Проектирование составов бетонных смесей с помощью современных информационных технологий. Монография
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Ɇɟɬɨɞɢɤɚ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɫɨɫɬɚɜɚ ɬɹɠɟɥɨɝɨ ɛɟɬɨɧɚ ɛɟɡ ɞɨɛɚɜɨɤ ɪɚɫɱɟɬɧɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɦɟɬɨɞɨɦ ɚɧɚɥɨɝɢɱɧɚ ɩɪɢɜɟɞɟɧɧɨɣ ɦɟ
ɬɨɞɢɤɟ ɢɡ ɮɨɪɦɭɥ ² ɫɥɟɞɭɟɬ ɢɫɤɥɸɱɢɬɶ ɜɟɥɢɱɢɧɭ Ⱦ
ɞ
Ⱦɚɥɟɟ ɩɪɨɢɡɜɨɞɹɬ ɩɟɪɟɪɚɫɱɟɬ ɤɨɥɢɱɟɫɬɜɚ ɡɚɩɨɥɧɢɬɟɥɟɣ ɫ ɭɱɟɬɨɦ ɢɯ ɜɥɚɠɧɨɫɬɢ ɢ ɫɜɨɣɫɬɜ ɜɜɨɞɢɦɨɣ ɯɢɦɢɱɟɫɤɨɣ ɞɨɛɚɜɤɢ ɢ ɩɟɪɟɞɚɸɬ ɫɨɫɬɚɜ ɧɚ ɩɪɨɢɡɜɨɞɫɬɜɨ > @
ǶȗȘȍȌȍȓȍȕȐȍ ȗȘȖȐȏȊȖȌșȚȊȍȕȕȖȋȖ șȖșȚȈȊȈ ȉȍȚȖȕȈ
ɇɚ ɩɪɨɢɡɜɨɞɫɬɜɟ ɱɚɫɬɨ ɩɪɢɦɟɧɹɸɬ ɩɪɢ ɢɡɝɨɬɨɜɥɟɧɢɢ ɛɟɬɨɧɚ ɜɥɚɠɧɵɟ ɡɚɩɨɥɧɢɬɟɥɢ Ʉɨɥɢɱɟɫɬɜɨ ɜɥɚɝɢ ɫɨɞɟɪɠɚɳɟɟɫɹ ɜ ɡɚɩɨɥɧɢɬɟ ɥɹɯ ɞɨɥɠɧɨ ɭɱɢɬɵɜɚɬɶɫɹ ɩɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɞɟɣɫɬɜɢɬɟɥɶɧɨɝɨ ɪɚɫɯɨɞɚ ɜɨɞɵ > @ Ⱦɥɹ ɷɬɨɝɨ ɨɩɪɟɞɟɥɹɸɬ ɫɨɞɟɪɠɚɧɢɟ ɜɨɞɵ ɜ ɩɟɫɤɟ ɢ ɳɟɛɧɟ ɩɨ ɮɨɪɦɭɥɚɦ
ȼɩ ɉWɩ |
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ȼɳ ɓWɳ |
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ɝɞɟɉ ɓ² ɤɨɥɢɱɟɫɬɜɨ ɩɟɫɤɚ ɢ ɳɟɛɧɹ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɤɝ |
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Wɩ Wɳ — ɜɥɚɠɧɨɫɬɶ ɩɟɫɤɚ ɢ ɳɟɛɧɹ |
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Ⱦɟɣɫɬɜɢɬɟɥɶɧɵɣ ɪɚɫɯɨɞ ɜɨɞɵ |
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ȼɞ ȼ íȼɩíȼɳ |
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Ʉɨɪɪɟɤɬɢɪɭɸɬ ɪɚɫɯɨɞ ɩɟɫɤɚ ɢ ɳɟɛɧɹ |
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ɉɞ |
ɉ ȼɩ |
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ɓɞ |
ɓ ȼɳ |
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ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɪɚɫɬɜɨɪɚ ɞɨɛɚɜɤɢ ɤɨɥɢɱɟɫɬɜɨ ɜɨɞɵ ɤɨɪɪɟɤɬɢ |
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ɪɭɸɬ ɫ ɭɱɟɬɨɦ ɜɨɞɵ ɧɚɯɨɞɹɳɟɣɫɹ ɜ ɪɚɫɬɜɨɪɟ ȼɵɱɢɫɥɹɸɬ ɪɚɫɯɨɞ ɞɨ
ɛɚɜɤɢ ɩɨ ɮɨɪɦɭɥɟ
Ⱦɞ |
ɐ Ⱦ |
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ɋ ɪɞ |
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ɝɞɟɐ² ɤɨɥɢɱɟɫɬɜɨ ɰɟɦɟɧɬɚ ɤɝ Ⱦ² ɤɨɥɢɱɟɫɬɜɨ ɞɨɛɚɜɤɢ ɨɬ ɦɚɫɫɵ ɰɟɦɟɧɬɚ ɋ² ɤɨɧɰɟɧɬɪɚɰɢɹ ɪɚɫɬɜɨɪɚ ɞɨɛɚɜɤɢ
ɪɞ ² ɩɥɨɬɧɨɫɬɶ ɪɚɫɬɜɨɪɚ ɞɨɛɚɜɤɢ ɝ ɫɦ
Ɉɤɨɧɱɚɬɟɥɶɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɜɨɞɵ ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ |
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ȼɞɞ ȼɞíȾɞ ɋ |
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ǸȈșȟȍȚ ȜȈȒȚȐȟȍșȒȖȋȖ ȘȈșȝȖȌȈ ȔȈȚȍȘȐȈȓȖȊ ȕȈ Ȕ ȉȍȚȖȕȈ
Ɂɧɚɹ ɩɥɨɬɧɨɫɬɶ ɩɨɥɭɱɟɧɧɨɣ ɛɟɬɨɧɧɨɣ ɫɦɟɫɢ ɢ ɪɚɫɯɨɞ ɦɚɬɟɪɢɚ ɥɨɜ ɧɚ ɩɪɨɛɧɵɣ ɡɚɦɟɫ ɨɩɪɟɞɟɥɹɸɬ ɮɚɤɬɢɱɟɫɤɢɣ ɪɚɫɯɨɞ ɦɚɬɟɪɢɚɥɨɜ ɧɚ ɦ ɛɟɬɨɧɚ ɉɥɨɬɧɨɫɬɶ ɛɟɬɨɧɧɨɣ ɫɦɟɫɢ ɪɚɜɧɚ
ɛ.ɫɦ ɐ ȼ ɉ ɓ Ⱦ
ɝɞɟɐ ȼ ɉ ɓ Ⱦ² ɪɚɫɯɨɞ ɰɟɦɟɧɬɚ ɜɨɞɵ ɩɟɫɤɚ ɳɟɛɧɹ ɞɨɛɚɜɤɢ ɫɨ ɨɬɜɟɬɫɬɜɟɧɧɨ
Ɏɚɤɬɢɱɟɫɤɢɣ ɪɚɫɯɨɞ ɦɚɬɟɪɢɚɥɨɜ ɧɚ ɦ ɛɟɬɨɧɚ ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɚɦ
ɐ |
ɐ ɛ |
ɛ.ɫɦ |
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ȼ |
ȼ ɛ |
ɛ.ɫɦ |
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ɉ ɛ |
ɛ.ɫɦ |
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ɓ |
ɓ ɛ |
ɛ.ɫɦ |
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Ⱦ ɛ |
ɛ.ɫɦ |
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ɝɞɟ ɛ² ɩɥɨɬɧɨɫɬɶ ɛɟɬɨɧɚ
ǸȈșȟȍȚ ȘȈșȝȖȌȈ ȔȈȚȍȘȐȈȓȖȊ ȕȈ ȖȌȐȕ ȏȈȔȍș ȉȍȚȖȕȖșȔȍșȐȚȍȓȧ
ɉɪɢ ɪɚɫɱɟɬɟ ɪɚɫɯɨɞɚ ɦɚɬɟɪɢɚɥɨɜ ɧɚ ɨɞɢɧ ɡɚɦɟɫ ɛɟɬɨɧɨɫɦɟɫɢɬɟɥɹ ɩɪɢɧɢɦɚɸɬ ɱɬɨ ɫɭɦɦɚ ɨɛɴɟɦɨɜ ɰɟɦɟɧɬɚ ɩɟɫɤɚ ɢ ɳɟɛɧɹ ɜ ɪɵɯɥɨɦ ɫɨ ɫɬɨɹɧɢɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɟɦɤɨɫɬɢ ɛɚɪɚɛɚɧɚ ɛɟɬɨɧɨɫɦɟɫɢɬɟɥɹ Ɍɨɝɞɚ ɨɛɴ ɟɦ ɛɟɬɨɧɚ ɥ ɩɨɥɭɱɚɟɦɵɣ ɢɡ ɨɞɧɨɝɨ ɡɚɦɟɫɚ ɜɵɱɢɫɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
Vɡ Vɛɫ |
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ɝɞɟ ɰ ɩ ɳ ɞ ² ɩɥɨɬɧɨɫɬɶ ɰɟɦɟɧɬɚ ɩɟɫɤɚ ɳɟɛɧɹ ɢ ɞɨɛɚɜɤɢ ɫɨ
ɨɬɜɟɬɫɬɜɟɧɧɨ ɝ ɫɦ Vɛɫ² ɟɦɤɨɫɬɶ ɛɟɬɨɧɨɫɦɟɫɢɬɟɥɹ ɥ
Ɋɚɫɯɨɞ ɦɚɬɟɪɢɚɥɨɜ ɤɝ ɧɚ ɨɞɢɧ ɡɚɦɟɫ ɛɟɬɨɧɨɫɦɟɫɢɬɟɥɹ ɜɵɱɢɫ ɥɹɸɬ ɩɨ ɮɨɪɦɭɥɚɦ
ɐɡ |
ɐ Vɡ |
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ȼɡ |
ȼ Vɡ |
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ɉɡ |
ɉ Vɡ |
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ɓɡ |
ɓ Vɡ |
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Ⱦɡ |
Ⱦ Vɡ |
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ǷȘȖȍȒȚȐȘȖȊȈȕȐȍ șȖșȚȈȊȈ ȓȍȋȒȖȋȖ ȉȍȚȖȕȈ
ɉɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɫɨɫɬɚɜɚ ɥɟɝɤɨɝɨ ɛɟɬɨɧɚ ɧɚ ɩɥɨɬɧɨɦ ɩɟɫɤɟ ɜɧɚɱɚɥɟ ɨɩɪɟɞɟɥɹɸɬ ɪɚɫɯɨɞ ɰɟɦɟɧɬɚ > @ ɇɚ ɨɫɧɨɜɟ ɪɟɤɨɦɟɧɞɚɰɢɣ ɢɡɥɨɠɟɧɧɵɯ ɜ ɥɢɬɟɪɚɬɭ ɪɟ ɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɛɵɥɚ ɩɨɥɭɱɟɧɚ ɪɟɝɪɟɫɫɢɨɧɧɚɹ ɡɚɜɢ ɫɢɦɨɫɬɶ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɪɚɫɯɨɞɚ ɰɟɦɟɧɬɚ
