chap7
.pdf
ɑɢɫɬɤɚ ȼ/Ɉ ɋ/ɉ ȼɵɱɢɫɥɟɧɢɟ
i ɋ/ɉ ] (ɩɨɫɥɟ ɜɜɨɞɚ ɤɚɠɞɨɣ i-ɣ ɩɚɪɵ ɧɚ ɢɧɞɢɤɚɬɨɪɟ ɩɨɹɜɥɹɟɬɫɹ ɬɟɤɭɳɟɟ
ɡɧɚɱɟɧɢɟ i, ɱɬɨ ɨɛɥɟɝɱɚɟɬ ɨɩɟɪɚɬɨɪɭ ɩɪɚɜɢɥɶɧɨɫɬɶ ɜɜɨɞɚ; 3 ɫɟɤ). ɉɨɫɥɟ ɜɜɨɞɚ ɜɫɟɯ ɩɚɪ ɱɢɫɟɥ ɧɚ ɢɧɞɢɤɚɬɨɪɟ ɞɨɥɠɧɨ ɩɨɹɜɢɬɶɫɹ ɡɚɞɚɧɧɨɟ ɱɢɫɥɨ n.
Ȼɉ 2 ɋ/ɉ (ɩɨɥɭɱɢɦU ; 5 ɫɟɤ), ɋ/ɉ (ɩɨɥɭɱɢɦ t; 5 ɫɟɤ).
Ʉɨɧɬɪɨɥɶɧɵɣ ɩɪɢɦɟɪ
ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ:
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Ɋɟɡɭɥɶɬɚɬɵ
U 0.7062935
t3.155016
Ɏɨɪɦɭɥɵ ɪɚɫɱɟɬɚ
ɋɦ. (V,8,4)
Ʉɪɢɬɢɱɟɫɤɢɟ ɡɧɚɱɟɧɢɹ. Ɍɚɛɥ. ɂ, ɉɪɢɥɨɠɟɧɢɟ 3.
Ʉɨɷɮɮɢɰɢɟɧɬ ɤɨɪɪɟɥɹɰɢɢ W , ɭɪɨɜɟɧɶ ɡɧɚɱɢɦɨɫɬɢ z
ɉɪɟɞɫɬɚɜɥɟɧɢɟ ɞɚɧɧɵɯ n - ɱɢɫɥɨ ɨɛɴɟɤɬɨɜ
x1, x2 ,...,xn - ɡɧɚɱɟɧɢɹ ɩɟɪɟɦɟɧɧɨɣ X (ɢɥɢ ɪɚɧɝɢ ɩɨ X) ɞɥɹ ɤɚɠɞɨɝɨ ɨɛɴɟɤɬɚ
y1, y2 ,..., yn - ɡɧɚɱɟɧɢɹ ɩɟɪɟɦɟɧɧɨɣ Y (ɢɥɢ ɠɟ ɪɚɧɝɢ ɩɨ Y) ɞɥɹ ɤɚɠɞɨɝɨ ɨɛɴɟɤɬɚ.
[234]
Ɋɟɡɭɥɶɬɚɬɵ
Ʉɨɷɮɮɢɰɢɟɧɬ ɤɨɪɪɟɥɹɰɢɢ W , ɞɥɹ ɧɟɫɜɹɡɧɵɯ ɢ ɞɥɹ ɫɜɹɡɧɵɯ ɪɚɧɝɨɜ, ɭɪɨɜɟɧɶ ɡɧɚɱɢɦɨɫɬɢ z (ɞɥɹ ɫɥɭɱɚɹ ɧɟɫɜɹɡɧɵɯ ɪɚɧɝɨɜ).
ȼɜɨɞ ɩɪɨɝɪɚɦɦɵ
ȼɵɱɢɫɥɟɧɢɟ
164
1. Cx Ɋ7 (ɱɢɫɬɤɚ) Ȼɉ FO x1 Ɋ2 y1 Ɋ3 [ xi n yi ɋ/ɉ] (4 ɫɟɤ.)
Ⱦɟɣɫɬɜɢɹ ɪɚɦɤɟ ɜɵɩɨɥɧɹɸɬɫɹ ɞɥɹ i = 2, 3,…, n. Ɂɚɬɟɦ x2 Ɋ2 y2 Ɋ3 [ xi n yi ɋ/ɉ] (i = 3, 4,…n) x3 P2 y3 P3 [ F 2 ɋ/ɉ] (i = 4, 5,…n) ɢ ɬɚɤ ɞɚɥɟɟ.
