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ɍɫɢɥɢɟ N 6 2 ɫɥɟɞɭɟɬ ɩɪɢɧɹɬɶ ɪɚɜɧɵɦ ɧɭɥɸ.ɇɨ ɤɚɤ ɬɨɥɶɤɨ ɦɵ ɩɪɢɪɚɜɧɹɟɦ ɭɫɢɥɢɟ N 6 2 ɧɭɥɸ, ɢɡ ɩɪɢɜɟɞɟɧɧɵɯ ɬɪɟɭɝɨɥɶɧɢɤɨɜ ɫɢɥɩɨɥɭɱɚɬɫɹ ɧɭɥɟɜɵɦɢ ɜɫɟ ɭɫɢɥɢɹ ɜ ɮɟɪɦɟ. Ɉɬɫɸɞɚ ɞɟɥɚɟɦ ɨɛɳɢɣ ɜɵɜɨɞ: ɬɚɤ ɤɚɤ ɫɨɛɥɸɞɚɟɬɫɹɧɟɨɛɯɨɞɢɦɨɟ ɭɫɥɨɜɢɟ n 0 ɢ ɩɪɢ ɧɭɥɟɜɨɣ ɧɚɝɪɭɡɤɟ ɜɫɟ ɭɫɢɥɢɹ ɪɚɜɧɵ ɧɭɥɸ, ɬɨ ɮɟɪɦɚɝɟɨɦɟɬɪɢɱɟɫɤɢ ɧɟɢɡɦɟɧɹɟɦɚ ɢ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɚ.110Ⱥɧɚɥɨɝɢɱɧɨɟ ɢɫɫɥɟɞɨɜɚɧɢɟ ɦɨɠɟɬ ɛɵɬɶ ɜɵɩɨɥɧɟɧɨ ɢ ɞɥɹ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ ɞɪɭɝɢɯɬɢɩɨɜ.ɉ ɪ ɢ ɦ ɟ ɪ 3. Ɋɚɫɫɦɨɬɪɢɦ ɪɚɦɭ, ɢɡɨɛɪɚɠɟɧɧɭɸ ɧɚ ɪɢɫ. 5.20, ɚ. Ⱦɥɹ ɧɟɟɭɞɨɜɥɟɬɜɨɪɹɟɬɫɹ ɧɟɨɛɯɨɞɢɦɨɟ ɭɫɥɨɜɢɟ ɫɬɚɬɢɱɟɫɤɨɣ ɨɩɪɟɞɟɥɢɦɨɫɬɢ ɢ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣɧɟɢɡɦɟɧɹɟɦɨɫɬɢ: n (nɨɩ 3nɤ ) (3 n1ɲ ) (5 3 ˜ 0) (3 2) 0 .Ɋɢɫ.

5.20ɉɪɨɜɟɪɤɭ Ƚɇ ɜɵɩɨɥɧɢɦ ɫɩɨɫɨɛɨɦ ɧɭɥɟɜɨɣ ɧɚɝɪɭɡɤɢ, ɜɵɩɨɥɧɢɜ ɫɥɟɞɭɸɳɢɟɪɚɫɫɭɠɞɟɧɢɹ.Ʌɢɧɢɹ ɞɟɣɫɬɜɢɹ ɩɨɥɧɨɣ ɪɟɚɤɰɢɢ ɜ ɨɩɨɪɟ A ɢɡ ɭɫɥɨɜɢɹ ɪɚɜɧɨɜɟɫɢɹ ɞɢɫɤɚ AD ɩɪɨɣɞɟɬɱɟɪɟɡ ɲɚɪɧɢɪ D . ɂɡ ɬɟɯ ɠɟ ɫɨɨɛɪɚɠɟɧɢɣ ɥɢɧɢɹ ɞɟɣɫɬɜɢɹ ɩɨɥɧɨɣ ɨɩɨɪɧɨɣ ɪɟɚɤɰɢɢ ɜ ɨɩɨɪɟC ɩɪɨɣɞɟɬ ɱɟɪɟɡ ɲɚɪɧɢɪ E . Ɉɛɟ ɥɢɧɢɢ ɞɟɣɫɬɜɢɹ ɩɟɪɟɫɟɤɭɬɫɹ ɜ ɬɨɱɤɟ O ɫ ɜɟɪɬɢɤɚɥɶɧɨɣɪɟɚɤɰɢɟɣ VB .Ɍɚɤ ɤɚɤ ɜɫɟ ɬɪɢ ɨɩɨɪɧɵɯ ɪɟɚɤɰɢɢ ɩɟɪɟɫɟɤɥɢɫɶ ɜ ɨɞɧɨɣ ɬɨɱɤɟ, ɬɨ, ɡɚɞɚɜɲɢɫɶ ɨɞɧɨɣ ɢɡɧɢɯ ɤɚɤ ɧɟɤɨɬɨɪɨɣ ɧɟ ɧɭɥɟɜɨɣ ɜɟɥɢɱɢɧɨɣ, ɦɨɠɟɦ ɢɡ ɬɪɟɭɝɨɥɶɧɢɤɚ ɫɢɥ, ɩɨɫɬɪɨɟɧɧɨɝɨ ɞɥɹɬɨɱɤɢ Ɉ , ɨɩɪɟɞɟɥɢɬɶ ɞɜɟ ɞɪɭɝɢɯ ɪɟɚɤɰɢɢ.