ɐ f Rɛ Rɰ Rɡ RɛíRɡíRɰ
ɝɞɟRɛ² ɩɪɨɱɧɨɫɬɶ ɛɟɬɨɧɚ Ɇɉɚ Rɰ² ɦɚɪɤɚ ɰɟɦɟɧɬɚ
Rɡ² ɦɚɪɤɚ ɩɨɪɢɫɬɨɝɨ ɡɚɩɨɥɧɢɬɟɥɹ ɩɨ ɩɪɨɱɧɨɫɬɢ ɡɟɪɧɚ
Ɂɚɬɟɦ ɨɩɪɟɞɟɥɹɸɬ ɧɚɱɚɥɶɧɵɣ ɪɚɫɯɨɞ ɜɨɞɵ
ɟɫɥɢ ɫɦɟɫɶ ɩɨɞɜɢɠɧɚɹ
ȼ f ɉ Ɇɤɪ |
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ɟɫɥɢ ɫɦɟɫɶ ɠɟɫɬɤɚɹ |
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ȼ f ɀ Ɇɤɪ |
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ɝɞɟɉ² ɩɨɞɜɢɠɧɨɫɬɶ ɫɦɟɫɢ ɫɦ ɀ² ɠɟɫɬɤɨɫɬɶ ɫɦɟɫɢ ɫ
Ɇɤɪ — ɧɚɢɛɨɥɶɲɢɣ ɪɚɡɦɟɪ ɡɟɪɟɧ ɤɪɭɩɧɨɝɨ ɡɚɩɨɥɧɢɬɟɥɹ ɦɦ
ɇɚ ɨɫɧɨɜɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɢ ɥɢɬɟɪɚɬɭɪɧɵɯ ɢɫɬɨɱɧɢ
ɤɨɜ ɛɵɥɢ ɩɨɥɭɱɟɧɵ ɫɥɟɞɭɸɳɢɟ ɡɚɜɢɫɢɦɨɫɬɢ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɤɨɥɢɱɟ
ɫɬɜɚ ɜɨɞɵ
ɞɥɹ ɩɨɞɜɢɠɧɨɣ ɛɟɬɨɧɧɨɣ ɫɦɟɫɢ ɧɚ ɤɟɪɚɦɡɢɬɨɜɨɦ ɝɪɚɜɢɢ ȼ ɉíɆɤɪíɉ Ɇɤɪ
ɞɥɹ ɩɨɞɜɢɠɧɨɣ ɛɟɬɨɧɧɨɣ ɫɦɟɫɢ ɧɚ ɤɟɪɚɦɡɢɬɨɜɨɦ ɳɟɛɧɟ ȼ ɉíɆɤɪíɉ Ɇɤɪ
ɞɥɹ ɠɟɫɬɤɨɣ ɛɟɬɨɧɧɨɣ ɫɦɟɫɢ ɧɚ ɤɟɪɚɦɡɢɬɨɜɨɦ ɝɪɚɜɢɢ
ȼ íɀíɆɤɪ ɀ Ɇɤɪ ɀ Ɇɤɪ
ɞɥɹ ɠɟɫɬɤɨɣ ɛɟɬɨɧɧɨɣ ɫɦɟɫɢ ɧɚ ɤɟɪɚɦɡɢɬɨɜɨɦ ɳɟɛɧɟ
ȼ íɀíɆɤɪ ɀ Ɇɤɪ ɀ Ɇɤɪ
Ⱦɚɥɟɟ ɨɩɪɟɞɟɥɹɸɬ ɨɛɴɟɦɧɭɸ ɤɨɧɰɟɧɬɪɚɰɢɸ ɤɪɭɩɧɨɝɨ ɡɚɩɨɥɧɢɬɟɥɹ
M f ɐ ȼ ɛ ɡ ȼɩ |
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ɝɞɟ ɛ ² ɩɥɨɬɧɨɫɬɶ ɛɟɬɨɧɚ ɤɝ ɦ ɡ ² ɩɥɨɬɧɨɫɬɶ ɡɟɪɟɧ ɤɪɭɩɧɨɝɨ ɡɚɩɨɥɧɢɬɟɥɹ ɜ ɰɟɦɟɧɬɧɨɦ ɬɟɫɬɟ
ɤɝ ɥ ȼɩ — ɜɨɞɨɩɨɬɪɟɛɧɨɫɬɶ ɩɟɫɤɚ
ɇɚ ɨɫɧɨɜɚɧɢɢ ɞɚɧɧɵɯ ɩɨɱɟɪɩɧɭɬɵɯ ɢɡ ɢɫɬɨɱɧɢɤɨɜ > @ ɛɵɥɚ ɩɨɥɭɱɟɧɚ ɫɥɟɞɭɸɳɚɹ ɪɟɝɪɟɫɫɢɨɧɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ
M í ɛ ɡ íȼɩíȼ
ɉɪɢ ɪɚɫɯɨɞɟ ɰɟɦɟɧɬɚ ɛɨɥɟɟ ɦɟɧɟɟ ɤɝ ɡɧɚɱɟɧɢɟM ɭɜɟɥɢɱɢɜɚ ɟɬɫɹ ɭɦɟɧɶɲɚɟɬɫɹ ɧɚ ɧɚ ɤɚɠɞɵɟ ɤɝ ɰɟɦɟɧɬɚ > @
Ɋɚɫɯɨɞ ɤɪɭɩɧɨɝɨ ɡɚɩɨɥɧɢɬɟɥɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
Ɂɤɪ f M |
ɡ M ɡ |
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Ɋɚɫɯɨɞ ɩɟɫɤɚ ɜɵɱɢɫɥɹɟɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ |
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ɛ íɐíɁɤɪ |
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Ɉɛɳɢɣ ɪɚɫɯɨɞ ɜɨɞɵ ɜɵɱɢɫɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ |
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ɝɞɟȼ ² ɧɚɱɚɥɶɧɵɣ ɪɚɫɯɨɞ ɜɨɞɵ
ȼ ²ɩɨɩɪɚɜɤɚɧɚɪɚɫɯɨɞɜɨɞɵɩɪɢɩɪɢɦɟɧɟɧɢɢɩɟɫɤɚɫɜɨɞɨɩɨ ɬɪɟɛɧɨɫɬɶɸ ɧɟ ɪɚɜɧɨɣ
ȼ ² ɩɨɩɪɚɜɤɚ ɧɚ ɪɚɫɯɨɞ ɜɨɞɵ ɩɪɢ ɜɵɫɨɤɢɯ ɪɚɫɯɨɞɚɯ ɰɟɦɟɧɬɚ ɛɨɥɶɲɟ ɤɝ ɦ
