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Файл:Каналы связи. Физические и компьютерные модели. Монография
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ȼ. Ʌ. ɏɚɡ
ɚɧ
ɄȺɇȺɅɕ ɋȼəɁɂ
ɎɂɁɂɑȿɋɄɂȿ ɂ ɄɈɆɉɖɘɌȿɊɇɕȿ ɆɈȾȿɅɂ
COMMUNICATION CHANNELS
PHYSICAL AND COMPUTER MODELS
Ɇɨɧɨɝɪɚɮɢɹ
Ɇɨɫɤɜɚ ȼɨɥɨɝɞɚ
«ɂɧɮɪɚ-ɂɧɠɟɧ
2024
ɟɪɢɹ»
ɍȾɄ 621.394
ȻȻɄ 32.881
ɏ15
Ɋɟɰɟɧɡɟɧɬɵ:
ɤɚɧɞ. ɮɢɡ.-ɦɚɬ. ɧɚɭɤ, ɫɬ. ɧɚɭɱ. ɫɨɬɪ. Ɉɇɐ ɋɈ ɊȺɇ (ɂɧɫɬɢɬɭɬ ɪɚɞɢɨɮɢɡɢɤɢ
ɢ ɮɢɡɢɱɟɫɤɨɣ ɷɥɟɤɬɪɨɧɢɤɢ – ɂɊɎɗ), ɭɱɟɧɵɣ ɫɟɤɪɟɬɚɪɶ ɇɌɋ ȺɈ «Ɉɦɫɤɢɣ ɇɂɂ
ɩɪɢɛɨɪɨɫɬɪɨɟɧɢɹ» Ⱦ. ȿ. Ɂɚɱɚɬɟɣɫɤɢɣ;
ɞ-ɪ ɬɟɯɧ. ɧɚɭɤ, ɜɟɞ. ɧɚɭɱ. ɫɨɬɪ. ɥɚɛɨɪɚɬɨɪɢɢ ɨɩɬɢɱɟɫɤɨɣ ɥɨɤɚɰɢɢ ɂɧɫɬɢɬɭɬɚ
ɨɩɬɢɤɢ ɚɬɦɨɫɮɟɪɵ ɢɦ. ɚɤɚɞ. ȼ. ȿ. Ɂɭɟɜɚ ɋɈ ɊȺɇ
ȼ. Ⱥ. ɏɚɧ
ɏɚɡɚɧ, ȼ. Ʌ.
ɏ15 Ʉɚɧɚɥɵ ɫɜɹɡɢ. Ɏɢɡɢɱɟɫɤɢɟ ɢ ɤɨɦɩɶɸɬɟɪɧɵɟ ɦɨɞɟɥɢ : ɦɨɧɨɝɪɚɮɢɹ /
ȼ. Ʌ. ɏɚɡɚɧ. – Ɇɨɫɤɜɚ ; ȼɨɥɨɝɞɚ : ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ, 2024. – 108 ɫ. : ɢɥ.,
ɬɚɛɥ.
ISBN 978-5-9729-1692-4
Ɋɚɫɫɦɨɬɪɟɧɵ ɮɢɡɢɱɟɫɤɢɟ ɢ ɤɨɦɩɶɸɬɟɪɧɵɟ ɦɨɞɟɥɢ ɤɚɧɚɥɨɜ ɫɜɹɡɢ. Ɋɚɡɪɚɛɨɬɚɧɧɵɟ ɚɜɬɨɪɨɦ ɦɨɞɟɥɢ ɹɜɥɹɸɬɫɹ ɢɧɫɬɪɭɦɟɧɬɨɦ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɪɚɡɥɢɱɧɵɯ ɷɥɟɦɟɧɬɨɜ ɩɪɢɟɦɨ-ɩɟɪɟɞɚɸɳɟɣ ɬɟɥɟɝɪɚɮɧɨɣ ɪɚɞɢɨɚɩɩɚɪɚɬɭɪɵ.
Ⱦɥɹ ɫɩɟɰɢɚɥɢɫɬɨɜ, ɡɚɧɢɦɚɸɳɢɯɫɹ ɪɚɡɪɚɛɨɬɤɨɣ
ɫɢɫɬɟɦ ɫɜɹɡɢ, ɚɫɩɢɪɚɧɬɨɜ ɢ ɫɬɭɞɟɧɬɨɜ ɜɵɫɲɢɯ ɬɟɯɧɢɱɟɫɤɢɯ ɭɱɟɛɧɵɯ ɡɚɜɟɞɟɧɢɣ ɪɚɞɢɨɬɟɯɧɢɱɟɫɤɨɝɨ ɩɪɨɮɢɥɹ.
ISBN 978-5-9729-1692-4
Ɉɦɫɤɢɣ ɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣ ɬɟɯɧɢɱɟɫɤɢɣ ɭɧɢɜɟɪɫɢɬɟɬ
ɏɚɡɚɧ ȼ. Ʌ., 2024
ɂɡɞɚɬɟɥɶɫɬɜɨ «ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ», 2024
Ɉɮɨɪɦɥɟɧɢɟ. ɂɡɞɚɬɟɥɶɫɬɜɨ «ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ», 2024
ɍȾɄ 621.394
ȻȻɄ 32.881
Ɇɨɟɣ ɞɨɪɨɝɨɣ ɠɟɧɟ
ɏɚɡɚɧ (ɋɚɥɨɦɚɬɨɜɨɣ) Ƚɚɥɢɧɟ Ʉɭɡɶɦɢɧɢɱɧɟ,
ɛɥɚɝɨɞɚɪɹ ɬɟɪɩɟɧɢɸ ɤɨɬɨɪɨɣ ɤ ɫɨɡɞɚɜɚɟɦɨɦɭ
ɦɧɨɣ ɞɢɫɤɨɦɮɨɪɬɭ ɜ ɫɟɦɟɣɧɨɣ ɠɢɡɧɢ ɢ ɧɚɫɬɨɹɬɟɥɶɧɨɦɭ ɩɨɨɳɪɟɧɢɸ ɫ ɟɟ ɫɬɨɪɨɧɵ (ɦɨɠɧɨ ɞɚɠɟ
ɫɤɚɡɚɬɶ, ɩɪɢɧɭɠɞɟɧɢɸ) ɢ ɩɨɹɜɢɥɚɫɶ ɷɬɚ ɤɧɢɝɚ.
