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Ɂɚɞɚɱɢ
Ɉɩɪɟɞɟɥɢɬɟɜɨɡɦɨɠɧɨɫɬɶɩɪɨɬɟɤɚɧɢɹɪɟɚɤɰɢɢ
ɝo&+ɝ
ɩɨɞɫɱɢɬɚɜ'6
Ɋɚɫɫɱɢɬɚɣɬɟ ɢɡɦɟɧɟɧɢɟɷɧɬɪɨɩɢɢɩɪɢ ɩɥɚɜɥɟɧɢɢ ɦɨɥɟɣɭɤɫɭɫɧɨɣ
ɤɢɫɥɨɬɵ&+
ɋɝɪɚɮɢɬ+
ɷɬɨɝɨɩɪɨɰɟɫɫɚ
&22+ɟɫɥɢɬɟɦɩɟɪɚɬɭɪɚɩɥɚɜɥɟɧɢɹ&+&22+ι&ɚɬɟɩɥɨɬɚ
ɩɥɚɜɥɟɧɢɹɤȾɠɝ
ȼɵɱɢɫɥɢɬɟ ɢɡɦɟɧɟɧɢɟ ɷɧɬɪɨɩɢɢ ɩɪɢ ɢɫɩɚɪɟɧɢɢ ɝ ɜɨɞɵ ɩɪɢ
ιɋ ɟɫɥɢ ɦɨɥɹɪɧɚɹ ɬɟɩɥɨɬɚ ɢɫɩɚɪɟɧɢɹ ɜɨɞɵ ɩɪɢ ɷɬɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɪɚɜɧɚ
ɤȾɠɦɨɥɶ
Ɍɟɩɥɨɬɚ ɢɫɩɚɪɟɧɢɹ ɛɪɨɦɛɟɧɡɨɥɚ ɩɪɢ Ʉ ɪɚɜɧɚ Ⱦɠɝ
Ɉɩɪɟɞɟɥɢɬɟ'6ɩɪɢɢɫɩɚɪɟɧɢɢɦɨɥɟɣɛɪɨɦɛɟɧɡɨɥɚ
ɂɡɦɟɧɟɧɢɟ ɷɧɬɪɨɩɢɢ ɩɪɢ ɩɥɚɜɥɟɧɢɢ ɝ ɦɟɞɢ ɪɚɜɧɨ ȾɠɄ
Ɋɚɫɫɱɢɬɚɣɬɟ ɭɞɟɥɶɧɭɸ ɬɟɩɥɨɬɭ ɩɥɚɜɥɟɧɢɹ ɦɟɞɢ ɟɫɥɢ ɬɟɦɩɟɪɚɬɭɪɚ ɩɥɚɜɥɟɧɢɹ
ɦɟɞɢ
ιɋ
ɍɞɟɥɶɧɚɹɬɟɩɥɨɬɚɩɥɚɜɥɟɧɢɹɥɶɞɚȾɠɤɝɈɩɪɟɞɟɥɢɬɟɢɡɦɟɧɟ
ɧɢɟɦɨɥɹɪɧɨɣɷɧɬɪɨɩɢɢɩɪɢɩɥɚɜɥɟɧɢɢɥɶɞɚ
Ɉɩɪɟɞɟɥɢɬɟ'6
ȼɨɡɦɨɠɧɚ ɥɢ ɫɥɟɞɭɸɳɚɹɪɟɚɤɰɢɹ +J
ɩɨɞɬɜɟɪɞɢɬɟɪɚɫɫɱɢɬɚɜ'*
Ɉɩɪɟɞɟɥɢɬɟ'*
ɫɢɫɬɟɦɵ+ɝ6ɤ +6ɝ
+J&O+J" Ɉɬɜɟɬ
ɷɬɨɣɫɢɫɬɟɦɵ
ɪɟɚɤɰɢɢ0H2ɤ&2ɝ 0H&2ɤɞɥɹɦɟ
&O
ɬɚɥɥɨɜɨɬ%Hɞɨ%Dɧɚɨɫɧɨɜɚɧɢɢɷɬɨɝɨɫɞɟɥɚɣɬɟɜɵɜɨɞɨɛɢɡɦɟɧɟɧɢɢɨɫɧɨɜɧɵɯ
ɫɜɨɣɫɬɜɨɤɫɢɞɨɜɷɬɢɯɦɟɬɚɥɥɨɜ
ɂɫɯɨɞɹ ɢɡ ɜɟɥɢɱɢɧ '*
ɨɩɪɟɞɟɥɢɬɟɜɨɡɦɨɠɧɚɥɢɪɟɚɤɰɢɹ$O
Ʉɚɤɚɹɢɡɩɪɢɜɟɞɟɧɧɵɯɪɟɚɤɰɢɣɪɚɡɥɨɠɟɧɢɹ.12
ɚ
.12
.122
ɛ
.12
ɜ
.12
.2122
.122
ȼɨɡɦɨɠɧɨ ɥɢ ɨɛɪɚɡɨɜɚɧɢɟ ɤɚɪɛɨɧɢɥɚ ɯɪɨɦɚ ɩɪɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɢ
ɫɨɟɞɢɧɟɧɢɣ ɭɱɚɫɬɜɭɸɳɢɯ ɜ ɪɟɚɤɰɢɢ
ɤ62ɝ $O62ɤ"
2
ɧɚɢɛɨɥɟɟɜɟɪɨɹɬɧɚ
ɯɪɨɦɚɫɨɤɫɢɞɨɦ ɭɝɥɟɪɨɞɚ"Ʉɚɤɢɟɭɫɥɨɜɢɹɹɜɥɹɸɬɫɹɨɩɬɢɦɚɥɶɧɵɦɢɞɥɹɩɪɨɬɟ
ɤɚɧɢɹɞɚɧɧɨɣɪɟɚɤɰɢɢ&U&2 &U&2
Ȼɭɞɭɬ ɥɢɩɪɢ ι& ɩɪɨɬɟɤɚɬɶɪɟɚɤɰɢɢ ɚ .++
ɛ.+ .