ȼ ² ɩɨɩɪɚɜɤɚ ɧɚ ɪɚɫɯɨɞ ɜɨɞɵ ɩɪɢ ɨɛɴɟɦɧɨɣ ɤɨɧɰɟɧɬɪɚɰɢɢ ɤɟ ɪɚɦɡɢɬɚ ɧɟ ɩɪɢɧɚɞɥɟɠɚɳɟɣ ɨɬɪɟɡɤɭ > @ ɜɵɱɢɫɥɹɟ ɦɵɟ ɩɨ ɮɨɪɦɭɥɚɦ
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ɉɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɫɨɫɬɚɜɚ ɥɟɝɤɨɝɨ ɛɟɬɨɧɚ ɧɚ ɩɨɪɢɫɬɨɦ ɢɥɢ ɫɦɟɲɚɧɧɨɦ ɩɟɫɤɟ ɪɚɫɯɨɞ ɰɟɦɟɧɬɚ ɧɚɱɚɥɶɧɵɣ ɪɚɫɯɨɞ ɜɨɞɵ ɨɛɴɟɦɧɭɸ ɤɨɧɰɟɧɬɪɚɰɢɸ ɤɪɭɩɧɨɝɨ ɡɚɩɨɥɧɢɬɟɥɹ ɢ ɪɚɫɯɨɞ ɤɪɭɩɧɨɝɨ ɡɚɩɨɥɧɢɬɟɥɹ ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɚɦ ²
Ⱦɚɥɟɟ ɜɵɱɢɫɥɹɸɬ ɜɫɩɨɦɨɝɚɬɟɥɶɧɵɟ ɜɟɥɢɱɢɧɵ ɩɨ ɮɨɪɦɭɥɚɦ
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ɝɞɟ ɩɩɨɪ ² ɩɥɨɬɧɨɫɬɶ ɡɟɪɟɧ ɦɟɥɤɨɝɨ ɡɚɩɨɥɧɢɬɟɥɹ ɩɨɪɢɫɬɨɝɨ ɩɟɫɤɚ ɜ ɰɟɦɟɧɬɧɨɦ ɬɟɫɬɟ
ɩɩɥ ² ɩɥɨɬɧɨɫɬɶ ɩɥɨɬɧɨɝɨ ɩɟɫɤɚ ȼɩɩɥ ȼɩɩɨɪ ² ɜɨɞɨɩɨɬɪɟɛɧɨɫɬɶ ɩɥɨɬɧɨɝɨ ɢ ɩɨɪɢɫɬɨɝɨ ɩɟɫɤɚ ɫɨɨɬ
ɜɟɬɫɬɜɟɧɧɨ
Ɋɚɫɯɨɞ ɩɨɪɢɫɬɨɝɨ ɩɟɫɤɚ ɜɵɱɢɫɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
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ɉɩɨɪ |
A QCɜɩɥ |
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ɋ ɜɩɨɪ ɋɜɩɥ |
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Ɋɚɫɯɨɞ ɩɥɨɬɧɨɝɨ ɩɟɫɤɚ ɜɵɱɢɫɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ |
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ɉɩɥ Q ɉɩɨɪ |
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Ɉɛɳɢɣ ɪɚɫɯɨɞ ɜɨɞɵ ɜɵɱɢɫɥɹɟɬɫɹ ɫ ɭɱɟɬɨɦ ɩɨɩɪɚɜɨɤ ² |
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ȼ |
ȼ ȼ1 ȼɩ.ɩɨɪ ȼ ȼ |
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ɝɞɟȼɩ.ɩɨɪ — ɩɨɩɪɚɜɤɚ ɧɚ ɜɨɞɨɩɨɬɪɟɛɧɨɫɬɶ ɩɨɪɢɫɬɨɝɨ ɩɟɫɤɚ ɜɵɱɢɫɥɹɟ
ɦɚɹ ɩɨ ɮɨɪɦɭɥɟ |
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ɉɩɨɪ |
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ɩɨɪ ɩ |
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ǷȘȖȍȒȚȐȘȖȊȈȕȐȍ șȖșȚȈȊȈ ȧȟȍȐșȚȖȋȖ ȉȍȚȖȕȈ
ɋɨɫɬɚɜ ɹɱɟɢɫɬɨɝɨ ɛɟɬɨɧɚ ɩɪɨɟɤɬɢɪɭɟɬɫɹ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɟɤɨ ɦɟɧɞɚɰɢɹɦɢ > @
ȼɧɚɱɚɥɟ ɜɵɱɢɫɥɹɟɬɫɹ ɪɚɫɯɨɞ ɜɹɠɭɳɟɝɨ ɩɨ ɮɨɪɦɭɥɟ
ɛ Vɛ |
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ȼɹɠ kc kɜ |
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ɝɞɟ ɛ ² ɩɥɨɬɧɨɫɬɶ ɹɱɟɢɫɬɨɝɨ ɛɟɬɨɧɚ ɜ ɜɵɫɭɲɟɧɧɨɦ ɫɨɫɬɨɹɧɢɢ Vɛ ² ɨɛɴɟɦ ɛɟɬɨɧɧɨɣ ɫɦɟɫɢ
kc ² ɤɨɷɮɮɢɰɢɟɧɬ ɭɱɢɬɵɜɚɸɳɢɣ ɫɜɹɡɚɧɧɭɸ ɜɨɞɭ ɜ ɦɚɬɟɪɢɚɥɟ
ɩɟɪɜɨɧɚɱɚɥɶɧɨ ɩɪɢɧɢɦɚɟɬɫɹ ɪɚɜɧɵɦ
