Davydov
.pdf| = d{ + e ɫ ɬɚɤɢɦɢ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ d ɢ e, ɱɬɨ ɮɭɧɤɰɢɹ ɞɜɭɯ ɩɟɪɟɦɟɧɧɵɯ
Xq
j(d>e) = (i({n) d{n e)2
n=0
ɩɪɢɧɢɦɚɟɬ ɧɚɢɦɟɧɶɲɟɟ ɡɧɚɱɟɧɢɟ.
1. ɉɭɫɬɶ q = 30. ɓɟɥɤɚɟɦ ɩɨ ɩɢɤɬɨɝɪɚɦɦɟ Pdwul{, ɜ ɩɨɹɜɢɜ- ɲɟɦɫɹ ɞɢɚɥɨɝɨɜɨɦ ɨɤɧɟ ɜɵɛɢɪɚɟɦ ɪɚɡɦɟɪɵ ɦɚɬɪɢɰɵ: ɬɪɢ ɫɬɪɨɤɢ ɢ ɨɞɢɧ ɫɬɨɥɛɟɰ (ɷɬɚ ɦɚɬɪɢɰɚ ɫɜɹɠɟɬ ɜɦɟɫɬɟ ɭɪɚɜɧɟɧɢɟ ɢ ɧɚɱɚɥɶɧɵɟ ɭɫɥɨɜɢɹ) ɢ ɳɟɥɤɚɟɦ ɩɨ ɤɧɨɩɤɟ RN. Ɂɚɬɟɦ ɜ ɩɟɪɜɨɣ ɫɬɪɨɤɟ ɲɚɛɥɨɧɚ ɦɚɬɪɢɰɵ ɧɚɛɢɪɚɟɦ ɭɪɚɜɧɟɧɢɟ
|00 + 30{|0 + | = 30{cos { + 31{,
ɩɪɢɱɟɦɩɪɢ ɧɚɛɨɪɟ ɲɬɪɢɯɨɜ ɩɪɢɦɟɧɹɟɦ ɬɨɥɶɤɨ ɤɥɚɜɢɲɭ ?'A (ɧɟɥɶ- ɡɹ ɩɪɢɦɟɧɹɬɶ ɤɥɚɜɢɲɭ ?"A), ɜɨ ɜɬɨɪɨɣ ɫɬɪɨɤɟ |(0) = 1 ɢ ɜ ɬɪɟɬɶɟɣ ɫɬɪɨɤɟ |0(0) = 1.
Ɍɟɩɟɪɶ ɫ ɩɨɦɨɳɶɸ ɤɨɦɚɧɞɵ Vroyh RGH + Qxphulf (ɤɭɪɫɨɪ ɧɚɯɨɞɢɬɫɹ ɜ ɩɨɥɟ ɦɚɬɪɢɰɵ) ɪɟɲɚɟɦ ɭɪɚɜɧɟɧɢɟ, ɢɫɩɨɥɶɡɭɹ ɩɪɢɛɥɢ- ɠɟɧɧɵɟ ɦɟɬɨɞɵ. SWP ɞɚɟɬ ɫɨɨɛɳɟɧɢɟ: Functions defined: |, ɬ.ɟ.
ɪɟɲɟɧɢɟ ɧɚɣɞɟɧɨ ɢ ɨ ɩ ɪ ɟ ɞ ɟ ɥ ɟ ɧ ɨ. |
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5 |
|00 + 30{|0 |
+ | = 30{cos { + 31{ |
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|(0) = 0 |
6 |
, Functions defined:|. |
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|0(0) = 2 |
8 |
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ɑɬɨɛɵ ɭɛɟɞɢɬɶɫɹ ɜ ɷɬɨɦ, ɢɫɩɨɥɶɡɭɹ ɩɢɤɬɨɝɪɚɦɦɭ Vkrz Ghilqlwlrqv, ɜɵɡɨɜɟɦ ɞɢɚɥɨɝɨɜɨɟ ɨɤɧɨ Definitions and Mappings,
ɝɞɟ ɭɜɢɞɢɦ: |, Numerical process number 1 (ɡɞɟɫɶ ɦɨɠɟɬ ɫɬɨɹɬɶ ɢ ɞɪɭɝɨɣ ɧɨɦɟɪ ɩɪɨɰɟɫɫɚ ɧɚɯɨɠɞɟɧɢɹ ɩɪɢɛɥɢɠɟɧɧɨɝɨ ɪɟɲɟɧɢɹ, ɟɫɥɢ ɪɚɧɟɟ ɩɪɢ ɪɟɞɚɤɬɢɪɨɜɚɧɢɢ ɞɨɤɭɦɟɧɬɚ ɭɠɟ ɩɪɢɦɟɧɹɥɢɫɶ ɩɪɢɛɥɢɠɟɧ- ɧɵɟ ɦɟɬɨɞɵ). ɉɪɢ ɠɟɥɚɧɢɢ ɦɨɠɧɨ ɧɚɣɬɢ ɡɧɚɱɟɧɢɟ ɪɟɲɟɧɢɹ | ɩɪɢ ɤɚɤɨɦ-ɧɢɛɭɞɶ ɡɧɚɱɟɧɢɢɚɪɝɭɦɟɧɬɚ {. ɇɚɩɪɢɦɟɪ, ɫ ɩɨɦɨɳɶɸɤɨɦɚɧɞɵ
Hydoxdwh ɧɚɯɨɞɢɦ |(1=5) = 2=4975.
