Введение в теорию вероятностей. Учебное пособие
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ɧɢɹ T ɨɫɬɚɟɬɫɹ ɧɟɢɡɜɟɫɬɧɵɦ Ⱦɥɹ ɟɝɨ ɨɰɟɧɤɢ ɞɨɫɬɚɬɨɱɧɨ ɢɦɟɬɶ ɨɞɧɨ ɭɪɚɜɧɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ɷɬɨɝɨ ɩɚɪɚɦɟɬɪɚ ɉɨɫɤɨɥɶɤɭ ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɠɢɞɚɧɢɟ P ɫɥɭ ɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ ɏ ɬɚɤɠɟ ɡɚɜɢɫɢɬ ɨɬ ɷɬɨɝɨ ɩɚɪɚɦɟɬɪɚ ɬ ɟ P Ɇ ɏ T ɬɨ ɢɦɟɟɦ ɫɦ ɩ ɫɥɟɞɭɸɳɟɟ ɩɪɢɛɥɢɠɟɧɧɨɟ ɪɚɜɟɧɫɬɜɨ ɞɥɹ ɧɚɯɨɠɞɟɧɢɹ T
xB | Ɇ ɏ T
ȿɫɥɢ ɮɭɧɤɰɢɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɞɜɭɦɹ ɧɟɢɡɜɟɫɬɧɵɦɢ ɩɚɪɚɦɟɬɪɚ ɦɢ ɬɨ ɟɫɬɶ ɢɦɟɟɬ ɜɢɞ F x T T ɬɨ ɞɥɹ ɢɯ ɨɰɟɧɤɢ ɧɟɨɛɯɨɞɢɦɵ ɞɜɚ ɭɪɚɜɧɟɧɢɹ ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɫɥɟɞɭɟɬ ɩɨɥɶɡɨɜɚɬɶɫɹ ɫɢɫɬɟɦɨɣ ɞɜɭɯ ɩɪɢɛɥɢɠɟɧɧɵɯ ɪɚɜɟɧɫɬɜ
xȼ | M X T T
®
¯Dȼ | D X T T
ɍɤɚɡɚɧɧɵɣ ɫɩɨɫɨɛ ɧɚɯɨɠɞɟɧɢɹ ɧɟɢɡɜɟɫɬɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɧɚɡɵɜɚɟɬɫɹ ɦɟɬɨɞɨɦ ɦɨɦɟɧɬɨɜ
ɇɚɣɞɟɦ ɧɚɩɪɢɦɟɪ ɦɟɬɨɞɨɦ ɦɨɦɟɧɬɨɜ ɨɰɟɧɤɭ ɩɚɪɚɦɟɬɪɨɜ a ɢ b ɪɚɜɧɨɦɟɪ ɧɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɪɚɜɧɨɦɟɪɧɨ ɪɚɫɩɪɟɞɟɥɟɧɧɨɝɨ ɤɨɥɢɱɟɫɬɜɟɧɧɨɝɨ ɩɪɢɡɧɚɤɚ ɝɟɧɟɪɚɥɶɧɨɣ ɫɨɜɨɤɭɩɧɨɫɬɢ ɂɦɟɟɦ ɫɢɫɬɟɦɭ
®xȼ | M X a b ¯Dȼ | D X a b
ɢɥɢ ɭɱɢɬɵɜɚɹ ɱɬɨ ɞɥɹ ɪɚɜɧɨɦɟɪɧɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ
M X a b ɢ D X b a
ɢɦɟɟɦ
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Ɋɟɲɢɜ ɷɬɭ ɫɢɫɬɟɦɭ ɩɨɥɭɱɢɦ ɢɫɤɨɦɵɟ ɨɰɟɧɤɢ
a x ȼ Vȼ b x ȼ Vȼ
ɝɞɟ Vȼ Dȼ
ɂɧɬɟɪɜɚɥɶɧɨɣ ɧɚɡɵɜɚɸɬ ɨɰɟɧɤɭ ɤɨɬɨɪɚɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɞɜɭɦɹ ɱɢɫɥɚ ɦɢ ± ɤɨɧɰɚɦɢ ɢɧɬɟɪɜɚɥɚ ɇɚɞɟɠɧɨɫɬɶɸ ɞɨɜɟɪɢɬɟɥɶɧɨɣ ɜɟɪɨɹɬɧɨɫɬɶɸ ɨɰɟɧ ɤɢ T ɧɚɡɵɜɚɸɬ ɜɟɪɨɹɬɧɨɫɬɶ J ɫ ɤɨɬɨɪɨɣ ɨɬɤɥɨɧɟɧɢɟ _T T _ ɨɤɚɡɵɜɚɟɬɫɹ ɡɚɞɚɧɧɨ ɦɚɥɵɦ
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ɇɚɢɛɨɥɟɟ ɱɚɫɬɨ ɡɚɞɚɸɬ ɧɚɞɟɠɧɨɫɬɶ ɪɚɜɧɭɸ ɂɧɬɟɪɜɚɥT ± G T G ɧɚɡɵɜɚɸɬ ɞɨɜɟɪɢɬɟɥɶɧɵɦ ɢɧɬɟɪɜɚɥɨɦ ɞɥɹ ɨɰɟɧɤɢ ɩɚɪɚɦɟɬɪɚ T
