Кубрин С.С. Теория анализа и синтеза информационно-аналитических систем оптимальной отработки шахтных полей и месторождений
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ɫɨɨɬɜɟɬɫɬɜɨɜɚɬɶ ɥɢɛɨ ɪɟɚɥɶɧɨ ɫɭɳɟɫɬɜɭɸɳɟɦɭ ɨɞɧɨɡɧɚɱɧɨ ɨɩɪɟɞɟɥɟɧɧɨɦɭ
ɨɛɴɟɤɬɭ ɥɢɛɨ ɩɨɧɹɬɢɸ, ɜɜɟɞɟɧɧɨɦɭ ɩɨ ɨɩɪɟɞɟɥɟɧɢɸ. ȼ ɨɛɨɢɯ ɫɥɭɱɚɹɯ
ɧɨɦɢɧɚɥɶɧɵɣ ɨɛɴɟɤɬ ɜɜɨɞɢɬɫɹ ɜ ɮɨɪɦɚɥɢɡɚɰɢɸ ɫɢɫɬɟɦɵ ɬɨɥɶɤɨ
ɚɤɫɢɨɦɚɬɢɱɟɫɤɢ. Ɉɩɪɟɞɟɥɟɧɢɟ ɧɨɦɢɧɚɥɶɧɨɝɨ ɨɛɴɟɤɬɚ ɞɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ
ɜɜɨɞɢɬɶ ɧɨɦɢɧɚɥɶɧɵɟ ɨɛɴɟɤɬɵ, ɨɩɢɫɵɜɚɸɳɢɟ ɩɨɧɹɬɢɹ, ɧɟ ɢɫɩɨɥɶɡɭɟɦɵɟ ɜ
ɝɟɨɥɨɝɢɢ ɢɥɢ ɜ ɞɪɭɝɢɯ ɟɫɬɟɫɬɜɟɧɧɵɯ ɧɚɭɤɚɯ. ȼɧɨɜɶ ɜɜɟɞɟɧɧɵɟ ɩɨɧɹɬɢɹ
(ɧɨɦɢɧɚɥɶɧɵɟ ɨɛɴɟɤɬɵ) ɩɨɡɜɨɥɹɬ ɩɨɥɧɟɟ ɩɪɨɚɧɚɥɢɡɢɪɨɜɚɬɶ ɜɧɭɬɪɟɧɧɸɸ
ɫɭɬɶ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɝɟɨɥɨɝɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɢ ɜɵɹɜɢɬɶ ɟɺ ɨɫɧɨɜɧɵɟ
ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ ɢ ɨɫɨɛɟɧɧɨɫɬɢ.
Ɉɫɧɨɜɧɵɟ ɚɫɩɟɤɬɵ ɩɪɨɬɢɜɨɩɨɫɬɚɜɥɟɧɢɹ ɧɨɦɢɧɚɥɶɧɵɯ ɢ ɪɟɚɥɶɧɵɯ
ɫɢɫɬɟɦ ɢ ɨɛɴɟɤɬɨɜ ɯɚɪɚɤɬɟɪɢɡɭɸɬ ɫɚɦ ɩɪɨɰɟɫɫ ɮɨɪɦɚɥɢɡɚɰɢɢ ɫɢɫɬɟɦɵ. ɗɬɨ
ɩɨɡɜɨɥɹɟɬ ɜɵɹɜɢɬɶ ɢ ɩɨɧɹɬɶ ɫɜɨɣɫɬɜɚ ɷɬɨɝɨ ɩɪɨɰɟɫɫɚ.
ɋɢɫɬɟɦɭ, ɫɨɫɬɨɹɳɭɸ ɢɡ ɧɨɦɢɧɚɥɶɧɵɯ ɨɛɴɟɤɬɨɜ, ɫɜɹɡɚɧɧɵɯ ɢ
ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ ɦɟɠɞɭ ɫɨɛɨɣ, ɢ ɤɨɬɨɪɚɹ ɹɜɥɹɟɬɫɹ ɮɨɪɦɚɥɶɧɵɦ
ɨɩɢɫɚɧɢɟɦ ɪɟɚɥɶɧɨɣ ɫɢɫɬɟɦɵ, ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ ɧɨɦɢɧɚɥɶɧɨɣ ɫɢɫɬɟɦɨɣ
NS
.
ɋɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɮɨɪɦɚɥɢɡɚɰɢɹ (
F
) ɪɟɚɥɶɧɨɣ ɫɢɫɬɟɦɵ (
RS
) ɟɫɬɶ
ɩɪɨɰɟɫɫ ɩɨɥɭɱɟɧɢɹ ɧɨɦɢɧɚɥɶɧɨɣ ɫɢɫɬɟɦɵ (
NS
). ɗɬɨɬ ɩɪɨɰɟɫɫ ɦɨɠɧɨ
ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ
NONSRS
F
o
. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɮɨɪɦɚɥɢɡɚɰɢɹ ɟɫɬɶ
ɩɪɨɰɟɫɫ ɧɚɯɨɠɞɟɧɢɹ ɨɬɨɛɪɚɠɟɧɢɹ ɪɟɚɥɶɧɨɣ ɫɢɫɬɟɦɵ ɜ ɧɨɦɢɧɚɥɶɧɭɸ, ɜ
ɯɨɞɟ ɤɨɬɨɪɨɝɨ ɩɪɨɢɫɯɨɞɢɬ ɩɨɫɬɪɨɟɧɢɟ ɧɨɦɢɧɚɥɶɧɵɯ ɨɛɴɟɤɬɨɜ. ɉɨ ɫɜɨɟɣ
ɫɭɬɢ ɮɨɪɦɚɥɢɡɚɰɢɹ ɹɜɥɹɟɬɫɹ ɧɟɤɨɬɨɪɵɦ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟɦ
RS
ɜ
NS
. ɋ
ɮɢɥɨɫɨɮɫɤɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ ɩɪɨɰɟɫɫ ɮɨɪɦɚɥɢɡɚɰɢɢ ɫɢɫɬɟɦɵ ɦɨɠɧɨ
ɨɬɨɠɞɟɫɬɜɢɬɶ ɫ ɩɪɨɰɟɫɫɨɦ ɟɺ ɢɡɭɱɟɧɢɹ. ɉɨ ɜɫɟɣ ɜɢɞɢɦɨɫɬɢ, ɫɭɳɟɫɬɜɭɟɬ
ɦɧɨɠɟɫɬɜɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ, ɨɫɭɳɟɫɬɜɥɹɸɳɢɯ ɧɚɯɨɠɞɟɧɢɟ ɨɬɨɛɪɚɠɟɧɢɹ
ɪɟɚɥɶɧɨɣ ɫɢɫɬɟɦɵ ɜ ɧɨɦɢɧɚɥɶɧɭɸ ɫɢɫɬɟɦɭ.
ɉɪɢ ɮɨɪɦɚɥɢɡɚɰɢɢ ɪɟɚɥɶɧɨɣ ɫɢɫɬɟɦɵ ɜɚɠɧɭɸ ɪɨɥɶ ɢɝɪɚɸɬ ɰɟɥɢ
(
RC
), ɤɨɬɨɪɵɟ ɨɧɚ ɞɨɥɠɧɚ ɪɟɲɚɬɶ. ȼ ɩɪɨɰɟɫɫɟ ɮɨɪɦɚɥɢɡɚɰɢɢ ɧɚ
ɨɫɧɨɜɚɧɢɢ ɷɬɢɯ ɰɟɥɟɣ ɨɩɪɟɞɟɥɹɸɬɫɹ ɤɪɢɬɟɪɢɢ ɢ ɨɝɪɚɧɢɱɟɧɢɹ ɧɨɦɢɧɚɥɶɧɨɣ
ɫɢɫɬɟɦɵ. ȼ ɯɨɞɟ ɮɨɪɦɚɥɢɡɚɰɢɢ ɨɱɟɧɶ ɱɚɫɬɨ ɤɨɧɤɪɟɬɢɡɢɪɭɸɬɫɹ ɢ
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ɭɬɨɱɧɹɸɬɫɹ ɰɟɥɢ, ɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɤɨɪɪɟɤɬɢɪɭɟɬɫɹ ɢ ɫɚɦ ɩɪɨɰɟɫɫ
ɮɨɪɦɚɥɢɡɚɰɢɢ. Ⱦɪɭɝɢɦɢ ɫɥɨɜɚɦɢ, ɮɨɪɦɚɥɢɡɚɰɢɹ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ
ɢɬɟɪɚɰɢɨɧɧɨ. ȼ ɨɛɳɟɦ ɜɢɞɟ ɩɪɨɰɟɫɫ ɮɨɪɦɚɥɢɡɚɰɢɢ ɩɪɟɞɫɬɚɜɢɦ ɜ ɜɢɞɟ
ɞɢɚɝɪɚɦɦɵ:
NONS
NC
F
RS
RC
o
m
o
.
Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɜɨɡɦɨɠɧɵɟ ɮɨɪɦɚɥɢɡɚɰɢɢ ɪɟɚɥɶɧɨɣ ɫɢɫɬɟɦɵ ɞɥɹ
ɞɨɫɬɢɠɟɧɢɹ ɤɨɧɤɪɟɬɧɵɯ ɰɟɥɟɣ
F
RC
ɹɜɥɹɸɬɫɹ ɥɢɲɶ ɱɚɫɬɶɸ ɜɫɟɯ
ɮɨɪɦɚɥɢɡɚɰɢɣ ɞɥɹ ɷɬɨɣ ɪɟɚɥɶɧɨɣ ɫɢɫɬɟɦɵ
F
RS
, ɬɨ ɟɫɬɶ
FF
RSRC
.