ɉɨɫɥɟɞɧɢɣ ɪɚɡ xn 1 Ɋ2 yn 1 Ɋ3 xn n yn ɋ/ɉ
2.nɊ3 Ȼɉ F u, ɋ/ɉ (2 ɫɟɤ.) xy P8 /—/ P,
3.ɉɭɧɤɬ 3 ɜɵɩɨɥɧɹɟɬɫɹ ɬɨɥɶɤɨ ɩɪɢ ɧɚɥɢɱɢɢ ɫɜɹɡɚɧɧɵɯ ɪɚɧɝɨɜ ɩɨ X – ɜ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɩɟɪɟɯɨɞɢɦ ɫɪɚɡɭ ɤ ɩ.6
4.F8 /—/ P
5.ɉɭɧɤɬ 5 ɜɵɩɨɥɧɹɟɬɫɹ ɥɢɲɶ ɜ ɬɨɦ ɫɥɭɱɚɟ ɟɫɥɢ ɟɫɬɶ ɫɜɹɡɚɧɧɵɟ ɪɚɧɝɢ ɩɨ Y, ɜ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɩɟɪɟɯɨɞɢɦ ɫɪɚɡɭ ɤ ɩ. 6
[ g i ɋ/ɉ] (2 ɫɟɤ.), gi - ɱɢɫɥɨ ɫɜɹɡɚɧɧɵɯ ɪɚɧɝɨɜ ɜ i-ɝɪɭɩɩɟ ɫɜɹɡɚɧɧɵɯ ɪɚɧɝɨɜ ɩɨ ɩɪɢɡɧɚɤɭ Y
6.Ɋ /—/ n Ȼɉ F4ɋ/ɉ (ɡɧɚɱɟɧɢɟ W ; 3 ɫɟɤ.)
7.ɋ/ɉ (2 ɫɟɤ.) F3 4 y ɋ/ɉ (ɡɧɚɱɟɧɢɟ z; 4 ɫɟɤ.)
Ʉɨɧɬɪɨɥɶɧɵɣ ɩɪɢɦɟɪ
ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ
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n=5 g=2 ɞɥɹ ɩɟɪɟɦɟɧɧɨɣ Y
Ɋɟɡɭɥɶɬɚɬɵ: W 0.5270463 , z 0.9797959
Ɏɨɪɦɭɥɵ ɞɥɹ ɪɚɫɱɟɬɚ16
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Ʉɪɢɬɢɱɟɫɤɢɟ ɡɧɚɱɟɧɢɹ
ɋɦ. ɬɚɛɥ. Ⱥ ɉɪɢɥɨɠɟɧɢɟ 3.
ɉɪɢɦɟɱɚɧɢɟ ɉɭɧɤɬ 1 ɩɪɨɝɪɚɦɦɵ ɜɵɱɢɫɥɟɧɢɹ W ɞɨɜɨɥɶɧɨ ɬɪɭɞɨɟɦɤɢɣ, ɢɧɨɝɞɚ ɢɦɟɟɬ ɫɦɵɫɥ ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ S, ɜɵɱɢɫɥɹɟɦɨɟ ɜ ɩɭɧɤɬɟ 1, ɜɪɭɱɧɭɸ (ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɨɛɴɟɤɬɵ ɪɚɧɠɢɪɭɸɬɫɹ ɩɨ ɡɧɚɱɟɧɢɹɦ ɨɞɧɨɣ ɢɡ ɩɟɪɟɦɟɧɧɵɯ). Ⱦɚɥɟɟ S ɡɚɧɨɫɢɬɫɹ ɜ «P7» ɢ ɜɵɱɢɫɥɟɧɢɟ ɩɨɜɬɨɪɹɟɬɫɹ, ɧɚɱɢɧɚɹ ɫ ɩ. 2.
Ʌɢɧɟɣɧɚɹ ɤɨɪɪɟɥɹɰɢɹ ɢ ɪɟɝɪɟɫɫɢɹ
ɉɪɟɞɫɬɚɜɥɟɧɢɟ ɞɚɧɧɵɯ
x1, x2 ,...,xn - ɡɧɚɱɟɧɢɹ ɩɪɢɡɧɚɤɚ ɏ y1, y2 ,..., yn - ɡɧɚɱɟɧɢɹ ɩɪɢɡɧɚɤɚ Y
16 Ɏɨɪɦɭɥɵ ɞɥɹ z ɜ ɫɥɭɱɚɟ ɫɜɹɡɚɧɧɵɯ ɪɚɧɝɨɜ ɫɦ. ɜ ɤɧ.: Ʉɟɧɞɷɥ Ɇ. Ɋɚɧɝɨɜɵɟ ɤɨɪɪɟɥɹɰɢɢ. Ɇ., 1975, ɫ. 66.
165
ɋɪɟɞɧɢɟ x ɢ ɭ, ɤɨɷɮɮɢɰɢɟɧɬ ɤɨɪɪɟɥɹɰɢɢ r , ɤɨɥɢɱɟɫɬɜɨ ɩɚɪ ɨɛɴɟɤɬɨɜ n ɢ ɩɚɪɚɦɟɬɪɵ ɚ ɢ b ɥɢɧɟɣɧɨɝɨ ɭɪɚɜɧɟɧɢɹ y ax b
ȼɜɨɞ ɩɪɨɝɪɚɦɦɵ
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ɑɢɫɬɤɚ |
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n /—/ (ɲɟɫɬɶ ɪɚɡ) |
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[236] |
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F7 y (ɩɨɥɭɱɢɦ r ) F6 y (ɡɧɚɱɟɧɢɟ a) n P/—/ P/—/ P/—/ (ɡɧɚɱɟɧɢɟ |
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n 5,r 0.9383148,a |
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Ɏɨɪɦɭɥɵ ɪɚɫɱɟɬɚ (ɫɦ. II,5,3), (III,1,11), (III,1,12). |
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Ʌɢɧɟɣɧɚɹ ɤɨɪɪɟɥɹɰɢɹ ɢ ɪɟɝɪɟɫɫɢɹ ɩɪɢ ɝɪɭɩɩɢɪɨɜɤɟ ɜ ɤɥɚɫɫɵ |
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ɉɪɟɞɫɬɚɜɥɟɧɢɟ ɞɚɧɧɵɯ |
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Ɉɛɳɟɟ ɱɢɫɥɨ ɪɟɫɩɨɧɞɟɧɬɨɜ N, ɫɪɟɞɧɢɟ ɡɧɚɱɟɧɢɟ |
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, ɤɨɷɮɮɢɰɢɟɧɬ ɤɨɪɪɟɥɹɰɢɢ r ɢ |
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ȼɜɨɞ ɩɪɨɝɪɚɦɦɵ |
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ɑɢɫɬɤɚ
Cx P /—/ (6 ɪɚɡ)
ȼɵɱɢɫɥɟɧɢɟ [ Ni ȼ/Ɉ ɋ/ɉ (2-3 ɫɟɤ.) xi ɋ/ɉ (4 ɫɟɤ.) yi ɋ/ɉ (6 ɫɟɤ.)] P /—/ (ɩɨɥɭɱɢɦ N) Ɋ2 Ɋ/—/ Ɋ3 Ȼɉ 5ɋ/ɉ (10ɫɟɤ.)
