chap2
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ɍɩɪɚɠɧɟɧɢɟ 41. ȼɵɱɢɫɥɢɬɶ ¦di2 ɩɪɢ N=2k+1
ɍɤɚɡɚɧɢɟ: ɫɩɟɪɜɚ ɪɚɫɫɦɨɬɪɟɬɶ N=7, ɩɨ ɚɧɚɥɨɝɢɢ ɫ N=6 (ɫɦ. ɜɵɲɟ), ɚ ɡɚɬɟɦ N=2k+1; ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ
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(ɫɦ. ɉɪɢɥɨɠɟɧɢɟ ʋ 2). Ɉɬɜɟɬ: |
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N( N 2 1) |
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ȿɫɥɢ ɩɨɥɨɠɢɬɶ f |
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N( N 2 1) |
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N ( N 2 1)
ɛɭɞɟɬ ɨɛɥɚɞɚɬɶ ɬɪɟɛɭɟɦɵɦ ɫɜɨɣɫɬɜɨɦ.
[94]
ɉɪɢɦɟɪ 18. ɂɡɭɱɚɹ ɫɜɹɡɶ ɦɟɠɞɭ ɫɭɛɴɟɤɬɢɜɧɵɦ ɨɬɧɨɲɟɧɢɟɦ ɪɚɛɨɬɧɢɤɨɜ ɤ ɬɪɭɞɭ (ɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɶ ɪɚɛɨɬɨɣ) ɢ ɨɛɴɟɤɬɢɜɧɵɦ (ɬɟɤɭɱɟɫɬɶ), ɦɵ, ɜ ɱɚɫɬɧɨɫɬɢ, ɨɰɟɧɢɜɚɥɢ ɟɟ ɫ ɩɨɦɨɳɶɸ ɤɨɷɮɮɢɰɢɟɧɬɚ ɋɩɢɪɦɟɧɚ ɜ «ɫɟɱɟɧɢɢ» ɜɨɡɪɚɫɬ. ȼɨ ɜɬɨɪɨɣ ɤɨɥɨɧɤɟ ɬɚɛɥɢɰɵ 26 ɡɧɚɱɟɧɢɹ ɢɧɞɟɤɫɨɜ ɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɢ ɪɚɛɨɬɨɣ ɪɚɡɥɢɱɧɵɯ ɜɨɡɪɚɫɬɧɵɯ ɝɪɭɩɩ ɪɚɛɨɬɧɢɤɨɜ Ɉɞɟɫɫɤɨɝɨ ɫɭɞɨɪɟɦɨɧɬɧɨɝɨ ɡɚɜɨɞɚ (ɈɋɊɁ).
Ʉɪɨɦɟ ɬɨɝɨ, ɧɚɦɢ ɢɡɭɱɚɥɚɫɶ ɬɟɤɭɱɟɫɬɶ ɪɚɛɨɬɧɢɤɨɜ. Ʉɚɠɞɚɹ ɜɨɡɪɚɫɬɧɚɹ ɝɪɭɩɩɚ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɨɩɪɟɞɟɥɟɧɧɵɦ ɤɨɷɮ-
Ɍɚɛɥɢɰɚ 26
ȼɵɱɢɫɥɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ ɋɩɢɪɦɟɧɚ U
ȼɨɡɪɚɫɬɧɵɟ |
ɂɧɞɟɤɫɵ |
Ʉɨɷɮɮɢɰɢɟɧɬ |
Ɋɚɧɝɢ ɩɨ |
Ɋɚɧɝɢ ɩɨ |
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ɝɪɭɩɩɵ |
ɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɢ |
ɬɟɤɭɱɟɫɬɢ |
ɄT, |
X (ip) |
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Y (KT) |
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d2 |
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ɪɚɛɨɬɨɣ ip |
% |
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1 |
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2 |
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3 |
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4 |
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5 |
6 |
7 |
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ɞɨ 18 ɥɟɬ |
0,57 |
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12,9 |
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5 |
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5 |
0 |
0 |
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18 – 19 |
0,38 |
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13,0 |
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7 |
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4 |
3 |
9 |
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20 – 21 |
0,35 |
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17,1 |
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8 |
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3 |
5 |
25 |
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22 – 24 |
0,24 |
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37,1 |
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9 |
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1 |
8 |
64 |
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25 – 30 |
0,39 |
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19,9 |
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6 |
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2 |
4 |
16 |
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31 – 40 |
0,59 |
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7,9 |
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4 |
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6 |
2 |
4 |
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41 – 50 |
0,69 |
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5,6 |
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3 |
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9 |
6 |
36 |
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51 – 60 |
0,76 |
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6,1 |
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2 |
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8 |
6 |
36 |
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ɫɜɵɲɟ 60 ɥɟɬ |
0,77 |
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6,4 |
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1 |
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7 |
6 |
36 |
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ɮɢɰɢɟɧɬɨɦ ɬɟɤɭɱɟɫɬɢ, ɡɧɚɱɟɧɢɹ ɷɬɢɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɧɚɯɨɞɹɬɫɹ ɜ ɬɪɟɬɶɟɣ ɤɨɥɨɧɤɟ |
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U 1 |
6x266 |
0,88 |
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ɍɩɪɚɠɧɟɧɢɟ 42. ȼ «ɫɟɱɟɧɢɢ» ɫɬɚɠ ɛɵɥɢ ɩɨɥɭɱɟɧɵ ɬɚɤɢɟ ɞɚɧɧɵɟ: |
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ɋɬɚɠ, ɥɟɬ |
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Ⱦɨ 5 |
0,41 |
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26,5 |
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5-10 |
0,46 |
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15,1 |
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10-15 |
0,58 |
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3,6 |
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15-20 |
0,65 |
3,3 |
ɋɜɵɲɟ 20 |
0,73 |
1,3 |
ȼɵɱɢɫɥɢɬɶ ȡ.
Ⱥɧɚɥɨɝɢɱɧɵɣ ɪɟɡɭɥɶɬɚɬ ɛɵɥ ɩɨɥɭɱɟɧ ɜ «ɫɟɱɟɧɢɢ» ɨɛɪɚɡɨɜɚɬɟɥɶɧɵɯ ɝɪɭɩɩ. ȼɫɟ ɷɬɨ ɩɨɡɜɨɥɢɥɨ ɡɚɤɥɸɱɢɬɶ, ɱɬɨ ɦɟɠɞɭ ɜɵɞɟɥɟɧɧɵɦɢ ɩɪɢɡɧɚɤɚɦɢ ɢɦɟɟɬɫɹ ɨɛɪɚɬɧɚɹ (ɨɬɪɢɰɚɬɟɥɶɧɚɹ)
[95]
ɫɜɹɡɶ, ɬ.ɟ. ɫɭɛɴɟɤɬɢɜɧɨɟ ɢ ɨɛɴɟɤɬɢɜɧɨɟ ɨɬɧɨɲɟɧɢɟ ɤ ɬɪɭɞɭ ɬɟɫɧɨ ɫɜɹɡɚɧɵ.
Ⱦɨ ɫɢɯ ɩɨɪ ɩɪɟɞɩɨɥɚɝɚɥɨɫɶ, ɱɬɨ ɜɫɟ ɪɚɧɝɢ ɪɚɡɥɢɱɧɵ. Ɇɨɠɟɬ, ɨɞɧɚɤɨ, ɫɥɭɱɢɬɶɫɹ, ɱɬɨ ɫ ɬɨɱɧɨɫɬɶɸ ɧɚɲɟɝɨ ɢɡɦɟɪɟɧɢɹ ɪɚɧɝɢ ɭ ɧɟɫɤɨɥɶɤɢɯ ɢɧɞɢɜɢɞɨɜ ɨɤɚɠɭɬɫɹ ɨɞɢɧɚɤɨɜɵɦɢ. ȿɫɥɢ, ɧɚɩɪɢɦɟɪ, ɞɚɧɧɵɣ ɩɪɢɡɧɚɤ ɜ ɦɚɤɫɢɦɚɥɶɧɨɣ ɫɬɟɩɟɧɢ ɩɪɢɫɭɳ Ⱥ ɢ ȼ, ɬɨ ɤɚɠɞɨɦɭ ɦɵ ɩɪɢɫɜɨɢɦ ɪɚɧɝ 1,5=(1+2)/2.
