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í ɜɫɩɨɦɨɝɚɬɟɥɶɧɵɟ ² ɩɚɪɚɦɟɬɪɵ ɢɫ ɩɨɥɶɡɭɟɦɵɟ ɫɨɜɦɟɫɬɧɨ ɫ
ɨɩɪɟɞɟɥɹɸɳɢɦɢ ɞɥɹ ɨɬɵɫɤɚɧɢɹ ɦɟɫɬ ɩɨɜ ɪɟɠɞɟɧɢɣ
í ɩɪɨɝɧɨɡɢɪɭɸɳɢɟ ² ɩɚɪɚɦɟɬɪɵ ɫɨɞɟɪɠɚɳɢɟ ɢɧɮɨɪɦɚɰɢɸ
ɧɟ ɨɛɯɨɞɢɦɭɸ ɞɥɹ ɩɪɨɝɧɨɡɚ ɬɟɯɧɢɱɟɫɤɨɝɨ ɫɨɫɬɨɹɧɢɹ ɫɢɫɬɟɦɵ
ɩɟɪɟ ɞɚɱɢ
í ɚɜɚɪɢɣɧɵɟ ² ɱɚɫɬɶ ɨɩɪɟɞɟɥɹɸɳɢɯ ɩɚɪɚɦɟɬɪɨɜ ɩɨ ɤɨɬɨɪɵɦ ɫɭ
ɞɹɬ ɨ ɩɪɢɛɥɢɠɟɧɢɢ ɚɜɚɪɢɣɧɵɯ ɪɟɠɢɦɨɜ ɜ ɪɚɛɨɬɟ ɫɢɫɬɟɦɵ ɫɜɹɡɢ
Ɉɛɵɱɧɨ ɩɪɢ ɜɵɛɨɪɟ ɤɨɧɬɪɨɥɢɪɭɟɦɵɯ ɩɚɪɚɦɟɬɪɨɜ ɩɪɨɜɨɞɹɬ
ɫɹ ɬɟɨɪɟɬɢɱɟɫɤɢɟ ɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɢɫɫɥɟɞɨɜɚɧɢɹ ɧɚ ɨɫɧɨɜɟ
ɪɟ ɡɭɥɶɬɚɬɨɜ ɤɨɬɨɪɵɯ ɨɩɪɟɞɟɥɹɸɬɫɹ ɱɢɫɥɨ ɩɚɪɚɦɟɬɪɨɜ ɩɨɞɥɟɠɚ
ɳɢɯ ɤɨɧɬɪɨɥɸ ɧɨɦɢɧɚɥɶɧɵɟ ɡɧɚɱɟ ɧɢɹ ɢɯ ɢ ɞɨɩɭɫɤɢ ɚ ɬɚɤɠɟ ɧɟ
ɨɛɯɨɞɢɦɨɟ ɜɪɟɦɹ ɤɨɧɬɪɨɥɹ
Ʉ ɧɚɫɬɨɹɳɟɦɭ ɜɪɟɦɟɧɢ ɪɚɡ ɪɚɛɨɬɚɧ ɪɹɞ ɦɟɬɨɞɨɜ ɩɨɡɜɨɥɹ ɸɳɢɯ
ɨɩɪɟɞɟɥɢɬɶ ɨɩɬɢɦɚɥɶɧɨɟ ɱɢɫɥɨ ɤɨɧɬɪɨɥɢɪɭɟɦɵɯ ɩɚɪɚ ɦɟɬɪɨɜ Ɇɟ
ɬɨɞɵ ɨɫɧɨɜɚɧɵ ɧɚ ɫɨɫɬɚɜɥɟɧɢɢ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɦɨɞɟɥɟɣ ɨɛɴɟɤɬɨɜ
ɤɨɧɬɪɨɥɹ ɩɭ ɬɟɦ ɚɧɚɥɢɬɢɱɟɫɤɨɝɨ ɢ ɫɬɚɬɢɫɬɢ ɱɟɫɤɨɝɨ ɢɯ ɨɩɢɫɚɧɢɹ ȼ
ɤɚɱɟɫɬ ɜɟ ɩɪɢɦɟɪɚ ɪɚɫɫɦɨɬɪɢɦ ɦɟɬɨɞ ɫɬɚɬɢɫɬɢɱɟɫɤɨɣ ɨɩɬɢɦɢɡɚɰɢɢ
ɩɨ ɤɪɢɬɟɪɢɸ ɦɚɤɫɢɦɚɥɶɧɨɣ ɜɟɪɨɹɬɧɨɫɬɢ ɨɬɤɚɡɚ ɩɚɪɚɦɟɬɪɚ ɨɫɧɨ
ɜɚɧɧɵɣ ɧɚ ɩɨɫɬɪɨɟɧɢɢ ɮɢɡɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɨɛɴɟɤɬɚ
Ɇɟɬɨɞ ɫɨɫɬɨɢɬ ɭɫɥɨɜɧɨ ɢɡ ɬɪɟɯ ɷɬɚɩɨɜ ɇɚ ɩɟɪɜɨɦ ɷɬɚɩɟ ɩɪɨ
