Планирование эксперимента. Учебное пособие-1
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ɉɪɢ ɷɬɨɦ¦xiu ɞɥɹ ɪɚɡɧɵɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɪɚɡɧɨɦɭ ɩɨ
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ɞɥɹ ɷɮɮɟɤɬɨɜ ɞɜɨɣɧɵɯ ɜɡɚɢɦɨɞɟɣɫɬɜɢɣb jl |
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ɞɥɹ ɤɜɚɞɪɚɬɢɱɧɵɯ ɷɮɮɟɤɬɨɜ ɬ ɟ ɞɥɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɩɪɢx j a
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ȼ ɫɥɭɱɚɟ ɈɐɄɉ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ ɫɜɨɣɫɬɜɨ ɧɨɪɦɢɪɨɜɚɧɧɨɫɬɢ ɧɟ ɫɨɛɥɸɞɚ
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ɟɬɫɹ ɬɚɤ ɤɚɤ¦xiu z N ɞɥɹ ɜɫɟɯ ɫɬɨɥɛɰɨɜ ɤɪɨɦɟ ɩɟɪɜɨɝɨ ɗɬɨ ɡɧɚɱɢɬ ɱɬɨ ɬɨɱ
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ɧɨɫɬɶ ɨɰɟɧɤɢ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɪɟɝɪɟɫɫɢɢ ɞɥɹ ɪɚɡɧɵɯ ɝɪɭɩɩ ɧɟɨɞɢɧɚɤɨɜɚɹ
Ɋɨɬɚɬɚɛɟɥɶɧɵɟ ɐɄɉ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ
ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɞɥɹ ɩɥɚɧɨɜ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ ɬɨɱɧɨɫɬɶ ɨɰɟɧɢɜɚɧɢɹ ɮɭɧɤɰɢɢ
ɨɬɤɥɢɤɚ ɹɜɥɹɟɬɫɹ ɧɟɨɞɢɧɚɤɨɜɨɣ ɩɨ ɪɚɡɥɢɱɧɵɦ ɧɚɩɪɚɜɥɟɧɢɹɦ ɮɚɤɬɨɪɧɨɝɨ ɩɪɨ ɫɬɪɚɧɫɬɜɚɄɚɤɩɪɚɜɢɥɨɡɚɪɚɧɟɟɧɟɢɡɜɟɫɬɧɨɜɤɚɤɢɯɬɨɱɤɚɯɮɚɤɬɨɪɧɨɝɨɩɪɨ ɫɬɪɚɧɫɬɜɚ ɦɨɠɟɬ ɜɨɡɧɢɤɧɭɬɶ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɧɚɯɨɠɞɟɧɢɹ ɨɰɟɧɨɤ ɮɭɧɤɰɢɢ