3
ɋɈȾȿɊɀȺɇɂȿ
ɉɊɂɇəɌɕȿ ɋɈɄɊȺɓȿɇɂə ɂ ɈȻɈɁɇȺɑȿɇɂə ................................................. 6
ȼȼȿȾȿɇɂȿ ................................................................................................................. 7
1. Ɏɢɡɢɱɟɫɤɢɟ ɦɨɞɟɥɢ ɤɚɧɚɥɨɜ ɫɜɹɡɢ ..................................................................... 12
1.1. Ɏɢɡɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɞɢɫɤɪɟɬɧɨɝɨ ɤɚɧɚɥɚ ɫɜɹɡɢ ɫ
ɩɨɫɬɨɹɧɧɵɦɢ ɩɚɪɚɦɟɬɪɚɦɢ ɢ ɚɞɞɢɬɢɜɧɵɦ ɛɟɥɵɦ
ɝɚɭɫɫɨɜɫɤɢɦ ɲɭɦɨɦ .................................................................................................. 12
1.2. Ɏɢɡɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɨɞɧɨɥɭɱɟɜɨɝɨ ɞɢɫɤɪɟɬɧɨɝɨ ɤɚɧɚɥɚ ɫɜɹɡɢ
ɫ ɩɟɪɟɦɟɧɧɵɦɢ ɩɚɪɚɦɟɬɪɚɦɢ .................................................................................. 15
1.3. Ɏɢɡɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɦɧɨɝɨɥɭɱɟɜɵɯ ɤɚɧɚɥɨɜ ɫɜɹɡɢ ........................... 18
1.4. Ɏɢɡɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɜɨɡɞɟɣɫɬɜɢɣ ɧɚ ɜɯɨɞ
Ɋɉɍ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɝɚɪɦɨɧɢɱɟɫɤɢɯ ɪɚɞɢɨɫɢɝɧɚɥɨɜ,
ɩɪɨɲɟɞɲɢɯ ɩɨ
1.5. Ɋɟɡɭɥɶɬɚɬɵ ɢɫɫɥɟɞɨɜɚɧɢɹ ɧɚɞɟɠɧɨɫɬɢ ɩɟɪɟɞɚɱɢ
ɫɨɨɛɳɟɧɢɣ ɧɚ ɲɢɪɨɬɧɵɯ ɬɪɚɫɫɚɯ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ
ɦɟɬɨɞɚ «ɗɄȼɂȼȺɅȿɇɌ» ........................................................................................ 25
1.6. ɂɦɢɬɚɰɢɨɧɧɚɹ ɦɨɞɟɥɶ ɤɚɧɚɥɚ ɫɜɹɡɢ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ
ɪɟɡɭɥɶɬɚɬɨɜ ɬɪɚɫɫɨɜɵɯ ɢɫɩɵɬɚɧɢɣ ......................................................................... 29
2. ɂɦɢɬɚɰɢɨɧɧɵɟ ɤɨɦɩɶɸɬɟɪɧɵɟ ɦɨɞɟɥɢ
ɤɚɧɚɥɨɜ ɫɜɹɡɢ ............................................................................................................ 32
2.1. Ʉɨɦɩɶɸɬɟɪɧɨɟ ɢɦɢɬɚɰɢɨɧɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ
ɨɞɧɨɦɟɪɧɵɯ ɤɚɧɚɥɨɜ ɫɜɹɡɢ ...................................................................................... 32
2.1.1. Ɉɫɨɛɟɧɧɨɫɬɢ ɢɦɢɬɚɰɢɨɧɧɵɯ ɤɨɦɩɶɸɬɟɪɧɵɯ
ɦɨɞɟɥɟɣ ɨɞɧɨɦɟɪɧɵɯ Ʉɋ ......................................................................................... 32
2.1.2. Ⱥɥɝɨɪɢɬɦɵ ɮɨɪɦɢɪɨɜɚɧɢɹ ɩɪɨɰɟɫɫɨɜ ɡɚɦɢɪɚɧɢɣ
ɫɢɝɧɚɥɚ ɜ Ʉɋ .............................................................................................................. 33
2.1.3.