166
F7 y (ɩɨɥɭɱɢɦ r ) F6 y (ɩɨɥɭɱɢɦ a ) n P/—/ P/—/ P/—/ (ɡɧɚɱɟɧɢɟ x ) u n P/—/ P/—/
(ɡɧɚɱɟɧɢɟ y) xy (ɡɧɚɱɟɧɢɟ b). |
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[237] |
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Ɋɟɡɭɥɶɬɚɬɵ: |
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N 26;r 0.5384615;a |
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Ɉɫɬɚɥɶɧɵɟ ɮɨɪɦɭɥɵ ɬɟ ɠɟ, ɱɬɨ ɢ ɜ ɩɪɟɞɵɞɭɳɟɦ ɫɥɭɱɚɟ (ɬ.ɟ. ɛɟɡ ɝɪɭɩɩɢɪɨɜɤɢ ɜ ɤɥɚɫɫɵ).
ɉɪɨɝɪɚɦɦɚ ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ ɩɨ ɬɚɛɥɢɰɟ k ul ɡɧɚɱɟɧɢɹ F2 , ɤɨɷɮɮɢɰɢɟɧɬɚ ɑɭɩɪɨɜɚ
Ɍ, ɤɨɷɮɮɢɰɢɟɧɬɚ Ʉɪɚɦɟɪɚ T.
ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ: Ɍɚɛɥɢɰɚ k ul (ɫɦ. § 2 ɝɥ. 11) Ɋɟɡɭɥɶɬɚɬɵ. ɁɧɚɱɟɧɢɟF2 , Ɍ ɢ Tc
ȼɜɨɞ ɩɪɨɝɪɚɦɦɵ
ȼɵɱɢɫɥɟɧɢɟ
ɑɢɫɬɤɚ Cx Ɋ8. NP3. Ȼɨɥɶɲɟɟ ɢɡ ɱɢɫɟɥ k 1 ɢ l 1 ɡɚɩɨɦɢɧɚɟɦ ɜ 4-ɣ (P4) ɦɟɧɶɲɟɟ - ɜ 5-ɣ ɹɱɟɣɤɟ (Ɋ5).
ɋɱɢɬɚɟɦ ɩɨ ɫɬɨɥɛɰɚɦ N y1 P2 N11 n N x1 ȼ/Ɉ ɋ/ɉ ɋ/ɉ ɢ ɞɚɥɟɟ ɜ ɰɢɤɥɟ
[ Ni1 n N xi |
ɋ/ɉ] i = 2, 3, ..., k (2 ɫɟɤ). Ɂɚɬɟɦ ɞɥɹ ɜɬɨɪɨɝɨ ɫɬɨɥɛɰɚ N y2 |
P2 [ Ni2 n N xi C/ɉ] l |
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= = 1, 2, ..., k ɢ ɬ.ɞ. ɉɨɫɥɟ ɜɜɨɞɚ ɜɫɟɯ ɫɬɨɥɛɰɨɜ Ȼɉ Ɋ u ɋ/ɉ (ɩɨɥɭɱɢɦ F2 ) |
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ɋ/ɉ (ɩɨɥɭɱɢɦ Ɍ ) ɋ/ɉ (ɩɨɥɭɱɢɦ T 2 |
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[238] |
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Ʉɨɧɬɪɨɥɶɧɵɣ ɩɪɢɦɟɪ |
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y1 |
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N xi |
43 |
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17 |
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Cx Ɋ8 120 Ɋ3 2Ɋ4 1Ɋ5 Ⱦɚɥɟɟ 43Ɋ2 29 n 80 ȼ/Ɉ ɋ/ɉ ɋ/ɉ 14 n40 ɋ/ɉ 60Ɋ2 36 n 80 ɋ/ɉ 24 n 40 ɋ/ɉ 17Ɋ2 15 n 80 ɋ/ɉ 2 n 40 ɋ/ɉ ȼɫɟ ɫɬɨɥɛɰɵ ɜɜɟɞɟɧɵ ȼɉ Ɋ u ɋ/ɉ (ɩɨɥɭɱɢɦ F2 = 4,770432) ɋ/ɉ (T = 0,1676604) ɋ/ɉ (Tc = 0.1993830)
Ɏɨɪɦɭɥɵ ɪɚɫɱɟɬɚ
ɋɦ. (II,2,1), (II,2,4), (II,2,5)
ɍɪɨɜɧɢ ɡɧɚɱɢɦɨɫɬɢ
Ɍɚɛɥ. Ȼ ɉɪɢɥɨɠɟɧɢɟ 3.
