ǙǛǑǒǝǚǕǔǕǝǛǏǍǚǚǍǬ ǏǛǘǛǗǛǚǚǛ-ǛǜǟǕǤǒǞǗǍǬ ǞǕǞǟǒǙǍ ǕǔǙǒǝǒǚǕǬ ǠǝǛǏǚǬ ǓǕǑǗǛǞǟǕ Ǖ. ǟ. ǚǭǴǭǽǻǯǭ, Ǒ. Ǖ. ǞDzǽDzǮǽȌǷǻǯ,

ǚǭDZDzdzǺǻǾǿȉ ǵ ǷǭȄDzǾǿǯǻ ǾǸǻdzǺȈȂ ǾǵǾǿDzǹ. Ȳ 4, 2013
ǠǑǗ 681.586.5
ǙǛǑǒǝǚǕǔǕǝǛǏǍǚǚǍǬ ǏǛǘǛǗǛǚǚǛ-ǛǜǟǕǤǒǞǗǍǬ
ǞǕǞǟǒǙǍ ǕǔǙǒǝǒǚǕǬ ǠǝǛǏǚǬ ǓǕǑǗǛǞǟǕ
ɇɚɡɚɪɨɜɚ ɂ. Ɍ., ɋɟɪɟɛɪɹɤɨɜ Ⱦ. ɂ., Ȼɪɨɫɬɢɥɨɜɚ Ɍ. ɘ., Ɇɭɪɚɲɤɢɧɚ Ɍ. ɂ.
Ɇɨɞɟɪɧɢɡɢɪɨɜɚɧɧɚɹ ɜɨɥɨɤɨɧɧɨ-ɨɩɬɢɱɟɫɤɚɹ ɫɢɫɬɟɦɚ ɢɡɦɟɪɟɧɢɹ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ
Ǖ. ǟ. ǚǭǴǭǽǻǯǭ, Ǒ. Ǖ. ǞDzǽDzǮǽȌǷǻǯ,
ǟ. ǫ. ǎǽǻǾǿǵǸǻǯǭ, ǟ. Ǖ. ǙȀǽǭȅǷǵǺǭ
ȼɜɟɞɟɧɢɟ
ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɫɨɜɪɟɦɟɧɧɵɟ ɢ ɩɟɪɫɩɟɤɬɢɜɧɵɟ ɪɚɡɪɚɛɨɬɤɢ ɚɜɢɚɰɢɨɧɧɨɣ, ɪɚɤɟɬɧɨɤɨɫɦɢɱɟɫɤɨɣ ɢ ɞɪɭɝɢɯ ɨɬɪɚɫɥɟɣ ɬɟɯɧɢɤɢ ɧɭɠɞɚɸɬɫɹ ɜ ɨɩɪɟɞɟɥɟɧɧɨɣ ɧɨɦɟɧɤɥɚɬɭɪɟ ɞɚɬɱɢɤɨɜ ɞɥɹ
ɢɧɮɨɪɦɚɰɢɨɧɧɨ-ɢɡɦɟɪɢɬɟɥɶɧɵɯ, ɤ ɤɨɬɨɪɵɦ ɩɪɟɞɴɹɜɥɹɸɬ ɩɨɜɵɲɟɧɧɵɟ ɬɪɟɛɨɜɚɧɢɹ, ɜ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ, ɪɚɛɨɬɨɫɩɨɫɨɛɧɨɫɬɶ ɜ ɠɟɫɬɤɢɯ ɭɫɥɨɜɢɹɯ ɷɤɫɩɥɭɚɬɚɰɢɢ ɢ ɨɛɟɫɩɟɱɟɧɢɟ ɛɟɡɨɩɚɫɧɨɫɬɢ. Ɉɫɨɛɟɧɧɨ ɷɬɨ ɚɤɬɭɚɥɶɧɨ ɩɪɢ ɢɡɦɟɪɟɧɢɢ ɭɪɨɜɧɹ ɜɡɪɵɜɨɨɩɚɫɧɵɯ ɠɢɞɤɨɫɬɟɣ.
ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɫɭɳɟɫɬɜɭɸɳɢɟ ɞɚɬɱɢɤɢ ɢ ɫɢɫɬɟɦɵ ɢɡɦɟɪɟɧɢɹ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ, ɨɫɧɨɜɚɧɧɵɟ ɧɚ ɬɚɤɢɯ ɮɢɡɢɱɟɫɤɢɯ ɩɪɢɧɰɢɩɚɯ, ɤɚɤ ɟɦɤɨɫɬɧɵɣ, ɢɧɞɭɤɬɢɜɧɵɣ ɢ ɞɪ., ɬɪɟɛɭɸɬ ɜ ɤɨɧɫɬɪɭɤɰɢɢ ɢɡɞɟɥɢɹ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɫɢɫɬɟɦ ɢ ɤɨɧɬɭɪɨɜ ɡɚɳɢɬɵ ɨɬ ɫɥɭɱɚɣɧɨɝɨ ɩɪɨɫɤɚɤɢɜɚɧɢɹ ɢɫɤɪɵ, ɬɚɤ
ɤɚɤ ɞɥɹ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢɡɦɟɪɢɬɟɥɶɧɨɣ ɢɧɮɨɪɦɚɰɢɢ ɢɫɩɨɥɶɡɭɸɬ ɷɥɟɤɬɪɢɱɟɫɤɢɟ ɫɢɝɧɚɥɵ. ɗɬɨ ɜ
ɫɜɨɸ ɨɱɟɪɟɞɶ ɩɪɢɜɨɞɢɬ ɤ ɭɜɟɥɢɱɟɧɢɸ ɦɚɫɫɵ ɚɜɢɚɰɢɨɧɧɨɣ, ɪɚɤɟɬɧɨɣ ɢ ɞɪɭɝɨɣ ɬɟɯɧɢɤɢ. ɋɬɨɢɬ ɡɚɞɚɱɚ ɜ ɫɨɡɞɚɧɢɢ ɫɢɫɬɟɦɵ ɢɡɦɟɪɟɧɢɹ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ, ɨɬɜɟɱɚɸɳɟɣ ɜɵɲɟɭɩɨɦɹɧɭɬɵɦ ɬɪɟɛɨɜɚɧɢɹɦ ɢ ɢɫɤɥɸɱɚɸɳɟɣ ɧɟɞɨɫɬɚɬɤɢ ɫɭɳɟɫɬɜɭɸɳɢɯ ɫɪɟɞɫɬɜ ɢɡɦɟɪɟɧɢɹ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ.
Ɉɩɢɫɚɧɢɟ ɤɨɧɫɬɪɭɤɰɢɢ
ȼ ɪɚɛɨɬɟ [1] ɨɩɢɫɚɧ ɜɨɥɨɤɨɧɧɨ-ɨɩɬɢɱɟɫɤɢɣ ɫɢɝɧɚɥɢɡɚɬɨɪ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ, ɤɨɬɨɪɵɣ ɱɚɫɬɢɱɧɨ ɪɟɲɚɟɬ ɩɨɫɬɚɜɥɟɧɧɭɸ ɡɚɞɚɱɭ. ɇɟɞɨɫɬɚɬɤɚɦɢ ɞɚɧɧɨɝɨ ɫɢɝɧɚɥɢɡɚɬɨɪɚ ɹɜɥɹɟɬɫɹ ɨɬɫɭɬɫɬɜɢɟ
ɜɨɡɦɨɠɧɨɫɬɢ ɤɨɧɬɪɨɥɢɪɨɜɚɬɶ ɧɟɫɤɨɥɶɤɨ ɡɧɚɱɟɧɢɣ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ.
Ⱦɥɹ ɩɨɥɧɨɝɨ ɪɟɲɟɧɢɹ ɩɨɫɬɚɜɥɟɧɧɨɣ ɡɚɞɚɱɢ ɛɵɥɚ ɩɪɟɞɥɨɠɟɧɚ ɤɨɧɫɬɪɭɤɰɢɹ ɜɨɥɨɤɨɧɧɨɨɩɬɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɢɡɦɟɪɟɧɢɹ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ (ȼɈɋɂɍɀ) [2].