ɂɦɢɬɚɰɢɨɧɧɨ-ɚɧɚɥɢɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɞɢɫɤɪɟɬɧɨɝɨ Ʉɋ
ɫ ɩɨɫɬɨɹɧɧɵɦɢ ɩɚɪɚɦɟɬɪɚɦɢ ................................................................................... 39
ɪɟɚɥɶɧɨɣ ɬɪɚɫɫɟ .............................................................................. 21
4
2.1.4. Ɏɟɧɨɦɟɧɨɥɨɝɢɱɟɫɤɢɟ ɢɦɢɬɚɰɢɨɧɧɵɟ ɦɨɞɟɥɢ
ɨɞɧɨɥɭɱɟɜɵɯ ɞɢɫɤɪɟɬɧɵɯ Ʉɋ ɫ ɩɟɪɟɦɟɧɧɵɦɢ ɩɚɪɚɦɟɬɪɚɦɢ ............................... 52
2.1.5. ɋɬɪɭɤɬɭɪɧɨ-ɮɭɧɤɰɢɨɧɚɥɶɧɨɟ ɢɦɢɬɚɰɢɨɧɧɨ-ɚɧɚɥɢɬɢɱɟɫɤɨɟ
ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɨɞɧɨɥɭɱɟɜɨɝɨ ɞɢɫɤɪɟɬɧɨɝɨ Ʉɋ
ɫ ɩɟɪɟɦɟɧɧɵɦɢ ɩɚɪɚɦɟɬɪɚɦɢ .................................................................................. 56
2.1.6. Ⱥɥɝɨɪɢɬɦ ɫɬɪɭɤɬɭɪɧɨ-ɮɭɧɤɰɢɨɧɚɥɶɧɨɣ
ɢɦɢɬɚɰɢɨɧɧɨ-ɚɧɚɥɢɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɨɞɧɨɥɭɱɟɜɨɝɨ ɞɢɫɤɪɟɬɧɨɝɨ
Ʉɋ ɫ ɩɟɪɟɦɟɧɧɵɦɢ ɩɚɪɚɦɟɬɪɚɦɢ ........................................................................... 59
2.1.7. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫɪɚɜɧɢɬɟɥɶɧɵɯ ɬɪɚɫɫɨɜɵɯ ɢɫɩɵɬɚɧɢɣ
ɫɢɫɬɟɦ ɫɜɹɡɢ ɫ ȺɌ ɢ ɑɌ ɫɢɝɧɚɥɚɦɢ ........................................................................ 68
2.1.8. ɂɦɢɬɚɰɢɨɧɧɨ-ɚɧɚɥɢɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɦɧɨɝɨɥɭɱɟɜɨɝɨ
ɞɢɫɤɪɟɬɧɨɝɨ
Ʉɋ ........................................................................................................ 70
2.1.9. Ɋɟɡɭɥɶɬɚɬɵ ɢɫɫɥɟɞɨɜɚɧɢɹ ɩɨɫɪɟɞɫɬɜɨɦ ɤɨɦɩɶɸɬɟɪɧɨɝɨ
ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɧɚɞɟɠɧɨɫɬɢ ɩɟɪɟɞɚɱɢ ɛɭɤɜɟɧɧɨ-ɰɢɮɪɨɜɵɯ
ɫɨɨɛɳɟɧɢɣ ɨɝɪɚɧɢɱɟɧɧɨɝɨ ɨɛɴɟɦɚ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ
ɜɵɫɨɤɨɫɤɨɪɨɫɬɧɵɯ ɢ ɧɢɡɤɨɫɤɨɪɨɫɬɧɵɯ ɦɨɞɟɦɨɜ ................................................. 73
2.1.10. ɂɦɢɬɚɰɢɨɧɧɨ-ɚɧɚɥɢɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ
ɞɢɫɤɪɟɬɧɨɝɨ ɤɚɧɚɥɚ ɫɜɹɡɢ ɫ ɤɪɚɟɜɵɦɢ ɢɫɤɚɠɟɧɢɹɦɢ ɢ
ɞɢɫɤɪɟɬɧɨ-ɧɟɩɪɟɪɵɜɧɨɝɨ ɤɚɧɚɥɚ ɫɜɹɡɢ ................................................................. 75
2.2. Ʉɨɦɩɶɸɬɟɪɧɨɟ ɢɦɢɬɚɰɢɨɧɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ
ɞɜɭɯɦɟɪɧɵɯ ɤɚɧɚɥɨɜ ɫɜɹɡɢ ..................................................................................... 84
2.3. Ʉɨɦɩɶɸɬɟɪɧɨɟ ɢɦɢɬɚɰɢɨɧɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɬɪɟɯɦɟɪɧɨɝɨ
ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨ-ɜɪɟɦɟɧɧɨɝɨ ɤɚɧɚɥɚ ɫɜɹɡɢ .......................................................... 91
ɁȺɄɅɘɑȿɇɂȿ
...................................................................................................... 102
ɋɉɂɋɈɄ ɅɂɌȿɊȺɌɍɊɕ ...................................................................................... 103
5