+"
"
2 .2+ +
Ʉɚɤ ɛɭɞɟɬ ɜɥɢɹɬɶ ɩɨɜɵɲɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɧɚ ɧɚɩɪɚɜɥɟɧɢɟ ɭɤɚɡɚɧɧɵɯ
ɩɪɨɰɟɫɫɨɜ"
Ʉɚɤɢɡɦɟɧɹɸɬɫɹɨɫɧɨɜɧɵɟɫɜɨɣɫɬɜɚɝɢɞɪɨɤɫɢɞɨɜɜɪɹɞɭ
/L2+o1D2+o.2+o5E2+o&V2+"
Ɉɬɜɟɬɞɚɣɬɟɪɚɫɫɱɢɬɚɜ'*
ɫɢɫɬɟɦɵ0H2+2o0H2+
Ʉɚɤɢɟ ɢɡ ɩɪɢɜɟɞɟɧɧɵɯ ɧɢɠɟ ɜɨɞɨɪɨɞɧɵɯ ɫɨɟɞɢɧɟɧɢɣ ɩɨɥɭɱɚɸɬ
ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɢɡ ɷɥɟɦɟɧɬɨɜ ɚ ɤɚɤɢɟ ɤɨɫɜɟɧɧɵɦ ɩɭɬɟɦ +
+
6Hɝ+7Hɝ"
Ɇɨɠɧɨ ɥɢɢɫɩɨɥɶɡɨɜɚɬɶɩɪɢɫɬɚɧɞɚɪɬɧɵɯɭɫɥɨɜɢɹɯɧɢɠɟɩɪɢɜɟɞɟɧ
2ɝ +6ɝ
ɧɭɸɪɟɚɤɰɢɸɞɥɹɩɨɥɭɱɟɧɢɹɚɦɦɢɚɤɚ
&Oɤ1D2+ɤ 1D&Oɤ+2ɝ1+n"
1+
ɉɪɢɦɟɧɟɧɢɟɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɯɮɭɧɤɰɢɣɞɥɹɯɚɪɚɤɬɟɪɢɫɬɢɤɢ
ɫɜɨɣɫɬɜɢɪɟɚɤɰɢɨɧɧɨɣɫɩɨɫɨɛɧɨɫɬɢɜɟɳɟɫɬɜ
ɉɪɢɦɟɪ
ȼɵɱɢɫɥɟɧɢɟ ɢɡɦɟɧɟɧɢɹ '*
ɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ ɩɨ ɡɧɚɱɟɧɢɹɦ ɫɬɚɧ
ɞɚɪɬɧɵɯɷɧɬɚɥɶɩɢɣɢɷɧɬɪɨɩɢɣɪɟɚɝɢɪɭɸɳɢɯɜɟɳɟɫɬɜ
ȼɵɱɢɫɥɢɬɟɫɬɚɧɞɚɪɬɧɨɟɢɡɦɟɧɟɧɢɟɷɧɟɪɝɢɢȽɢɛɛɫɚɯɢɦɢɱɟɫɤɨɝɨɩɪɨɰɟɫɫɚ
ɩɪɢ
ιɋ1+
ɝ+ɋOɝ 1+&Oɤɟɫɥɢɡɧɚɱɟɧɢɟ'+
ɢ6
ɳɢɯɜɟɳɟɫɬɜɫɥɟɞɭɸɳɢɟ
ȼɟɳɟɫɬɜɨ 1+
'+
ɤȾɠɦɨɥɶ
ȾɠɦɨɥɶÂɄ
6
+ɋO1+
± ± ±
&O
Ɋɟɲɟɧɢɟ
+'
&O1+
ɪɟɚɤɰɢɢ
+'
±
1+
+'
±±±±
+&O
Ɉɩɪɟɞɟɥɹɟɦ'+
'+
±ɤȾɠɦɨɥɶ
ɂɡɦɟɧɟɧɢɟɷɧɬɪɨɩɢɢɪɟɚɤɰɢɢ
'6
6
6
±
&O1+
1+
6
±
+&O
±ȾɠɦɨɥɶÂɄ
ɂɫɩɨɥɶɡɭɹ ɭɪɚɜɧɟɧɢɟ ȽɢɛɛɫɚȽɟɥɶɦɝɨɥɶɰɚ ɧɚɯɨɞɢɦ ɢɡɦɟɧɟɧɢɟ ɷɧɟɪɝɢɢ
Ƚɢɛɛɫɚ
'+±7Â'6 ±Âí ±
'*
±ɤȾɠɦɨɥɶ
Ɍɚɤɤɚɤ'*
ɞɚɧɧɚɹɪɟɚɤɰɢɹɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɜɨɡɦɨɠɧɚɩɪɨɬɟɤɚɟɬ
ɫɚɦɨɩɪɨɢɡɜɨɥɶɧɨɢɹɜɥɹɟɬɫɹɷɤɡɨɬɟɪɦɢɱɟɫɤɨɣ
ɪɟɚɝɢɪɭɸ
Ɂɚɞɚɱɢ
ɍɤɚɠɢɬɟ ɤɚɤɢɟ ɢɡ ɩɪɢɜɟɞɟɧɧɵɯ ɪɟɚɤɰɢɣ ɩɪɨɬɟɤɚɸɬ ɫɚɦɨɩɪɨɢɡ
ɜɨɥɶɧɨɢɹɜɥɹɸɬɫɹɷɤɡɨɬɟɪɦɢɱɟɫɤɢɦɢ
ɚ
+
ɠ +2ɠ2ɝ
2
+
ɝ1ɝ 1+ɝ
ɛ
1
ɜ
ɚ
ɛ
ɇɟɨɛɯɨɞɢɦɵɟɞɥɹ ɪɚɫɱɟɬɚɜɟɥɢɱɢɧɵ '*
ɝl12ɝ
2
ɍɤɚɠɢɬɟɤɚɤɚɹɢɡɞɜɭɯɪɟɚɤɰɢɣɛɭɞɟɬɩɪɨɬɟɤɚɬɶɫɚɦɨɩɪɨɢɡɜɨɥɶɧɨ
)Hɤ$O
$Oɤ)H
ɤ $Oɤ)H2ɤ
2
ɤ )Hɤ$O2ɤ
2
ɡɧɚɱɟɧɢɹ '+
ɢ6
ɢɡɉɪɢɥɨɠɟɧɢɹ
ȼɵɱɢɫɥɢɬɟɡɧɚɱɟɧɢɟ'+
0H&2
ɤo0H2ɤ&2ɝ
ɢɫɨɫɬɚɜɶɬɟɪɹɞɬɟɪɦɢɱɟɫɤɨɣɫɬɚɛɢɥɶɧɨɫɬɢ ɤɚɪɛɨɧɚɬɨɜ 0J&2
'*
'6
ɞɥɹɩɪɨɰɟɫɫɚ
%D&2&D&2
Ʉɚɤɜɥɢɹɟɬɧɚɬɟɱɟɧɢɟɷɬɢɯɩɪɨɰɟɫɫɨɜɬɟɦɩɟɪɚɬɭɪɚ"
ɥɢɬɟ'*
ɚ
ɛ
ɜ
ɇɚ ɨɫɧɨɜɚɧɢɢɜɟɥɢɱɢɧ'+
ɞɥɹɫɥɟɞɭɸɳɢɯɩɪɨɰɟɫɫɨɜ
62
ɝ2l62ɝ
&2ɝ+