ɢɡɜɨɞɢɬɫɹ ɢɫɫɥɟɞɨɜɚɧɢɟ ɢ ɚɧɚɥɢɡ ɪɚɛɨɬɵ ɮɭɧɤɰɢɨɧɚɥɶɧɵɯ ɭɡɥɨɜ
ɚɩɩɚɪɚɬɭɪɵ ɢ ɫɢɫɬɟɦɵ ɩɟɪɟɞɚɱɢ ɜ ɰɟɥɨɦ ɭɫɬɚɧɚɜɥɢɜɚɸɬɫɹ ɡɚɜɢ
ɫɢɦɨɫɬɢ ɜɵɯɨɞɧɵɯ ɫɢɝɧɚɥɨɜ ɨɬ ɜɯɨɞɧɵɯ ɢ ɨɬ ɜɧɭɬɪɟɧɧɢɯ ɢ ɜɧɟɲ ɧɢɯ
ɩɨɦɟɯ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɡɚɢɦɧɚɹ ɫɜɹɡɶ ɭɡɥɨɜ ɚɩɩɚɪɚɬɭɪɵ ɢ ɢɯ ɩɚɪɚɦɟ
ɬɪɨɜ ɜɵɛɢɪɚɟɬɫɹ ɢɫɯɨɞɧɨɟ ɱɢɫɥɨ ɤɨɧɬɪɨɥɢɪɭɟɦɵɯ ɩɚɪɚɦɟɬɪɨɜ
ɋɬɟɩɟɧɶ ɫɜɹɡɢ ɦɟɠɞɭ ɩɚɪɚɦɟɬɪɚɦɢ h ɢ h ɨɩɪɟɞɟɥɹɟɬɫɹ ɫ ɩɨɦɨ
i j
ɳɶɸ ɜɵɪɚɠɟɧɢɹ ɩɪɟɞɟɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɚ ɤɨɪɪɟɥɹɰɢɢ
z n / n n ,
,
hi hj j,o. i j
ɝɞɟ n ɢ n ² ɱɢɫɥɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɜɥɢɹɸɳɢɯ ɧɚ ɩɚ
i
j
ɪɚɦɟɬɪɵ h ɢ h n ² ɱɢɫɥɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɨɛɳɢɯ
i M ɨɛɳ
ɞɥɹ ɩɚɪɚɦɟɬɪɨɜ h ɢ h
L M
ɂɫɯɨɞɧɨɟ ɱɢɫɥɨ ɩɚɪɚɦɟɬɪɨɜ ɜɵɛɢɪɚɟɬɫɹ ɬɚɤɢɦ ɨɛɪɚɡɨɦ ɱɬɨɛɵ
ɤɨɧɬɪɨɥɟɦ ɛɵɥɢ ɨɯɜɚɱɟɧɵ ɜɫɟ ɷɥɟɦɟɧɬɵ ɫɢɫɬɟɦɵ Ⱦɨɫɬɚɬɨɱɧɨɫɬɶ ɢɫ
ɯɨɞɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɩɪɨɜɟɪɹɟɬɫɹ ɪɚɫɱɟɬɨɦ ɤɨɷɮɮɢɰɢɟɧɬɚ ɩɨɥɧɨ ɬɵ
ɤɨɧɬɪɨɥɹ
ɇɚ ɜɬɨɪɨɦ ɷɬɚɩɟ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɜɟɪɨɹɬɧɨɫɬɶ ɨɬɤɚɡɚ ɮɭɧɤɰɢ
ɨɧɚɥɶɧɵɯ ɭɡɥɨɜ ɢɥɢ ɚɩɩɚɪɚɬɭɪɵ ɤɚɧɚɥɚ ɩɟɪɟɞɚɱɢ ɢ ɧɚ ɨɫɧɨɜɟ ɩɨ
ɥɭɱɟɧɧɵɯ ɞɚɧɧɵɯ ɢ ɪɟɡɭɥɶɬɚɬɨɜ ɪɚɛɨɬɵ ɩɟɪɜɨɝɨ ɷɬɚɩɚ ɫɨɫɬɚɜ ɥɹɟɬɫɹ