ɉɊɂɇəɌɕȿ ɋɈɄɊȺɓȿɇɂə ɂ ɈȻɈɁɇȺɑȿɇɂə
ȺɆ – ɚɦɩɥɢɬɭɞɧɚɹ ɦɚɧɢɩɭɥɹɰɢɹ;
Ⱥɏ – ɚɦɩɥɢɬɭɞɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ;
Ⱥɑɏ – ɚɦɩɥɢɬɭɞɧɨ-ɱɚɫɬɨɬɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ;
Ƚɉ
– ɝɟɧɟɪɚɬɨɪ ɩɨɬɨɤɚ ɨɲɢɛɨɤ;
ɨɲ
Ƚɋɑ – ɝɟɧɟɪɚɬɨɪ ɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ;
ȾɄɍ – ɞɟɤɨɞɢɪɭɸɳɟɟ ɭɫɬɪɨɣɫɬɜɨ;
ɂɉɆ – ɢɦɢɬɚɰɢɨɧɧɨ-ɩɚɪɚɦɟɬɪɢɱɟɫɤɚɹ ɦɨɞɟɥɶ;
ɄɂȾ – ɤɨɷɮɮɢɰɢɟɧɬ ɢɫɩɪɚɜɧɨɝɨ ɞɟɣɫɬɜɢɹ;
Ʉɋ – ɤɚɧɚɥ ɫɜɹɡɢ;
ɆɈ – ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɠɢɞɚɧɢɟ;
ɈɎɆ – ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɮɚɡɨɜɚɹ ɦɚɧɢɩɭɥɹɰɢɹ;
ɉɪɞɍ – ɪɚɞɢɨɩɟɪɟɞɚɸɳɟɟ ɭɫɬɪɨɣɫɬɜɨ;
ɉɏ – ɩɪɨɯɨɞɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ;
Ɋɉɍ – ɪɚɞɢɨɩɪɢɟɦɧɨɟ ɭɫɬɪɨɣɫɬɜɨ;
ɋɄɈ – ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɟɫɤɨɟ ɨɬɤɥɨɧɟɧɢɟ;
ɌɅȽ – ɬɟɥɟɝɪɚɦɦɚ;
ɍɌ – ɭɫɢɥɢɬɟɥɶɧɵɣ ɬɪɚɤɬ;
ɍɐɈɋ – ɭɫɬɪɨɣɫɬɜɨ ɰɢɮɪɨɜɨɣ ɨɛɪɚɛɨɬɤɢ ɫɢɝɧɚɥɚ;
ɎɆ – ɮɚɡɨɜɚɹ ɦɚɧɢɩɭɥɹɰɢɹ;
Ɏɇɑ – ɮɢɥɶɬɪ ɧɢɠɧɢɯ ɱɚɫɬɨɬ;
ɎɈɂ – ɮɢɥɶɬɪ ɨɫɧɨɜɧɨɣ ɢɡɛɢɪɚɬɟɥɶɧɨɫɬɢ;
Ɏɉɋ – ɮɢɥɶɬɪ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɣ ɫɟɥɟɤɰɢɢ;
Ɏɑɏ – ɮɚɡɨ-ɱɚɫɬɨɬɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ;
ɑɆ – ɱɚɫɬɨɬɧɚɹ ɦɚɧɢɩɭɥɹɰɢɹ;
ent[x] – ɰɟɥɚɹ ɱɚɫɬɶ ɱɢɫɥɚ ɯ;
(+)–ɫɭɦɦɚɬɨɪ «ɩɨ ɦɨɞɭɥɸ ɞɜɚ».
6
ȼȼȿȾȿɇɂȿ
ɉɨɞ ɤɚɧɚɥɚɦɢ ɫɜɹɡɢ (Ʉɋ) ɩɨɧɢɦɚɸɬɫɹ ɫɪɟɞɚ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɫɢɝɧɚɥɚ ɢ ɬɟɯɧɢɱɟɫɤɢɟ ɫɪɟɞɫɬɜɚ, ɫ ɩɨɦɨɳɶɸ ɤɨɬɨɪɵɯ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɟɪɟɞɚɱɚ ɢɧɮɨɪɦɚɰɢɢ
ɨɬ ɢɫɬɨɱɧɢɤɚ ɞɨ ɩɨɥɭɱɚɬɟɥɹ ɫɨɨɛɳɟɧɢɹ.
ɇɚ ɪɢɫɭɧɤɟ 1 ɢɡɨɛɪɚɠɟɧɚ ɛɥɨɤ-ɫɯɟɦɚ ɦɨɞɟɥɢ ɬɢɩɨɜɨɝɨ Ʉɋ, ɜɤɥɸɱɚɸɳɚɹ ɜ
ɫɟɛɹ ɦɧɨɝɨɥɭɱɟɜɭɸ ɫɪɟɞɭ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɫɢɝɧɚɥɚ ɫ ɪɚɡɥɢɱɧɨɝɨ ɪɨɞɚ ɚɞɞɢɬɢɜɧɵɦɢ ɩɨɦɟɯɚɦɢ ɢ ɨɫɧɨɜɧɵɟ ɮɭɧɤɰɢɨɧɚɥɶɧɵɟ ɷɥɟɦɟɧɬɵ ɩɟɪɟɞɚɸɳɟɝɨ ɢ
ɩɪɢɟɦ-
ɧɨɝɨ ɭɫɬɪɨɣɫɬɜ.
ɇɚ ɪɢɫɭɧɤɟ ɨɛɨɡɧɚɱɟɧɨ: ɂɋ – ɢɫɬɨɱɧɢɤ ɫɨɨɛɳɟɧɢɣ; Ʉɍ – ɤɨɞɢɪɭɸɳɟɟ
ɭɫɬɪɨɣɫɬɜɨ; Ɇ – ɦɨɞɭɥɹɬɨɪ ɫɢɝɧɚɥɚ; Ɍɉ – ɭɫɢɥɢɬɟɥɶɧɵɣ ɬɪɚɤɬ ɩɟɪɟɞɚɬɱɢɤɚ;
Ɏɉɂ – ɮɢɥɶɬɪ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɣ ɢɡɛɢɪɚɬɟɥɶɧɨɫɬɢ ɩɪɢɟɦɧɢɤɚ; Ɍɉɪ – ɭɫɢɥɢɬɟɥɶɧɵɣ ɬɪɚɤɬ ɩɪɢɟɦɧɢɤɚ; ɎɈɂ – ɮɢɥɶɬɪ ɨɫɧɨɜɧɨɣ ɢɡɛɢɪɚɬɟɥɶɧɨɫɬɢ; Ⱦ – ɞɟɬɟɤɬɨɪ;
Ɏɇɑ – ɮɢɥɶɬɪ ɧɢɠɧɢɯ ɱɚɫɬɨɬ; ɌɊ – ɬɪɢɝɝɟɪ; ɊȽ – ɪɟɝɟɧɟɪɚɬɨɪ; ȾɄɍ – ɞɟɤɨɞɢɪɭɸɳɟɟ ɭɫɬɪɨɣɫɬɜɨ; ɉɋ – ɩɨɥɭɱɚɬɟɥɶ
ɡɚɞɟɪɠɤɢ; K
– ɤɨɦɩɥɟɤɫɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɞɚɱɢ ɩɨ ɧɚɩɪɹɠɟɧɢɸ ɞɥɹ i-ɝɨ
i
ɫɨɨɛɳɟɧɢɹ; ȾɆ – ɞɟɦɨɞɭɥɹɬɨɪ; ɅɁ – ɥɢɧɢɹ
ɥɭɱɚ; ɂɒ – ɢɫɬɨɱɧɢɤ ɲɭɦɚ; ɂɋɉ – ɢɫɬɨɱɧɢɤ ɫɬɚɧɰɢɨɧɧɵɯ ɩɨɦɟɯ; ɂɂɉ – ɢɫɬɨɱɧɢɤ ɢɦɩɭɥɶɫɧɵɯ ɩɨɦɟɯ; ɋɊ – ɫɪɟɞɚ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɫɢɝɧɚɥɚ; A, B, C, D, E,
F, G, H, J, I – ɝɪɚɧɢɰɵ ɦɟɠɞɭ ɮɭɧɤɰɢɨɧɚɥɶɧɵɦɢ ɷɥɟɦɟɧɬɚɦɢ ɩɟɪɟɞɚɸɳɟɣ ɢ ɩɪɢɟɦɧɨɣ ɚɩɩɚɪɚɬɭɪɵ Ʉɋ.