Ʉɨɷɮɮɢɰɢɟɧɬɵ ɫɜɹɡɢ ɞɥɹ ɬɚɛɥɢɰɵ 2u2:Q,) ɢ F2
ɉɪɟɞɫɬɚɜɥɟɧɢɟ ɞɚɧɧɵɯ:
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y1 |
y2 |
x1 |
N11 |
N12 |
x2 |
N21 |
N22 |
Ɋɟɡɭɥɶɬɚɬɵ
Ʉɨɷɮɮɢɰɢɟɧɬ ɘɥɚ Q, ɤɨɷɮɮɢɰɢɟɧɬ ɤɨɧɬɢɧɝɟɧɰɢɢ Ɏ, ɩɨɤɚɡɚɬɟɥɶ F2 .
ȼɜɨɞ ɩɪɨɝɪɚɦɦɵ
ȼɵɱɢɫɥɟɧɢɟ N11P2 N12 P3N21P4N22 P5 ȼ/Ɉ ɋ/ɉ (ɩɨɥɭɱɢɥɢ Q; 8 ɫɟɤ.) ɋ/ɉ (ɩɨɥɭɱɢɥɢ Ɏ; 2 ɫɟɤ.) Fx2 ɋ/ɉ (ɩɨɥɭɱɢɥɢ F2 ; 1 ɫɟɤ.)
[239]
Ʉɨɧɬɪɨɥɶɧɵɣ ɩɪɢɦɟɪ:
ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ: ɬɚɛɥɢɰɚ
1 2
34
Ɋɟɡɭɥɶɬɚɬɵ:
Q 0,20 ) 0.08908708 F2 0.07936508
Ɏɨɪɦɭɥɵ ɪɚɫɱɟɬɚ
ɋɦ (ɫ. 86), (ɫ. 88), (II,2,1).
Ʉɨɷɮɮɢɰɢɟɧɬɵ ɱɚɫɬɧɨɣ ɤɨɪɪɟɥɹɰɢɢ (ɞɥɹ r ɢ W ).
ɉɪɟɞɫɬɚɜɥɟɧɢɟ ɞɚɧɧɵɯ:
Ʉɨɷɮɮɢɰɢɟɧɬɵ ɩɚɪɧɨɣ ɤɨɪɪɟɥɹɰɢɢ r01 , r02 ɢ r12 (ɢɥɢ W01,W02 ɢ W12 ) ɞɥɹ ɤɨɷɮɮɢɰɢɟɧɬɚ
ɱɚɫɬɧɨɣ ɤɨɪɪɟɥɹɰɢɢ r01.2 ɢɥɢ W01.2 ; ɤɨɷɮɮɢɰɢɟɧɬɵ r01.2 ,r03.2 ɢ r13.2 ɞɥɹ ɤɨɷɮɮɢɰɢɟɧɬɚ r01.23 ɢ ɬ.ɞ.
Ɋɟɡɭɥɶɬɚɬɵ
168
Ʉɨɷɮɮɢɰɢɟɧɬɵ ɱɚɫɬɧɨɣ ɤɨɪɪɟɥɹɰɢɢ ɥɸɛɨɝɨ ɩɨɪɹɞɤɚ (ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ n-ɨɝɨ ɩɨɪɹɞɤɚ ɫɧɚɱɚɥɚ ɜɵɱɢɫɥɹɸɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɵ ( n 1)-ɝɨ ɩɨɪɹɞɤɚ)
ȼɜɨɞ ɩɪɨɝɪɚɦɦɵ
ȼɵɱɢɫɥɟɧɢɟ.
Ⱦɥɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɩɟɪɜɨɝɨ ɩɨɪɹɞɤɚ r01P,r02 P,r12 P, ȼ/Ɉ ɋ/ɉ (ɩɨɥɭɱɢɦ r01.2 , 7 ɫɟɤ). Ⱦɥɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ r01.3P,r02.3P,r13.2 P, ȼ/Ɉ ɋ/ɉ (ɩɨɥɭɱɢɦ r01.23 ;7 ɫɟɤ) ɢ
ɬ.ɞ.
Ⱥɧɚɥɨɝɢɱɧɨ ɜɵɱɢɫɥɹɸɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɵ W01.2 ;W01.23 ɢ ɬ.ɞ.
Ʉɨɧɬɪɨɥɶɧɵɣ ɩɪɢɦɟɪ
r01.3 0.620 r03.2 0.240 r13.2 0.171 r01.23 0.6911214
Ɏɨɪɦɭɥɵ ɪɚɫɱɟɬɚ
(III,2,3 - III,2,5), (III,2,6), (III,2,7)
Ʉɨɷɮɮɢɰɢɟɧɬ ɦɧɨɠɟɫɬɜɟɧɧɨɣ ɤɨɪɪɟɥɹɰɢɢ
ɉɪɟɞɫɬɚɜɥɟɧɢɟ ɞɚɧɧɵɯ
ɑɚɫɬɧɵɟ ɤɨɷɮɮɢɰɢɟɧɬɵ ɤɨɪɪɟɥɹɰɢɢ, ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɪɚɫɱɟɬɚ ɤɨɷɮɮɢɰɢɟɧɬɚ
ɦɧɨɠɟɫɬɜɟɧɧɨɣ ɤɨɪɪɟɥɹɰɢɢ R0.12...n : r01;r02.1;r03.12 ;...;r0n.12...(n 1)
[240]
Ɋɟɡɭɥɶɬɚɬɵ
Ʉɨɷɮɮɢɰɢɟɧɬ R0.12...n
ȼɜɨɞ ɩɪɨɝɪɚɦɦɵ.
