Оригинальное применение математического ожидания к вычислению вероятностей: модельная задача, программная реализация, особенности алгоритма
Выпуск:
ART 96353
Библиографическое описание статьи для цитирования:
Александров
П.
О.,
Орлик
Л.
К. Оригинальное применение математического ожидания к вычислению вероятностей: модельная задача, программная реализация, особенности алгоритма // Научно-методический электронный журнал «Концепт». –
2016. – Т. 15. – С.
2166–2170. – URL:
http://e-koncept.ru/2016/96353.htm.
Аннотация. В статье изложено оригинальное решение вероятностной задачи на классическую схему без использования комбинаторных формул, основанное на применении математического ожидания. Представлены нестандартные вычислительные алгоритмы с программной реализацией, и получены оценки их скорости роста. Проанализированы факторы, ускоряющие процесс вычислений.
Текст статьи
Ɍɷɱɶɽɬɹɰɼɺɮɛɬɮɱɷ ɚɷɱɯɺɮɴʃ,ɽɾɿɰɱɹɾ 3ɶɿɼɽɬ ɭɬɶɬɷɬɮɼɴɬɾɬʀɬɶɿɷʈɾɱɾɬ ɴɹʀɺɼɸɬʂɴɺɹɹʇʁ ɾɱʁɹɺɷɺɯɴɵ ɴ ɾɱʁɹɺɽʀɱɼɹɺɵɭɱɳɺɻɬɽɹɺɽɾɴ.ɜɺɽɽɴɵɽɶɴɵ ɏɺɽɿɰɬɼɽɾɮɱɹɹʇɵ ɝɺʂɴɬɷʈɹʇɵ ɟɹɴɮɱɼɽɴɾɱɾ. ɯ. ɘɺɽɶɮɬpavelÃaleksandrov@mail.ru
ɚɼɷɴɶɗʊɭɺɮʈ ɖɺɹɽɾɬɹɾɴɹɺɮɹɬ,ɻɼɺʀɱɽɽɺɼ, ɶɬɹɰɴɰɬɾ ʀɴɳɴɶɺÃɸɬɾɱɸɬɾɴʃɱɽɶɴʁ ɹɬɿɶ, ɻɼɺʀɱɽɽɺɼ ɶɬʀɱɰɼʇ ɻɼɴɶɷɬɰɹɺɵ ɸɬɾɱɸɬɾɴɶɴ. ɜɺɽɽɴɵɽɶɴɵ ɏɺɽɿɰɬɼɽɾɮɱɹɹʇɵ ɝɺʂɴɬɷʈɹʇɵ ɟɹɴɮɱɼɽɴɾɱɾ. ɯ. ɘɺɽɶɮɬLubov.orlik@gmail.com