ɇɨɦɢɧɚɥɶɧɵɟ ɫɢɫɬɟɦɵ, ɩɨɫɬɪɨɟɧɧɵɟ ɞɥɹ ɞɨɫɬɢɠɟɧɢɹ ɪɚɡɥɢɱɧɵɯ ɰɟɥɟɣ
RC
, ɦɨɝɭɬ, ɧɨ ɧɟ ɨɛɹɡɚɧɵ ɨɬɥɢɱɚɬɶɫɹ.
Ɋɟɡɸɦɢɪɭɹ ɜɵɲɟɢɡɥɨɠɟɧɧɨɟ, ɫɬɚɜɢɬɫɹ ɩɪɨɛɥɟɦɚ ɪɚɡɪɚɛɨɬɚɬɶ ɢ
ɨɩɢɫɚɬɶ ɦɟɯɚɧɢɡɦ, ɩɨɡɜɨɥɹɸɳɢɣ ɫɨɡɞɚɜɚɬɶ ɧɨɦɢɧɚɥɶɧɭɸ ɫɢɫɬɟɦɭ ɞɥɹ
ɨɩɢɫɚɧɢɹ ɪɟɚɥɶɧɨɣ ɫɢɫɬɟɦɵ. ɉɪɨɰɟɫɫ ɩɨɫɬɪɨɟɧɢɹ ɧɨɦɢɧɚɥɶɧɨɣ ɫɢɫɬɟɦɵ
ɫɨɫɬɨɢɬ ɜ ɪɚɡɞɟɥɟɧɢɢ ɫɢɫɬɟɦɵ ɧɚ ɟɺ ɜɧɭɬɪɟɧɧɢɟ ɤɨɦɩɨɧɟɧɬɵ, ɩɨɞɫɢɫɬɟɦɵ,
ɜɵɞɟɥɟɧɢɟ ɢɥɢ ɚɤɫɢɨɦɚɬɢɱɟɫɤɨɟ ɨɩɪɟɞɟɥɟɧɢɟ ɧɨɦɢɧɚɥɶɧɵɯ ɨɛɴɟɤɬɨɜ,
ɚɧɚɥɢɡɚ ɫɭɳɟɫɬɜɭɸɳɢɯ ɢ ɪɚɡɪɚɛɨɬɤɢ ɨɬɫɭɬɫɬɜɭɸɳɢɯ ɦɨɞɟɥɟɣ, ɜɵɹɫɧɟɧɢɢ
ɢ ɨɩɪɟɞɟɥɟɧɢɢ ɰɟɥɟɣ, ɤɨɬɨɪɵɟ ɧɟɨɛɯɨɞɢɦɨ ɞɨɫɬɢɱɶ. ɉɨɥɧɨɬɚ ɩɨɫɬɪɨɟɧɧɨɣ
ɧɨɦɢɧɚɥɶɧɨɣ ɫɢɫɬɟɦɵ ɡɚɜɢɫɢɬ ɨɬ ɭɪɨɜɧɹ ɪɚɡɜɢɬɢɹ ɡɧɚɧɢɣ ɨ ɪɟɚɥɶɧɵɯ
ɨɛɴɟɤɬɚɯ, ɫɜɹɡɹɯ ɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɢ ɢɯ ɦɟɠɞɭ ɫɨɛɨɣ ɜ ɯɨɞɟ ɩɪɨɰɟɫɫɚ
ɞɨɛɵɱɢ, ɨɛɨɝɚɳɟɧɢɹ ɢ ɬɪɚɧɫɩɨɪɬɢɪɨɜɤɢ ɭɝɥɹ.
ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɨɱɟɧɶ ɫɥɚɛɨ ɪɚɡɪɚɛɨɬɚɧ ɢɦɟɧɧɨ ɚɩɩɚɪɚɬ
ɩɨɫɬɪɨɟɧɢɹ ɧɨɦɢɧɚɥɶɧɵɯ ɫɢɫɬɟɦ. ȼ ɥɢɬɟɪɚɬɭɪɟ ɜ ɨɫɧɨɜɧɨɦ ɩɪɢɜɨɞɹɬɫɹ
ɧɟɛɨɥɶɲɢɟ ɩɪɢɦɟɪɵ, ɫɜɹɡɚɧɧɵɟ ɫ ɬɟɯɧɢɱɟɫɤɢɦɢ ɫɢɫɬɟɦɚɦɢ, ɮɨɪɦɚɥɢɡɚɰɢɹ
ɤɨɬɨɪɵɯ ɧɟ ɩɪɟɞɫɬɚɜɥɹɟɬ ɨɫɨɛɨɣ ɫɥɨɠɧɨɫɬɢ. ɋ ɪɨɫɬɨɦ ɪɚɡɦɟɪɧɨɫɬɢ ɜɟɤɬɨɪɚ
ɩɨɤɚɡɚɬɟɥɟɣ ɩɨɹɜɥɹɸɬɫɹ ɧɟ ɬɨɥɶɤɨ ɬɟɯɧɢɱɟɫɤɢɟ ɫɥɨɠɧɨɫɬɢ, ɧɨ ɫɥɨɠɧɨɫɬɢ
ɩɪɢɧɰɢɩɢɚɥɶɧɨɝɨ ɯɚɪɚɤɬɟɪɚ. ɉɨɷɬɨɦɭ ɮɨɪɦɚɥɢɡɚɰɢɹ ɛɨɥɶɲɢɯ ɢ
ɝɪɨɦɨɡɞɤɢɯ ɫɢɫɬɟɦ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɛɨɥɶɲɭɸ ɫɥɨɠɧɨɫɬɶ ɢ ɩɨɥɧɨɟ
ɨɬɫɭɬɫɬɜɢɟ ɤɚɤɢɯ-ɥɢɛɨ ɮɨɪɦɚɥɶɧɵɯ ɦɟɬɨɞɨɜ ɢ ɩɪɢɟɦɨɜ ɩɪɢɜɨɞɢɬ ɤ ɬɨɦɭ,
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ɱɬɨ ɷɬɨɬ ɩɪɨɰɟɫɫ ɫɬɚɧɨɜɢɬɫɹ ɧɟɭɩɪɚɜɥɹɟɦɵɦ ɢ ɧɟ ɩɨɞɚɸɳɢɦɫɹ ɜɧɟɲɧɟɦɭ
ɤɨɧɬɪɨɥɸ.
ɋɨɡɞɚɞɢɦ ɦɟɬɨɞɵ ɩɨɫɬɪɨɟɧɢɹ ɧɨɦɢɧɚɥɶɧɨɣ ɫɢɫɬɟɦɵ ɫ ɩɨɦɨɳɶɸ
ɢɧɮɨɪɦɚɰɢɢ, ɨɩɢɫɵɜɚɸɳɟɣ ɪɟɚɥɶɧɭɸ ɫɥɨɠɧɭɸ ɫɢɫɬɟɦɭ. ɉɪɟɞɫɬɚɜɢɦ
ɫɬɨɹɳɭɸ ɩɟɪɟɞ ɧɚɦɢ ɡɚɞɚɱɭ ɜ ɫɥɟɞɭɸɳɟɦ ɜɢɞɟ. ɋɭɳɟɫɬɜɭɟɬ ɛɨɥɶɲɚɹ,
ɫɥɨɠɧɚɹ ɪɟɚɥɶɧɚɹ ɫɢɫɬɟɦɚ -
RS
, ɞɥɹ ɤɨɬɨɪɨɣ ɞɨɫɬɭɩɧɨ ɦɧɨɠɟɫɬɜɨ
ɮɨɪɦɚɥɢɡɚɰɢɣ -
FF
RSRC
. ɂɡ ɜɫɟɝɨ ɦɧɨɠɟɫɬɜɚ
F
RC
ɮɨɪɦɚɥɢɡɚɰɢɣ
ɧɟɨɛɯɨɞɢɦɨ ɜɵɛɪɚɬɶ ɬɚɤɭɸ, ɤɨɬɨɪɚɹ ɫɨɨɬɜɟɬɫɬɜɨɜɚɥɚ ɛɵ ɢɫɤɨɦɨɣ
ɧɨɦɢɧɚɥɶɧɨɣ ɫɢɫɬɟɦɟ
NONS
, ɚɞɟɤɜɚɬɧɨ ɨɩɢɫɵɜɚɸɳɟɣ ɪɟɚɥɶɧɭɸ
ɫɢɫɬɟɦɭ. ɂɧɬɭɢɬɢɜɧɨ ɩɨɧɹɬɧɨ, ɱɬɨ ɞɚɧɧɚɹ ɡɚɞɚɱɚ ɢɦɟɟɬ ɜɟɥɢɤɨɟ ɦɧɨɠɟɫɬɜɨ
ɪɟɲɟɧɢɣ. ɑɬɨɛɵ ɤɚɤ-ɬɨ ɫɭɡɢɬɶ ɨɛɥɚɫɬɶ ɪɟɲɟɧɢɣ, ɧɟɨɛɯɨɞɢɦɨ ɩɨɬɪɟɛɨɜɚɬɶ,
ɱɬɨɛ ɨɩɢɫɚɧɢɟ ɨɛɪɚɡɨɜ ɧɨɦɢɧɚɥɶɧɵɯ ɨɛɴɟɤɬɨɜ ɢ ɜɫɟɣ ɧɨɦɢɧɚɥɶɧɨɣ
ɫɢɫɬɟɦɵ ɜ ɰɟɥɨɦ ɛɵɥɨ ɛɵ ɨɩɬɢɦɚɥɶɧɨ. ɉɪɢ ɷɬɨɦ ɞɨɥɠɧɨ ɜɵɩɨɥɧɹɬɶɫɹ
ɨɝɪɚɧɢɱɟɧɢɟ – ɧɨɦɢɧɚɥɶɧɚɹ ɫɢɫɬɟɦɚ ɞɨɥɠɧɚ ɛɵɬɶ ɭɧɢɜɟɪɫɚɥɶɧɨɣ. Ɍɨ ɟɫɬɶ
ɫɢɫɬɟɦɚ ɞɨɥɠɧɚ ɪɚɛɨɬɚɬɶ ɩɪɢ ɥɸɛɵɯ ɜɨɡɦɨɠɧɵɯ ɜ ɩɪɢɪɨɞɟ ɫɨɨɬɧɨɲɟɧɢɹɯ
ɞɚɧɧɵɯ ɢ ɧɟ ɡɚɜɢɫɟɬɶ ɨɬ ɨɫɨɛɟɧɧɨɫɬɟɣ ɦɟɫɬɨɪɨɠɞɟɧɢɹ, ɭɫɥɨɜɢɣ ɞɨɛɵɱɢ
ɭɝɥɹ, ɜɢɞɚ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɤɚɦɟɧɧɨɝɨ ɬɨɩɥɢɜɚ ɢ ɬɚɤ ɞɚɥɟɟ. ɋɢɫɬɟɦɚ ɞɨɥɠɧɚ
ɢɦɟɬɶ ɜɨɡɦɨɠɧɨɫɬɶ ɪɚɡɜɢɬɢɹ ɢ ɫɨɜɟɪɲɟɧɫɬɜɨɜɚɧɢɹ ɩɨ ɦɟɪɟ ɩɪɢɨɛɪɟɬɟɧɢɹ
ɡɧɚɧɢɣ ɨ ɩɪɟɞɦɟɬɧɨɣ ɨɛɥɚɫɬɢ ɢ ɭɬɨɱɧɟɧɢɢ ɰɟɥɟɣ.