ɉɪɢ ɷɬɨɦ ɧɟ ɜɫɬɪɟɬɢɦ ɧɢɤɚɤɨɝɨ ɩɪɨɬɢɜɨɪɟɱɢɹ:ɬɪɟɭɝɨɥɶɧɢɤ ɫɢɥ ɛɭɞɟɬ ɡɚɦɤɧɭɬ, ɢ ɜɫɹ ɫɢɫɬɟɦɚ ɛɭɞɟɬ ɧɚɯɨɞɢɬɶɫɹ ɜ ɪɚɜɧɨɜɟɫɢɢ.Ɉɬɫɸɞɚ ɩɨɥɭɱɚɟɦ ɜɵɜɨɞ: ɧɚɲɟ ɞɨɩɭɳɟɧɢɟ ɨ ɜɨɡɦɨɠɧɨɫɬɢ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɪɟɚɤɰɢɣ ɢɛɟɡ ɧɚɝɪɭɡɤɢ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɫɢɫɬɟɦɚ, ɧɟɫɦɨɬɪɹ ɧɚ ɜɵɩɨɥɧɟɧɢɟ ɭɫɥɨɜɢɹ n 0 , ɹɜɥɹɟɬɫɹɝɟɨɦɟɬɪɢɱɟɫɤɢ ɢɡɦɟɧɹɟɦɨɣ ɫɢɫɬɟɦɨɣ.ȿɫɥɢ ɫɞɜɢɧɭɬɶ ɲɚɪɧɢɪ D ɢɥɢ E (ɫɦ. ɪɢɫ. 5.20, ɛ), ɬɨ ɥɢɧɢɢ ɞɟɣɫɬɜɢɹ ɪɟɚɤɰɢɣ ɧɟɛɭɞɭɬ ɩɟɪɟɫɟɤɚɬɶɫɹ ɜ ɨɞɧɨɣ ɬɨɱɤɟ.ȼ ɷɬɨɦ ɫɥɭɱɚɟ, ɩɪɢ ɩɪɟɞɩɨɥɨɠɟɧɢɢ ɨ ɜɨɡɦɨɠɧɨɫɬɢ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɨɞɧɨɣ ɢɡ ɪɟɚɤɰɢɣ,ɩɨɥɭɱɢɦ ɩɪɨɬɢɜɨɪɟɱɢɟ: ɪɚɦɚ ɧɟ ɛɭɞɟɬ ɧɚɯɨɞɢɬɶɫɹ ɜ ɪɚɜɧɨɜɟɫɢɢ.Ɂɧɚɱɢɬ, ɥɸɛɚɹ ɢɡ ɪɟɚɤɰɢɣ ɜ ɜɚɪɢɚɧɬɟ ɛ ɪɚɦɵ ɪɚɜɧɚ ɧɭɥɸ, ɚ ɡɧɚɱɢɬ, ɪɚɜɧɵ ɧɭɥɸ ɢ ɜɫɟɭɫɢɥɢɹ ɜ ɫɟɱɟɧɢɹɯ ɫɬɟɪɠɧɟɣ ɪɚɦɵ.ɗɬɨ ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɫɢɫɬɟɦɚ ɩɪɚɜɢɥɶɧɨ ɨɛɪɚɡɨɜɚɧɚ ɢ ɹɜɥɹɟɬɫɹɝɟɨɦɟɬɪɢɱɟɫɤɢ ɧɟɢɡɦɟɧɹɟɦɨɣ ɢ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɨɣ.1115.9.

ɉɨɧɹɬɢɟ ɨ ɥɢɧɢɹɯ ɜɥɢɹɧɢɹ ɢ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɩɪɢ ɪɚɫɱɟɬɟɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦȼɜɟɞɟɧɢɟȾɨ ɫɢɯ ɩɨɪ ɜ ɷɬɨɦ ɪɚɡɞɟɥɟ ɩɨɫɨɛɢɹ ɪɚɫɫɦɚɬɪɢɜɚɥɚɫɶ ɦɟɬɨɞɢɤɚɨɩɪɟɞɟɥɟɧɢɹ ɭɫɢɥɢɣ ɫɬɚɬɢɱɟɫɤɢɦ ɦɟɬɨɞɨɦ (ɫ ɩɨɦɨɳɶɸ ɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ)ɜ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɵɯ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦɚɯ ɨɬ ɞɟɣɫɬɜɢɹ ɧɚ ɧɢɯɧɟɩɨɞɜɢɠɧɨɣ ɧɚɝɪɭɡɤɢ.Ɉɞɧɚɤɨ, ɧɚ ɧɟɤɨɬɨɪɵɟ ɫɨɨɪɭɠɟɧɢɹ ɞɟɣɫɬɜɭɸɬ ɢ ɩɨɞɜɢɠɧɵɟ ɧɚɝɪɭɡɤɢ,ɉɪɢɦɟɪɨɦ ɦɨɠɟɬ ɫɥɭɠɢɬɶ ɩɪɨɦɵɲɥɟɧɧɨɟ ɡɞɚɧɢɟ, ɜ ɤɨɬɨɪɨɦ ɩɪɢ ɟɝɨɷɤɫɩɥɭɚɬɚɰɢɢ ɩɪɟɞɭɫɦɨɬɪɟɧɨ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɤɪɚɧɚ.ɋɬɚɧɢɧɚ ɤɪɚɧɚ ɦɨɠɟɬ ɩɟɪɟɦɟɳɚɬɶɫɹ, ɧɚɩɪɢɦɟɪ, ɜɞɨɥɶ ɦɚɲɢɧɧɨɝɨ ɡɚɥɚɷɥɟɤɬɪɨɫɬɚɧɰɢɢ ɩɨ ɫɩɟɰɢɚɥɶɧɵɦ ɩɨɞɤɪɚɧɨɜɵɦ ɛɚɥɤɚɦ.