ȿɫɥɢ, ɧɚɩɪɢɦɟɪ, ɜɫɥɟɞ ɡɚ ɧɢɦɢ ɢɞɭɬ ɋ, D, ȿ ɫ ɨɞɢɧɚɤɨɜɨɣ ɫɬɟɩɟɧɶɸ ɩɪɢɡɧɚɤɚ, ɬɨ ɤɚɠɞɨɦɭ ɢɡ ɢɧɞɢɜɢɞɨɜ ɦɵ ɩɪɢɫɜɨɢɦ ɪɚɧɝ (3+4+5)/3=4. ȼ ɬɚɤɢɯ ɫɥɭɱɚɹɯ ɝɨɜɨɪɹɬ ɨɛ ɨɛɴɟɞɢɧɟɧɢɢ ɪɚɧɝɨɜ. ȼɵɜɟɞɟɧɧɚɹ ɮɨɪɦɭɥɚ ɞɥɹ ɫɥɭɱɚɹ ɨɛɴɟɞɢɧɟɧɧɵɯ ɪɚɧɝɨɜ ɦɨɠɟɬ ɛɵɬɶ ɨɛɨɛɳɟɧɚ (ɦɵ ɷɬɨ ɫɞɟɥɚɟɦ ɜ §5). ɋɟɣɱɚɫ ɠɟ ɭɤɚɠɟɦ ɤɨɧɟɱɧɵɣ ɪɟɡɭɥɶɬɚɬ. ȿɫɥɢ ɫɪɟɞɢ ɪɚɧɝɨɜ ɩɨ X ɜɫɬɪɟɱɚɟɬɫɹ ɪ ɪɚɡɥɢɱɧɵɯ ɨɛɴɟɞɢɧɟɧɢɣ ɢ ɜ s-ɨɦ ɨɛɴɟɞɢɧɟɧɨ ts ɨɛɴɟɤɬɨɜ (ɪɚɧɝɨɜ), ɝɞɟ
s 1, p , ɚ ɫɪɟɞɢ ɪɚɧɝɨɜ Y ɢɦɟɟɬɫɹ q ɨɛɴɟɞɢɧɟɧɢɣ ɩɨ ur ɨɛɴɟɤɬɨɜ ɜ ɤɚɠɞɨɦ, ɝɞɟ r 1 , q ,
ɬɨ U |
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12 r 1 |
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ɉɨɫɥɟɞɧɹɹ ɮɨɪɦɭɥɚ, ɤɚɤ ɥɟɝɤɨ ɜɢɞɟɬɶ, ɜ ɫɥɭɱɚɟ ɨɬɫɭɬɫɬɜɢɹ ɨɛɴɟɞɢɧɟɧɢɣ ɥɟɝɤɨ ɩɪɟɜɪɚɳɚɟɬɫɹ ɜ ɪɚɧɟɟ ɩɨɥɭɱɟɧɧɭɸ (11,4,1). Ɋɚɫɫɦɨɬɪɟɧɢɟ ɪɚɧɝɨɜɨɣ ɤɨɪɪɟɥɹɰɢɢ ɧɚ ɷɬɨɦ ɦɵ ɧɟ ɡɚɤɚɧɱɢɜɚɟɦ. ȼ ɞɚɥɶɧɟɣɲɟɦ (§ 6) ɛɭɞɟɬ ɜɜɟɞɟɧ ɞɪɭɝɨɣ ɤɨɷɮɮɢɰɢɟɧɬ ɪɚɧɝɨɜɨɣ ɤɨɪɪɟɥɹɰɢɢ, ɩɪɟɞɥɨɠɟɧɧɵɣ Ʉɟɧɞɷɥɨɦ.
Ʉɪɨɦɟ ɬɨɝɨ, ɞɥɹ ɭɹɫɧɟɧɢɹ ɫɦɵɫɥɚ ɤɨɷɮɮɢɰɢɟɧɬɚ ɋɩɢɪɦɟɧɚ ɦɵ ɩɪɨɫɥɟɞɢɦ ɟɝɨ ɫɜɹɡɶ ɫ ɬɚɤ ɧɚɡɵɜɚɟɦɵɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɩɚɪɧɨɣ ɤɨɪɪɟɥɹɰɢɢ ɉɢɪɫɨɧɚ — Ȼɪɚɜɟ. ɗɬɨ ɩɨɡɜɨɥɢɬ ɭɬɨɱɧɢɬɶ ɭɫɥɨɜɢɹ ɢ ɨɛɥɚɫɬɶ ɩɪɢɦɟɧɟɧɢɹ ɫɩɢɪɦɟɧɨɜɫɤɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ.
Ʉɨɷɮɮɢɰɢɟɧɬ ɉɢɪɫɨɧɚ — Ȼɪɚɜɟ, ɤ ɪɚɫɫɦɨɬɪɟɧɢɸ ɤɨɬɨɪɨɝɨ ɦɵ ɩɟɪɟɯɨɞɢɦ, ɬɚɤɠɟ ɨɫɧɨɜɚɧ ɧɚ ɩɪɢɧɰɢɩɟ ɤɨɜɚɪɢɚɰɢɢ. Ɉɧ ɩɪɢɦɟɧɢɦ ɬɨɥɶɤɨ ɤ ɤɨɥɢɱɟɫɬɜɟɧɧɵɦ ɩɪɢɡɧɚɤɚɦ.
[96]
5. Ʉɨɷɮɮɢɰɢɟɧɬ ɩɚɪɧɨɣ ɤɨɪɪɟɥɹɰɢɢ ɢ ɟɝɨ ɫɜɹɡɶ ɫ ɞɪɭɝɢɦɢ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ
ȼɧɚɱɚɥɟ ɩɪɢɞɟɦ ɤ ɤɨɷɮɮɢɰɢɟɧɬɭ ɩɚɪɧɨɣ ɤɨɪɪɟɥɹɰɢɢ ɩɨɥɭɤɚɱɟɫɬɜɟɧɧɵɦ ɨɛɪɚɡɨɦ (ɚɧɚɥɨɝɢɱɧɨ ɜɵɜɨɞɭ ȡ). Ɍɚɤɨɣ ɧɟɫɬɪɨɝɢɣ ɜɵɜɨɞ, ɨɞɧɚɤɨ, ɩɨɥɟɡɟɧ, ɬɚɤ ɤɚɤ ɩɨɦɨɝɚɟɬ ɩɨɧɹɬɶ ɫɦɵɫɥ ɤɨɷɮɮɢɰɢɟɧɬɚ.
ɂɬɚɤ, ɞɚɧɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɨɞɢɧ ɢɡ ɩɨɤɚɡɚɬɟɥɟɣ ɤɨɪɪɟɥɹɰɢɨɧɧɨɣ ɫɜɹɡɢ. Ɉɫɧɨɜɧɵɟ ɡɚɞɚɱɢ ɤɨɪɪɟɥɹɰɢɨɧɧɨɝɨ ɚɧɚɥɢɡɚ ɫɨɫɬɨɹɬ ɜ ɭɫɬɚɧɨɜɥɟɧɢɢ ɮɨɪɦɵ ɫɜɹɡɢ, ɬ.ɟ. ɨɩɪɟɞɟɥɟɧɢɢ ɜɢɞɚ ɤɨɪɪɟɥɹɰɢɨɧɧɨɝɨ ɭɪɚɜɧɟɧɢɹ (ɤɚɤ ɷɬɨ ɞɟɥɚɟɬɫɹ, ɦɵ ɪɚɫɫɦɨɬɪɢɦ ɜ ɫɥɟɞɭɸɳɟɣ ɝɥɚɜɟ), ɚ ɬɚɤɠɟ ɜ ɨɩɪɟɞɟɥɟɧɢɢ ɬɟɫɧɨɬɵ, «ɫɢɥɵ» ɫɜɹɡɢ, ɬ.ɟ. ɨɰɟɧɤɟ ɫɬɟɩɟɧɢ ɪɚɫɫɟɹɧɢɹ ɷɦɩɢɪɢɱɟɫɤɢɯ ɡɧɚɱɟɧɢɣ y ɨɤɨɥɨ ɥɢɧɢɢ ɪɟɝɪɟɫɫɢɢ ɞɥɹ ɪɚɡɧɵɯ ɯ.
65
Ɋɢɫ. 20. Ɉɛɥɚɫɬɢ ɤɨɪɪɟɥɹɰɢɨɧɧɨɝɨɩɨɥɹ
Ɇɟɪɨɣ ɬɟɫɧɨɬɵ ɫɜɹɡɢ ɜ ɫɥɭɱɚɟ ɥɢɧɟɣɧɨɣ ɤɨɪɪɟɥɹɰɢɨɧɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ, ɤɚɤ ɦɵ ɭɜɢɞɢɦ, ɹɜɥɹɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬ ɩɚɪɧɨɣ ɤɨɪɪɟɥɹɰɢɢ, ɚ ɩɪɢ ɤɪɢɜɨɥɢɧɟɣɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ — ɤɨɪɪɟɥɹɰɢɨɧɧɨɟ ɨɬɧɨɲɟɧɢɟ.
Ɉɫɬɚɧɨɜɢɦɫɹ ɧɟɫɤɨɥɶɤɨ ɩɨɞɪɨɛɧɟɟ ɧɚ ɩɨɧɹɬɢɢ ɬɟɫɧɨɬɵ ɫɜɹɡɢ. ȿɫɥɢ ɧɚɧɟɫɬɢ ɜɫɟ ɩɚɪɵ ɯ ɢ ɭ ɜ ɜɢɞɟ ɬɨɱɟɤ ɧɚ ɩɥɨɫɤɨɫɬɢ, ɬɨ ɩɨɥɭɱɢɬɫɹ, ɤɚɤ ɭɩɨɦɢɧɚɥɨɫɶ, ɤɨɪɪɟɥɹɰɢɨɧɧɨɟ ɩɨɥɟ. ȿɝɨ ɬɨɱɤɢ ɪɚɫɩɨɥɚɝɚɸɬɫɹ ɜ ɨɤɪɟɫɬɧɨɫɬɢ ɥɢɧɢɢ ɪɟɝɪɟɫɫɢɢ, ɤɨɦɩɚɤɬɧɨ ɢɥɢ ɪɚɡɛɪɨɫɚɧɨ. ɉɨɹɫɧɢɦ ɷɬɨ ɩɪɢɦɟɪɨɦ.