Ʉɋ ɦɨɝɭɬ ɛɵɬɶ ɨɞɧɨɦɟɪɧɵɦɢ, ɞɜɭɯɦɟɪɧɵɦɢ ɢ ɬɪɟɯɦɟɪɧɵɦɢ. Ɉɞɧɨɦɟɪɧɵɟ
ɤɚɧɚɥɵ ɫɜɹɡɢ ɹɜɥɹɸɬɫɹ ɧɢɡɤɨɱɚɫɬɨɬɧɵɦɢ ɢ ɯɚɪɚɤɬɟɪɢɡɭɸɬɫɹ
ɜɵɯɨɞɧɵɦ ɫɢɝɧɚɥɨɦ ɫ ɨɞɧɢɦ ɩɚɪɚɦɟɬɪɨɦ – ɧɚɩɪɹɠɟɧɢɟɦ, ɤɨɬɨɪɨɟ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɜɪɟɦɟɧɢ
(ɫɟɱɟɧɢɹ H, J ɢ I).
Ⱦɜɭɯɦɟɪɧɵɟ Ʉɋ ɹɜɥɹɸɬɫɹ ɜɵɫɨɤɨɱɚɫɬɨɬɧɵɦɢ, ɨɬɧɨɫɢɬɟɥɶɧɨ ɭɡɤɨɩɨɥɨɫɧɵɦɢ ɢ ɯɚɪɚɤɬɟɪɢɡɭɸɬɫɹ ɜɵɯɨɞɧɵɦ ɫɢɝɧɚɥɨɦ ɫ ɞɜɭɦɹ ɡɚɜɢɫɹɳɢɦɢ ɨɬ ɜɪɟɦɟɧɢ
ɩɚɪɚɦɟɬɪɚɦɢ: ɚɦɩɥɢɬɭɞɨɣ ɢ ɮɚɡɨɣ ɪɚɞɢɨɫɢɝɧɚɥɚ (ɫɟɱɟɧɢɹ E, F ɢ G). Ɍɪɟɯɦɟɪɧɵɟ
Ʉɋ ɯɚɪɚɤɬɟɪɢɡɭɸɬɫɹ ɬɪɟɦɹ ɡɚɜɢɫɹɳɢɦɢ ɨɬ ɜɪɟɦɟɧɢ ɩɚɪɚɦɟɬɪɚɦɢ:
ɦɨɞɭɥɟɦ ɜɟɤɬɨɪɚ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɢ ɞɜɭɦɹ ɟɝɨ ɭɝɥɚɦɢ: ɨɞɧɢɦ – ɲɢɪɨɬɵ ɢ ɞɪɭɝɢɦ – ɞɨɥɝɨɬɵ (ɫɟɱɟɧɢɟ D).
7
ˁˀ
ʸʯ
B
ʰˁʿ
N
ʶ
2
ʶ
1
ʶ
˃ʿ
C
ʰʰʿ
+
ʰˌ
ʿˁ
ʪʶ˄
ˀʧ
ˇʽʰ ʪ ˇʻˋ ˃ˀ
JH
ʪʺ
G I
F
Ɋɢɫ. 1. Ȼɥɨɤ-ɫɯɟɦɚ ɦɨɞɟɥɢ ɬɢɩɨɜɨɝɨ ɤɚɧɚɥɚ ɫɜɹɡɢ
3
A
ʶ˄ ʺ
ʰˁ
D
˃ʿ
ˇʿʰ
E
Ʉɨɞɟɤ Ʉɋ ɨɛɟɫɩɟɱɢɜɚɟɬ ɨɛɧɚɪɭɠɟɧɢɟ ɢ ɢɫɩɪɚɜɥɟɧɢɟ ɨɲɢɛɨɤ ɧɚ ɩɪɢɟɦɧɨɣ
ɫɬɨɪɨɧɟ ɪɚɞɢɨɥɢɧɢɢ ɡɚ ɫɱɟɬ ɢɧɮɨɪɦɚɰɢɨɧɧɨɣ ɢɡɛɵɬɨɱɧɨɫɬɢ, ɜɧɟɫɟɧɧɨɣ ɩɨ
ɨɩɪɟɞɟɥɟɧɧɵɦ ɩɪɚɜɢɥɚɦ ɜ ɩɟɪɟɞɚɜɚɟɦɨɟ ɫɨɨɛɳɟɧɢɟ. Ɂɚɞɚɱɟɣ ɤɨɞɢɪɭɸɳɟɝɨ
ɭɫɬɪɨɣɫɬɜɚ ɹɜɥɹɟɬɫɹ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ ɩɟɪɟɞɚɜɚɟɦɨɝɨ ɡɧɚɤɚ (ɮɪɚɝɦɟɧɬɚ) ɫɨɨɛɳɟɧɢɹ ɜ ɤɨɞɨɜɭɸ ɤɨɦɛɢɧɚɰɢɸ (ɫɟɱɟɧɢɟ A). Ⱦɟɤɨɞɢɪɭɸɳɟɟ ɭɫɬɪɨɣɫɬɜɨ ɧɚ ɩɪɢɟɦɧɨɣ ɫɬɨɪɨɧɟ Ʉɋ ɨɫɭɳɟɫɬɜɥɹɟɬ ɨɛɪɚɬɧɨɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ ɤɨɞɨɜɵɯ ɤɨɦɛɢɧɚɰɢɣ