ɨɬɤɥɢɤɚ ɗɬɨ ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ ɜɵɡɵɜɚɟɬ ɨɩɪɟɞɟɥɟɧɧɵɟ ɡɚɬɪɭɞɧɟɧɢɹ ɩɪɢ ɢɫɫɥɟɞɨ ɜɚɧɢɢɊɨɬɚɬɚɛɟɥɶɧɵɟɩɥɚɧɵɭɫɬɪɚɧɹɸɬɞɚɧɧɨɟ ɡɚɬɪɭɞɧɟɧɢɟɢɨɛɟɫɩɟɱɢɜɚɸɬ ɨɞɢɧɚɤɨɜɭɸ ɬɨɱɧɨɫɬɶ ɮɭɧɤɰɢɢ ɨɬɤɥɢɤɚ ɩɨ ɪɚɡɥɢɱɧɵɦ ɧɚɩɪɚɜɥɟɧɢɹɦ ɮɚɤɬɨɪɧɨ ɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ
Ɋɨɬɚɬɚɛɟɥɶɧɵɟ ɩɥɚɧɵ ± ɷɬɨ ɩɥɚɧɵ ɭ ɤɨɬɨɪɵɯ ɬɨɱɤɢ ɩɥɚɧɚ ɪɚɫɩɨɥɚɝɚɸɬɫɹ
ɧɚ ɨɤɪɭɠɧɨɫɬɹɯ ɫɮɟɪɚɯ ɝɢɩɟɪɫɮɟɪɚɯ ɍ ɪɨɬɚɬɚɛɟɥɶɧɨɝɨ ɩɥɚɧɚ ɩɟɪɜɨɝɨ ɩɨɪɹɞ
ɤɚ ɬɨɱɤɢ ɩɥɚɧɚ ɪɚɫɩɨɥɚɝɚɸɬɫɹ ɧɚ ɨɞɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɫɮɟɪɟ ɝɢɩɟɪɫɮɟɪɟ ɫ ɪɚ ɞɢɭɫɨɦR
n
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ɝɞɟ |
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± ɧɨɦɟɪ ɬɨɱɤɢ ɩɥɚɧɚ |
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ȼ ɬɚɤɨɦ ɫɥɭɱɚɟ ɬɨɱɧɨɫɬɶ ɨɰɟɧɢɜɚɧɢɹ ɮɭɧɤɰɢɢ ɨɬɤɥɢɤɚ ɩɨ ɥɸɛɨɦɭ ɧɚɩɪɚɜ
ɥɟɧɢɸ ɮɚɤɬɨɪɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɞɥɹ ɜɫɟɯ ɬɨɱɟɤ ɩɥɚɧɚ ɨɞɢɧɚɤɨɜɚɹ
Ɋɨɬɚɬɚɛɟɥɶɧɵɣ ɩɥɚɧ ɦɨɠɟɬ ɛɵɬɶ ɫɢɦɦɟɬɪɢɱɧɵɦ ɤɨɝɞɚ ɬɨɱɤɢ ɩɥɚɧɚ ɪɚɫɩɨ ɥɚɝɚɸɬɫɹ ɫɢɦɦɟɬɪɢɱɧɨ Ɋɚɫɫɦɨɬɪɟɧɧɵɣ ɪɚɧɟɟ ɩɥɚɧ ɉɎɗ n ± ɪɨɬɚɬɚɛɟɥɶɧɵɣ ɫɢɦɦɟɬɪɢɱɧɵɣ ɩɥɚɧ ɩɟɪɜɨɝɨ ɩɨɪɹɞɤɚ
ɍ ɪɨɬɚɬɚɛɟɥɶɧɵɯ ɩɥɚɧɨɜ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ ɬɨɱɤɢ ɩɥɚɧɚ ɪɚɫɩɨɥɚɝɚɸɬɫɹ ɧɚ ɞɜɭɯ ɤɨɧɰɟɧɬɪɢɱɟɫɤɢɯ ɝɢɩɟɪɫɮɟɪɚɯ ɫ ɪɚɞɢɭɫɚɦɢR ɢR ȼ ɬɚɤɢɯ ɩɥɚɧɚɯ