+
ɝ2ɝl+2ɝ
2ɝl&2ɝ+ɝ
ɢ6
ɪɟɚɝɢɪɭɸɳɢɯɜɟɳɟɫɬɜ ɜɵɱɢɫ
ɍɤɚɠɢɬɟɜɤɚɤɨɦɧɚɩɪɚɜɥɟɧɢɢɷɬɢɪɟɚɤɰɢɢɛɭɞɭɬɩɪɨɬɟɤɚɬɶɩɪɢɛɥɢɠɚɹɫɶ
ɤɪɚɜɧɨɜɟɫɢɸ
ȼɵɱɢɫɥɢɜ'*
ɪɟɚɝɢɪɭɸɳɢɯɜɟɳɟɫɬɜɨɩɪɟɞɟɥɢɬɟɜɨɡɦɨɠɧɚɥɢɷɬɚɪɟɚɤɰɢɹ
6
Ɉɩɪɟɞɟɥɢɬɟ ɬɟɩɥɨɜɨɣɷɮɮɟɤɬ ɪɟɚɤɰɢɢ
ɡɭɹɡɧɚɱɟɧɢɟ'*
ɡɧɚɹ'+
12
ȼɵɱɢɫɥɢɬɟɢɡɦɟɧɟɧɢɟɷɧɟɪɝɢɢȽɢɛɛɫɚɩɪɢιɋɞɥɹɩɪɨɰɟɫɫɚ
ɢ6
ɪɟɚɝɢɪɭɸɳɢɯɜɟɳɟɫɬɜ ɢ ɫɬɚɧɞɚɪɬɧɭɸɬɟɩɥɨɬɭɫɝɨɪɚɧɢɹ ɦɟ
ɫɢɫɬɟɦɵ3E23E 3E2ɧɚɨɫɧɨɜɚɧɢɢ'+
6
ɪɟɚɝɢɪɭɸɳɢɯɜɟɳɟɫɬɜ
ɋɝɪɚɮɢɬɇ
ɝ ɋɇɝ
12l 12 ɢɫɩɨɥɶ
ɬɚɧɚ
ɉɪɢɤɚɤɨɣɬɟɦɩɟɪɚɬɭɪɟɧɚɫɬɭɩɢɬɪɚɜɧɨɜɟɫɢɟɫɢɫɬɟɦɵ
ɜɡɹɬɶ
ɢ
+&Oɝ2
ɝl+2ɝ&Oɝ'+ íɤȾɠ"
ɏɥɨɪɢɥɢɤɢɫɥɨɪɨɞɜɷɬɨɣɫɢɫɬɟɦɟɹɜɥɹɟɬɫɹɛɨɥɟɟɫɢɥɶɧɵɦɨɤɢɫɥɢɬɟɥɟɦɢ
ɩɪɢɤɚɤɢɯɬɟɦɩɟɪɚɬɭɪɚɯ"
ȼɨɫɫɬɚɧɨɜɥɟɧɢɟ)H
)H
2
ɨɤɫɢɞɨɦɭɝɥɟɪɨɞɚɢɞɟɬɩɨɭɪɚɜɧɟɧɢɸ
2
ɤ&2ɝ )H2ɤ&2 ɝ
ȼɵɱɢɫɥɢɬɟ '*
ɢ ɫɞɟɥɚɣɬɟ ɜɵɜɨɞ ɨ ɜɨɡɦɨɠɧɨɫɬɢ ɫɚɦɨɩɪɨɢɡɜɨɥɶɧɨɝɨ
ɩɪɨɬɟɤɚɧɢɹɷɬɨɣɪɟɚɤɰɢɢɩɪɢɫɬɚɧɞɚɪɬɧɵɯɭɫɥɨɜɢɹɯɑɟɦɭɪɚɜɧɚ '6
ɩɪɨɰɟɫɫɟ"
Ɋɟɚɤɰɢɹɝɨɪɟɧɢɹɚɰɟɬɢɥɟɧɚɢɞɟɬɩɨɭɪɚɜɧɟɧɢɸ
ɝ2ɝ &2ɝ+2ɠ
&
+
ȼɵɱɢɫɥɢɬɟ'*
ɢ'6
Ɉɛɴɹɫɧɢɬɟɭɦɟɧɶɲɟɧɢɟɷɧɬɪɨɩɢɢɜɪɟɡɭɥɶɬɚɬɟ
ɷɬɨɣɪɟɚɤɰɢɢ
ɑɟɦ ɦɨɠɧɨ ɨɛɴɹɫɧɢɬɶ ɱɬɨɩɪɢ ɫɬɚɧɞɚɪɬɧɵɯɭɫɥɨɜɢɹɯ ɧɟɜɨɡɦɨɠɧɚ
ɷɤɡɨɬɟɪɦɢɱɟɫɤɚɹɪɟɚɤɰɢɹ
ɝɋ2ɝ &2ɝ+2ɠ'+ ±ɤȾɠ"
+
Ɂɧɚɹɬɟɩɥɨɜɨɣ ɷɮɮɟɤɬɪɟɚɤɰɢɢ ɢɚɛɫɨɥɸɬɧɵɟ ɫɬɚɧɞɚɪɬɧɵɟɷɧɬɪɨɩɢɢ ɫɨ
ɨɬɜɟɬɫɬɜɭɸɳɢɯɜɟɳɟɫɬɜɨɩɪɟɞɟɥɢɬɟ'*
ɉɪɹɦɚɹ ɢɥɢ ɨɛɪɚɬɧɚɹ ɪɟɚɤɰɢɹ ɛɭɞɟɬ ɩɪɨɬɟɤɚɬɶ ɩɪɢ ɫɬɚɧɞɚɪɬɧɵɯ
ɭɫɥɨɜɢɹɯɜɫɢɫɬɟɦɟ12ɝ2
ɩɪɹɦɨɣɪɟɚɤɰɢɢ
'*
ɂɫɯɨɞɹɢɡɡɧɚɱɟɧɢɣɫɬɚɧɞɚɪɬɧɵɯɬɟɩɥɨɬɨɛɪɚɡɨɜɚɧɢɹɢɚɛɫɨɥɸɬɧɵɯ
ɝl12ɝ"Ɉɬɜɟɬɦɨɬɢɜɢɪɭɣɬɟɜɵɱɢɫɥɢɜ
ɫɬɚɧɞɚɪɬɧɵɯ ɷɧɬɪɨɩɢɣ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɜɟɳɟɫɬɜ ɜɵɱɢɫɥɢɬɟ '*
ɷɬɨɣɪɟɚɤɰɢɢ
ɩɪɨɬɟɤɚɸɳɟɣɩɨɭɪɚɜɧɟɧɢɸ
ɝ+ɋOɝ 1+&Oɤ
1+
Ɇɨɠɟɬɥɢɷɬɚɪɟɚɤɰɢɹɩɪɢɫɬɚɧɞɚɪɬɧɵɯɭɫɥɨɜɢɹɯɢɞɬɢɫɚɦɨɩɪɨɢɡɜɨɥɶɧɨ"
ɉɪɢɤɚɤɨɣɬɟɦɩɟɪɚɬɭɪɟɧɚɫɬɭɩɢɬɪɚɜɧɨɜɟɫɢɟɫɢɫɬɟɦɵ
ɜɷɬɨɦ
ɪɟɚɤɰɢɢ
&2ɝ+
ɉɪɢɤɚɤɨɣɬɟɦɩɟɪɚɬɭɪɟɧɚɫɬɭɩɢɬɪɚɜɧɨɜɟɫɢɟɫɢɫɬɟɦɵ
ɝ&2ɝ &2ɝ+ɝ'+ ɤȾɠ"
&+
ɇɚɨɫɧɨɜɚɧɢɢɫɬɚɧɞɚɪɬɧɵɯɬɟɩɥɨɬɨɛɪɚɡɨɜɚɧɢɹɢɚɛɫɨɥɸɬɧɵɯɫɬɚɧ
ɝl&+2+ɠ'+ ±ɤȾɠ"
ɞɚɪɬɧɵɯɷɧɬɪɨɩɢɣɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯɜɟɳɟɫɬɜɜɵɱɢɫɥɢɬɟ'*
ɤɚɸɳɟɣɩɨɭɪɚɜɧɟɧɢɸ1+
ɝ2ɝ 12ɝ+2ɝȼɨɡɦɨɠɧɚɥɢɷɬɚ
ɪɟɚɤɰɢɹɩɪɢɫɬɚɧɞɚɪɬɧɵɯɭɫɥɨɜɢɹɯ"