ɇɟɞɨɫɬɚɬɤɚɦɢ ɞɚɧɧɨɣ ɫɢɫɬɟɦɵ ɹɜɥɹɟɬɫɹ ɫɥɟɞɭɸɳɟɟ:
– ɩɪɢ ɪɟɝɢɫɬɪɚɰɢɢ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ, ɞɜɢɠɭɳɟɣɫɹ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɤ ɨɩɬɢɱɟɫɤɨɣ ɨɫɢ
ɭɪɨɜɧɟɦɟɪɚ (ɧɚɩɪɢɦɟɪ, ɦɨɪɫɤɚɹ ɜɨɥɧɚ), ɬɨɱɧɨɫɬɶ ɪɟɝɢɫɬɪɚɰɢɢ ɛɭɞɟɬ ɧɟɜɵɫɨɤɨɣ;
– ɬɟɯɧɨɥɨɝɢɱɟɫɤɢ ɫɥɨɠɧɨ ɢɡɝɨɬɨɜɢɬɶ ɧɚɤɨɧɟɱɧɢɤ ɜ ɜɢɞɟ ɤɨɧɭɫɚ;
– ɩɪɢ ɫɛɨɪɤɟ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢ ɬɪɭɞɧɨ ɩɪɨɬɹɧɭɬɶ ɱɟɪɟɡ ɞɥɢɧɧɭɸ ɬɪɭɛɭ ɨɩɬɢɱɟɫɤɢɟ ɜɨɥɨɤɧɚ,
ɫɨɛɪɚɧɧɵɟ ɜ ɠɝɭɬɵ, ɤɪɨɦɟ ɬɨɝɨ, ɩɪɢ ɷɬɨɦ ɦɨɠɧɨ ɜ ɦɟɫɬɚɯ ɫɬɵɤɚ ɬɪɭɛɵ ɢ ɤɨɪɩɭɫɨɜ ɫɥɨɦɚɬɶ ɨɬɞɟɥɶɧɵɟ ɜɨɥɨɤɧɚ, ɚ ɨɩɪɟɞɟɥɢɬɶ ɦɟɫɬɨ ɩɨɥɨɦɤɢ ɜɨɡɦɨɠɧɨ ɬɨɥɶɤɨ ɩɨɫɥɟ ɩɨɞɫɬɵɤɨɜɤɢ ɨɩɬɢɱɟɫɤɢɯ
ɜɨɥɨɤɨɧ ɤ ɩɪɢɟɦɧɢɤɚɦ ɢɡɥɭɱɟɧɢɹ;
– ɩɨɥɢɪɨɜɚɬɶ ɜɨɥɨɤɧɚ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɩɨɫɥɟ ɜɤɥɟɢɜɚɧɢɹ ɜɨ ɜɬɭɥɤɢ, ɜ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɜ
ɩɪɨɰɟɫɫɟ ɫɛɨɪɤɢ ɩɨɥɢɪɨɜɚɧɧɚɹ ɩɨɜɟɪɯɧɨɫɬɶ ɦɨɠɟɬ ɛɵɬɶ ɩɨɰɚɪɚɩɚɧɚ;
– ɟɫɥɢ ɢɡɦɟɪɹɟɬɫɹ ɭɪɨɜɟɧɶ ɚɝɪɟɫɫɢɜɧɨɣ ɫɪɟɞɵ (ɧɚɩɪɢɦɟɪ, ɤɢɫɥɨɬɧɵɣ ɷɥɟɤɬɪɨɥɢɬ), ɬɨ ɜɨɡɦɨɠɧɨ ɧɚɪɭɲɟɧɢɟ ɝɟɪɦɟɬɢɱɧɨɫɬɢ ɭɡɥɚ «ɫɬɟɪɠɟɧɶ-ɧɚɤɨɧɟɱɧɢɤ» ɢɡ-ɡɚ ɪɚɫɬɜɨɪɟɧɢɹ ɤɥɟɹɳɟɝɨ ɫɨɫɬɚɜɚ.
ɉɨɷɬɨɦɭ ɩɪɟɞɥɨɠɟɧ ɦɨɞɟɪɧɢɡɢɪɨɜɚɧɧɵɣ ɜɚɪɢɚɧɬ ȼɈɋɂɍɀ, ɜ ɤɨɬɨɪɨɦ ɞɚɧɧɵɟ ɧɟɞɨɫɬɚɬɤɢ
ɭɫɬɪɚɧɟɧɵ (ɪɢɫ. 1).
ȼɈɋɂɍɀ ɫɨɞɟɪɠɢɬ ɢɫɬɨɱɧɢɤɢ ɢɡɥɭɱɟɧɢɹ 1, ɧɚɩɪɢɦɟɪ ɩɨɥɭɩɪɨɜɨɞɧɢɤɨɜɵɟ ɫɜɟɬɨɞɢɨɞɵ (ɥɚɡɟɪɵ), ɩɨɞɜɨɞɹɳɢɟ 2 ɢ ɨɬɜɨɞɹɳɢɟ 3 ɨɩɬɢɱɟɫɤɢɟ ɜɨɥɨɤɧɚ, ɨɩɬɢɱɟɫɤɢɟ ɫɬɟɪɠɧɢ 4, Ƚ-ɨɛɪɚɡɧɵɟ ɤɨɪɩɭɫɚ 5, ɫɨɫɬɨɹɳɢɟ ɢɡ ɬɪɟɯ ɱɚɫɬɟɣ 6, 7, 8, ɬɪɭɛɭ 9, ɡɚɝɥɭɲɤɭ 10, ɩɪɢɟɦɧɢɤɢ ɢɡɥɭɱɟɧɢɹ 11, ɧɚɩɪɢɦɟɪ
ɮɨɬɨɞɢɨɞɵ.
ɋ ɢɫɬɨɱɧɢɤɚɦɢ ɢɡɥɭɱɟɧɢɹ 1 ɫɨɫɬɵɤɨɜɚɧɵ ɩɨɞɜɨɞɹɳɢɟ ɨɩɬɢɱɟɫɤɢɟ ɜɨɥɨɤɧɚ 2, ɤɨɥɢɱɟɫɬɜɨ
ɤɨɬɨɪɵɯ ɪɚɜɧɨ ɤɨɥɢɱɟɫɬɜɭ ɬɨɱɟɤ ɫɴɟɦɚ ɢɧɮɨɪɦɚɰɢɢ ɨɛ ɭɪɨɜɧɟ ɠɢɞɤɨɫɬɢ.
ȼɨɥɨɤɨɧɧɨ-ɨɩɬɢɱɟɫɤɢɣ ɭɪɨɜɧɟɦɟɪ ɫɨɞɟɪɠɢɬ ɢɫɬɨɱɧɢɤɢ ɢɡɥɭɱɟɧɢɹ 1, ɧɚɩɪɢɦɟɪ ɩɨɥɭɩɪɨɜɨɞɧɢɤɨɜɵɟ ɫɜɟɬɨɞɢɨɞɵ, ɩɨɞɜɨɞɹɳɢɟ (ɉɈȼ) 2 ɢ ɨɬɜɨɞɹɳɢɟ (ɈɈȼ) 3 ɨɩɬɢɱɟɫɤɢɟ ɜɨɥɨɤɧɚ, ɨɩɬɢɱɟ-
54
ǟDzȂǺǻǸǻǰǵȄDzǾǷǵDz ǻǾǺǻǯȈ ǼǻǯȈȅDzǺǵȌ ǺǭDZDzdzǺǻǾǿǵ ǵ ǷǭȄDzǾǿǯǭ ǵǴDZDzǸǵǶ
ɫɤɢɟ ɫɬɟɪɠɧɢ 4, ɤɨɪɩɭɫɚ 5, ɫɨɫɬɨɹɳɢɟ ɢɡ ɬɪɟɯ ɱɚɫɬɟɣ: ɩɨɥɵɯ ɬɪɭɛɨɤ 6, ɜɬɭɥɨɤ 7 ɫɨ ɫɤɜɨɡɧɵɦ ɜɧɭɬɪɟɧɧɢɦ ɨɬɜɟɪɫɬɢɟɦ, ɧɚɤɨɧɟɱɧɢɤɨɜ 8 ɫ ɰɢɥɢɧɞɪɢɱɟɫɤɢɦ ɫɤɜɨɡɧɵɦ ɨɬɜɟɪɫɬɢɟɦ, ɬɪɭɛɭ 9, ɡɚɝɥɭɲɤɭ 10, ɩɪɢɟɦɧɢɤɢ ɢɡɥɭɱɟɧɢɹ 11, ɧɚɩɪɢɦɟɪ ɮɨɬɨɞɢɨɞɵ.