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¦xiv |
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ȼɬɨɪɚɹ ɫɮɟɪɚ ɜɵɪɨɠɞɟɧɧɚɹ ɢR |
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Ɋɚɫɫɦɨɬɪɟɧɧɵɣ ɪɚɧɟɟ ɨɪɬɨɝɨɧɚɥɶɧɵɣ ɰɟɧɬɪɚɥɶɧɨ ɤɨɦɩɨɡɢɰɢɨɧɧɵɣ ɩɥɚɧ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ ɈɐɄɉ ɧɟ ɹɜɥɹɟɬɫɹ ɪɨɬɚɬɚɛɟɥɶɧɵɦ ɩɥɚɧɨɦ ɬɚɤ ɤɚɤ ɟɝɨ ɬɨɱɤɢ ɥɟɠɚɬ ɧɚ ɬɪɟɯ ɤɨɧɰɟɧɬɪɢɱɟɫɤɢɯ ɨɤɪɭɠɧɨɫɬɹɯ ɫɮɟɪɚɯ ɝɢɩɟɪɫɮɟɪɚɯ ɉɪɢ n ɷɬɨ ɨɱɟɜɢɞɧɨ ɢɡ ɪɢɫ ©ɡɜɟɡɞɧɵɟª ɬɨɱɤɢ ɩɥɚɧɚ ɢ ɬɨɱɤɢ ɩɥɚɧɚ ɉɎɗ ɥɟɠɚɬ ɧɚ ɪɚɡɧɵɯ ɨɤɪɭɠɧɨɫɬɹɯ ɚ ɬɪɟɬɶɹ ɨɤɪɭɠɧɨɫɬɶ ɜɵɪɨɠɞɟɧɧɚɹ ± ɰɟɧɬɪ ɩɥɚɧɚ
ɊɢɫɊɚɫɩɨɥɨɠɟɧɢɟ ɬɨɱɟɤ ɈɐɄɉ ɧɚ ɬɪɟɯ ɨɤɪɭɠɧɨɫɬɹɯ ɩɪɢn
Ɋɨɬɚɬɚɛɟɥɶɧɵɣ ɩɥɚɧ ɦɨɠɟɬ ɛɵɬɶ ɨɪɬɨɝɨɧɚɥɶɧɵɦ ɟɫɥɢ ɜɵɩɨɥɧɹɟɬɫɹ ɭɫɥɨ
ɜɢɟ
N
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ɝɞɟi m j m i z j ± ɧɨɦɟɪɚ ɫɬɨɥɛɰɨɜ ɩɥɚɧɚ
Ɋɨɬɚɬɚɛɟɥɶɧɵɣ ɨɪɬɨɝɨɧɚɥɶɧɵɣ
ɰɟɧɬɪɚɥɶɧɨ ɤɨɦɩɨɡɢɰɢɨɧɧɵɣ ɩɥɚɧ
Ɋɨɬɚɬɚɛɟɥɶɧɵɣ ɨɪɬɨɝɨɧɚɥɶɧɵɣ ɰɟɧɬɪɚɥɶɧɨ ɤɨɦɩɨɡɢɰɢɨɧɧɵɣ ɩɥɚɧ ɊɈɐɄɉ ɫɬɪɨɢɬɫɹ ɚɧɚɥɨɝɢɱɧɨ ɪɚɫɫɦɨɬɪɟɧɧɨɦɭ ɪɚɧɟɟ ɈɐɄɉ Ʉ ɢɫɩɨɥɶɡɨɜɚɧ ɧɨɦɭ ɜ ɤɚɱɟɫɬɜɟ ɹɞɪɚ ɩɥɚɧɭ ɉɎɗ n ɞɨɛɚɜɥɹɸɬɫɹ ©ɡɜɟɡɞɧɵɟª ɬɨɱɤɢ ± ɩɨ ɞɜɟ ɧɚ ɤɚɠɞɵɣ ɮɚɤɬɨɪ ɢ ɧɟɫɤɨɥɶɤɨ ɬɨɱɟɤ ɜ ɰɟɧɬɪɟ ɩɥɚɧɚ ©Ɂɜɟɡɞɧɵɟª ɬɨɱɤɢ ɞɨɥɠɧɵ ɪɚɫɩɨɥɚɝɚɬɶɫɹ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɝɢɩɟɪɫɮɟɪɵ ɫ ɪɚɞɢɭɫɨɦ R ɧɚ ɤɨɬɨɪɨɣ ɥɟɠɚɬ ɢɬɨɱɤɢɩɥɚɧɚ ɉɎɗ n ɬɨɟɫɬɶɜɟɥɢɱɢɧɚɩɥɟɱɚ©ɡɜɟɡɞɧɵɯªɬɨɱɟɤ D ɞɨɥɠ ɧɚ ɪɚɜɧɹɬɶɫɹ ɪɚɞɢɭɫɭR ɗɬɨ ɦɨɠɟɬ ɛɵɬɶ ɨɛɟɫɩɟɱɟɧɨ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɭɫɥɨɜɢɹ ɨɪɬɨɝɨɧɚɥɶɧɨɫɬɢ ɢ ɬɨɥɶɤɨ ɩɪɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɦ ɜɵɛɨɪɟ ɱɢɫɥɚ ɧɚɛɥɸɞɟɧɢɣ ɜ ɰɟɧɬɪɚɥɶɧɨɣ ɧɭɥɟɜɨɣ ɬɨɱɤɟ ɩɥɚɧɚ n Ⱦɥɹ ɊɈɐɄɉ n ɡɚɜɢɫɢɬ ɨɬ ɱɢɫɥɚ ɮɚɤɬɨɪɨɜnɇɚɩɨɦɧɢɦ ɱɬɨ ɜ ɈɐɄɉn ɞɥɹ ɥɸɛɨɝɨ ɱɢɫɥɚ ɮɚɤɬɨɪɨɜn
Ɋɚɞɢɭɫ ɫɮɟɪɵ ɧɚ ɤɨɬɨɪɨɣ ɥɟɠɚɬ ɬɨɱɤɢ ɩɥɚɧɚ ɉɎɗ n ɩɪɢ ɞɜɭɯ ɭɪɨɜɧɹɯ ɜɚɪɶɢɪɨɜɚɧɢɹ ɮɚɤɬɨɪɨɜ ɫ ɞɢɚɩɚɡɨɧɨɦ ɨɬ ± ɞɨ ɩɪɟɞɫɬɚɜɥɟɧ ɧɚ ɪɢɫ
Ɍɚɤ ɩɪɢn R |
ɪɢɫɚ |
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ɩɪɢn |
R |
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ɪɢɫɛ |
ɩɪɢn |
R |
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ɪɢɫɜ |
ɚ |
ɛ |
ɜ |
ɊɢɫɊɚɞɢɭɫ ɨɤɪɭɠɧɨɫɬɢ ɫɮɟɪɵ ɧɚ ɤɨɬɨɪɨɣ ɥɟɠɚɬ ɬɨɱɤɢ ɩɥɚɧɚ ɉɎɗn ɩɪɢ ɞɢɚɩɚɡɨɧɟ ɜɚɪɶɢɪɨɜɚɧɢɹ ɮɚɤɬɨɪɨɜ ɨɬ ± ɞɨ
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɩɪɢ ɩɨɫɬɪɨɟɧɢɢ ɊɈɐɄɉ ɫ ɹɞɪɨɦ ɢɡ ɩɥɚɧɚ ɉɎɗ n ɩɥɟɱɨ ©ɡɜɟɡɞɧɵɯª ɬɨɱɟɤ ɨɩɪɟɞɟɥɹɟɬɫɹ ɱɢɫɥɨɦ ɮɚɤɬɨɪɨɜ
D
n
ɊɚɧɧɟɟɩɪɢɨɩɪɟɞɟɥɟɧɢɢɩɚɪɚɦɟɬɪɨɜɈɐɄɉɜɬɨɪɨɝɨɩɨɪɹɞɤɚɫɹɞɪɨɦɢɡ ɩɥɚɧɚ ɉɎɗnɛɵɥɨ ɩɨɥɭɱɟɧɨ ɩɥɟɱɨ ©ɡɜɟɡɞɧɵɯª ɬɨɱɟɤ
DNN N
ɢ ɤɨɧɫɬɚɧɬɚ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɷɥɟɦɟɧɬɨɜ ɫɬɨɥɛɰɨɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɤɜɚɞɪɚɬɚɦ
ɮɚɤɬɨɪɨɜ