ɚɼɴɯɴɹɬɷʈɹɺɱ ɻɼɴɸɱɹɱɹɴɱ ɸɬɾɱɸɬɾɴʃɱɽɶɺɯɺ ɺɲɴɰɬɹɴʋ ɶ ɮʇʃɴɽɷɱɹɴʊ ɮɱɼɺʋɾɹɺɽɾɱɵ: ɸɺɰɱɷʈɹɬʋ ɳɬɰɬʃɬ, ɻɼɺɯɼɬɸɸɹɬʋ ɼɱɬɷɴɳɬʂɴʋ, ɺɽɺɭɱɹɹɺɽɾɴ ɬɷɯɺɼɴɾɸɬ
Ɍɹɹɺɾɬʂɴʋ. Ɏ ɽɾɬɾʈɱ ɴɳɷɺɲɱɹɺɺɼɴɯɴɹɬɷʈɹɺɱ ɼɱʄɱɹɴɱ ɮɱɼɺʋɾɹɺɽɾɹɺɵ ɳɬɰɬʃɴ ɹɬ ɶɷɬɽɽɴʃɱɽɶɿʊ ɽʁɱɸɿ ɭɱɳ ɴɽɻɺɷʈɳɺɮɬɹɴʋ ɶɺɸɭɴɹɬɾɺɼɹʇʁ ʀɺɼɸɿɷ, ɺɽɹɺɮɬɹɹɺɱ ɹɬ ɻɼɴɸɱɹɱɹɴɴ ɸɬɾɱɸɬɾɴʃɱɽɶɺɯɺ ɺɲɴɰɬɹɴʋ. ɛɼɱɰɽɾɬɮɷɱɹʇ ɹɱɽɾɬɹɰɬɼɾɹʇɱ ɮʇʃɴɽɷɴɾɱɷʈɹʇɱ ɬɷɯɺɼɴɾɸʇ ɽ ɻɼɺɯɼɬɸɸɹɺɵ ɼɱɬɷɴɳɬʂɴɱɵ ɴ ɻɺɷɿʃɱɹʇɺʂɱɹɶɴ ɴʁ ɽɶɺɼɺɽɾɴ ɼɺɽɾɬ. ɛɼɺɬɹɬɷɴɳɴɼɺɮɬɹʇ ʀɬɶɾɺɼʇ, ɿɽɶɺɼʋʊʅɴɱ ɻɼɺʂɱɽɽ ɮʇʃɴɽɷɱɹɴɵ.ɖɷʊʃɱɮʇɱ ɽɷɺɮɬ: ɾɱɺɼɴʋ ɮɱɼɺʋɾɹɺɽɾɱɵ, ɸɬɾɱɸɬɾɴʃɱɽɶɺɱ ɺɲɴɰɬɹɴɱ, ɯɼɬʀɰɱɼɱɮɺ, ɺɻɾɴɸɴɳɬʂɴʋ ɮʇʃɴɽɷɱɹɴɵ
ɐɬɹɹɬʋ ɼɬɭɺɾɬ ʋɮɷʋɱɾɽʋ ɻɼɺɰɺɷɲɱɹɴɱɸ ʂɴɶɷɬ ɽɾɬɾʈɱɵ, ɻɺɽɮʋʅʌɹɹʇʁ ɽɼɬɮɹɴɾɱɷʈɹɺɸɿ ɬɹɬɷɴɳɿ ɮʇʃɴɽɷɴɾɱɷʈɹʇʁ ɳɬɾɼɬɾ ɻɼɴ ɼɱɬɷɴɳɬʂɴɴ ɽɾɬɹɰɬɼɾɹɺɯɺ ɴ ɺɼɴɯɴɹɬɷʈɹɺɯɺ ɬɷɯɺɼɴɾɸɺɮ ɼɱʄɱɹɴʋ ɺɭɺɭʅʌɹɹɺɵ ɳɬɰɬʃɴ ɍɱɼɹʄɾɱɵɹɬ ɝ.ə.PQ,ɽ. 91].ɝɾɬɹɰɬɼɾɹʇɵ ɸɱɾɺɰ ɻɼɱɰɻɺɷɬɯɬɱɾ ɴɽɻɺɷʈɳɺɮɬɹɴɱ ɶɺɸɭɴɹɬɾɺɼɹʇʁ ʀɺɼɸɿɷ, ɺɼɴɯɴɹɬɷʈɹʇɵ Ãɻɼɴɸɱɹɱɹɴɱ ɸɬɾɱɸɬɾɴʃɱɽɶɺɯɺ ɺɲɴɰɬɹɴʋP2,3R.Ɏɬɲɹɺ ɺɾɸɱɾɴɾʈ ɻɼɴɶɷɬɰɹɺɱ ɳɹɬʃɱɹɴɱ ɰɬɹɹʇʁ ɾɱɺɼɱɾɴʃɱɽɶɴʁ ɴɳʇɽɶɬɹɴɵ. ɛɼɴɮɱɰʌɸ ɻɼɴɸɱɼ ɳɬɰɬʃɴ, ɮ ɶɺɾɺɼɺɵ ɼɱɬɷɴɳɺɮɬɹ ɺɼɴɯɴɹɬɷʈɹʇɵ ɻɺɰʁɺɰ ɶ ɼɱʄɱɹɴʊ, ɬ ɴɸɱɹɹɺ: ɸɬɾɱɸɬɾɴʃɱɽɶɺɱ ɸɺɰɱɷɴɼɺɮɬɹɴɱ ɮʇɭɺɼɺʃɹɺɯɺ ɾɬɸɺɲɱɹɹɺɯɺ ɶɺɹɾɼɺɷʋ.