ȼɵɱɢɫɥɟɧɢɟ
ȼ/Ɉ ɋ/ɉ r01 C/ɉ (3 ɫɟɤ) r02.1 ɋ/ɉ (3 ɫɟɤ)... r0n.12...(n 1) ɋ/ɉ (3 ɫɟɤ) ɉɨɫɥɟ ɜɜɨɞɚ ɜɫɟɯ ɱɚɫɬɧɵɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɤɨɪɪɟɥɹɰɢɢ Ȼɉ P u ɋ/ɉ (ɩɨɥɭɱɢɦ R01.2...n ;3 ɫɟɤ)
Ʉɨɧɬɪɨɥɶɧɵɣ ɩɪɢɦɟɪ.
r01 0.705 r02.1 0.479 r03.12 0.342 R01.23 0.8110240
Ɏɨɪɦɭɥɵ ɪɚɫɱɟɬɚ
(III,3,7)
Ɂɧɚɱɢɦɨɫɬɶ ɪɚɡɥɢɱɢɹ ɞɨɥɟɣ (ɩɪɨɰɟɧɬɨɜ)
ɉɪɟɞɫɬɚɜɥɟɧɢɟ ɞɚɧɧɵɯ
169
v1,v2 - ɫɪɚɜɧɢɜɚɟɦɵɟ ɞɨɥɢ ɩɪɢɡɧɚɤɨɜ (ɩɪɨɰɟɧɬɵ)
n1,n2 - ɨɛɴɟɦɵ ɜɵɛɨɪɨɤ, ɩɨ ɤɨɬɨɪɵɦ ɪɚɫɫɱɢɬɵɜɚɥɢɫɶ v1 ɢ v2 ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ.
Ɋɟɡɭɥɶɬɚɬɵ
Ʉɪɢɬɟɪɢɣ ɡɧɚɱɢɦɨɫɬɢ ɪɚɡɥɢɱɢɣ ɞɨɥɟɣ z (ɦɨɠɟɬ ɢɫɩɨɥɶɡɨɜɚɬɶɫɹ, ɟɫɥɢ ɜɵɩɨɥɧɹɟɬɫɹ ɤɚɠɞɨɟ ɢɡ ɫɥɟɞɭɸɳɢɯ ɭɫɥɨɜɢɣ: n1 t50,n2 t50,np !5,n(1 p) !5 , ɮɨɪɦɭɥɚ ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ ɩɪɢɜɟɞɟɧɚ ɧɢɠɟ).
ȼɜɨɞ ɩɪɨɝɪɚɦɦɵ
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ɋɱɟɬ |
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ȿɫɥɢ v1 |
ɢ v2 ɜɵɪɚɠɟɧɵ ɜ ɞɨɥɹɯ, ɜɜɨɞɢɦ: 1Ɋ8, ɟɫɥɢ ɜ ɩɪɨɰɟɧɬɚɯ: 100P8 |
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n1P2 n2 P3 v1 n v2 ȼ/Ɉ ɋ/ɉ (ɩɨɥɭɱɢɦ z; 9 ɫɟɤ) |
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Ʉɨɧɬɪɨɥɶɧɵɣ ɩɪɢɦɟɪ |
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ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ: |
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[241] |
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n1 |
392 , |
v1 |
0.296, |
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29.6% , |
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n2 |
277 |
v2 |
0.209 |
ɢɥɢ |
v2 |
20.9% , |
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Ɋɟɡɭɥɶɬɚɬ: z = 2,526962
Ɏɨɪɦɭɥɵ ɪɚɫɱɟɬɚ
ɋɦ (V,5,1).
Ʉɪɢɬɢɱɟɫɤɢɟ ɡɧɚɱɟɧɢɹ
ɋɦ. ɬɚɛɥ. Ⱥ ɉɪɢɥɨɠɟɧɢɹ 3.
Ɂɧɚɱɢɦɨɫɬɶ ɪɚɡɥɢɱɢɣ ɫɪɟɞɧɢɯ ɚɪɢɮɦɟɬɢɱɟɫɤɢɯ
ɉɪɟɞɫɬɚɜɥɟɧɢɟ ɞɚɧɧɵɯ
x1,s1, x2 ,s2 - ɫɪɟɞɧɢɟ ɚɪɢɮɦɟɬɢɱɟɫɤɢɟ ɢ ɨɰɟɧɤɢ ɫɪɟɞɧɢɯ ɤɜɚɞɪɚɬɢɱɟɫɤɢɯ ɨɬɤɥɨɧɟɧɢɣ, ɪɚɫɫɱɢɬɚɧɧɵɟ ɩɨ ɜɵɛɨɪɤɚɦ ɨɛɴɟɦɚ n1 ɢ n2 ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ.