Ɋɚɫɫɦɨɬɪɢɦ ɬɚɤ ɧɚɡɵɜɚɟɦɵɟ ɞɨɜɟɪɢɬɟɥɶɧɵɟ ɢɧɬɟɪɜɚɥɵ ɞɥɹ ɨɰɟɧɤɢ ɦɚ ɬɟɦɚɬɢɱɟɫɤɨɝɨ ɨɠɢɞɚɧɢɹ ɧɨɪɦɚɥɶɧɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɪɢ ɢɡɜɟɫɬɧɨɦ ɫɪɟɞ ɧɟɦ ɤɜɚɞɪɚɬɢɱɟɫɤɨɦ ɨɬɤɥɨɧɟɧɢɢ V ɉɭɫɬɶ ɤɨɥɢɱɟɫɬɜɟɧɧɵɣ ɩɪɢɡɧɚɤ ɏ ɝɟɧɟɪɚɥɶ ɧɨɣ ɫɨɜɨɤɭɩɧɨɫɬɢ ɪɚɫɩɪɟɞɟɥɟɧ ɫ ɩɥɨɬɧɨɫɬɶɸ
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ɧɨɪɦɚɥɶɧɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɡɞɟɫɶ ɩɚɪɚɦɟɬɪ ɚ ɟɫɬɶ ɡɧɚɱɟɧɢɟ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɨɠɢɞɚɧɢɹ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ ɏ
ɉɪɟɞɩɨɥɨɠɢɦ ɱɬɨ ɫɪɟɞɧɟɟ ɤɜɚɞɪɚɬɢɱɟɫɤɨɟ ɨɬɤɥɨɧɟɧɢɟ V ɷɬɨɝɨ ɪɚɫɩɪɟɞɟ ɥɟɧɢɹ ɢɡɜɟɫɬɧɨ ɢ ɢɡɜɥɟɱɟɧɚ ɜɵɛɨɪɤɚ ɨɛɴɟɦɚ n Ɍɪɟɛɭɟɬɫɹ ɨɰɟɧɢɬɶ ɧɟɢɡɜɟɫɬɧɨɟ ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɠɢɞɚɧɢɟ ɚ ɩɨ ɜɵɛɨɪɨɱɧɨɣ ɫɪɟɞɧɟɣ ɫ ɡɚɞɚɧɧɨɣ ɧɚɞɟɠɧɨɫɬɶɸ J
ȿɫɥɢ
P _xB ± a_ G J
ɬɨ ɡɧɚɱɟɧɢɟ G ɪɚɞɢɭɫ ɞɨɜɟɪɢɬɟɥɶɧɨɝɨ ɢɧɬɟɪɜɚɥɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜ ɜɢɞɟ
G t Vn
ɝɞɟ ɱɢɫɥɨ t ɦɨɠɟɬ ɛɵɬɶ ɧɚɣɞɟɧɨ ɢɡ ɫɨɨɬɧɨɲɟɧɢɹ Ɏ t J ɩɨ ɬɚɛɥ ɉɪɢɥɨɠɟ
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ɧɢɣ ɋɥɟɞɨɜɚɬɟɥɶɧɨ ɫ ɧɚɞɟɠɧɨɫɬɶɸ J ɞɨɜɟɪɢɬɟɥɶɧɵɣ ɢɧɬɟɪɜɚɥ |
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ɩɨɤɪɵɜɚɟɬ ɧɟɢɡɜɟɫɬɧɵɣ ɩɚɪɚɦɟɬɪ ɚ ɬɨɱɧɨɫɬɶ ɨɰɟɧɤɢ ɟɫɬɶ G t |
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3. Метод наименьших квадратов
ɉɪɟɞɩɨɥɨɠɢɦ ɱɬɨ ɷɦɩɢɪɢɱɟɫɤɢɦ ɩɭɬɟɦ ɜɵɹɜɥɟɧɚ ɡɚɜɢɫɢɦɨɫɬɶ ɦɟɠɞɭ ɜɟɥɢɱɢɧɚɦɢ X ɢ Y ɝɞɟ Y ± ɫɥɭɱɚɣɧɚɹ ɜɟɥɢɱɢɧɚ ɇɚɩɪɢɦɟɪ ɷɤɫɩɟɪɢɦɟɧɬ ɦɨ ɠɟɬ ɫɨɫɬɨɹɬɶ ɜ ɢɡɦɟɪɟɧɢɢ ɡɧɚɱɟɧɢɣ ɭ ɭ ɭɩ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ Y ɜ ɬɨɱ ɤɚɯ ɯ ɯ ɯɩ ɉɨɥɭɱɟɧɧɚɹ ɧɚ ɤɨɨɪɞɢɧɚɬɧɨɣ ɩɥɨɫɤɨɫɬɢ ɫɢɫɬɟɦɚ ɬɨɱɟɤ ɯi yj j n ɧɚɡɵɜɚɟɬɫɹ ɞɢɚɝɪɚɦɦɨɣ ɪɚɫɫɟɹɧɢɹ ɉɪɢ ɷɬɨɦ ɩɨ ɯɚɪɚɤɬɟɪɭ ɪɚɫɩɨɥɨɠɟ ɧɢɹ ɬɨɱɟɤ ɦɨɠɟɬ ɛɵɬɶ ɫɞɟɥɚɧ ɜɵɜɨɞ ɨ ɜɨɡɦɨɠɧɨɦ ɜɢɞɟ ɨɛɴɟɤɬɢɜɧɨ ɢɦɟɸɳɟɣɫɹ ɮɭɧɤɰɢɨɧɚɥɶɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɭ M ɯ ɩɨɫɥɟɞɧɟɟ ɭɪɚɜɧɟɧɢɟ ɧɚɡɵɜɚɟɬɫɹ ɭɪɚɜ