ɉɨ ɜɫɟɣ ɜɢɞɢɦɨɫɬɢ, ɷɬɨ ɨɩɬɢɦɚɥɶɧɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɫɢɫɬɟɦɵ ɧɟ
ɹɜɥɹɟɬɫɹ ɫɬɚɬɢɱɟɫɤɢɦ, ɚ ɛɭɞɟɬ ɢɡɦɟɧɹɬɶɫɹ ɩɨ ɦɟɪɟ ɢɡɭɱɟɧɢɹ ɪɟɚɥɶɧɨɣ
ɫɢɫɬɟɦɵ, ɬɨ ɟɫɬɶ ɩɨ ɦɟɪɟ ɪɚɡɜɟɞɵɜɚɟɦɨɫɬɢ ɢ ɪɚɡɪɚɛɨɬɤɢ ɦɟɫɬɨɪɨɠɞɟɧɢɹ.
ɋɨɡɞɚɧɢɟ ɧɨɦɢɧɚɥɶɧɵɯ ɫɢɫɬɟɦ ɜ ɩɪɨɰɟɫɫɟ ɮɨɪɦɚɥɢɡɚɰɢɢ ɞɨɥɠɧɨ
ɩɪɨɢɫɯɨɞɢɬɶ ɜ ɪɚɦɤɚɯ ɬɟɨɪɟɬɢɤɨ-ɦɧɨɠɟɫɬɜɟɧɧɨɝɨ ɩɨɞɯɨɞɚ, ɩɨɷɬɨɦɭ
ɜɧɚɱɚɥɟ ɧɟɨɛɯɨɞɢɦɨ ɪɚɫɫɦɨɬɪɟɬɶ ɢ ɨɩɪɟɞɟɥɢɬɶ ɨɩɢɫɚɧɢɟ ɧɨɦɢɧɚɥɶɧɨɝɨ
ɨɛɴɟɤɬɚ. Ɍɨ ɟɫɬɶ ɨɩɪɟɞɟɥɢɬɶ ɷɥɟɦɟɧɬɵ, ɢɡ ɤɨɬɨɪɵɯ ɫɨɫɬɨɹɬ ɧɨɦɢɧɚɥɶɧɵɟ
ɫɢɫɬɟɦɵ.
54
2.3 Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɧɨɦɢɧɚɥɶɧɵɯ ɨɛɴɟɤɬɨɜ
ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɜɜɟɞɟɧɧɵɦɢ ɚɩɪɢɨɪɧɨ ɩɨɧɹɬɢɹɦɢ ɨ ɧɨɦɢɧɚɥɶɧɨɣ
ɫɢɫɬɟɦɟ ɢ ɧɨɦɢɧɚɥɶɧɨɦ ɨɛɴɟɤɬɟ, ɨɞɧɨɡɧɚɱɧɨɝɨ ɪɟɲɟɧɢɹ ɩɨ ɜɵɞɟɥɟɧɢɸ
ɧɨɦɢɧɚɥɶɧɵɯ ɨɛɴɟɤɬɨɜ ɩɪɢ ɢɡɭɱɟɧɢɢ ɪɟɚɥɶɧɨɣ ɫɢɫɬɟɦɵ ɧɟɬ.
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɧɟɬ ɧɢɤɚɤɨɣ ɜɨɡɦɨɠɧɨɫɬɢ ɨɞɧɨɡɧɚɱɧɨ
ɜɵɱɥɟɧɢɬɶ ɬɨɬ ɢɥɢ ɢɧɨɣ ɨɛɴɟɤɬ ɢɡ ɪɟɚɥɶɧɨɣ ɫɢɫɬɟɦɵ. Ɇɨɠɧɨ ɬɨɥɶɤɨ
ɨɞɧɨɡɧɚɱɧɨ ɡɚɞɚɬɶ ɟɝɨ ɨɩɢɫɚɧɢɟ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɧɟɤɨɬɨɪɨɣ
ɮɨɪɦɚɥɢɡɚɰɢɢ. Ⱦɚɥɟɟ, ɢɫɩɨɥɶɡɭɹ ɷɬɨ ɨɩɢɫɚɧɢɟ, ɦɨɠɧɨ ɩɨɫɬɪɨɢɬɶ
ɧɨɦɢɧɚɥɶɧɭɸ ɫɢɫɬɟɦɭ.
Ɋɚɫɫɦɨɬɪɢɦ, ɤ ɩɪɢɦɟɪɭ, ɜɨɩɪɨɫɵ ɡɚɞɚɧɢɹ ɝɟɨɦɟɬɪɢɢ ɭɝɨɥɶɧɨɝɨ
ɩɥɚɫɬɚ. Ɉɩɢɫɚɬɶ ɭɝɨɥɶɧɵɣ ɩɥɚɫɬ ɦɨɠɧɨ ɦɧɨɝɢɦɢ ɪɚɡɥɢɱɧɵɦɢ ɫɩɨɫɨɛɚɦɢ:
ɧɟɫɤɨɥɶɤɢɦɢ ɬɪɟɯɦɟɪɧɵɦɢ ɬɟɥɚɦɢ, ɧɚɛɨɪɨɦ ɬɨɩɨɥɨɝɢɱɟɫɤɢɯ
ɩɨɜɟɪɯɧɨɫɬɟɣ, ɢɡɨɝɢɩɫɚɦɢ, ɢɡɨɥɢɧɢɹɦɢ ɤɚɱɟɫɬɜɚ. ɉɪɢɜɟɞɟɧɧɵɟ ɨɩɢɫɚɧɢɹ
ɭɝɨɥɶɧɨɝɨ ɩɥɚɫɬɚ ɩɨɥɭɱɚɸɬɫɹ ɜ ɯɨɞɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɝɟɨɦɟɬɪɢɢ ɩɨɞɨɲɜɵ
ɫɥɨɹ ɢ ɢɯ ɦɨɠɧɨ ɭɫɥɨɜɧɨ ɧɚɡɜɚɬɶ ɦɨɞɟɥɶɧɵɦɢ (ɬɨɱɧɟɟ,
ɫɦɨɞɟɥɢɪɨɜɚɧɧɵɦɢ) ɨɩɢɫɚɧɢɹɦɢ.
ɇɨ ɤɪɨɦɟ ɬɚɤɢɯ ɨɩɢɫɚɧɢɣ, ɭɝɨɥɶɧɵɣ ɩɥɚɫɬ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ
ɩɪɨɫɬɵɦ ɧɚɛɨɪɨɦ ɬɨɱɟɤ ɜ ɬɪɟɯɦɟɪɧɨɦ (ɢɥɢ ɩɪɢ ɟɝɨ ɪɚɡɪɚɛɨɬɤɟ, ɤɨɝɞɚ
ɩɪɨɢɫɯɨɞɢɬ ɞɜɢɠɟɧɢɟ ɮɪɨɧɬɚ ɝɨɪɧɵɯ ɪɚɛɨɬ, ɜ ɱɟɬɵɪɟɯɦɟɪɧɨɦ)
ɩɪɨɫɬɪɚɧɫɬɜɟ. Ɍɨ ɟɫɬɶ, ɬɟɦ ɧɚɛɨɪɨɦ ɬɨɱɟɤ, ɤɨɬɨɪɵɣ ɹɜɥɹɟɬɫɹ ɢɫɯɨɞɧɵɦ ɞɥɹ
ɡɚɞɚɱɢ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɝɟɨɦɟɬɪɢɢ ɩɥɚɫɬɚ. ɉɨ ɜɫɟɣ ɜɢɞɢɦɨɫɬɢ, ɷɬɢ ɨɩɢɫɚɧɢɹ
ɨɬɥɢɱɚɸɬɫɹ ɥɢɲɶ ɬɟɦ, ɱɬɨ ɧɚɛɨɪ ɬɨɱɟɤ ɹɜɥɹɟɬɫɹ, ɤɚɤ ɛɵ ɩɟɪɜɢɱɧɨɣ
ɢɧɮɨɪɦɚɰɢɨɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ, ɚ, ɬɚɤ ɫɤɚɡɚɬɶ, ɦɨɞɟɥɶɧɵɟ ɢɥɢ
ɫɦɨɞɟɥɢɪɨɜɚɧɧɵɟ ɨɩɢɫɚɧɢɹ ɩɨɹɜɥɹɸɬɫɹ ɩɨɫɥɟ ɧɟɤɨɬɨɪɵɯ ɪɚɫɱɟɬɨɜ,
ɜɵɱɢɫɥɟɧɢɣ, ɜɵɩɨɥɧɹɟɦɵɯ ɫ ɩɨɦɨɳɶɸ ɪɚɡɥɢɱɧɵɯ ɦɨɞɟɥɟɣ, ɨɫɧɨɜɚɧɧɵɯ ɧɚ
ɪɚɡɥɢɱɧɵɯ ɩɪɟɞɩɨɥɨɠɟɧɢɹɯ ɢ ɞɨɩɭɳɟɧɢɹɯ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɫɭɳɟɫɬɜɭɸɬ
ɤɚɤ ɩɟɪɜɢɱɧɵɟ, ɬɚɤ ɢ ɜɬɨɪɢɱɧɵɟ ɨɩɢɫɚɧɢɹ ɧɨɦɢɧɚɥɶɧɵɯ ɨɛɴɟɤɬɨɜ.