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Ɂɚɬɚɛɭɥɢɪɭɟɦ ɡɧɚɱɟɧɢɹ ɪɟɲɟɧɢɹ |({). Ⱦɥɹ ɷɬɨɝɨ ɜɜɟɞɟɦ ɜɫɩɨɦɨ- ɝɚɬɟɥɶɧɭɸ ɮɭɧɤɰɢɸ j(q) = 0=1q ɢ ɨɩɪɟɞɟɥɢɦ ɟɟ ɫ ɩɨɦɨɳɶɸ ɩɢɤɬɨ- ɝɪɚɦɦɵ Qhz Ghilqlwlrq ɧɚ ɩɚɧɟɥɢ ɢɧɫɬɪɭɦɟɧɬɨɜ Frpsxwh. Ɂɚɬɟɦ ɢɫɩɨɥɶɡɭɟɦ ɤɨɦɚɧɞɭ Pdwulfhv + Iloo Pdwul{, ɤɨɬɨɪɚɹ ɨɬɤɪɵɜɚɟɬ ɞɢɚɥɨɝɨɜɨɟ ɨɤɧɨ Fill Matrix, ɝɞɟ ɜ ɩɨɥɹɯ Dimensions ɜɵɛɢɪɚɟɦ 10 ɫɬɪɨɤ ɢ 1 ɫɬɨɥɛɟɰ, ɚ ɜ ɩɨɥɟ Fill with ɜɵɛɢɪɚɟɦ Defined by function, ɩɨɫɥɟ ɱɟɝɨ ɩɨɹɜɥɹɟɬɫɹ ɩɨɞɨɤɧɨ, ɝɞɟ ɩɪɟɞɥɚɝɚɟɬɫɹ ɧɚɛɪɚɬɶ ɢɦɹ ɮɭɧɤɰɢɢ j. Ɂɚɤɪɵɜɚɟɦ ɨɤɧɨ (RN), ɢ ɧɚ ɷɤɪɚɧɟ ɩɨɹɜɥɹɟɬɫɹ ɬɚɛɥɢɰɚ ɢɡ ɞɟɫɹɬɢ ɫɬɪɨɤ. ȼɵɞɟɥɢɦ (ɡɚɤɪɚɫɢɦ) ɷɬɭ ɬɚɛɥɢɰɭ ɢ ɫ ɩɨɦɨɳɶɸ ɩɢɤɬɨɝɪɚɦɦɵ Eudfnhwv ɧɚ ɩɚɧɟɥɢ ɢɧɫɬɪɭɦɟɧɬɨɜ ɜɨɡɶɦɟɦ ɟɟ ɜ ɤɜɚɞ- ɪɚɬɧɵɟ ɫɤɨɛɤɢ.
Ɍɟɩɟɪɶ ɧɚɛɢɪɚɟɦ | (ɢɦɹ ɪɟɲɟɧɢɹ ɭɪɚɜɧɟɧɢɹ) ɩɟɪɟɞ ɨɬɤɪɵɜɚɸ- ɳɟɣɫɹ ɤɜɚɞɪɚɬɧɨɣ ɫɤɨɛɤɨɣ (ɧɟ ɡɚɛɭɞɶɬɟ ɩɨɫɬɚɜɢɬɶ ɩɟɪɟɤɥɸɱɚɬɟɥɶ (T-M) ɜ ɩɨɡɢɰɢɸ 
M 
, ɢɫɩɨɥɶɡɭɹ, ɧɚɩɪɢɦɟɪ, ɤɥɚɜɢɲɧɭɸ ɤɨɦɛɢɧɚ- ɰɢɸ ?Ctrl + MA), ɩɨɫɥɟ ɱɟɝɨ ɫ ɩɨɦɨɳɶɸ ɤɨɦɚɧɞɵ Hydoxdwh ɩɨɥɭ- ɱɚɟɦ ɬɚɛɥɢɰɭ ɡɧɚɱɟɧɢɣ ɪɟɲɟɧɢɹ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɧɚ ɢɧɬɟɪɜɚɥɟ [0; 1] ɫ ɲɚɝɨɦ k = 0=1:
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5 |
0=1 |
6 |
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5 |
0=19983 |
6 |
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5 |
{ |
|({) |
6 |
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0=1 |
0=19983 |
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0=2 |
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0=39867 |
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9 |
0=2 |
0=39867 |
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9 |
0=3 |
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9 |
0=59552 |
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0=4 |
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0=78942 |
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9 |
0=3 |
0=59552 |
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9 |
0=5 |
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9 |
0=97943 |
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9 |
0=4 |
0=78942 |
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9 |
: |
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9 |
: |
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9 |
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: |
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9 |
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: |
= |
9 |
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: |
, ɢɥɢ |
9 |
0=5 |
0=97943 |
: |
9 |
0=6 |
: |
9 |
1=1646 |
: |
9 |
:. |
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9 |
: |
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9 |
: |
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9 |
0=6 |
1=1646 |
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9 |
0=7 |
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9 |
1=3442 |
: |
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9 |
: |
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9 |
: |
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9 |
: |
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9 |
0=7 |
1=3442 |
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9 |
0=8 |
: |
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9 |
1=5174 |
: |
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9 |
: |
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9 |
: |
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9 |
: |
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9 |
0=8 |
1=5174 |
: |
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9 |
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: |
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9 |
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: |
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9 |
: |
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9 |
0=9 |
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9 |
1=6833 |
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9 |
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9 |
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9 |
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: |
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9 |
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: |
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7 |
0=9 |
1=6833 |
8 |
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1=0 |
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1=8415 |
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9 |
: |
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9 |
: |
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9 |
: |
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9 |
1=0 |
1=8415 |
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7 |
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8 |
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7 |
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8 |
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9 |
: |
ɉɨɫɥɟɞɧɟɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɩɨɥɭɱɟɧɨ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ. ɉɨ- ɫɬɚɜɢɦ ɞɜɟ ɦɚɬɪɢɰɵ ɪɹɞɨɦ ɢ ɨɛɴɟɞɢɧɢɦ ɢɯ ɜ ɨɞɧɭ ɫ ɩɨɦɨɳɶɸ ɤɨɦɚɧɞɵ Pdwulflhv + Frqfdwhqdwh. ɋɧɚɛɞɢɦ ɫɬɨɥɛɰɵ ɩɨɥɭɱɟɧɧɨɣ ɦɚɬɪɢɰɵ ɡɚɝɨɥɨɜɤɚɦɢ («ɲɚɩɤɚɦɢ»). Ⱦɥɹ ɷɬɨɝɨ ɧɚɞɨ ɞɨɛɚɜɢɬɶ ɜɜɟɪɯɭ
22
ɧɨɜɭɸ ɫɬɪɨɤɭ. ɉɨɫɬɚɜɢɦ ɤɭɪɫɨɪ ɜ ɩɨɥɟ ɦɚɬɪɢɰɵ ɢ, ɢɫɩɨɥɶɡɭɹ ɤɨɦɚɧ- ɞɭ Hglw + Lqvhuw Urzv, ɨɬɤɪɨɟɦ ɞɢɚɥɨɝɨɜɨɟ ɨɤɧɨ, ɝɞɟ ɜɵɛɢɪɚɟɦ
1 ɤɚɤ Number to Insert ɢ 1 ɤɚɤ At Position, ɩɨɫɥɟ ɱɟɝɨ ɡɚɤɪɵɜɚɟɦ ɨɤɧɨ (RN). ȼ ɩɨɹɜɢɜɲɟɣɫɹ ɫɬɪɨɤɟ ɧɚɛɢɪɚɟɦ { ɢ |({).