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ɧɟɧɢɟɦ ɪɟɝɪɟɫɫɢɢ ɇɚɩɪɢɦɟɪ ɪɟɱɶ ɦɨɠɟɬ ɢɞɬɢ ɨ ɪɟɝɪɟɫɫɢɢ ɡɚɜɢɫɢɦɨɫɬɢ |
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ɦɟɬɪɨɜ a b ɨɫɬɚɸɬɫɹ ɧɟɢɡɜɟɫɬɧɵɦɢ ɧɚ ɨɫɧɨɜɟ ɩɨɥɭɱɟɧɧɵɯ ɷɤɫɩɟɪɢɦɟɧ |
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ɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɦɨɠɧɨ ɝɨɜɨɪɢɬɶ ɥɢɲɶ ɨ ɬɨɱɟɱɧɵɯ ɨɰɟɧɤɚɯ D E ɩɚɪɚɦɟɬ |
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ɪɨɜ a b ɂɬɚɤ ɦɵ ɢɳɟɦ ɡɚɜɢɫɢɦɨɫɬɶ y |
M x D E ©ɧɚɢɥɭɱɲɢɦ ɨɛɪɚɡɨɦª |
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ɨɩɢɫɵɜɚɸɳɭɸ ɪɚɫɩɨɥɨɠɟɧɢɟ ɬɨɱɟɤ ɧɚ ɞɢɚɝɪɚɦɦɟ ɪɚɫɫɟɹɧɢɹ ɬɚɤ ɧɚɡɵɜɚɟɦɨɟ |
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ɜɵɛɨɪɨɱɧɨɟ ɭɪɚɜɧɟɧɢɟ ɪɟɝɪɟɫɫɢɢ ɉɨɥɶɡɭɹɫɶ ɜɵɲɟɩɪɢɜɟɞɟɧɧɵɦɢ ɫɦ ɩ |
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ɪɚɫɫɭɠɞɟɧɢɹɦɢ ɨ ɰɟɥɟɫɨɨɛɪɚɡɧɨɫɬɢ ɪɚɫɫɦɨɬɪɟɧɢɹ ɤɜɚɞɪɚɬɨɜ ɭɤɥɨɧɟɧɢɣ ɤɨɬɨ |
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ɪɵɟ ɭɤɥɨɧɟɧɢɹ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɢɦɟɸɬ ɜɢɞ |
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ɫɤɨɥɶɤɭ ɦɧɨɠɟɫɬɜɨ ɜɫɟɯ ɡɧɚɱɟɧɢɣ ɬɚɤɨɣ ɫɭɦɦɵ ɨɝɪɚɧɢɱɟɧɨ ɫɧɢɡɭ ɧɭɥɟɦ |
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ȿɫɥɢ ɱɢɫɥɚ D E ɪɟɲɟɧɢɟ ɷɬɨɣ ɫɢɫɬɟɦɵ ɨɩɪɟɞɟɥɹɬɫɹ ɨɞɧɨɡɧɚɱɧɵɦ ɨɛ ɪɚɡɨɦ ɬɨ ɨɧɢ ɢ ɛɭɞɭɬ ɢɫɤɨɦɵɦɢ ɬɨɱɟɱɧɵɦɢ ɨɰɟɧɤɚɦɢ ɩɚɪɚɦɟɬɪɨɜ a b ɬɟɦ ɫɚɦɵɦ ɡɚɞɚɱɚ ɨ ɩɨɢɫɤɟ ɜɵɛɨɪɨɱɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɪɟɝɪɟɫɫɢɢ y M x D E ɛɭɞɟɬ ɪɟɲɟɧɚ
ȼ ɫɥɭɱɚɟ ɥɢɧɟɣɧɨɣ ɪɟɝɪɟɫɫɢɢ y ax b ɫɢɫɬɟɦɚ ɭɪɚɜɧɟɧɢɣ ɩ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɬɨɱɟɱɧɵɯ ɨɰɟɧɨɤ D E ɩɚɪɚɦɟɬɪɨɜ a b ɩɪɢɧɢɦɚɟɬ ɜɢɞ
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ɂɫɤɨɦɵɟ ɡɧɚɱɟɧɢɹ D ɢ E ɧɚɯɨɞɢɦ ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɟɲɟɧɢɹ ɩɨɥɭɱɟɧɧɨɣ ɞɥɹ ɧɢɯ ɫɢɫɬɟɦɵ ɭɪɚɜɧɟɧɢɣ