Ⱥ-Ⱥ
11
11
1
.
..
11
...
À
À
I
2 3 5
14
R
d ɨɜ
d ɨɜ
d ɨɜ/2
17
18
9
15 6
7
12 13 8 4
20
19
10
I
Ɋɢɫ. 1. Ʉɨɧɫɬɪɭɤɬɢɜɧɨɟ ɢɫɩɨɥɧɟɧɢɟ ɦɨɞɟɪɧɢɡɢɪɨɜɚɧɧɨɣ ɜɨɥɨɤɨɧɧɨ-ɨɩɬɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ
ɢɡɦɟɪɟɧɢɹ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ
ɇɚɤɨɧɟɱɧɢɤ 8 ɜɵɩɨɥɧɟɧ ɜ ɜɢɞɟ ɰɢɥɢɧɞɪɚ ɢ ɭɫɟɱɟɧɧɨɝɨ ɤɨɧɭɫɚ, ɩɪɢɱɟɦ ɰɢɥɢɧɞɪ ɹɜɥɹɟɬɫɹ
ɨɫɧɨɜɚɧɢɟɦ ɞɥɹ ɭɫɟɱɟɧɧɨɝɨ ɤɨɧɭɫɚ, ɦɚɥɨɟ ɨɫɧɨɜɚɧɢɟ ɤɨɬɨɪɨɝɨ ɨɛɪɚɳɟɧɨ ɜ ɫɬɨɪɨɧɭ ɲɚɪɨɜɢɞɧɨɝɨ
ɫɟɝɦɟɧɬɚ ɫɬɟɪɠɧɹ 4.
ɋ ɢɫɬɨɱɧɢɤɚɦɢ ɢɡɥɭɱɟɧɢɹ 1 ɫɨɫɬɵɤɨɜɚɧɵ ɉɈȼ 2, ɤɨɥɢɱɟɫɬɜɨ ɤɨɬɨɪɵɯ ɪɚɜɧɨ ɤɨɥɢɱɟɫɬɜɭ ɬɨɱɟɤ ɫɴɟɦɚ ɢɧɮɨɪɦɚɰɢɢ ɨɛ ɭɪɨɜɧɟ ɠɢɞɤɨɫɬɢ.
ɋɬɟɪɠɧɢ 4 ɢɦɟɸɬ ɤɪɭɝɥɨɟ ɫɟɱɟɧɢɟ ɢ ɜɵɩɨɥɧɟɧɵ ɫ ɲɚɪɨɜɢɞɧɵɦɢ ɫɟɝɦɟɧɬɚɦɢ ɧɚ ɪɚɛɨɱɟɦ
ɬɨɪɰɟ, ɨɛɪɚɳɟɧɧɵɦɢ ɜ ɫɬɨɪɨɧɭ ɠɢɞɤɨɫɬɢ, ɪɚɞɢɭɫɨɦ R, ɨɩɪɟɞɟɥɹɟɦɵɦ ɜɵɪɚɠɟɧɢɟɦ
dɨɜ d R d 1,5dɨɜ,
55
(1)
ǚǭDZDzdzǺǻǾǿȉ ǵ ǷǭȄDzǾǿǯǻ ǾǸǻdzǺȈȂ ǾǵǾǿDzǹ. Ȳ 4, 2013
ɝɞɟ dɨɜ – ɞɢɚɦɟɬɪ ɨɛɨɥɨɱɤɢ ɨɩɬɢɱɟɫɤɨɝɨ ɜɨɥɨɤɧɚ ɢɡ ɨɩɬɢɱɟɫɤɢ ɩɪɨɡɪɚɱɧɨɝɨ ɦɚɬɟɪɢɚɥɚ, ɧɚɩɪɢɦɟɪ,
ɢɡ ɤɜɚɪɰɟɜɨɝɨ ɫɬɟɤɥɚ, ɞɥɹ ɤɨɬɨɪɨɝɨ ɜɵɩɨɥɧɹɟɬɫɹ ɭɫɥɨɜɢɟ:
nɋɊ < nɀ < n1,
(2)
ɝɞɟ nɋɊ, nɀ, n1 – ɩɨɤɚɡɚɬɟɥɢ ɩɪɟɥɨɦɥɟɧɢɹ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ, ɠɢɞɤɨɫɬɢ ɢ ɫɬɟɪɠɧɹ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ.
ɐɢɥɢɧɞɪɢɱɟɫɤɚɹ ɱɚɫɬɶ ɫɬɟɪɠɧɟɣ 4 ɡɚɤɪɟɩɥɹɟɬɫɹ ɜ ɧɚɤɨɧɟɱɧɢɤɟ 8 ɤɨɪɩɭɫɚ 5 ɫɩɟɤɚɧɢɟɦ ɩɪɢ
ɜɵɫɨɤɨɣ ɬɟɦɩɟɪɚɬɭɪɟ, ɩɪɢ ɷɬɨɦ ɲɚɪɨɜɨɣ ɫɟɝɦɟɧɬ ɜɵɫɬɭɩɚɟɬ ɡɚ ɩɪɟɞɟɥɵ ɱɚɫɬɢ 8 ɤɨɪɩɭɫɚ 5 ɧɚ ɡɧɚɱɟɧɢɟ, ɪɚɜɧɨɟ R.
ɉɨɞɜɨɞɹɳɟɟ ɨɩɬɢɱɟɫɤɨɟ ɜɨɥɨɤɧɨ 2 ɢ ɨɬɜɨɞɹɳɟɟ ɨɩɬɢɱɟɫɤɨɟ ɜɨɥɨɤɧɨ 3 ɡɚɤɪɟɩɥɟɧɵ ɜɨ ɜɬɭɥɤɟ 7
ɤɨɪɩɭɫɚ 5 ɫ ɩɨɦɨɳɶɸ ɤɥɟɹ 12, ɨɛɥɚɞɚɸɳɟɝɨ ɛɨɥɶɲɨɣ ɭɩɪɭɝɨɫɬɶɸ. ȼɬɭɥɤɢ 7 ɭɫɬɚɧɚɜɥɢɜɚɸɬɫɹ ɜ
ɩɚɡ 13 ɧɚɤɨɧɟɱɧɢɤɨɜ 8. ɑɚɫɬɢ 6, 7, 8 ɤɨɪɩɭɫɚ 5 ɫɨɟɞɢɧɟɧɵ ɦɟɠɞɭ ɫɨɛɨɣ ɫ ɩɨɦɨɳɶɸ ɫɜɚɪɤɢ 14, ɩɪɢ
ɷɬɨɦ ɰɟɧɬɪɵ ɬɨɪɰɨɜ ɩɨɞɜɨɞɹɳɟɝɨ ɨɩɬɢɱɟɫɤɨɝɨ ɜɨɥɨɤɧɚ 2 ɢ ɨɬɜɨɞɹɳɟɝɨ ɨɩɬɢɱɟɫɤɨɝɨ ɜɨɥɨɤɧɚ 3
ɫɦɟɳɟɧɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɰɟɧɬɪɚ ɬɨɪɰɚ ɫɬɟɪɠɧɹ 4 ɧɚ ɡɧɚɱɟɧɢɟ, ɪɚɜɧɨɟ (dɨɜ/2 …1,5dɨɜ/2). ȼɧɭɬɪɟɧɧɹɹ
ɩɨɥɨɫɬɶ 15 ɤɨɪɩɭɫɚ 5 ɡɚɩɨɥɧɹɟɬɫɹ ɝɟɪɦɟɬɢɤɨɦ 16 (ɧɚ ɮɢɝ. 1 ɧɟ ɩɨɤɚɡɚɧ) ɜ ɰɟɥɹɯ ɢɫɤɥɸɱɟɧɢɹ ɩɨɥɨɦɨɤ ɨɩɬɢɱɟɫɤɢɯ ɜɨɥɨɤɨɧ ɩɪɢ ɜɨɡɞɟɣɫɬɜɢɢ ɜɢɛɪɚɰɢɢ, ɭɞɚɪɨɜ ɢ ɬ.ɩ.