Ɍɨɱɧɨɟ ɪɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ i({) = sin {+cos {. Ɂɧɚɱɟɧɢɟ i(1=5), ɧɚɣɞɟɧɧɨɟ ɩɨ ɬɨɱɧɨɦɭ ɪɟɲɟɧɢɸ, ɫɨɜɩɚɞɚɟɬ ɫ ɩɪɢɛɥɢɠɟɧɧɵɦ ɡɧɚɱɟ- ɧɢɟɦ ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɱɟɬɵɪɟɯ ɰɢɮɪ ɩɨɫɥɟ ɡɚɩɹɬɨɣ (ɬɚɤ ɩɪɢɧɹɬɨ ɝɨɜɨɪɢɬɶ ɭ ɧɚɫ, ɯɨɬɹ ɧɚ ɷɤɪɚɧɟ PC ɡɚɩɹɬɚɹ ɷɬɨ ɬɨɱɤɚ). Ɉɬɦɟɬɢɦ, ɱɬɨ ɬɨɱɧɨɫɬɶ ɜɵɱɢɫɥɟɧɢɣ ɢ ɤɨɥɢɱɟɫɬɜɨ ɰɢɮɪ, ɜɵɜɨɞɢɦɵɯ ɧɚ ɷɤɪɚɧ, ɦɨɠɧɨ ɭɫɬɚɧɨɜɢɬɶ ɫ ɩɨɦɨɳɶɸ ɤɨɦɚɧɞɵ Frpsxwh + Vhwwlqjv, ɤɨɬɨ- ɪɚɹ ɨɬɤɪɵɜɚɟɬ ɞɢɚɥɨɝɨɜɨɟ ɨɤɧɨ, ɝɞɟ ɜ ɪɚɡɞɟɥɟ General ɢɦɟɸɬɫɹ ɩɨɥɹ: Digits Used in Computations ɢ Digits Used in Display. ɋɨɝɥɚɫɧɨ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɣ ɧɚɫɬɪɨɣɤɟ SWP (ɩɨ ɭɦɨɥɱɚɧɢɸ) ɩɪɢɛɥɢɠɟɧɧɵɟ ɜɵɱɢɫɥɟɧɢɹ ɩɪɨɢɡɜɨɞɹɬɫɹ ɫ 10 ɰɢɮɪɚɦɢ, ɚ ɧɚ ɷɤɪɚɧ ɜɵɜɨɞɢɬɫɹ 5 ɰɢɮɪ. ȼ ɷɬɨɦ ɞɢɚɥɨɝɨɜɨɦ ɨɤɧɟ ɩɨɥɶɡɨɜɚɬɟɥɶ ɦɨɠɟɬ ɭɫɬɚɧɨɜɢɬɶ ɧɭɠɧɨɟ ɟɦɭ ɤɨɥɢɱɟɫɬɜɨ ɰɢɮɪ ɤɚɤ ɩɪɢ ɜɵɱɢɫɥɟɧɢɹɯ, ɬɚɤ ɢ ɩɪɢ ɜɵɜɨɞɟ ɪɟɡɭɥɶɬɚɬɨɜ ɧɚ ɷɤɪɚɧ ɦɨɧɢɬɨɪɚ.
2.Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ ɝɪɚɮɢɤɚ ɧɚɛɢɪɚɟɦ ɧɚ ɧɨɜɨɣ ɫɬɪɨɤɟ (ɜ ɦɚɬɟ- ɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟ): | ɢ ɜɵɡɵɜɚɟɦ ɤɨɦɚɧɞɭ Sorw 2G + Uhfwdqjxodu (ɢɥɢ ɳɟɥɤɚɟɦ ɩɨ ɩɢɤɬɨɝɪɚɦɦɟ Sorw 2G Uhfwdqjxodu ɧɚ ɩɚɧɟɥɢ Frpsxwh). Ƚɪɚɮɢɤ ɩɨɫɬɪɨɟɧ, ɧɨ ɟɝɨ ɧɚɞɨ ɩɨɞɤɨɪɪɟɤɬɢɪɨɜɚɬɶ ɫ ɩɨɦɨɳɶɸ ɨɤɧɚ, ɜɵɡɵɜɚɟɦɨɝɨ ɩɢɤɬɨɝɪɚɦɦɨɣ Surshuwlhv, ɝɞɟ ɧɚɛɢ- ɪɚɟɦ ɨɛɥɚɫɬɶ ɢɡɦɟɧɟɧɢɹ ɞɥɹ {: { 5 [0; 5] (SWP ɧɚɫɬɪɨɟɧ ɧɚ ɢɧɬɟɪ- ɜɚɥ [ 5; 5]). ɉɨɥɭɱɚɟɦ ɧɭɠɧɵɣ ɝɪɚɮɢɤ (ɪɢɫ. 2).