ɉɪɢɦɟɪ ɇɚɣɬɢ ɜɵɛɨɪɨɱɧɨɟ ɭɪɚɜɧɟɧɢɟ ɥɢɧɟɣɧɨɣ ɪɟɝɪɟɫɫɢɢ ɩɨ ɫɥɟɞɭ ɸɳɢɦ ɞɚɧɧɵɦ ɢɡɦɟɪɟɧɢɣ
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Ɋɟɲɟɧɢɟɇɚɯɨɞɢɦ ɡɧɚɱɟɧɢɹ ɫɭɦɦ ɤɨɬɨɪɵɟ ɹɜɥɹɸɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ ɩɪɢ |
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D ɢ E ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɫɢɫɬɟɦɟ ɭɪɚɜɧɟɧɢɣ |
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84
Ɂɚɩɢɫɵɜɚɟɦ ɬɟɩɟɪɶ ɭɪɚɜɧɟɧɢɹ ɫɢɫɬɟɦɵ ɩ
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ɨɬɤɭɞɚ ɧɚɯɨɞɢɦ D E ɬɚɤ ɱɬɨ ɜɵɛɨɪɨɱɧɨɟ ɥɢɧɟɣɧɨɣ ɭɪɚɜɧɟɧɢɟ ɪɟ ɝɪɟɫɫɢɢ ɩɪɢɧɢɦɚɟɬ ɜɢɞ ɭ ɯ
4. Математическая статистика: типовые задачи
Задача 4.1. ɂɡ ɝɟɧɟɪɚɥɶɧɨɣ ɫɨɜɨɤɭɩɧɨɫɬɢ ɢɡɜɥɟɱɟɧɚ ɜɵɛɨɪɤɚ ɂɡɜɟɫɬɟɧ ɜɚɪɢɚɰɢɨɧɧɵɣ ɪɹɞ
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ɍɤɚɡɚɬɶ ɪɚɡɦɚɯ ɜɚɪɶɢɪɨɜɚɧɢɹ ɦɨɞɭ ɦɟɞɢɚɧɭ ɜɚɪɢɚɰɢɨɧɧɨɝɨ ɪɹɞɚ ɇɚɣɬɢ ɚ ɜɵɛɨɪɨɱɧɭɸ ɫɪɟɞɧɸɸ ɛ ɜɵɛɨɪɨɱɧɭɸ ɞɢɫɩɟɪɫɢɸ
Ɋɟɲɟɧɢɟ Ɋɚɡɦɚɯ
R = xPD[ – xPLQ –
Ɇɨɞɚ Ɇɨ ɬ ɤ ɷɬɚ ɜɚɪɢɚɧɬɚ ɨɛɥɚɞɚɟɬ ɧɚɢɛɨɥɶɲɟɣ ɱɚɫɬɨɬɨɣ ɪɚɜ ɧɨɣ Ɇɟɞɢɚɧɚ ɆH ɩɨɫɤɨɥɶɤɭ ɷɬɚ ɜɚɪɢɚɧɬɚ ɪɚɫɩɨɥɨɠɟɧɚ ɜ ɫɟɪɟɞɢɧɟ ɜɚ ɪɢɚɰɢɨɧɧɨɝɨ ɪɹɞɚ Ɉɛɴɟɦ ɜɵɛɨɪɤɢ
n
ɚ ɉɨ ɮɨɪɦɭɥɟ ɩ ɢɦɟɟɦ |
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ɛ ɋɨɝɥɚɫɧɨ ɩ |
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Задача 4.2. ɋɥɭɱɚɣɧɚɹ ɜɟɥɢɱɢɧɚ ɏ ɢɦɟɟɬ ɧɨɪɦɚɥɶɧɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɫ ɢɡɜɟɫɬɧɵɦ ɫɪɟɞɧɢɦ ɤɜɚɞɪɚɬɢɱɧɵɦ ɨɬɤɥɨɧɟɧɢɟɦ V ɇɚɣɬɢ ɞɨɜɟɪɢɬɟɥɶɧɵɣ ɢɧ ɬɟɪɜɚɥ ɞɥɹ ɨɰɟɧɤɢ ɧɟɢɡɜɟɫɬɧɨɝɨ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɨɠɢɞɚɧɢɹ ɚ ɩɨ ɜɵɛɨɪɨɱɧɨɣ ɫɪɟɞɧɟɣ xB ɟɫɥɢ ɨɛɴɟɦ ɜɵɛɨɪɤɢ n ɢ ɡɚɞɚɧɚ ɧɚɞɟɠɧɨɫɬɶ ɨɰɟɧɤɢ J
ɇɚɣɞɟɦ t ɢɡ ɫɨɨɬɧɨɲɟɧɢɹ Ɏ t ɉɨ ɬɚɛɥ ɉɪɢɥ ɧɚɯɨɞɢɦ
t ɇɚɣɞɟɦ ɬɨɱɧɨɫɬɶ ɨɰɟɧɤɢ G ɋɥɟɞɨɜɚɬɟɥɶɧɨ ɞɨɜɟɪɢ
85
ɬɟɥɶɧɵɣ ɢɧɬɟɪɜɚɥ ɢɦɟɟɬ ɜɢɞ ± ɂɧɚɱɟ ɝɨɜɨɪɹ ɫ ɧɚɞɟɠɧɨ ɫɬɶɸ J ɢɦɟɟɬ ɦɟɫɬɨ ɧɟɪɚɜɟɧɫɬɜɨ a
КОНТРОЛЬНЫЙ МОДУЛЬ
ɌȿɈɊȿɌɂɑȿɋɄɂȿ ɍɉɊȺɀɇȿɇɂə