Ɋɟɡɭɥɶɬɚɬɵ,
Ʉɪɢɬɟɪɢɣ ɡɧɚɱɢɦɨɫɬɢ ɪɚɡɥɢɱɢɣ t, ɱɢɫɥɨ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ f
ȼɜɨɞ ɩɪɨɝɪɚɦɦɵ
ȼɵɱɢɫɥɟɧɢɟ
ȼ/Ɉ ɋ ɉ (1 ɫɟɤ) n1 n s1 ɋ/ɉ ( |4 ɫɟɤ) n2 n s2 ɋ/ɉ (ɩɨɥɭɱɢɦ v; |5 ɫɟɤ)
x1 n x2 ɋ/ɉ (ɩɨɥɭɱɢɦ ɤɪɢɬɟɪɢɣ t; 1 ɫɟɤ)
Ʉɨɧɬɪɨɥɶɧɵɣ ɩɪɢɦɟɪ
170
ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ:
x1 15,s1 4, x2 11,s2 0.1,n1 30,n2 65
Ɋɟɡɭɥɶɬɚɬɵ: v = 29,01788 t = 5,476435
Ɏɨɪɦɭɥɵ ɪɚɫɱɟɬɚ
ɋɦ. (V,6,1), (V,6,2)
Ʉɪɢɬɢɱɟɫɤɢɟ ɡɧɚɱɟɧɢɹ
ɋɦ. ɬɚɛɥ. Ⱥ ɉɪɢɥɨɠɟɧɢɟ ɂ.
Ɂɧɚɱɢɦɨɫɬɶ ɪɚɡɥɢɱɢɣ ɞɜɭɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɤɨɪɪɟɥɹɰɢɢ
ɉɪɟɞɫɬɚɜɥɟɧɢɟ ɞɚɧɧɵɯ
Ʉɨɷɮɮɢɰɢɟɧɬɵ ɤɨɪɪɟɥɹɰɢɢ r1 ɢ r2 ɪɚɫɫɱɢɬɚɧɧɵɟ ɩɨ ɜɵɛɨɪɤɚɦ n1 ɢ n2 ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ.
[242]
Ɋɟɡɭɥɶɬɚɬɵ
ɍɪɨɜɟɧɶ ɡɧɚɱɢɦɨɫɬɢ ɪɚɡɥɢɱɢɣ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɤɨɪɪɟɥɹɰɢɢ z.
ȼɜɨɞ ɩɪɨɝɪɚɦɦɵ
ȼɵɱɢɫɥɟɧɢɟ
ɇɟ ɨɛɪɚɳɚɹ ɜɧɢɦɚɧɢɹ ɧɚ ɱɢɫɥɚ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɩɨɹɜɢɬɶɫɹ ɢɡ ɫɬɟɤɚ, ɜɵɩɨɥɧɹɟɦ: r1P,r2 P,n1P,n2 ȼ/Ɉ ɋ/ɉ (ɩɨɥɭɱɢɦ z; 9 ɫɟɤ)
Ʉɨɧɬɪɨɥɶɧɵɣ ɩɪɢɦɟɪ
ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ:
r1 =0.6 |
n1 =28 |
r2 =0.8 |
n2 =23 |
Ɋɟɡɭɥɶɬɚɬɵ: z = 1,351550 Ɏɨɪɦɭɥɵ ɪɚɫɱɟɬɚ
ɋɦ. (V,9,1).
Ʉɪɢɬɢɱɟɫɤɢɟ ɡɧɚɱɟɧɢɹ
ɋɦ. ɬɚɛɥ. Ⱥ ɩɪɢɥɨɠɟɧɢɹ 3
Ɂɧɚɱɢɦɨɫɬɶ ɪɚɡɥɢɱɢɣ ɪɚɫɩɪɟɞɟɥɟɧɢɣ (ɤɪɢɬɟɪɢɣ F2 )
ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ
Ɍɚɛɥɢɰɚ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɞɜɭɯ ɫɨɜɨɤɭɩɧɨɫɬɟɣ ɪɟɫɩɨɧɞɟɧɬɨɜ ɩɨ ɧɟɤɨɬɨɪɨɦɭ ɩɪɢɡɧɚɤɭ ɏ:
k1k2...kn |
K |
l1l2...ln |
L |
ɝɞɟ ki ɢ li - ɱɚɫɬɨɬɵ; ki - ɱɢɫɥɨ ɪɟɫɩɨɧɞɟɧɬɨɜ ɢɡ ɩɟɪɜɨɣ ɫɨɜɨɤɭɩɧɨɫɬɢ, ɜɵɛɪɚɜɲɢɯ i-ɸ ɝɪɚɞɚɰɢɸ ɩɪɢ ɨɬɜɟɬɟ ɧɚ ɜɨɩɪɨɫ ɏ; li - ɚɧɚɥɨɝɢɱɧɚɹ ɱɚɫɬɨɬɚ ɞɥɹ ɜɬɨɪɨɣ ɝɪɭɩɩɵ ɪɟɫɩɨɧɞɟɧɬɨɜ. K ɢ L -- ɫɭɦɦɵ ɱɚɫɬɨɬ:
171
nn
K ¦ki L ¦li
i 1 |
i 1 |
Ɋɟɡɭɥɶɬɚɬɵ
[243]
Ʉɪɢɬɟɪɢɣ F2 , ɩɨɤɚɡɵɜɚɸɳɢɣ ɡɧɚɱɢɦɨɫɬɶ ɪɚɡɥɢɱɢɣ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɩɪɢɡɧɚɤɚ ɏ ɜ 2
ɝɪɭɩɩɚɯ ɪɟɫɩɨɧɞɟɧɬɨɜ17.