ɋ ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ, ɫɚɦɢ ɬɨɱɤɢ, ɭɱɚɫɬɜɭɸɳɢɟ ɜ ɩɟɪɜɢɱɧɨɦ ɨɩɢɫɚɧɢɢ
ɭɝɨɥɶɧɨɝɨ ɩɥɚɫɬɚ, ɩɨɥɭɱɚɸɬɫɹ ɜ ɯɨɞɟ ɪɚɡɥɢɱɧɵɯ ɜɵɱɢɫɥɟɧɢɣ, ɛɭɞɶ ɬɨ
ɪɚɫɱɟɬ ɬɟɨɞɨɥɢɬɧɨɝɨ ɯɨɞɚ, ɜɵɱɢɫɥɟɧɢɟ ɤɨɨɪɞɢɧɚɬ ɩɨɞɫɟɱɟɤ ɩɨɞɨɲɜɵ ɫɥɨɟɜ
55
ɩɨ ɞɚɧɧɵɦ ɡɚɦɟɪɨɜ ɢɫɤɪɢɜɥɟɧɢɹ ɨɫɢ ɫɤɜɚɠɢɧɵ ɢɥɢ ɡɚɦɟɪɵ ɩɨɞɪɨɛɧɨɫɬɟɣ ɜ
ɡɚɛɨɹɯ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɪɢɧɰɢɩɢɚɥɶɧɵɯ ɨɬɥɢɱɢɣ ɪɚɡɥɢɱɧɵɯ ɨɩɢɫɚɧɢɣ
ɞɪɭɝ ɨɬ ɞɪɭɝɚ, ɫɜɹɡɚɧɧɵɯ ɫ ɩɨɝɪɟɲɧɨɫɬɹɦɢ ɪɚɫɱɟɬɚ, ɧɟɬ.
Ʉɚɤɨɟ ɢɡ ɩɟɪɟɱɢɫɥɟɧɧɵɯ ɨɩɢɫɚɧɢɣ ɫɥɟɞɭɟɬ ɢɫɩɨɥɶɡɨɜɚɬɶ ɢɥɢ
ɧɟɨɛɯɨɞɢɦɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɜɫɟ ɩɪɢɜɟɞɟɧɧɵɟ ɨɩɢɫɚɧɢɹ? Ɉɬɜɟɬɢɬɶ ɧɚ
ɩɨɫɬɚɜɥɟɧɧɵɣ ɜɨɩɪɨɫ ɧɟɜɨɡɦɨɠɧɨ. ɋɪɚɡɭ ɠɟ ɞɨɥɠɧɵ ɛɵɬɶ ɩɪɢɧɹɬɵ ɜɨ
ɜɧɢɦɚɧɢɟ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɚɫɩɟɤɬɵ, ɫɜɹɡɚɧɧɵɟ ɫ ɰɟɥɹɦɢ, ɞɥɹ ɤɨɬɨɪɵɯ
ɫɬɪɨɢɬɫɹ ɫɢɫɬɟɦɚ. ɉɨ ɜɫɟɣ ɜɢɞɢɦɨɫɬɢ, ɮɨɪɦɚɥɢɡɚɰɢɹ ɨɞɧɨɡɧɚɱɧɨ
ɨɩɪɟɞɟɥɹɟɬ ɜɫɟ ɧɨɦɢɧɚɥɶɧɵɟ ɨɛɴɟɤɬɵ.
Ɋɟɡɸɦɢɪɭɹ ɜɵɲɟɢɡɥɨɠɟɧɧɨɟ, ɦɨɠɧɨ ɫɤɚɡɚɬɶ, ɱɬɨ ɞɥɹ ɡɚɞɚɧɢɹ
ɧɨɦɢɧɚɥɶɧɨɝɨ ɨɛɴɟɤɬɚ ɧɟɨɛɯɨɞɢɦɨ ɧɟɤɨɬɨɪɨɟ ɢɧɮɨɪɦɚɰɢɨɧɧɨɟ ɨɩɢɫɚɧɢɟ ɢ
ɫɩɢɫɨɤ ɦɟɬɨɞɨɜ, ɦɨɞɟɥɟɣ, ɞɥɹ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɟɝɨ ɜ ɫɢɫɬɟɦɟ. Ⱦɥɹ ɨɩɢɫɚɧɢɹ
ɧɨɦɢɧɚɥɶɧɨɝɨ ɨɛɴɟɤɬɚ ɜ ɞɚɥɶɧɟɣɲɟɦ ɛɭɞɟɦ ɢɫɩɨɥɶɡɨɜɚɬɶ ɩɨɧɹɬɢɟ ɨɛɪɚɡ
ɧɨɦɢɧɚɥɶɧɨɝɨ ɨɛɴɟɤɬɚ. ɉɨɞ ɨɛɪɚɡɨɦ ɧɨɦɢɧɚɥɶɧɨɝɨ ɨɛɴɟɤɬɚ ɢɥɢ, ɞɥɹ
ɤɪɚɬɤɨɫɬɢ, ɨɛɪɚɡɨɦ ɨɛɴɟɤɬɚ
IdefObr ,
ɛɭɞɟɦ ɩɨɧɢɦɚɬɶ ɟɝɨ
ɚɤɫɢɨɦɚɬɢɱɟɫɤɨɟ ɨɩɪɟɞɟɥɟɧɢɟ
def
ɢ ɢɧɮɨɪɦɚɰɢɨɧɧɨɟ ɨɩɢɫɚɧɢɹ ɨɛɴɟɤɬɚ
I
. ɂɬɚɤ, ɫɨɜɨɤɭɩɧɨɫɬɶ ɨɛɪɚɡɚ ɧɨɦɢɧɚɥɶɧɨɝɨ ɨɛɴɟɤɬɚ ɢ ɧɚɛɨɪ ɟɝɨ ɦɨɞɟɥɟɣ
M
, ɨɩɢɫɵɜɚɸɳɢɯ ɩɨɜɟɞɟɧɢɟ ɷɬɨɝɨ ɨɛɴɟɤɬɚ ɜ ɫɢɫɬɟɦɟ, – ɷɥɟɦɟɧɬɵ,
ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɨɩɢɫɚɧɢɹ ɧɨɦɢɧɚɥɶɧɨɣ ɫɢɫɬɟɦɵ.
ȼɟɪɧɟɦɫɹ ɤ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦɭ ɩɪɢɦɟɪɭ. Ɉɛɳɟɢɡɜɟɫɬɧɨ, ɱɬɨ ɨɞɧɨɣ
ɝɟɨɦɟɬɪɢɢ ɞɥɹ ɨɩɢɫɚɧɢɹ ɩɥɚɫɬɚ ɧɟɞɨɫɬɚɬɨɱɧɨ. Ƚɟɨɥɨɝ ɫ ɩɥɚɫɬɨɦ
ɚɫɫɨɰɢɢɪɭɟɬ ɞɚɧɧɵɟ ɨ ɜɡɹɬɵɯ ɩɪɨɛɚɯ, ɤɚɤ ɫɚɦɨɝɨ ɩɨɥɟɡɧɨɝɨ ɢɫɤɨɩɚɟɦɨɝɨ,
ɬɚɤ ɢ ɜɦɟɳɚɸɳɢɯ ɩɨɪɨɞ, ɜɨɞɵ, ɝɚɡɨɜ ɢ ɧɟɮɬɟɩɪɨɹɜɥɟɧɢɣ. Ɇɧɨɝɢɟ ɝɨɪɧɵɟ
ɜɵɪɚɛɨɬɤɢ ɩɪɨɯɨɞɹɬɫɹ ɩɨ ɩɥɚɫɬɭ, ɢ ɨɧɢ ɧɟɪɚɡɪɵɜɧɨ ɫɜɹɡɚɧɵ ɫ ɧɢɦ. ȼ
ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɤɚɱɟɫɬɜɚ ɭɝɥɹ, ɦɨɳɧɨɫɬɢ, ɷɥɟɦɟɧɬɨɜ ɡɚɥɟɝɚɧɢɹ ɩɥɚɫɬ
ɪɚɡɛɢɜɚɟɬɫɹ ɧɚ ɩɨɞɫɱɟɬɧɵɟ ɛɥɨɤɢ, ɩɨ ɤɨɬɨɪɵɦ ɩɪɨɢɫɯɨɞɢɬ ɩɨɞɫɱɟɬ ɢ ɭɱɟɬ
ɞɜɢɠɟɧɢɹ ɡɚɩɚɫɨɜ. ɉɨɞɨɛɧɚɹ ɢɧɮɨɪɦɚɰɢɹ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɧɟɤɨɬɨɪɭɸ
ɜɧɭɬɪɟɧɧɸɸ ɫɬɪɭɤɬɭɪɭ ɬɚɤɨɝɨ ɫɥɨɠɧɨɝɨ ɨɛɴɟɤɬɚ, ɤɚɤ ɭɝɨɥɶɧɵɣ ɩɥɚɫɬ. Ɍɚɤ
56
ɠɟ ɨɧɚ ɨɩɪɟɞɟɥɹɟɬ ɨɫɨɛɟɧɧɨɫɬɢ ɫɜɹɡɟɣ ɭɝɨɥɶɧɨɝɨ ɩɥɚɫɬɚ ɫ ɞɪɭɝɢɦɢ
ɝɨɪɧɵɦɢ ɨɛɴɟɤɬɚɦɢ.
