ɚɤɬɢɜɧɨɫɬɶ ɢɨɧɚ 3E+ɪɚɜɧɚ
ɪɇ Ɍ .
Ɉɩɪɟɞɟɥɢɬɟ ɡɧɚɱɟɧɢɟ ɷɥɟɤɬɪɨɞɧɨɝɨɩɨɬɟɧɰɢɚɥɚɦɟɞɢɩɨɝɪɭɠɟɧɧɨɣ
ɜɧɋX12
ȼɵɱɢɫɥɢɬɟ ɩɨɬɟɧɰɢɚɥ ɜɨɞɨɪɨɞɧɨɝɨ ɷɥɟɤɬɪɨɞɚɟɫɥɢ ɋ
ɪɚɜɧɚÂ
í
ȼɵɱɢɫɥɢɬɟ ɩɨɬɟɧɰɢɚɥɠɟɥɟɡɧɨɝɨɷɥɟɤɬɪɨɞɚɨɩɭɳɟɧɧɨɝɨɜɪɚɫɬɜɨɪ
ɫɨɞɟɪɠɚɳɢɣɝ)H&O
ɉɨɬɟɧɰɢɚɥ ɜɨɞɨɪɨɞɧɨɝɨ ɷɥɟɤɬɪɨɞɚɪɚɜɟɧ ±ȼ Ɉɩɪɟɞɟɥɢɬɟ ɪɇ
ɪɚɫɬɜɨɪɚ ɢ ɚɤɬɢɜɧɨɫɬɶ ɢɨɧɨɜ ɜɨɞɨɪɨɞɚ ɜ ɪɚɫɬɜɨɪɟ Ʉɨɷɮɮɢɰɢɟɧɬ ɚɤɬɢɜɧɨɫɬɢ
ɢɨɧɚɇ
ɪɚɜɟɧ
ȼɵɱɢɫɥɢɬɟ ɩɨɬɟɧɰɢɚɥɜɨɞɨɪɨɞɧɨɝɨ ɷɥɟɤɬɪɨɞɚ ɩɪɢ ɪɇ ɢɫɬɚɧ
ɦɨɥɶɥ
ɜɥ
ɜɪɚɫɬɜɨɪɟ
ɇ
ɞɚɪɬɧɨɦɞɚɜɥɟɧɢɢ
ɉɨɬɟɧɰɢɚɥɤɚɞɦɢɟɜɨɝɨɷɥɟɤɬɪɨɞɚɩɪɢ.ɜɪɚɫɬɜɨɪɟɟɝɨɫɨɥɢɪɚ
ɜɟɧȼɊɚɫɫɱɢɬɚɣɬɟɚɤɬɢɜɧɨɫɬɶɢɨɧɨɜɤɚɞɦɢɹ
ɉɪɢ ɤɚɤɨɣɚɤɬɢɜɧɨɫɬɢ ɢɨɧɨɜɊɖ
ɪɚɜɧɨɜɟɫɧɵɣ ɩɨɬɟɧɰɢɚɥ ɫɜɢɧɰɨ
ɜɨɝɨ ɷɥɟɤɬɪɨɞɚ ɩɪɢ . ɛɭɞɟɬ ɪɚɜɟɧ ɫɬɚɧɞɚɪɬɧɨɦɭ ɩɨɬɟɧɰɢɚɥɭ ɧɢɤɟɥɟɜɨɝɨ
ɷɥɟɤɬɪɨɞɚ"
Ɋɚɫɫɱɢɬɚɣɬɟ ɩɨɬɟɧɰɢɚɥɷɥɟɤɬɪɨɞɚɧɚɤɨɬɨɪɨɦɩɪɢ.ɭɫɬɚɧɨɜɢ
ɥɨɫɶɪɚɜɧɨɜɟɫɢɟ
Hl&Oí
&O
ɩɪɢ
S
&O
ɢ
D
íɦɨɥɶɥȿ
&O
Ɋɚɫɫɱɢɬɚɣɬɟ ɩɨɬɟɧɰɢɚɥɷɥɟɤɬɪɨɞɚɧɚɤɨɬɨɪɨɦɩɪɢ.ɭɫɬɚɧɨɜɢ
ɥɨɫɶɪɚɜɧɨɜɟɫɢɟ
Hl)í
)