Ⱦɨɩɭɫɬɢɦ, ɱɬɨ ɫɨɩɨɫɬɚɜɥɹɟɬɫɹ ɜɨɡɪɚɫɬ ɭɱɚɳɟɝɨɫɹ (Y) ɢ ɝɨɞ ɨɛɭɱɟɧɢɹ (X). ȿɫɥɢ ɪɟɱɶ ɢɞɟɬ ɨ ɲɤɨɥɶɧɢɤɚɯ, ɬɨ ɡɚɜɢɫɢɦɨɫɬɶ ɩɪɹɦɚɹ ɮɭɧɤɰɢɨɧɚɥɶɧɚɹ: ɬɚɤ ɜ ɩɟɪɜɨɦ ɤɥɚɫɫɟ, ɜ ɨɫɧɨɜɧɨɦ, ɞɟɬɢ ɫɟɦɢɥɟɬɧɟɝɨ ɜɨɡɪɚɫɬɚ, ɜɨ ɜɬɨɪɨɦ — ɜɨɫɶɦɢɥɟɬɧɟɝɨ ɢ ɬ.ɞ. ȼɬɨɪɨɝɨɞɧɢɱɟɫɬɜɨ, ɨɛɭɫɥɨɜɥɟɧɧɨɟ ɛɨɥɟɡɧɹɦɢ, ɪɟɠɟ — ɩɥɨɯɨɣ ɭɫɩɟɜɚɟɦɨɫɬɶɸ, ɧɟɫɤɨɥɶɤɨ «ɪɚɡɦɵɜɚɟɬ» ɡɚɜɢɫɢɦɨɫɬɶ, ɞɟɥɚɟɬ ɟɟ ɤɨɪɪɟɥɹɰɢɨɧɧɨɣ, ɧɨ ɬɨɱɤɢ ɤɨɪɪɟɥɹɰɢɨɧɧɨɝɨ ɩɨɥɹ ɬɟɫɧɨ ɪɚɫɩɨɥɚɝɚɸɬɫɹ ɜ ɨɤɪɟɫɬɧɨɫɬɢ ɩɪɹɦɨɣ ɪɟɝɪɟɫɫɢɢ.
ɉɟɪɟɣɞɟɦ ɤ ɪɚɫɫɦɨɬɪɟɧɢɸ ɨɛɭɱɟɧɢɹ ɜ ɜɭɡɟ. ɇɟ ɜɫɟ ɫɬɭɞɟɧɬɵ—ɜɱɟɪɚɲɧɢɟ ɲɤɨɥɶɧɢɤɢ, ɦɧɨɝɢɟ ɩɪɢɯɨɞɹɬ ɜ ɜɭɡ ɩɨɫɥɟ ɚɪɦɢɢ, ɪɚɛɨɬɵ ɜ ɧɚɪɨɞɧɨɦ ɯɨɡɹɣɫɬɜɟ, ɩɨɷɬɨɦɭ ɪɚɡɛɪɨɫ ɡɧɚɱɟɧɢɣ ɜɨɡɪɚɫɬɚ ɫɬɭɞɟɧɬɨɜ ɧɚ ɪɚɡɧɵɯ ɤɭɪɫɚɯ ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɶɲɟ, ɱɟɦ ɜ ɪɚɡɧɵɯ ɤɥɚɫɫɚɯ ɲɤɨɥɵ: ɤɨɪɪɟɥɹɰɢɨɧɧɨɟ ɩɨɥɟ «ɪɚɡɦɵɜɚɟɬɫɹ».
[97]
ɉɪɨɰɟɧɬ ɩɪɢɯɨɞɹɳɢɯ ɜ ɚɫɩɢɪɚɧɬɭɪɭ ɩɨɫɥɟ ɪɚɛɨɬɵ ɡɧɚɱɢɬɟɥɶɧɨ ɜɵɲɟ, ɩɪɢɱɟɦ ɩɪɢɯɨɞɹɬ ɥɸɞɢ ɩɨɫɥɟ ɪɚɡɧɵɯ ɩɟɪɟɪɵɜɨɜ ɜ ɭɱɟɛɟ, ɪɚɡɛɪɨɫ ɡɧɚɱɟɧɢɣ ɜɨɡɪɚɫɬɚ ɚɫɩɢɪɚɧɬɨɜ ɧɚ ɤɚɠɞɨɦ ɤɭɪɫɟ ɜɵɲɟ, ɱɟɦ ɭ ɫɬɭɞɟɧɬɨɜ, ɤɨɪɪɟɥɹɰɢɨɧɧɨɟ ɩɨɥɟ ɟɳɟ ɛɨɥɟɟ «ɪɚɡɦɵɬɨ».
Ɉɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶ «ɪɚɡɦɵɬɨɫɬɶ» ɷɬɨɝɨ ɩɨɥɹ ɦɨɠɧɨ ɫ ɩɨɦɨɳɶɸ ɨɬɤɥɨɧɟɧɢɣ ɢɧɞɢɜɢɞɭɚɥɶɧɵɯ ɷɦɩɢɪɢɱɟɫɤɢɯ ɡɧɚɱɟɧɢɣ ɨɬ ɫɪɟɞɧɢɯ, ɬ.ɟ. xi x ɢ yi y. ȿɫɥɢ ɡɧɚɱɟɧɢɸ ɯ,
ɦɟɧɶɲɟɦɭ ɫɪɟɞɧɟɝɨ, ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɡɧɚɱɟɧɢɟ, ɭ ɬɨɠɟ ɦɟɧɶɲɟɟ ɫɪɟɞɧɟɝɨ (ɚ ɛɨɥɶɲɟɦɭ — ɛɨɥɶɲɟɟ), ɬɨ ɷɬɨ ɫɜɢɞɟɬɟɥɶɫɬɜɭɟɬ ɨɛ ɭɩɨɪɹɞɨɱɟɧɧɨɫɬɢ, ɨ ɧɚɥɢɱɢɢ ɫɜɹɡɢ, ɦɟɪɨɣ ɤɨɬɨɪɨɣ ɦɨɠɟɬ ɫɥɭɠɢɬɶ ɜɟɥɢɱɢɧɚ
N
S ¦( x i x )( yi y).
i 1
Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɱɟɦ ɛɨɥɶɲɟ ɫɨɜɩɚɞɟɧɢɣ ɡɧɚɤɨɜ ɭɩɨɦɹɧɭɬɵɯ ɨɬɤɥɨɧɟɧɢɣ, ɬ.ɟ. ɱɟɦ ɛɨɥɶɲɟ ɭɩɨɪɹɞɨɱɟɧɧɨɫɬɶ, ɬɟɦ ɛɨɥɶɲɟ S. ɉɪɢ ɧɟɫɨɜɩɚɞɟɧɢɢ ɡɧɚɤɨɜ ɨɬɤɥɨɧɟɧɢɣ ɜ ɫɭɦɦɟ ɩɨɹɜɥɹɸɬɫɹ ɨɬɪɢɰɚɬɟɥɶɧɵɟ ɫɥɚɝɚɟɦɵɟ, ɢ ɨɧɚ ɭɦɟɧɶɲɚɟɬɫɹ. ȿɫɥɢ ɫɜɹɡɢ ɧɟɬ, ɬɨ ɩɨɥɨɠɢɬɟɥɶɧɵɟ ɢ ɨɬɪɢɰɚɬɟɥɶɧɵɟ ɫɥɚɝɚɟɦɵɟ ɩɪɢɦɟɪɧɨ ɭɪɚɜɧɨɜɟɫɹɬɫɹ ɢ ɫɭɦɦɚ S ɛɭɞɟɬ ɛɥɢɡɤɚ ɤ ɧɭɥɸ.
Ɂɚɦɟɬɢɦ, ɱɬɨ ɩɨɤɚ ɪɟɱɶ ɲɥɚ ɨ ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɫɜɹɡɢ. ɋɜɹɡɶ ɦɨɠɟɬ ɛɵɬɶ ɨɬɪɢɰɚɬɟɥɶɧɨɣ, ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɡɧɚɤɢ ɨɬɤɥɨɧɟɧɢɣ ¨xi ɢ ¨yi ɩɪɟɢɦɭɳɟɫɬɜɟɧɧɨ ɫɨɜɩɚɞɚɬɶ ɧɟ ɛɭɞɭɬ ɢ ɜɟɥɢɱɢɧɚ S ɫɬɚɧɨɜɢɬɫɹ ɨɬɪɢɰɚɬɟɥɶɧɨɣ. Ɍɟɩɟɪɶ ɫɨɜɩɚɞɟɧɢɹ ɡɧɚɤɨɜ ɢɧɞɢɜɢɞɭɚɥɶɧɵɯ ɨɬɤɥɨɧɟɧɢɣ ɭɦɟɧɶɲɚɸɬ S ɩɨ ɚɛɫɨɥɸɬɧɨɣ ɜɟɥɢɱɢɧɟ, ɩɪɢɛɥɢɠɚɹ ɟɟ ɤ ɧɭɥɸ.
ɉɟɪɟɣɞɟɦ ɤ ɝɪɚɮɢɱɟɫɤɨɣ ɢɧɬɟɪɩɪɟɬɚɰɢɢ.
ɇɚ ɪɢɫ. 20 ɩɪɹɦɵɟ y y ɢ x x ɪɚɡɛɢɜɚɸɬ ɤɨɨɪɞɢɧɚɬɧɭɸ ɩɥɨɫɤɨɫɬɶ ɧɚ 4 ɱɚɫɬɢ: a, b, ɫ, d. ɉɨɥɨɠɢɬɟɥɶɧɨɫɬɶ S ɨɡɧɚɱɚɟɬ ɩɪɟɢɦɭɳɟɫɬɜɟɧɧɨɟ ɪɚɫɩɨɥɨɠɟɧɢɟ ɬɨɱɟɤ ɤɨɪɪɟɥɹɰɢɨɧɧɨɝɨ
66
ɩɨɥɹ ɜ ɨɛɥɚɫɬɹɯ a ɢ ɫ (ɨɬɪɢɰɚɬɟɥɶɧɨɫɬɶ — b ɢ d). ȼɟɥɢɱɢɧɚ S ɛɥɢɡɤɚ ɤ ɧɭɥɸ, ɟɫɥɢ ɩɨɥɟ ɪɚɜɧɨɦɟɪɧɨ «ɪɚɡɦɚɡɚɧɨ».