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a |
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ɝɞɟN |
n ± ɱɢɫɥɨ ɬɨɱɟɤ ɩɥɚɧɚ ɉɎɗ |
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N |
N n n ± ɨɛɳɟɟ ɱɢɫɥɨ ɬɨɱɟɤ ɤɨɦɩɨɡɢɰɢɨɧɧɨɝɨ ɩɥɚɧɚ ɜɬɨɪɨɝɨ ɩɨ |
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ɪɹɞɤɚ ɩɪɢ ɷɬɨɦ ɱɢɫɥɨ ɬɨɱɟɤ ɜ ɰɟɧɬɪɟ ɩɥɚɧɚ ɤɚɤ ɩɪɚɜɢɥɨ ɪɚɜɧɨn
ȼ ɊɈɐɄɉ ɱɢɫɥɨ ɬɨɱɟɤ ɜ ɰɟɧɬɪɟ ɩɥɚɧɚn ɞɨɥɠɧɨ ɛɵɬɶ ɫɬɪɨɝɨ ɨɩɪɟɞɟɥɟɧ ɧɵɦ ɢ ɡɚɜɢɫɢɬ ɨɬ ɱɢɫɥɚ ɮɚɤɬɨɪɨɜ
n |
n |
n |
n |
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ɗɬɨ ɱɢɫɥɨ ɩɨɥɭɱɚɟɬɫɹ ɢɡ ɫɨɨɬɧɨɲɟɧɢɣ
n NN N ɢN N n n
ȿɫɥɢ n ɨɤɚɡɚɥɨɫɶ ɧɟ ɰɟɥɨɟ ɬɨ ɩɪɢ ɩɪɚɤɬɢɱɟɫɤɨɦ ɩɨɫɬɪɨɟɧɢɢ ɩɥɚɧɚ ɟɝɨ ɨɤɪɭɝɥɹɸɬ ɞɨ ɰɟɥɨɝɨ ɧɨ ɬɨɝɞɚ ɩɥɚɧ ɩɟɪɟɫɬɚɟɬ ɛɵɬɶ ɨɪɬɨɝɨɧɚɥɶɧɵɦ
ɉɚɪɚɦɟɬɪɵ ɊɈɐɄɉ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɱɢɫɥɚ ɮɚɤɬɨɪɨɜ ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥɢ
ɰɟ
Ɍ ɚ ɛ ɥ ɢ ɰ ɚ
ɉɚɪɚɦɟɬɪɵ ɊɈɐɄɉ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɱɢɫɥɚ ɮɚɤɬɨɪɨɜ
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ɉɪɢɦɟɪ. ɉɨɫɬɪɨɢɬɶ ɪɨɬɚɬɚɛɟɥɶɧɵɣ ɨɪɬɨɝɨɧɚɥɶɧɵɣ ɰɟɧɬɪɚɥɶɧɵɣ ɤɨɦɩɨɡɢ |
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ɰɢɨɧɧɵɣ ɩɥɚɧ ɞɥɹn |
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ɉɚɪɚɦɟɬɪɵ ɩɥɚɧɚ |
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ɊɈɐɄɉ ɞɥɹn |