ɜ ɡɧɚɤɢ
(ɮɪɚɝɦɟɧɬɵ) ɫɨɨɛɳɟɧɢɹ. ɉɪɢ ɧɚɥɢɱɢɢ ɩɨɦɟɯ ɜ Ʉɋ ɫɭɳɟɫɬɜɭɟɬ ɜɟɪɨɹɬ-
ɧɨɫɬɶ ɨɲɢɛɨɱɧɨɝɨ ɞɟɤɨɞɢɪɨɜɚɧɢɹ ɡɧɚɤɚ (ɮɪɚɝɦɟɧɬɚ) ɫɨɨɛɳɟɧɢɹ. ɗɬɚ ɜɟɪɨɹɬɧɨɫɬɶ ɡɚɜɢɫɢɬ ɨɬ ɜɟɪɨɹɬɧɨɫɬɢ ɨɲɢɛɨɱɧɨɝɨ ɩɪɢɟɦɚ ɷɥɟɦɟɧɬɨɜ ɫɨɨɛɳɟɧɢɹ (ɫɟɱɟɧɢɟ I) ɢ ɨɬ ɢɡɛɵɬɨɱɧɨɫɬɢ ɤɨɞɚ. ɉɪɢ ɧɚɥɢɱɢɢ ɜ ɤɨɞɨɜɨɣ ɤɨɦɛɢɧɚɰɢɢ ɨɩɪɟɞɟɥɟɧɧɨɣ ɢɡɛɵɬɨɱɧɨɫɬɢ ɧɚ ɩɪɢɟɦɧɨɣ ɫɬɨɪɨɧɟ ɤɚɧɚɥɚ ɫɜɹɡɢ ɜɨɡɦɨɠɧɨ ɨɛɧɚɪɭɠɟɧɢɟ
ɨɲɢɛɨɱɧɨ ɩɪɢɧɹɬɵɯ ɡɧɚɤɨɜ (
ɮɪɚɝɦɟɧɬɨɜ) ɫɨɨɛɳɟɧɢɹ, a ɟɫɥɢ ɢɡɛɵɬɨɱɧɨɫɬɶ
ɤɨɞɚ ɞɨɫɬɚɬɨɱɧɨ ɜɟɥɢɤɚ, ɬɨ ɜɨɡɦɨɠɧɨ ɧɟ ɬɨɥɶɤɨ ɨɛɧɚɪɭɠɟɧɢɟ ɨɲɢɛɨɤ, ɧɨ ɢ ɜɨɫɫɬɚɧɨɜɥɟɧɢɟ ɡɧɚɤɨɜ (ɮɪɚɝɦɟɧɬɨɜ) ɫɨɨɛɳɟɧɢɹ ɜ ɩɟɪɜɨɧɚɱɚɥɶɧɨɦ ɜɢɞɟ. ɉɨ ɱɚɫɬɨɫɬɢ ɨɛɧɚɪɭɠɟɧɧɵɯ ɨɲɢɛɨɤ ɜ ɡɧɚɤɚɯ (ɮɪɚɝɦɟɧɬɚɯ) ɫɨɨɛɳɟɧɢɹ ɦɨɠɧɨ ɩɪɨɢɡɜɨɞɢɬɶ ɨɰɟɧɤɭ ɤɚɱɟɫɬɜɚ ɩɪɢɟɦɚ ɨɬɞɟɥɶɧɵɯ ɢɧɞɢɜɢɞɭɚɥɶɧɵɯ ɩɚɤɟɬɨɜ ɢ ɜɫɟɝɨ
ɫɨɨɛɳɟɧɢɹ ɜ ɰɟɥɨɦ. ȼ ɫɟɱɟɧɢɹɯ A ɢ I
ɢɦɟɸɬ ɦɟɫɬɨ ɛɢɧɚɪɧɵɟ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɢɦɩɭɥɶɫɨɜ, ɞɥɢɬɟɥɶɧɨɫɬɢ ɤɨɬɨɪɵɯ ɤɪɚɬɧɵ ɨɩɪɟɞɟɥɟɧɧɨɣ ɜɟɥɢɱɢɧɟ, ɨɛɭɫɥɨɜɥɟɧɧɨɣ ɢɧɮɨɪɦɚɰɢɨɧɧɨɣ ɫɤɨɪɨɫɬɶɸ ɩɟɪɟɞɚɱɢ ɫɨɨɛɳɟɧɢɹ, ɢɡɦɟɪɹɟɦɨɣ ɜ
ɛɢɬ/ɫ. Ⱦɥɹ ɪɚɡɪɚɛɨɬɤɢ ɢ ɫɪɚɜɧɟɧɢɹ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɤɨɞɟɤɨɜ ɧɟɨɛɯɨɞɢɦɨ ɭɦɟɬɶ
ɦɨɞɟɥɢɪɨɜɚɬɶ ɨɞɧɨɦɟɪɧɵɣ ɤɚɧɚɥ ɫɜɹɡɢ ɫ ɞɢɫɤɪɟɬɧɵɦɢ ɜɯɨɞɨɦ (ɫɟɱɟɧɢɟ Ⱥ) ɢ
ɞɢɫɤɪɟɬɧɵɦ ɜɵɯɨɞɨɦ (ɫɟɱɟɧɢɟ I).