Ɋɚɫɫɦɨɬɪɢɦ, ɞɥɹ ɨɩɪɟɞɟɥɟɧɧɨɫɬɢ, S>0. ɑɟɦ ɛɨɥɶɲɟ S, ɬɟɦ ɛɨɥɟɟ ɭɩɨɪɹɞɨɱɟɧɨ ɤɨɪɪɟɥɹɰɢɨɧɧɨɟ ɩɨɥɟ. ȼ ɤɚɤɨɦ ɫɥɭɱɚɟ ɭɩɨɪɹɞɨɱɟɧɧɨɫɬɶ ɦɚɤɫɢɦɚɥɶɧɚ? ȿɫɥɢ ɡɚɜɢɫɢɦɨɫɬɶ ɮɭɧɤɰɢɨɧɚɥɶɧɚɹ, ɩɪɹɦɨɥɢɧɟɣɧɚɹ, ɬɨ, ɨɱɟɜɢɞɧɨ, ɤɨɝɞɚ ɜɫɟ ɬɨɱɤɢ ɥɟɠɚɬ ɧɚ ɩɪɹɦɨɣ, ɫɤɚɠɟɦ,
(Ⱥȼ).
ȼ ɤɚɱɟɫɬɜɟ ɦɟɪɵ ɬɟɫɧɨɬɵ ɫɜɹɡɢ ɭɞɨɛɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɨɬɧɨɲɟɧɢɟ S ɤ ɟɝɨ ɦɚɤɫɢɦɚɥɶɧɨ ɜɨɡɦɨɠɧɨɦɭ ɡɧɚɱɟɧɢɸ. ɗɬɨ ɨɬɧɨɲɟɧɢɟ r, ɧɚɡɵɜɚɟɦɨɟ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɩɚɪɧɨɣ ɤɨɪɪɟɥɹɰɢɢ, ɨɱɟɜɢɞɧɨ, ɩɪɢɧɢɦɚɟɬ ɡɧɚɱɟɧɢɟ +1, ɟɫɥɢ ɫɜɹɡɶ ɩɪɹɦɨ-
[98]
ɥɢɧɟɣɧɚɹ ɩɨɥɨɠɢɬɟɥɶɧɚɹ; –1 — ɟɫɥɢ ɩɪɹɦɨɥɢɧɟɣɧɚɹ ɨɬɪɢɰɚɬɟɥɶɧɚɹ; 0 — ɟɫɥɢ ɫɜɹɡɢ ɧɟɬ16. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɞɥɹ ɬɨɝɨ ɱɬɨɛɵ ɩɨɥɧɨɫɬɶɸ ɨɩɪɟɞɟɥɢɬɶ r, ɨɫɬɚɟɬɫɹ ɧɚɣɬɢ ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɜɟɥɢɱɢɧɵ S. Ɍɚɤ ɤɚɤ ɩɪɢ ɩɪɹɦɨɥɢɧɟɣɧɨɣ ɫɜɹɡɢ yi=axi+b, ɬɨ ¨yi=yi–y=a•¨xi, ɨɬɤɭɞɚ
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ɉɨɷɬɨɦɭ S max a¦( 'xi )2 ɢ |
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ɜ ɬɨ ɠɟ ɜɪɟɦɹ |
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ɨɫɜɨɛɨɞɢɬɶɫɹ ɨɬ ɚ, ɡɚɩɢɲɟɦ S max |
S max S min |
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Ɉɤɨɧɱɚɬɟɥɶɧɨ: |
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Ɏɨɪɦɭɥɭ (II,5,1) ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ |
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ɟɫɥɢ ɢɫɩɨɥɶɡɨɜɚɬɶ ɨɩɪɟɞɟɥɟɧɢɟ ɫɪɟɞɧɟɝɨ ɤɜɚɞɪɚɬɢɱɟɫɤɨɝɨ ɨɬɤɥɨɧɟɧɢɹ.
ɍɩɪɚɠɧɟɧɢɟ 43. ɉɨɤɚɡɚɬɶ, ɱɬɨ ɤɨɷɮɮɢɰɢɟɧɬ ɩɚɪɧɨɣ ɤɨɪɪɟɥɹɰɢɢ ɦɨɠɟɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧ ɜ ɜɢɞɟ
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ɍɤɚɡɚɧɢɟ: ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɨɨɬɧɨɲɟɧɢɟ (I,4,3) ɞɥɹ ɨɛɟɢɯ ɩɟɪɟɦɟɧɧɵɯ — X ɢ Y, ɚ ɬɚɤɠɟ ɨɩɪɟɞɟɥɟɧɢɟ ɫɪɟɞɧɢɯ.
Ⱦɥɹ ɭɹɫɧɟɧɢɹ ɫɦɵɫɥɚ r ɩɨɥɟɡɧɨ ɨɛɪɚɬɢɬɶɫɹ ɤ ɧɟɤɨɬɨɪɵɦ ɱɚɫɬɧɵɦ ɫɥɭɱɚɹɦ, ɝɞɟ ɫɜɹɡɶ ɩɪɨɫɦɚɬɪɢɜɚɟɬɫɹ ɧɚɝɥɹɞɧɨ.
1.ɉɭɫɬɶ X ɢ Y ɩɪɢɧɢɦɚɸɬ ɬɚɤɢɟ ɡɧɚɱɟɧɢɹ:
X |
1 |
2 |
3 |
4 |
5 |
Y |
12 |
13 |
14 |
15 |
16 |
əɫɧɨ, ɱɬɨ ɭ=ɯ+11, ɬ.ɟ. ɢɦɟɟɬ ɦɟɫɬɨ ɩɪɹɦɨɥɢɧɟɣɧɚɹ ɩɨɥɨɠɢɬɟɥɶɧɚɹ ɫɜɹɡɶ |
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10,r 1 (ȼɵɱɢɫɥɟɧɢɟ ɩɪɢɜɟɞɟɧɧɵɯ |
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ɡɧɚɱɟɧɢɣ ɫɨɫɬɚɜɥɹɟɬ ɫɨɞɟɪɠɚɧɢɟ ɭɩɪɚɠɧɟɧɢɹ 44).
2.ɉɭɫɬɶ X ɢ Y ɩɪɢɧɢɦɚɸɬ ɡɧɚɱɟɧɢɹ:
X |
1 |
2 |
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4 |
5 |
Y |
16 |
15 |
14 |
13 |
12 |
r= —1 (ɍɩɪɚɠɧɟɧɢɟ 45. ɉɨɤɚɡɚɬɶ ɷɬɨ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ).
[99]
16 ɇɢɠɟ ɦɵ ɨɫɬɚɧɨɜɢɦɫɹ ɩɨɞɪɨɛɧɟɟ ɧɚ ɫɥɭɱɚɟ S=0.
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ɍɩɪɚɠɧɟɧɢɟ 46. Ⱦɥɹ ɞɚɧɧɵɯ ɫɥɟɞɭɸɳɟɣ ɬɚɛɥɢɰɵ ɜɵɱɢɫɥɢɬɶ r.
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Ɉɬɜɟɬ: r=0
ɋɩɟɰɢɚɥɶɧɨ ɨɫɬɚɧɨɜɢɦɫɹ ɧɚ ɪɚɫɫɦɨɬɪɟɧɢɢ ɫɥɭɱɚɟɜ, ɤɨɝɞɚ r ɪɚɜɧɨ ɢɥɢ ɛɥɢɡɤɨ ɤ ɧɭɥɸ. ȼɫɟɝɞɚ ɥɢ ɷɬɨ ɨɡɧɚɱɚɟɬ ɨɬɫɭɬɫɬɜɢɟ ɫɜɹɡɢ?
ȼɨɨɛɳɟ ɝɨɜɨɪɹ, ɧɟɬ. ȼɫɩɨɦɧɢɦ, ɱɬɨ ɦɟɪɚ r ɩɪɢɫɩɨɫɨɛɥɟɧɚ ɤ ɢɡɭɱɟɧɢɸ ɩɪɹɦɨɥɢɧɟɣɧɵɯ ɡɚɜɢɫɢɦɨɫɬɟɣ, r ɦɨɠɟɬ ɛɵɬɶ ɦɚ-
Ɋɢɫ.21. Ʉɪɢɜɨɥɢɧɟɣɧɚɹ ɮɭɧɤɰɢɨɧɚɥɶɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ
ɥɵɦ ɢɥɢ ɞɚɠɟ ɪɚɜɧɵɦ ɧɭɥɸ ɧɟ ɩɨɬɨɦɭ, ɱɬɨ ɫɜɹɡɢ ɧɟɬ, ɚ ɩɨɬɨɦɭ, ɱɬɨ ɨɧɚ ɤɪɢɜɨɥɢɧɟɣɧɚ. ɗɬɨ ɩɨɦɨɝɚɟɬ ɩɨɧɹɬɶ ɩɪɨɫɬɨɣ ɩɪɢɦɟɪ. ɉɭɫɬɶ X ɢ Y ɡɚɞɚɧɵ ɫ ɩɨɦɨɳɶɸ ɫɥɟɞɭɸɳɟɣ ɬɚɛɥɢɰɵ:
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ȼɵɱɢɫɥɢɦ r ɞɥɹ ɷɬɢɯ ɞɚɧɧɵɯ. əɫɧɨ, ɱɬɨ x |
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Ɉɞɧɨɜɪɟɦɟɧɧɨ ɥɟɝɤɨ ɜɢɞɟɬɶ, ɱɬɨ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɟ ɜɟɥɢɱɢɧɵ ɯ ɢ ɭ ɫɜɹɡɚɧɵ |
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ɮɭɧɤɰɢɨɧɚɥɶɧɨ: y |
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ɉɪɟɞɫɬɚɜɢɦ ɷɬɭ ɡɚɜɢɫɢɦɨɫɬɶ ɝɪɚɮɢɱɟɫɤɢ (ɪɢɫ. 21).