ɩɪɟɞɫɬɚɜɥɟɧ ɜ ɬɚɛɥɢɰɟ |
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ɂɫɩɨɥɶɡɭɟɦ ɪɚɫɫɦɨɬɪɟɧɧɵɣ ɪɚɧɟɟ ɩɥɚɧ ɈɐɄɉ ɬɚɛɥɢɰɚ ɢ ɫ ɭɱɟɬɨɦ
ɩɪɢɜɟɞɟɧɧɵɯ ɜɵɲɟ ɩɚɪɚɦɟɬɪɨɜ ɊɈɐɄɉ ɜ ɱɚɫɬɧɨɫɬɢ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɱɢɫɥɚ ɨɩɵ ɬɨɜ ɜ ɰɟɧɬɪɟ ɩɥɚɧɚ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟn ɞɨɛɚɜɥɹɟɦ ɫɬɪɨɤɢ ±
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Ɍ ɚ ɛ ɥ ɢ ɰ ɚ |
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ɊɈɐɄɉ ɞɥɹn |
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ɉɥɚɧ |
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ɉɎɗ |
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©Ɂɜɟɡɞɧɵɣª |
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ɐɟɧɬɪ ɩɥɚɧɚ |
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ɇɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɩɪɨɜɨɞɢɬɶ ɜɨɫɟɦɶ ɪɚɡ ɬɨɱɤɢ ɫ ɩɨ ɨɩɵɬɵ ɜ ɰɟɧɬ ɪɟɩɥɚɧɚɄɚɤɩɪɚɜɢɥɨɞɨɫɬɚɬɨɱɧɨɩɪɨɜɟɫɬɢɷɬɨɬɨɩɵɬɨɞɢɧɪɚɡɢ ɡɚɩɢɫɚɬɶ ɪɟɡɭɥɶɬɚɬɜɨɜɫɟɜɨɫɟɦɶɫɬɪɨɤɋɬɪɨɤɢɫɨɤɪɚɳɚɬɶɧɟɥɶɡɹɬɚɤɤɚɤɧɚɪɭɲɚɟɬ ɫɹ ɫɜɨɣɫɬɜɨ ɨɪɬɨɝɨɧɚɥɶɧɨɫɬɢ ɢ ɤɨɷɮɮɢɰɢɟɧɬɵ ɩɨɥɢɧɨɦɚ ɛɭɞɭɬ ɨɩɪɟɞɟɥɟɧɵ ɧɟ ɜɟɪɧɨ
Ʉɨɷɮɮɢɰɢɟɧɬɵ ɤɜɚɞɪɚɬɢɱɧɨɝɨ ɩɨɥɢɧɨɦɚ ɪɚɫɫɱɢɬɚɸɬɫɹ ɤɚɤ ɢ ɪɚɧɟɟ
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ɉɨɥɢɧɨɦ ɩɪɢɧɢɦɚɟɬ ɜɢɞ
yɊɈɐɄɉ b b x b x b x x b x a b x a |