ɩɪɢ ɫɬɚɧɞɚɪɬɧɨɦ ɞɚɜɥɟɧɢɢ ɢ ɚɤɬɢɜɧɨɫɬɢ ɢɨɧɨɜ ɮɬɨɪɚ ɪɚɜɧɨɣ
ȼ
ȿ
Ɋɚɫɫɱɢɬɚɣɬɟ ɷɥɟɤɬɪɨɞɧɵɟɩɨɬɟɧɰɢɚɥɵ ɦɚɝɧɢɹ ɜ ɪɚɫɬɜɨɪɟ ɟɝɨ ɫɨɥɢ
ɩɪɢɤɨɧɰɟɧɬɪɚɰɢɹɯɢɨɧɚɦɚɝɧɢɹɢɦɨɥɶɥ
í
ɦɨɥɶɥ
ȼɵɱɢɫɥɢɬɟ ɩɨɬɟɧɰɢɚɥ ɜɨɞɨɪɨɞɧɨɝɨɷɥɟɤɬɪɨɞɚ ɩɨɝɪɭɠɟɧɧɨɝɨ ɜ ɱɢ
ɫɬɭɸɜɨɞɭɜɪɚɫɬɜɨɪɫɪɇ ɜɪɚɫɬɜɨɪɫɪɇ
ɉɨɬɟɧɰɢɚɥ ɜɨɞɨɪɨɞɧɨɝɨ ɷɥɟɤɬɪɨɞɚ ɜ ɜɨɞɧɨɦ ɪɚɫɬɜɨɪɟ ɪɚɜɟɧ ±
ɦȼȼɵɱɢɫɥɢɬɟɚɤɬɢɜɧɨɫɬɶɢɨɧɨɜɇ
ɜɷɬɨɦɪɚɫɬɜɨɪɟ
Ƚɚɥɶɜɚɧɢɱɟɫɤɢɟɷɥɟɦɟɧɬɵ
ɍɫɬɪɨɣɫɬɜɚɜɤɨɬɨɪɵɯɷɧɟɪɝɢɹɨɤɢɫɥɢɬɟɥɶɧɨɜɨɫɫɬɚɧɨɜɢɬɟɥɶɧɵɯɪɟɚɤɰɢɣ
ɩɪɟɜɪɚɳɚɟɬɫɹ ɜ ɷɥɟɤɬɪɢɱɟɫɤɭɸ ɧɚɡɵɜɚɸɬɫɹ
ɬɚɦɢ (Ƚɗ).
ȼɫɹɤɢɣ ɝɚɥɶɜɚɧɢɱɟɫɤɢɣ ɷɥɟɦɟɧɬ ɫɨɫɬɨɢɬ ɢɡ ɞɜɭɯ ɷɥɟɤɬɪɨɞɨɜ±ɦɟɬɚɥɥɨɜ
ɩɨɝɪɭɠɟɧɧɵɯ ɜ ɪɚɫɬɜɨɪɵ ɷɥɟɤɬɪɨɥɢɬɨɜ ɩɨɫɥɟɞɧɢɟ ɫɨɨɛɳɚɸɬɫɹɞɪɭɝ ɫɞɪɭɝɨɦ
ɨɛɵɱɧɨɱɟɪɟɡɩɨɪɢɫɬɭɸɩɟɪɟɝɨɪɨɞɤɭȿɫɥɢɞɚɧɧɵɟ ɷɥɟɤɬɪɨɞɵ ɫɨɟɞɢɧɢɬɶɜɧɟɲ
ɧɢɦɩɪɨɜɨɞɧɢɤɨɦ ɬɨɜɨ ɜɧɟɲɧɟɣɰɟɩɢ ɦɨɠɧɨɡɚɪɟɝɢɫɬɪɢɪɨɜɚɬɶ ɷɥɟɤɬɪɢɱɟɫɤɢɣ
ɬɨɤɫɩɨɦɨɳɶɸɝɚɥɶɜɚɧɨɦɟɬɪɚɉɪɢɷɬɨɦɦɟɬɚɥɥɫɛɨɥɶɲɟɣɯɢɦɢɱɟɫɤɨɣɚɤɬɢɜ
ɧɨɫɬɶɸɛɭɞɟɬɩɟɪɟɯɨɞɢɬɶɜɪɚɫɬɜɨɪɬɟ