Ʉɨɥɢɱɟɫɬɜɨ ɤɨɪɩɭɫɨɜ 5 ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɤɨɥɢɱɟɫɬɜɭ ɬɨɱɟɤ ɫɴɟɦɚ ɢɧɮɨɪɦɚɰɢɢ ɨɛ ɭɪɨɜɧɟ ɠɢɞɤɨɫɬɢ.
Ɍɪɭɛɚ 9 ɢɡɝɨɬɚɜɥɢɜɚɟɬɫɹ ɞɥɢɧɨɸ ɧɟ ɦɟɧɟɟ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɢɡɦɟɪɹɟɦɨɝɨ ɭɪɨɜɧɹ
ɠɢɞɤɨɫɬɢ. ɉɨɩɟɪɟɱɧɨɟ ɫɟɱɟɧɢɟ ɬɪɭɛɵ 9 ɦɨɠɟɬ ɛɵɬɶ ɤɪɭɝɥɵɦ ɢɥɢ ɩɪɹɦɨɭɝɨɥɶɧɵɦ. ɇɚ ɪɢɫ. 1 ɞɥɹ
ɩɪɢɦɟɪɚ ɩɪɢɜɟɞɟɧɚ ɤɪɭɝɥɚɹ ɬɪɭɛɚ. ȼ ɬɪɭɛɟ 9 ɩɪɨɫɜɟɪɥɟɧɵ ɫɤɜɨɡɧɵɟ ɨɬɜɟɪɫɬɢɹ 17 ɬɚɤ, ɱɬɨ ɢɯ ɨɫɢ
ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɵ ɩɪɨɞɨɥɶɧɨɣ ɨɫɢ ɬɪɭɛɵ. ɇɚɩɪɢɦɟɪ, ɤɚɤ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 1, ɨɬɜɟɪɫɬɢɹ 17 ɜɵɩɨɥɧɟɧɵ ɪɚɜɧɨɦɟɪɧɨ ɩɨ ɫɩɢɪɚɥɢ ɫ ɪɚɜɧɨɦɟɪɧɵɦ ɲɚɝɨɦ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦ ɪɚɫɫɬɨɹɧɢɸ ɦɟɠɞɭ ɬɨɱɤɚɦɢ ɫɴɟɦɚ ɢɧɮɨɪɦɚɰɢɢ. Ʉɨɥɢɱɟɫɬɜɨ ɨɬɜɟɪɫɬɢɣ 17 ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɤɨɥɢɱɟɫɬɜɭ ɬɨɱɟɤ ɫɴɟɦɚ ɢɧɮɨɪɦɚɰɢɢ ɨɛ ɭɪɨɜɧɟ ɠɢɞɤɨɫɬɢ.
Ʉɨɪɩɭɫɚ 5 ɤɪɟɩɹɬɫɹ ɤ ɬɪɭɛɟ 9 ɫ ɩɨɦɨɳɶɸ ɫɜɚɪɤɢ 18 ɬɚɤ, ɱɬɨɛɵ ɨɬɜɟɪɫɬɢɹ ɜ ɜɟɪɯɧɟɣ ɱɚɫɬɢ
ɤɨɪɩɭɫɚ 5 ɛɵɥɢ ɫɨɜɦɟɳɟɧɵ ɫ ɨɬɜɟɪɫɬɢɹɦɢ ɜ ɬɪɭɛɟ 9.
Ƚɟɪɦɟɬɢɡɚɰɢɹ ɬɪɭɛɵ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɡɚɝɥɭɲɤɢ 10, ɤɨɬɨɪɚɹ ɤɪɟɩɢɬɫɹ ɤ ɬɪɭɛɟ 9 ɫ
ɩɨɦɨɳɶɸ ɫɜɚɪɤɢ 19. ȼɧɭɬɪɟɧɧɹɹ ɩɨɥɨɫɬɶ 20 ɬɪɭɛɵ 9 ɡɚɩɨɥɧɹɟɬɫɹ ɝɟɪɦɟɬɢɤɨɦ 21 (ɧɚ ɪɢɫ. 1 ɧɟ ɩɨɤɚɡɚɧ) ɜ ɰɟɥɹɯ ɢɫɤɥɸɱɟɧɢɹ ɩɨɥɨɦɨɤ ɨɩɬɢɱɟɫɤɢɯ ɜɨɥɨɤɨɧ ɩɪɢ ɜɨɡɞɟɣɫɬɜɢɢ ɜɢɛɪɚɰɢɢ, ɭɞɚɪɨɜ ɢ ɬ.ɩ.
Ɉɬɜɨɞɹɳɢɟ ɨɩɬɢɱɟɫɤɢɟ ɜɨɥɨɤɧɚ 3, ɤɨɥɢɱɟɫɬɜɨ ɤɨɬɨɪɵɯ ɪɚɜɧɨ ɤɨɥɢɱɟɫɬɜɭ ɬɨɱɟɤ ɫɴɟɦɚ ɢɧɮɨɪɦɚɰɢɢ ɨɛ ɭɪɨɜɧɟ ɠɢɞɤɨɫɬɢ, ɫɨɟɞɢɧɟɧɵ ɫ ɩɪɢɟɦɧɢɤɚɦɢ ɢɡɥɭɱɟɧɢɹ 11.
Ɉɩɬɢɱɟɫɤɢɟ ɜɨɥɨɤɧɚ 2 ɢ 3 ɩɪɨɯɨɞɹɬ ɜɧɭɬɪɢ ɬɪɭɛɵ 9 ɢ ɱɟɪɟɡ ɨɬɜɟɪɫɬɢɹ 17 ɜ ɬɪɭɛɟ 9 ɩɪɨɬɹɧɭɬɵ ɤ ɩɪɢɟɦɧɨɦɭ ɬɨɪɰɭ ɫɬɟɪɠɧɹ 4.
