Проектирование составов бетонных смесей с помощью современных информационных технологий. Монография
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ɦɨɪɨɡɨɫɬɨɣɤɨɫɬɶ ɰɢɤɥɵ |
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F íɏ ɏ íɏ |
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ɏ ɏ ɏ ɏ ɏ ɏ íɏ ɏ |
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ɏ ɏ íɏ ɏ |
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ɝɞɟɏ — ɤɨɥɢɱɟɫɬɜɨ ɰɟɦɟɧɬɚ ɤɝ ɏ — ɜɨɞɨɰɟɦɟɧɬɧɨɟ ɨɬɧɨɲɟɧɢɟ
ɏ — ɨɬɧɨɲɟɧɢɟ ɩɨ ɦɚɫɫɟ ɦɟɠɞɭ ɩɟɫɤɨɦ ɢ ɳɟɛɧɟɦ
ɏ ² ɩɪɨɱɧɨɫɬɶ ɩɪɢ ɫɠɚɬɢɢ Ɇɉɚ
Ɂɚɬɟɦ ɩɨ ɦɟɬɨɞɢɤɟ ɨɩɢɫɚɧɧɨɣ ɜ ɩ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɤɪɢɬɟ
ɪɢɹ ɋɬɶɸɞɟɧɬɚ ɛɵɥ ɩɪɨɜɟɞɟɧ ɫɬɚɬɢɫɬɢɱɟɫɤɢɣ ɚɧɚɥɢɡ ɩɨɥɭɱɟɧɧɵɯ ɤɨ
ɷɮɮɢɰɢɟɧɬɨɜ ɬɚɛɥ ɉ ɉ ɉ
ɉɪɨɜɟɪɤɚ ɚɞɟɤɜɚɬɧɨɫɬɢ ɩɨɥɭɱɟɧɧɵɯ ɭɪɚɜɧɟɧɢɣ ɩɪɨɜɨɞɢɥɚɫɶ ɜ ɫɨ
ɨɬɜɟɬɫɬɜɢɢ ɫ ɦɟɬɨɞɢɤɨɣ ɨɩɢɫɚɧɧɨɣ ɜ ɩ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɤɪɢɬɟ
ɪɢɹ Ɏɢɲɟɪɚ Ⱥɧɚɥɢɡ ɩɨɥɭɱɟɧɧɵɯ ɭɪɚɜɧɟɧɢɣ ɩɨɤɚɡɚɥ ɢɯ ɚɞɟɤɜɚɬɧɨɫɬɶ
ɬɚɛɥ ɉ ɉ ɉ
Ⱦɥɹ ɢɫɫɥɟɞɨɜɚɧɢɹ ɜɥɢɹɧɢɹ ɪɚɡɥɢɱɧɵɯ ɮɚɤɬɨɪɨɜ ɧɚ ɫɜɨɣɫɬɜɚ ɥɟɝ ɤɨɝɨ ɛɟɬɨɧɚ ɫ ɩɥɚɫɬɢɮɢɰɢɪɭɸɳɟɣ ɞɨɛɚɜɤɨɣ ɛɵɥɢ ɜɵɛɪɚɧɵ ɫɥɟɞɭɸ ɳɢɟ ɮɚɤɬɨɪɵ ɜɨɞɨɰɟɦɟɧɬɧɨɟ ɨɬɧɨɲɟɧɢɟ ɫɦɟɫɢȼ/ɐɤɨɥɢɱɟɫɬɜɨ ɰɟ
ɦɟɧɬɚɐɫɨɨɬɧɨɲɟɧɢɟ ɩɨ ɦɚɫɫɟ ɦɟɠɞɭ ɩɟɫɤɨɦ ɢ ɤɪɭɩɧɵɦ ɡɚɩɨɥɧɢ ɬɟɥɟɦɉ/Ʉɤɨɥɢɱɟɫɬɜɨ ɞɨɛɚɜɤɢȾ
ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɞɚɧɧɵɟ ɩɪɢɜɟɞɟɧɵ ɜ ɩɪɢɥ ɩɪɨɱɧɨɫɬɶ ɬɚɛɥ ɉ ɩɥɨɬɧɨɫɬɶ ɬɚɛɥ ɉ ɦɨɪɨɡɨɫɬɨɣɤɨɫɬɶ ɬɚɛɥ ɉ ȼ ɪɟɡɭɥɶɬɚɬɟ ɨɛɪɚɛɨɬɤɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɛɵɥɢ ɩɨɥɭ
ɱɟɧɵ ɫɥɟɞɭɸɳɢɟ ɭɪɚɜɧɟɧɢɹ ɪɟɝɪɟɫɫɢɢ
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ɩɪɨɱɧɨɫɬɶ ɩɪɢ ɫɠɚɬɢɢ Ɇɉɚ |
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Rɫɠ ɏ íɏ íɏ íɏ íɏ ɏ |
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ɏ ɏ íɏ ɏ ɏ ɏ |
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ɏ ɏ ɏ ɏ |
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ɩɥɨɬɧɨɫɬɶ ɤɝ ɦ |
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íɏ íɏ íɏ ɏ í |
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íɏ ɏ ɏ ɏ íɏ ɏ ɏ ɏ |
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ɏ ɏ íɏ ɏ |
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ɦɨɪɨɡɨɫɬɨɣɤɨɫɬɶ ɰɢɤɥɵ
F íɏ ɏ ɏ ɏ í
íɏ ɏ íɏ ɏ ɏ ɏ ɏ ɏ ííɏ ɏ íɏ ɏ ɝɞɟɏ — ɤɨɥɢɱɟɫɬɜɨ ɰɟɦɟɧɬɚ ɤɝ
ɏ — ɜɨɞɨɰɟɦɟɧɬɧɨɟ ɨɬɧɨɲɟɧɢɟ ɏ — ɨɬɧɨɲɟɧɢɟ ɩɨ ɦɚɫɫɟ ɦɟɠɞɭ ɩɟɫɤɨɦ ɢ ɳɟɛɧɟɦ
ɏ ² ɤɨɥɢɱɟɫɬɜɨ ɞɨɛɚɜɤɢ ɨɬ ɦɚɫɫɵ ɰɟɦɟɧɬɚ
Ɂɚɬɟɦ ɩɨ ɦɟɬɨɞɢɤɟ ɨɩɢɫɚɧɧɨɣ ɜ ɩ ɢɫɩɨɥɶɡɭɹ ɤɪɢɬɟɪɢɣ ɋɬɶɸɞɟɧɬɚ ɛɵɥ ɩɪɨɜɟɞɟɧ ɫɬɚɬɢɫɬɢɱɟɫɤɢɣ ɚɧɚɥɢɡ ɩɨɥɭɱɟɧɧɵɯ ɤɨɷɮ ɮɢɰɢɟɧɬɨɜ ɬɚɛɥ ɉ ɉ ɉ ɉɪɨɜɟɪɤɚ ɚɞɟɤɜɚɬɧɨɫɬɢ ɩɨɥɭ ɱɟɧɧɵɯ ɭɪɚɜɧɟɧɢɣ ɩɪɨɜɨɞɢɥɚɫɶ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɦɟɬɨɞɢɤɨɣ ɨɩɢɫɚɧ ɧɨɣ ɜ ɩ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɤɪɢɬɟɪɢɹ Ɏɢɲɟɪɚ Ⱥɧɚɥɢɡ ɩɨɥɭɱɟɧɧɵɯ ɭɪɚɜɧɟɧɢɣ ɩɨɤɚɡɚɥ ɢɯ ɚɞɟɤɜɚɬɧɨɫɬɶ ɬɚɛɥ ɉ ɉ ɉ
ȅȒșȗȍȘȐȔȍȕȚȈȓȤȕȣȍ ȐșșȓȍȌȖȊȈȕȐȧ ȊȓȐȧȕȐȧ
ȘȈȏȓȐȟȕȣȝ ȜȈȒȚȖȘȖȊ ȕȈ șȊȖȑșȚȊȈ ȧȟȍȐșȚȖȋȖ ȉȍȚȖȕȈ
ɂɫɫɥɟɞɨɜɚɧɢɟ ɜɥɢɹɧɢɹ ɪɚɡɥɢɱɧɵɯ ɮɚɤɬɨɪɨɜ ɧɚ ɫɜɨɣɫɬɜɚ ɩɟ ɧɨɛɟɬɨɧɚ ɩɪɨɜɨɞɢɥɨɫɶ ɧɚ ɨɫɧɨɜɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɥɚɛɨ ɪɚɬɨɪɢɣ ɡɚɜɨɞɨɜ ɠɟɥɟɡɨɛɟɬɨɧɧɵɯ ɢɡɞɟɥɢɣ Ɉɦɫɤɚ Ⱦɚɧɧɵɟ ɩɪɢɜɟɞɟ ɧɵ ɜ ɩɪɢɥ ɩɥɨɬɧɨɫɬɶ ɬɚɛɥ ɉ ɩɪɨɱɧɨɫɬɶ ɩɪɢ ɫɠɚɬɢɢ ɬɚɛɥ ɉ
ɇɚɢɛɨɥɟɟ ɫɭɳɟɫɬɜɟɧɧɨɟ ɜɥɢɹɧɢɟ ɧɚ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɟ ɫɜɨɣɫɬɜɚ ɩɟɧɨɛɟɬɨɧɚ ɨɤɚɡɵɜɚɸɬ ɫɥɟɞɭɸɳɢɟ ɮɚɤɬɨɪɵ ɜɨɞɨɬɜɟɪɞɨɟ ɨɬɧɨɲɟɧɢɟ ɫɦɟɫɢ ȼ/Ɍ ɨɬɧɨɲɟɧɢɟ ɤɪɟɦɧɟɡɟɦɢɫɬɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɤ ɜɹɠɭɳɟɦɭɄɪ/ȼɹɠɤɨɥɢɱɟɫɬɜɨ ɩɟɧɨɨɛɪɚɡɭɸɳɟɣ ɞɨɛɚɜɤɢȾ
ȼ ɪɟɡɭɥɶɬɚɬɟ ɨɛɪɚɛɨɬɤɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɛɵɥɢ ɩɨɥɭ ɱɟɧɵ ɫɥɟɞɭɸɳɢɟ ɭɪɚɜɧɟɧɢɹ ɪɟɝɪɟɫɫɢɢ
ɩɪɨɱɧɨɫɬɶ ɩɪɢ ɫɠɚɬɢɢ Ɇɉɚ
Rɫɠ íɏ íɏ íɏ ɏ ɏ
ɏ ɏ ɏ ɏ ɏ ɏ ɏ ɏ ɏ ɏ í íɏ ɏ ɏ ɏ ɏ íɏ íɏ
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ɩɥɨɬɧɨɫɬɶ ɤɝ ɦ |
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íɏ ɏ ɏ ɏ ɏ |
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ɏ ɏ íɏ ɏ |
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ɝɞɟɏ — ɜɨɞɨɬɜɟɪɞɨɟ ɨɬɧɨɲɟɧɢɟ ɏ — ɨɬɧɨɲɟɧɢɟ ɤɪɟɦɧɟɡɟɦɢɫɬɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɤ ɜɹɠɭɳɟɦɭ
ɏ — ɤɨɥɢɱɟɫɬɜɨ ɩɟɧɨɨɛɪɚɡɭɸɳɟɣ ɞɨɛɚɜɤɢ ɨɬ ɦɚɫɫɵ ɰɟɦɟɧɬɚ
ɏ ² ɩɥɨɬɧɨɫɬɶ ɛɟɬɨɧɚ ɤɝ ɦ
ɉɨ ɦɟɬɨɞɢɤɟ ɨɩɢɫɚɧɧɨɣ ɜ ɩ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɤɪɢɬɟɪɢɹ ɋɬɶɸɞɟɧɬɚ ɛɵɥ ɩɪɨɜɟɞɟɧ ɫɬɚɬɢɫɬɢɱɟɫɤɢɣ ɚɧɚɥɢɡ ɩɨɥɭɱɟɧɧɵɯ ɤɨɷɮ ɮɢɰɢɟɧɬɨɜ ɬɚɛɥ ɉ ɉ
ɉɪɨɜɟɪɤɚ ɚɞɟɤɜɚɬɧɨɫɬɢ ɩɨɥɭɱɟɧɧɵɯ ɭɪɚɜɧɟɧɢɣ ɩɪɨɜɨɞɢɥɚɫɶ ɜ ɫɨ
ɨɬɜɟɬɫɬɜɢɢ ɫ ɦɟɬɨɞɢɤɨɣ ɨɩɢɫɚɧɧɨɣ ɜ ɩ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɤɪɢɬɟ
ɪɢɹ Ɏɢɲɟɪɚ Ⱥɧɚɥɢɡ ɩɨɥɭɱɟɧɧɵɯ ɭɪɚɜɧɟɧɢɣ ɩɨɤɚɡɚɥ ɢɯ ɚɞɟɤɜɚɬɧɨɫɬɶ
ɬɚɛɥ ɉ ɉ
ɇɚ ɨɫɧɨɜɟ ɤɨɪɪɟɥɹɰɢɨɧɧɨɝɨ ɚɧɚɥɢɡɚ ɞɚɧɧɵɯ ɬɚɛɥ ɉ ɩɨɥɭ
ɱɟɧɚ ɡɚɜɢɫɢɦɨɫɬɶ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢ ɩɟɧɨɛɟɬɨɧɚ ɨɬ ɟɝɨ ɩɥɨɬɧɨɫɬɢ
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Ʉɨɷɮɮɢɰɢɟɧɬ ɩɚɪɧɨɣ ɤɨɪɪɟɥɹɰɢɢ ɪɚɜɧɵɣ ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɵɲɚɟɬ ɤɪɢɬɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ ɱɬɨ ɝɨɜɨɪɢɬ ɨɛ ɚɞɟɤɜɚɬɧɨɫɬɢ ɩɨɥɭɱɟɧɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɪɟɝɪɟɫɫɢɢ
ǷǶǹǺǸǶǭǵǰǭ ǴǨǺǭǴǨǺǰǿǭǹDzǶDZ ǴǶǬǭdzǰ ǷǸǶǾǭǹǹǨ ǷǸǶǭDzǺǰǸǶǪǨǵǰȇ ǹǶǹǺǨǪǶǪ
ǩǭǺǶǵǵȃǽ ǹǴǭǹǭDZ
Ɋɚɫɫɦɨɬɪɢɦ ɨɛɳɭɸ ɫɯɟɦɭ ɩɪɨɰɟɫɫɚ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɫɨɫɬɚɜɚ ɛɟ ɬɨɧɧɨɣ ɫɦɟɫɢ ɪɢɫ
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ǸȐș ǹȝȍȔȈ ȗȘȖȞȍșșȈ ȗȘȖȍȒȚȐȘȖȊȈȕȐȧ șȖșȚȈȊȈ ȉȍȚȖȕȕȖȑ șȔȍșȐ
ɇɚ ɞɚɧɧɨɣ ɫɯɟɦɟ ɜɵɞɟɥɟɧɵ ɜɯɨɞɧɵɟ ɢ ɜɵɯɨɞɧɵɟ ɩɚɪɚɦɟɬɪɵ ɇɚ ɜɯɨɞɟ ɮɭɧɤɰɢɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɡɚɩɨɥɧɢɬɟɥɟɣZɬɪɟɛɭɟɦɵɯ ɯɚɪɚɤ ɬɟɪɢɫɬɢɤ ɛɟɬɨɧɧɨɣ ɫɦɟɫɢ ɢ ɛɟɬɨɧɚ B ɚ ɬɚɤɠɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɯɢɦɢ ɱɟɫɤɢɯ ɞɨɛɚɜɨɤDɇɚ ɜɵɯɨɞɟ ɛɭɞɭɬ ɦɚɫɫɨɜɵɟ ɩɨɤɚɡɚɬɟɥɢ ɤɨɦɩɨɧɟɧ
ɬɨɜ ɝɨɬɨɜɨɣ ɛɟɬɨɧɧɨɣ ɫɦɟɫɢ ɰɟɦɟɧɬɚ ɐ ɩɟɫɤɚ ɉ ɤɪɭɩɧɨɝɨ ɡɚ ɩɨɥɧɢɬɟɥɹ ɓ ɜɨɞɵ ȼ ɯɢɦɢɱɟɫɤɢɯ ɞɨɛɚɜɨɤ Ⱦ ɇɚ ɨɫɧɨɜɚ ɧɢɢ ɩɪɟɞɫɬɚɜɥɟɧɧɨɣ ɫɯɟɦɵ ɢ ɢɡɥɨɠɟɧɧɨɣ ɜ ɥɢɬɟɪɚɬɭɪɟ ɢ ɋɇɢɉɟ ɦɟɬɨɞɢɤɢ ɪɚɫɱɟɬɚ ɫɨɫɬɚɜɚ ɛɟɬɨɧɧɨɣ ɫɦɟɫɢ > @ ɩɨɫɬɪɨɢɦ ɦɚɬɟ ɦɚɬɢɱɟɫɤɭɸ ɦɨɞɟɥɶ ɪɚɫɱɟɬɚ ɫɨɫɬɚɜɨɜ ɬɹɠɟɥɵɯ ɛɟɬɨɧɨɜ ɪɚɫɱɟɬɧɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɦɟɬɨɞɨɦ
ȼɵɯɨɞɧɚɹ ɮɭɧɤɰɢɹ ɤɨɧɟɱɧɨɝɨ ɫɨɫɬɚɜɚ ɛɟɬɨɧɧɨɣ ɫɦɟɫɢ ɫɨɝɥɚɫɧɨ ɬɪɟɛɨɜɚɧɢɹɦ ɋɇɢɉɚ > @ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ
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ɤɚɠɞɚɹ ɢɡ ɜɯɨɞɧɵɯ ɮɭɧɤɰɢɣ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ |
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ɰ ɩ ɤɪ Ɇɤɪ Wɩ Wɤɪ r |
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f Rɛ ȼ ɐ ɉɀ |
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f Ʉɞ ɞ ɋɞ ɪɞ |
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ɝɞɟRɰ — ɚɤɬɢɜɧɨɫɬɶ ɰɟɦɟɧɬɚ Ɇɉɚ
ɰ² ɩɥɨɬɧɨɫɬɶ ɰɟɦɟɧɬɚ ɝ ɫɦ
ɩ — ɩɥɨɬɧɨɫɬɶ ɩɟɫɤɚ ɝ ɫɦ
ɤɪ² ɩɥɨɬɧɨɫɬɶ ɤɪɭɩɧɨɝɨ ɡɚɩɨɥɧɢɬɟɥɹ ɝ ɫɦ Ɇɤɪ² ɧɚɢɛɨɥɶɲɢɣ ɪɚɡɦɟɪ ɡɟɪɟɧ ɤɪɭɩɧɨɝɨ ɡɚɩɨɥɧɢɬɟɥɹ ɦɦ Wɩ — ɜɥɚɠɧɨɫɬɶ ɩɟɫɤɚ Wɤɪ² ɜɥɚɠɧɨɫɬɶ ɤɪɭɩɧɨɝɨ ɡɚɩɨɥɧɢɬɟɥɹ
r² ɬɪɟɛɭɟɦɨɟ ɫɨɨɬɧɨɲɟɧɢɟ ɦɟɠɞɭ ɩɟɫɤɨɦ ɢ ɤɪɭɩɧɵɦ ɡɚɩɨɥɧɢ
ɬɟɥɟɦ ɩɨ ɦɚɫɫɟ
Rɛ² ɬɪɟɛɭɟɦɨɟ ɡɧɚɱɟɧɢɟ ɩɪɨɱɧɨɫɬɢ ɛɟɬɨɧɚ ɧɚ ɟ ɫɭɬɤɢ ɩɨɫɥɟ
ɢɡɝɨɬɨɜɥɟɧɢɹ ɛɟɬɨɧɧɨɣ ɫɦɟɫɢ Ɇɉɚ ȼ/ɐ — ɜɨɞɨɰɟɦɟɧɬɧɨɟ ɨɬɧɨɲɟɧɢɟ
ɉɀ — ɬɪɟɛɭɟɦɨɟ ɡɧɚɱɟɧɢɟ ɩɨɞɜɢɠɧɨɫɬɢ ɫɦ ɢɥɢ ɠɟɫɬɤɨɫɬɢ ɫ
ɛɟɬɨɧɧɨɣ ɫɦɟɫɢ Ʉɞ² ɤɨɥɢɱɟɫɬɜɨ ɫɭɯɨɝɨ ɜɟɳɟɫɬɜɚ ɞɨɛɚɜɤɢ ɨɬ ɦɚɫɫɵ ɰɟɦɟɧɬɚ
ɞ — ɩɥɨɬɧɨɫɬɶ ɞɨɛɚɜɤɢ ɝ ɫɦ
ɋɞ² ɤɨɧɰɟɧɬɪɚɰɢɹ ɪɚɫɬɜɨɪɚ ɞɨɛɚɜɤɢ ɪɞ — ɩɥɨɬɧɨɫɬɶ ɪɚɫɬɜɨɪɚ ɞɨɛɚɜɤɢ ɝ ɫɦ
ȼɫɟ ɩɚɪɚɦɟɬɪɵ ɮɭɧɤɰɢɣZɢD ɢɡɦɟɪɹɸɬɫɹ ɫɩɟɰɢɚɥɶɧɵɦɢ ɩɪɢɛɨ ɪɚɦɢ ȼ ɤɚɱɟɫɬɜɟ ɩɚɪɚɦɟɬɪɨɜ ɮɭɧɤɰɢɢB ɛɟɪɭɬɫɹ ɬɪɟɛɭɟɦɵɟ ɡɧɚɱɟɧɢɹ
ɩɪɨɱɧɨɫɬɢɛɟɬɨɧɧɨɣɫɦɟɫɢɜɨɞɨɰɟɦɟɧɬɧɨɝɨɨɬɧɨɲɟɧɢɹɢɩɨɞɜɢɠɧɨ ɫɬɢ ɠɟɫɬɤɨɫɬɢ ɛɟɬɨɧɧɨɣ ɫɦɟɫɢ
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ǸȈșȟȍȚ șȖșȚȈȊȈ ȚȧȎȍȓȖȋȖ ȉȍȚȖȕȈ |
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Ɂɚ ɨɫɧɨɜɭ ɪɚɫɱɟɬɚ ɫɨɫɬɚɜɚ ɬɹɠɟɥɨɝɨ ɛɟɬɨɧɚ ɛɵɥɚ ɜɵɛɪɚɧɚ ɦɟɬɨ ɞɢɤɚ ɨɩɢɫɚɧɧɚɹ ɜ ɋɇɢɉɟ > @ ɚ ɬɚɤɠɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɧɨɪɦɚɬɢɜ ɧɵɟ ɞɨɤɭɦɟɧɬɵ > @
ɉɟɪɜɨɧɚɱɚɥɶɧɨ ɨɩɪɟɞɟɥɹɸɬ ɨɪɢɟɧɬɢɪɨɜɨɱɧɨɟ ɡɧɚɱɟɧɢɟ ɜɨɞɨɰɟ ɦɟɧɬɧɨɝɨ ɨɬɧɨɲɟɧɢɹ
ȼ ɥɢɬɟɪɚɬɭɪɟ ɢ ɧɨɪɦɚɬɢɜɧɵɯ ɞɨɤɭɦɟɧɬɚɯ ɩɪɟɞɥɚɝɚɸɬɫɹ ɪɚɡɥɢɱ ɧɵɟ ɡɚɜɢɫɢɦɨɫɬɢ
ɚ ɋɇɢɉ > @
ȼ/ɐ f Rɰ Rɛ |
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ɛ ȽɈɋɌ > @
ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɞɨɛɚɜɤɢ ɩɥɚɫɬɢɮɢɤɚɬɨɪɚ
ȼ/ɐ f Rɰ Rɛ |
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ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɞɨɛɚɜɤɢ ɫɭɩɟɪɩɥɚɫɬɢɮɢɤɚɬɨɪɚ
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ɜ Ȼ Ƚ ɋɤɪɚɦɬɚɟɜ ɘ Ɇ Ȼɚɠɟɧɨɜ > |
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ȼ/ɐ f Rɰ Rɛ Ⱥ |
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ɝɞɟȺ² ɤɨɷɮɮɢɰɢɟɧɬ ɤɚɱɟɫɬɜɚ ɡɚɩɨɥɧɢɬɟɥɟɣ
ɇɚ ɨɫɧɨɜɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɛɵɥɚ ɩɨɥɭɱɟɧɚ ɫɥɟɞɭɸɳɚɹ
ɡɚɜɢɫɢɦɨɫɬɶ
ȼ/ɐ f Rɰ Rɛ |
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ɉɨ ɡɧɚɱɟɧɢɹɦ ɧɚɢɛɨɥɶɲɟɣ ɤɪɭɩɧɨɫɬɢ ɡɟɪɟɧ ɤɪɭɩɧɨɝɨ ɡɚɩɨɥɧɢɬɟ ɥɹ ɢ ɬɪɟɛɭɟɦɨɣ ɩɨɞɜɢɠɧɨɫɬɢ ɢɥɢ ɠɟɫɬɤɨɫɬɢ ɫɦɟɫɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɨ ɥɢɱɟɫɬɜɨ ɜɨɞɵ ɞɥɹ ɡɚɬɜɨɪɟɧɢɹ ɦ ɛɟɬɨɧɧɨɣ ɫɦɟɫɢ ɧɟɨɛɯɨɞɢɦɨɣ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɬɪɟɛɭɟɦɨɣ ɭɞɨɛɨɭɤɥɚɞɵɜɚɟɦɨɫɬɢ
Ʉɨɥɢɱɟɫɬɜɨ ɜɨɞɵ ɡɚɜɢɫɢɬ ɨɬ ɭɞɨɛɨɭɤɥɚɞɵɜɚɟɦɨɫɬɢ ɛɟɬɨɧɧɨɣ ɫɦɟɫɢ ɩɨɞɜɢɠɧɨɫɬɢ ɢɥɢ ɠɟɫɬɤɨɫɬɢ ɢ ɦɨɞɭɥɹ ɤɪɭɩɧɨɫɬɢ ɝɪɚɜɢɹ ɳɟɛɧɹ
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ȼ f ɉɀ Ɇɤɪ |
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Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɤɨɥɢɱɟɫɬɜɚ ɜɨɞɵ ɛɵɥɢ ɩɨɥɭɱɟɧɵ ɡɚɜɢɫɢɦɨɫɬɢ |
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Ⱦɥɹ ɩɨɞɜɢɠɧɵɯ ɫɦɟɫɟɣ |
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u í u ɩɪɢɆɤɪ |
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u í u ɩɪɢɆɤɪ |
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ȼ u í u ɩɪɢɆɤɪ |
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ɢɥɢ |
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ȼ í u u Ɇɤɪ í Ɇɤɪ
ɝɞɟɆɤɪ — ɧɚɢɛɨɥɶɲɢɣ ɪɚɡɦɟɪ ɡɟɪɟɧ ɝɪɚɜɢɹ ɦɦ u² ɩɨɞɜɢɠɧɨɫɬɶ ɛɟɬɨɧɧɨɣ ɫɦɟɫɢ ɫɦ
Ⱦɥɹ ɠɟɫɬɤɢɯ ɫɦɟɫɟɣ |
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í u u ɩɪɢɆɤɪ |
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ɢɥɢ |
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ȼ u í u Ɇɤɪ í Ɇɤɪ
ɝɞɟɆɤɪ — ɧɚɢɛɨɥɶɲɢɣ ɪɚɡɦɟɪ ɡɟɪɟɧ ɝɪɚɜɢɹ ɦɦ u² ɠɟɫɬɤɨɫɬɶ ɛɟɬɨɧɧɨɣ ɫɦɟɫɢ ɫ
ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɳɟɛɧɹ ɪɚɫɯɨɞ ɜɨɞɵ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɧɚ ɥ ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɩɟɫɤɚ ɫ ɜɨɞɨɩɨɬɪɟɛɧɨɫɬɶɸ ɛɨɥɟɟ ɦɟɧɟɟ ɪɚɫ ɯɨɞ ɜɨɞɵ ɭɜɟɥɢɱɢɜɚɸɬ ɭɦɟɧɶɲɚɸɬ ɧɚ ɥ ɧɚ ɤɚɠɞɵɣ ɩɪɨɰɟɧɬ ɭɜɟɥɢ ɱɟɧɢɹ ɭɦɟɧɶɲɟɧɢɹ ɜɨɞɨɩɨɬɪɟɛɧɨɫɬɢ
ɉɪɨɢɡɜɨɞɹɬ ɤɨɪɪɟɤɬɢɪɨɜɤɭ ɤɨɥɢɱɟɫɬɜɚ ɜɨɞɵ ɫ ɭɱɟɬɨɦ ɜɜɟɞɟɧɢɹ ɞɨɛɚɜɤɢ ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɞɨɛɚɜɤɢ ɩɥɚɫɬɢɮɢɤɚɬɨɪɚ ɤɨɥɢɱɟɫɬɜɨ ɜɨ ɞɵ ɭɦɟɧɶɲɚɸɬ ɧɚ ɥ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɫɭɩɟɪɩɥɚɫɬɢɮɢɤɚɬɨɪɚ ² ɧɚ ɥ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɝɢɩɟɪɩɥɚɫɬɢɮɢɤɚɬɨɪɚ ² ɧɚ ɥ
ɉɨ ɜɨɞɨɰɟɦɟɧɬɧɨɦɭ ɨɬɧɨɲɟɧɢɸ ɢ ɤɨɥɢɱɟɫɬɜɭ ɜɨɞɵ ɨɩɪɟɞɟɥɹɸɬ ɪɚɫɯɨɞ ɰɟɦɟɧɬɚ ɧɚ ɦ ɛɟɬɨɧɧɨɣ ɫɦɟɫɢ
ɐ f ȼ/ɐ ȼ |
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f ɉɀ Ɇ ɤɪ |
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ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɞɨɛɚɜɤɢ ɩɥɚɫɬɢɮɢɤɚɬɨɪɚ ɪɚɫɯɨɞ ɰɟɦɟɧɬɚ ɤɨɪɪɟɤɬɢɪɭɟɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ > @
ɐ k ɐ |
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ɝɞɟk² ɩɨɩɪɚɜɨɱɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɬɚɛɥ |
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Ɂɚɬɟɦ ɫɪɚɜɧɢɜɚɸɬ ɧɚɣɞɟɧɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɰɟɦɟɧɬɚ ɫ ɫɨɨɬɜɟɬɫɬɜɭ ɸɳɢɦɢ ɧɨɪɦɚɦɢ ɪɚɫɯɨɞɚ ɰɟɦɟɧɬɚ ɢ ɩɪɨɢɡɜɨɞɹɬ ɤɨɪɪɟɤɬɢɪɨɜɤɭ
ǺȈȉȓȐȞȈ
ǯȕȈȟȍȕȐȧ ȗȖȗȘȈȊȖȟȕȖȋȖ ȒȖȥȜȜȐȞȐȍȕȚȈ
ǪȐȌ ȌȖȉȈȊȒȐ |
DzȖȥȜȜȐȞȐȍȕȚ |
ǷȓȈșȚȐȜȐȒȈȚȖȘ |
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ǹțȗȍȘȗȓȈșȚȐȜȐȒȈȚȖȘ |
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ǫȐȗȍȘȗȓȈșȚȐȜȐȒȈȚȖȘ |
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ǺȈȉȓȐȞȈ
ǯȕȈȟȍȕȐȧ ȗȖȗȘȈȊȖȟȕȖȋȖ ȒȖȥȜȜȐȞȐȍȕȚȈ
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ǪȐȌ ȌȖȉȈȊȒȐ |
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ǸȈșȝȖȌ ȞȍȔȍȕȚȈ |
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Ǵȍȕȍȍ Ȓȋ |
Ȓȋ |
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ǪȖȏȌțȝȖȊȖȊȓȍȒȈȦȡȈȧ |
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ǻșȒȖȘȐȚȍȓȤ ȚȊȍȘȌȍȕȐȧ |
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ɇɚ ɨɫɧɨɜɚɧɢɢ ɬɪɟɛɨɜɚɧɢɣ ɋɇɢɉɚ > @ ɛɵɥɚ ɩɨɥɭɱɟɧɚ ɪɟɝɪɟɫɫɢ ɨɧɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɧɨɪɦɵ ɪɚɫɯɨɞɚ ɰɟɦɟɧɬɚ ɦɚɪɤɢ Ɇɞɥɹɬɹɠɟɥɨɝɨɛɟɬɨɧɚɫɦɚɪɤɨɣɩɨɭɞɨɛɨɭɤɥɚɞɵɜɚɟɦɨɫɬɢ ɉɧɚ ɡɚɩɨɥɧɢɬɟɥɟ ɫ ɧɚɢɛɨɥɶɲɟɣ ɤɪɭɩɧɨɫɬɶɸ ɦɦ
ɇɐ f Rɛ Rɛ Rɛ |
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ɝɞɟK² ɩɨɩɪɚɜɨɱɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ |
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ǺȈȉȓȐȞȈ |
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ǯȕȈȟȍȕȐȧ ȗȖȗȘȈȊȖȟȕȖȋȖ ȒȖȥȜȜȐȞȐȍȕȚȈ |
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ǵȈȐȉȖȓȤȠȈȧ ȒȘțȗȕȖșȚȤ |
DzȓȈșș ȉȍȚȖȕȈ ȗȖ ȗȘȖȟȕȖșȚȐ |
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ȏȍȘȍȕ ȏȈȗȖȓȕȐȚȍȓȧ |
ȕȈ șȎȈȚȐȍ |
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ȔȔ |
ȌȖ Ǫ ȊȒȓȦȟȐȚȍȓȤȕȖ |
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ǯȕȈȟȍȕȐȧ ȗȖȗȘȈȊȖȟȕȖȋȖ ȒȖȥȜȜȐȞȐȍȕȚȈ |
ǺȈȉȓȐȞȈ |
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ǴȈȘȒȈ ȉȍȚȖȕȈ ȗȖ |
ǷȖȌȊȐȎȕȖșȚȤ șȔ |
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ǯȕȈȟȍȕȐȧ ȗȖȗȘȈȊȖȟȕȖȋȖ ȒȖȥȜȜȐȞȐȍȕȚȈ |
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ǴȈȘȒȈ ȞȍȔȍȕȚȈ |
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Ⱦɚɥɶɧɟɣɲɢɣ ɪɚɫɱɟɬ ɜɟɞɟɬɫɹ ɢɫɯɨɞɹ ɢɡ ɬɨɝɨ ɱɬɨ ɫɭɦɦɚ ɚɛɫɨɥɸɬ ɧɵɯ ɨɛɴɟɦɨɜ ɫɨɫɬɚɜɥɹɸɳɢɯ ɦɚɬɟɪɢɚɥɨɜ ɪɚɜɧɚ ɦ ɩɥɨɬɧɨ ɭɥɨɠɟɧɧɨɣ ɛɟɬɨɧɧɨɣ ɫɦɟɫɢ Ɉɩɪɟɞɟɥɹɸɬ ɚɛɫɨɥɸɬɧɵɣ ɨɛɴɟɦ ɰɟɦɟɧɬɧɨɝɨ ɬɟɫɬɚ ɢ ɚɛɫɨɥɸɬɧɵɣ ɨɛɴɟɦ ɫɦɟɫɢ ɡɚɩɨɥɧɢɬɟɥɟɣ ɚ ɬɚɤɠɟ ɦɚɫɫɭ ɤɚɠɞɨɝɨ ɡɚɩɨɥ ɧɢɬɟɥɹ ɢ ɯɢɦɢɱɟɫɤɢɯ ɞɨɛɚɜɨɤ ɜ ɦ > @
Ⱥɛɫɨɥɸɬɧɵɣ ɨɛɴɟɦ ɰɟɦɟɧɬɧɨɝɨ ɬɟɫɬɚ ɜɵɱɢɫɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
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Ⱥɛɫɨɥɸɬɧɵɣ ɨɛɴɟɦ ɫɦɟɫɢ ɡɚɩɨɥɧɢɬɟɥɟɣ ɜɵɱɢɫɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ |
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Ɂɚɬɟɦ ɨɩɪɟɞɟɥɹɸɬ ɦɚɫɫɭ ɡɚɩɨɥɧɢɬɟɥɟɣ ɩɨ ɮɨɪɦɭɥɟ |
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ɝɞɟ Ɂ ² ɩɪɢɜɟɞɟɧɧɚɹ ɩɥɨɬɧɨɫɬɶ ɫɦɟɫɢ ɡɚɩɨɥɧɢɬɟɥɟɣ ɪɚɜɧɚɹ
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ɡɞɟɫɶr — ɡɚɞɚɧɧɨɟ ɫɨɨɬɧɨɲɟɧɢɟ ɩɨ ɦɚɫɫɟ ɦɟɠɞɭ ɩɟɫɤɨɦ ɢ ɳɟɛɧɟɦ |
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Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɦɚɫɫɚ ɡɚɩɨɥɧɢɬɟɥɟɣ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ |
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Ʉɨɥɢɱɟɫɬɜɨ ɳɟɛɧɹ ɜɵɱɢɫɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ |
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ɧɢɬɟɥɟɣɁɢ ɦɚɫɫɨɣ ɳɟɛɧɹɓ |
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