3.Ⱦɥɹ ɧɚɯɨɠɞɟɧɢɹ ɢɧɬɟɪɩɨɥɹɰɢɨɧɧɨɝɨ ɦɧɨɝɨɱɥɟɧɚ ɩɨɥɭɱɢɦ ɤɨɨɪɞɢɧɚɬɵ 5 ɬɨɱɟɤ ɧɚ ɝɪɚɮɢɤɟ. Ⱦɥɹ ɷɬɨɝɨ ɩɪɨɜɟɞɟɦ ɞɜɨɣɧɨɣ ɳɟɥ- ɱɨɤ ɦɵɲɶɸ ɜ ɩɨɥɟ ɝɪɚɮɢɤɚ ɢ ɫɪɟɞɢ ɩɨɹɜɢɜɲɢɯɫɹ ɫɩɪɚɜɚ ɜɜɟɪɯɭ ɤɜɚɞɪɚɬɢɤɨɜ ɜɵɛɟɪɟɦ x,y , ɩɨɫɥɟ ɱɟɝɨ ɤɭɪɫɨɪ ɦɵɲɢ ɩɪɢɧɢɦɚɟɬ ɮɨɪɦɭ ɤɪɟɫɬɚ, ɢ ɩɨɹɜɥɹɟɬɫɹ ɨɤɧɨ Plot Coordinates, ɤɨɬɨɪɨɟ ɧɚɞɨ ɫɞɜɢɧɭɬɶ ɜ ɫɬɨɪɨɧɭ, ɱɬɨɛɵ ɨɧɨ ɧɟ ɡɚɝɨɪɚɠɢɜɚɥɨ ɝɪɚɮɢɤ ɪɟɲɟɧɢɹ |({) ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ ɭɪɚɜɧɟɧɢɹ. ɋ ɩɨɦɨɳɶɸ ɦɵɲɢ ɜɵɛɢɪɚɟɦ ɧɚ ɝɪɚɮɢɤɟ ɬɨɱɤɭ ɫ ɚɛɫɰɢɫɫɨɣ ɩɪɢɛɥɢɡɢɬɟɥɶɧɨ ɪɚɜɧɨɣ 0 (ɤɨɨɪɞɢɧɚ- ɬɵ ɬɨɱɤɢ ɜɵɫɜɟɱɢɜɚɸɬɫɹ ɜ ɞɢɚɥɨɝɨɜɨɦ ɨɤɧɟ) ɢ ɩɪɨɢɡɜɨɞɢɦ ɳɟɥɱɨɤ.
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Ɋɢɫ. 2. Ƚɪɚɮɢɤ ɪɟɲɟɧɢɹ | ɞɢɮ. ɭɪɚɜɧɟɧɢɹ
Ʉɨɨɪɞɢɧɚɬɵ ɩɟɪɜɨɣ ɬɨɱɤɢ ɩɨɹɜɥɹɸɬɫɹ ɜ ɨɤɧɟ. Ⱥɧɚɥɨɝɢɱɧɵɦ ɨɛɪɚ- ɡɨɦ ɩɨɥɭɱɚɟɦ ɤɨɨɪɞɢɧɚɬɵ ɟɳɟ 4 ɬɨɱɟɤ ɫ ɡɚɞɚɧɧɵɦɢ ɚɛɫɰɢɫɫɚɦɢ, ɩɨɫɥɟ ɱɟɝɨ ɜɵɞɟɥɹɟɦ (ɡɚɤɪɚɲɢɜɚɟɦ) ɢɯ ɫ ɩɨɦɨɳɶɸ ɤɧɨɩɤɢ Vhohfw Doo.
ɉɪɨɢɡɜɨɞɢɦ ɳɟɥɱɨɤ ɜɧɟ ɩɨɥɹ ɝɪɚɮɢɤɚ, ɱɬɨɛɵ ɨɬɦɟɧɢɬɶ ɟɝɨ ɜɵɞɟɥɟɧɢɟ, ɡɚɬɟɦ ɜ ɞɢɚɥɨɝɨɜɨɦ ɨɤɧɟ ɜɵɛɪɚɬɶ ɤɧɨɩɤɭ Sdvwh, ɩɨɫɥɟ ɱɟɝɨ ɜ ɪɟɞɚɤɬɢɪɭɟɦɨɦ ɞɨɤɭɦɟɧɬɟ ɩɨɹɜɥɹɟɬɫɹ ɦɚɬɪɢɰɚ ɫ ɤɨɨɪɞɢɧɚɬɚ- ɦɢ ɜɵɛɪɚɧɧɵɯ 5 ɬɨɱɟɤ. Ⱦɨɛɚɜɢɦ ɤ ɦɚɬɪɢɰɟ ɟɳɟ ɨɞɧɭ ɫɬɪɨɤɭ ɫ ɩɨɦɨɳɶɸ ɤɨɦɚɧɞɵ Hglw + Lqvhuw Urz(v) (ɩɪɢ ɷɬɨɦ ɬɟɤɫɬɨɜɨɣ ɤɭɪɫɨɪ ɞɨɥɠɟɧ ɧɚɯɨɞɢɬɶɫɹ ɜ ɩɨɥɟ ɦɚɬɪɢɰɵ) ɢ ɧɚɛɟɪɟɦ ɜ ɧɟɣ ɧɚɡɜɚ- ɧɢɹ ɤɨɨɪɞɢɧɚɬ (ɷɬɚ ɫɨɫɬɨɹɳɚɹ ɢɡ ɛɭɤɜɟɧɧɵɯ ɫɢɦɜɨɥɨɜ ɫɬɪɨɤɚ ɛɭɞɟɬ ɢɝɧɨɪɢɪɨɜɚɬɶɫɹ ɩɪɢ ɞɚɥɶɧɟɣɲɟɣ ɪɚɛɨɬɟ).