ȼɜɨɞ ɩɪɨɝɪɚɦɦɵ
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Ɂɚɧɨɫɢɦ Ʉ ɜ Ɋ2; L ɜ P3. ȼ/Ɉ ɋ/ɉ (1 ɫɟɤ) |
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ɋ/ɉ] (t | 4 ɫɟɤ) Ȼɉ Ɋ5 ɋ/ɉ (ɩɨɥɭɱɢɦ F2 ) |
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Ʉɨɧɬɪɨɥɶɧɵɣ ɩɪɢɦɟɪ |
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ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ: |
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Ɋɟɡɭɥɶɬɚɬ: F2 = 4,770444 |
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Ɏɨɪɦɭɥɵ ɪɚɫɱɟɬɚ |
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¬i 1 © K L ¹ki |
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Ʉɪɢɬɢɱɟɫɤɢɟ ɡɧɚɱɟɧɢɹ
ɋɦ. ɬɚɛɥ. Ȼ ɉɪɢɥɨɠɟɧɢɟ 3.
ɑɬɨ ɤɚɫɚɟɬɫɹ ɪɚɫɱɟɬɚ ɫɩɟɰɢɚɥɶɧɵɯ ɩɨɤɚɡɚɬɟɥɟɣ, ɬɨ ɜɨ ɦɧɨɝɢɯ ɫɥɭɱɚɹɯ (ɜ ɱɚɫɬɧɨɫɬɢ, ɩɪɢ ɪɚɫɱɟɬɟ ɢɧɞɟɤɫɨɜ ɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɢ, ɩɪɟɫɬɢɠɚ ɢ ɬ.ɩ.) ɦɨɠɧɨ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɩɪɨɝɪɚɦɦɨɣ ɜɵɱɢɫɥɟɧɢɹ ɫɪɟɞɧɢɯ ɚɪɢɮɦɟɬɢɱɟɫɤɢɯ ɞɥɹ ɫɝɪɭɩɩɢɪɨɜɚɧɧɵɯ ɞɚɧɧɵɯ (ɜɦɟɫɬɨ ɫɟɪɟɞɢɧ ɢɧɬɟɪɜɚɥɨɜ ɜɡɹɬɶ ɡɧɚɱɟɧɢɹ ɜɟɫɨɜ ɬɟɯ ɢɥɢ ɢɧɵɯ ɜɚɪɢɚɧɬɨɜ ɨɬɜɟɬɚ). ɉɪɢ ɛɨɥɶɲɨɦ ɱɢɫɥɟ ɢɧɞɟɤɫɨɜ ɩɪɢ ɧɟɢɡɦɟɧɧɵɯ ɜɟɫɚɯ ɞɥɹ ɭɫɤɨɪɟɧɢɹ ɪɚɫɱɟɬɨɜ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɩɟɰɢɚɥɶɧɵɟ ɩɪɨɝɪɚɦɦɵ. ɉɪɢɜɟɞɟɦ ɩɪɢɦɟɪ ɬɚɤɨɝɨ ɪɨɞɚ ɩɪɨɝɪɚɦɦɵ.
Ɋɚɫɱɟɬ ɢɧɞɟɤɫɚ ɞɥɹ ɩɹɬɢɛɚɥɥɶɧɵɯ ɲɤɚɥ
ɉɪɟɞɫɬɚɜɥɟɧɢɟ ɞɚɧɧɵɯ
Ɉɞɧɨɦɟɪɧɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨ ɩɪɢɡɧɚɤɭ, ɢɦɟɸɳɟɦɭ 5 ɜɚɪɢɚɧɬɨɜ ɱɚɫɬɨɬɵ: N1, N2 , N3 , N4 , N5 . ɋɭɦɦɚ ɱɚɫɬɨɬ ɪɚɜɧɚ N. Ʉɚɠɞɵɣ ɢɡ ɜɚɪɢɚɧɬɨɜ ɢɦɟɟɬ ɜɟɫ: E1,E2 ,E3 ,E4 ,E5
[244]
Ɋɟɡɭɥɶɬɚɬ ɢ ɮɨɪɦɭɥɚ ɪɚɫɱɟɬɚ
ɇɟɤɨɬɨɪɵɣ ɢɧɞɟɤɫ
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ȼɜɨɞ ɩɪɨɝɪɚɦɦɵ
17 ȼ ɰɢɬ. ɤɧɢɝɟ Ʌ. Ɏɪɚɧɰɟɜɢɱɚ ɟɫɬɶ ɩɪɨɝɪɚɦɦɚ ɪɚɫɱɟɬɚ ɤɪɢɬɟɪɢɹ ɜ ɫɥɭɱɚɟ, ɟɫɥɢ ɡɧɚɱɟɧɢɟ Ʉ ɢ L ɧɟ ɡɚɞɚɧɵ.