Ⱦɨɤɚɡɚɬɶ ɱɬɨ ɜɵɛɨɪɨɱɧɚɹ ɫɪɟɞɧɹɹ xB ɩɪɢɧɢɦɚɟɬ ɡɧɚɱɟɧɢɹ
xB >xPLQ xPD[@
ɝɞɟ xPD[ ɢ xPLQ ± ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɧɚɢɛɨɥɶɲɟɟ ɢ ɧɚɢɦɟɧɶɲɟɟ ɡɧɚɱɟɧɢɹ ɜɚɪɢɚɧɬ xk
Ʉɨɥɢɱɟɫɬɜɟɧɧɵɣ ɩɪɢɡɧɚɤ ɪɚɫɩɪɟɞɟɥɟɧ ɩɨ ɩɨɤɚɡɚɬɟɥɶɧɨɦɭ ɡɚɤɨɧɭ ɫ ɩɚ ɪɚɦɟɬɪɨɦ O ɬ ɟ ɩɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɢɦɟɟɬ ɜɢɞ
f x Oe Ox x ! f x x ɂɡɜɥɟɱɟɧɚ ɜɵɛɨɪɤɚ ɢ ɜɵɱɢɫɥɟɧɚ ɜɵɛɨɪɨɱɧɚɹ ɫɪɟɞɧɹɹ xB ɂɫɩɨɥɶɡɭɹ ɦɟɬɨɞ
ɦɨɦɟɧɬɨɜ ɧɚɣɬɢ ɬɨɱɟɱɧɭɸ ɨɰɟɧɤɭ ɩɚɪɚɦɟɬɪɚ O
ɁȺȾȺɑɂ ȾɅə ɋȺɆɈɋɌɈəɌȿɅɖɇɈȽɈ Ɋȿɒȿɇɂə
ȼ ɬɟɱɟɧɢɟ ɛɢɪɠɟɜɵɯ ɬɨɪɝɨɜ ɤɭɪɫ ɞɨɥɥɚɪɚ ɫɨɫɬɚɜɢɥ ɫɥɟɞɭɸɳɢɟ ɡɧɚɱɟ ɧɢɹ ɜ ɪɭɛɥɹɯ
ɇɚɣɬɢ ɚ ɦɨɞɭ Ɇɨ ɛ ɦɟɞɢɚɧɭ ɆH ɜ ɪɚɡɦɚɯ ɜɚɪɶɢɪɨɜɚɧɢɹ R ɝ ɫɪɟɞɧɢɣ ɤɭɪɫ ɞɨɥɥɚɪɚ
ɂɡ ɝɟɧɟɪɚɥɶɧɨɣ ɫɨɜɨɤɭɩɧɨɫɬɢ ɡɚɞɟɪɠɚɧɧɵɯ ɧɚ ɬɚɦɨɠɧɟ ɤɨɧɬɪɚɮɚɤɬɧɵɯ ɬɨɜɚɪɨɜ ɫɞɟɥɚɧɚ ɜɵɛɨɪɤɚ ɂɡɜɟɫɬɧɵ ɩɪɢɦɟɪɧɵɟ ɪɵɧɨɱɧɵɟ ɰɟɧɵ ɚɧɚɥɨɝɢɱɧɵɯ ɬɨɜɚɪɨɜ ɩɪɢɡɧɚɧɧɵɯ ɛɪɟɧɞɨɜ ɜ ɬɵɫ ɪɭɛ ɯi ɢ ɱɚɫɬɨɬɵ ni ɢɯ ɡɧɚɱɟɧɢɣ ɜ ɜɵɛɨɪɨɱ ɧɨɣ ɫɨɜɨɤɭɩɧɨɫɬɢ
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ɇɚɣɬɢ ɜɵɛɨɪɨɱɧɭɸ ɫɪɟɞɧɸɸ ɪɵɧɨɱɧɨɣ ɰɟɧɵ ɤɨɧɬɪɚɮɚɤɬɚ ɢ ɟɟ ɜɵɛɨɪɨɱ ɧɨɟ ɫɪɟɞɧɟ ɤɜɚɞɪɚɬɢɱɟɫɤɨɟ ɨɬɤɥɨɧɟɧɢɟ
86
ɇɚɣɬɢ ɞɨɜɟɪɢɬɟɥɶɧɵɣ ɢɧɬɟɪɜɚɥ ɞɥɹ ɨɰɟɧɤɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɨɠɢɞɚɧɢɹ D ɧɨɪɦɚɥɶɧɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɫ ɧɚɞɟɠɧɨɫɬɶɸ J ɡɧɚɹ ɜɵɛɨɪɨɱɧɭɸ ɫɪɟɞɧɸɸ xB ɨɛɴɟɦ ɜɵɛɨɪɤɢ n ɢ ɫɪɟɞɧɟɟ ɤɜɚɞɪɚɬɢɱɧɨɟ ɨɬɤɥɨɧɟ ɧɢɟ V
ɂɡ ɝɟɧɟɪɚɥɶɧɨɣ ɫɨɜɨɤɭɩɧɨɫɬɢ ɦɟɬɚɥɥɢɱɟɫɤɢɯ ɲɚɣɛ ɫɞɟɥɚɧɚ ɜɵɛɨɪɤɚ ɂɡɜɟɫɬɧɵ ɜɧɭɬɪɟɧɧɢɟ ɞɢɚɦɟɬɪɵ xi ɢ ɱɚɫɬɨɬɵ ni ɷɬɢɯ ɡɧɚɱɟɧɢɣ ɜ ɜɵɛɨɪɨɱɧɨɣ ɫɨ ɜɨɤɭɩɧɨɫɬɢ ɪɚɡɦɟɪɵ ɞɚɧɵ ɜ ɦɢɥɥɢɦɟɬɪɚɯ ɇɚɣɬɢ ɜɵɛɨɪɨɱɧɭɸ ɫɪɟɞɧɸɸ
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ȼɪɚɱɢ ɪɟɤɨɦɟɧɞɭɸɬ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɬɨɧɨɦɟɬɪɨɜ ɚɜɬɨɦɚɬɨɜ ɩɪɨɢɡɜɨ ɞɢɬɶ ɢɡɦɟɪɟɧɢɹ ɚɪɬɟɪɢɚɥɶɧɨɝɨ ɞɚɜɥɟɧɢɹ ȺȾ ɧɟɫɤɨɥɶɤɨ ɪɚɡ ɢ ɩɪɢɧɢɦɚɬɶ ɡɚ ɩɪɚɜɢɥɶɧɵɣ ɪɟɡɭɥɶɬɚɬ ɫɪɟɞɧɟɟ ɚɪɢɮɦɟɬɢɱɟɫɤɨɟ ɢɡɦɟɪɟɧɢɣ Ɉɫɨɛɨ ɦɧɢɬɟɥɶɧɵɣ ɩɚɰɢɟɧɬ ɢɡɦɟɪɢɥ ɞɚɜɥɟɧɢɟ ɪɚɡ Ʉɚɤɨɜɨ ɢɫɬɢɧɧɨɟ ɜɟɪɯɧɟɟ ɡɧɚɱɟɧɢɟ ȺȾ ɟɫɥɢ ɞɥɹ ɧɟɝɨ ɨɧ ɩɨɥɭɱɢɥ ɫɥɟɞɭɸɳɢɟ ɪɟɡɭɥɶɬɚɬɵ ɢɡɦɟɪɟɧɢɣ