ɠɿɼʇ ɽ ɶɺɹɾɼɬɭɬɹɰɹʇɸɴ ɯɼɿɳɬɸɴ ɼɱɯɿɷʋɼɹɺ ɳɬɰɱɼɲɴɮɬʊɾɽʋ ɹɬ ɾɬɸɺɲɹɱ ɳɬ ɹɬɼɿʄɱɹɴɱ ɼɱɲɴɸɬ ɽɬɹɶʂɴɵ ɴ ɬɹɾɴɽɬɹɶʂɴɵ. Ɏ ɽɮʋɳɴ ɽ ʉɾɴɸ ɬɶɾɿɬɷʈɹʇɸ ʋɮɷʋɱɾɽʋ ɮɺɻɼɺɽ ɺɭ ʉʀʀɱɶɾɴɮɹɺɽɾɴ ɮʇɭɺɼɺʃɹɺɯɺ ɾɬɸɺɲɱɹɹɺɯɺ ɶɺɹɾɼɺɷʋ. əɱ ɮ ɿʅɱɼɭ ɺɭʅɹɺɽɾɴ ɼɬɽɽɿɲɰɱɹɴɵ ɰɷʋ ɻɼɺɽɾɺɾʇ ɴɳɷɺɲɱɹɴʋ ɼɬɽɽɸɺɾɼɴɸ ɸɬɾɱɸɬɾɴʃɱɽɶɿʊ ɸɺɰɱɷʈ ɮʇɭɺɼɺʃɹɺɯɺ ɰɺɽɸɺɾɼɬʀɿɼ ɮ N(N= 11) ɼɱɯɴɺɹɬʁ.ɛɺ ɺɻɱɼɬɾɴɮɹʇɸ ɰɬɹɹʇɸ ɴɳɮɱɽɾɹɺ ɶɺɷɴʃɱɽɾɮɺ ʀɿɼ ɮ ɼɱɯɴɺɹɱ ɽ ɶɺɹɾɼɬɭɬɹɰɹʇɸɴ ɯɼɿɳɬɸɴ ɴ ɹɱ ɹɬɼɿʄɬʊʅɴɸɴ ɼɱɲɴɸ ɽɬɹɶʂɴɵ/ɬɹɾɴɽɬɹɶʂɴɵ, ɬ ɾɬɶɲɱ ʃɴɽɷɺ ɮɹɺɮʈ ɻɼɴɭʇɮʄɴʁ.Ɏ ʃɱɾʇɼʌʁ ɿɼɺɮɹɱɮɺɵ ɴɱɼɬɼʁɴɴ ɶɺɼɹɱɮʇɸ ɿɳɷɺɸ ʋɮɷʋɱɾɽʋ Customs(ɞɬɸɺɲɹʋ). ɚɹɬ ɽɮʋɳɬɹɬ ɽ ɻʋɾʈʊ ɼɱɯɴɺɹɬɸɴAthenaeum, Sanctury, Blackquarter, Middleheim, Elfwind, ɶɬɲɰʇɵ ɴɳ ɶɺɾɺɼʇʁ, ɽɮʋɳɬɹ ɽ ɼɱɯɴɺɹɬɸɴɴɳ ɻɱɼɱʃɴɽɷɱɹɴʋEquinox, DragoBreach, Silverwing, Rainhaven(0, 1, 1, 2, 0
ʃɴɽɷɺ ɽɮʋɳɱɵ ɽɺɺɾɮɱɾɽɾɮɱɹɹɺ), ɴ ɰɬɷɱɱ ɹɬ ɻɺɽɷɱɰɹɱɸ ɿɼɺɮɹɱ ɴɱɼɬɼʁɴɴDragoBreachɽɮʋɳɬɹ ɽ Rockwarren(ɼɴɽɿɹɺɶ Q).ɠɿɼʇ ɻɱɼɱɸɱʅɬʊɾɽʋ ɺɾ ɰɺʃɱɼɹɴʁ ɿɳɷɺɮ ɶ ɼɺɰɴɾɱɷʈɽɶɴɸ.ɖɬɶɺɮɬ ɮɱɼɺʋɾɹɺɽɾʈ ɾɺɯɺ, ʃɾɺ ɹɬɿɯɬɰ ɺɽɾɬɹɺɮɷɱɹɹɬʋ ɰɷʋ ɰɺɽɸɺɾɼɬ ʀɿɼɬ, ɻɱɼɱɮɺɳɴɾ ɶɺɹɾɼɬɭɬɹɰɹʇɱ ɯɼɿɳʇ.ɐɷʋ ɼɱʄɱɹɴʋ ɳɬɰɬʃɴ ɴɽɻɺɷʈɳɺɮɬɹ ɸɱɾɺɰ, ɺɻɿɭɷɴɶɺɮɬɹɹʇɵ ɮ ɼɬɭɺɾɱ[3].Ɏ ɹɱɵ ɻɼɱɰɷɬɯɬɱɾɽʋ ɬɷɯɺɼɴɾɸ ɻɺɴɽɶɬ ɮɱɼɺʋɾɹɺɽɾɴ ʃɱɼɱɳ ɸɬɾɱɸɬɾɴʃɱɽɶɺɱ ɺɲɴɰɬɹɴɱ ɴ ɰɺɶɬɳʇɮɱɾɽʋ ɱɯɺ ʉʀʀɱɶɾɴɮɹɺɽɾʈ ɻɱɼɱɰ ɸɱɾɺɰɺɸ ɶɺɸɭɴɹɬɾɺɼɹɺɯɺ ɻɱɼɱɭɺɼɬ ɮɽɱʁ ɮɺɳɸɺɲɹʇʁ ɮɬɼɴɬɹɾɺɮ. ɛɼɴɮɱɰɱɹɬ ɶɺɷɴʃɱɽɾɮɱɹɹɬʋɺʂɱɹɶɬ ɮʇʃɴɽɷɴɾɱɷʈɹʇʁ ɳɬɾɼɬɾ ɻɼɴ ɺɻɾɴɸɴɳɬʂɴɴ ɬɷɯɺɼɴɾɸɺɮ ɻɼɺɯɹɺɳɴɼɺɮɬɹɴʋ.