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɧɚɲɟɦ ɫɥɭɱɚɟ ɩɪɢ r=0 ɢɦɟɟɬ ɦɟɫɬɨ ɤɪɢɜɨɥɢɧɟɣɧɚɹ (ɞɚɠɟ ɮɭɧɤɰɢɨɧɚɥɶɧɚɹ) ɡɚɜɢɫɢɦɨɫɬɶ.
ɂɬɚɤ, ɟɫɥɢ r=0 (ɥɢɛɨ ɛɥɢɡɤɨ ɤ ɧɭɥɸ), ɬɨ ɷɬɨ ɨɡɧɚɱɚɟɬ ɨɬɫɭɬɫɬɜɢɟ ɩɪɹɦɨɥɢɧɟɣɧɨɣ ɫɜɹɡɢ, ɧɨ ɦɨɠɟɬ ɢɦɟɬɶ ɦɟɫɬɨ ɤɪɢɜɨɥɢɧɟɣɧɚɹ (ɨɛɵɱɧɨ ɤɨɪɪɟɥɹɰɢɨɧɧɚɹ) ɫɜɹɡɶ ɦɟɠɞɭ ɢɡɭɱɚɟɦɵɦɢ ɜɟɥɢɱɢɧɚɦɢ.
ɍɩɪɚɠɧɟɧɢɟ 47. ɉɨɤɚɡɚɬɶ, ɱɬɨ ɜ ɫɥɭɱɚɟ ɤɨɪɪɟɥɹɰɢɨɧɧɨɣ ɬɚɛɥɢɰɵ ^N ij ` ɤɨɷɮɮɢɰɢɟɧɬ ɤɨɪɪɟɥɹɰɢɢ ɉɢɪɫɨɧɚ — Ȼɪɚɜɟ
[100]
ɩɪɢɧɢɦɚɟɬ ɜɢɞ:
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ɍɤɚɡɚɧɢɟ: ɢɫɩɨɥɶɡɨɜɚɬɶ (II,5,3).
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Ʉɚɤ ɭɠɟ ɨɬɦɟɱɚɥɨɫɶ, r=1 ɨɡɧɚɱɚɟɬ ɧɚɥɢɱɢɟ ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɩɪɹɦɨɥɢɧɟɣɧɨɣ ɫɜɹɡɢ, r=— 1 — ɨɬɪɢɰɚɬɟɥɶɧɨɣ, ɚ r=0 — ɨɬɫɭɬɫɬɜɢɟ ɩɪɹɦɨɥɢɧɟɣɧɨɣ ɤɨɪɪɟɥɹɰɢɨɧɧɨɣ ɫɜɹɡɢ. Ɂɧɚɱɟɧɢɹ, ɩɨɥɭɱɚɟɦɵɟ ɧɚ ɩɪɚɤɬɢɤɟ, ɨɛɵɱɧɨ ɬɚɤɨɜɵ, ɱɬɨ0 r 1. ȼɨɩɪɨɫ ɨ ɫɭɳɟɫɬɜɟɧɧɨɫɬɢ r ɫɦ. ɜ § 8
ɝɥɚɜɵ V.
Ɂɚɦɟɬɢɦ, ɱɬɨ ɛɟɡ ɨɛɨɫɧɨɜɚɧɢɹ ɥɢɧɟɣɧɨɫɬɢ ɫɜɹɡɢ ɢɫɩɨɥɶɡɨɜɚɧɢɟ r ɧɟ ɹɜɥɹɟɬɫɹ ɡɚɤɨɧɧɵɦ, ɯɨɬɹ ɢ ɩɨɥɭɱɢɥɨ ɲɢɪɨɤɨɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ.
Ⱦɥɹ ɧɟɥɢɧɟɣɧɵɯ ɡɚɜɢɫɢɦɨɫɬɟɣ, ɤɚɤɢɦɢ ɱɚɫɬɨ ɹɜɥɹɸɬɫɹ ɫɨɰɢɚɥɶɧɵɟ, ɧɭɠɧɨ ɩɪɢɦɟɧɹɬɶ ɤɨɪɪɟɥɹɰɢɨɧɧɨɟ ɨɬɧɨɲɟɧɢɟ. ɗɬɨɬ ɤɨɷɮɮɢɰɢɟɧɬ ɛɭɞɟɬ ɩɨɞɪɨɛɧɨ ɩɪɨɚɧɚɥɢɡɢɪɨɜɚɧ ɜ ɫɥɟɞɭɸɳɟɣ ɝɥɚɜɟ. Ɂɞɟɫɶ ɠɟ ɦɵ ɩɪɢɞɟɦ ɤ ɧɟɦɭ ɢɡ ɤɚɱɟɫɬɜɟɧɧɵɯ ɫɨɨɛɪɚɠɟɧɢɣ. ȼ ɫɥɭɱɚɟ ɤɨɪɪɟɥɹɰɢɨɧɧɨɣ ɫɜɹɡɢ ɤɚɠɞɨɦɭ xi ɫɨɨɬɜɟɬɫɬɜɭɟɬ
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ɬɚɤ ɧɚɡɵɜɚɟɦɨɟ ɭɫɥɨɜɧɨɟ ɫɪɟɞɧɟɟ (ɭɫɥɨɜɢɟ: X=xi). |
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ȼɨɨɛɳɟ ɝɨɜɨɪɹ, y i ɧɟ ɫɨɜɩɚɞɚɸɬ ɫɨ ɫɪɟɞɧɢɦ ɡɧɚɱɟɧɢɟɦ |
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Ɇɟɪɨɣ ɨɬɤɥɨɧɟɧɢɹ ɷɦɩɢɪɢɱɟɫɤɢɯ y i ɨɬ y ɦɨɠɟɬ ɫɥɭɠɢɬɶ ɜɟɥɢɱɢɧɚ |
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ɤɨɬɨɪɚɹ ɜ ɬɟɪɦɢɧɚɯ § 3 ɝɥɚɜɵ II ɦɨɠɟɬ ɪɚɫɫɦɚɬɪɢɜɚɬɶɫɹ ɤɚɤ ɦɟɠɝɪɭɩɩɨɜɚɹ ɞɢɫɩɟɪɫɢɹ |
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(ɬɚɦ ɷɬɚ ɞɢɫɩɟɪɫɢɹ ɨɛɨɡɧɚɱɚɥɚɫɶ į). |
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Ʉɨɪɪɟɥɹɰɢɨɧɧɵɦ ɨɬɧɨɲɟɧɢɟɦ Ș ɧɚɡɵɜɚɟɬɫɹ ɨɬɧɨɲɟɧɢɟ |
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ɜɟɥɢɱɢɧɚ ɞɟɣɫɬɜɢɬɟɥɶɧɨ ɢɦɟɟɬ ɫɦɵɫɥ ɦɟɪɵ ɬɟɫɧɨɬɵ ɤɨɪɪɟɥɹɰɢɢ ɜ ɫɥɭɱɚɟ ɤɪɢɜɨɥɢɧɟɣɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ. ȿɫɥɢɡɚɜɢɫɢɦɨɫɬɢɧɟɬ, ɬɨ yi ɧɟɛɭɞɟɬɨɬɥɢɱɚɬɶɫɹɨɬ y , ɬ.ɟ. Vy = 0 ɢȘ = 0.
ȿɫɥɢ ɡɚɜɢɫɢɦɨɫɬɶ ɮɭɧɤɰɢɨɧɚɥɶɧɚɹ, ɬ.ɟ. ɤɚɠɞɨɦɭ X ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɨɞɧɨ ɨɩɪɟɞɟɥɟɧɧɨɟ
ɡɧɚɱɟɧɢɟ V, ɬɨ ɱɚɫɬɧɵɟ ɞɢɫɩɟɪɫɢɢ Vi2 (ɭ) = Ɉ (i = 1, Ʉ) ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɢɯ ɫɪɟɞɧɹɹ V 2 ɬɨɠɟ ɪɚɜɧɚ 0.
ɉɨɷɬɨɦɭɬɟɨɪɟɦɚɫɥɨɠɟɧɢɹɞɢɫɩɟɪɫɢɣ (I,4,8) ɜɷɬɨɦɫɥɭɱɚɟɞɚɟɬ: V 2 |
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ɂɬɚɤ, 0 Ș 1, ɝɞɟ 0 ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɨɬɫɭɬɫɬɜɢɸ ɫɜɹɡɢ, 1 – ɮɭɧɤɰɢɨɧɚɥɶɧɨɣ, ɚ Ș, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɟ ɭɫɥɨɜɢɸ 0 < Ș < 1, – ɤɨɪɪɟɥɹɰɢɨɧɧɨɣ. ɑɟɦ ɛɥɢɠɟ Ș ɤ 1, ɬɟɦ ɬɟɫɧɟɟ ɫɜɹɡɶ, ɬɟɦ ɛɥɢɠɟɨɧɚɤɮɭɧɤɰɢɨɧɚɥɶɧɨɣ.