kɜ ² ɨɬɧɨɲɟɧɢɟ ɤɪɟɦɧɟɡɟɦɢɫɬɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɤ ɜɹɠɭɳɟɦɭ
Ɋɚɫɯɨɞ ɰɟɦɟɧɬɚ ɜɵɱɢɫɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ |
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ɐ ȼɹɠ n |
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ɝɞɟ n² ɞɨɥɹ ɰɟɦɟɧɬɚ ɜ ɫɦɟɲɚɧɧɨɦ ɜɹɠɭɳɟɦ |
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Ɂɚɬɟɦ ɜɵɱɢɫɥɹɟɬɫɹ ɪɚɫɯɨɞ ɤɪɟɦɧɟɡɟɦɢɫɬɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɩɨ ɮɨɪ |
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ɦɭɥɟ |
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Ʉɪ ȼɹɠ kɜ |
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Ɋɚɫɯɨɞ ɜɨɞɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ |
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ȼ ȼɹɠ Ʉɪ ȼ/Ɍ |
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ɝɞɟȼ/Ɍ² ɜɨɞɨɬɜɟɪɞɨɟ ɨɬɧɨɲɟɧɢɟ ɫɦɟɫɢ |
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Ɂɚɬɟɦ ɜɵɱɢɫɥɹɟɬɫɹ ɩɨɪɢɫɬɨɫɬɶ ɛɟɬɨɧɚ ɩɨ ɮɨɪɦɭɥɟ
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ɝɞɟ ɰ Ʉɪ ² ɩɥɨɬɧɨɫɬɶ ɰɟɦɟɧɬɚ ɢ ɤɪɟɦɧɟɡɟɦɢɫɬɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɫɨ ɨɬɜɟɬɫɬɜɟɧɧɨ
Ⱦɚɥɶɧɟɣɲɢɟ ɪɚɫɱɟɬɵ ɡɚɜɢɫɹɬ ɨɬ ɜɢɞɚ ɹɱɟɢɫɬɨɝɨ ɛɟɬɨɧɚ
ɉɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɫɨɫɬɚɜɚ ɩɟɧɨɛɟɬɨɧɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɚɫɯɨɞ ɪɚ
ɛɨɱɟɝɨ ɪɚɫɬɜɨɪɚ ɩɟɧɨɨɛɪɚɡɭɸɳɟɣ ɞɨɛɚɜɤɢ ɩɨ ɮɨɪɦɭɥɟ |
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Ⱦɉ Vɉ Ʉɉ |
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ɝɞɟɄɉ² ɤɪɚɬɧɨɫɬɶ ɩɟɧɵ |
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Ɋɚɫɯɨɞ ɤɨɧɰɟɧɬɪɢɪɨɜɚɧɧɨɣ ɩɟɧɨɨɛɪɚɡɭɸɳɟɣ ɞɨɛɚɜɤɢ ɜɵɱɢɫɥɹɟɬ
ɫɹ ɩɨ ɮɨɪɦɭɥɟ |
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ȾɉɄ Ⱦɉ N |
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ɝɞɟN² ɤɪɚɬɧɨɫɬɶ ɪɚɡɛɚɜɥɟɧɢɹ ɤɨɧɰɟɧɬɪɢɪɨɜɚɧɧɨɣ ɩɟɧɨɨɛɪɚɡɭɸɳɟɣ
ɞɨɛɚɜɤɢ ɩɪɢ ɩɪɢɝɨɬɨɜɥɟɧɢɢ ɪɚɛɨɱɟɝɨ ɪɚɫɬɜɨɪɚ
ɉɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɫɨɫɬɚɜɚ ɝɚɡɨɛɟɬɨɧɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɚɫɯɨɞ ɢɡ
ɜɟɫɬɢ ɩɨ ɮɨɪɦɭɥɟ
ɂ ȼɹɠ ín Ⱥɂ |
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ɝɞɟȺɂ² ɚɤɬɢɜɧɨɫɬɶ ɢɡɜɟɫɬɢ |