ɜɴɽɿɹɺɶ 1
ɍɿɰɱɸ ɻɺɹɴɸɬɾʈ ɻɺɰ ɿɼɹɬɸɴ Ãɼɱɯɴɺɹʇ, ɻɺɰ ɶɼɬɽɹʇɸɴ ʄɬɼɬɸɴ Ãʀɿɼʇ ɽ ɶɺɹɾɼɬɭɬɹɰɹʇɸɴ ɯɼɿɳɬɸɴ, ɻɺɰ ɽɴɹɴɸɴ Ãʀɿɼʇ, ɹɱ ɹɬɼɿʄɬʊʅɴɱ ɽɬɹɶʂɴɺɹɹʇɵ ɼɱɲɴɸ.Ɏɮɱɰɱɸ ɽɷɱɰɿʊʅɴɱ ɺɭɺɳɹɬʃɱɹɴʋ ɰɷʋ iÃɺɵ ɿɼɹʇ: red[i]Ãɶɺɷɴʃɱɽɾɮɺ ɶɼɬɽɹʇʁ ʄɬɼɺɮ, blue[i]Ãɶɺɷɴʃɱɽɾɮɺ ɽɴɹɴʁ, takeOut[i]Ãɶɺɷɴʃɱɽɾɮɺ ɴɳɮɷɱɶɬɱɸʇʁ ɴɳ iÃɺɵɿɼɹʇ ʄɬɼɺɮ. i=΅dzݙശശശശശ, k2, ɯɰɱ kÃʃɴɽɷɺ ɿɼɹ.ɜɬɽɽɸɺɾɼɴɸ ɽʁɱɸɿ ɴɳ ɻɺɽɷɱɰɺɮɬɾɱɷʈɹɺɵ ʂɱɻɺʃɶɴ ɿɼɹ. ɔɳ ɻɱɼɮɺɵ ɿɼɹʇ ɹɬɿɰɬʃɿ ɴɳɮɷɱɶɬɱɾɽʋ ɹɱɽɶɺɷʈɶɺ ʄɬɼɺɮ ɴ ɻɱɼɱɶɷɬɰʇɮɬɱɾɽʋ ɮɺ ɮɾɺɼɿʊ. Ɏ ɽɮɺʊ ɺʃɱɼɱɰʈ, ɴɳ ɮɾɺɼɺɵ ɮ ɾɼɱɾʈʊ ɻɱɼɱɶɷɬɰʇɮɬɱɾɽʋ ɶɬɶɺɱÃɾɺ ɶɺɷɴʃɱɽɾɮɺ ʄɬɼɺɮ ɴ ɾɬɶ ɰɬɷɱɱ. ɔ ɰɷʋɹɬʁɺɲɰɱɹɴʋ ɮɱɼɺʋɾɹɺɽɾɴ ɴɳɮɷɱʃɱɹɴʋɶɼɬɽɹʇɵ ʄɬɼ ɴɳ ɻɺɽɷɱɰɹɱɵ ɿɼɹʇ ɴɽɻɺɷʈɳɺɮɬɷɽʋ ɽɷɱɰɿʊʅɴɵ ɬɷɯɺɼɴɾɸ(ɼɴɽɿɹɺɶ 2).
ɜɴɽɿɹɺɶ 2
ɝɹɬʃɬɷɬɹɬʁɺɰɴɸɸɬɾɱɸɬɾɴʃɱɽɶɺɱɺɲɴɰɬɹɴɱɴɳɮɷɱʃɱɹɴʋɶɼɬɽɹɺɯɺʄɬɼɬɰɷʋɻɱɼɮɺɵɿɼɹʇ. ɛɺɾɺɸɮʂɴɶɷɱɴʅɱɾɽʋɸɬɾɱɸɬɾɴʃɱɽɶɺɱɺɲɴɰɬɹɴɱ ɰɷʋ ɻɺɽɷɱɰɿʊʅɴʁ ɿɼɹ ɽ ɿʃʌɾɺɸ ɸɬɾɱɸɬɾɴʃɱɽɶɺɯɺ ɺɲɴɰɬɹɴʋ ɰɷʋ ɻɼɱɰʇɰɿʅɴʁ. ɓɬɾɱɸ ɹɬʁɺɰɴɸ ɮɱɼɺʋɾɹɺɽɾʈ ɴɳɮɷɱʃɱɹɴʋ ɶɼɬɽɹɺɯɺ ʄɬɼɬ ɴɳ ɻɺɽɷɱɰɹɱɵ ɿɼɹʇ. ɓɹɬʃɱɹɴɱ ɮɱɼɺʋɾɹɺɽɾɴ ɮɺɳɮɼɬʅɬɱɾɽʋ ɮ ɻɼɺɯɼɬɸɸɿ.Ɏ ɽɷɿʃɬɱ ɻɱɼɱʁɺɰɬ ɺɾ ɻɺɽɷɱɰɺɮɬɾɱɷʈɹɺɯɺ ɼɬɽɻɺɷɺɲɱɹɴʋ ɿɼɹ ɶ ɸɺɰɱɷɴɼɿɱɸɺɵ ɽɾɼɿɶɾɿɼɱ ɰɱɼɱɮɬ ɽ ɶɺɼɹɱɮʇɸ ɿɳɷɺɸ Customs, ɽ ɿɳɷɬɸɴ ɮɱɾɮɷɱɹɴʋ Sanctury, Blackquarter, Middleheim,DragoBreachɴ ɷɴɽɾʈʋɸɴ Athenaeum, Elfwind, Equinox, Silverwing, Rainhaven, Rockwarrenɬɷɯɺɼɴɾɸ ɾɼɱɭɿɱɾ ɸɺɰɴʀɴɶɬʂɴɴ ɴɳɳɬ ɾɺɯɺ, ʃɾɺ ɾɱɻɱɼʈ ɿɳɱɷ ɸɺɲɱɾ ɴɸɱɾʈ ɭɺɷɱɱ ɺɰɹɺɯɺ ɰɺʃɱɼɹɱɯɺ ɿɳɷɬ.ɔɽɻɺɷʈɳɺɮɬɹɴɱ ɸɬɽɽɴɮɺɮ ɹɱ ɻɼɱɰɽɾɬɮɷʋɱɾɽʋ ɮɺɳɸɺɲɹʇɸ, ɻɺʉɾɺɸɿ,ʃɾɺɭʇ ɴɳɭɬɮɴɾʈɽʋ ɺɾ ɹɱɺɭʁɺɰɴɸɺɽɾɴ ɮ ɹɴʁ,ɭɿɰɱɸ ɴɽɻɺɷʈɳɺɮɬɾʈ ɼɱɶɿɼɽɴʊ (ɼɴɽɿɹɺɶ 3).