ȼɞɨɥɶ ɩɨɞɤɪɚɧɨɜɵɯɛɚɥɨɤ ɭɥɨɠɟɧɵ ɪɟɥɶɫɵ, ɧɚ ɤɨɬɨɪɵɟ ɱɟɪɟɡ ɤɨɥɟɫɚ ɫɬɚɧɢɧɵ ɤɪɚɧɚ ɩɟɪɟɞɚɸɬɫɹɫɢɥɵ ɞɚɜɥɟɧɢɹ ɨɬ ɫɨɛɫɬɜɟɧɧɨɝɨ ɜɟɫɚ ɤɪɚɧɚ ɢ ɧɟɫɭɳɟɝɨ ɢɦ ɝɪɭɡɚ.Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɢ ɞɜɢɠɟɧɢɢ ɤɪɚɧɚ ɩɨɞɤɪɚɧɨɜɚɹ ɛɚɥɤɚ ɛɭɞɟɬɢɫɩɵɬɵɜɚɬɶ ɞɚɜɥɟɧɢɟ ɤɨɥɟɫ ɤɪɚɧɚ ɜ ɜɢɞɟ ɝɪɭɩɩɵ ɩɨɞɜɢɠɧɵɯ ɫɨɫɪɟɞɨɬɨɱɟɧɧɵɯɫɢɥ.ɉɨɫɤɨɥɶɤɭ ɩɨɞɤɪɚɧɨɜɚɹ ɛɚɥɤɚ ɨɩɢɪɚɟɬɫɹ ɧɚ ɩɨɩɟɪɟɱɧɵɟ ɪɚɦɵɩɪɨɦɵɲɥɟɧɧɨɝɨ ɡɞɚɧɢɹ, ɬɨ ɞɟɣɫɬɜɢɟ ɩɨɞɜɢɠɧɨɣ ɧɚɝɪɭɡɤɢ ɩɟɪɟɞɚɟɬɫɹ ɢ ɧɚɩɨɩɟɪɟɱɧɵɟ ɪɚɦɵ ɡɞɚɧɢɹ ɢ ɧɚ ɢɯ ɮɭɧɞɚɦɟɧɬ.ȼɬɨɪɵɦ ɩɪɢɦɟɪɨɦ ɫɨɨɪɭɠɟɧɢɣ, ɜɨɫɩɪɢɧɢɦɚɸɳɢɯ ɩɨɞɜɢɠɧɵɟ ɧɚɝɪɭɡɤɢ,ɹɜɥɹɸɬɫɹ ɦɨɫɬɵ. ɉɪɢ ɷɬɨɦ ɫɢɥɵ ɞɚɜɥɟɧɢɹ ɧɚ ɦɨɫɬ ɦɨɝɭɬ ɛɵɬɶ ɫɚɦɵɟɪɚɡɧɨɨɛɪɚɡɧɵɟ (ɨɬ ɝɪɭɩɩɵ ɫɨɫɪɟɞɨɬɨɱɟɧɧɵɯ ɞɚɜɥɟɧɢɣ ɤɨɥɟɫ ɩɨɟɡɞɚ ɢɥɢ ɨɬɦɧɨɝɨɱɢɫɥɟɧɧɨɝɨ ɢ ɪɚɡɧɨɨɛɪɚɡɧɨɝɨ ɚɜɬɨɬɪɚɧɫɩɨɪɬɚ, ɨɬ ɪɚɫɩɪɟɞɟɥɟɧɧɨɝɨɞɚɜɥɟɧɢɹ ɩɨ ɤɚɤɨɣ-ɬɨ ɞɥɢɧɟ ɦɨɫɬɚ, ɧɚɩɪɢɦɟɪ, ɨɬ ɞɜɢɠɭɳɟɣɫɹ ɤɨɥɨɧɧɵ ɥɸɞɟɣ ɢɬ.