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Ɋɚɫɫɱɢɬɚɧɧɵɟ ɡɧɚɱɟɧɢɹ ɮɭɧɤɰɢɢ ɢ ɪɚɫɯɨɠɞɟɧɢɹ ɫ ɨɩɵɬɧɵɦɢ ɞɚɧɧɵɦɢ ɩɪɟɞɫɬɚɜɥɟɧɵ ɜ ɩɨɫɥɟɞɧɟɦ ɢ ɩɪɟɞɩɨɫɥɟɞɧɟɦ ɫɬɨɥɛɰɚɯ ɩɥɚɧɚ ɬɚɛɥɢɰɚ
Ɋɚɧɟɟ ɞɥɹ ɈɐɄɉ ɩɪɢ ɧɟɫɤɨɥɶɤɨ ɨɬɥɢɱɚɸɳɟɣɫɹ ɩɨɜɟɪɯɧɨɫɬɢ ɮɭɧɤɰɢɢ ɛɵɥ
ɩɨɥɭɱɟɧ ɛɥɢɡɤɢɣ ɩɨɥɢɧɨɦ ɜ ɜɢɞɟ
yɈɐɄɉ x x x x x x
Ⱦɥɹ n ɱɢɫɥɨ ɱɥɟɧɨɜ ɤɜɚɞɪɚɬɢɱɧɨɝɨ ɩɨɥɢɧɨɦɚ ɫɨɫɬɚɜɥɹɟɬ ɲɟɫɬɶ ȼ ɈɐɄɉ ɢ ɊɈɐɄɉ ɧɟɨɛɯɨɞɢɦɨ ɩɪɨɜɟɫɬɢ ɞɟɜɹɬɶ ɨɬɥɢɱɚɸɳɢɯɫɹ ɨɩɵɬɨɜ ɩɪɢ ɩɹɬɢ ɭɪɨɜɧɹɯ ɜɚɪɶɢɪɨɜɚɧɢɹ ɮɚɤɬɨɪɨɜ ɉɨɷɬɨɦɭ ɈɐɄɉ ɢ ɊɈɐɄɉ ± ɧɟɧɚɫɵɳɟɧɧɵɟ ɩɥɚɧɵɌɚɤɨɟɱɢɫɥɨɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯɬɨɱɟɤɦɨɠɟɬɛɵɬɶɢɫɩɨɥɶɡɨɜɚɧɨɞɥɹ ɩɨɫɬɪɨɟɧɢɹ ɧɚɩɪɢɦɟɪ ɩɨɥɢɧɨɦɨɜ ɬɪɟɬɶɟɣ ɫɬɟɩɟɧɢ
ȼ ɈɐɄɉ ɢ ɊɈɐɄɉ ©ɡɜɟɡɞɧɵɟª ɬɨɱɤɢ ɨɩɪɟɞɟɥɹɟɦɵɟ ɤɚɤ
DNN N
ɩɪɢɧɢɦɚɸɬ ɡɧɚɱɟɧɢɹD ɩɪɢn ɢD ! ɩɪɢn ! ɢ ɬɚɤɢɦ ɨɛɪɚɡɨɦ ɦɨɝɭɬ ɜɵɯɨɞɢɬɶ ɡɚ ɩɪɟɞɟɥɵ ɟɞɢɧɢɱɧɨɝɨ ɝɢɩɟɪɤɭɛɚ ɢ ɟɞɢɧɢɱɧɨɝɨ ɝɢɩɟɪɲɚɪɚ Ⱦɥɹ ɜɩɢ ɫɵɜɚɧɢɹ ɩɥɚɧɚ ɜ ɨɛɥɚɫɬɶ ɟɞɢɧɢɱɧɨɝɨ ɝɢɩɟɪɲɚɪɚ ɧɟɨɛɯɨɞɢɦɨ ɢɡɦɟɧɢɬɶ ɡɧɚɱɟɧɢɹ ɮɚɤɬɨɪɨɜ ɩɭɬɟɦ ɭɦɧɨɠɟɧɢɹ ɢɯ ɧɚ ɤɨɷɮɮɢɰɢɟɧɬ
ɋn
Ɍɚɤ ɩɪɢn ɷɬɨɬ ɤɨɷɮɮɢɰɢɟɧɬ ɪɚɜɟɧ ɉɪɢ ɩɟɪɟɯɨɞɟ ɤ ɟɞɢɧɢɱɧɨɦɭ ɝɢɩɟɪɲɚɪɭɩɪɟɨɛɪɚɡɨɜɚɧɧɵɟɡɧɚɱɟɧɢɹɮɚɤɬɨɪɨɜɩɪɢ n ɞɥɹɩɥɚɧɨɜɈɐɄɉ ɢ ɊɈɐɄɉ ɩɪɟɞɫɬɚɜɥɟɧɵ ɜ ɬɚɛɥɢɰɟ
Ɍ ɚ ɛ ɥ ɢ ɰ ɚ
Ɂɧɚɱɟɧɢɟ ɮɚɤɬɨɪɨɜ ɜ ɈɐɄɉ ɢ ɊɈɐɄɉ ɩɪɢ ɩɟɪɟɯɨɞɟ ɤ ɟɞɢɧɢɱɧɨɦɭ ɝɢɩɟɪɲɚɪɭ ɩɪɢn
u |
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ȼɨɩɪɨɫɵ