ɋɩɨɫɨɛ ɢɡɝɨɬɨɜɥɟɧɢɹ ȼɈɋɂɍɀ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɫɥɟɞɭɸɳɟɦ (ɪɢɫ. 2):
1) ɧɚɪɟɡɚɸɬ ɨɩɬɢɱɟɫɤɢɟ ɜɨɥɨɤɧɚ ɜ ɤɨɥɢɱɟɫɬɜɟ 2n, ɝɞɟ n – ɤɨɥɢɱɟɫɬɜɨ ɤɨɧɬɪɨɥɢɪɭɟɦɵɯ ɬɨɱɟɤ
ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ, ɩɪɢɱɟɦ ɞɥɢɧɚ Li ɞɜɭɯ ɨɬɞɟɥɶɧɵɯ i-ɯ ɜɨɥɨɤɨɧ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɹɦɢ (3),
ɤɨɝɞɚ ɬɨɱɤɢ ɤɨɧɬɪɨɥɹ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ ɪɚɜɧɨɭɞɚɥɟɧɵ, ɫɨɨɬɧɨɲɟɧɢɹɦɢ (4), ɤɨɝɞɚ ɬɨɱɤɢ ɤɨɧɬɪɨɥɹ
ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ ɪɚɫɩɪɟɞɟɥɟɧɵ ɩɨ ɞɥɢɧɟ ɟɦɤɨɫɬɢ ɧɟɪɚɜɧɨɦɟɪɧɨ;
2) ɪɚɜɧɵɟ ɩɨ ɞɥɢɧɟ ɨɞɧɨ ɉɈȼ 2 ɢ ɨɞɧɨ ɈɈȼ 3 ɩɪɨɩɭɫɤɚɸɬ (ɧɚɱɢɧɚɹ ɫ ɫɚɦɵɯ ɞɥɢɧɧɵɯ ɢ ɞɚɥɟɟ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɩɨ ɦɟɪɟ ɭɦɟɧɶɲɟɧɢɹ ɢɯ ɞɥɢɧɵ) ɱɟɪɟɡ ɩɨɥɵɟ ɬɪɭɛɤɢ 6 ɤɨɪɩɭɫɨɜ 5;
3) ɜɤɥɟɢɜɚɸɬ ɨɩɬɢɱɟɫɤɢɟ ɜɨɥɨɤɧɚ 2 ɢ 3 ɫ ɩɨɦɨɳɶɸ ɤɥɟɹɳɟɝɨ ɫɨɫɬɚɜɚ 12 ɜɨ ɜɬɭɥɤɢ 7 ɬɚɤɢɦ
ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɪɚɛɨɱɢɟ ɬɨɪɰɵ ɨɩɬɢɱɟɫɤɢɯ ɜɨɥɨɤɨɧ 2 ɢ 3 ɛɵɥɢ ɪɚɫɩɨɥɨɠɟɧɵ ɜ ɩɥɨɫɤɨɫɬɢ ɩɨɜɟɪɯɧɨɫɬɢ ɜɬɭɥɨɤ 7, ɨɛɪɚɳɟɧɧɵɯ ɤ ɧɚɤɨɧɟɱɧɢɤɭ 8. ɇɚɥɢɱɢɟ ɤɥɟɹɳɟɝɨ ɫɨɫɬɚɜɚ 12 ɧɚ ɪɚɛɨɱɢɯ ɬɨɪɰɚɯ
ɜɨɥɨɤɨɧ 2, 3 ɧɟ ɞɨɩɭɫɤɚɟɬɫɹ;
4) ɬɨɪɰɵ ɨɩɬɢɱɟɫɤɢɯ ɜɨɥɨɤɨɧ 2 ɢ 3, ɡɚɤɪɟɩɥɟɧɧɵɯ ɜɨ ɜɬɭɥɤɟ 7, ɩɨɥɢɪɭɸɬ;
5) ɫɩɟɤɚɧɢɟɦ ɩɪɢ ɜɵɫɨɤɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɠɟɫɬɤɨ ɡɚɤɪɟɩɥɹɸɬ ɫɬɟɪɠɧɢ 4 ɜ ɧɚɤɨɧɟɱɧɢɤɚɯ 8 ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɫɮɟɪɢɱɟɫɤɢɟ ɫɟɝɦɟɧɬɵ ɪɚɫɩɨɥɚɝɚɥɢɫɶ ɫ ɭɡɤɨɣ ɫɬɨɪɨɧɵ ɤɨɧɭɫɨɜ ɧɚɤɨɧɟɱɧɢɤɨɜ 8, ɚ ɩɥɨɫɤɨɫɬɢ ɞɪɭɝɢɯ ɬɨɪɰɨɜ ɫɬɟɪɠɧɟɣ 4 ɫɨɜɩɚɞɚɥɢ ɫ ɨɫɧɨɜɚɧɢɹɦɢ ɰɢɥɢɧɞɪɨɜ ɧɚɤɨɧɟɱɧɢɤɨɜ 8;
6) ɜɬɭɥɤɢ 7 ɭɫɬɚɧɚɜɥɢɜɚɸɬ ɜ ɩɚɡ 13 ɧɚɤɨɧɟɱɧɢɤɨɜ 8;
7) ɧɚɤɨɧɟɱɧɢɤɚɦɢ 8 ɩɪɢɠɢɦɚɸɬ ɜɬɭɥɤɢ 7 ɫ ɨɩɬɢɱɟɫɤɢɦɢ ɜɨɥɨɤɧɚɦɢ 2 ɢ 3 ɤ ɨɞɧɨɦɭ ɬɨɪɰɭ
ɩɨɥɵɯ ɬɪɭɛɨɤ 6 ɤɨɪɩɭɫɨɜ 5;
8) ɱɚɫɬɢ 6, 7, 8 ɤɨɪɩɭɫɚ 5 ɜ ɦɟɫɬɚɯ ɢɯ ɫɨɟɞɢɧɟɧɢɣ ɫɜɚɪɢɜɚɸɬ ɦɟɠɞɭ ɫɨɛɨɣ ɫɜɚɪɤɨɣ 14;
56
ǟDzȂǺǻǸǻǰǵȄDzǾǷǵDz ǻǾǺǻǯȈ ǼǻǯȈȅDzǺǵȌ ǺǭDZDzdzǺǻǾǿǵ ǵ ǷǭȄDzǾǿǯǭ ǵǴDZDzǸǵǶ
ɚ)
ɛ)
Ɋɢɫ. 2. ɋɩɨɫɨɛ ɢɡɝɨɬɨɜɥɟɧɢɹ ȼɈɋɂɍɀ:
ɚ – ɤ ɨɩɪɟɞɟɥɟɧɢɸ ɞɥɢɧɵ ɨɩɬɢɱɟɫɤɢɯ ɜɨɥɨɤɨɧ;
ɛ – ɫɯɟɦɚ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɫɜɟɬɚ ɜ ɨɩɬɢɱɟɫɤɨɦ ɤɚɧɚɥɟ ȼɈɋɂɍ
57
ǚǭDZDzdzǺǻǾǿȉ ǵ ǷǭȄDzǾǿǯǻ ǾǸǻdzǺȈȂ ǾǵǾǿDzǹ. Ȳ 4, 2013
9) ɜɧɭɬɪɟɧɧɹɹ ɩɨɥɨɫɬɶ 15 ɫɨɛɪɚɧɧɵɯ ɤɨɪɩɭɫɨɜ 5 ɡɚɩɨɥɧɹɟɬɫɹ ɝɟɪɦɟɬɢɤɨɦ 16 (ɧɚ ɪɢɫ. 1 ɧɟ
ɩɨɤɚɡɚɧ);
10) ɫ ɩɨɦɨɳɶɸ ɩɪɢɫɩɨɫɨɛɥɟɧɢɹ ɜ ɜɢɞɟ ɤɪɸɱɤɚ ɱɟɪɟɡ ɨɬɜɟɪɫɬɢɹ 17 ɜ ɬɪɭɛɟ 9, ɧɚɱɢɧɚɹ ɫ ɫɚɦɨɝɨ ɧɢɠɧɟɝɨ ɢ ɩɟɪɟɦɟɳɚɹɫɶ ɜɜɟɪɯ ɩɨ ɬɪɭɛɟ 9, ɩɪɨɬɹɝɢɜɚɸɬ ɫɜɨɛɨɞɧɵɟ ɤɨɧɰɵ ɨɞɧɨɝɨ ɩɨɞɜɨɞɹɳɟɝɨ ɨɩɬɢɱɟɫɤɨɝɨ ɜɨɥɨɤɧɚ 2 ɢ ɨɞɧɨɝɨ ɨɬɜɨɞɹɳɟɝɨ ɨɩɬɢɱɟɫɤɨɝɨ ɜɨɥɨɤɧɚ 3 ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɧɚɱɢɧɚɹ ɫ
ɫɚɦɵɯ ɞɥɢɧɧɵɯ, ɜ ɫɬɨɪɨɧɭ ɢɫɬɨɱɧɢɤɨɜ ɢɡɥɭɱɟɧɢɹ 1 ɢ ɩɪɢɟɦɧɢɤɨɜ ɢɡɥɭɱɟɧɢɹ 11;
11) ɤɨɪɩɭɫɚ 5 ɫɨɟɞɢɧɹɸɬ ɫ ɬɪɭɛɨɣ 9 ɜ ɦɟɫɬɚɯ ɨɬɜɟɪɫɬɢɣ 17 ɫ ɩɨɦɨɳɶɸ ɫɜɚɪɤɢ 18;
12) ɡɚɝɥɭɲɤɨɣ 10 ɡɚɤɪɵɜɚɸɬ ɫ ɧɢɠɧɟɝɨ ɤɨɧɰɚ ɬɪɭɛɭ 9 ɢ ɡɚɤɪɟɩɥɹɸɬ ɫ ɩɨɦɨɳɶɸ ɫɜɚɪɤɢ 19;
13) ɝɟɪɦɟɬɢɤɨɦ 21 (ɧɚ ɪɢɫ. 1 ɧɟ ɩɨɤɚɡɚɧ) ɡɚɩɨɥɧɹɸɬ ɜɧɭɬɪɟɧɧɸɸ ɩɨɥɨɫɬɶ 20 ɬɪɭɛɵ 9;
14) ɫɜɨɛɨɞɧɵɟ ɬɨɪɰɵ ɩɨɞɜɨɞɹɳɢɯ ɨɩɬɢɱɟɫɤɢɯ ɜɨɥɨɤɨɧ 2 ɩɨɞɜɨɞɹɬ ɤ ɢɫɬɨɱɧɢɤɚɦ ɢɡɥɭɱɟɧɢɹ 1,
ɚ ɨɬɜɨɞɹɳɢɯ ɨɩɬɢɱɟɫɤɢɯ ɜɨɥɨɤɨɧ 3 – ɤ ɩɪɢɟɦɧɢɤɚɦ ɢɡɥɭɱɟɧɢɹ 11.