ɇɚɨɫɧɨɜɚɧɢɢɫɬɚɧɞɚɪɬɧɵɯɬɟɩɥɨɬɨɛɪɚɡɨɜɚɧɢɹɢɚɛɫɨɥɸɬɧɵɯɫɬɚɧ
ɞɚɪɬɧɵɯɷɧɬɪɨɩɢɣɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯɜɟɳɟɫɬɜɜɵɱɢɫɥɢɬɟ'*
ɤɚɸɳɟɣɩɨɭɪɚɜɧɟɧɢɸ&2
ɝ+ɝ &+ɝ+2ɠȼɨɡɦɨɠɧɚɥɢɷɬɚ
ɪɟɚɤɰɢɹɩɪɢɫɬɚɧɞɚɪɬɧɵɯɭɫɥɨɜɢɹɯ"
ȼɵɱɢɫɥɢɬɟ'+
ȼɨɡɦɨɠɧɚɥɢɷɬɚɪɟɚɤɰɢɹɜɨɫɫɬɚɧɨɜɥɟɧɢɹ)H
'6'*ɪɟɚɤɰɢɢɩɪɨɬɟɤɚɸɳɟɣɩɨɭɪɚɜɧɟɧɢɸ
)H
ɤ+ɝ )Hɤ+2ɝ
2
ɜɨɞɨɪɨɞɨɦɩɪɢɬɟɦɩɟɪɚ
2
ɬɭɪɚɯɢɄ"
ɪɟɚɤɰɢɢɩɪɨɬɟ
ɪɟɚɤɰɢɢɩɪɨɬɟ
ȼɵɱɢɫɥɢɬɟ'+
ȼɨɡɦɨɠɧɚɥɢɷɬɚɪɟɚɤɰɢɹɜɨɫɫɬɚɧɨɜɥɟɧɢɹ7L2
'6'*ɪɟɚɤɰɢɢɩɪɨɬɟɤɚɸɳɟɣɩɨɭɪɚɜɧɟɧɢɸ
ɤ&ɤ 7Lɤ&2ɝ
7L2
ɭɝɥɟɪɨɞɨɦɩɪɢɬɟɦɩɟɪɚɬɭ
ɪɚɯɢɄ"
ɇɚɨɫɧɨɜɚɧɢɢɫɬɚɧɞɚɪɬɧɵɯɬɟɩɥɨɬɨɛɪɚɡɨɜɚɧɢɹɢɚɛɫɨɥɸɬɧɵɯɫɬɚɧ
ɞɚɪɬɧɵɯɷɧɬɪɨɩɢɣɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯɜɟɳɟɫɬɜɜɵɱɢɫɥɢɬɟ'*
ɪɟɚɤɰɢɢɩɪɨɬɟ
ɤɚɸɳɟɣɩɨɭɪɚɜɧɟɧɢɸ
ɝ2ɝ &2ɝ+2ɠ
&
+
ȼɨɡɦɨɠɧɚɥɢɷɬɚɪɟɚɤɰɢɹɩɪɢɫɬɚɧɞɚɪɬɧɵɯɭɫɥɨɜɢɹɯ"
Ɉɩɪɟɞɟɥɢɬɟ ɩɪɢɤɚɤɨɣɬɟɦɩɟɪɚɬɭɪɟɧɚɱɧɟɬɫɹɪɟɚɤɰɢɹɜɨɫɫɬɚɧɨɜɥɟ
ɧɢɹ)H
ɩɪɨɬɟɤɚɸɳɚɹɩɨɭɪɚɜɧɟɧɢɸ
2
ɤ&2ɝ )H2ɤ&2ɝ'+ ɤȾɠ
)H
2
Ɉɤɫɢɞɚɡɨɬɚ,,ɧɟɨɛɯɨɞɢɦɵɣɞɥɹɩɪɨɢɡɜɨɞɫɬɜɚɚɡɨɬɧɨɣɤɢɫɥɨɬɵɢ
ɚɡɨɬɧɵɯɭɞɨɛɪɟɧɢɣɡɚɦɚɧɱɢɜɨɩɨɥɭɱɚɬɶɢɡɜɨɡɞɭɯɚɩɨɪɟɚɤɰɢɢ
1
ɝ2ɝ 12ɝ
Ɋɚɫɫɱɢɬɚɣɬɟɩɪɢɤɚɤɨɣɬɟɦɩɟɪɚɬɭɪɟɷɬɚɪɟɚɤɰɢɹɜɨɡɦɨɠɧɚɢɨɰɟɧɢɬɟɬɟɯ
ɧɢɱɟɫɤɭɸɨɫɭɳɟɫɬɜɢɦɨɫɬɶɩɪɨɜɟɞɟɧɢɹɷɬɨɣɪɟɚɤɰɢɢ
Ɋɚɡɥɨɠɟɧɢɟ ɧɢɬɪɚɬɚ ɚɦɦɨɧɢɹ ɩɪɢ ɧɚɝɪɟɜɚɧɢɢ ɜɨɡɦɨɠɧɨ ɩɨ ɞɜɭɦ
ɧɚɩɪɚɜɥɟɧɢɹɦ
ɚ 1+
ɛ 1+12
ɤ 1
12
ɤ 1ɝò2ɝ+
2ɝ+2ɝ
2ɝ
Ʉɚɤɨɟɢɡɧɢɯɛɨɥɟɟɜɟɪɨɹɬɧɨɩɪɢιɋ"
ȼɨɫɫɬɚɧɚɜɥɢɜɚɬɶɠɟɥɟɡɨɢɡɨɤɫɢɞɚɠɟɥɟɡɚ,,ɦɨɠɧɨɭɝɥɟɪɨɞɨɦɢɥɢ
ɨɤɫɢɞɨɦɭɝɥɟɪɨɞɚ,,
ɚ
)H2&ɝɪɚɮɢɬ )H&2
ɛ
)H2&2 )H&2
Ʉɚɤɚɹɢɡɷɬɢɯɪɟɚɤɰɢɣɛɨɥɟɟɜɟɪɨɹɬɧɚɩɪɢɫɬɚɧɞɚɪɬɧɨɣɬɟɦɩɟɪɚɬɭɪɟɢɩɪɢ
ɬɟɦɩɟɪɚɬɭɪɟ
ιɋ"
ɊȺɁȾȿɅɏɂɆɂɑȿɋɄȺəɄɂɇȿɌɂɄȺɂɊȺȼɇɈȼȿɋɂȿ
Ɂɚɜɢɫɢɦɨɫɬɶɫɤɨɪɨɫɬɢɯɢɦɢɱɟɫɤɨɣɪɟɚɤɰɢɢɨɬɤɨɧɰɟɧɬɪɚɰɢɢ
ɪɟɚɝɢɪɭɸɳɢɯɜɟɳɟɫɬɜ
ɋɨɝɥɚɫɧɨɡɚɤɨɧɭ ɞɟɣɫɬɜɢɹɦɚɫɫɡɞɦɩɪɢɩɨɫɬɨɹɧɧɨɣɬɟɦɩɟɪɚ
ɬɭɪɟɫɤɨɪɨɫɬɶɯɢɦɢɱɟɫɤɨɣɪɟɚɤɰɢɢɩɪɹɦɨɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚɩɪɨɢɡɜɟɞɟɧɢɸɤɨɧ
ɰɟɧɬɪɚɰɢɣɪɟɚɝɢɪɭɸɳɢɯɜɟɳɟɫɬɜɜɡɹɬɵɯɜɫɬɟɩɟɧɹɯɪɚɜɧɵɯɤɨɷɮɮɢɰɢɟɧɬɚɦɜ
ɭɪɚɜɧɟɧɢɢɪɟɚɤɰɢɣ
ȾɥɹɪɟɚɤɰɢɢDÂ$EÂ%oGÂ'ɟÂȿɦɚɬɟɦɚɬɢɱɟɫɤɨɟɜɵɪɚɠɟɧɢɟɡɞɦɢɦɟ
ɟɬɜɢɞ
9 NÂ&
ɝɞɟ 9±ɫɤɨɪɨɫɬɶɪɟɚɤɰɢɢɦɨɥɶɥ