ɜɴɽɿɹɺɶ 3
ɛɼɴɹɬɲɬɾɴɴɶɹɺɻɶɴ"count" ɹɬɶɬɶɺɸɷɴɭɺɿɳɷɱɳɬɻɿɽɶɬɱɾɽʋʉɾɬʀɿɹɶʂɴʋɽɻɬɼɬɸɱɾɼɺɸisRoot= true. ɩɾɺɾɿɳɱɷɽʃɴɾɬɱɾ ɽɿɸɸɿ ɸɬɾɱɸɬɾɴʃɱɽɶɴʁ ɺɲɴɰɬɹɴɵ ɰɺʃɱɼɹɴʁ ɿɳɷɺɮ, ɳɬɻɼɬʄɴɮɬʋ ɱɯɺ ɿ ɹɴʁ ɽ ɻɬɼɬɸɱɾɼɺɸ isRoot( [VahZ, ɴ, ɴɽɻɺɷʈɳɿʋ ʉɾɺ ɳɹɬʃɱɹɴɱ,ɻɺɰɽʃɴɾʇɮɬɱɾ ɮɱɼɺʋɾɹɺɽɾʈ ɺɭɹɬɼɿɲɱɹɴʋ ʀɿɼʇ ɽ ɽɬɹɶʂɴɺɹɹʇɸ ɯɼɿɳɺɸ. ɐɺʃɱɼɹɴɱ ɿɳɷʇ, ɮ ɽɮɺʊ ɺʃɱɼɱɰʈ, ɾɺʃɹɺ ɾɬɶɲɱ ɽʃɴɾɬʊɾ ɽɿɸɸɿ ɸɬɾɱɸɬɾɴʃɱɽɶɴʁ ɺɲɴɰɬɹɴɵ ɽɮɺɴʁ ɰɺʃɱɼɹɴʁ ɿɳɷɺɮ, ɹɺ ɾɬɶ ɶɬɶ ɴɸ ɻɱɼɱɰɬɹ ɻɬɼɬɸɱɾɼ isRoot( [VahZ, ɾɺɺɹɴɮɺɳɮɼɬɾʋɾ ɹɱ ɮɱɼɺʋɾɹɺɽɾʈɺɭɹɬɼɿɲɱɹɴʋ, ɬ ɸɬɾɱɸɬɾɴʃɱɽɶɺɱ ɺɲɴɰɬɹɴɱ.
ɛɺɷɿʃɱɹ ɮɴɳɿɬɷɴɳɴɼɺɮɬɹɹʇɵ ɰɴɹɬɸɴʃɱɽɶɴɵ ɮɬɼɴɬɹɾ ɼɬɭɺɾʇ ɾɬɸɺɲɹɴ Customs. ɛɼɺɯɼɬɸɸɬ ɮɴɳɿɬɷɴɳɬʂɴɴ ɼɱɬɷɴɳɺɮɬɹɬ ɹɬ ʋɳʇɶɱ ɻɼɺɯɼɬɸɸɴɼɺɮɬɹɴʋ Java.ɚɭɺɭʅɴɸ ɻɺɽɾɬɹɺɮɶɿ ɻɼɱɰʇɰɿʅɱɵ ɳɬɰɬʃɴ. ɑɽɷɴ ɮ ɭɬɳɺɮɺɵ ɽʁɱɸɱɿɼɹ ɴɳ ɻɺɽɷɱɰɹɱɵ ɿɼɹʇ ɴɳɮɷɱɶɬɷɽʋ ɺɰɴɹ ʄɬɼ, ɾɱɻɱɼʈ Ãnʄɬɼɺɮ ɺɰɹɺɯɺ ʂɮɱɾɬ.ɛɼɱɰʇɰɿʅɴɵ ɬɷɯɺɼɴɾɸ ɻɺɳɮɺɷʋɱɾ ɮʇʃɴɽɷɴɾʈɮɱɼɺʋɾɹɺɽɾʈ ɾɺɯɺ, ʃɾɺ ɻɱɼɮʇɵ ɴɳɮɷɱʃʌɹɹʇɵ ɴɳ ɶɺɼɹɱɮɺɯɺ ɿɳɷɬʄɬɼ ɶɼɬɽɹʇɵ.