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Ɋɚɫɯɨɞ ɩɨɪɨɨɛɪɚɡɨɜɚɬɟɥɹ ɜɵɱɢɫɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ |
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Ɋɩ |
Vɉ Vɛ |
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ɝɞɟ ɚ² ɤɨɷɮɮɢɰɢɟɧɬ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɩɨɪɨɨɛɪɚɡɨɜɚɬɟɥɹ ɩɟɪɜɨɧɚ ɱɚɥɶɧɨ ɩɪɢɧɢɦɚɟɬɫɹ ɪɚɜɧɵɦ
k² ɤɨɷɮɮɢɰɢɟɧɬ ɜɵɯɨɞɚ ɩɨɪɨɨɛɪɚɡɨɜɚɬɟɥɹ ɞɥɹ ɝɚɡɨɛɟɬɨɧɚ k
DzȖȘȘȍȒȚȐȘȖȊȒȈ șȖșȚȈȊȈ ȧȟȍȐșȚȖȋȖ ȉȍȚȖȕȈ
ɋɨɫɬɚɜ ɹɱɟɢɫɬɨɝɨ ɛɟɬɨɧɚ ɤɨɪɪɟɤɬɢɪɭɟɬɫɹ ɫ ɭɱɟɬɨɦ ɮɚɤɬɢɱɟɫɤɨɣ ɩɥɨɬɧɨɫɬɢ ɛɟɬɨɧɚ Ɉɩɪɟɞɟɥɹɟɬɫɹ ɮɚɤɬɢɱɟɫɤɚɹ ɩɨɪɢɫɬɨɫɬɶ ɛɟɬɨɧɚ ɩɨ ɮɨɪɦɭɥɟ
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ɹɮɫ ² ɮɚɤɬɢɱɟɫɤɚɹ ɫɪɟɞɧɹɹ ɩɥɨɬɧɨɫɬɶ ɹɱɟɢɫɬɨ ɛɟɬɨɧɧɨɣ ɫɦɟɫɢ |
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ɮɪ ² ɮɚɤɬɢɱɟɫɤɚɹ ɫɪɟɞɧɹɹ ɩɥɨɬɧɨɫɬɶ ɪɚɫɬɜɨɪɧɨɣ ɫɦɟɫɢ |
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ɍɬɨɱɧɹɟɬɫɹ ɡɧɚɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ ɭɱɢɬɵɜɚɸɳɟɝɨ ɫɜɹɡɚɧɧɭɸ |
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ɜɨɞɭ ɜ ɦɚɬɟɪɢɚɥɟ |
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cɮ ² ɮɚɤɬɢɱɟɫɤɚɹ ɫɪɟɞɧɹɹ ɩɥɨɬɧɨɫɬɶ ɹɱɟɢɫɬɨɝɨ ɛɟɬɨɧɚ ɜ ɫɭɯɨɦ |
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ɫɨɫɬɨɹɧɢɢ |
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ȼ/Ɍ² ɜɨɞɨɬɜɟɪɞɨɟ ɨɬɧɨɲɟɧɢɟ |
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Ⱦɚɥɟɟ ɭɬɨɱɧɹɟɬɫɹ ɡɧɚɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɩɨɪɨ |
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ɨɛɪɚɡɨɜɚɬɟɥɹ ɩɨ ɮɨɪɦɭɥɟ |
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ɝɞɟɊɩ² ɪɚɫɯɨɞ ɩɨɪɨɨɛɪɚɡɨɜɚɬɟɥɹ
Ɂɚɬɟɦ ɜɵɱɢɫɥɹɟɬɫɹ ɪɚɫɯɨɞ ɦɚɬɟɪɢɚɥɨɜ ɩɨ ɮɨɪɦɭɥɚɦ ²
ǶȗȚȐȔȐȏȈȞȐȧ șȖșȚȈȊȈ ȉȍȚȖȕȕȖȑ șȔȍșȐ
ȊȣȉȖȘ ȒȘȐȚȍȘȐȍȊ ȥȜȜȍȒȚȐȊȕȖșȚȐ
Ⱦɥɹ ɭɫɩɟɲɧɨɝɨ ɩɪɢɦɟɧɟɧɢɹ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɦɟɬɨɞɨɜ ɢ ɭɩɪɚɜɥɟ ɧɢɹ ɬɟɯɧɨɥɨɝɢɟɣ ɛɟɬɨɧɚ ɢ ɠɟɥɟɡɨɛɟɬɨɧɚ ɛɨɥɶɲɨɟ ɡɧɚɱɟɧɢɟ ɢɦɟɸɬ ɩɪɚɜɢɥɶɧɚɹ ɨɰɟɧɤɚ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɮɚɤɬɨɪɨɜ ɢ ɜɵɛɨɪ ɫɨɨɬɜɟɬɫɬɜɭ ɸɳɢɯ ɤɪɢɬɟɪɢɟɜ ȼ ɪɹɞɟ ɫɥɭɱɚɟɜ ɷɬɨ ɬɪɟɛɭɟɬ ɫɨɜɟɪɲɟɧɫɬɜɨɜɚɧɢɹ