Ɇɟɠɞɭ ɜɟɪɯɧɢɦ ɢ ɧɢɠɧɢɦ ɡɧɚɱɟɧɢɹɦɢ ɩɨɤɚɡɚɬɟɥɟɣ ɚɪɬɟɪɢɚɥɶɧɨɝɨ ɞɚɜ ɥɟɧɢɹ X ɢ Y ɫɭɳɟɫɬɜɭɟɬ ɡɚɜɢɫɢɦɨɫɬɶ ɋɱɢɬɚɹ ɟɺ ɥɢɧɟɣɧɨɣ ɪɟɝɪɟɫɫɢɟɣ ɧɚɣɬɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɭɪɚɜɧɟɧɢɟ ɟɫɥɢ ɞɚɧɧɵɟ ɢɡɦɟɪɟɧɢɣ ± ɫɥɟɞɭɸɳɢɟ
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ɉɨ ɭɪɚɜɧɟɧɢɸ ɥɢɧɟɣɧɨɣ ɪɟɝɪɟɫɫɢɢ ɨɩɪɟɞɟɥɢɬɶ ɧɢɠɧɟɟ ɡɧɚɱɟɧɢɟ ȺȾ ɟɫɥɢ ɜɟɪɯɧɟɟ ɡɧɚɱɟɧɢɟ ɞɨɫɬɢɝɧɟɬ ɟɞ
87
ЗАКЛЮЧЕНИЕ
ɋɭɬɶ ɤɨɦɩɟɬɟɧɬɧɨɫɬɧɨɝɨ ɩɨɞɯɨɞɚ ɜ ɦɚɬɟɦɚɬɢɱɟɫɤɨɦ ɨɛɪɚɡɨɜɚɧɢɢ ɫɨɫɬɨɢɬ ɜ ɮɨɪɦɢɪɨɜɚɧɢɢ ɭ ɨɛɭɱɚɸɳɢɯɫɹ ɫɩɨɫɨɛɧɨɫɬɢ ɩɟɪɟɧɨɫɢɬɶ ɩɨɥɭɱɟɧɧɵɟ ɡɧɚɧɢɹ ɢ ɭɦɟɧɢɹ ɜ ɧɨɜɵɟ ɭɫɥɨɜɢɹ ɧɚ ɜɧɨɜɶ ɨɫɜɚɢɜɚɟɦɵɟ ɨɛɴɟɤɬɵ ɢɫɫɥɟɞɨɜɚɧɢɹ ɢ ɬ ɩ Ɍɚɤɢɦɢ ɨɛɴɟɤɬɚɦɢ ɦɨɝɭ ɛɵɬɶ ɢ ɫɚɦɢ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɬɟɨɪɢɢ ɂɡɭɱɟɧɢɟ ɬɟɨɪɢɢ ɜɟɪɨɹɬɧɨɫɬɟɣ ɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɫɬɚɬɢɫɬɢɤɢ ɤɚɤ ɩɪɚɜɢɥɨ ɫɥɟɞɭɟɬ ɡɚ ɢɡɭɱɟɧɢɟɦɢɥɢ ɩɚɪɚɥɥɟɥɶɧɨ ɢɡɭɱɟɧɢɸ ɷɥɟɦɟɧɬɨɜ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɥɨɝɢɤɢ ɥɢɧɟɣɧɨɣ ɚɥ ɝɟɛɪɵ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɚɧɚɥɢɡɚ ɢ ɞɪ ɉɨɷɬɨɦɭ ɫɥɟɞɭɟɬ ɨɛɪɚɬɢɬɶ ɜɧɢɦɚɧɢɟ ɨɛɭ ɱɚɸɳɢɯɫɹ ɧɚ ©ɩɪɨɧɢɤɧɨɜɟɧɢɟª ɦɟɬɨɞɨɜ ɞɢɫɤɪɟɬɧɨɣ ɦɚɬɟɦɚɬɢɤɢ ɤɨɦɛɢɧɚɬɨɪɢ ɤɢ ɬɟɨɪɢɢ ɦɧɨɠɟɫɬɜ ɚɥɝɟɛɪɵ ɢ ɚɧɚɥɢɡɚ ɜ ɜɨɩɪɨɫɵ ɫɬɨɯɚɫɬɢɤɢ Ɍɚɤɢɟ ɦɟɬɨɞɵ ɫɩɨɫɨɛɫɬɜɭɸɬ ɭɤɪɟɩɥɟɧɢɸ ɜɧɭɬɪɢɩɪɟɞɦɟɬɧɵɯ ɫɜɹɡɟɣ ɮɨɪɦɢɪɨɜɚɧɢɸ ɭ ɨɛɭɱɚ ɸɳɢɯɫɹ ɩɪɟɞɫɬɚɜɥɟɧɢɣ ɨ ɰɟɥɨɫɬɧɨɫɬɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɧɚɭɤɢ ɨɛɳɧɨɫɬɢ ɢ ɭɧɢ ɜɟɪɫɚɥɶɧɨɫɬɢ ɟɺ ɨɫɧɨɜɧɵɯ ɢɞɟɣ
88
ПРИЛОЖЕНИЕ
ɌȺȻɅɂɐɕ ɁɇȺɑȿɇɂɃ ɎɍɇɄɐɂɃ ɅȺɉɅȺɋȺ ɂ ɗɄɋɉɈɇȿɇɌɕ
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ɂɇɇɈȼȺɐɂɈɇɇɕɃ ɁȺȾȺɑɇɕɃ ɆȺɌȿɊɂȺɅ