N±ɤɨɧɫɬɚɧɬɚɫɤɨɪɨɫɬɢɯɢɦɢɱɟɫɤɨɣɪɟɚɤɰɢɢ
&
ɢ&%±ɤɨɧɰɟɧɬɪɚɰɢɢɜɟɳɟɫɬɜ$ɢ%
$
DE±ɤɨɷɮɮɢɰɢɟɧɬɵɩɟɪɟɞɜɟɳɟɫɬɜɚɦɢ$ɢ%ɜɭɪɚɜɧɟɧɢɢɪɟɚɤɰɢɢ
ɋɤɨɪɨɫɬɶɝɟɬɟɪɨɝɟɧɧɵɯɯɢɦɢɱɟɫɤɢɯɪɟɚɤɰɢɣɡɚɜɢɫɢɬɨɬɤɨɧɰɟɧɬɪɚɰɢɣɝɚ
ɡɨɨɛɪɚɡɧɵɯɢɥɢɠɢɞɤɢɯɪɟɚɝɟɧɬɨɜɢɧɟɡɚɜɢɫɢɬɨɬɤɨɧɰɟɧɬɪɚɰɢɢɬɜɟɪɞɨɣɮɚɡɵ
ȿɫɥɢ ɜ ɪɟɚɤɰɢɢ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɭɱɚɫɬɜɭɟɬ ɬɜɟɪɞɨɟ ɜɟɳɟɫɬɜɨ ɬɨ ɜ ɤɢɧɟɬɢɱɟ
ɫɤɨɟɭɪɚɜɧɟɧɢɟɧɟ ɜɯɨɞɢɬ ɟɝɨɤɨɧɰɟɧɬɪɚɰɢɹɬɚɤ ɤɚɤ ɨɧɚ ɩɨɫɬɨɹɧɧɚȾɥɹɪɟɚɤ
ɰɢɢɨɤɢɫɥɟɧɢɹɫɟɪɵ62
ɉɪɢɦɟɪɵ
ȼɨɫɤɨɥɶɤɨɪɚɡɢɡɦɟɧɹɟɬɫɹɫɤɨɪɨɫɬɶɩɪɹɦɨɣɢɨɛɪɚɬɧɨɣɪɟɚɤɰɢɣɜɫɢ
ɫɬɟɦɟɟɫɥɢɭɜɟɥɢɱɢɬɶɞɚɜɥɟɧɢɟɜɞɜɚɪɚɡɚ"
$
o62
D
E
Â&
ɢɥɢ9 NÂ>$@DÂ>%@E
%
Âɫ
ɭɪɚɜɧɟɧɢɟɡɞɦɩɪɢɧɢɦɚɟɬɜɢɞ9 NÂ>2
@
ɝ2ɝl62ɝ
62
Ɋɟɲɟɧɢɟ
ɍɜɟɥɢɱɟɧɢɟ ɞɚɜɥɟɧɢɹ ɜ ɫɢɫɬɟɦɟ ɜ ɪɚɡɚ ɜɵɡɨɜɟɬ ɭɦɟɧɶɲɟɧɢɟ ɨɛɴɟɦɚ ɜ
ɞɜɚ ɪɚɡɚ ɚ ɤɨɧɰɟɧɬɪɚɰɢɹ ɜɟɳɟɫɬɜɚ ɜɨɡɪɚɫɬɚɟɬ ɜ ɪɚɡɚ ɋɨɝɥɚɫɧɨɡɞɦ
ɧɚɱɚɥɶɧɚɹɫɤɨɪɨɫɬɶɩɪɹɦɨɣɪɟɚɤɰɢɢɪɚɜɧɚ
ɞɚɜɥɟɧɢɹ
9 N & & N & &
ɩɪ ɩɪ 62 2 ɩɪ 62 2
9N&&
ɩɪ 62 2
ɩɨɫɥɟɭɜɟɥɢɱɟɧɢɹ
ɉɨɫɥɟ ɭɜɟɥɢɱɟɧɢɹ ɞɚɜɥɟ
ɧɢɹɜɞɜɚɪɚɡɚɫɤɨɪɨɫɬɶɩɪɹɦɨɣɪɟɚɤɰɢɢɜɨɡɪɨɫɥɚɜɪɚɡ
ɋɤɨɪɨɫɬɶ ɨɛɪɚɬɧɨɣ ɪɟɚɤɰɢɢ ɩɨ ɡ ɞ ɦ ɜ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɪɚɜɧɚ
9N&
ɨɛ ɨɛ 62
ɩɨɫɥɟɭɜɟɥɢɱɟɧɢɹɞɚɜɥɟɧɢɹ
9N&N&
ɨɛ ɨɛ 62 ɨɛ 62
ɉɨɫɥɟɭɜɟɥɢɱɟɧɢɹɞɚɜɥɟɧɢɹɜɪɚɡɚɫɤɨɪɨɫɬɶɨɛɪɚɬɧɨɣɪɟɚɤɰɢɢɜɨɡɪɨɫɥɚ
1
ɜɪɚɡɚ
ɇɚɩɢɫɚɬɶɜɵɪɚɠɟɧɢɟɡɚɤɨɧɚɞɟɣɫɬɜɢɹɦɚɫɫɞɥɹɪɟɚɤɰɢɣ
1
ɝ+ɝo1+ɝ
ɚ
ɋDɋ2
ɛ
ɬɜoɋɚ2ɬɜɋ2ɝ
Ɋɟɲɟɧɢɟ
ɚ
9N& &
=
&
ɛ9
+
±ɩɨɫɤɨɥɶɤɭɤɚɪɛɨɧɚɬɤɚɥɶɰɢɹ±ɬɜɟɪɞɨɟɜɟɳɟɫɬɜɨɫɤɨɪɨɫɬɶ
&2
ɪɟɚɤɰɢɢɧɟɡɚɜɢɫɢɬɨɬɤɨɧɰɟɧɬɪɚɰɢɢɬɜɟɪɞɨɣɮɚɡɵ
ɊɟɚɤɰɢɹɩɪɨɬɟɤɚɟɬɫɨɝɥɚɫɧɨɭɪɚɜɧɟɧɢɸȺ ȼ ɋɤɨɧɰɟɧɬɪɚɰɢɹɜɟ
ɳɟɫɬɜɚȺ ɦɨɥɶɥɚɜɟɳɟɫɬɜɚ% ɦɨɥɶɥɄɨɧɫɬɚɧɬɚɫɤɨɪɨɫɬɢ ɪɚɜɧɚ
N ɥ
Âɦɨɥɶ±Âɫ±ȼɵɱɢɫɥɢɬɶɫɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢɜɧɚɱɚɥɶɧɵɣɦɨɦɟɧɬɢɤɨɝɞɚ
ɨɫɬɚɧɟɬɫɹɜɟɳɟɫɬɜɚȺ
Ɋɟɲɟɧɢɟ
ɋɨɝɥɚɫɧɨɡɞɦ9 NÂ&$Â&
9
ɋɤɨɪɨɫɬɶɪɟɚɤɰɢɢɜɧɚɱɚɥɶɧɵɣɦɨɦɟɧɬ
%
= ÂÂ ɦɨɥɶɥÂɫ
ɄɨɝɞɚɨɫɬɚɧɟɬɫɹɜɟɳɟɫɬɜɚȺɤɨɧɰɟɧɬɪɚɰɢɹɟɝɨɫɬɚɧɟɬ
ή ɦɨɥɶɥ
ɁɧɚɱɢɬɤɨɧɰɟɧɬɪɚɰɢɹɜɟɳɟɫɬɜɚȺɭɦɟɧɶɲɢɬɫɹɧɚ± ɦɨɥɶɥ
ɌɚɤɤɚɤɜɟɳɟɫɬɜɚȺɢȼ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɬ ɦɟɠɞɭ ɫɨɛɨɣ ɜɫɨɨɬɧɨɲɟɧɢɢɬɨ
ɤɨɧɰɟɧɬɪɚɰɢɹɜɟɳɟɫɬɜɚȼɭɦɟɧɶɲɢɥɚɫɶɧɚɦɨɥɶɥÂɢɫɬɚɥɚ ɪɚɜɧɨɣ
ɦɨɥɶɥ±ɋɥɟɞɨɜɚɬɟɥɶɧɨ
= ÂÂ ɦɨɥɶɥÂɫ
9
Ɂɚɞɚɱɢ
Ɋɚɫɫɱɢɬɚɣɬɟ ɧɚɱɚɥɶɧɭɸ ɫɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢ Ⱥ ȼ o ɋ ɢ ɫɤɨɪɨɫɬɶ
ɷɬɨɣ ɪɟɚɤɰɢɢ ɱɟɪɟɡ ɧɟɤɨɬɨɪɨɟ ɜɪɟɦɹ ɤɨɝɞɚ ɤɨɧɰɟɧɬɪɚɰɢɹ Ⱥ ɭɦɟɧɶɲɢɬɫɹ ɧɚ
ɦɨɥɶɥ ɇɚɱɚɥɶɧɚɹ ɤɨɧɰɟɧɬɪɚɰɢɹ ɜɟɳɟɫɬɜɚ Ⱥɪɚɜɧɚ ɦɨɥɶɥɚɜɟɳɟɫɬɜɚ
ȼ±ɦɨɥɶɥɄɨɧɫɬɚɧɬɚɫɤɨɪɨɫɬɢɪɟɚɤɰɢɢɪɚɜɧɚɥ
Ɋɚɫɫɱɢɬɚɣɬɟɢɡɦɟɧɟɧɢɟɫɤɨɪɨɫɬɢɯɢɦɢɱɟɫɤɨɣɪɟɚɤɰɢɢ
Âɦɨɥɶ±Âɫ±
&2ɝ2
ɝo&2ɝ
ɩɪɢɭɦɟɧɶɲɟɧɢɢɞɚɜɥɟɧɢɹɜɫɢɫɬɟɦɟɡɚɫɱɟɬɟɟɪɚɫɲɢɪɟɧɢɹɜɪɚɡɌɟɦɩɟɪɚ
ɬɭɪɚɫɢɫɬɟɦɵɩɨɞɞɟɪɠɢɜɚɟɬɫɹɩɨɫɬɨɹɧɧɨɣ
ȼɧɚɱɚɥɶɧɵɣɦɨɦɟɧɬɩɪɨɬɟɤɚɧɢɹɪɟɚɤɰɢɢ1
ɬɪɚɰɢɢɛɵɥɢɪɚɜɧɵɦɨɥɶɥ>1
@ >+@ >1+@ Ʉɚɤɨɜɵɤɨɧɰɟɧɬɪɚ
+l1+ɤɨɧɰɟɧ
ɰɢɢɚɡɨɬɚɢɜɨɞɨɪɨɞɚɬɨɝɞɚɤɨɝɞɚɤɨɧɰɟɧɬɪɚɰɢɹɚɦɦɢɚɤɚɦɨɥɶɥ"
ɇɚɱɚɥɶɧɵɟɤɨɧɰɟɧɬɪɚɰɢɢɜɟɳɟɫɬɜɜɪɟɚɤɰɢɢ&2+
2l&2+
ɛɵɥɢɪɚɜɧɵɦɨɥɶɥ>&2@ >+2@ >&2@ >+@ ȼɵɱɢɫɥɢɬɟ
ɤɨɧɰɟɧɬɪɚɰɢɢɜɫɟɯɭɱɚɫɬɜɭɸɳɢɯɜ ɪɟɚɤɰɢɢ ɜɟɳɟɫɬɜ ɩɨɫɥɟɬɨɝɨɤɚɤɩɪɨɪɟɚɝɢ
ɪɨɜɚɥɨ+
2
Ʉɨɧɫɬɚɧɬɚ ɫɤɨɪɨɫɬɢ ɪɟɚɤɰɢɢ Ⱥ % l ɋ ɪɚɜɧɚ ɥ
Âɦɨɥɶ±Âɫ±
ɇɚɱɚɥɶɧɵɟ ɤɨɧɰɟɧɬɪɚɰɢɢ >$@ ɢ >%@ ɦɨɥɶɥ ȼ ɪɟɡɭɥɶɬɚɬɟ ɪɟɚɤɰɢɢ
ɤɨɧɰɟɧɬɪɚɰɢɢɜɟɳɟɫɬɜɚȼɨɤɚɡɚɥɚɫɶɪɚɜɧɨɣɦɨɥɶɥȼɵɱɢɫɥɢɬɟɤɚɤɨɜɚɤɨɧ
ɰɟɧɬɪɚɰɢɹɜɟɳɟɫɬɜɚȺɢɫɤɨɪɨɫɬɶɪɟɚɤɰɢɢ
Ɋɟɚɤɰɢɹɢɞɟɬɩɨɭɪɚɜɧɟɧɢɸ1+
2l12+2Ʉɚɤɢɡɦɟ
ɧɢɬɫɹɫɤɨɪɨɫɬɶɪɟɚɤɰɢɢɟɫɥɢɭɜɟɥɢɱɢɬɶɞɚɜɥɟɧɢɟɜɪɚɡɚ"
ɊɟɚɤɰɢɹɦɟɠɞɭɜɟɳɟɫɬɜɚɦɢȺɢȼɜɵɪɚɠɚɟɬɫɹɭɪɚɜɧɟɧɢɟɦ
Ⱥȼlɋ
ɇɚɱɚɥɶɧɚɹ ɤɨɧɰɟɧɬɪɚɰɢɹ ɜɟɳɟɫɬɜɚ Ⱥ ɪɚɜɧɚ ɦɨɥɶɥ ɚ ɜɟɳɟɫɬɜɚ ȼ
ɦɨɥɶɥɄɨɧɫɬɚɧɬɚɫɤɨɪɨɫɬɢɪɟɚɤɰɢɢɪɚɜɧɚ ɥ
Âɦɨɥɶ±Âɦɢɧ±Ɋɚɫɫɱɢɬɚɣɬɟ
ɧɚɱɚɥɶɧɭɸɫɤɨɪɨɫɬɶɪɟɚɤɰɢɢɩɨɢɫɬɟɱɟɧɢɢɧɟɤɨɬɨɪɨɝɨɜɪɟɦɟɧɢɤɨɝɞɚɤɨɧɰɟɧ
ɬɪɚɰɢɹɜɟɳɟɫɬɜɚȺɭɦɟɧɶɲɚɟɬɫɹɧɚɦɨɥɶ
Ɋɚɡɥɨɠɟɧɢɟ 1
ɩɪɨɬɟɤɚɟɬɩɨɭɪɚɜɧɟɧɢɸ 1
ɰɢɢ ɪɚɜɧɚ Â
±ɥ
2ɧɚɩɨɜɟɪɯɧɨɫɬɢɡɨɥɨɬɚɩɪɢɜɵɫɨɤɢɯɬɟɦɩɟɪɚɬɭɪɚɯ
2l12Ʉɨɧɫɬɚɧɬɚɫɤɨɪɨɫɬɢ ɞɚɧɧɨɣ ɪɟɚɤ
Âɦɨɥɶ±Âɫ± ɩɪɢ Ʉ ɇɚɱɚɥɶɧɚɹ ɤɨɧɰɟɧɬɪɚɰɢɹ 12 ±
ɦɨɥɶɥ Ɉɩɪɟɞɟɥɢɬɟ ɫɤɨɪɨɫɬɶ ɩɪɢ ɡɚɞɚɧɧɨɣɬɟɦɩɟɪɚɬɭɪɟ ɜ ɧɚɱɚɥɶɧɵɣɦɨ
ɦɟɧɬɢɜɬɨɬɦɨɦɟɧɬɤɨɝɞɚɪɚɡɥɨɠɢɬɫɹ1
Ɋɟɚɤɰɢɹ ɢɞɟɬ ɩɨ ɭɪɚɜɧɟɧɢɸ 12 2
ɝɢɪɭɸɳɢɯ ɜɟɳɟɫɬɜ ɛɵɥɢ ɦɨɥɶɥ >12@ >2
2
12Ʉɨɧɰɟɧɬɪɚɰɢɢɪɟɚ
@ Ʉɚɤɢɡɦɟɧɢɬɫɹɫɤɨ
ɪɨɫɬɶɪɟɚɤɰɢɢ ɟɫɥɢɤɨɧɰɟɧɬɪɚɰɢɸ ɤɢɫɥɨɪɨɞɚ ɭɜɟɥɢɱɢɬɶ ɞɨ ɦɨɥɶɥ ɚ ɤɨɧ
ɰɟɧɬɪɚɰɢɸɨɤɫɢɞɚɚɡɨɬɚɞɨɦɨɥɶɥ"