Ʉɪɨɦɟ ɷɬɨɝɨ, ɭɝɨɥɶɧɵɣ ɩɥɚɫɬ ɢɦɟɟɬ ɝɟɨɥɨɝɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ
ɜɨɡɪɚɫɬɧɨɝɨ ɩɥɚɧɚ. Ɍɚɤ, ɨɧ ɫɬɪɚɬɢɝɪɚɮɢɱɟɫɤɢ ɪɚɫɩɨɥɨɠɟɧ ɜ ɧɟɤɨɬɨɪɨɦ
ɩɚɤɟɬɟ, ɩɨɞɫɜɢɬɟ, ɫɜɢɬɟ, ɫɟɪɢɢ. Ɉɞɢɧ ɢ ɬɨɬ ɠɟ ɩɥɚɫɬ ɱɚɫɬɨ ɩɪɨɫɥɟɠɢɜɚɟɬɫɹ
ɧɚ ɪɚɡɥɢɱɧɵɯ ɲɚɯɬɧɵɯ ɩɨɥɹɯ, ɦɟɫɬɨɪɨɠɞɟɧɢɹɯ, ɜ ɩɪɟɞɟɥɚɯ ɨɞɧɨɝɨ
ɭɝɨɥɶɧɨɝɨ ɛɚɫɫɟɣɧɚ. ɗɬɢ ɨɩɢɫɚɧɢɹ ɩɨɤɚɡɵɜɚɸɬ, ɤɚɤ ɩɥɚɫɬ ɜɯɨɞɢɬ ɜ ɛɨɥɟɟ
ɫɥɨɠɧɵɟ ɨɛɴɟɤɬɵ. Ɍɚɤɢɯ ɩɪɢɦɟɪɨɜ ɦɨɠɧɨ ɩɪɢɜɟɫɬɢ ɦɚɫɫɭ ɞɥɹ ɥɸɛɵɯ
ɝɨɪɧɨ-ɝɟɨɥɨɝɢɱɟɫɤɢɯ ɨɛɴɟɤɬɨɜ.
Ɋɚɫɫɦɨɬɪɢɦ ɨɬɧɨɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟɨɛɯɨɞɢɦɨ ɨɬɪɚɠɚɬɶ ɜ
ɧɨɦɢɧɚɥɶɧɨɣ ɫɢɫɬɟɦɟ. ɉɭɫɬɶ ɞɚɧɨ ɧɟɤɨɬɨɪɨɟ ɨɬɧɨɲɟɧɢɟ
, ɜ ɤɨɬɨɪɨɦ
ɦɨɝɭɬ ɧɚɯɨɞɢɬɶɫɹ ɧɨɦɢɧɚɥɶɧɵɟ ɨɛɴɟɤɬɵ
1
NO
ɢ
2
NO
. ɗɬɢ ɧɨɦɢɧɚɥɶɧɵɟ
ɨɛɴɟɤɬɵ ɦɨɝɭɬ ɫɨɫɬɨɹɬɶ
21
NONO
ɢɥɢ ɧɟ ɫɨɫɬɨɹɬɶ
21
NONO
ɜ
ɡɚɞɚɧɧɨɦ ɨɬɧɨɲɟɧɢɢ. ɉɪɢɱɟɦ ɨɬɧɨɲɟɧɢɟ
21
NONO
ɧɟ ɬɨɠɞɟɫɬɜɟɧɧɨ
ɨɬɧɨɲɟɧɢɸ
12
NONO
, ɬɨ ɟɫɬɶ ɩɨɪɹɞɨɤ ɫɥɟɞɨɜɚɧɢɹ ɧɨɦɢɧɚɥɶɧɵɯ
ɨɛɴɟɤɬɨɜ ɜ ɨɬɧɨɲɟɧɢɢ ɫɭɳɟɫɬɜɟɧɟɧ. ɋɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɞɥɹ ɧɨɦɢɧɚɥɶɧɨɣ
ɫɢɫɬɟɦɵ ɫɭɳɟɫɬɜɭɟɬ ɧɟɤɨɬɨɪɨɟ ɦɧɨɠɟɫɬɜɨ
R
, ɨɩɪɟɞɟɥɹɟɦɨɟ ɤɚɤ
ɩɨɞɦɧɨɠɟɫɬɜɨ
NSNSR u
ɜɫɟɯ ɩɚɪ ɧɨɦɢɧɚɥɶɧɵɯ ɨɛɴɟɤɬɨɜ, ɞɥɹ ɤɨɬɨɪɵɯ
ɫɭɳɟɫɬɜɭɟɬ
21
NONO
. Ɋɚɫɫɦɨɬɪɟɧɧɨɟ ɨɬɧɨɲɟɧɢɟ ɹɜɥɹɟɬɫɹ ɛɢɧɚɪɧɵɦ
(ɞɜɭɯɦɟɫɬɧɵɦ). ɑɢɫɥɨ ɫɨɦɧɨɠɢɬɟɥɟɣ ɜ ɜɟɤɬɨɪɧɨɦ ɩɪɨɢɡɜɟɞɟɧɢɢ
ɨɩɪɟɞɟɥɹɟɬ ɪɚɡɦɟɪɧɨɫɬɶ ɨɬɧɨɲɟɧɢɣ. ȼ ɞɚɥɶɧɟɣɲɟɦ ɪɚɫɫɦɨɬɪɟɧɢɟ
ɨɝɪɚɧɢɱɢɦ ɬɨɥɶɤɨ ɭɧɚɪɧɵɦɢ ɢ ɛɢɧɚɪɧɵɦɢ ɨɬɧɨɲɟɧɢɹɦɢ ɦɟɠɞɭ
ɧɨɦɢɧɚɥɶɧɵɦɢ ɨɛɴɟɤɬɚɦɢ.
ȼɜɟɞɟɦ ɨɩɪɟɞɟɥɟɧɢɹ. Ɉɞɧɨɦɟɫɬɧɨɟ (ɭɧɚɪɧɨɟ) ɨɬɧɨɲɟɧɢɟ ɛɭɞɟɦ
ɧɚɡɵɜɚɬɶ ɫɜɨɣɫɬɜɨɦ ɧɨɦɢɧɚɥɶɧɨɝɨ ɨɛɴɟɤɬɚ
Q
I
. Ⱦɜɭɯɦɟɫɬɧɨɟ (ɛɢɧɚɪɧɨɟ)
ɨɬɧɨɲɟɧɢɟ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɩɨɧɹɬɢɸ «ɱɚɫɬɶ», ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ
ɫɜɹɡɹɦɢ ɧɨɦɢɧɚɥɶɧɨɝɨ ɨɛɴɟɤɬɚ
S
I
.
57
Ⱦɪɭɝɢɦɢ ɫɥɨɜɚɦɢ, ɢɧɮɨɪɦɚɰɢɹ, ɨɩɢɫɵɜɚɸɳɚɹ ɨɛɴɟɤɬ, ɞɟɥɢɬɫɹ ɧɚ ɞɜɟ
ɤɚɬɟɝɨɪɢɢ. Ɉɞɧɚ ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɫɜɨɣɫɬɜɚ ɫɚɦɨɝɨ ɨɛɴɟɤɬɚ, ɞɪɭɝɚɹ ɨɩɢɫɵɜɚɟɬ
ɟɝɨ ɫɜɹɡɢ ɫ ɞɪɭɝɢɦɢ ɨɛɴɟɤɬɚɦɢ, ɚ ɬɚɤ ɠɟ ɟɝɨ ɜɧɭɬɪɟɧɧɸɸ ɨɪɝɚɧɢɡɚɰɢɨɧɧɭɸ
ɫɬɪɭɤɬɭɪɭ. Ɇɨɠɧɨ ɫɤɚɡɚɬɶ, ɱɬɨ ɫɜɹɡɢ ɨɛɪɚɡɚ ɨɛɴɟɤɬɚ ɹɜɥɹɸɬɫɹ
ɢɧɮɨɪɦɚɰɢɟɣ ɨ ɫɬɪɭɤɬɭɪɟ ɢ ɨɩɢɫɵɜɚɸɬ ɨɪɝɚɧɢɡɚɰɢɸ ɤɨɧɤɪɟɬɧɨɝɨ
ɧɨɦɢɧɚɥɶɧɨɝɨ ɨɛɴɟɤɬɚ, ɩɨɞɫɢɫɬɟɦɵ ɢɥɢ ɫɢɫɬɟɦɵ ɜ ɰɟɥɨɦ.