ɞ.).ɉɪɢ ɞɜɢɠɭɳɟɣɫɹ ɩɨ ɫɨɨɪɭɠɟɧɢɸ ɢɥɢ ɟɝɨ ɷɥɟɦɟɧɬɭ ɧɚɝɪɭɡɤɟ ɜɫɟɜɧɭɬɪɟɧɧɢɟ ɭɫɢɥɢɹ ɢ ɨɩɨɪɧɵɟ ɪɟɚɤɰɢɢ ɛɭɞɭɬ ɢɡɦɟɧɹɬɶɫɹ ɩɨ ɫɜɨɟɦɭ ɡɧɚɱɟɧɢɸ ɢɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɞɟɣɫɬɜɢɹ.ɉɨɷɬɨɦɭ ɜɨɡɧɢɤɚɟɬ ɜɨɩɪɨɫ ɨ ɦɟɬɨɞɢɤɟ ɪɚɫɱɟɬɚ ɫɨɨɪɭɠɟɧɢɣ ɢ ɢɯɷɥɟɦɟɧɬɨɜ ɨɬ ɩɨɞɜɢɠɧɨɣ ɧɚɝɪɭɡɤɢ.Ⱦɜɢɠɭɳɚɹɫɹ ɧɚɝɪɭɡɤɚ ɦɨɠɟɬ ɛɵɬɶ ɪɚɫɫɦɨɬɪɟɧɚ ɢ ɤɚɤ ɫɬɚɬɢɱɟɫɤɚɹ (ɧɟɜɵɡɵɜɚɸɳɚɹ ɩɨɹɜɥɟɧɢɹ ɞɨɩɨɥɧɢɬɟɥɶɧɨɣ ɧɚɝɪɭɡɤɢ ɜ ɜɢɞɟ ɫɢɥ ɢɧɟɪɰɢɢ) ɢ ɤɚɤɞɢɧɚɦɢɱɟɫɤɚɹ (ɤɨɝɞɚ ɩɨɹɜɥɹɸɬɫɹ ɫɢɥɵ ɢɧɟɪɰɢɢ, ɤɨɬɨɪɵɟ ɧɟɨɛɯɨɞɢɦɨɭɱɢɬɵɜɚɬɶ ɤɚɤ ɞɨɩɨɥɧɢɬɟɥɶɧɭɸ ɧɚɝɪɭɡɤɭ ɧɚ ɫɨɨɪɭɠɟɧɢɟ).Ʉɚɤ ɩɨɤɚɡɚɧɨ ɜ ɩɨɞɪɚɡɞɟɥɟ 1.4 ɭɱɟɛɧɨɝɨ ɩɨɫɨɛɢɹ ɧɚ ɫɯɟɦɟ ɪɚɡɞɟɥɟɧɢɹ112ɫɬɪɨɢɬɟɥɶɧɨɣ ɦɟɯɚɧɢɤɢ ɧɚ «ɫɬɚɬɢɤɭ ɫɨɨɪɭɠɟɧɢɣ» ɢ ɧɚ «ɞɢɧɚɦɢɤɭɫɨɨɪɭɠɟɧɢɣ», ɞɚɧɧɨɟ ɭɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɱɚɫɬɢ «ɋɬɚɬɢɤɚɫɨɨɪɭɠɟɧɢɣ».ɉɨɷɬɨɦɭ ɩɨɞɜɢɠɧɭɸ ɧɚɝɪɭɡɤɭ ɜ ɞɚɧɧɨɦ ɩɨɫɨɛɢɢ ɛɭɞɟɦ ɪɚɫɫɦɚɬɪɢɜɚɬɶɤɚɤ ɫɬɚɬɢɱɟɫɤɭɸ.

ȼɨɩɪɨɫɵ ɞɢɧɚɦɢɤɢ ɛɭɞɭɬ ɢɡɭɱɚɬɶɫɹ ɜ ɱɚɫɬɢ «Ⱦɢɧɚɦɢɤɚɫɨɨɪɭɠɟɧɢɢ».ɂɡɭɱɟɧɢɟ ɜɨɩɪɨɫɚ ɨ ɪɚɫɱɟɬɟ ɫɨɨɪɭɠɟɧɢɣ ɧɚ ɫɬɚɬɢɱɟɫɤɭɸ ɩɨɞɜɢɠɧɭɸɧɚɝɪɭɡɤɭ ɧɚɱɧɟɦ ɫ ɩɨɧɹɬɢɹ ɨ ɥɢɧɢɹɯ ɜɥɢɹɧɢɹ.ɉɨɧɹɬɢɟ ɨ ɥɢɧɢɹɯ ɜɥɢɹɧɢɹ ɞɥɹ ɭɫɢɥɢɣɊɚɫɫɦɨɬɪɢɦ ɨɞɧɨɩɪɨɥɟɬɧɭɸ ɛɚɥɤɭ, ɩɨ ɤɨɬɨɪɨɣ ɞɜɢɠɟɬɫɹ ɫɨɫɪɟɞɨɬɨɱɟɧɧɚɹɫɢɥɚ P 1 ɤɇ.ɉɪɢɭɤɚɡɚɧɧɨɦɩɨɥɨɠɟɧɢɢȽɪɭɡ ɫɩɪɚɜɚȽɪɭɡ ɫɥɟɜɚɟɞɢɧɢɱɧɨɝɨɝɪɭɡɚɢɡɭɪɚɜɧɟɧɢɣ1xɪɚɜɧɨɜɟɫɢɹ ɨɩɨɪɧɵɟ ɪɟɚɤɰɢɢ ɜɵɪɚɡɹɬɫɹknmɤɚɤ ɥɢɧɟɣɧɵɟ ɮɭɧɤɰɢɢ ɤɨɨɪɞɢɧɚɬɵ x:VAVBllxxɥ.ɜ.VAVA 1 ˜; VB 1 ˜(5.22)ll1ɗɬɢ ɮɭɧɤɰɢɢ ɹɜɥɹɸɬɫɹ ɮɭɧɤɰɢɹɦɢɥ.ɜ.Vȼɜɥɢɹɧɢɹ ɟɞɢɧɢɱɧɨɣ ɫɢɥɵ ɧɚ ɜɟɥɢɱɢɧɵ1(ɧɚ ɡɧɚɱɟɧɢɹ ɢ ɡɧɚɤɢ) ɨɩɨɪɧɵɯ ɪɟɚɤɰɢɣ.Ƚɪɚɮɢɤɢ ɷɬɢɯ ɮɭɧɤɰɢɣ ɜɥɢɹɧɢɹɥ.ɜ.Mkɧɚɡɵɜɚɸɬɫɹɥɢɧɢɹɦɢɜɥɢɹɧɢɹmɟɞɢɧɢɱɧɨɣ ɫɢɥɵ ɧɚ ɜɟɥɢɱɢɧɵ ɨɩɨɪɧɵɯnmn/lɪɟɚɤɰɢɣ.Ƚɪɚɮɢɤɢɥɢɧɟɣɧɵɯɮɭɧɤɰɢɣɜɥɢɹɧɢɹ ɦɨɠɧɨ ɩɨɫɬɪɨɢɬɶ ɩɨ ɞɜɭɦɥ.ɜ.Qk1ɨɪɞɢɧɚɬɚɦ, ɧɚɩɪɢɦɟɪ, ɩɪɢ x 0 ɢ x l(ɪɢɫ.