Ɇɨɞɟɦ Ʉɋ ɨɩɪɟɞɟɥɹɟɬ ɬɢɩ ɦɨɞɭɥɹɰɢɢ ɫɢɝɧɚɥɚ. Ɇɨɞɭɥɹɬɨɪ
ɩɟɪɟɞɚɸɳɟɝɨ
ɭɫɬɪɨɣɫɬɜɚ ɨɫɭɳɟɫɬɜɥɹɟɬ ɢɡɦɟɧɟɧɢɟ ɩɚɪɚɦɟɬɪɨɜ (ɚɦɩɥɢɬɭɞɵ, ɱɚɫɬɨɬɵ ɢ ɮɚɡɵ)
ɧɟɫɭɳɟɝɨ ɤɨɥɟɛɚɧɢɹ ɩɨ ɨɩɪɟɞɟɥɟɧɧɵɦ ɡɚɤɨɧɚɦ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɟɪɟɞɚɜɚɟɦɨɣ
ɰɢɮɪɨɜɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶɸ (ɫɟɱɟɧɢɟ B) [1]. Ɉɞɢɧ ɷɥɟɦɟɧɬ ɡɧɚɤɚ ɢɦɟɟɬ
ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ, ɤɨɬɨɪɚɹ ɨɛɭɫɥɨɜɥɟɧɚ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɫɤɨɪɨɫɬɶɸ ɦɚɧɢɩɭɥɹɰɢɢ, ɢɡɦɟɪɹɟɦɨɣ ɜ Ȼɨɞɚɯ. Ⱦɟɦɨɞɭɥɹɬɨɪ ɩɪɢɟɦɧɨɝɨ ɭɫɬɪɨɣɫɬɜɚ ɞɨɥɠɟɧ ɜɨɫɫɬɚɧɚɜɥɢɜɚɬɶ ɩɟɪɟɞɚɜɚɟɦɭɸ ɛɢɧɚɪɧɭɸ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ (ɫɟɱɟɧɢɟ I) ɫ ɦɢɧɢɦɚɥɶɧɨ ɜɨɡɦɨɠɧɨɣ
ɜɟɪɨɹɬɧɨɫɬɶɸ ɨɲɢɛɤɢ ɷɥɟɦɟɧɬɨɜ, ɤɨɬɨɪɚɹ ɨɛɭɫɥɨɜɥɟɧɚ
9
ɦɟɬɨɞɨɦ ɦɚɧɢɩɭɥɹɰɢɢ ɢ ɨɬɧɨɲɟɧɢɟɦ ɫɢɝɧɚɥ/ɩɨɦɟɯɚ ɧɚ ɜɵɯɨɞɟ ɮɢɥɶɬɪɚ ɨɫɧɨɜɧɨɣ ɢɡɛɢɪɚɬɟɥɶɧɨɫɬɢ (ɫɟɱɟɧɢɟ G). ȼ ɚɫɢɧɯɪɨɧɧɵɯ ɫɢɫɬɟɦɚɯ ɫɜɹɡɢ ɧɚ ɜɯɨɞɟ ɪɟɝɟɧɟɪɚɬɨɪɚ (ɫɟɱɟɧɢɟ J) ɛɢɧɚɪɧɚɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɢɦɟɟɬ ɤɪɚɟɜɵɟ ɢɫɤɚɠɟɧɢɹ ɷɥɟɦɟɧɬɨɜ, ɬɨ ɟɫɬɶ ɨɬɤɥɨɧɟɧɢɟ ɮɪɨɧɬɨɜ ɷɥɟɦɟɧɬɨɜ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɪɚɡɥɢɱɧɨɝɨ ɪɨɞɚ ɩɨɦɟɯ ɨɬ ɢɯ ɬɨɱɧɨɝɨ ɦɟɫɬɨɩɨɥɨɠɟɧɢɹ. Ɂɞɟɫɶ ɠɟ ɢɦɟɸɬ ɦɟɫɬɨ ɞɪɨɛ
-
ɥɟɧɢɹ ɷɥɟɦɟɧɬɨɜ, ɡɚɤɥɸɱɚɸɳɢɟɫɹ ɜ ɤɪɚɬɤɨɜɪɟɦɟɧɧɨɦ ɢɡɦɟɧɟɧɢɢ ɡɧɚɱɟɧɢɹ
ɷɥɟɦɟɧɬɚ ɧɚ ɢɧɬɟɪɜɚɥɟ ɟɝɨ ɞɥɢɬɟɥɶɧɨɫɬɢ. ɉɨ ɜɟɥɢɱɢɧɟ ɤɪɚɟɜɵɯ ɢɫɤɚɠɟɧɢɣ ɛɢɧɚɪɧɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɜ ɬɚɤɨɝɨ ɪɨɞɚ ɦɨɞɟɦɚɯ ɜɨɡɦɨɠɧɨ ɨɰɟɧɢɜɚɬɶ ɤɚɱɟɫɬɜɨ ɨɬɞɟɥɶɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɩɪɢɧɢɦɚɟɦɨɝɨ ɫɨɨɛɳɟɧɢɹ. Ⱦɥɹ ɢɫɫɥɟɞɨɜɚɧɢɹ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɪɚɛɨɬɵ ɪɟɝɟɧɟɪɚɬɨɪɨɜ ɢ ɦɟɬɨɞɨɜ ɨɰɟɧɤɢ ɤɚɱɟɫɬɜɚ ɩɪɢɧɢɦɚɟɦɨɝɨ
ɫɨɨɛɳɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨ ɢɦɟɬɶ ɦɨɞɟɥɶ ɨɞɧɨɦɟɪɧɨɝɨ Ʉɋ ɫ ɞɢɫɤɪɟɬɧɵɦ
ɜɯɨɞɨɦ (ɫɟ-
ɱɟɧɢɟ Ⱥ) ɢ ɞɢɫɤɪɟɬɧɵɦ ɜɵɯɨɞɨɦ (ɫɟɱɟɧɢɟ J).