ɂɡ ɨɩɪɟɞɟɥɟɧɢɹ ɧɨɦɢɧɚɥɶɧɨɝɨ ɨɛɴɟɤɬɚ ɫɥɟɞɭɟɬ, ɱɬɨ
Q
I
ɢ
S
I
ɹɜɥɹɸɬɫɹ ɩɨɞɦɧɨɠɟɫɬɜɚɦɢ ɢɧɮɨɪɦɚɰɢɨɧɧɨɝɨ ɨɩɢɫɚɧɢɹ ɨɛɴɟɤɬɚ
I
.
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɞɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɩɪɨɢɡɨɲɥɨ ɡɚɦɵɤɚɧɢɟ
SQ
III
,
ɭɬɨɱɧɢɦ ɨɩɪɟɞɟɥɟɧɢɟ ɨɛɪɚɡɚ ɧɨɦɢɧɚɥɶɧɨɝɨ ɨɛɴɟɤɬɚ. ȼ ɞɚɥɶɧɟɣɲɟɦ, ɩɨɞ
ɨɛɪɚɡɨɦ ɧɨɦɢɧɚɥɶɧɨɝɨ ɨɛɴɟɤɬɚ
SQ
IIdefObr ,,
ɛɭɞɟɦ ɩɨɧɢɦɚɬɶ
ɚɤɫɢɨɦɚɬɢɱɟɫɤɨɟ ɨɩɪɟɞɟɥɟɧɢɟ
def
, ɫɨɜɨɤɭɩɧɨɫɬɶ ɫɜɨɣɫɬɜ ɨɛɴɟɤɬɚ
Q
I
, ɚ
ɬɚɤ ɠɟ ɟɝɨ ɫɜɹɡɢ ɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɫ ɞɪɭɝɢɦɢ ɨɛɴɟɤɬɚɦɢ ɫɢɫɬɟɦɵ
S
I
.
ɂɬɚɤ, ɨɛɪɚɡ ɧɨɦɢɧɚɥɶɧɨɝɨ ɨɛɴɟɤɬɚ ɫɨɫɬɨɢɬ ɢɡ ɨɩɪɟɞɟɥɟɧɢɹ,
ɢɧɮɨɪɦɚɰɢɨɧɧɨɝɨ ɨɩɢɫɚɧɢɹ, ɢ ɟɝɨ ɫɜɹɡɟɣ ɫ ɪɚɡɥɢɱɧɵɦɢ ɧɨɦɢɧɚɥɶɧɵɦɢ
ɨɛɴɟɤɬɚɦɢ. Ɍɚɤɨɣ ɩɨɞɯɨɞ ɩɨɡɜɨɥɹɟɬ ɨɬɞɟɥɢɬɶ ɢɧɮɨɪɦɚɰɢɸ,
ɯɚɪɚɤɬɟɪɢɡɭɸɳɭɸ ɤɨɧɤɪɟɬɧɵɣ ɨɛɴɟɤɬ, ɨɬ ɢɧɮɨɪɦɚɰɢɢ, ɨɩɢɫɵɜɚɸɳɟɣ ɟɝɨ
ɩɨɥɨɠɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ɞɪɭɝɢɯ ɨɛɴɟɤɬɨɜ, ɢ ɜ ɫɢɫɬɟɦɟ ɜ ɰɟɥɨɦ. Ʉɪɨɦɟ
ɷɬɨɝɨ, ɨɬɦɟɬɢɦ, ɱɬɨ ɡɞɟɫɶ ɧɟɬ ɩɪɢɧɰɢɩɢɚɥɶɧɨɝɨ ɪɚɡɥɢɱɢɹ ɜ
ɢɧɮɨɪɦɚɰɢɨɧɧɨɦ ɨɩɢɫɚɧɢɢ ɨɛɴɟɤɬɚ ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɩɟɪɜɢɱɧɨɝɨ ɢ
ɜɬɨɪɢɱɧɨɝɨ (ɦɨɞɟɥɶɧɨɝɨ) ɧɚɛɨɪɚ ɞɚɧɧɵɯ. ɂɧɬɭɢɬɢɜɧɨ ɩɨɧɹɬɧɨ, ɱɬɨ ɦɨɞɟɥɢ
ɞɥɹ ɜɫɟɯ ɨɛɪɚɡɨɜ ɧɨɦɢɧɚɥɶɧɵɯ ɨɛɴɟɤɬɨɜ, ɭ ɤɨɬɨɪɵɯ ɨɞɧɨ ɢ ɬɨ ɠɟ
ɚɤɫɢɨɦɚɬɢɱɟɫɤɨɟ ɨɩɪɟɞɟɥɟɧɢɟ, ɨɞɧɢ ɢ ɬɟ ɠɟ. ɇɟɥɶɡɹ ɫɞɟɥɚɬɶ ɬɚɤɨɟ ɠɟ
ɭɬɜɟɪɠɞɟɧɢɟ ɨɛ ɢɧɮɨɪɦɚɰɢɨɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ, ɨɧɚ ɭ ɤɚɠɞɨɝɨ ɨɛɴɟɤɬɚ
ɪɚɡɥɢɱɧɚ, ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɥɢ ɨɧɚ ɫɜɨɣɫɬɜɚ ɨɛɴɟɤɬɚ ɢɥɢ ɟɝɨ ɫɜɹɡɢ.
ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɭ ɧɚɫ ɟɫɬɶ ɷɤɫɩɟɪɬɧɚɹ ɨɛɥɚɫɬɶ ɝɟɨɥɨɝɢɱɟɫɤɢɯ
ɡɧɚɧɢɣ, ɫ ɩɨɦɨɳɶɸ ɤɨɬɨɪɨɣ ɦɨɠɧɨ ɜɵɩɨɥɧɢɬɶ ɪɹɞ ɬɟɫɬɨɜ. Ɋɟɡɭɥɶɬɚɬɵ
ɤɚɠɞɨɝɨ ɬɟɫɬɚ ɪɚɡɛɢɜɚɸɬ ɨɛɥɚɫɬɶ, ɫɨɞɟɪɠɚɳɭɸ ɝɨɪɧɨ-ɝɟɨɥɨɝɢɱɟɫɤɭɸ
58
ɢɧɮɨɪɦɚɰɢɸ ɧɚ ɪɹɞ ɧɟɩɟɪɟɫɟɤɚɸɳɢɯɫɹ ɤɚɬɟɝɨɪɢɣ ɷɤɜɢɜɚɥɟɧɬɧɨɫɬɢ,
ɨɩɢɫɵɜɚɸɳɢɯ ɧɨɦɢɧɚɥɶɧɵɟ ɨɛɴɟɤɬɵ:
iii
ModGObGG ,
, ɝɞɟ
i
ObG
-
ɤɥɚɫɫ ɩɨɧɹɬɢɣ ɤɚɬɟɝɨɪɢɢ, ɚ
i
ModG
- ɤɥɚɫɫ ɦɨɞɟɥɟɣ ɤɚɬɟɝɨɪɢɢ. Ɍɨɝɞɚ ɨɛɳɟɟ
ɦɧɨɠɟɫɬɜɨ ɝɟɨɥɨɝɢɱɟɫɤɢɯ ɩɨɧɹɬɢɣ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɨɩɢɫɚɧɢɹɦ
ɧɨɦɢɧɚɥɶɧɵɯ ɨɛɴɟɤɬɨɜ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ ɨɛɴɟɞɢɧɟɧɢɟ -
n
i
i
GGEO
1
, ɞɥɹ
ɤɨɬɨɪɵɯ ɩɨ ɩɚɪɧɵɟ ɩɟɪɟɫɟɱɟɧɢɹ ɩɭɫɬɵ
ji
GG
ɞɥɹ ɜɫɟɯ
ji z
. ȿɫɥɢ
ɠɟ ɬɟɫɬ ɧɟ ɞɚɟɬ ɬɚɤɢɯ ɪɟɡɭɥɶɬɚɬɨɜ, ɬɨ ɟɝɨ ɧɟɨɛɯɨɞɢɦɨ ɦɨɞɢɮɢɰɢɪɨɜɚɬɶ
(ɞɟɬɚɥɢɡɢɪɨɜɚɬɶ, ɭɬɨɱɧɢɬɶ), ɡɚɦɟɧɢɬɶ ɢɥɢ ɨɬɛɪɨɫɢɬɶ. Ʉɚɠɞɭɸ ɩɨɥɭɱɟɧɧɭɸ
ɬɚɤɢɦ ɨɛɪɚɡɨɦ ɤɚɬɟɝɨɪɢɸ ɛɭɞɟɦ ɫɱɢɬɚɬɶ ɫɜɨɣɫɬɜɨɦ ɧɨɦɢɧɚɥɶɧɨɝɨ ɨɛɴɟɤɬɚ.
Ɍɨɝɞɚ, ɨ ɧɟɤɨɬɨɪɨɦ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ ɝɟɨɥɨɝɢɱɟɫɤɨɦ ɩɨɧɹɬɢɢ ɦɨɠɧɨ
ɫɞɟɥɚɬɶ ɞɜɚ ɷɤɜɢɜɚɥɟɧɬɧɵɯ ɭɬɜɟɪɠɞɟɧɢɹ: ɪɟɡɭɥɶɬɚɬ ɩɪɢɦɟɧɟɧɢɹ ɬɟɫɬɚ
T
ɟɫɬɶ
i
t
, ɢ ɩɨɧɹɬɢɟ
i
t
ɩɪɢɧɚɞɥɟɠɢɬ ɪɚɡɛɢɟɧɢɸ
T
.