ɫɭɳɟɫɬɜɭɸɳɢɯ ɦɟɬɨɞɨɜ ɨɩɪɟɞɟɥɟɧɢɹ ɫɜɨɣɫɬɜ ɦɚɬɟɪɢɚɥɨɜ ɢ ɩɚɪɚɦɟɬ ɪɨɜ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ ɪɚɡɪɚɛɨɬɤɢ ɬɚɤɢɯ ɦɟɬɨɞɨɜ ɢɫɩɵɬɚɧɢɣ ɢ ɜɵɛɨɪɚ ɩɚɪɚɦɟɬɪɨɜ ɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɦɚɬɟɪɢɚɥɨɜ ɤɨɬɨɪɵɟ ɨɬɜɟɱɚɸɬ ɩɨ ɬɨɱɧɨɫɬɢ ɢ ɞɨɫɬɨɜɟɪɧɨɫɬɢ ɩɪɢɦɟɧɹɟɦɵɦ ɦɟɬɨɞɚɦ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɢɫɫɥɟɞɨɜɚɧɢɣ ɢ ɚɧɚɥɢɡɭ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɫɢɫɬɟɦ
ɋɢɫɬɟɦɵ ɦɨɠɧɨ ɪɚɡɞɟɥɢɬɶ ɧɚ ɞɜɚ ɤɥɚɫɫɚ ɞɟɬɟɪɦɢɧɢɪɨɜɚɧɧɵɟ ɢ ɫɬɨɯɚɫɬɢɱɟɫɤɢɟ, ɯɨɬɹ ɜ ɩɪɚɤɬɢɤɟ ɩɪɨɢɡɜɨɞɫɬɜɚ ɢɫɫɥɟɞɭɟɦɵɟ ɫɢɫɬɟ
ɦɵ ɱɚɫɬɨ ɧɟ ɞɟɥɹɬɫɹ ɫɬɨɥɶ ɱɟɬɤɨ > @ Ʉ ɞɟɬɟɪɦɢɧɢɪɨɜɚɧɧɵɦ ɨɬɧɨɫɹɬ ɫɢɫɬɟɦɵ ɜ ɤɨɬɨɪɵɯ ɫɨɫɬɚɜɧɵɟ ɱɚ
ɫɬɢ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɬ ɬɨɱɧɨ ɩɪɟɞɜɢɞɢɦɵɦ ɨɛɪɚɡɨɦ ɉɪɢ ɢɫɫɥɟɞɨɜɚ ɧɢɢ ɞɟɬɟɪɦɢɧɢɪɨɜɚɧɧɨɣ ɫɢɫɬɟɦɵ ɧɟ ɜɨɡɧɢɤɚɟɬ ɧɢɤɚɤɨɣ ɧɟɨɩɪɟɞɟɥɟɧ ɧɨɫɬɢ ɂɡɦɟɧɟɧɢɟ ɨɞɧɨɝɨ ɢɡ ɷɥɟɦɟɧɬɨɜ ɫɢɫɬɟɦɵ ɧɚ ɧɟɤɨɬɨɪɭɸ ɜɟɥɢ ɱɢɧɭ ɜɫɟɝɞɚ ɜɵɡɵɜɚɟɬ ɢɡɦɟɧɟɧɢɟ ɞɪɭɝɨɝɨ ɢɥɢ ɞɪɭɝɢɯ ɧɚ ɫɬɪɨɝɨ ɨɩɪɟ ɞɟɥɟɧɧɭɸ ɜɟɥɢɱɢɧɭ
ȼ ɬɟɪɦɢɧɚɯ ɬɟɯɧɨɥɨɝɢɢ ɛɟɬɨɧɚ ɷɬɨ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɥɟɞɭɸɳɟɦɭ ɟɫɥɢ ɜɟɥɢɱɢɧɚ ɤɚɤɨɝɨ ɬɨ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɮɚɤɬɨɪɚ ɏi ɢɡɦɟɧɢɬɫɹ ɧɚ 'ɏ ɬɨ ɫɜɨɣɫɬɜɨ Yi ɜɫɟɝɞɚ ɢɡɦɟɧɢɬɫɹ ɧɚ 'ɍ. Ɉɬɞɟɥɶɧɵɟ ɩɨɞɫɢɫɬɟɦɵ
ɬɟɯɧɨɥɨɝɢɢ ɛɟɬɨɧɚ ɦɨɠɧɨ ɨɬɧɟɫɬɢ ɤ ɞɟɬɟɪɦɢɧɢɪɨɜɚɧɧɵɦ ɧɚɩɪɢɦɟɪ ɭɦɟɧɶɲɟɧɢɟ ɞɢɚɦɟɬɪɚ ɲɚɪɢɤɨɜɢɞɧɵɯ ɡɟɪɟɧ ɩɪɢɜɨɞɢɬ ɤ ɭɜɟɥɢɱɟɧɢɸ ɢɯ ɭɞɟɥɶɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ
Ⱦɥɹ ɫɬɨɯɚɫɬɢɱɟɫɤɨɣ ɜɟɪɨɹɬɧɨɫɬɧɨɣ ɫɢɫɬɟɦɵ ɧɟɥɶɡɹ ɫɞɟɥɚɬɶ ɬɨɱɧɨɝɨ ɞɟɬɚɥɶɧɨɝɨ ɩɪɟɞɫɤɚɡɚɧɢɹ Ɍɚɤɭɸ ɫɢɫɬɟɦɭ ɦɨɠɧɨ ɬɳɚɬɟɥɶɧɨ ɢɫɫɥɟɞɨɜɚɬɶ ɢ ɭɫɬɚɧɨɜɢɬɶ ɫ ɛɨɥɶɲɨɣ ɫɬɟɩɟɧɶɸ ɜɟɪɨɹɬɧɨɫɬɢ ɤɚɤ ɨɧɚ ɛɭɞɟɬ ɫɟɛɹ ɜɟɫɬɢ ɜ ɥɸɛɵɯ ɡɚɞɚɧɧɵɯ ɭɫɥɨɜɢɹɯ Ɉɞɧɚɤɨ ɫɢɫɬɟɦɚ ɜɫɟ ɬɚɤɢ ɨɫɬɚɟɬɫɹ ɧɟɨɩɪɟɞɟɥɟɧɧɨɣ ɢ ɥɸɛɨɟ ɩɪɟɞɫɤɚɡɚɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ɟɟ ɩɨɜɟɞɟɧɢɹɧɢɤɨɝɞɚɧɟɦɨɠɟɬɜɵɣɬɢɡɚɥɨɝɢɱɟɫɤɢɟɪɚɦɤɢɜɟɪɨɹɬɧɨɫɬ ɧɵɯ ɤɚɬɟɝɨɪɢɣ ɫ ɩɨɦɨɳɶɸ ɤɨɬɨɪɵɯ ɷɬɨ ɩɨɜɟɞɟɧɢɟ ɨɩɢɫɵɜɚɟɬɫɹ ȼ ɫɬɨɯɚɫɬɢɱɟɫɤɢɯ ɫɢɫɬɟɦɚɯ ɢɡɦɟɧɟɧɢɟ ɨɞɧɨɝɨ ɢɡ ɷɥɟɦɟɧɬɨɜ ɧɟ ɜɫɟɝɞɚ ɜɵɡɵɜɚɟɬ ɢɡɦɟɧɟɧɢɟ ɞɪɭɝɨɝɨ ɫɜɹɡɚɧɧɨɝɨ ɫ ɧɢɦ ɚ ɬɨɥɶɤɨ ɜ ɧɟɤɨɬɨɪɵɯ ɫɥɭɱɚɹɯ ȿɫɥɢ Xi ɢɡɦɟɧɢɥɫɹ ɧɚ 'ɏ ɬɨ RK ɢɡɦɟɧɢɬɫɹ ɧɚ 'R M ɝɞɟM — ɫɥɭɱɚɣɧɚɹ ɜɟɥɢɱɢɧɚ
ȿɫɥɢ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɥɭɱɚɣɧɨɫɬɢ M = –'R ɬɨ ɜɥɢɹɧɢɟ ɏi ɧɚ RK
ɜɨɨɛɳɟ ɜ ɞɚɧɧɨɦ ɧɚɛɥɸɞɟɧɢɢ ɨɛɧɚɪɭɠɟɧɨ ɧɟ ɛɭɞɟɬ