Ɋɟɚɤɰɢɹɩɪɨɬɟɤɚɟɬɩɨɭɪɚɜɧɟɧɢɸ
1D
+62 1D62+626
62
Ʉɚɤɢɡɦɟɧɢɬɫɹɫɤɨɪɨɫɬɶɪɟɚɤɰɢɢɩɨɫɥɟɪɚɡɛɚɜɥɟɧɢɹɪɟɚɝɢɪɭɸɳɟɣɫɦɟɫɢɜ
ɪɚɡɚ"
Ɋɟɚɤɰɢɹ ɜɵɪɚɠɚɟɬɫɹɭɪɚɜɧɟɧɢɟɦɇɋO2
l+2&Oɑɟɪɟɡ
ɧɟɤɨɬɨɪɨɟ ɜɪɟɦɹ ɩɨɫɥɟ ɧɚɱɚɥɚ ɪɟɚɤɰɢɢ ɤɨɧɰɟɧɬɪɚɰɢɢ ɭɱɚɫɬɜɭɸɳɢɯ ɜɧɟɣɜɟ
ɳɟɫɬɜɫɬɚɥɢɦɨɥɶɥ>+&O@ >2
ɰɟɧɬɪɚɰɢɢ+&Oɢ2
ɇɚɣɬɢɡɧɚɱɟɧɢɟɤɨɧɫɬɚɧɬɵɫɤɨɪɨɫɬɢɪɟɚɤɰɢɢȺȼoȺȼɟɫɥɢɩɪɢ
ɤɨɧɰɟɧɬɪɚɰɢɹɯɜɟɳɟɫɬɜȺɢȼɪɚɜɧɵɯɫɨɨɬɜɟɬɫɬɜɟɧɧɨɢ ɦɨɥɶɥ ɫɤɨ
ɪɨɫɬɶɪɟɚɤɰɢɢɪɚɜɧɚÂ
ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɢɡɦɟɧɢɬɫɹ ɫɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢ Ⱥ ȼoȺ
ɜɧɚɱɚɥɟɪɟɚɤɰɢɢ"
±
ɦɨɥɶɥÂɦɢɧ
@ >&O@ Ʉɚɤɢɦɢ ɛɵɥɢɤɨɧ
ȼ ɟɫɥɢ
ɤɨɧɰɟɧɬɪɚɰɢɸ ɜɟɳɟɫɬɜɚ Ⱥ ɭɜɟɥɢɱɢɬɶ ɜ ɪɚɡɚ ɚ ɤɨɧɰɟɧɬɪɚɰɢɸ ɜɟɳɟɫɬɜɚ ȼ
ɭɦɟɧɶɲɢɬɶɜɪɚɡɚ"
ȼɨɫɤɨɥɶɤɨɪɚɡɫɥɟɞɭɟɬɭɜɟɥɢɱɢɬɶɤɨɧɰɟɧɬɪɚɰɢɸɜɟɳɟɫɬɜɚȼɜɫɢ
ɫɬɟɦɟȺ
ɝȼɝ Ⱥȼɝɱɬɨɛɵɩɪɢɭɦɟɧɶɲɟɧɢɢɤɨɧɰɟɧɬɪɚɰɢɢɜɟɳɟɫɬɜɚ
Ⱥɜɪɚɡɚɫɤɨɪɨɫɬɶɩɪɹɦɨɣɪɟɚɤɰɢɢɧɟɢɡɦɟɧɢɥɚɫɶ"
ȼɫɢɫɬɟɦɟ&2&O
&2&OɤɨɧɰɟɧɬɪɚɰɢɸɋɈɭɜɟɥɢɱɢɥɢɨɬɞɨ
ɦɨɥɶɥɚɤɨɧɰɟɧɬɪɚɰɢɸɯɥɨɪɚ±ɨɬɞɨɦɨɥɶɥȼɨɫɤɨɥɶɤɨɪɚɡɜɨɡ
ɪɨɫɥɚɫɤɨɪɨɫɬɶɩɪɹɦɨɣɪɟɚɤɰɢɢ"
ɊɟɚɤɰɢɹɦɟɠɞɭɜɟɳɟɫɬɜɚɦɢȺɢȼɜɵɪɚɠɚɟɬɫɹɭɪɚɜɧɟɧɢɟɦȺȼo
o ɋ ɇɚɱɚɥɶɧɵɟ ɤɨɧɰɟɧɬɪɚɰɢɢ ɫɨɫɬɚɜɥɹɸɬ >$
@ ɦɨɥɶɥ >%@
ɦɨɥɶɥ Ʉɨɧɫɬɚɧɬɚ ɫɤɨɪɨɫɬɢ ɪɟɚɤɰɢɢ ɪɚɜɧɚ ɇɚɣɬɢɧɚɱɚɥɶɧɭɸ ɫɤɨ
ɪɨɫɬɶɪɟɚɤɰɢɢɫɤɨɪɨɫɬɶɪɟɚɤɰɢɢɩɨɢɫɬɟɱɟɧɢɢɧɟɤɨɬɨɪɨɝɨɜɪɟɦɟɧɢɤɨɝɞɚɤɨɧ
ɰɟɧɬɪɚɰɢɹɜɟɳɟɫɬɜɚȺɭɦɟɧɶɲɢɬɫɹɧɚɦɨɥɶɥ
Ʉɚɤ ɢɡɦɟɧɢɬɫɹ ɫɤɨɪɨɫɬɶ ɪɟɚɤɰɢɢ 12ɝ 2
ɝ o12ɝ ɟɫɥɢ
ɚɭɜɟɥɢɱɢɬɶɞɚɜɥɟɧɢɟɜɫɢɫɬɟɦɟɜɪɚɡɚɛɭɦɟɧɶɲɢɬɶɨɛɴɟɦɫɢɫɬɟɦɵɜɪɚɡɚ
ɜɩɨɜɵɫɢɬɶɤɨɧɰɟɧɬɪɚɰɢɸ12ɜɪɚɡɚ"
Ʉɨɧɫɬɚɧɬɚ ɫɤɨɪɨɫɬɢɩɪɨɫɬɨɣɪɟɚɤɰɢɢ+
ɝ,ɝ +,ɝɩɪɢɧɟ
ɤɨɬɨɪɨɣɬɟɦɩɟɪɚɬɭɪɟɪɚɜɧɚɂɫɯɨɞɧɵɟɤɨɧɰɟɧɬɪɚɰɢɢɜɨɞɨɪɨɞɚɢɣɨɞɚɪɚɜ
ɧɵɢɦɨɥɶɥɈɩɪɟɞɟɥɢɬɟɧɚɱɚɥɶɧɭɸɫɤɨɪɨɫɬɶɪɟɚɤɰɢɢɢɫɤɨɪɨɫɬɶɟɺɜ
ɬɨɬɦɨɦɟɧɬɤɨɝɞɚɤɨɧɰɟɧɬɪɚɰɢɹɜɨɞɨɪɨɞɚɭɦɟɧɶɲɢɥɚɫɶɜɞɜɨɟ
Ɂɚɜɢɫɢɦɨɫɬɶɫɤɨɪɨɫɬɢɯɢɦɢɱɟɫɤɨɣɪɟɚɤɰɢɢɨɬɬɟɦɩɟɪɚɬɭɪɵ
ɗɧɟɪɝɢɹɚɤɬɢɜɚɰɢɢ
Ɂɚɜɢɫɢɦɨɫɬɶ ɫɤɨɪɨɫɬɢ ɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɜɵɪɚɠɚɟɬɫɹ
ɷɦɩɢɪɢɱɟɫɤɢɦ
ιɋɫɤɨɪɨɫɬɶɛɨɥɶɲɢɧɫɬɜɚɝɨɦɨɝɟɧɧɵɯɪɟɚɤɰɢɣɭɜɟɥɢɱɢɜɚɟɬɫɹɜ±ɪɚɡɚ
Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹɮɨɪɦɭɥɚɷɬɨɝɨɩɪɚɜɢɥɚ
9
ɝɞɟ