ȼɟɪɧɟɦɫɹ ɤ ɪɚɫɫɦɨɬɪɟɧɢɸ r. ɇɟ ɹɜɥɹɟɬɫɹ ɡɚɤɨɧɧɵɦ ɢɫɩɨɥɶɡɨɜɚɧɢɟ r ɬɚɤɠɟ ɜ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɩɪɢɡɧɚɤɢ ɧɟ ɤɨɥɢɱɟɫɬɜɟɧɧɵɟ. Ɋɚɫɫɦɨɬɪɢɦ ɨɞɢɧ ɢɡ ɬɢɩɢɱɧɵɯ ɩɪɢɦɟɪɨɜ. ȼ ɢɫɫɥɟɞɨɜɚɧɢɢ «ɑɟɥɨɜɟɤɢɟɝɨɪɚɛɨɬɚ», ɜɱɚɫɬɧɨɫɬɢ, ɢɡɭɱɚɥɚɫɶɫɜɹɡɶɦɟɠɞɭɬɚɤɢɦɢɩɪɢɡɧɚɤɚɦɢ, ɤɚɤɫɨɞɟɪɠɚɧɢɟ ɬɪɭɞɚɢɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɶɫɩɟɰɢɚɥɶɧɨɫɬɶɸ. ɉɪɨɮɟɫɫɢɢɝɪɭɩɩɢɪɨɜɚɥɢɫɶɩɨɫɨɞɟɪɠɚɧɢɸɬɪɭɞɚɫ ɭɱɟɬɨɦ ɤɪɢɬɟɪɢɟɜ, ɫɜɹɡɚɧɧɵɯ ɫ ɬɜɨɪɱɟɫɤɢɦɢ ɜɨɡɦɨɠɧɨɫɬɹɦɢ ɬɪɭɞɨɜɨɣ ɞɟɹɬɟɥɶɧɨɫɬɢ (ɭɪɨɜɟɧɶ ɦɟɯɚɧɢɡɚɰɢɢ, ɭɪɨɜɟɧɶ ɤɜɚɥɢɮɢɤɚɰɢɢ, ɫɨɨɬɧɨɲɟɧɢɟ ɡɚɬɪɚɬ ɭɦɫɬɜɟɧɧɨɝɨ ɢ ɮɢɡɢɱɟɫɤɨɝɨ ɬɪɭɞɚ)17. Ȼɵɥɢ ɜɵɞɟɥɟɧɵ ɬɚɤɢɟ ɝɪɭɩɩɵ: 1) ɪɭɱɧɨɣ ɬɪɭɞ, ɧɟ ɬɪɟɛɭɸɳɢɣ ɫɩɟɰɢɚɥɶɧɨɣ ɩɨɞɝɨɬɨɜɤɢ; 2) ɬɪɭɞ ɧɚ ɤɨɧɜɟɣɟɪɟ; 3) ɦɟɯɚɧɢɡɢɪɨɜɚɧɧɵɣ ɬɪɭɞ (ɫɬɚɧɨɱɧɵɣ); 4) ɚɜɬɨɦɚɬɱɢɤɢ ɛɟɡ ɧɚɜɵɤɨɜ ɧɚɥɚɞɤɢ; 5) ɪɭɱɧɨɣɬɪɭɞ, ɬɪɟɛɭɸɳɢɣɜɵɫɲɟɣɤɜɚɥɢɮɢɤɚɰɢɢ; 6) ɩɭɥɶɬɨɜɢɤɧ-ɧɚɥɚɞɱɢɤɢ.
17 ɑɟɥɨɜɟɤ ɢ ɟɝɨ ɪɚɛɨɬɚ. Ɇ., 1967, ɫ.30-38.
69
əɫɧɨ, ɱɬɨ ɷɬɢ ɝɪɭɩɩɵ – ɩɭɧɤɬɵ ɜ ɥɭɱɲɟɦ ɫɥɭɱɚɟ ɩɨɪɹɞɤɨɜɨɣ ɲɤɚɥɵ. ɍɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɶ ɫɩɟɰɢɚɥɶɧɨɫɬɶɸ ɨɩɪɟɞɟɥɹɥɚɫɶ ɩɨ ɨɬɜɟɬɚɦ ɧɚ ɜɨɩɪɨɫɵ ɚɧɤɟɬɵ, ɭɩɨɪɹɞɨɱɟɧɧɵɦ ɩɨ ɫɯɟɦɟ «ɥɨɝɢɱɟɫɤɨɝɨ ɤɜɚɞɪɚɬɚ», ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɬɚɤɠɟ ɩɨ ɩɨɪɹɞɤɨɜɨɣ ɲɤɚɥɟ. Ʉɨɪɪɟɥɹɰɢɹ ɠɟ ɦɟɠɞɭ ɜɵɞɟɥɟɧɧɵɦɢ ɩɪɢɡɧɚɤɚɦɢ ɢɡɭɱɚɥɚɫɶ ɫ ɩɨɦɨɳɶɸ ɤɨɷɮɮɢɰɢɟɧɬɚ ɉɢɪɫɨɧɚ – Ȼɪɚɜɟ, ɩɪɢɦɟɧɢɦɨɝɨ ɥɢɲɶ ɜ ɫɥɭɱɚɟ ɦɟɬɪɢɱɟɫɤɢɯ ɲɤɚɥ, ɬɚɤ ɤɚɤ ɨɧ ɛɚɡɢɪɭɟɬɫɹ ɧɚ ɩɨɧɹɬɢɢ ɨɬɤɥɨɧɟɧɢɹ ɨɬ ɫɪɟɞɧɟɝɨ, ɤɨɬɨɪɨɟ ɢɦɟɟɬ ɫɦɵɫɥ ɥɢɲɶ ɬɨɝɞɚ, ɤɨɝɞɚ ɱɢɫɥɚ ɧɟɫɭɬ ɢɧɮɨɪɦɚɰɢɸ ɨɛ «ɚɛɫɨɥɸɬɧɨɣ» ɢɧɬɟɧɫɢɜɧɨɫɬɢɫɜɨɣɫɬɜɚ. Ɍɚɤɢɦɨɛɪɚɡɨɦ,
[102]
ɢɫɩɨɥɶɡɨɜɚɥɚɫɶ ɢɧɮɨɪɦɚɰɢɹ, ɤɨɬɨɪɨɣ ɮɚɤɬɢɱɟɫɤɢ ɢɫɫɥɟɞɨɜɚɬɟɥɢ ɧɟ ɪɚɫɩɨɥɚɝɚɥɢ. ɇɚɤɨɧɟɰ, r ɩɪɢɦɟɧɹɥɫɹ ɛɟɡ ɨɛɨɫɧɨɜɚɧɢɹ ɥɢɧɟɣɧɨɫɬɢ ɫɜɹɡɢ. ɉɨɤɚɠɟɦ, ɱɬɨ ɤɨɷɮɮɢɰɢɟɧɬ ɋɩɢɪɦɟɧɚ ɹɜɥɹɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɉɢɪɫɨɧɚ – Ȼɪɚɜɟ, ɩɪɢɦɟɧɟɧɧɵɦ ɤ ɪɚɧɝɚɦ. Ɋɚɧɝ ɩɨ X, ɤɚɤ ɢ ɪɚɧɝɢ ɩɨ ɍ,
ɩɪɢɧɢɦɚɸɬ ɡɧɚɱɟɧɢɟ ɨɬ 1 ɞɨ N. ɋɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɪɚɧɝɚ 1 N , ɚ ɨɬɤɥɨɧɟɧɢɟ i-ɝɨ ɪɚɧɝɚ ɨɬ
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(ɫɦ. ɉɪɢɥɨɠɟɧɢɟ 2). Ⱥɧɚɥɨɝɢɱɧɨ
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[103] |
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ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɬɟɩɟɪɶ |
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Ɂɚɜɟɪɲɢɦ ɡɞɟɫɶ ɪɚɫɫɦɨɬɪɟɧɢɟ p ɜɵɜɨɞɨɦɮɨɪɦɭɥɵɞɥɹɫɥɭɱɚɹɨɛɴɟɞɢɧɟɧɧɵɯɪɚɧɝɨɜ. |
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ɍ ɧɚɫ |
i 1, N . |
Ⱦɨɩɭɫɬɢɦ, ɱɬɨ ɪɚɧɝɢ ɭ ɧɟɫɤɨɥɶɤɢɯ ɨɛɴɟɤɬɨɜ, ɧɚɩɪɢɦɟɪ, ɫ l+1 ɩɨ l+t |
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ɨɞɢɧɚɤɨɜɵ. Ʉɚɠɞɨɦɭ ɢɡ ɷɬɢɯ t ɨɛɴɟɤɬɨɜ ɟɫɬɟɫɬɜɟɧɧɨ ɩɪɢɩɢɫɚɬɶ ɫɪɟɞɧɢɣ ɪɚɧɝ, ɤɨɬɨɪɵɣ ɪɚɜɟɧ l 1 t . ɇɚɣɞɟɦɫɭɦɦɭɤɜɚɞɪɚɬɨɜɨɛɴɟɞɢɧɟɧɧɵɯɪɚɧɝɨɜ:
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ȿɫɥɢɛɵɨɛɴɟɞɢɧɟɧɢɹɧɟɛɵɥɨ, ɬɨɫɭɦɦɚɤɜɚɞɪɚɬɨɜɪɚɧɝɨɜɬɟɯɠɟɨɛɴɟɤɬɨɜɛɵɥɚɛɵ |
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Ɂɞɟɫɶɦɵɜɨɫɩɨɥɶɡɨɜɚɥɢɫɶɮɨɪɦɭɥɚɦɢɉɪɢɥɨɠɟɧɢɹ 2. |
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Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɢ ɨɛɴɟɞɢɧɟɧɢɢ ɪɚɧɝɨɜ ɨɛɳɚɹ ɫɭɦɦɚ ɤɜɚɞɪɚɬɨɜ ɨɤɚɠɟɬɫɹ ɭɦɟɧɶɲɟɧɧɨɣ |
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ɧɚɜɟɥɢɱɢɧɭ B A |
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12
Ɇɵ ɪɚɫɫɦɨɬɪɟɥɢ ɫɥɭɱɚɣ ɨɞɧɨɝɨ ɨɛɴɟɞɢɧɟɧɢɹ (ɨɬ l 1 ɞɨ l t ), ɟɫɥɢ ɨɛɴɟɞɢɧɟɧɢɣ ɧɟɫɤɨɥɶɤɨ, ɫɤɚɠɟɦ, p , ɩɪɢɱɟɦɜ s-ɨɦɫɥɭɱɚɟɨɛɴɟɞɢɧɟɧɨ ts ɪɚɧɝɨɜ, ɬɨɨɛɳɟɟɭɦɟɧɶɲɟɧɢɟ
Tx |
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ts ts2 1 |
, (II, 5, 6) |
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ɟɫɥɢɨɛɴɟɞɢɧɢɬɶɪɚɧɝɢɏ. |
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Ⱥɧɚɥɨɝɢɱɧɵɣɜɤɥɚɞ Ty ɞɚɟɬɨɛɴɟɞɢɧɟɧɢɟɪɚɧɝɨɜɩɨɍ: |
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ur ur2 1 |
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Y, ur - ɱɢɫɥɨ ɪɚɧɝɨɜ ɜ r-ɨɦ |
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ɨɛɴɟɞɢɧɟɧɢɢ. |
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[104] |
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ȼɜɟɞɟɦɷɬɢɩɨɩɪɚɜɤɢɜɮɨɪɦɭɥɭɞɥɹ p. ɂɫɯɨɞɧɵɦɩɪɢɷɬɨɦɛɭɞɟɬɬɚɤɨɟɩɪɟɞɫɬɚɜɥɟɧɢɟ: |
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Ɍɚɤɢɦɨɛɪɚɡɨɦ,
71
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ȼɡɚɤɥɸɱɟɧɢɟɩɚɪɚɝɪɚɮɚɩɪɢɜɟɞɟɦɩɪɢɦɟɪɜɵɱɢɫɥɟɧɢɹ ȡ ɫɨɛɴɟɞɢɧɟɧɢɟɦɪɚɧɝɨɜ.