5.21).Ʌɢɧɢɢ ɜɥɢɹɧɢɹ ɦɨɠɧɨ ɩɨɫɬɪɨɢɬɶ ɢɞɥɹ ɭɫɢɥɢɣ Mk ɢ Qk ɜ ɥɸɛɨɦ ɫɟɱɟɧɢɢ k1ɩɪɨɥɟɬɚ ɛɚɥɤɢ.ɉɪɢ ɷɬɨɦ ɨɬɞɟɥɶɧɨ ɫɬɪɨɹɬɫɹ ɞɜɚɊɢɫ. 5.21ɝɪɚɮɢɤɚ ɞɥɹ ɤɚɠɞɨɝɨ ɭɫɢɥɢɹ: ɤɨɝɞɚ ɝɪɭɡɧɚɯɨɞɢɬɫɹ ɫɥɟɜɚ ɨɬ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ ɫɟɱɟɧɢɹ k ɢ ɤɨɝɞɚ ɨɧ ɧɚɯɨɞɢɬɫɹ ɫɩɪɚɜɚ ɨɬɫɟɱɟɧɢɹ. ɉɨɥɭɱɚɟɬɫɹ ɜɟɬɜɢ ɥ.ɜ.Mk ɢ ɥ.ɜ.Qk ɫɥɟɜɚ ɢ ɫɩɪɚɜɚ ɨɬ ɫɟɱɟɧɢɹ k(ɫɦ.

ɪɢɫ. 5.21).113ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɥɢɧɢɣ ɜɥɢɹɧɢɹ ɞɥɹ ɭɫɢɥɢɣɫ ɰɟɥɶɸ ɨɩɪɟɞɟɥɟɧɢɹ ɢɫɤɨɦɨɝɨ ɭɫɢɥɢɹ ɨɬ ɝɪɭɩɩɵ ɫɢɥɅɢɧɢɸ ɜɥɢɹɧɢɹ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɜɟɥɢɱɢɧɵ ɭɫɢɥɢɹ,ɞɥɹ ɤɨɬɨɪɨɝɨ ɨɧɚ ɩɨɫɬɪɨɟɧɚ, ɨɬ ɥɸɛɨɣ ɝɪɭɩɩɵ ɫɢɥ, ɞɟɣɫɬɜɭɸɳɢɯ ɧɚɪɚɫɫɦɚɬɪɢɜɚɟɦɭɸ ɤɨɧɫɬɪɭɤɰɢɸ (ɜ ɞɚɧɧɨɦ ɩɪɢɦɟɪɟ – ɧɚ ɩɪɨɫɬɭɸ ɛɚɥɤɭ).ȼɵɱɢɫɥɟɧɢɟ ɢɫɤɨɦɨɝɨ ɭɫɢɥɢɹ ɨɬ ɝɪɭɩɩɵ ɫɨɫɪɟɞɨɬɨɱɟɧɧɵɯ ɫɢɥ Pi ɫɧɨɦɟɪɨɦ i ɢ ɨɬ ɝɪɭɩɩɵ ɪɚɜɧɨɦɟɪɧɨ ɪɚɫɩɪɟɞɟɥɟɧɧɵɯ ɧɚɝɪɭɡɨɤ ɢɧɬɟɧɫɢɜɧɨɫɬɶɸq j ɫ ɧɨɦɟɪɨɦ j ɛɭɞɟɬ ɜɵɩɨɥɧɹɬɶɫɹ ɩɨ ɮɨɪɦɭɥɟ:ɍɫɢɥɢɟ ¦ Pi ˜ zi + ¦ q j ˜ Z j .ij(5.23)Ɂɞɟɫɶ zi ɹɜɥɹɟɬɫɹ ɨɪɞɢɧɚɬɨɣ ɥɢɧɢɢ ɜɥɢɹɧɢɹ ɞɥɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨɭɫɢɥɢɹ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɫɨɫɪɟɞɨɬɨɱɟɧɧɨɣ ɫɢɥɟ Pi ; Z j ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣɩɥɨɳɚɞɶ ɥɢɧɢɢ ɜɥɢɹɧɢɹ ɧɚɯɨɞɹɳɟɣɫɹ ɩɨɞ ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ ɧɚɝɪɭɡɤɨɣɢɧɬɟɧɫɢɜɧɨɫɬɢ q j .