ɑɟɦ ɜɵɡɜɚɧɚ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɩɟɪɟɯɨɞɚ ɤ ɩɥɚɧɚɦ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ"
ɋɤɨɥɶɤɨ ɱɥɟɧɨɜ ɢ ɧɟɢɡɜɟɫɬɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɤɚɤ ɩɪɚɜɢɥɨ ɫɨɞɟɪɠɢɬ ɩɨ ɥɢɧɨɦ ɜɬɨɪɨɣ ɫɬɟɩɟɧɢ"
ȼ ɱɟɦ ɧɟɞɨɫɬɚɬɨɤ ɩɥɚɧɨɜ ɉɎɗ n ɫ ɬɪɟɦɹ ɭɪɨɜɧɹɦɢ ɜɚɪɶɢɪɨɜɚɧɢɹ
ɮɚɤɬɨɪɨɜ ɜ ɨɬɥɢɱɢɟ ɨɬ ɩɥɚɧɨɜ ɉɎɗn "
ɋɤɨɥɶɤɨ ɭɪɨɜɧɟɣ ɜɚɪɶɢɪɨɜɚɧɢɹ ɮɚɤɬɨɪɨɜ ɜ ɰɟɧɬɪɚɥɶɧɨɦ ɤɨɦɩɨɡɢɰɢɨɧ ɧɨɦ ɩɥɚɧɟ ɐɄɉ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ"
Ɂɚɱɟɦ ɧɭɠɧɵ ɬɚɤ ɧɚɡɵɜɚɟɦɵɟ ©ɡɜɟɡɞɧɵɟª ɬɨɱɤɢ"
Ʉɚɤɨɣ ɩɥɚɧ ɧɚɡɵɜɚɟɬɫɹ ɰɟɧɬɪɚɥɶɧɵɦ"
Ʉɚɤɨɣ ɩɥɚɧ ɧɚɡɵɜɚɟɬɫɹ ɰɟɧɬɪɚɥɶɧɵɦ ɤɨɦɩɨɡɢɰɢɨɧɧɵɦ ɩɥɚɧɨɦ ɐɄɉ "
ɑɟɦɭ ɪɚɜɧɨ ɨɛɳɟɟ ɱɢɫɥɨ ɫɬɪɨɤ ɐɄɉ ɩɥɚɧɚ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ"
ɑɟɦɭ ɪɚɜɧɨ ɱɢɫɥɨ ɪɚɡɥɢɱɧɵɯ ɫɬɪɨɤ ɐɄɉ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ"
Ⱦɚɣɬɟ ɨɩɪɟɞɟɥɟɧɢɟ ɩɥɚɧɚ Ȼɨɤɫɚ
ȼ ɱɟɦ ɩɪɟɢɦɭɳɟɫɬɜɚ ɢ ɧɟɞɨɫɬɚɬɤɢ ɩɥɚɧɨɜ ɏɚɪɬɥɢ"
Ʉɚɤɨɣ ɩɥɚɧ ɧɚɡɵɜɚɟɬɫɹ ɨɪɬɨɝɨɧɚɥɶɧɵɦ ɐɄɉ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ"
ɄɚɤɨɟɬɪɟɛɨɜɚɧɢɟɞɨɥɠɧɨɜɵɩɨɥɧɹɬɶɫɹɱɬɨɛɵɐɄɉɜɬɨɪɨɝɨɩɨɪɹɞɤɚ ɛɵɥ ɨɪɬɨɝɨɧɚɥɶɧɵɦ"
ɉɨɫɬɪɨɣɬɟ ɩɥɚɧ ɈɐɄɉ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ ɞɥɹn
ȼ ɱɟɦ ɩɪɟɢɦɭɳɟɫɬɜɨ ɪɨɬɚɬɚɛɟɥɶɧɵɯ ɐɄɉ"
Ʉɚɤɨɣ ɩɥɚɧ ɧɚɡɵɜɚɟɬɫɹ ɪɨɬɚɬɚɛɟɥɶɧɵɦ ɨɪɬɨɝɨɧɚɥɶɧɵɦ ɐɄɉ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ"