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ɈȺȻɭɲɭɟɜɚȾɇɄɨɪɦɢɥɢɰɵɧɘɋɆɟɲɤɨɜɚ
ɍɉɊȺȼɅȿɇɂȿɍɊɈȼɇəɆɂɇȺɉɊəɀȿɇɂə
ȼ ɊȺɋɉɊȿȾȿɅɂɌȿɅɖɇɕɏɗɅȿɄɌɊɂɑȿɋɄɂɏɋȿɌəɏ
ɍɱɟɛɧɨɟɩɨɫɨɛɢɟ
Ɇɨɫɤɜɚȼɨɥɨɝɞɚ
©ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹª
2025
1
ɍȾɄ 621.316
ȻȻɄ 31.27
Ȼ
ɤɬɧ ȺȺɋɤɨɪɨɛɨɝɚɬɨɜɎȽȻɈɍȼɈ©ɂɜɚɧɨɜɫɤɢɣɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣ
ɷɧɟɪɝɟɬɢɱɟɫɤɢɣɭɧɢɜɟɪɫɢɬɟɬɢɦɟɧɢȼɂɅɟɧɢɧɚª
ɡɚɦɝɥɚɜɧɨɝɨɢɧɠɟɧɟɪɚɧɚɱɚɥɶɧɢɤɪɚɣɨɧɚɷɥɟɤɬɪɢɱɟɫɤɢɯɫɟɬɟɣ
ɉȺɈ©Ɋɨɫɫɟɬɢɐɟɧɬɪɢɉɪɢɜɨɥɠɶɟª– ɮɢɥɢɚɥ©ɂɜɷɧɟɪɝɨª ɋȺɄɢɬɚɟɜ
Ɋɟɰɟɧɡɟɧɬɵ
ȻɭɲɭɟɜɚɈȺ
Ȼ94 ɍɩɪɚɜɥɟɧɢɟ ɭɪɨɜɧɹɦɢ ɧɚɩɪɹɠɟɧɢɹ ɜ ɪɚɫɩɪɟɞɟɥɢɬɟɥɶɧɵɯ ɷɥɟɤɬɪɢɱɟ
ɫɤɢɯ ɫɟɬɹɯ ɭɱɟɛɧɨɟ ɩɨɫɨɛɢɟ Ɉ Ⱥ Ȼɭɲɭɟɜɚ Ⱦ ɇ Ʉɨɪɦɢɥɢɰɵɧ
ɘ ɋ Ɇɟɲɤɨɜɚ– Ɇɨɫɤɜɚȼɨɥɨɝɞɚɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ– ɫ
ɢɥɬɚɛɥ
ISBN -5---6
Ⱦɚɧɵ ɨɫɧɨɜɵ ɬɟɨɪɢɢ ɭɩɪɚɜɥɟɧɢɹ ɪɟɠɢɦɚɦɢ ɧɚɩɪɹɠɟɧɢɹ ɜ ɪɚɫɩɪɟɞɟɥɢɬɟɥɶɧɵɯ
ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɫɟɬɹɯ Ɋɚɫɫɦɨɬɪɟɧɵ ɫɩɨɫɨɛɵ ɢ ɦɟɬɨɞɵ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɧɚɩɪɹɠɟɧɢɹ
ɉɪɢɜɟɞɟɧɵɩɪɢɦɟɪɵɪɟɲɟɧɢɹɡɚɞɚɱɫɩɨɞɪɨɛɧɵɦɢɩɨɹɫɧɟɧɢɹɦɢɡɚɞɚɱɢɞɥɹɫɚɦɨɫɬɨ
ɹɬɟɥɶɧɨɝɨɪɟɲɟɧɢɹɢɤɨɧɬɪɨɥɶɧɵɟɜɨɩɪɨɫɵȼɩɪɢɥɨɠɟɧɢɢɞɚɧɵɫɩɪɚɜɨɱɧɵɟɦɚɬɟɪɢ
ɚɥɵɞɥɹɪɟɲɟɧɢɹɡɚɞɚɱ
Ⱦɥɹɨɛɭɱɚɸɳɢɯɫɹɩɨɧɚɩɪɚɜɥɟɧɢɸ ©ɗɥɟɤɬɪɨɷɧɟɪɝɟɬɢɤɚ ɢ ɷɥɟɤɬɪɨɬɟɯɧɢ
ɤɚª ɩɪɢ ɢɡɭɱɟɧɢɢ ɞɢɫɰɢɩɥɢɧ ©ɗɥɟɤɬɪɨɷɧɟɪɝɟɬɢɱɟɫɤɢɟ ɫɢɫɬɟɦɵ ɢ ɫɟɬɢªɢ©ɋɢɫɬɟɦɵ
ɷɥɟɤɬɪɨɫɧɚɛɠɟɧɢɹɝɨɪɨɞɨɜɢ ɩɪɨɦɵɲɥɟɧɧɵɯ ɩɪɟɞɩɪɢɹɬɢɣªɚɬɚɤɠɟɦɨɠɟɬ ɛɵɬɶ ɩɨ
ɥɟɡɧɨ ɞɥɹ ɫɥɭɲɚɬɟɥɟɣ ɰɟɧɬɪɨɜ ɩɨɜɵɲɟɧɢɹ ɤɜɚɥɢɮɢɤɚɰɢɢ ɩɟɪɫɨɧɚɥɚɷɧɟɪɝɟɬɢɱɟɫɤɢɯ
ɫɥɭɠɛɨɛɴɟɤɬɨɜɫɟɬɟɜɨɝɨɪɚɫɩɪɟɞɟɥɢɬɟɥɶɧɨɝɨɤɨɦɩɥɟɤɫɚɊɨɫɫɢɢ
ɍȾɄ 621.316
ȻȻɄ 31.27
ISBN -5---6 ȻɭɲɭɟɜɚɈȺɄɨɪɦɢɥɢɰɵɧȾɇɆɟɲɤɨɜɚɘɋ
ɂɡɞɚɬɟɥɶɫɬɜɨ©ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹª25
Ɉɮɨɪɦɥɟɧɢɟɂɡɞɚɬɟɥɶɫɬɜɨ©ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹª25
2
ɈȽɅȺȼɅȿɇɂȿ
ȼȼȿȾȿɇɂȿ .................................................................................................................. 5
ɋɉɂɋɈɄɂɋɉɈɅɖɁɈȼȺɇɇɕɏɋɈɄɊȺɓȿɇɂɃ ................................................. 6
1. ɋɈȼɊȿɆȿɇɇȺəɇɈɊɆȺɌɂȼɇȺəȻȺɁȺɇɈɆɂɇȺɅɖɇɕɏ
ɂȾɈɉɍɋɌɂɆɕɏɁɇȺɑȿɇɂɃɇȺɉɊəɀȿɇɂə
ȼɊȺɋɉɊȿȾȿɅɂɌȿɅɖɇɕɏɗɅȿɄɌɊɂɑȿɋɄɂɏɋȿɌəɏ ....................................
ɋɬɚɧɞɚɪɬɵɧɨɦɢɧɚɥɶɧɵɯɧɚɩɪɹɠɟɧɢɣ ...............................................................
Ⱦɨɩɭɫɬɢɦɵɟɡɧɚɱɟɧɢɹɧɚɩɪɹɠɟɧɢɣ ....................................................................
2. ȼɅɂəɇɂȿɈɌɄɅɈɇȿɇɂəɇȺɉɊəɀȿɇɂəɇȺɊȺȻɈɌɍ
ɉɊɂȿɆɇɂɄɈȼɗɅȿɄɌɊɂɑȿɋɄɈɃɗɇȿɊȽɂɂ
ɂɗɅȿɄɌɊɂɑȿɋɄɂȿɋȿɌɂ .................................................................................... 13
ɉȺȾȿɇɂȿɂɉɈɌȿɊəɇȺɉɊəɀȿɇɂəȼɌɊȿɏɎȺɁɇɈɃɅɗɉ
ɋ ɋɂɆɆȿɌɊɂɑɇɈɃɇȺȽɊɍɁɄɈɃ ....................................................................... 17
ɋɉɈɋɈȻɕɂɋɊȿȾɋɌȼȺɊȿȽɍɅɂɊɈȼȺɇɂəɇȺɉɊəɀȿɇɂə ................... 20
ɋɩɨɫɨɛɵɪɟɝɭɥɢɪɨɜɚɧɢɹɧɚɩɪɹɠɟɧɢɹ ............................................................... 20
Ⱦɜɭɯɫɬɭɩɟɧɱɚɬɨɟɪɟɝɭɥɢɪɨɜɚɧɢɟɧɚɩɪɹɠɟɧɢɹ ......................................... 20
ɋɬɚɛɢɥɢɡɚɰɢɹɧɚɩɪɹɠɟɧɢɹ ......................................................................... 21
ȼɫɬɪɟɱɧɨɟɪɟɝɭɥɢɪɨɜɚɧɢɟɧɚɩɪɹɠɟɧɢɹ .....................................................
ɋɪɟɞɫɬɜɚɪɟɝɭɥɢɪɨɜɚɧɢɹɧɚɩɪɹɠɟɧɢɹ .............................................................. 27
ɊȿȽɍɅɂɊɈȼȺɇɂȿɇȺɉɊəɀȿɇɂəɇȺɗɅȿɄɌɊɂɑȿɋɄɂɏ
ɋɌȺɇɐɂəɏ ...............................................................................................................
ɊȿȽɍɅɂɊɈȼȺɇɂȿɇȺɉɊəɀȿɇɂəɇȺɉɈȾɋɌȺɇɐɂəɏ ........................... 31
ɉɪɢɧɰɢɩɪɟɝɭɥɢɪɨɜɚɧɢɹɧɚɩɪɹɠɟɧɢɹɫɢɥɨɜɵɦɢɬɪɚɧɫɮɨɪɦɚɬɨɪɚɦɢ .......... 31
ɋɯɟɦɚɡɚɦɟɳɟɧɢɹɞɜɭɯɨɛɦɨɬɨɱɧɨɝɨɬɪɚɧɫɮɨɪɦɚɬɨɪɚ ...................................
ȾɜɭɯɨɛɦɨɬɨɱɧɵɟɬɪɚɧɫɮɨɪɦɚɬɨɪɵɫɊɉɇ ....................................................... 35
ȼɵɛɨɪɪɟɝɭɥɢɪɨɜɨɱɧɨɝɨɨɬɜɟɬɜɥɟɧɢɹɊɉɇ ..............................................
ȾɜɭɯɨɛɦɨɬɨɱɧɵɟɬɪɚɧɫɮɨɪɦɚɬɨɪɵɫɉȻȼ .......................................................
Ɍɪɟɯɨɛɦɨɬɨɱɧɵɟɬɪɚɧɫɮɨɪɦɚɬɨɪɵ ...................................................................
ȼɵɛɨɪɪɟɝɭɥɢɪɨɜɨɱɧɵɯɨɬɜɟɬɜɥɟɧɢɣɊɉɇɢɉȻȼ ...................................
Ⱥɜɬɨɬɪɚɧɫɮɨɪɦɚɬɨɪɵ ......................................................................................... 51
ȺɜɬɨɬɪɚɧɫɮɨɪɦɚɬɨɪɵɫɊɉɇɧɚɨɛɦɨɬɤɟɋɇ ........................................... 52
ȼɵɛɨɪɪɟɝɭɥɢɪɨɜɨɱɧɨɝɨɨɬɜɟɬɜɥɟɧɢɹɊɉɇɧɚɨɛɦɨɬɤɟɋɇ
ɚɜɬɨɬɪɚɧɫɮɨɪɦɚɬɨɪɨɜ ................................................................................................ 53
ȺɜɬɨɬɪɚɧɫɮɨɪɦɚɬɨɪɵɫɊɉɇɜɧɟɣɬɪɚɥɢ .................................................. 56
Ʌɢɧɟɣɧɵɣɪɟɝɭɥɢɪɨɜɨɱɧɵɣɬɪɚɧɫɮɨɪɦɚɬɨɪ ................................................... 60
ȼɨɥɶɬɨɞɨɛɚɜɨɱɧɵɣɬɪɚɧɫɮɨɪɦɚɬɨɪ .................................................................. 63
3
7. ȼɈɅɖɌɈȾɈȻȺȼɈɑɇɕȿɌɊȺɇɋɎɈɊɆȺɌɈɊɕȻɍɋɌȿɊɕ
ȼɊȺɋɉɊȿȾȿɅɂɌȿɅɖɇɕɏɋȿɌəɏɄȼ .........................................................
ɇɚɡɧɚɱɟɧɢɟɭɫɬɪɨɣɫɬɜɨɢɩɪɢɧɰɢɩɪɚɛɨɬɵ ....................................................
ɍɫɬɚɧɨɜɤɚɛɭɫɬɟɪɨɜ ............................................................................................ 72
ɊȿȽɍɅɂɊɈȼȺɇɂȿɇȺɉɊəɀȿɇɂəɂɁɆȿɇȿɇɂȿɆɉɈɌɈɄɈȼ
ɊȿȺɄɌɂȼɇɈɃɆɈɓɇɈɋɌɂȼɗɅȿɄɌɊɂɑȿɋɄɂɏɋȿɌəɏ............................ 73
Ȼɚɥɚɧɫɦɨɳɧɨɫɬɢɜɫɟɬɢɢɟɝɨɫɜɹɡɶɫ ɭɪɨɜɧɹɦɢɧɚɩɪɹɠɟɧɢɹ ....................... 73
ɉɪɢɧɰɢɩɪɟɝɭɥɢɪɨɜɚɧɢɹɧɚɩɪɹɠɟɧɢɹɢɡɦɟɧɟɧɢɟɦɩɨɬɨɤɨɜɪɟɚɤɬɢɜɧɨɣ
ɦɨɳɧɨɫɬɢɜɷɥɟɤɬɪɢɱɟɫɤɢɯɫɟɬɹɯ ............................................................................
ɍɫɬɚɧɨɜɤɢɤɨɦɩɟɧɫɚɰɢɢɪɟɚɤɬɢɜɧɨɣɦɨɳɧɨɫɬɢɢ ɢɯɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ......... 77
ɋɢɧɯɪɨɧɧɵɟɤɨɦɩɟɧɫɚɬɨɪɵ ........................................................................ 77
Ȼɚɬɚɪɟɢɤɨɧɞɟɧɫɚɬɨɪɨɜ ...............................................................................
ȼɵɛɨɪɦɨɳɧɨɫɬɢɍɄɊɆɩɨɭɫɥɨɜɢɹɦɪɟɝɭɥɢɪɨɜɚɧɢɹɧɚɩɪɹɠɟɧɢɹ .............
ɊȿȽɍɅɂɊɈȼȺɇɂȿɇȺɉɊəɀȿɇɂəɂɁɆȿɇȿɇɂȿɆ
ɉȺɊȺɆȿɌɊɈȼɋȿɌɂ ..............................................................................................
ɄɈɇɌɊɈɅɖɇɕȿȼɈɉɊɈɋɕ ............................................................................
ɁȺȾȺɑɂȾɅəɋȺɆɈɋɌɈəɌȿɅɖɇɈȽɈɊȿɒȿɇɂə ....................................
ɁȺȾȺɇɂəȾɅəɉɊɈȼȿȾȿɇɂəɄɈɇɌɊɈɅəɁɇȺɇɂɃ ............................. 101
ȻɂȻɅɂɈȽɊȺɎɂɑȿɋɄɂɃɋɉɂɋɈɄ .................................................................... 111
ɉɊɂɅɈɀȿɇɂȿ. ɋɉɊȺȼɈɑɇɕȿɆȺɌȿɊɂȺɅɕ ............................................... 112
ȼȼȿȾȿɇɂȿ
Ɋɚɫɩɪɟɞɟɥɢɬɟɥɶɧɵɟɷɥɟɤɬɪɢɱɟɫɤɢɟɫɟɬɢ ɩɪɟɞɧɚɡɧɚɱɟɧɵ ɞɥɹɪɚɫɩɪɟɞɟɥɟɧɢɹ
ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɩɨɥɭɱɚɟɦɨɣ ɨɬ ɢɫɬɨɱɧɢɤɨɜ ɩɢɬɚɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɢɯ
ɫɬɚɧɰɢɣ ɢɩɨɧɢɠɚɸɳɢɯ ɩɨɞɫɬɚɧɰɢɣ ɩɨɬɟɪɪɢɬɨɪɢɢ ɪɚɣɨɧɚ ɷɧɟɪɝɨɫɢɫɬɟɦɵ ɢ
ɩɟɪɟɞɚɱɟɟɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨɩɨɬɪɟɛɢɬɟɥɹɦ
ȼɚɠɧɟɣɲɟɣ ɡɚɞɚɱɟɣ ɪɚɫɩɪɟɞɟɥɢɬɟɥɶɧɵɯ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɫɟɬɟɣ ɹɜɥɹɟɬɫɹ
ɨɛɟɫɩɟɱɟɧɢɟɤɚɱɟɫɬɜɚɷɥɟɤɬɪɨɷɧɟɪɝɢɢɭɩɨɬɪɟɛɢɬɟɥɟɣɤɨɬɨɪɨɟɪɟɝɥɚɦɟɧɬɢɪɭɟɬ
ɫɹɦɟɠɝɨɫɭɞɚɪɫɬɜɟɧɧɵɦɫɬɚɧɞɚɪɬɨɦ [1].
Ɉɞɧɢɦɢɡɨɫɧɨɜɧɵɯɩɨɤɚɡɚɬɟɥɟɣɤɚɱɟɫɬɜɚɷɥɟɤɬɪɢɱɟɫɤɨɣɷɧɟɪɝɢɢɹɜɥɹɟɬ
ɫɹɨɬɤɥɨɧɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹɤɨɬɨɪɨɟ ɨɤɚɡɵɜɚɟɬ ɜɥɢɹɧɢɟɤɚɤ ɧɚɪɚɛɨɬɭ ɩɪɢɟɦ
ɧɢɤɨɜɷɥɟɤɬɪɨɷɧɟɪɝɢɢɬɚɤɢɧɚɬɟɯɧɢɤɨ-ɷɤɨɧɨɦɢɱɟɫɤɢɟɩɨɤɚɡɚɬɟɥɢɷɥɟɤɬɪɢɱɟ
ɫɤɢɯɫɟɬɟɣ
Ɋɟɠɢɦɷɥɟɤɬɪɢɱɟɫɤɢɯɫɟɬɟɣɹɜɥɹɟɬɫɹɞɨɩɭɫɬɢɦɵɦɩɪɢɭɫɥɨɜɢɢɱɬɨɧɚɩɪɹ
ɠɟɧɢɟɭɩɨɬɪɟɛɢɬɟɥɹɩɨɞɞɟɪɠɢɜɚɟɬɫɹɜɧɨɪɦɚɬɢɜɧɵɯ ɩɪɟɞɟɥɚɯ.
Ɉɫɧɨɜɧɵɦ ɢɧɫɬɪɭɦɟɧɬɨɦ ɨɝɪɚɧɢɱɟɧɢɹ ɨɬɤɥɨɧɟɧɢɣ ɧɚɩɪɹɠɟɧɢɹ ɹɜɥɹɟɬɫɹ
ɭɩɪɚɜɥɟɧɢɟɪɟɠɢɦɚɦɢɷɥɟɤɬɪɢɱɟɫɤɢɯ ɫɟɬɟɣɢɪɟɝɭɥɢɪɨɜɚɧɢɟɧɚɩɪɹɠɟɧɢɹ ɫɩɨ
ɦɨɳɶɸɪɚɡɥɢɱɧɵɯɦɟɬɨɞɨɜɢɫɪɟɞɫɬɜ
Ɉɬɥɢɱɢɬɟɥɶɧɨɣɨɫɨɛɟɧɧɨɫɬɶɸɭɱɟɛɧɨɝɨɩɨɫɨɛɢɹɹɜɥɹɟɬɫɹɟɝɨɩɪɚɤɬɢɱɟɫɤɚɹ
ɧɚɩɪɚɜɥɟɧɧɨɫɬɶ ɩɪɢ ɢɡɭɱɟɧɢɢ ɞɢɫɰɢɩɥɢɧ ©ɗɥɟɤɬɪɨɷɧɟɪɝɟɬɢɱɟɫɤɢɟ ɫɢɫɬɟɦɵ ɢ
ɫɟɬɢªɢ©ɋɢɫɬɟɦɵɷɥɟɤɬɪɨɫɧɚɛɠɟɧɢɹɝɨɪɨɞɨɜɢɩɪɨɦɵɲɥɟɧɧɵɯɩɪɟɞɩɪɢɹɬɢɣª
ɨɬɧɨɫɹɳɢɯɫɹ ɤ ɩɪɨɮɟɫɫɢɨɧɚɥɶɧɨɦɭ ɰɢɤɥɭ ɞɢɫɰɢɩɥɢɧ ɭɱɟɛɧɨɝɨ ɩɥɚɧɚ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ©ɗɥɟɤɬɪɨɷɧɟɪɝɟɬɢɤɚɢɷɥɟɤɬɪɨɬɟɯɧɢɤɚª
ȼ ɭɱɟɛɧɨɦ ɩɨɫɨɛɢɢ ɞɚɧɵ ɨɫɧɨɜɵ ɬɟɨɪɢɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɪɟɝɭɥɢɪɭɸɳɢɯ
ɭɫɬɪɨɣɫɬɜ ɫɩɨɫɨɛɵ ɢɦɟɬɨɞɵ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɩɪɢ ɭɩɪɚɜɥɟɧɢɢ ɪɟ
ɠɢɦɚɦɢɪɚɫɩɪɟɞɟɥɢɬɟɥɶɧɵɯɷɥɟɤɬɪɢɱɟɫɤɢɯɫɟɬɟɣ
ɉɨɫɨɛɢɟɫɨɞɟɪɠɢɬɩɪɢɦɟɪɵ ɪɟɲɟɧɢɹɡɚɞɚɱɫɩɨɞɪɨɛɧɵɦɢ ɩɨɹɫɧɟɧɢɹɦɢɚ
ɬɚɤɠɟɡɚɞɚɱɢɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨɪɟɲɟɧɢɹɢɤɨɧɬɪɨɥɶɧɵɟ ɜɨɩɪɨɫɵɩɪɢɩɨɞ
ɝɨɬɨɜɤɟɤɩɪɨɦɟɠɭɬɨɱɧɨɦɭɢɢɬɨɝɨɜɨɦɭɤɨɧɬɪɨɥɹɦɡɧɚɧɢɣ ɉɪɢɜɟɞɟɧɵɧɟɤɨɬɨ
ɪɵɟɫɩɪɚɜɨɱɧɵɟɦɚɬɟɪɢɚɥɵɧɟɨɛɯɨɞɢɦɵɟɞɥɹɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨɪɟɲɟɧɢɹɡɚɞɚɱ
Ɇɚɬɟɪɢɚɥ ɩɨɫɨɛɢɹ ɦɨɠɟɬ ɛɵɬɶ ɩɨɥɟɡɟɧ ɞɥɹ ɜɵɩɨɥɧɟɧɢɹ ɨɛɭɱɚɸɳɢɦɢɫɹ
ɤɭɪɫɨɜɵɯɩɪɨɟɤɬɨɜɩɨɭɤɚɡɚɧɧɵɦɜɵɲɟɞɢɫɰɢɩɥɢɧɚɦɚɬɚɤɠɟɫɥɭɲɚɬɟɥɹɦ ɤɭɪ
ɫɨɜɩɨɜɵɲɟɧɢɹɤɜɚɥɢɮɢɤɚɰɢɢɩɨɷɥɟɤɬɪɨɷɧɟɪɝɟɬɢɱɟɫɤɢɦɫɩɟɰɢɚɥɶɧɨɫɬɹɦ
Ⱥɜɬɨɪɵɧɟɩɪɟɬɟɧɞɭɸɬɧɚɩɨɥɧɨɟɢɡɥɨɠɟɧɢɟɜɨɩɪɨɫɨɜɫɜɹɡɚɧɧɵɯɫɭɩɪɚɜ
ɥɟɧɢɟɦɭɪɨɜɧɹɦɢ ɧɚɩɪɹɠɟɧɢɹ ɜɷɥɟɤɬɪɨɷɧɟɪɝɟɬɢɱɟɫɤɢɯɫɢɫɬɟɦɚɯɩɨɷɬɨɦɭ ɨɧɨ
ɧɟɦɨɠɟɬɡɚɦɟɧɢɬɶɜɩɨɥɧɨɣɦɟɪɟɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟɭɱɟɛɧɢɤɢɢɞɪɭɝɢɟɭɱɟɛɧɵɟ
ɩɨɫɨɛɢɹ.
5
ɋɉɂɋɈɄɂɋɉɈɅɖɁɈȼȺɇɇɕɏɋɈɄɊȺɓȿɇɂɃ
ȺȾ – ɚɫɢɧɯɪɨɧɧɵɣɞɜɢɝɚɬɟɥɶ
ȺɊȼ – ɚɜɬɨɦɚɬɢɱɟɫɤɨɟɪɟɝɭɥɢɪɨɜɚɧɢɟɜɨɡɛɭɠɞɟɧɢɹ
ȺɋɄ – ɚɫɢɧɯɪɨɧɢɡɢɪɨɜɚɧɧɵɣɫɢɧɯɪɨɧɧɵɣɤɨɦɩɟɧɫɚɬɨɪ
ȻȺɍɊɉɇ – ɛɥɨɤɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨɭɩɪɚɜɥɟɧɢɹɪɟɝɭɥɹɬɨɪɨɦɩɨɞɧɚɝɪɭɡɤɨɣ
ȻɌ – ɛɥɨɱɧɵɣɬɪɚɧɫɮɨɪɦɚɬɨɪ
ȻɄ – ɛɚɬɚɪɟɹɤɨɧɞɟɧɫɚɬɨɪɨɜ
ȼȾɌ – ɜɨɥɶɬɨɞɨɛɚɜɨɱɧɵɣɬɪɚɧɫɮɨɪɦɚɬɨɪ
ȼɅ – ɜɨɡɞɭɲɧɚɹɥɢɧɢɹ
ȼɇ – ɜɵɫɲɟɟɧɚɩɪɹɠɟɧɢɟ
ȼɊɍ – ɜɜɨɞɧɨɟɪɚɫɩɪɟɞɟɥɢɬɟɥɶɧɨɟɭɫɬɪɨɣɫɬɜɨ
Ƚ – ɝɟɧɟɪɚɬɨɪ
Ⱦɋɉ – ɞɭɝɨɜɚɹɫɬɚɥɟɩɥɚɜɢɥɶɧɚɹɩɟɱɶ
ɂɉ – ɢɫɬɨɱɧɢɤɩɢɬɚɧɢɹ
ɂɊɆ – ɢɫɬɨɱɧɢɤɪɟɚɤɬɢɜɧɨɣɦɨɳɧɨɫɬɢ
ɂɌ – ɢɞɟɚɥɶɧɵɣɬɪɚɧɫɮɨɪɦɚɬɨɪ
ɄɁ – ɤɨɪɨɬɤɨɟɡɚɦɵɤɚɧɢɟ
ɅɊ – ɥɢɧɟɣɧɵɣɪɟɝɭɥɢɪɨɜɨɱɧɵɣɬɪɚɧɫɮɨɪɦɚɬɨɪ
Ʌɗɉ – ɥɢɧɢɹɷɥɟɤɬɪɨɩɟɪɟɞɚɱɢ
ɇɇ – ɧɢɡɲɟɟɧɚɩɪɹɠɟɧɢɟ
Ɉȼ – ɨɛɦɨɬɤɚɜɨɡɛɭɠɞɟɧɢɹ
ɉȻȼ – ɩɟɪɟɤɥɸɱɟɧɢɟɛɟɡɜɨɡɛɭɠɞɟɧɢɹ
ɉɋ – ɩɨɞɫɬɚɧɰɢɹ
ɉɌɗ – ɩɪɚɜɢɥɚɬɟɯɧɢɱɟɫɤɨɣɷɤɫɩɥɭɚɬɚɰɢɢ
ɉɍɗ – ɩɪɚɜɢɥɚɭɫɬɪɨɣɫɬɜɚɷɥɟɤɬɪɨɭɫɬɚɧɨɜɨɤ
– ɩɨɬɪɟɛɢɬɟɥɢɷɥɟɤɬɪɢɱɟɫɤɨɣɷɧɟɪɝɢɢ
ɉɗɗ
Ɋɟɝɍ – ɪɟɝɭɥɢɪɨɜɨɱɧɨɟɭɫɬɪɨɣɫɬɜɨ
Ɋɉɇ – ɪɟɝɭɥɢɪɨɜɚɧɢɟɩɨɞɧɚɝɪɭɡɤɨɣ
ɋȾ – ɫɢɧɯɪɨɧɧɵɣɞɜɢɝɚɬɟɥɶ
ɋɄ – ɫɢɧɯɪɨɧɧɵɣɤɨɦɩɟɧɫɚɬɨɪ
ɋɄɍ – ɫɬɚɬɢɱɟɫɤɨɟɤɨɦɩɟɧɫɢɪɭɸɳɟɟɭɫɬɪɨɣɫɬɜɨ
ɋɇ – ɫɪɟɞɧɟɟɧɚɩɪɹɠɟɧɢɟ
ɋɌɄ – ɫɬɚɬɢɱɟɫɤɢɣɬɢɪɢɫɬɨɪɧɵɣɤɨɦɩɟɧɫɚɬɨɪ
ɋɏɇ – ɫɬɚɬɢɱɟɫɤɚɹɯɚɪɚɤɬɟɪɢɫɬɢɤɚɧɚɝɪɭɡɤɢ
Ɍ – ɬɪɚɧɫɮɨɪɦɚɬɨɪ
Ɍɇ – ɬɪɚɧɫɮɨɪɦɚɬɨɪɧɚɩɪɹɠɟɧɢɹ
Ɍɉ – ɬɪɚɧɫɮɨɪɦɚɬɨɪɧɚɹɩɨɞɫɬɚɧɰɢɹ
ɌɌ – ɬɪɚɧɫɮɨɪɦɚɬɨɪɬɨɤɚ
6
ɍȻɄ – ɭɩɪɚɜɥɹɟɦɵɟɛɚɬɚɪɟɢɤɨɧɞɟɧɫɚɬɨɪɨɜ
ɍɄɊɆ – ɭɫɬɚɧɨɜɤɚɤɨɦɩɟɧɫɚɰɢɢɪɟɚɤɬɢɜɧɨɣɦɨɳɧɨɫɬɢ
ɍɊ – ɭɫɬɚɧɨɜɢɜɲɢɣɫɹɪɟɠɢɦ
ɍɒɊ – ɭɩɪɚɜɥɹɟɦɵɣɲɭɧɬɢɪɭɸɳɢɣɪɟɚɤɬɨɪ
ɐɉ – ɰɟɧɬɪɩɢɬɚɧɢɹ
ɒɊ – ɲɭɧɬɢɪɭɸɳɢɣɪɟɚɤɬɨɪ
ɗȼɆ – ɷɥɟɤɬɪɨɧɧɚɹɜɵɱɢɫɥɢɬɟɥɶɧɚɹɦɚɲɢɧɚ
ɗȾɋ – ɷɥɟɤɬɪɨɞɜɢɠɭɳɚɹɫɢɥɚ
ɗɋ – ɷɧɟɪɝɨɫɢɫɬɟɦɚ
ɗɗɋ – ɷɥɟɤɬɪɨɷɧɟɪɝɟɬɢɱɟɫɤɚɹɫɢɫɬɟɦɚ.
7
ɋɈȼɊȿɆȿɇɇȺəɇɈɊɆȺɌɂȼɇȺəȻȺɁȺ
ɇɈɆɂɇȺɅɖɇɕɏɂȾɈɉɍɋɌɂɆɕɏɁɇȺɑȿɇɂɃ
ɇȺɉɊəɀȿɇɂəȼɊȺɋɉɊȿȾȿɅɂɌȿɅɖɇɕɏ
ɗɅȿɄɌɊɂɑȿɋɄɂɏɋȿɌəɏ
ɋɬɚɧɞɚɪɬɵɧɨɦɢɧɚɥɶɧɵɯɧɚɩɪɹɠɟɧɢɣ
ɇɨɦɢɧɚɥɶɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɫɟɬɢ – ɧɚɩɪɹɠɟɧɢɟ ɞɥɹ ɤɨɬɨɪɨɝɨ ɩɪɟɞɧɚɡɧɚ
ɱɟɧɚɢɥɢ ɢɞɟɧɬɢɮɢɰɢɪɨɜɚɧɚɷɥɟɤɬɪɢɱɟɫɤɚɹ ɫɟɬɶɢ ɩɪɢɦɟɧɢɬɟɥɶɧɨɤ ɤɨɬɨɪɨɦɭ
ɭɫɬɚɧɚɜɥɢɜɚɸɬɟɟɪɚɛɨɱɢɟɯɚɪɚɤɬɟɪɢɫɬɢɤɢ [1].
ȼɫɨɜɪɟɦɟɧɧɨɣɷɥɟɤɬɪɨɷɧɟɪɝɟɬɢɤɟɪɨɥɶɪɚɫɩɪɟɞɟɥɢɬɟɥɶɧɵɯɜɵɩɨɥɧɹɸɬ ɪɚɡ
ɜɟɬɜɥɺɧɧɵɟɷɥɟɤɬɪɢɱɟɫɤɢɟɫɟɬɢɛɨɥɶɲɨɝɨɞɢɚɩɚɡɨɧɚɧɨɦɢɧɚɥɶɧɵɯɧɚɩɪɹɠɟɧɢɣ
– ɫɟɬɢɞɨȼ– ɜɩɪɟɞɟɥɚɯɤɜɚɪɬɚɥɨɜɝɨɪɨɞɨɜɢɥɢɧɟɤɪɭɩɧɵɯɩɨɫɺɥɤɨɜ
ɰɟɯɨɜɩɪɨɦɵɲɥɟɧɧɵɯɩɪɟɞɩɪɢɹɬɢɣɩɪɨɢɡɜɨɞɫɬɜɟɧɧɵɯɨɛɴɟɤɬɨɜ ɫɟɥɶɫɤɨɝɨɯɨ
ɡɹɣɫɬɜɚɠɢɥɵɯɢɨɛɳɟɫɬɜɟɧɧɵɯɡɞɚɧɢɣɢɬɩ
– ɫɟɬɢ ɢ ɤȼ– ɜɩɪɟɞɟɥɚɯɦɢɤɪɨɪɚɣɨɧɨɜ ɝɨɪɨɞɨɜɤɪɭɩɧɵɯ ɩɨɫɺɥ
ɤɨɜɩɪɨɦɵɲɥɟɧɧɵɯɩɪɟɞɩɪɢɹɬɢɣɫɟɥɶɫɤɨɯɨɡɹɣɫɬɜɟɧɧɵɯɪɚɣɨɧɨɜ
– ɫɟɬɢɢɤȼ– ɧɚɪɚɫɫɬɨɹɧɢɹɨɬɟɞɢɧɢɰɞɨɧɟɫɤɨɥɶɤɢɯɞɟɫɹɬɤɨɜ
ɤɢɥɨɦɟɬɪɨɜɨɬɩɨɞɫɬɚɧɰɢɣɷɧɟɪɝɨɫɢɫɬɟɦɞɨɩɨɬɪɟɛɢɬɟɥɹ
ɇɨɦɢɧɚɥɶɧɵɟɧɚɩɪɹɠɟɧɢɹɪɚɫɩɪɟɞɟɥɢɬɟɥɶɧɵɯɷɥɟɤɬɪɢɱɟɫɤɢɯɫɟɬɟɣɢɷɥɟɤ
ɬɪɨɨɛɨɪɭɞɨɜɚɧɢɹɭɫɬɚɧɨɜɥɟɧɵɜɫɬɚɧɞɚɪɬɚɯ [2–@ ɢɩɪɢɜɟɞɟɧɵɜɬɚɛɥɢɰɟ 1.1.
Ɍɚɛɥɢɰɚ1.1
ɇɨɦɢɧɚɥɶɧɵɟɧɚɩɪɹɠɟɧɢɹɩɟɪɟɦɟɧɧɨɝɨɬɨɤɚɞɥɹɱɚɫɬɨɬɵȽɰ
ɪɚɫɩɪɟɞɟɥɢɬɟɥɶɧɵɯɷɥɟɤɬɪɢɱɟɫɤɢɯɫɟɬɟɣɢɷɥɟɤɬɪɨɨɛɨɪɭɞɨɜɚɧɢɹ
ɇɨɦɢɧɚɥɶɧɨɟ
ɧɚɩɪɹɠɟɧɢɟɤȼ
ȽɈɋɌ- [2]
6 6
ɇɨɦɢɧɚɥɶɧɨɟ
ɧɚɩɪɹɠɟɧɢɟɤȼ
ȽɈɋɌ- [3]
ɇɨɦɢɧɚɥɶɧɨɟ
ɧɚɩɪɹɠɟɧɢɟɤȼ
ȽɈɋɌ- >@
10 10
20 20
35 35 –
110 –
220 –
– –
ɉɪɢɦɟɱɚɧɢɟ ȼ >@ ɭɫɬɚɧɨɜɥɟɧɵɧɨɦɢɧɚɥɶɧɵɟɡɧɚɱɟɧɢɹɧɚɩɪɹɠɟɧɢɣɞɥɹɢɫɬɨɱɧɢɤɨɜɩɢɬɚɧɢɹ
ɱɢɫɥɢɬɟɥɶɫɟɬɟɣɢɩɪɢɟɦɧɢɤɨɜɷɥɟɤɬɪɢɱɟɫɤɨɣɷɧɟɪɝɢɢɡɧɚɦɟɧɚɬɟɥɶɧɚɩɪɢɦɟɪ
Ⱦɨɩɭɫɬɢɦɵɟɡɧɚɱɟɧɢɹɧɚɩɪɹɠɟɧɢɣ
ɋɬɚɧɞɚɪɬ [1] ɭɫɬɚɧɚɜɥɢɜɚɟɬ ɧɨɪɦɚɬɢɜɧɨɟ ɡɧɚɱɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɩɨ ɨɫɧɨɜ
ɧɨɦɭɩɨɤɚɡɚɬɟɥɸ ɤɚɱɟɫɬɜɚɷɥɟɤɬɪɨɷɧɟɪɝɢɢ – ɨɬɤɥɨɧɟɧɢɸɧɚɩɪɹɠɟɧɢɹ ɨɬɧɨ
ɫɹɳɟɝɨɫɹɤɦɟɞɥɟɧɧɨɦɭɢɡɦɟɧɟɧɢɸɧɚɩɪɹɠɟɧɢɹ ɜɬɨɱɤɚɯɩɟɪɟɞɚɱɢɟɟɩɨɬɪɟ
ɛɢɬɟɥɹɦɷɥɟɤɬɪɢɱɟɫɤɢɯɫɟɬɟɣɞɥɹɤɨɬɨɪɨɝɨɭɫɬɚɧɨɜɥɟɧɵɧɨɪɦɵ %.
Ɉɬɤɥɨɧɟɧɢɹɧɚɩɪɹɠɟɧɢɹɨɩɪɟɞɟɥɹɸɬɫɹɩɨɜɵɪɚɠɟɧɢɹɦ [1]
– ɨɬɪɢɰɚɬɟɥɶɧɨɟɨɬɤɥɨɧɟɧɢɟɧɚɩɪɹɠɟɧɢɹ
ªº
UU
0
m
G
«»
U
«»
¬¼
U
0
– ɩɨɥɨɠɢɬɟɥɶɧɨɟɨɬɤɥɨɧɟɧɢɟɧɚɩɪɹɠɟɧɢɹU
ªº
UU
m
G
«»
U
«»
¬¼
U
0
0
ɝɞɟ
ɷɥɟɤɬɪɢɱɟɫɤɚɹɫɬɚɧɰɢɹɦɟɧɶɲɟU
ɢɧɬɟɪɜɚɥɟɜɪɟɦɟɧɢ ɦɢɧ U
mU
ɢ
– ɡɧɚɱɟɧɢɹɧɚɩɪɹɠɟɧɢɹɢɫɬɨɱɧɢɤɚ ɩɢɬɚɧɢɹɩɨɞɫɬɚɧɰɢɹɢɥɢ
mU
ɢɛɨɥɶɲɟU0 ɫɨɨɬɜɟɬɫɬɜɟɧɧɨɭɫɪɟɞɧɟɧɧɵɟɜ
0
– ɧɚɩɪɹɠɟɧɢɟɪɚɜɧɨɟ ɫɬɚɧɞɚɪɬɧɨɦɭɧɨɦɢɧɚɥɶ
0
ɧɨɦɭ ɧɚɩɪɹɠɟɧɢɸ ȽɈɋɌ 721- ɢɥɢ ȽɈɋɌ - ɢɥɢ ɫɨɝɥɚɫɨɜɚɧɧɨɦɭ
ɧɚɩɪɹɠɟɧɢɸɬɨɥɶɤɨɞɥɹɧɚɩɪɹɠɟɧɢɹ ɢɤȼ
ɍɫɬɚɧɨɜɥɟɧɧɵɟ ɧɨɪɦɵ ɞɥɹ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɢ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɨɬɤɥɨɧɟɧɢɣ
ɧɚɩɪɹɠɟɧɢɹ ɧɟ ɞɨɥɠɧɵ ɩɪɟɜɵɲɚɬɶ % ɧɨɦɢɧɚɥɶɧɨɝɨ ɢɥɢ ɫɨɝɥɚɫɨɜɚɧɧɨɝɨ
ɡɧɚɱɟɧɢɹɧɚɩɪɹɠɟɧɢɹɜɬɨɱɤɟɩɟɪɟɞɚɱɢɷɥɟɤɬɪɨɷɧɟɪɝɢɢɜɬɟɱɟɧɢɟ % ɜɪɟɦɟ
ɧɢ ɢɧɬɟɪɜɚɥɚɜɨɞɧɭɧɟɞɟɥɸ [1].