ȼɫɟ ɩɪɨɢɡɜɟɞɟɧɢɹ ɜ ɮɨɪɦɭɥɟ (5.23) ɛɟɪɭɬɫɹ ɫɨ ɫɜɨɢɦɢɡɧɚɤɚɦɢ.Ⱦɥɹ ɩɨɥɭɱɟɧɢɹ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɢɫɤɨɦɨɝɨ ɭɫɢɥɢɹ ɧɟɨɛɯɨɞɢɦɨɪɚɡɦɟɫɬɢɬɶ ɝɪɭɡɵ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɜɵɱɢɫɥɟɧɢɟ ɩɨ ɮɨɪɦɭɥɟ (5.23) ɞɚɥɨ ɷɬɨɡɧɚɱɟɧɢɟ.ȼɨɩɪɨɫ ɨ ɩɨɫɬɪɨɟɧɢɢ ɥɢɧɢɣ ɜɥɢɹɧɢɹ ɛɵɥ ɩɪɨɞɟɦɨɧɫɬɪɢɪɨɜɚɧ ɧɚ ɩɪɢɦɟɪɟɩɪɨɫɬɨɣ ɨɞɧɨɩɪɨɥɟɬɧɨɣ ɛɚɥɤɢ. Ⱥɧɚɥɨɝɢɱɧɨ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɭɪɚɜɧɟɧɢɣɪɚɜɧɨɜɟɫɢɹ ɦɨɠɧɨ ɩɨɫɬɪɨɢɬɶ ɥɢɧɢɢ ɜɥɢɹɧɢɹ ɞɥɹ ɨɩɨɪɧɵɯ ɪɟɚɤɰɢɣ ɢɜɧɭɬɪɟɧɧɢɯ ɭɫɢɥɢɣ M, Q, N ɜ ɫɟɱɟɧɢɹɯ ɫɬɟɪɠɧɟɣ ɥɸɛɵɯ ɫɬɚɬɢɱɟɫɤɢɨɩɪɟɞɟɥɢɦɵɯ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ (ɲɚɪɧɢɪɧɵɯ ɛɚɥɨɤ, ɪɚɦ, ɬɪɟɯɲɚɪɧɢɪɧɵɯ ɚɪɨɤɢ ɮɟɪɦ) [7, 10].Ɂɧɚɱɢɬɟɥɶɧɨ ɛɨɥɟɟ ɫɥɨɠɧɨ ɥɢɧɢɢ ɜɥɢɹɧɢɹ ɞɥɹ ɢɫɤɨɦɵɯ ɭɫɢɥɢɣ ɫɬɪɨɹɬɫɹɞɥɹ ɫɬɚɬɢɱɟɫɤɢ ɧɟɨɩɪɟɞɟɥɢɦɵɯ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ.

Ɉɞɧɚɤɨ ɢɫɩɨɥɶɡɨɜɚɧɢɟɫɨɜɪɟɦɟɧɧɵɯ ɩɪɨɝɪɚɦɦɧɵɯ ɤɨɦɩɥɟɤɫɨɜ (ɧɚɩɪɢɦɟɪ, ɩɪɨɝɪɚɦɦɵ SCAD)ɩɨɡɜɨɥɹɟɬ ɞɨɫɬɚɬɨɱɧɨ ɛɵɫɬɪɨ ɨɩɪɟɞɟɥɹɬɶ ɢɫɤɨɦɵɟ ɭɫɢɥɢɹ ɨɬ ɥɸɛɨɣ ɧɚɝɪɭɡɤɢɩɪɢ ɥɸɛɨɦ ɟɟ ɤɨɧɤɪɟɬɧɨɦ ɩɨɥɨɠɟɧɢɢ ɜ ɩɪɨɰɟɫɫɟ ɩɟɪɟɞɜɢɠɟɧɢɹ ɩɨɫɨɨɪɭɠɟɧɢɸ.5.10. ɂɧɮɨɪɦɚɰɢɹ ɨ ɫɛɨɪɧɢɤɟ ɡɚɞɚɧɢɣ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɵɯ ɪɚɫɱɟɬɧɵɯɪɚɛɨɬ ɫɬɭɞɟɧɬɨɜ ɧɚ ɬɟɦɭ «Ɉɩɪɟɞɟɥɟɧɢɟ ɭɫɢɥɢɣ ɢ ɩɨɫɬɪɨɟɧɢɟ ɷɩɸɪ M , Q, Nɜ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɵɯ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦɚɯ»ɂɡɭɱɟɧɢɟ ɪɚɰɢɨɧɚɥɶɧɵɯ ɫɩɨɫɨɛɨɜ ɨɩɪɟɞɟɥɟɧɢɹ ɭɫɢɥɢɣ ɜ ɫɬɚɬɢɱɟɫɤɢɨɩɪɟɞɟɥɢɦɵɯ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦɚɯ ɫ ɭɱɟɬɨɦ ɢɯ ɤɨɧɫɬɪɭɤɬɢɜɧɵɯ ɨɫɨɛɟɧɧɨɫɬɟɣɹɜɥɹɟɬɫɹ ɨɱɟɧɶ ɜɚɠɧɵɦ ɷɬɚɩɨɦ ɭɱɟɛɧɨɝɨ ɩɪɨɰɟɫɫɚ ɩɨ ɞɢɫɰɢɩɥɢɧɟ114«ɋɬɪɨɢɬɟɥɶɧɚɹ ɦɟɯɚɧɢɤɚ».ɍɦɟɧɢɟ ɨɩɪɟɞɟɥɹɬɶ ɭɫɢɥɢɹ ɫ ɩɨɦɨɳɶɸ ɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ ɜɪɚɡɥɢɱɧɵɯ ɬɢɩɚɯ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɵɯ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ (ɛɚɥɨɤ, ɪɚɦ,ɚɪɨɤ, ɮɟɪɦ) ɩɨɡɜɨɥɹɟɬ ɭɱɚɳɟɦɭɫɹ ɥɭɱɲɟ ɩɨɧɢɦɚɬɶ ɢɯ ɨɛɳɢɟ ɫɜɨɣɫɬɜɚ ɢɪɚɡɥɢɱɢɟ, ɨɩɪɟɞɟɥɹɟɦɨɟ ɤɨɧɫɬɪɭɤɬɢɜɧɵɦɢ ɨɫɨɛɟɧɧɨɫɬɹɦɢ.ȼ ɬɨɠɟ ɜɪɟɦɹ, ɤɚɤ ɨɬɦɟɱɚɥɨɫɶ ɜ ɩɪɟɞɢɫɥɨɜɢɢ ɤ ɩɨɫɨɛɢɸ, ɩɪɢ ɜɵɩɨɥɧɟɧɢɢɡɚɞɚɱ ɩɨɫɬɪɨɟɧɢɹ ɷɩɸɪ ɭɫɢɥɢɣ ɜ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɵɯ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦɚɯɭɱɚɳɢɣɫɹ ɞɨɥɠɟɧ ɧɚɱɚɬɶ ɢɡɭɱɟɧɢɟ ɫɨɜɪɟɦɟɧɧɨɣ ɦɟɬɨɞɢɤɢ ɪɚɫɱɟɬɚ ɫɬɟɪɠɧɟɜɵɯɫɢɫɬɟɦ ɧɚ ɉɄ.