ȼ ɭɫɥɨɜɢɹɯ ɩɟɪɟɯɨɞɚ ɨɬ ɡɧɚɧɢɟɜɨɣ ɤ ɤɨɦɩɟɬɟɧɬɧɨɫɬɧɨɣ ɩɚɪɚɞɢɝɦɟ ɨɛɭɱɟ ɧɢɹ ɧɚ ɰɟɧɬɪɚɥɶɧɨɟ ɦɟɫɬɨ ɜɵɯɨɞɢɬ ɫɢɫɬɟɦɧɨ ɞɟɹɬɟɥɶɧɨɫɬɧɵɣ ɩɨɞɯɨɞ ɤ ɨɛɪɚɡɨ ɜɚɬɟɥɶɧɨɦɭ ɩɪɨɰɟɫɫɭ ȼɟɞɭɳɚɹ ɪɨɥɶ ɬɟɩɟɪɶ ɨɬɜɨɞɢɬɫɹ ɚɤɬɢɜɧɨɣ ɪɚɡɧɨɫɬɨɪɨɧ ɧɟɣ ɢ ɦɚɤɫɢɦɚɥɶɧɨ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɣ ɩɨɡɧɚɜɚɬɟɥɶɧɨɣ ɞɟɹɬɟɥɶɧɨɫɬɢ ɨɛɭɱɚɸɳɟ ɝɨɫɹ ȼ ɫɜɨɸ ɨɱɟɪɟɞɶ ɜ ɪɚɦɤɚɯ ɞɟɹɬɟɥɶɧɨɫɬɧɨɝɨ ɩɨɞɯɨɞɚ ɦɵ ɪɚɫɫɦɚɬɪɢɜɚɟɦ ɡɚ ɞɚɱɧɵɣ ɩɨɞɯɨɞ ɤɚɤ ɢɧɫɬɪɭɦɟɧɬ ɮɨɪɦɢɪɨɜɚɧɢɹ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɜ ɬɨɦ ɱɢɫɥɟ ɫɬɨɯɚɫɬɢɱɟɫɤɢɯ ɡɧɚɧɢɣ ɢ ɭɦɟɧɢɣ ɫɪɟɞɫɬɜɚɦɢ ɪɟɲɟɧɢɹ ɫɢɫɬɟɦ ɭɱɟɛɧɵɯ ɡɚɞɚɱ ȼ ɷɬɨɣ ɫɜɹɡɢ ɦɵ ɩɪɟɞɥɚɝɚɟɦ ɤɨɧɬɟɤɫɬɧɵɣ ɡɚɞɚɱɧɵɣ ɦɚɬɟɪɢɚɥ ɜɤɥɸɱɚɸɳɢɣ ɜ ɫɟɛɹ ɡɚɞɚɱɢ ɤɟɣɫɵ ɡɚɞɚɱɢ ɬɪɚɧɫɮɨɪɦɟɪɵ ɬɟɪɦɢɧ ± ɧɚɲ ɢ ɨɛɪɚɬɧɵɟ ɫɬɨɯɚɫɬɢ ɱɟɫɤɢɟ ɡɚɞɚɱɢ ɋɸɠɟɬɵ ɡɚɞɚɧɢɣ ɧɨɫɹɬ ɜ ɨɫɧɨɜɧɨɦ ɩɪɢɤɥɚɞɧɨɣ ɯɚɪɚɤɬɟɪ ɋɨɨɬ ɜɟɬɫɬɜɭɸɳɢɣ ɡɚɞɚɱɧɵɣ ɦɚɬɟɪɢɚɥ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɢɧɧɨɜɚɰɢɨɧɧɵɦ ɜ ɫɨɨɬɜɟɬ ɫɬɜɢɢ ɫ ɤɨɧɰɟɩɰɢɟɣ ɫɨɝɥɚɫɧɨ ɤɨɬɨɪɨɣ ɢɧɧɨɜɚɰɢɢ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɨɩɪɟɞɟɥɺɧ ɧɨɣ ɫɬɟɩɟɧɶɸ ɧɨɜɢɡɧɵ ɜɨɫɩɪɨɢɡɜɨɞɢɦɨɫɬɶɸ ɢ ɧɚɰɟɥɟɧɧɨɫɬɶɸ ɧɚ ɜɨɫɬɪɟɛɨɜɚɧ ɧɵɣ ɪɟɡɭɥɶɬɚɬ ȼ ɤɚɱɟɫɬɜɟ ɬɚɤɨɝɨ ɪɟɡɭɥɶɬɚɬɚ ɦɵ ɪɚɫɫɦɚɬɪɢɜɚɟɦ ɪɚɡɜɢɬɢɟ ɦɨɬɢ ɜɚɰɢɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɞɟɹɬɟɥɶɧɨɫɬɢ ɢ ɮɨɪɦɢɪɨɜɚɧɢɟ ɫɢɫɬɟɦɧɨɫɬɢ ɦɚɬɟɦɚɬɢɱɟ ɫɤɨɝɨ ɫɬɨɯɚɫɬɢɱɟɫɤɨɝɨ ɡɧɚɧɢɹ
89
Ⱥɧɚɥɢɡ ɨɬɞɟɥɶɧɵɯ ɷɥɟɦɟɧɬɨɜ ɩɪɟɞɥɚɝɚɟɦɨɝɨ ɡɚɞɚɱɧɨɝɨ ɦɚɬɟɪɢɚɥɚ ɹɜɥɹɟɬɫɹ ɰɟɥɶɸ ɧɚɫɬɨɹɳɟɣ ɪɚɫɫɦɨɬɪɟɧɢɹ
ɋɮɟɪɚ ɦɨɬɢɜɚɰɢɢ ± ɜɚɠɧɟɣɲɚɹ ɜ ɞɟɹɬɟɥɶɧɨɫɬɧɨɦ ɩɨɞɯɨɞɟ Ɋɨɫɬ ɢɧɬɟɪɟɫɚ ɤ ɫɬɨɯɚɫɬɢɱɟɫɤɢɦ ɮɚɤɬɚɦ ɢ ɦɟɬɨɞɚɦ ɞɨɫɬɢɝɚɟɬɫɹ ɬɳɚɬɟɥɶɧɵɦ ɨɬɛɨɪɨɦ ɫɸɠɟ ɬɨɜ ɡɚɞɚɧɢɣ ɡɚɞɚɧɢɟ ɞɨɥɠɧɨ ɛɵɬɶ ɢɧɬɟɪɟɫɧɵɦ ɩɨɡɧɚɜɚɬɟɥɶɧɵɦ ɩɪɢɤɥɚɞɧɵɦ ɢ ɬ ɩ Ɍɚɤ ɦɥɚɞɲɢɦ ɲɤɨɥɶɧɢɤɚɦ ɦɨɝɭɬ ɛɵɬɶ ɩɪɟɞɥɨɠɟɧɵ ɫɸɠɟɬɵ ɫɜɹɡɚɧɧɵɣ ɫ ɝɟɪɨɹɦɢ ɩɨɩɭɥɹɪɧɵɯ ɫɤɚɡɨɤ ɧɚɩɪɢɦɟɪ ɫ ɤɚɤɨɣ ɜɟɪɨɹɬɧɨɫɬɶɸ ȼɢɧɢ ɉɭɯ ɢ ɟɝɨ ɞɪɭɡɶɹ ɧɟ ɡɚɛɭɞɭɬ ɩɨɡɞɪɚɜɢɬɶ ɨɫɥɢɤɚ ɂɚ ɂɚ ɫ ɟɝɨ ɞɧɺɦ ɪɨɠɞɟɧɢɹ ɢ ɬ ɩ Ɋɨɫɬɭ ɦɨɬɢɜɚɰɢɢ ɞɟɹɬɟɥɶɧɨɫɬɢ ɜ ɨɛɥɚɫɬɢ ɫɬɨɯɚɫɬɢɤɢ ɫɩɨɫɨɛɫɬɜɭɸɬ ɡɚɞɚɱɢ ɫ ɩɪɚɤɬɢɤɨ ɨɪɢɟɧɬɢɪɨɜɚɧɧɵɦɢ ɫɸɠɟɬɚɦɢ ɭɪɨɜɟɧɶ ɨɫɧɨɜɧɨɣ ɢ ɫɬɚɪɲɟɣ ɲɤɨ ɥɵ ɢ ɩɪɨɫɬɟɣɲɢɟ ɩɪɨɮɟɫɫɢɨɧɚɥɶɧɨ ɨɪɢɟɧɬɢɪɨɜɚɧɧɵɟ ɡɚɞɚɱɢ ɫɩɨɫɨɛɫɬɜɭɸ ɳɢɟ ɩɪɨɮɟɫɫɢɨɧɚɥɶɧɨɦɭ ɫɚɦɨɨɩɪɟɞɟɥɟɧɢɸ ɫɬɚɪɲɚɹ ɲɤɨɥɚ Ɂɚɞɚɧɢɹ ɩɪɚɤɬɢɤɨ ɨɪɢɟɧɬɢɪɨɜɚɧɧɨɝɨ ɯɚɪɚɤɬɟɪɚ ɢɦɟɸɬɫɹ ɜ ɦɧɨɝɨɱɢɫɥɟɧɧɵɯ ɢɫɬɨɱɧɢɤɚɯ ȼ ɤɚɱɟ ɫɬɜɟ ɡɚɞɚɧɢɣ ©ɩɪɟɞɪɨɮɟɫɫɢɨɧɚɥɶɧɨɝɨª ɯɚɪɚɤɬɟɪɚ ɧɚɩɪɢɦɟɪ ɩɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɰɢɤɥɭ ɫɬɪɨɢɬɟɥɶɧɵɯ ɫɩɟɰɢɚɥɶɧɨɫɬɟɣ ɦɨɝɭɬ ɛɵɬɶ ɩɪɟɞɥɨɠɟɧɵ ɫɥɟɞɭɸɳɢɟ
Ⱦɥɹ ɩɪɢɝɨɬɨɜɥɟɧɢɹ ɪɚɫɬɜɨɪɚ ɧɭɠɧɨ ɜɡɹɬɶ ɦɟɲɨɤ ɰɟɦɟɧɬɚ ɦɚɪɤɢ Ɇ ɢ ɦɟɲɨɤ ɰɟɦɟɧɬɚ Ɇ ɇɚ ɫɤɥɚɞɟ ɢɦɟɸɬɫɹ ɦɟɲɤɨɜ ɦɚɪɤɢ Ɇ ɢ ɦɟɲ ɤɨɜ ɦɚɪɤɢ Ɇ ɋɤɨɥɶɤɨ ɫɭɳɟɫɬɜɭɟɬ ɫɩɨɫɨɛɨɜ ɜɵɛɪɚɬɶ ɩɚɪɭ ɦɟɲɤɨɜ ɭɤɚɡɚɧ ɧɵɯ ɦɚɪɨɤ"
Ɍɪɢ ɛɚɥɤɢ ɩɟɪɟɤɪɵɬɢɹ ɢɫɩɵɬɵɜɚɸɬ ɧɚ ɩɪɨɱɧɨɫɬɶ ȼɟɪɨɹɬɧɨɫɬɶ ɩɨɜɪɟ ɠɞɟɧɢɹ ɛɚɥɤɢ ɩɨɞ ɤɨɧɬɪɨɥɶɧɨɣ ɧɚɝɪɭɡɤɨɣ ɪɚɜɧɚ Ʉɚɤɨɜɚ ɜɟɪɨɹɬɧɨɫɬɶ ɱɬɨ ɜɫɟ ɛɚɥɤɢ ɨɤɚɠɭɬɫɹ ɩɨɜɪɟɠɞɺɧɧɵɦɢ"
Ɉɛɫɭɞɢɦ ɬɟɩɟɪɶ ɫɨɞɟɪɠɚɧɢɟ ɡɚɞɚɱɧɨɝɨ ɦɚɬɟɪɢɚɥɚ ɧɚɩɪɚɜɥɟɧɧɨɝɨ ɧɚ ɮɨɪ ɦɢɪɨɜɚɧɢɟ ɫɢɫɬɟɦɧɨɫɬɢ ɢ ɰɟɥɨɫɬɧɨɫɬɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɡɧɚɧɢɹ ɢ ɦɵɲɥɟɧɢɹ
ɋɬɨɯɚɫɬɢɱɟɫɤɢɟ ɤɟɣɫɵ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɸ ɤɨɦɩɥɟɤɫɧɵɟ ɤɨɦɩɟɬɟɧɬɧɨɫɬɧɨ ɨɪɢɟɧɬɢɪɨɜɚɧɧɟ ɭɱɟɛɧɵɟ ɡɚɞɚɧɢɹ ɩɨ ɦɨɞɟɥɢɪɨɜɚɧɢɸ ɫɬɨɯɚɫɬɢɱɟɫɤɢɯ ɫɢɬɭɚɰɢɣ ɂɯ ɪɟɲɟɧɢɟ ɬɪɟɛɭɟɬ ɨɩɬɢɦɚɥɶɧɨɝɨ ɫɨɱɟɬɚɧɢɹ ɬɟɨɪɢɢ ɢ ɩɪɚɤɬɢɱɟɫɤɨɝɨ ɡɧɚɧɢɹ ɚ ɬɚɤɠɟ ɭɦɟɧɢɣ ɨɩɢɪɚɸɳɢɯɫɹ ɧɚ ɩɪɟɞɵɞɭɳɢɣ ɨɩɵɬ ɩɪɚɤɬɢɱɟɫɤɨɣ ɞɟɹɬɟɥɶɧɨ ɫɬɢ ɨɛɭɱɚɸɳɢɯɫɹ ɉɪɢɦɟɪɨɦ ɦɨɠɟɬ ɫɥɭɠɢɬɶ ɫɥɟɞɭɸɳɟɟ ɡɚɞɚɧɢɟ ɧɚ ɩɨɫɬɪɨɟɧɢɟ ɪɹɞɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɞɢɫɤɪɟɬɧɨɣ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ ɢ ɧɚɯɨɠɞɟɧɢɟ ɯɚɪɚɤɬɟɪɢ ɫɬɢɤ ɪɚɫɩɪɟɞɟɥɟɧɢɹ
ɇɚ ɩɭɬɢ ɚɜɬɨɦɨɛɢɥɹ ɩɨ ɭɥɢɰɟ Ɂɟɥɺɧɨɣ ɫɜɟɬɨɮɨɪɚ ɤɚɠɞɵɣ ɢɡ ɤɨɬɨɪɵɯ
ɦɨɠɟɬ ɨɫɬɚɧɨɜɢɬɶ ɚɜɬɨɦɨɛɢɥɶ ɫ ɜɟɪɨɹɬɧɨɫɬɶɸ ɪ
Ʉɚɤɨɜɚ ɜɟɪɨɹɬɧɨɫɬɶ ɯɨɬɹ ɛɵ ɨɞɧɨɣ ɨɫɬɚɧɨɜɤɢ ɚɜɬɨɦɨɛɢɥɹ ɩɪɢ ɞɜɢɠɟɧɢɢ ɩɨ ɷɬɨɣ ɭɥɢɰɟ" Ʉɚɤɨɜɚ ɜɟɪɨɹɬɧɨɫɬɶ ɪɨɜɧɨ ɯ ɨɫɬɚɧɨɜɨɤ" ɇɟ ɦɟɧɟɟ ɯ ɨɫɬɚɧɨ ɜɨɤ"
ɉɨɫɬɪɨɣɬɟ ɪɹɞ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɱɢɫɥɚ ɨɫɬɚɧɨɜɨɤ ɧɚ ɫɜɟɬɨɮɨɪɚɯ Ʉɚɤɨɜɨ ɫɪɟɞɧɟɟ ɱɢɫɥɨ ɨɫɬɚɧɨɜɨɤ ɩɪɢ ɩɨɫɬɨɹɧɧɨɣ ɟɡɞɟ ɩɨ ɭɥ Ɂɟɥɺɧɨɣ"
90