ɉɪɢɦɟɪ 19. ɂɡɭɱɚɹ ɫɜɹɡɶ ɦɟɠɞɭ ɩɨɥɨɠɢɬɟɥɶɧɵɦɢ ɨɬɜɟɬɚɦɢ ɧɚ ɜɨɩɪɨɫɵ «ɢɧɬɟɪɟɫɧɚɹ ɪɚɛɨɬɚ» (ɏ) ɢ «ɨɛɪɚɡɨɜɚɧɢɟ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɪɚɛɨɬɟ» (Y), ɫɨɰɢɨɥɨɝɢ Ʉɚɡɚɧɫɤɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ ɢɡ 14 ɩɪɨɮɟɫɫɢɨɧɚɥɶɧɵɯɝɪɭɩɩɪɚɛɨɱɢɯ (N=14) ɩɨɥɭɱɢɥɢɬɚɤɢɟɞɚɧɧɵɟ18 ( ɬɚɛɥ. 27, ɞɚɧɧɵɟ 1963ɝ.):
¦2di 286,5; p=0,354.
ɂɦɟɟɦ Tx = 10,5; Ty = 1;
Ɉɬɦɟɬɢɦ, ɱɬɨ ɜ «Ɇɟɬɨɞɢɤɟ ɢ ɬɟɯɧɢɤɟ…» ɢ ɜ «ɋɬɚɬɢɫɬɢɱɟɫɤɢɯ ɦɟɬɨɞɚɯ…», ɨɬɤɭɞɚ ɜɡɹɬ ɷɬɨɬɩɪɢɦɟɪ, ɡɧɚɱɟɧɢɟ ȡɪɚɜɧɨ 0,345. ɉɨɥɭɱɟɧɧɨɟɪɚɫɯɨɠɞɟɧɢɟɜɵɡɜɚɧɨɬɟɦ, ɱɬɨɜɨɛɟɢɯ
[105]
ɤɧɢɝɚɯɢɫɩɨɥɶɡɨɜɚɥɚɫɶɫɥɟɞɭɸɳɚɹɮɨɪɦɭɥɚɞɥɹɪɚɫɱɟɬɚȡ:
§ |
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Ʉɚɤ ɨɧɚ ɫɨɨɬɧɨɫɢɬɫɹ ɫ ɜɵɜɟɞɟɧɧɨɣ ɧɚɦɢ ɮɨɪɦɭɥɨɣ? ɉɪɟɨɛɪɚɡɭɹ ɮɨɪɦɭɥɭ (III,5,7), ɩɨɥɭɱɚɟɦ:
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ȿɫɥɢ ɜ ɷɬɨɣ ɮɨɪɦɭɥɟ ɩɪɟɧɟɛɪɟɱɶ ɜɟɥɢɱɢɧɚɦɢ, ɜɵɱɢɬɚɸɳɢɦɢɫɹ ɢɡ 1 ɩɨɞ ɤɨɪɧɟɦ, ɬɨ ɩɨɞɤɨɪɟɧɧɨɟɜɵɪɚɠɟɧɢɟɫɬɚɧɟɬɪɚɜɧɨ
Ɍɚɛɥɢɰɚ27
ɉɪɢɦɟɪ ɜɵɱɢɫɥɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɚ ɋɩɢɪɦɟɧɚ ȡɫɨɛɴɟɞɢɧɟɧɢɟɦ ɪɚɧɝɨɜ
ɇɨɦɟɪ |
X (%) |
Y(5) |
RX |
RY |
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d 2 |
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ɝɪɭɩɩɵ |
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100 |
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3 |
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4 |
2 |
100 |
87,5 |
3 |
5,5 |
2,5 |
6,25 |
3 |
100 |
77 |
3 |
9 |
6 |
36 |
4 |
100 |
75 |
3 |
10 |
7 |
49 |
5 |
100 |
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3 |
11,5 |
8,5 |
72,25 |
6 |
83,5 |
92 |
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3 |
3,5 |
12,25 |
7 |
83,5 |
83 |
6,5 |
8 |
1,5 |
2,25 |
8 |
83,0 |
90 |
8 |
4 |
4,0 |
16,00 |
9 |
82,5 |
94,5 |
9 |
2 |
7,0 |
49,00 |
10 |
71,0 |
87,0 |
10 |
7 |
3,0 |
9,0 |
11 |
55,5 |
87,5 |
11 |
5,5 |
5,5 |
30,25 |
12 |
50,0 |
50,0 |
12 |
11,5 |
0,5 |
0,25 |
13 |
28,5 |
43,0 |
13 |
13 |
0 |
0 |
14 |
0 |
0 |
14 |
14 |
0 |
0 |
18 Ɇɟɬɨɞɢɤɚ ɢ ɬɟɯɧɢɤɚ ɫɬɚɬɢɫɬɢɱɟɫɤɨɣ ɨɛɪɚɛɨɬɤɢ ɩɟɪɜɢɱɧɨɣ ɫɨɰɢɨɥɨɝɢɱɟɫɤɨɣ ɢɧɮɨɪɦɚɰɢɢ. Ɇ., 1968 ɝ., ɫ. 169, 170; ɷɬɨɬ ɠɟ ɩɪɢɦɟɪ ɫɦ.: ɋɬɚɬɢɫɬɢɱɟɫɤɢɟ ɦɟɬɨɞɵ ɚɧɚɥɢɡɚ ɢɧɮɨɪɦɚɰɢɢ ɜ ɫɨɰɢɨɥɨɝɢɱɟɫɤɢɯ ɢɫɫɥɟɞɨɜɚɧɢɹɯ. Ɇ., 1979, ɫ.111, 112.
72
1 ɢ (II,5,9) ɩɪɟɨɛɪɚɡɭɟɬɫɹ ɜ (II,5,8). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, (II,5,8) ɹɜɥɹɟɬɫɹ ɩɪɢɛɥɢɠɟɧɧɵɦ ɜɵɪɚɠɟɧɢɟɦɞɥɹ (II,5,7).
Ⱦɭɦɚɟɬɫɹ, ɱɬɨ ɩɪɢ ɧɚɥɢɱɢɢ ɨɛɴɟɞɢɧɟɧɧɵɯ ɪɚɧɝɨɜ ɧɢ (II,5,7), ɧɢ (II,5,8) ɧɟ ɞɚɸɬ ɫɭɳɟɫɬɜɟɧɧɨɝɨ ɭɩɪɨɳɟɧɢɹ ɪɚɫɱɟɬɨɜ, ɩɨɷɬɨɦɭ ɦɨɠɧɨ ɪɟɤɨɦɟɧɞɨɜɚɬɶ ɢɫɩɨɥɶɡɨɜɚɬɶ ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ ȡ ɮɨɪɦɭɥɭ, ɩɨ ɤɨɬɨɪɨɣ ɜɵɱɢɫɥɹɟɬɫɹ r – (II,5,1), (II,5,2) ɢɥɢ (II,5,3). ɉɨɫɤɨɥɶɤɭ, ɤɚɤ ɦɵɩɨɤɚɡɚɥɢ, ȡ ɹɜɥɹɟɬɫɹɤɨɷɮɮɢɰɢɟɧɬɨɦ r, ɩɪɢɦɟɧɟɧɧɵɦɤɪɚɧɝɚɦ, ɪɟɡɭɥɶɬɚɬɛɭɞɟɬɬɨɬɠɟ, ɱɬɨɢ ɩɨɮɨɪɦɭɥɟ (II,5,7). ȼɱɚɫɬɧɨɫɬɢ, ɩɪɢɢɫɩɨɥɶɡɨɜɚɧɢɢ(II,5,1) ɞɥɹɩɪɢɦɟɪɚ 19 ɩɨɥɭɱɢɦ 0,354.
[106]
6.Ʉɨɷɮɮɢɰɢɟɧɬ ɪɚɧɝɨɜɨɣ ɤɨɪɪɟɥɹɰɢɢ Ʉɟɧɞɷɥɚ
ȼɫɨɰɢɨɥɨɝɢɱɟɫɤɢɯ ɢɫɫɥɟɞɨɜɚɧɢɹɯ ɱɚɫɬɨ ɭɞɚɟɬɫɹ ɨɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶ ɨɛɴɟɤɬ ɧɟ ɩɨ ɚɛɫɨɥɸɬɧɨɣ, ɚ ɥɢɲɶ ɩɨ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɧɟɤɨɬɨɪɨɝɨ ɫɜɨɣɫɬɜɚ (ɤɚɱɟɫɬɜɟɧɧɵɟ ɩɪɢɡɧɚɤɢ: ɨɰɟɧɤɢ, ɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɶ ɢ ɬ.ɞ.). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɢɡɜɟɫɬɧɚ ɥɢɲɶ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ, ɜ ɤɨɬɨɪɨɣ ɪɚɫɩɨɥɚɝɚɸɬɫɹ ɨɛɴɟɤɬɵ, ɬ.ɟ. ɤɚɠɞɵɣ ɨɛɴɟɤɬ ɨɩɢɫɵɜɚɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɪɚɧɝɨɜ ɩɨ ɤɚɠɞɨɦɭ ɩɪɢɡɧɚɤɭ. əɫɧɨ, ɱɬɨ ɱɟɦ ɛɨɥɟɟ ɫɨɝɥɚɫɨɜɚɧɵ ɪɚɧɝɨɜɵɟ ɪɹɞɵ, ɬɟɦ ɛɨɥɶɲɟɫɜɹɡɶɦɟɠɞɭɩɪɢɡɧɚɤɚɦɢ.
Ɉɞɧɚɤɨ ɩɪɢ ɫɬɪɨɝɨɦ ɩɨɞɯɨɞɟ ɧɢ r, ɧɢ ȡ ɧɟ ɦɨɝɭɬ ɢɫɩɨɥɶɡɨɜɚɬɶɫɹ ɤɚɤ ɧɚɞɟɠɧɚɹ ɦɟɪɚ ɫɜɹɡɢ ɞɜɭɯ ɤɚɱɟɫɬɜɟɧɧɵɯ ɩɪɢɡɧɚɤɨɜ (ɥɢɛɨ ɤɚɱɟɫɬɜɟɧɧɨɝɨ ɢ ɤɨɥɢɱɟɫɬɜɟɧɧɨɝɨ), ɩɨɫɤɨɥɶɤɭ ɷɦɩɢɪɢɱɟɫɤɢ ɧɟɨɛɨɫɧɨɜɚɧɵɨɬɧɨɲɟɧɢɹ, ɢɫɩɨɥɶɡɭɟɦɵɟɩɪɢɩɨɫɬɪɨɟɧɢɢɷɬɢɯɤɨɷɮɮɢɰɢɟɧɬɨɜ.
ɉɪɟɞɥɨɠɟɧɧɵɣ Ʉɟɧɞɷɥɨɦ ɤɨɷɮɮɢɰɢɟɧɬ ɫɬɪɨɢɬɫɹ ɧɚ ɨɫɧɨɜɟ ɨɬɧɨɲɟɧɢɣ ɬɢɩɚ «ɛɨɥɶɲɟ – ɦɟɧɶɲɟ», ɫɩɪɚɜɟɞɥɢɜɨɫɬɶɤɨɬɨɪɵɯɭɫɬɚɧɨɜɥɟɧɚɩɪɢɩɨɫɬɪɨɟɧɢɢɲɤɚɥ.
Ɋɚɫɫɦɨɬɪɢɦ ɥɨɝɢɤɭ ɜɵɜɨɞɚ ɷɬɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ. ɉɭɫɬɶ ɢɦɟɸɬɫɹ N ɨɛɴɟɤɬɨɜ. ɂɡ ɧɢɯ
ɦɨɠɧɨ ɜɵɛɪɚɬɶ C2 N(N 1) ɪɚɡɥɢɱɧɵɯ ɩɚɪ. ɉɨ ɩɪɟɞɩɨɥɨɠɟɧɢɸ, ɢɡɜɟɫɬɧɵ ɪɚɧɝɢ ɤɚɠɞɨɝɨ
N
2
ɨɛɴɟɤɬɚɢɩɨɩɪɢɡɧɚɤɭ X ɢɩɨɩɪɢɡɧɚɤɭ Y.
ȼɵɞɟɥɢɦ ɩɚɪɭ ɨɛɴɟɤɬɨɜ ɢ ɫɪɚɜɧɢɦ ɢɯ ɪɚɧɝɢ ɩɨ ɨɞɧɨɦɭ ɩɪɢɡɧɚɤɭ ɢ ɩɨ ɞɪɭɝɨɦɭ. ȿɫɥɢ ɩɨ ɞɚɧɧɨɦɭ ɩɪɢɡɧɚɤɭ ɪɚɧɝɢ ɨɛɪɚɡɭɸɬ ɩɪɹɦɨɣ ɩɨɪɹɞɨɤ (ɬ.ɟ. ɩɨɪɹɞɨɤ ɧɚɬɭɪɚɥɶɧɨɝɨ ɪɹɞɚ), ɬɨ ɩɚɪɟ ɩɪɢɩɢɫɵɜɚɟɬɫɹ +1, ɟɫɥɢ ɨɛɪɚɬɧɵɣ, ɬɨ –1. Ⱦɥɹ ɜɵɞɟɥɟɧɧɨɣ ɩɚɪɵ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɩɥɸɫ – ɦɢɧɭɫ ɟɞɢɧɢɰɵ (ɩɨ ɩɪɢɡɧɚɤɭ X ɢ ɩɨ ɩɪɢɡɧɚɤɭ Y) ɩɟɪɟɦɧɨɠɚɸɬɫɹ. Ɋɟɡɭɥɶɬɚɬ, ɨɱɟɜɢɞɧɨ, ɪɚɜɟɧ +1; ɟɫɥɢ ɪɚɧɝɢ ɩɚɪɵ ɨɛɨɢɯ ɩɪɢɡɧɚɤɨɜ ɪɚɫɩɨɥɨɠɟɧɵ ɜ ɨɞɢɧɚɤɨɜɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ, ɢ –1, ɟɫɥɢ ɜ ɨɛɪɚɬɧɨɣ.
ȿɫɥɢ ɩɨɪɹɞɤɢ ɪɚɧɝɨɜ ɩɨ ɨɛɨɢɦ ɩɪɢɡɧɚɤɚɦ ɭ ɜɫɟɯ ɩɚɪ ɨɞɢɧɚɤɨɜɵ, ɬɨ ɫɭɦɦɚ ɟɞɢɧɢɰ, ɩɪɢɩɢɫɚɧɧɵɯ ɜɫɟɦ ɩɚɪɚɦ ɨɛɴɟɤɬɨɜ, ɦɚɤɫɢɦɚɥɶɧɚ ɢ ɪɚɜɧɚ ɱɢɫɥɭ ɩɚɪ. ȿɫɥɢ ɩɨɪɹɞɤɢ ɪɚɧɝɨɜ ɜɫɟɯ ɩɚɪ ɨɛɪɚɬɧɵ, ɬɨ –CN2 . ȼ ɨɛɳɟɦ ɫɥɭɱɚɟCN2 P Q , ɝɞɟ P – ɱɢɫɥɨ ɩɨɥɨɠɢɬɟɥɶɧɵɯ, ɚ Q. – ɨɬɪɢɰɚɬɟɥɶɧɵɯɟɞɢɧɢɰ, ɩɪɢɩɢɫɚɧɧɵɯɩɚɪɚɦɩɪɢɫɨɩɨɫɬɚɜɥɟɧɢɢɢɯɪɚɧɝɨɜɩɨɨɛɨɢɦɩɪɢɡɧɚɤɚɦ.
ȼɟɥɢɱɢɧɚ |
|
|
W |
P Q |
(II, 6,1) |
1 N N 1 |
||
2
ɧɚɡɵɜɚɟɬɫɹɤɨɷɮɮɢɰɢɟɧɬɨɦɄɟɧɞɷɥɚ.
[107]
ɍɩɪɚɠɧɟɧɢɟ 48. 1. ɍɛɟɞɢɬɶɫɹ, ɱɬɨ ɜ ɫɥɭɱɚɟ ɫɨɜɩɚɞɟɧɢɹ ɩɨɪɹɞɤɨɜ ɪɚɧɝɨɜ ɜɫɟɯ ɨɛɴɟɤɬɨɜ ɩɨ ɨɛɨɢɦɩɪɢɡɧɚɤɚɦIJ = +1, ɚɜɫɥɭɱɚɟɨɛɪɚɬɧɨɝɨɩɨɪɹɞɤɚIJ= –1.
2. ɉɨɤɚɡɚɬɶ, ɱɬɨ
4Q
ɚ) W 1 N N 1 (II, 6, 2)
73