ɚɧɨɞɨɦɢɢɦɟɟɬɡɧɚɤ±ɗɥɟɤɬɪɨɧɵɧɚɤɚɩɥɢɜɚɸɬɫɹɧɚɚɧɨɞɟɢɡɚɪɹɠɚɸɬ
ɟɬɫɹ
ɟɝɨɨɬɪɢɰɚɬɟɥɶɧɨ ɉɨ ɜɧɟɲɧɟɦɭɩɪɨɜɨɞɧɢɤɭ ɷɥɟɤɬɪɨɧɵ ɛɭɞɭɬɩɟɪɟɦɟɳɚɬɶɫɹɤ
ɦɟɧɟɟɚɤɬɢɜɧɨɦɭ ɦɟɬɚɥɥɭɦɟɞɢ ɢ ɩɪɨɢɡɨɣɞɟɬɪɚɡɪɹɞ ɢɨɧɨɜɦɟɞɢɬɟ
ɫɬɚɧɨɜɥɟɧɢɟ
ɗɬɨɬɷɥɟɤɬɪɨɞɧɚɡɵɜɚɟɬɫɹɤɚɬɨɞɨɦɢɢɦɟɟɬɡɧɚɤ
ɋɭɦɦɚɪɧɚɹ ɨɤɢɫɥɢɬɟɥɶɧɨɜɨɫɫɬɚɧɨɜɢɬɟɥɶɧɚɹ ɪɟɚɤɰɢɹ ɩɪɨɬɟɤɚɸɳɚɹ ɧɚ
ɷɥɟɤɬɪɨɞɚɯɧɚɡɵɜɚɟɬɫɹɬ ɨ ɤ ɨ ɨ ɛ ɪ ɚ ɡ ɭ ɸ ɳ ɟ ɣ
ɋɯɟɦɚɬɢɱɟɫɤɢɝɚɥɶɜɚɧɢɱɟɫɤɢɣ ɷɥɟɦɟɧɬ ɜɨɫɧɨɜɟ ɪɚɛɨɬɵ ɤɨɬɨɪɨɝɨɥɟɠɢɬ
ɪɟɚɤɰɢɹ
=Q&X62
=Q62&X
ɢɡɨɛɪɚɠɚɟɬɫɹɫɥɟɞɭɸɳɢɦɨɛɪɚɡɨɦ
ɝɚɥɶɜɚɧɢɱɟɫɤɢɦɢ ɷɥɟɦɟɧ-
ɨɤɢɫɥɹɬɶɫɹɗɬɨɬɷɥɟɤɬɪɨɞɧɚɡɵɜɚ
ɜɨɫ-
=Q_=Q62
__&X62_&X
ɢɥɢɜɢɨɧɧɨɦɜɢɞɟ
=Q_=Q
__&X_&X
ɇɚɷɥɟɤɬɪɨɞɚɯɩɪɨɬɟɤɚɸɬɫɥɟɞɭɸɳɢɟɩɪɨɰɟɫɫɵ
ɚɧɨɞɧɵɣ=Q±ɟ =Q
ɤɚɬɨɞɧɵɣ&X
ɬɨɤɨɨɛɪɚɡɭɸɳɚɹ ɪɟɚɤɰɢɹ=Q&X62
ɟ &X
=Q62&X
ɊɚɛɨɬɭȽɗɦɨɠɧɨɨɰɟɧɢɬɶɜɟɥɢɱɢɧɨɣɟɝɨ ɷɥɟɤɬɪɨɞɜɢɠɭɳɟɣ ɫɢɥɵíɗȾɋ
ȿɈɧɚɪɚɜɧɚɪɚɡɧɨɫɬɢɪɚɜɧɨɜɟɫɧɵɯɩɨɬɟɧɰɢɚɥɨɜɤɚɬɨɞɚȿ
ɢɚɧɨɞɚȿɚɷɥɟɤ
ɤ
ɬɪɨɞɨɜ
ȿ ȿ
±ȿɚ
ɤ
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