Ɍɨɱɤɚ ɩɟɪɟɞɚɱɢ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ – ɬɨɱɤɚ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɫɟɬɢ
ɧɚɯɨɞɹɳɚɹɫɹɧɚɥɢɧɢɢɪɚɡɞɟɥɚɨɛɴɟɤɬɨɜɷɥɟɤɬɪɨɷɧɟɪɝɟɬɢɤɢɦɟɠɞɭɜɥɚɞɟɥɶɰɚɦɢ
ɩɨɩɪɢɡɧɚɤɭ ɫɨɛɫɬɜɟɧɧɨɫɬɢɢɥɢ ɜɥɚɞɟɧɢɹɧɚ ɢɧɨɦɩɪɟɞɭɫɦɨɬɪɟɧɧɨɦ ɡɚɤɨɧɚɦɢ
ɨɫɧɨɜɚɧɢɢɨɩɪɟɞɟɥɟɧɧɚɹɜɩɪɨɰɟɫɫɟɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨɩɪɢɫɨɟɞɢɧɟɧɢɹ [1].
Ʉɚɤ ɩɪɚɜɢɥɨ ɬɨɱɤɨɣ ɩɟɪɟɞɚɱɢ ɷɥɟɤɬɪɨɷɧɟɪɝɢɢ ɹɜɥɹɟɬɫɹ ɬɨɱɤɚ ɤɨɬɨɪɚɹ
ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɚɤɬɨɦ ɪɚɡɝɪɚɧɢɱɟɧɢɹ ɛɚɥɚɧɫɨɜɨɣ ɩɪɢɧɚɞɥɟɠɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟ
ɫɤɢɯɫɟɬɟɣɢɷɤɫɩɥɭɚɬɚɰɢɨɧɧɨɣɨɬɜɟɬɫɬɜɟɧɧɨɫɬɢɫɬɨɪɨɧɩɨɬɪɟɛɢɬɟɥɹɢɫɟɬɟɜɨɣ
ɨɪɝɚɧɢɡɚɰɢɢ
U
G
(1.1
100
100
(1.2
ɉɪɢɦɟɪ
ȼ ɫɯɟɦɟ ɪɢɫɭɧɤɚ ɩɭɧɤɬɢɪɧɨɣ ɥɢɧɢɟɣ ɩɨɤɚɡɚɧɚ ɝɪɚɧɢɰɚ ɛɚɥɚɧɫɨɜɨɣ
ɩɪɢɧɚɞɥɟɠɧɨɫɬɢɩɢɬɚɸɳɟɣ ɷɥɟɤɬɪɢɱɟɫɤɨɣɫɟɬɢ ɤȼ ɫɩɨɞɫɬɚɧɰɢɹɦɢ ɢ
ɩɪɢɧɚɞɥɟɠɚɳɢɦɢɷɧɟɪɝɨɫɢɫɬɟɦɟɢɩɨɬɪɟɛɢɬɟɥɹ– ɩɪɨɦɵɲɥɟɧɧɨɝɨɩɪɟɞɩɪɢɹɬɢɹ
ɩɨ ɩɟɪɟɪɚɛɨɬɤɟ ɧɟɮɬɟɩɪɨɞɭɤɬɨɜ ɫ ɫɨɛɫɬɜɟɧɧɵɦɢ ɝɥɚɜɧɵɦɢ ɩɨɧɢɡɢɬɟɥɶɧɵɦɢ
ɩɨɞɫɬɚɧɰɢɹɦɢ ȽɉɉɢȽɉɉ
ɉɋɇɉɁ220/110/35 ɉɋɋɉɉ110/10
ɗɗɋɉɨɬɪɟɛɢɬɟɥɶ
Ƚɪɚɧɢɰɚ
ɛɚɥɚɧɫɨɜɨɣ
1Ƚɉɉ
ɩɪɢɧɚɞɥɟɠɧɨɫɬɢ
ɈɊɍ-110ɤȼ
2Ƚɉɉ
ɈɊɍ-110ɤȼ
ɁɊɍ-6ɤȼ ɁɊɍ-6ɤȼ
Ɋɢɫ 1.1. ɋɯɟɦɚɪɚɡɝɪɚɧɢɱɟɧɢɹɫɟɬɟɜɨɣɤɨɦɩɚɧɢɢɢɩɨɬɪɟɛɢɬɟɥɹɫɭɤɚɡɚɧɢɟɦ
ɝɪɚɧɢɰɵɛɚɥɚɧɫɨɜɨɣɩɪɢɧɚɞɥɟɠɧɨɫɬɢ
ɇɚɢɛɨɥɶɲɟɟɪɚɛɨɱɟɟɧɚɩɪɹɠɟɧɢɟ ɷɥɟɤɬɪɨɨɛɨɪɭɞɨɜɚɧɢɹ ɜɪɚɫɩɪɟɞɟɥɢ
ɬɟɥɶɧɵɯ ɫɟɬɹɯ ɢ ɤȼ ɩɪɢɥɨɠɟɧɢɟ ɤɨɬɨɪɨɝɨ ɤ ɡɚɠɢɦɚɦ
ɪɚɡɧɵɯɮɚɡɩɨɥɸɫɨɜɷɥɟɤɬɪɨɨɛɨɪɭɞɨɜɚɧɢɹɞɨɩɭɫɬɢɦɨɩɨɭɫɥɨɜɢɹɦɪɚɛɨɬɵ
ɟɝɨɢɡɨɥɹɰɢɢ ɭɤɚɡɚɧɨɜɫɬɚɧɞɚɪɬɚɯȽɈɋɌ-ɢȽɈɋɌ-ɢɜɬɚɛ
ɥɢɰɟ 1.2.
10
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