ɉɪɟɞɜɚɪɢɬɟɥɶɧɵɟ ɫɜɟɞɟɧɢɹ ɩɨ ɷɬɨɦɭ ɜɨɩɪɨɫɭ ɛɵɥɢ ɞɚɧɵ ɜɩɨɫɨɛɢɢ ɜ ɪɚɡɞɟɥɚɯ 3 ɢ 4.ɋ ɰɟɥɶɸ ɜɵɪɚɛɨɬɤɢ ɡɧɚɧɢɣ ɢ ɭɦɟɧɢɣ ɫɬɭɞɟɧɬɨɜ ɩɨ ɷɬɢɦ ɞɜɭɦ ɦɟɬɨɞɢɤɚɦɢɦ ɡɚɞɚɸɬɫɹ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ ɪɹɞ ɪɚɫɱɟɬɧɵɯ ɪɚɛɨɬ ɢɡ ɫɛɨɪɧɢɤɚɡɚɞɚɧɢɣ ɢ ɡɚɞɚɱ [6]. ɑɚɫɬɶ ɡɚɞɚɧɢɣ ɜ ɫɛɨɪɧɢɤɟ, ɨɬɧɨɫɹɳɢɯɫɹ ɤ ɪɚɡɞɟɥɭ «Ɋɚɫɱɟɬɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɵɯ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ», ɩɪɢɜɟɞɟɧɚ ɜ ɩɪɢɥɨɠɟɧɢɢ 1.Ɋɚɫɱɟɬɧɵɟ ɪɚɛɨɬɵ ɩɨ ɩɨɫɬɪɨɟɧɢɸ ɷɩɸɪ ɭɫɢɥɢɣ ɜ ɫɬɚɬɢɱɟɫɤɢɨɩɪɟɞɟɥɢɦɵɯ ɛɚɥɤɚɯ, ɪɚɦɚɯ ɢ ɮɟɪɦɚɯ ɫɨɫɬɨɹɬ ɢɡ ɞɜɭɯ ɪɚɡɞɟɥɨɜ:1. Ɋɚɫɱɟɬɵ ɧɚ ɉɄ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɪɨɝɪɚɦɦɵ SCAD, ɪɟɚɥɢɡɭɸɳɟɣɆɄɗ.2. Ʉɨɧɬɪɨɥɶ ɪɟɡɭɥɶɬɚɬɨɜ ɪɚɫɱɟɬɚ ɜɪɭɱɧɭɸ (ɛɟɡ ɩɪɢɦɟɧɟɧɢɹ ɉɄ). ɉɪɢ ɷɬɨɦɢɫɩɨɥɶɡɭɸɬɫɹ ɩɪɢɡɧɚɤɢ (ɫɜɨɣɫɬɜɚ) ɩɪɚɜɢɥɶɧɵɯ ɷɩɸɪ, ɩɪɢɜɟɞɟɧɧɵɟ ɜ ɪɚɡɞɟɥɟ 4,ɢ ɪɚɰɢɨɧɚɥɶɧɵɟ ɫɩɨɫɨɛɵ ɩɪɢɦɟɧɟɧɢɹ ɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ.Ⱦɥɹ ɩɨɞɝɨɬɨɜɤɢ ɭɱɚɳɢɯɫɹ ɩɨ ɢɫɩɨɥɶɡɨɜɚɧɢɸ ɩɪɨɝɪɚɦɦɵ SCAD ɧɚ ɭɪɨɜɧɟ«ɉɨɥɶɡɨɜɚɬɟɥɹ» ɤɪɨɦɟ ɩɪɟɞɜɚɪɢɬɟɥɶɧɵɯ ɞɚɧɧɵɯ, ɩɪɢɜɟɞɟɧɧɵɯ ɜ ɪɚɡɞɟɥɟ 3,ɜ ɪɚɡɞɟɥɚɯ 6 – 9 ɩɨɫɨɛɢɹ ɩɪɢɜɟɞɟɧɵ ɦɟɬɨɞɢɱɟɫɤɢɟ ɭɤɚɡɚɧɢɹ ɩɨ ɩɪɢɦɟɧɟɧɢɸɷɬɨɣ ɩɪɨɝɪɚɦɦɵ ɧɚ ɩɪɢɦɟɪɚɯ ɪɚɫɱɟɬɚ ɦɧɨɝɨɩɪɨɥɟɬɧɨɣ ɛɚɥɤɢ, ɪɚɦɵ ɢ ɮɟɪɦɵ.ɢɩɨɫɬɪɨɟɧɢɸɊɚɫɱɟɬɧɚɹɪɚɛɨɬɚɩɨɨɩɪɟɞɟɥɟɧɢɸɭɫɢɥɢɣɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɷɩɸɪ ɜ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɨɣ ɬɪɟɯɲɚɪɧɢɪɧɨɣ ɚɪɤɟɜɵɩɨɥɧɟɧɚ ɜ ɩɨɫɨɛɢɢ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɧɟ ɩɪɨɝɪɚɦɦɵ SCAD, ɚ ɩɪɨɝɪɚɦɦɵARKA [21], ɪɟɚɥɢɡɭɸɳɟɣ ɪɚɫɱɟɬ ɩɨ ɮɨɪɦɭɥɚɦ, ɩɪɢɜɟɞɟɧɧɵɦ ɜ ɩɨɞɪɚɡɞɟɥɟ 5.5.