Ʉ ɩɨɥɭɱɟɧɧɨɣ ɦɚɬɪɢɰɟ ɩɪɢɦɟɧɹɟɦ ɤɨɦɚɧɞɭ Vwdwlvwlfv + Ilw Fxuyh wr Gdwd, ɤɨɬɨɪɚɹ ɨɬɤɪɵɜɚɟɬ ɞɢɚɥɨɝɨɜɨɟ ɨɤɧɨ, ɝɞɟ ɜɵɛɢɪɚɟɦ ɤɧɨɩɤɢ Last Column ɤɚɤ Location of Dependent Variable ɢ Polynomial of Degree, ɡɚɬɟɦ ɭɤɚɡɵɜɚɟɦ ɫɬɟɩɟɧɶ 4, ɩɨɫɥɟ ɱɟɝɨ ɡɚɤɪɵɜɚɟɦ
24
ɨɤɧɨ (RN) ɢ ɩɨɥɭɱɚɟɦ:
5 6
{|
99 0=025479 0=008814 ::
99 2=004164 2=932125 ::, Polynomial fit:
99 3=036521 3=166615 :: 7 4=007429 3=260411 8 5=002916 4=088943
| = 0=05635 + 2=5716{ 0=54854{2 0=018872{3 + 0=011769{4.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɩɨɥɭɱɟɧ ɢɫɤɨɦɵɣ ɢɧɬɟɪɩɨɥɹɰɢɨɧɧɵɣ ɦɧɨɝɨɱɥɟɧ
i({) = 0=05635+2=5716{ 0=54854{2 0=018872{3 +0=011769{4.
ȿɫɥɢ ɩɨɫɬɪɨɢɬɶ ɟɝɨ ɝɪɚɮɢɤ ɧɚ ɨɞɧɨɦ ɪɢɫɭɧɤɟ ɫ ɝɪɚɮɢɤɨɦ ɪɟɲɟɧɢɹ |({) ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ ɭɪɚɜɧɟɧɢɹ, ɬɨ ɨɧɢ ɩɨɱɬɢ ɫɨɥɶɸɬɫɹ ɜ ɨɞɧɭ ɤɪɢɜɭɸ (ɬɨɥɶɤɨ ɧɚ ɢɧɬɟɪɜɚɥɟ [0=2; 2=1] ɨɧɢ ɧɟ ɫɥɢɜɚɸɬɫɹ). ɉɨɷɬɨɦɭ ɩɪɢɛɚɜɢɦ 0.1 ɤ ɩɪɚɜɨɣ ɱɚɫɬɢ ɢɧɬɟɪɩɨɥɹɰɢɨɧɧɨɝɨ ɦɧɨɝɨɱɥɟɧɚ, ɜɵ- ɞɟɥɢɦ (ɡɚɤɪɚɫɢɦ) ɩɨɥɭɱɟɧɧɭɸ ɩɪɚɜɭɸ ɱɚɫɬɶ ɢ ɨɬɛɭɤɫɢɪɭɟɦ ɟɟ ɜ ɩɨɥɟ ɝɪɚɮɢɤɚ ɪɟɲɟɧɢɹ |({), ɝɞɟ ɨɬɩɭɫɬɢɦ ɥɟɜɭɸ ɤɧɨɩɤɭ ɦɵɲɢ. ɉɨɥɭɱɚɟɦ ɞɜɟ «ɩɚɪɚɥɥɟɥɶɧɵɟ» ɤɪɢɜɵɟ (ɪɢɫ. 3).
Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɩɪɢ ɜɵɛɨɪɟ ɛɨɥɶɲɟɝɨ ɱɢɫɥɚ ɬɨɱɟɤ ɧɚ ɝɪɚɮɢɤɟ ɪɟɲɟɧɢɹ |({) ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɥɭɱɲɟɟ ɩɪɢɛɥɢɠɟɧɢɟ ɫ ɩɨɦɨɳɶɸ ɢɧɬɟɪɩɨɥɹɰɢɨɧɧɨɝɨ ɦɧɨɝɨɱɥɟɧɚ ɛɨɥɟɟ ɜɵɫɨɤɨɣ ɫɬɟɩɟɧɢ. ɉɪɢ ɷɬɨɦ ɧɚɞɨ ɫɬɚɪɚɬɶɫɹ ɬɳɚɬɟɥɶɧɨ ɜɵɛɢɪɚɬɶ ɬɨɱɤɢ ɧɚ ɝɪɚɮɢɤɟ (ɷɬɨ ɡɚɜɢɫɢɬ ɨɬ ɦɨɧɢɬɨɪɚ, ɦɵɲɢ ɢ ɩɨɥɶɡɨɜɚɬɟɥɹ).
ɂɦɟɟɬɫɹ ɢ ɞɪɭɝɚɹ ɜɨɡɦɨɠɧɨɫɬɶ ɚɩɩɪɨɤɫɢɦɢɪɨɜɚɬɶ ɪɟɲɟɧɢɟ |({) ɩɨ ɟɝɨ ɝɪɚɮɢɤɭ. ɇɚ ɭɱɚɫɬɤɟ [0; d1], ɝɞɟ ɝɪɚɮɢɤ ɝɥɚɞɤɢɣ, ɜɵɛɢɪɚɸɬ ɩɨɱɚɳɟ, ɧɚɩɪɢɦɟɪ, 4 ɬɨɱɤɢ (ɱɬɨɛɵ ɫɬɟɩɟɧɶ ɦɧɨɝɨɱɥɟɧɚ ɧɟ ɛɵɥɚ ɛɨɥɶɲɨɣ) ɢ ɩɨ ɧɢɦ ɫɬɪɨɹɬ ɢɧɬɟɪɩɨɥɹɰɢɨɧɧɵɣ ɦɧɨɝɨɱɥɟɧ. ɇɚ ɫɥɟɞɭ- ɸɳɟɦ ɭɱɚɫɬɤɟ [d1; d2], ɝɞɟ ɝɪɚɮɢɤ ɝɥɚɞɤɢɣ, ɜɵɛɢɪɚɸɬ ɩɨɱɚɳɟ ɫɧɨɜɚ 4 ɬɨɱɤɢ, ɩɟɪɜɚɹ ɢɡ ɤɨɬɨɪɵɯ ɹɜɥɹɟɬɫɹ ɩɨɫɥɟɞɧɟɣ ɜ ɩɪɟɞɵɞɭɳɟɦ ɧɚɛɨɪɟ, ɢ ɩɨ ɧɢɦ ɫɬɪɨɹɬ ɢɧɬɟɪɩɨɥɹɰɢɨɧɧɵɣ ɦɧɨɝɨɱɥɟɧ ɢ ɬ.ɞ. ɉɨɫɥɟ ɷɬɨɝɨ ɧɚ ɛɚɡɟ ɩɨɫɬɪɨɟɧɧɵɯ ɦɧɨɝɨɱɥɟɧɨɜ ɨɩɪɟɞɟɥɹɸɬ ɮɭɧɤɰɢɸ S({) ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ.