ȼ ɬɟɯɧɨɥɨɝɢɢ ɛɟɬɨɧɚ ɢ ɠɟɥɟɡɨɛɟɬɨɧɚ ɫɬɨɯɚɫɬɢɱɟɫɤɢɟ ɫɢɫɬɟɦɵ ɢɦɟɸɬ ɛɨɥɶɲɨɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɇɚɩɪɢɦɟɪ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɫɨɫɬɚɜ ɥɹɸɳɢɯ ɢ ɷɥɟɦɟɧɬɨɜ ɫɬɪɭɤɬɭɪɵ ɩɨɞɱɢɧɹɟɬɫɹ ɜɟɪɨɹɬɧɨɫɬɧɨ ɫɬɚɬɢɫɬɢɱɟɫɤɢɦ ɡɚɤɨɧɨɦɟɪɧɨɫɬɹɦ ɪɨɥɶ ɫɥɭɱɚɣɧɨɝɨ ɷɮɮɟɤɬɚ ɜɨɡɪɚɫɬɚ ɟɬ ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɨɛɴɟɦɨɜ ɩɪɢ ɩɟɪɟɯɨɞɟ ɨɬ ɥɚɛɨɪɚɬɨɪɧɵɯ ɨɛɪɚɡ ɰɨɜ ɤ ɢɡɞɟɥɢɹɦ ɚ ɬɚɤɠɟ ɩɪɢ ɩɟɪɟɯɨɞɟ ɨɬ ɟɞɢɧɢɱɧɨɣ ɤ ɦɚɫɫɨɜɨɣ ɩɪɨ ɞɭɤɰɢɢ
ȼ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɣ ɫɢɫɬɟɦɟ ɞɟɣɫɬɜɭɟɬ ɛɨɥɶɲɨɟ ɱɢɫɥɨ ɜɡɚɢɦɨɫɜɹ ɡɚɧɧɵɯ ɮɚɤɬɨɪɨɜ ɏi ɂɡ ɧɢɯ ɬɨɥɶɤɨ ɱɚɫɬɶ ɦɨɠɧɨ ɞɟɬɟɪɦɢɧɢɪɨɜɚɧɧɨ
ɭɱɟɫɬɶɚɨɫɬɚɥɶɧɵɟɮɚɤɬɨɪɵɜɫɟɝɞɚɫɨɡɞɚɞɭɬɫɥɭɱɚɣɧɵɣɷɮɮɟɤɬɩɨ ɷɬɨɦɭ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɫɬɨɯɚɫɬɢɱɟɫɤɢɯ ɫɢɫɬɟɦ ɜ ɬɟɯɧɨɥɨɝɢɢ ɫɛɨɪɧɨɝɨ ɠɟɥɟɡɨɛɟɬɨɧɚ ɩɨɡɜɨɥɹɟɬ ɭɫɩɟɲɧɨ ɪɟɲɚɬɶ ɦɧɨɝɢɟ ɡɚɞɚɱɢ ɭɩɪɚɜɥɟɧɢɹ ɤɚɱɟɫɬɜɨɦ ɢ ɩɪɨɢɡɜɨɞɫɬɜɨɦ
ɉɪɢ ɷɬɨɦ ɜɨɩɪɨɫ ɮɨɪɦɭɥɢɪɨɜɤɢ ɰɟɥɢ ɪɟɲɚɟɬɫɹ ɜ ɤɚɠɞɨɦ ɨɬɞɟɥɶ ɧɨɦ ɫɥɭɱɚɟ ɧɚ ɨɫɧɨɜɟ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɢ ɷɤɨɧɨɦɢɱɟɫɤɢɯ ɭɫɥɨɜɢɣ ɐɟɥɶɸ ɦɨɠɟɬ ɛɵɬɶ ɧɚɩɪɢɦɟɪ ɞɨɫɬɢɠɟɧɢɟ ɠɟɥɟɡɨɛɟɬɨɧɨɦ ɨɩ ɬɢɦɚɥɶɧɨɝɨ ɤɚɱɟɫɬɜɚ ɢ ɩɨɞɞɟɪɠɚɧɢɟ ɟɝɨ ɧɚ ɷɬɨɦ ɭɪɨɜɧɟ ɫ ɦɚɤɫɢɦɚɥɶ ɧɨɣ ɫɬɚɛɢɥɶɧɨɫɬɶɸ ɋɪɟɞɫɬɜɨɦ ɤ ɞɨɫɬɢɠɟɧɢɸ ɰɟɥɢ ɹɜɥɹɟɬɫɹ ɭɩɪɚɜɥɟ ɧɢɟ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɦɢ ɮɚɤɬɨɪɚɦɢ ɏi ɞɟɣɫɬɜɭɸɳɢɦɢ ɜ ɬɟɯɧɨɥɨɝɢɢ
ɤɚɤ ɜ ɫɥɨɠɧɨɣ ɫɬɨɯɚɫɬɢɱɟɫɤɨɣ ɫɢɫɬɟɦɟ ɇɟɨɛɯɨɞɢɦɨ ɩɪɢɣɬɢ ɤ ɰɟɥɢ ɧɚɩɪɢɦɟɪ ɩɨɥɭɱɟɧɢɸ ɡɚɞɚɧɧɨɣ
ɩɪɨɱɧɨɫɬɢR, ɜɵɛɢɪɚɹɜɢɞɨɫɧɨɜɧɵɯɤɨɦɩɨɧɟɧɬɨɜɛɟɬɨɧɚɟɝɨɪɟɰɟɩ
ɬɭɪɵ ɬɢɩ ɨɛɨɪɭɞɨɜɚɧɢɹ ɢ ɪɟɠɢɦɵ ɪɚɛɨɬɵ ɋɬɟɩɟɧɶ ɞɨɫɬɢɠɟɧɢɹ ɰɟɥɢ ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɩɨɤɚɡɚɬɟɥɶ ɤɨɬɨɪɵɣ
ɧɚɡɵɜɚɸɬ ɤɪɢɬɟɪɢɟɦ ɷɮɮɟɤɬɢɜɧɨɫɬɢ, ɢɥɢ ɨɩɬɢɦɚɥɶɧɨɫɬɢ. ȼ ɤɚɱɟ
ɫɬɜɟ ɤɪɢɬɟɪɢɹ ɦɨɝɭɬ ɛɵɬɶ ɜɵɛɪɚɧɵ ɪɚɡɥɢɱɧɵɟ ɩɨɤɚɡɚɬɟɥɢ ɩɪɨɱɧɨɫɬɶ
ɢɥɢ ɞɪɭɝɢɟ ɫɜɨɣɫɬɜɚ ɛɟɬɨɧɚ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɡɚɜɨɞɚ ɢɥɢ ɰɟɯɚ ɫɟ ɛɟɫɬɨɢɦɨɫɬɶ ɩɪɨɞɭɤɰɢɢ ɢ ɞɪ ȼɵɛɨɪ ɤɪɢɬɟɪɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɧɚɡɧɚ ɱɟɧɢɟɦɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣɫɢɫɬɟɦɵɄɚɠɞɨɦɭɜɚɪɢɚɧɬɭɪɟɲɟɧɢɹɫɨɨɬ ɜɟɬɫɬɜɭɟɬɨɩɪɟɞɟɥɟɧɧɨɟɡɧɚɱɟɧɢɟɜɵɛɪɚɧɧɨɝɨɤɪɢɬɟɪɢɹɢɡɚɞɚɱɚɨɩ ɬɢɦɚɥɶɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɫɨɫɬɨɢɬ ɜ ɬɨɦ ɱɬɨɛɵ ɜɵɛɪɚɬɶ ɢ ɪɟɚɥɢɡɨ ɜɚɬɶ ɬɚɤɨɣ ɜɚɪɢɚɧɬ ɩɪɢ ɤɨɬɨɪɨɦ ɤɪɢɬɟɪɢɣ ɢɦɟɟɬ ɷɤɫɬɪɟɦɚɥɶɧɨɟ ɦɚɤ ɫɢɦɚɥɶɧɨɟ ɢɥɢ ɦɢɧɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɩɪɢ ɞɚɧɧɵɯ ɭɫɥɨɜɢɹɯ ɩɪɨɢɡ ɜɨɞɫɬɜɚ