ȼ ɫɟɱɟɧɢɢ H ɧɚ ɜɵɯɨɞɟ Ɏɇɑ ɢɦɟɟɬ ɦɟɫɬɨ ɧɢɡɤɨɱɚɫɬɨɬɧɵɣ ɤɨɧɬɢɧɭɚɥɶɧɵɣ
ɫɢɝɧɚɥ, ɤɚɱɟɫɬɜɨ ɤɨɬɨɪɨɝɨ ɡɚɜɢɫɢɬ ɨɬ ɨɬɧɨɲɟɧɢɹ ɫɢɝɧɚɥ/ɩɨɦɟɯɚ ɧɚ ɜɵɯɨɞɟ ɮɢɥɶɬɪɚ ɨɫɧɨɜɧɨɣ ɢɡɛɢɪɚɬɟɥɶɧɨɫɬɢ (ɫɟɱɟɧɢɟ G). Ɇɨɞɟɥɶ ɨɞɧɨɦɟɪɧɨɝɨ Ʉɋ ɫ ɞɢɫɤɪɟɬɧɵɦ ɜɯɨɞɨɦ (ɫɟɱɟɧɢɟ Ⱥ) ɢ ɚɧɚɥɨɝɨɜɵɦ ɜɵɯɨɞɨɦ (ɫɟɱɟɧɢɟ G) ɦɨɠɟɬ ɛɵɬɶ
ɢɫɩɨɥɶɡɨɜɚɧɚ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɭɫɬɪɨɣɫɬɜ ɩɨɷɥɟɦɟɧɬɧɨɣ ɨɰɟɧɤɢ ɤɚɱɟɫɬɜɚ
ɩɪɢɧɢɦɚɟɦɨɝɨ ɫɨɨɛɳɟɧɢɹ.
ȼ ɫɨɜɪɟɦɟɧɧɵɯ ɪɚɞɢɨɩɪɢɟɦɧɵɯ ɭɫɬɪɨɣɫɬɜɚɯ ɫ ɩɪɹɦɵɦ ɚɧɚɥɨɝɨ-ɰɢɮɪɨɜɵɦ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟɦ ɧɚɱɢɧɚɹ ɫ ɫɟɱɟɧɢɹ F (a ɬɨ ɢ E) ɨɛɪɚɛɨɬɤɚ ɫɢɝɧɚɥɚ ɩɪɨɢɡɜɨɞɢɬɫɹ ɰɢɮɪɨɜɵɦɢ ɦɟɬɨɞɚɦɢ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɧɚɱɢɧɚɹ ɫ ɷɬɢɯ ɫɟɱɟɧɢɣ, ɪɟɚɥɢɡɨɜɚɧɧɵɟ ɧɚ ɗȼɆ ɚɥɝɨɪɢɬɦɵ ɢɦɢɬɚɰɢɨɧɧɵɯ ɦɨɞɟɥɟɣ ɬɟɯɧɢɱɟɫɤɨɣ ɱɚɫɬɢ
ɤɚɧɚɥɚ ɫɜɹɡɢ ɦɚɥɨ ɱɟɦ ɨɬɥɢɱɚɸɬɫɹ ɨɬ ɢɫɬɢɧɧɵɯ ɚɥɝɨɪɢɬɦɨɜ ɰɢɮɪɨɜɨɣ ɨɛɪɚɛɨɬɤɢ
ɫɢɝɧɚɥɚ ɜ ɪɟɚɥɶɧɨɦ ɩɪɢɟɦɧɨɦ ɭɫɬɪɨɣɫɬɜɟ. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɷɮɮɟɤɬɢɜɧɨɫɬɢ
ɚɥɝɨɪɢɬɦɨɜ ɰɢɮɪɨɜɨɣ ɨɛɪɚɛɨɬɤɢ ɫɢɝɧɚɥɨɜ ɧɟɨɛɯɨɞɢɦɵ ɦɨɞɟɥɢ ɞɜɭɯɦɟɪɧɵɯ
Ʉɋ ɫ ɞɢɫɤɪɟɬɧɵɦ ɜɯɨɞɨɦ (ɫɟɱɟɧɢɟ Ⱥ) ɢ ɞɜɭɯɦɟɪɧɵɦ ɜɟɤɬɨɪɧɵɦ ɜɵɯɨɞɨɦ (ɫɟɱɟɧɢɹ E ɢ F).
ɋɟɱɟɧɢɟ D ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɩɪɨɫɬɪɚɧɫɬɜɭ ɜ ɬɨɱɤɟ ɩɪɢɟɦɚ. ɉɪɨɫɬɪɚɧɫɬɜɟɧɧɨ-
ɜɪɟɦɟɧɧɚɹ ɦɨɞɟɥɶ
Ʉɋ ɫ ɤɨɧɬɢɧɭɚɥɶɧɵɦ ɬɪɟɯɦɟɪɧɵɦ ɜɟɤɬɨɪɧɵɦ ɜɵɯɨɞɨɦ ɞɥɹ
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