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Ɋɢɫ. 3. Ƚɪɚɮɢɤɢ |({) ɢ i({) + 0=1
•ɇɚɛɢɪɚɸɬ ɜ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟ S({) =
•ɋ ɩɨɦɨɳɶɸ ɩɢɤɬɨɝɪɚɦɦɵ Eudfnhwv ɜɵɜɨɞɹɬ ɧɚ ɷɤɪɚɧ ɥɟɜɵɣ ɪɚɡɞɟɥɢɬɟɥɶ ɜ ɜɢɞɟ ɮɢɝɭɪɧɨɣ ɫɤɨɛɤɢ ɢ ɩɪɚɜɵɣ ɪɚɡɞɟɥɢɬɟɥɶ ɜ ɜɢɞɟ ɬɨɱɟɱɧɨɣɜɟɪɬɢɤɚɥɶɧɨɣ ɥɢɧɢɢ (ɧɟɜɢɞɢɦɨɣ ɩɪɢ ɩɪɨɫɦɨɬɪɟ ɢ ɩɟɱɚɬɢ).
•ɋ ɩɨɦɨɳɶɸ ɩɢɤɬɨɝɪɚɦɦɵ Pdwul{w ɜɵɜɨɞɹɬ ɧɚ ɷɤɪɚɧ ɲɚɛɥɨɧ ɦɚɬɪɢɰɵ (ɜ ɧɚɲɟɦ ɫɥɭɱɚɟ ɫ 3 ɫɬɪɨɤɚɦɢ ɢ ɬɪɟɦɹ ɫɬɨɥɛɰɚɦɢ).
•Ɂɚɩɨɥɧɹɟɦ ɤɥɟɬɨɱɤɢ ɦɚɬɪɢɰɵ. ɉɨɥɭɱɚɟɦ
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ɩɪɚɜɚɹ ɱɚɫɬɶ ɩɟɪɜɨɝɨ ɦɧɨɝɨɱɥɟɧɚ |
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S({) = |
ɩɪɚɜɚɹ ɱɚɫɬɶ ɜɬɨɪɨɝɨ ɦɧɨɝɨɱɥɟɧɚ |
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? ɩɪɚɜɚɹ ɱɚɫɬɶ ɬɪɟɬɶɟɝɨ ɦɧɨɝɨɱɥɟɧɚ |
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Ⱦɥɹ ɩɪɢɦɟɪɚ ɨɩɪɟɞɟɥɢɦ ɜ ɫɪɟɞɟ SWP ɫɥɟɞɭɸɳɭɸ ɮɭɧɤɰɢɸ
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S({) = = {2 li 1 { ? 2 .
4li 2 { 3
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Ʉɨɦɚɧɞɚ Hydoxdwh ɞɚɟɬ: S(0=25) = 0=25, S(1=5) = 2=25, S(3) = 4 ɢ ɬ.ɞ. Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ ɝɪɚɮɢɤɚ ɷɬɨɣ ɮɭɧɤɰɢɢ ɧɚɛɢɪɚɟɦ S ɢ ɩɪɢɦɟɧɹɟɦ ɤɨɦɚɧɞɭ Sorw 2G + Uhfwdqjxodu.
4. ɇɚɣɞɟɦ ɤɨɨɪɞɢɧɚɬɵ ɟɳɟ ɨɞɧɨɣ ɬɨɱɤɢ ɫ ɚɛɫɰɢɫɫɨɣ 1 ɧɚ ɝɪɚɮɢɤɟ ɪɟɲɟɧɢɹ (ɫɦ. ɪɢɫ. 2) ɢ ɜɫɬɚɜɢɦ ɢɯ ɜ ɦɚɬɪɢɰɭ, ɫ ɩɨɦɨɳɶɸ ɤɨɬɨɪɨɣ ɫɬɪɨɢɥɢ ɢɧɬɟɪɩɨɥɹɰɢɨɧɧɵɣ ɦɧɨɝɨɱɥɟɧ. Ʉɩɨɥɭɱɟɧɧɨɣ ɦɚɬɪɢɰɟ ɩɪɢ- ɦɟɧɹɟɦ ɤɨɦɚɧɞɭ Vwdwlvwlfv + Ilw Fxuyh wr Gdwd, ɤɨɬɨɪɚɹ ɨɬɤɪɵɜɚɟɬ ɞɢɚɥɨɝɨɜɨɟ ɨɤɧɨ, ɝɞɟ ɜɵɛɢɪɚɟɦ ɤɧɨɩɤɢ Last Column ɤɚɤ Location of Dependent Variable ɢ Multiple Regression, ɩɨɫɥɟ ɱɟɝɨ ɡɚɤɪɵɜɚɟɦ ɨɤɧɨ (RN) ɢ ɩɨɥɭɱɚɟɦ ɭɪɚɜɧɟɧɢɟ ɥɢɧɢɢ ɪɟɝɪɟɫɫɢɢ | ɧɚ {:
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, Regression is: | = 0=76304 + 0=71144{. |
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ɍɛɟɪɟɦ ɭ ɩɨɫɥɟɞɧɟɣ ɦɚɬɪɢɰɵ ɩɟɪɜɭɸ ɫɬɪɨɤɭ ɫ ɛɭɤɜɟɧɧɵɦɢ ɫɢɦɜɨɥɚɦɢ ɢ ɫ ɩɨɦɨɳɶɸ ɤɨɦɚɧɞɵ Sorw 2G Uhfwdqjxodu ɩɨɫɬɪɨɢɦ ɥɨɦɚɧɭɸ ɥɢɧɢɸ ɫ ɜɟɪɲɢɧɚɦɢ, ɤɨɨɪɞɢɧɚɬɵ ɤɨɬɨɪɵɯ ɭɤɚɡɚɧɵ ɜ ɦɚɬ- ɪɢɰɟ, ɩɨɫɥɟ ɱɟɝɨ ɩɨɞɤɨɪɪɟɤɬɢɪɭɟɦ ɩɨɥɭɱɟɧɧɵɣ ɝɪɚɮɢɤ, ɢɫɩɨɥɶɡɭɹ ɩɢɤɬɨɝɪɚɦɦɭ Surshuwlhv. ȼ ɪɚɡɞɟɥɟ Items Plotted ɜɵɛɢɪɚɟɦ Point ɤɚɤ Plot Style, Circle ɤɚɤ Point Marker ɢ ɡɚɤɪɵɜɚɟɦ ɞɢɚɥɨɝɨɜɨɟ ɨɤɧɨ
(RN).