Ɉɞɢɧ ɢɡɦɟɪɢɬɟɥɶɧɵɣ ɤɚɧɚɥ ɜɨɥɨɤɨɧɧɨ-ɨɩɬɢɱɟɫɤɨɝɨ ɭɪɨɜɧɟɦɟɪɚ ɪɚɛɨɬɚɟɬ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ.
ɂɡɥɭɱɟɧɢɟ ɢɫɬɨɱɧɢɤɚ ɢɡɥɭɱɟɧɢɹ 1 ɧɚɩɪɚɜɥɹɟɬɫɹ ɩɨ ɉɈȼ 2 ɤ ɫɬɟɪɠɧɸ 4. ɉɨɬɨɤ ɢɡɥɭɱɟɧɢɹ,
ɢɡɥɭɱɚɟɦɵɣ ɬɨɪɰɨɦ ɉɈȼ 2, ɩɚɞɚɟɬ ɧɚ ɜɯɨɞɧɨɣ ɬɨɪɟɰ ɫɬɟɪɠɧɹ 4, ɩɪɟɥɨɦɥɹɟɬɫɹ ɢ ɪɚɫɩɪɨɫɬɪɚɧɹɟɬɫɹ
ɩɨ ɧɟɦɭ ɩɭɬɟɦ ɩɟɪɟɨɬɪɚɠɟɧɢɹ ɨɬ ɰɢɥɢɧɞɪɢɱɟɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɞɨ ɲɚɪɨɜɨɝɨ ɫɟɝɦɟɧɬɚ [3].
ɉɪɢ ɨɬɫɭɬɫɬɜɢɢ ɤɨɧɬɚɤɬɚ ɲɚɪɨɜɨɝɨ ɫɟɝɦɟɧɬɚ ɫɬɟɪɠɧɹ 4 ɫ ɠɢɞɤɨɫɬɶɸ ɥɭɱɢ ɫɜɟɬɚ ɡɚ ɫɱɟɬ ɜɵɩɨɥɧɟɧɢɹ ɭɫɥɨɜɢɹ ɩɨɥɧɨɝɨ ɜɧɭɬɪɟɧɧɟɝɨ ɨɬɪɚɠɟɧɢɹ ɨɬɪɚɠɚɸɬɫɹ ɨɬ ɩɨɜɟɪɯɧɨɫɬɢ ɫɬɪɟɠɧɹ 4 ɢ ɜɨɡɜɪɚɳɚɸɬɫɹ ɨɛɪɚɬɧɨ ɤ ɜɯɨɞɧɨɦɭ ɬɨɪɰɭ ɫɬɟɪɠɧɹ 4, ɩɪɟɥɨɦɥɹɸɬɫɹ ɢ ɜɵɯɨɞɹɬ ɢɡ ɫɬɟɪɠɧɹ 4, ɩɚɞɚɹ ɧɚ
ɩɪɢɟɦɧɵɣ ɬɨɪɟɰ ɈɈȼ 3. ɉɨ ɈɈȼ 3 ɩɨɬɨɤ ɢɡɥɭɱɟɧɢɹ ɪɚɫɩɪɨɫɬɪɚɧɹɟɬɫɹ ɞɨ ɩɪɢɟɦɧɢɤɚ ɢɡɥɭɱɟɧɢɹ 11,
ɝɞɟ ɩɪɨɢɫɯɨɞɢɬ ɟɝɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ ɜ ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɫɢɝɧɚɥ.
ɉɪɢ ɤɨɧɬɚɤɬɟ ɲɚɪɨɜɨɝɨ ɫɟɝɦɟɧɬɚ ɫɬɟɪɠɧɹ 4 ɫ ɠɢɞɤɨɫɬɶɸ ɩɪɨɢɫɯɨɞɢɬ ɧɚɪɭɲɟɧɢɟ ɭɫɥɨɜɢɹ ɩɨɥɧɨɝɨ ɜɧɭɬɪɟɧɧɟɝɨ ɨɬɪɚɠɟɧɢɹ, ɢ ɛɨɥɶɲɚɹ ɱɚɫɬɶ ɢɡɥɭɱɟɧɢɹ ɜɵɯɨɞɢɬ ɢɡ ɫɬɟɪɠɧɹ (ɬɨɱɤɚ Ⱥ ɧɚ ɪɢɫ. 2),
ɨɫɬɚɜɲɚɹɫɹ ɦɟɧɶɲɚɹ ɱɚɫɬɶ ɩɨ ɈɈȼ 3 ɪɚɫɩɪɨɫɬɪɚɧɹɟɬɫɹ ɞɨ ɩɪɢɟɦɧɢɤɚ ɢɡɥɭɱɟɧɢɹ 11.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɧɚɥɢɱɢɸ ɠɢɞɤɨɫɬɢ ɜ ɡɨɧɟ ɢɡɦɟɪɟɧɢɹ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɜɵɫɨɤɢɣ ɭɪɨɜɟɧɶ
ɧɚɩɪɹɠɟɧɢɹ ɩɪɢɟɦɧɢɤɚ ɢɡɥɭɱɟɧɢɹ 11, ɨɬɫɭɬɫɬɜɢɸ ɠɢɞɤɨɫɬɢ – ɧɢɡɤɢɣ ɭɪɨɜɟɧɶ ɧɚɩɪɹɠɟɧɢɹ.
Ⱥɧɚɥɨɝɢɱɧɵɦ ɨɛɪɚɡɨɦ ɪɚɛɨɬɚɸɬ ɞɪɭɝɢɟ ɢɡɦɟɪɢɬɟɥɶɧɵɟ ɤɚɧɚɥɵ ɜɨɥɨɤɨɧɧɨ-ɨɩɬɢɱɟɫɤɨɝɨ
ɭɪɨɜɧɟɦɟɪɚ.