Ɇɟɬɨɞɢɱɟɫɤɢɟ ɭɤɚɡɚɧɢɹ ɩɨ ɨɮɨɪɦɥɟɧɢɸ ɪɚɫɱɟɬɧɵɯ ɪɚɛɨɬ (ɡɚɞɚɧɢɣ) ɩɪɢɜɵɩɨɥɧɟɧɢɢ ɭɤɚɡɚɧɧɵɯ ɜɵɲɟ ɞɜɭɯ ɪɚɡɞɟɥɨɜ ɩɪɢɜɟɞɟɧɵ ɜ ɩɨɫɨɛɢɢ [4] ɢ (ɞɥɹɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɵɯ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ) ɜ ɪɚɡɞɟɥɚɯ 6 – 11.Ⱦɨɩɨɥɧɢɬɟɥɶɧɨ ɤ ɫɛɨɪɧɢɤɭ ɡɚɞɚɧɢɣ ɩɨ ɩɨɫɬɪɨɟɧɢɸ ɷɩɸɪ ɭɫɢɥɢɣ ɜɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɵɯ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦɚɯ ɜ ɩɪɢɥɨɠɟɧɢɢ 2 ɩɪɢɜɟɞɟɧɵɤɨɧɬɪɨɥɶɧɵɟ ɡɚɞɚɱɢ, ɚ ɜ ɩɪɢɥɨɠɟɧɢɢ 3 – ɜɨɩɪɨɫɵ ɞɥɹ ɩɨɞɝɨɬɨɜɤɢ ɤ ɡɚɱɟɬɭ ɢɷɤɡɚɦɟɧɭ ɩɨ ɦɟɬɨɞɢɤɚɦ ɪɚɫɱɟɬɚ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɵɯ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ.1156.

ɈȻɓɂȿ ȼɈɉɊɈɋɕ ɉɊɂɆȿɇȿɇɂə ɉɊɈȽɊȺɆɆɕ SCADȾɅə ɊȺɋɑȿɌȺ ɉɅɈɋɄɂɏ ɋɌȿɊɀɇȿȼɕɏ ɋɂɋɌȿɆɉɊɂ ɋɌȺɌɂɑȿɋɄɈɃ ɇȺȽɊɍɁɄȿȼɜɟɞɟɧɢɟȼ ɞɚɧɧɨɦ ɭɱɟɛɧɨɦ ɩɨɫɨɛɢɢ ɩɪɨɰɟɞɭɪɚ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɩɨ ɨɩɪɟɞɟɥɟɧɢɸɇȾɋ ɩɥɨɫɤɢɯ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ ɫ ɩɨɦɨɳɶɸ ɩɪɨɝɪɚɦɦɵ SCAD ɭɫɥɨɜɧɨɪɚɡɞɟɥɟɧɚ ɧɚ ɫɥɟɞɭɸɳɢɟ ɷɬɚɩɵ.1. Ɂɚɩɭɫɤ ɩɪɨɝɪɚɦɦɵ ɢ ɩɨɞɝɨɬɨɜɤɚ ɤ ɫɨɡɞɚɧɢɸ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ1.1. Ɂɚɩɭɫɤ ɩɪɨɝɪɚɦɦɵ SCAD.1.2. ɋɨɡɞɚɧɢɟ ɧɨɜɨɝɨ ɩɪɨɟɤɬɚ ɞɥɹ ɜɵɩɨɥɧɟɧɢɹ ɪɚɫɱɟɬɚ ɡɚɞɚɧɧɨɣɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ ɢ ɟɝɨ ɧɚɢɦɟɧɨɜɚɧɢɟ.1.3. Ɂɚɞɚɧɢɟ ɢɦɟɧɢ ɮɚɣɥɚ ɜ ɞɢɪɟɤɬɨɪɢɢ SDATA, ɜ ɤɨɬɨɪɨɦ ɛɭɞɟɬɫɨɯɪɚɧɹɬɶɫɹ ɜɫɹ ɢɧɮɨɪɦɚɰɢɹ ɩɨ ɜɜɟɞɟɧɧɵɦ ɢɫɯɨɞɧɵɦ ɞɚɧɧɵɦ.

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