ȼɵɞɟɥɹɟɦ ɩɪɚɜɭɸ ɱɚɫɬɶ ɭɪɚɜɧɟɧɢɹ ɥɢɧɢɢ ɪɟɝɪɟɫɫɢɢ ɢ ɛɭɤɫɢɪɭ- ɟɦ ɟɟ ɜ ɩɨɥɟ ɩɨɫɥɟɞɧɟɝɨ ɝɪɚɮɢɤɚ. ɋɧɨɜɚ ɢɫɩɨɥɶɡɭɟɦ ɩɢɤɬɨɝɪɚɦɦɭ
Surshuwlhv. ȼ ɪɚɡɞɟɥɟ Items Plotted ɜɵɛɢɪɚɟɦ 2 ɤɚɤ Item Number (ɫɩɪɚɜɚ ɜɜɟɪɯɭ), Line ɤɚɤ Plot Style, ɳɟɥɤɚɟɦ ɩɨ ɩɪɹɦɨɭɝɨɥɶɧɢɤɭ Variables and Intervals, ɜɵɛɢɪɚɟɦ ɨɛɥɚɫɬɶ ɢɡɦɟɧɟɧɢɹ ɞɥɹ { ɨɬ 0=2 ɞɨ 5=2 ɢ ɡɚɤɪɵɜɚɟɦ ɞɢɚɥɨɝɨɜɨɟ ɨɤɧɨ (ɞɜɚ ɪɚɡɚ RN). ɉɨɥɭɱɚɟɦ ɧɚ ɨɞɧɨɦ ɪɢɫɭɧɤɟ ɥɢɧɢɸ ɪɟɝɪɟɫɫɢɢ ɢ ɬɨɱɤɢ, ɩɨ ɤɨɬɨɪɵɦ ɨɧɚ ɩɨɫɬɪɨɟɧɚ
(ɪɢɫ. 4).
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Ɋɢɫ. 4. Ƚɪɚɮɢɤ ɥɢɧɢɢ ɪɟɝɪɟɫɫɢɢ | ɧɚ {
13. Ʌɚɛɨɪɚɬɨɪɧɚɹ ɪɚɛɨɬɚ 7. Ɇɚɬɪɢɱɧɵɟ ɢɝɪɵ
1) ɂɦɟɟɬɫɹ ɬɪɢ ɫɢɫɬɟɦɵ ɩɪɨɬɢɜɨɜɨɡɞɭɲɧɨɣ ɨɛɨɪɨɧɵ D1, D2 ɢ D3. ɉɪɨɬɢɜɧɢɤ ɩɪɢɦɟɧɹɟɬ ɬɪɢ ɬɢɩɚ ɛɨɦɛɚɪɞɢɪɨɜɳɢɤɨɜ E1, E2 ɢ E3. ɋɢɫɬɟɦɚ D1 ɫɛɢɜɚɟɬ ɫɚɦɨɥɟɬɵ ɬɢɩɚ E1, E2 ɢ E3 ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɫ ɜɟɪɨɹɬɧɨɫɬɹɦɢ 0=1 + 0=1(Q mod 8), 0=6, 0=3; ɫɢɫɬɟɦɚ D2 ɫɛɢɜɚɟɬ ɫɚɦɨɥɟɬɵ ɬɢɩɚ E1, E2 ɢ E3 ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɫ ɜɟɪɨɹɬɧɨɫɬɹɦɢ 0=3, 0=3+0=1(Q mod 5), 0=5; ɫɢɫɬɟɦɚ D3 ɫɛɢɜɚɟɬ ɫɚɦɨɥɟɬɵ ɬɢɩɚ E1, E2 ɢE3 ɫɨɨɬɜɟɬɫɬɜɟɧ- ɧɨ ɫ ɜɟɪɨɹɬɧɨɫɬɹɦɢ 0=9, 0=5, 0=6 + 0=1(Q mod 2) (Q ɧɨɦɟɪ ɫɬɭɞɟɧɬɚ ɩɨ ɫɩɢɫɤɭ ɝɪɭɩɩɵ). ɇɚɣɬɢ ɧɢɠɧɸɸ ɢ ɜɟɪɯɧɸɸ ɰɟɧɵ ɢɝɪɵ.
2) ɇɚɣɬɢ ɨɩɬɢɦɚɥɶɧɭɸ ɫɬɪɚɬɟɝɢɸ ¯ ɩɪɢɦɟɧɟɧɢɹ ɫɢɫɬɟɦ ɩɪɨ-
VD
ɬɢɜɨɜɨɡɞɭɲɧɨɣ ɨɛɨɪɨɧɵ ɢ ɨɩɬɢɦɚɥɶɧɭɸ ɰɟɧɭ ɢɝɪɵ y¯.