ɉɨɜɵɲɟɧɢɟ ɢɥɢ ɩɨɧɢɠɟɧɢɟ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ ɜ ɟɦɤɨɫɬɢ 22 ɜɟɞɟɬ ɤ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɦɭ ɫɪɚɛɚɬɵɜɚɧɢɸ ɢɡɦɟɪɢɬɟɥɶɧɵɯ ɤɚɧɚɥɨɜ. ɋɢɝɧɚɥɵ ɫ ɩɪɢɟɦɧɢɤɨɜ ɢɡɥɭɱɟɧɢɹ 11 ɜ ɞɚɥɶɧɟɣɲɟɦ ɦɨɝɭɬ ɩɟɪɟɞɚɜɚɬɶɫɹ ɜ ɫɢɫɬɟɦɭ ɨɛɪɚɛɨɬɤɢ ɢɧɮɨɪɦɚɰɢɢ, ɤɨɬɨɪɚɹ ɦɨɠɟɬ ɜɵɞɚɜɚɬɶ ɫɢɝɧɚɥ ɜ ɜɢɞɟ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɞɢɫɤɪɟɬɧɨɝɨ ɩɨɜɵɲɟɧɢɹ ɢɥɢ ɩɨɧɢɠɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɩɪɢ ɩɨɜɵɲɟɧɢɢ ɢ
ɩɨɧɢɠɟɧɢɢ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ, ɢɥɢ ɨɛɪɚɛɚɬɵɜɚɬɶ ɢɧɞɢɜɢɞɭɚɥɶɧɨ ɫɢɝɧɚɥɵ ɫ ɤɚɠɞɨɝɨ ɢɡɦɟɪɢɬɟɥɶɧɨɝɨ ɤɚɧɚɥɚ.
ȼ ɩɪɟɞɥɚɝɚɟɦɨɣ ɤɨɧɫɬɪɭɤɰɢɢ ɜɨɥɨɤɨɧɧɨ-ɨɩɬɢɱɟɫɤɨɝɨ ɭɪɨɜɧɟɦɟɪɚ ɪɟɚɥɢɡɨɜɚɧɨ ɞɢɫɤɪɟɬɧɨɟ
ɢɡɦɟɪɟɧɢɟ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ, ɱɬɨ ɩɨɡɜɨɥɹɟɬ ɤɨɧɬɪɨɥɢɪɨɜɚɬɶ ɧɟɫɤɨɥɶɤɨ ɡɧɚɱɟɧɢɣ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ.
ɉɪɟɞɥɚɝɚɟɦɚɹ ɧɨɜɚɹ ɤɨɧɫɬɪɭɤɰɢɹ ɜɨɥɨɤɨɧɧɨ-ɨɩɬɢɱɟɫɤɨɝɨ ɭɪɨɜɧɟɦɟɪɚ ɩɨɡɜɨɥɹɟɬ ɩɪɨɢɡɜɨɞɢɬɶ ɤɨɧɬɪɨɥɶ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ ɜ ɬɪɟɛɭɟɦɵɯ ɬɨɱɤɚɯ ɟɦɤɨɫɬɟɣ, ɪɚɛɨɬɨɫɩɨɫɨɛɧɚ ɜ ɠɟɫɬɤɢɯ ɭɫɥɨɜɢɹɯ ɊɄɌ, ɨɛɥɚɞɚɟɬ ɚɛɫɨɥɸɬɧɨɣ ɢɫɤɪɨ-, ɜɡɪɵɜɨ-, ɩɨɠɚɪɨɛɟɡɨɩɚɫɧɨɫɬɶɸ ɢ ɧɟ ɬɪɟɛɭɟɬ ɫɥɨɠɧɵɯ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɢ ɢɡɦɟɪɢɬɟɥɶɧɵɯ ɨɩɟɪɚɰɢɣ ɩɪɢ ɢɡɝɨɬɨɜɥɟɧɢɢ.
Ɉɛɳɟɟ ɤɨɥɢɱɟɫɬɜɨ ɨɩɬɢɱɟɫɤɢɯ ɜɨɥɨɤɨɧ ȼɈɋɂɍ ɪɚɜɧɨ 2n, ɝɞɟ n – ɤɨɥɢɱɟɫɬɜɨ ɤɨɧɬɪɨɥɢɪɭɟɦɵɯ ɬɨɱɟɤ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ, ɩɪɢɱɟɦ ɞɥɢɧɚ Li ɞɜɭɯ ɨɬɞɟɥɶɧɵɯ i-ɯ ɜɨɥɨɤɨɧ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɹɦɢ (ɫɦ. ɪɢɫ. 2):
ɚ) ɤɨɝɞɚ ɬɨɱɤɢ ɤɨɧɬɪɨɥɹ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ ɪɚɜɧɨɭɞɚɥɟɧɵ:
Li • L + [H – (i–1)¨i],
ɛ) ɤɨɝɞɚ ɬɨɱɤɢ ɤɨɧɬɪɨɥɹ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ ɪɚɫɩɪɟɞɟɥɟɧɵ ɩɨ ɞɥɢɧɟ ɟɦɤɨɫɬɢ ɧɟɪɚɜɧɨɦɟɪɧɨ:
¦ 'i ),
n
Li • L +(H –
i 1
ɝɞɟ L – ɞɥɢɧɚ ɭɱɚɫɬɤɚ ɨɬ ɢɫɬɨɱɧɢɤɚ 1 ɢɥɢ ɩɪɢɟɦɧɢɤɚ ɢɡɥɭɱɟɧɢɹ 11 ɞɨ ɟɦɤɨɫɬɢ 19 (ɫɦ. ɪɢɫ. 3);
H – ɜɵɫɨɬɚ ɟɦɤɨɫɬɢ 19 (ɢɥɢ ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɜɟɪɯɧɟɣ ɝɪɚɧɢɰɵ ɟɦɤɨɫɬɢ ɞɨ ɩɨɫɥɟɞɧɟɣ ɬɨɱɤɢ ɫɴɟɦɚ ɢɧɮɨɪɦɚɰɢɢ); ¨i – ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɛɥɢɠɚɣɲɢɦɢ ɬɨɱɤɚɦɢ ɤɨɧɬɪɨɥɹ (ɫɦ. ɪɢɫɭɧɨɤ 2); i = 1, 2, …, n – ɩɨɪɹɞɤɨɜɵɣ ɧɨɦɟɪ ɬɨɱɤɢ.
Ɂɚɤɥɸɱɟɧɢɟ
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɟɞɥɚɝɚɟɦɚɹ ɤɨɧɫɬɪɭɤɰɢɹ ȼɈɋɂɍ ɪɟɚɥɢɡɭɟɬ ɞɢɫɤɪɟɬɧɨɟ ɢɡɦɟɪɟɧɢɟ ɭɪɨɜɧɹ
ɠɢɞɤɨɫɬɢ, ɱɬɨ ɩɨɡɜɨɥɹɟɬ ɤɨɧɬɪɨɥɢɪɨɜɚɬɶ ɧɟɫɤɨɥɶɤɨ ɡɧɚɱɟɧɢɣ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ ɜ ɬɪɟɛɭɟɦɵɯ ɬɨɱ-
58
ǟDzȂǺǻǸǻǰǵȄDzǾǷǵDz ǻǾǺǻǯȈ ǼǻǯȈȅDzǺǵȌ ǺǭDZDzdzǺǻǾǿǵ ǵ ǷǭȄDzǾǿǯǭ ǵǴDZDzǸǵǶ
ɤɚɯ ɟɦɤɨɫɬɢ, ɪɚɛɨɬɨɫɩɨɫɨɛɧɚ ɜ ɠɟɫɬɤɢɯ ɭɫɥɨɜɢɹɯ, ɨɛɥɚɞɚɟɬ ɚɛɫɨɥɸɬɧɨɣ ɢɫɤɪɨ-, ɜɡɪɵɜɨ-, ɩɨɠɚɪɨɛɟɡɨɩɚɫɧɨɫɬɶɸ, ɬɚɤ ɤɚɤ ɜ ɤɚɱɟɫɬɜɟ ɩɟɪɟɞɚɸɳɟɣ ɫɪɟɞɵ ɢɫɩɨɥɶɡɭɟɬɫɹ ɫɜɟɬɨɜɨɣ ɩɨɬɨɤ ɢ ɧɟ ɬɪɟɛɭɟɬ
ɫɥɨɠɧɵɯ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɢ ɢɡɦɟɪɢɬɟɥɶɧɵɯ ɨɩɟɪɚɰɢɣ ɩɪɢ ɢɡɝɨɬɨɜɥɟɧɢɢ.