Ɏɺɳɹɴɶɬɱɾɮɺɻɼɺɽ:ɶɬɶ ɸɱɹʋɱɾɽʋ ɮɱɼɺʋɾɹɺɽɾʈ ɴɳɮɷɱʃɱɹɴʋ ɮɾɺɼɺɯɺ ɶɼɬɽɹɺɯɺ ʄɬɼɬ ɮ ɳɬɮɴɽɴɸɺɽɾɴ ɺɾ ɶɺɹɶɼɱɾɹɺɯɺ ɿɳɷɬ, ɴɳ ɶɺɾɺɼɺɯɺ ɭʇɷ ɴɳɮɷɱʃʌɹɻɱɼɮʇɵ ʄɬɼ. ɐɷʋ ɶɬɲɰɺɯɺ ɿɳɷɬ ɴɸɱɱɾ ɸɱɽɾɺ ɹɺɮɺɱ ɳɹɬʃɱɹɴɱ ɮɱɼɺʋɾɹɺɽɾɴ.ɚɾɮɱɾ ɹɬ ɻɺɽɾɬɮɷɱɹɹʇɵ ɮɺɻɼɺɽ ɽɺɽɾɺɴɾ ɴɳ ɹɱɽɶɺɷʈɶɴʁʉɾɬɻɺɮ. ɚɽɺɭɱɹɹɺɽɾʈ ɮʇɭɼɬɹɹɺɵ ɾɼɬɱɶɾɺɼɴɴ ɰɮɴɲɱɹɴʋɻɺ ɰɱɼɱɮɿ ɽɺɽɾɺɴɾ ɮ ɹɬɻɼɬɮɷɱɹɴɴɺɾ ɷɴɽɾʈɱɮ ɶ ɶɺɼɹʊ. ɛɼɱɰɻɺʃɾɴɾɱɷʈɹɺɽɾʈ ɾɬɶɺɯɺ ɬɷɯɺɼɴɾɸɬ ɺɭɿɽɷɺɮɷɱɹɬ ɺɾɽɿɾɽɾɮɴɱɸ ɻɺɾɺɸɶɺɮ ɿ ɷɴɽɾʈɱɮ. ɐɷʋ ɺɻɼɱɰɱɷɱɹɴʋ ɮɱɼɺʋɾɹɺɽɾɴɾɺɯɺ, ʃɾɺ ɻɱɼɮʇɵ ʄɬɼ Ãɶɼɬɽɹʇɵ, ɰɱɷɴɸ ɶɺɷɴʃɱɽɾɮɺ ɶɼɬɽɹʇʁ ʄɬɼɺɮrɹɬ ɶɺɷɴʃɱɽɾɮɺ ʄɬɼɺɮr+bɮ ɿɳɷɱ. Ɏʇʃɴɽɷɱɹɴɱ ɸɬɾɱɸɬɾɴʃɱɽɶɺɯɺ ɺɲɴɰɬɹɴʋ Mɮɶɷʊʃɬɱɾɽʋ ɮ ɽɱɭʋ ɿɸɹɺɲɱɹɴɱ ɻɺɷɿʃɱɹɹɺɯɺ ɼɱɳɿɷʈɾɬɾɬ ɹɬ ɶɺɷɴʃɱɽɾɮɺ ɴɳɮɷɱɶɬɱɸʇʁʄɬɼɺɮt.ɞɺ ɱɽɾʈ ɰɷʋ ɻɱɼɮɺɯɺ ʄɬɼɬPେ൞௷௷௧, Mେ൞݄େݢ,ɾɺɯɰɬ ɰɷʋjÃɺɯɺ ʄɬɼɬ݄௯൞௷(௯େ)௷௧(௯େ), ݁௯൞݄௯(ݢ−(ݘ−΅)).ɝʀɺɼɸɴɼɿɱɸ ɮɱɶɾɺɼ ɰɷʋ iÃɺɯɺ ɿɳɷɬ݁௮൞(ݛ௮େdzݛ௮ୈdzǷdzݛ௮௳), ݛ௮௯൞݁௯Ƕɐɷʋ ɹɱ ɷɴɽɾɺɮɺɯɺ ɿɳɷɬ, ɴɸɱʊʅɱɯɺ k
1ɰɺʃɱɼɹɴʁ ɿɳɷɺɮ Ãɷɴɽɾʈɱɮ, ɼɬɽɽɸɺɾɼɴɸ ɸɬɾɼɴʂɿMɼɬɳɸɱɼɹɺɽɾʈʊ kĀ n, ɻɺɷɺɲɴɮ ݠ௯൞ݠ−(ݘ−΅)൞ݛେ௯ÃjÃɺɱ ɸɬɾɱɸɬɾɴʃɱɽɶɺɱ ɺɲɴɰɬɹɴɱ ɼɬɽɽɸɬɾɼɴɮɬɱɸɺɯɺ ɿɳɷɬ, ݛ௮େdz௯Ã jÃɺɱ ɸɬɾɱɸɬɾɴʃɱɽɶɺɱ ɺɲɴɰɬɹɴɱiÃɺɯɺ ɰɺʃɱɼɹɱɯɺ ɿɳɷɬɰɷʋ ɼɬɽɽɸɬɾɼɴɮɬɱɸɺɯɺ, ɾɺ ɱɽɾʈ jÃɬʋ ɶɺɺɼɰɴɹɬɾɬ ɮɱɶɾɺɼɬ Mi.