172
ȼɵɱɢɫɥɟɧɢɟ
ɚ) E1P2 E2 P3, E3P4 E4 P5 E5 P6,
ɛ) NP7
ɜ) ȼ/Ɉ ɋ/ɉ (1 ɫɟɤ.) N1 ɋ/ɉ (3 ɫɟɤ) N2 ɋ/ɉ (3 ɫɟɤ) N3 ɋ/ɉ (3 ɫɟɤ) N4 ɋ/ɉ (3 ɫɟɤ) N5 ɋ/ɉ (ɩɨɥɭɱɢɦ ɢɧɞɟɤɫ I).
ɉɪɢ ɧɟɢɡɦɟɧɧɵɯ ɛɚɥɥɚɯ ɞɥɹ ɪɚɫɱɟɬɚ ɧɨɜɨɝɨ ɢɧɞɟɤɫɚ ɧɚɱɢɧɚɬɶ ɫ ɩ. ɛ., ɚ ɩɪɢ ɧɟɢɡɦɟɧɧɨɦ N - ɫ ɩɭɧɤɬɚ ɜ.
Ʉɨɧɬɪɨɥɶɧɵɣ ɩɪɢɦɟɪ
Ei |
1 |
0.5 |
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30 |
10 |
10 |
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Ɋɟɡɭɥɶɬɚɬ: I = 0,1666666
ɇɢɠɟ ɩɪɢɜɨɞɢɬɫɹ ɩɪɨɝɪɚɦɦɚ ɪɚɫɱɟɬɚ ɟɜɤɥɢɞɨɜɵɯ ɪɚɫɫɬɨɹɧɢɣ ɦɟɠɞɭ ɜɟɤɬɨɪɚɦɢ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɦɢ ɫɨɰɢɨɥɨɝɢɱɟɫɤɢɟ ɨɛɴɟɤɬɵ (ɪɟɫɩɨɧɞɟɧɬɨɜ, ɝɪɭɩɩ ɪɟɫɩɨɧɞɟɧɬɨɜ). Ɍɚɤɨɝɨ ɪɨɞɚ ɪɚɫɫɬɨɹɧɢɹ ɢɫɩɨɥɶɡɭɸɬɫɹ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɛɥɢɡɨɫɬɢ ɨɛɴɟɤɬɨɜ ɜ ɧɟɤɨɬɨɪɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ ɩɪɢɡɧɚɤɨɜ (ɬɢɩɢɱɧɵɣ ɩɪɢɦɟɪ - ɪɚɡɛɢɟɧɢɟ ɦɚɫɫɢɜɚ ɨɩɪɨɲɟɧɧɵɯ ɧɚ ɧɟɤɨɬɨɪɵɟ ɬɢɩɵ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɫɨɞɟɪɠɚɬɟɥɶɧɵɦɢ ɝɢɩɨɬɟɡɚɦɢ ɢ ɩɪɨɜɟɪɤɚ ɬɨɝɨ, ɧɚɫɤɨɥɶɤɨ ɭɞɚɱɧɨ ɜɜɟɞɟɧɵ ɬɢɩɵ, ɩɭɬɟɦ ɪɚɫɱɟɬɚ ɪɚɫɫɬɨɹɧɢɣ ɦɟɠɞɭ ɧɢɦɢ). ɗɬɚ ɩɪɨɝɪɚɦɦɚ ɩɪɟɞɫɬɚɜɥɹɟɬ ɢɧɬɟɪɟɫ ɬɟɦ, ɱɬɨ ɪɟɡɭɥɶɬɚɬɨɦ ɫɱɟɬɚ ɹɜɥɹɟɬɫɹ ɧɟ ɨɞɧɨ ɱɢɫɥɨ, ɚ ɦɚɬɪɢɰɚ ɪɚɫɫɬɨɹɧɢɣ 4 u 4 (ɬ.ɟ. 6 ɱɢɫɟɥ, ɬɚɤ ɤɚɤ ɦɚɬɪɢɰɚ ɫɢɦɦɟɬɪɢɱɧɚ).
[245]
ɉɪɨɝɪɚɦɦɚ ɪɚɫɱɟɬɚ ɦɚɬɪɢɰɵ ɪɚɫɫɬɨɹɧɢɣ ɦɟɠɞɭ 4-ɦɹ ɜɟɤɬɨɪɚɦɢ
ɉɪɟɞɫɬɚɜɥɟɧɢɟ ɞɚɧɧɵɯ
ȼɟɤɬɨɪɚ:
X |
^x1, , x2 ,..., xn ` |
Y |
^y1, y2 ,..., yn ` |
Z |
^z1, z2 ,..., zn ` |
U |
^u1,u2 ,...,un `ɝɞɟ ɢ - ɱɢɫɥɨ ɩɪɢɡɧɚɤɨɜ, xi , yi , zi ,ui — ɡɧɚɱɟɧɢɟ i-ɝɨ ɩɪɢɡɧɚɤɚ ɞɥɹ |
ɜɟɤɬɨɪɨɜ ɏ, Y, Z, U ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ.
Ɋɟɡɭɥɶɬɚɬɵ
Ɇɚɬɪɢɰɚ ɪɚɫɫɬɨɹɧɢɣ Ɇ ɦɟɠɞɭ ɜɟɤɬɨɪɚɦɢ ɏ, Y, Z, U:
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dXZ |
dXU º |
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«dYX |
dYY |
dYZ |
dYU » |
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ZX |
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ZY |
d |
ZZ |
d |
ZU |
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¬dUX |
dUY |
dUZ |
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ȼɜɨɞ ɩɪɨɝɪɚɦɦɵ
173