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɫɪɟɞɚ ɝɨɪɧɨ-ɝɟɨɥɨɝɢɱɟɫɤɢɯ ɡɧɚɧɢɣ
G
, ɩɪɟɞɫɬɚɜɢɦɚ ɜ
ɜɢɞɟ ɩɚɪɵ
3
,UG
, ɦɧɨɠɟɫɬɜɚ ɝɨɪɧɨ-ɝɟɨɥɨɝɢɱɟɫɤɢɯ ɩɨɧɹɬɢɣ -
U
ɢ
ɫɟɦɟɣɫɬɜɚ ɢɯ ɪɚɡɛɢɟɧɢɣ -
3
ɩɨ ɪɚɡɥɢɱɧɵɦ ɫɜɨɣɫɬɜɚɦ. Ʉɚɠɞɵɣ ɷɥɟɦɟɧɬ ɢɡ
ɦɧɨɠɟɫɬɜɚ
3
ɟɫɬɶ ɫɜɨɣɫɬɜɨ. ȿɫɥɢ
P
- ɫɜɨɣɫɬɜɨ, ɬɨ ɤɚɠɞɵɣ ɷɥɟɦɟɧɬ
ɦɧɨɠɟɫɬɜɚ
P
(
Pp
) ɧɚɡɵɜɚɟɬɫɹ ɡɧɚɱɟɧɢɟɦ ɷɬɨɝɨ ɫɜɨɣɫɬɜɚ. Ɉɞɧɢɦ ɢɡ
ɜɚɠɧɵɯ ɢ ɩɨɧɹɬɧɵɯ ɝɨɪɧɵɦ ɫɩɟɰɢɚɥɢɫɬɚɦ ɪɚɡɛɢɟɧɢɟɦ ɝɨɪɧɨ-
ɝɟɨɥɨɝɢɱɟɫɤɢɯ ɩɨɧɹɬɢɣ ɟɫɬɶ ɪɚɡɛɢɟɧɢɟ ɧɚ ɨɛɴɟɤɬɵ. ɗɥɟɦɟɧɬ
obj
P
ɢɡ
ɦɧɨɠɟɫɬɜɚ
3
ɨɩɪɟɞɟɥɹɟɬ ɩɟɪɟɱɟɧɶ ɧɨɦɢɧɚɥɶɧɵɯ ɨɛɴɟɤɬɨɜ.
Ⱥɤɫɢɨɦɚɬɢɱɟɫɤɨɟ ɨɩɪɟɞɟɥɟɧɢɟ
def
ɨɛɪɚɡɚ ɧɨɦɢɧɚɥɶɧɨɝɨ ɨɛɴɟɤɬɚ
ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɡɧɚɱɟɧɢɸ ɫɜɨɣɫɬɜɚ
obj
P
. ɋɨɜɨɤɭɩɧɨɫɬɶ ɜɫɟɯ ɨɛɪɚɡɨɜ
SQ
IIdefObr ,,
ɧɨɦɢɧɚɥɶɧɵɯ ɨɛɴɟɤɬɨɜ ɫ ɪɚɡɥɢɱɧɵɦɢ ɨɩɪɟɞɟɥɟɧɢɹɦɢ
def
ɨɛɪɚɡɭɟɬ ɤɥɚɫɫ
obj
ObP
.
Ɉɬɦɟɬɢɦ ɨɫɧɨɜɧɵɟ ɬɪɟɛɨɜɚɧɢɹ, ɤɨɬɨɪɵɦ ɞɨɥɠɧɨ ɭɞɨɜɥɟɬɜɨɪɹɬɶ
ɨɩɢɫɚɧɢɟ ɨɛɪɚɡɨɜ ɧɨɦɢɧɚɥɶɧɵɯ ɨɛɴɟɤɬɨɜ. ȼɨ-ɩɟɪɜɵɯ, ɷɬɢ ɨɩɢɫɚɧɢɹ
59
ɞɨɥɠɧɵ ɫɬɪɨɢɬɶɫɹ ɜ ɪɚɦɤɚɯ ɮɨɪɦɚɥɶɧɨɝɨ ɹɡɵɤɚ. ȼɨ-ɜɬɨɪɵɯ, ɨɩɢɫɚɧɢɹ
ɨɛɪɚɡɨɜ ɞɨɥɠɧɵ ɢɦɟɬɶ ɨɞɢɧɚɤɨɜɵɣ ɭɪɨɜɟɧɶ ɚɛɫɬɪɚɤɰɢɢ. ȼ-ɬɪɟɬɶɢɯ,
ɞɨɥɠɧɚ ɭɱɢɬɵɜɚɬɶɫɹ ɞɢɧɚɦɢɤɚ ɢ ɜɡɚɢɦɨɫɜɹɡɶ ɫ ɞɪɭɝɢɦɢ ɧɨɦɢɧɚɥɶɧɵɦɢ
ɨɛɴɟɤɬɚɦɢ. ȼ-ɱɟɬɜɟɪɬɵɯ, ɨɩɢɫɚɧɢɸ ɨɛɪɚɡɚ ɞɨɥɠɧɵ ɛɵɬɶ ɩɪɢɫɭɳɢ
ɷɜɨɥɸɰɢɨɧɧɵɟ ɫɜɨɣɫɬɜɚ. Ɍɚɤ, ɩɨ ɦɟɪɟ ɪɚɡɜɢɬɢɹ ɡɧɚɧɢɣ ɨ ɪɟɚɥɶɧɨɣ
ɝɟɨɥɨɝɢɱɟɫɤɨɣ ɫɢɫɬɟɦɟ ɢ ɨɛ ɨɛɴɟɤɬɚɯ, ɢɡ ɤɨɬɨɪɵɯ ɨɧɚ ɫɨɫɬɨɢɬ, ɨɛɪɚɡ
ɨɞɧɨɝɨ ɢ ɬɨɝɨ ɠɟ ɪɟɚɥɶɧɨɝɨ ɨɛɴɟɤɬɚ ɞɨɥɠɟɧ ɪɚɡɜɢɜɚɬɶɫɹ ɷɜɨɥɸɰɢɨɧɧɵɦ
ɩɭɬɟɦ. ɂ, ɧɚɤɨɧɟɰ, ɜ-ɩɹɬɵɯ, ɫɨɡɞɚɧɧɵɟ ɨɩɢɫɚɧɢɹ ɞɨɥɠɧɵ ɛɵɬɶ
ɭɧɢɜɟɪɫɚɥɶɧɵ. ɂɡ ɷɬɨɝɨ, ɜ ɱɚɫɬɧɨɫɬɢ, ɫɥɟɞɭɟɬ, ɱɬɨ ɷɥɟɦɟɧɬɵ ɤɥɚɫɫɚ
obj
ObP
ɞɨɥɠɧɵ ɢɦɟɬɶ ɨɞɧɭ ɨɛɳɭɸ ɫɬɪɭɤɬɭɪɭ. ɉɨɩɵɬɚɟɦɫɹ ɟɺ ɩɨɫɬɪɨɢɬɶ.
Ɋɚɫɫɦɨɬɪɢɦ ɬɟɩɟɪɶ ɜɨɩɪɨɫɵ ɩɨɫɬɪɨɟɧɢɹ ɢɧɮɨɪɦɚɰɢɨɧɧɨɣ
ɫɨɫɬɚɜɥɹɸɳɟɣ ɨɛɪɚɡɨɜ ɧɨɦɢɧɚɥɶɧɵɯ ɨɛɴɟɤɬɨɜ. Ȼɭɞɟɦ ɫɱɢɬɚɬɶ, ɱɬɨ ɞɚɧɨ
ɧɟɤɨɬɨɪɨɟ ɦɧɨɠɟɫɬɜɨ ɧɨɦɢɧɚɥɶɧɵɯ ɨɛɴɟɤɬɨɜ ɢ ɧɟɨɛɯɨɞɢɦɨ ɫɨɡɞɚɬɶ ɤɥɚɫɫ
ɢɯ ɨɛɪɚɡɨɜ ɢ ɨɩɢɫɚɬɟɥɶɧɵɣ ɹɡɵɤ, ɤɨɬɨɪɵɣ ɫɨɡɞɚɟɬ ɩɪɨɫɬɵɟ ɢ ɭɞɨɛɧɵɟ
ɨɩɢɫɚɧɢɹ ɢɧɮɨɪɦɚɰɢɨɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɨɛɪɚɡɨɜ ɷɥɟɦɟɧɬɨɜ. ɉɪɟɠɞɟ
ɜɫɟɝɨ, ɨɩɪɟɞɟɥɢɦ ɩɨɧɹɬɢɟ ɩɪɨɫɬɨɝɨ ɢɧɮɨɪɦɚɰɢɨɧɧɨɝɨ ɨɩɢɫɚɧɢɹ. ɉɨɞ
ɩɪɨɫɬɵɦ ɨɩɢɫɚɧɢɟɦ ɢɧɮɨɪɦɚɰɢɨɧɧɵɯ ɫɜɨɣɫɬɜ ɧɨɦɢɧɚɥɶɧɨɝɨ ɨɛɴɟɤɬɚ
ɛɭɞɟɦ ɩɨɧɢɦɚɬɶ ɫɬɪɭɤɬɭɪɭ ɨɛɪɚɡɚ, ɜ ɤɨɬɨɪɨɣ ɤɚɠɞɨɦɭ ɫɜɨɣɫɬɜɭ ɨɛɴɟɤɬɚ
ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɨɞɧɨ ɨɩɢɫɚɧɢɟ. Ⱦɪɭɝɢɦɢ ɫɥɨɜɚɦɢ, ɩɪɨɫɬɨɟ ɢɧɮɨɪɦɚɰɢɨɧɧɨɟ
ɨɩɢɫɚɧɢɟ ɫɜɨɣɫɬɜ ɨɛɪɚɡɚ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜ ɜɢɞɟ ɧɟɤɨɬɨɪɨɣ ɫɬɪɭɤɬɭɪɵ,
ɫɨɞɟɪɠɚɳɟɣ ɩɟɪɟɱɟɧɶ ɫɜɨɣɫɬɜ
n
PPPɉ ,,,
21
, ɫ ɢɯ ɜɨɡɦɨɠɧɵɦɢ
ɡɧɚɱɟɧɢɹɦɢ
n
k
nnnn
kk
pppPpppPpppPɉ ,,,,,,,,,
21
2
2
2
2
1
22
1
1
2
1
1
11
.