3) ɇɚɣɬɢ ɨɩɬɢɦɚɥɶɧɭɸ ɫɬɪɚɬɟɝɢɸ ¯ ɩɪɢɦɟɧɟɧɢɹ ɪɚɡɥɢɱɧɵɯ
VE
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ɬɢɩɨɜ ɛɨɦɛɚɪɞɢɪɨɜɳɢɤɨɜ.
14.ɉɪɢɦɟɪ ɜɵɩɨɥɧɟɧɢɹ ɪɚɛɨɬɵ 7
1.ɉɭɫɬɶ ɬɚɛɥɢɰɚ ɢɝɪɵ ɢɦɟɟɬ ɜɢɞ
E1 
E2 
E3 
D1 
0=9 
0=4 
0=2 
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D2 0=3 0=6 0=8
D3 
0=5 
0=7 
0=2
Ɍɨɝɞɚ ɦɚɬɪɢɰɚ ɢɝɪɵ d ɞɥɹ ɫɢɫɬɟɦɵ ɨɛɨɪɨɧɵ ɢɦɟɟɬ ɜɢɞ
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0=9 0=4 0=2
d = 7 0=3 0=6 0=8 8. 0=5 0=7 0=2
ɋ ɩɨɦɨɳɶɸ ɤɨɦɚɧɞɵ Ghilqlwlrqv + Qhz Ghilqlwlrq ɨɩɪɟɞɟ-
ɥɢɦ ɷɬɭ ɦɚɬɪɢɰɭ ɜ ɫɪɟɞɟ SWP ɢ, ɢɫɩɨɥɶɡɭɹ ɤɨɦɚɧɞɭ Hydoxdwh> ɧɚɣɞɟɦ ɧɢɠɧɸɸ ɰɟɧɭ ɢɝɪɵ ɢ ɜɟɪɯɧɸɸ ɰɟɧɭ ɢɝɪɵ .
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min dl>m = 0=3, |
= min max dl>m = 0=7. |
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1$l$3 1$m$3 |
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1$m$3 1$l$3 |
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2. Ɋɚɫɫɦɨɬɪɢɦ ɫɬɪɚɬɟɝɢɢ VD ɞɥɹ ɫɢɫɬɟɦ ɨɛɨɪɨɧɵ |
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VD = µ s11 |
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s33 ¶ , |
ɝɞɟ S = |
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ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɱɚɫɬɨɬɵ ɩɪɢɦɟɧɟɧɢɹ ɤɚɠɞɨɣ |
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ɢɡ ɫɢɫɬɟɦ£ |
ɨɛɨɪɨɧɵ1 2 , |
3s1¤+ s2 + s3 = 1. |
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ɂɡɜɟɫɬɧɨ, ɱɬɨ ɧɚɯɨɠɞɟɧɢɟ ɨɩɬɢɦɚɥɶɧɨɣ ɫɬɪɚɬɟɝɢɢ ɫɜɨɞɢɬɫɹ ɤ |
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ɪɟɲɟɧɢɸ ɡɚɞɚɱɢ ɥɢɧɟɣɧɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɫ ɦɚɬɪɢɰɟɣ dW |
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d11{1 + d21{2 + d31{3 > 1, |
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; d12{1 + d22{2 + d32{3 > 1, |
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A d13{1 + d23{2 + d33{3 > 1, |
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ɝɞɟ {l = |
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ɢ y ɰɟɧɚ ɢɝɪɵ. Ɍɚɤ ɤɚɤ } = |
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ɧɚɞɨ ɪɟɲɚɬɶ ɡɚɞɚɱɭ ɧɚ ɦɢɧɢɦɭɦ, ɱɬɨɛɵ ɢɦɟɬɶ ɦɚɤɫɢɦɚɥɶɧɭɸ ɰɟɧɭ ɢɝɪɵ y (ɫɬɨɪɨɧɚ D ɢɝɪɚɟɬ ɧɚ ɦɚɤɫɢɦɭɦ).
ɂɬɚɤ, ɜɵɡɵɜɚɟɦ ɲɚɛɥɨɧ 7×1-ɦɚɬɪɢɰɵ ɢ ɜ ɩɟɪɜɨɣ ɫɬɪɨɤɟ ɧɚɛɢ- ɪɚɟɦ ɜɵɪɚɠɟɧɢɟ ɩɪɚɜɨɣ ɱɚɫɬɢ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ }, ɚ ɜ ɨɫɬɚɥɶɧɵɯ ɫɬɪɨɤɚɯ ɨɝɪɚɧɢɱɟɧɢɹ, ɜɤɥɸɱɚɹ ɧɟɨɬɪɢɰɚɬɟɥɶɧɨɫɬɶ ɧɟɢɡɜɟɫɬɧɵɯ.
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ɉɪɢɦɟɧɹɹ ɤɨɦɚɧɞɭ Vlpsoh{ + Plqlpl}h, ɩɨɥɭɱɚɟɦ |
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Minimum is at: ½{3 = |
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ɇɚɯɨɞɢɦ }min = }¯ = {1 + {2 |
+ {3 |
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. ɉɨɥɭɱɚɟɦ, ɱɬɨ |
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ɨɩɬɢɦɚɥɶɧɚɹ ɰɟɧɚ ɢɝɪɵ y¯ = |
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ɚ ɫɥɟɞɨɜɚɬɟɥɶɧɨ, s¯1 = {1y¯ = |
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. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɨɥɭɱɟɧɵ |
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ɢ ɨɩɬɢɦɚɥɶɧɚɹ ɰɟɧɚ ɢɝɪɵ y¯ ɞɥɹ ɫɢɫɬɟɦ |
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ɨɩɬɢɦɚɥɶɧɚɹ ɫɬɪɚɬɟɝɢɹ VD |
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ɨɛɨɪɨɧɵ: |
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V¯D = Ã |
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3. Ɋɚɫɫɦɨɬɪɢɦ ɫɬɪɚɬɟɝɢɢ VE ɞɥɹ ɛɨɦɛɚɪɞɢɪɨɜɳɢɤɨɜ |
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VE = µ t11 |
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t22 |
t33 |
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