7
J ± ɬɟɦɩɟɪɚɬɭɪɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɫɤɨɪɨɫɬɢ ɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ Ɇɟɠɞɭ
ɫɤɨɪɨɫɬɶɸɩɪɨɬɟɤɚɧɢɹɪɟɚɤɰɢɣɢɢɯɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶɸɫɭɳɟɫɬɜɭɟɬɨɛ
ɪɚɬɧɨɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚɹɡɚɜɢɫɢɦɨɫɬɶ
ɝɞɟ W
ɢW ± ɜɪɟɦɹ ɩɪɨɬɟɤɚɧɢɹ ɪɟɚɤɰɢɢ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɚɯ 7ɢ7 Ɍɨɝɞɚ ɩɨ
ɩɪɚɜɢɥɭȼɚɧɬȽɨɮɮɚ
ɩɪɚɜɢɥɨɦȼɚɧɬȽɨɮɮɚ ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ ɧɚ
77
99Ȗ
77
9
ɢ
±ɫɤɨɪɨɫɬɢɯɢɦɢɱɟɫɤɢɯɪɟɚɤɰɢɣɩɪɢɬɟɦɩɟɪɚɬɭɪɚɯ7ɢ7
7
9
7
9W
7
W
77
W
W
Ʉɚɠɞɚɹ ɯɢɦɢɱɟɫɤɚɹ ɪɟɚɤɰɢɹ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɨɩɪɟɞɟɥɟɧɧɵɦ
ɱɟɫɤɢɦ ɛɚɪɶɟɪɨɦ
ɤɨɬɨɪɵɣɩɪɟɨɞɨɥɟɜɚɸɬ ɦɨɥɟɤɭɥɵ ɱɬɨɛɵɜɫɬɭɩɢɬɶɜɪɟɚɤ
Ȗ
ɷɧɟɪɝɟɬɢ-
ɰɢɸɢɨɛɪɚɡɨɜɚɬɶɧɨɜɵɟɜɟɳɟɫɬɜɚȾɥɹɨɫɭɳɟɫɬɜɥɟɧɢɹɯɢɦɢɱɟɫɤɨɝɨɜɡɚɢɦɨɞɟɣ
ɫɬɜɢɹ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɢ ɦɨɥɟɤɭɥɵ ɞɨɥɠɧɵɨɛɥɚɞɚɬɶ ɢɡɛɵɬɨɱɧɨɣ ɷɧɟɪɝɢɟɣ ɩɨ
ɫɪɚɜɧɟɧɢɸɫɨɫɪɟɞɧɢɦɡɚɩɚɫɨɦɷɧɟɪɝɢɢɜɫɟɯɦɨɥɟɤɭɥ
ɂɡɛɵɬɨɱɧɚɹ ɷɧɟɪɝɢɹ ɤɨɬɨɪɨɣ ɨɛɥɚɞɚɸɬ ɦɨɥɟɤɭɥɵ ɜɫɬɭɩɚɸɳɢɟ ɜ ɯɢɦɢ
ɱɟɫɤɨɟɜɡɚɢɦɨɞɟɣɫɬɜɢɟɧɚɡɵɜɚɟɬɫɹ±
ɷɧɟɪɝɢɹ ɚɤɬɢɜɚɰɢɢ ȿ
ɚ
Ɂɚɜɢɫɢɦɨɫɬɶ ɤɨɧɫɬɚɧɬɵ ɫɤɨɪɨɫɬɢ ɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ
ɨɩɪɟɞɟɥɹɟɬɫɹ
ɭɪɚɜɧɟɧɢɟɦ Ⱥɪɪɟɧɢɭɫɚ
ɝɞɟ
.
7
OJ
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7
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.
±ɤɨɧɫɬɚɧɬɵɫɤɨɪɨɫɬɢɪɟɚɤɰɢɢɩɪɢɬɟɦɩɟɪɚɬɭɪɚɯɌɢɌ
7
7
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©¹
5±ɭɧɢɜɟɪɫɚɥɶɧɚɹɝɚɡɨɜɚɹɩɨɫɬɨɹɧɧɚɹȾɠɦɨɥɶÂɄ
ȿ
±ɷɧɟɪɝɢɹɚɤɬɢɜɚɰɢɢɤȾɠɦɨɥɶ
D
ɉɪɢɦɟɪɵ
Ɍɟɦɩɟɪɚɬɭɪɧɵɣɤɨɷɮɮɢɰɢɟɧɬ ɫɤɨɪɨɫɬɢɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ ɪɚɜɟɧ
Ʉɚɤɢɡɦɟɧɢɬɫɹɫɤɨɪɨɫɬɶɷɬɨɣɪɟɚɤɰɢɢɩɪɢɭɜɟɥɢɱɟɧɢɢɬɟɦɩɟɪɚɬɭɪɵɨɬ
ιɋ"
ιɋɞɨ
Ɋɟɲɟɧɢɟ
ɉɨɩɪɚɜɢɥɭȼɚɧɬȽɨɮɮɚ
77
9
9
7
Ȗ
7
ɋɤɨɪɨɫɬɶɪɟɚɤɰɢɢɜɨɡɪɚɫɬɚɟɬɜɪɚɡ
ɉɪɢ Ʉ ɪɟɚɤɰɢɹ ɡɚɤɚɧɱɢɜɚɟɬɫɹ ɡɚ ɫ ɋɤɨɥɶɤɨ ɜɪɟɦɟɧɢ ɛɭɞɟɬ
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