ɉɪɢɱɟɦ ɡɧɚɱɟɧɢɹ ɫɜɨɣɫɬɜ ɹɜɥɹɸɬɫɹ ɩɨ ɩɚɪɧɨ ɧɟɩɟɪɟɫɟɤɚɸɳɢɟɫɹ
ɦɧɨɠɟɫɬɜɚ
ji
PP
ɞɥɹ ɜɫɟɯ
ji z
.
2.4 Ɉɩɪɟɞɟɥɟɧɢɟ ɩɟɪɟɱɧɹ ɬɢɩɨɜɵɯ ɫɜɨɣɫɬɜ ɨɛɪɚɡɨɜ ɝɨɪɧɨ-
ɝɟɨɥɨɝɢɱɟɫɤɢɯ ɨɛɴɟɤɬɨɜ.
ɉɪɨɚɧɚɥɢɡɢɪɭɟɦ ɜɨɡɦɨɠɧɨɟ ɦɧɨɠɟɫɬɜɨ ɬɢɩɨɜ ɫɜɨɣɫɬɜ, ɧɟɨɛɯɨɞɢɦɵɯ
ɞɥɹ ɨɩɢɫɚɧɢɹ ɝɟɨɥɨɝɢɱɟɫɤɢɯ ɨɛɴɟɤɬɨɜ.
60
ȼ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨ-ɜɪɟɦɟɧɧɨɦ ɤɨɧɬɢɧɭɭɦɟ ɬɪɚɟɤɬɨɪɢɢ ɬɨɱɟɤ ɝɨɪɧɨ-
ɝɟɨɥɨɝɢɱɟɫɤɢɯ ɨɛɴɟɤɬɨɜ, ɩɪɟɞɫɬɚɜɥɟɧɧɵɟ ɜ ɧɨɦɢɧɚɥɶɧɨɣ ɫɢɫɬɟɦɟ
ɧɨɦɢɧɚɥɶɧɵɦɢ ɨɛɴɟɤɬɚɦɢ, ɨɩɪɟɞɟɥɹɸɬɫɹ ɱɟɬɵɪɶɦɹ ɤɨɨɪɞɢɧɚɬɚɦɢ -
x
,
y
,
z
,
t
. Ɋɚɫɫɦɨɬɪɢɦ ɛɨɥɟɟ ɩɨɞɪɨɛɧɨ ɞɜɢɠɟɧɢɟ ɩɨ ɜɪɟɦɟɧɧɨɣ ɤɨɨɪɞɢɧɚɬɟ -
t
.
Ⱦɨɛɵɱɚ ɩɨɥɟɡɧɨɝɨ ɢɫɤɨɩɚɟɦɨɝɨ - ɞɥɢɬɟɥɶɧɵɣ ɢ ɞɨɜɨɥɶɧɨ ɦɟɞɥɟɧɧɨ
ɪɚɡɜɢɜɚɸɳɢɣɫɹ ɩɪɨɰɟɫɫ. ɂɧɬɟɪɜɚɥɵ ɜɪɟɦɟɧɢ ɢɫɱɢɫɥɹɸɬɫɹ ɫɭɬɤɚɦɢ,
ɧɟɞɟɥɹɦɢ, ɦɟɫɹɰɚɦɢ. Ɉɞɧɚɤɨ, ɤɪɨɦɟ ɬɨɝɨ, ɩɪɢɫɭɬɫɬɜɭɸɬ ɛɵɫɬɪɨ ɬɟɤɭɳɢɟ
ɩɪɨɰɟɫɫɵ (ɱɚɳɟ ɜɫɟɝɨ ɧɟɝɚɬɢɜɧɵɟ - ɝɨɪɧɵɟ ɭɞɚɪɵ, ɜɵɛɪɨɫɵ, ɜɡɪɵɜɵ), ɫɱɟɬ
ɜɪɟɦɟɧɢ ɜ ɤɨɬɨɪɵɯ ɢɞɟɬ ɧɚ ɞɨɥɢ ɫɟɤɭɧɞɵ. Ɇɧɨɝɢɟ ɝɨɪɧɨ-ɝɟɨɥɨɝɢɱɟɫɤɢɟ
ɨɛɴɟɤɬɵ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɦɟɧɹɸ ɫɜɨɟ ɩɨɥɨɠɟɧɢɟ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ. Ⱦɪɭɝɢɟ ɠɟ
ɧɟ ɦɟɧɹɸɬ ɫɜɨɢɯ ɫɜɨɣɫɬɜ ɫɨ ɜɪɟɦɟɧɟɦ. ɋɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɞɥɹ ɨɩɢɫɚɧɢɹ
ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨ-ɜɪɟɦɟɧɧɵɯ ɫɜɨɣɫɬɜ ɝɨɪɧɨ-ɝɟɨɥɨɝɢɱɟɫɤɢɯ ɨɛɴɟɤɬɨɜ
ɧɟɨɛɯɨɞɢɦɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɪɚɡɞɟɥɶɧɨ ɬɪɢ ɫɜɨɣɫɬɜɚ: ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɚɹ
ɤɨɧɮɢɝɭɪɚɰɢɹ ɨɛɪɚɡɚ ɨɛɴɟɤɬɚ
xyz
P
, ɞɚɬɚ
Data
P
ɢ ɜɪɟɦɹ
t
P
ɧɚɛɥɸɞɟɧɢɹ
ɫɜɨɣɫɬɜ ɨɛɴɟɤɬɚ.
ȼɵɹɫɧɢɦ, ɤɚɤɢɦɢ ɩɪɢɡɧɚɤɚɦɢ ɨɛɥɚɞɚɸɬ ɨɫɬɚɥɶɧɵɟ ɫɜɨɣɫɬɜɚ. ȼɨ-
ɩɟɪɜɵɯ, ɫɜɨɣɫɬɜɚ ɨɬɥɢɱɚɸɬɫɹ ɞɪɭɝ ɨɬ ɞɪɭɝɚ ɦɨɳɧɨɫɬɶɸ ɦɧɨɠɟɫɬɜɚ
ɡɧɚɱɟɧɢɣ. Ɍɚɤ, ɧɟɤɨɬɨɪɵɟ ɫɜɨɣɫɬɜɚ ɨɛɥɚɞɚɸɬ ɤɨɧɟɱɧɵɦ ɩɟɪɟɱɧɟɦ ɡɧɚɱɟɧɢɣ
^`
n
nP
ppppP ,,,,
321
, ɚ ɢɧɵɟ ɫɜɨɣɫɬɜɚ ɦɨɝɭɬ ɩɪɢɧɢɦɚɬɶ ɛɟɫɤɨɧɟɱɧɨɟ
ɱɢɫɥɨ ɡɧɚɱɟɧɢɣ
^`
,,,
321
pppP
P
f
. ɇɚɩɪɢɦɟɪ, ɫɜɨɣɫɬɜɨ, ɨɩɢɫɵɜɚɸɳɟɟ
ɦɨɪɮɨɥɨɝɢɸ ɬɪɟɳɢɧ, ɨɛɥɚɞɚɟɬ ɤɨɧɟɱɧɵɦ ɩɟɪɟɱɧɟɦ ɡɧɚɱɟɧɢɣ: ɜɨɥɨɫɬɧɵɟ
ɬɪɟɳɢɧɵ, ɡɚɤɪɵɬɵɟ, ɡɚɩɨɥɧɟɧɧɵɟ, ɨɬɤɪɵɬɵɟ, ɩɨɥɵɟ ɬɪɟɳɢɧɵ ɢ ɬ. ɞ. Ⱥ
ɫɜɨɣɫɬɜɨ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɟɟ ɦɨɳɧɨɫɬɶ ɩɥɚɫɬɚ – ɢɦɟɟɬ ɛɟɫɤɨɧɟɱɧɨɟ ɱɢɫɥɨ
ɡɧɚɱɟɧɢɣ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɪɢɡɧɚɤ «ɫɱɺɬɧɨɫɬɢ» ɡɧɚɱɟɧɢɣ ɫɜɨɣɫɬɜɚ
ɫɨɞɟɪɠɢɬ ɞɜɚ ɷɥɟɦɟɧɬɚ
^`
f ,qQ
P
(ɱɢɫɥɨ ɡɧɚɱɟɧɢɣ ɤɨɧɟɱɧɨ ɢɥɢ ɱɢɫɥɨ
ɡɧɚɱɟɧɢɣ ɫɱɟɬɧɨ).
ȼɨ-ɜɬɨɪɵɯ, ɧɟɤɨɬɨɪɵɟ ɫɜɨɣɫɬɜɚ ɹɜɥɹɸɬɫɹ ɪɟɡɭɥɶɬɚɬɨɦ ɤɚɤɢɯ-ɥɢɛɨ
ɢɡɦɟɪɟɧɢɣ ɢɥɢ ɜɵɱɢɫɥɟɧɢɣ ɢ ɦɨɝɭɬ ɛɵɬɶ ɜɵɪɚɠɟɧɵ ɱɢɫɥɨɦ
R
P
(ɦɨɳɧɨɫɬɶ