ɋɩɢɫɨɤ ɥɢɬɟɪɚɬɭɪɵ
1. ɉɚɬɟɧɬ ɊɎ ʋ 2297602, ɆɉɄ G 01 F 23/22. ȼɨɥɨɤɨɧɧɨ-ɨɩɬɢɱɟɫɤɢɣ ɫɢɝɧɚɥɢɡɚɬɨɪ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ /
Ⱦ. ɂ. ɋɟɪɟɛɪɹɤɨɜ, Ɍ. ɂ. Ɇɭɪɚɲɤɢɧɚ. – Ɂɚɪɟɝ. ɜ ɝɨɫɪɟɟɫɬɪɟ 20.04.2007.
2. ɉɚɬɟɧɬ ɊɎ ʋ 2399887. ȼɨɥɨɤɨɧɧɨ-ɨɩɬɢɱɟɫɤɢɣ ɭɪɨɜɧɟɦɟɪ ɢ ɫɩɨɫɨɛ ɟɝɨ ɢɡɝɨɬɨɜɥɟɧɢɹ / Ⱦ. ɂ. ɋɟɪɟɛɪɹɤɨɜ,
Ɍ. ɂ. Ɇɭɪɚɲɤɢɧɚ, Ⱥ. Ƚ. ɉɢɜɤɢɧ, Ⱥ. ȼ. Ⱥɪɯɢɩɨɜ, Ⱥ. ȼ. Ɇɵɬɚɪɟɜ. – Ɂɚɪɟɝ. ɜ ɝɨɫɪɟɟɫɬɪɟ 20.09.2010.
3. ɉɚɬɟɧɬ ɊɎ ʋ 2297602. ȼɨɥɨɤɨɧɧɨ-ɨɩɬɢɱɟɫɤɢɣ ɫɢɝɧɚɥɢɡɚɬɨɪ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ / Ⱦ. ɂ. ɋɟɪɟɛɪɹɤɨɜ,
Ɍ. ɂ. Ɇɭɪɚɲɤɢɧɚ. – Ɉɩɭɛɥ. 20.04.2007, Ȼɸɥ. ʋ 11.
ɍȾɄ 681.586.5
Ɇɨɞɟɪɧɢɡɢɪɨɜɚɧɧɚɹ ɜɨɥɨɤɨɧɧɨ-ɨɩɬɢɱɟɫɤɚɹ ɫɢɫɬɟɦɚ ɢɡɦɟɪɟɧɢɹ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ / ɂ. Ɍ. ɇɚɡɚɪɨɜɚ, Ⱦ. ɂ. ɋɟɪɟɛɪɹɤɨɜ, Ɍ. ɘ. Ȼɪɨɫɬɢɥɨɜɚ, Ɍ. ɂ. Ɇɭɪɚɲɤɢɧɚ // ɇɚɞɟɠɧɨɫɬɶ ɢ ɤɚɱɟɫɬɜɨ ɫɥɨɠɧɵɯ ɫɢɫɬɟɦ. – 2013. –
ʋ 4. – ɋ. 54 –59.
ɇɚɡɚɪɨɜɚ ɂɧɧɚ Ɍɚɞɠɢɞɞɢɧɨɜɧɚ
ɚɫɩɢɪɚɧɬ,
ɤɚɮɟɞɪɚ ɩɪɢɛɨɪɨɫɬɪɨɟɧɢɹ,
ɉɟɧɡɟɧɫɤɢɣ ɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣ ɭɧɢɜɟɪɫɢɬɟɬ
(440026, Ɋɨɫɫɢɹ, ɝ. ɉɟɧɡɚ, ɭɥ. Ʉɪɚɫɧɚɹ, 40)
(8412) 36-84-59
E-mail: uncate@yandex.ru
Nazarova Inna Tadzhiddinovna
postgraduate student,
sub-department of instrumentation,
Penza State University
(440026, 40 Krasnaya street, Penza, Russia)
ɋɟɪɟɛɪɹɤɨɜ Ⱦɦɢɬɪɢɣ ɂɝɨɪɟɜɢɱ
ɧɚɱɚɥɶɧɢɤ ɥɚɛɨɪɚɬɨɪɢɢ,
ɇɚɭɱɧɨ-ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɢɣ ɢɧɫɬɢɬɭɬ
ɮɢɡɢɱɟɫɤɢɯ ɢɡɦɟɪɟɧɢɣ
(440026, Ɋɨɫɫɢɹ, ɝ. ɉɟɧɡɚ, ɭɥ. ȼɨɥɨɞɚɪɫɤɨɝɨ, 8/10)
89063972491
Serebryakov Dmitriy Igorevich
head of laboratory,
Research Institute physical measurements
(440026, 8/10 Volodarskogo street, Penza, Russia)
Ȼɪɨɫɬɢɥɨɜɚ Ɍɚɬɶɹɧɚ ɘɪɶɟɜɧɚ
ɤɚɧɞɢɞɚɬ ɬɟɯɧɢɱɟɫɤɢɯ ɧɚɭɤ, ɞɨɰɟɧɬ,
ɤɚɮɟɞɪɚ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɵɯ
ɷɥɟɤɬɪɨɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɫɢɫɬɟɦ,
ɉɟɧɡɟɧɫɤɢɣ ɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣ ɭɧɢɜɟɪɫɢɬɟɬ
(440026, Ɋɨɫɫɢɹ, ɝ. ɉɟɧɡɚ, ɭɥ. Ʉɪɚɫɧɚɹ, 40)
(8412) 36-84-59
E-mail: tat-krupkina@yandex.ru
Brostilova Tat'yana Yur'evna
candidate of technical sciences, associate professor,
sub-department of automated electric power systems,
Penza State University
(440026, 40 Krasnaya street, Penza, Russia)
Ɇɭɪɚɲɤɢɧɚ Ɍɚɬɶɹɧɚ ɂɜɚɧɨɜɧɚ
ɞɨɤɬɨɪ ɬɟɯɧɢɱɟɫɤɢɯ ɧɚɭɤ, ɩɪɨɮɟɫɫɨɪ,
ɤɚɮɟɞɪɚ ɩɪɢɛɨɪɨɫɬɪɨɟɧɢɹ,
ɉɟɧɡɟɧɫɤɢɣ ɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣ ɭɧɢɜɟɪɫɢɬɟɬ
(440026, Ɋɨɫɫɢɹ, ɝ. ɉɟɧɡɚ, ɭɥ. Ʉɪɚɫɧɚɹ, 40)
(8412) 36-84-59
E-mail: timurashkina.pgu@mail.ru
Murashkina Tat'yana Ivanovna
doctor of technical sciences, professor,
sub-department of instrumentation,
Penza State University
(440026, 40 Krasnaya street, Penza, Russia)
Ⱥɧɧɨɬɚɰɢɹ. ɉɪɨɜɟɞɟɧ ɚɧɚɥɢɡ ɫɭɳɟɫɬɜɭɸɳɢɯ ɞɚɬɱɢɤɨɜ ɢ ɫɢɫɬɟɦ ɢɡɦɟɪɟɧɢɹ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ. ȼɵɹɜɥɟɧɵ ɢɯ ɧɟɞɨɫɬɚɬɤɢ ɢ ɩɪɟɞɥɚɝɚɟɬɫɹ ɦɨɞɟɪɧɢɡɢɪɨɜɚɧɧɚɹ ɤɨɧɫɬɪɭɤɰɢɹ ɜɨɥɨɤɨɧɧɨ-ɨɩɬɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ
ɢɡɦɟɪɟɧɢɹ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ.
Abstract. The analysis of existing sensors and liquid level
measurement. Revealed their shortcomings and offers
streamlined design of fiber-optic liquid level measurement system.
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɜɨɥɨɤɨɧɧɨ-ɨɩɬɢɱɟɫɤɢɣ ɫɢɝɧɚɥɢɡɚɬɨɪ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ, ɨɩɬɢɱɟɫɤɢɟ ɜɨɥɨɤɧɚ, ɢɡɦɟɪɢɬɟɥɶɧɵɣ ɤɚɧɚɥ, ɢɫɬɨɱɧɢɤ ɢɡɥɭɱɟɧɢɹ.
Key words: system analysis, techniques of systems
analysis, systems approach, a complex technical system,
structure, system, method of peer review.
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