ɩɾɬ ɸɬɾɼɴʂɬ ɴɸɱɱɾ ɮɴɰ݁൞ۛۚۙݠେǷݠ௳ݛୈେǷݛୈ௳ݛେǷݛ௳ǷǷǷݛ௰େǷݛ௰௳۞ۜǶɎɮɱɰʌɸ ɮ ɼɬɽɽɸɺɾɼɱɹɴɱ ɮɱɶɾɺɼ ܹ൞(ܹେǴܹୈǴǷǴܹ௳),ɬɾɬɶɲɱ sÃɺɱ ɽɺɽɾɺʋɹɴɱjÃɺɯɺ ʄɬɯɬ ɰɷʋ iÃɺɯɺ ɿɳɷɬ Ãʃɴɽɷɺ ɶɼɬɽɹʇʁ ݠ௯௸, ɽɴɹɴʁ ݐ௯௸, ɴ ɴɳɮɷɱɶɬɱɸʇʁ ݢ௯௸ʄɬɼɺɮ.ɛɼɴʃʌɸ jÃʇɵ ʄɬɯ ɻɼɱɰɻɺɷɬɯɬɱɾ ɹɬɷɴʃɴɱ jɽɺɽɾɺʋɹɴɵ s.ɛɼɴ ɽɺɽɾɺʋɹɴɴ s=1ɹɬ
jÃɺɸ ʄɬɯɱɴɸɱɱɸݠ௯େ൞ݠ௯dzݐ௯େ൞ݐ௯dzݢ௯େ൞ݢ௯Ƕɛɼɴ ɽɺɽɾɺʋɹɴɴ s=2ɹɬ jɺɸ ʄɬɯɱ ɴɸɱɱɸ ݠ௯ୈ൞ݠ௯େdzݐ௯ୈ൞ݐ௯େdzݢ௯ୈ൞ݢ௯େǶɛɼɴ ɽɺɽɾɺʋɹɴɴ s=lɹɬ jÃɺɸ ʄɬɯɱ ɴɸɱɱɸ ݠ௯௱൞ݠ௯(௱େ)dzݐ௯௱൞ݐ௯(௱େ)dzݢ௯௱൞ݢ௯(௱େ)Ƕɛɼɴ ɽɺɽɾɺʋɹɴɴ s=j ɽɺɺɾɮɱɾɽɾɮɱɹɹɺ ɴɸɱɱɸ ݠ௯௯൞ݠେdzݐ௯௯൞ݐେdzݢ௯௯൞ݢେǶɚɭɺɳɹɬʃɴɸ ɮɱɼɺʋɾɹɺɽɾʈ ɹɬɽɾɿɻɷɱɹɴʋ sÃɺɯɺ ɽɺɽɾɺʋɹɴʋ ɰɷʋ jÃɺɯɺ ʄɬɯɬ iÃɺɯɺ ɿɳɷɬ ݄௮௯௸. ɡɬɼɬɶɾɱɼɴɽɾɴɶɺɵ ɶɬɲɰɺɯɺ jÃɺɯɺ ʄɬɯɬiÃɺɯɺ ɿɳɷɬ ʋɮɷʋɱɾɽʋ ܺ௮௯൞ෟPijஃ௯௸େݛ௮௸dzɬ ɽɿɸɸɬ ʉɾɴʁ ʁɬɼɬɶɾɱɼɴɽɾɴɶ ɹɬ jÃɺɸ ʄɬɯɱ ɰɷʋ ɮɽɱʁ ɿɳɷɺɮ ɺɭɼɬɳɿɱɾ jÃɿʊ ɶɺɺɼɰɴɹɬɾɿ Ejɮɱɶɾɺɼɬ E.ܹ௯൞ෟܺ௮௯௰iେǶəɬ ɻɱɼɮɺɸ ʄɬɯɱ ɰɷʋ ɶɬɲɰɺɯɺ ɿɳɷɬ ɽɿʅɱɽɾɮɿɱɾ ɱɰɴɹɽɾɮɱɹɹɺɱ ɽɺɽɾɺʋɹɴɱ, ɴ ɻɺʉɾɺɸɿ ɮɱɼɺʋɾɹɺɽɾʈ ɹɬɽɾɿɻɷɱɹɴʋ ʉɾɺɯɺ ɽɺɽɾɺʋɹɴɱ ɼɬɮɹɬ Q. ɡɬɼɬɶɾɱɼɴɽɾɴɶɬ ɻɱɼɮɺɯɺ ʄɬɯɬ iɺɯɺ ɿɳɷɬܺ௮େ൞݄௮େେπݛ௮େ൞ݛ௮େəɬɻɺɸɹɴɸ, ʃɾɺ ݛ௮େÃʉɷɱɸɱɹɾʇ ɻɱɼɮɺɯɺ ɽɾɺɷɭʂɬ ɸɬɾɼɴʂʇ M. ɑʌ ɻɱɼɮʇɵ ɽɾɺɷɭɱʂ, ɴ ɾɺɷʈɶɺ ɻɱɼɮʇɵ, ɽɺɮɻɬɰɬɱɾ ɽ ʁɬɼɬɶɾɱɼɴɽɾɴɶɬɸɴ ɻɱɼɮɺɯɺ ʄɬɯɬ ɰɷʋ ɮɽɱʁ ɿɳɷɺɮ. ɞɬɶɴɸ ɺɭɼɬɳɺɸ, ɻɱɼɮɬʋ ɶɺɺɼɰɴɹɬɾɬ ܹେɮɱɶɾɺɼɬ Eɼɬɮɹɬ ɽɿɸɸɱɶɺɺɼɰɴɹɬɾ ɻɱɼɮɺɯɺ ɽɾɺɷɭʂɬ ɸɬɾɼɴʂʇ M.ܹେ൞ෟܺ௮େ௰iେ൞ෟݛ௮େ௰iେǶ
əɬ ɶɬɲɰɺɸ ɻɺɽɷɱɰɿʊʅɱɸ ʄɬɯɱ, ɮ ɺɾɷɴʃɴɱ ɺɾ ɻɱɼɮɺɯɺ, ɴɸɱɱɸ ɶɺɷɴʃɱɽɾɮɺ ɽɺɽɾɺʋɹɴɵ ݡ൞΅dzଦശശശശ,ɭɺɷɱɱ ɺɰɹɺɯɺ.ɣɴɽɷɺ ɽɷɬɯɬɱɸʇʁ ɮ ʁɬɼɬɶɾɱɼɴɽɾɴɶɱ ʄɬɯɬ ɺɻɼɱɰɱɷʋɱɾɽʋ ɶɺɷɴʃɱɽɾɮɺɸ ɽɺɽɾɺʋɹɴɵ ɹɬ ʉɾɺɸ ʄɬɯɱ.əɬ ɮɾɺɼɺɸ ʄɬɯɱ ɴɸɱɱɸ ɰɮɬ ɽɺɽɾɺʋɹɴʋ, ɮɱɼɺʋɾɹɺɽɾɴ ɶɺɾɺɼʇʁ ɰɷʋ iÃɺɯɺ ɿɳɷɬ ɮʇʃɴɽɷʋʊɾɽʋ ɻɺ ʀɺɼɸɿɷɬɸPiୈୈ൞ܺ௮େܹେdzPiୈେ൞΅−PiୈୈǶɞɬɶɴɸ ɺɭɼɬɳɺɸ, ʁɬɼɬɶɾɱɼɴɽɾɴɶɬ ɮɾɺɼɺɯɺ ʄɬɯɬ ɰɷʋ iÃɺɯɺ ɿɳɷɬ ɳɬɰɬʌɾɽʋ ʀɺɼɸɿɷɺɵܺ௮ୈ൞݄iୈୈݛ௮ୈ+Piୈେݛ௮େǶɝɷɱɰɺɮɬɾɱɷʈɹɺ,ܹୈ൞ෟܺ௮ୈ௰iେǶɝ ɴɳɮɷɱʃɱɹɴɱɸ ɾɼɱɾʈɱɯɺ ʄɬɼɬ ɽɮʋɳɬɹɺ ɾɼɴ ɼɬɳɹʇʁ ɽɺɽɾɺʋɹɴʋ ɰɷʋ ɶɬɲɰɺɯɺ ɿɳɷɬ. əɬ ʉɾɺɸ ʉɾɬɻɱ ɺɻɼɱɰɱɷɱɹɴɱ ɮɱɼɺʋɾɹɺɽɾɱɵ ɹɬɽɾɿɻɷɱɹɴɵ ɹɺɮʇʁ ɽɺɽɾɺʋɹɴɵ ɺɻɼɱɰɱɷʋɱɾɽʋ ɻɺ ɹɺɮɺɵ ɽʁɱɸɱ. Ɍ ɴɸɱɹɹɺ, ɮ ɹɬʃɬɷɱ,ɹɬɵɰʌɸ ɮɱɼɺʋɾɹɺɽɾʈ Qɾɺɯɺ, ʃɾɺ ɻɼɱɰʇɰɿʅɴɵ ʄɬɼ ɭʇɷ ɴɳɮɷɱʃʌɹ ɴɳ iɺɯɺ ɿɳɷɬ. ɜɬɹʈʄɱ ɮ ʉɾɺɸ ɹɱ ɭʇɷɺ ɹɱɺɭʁɺɰɴɸɺɽɾɴ.ɞɬɶɴɸ ɺɭɼɬɳɺɸ, ɰɷʋ ɶɬɲɰɺɯɺ iɺɯɺ ɿɳɷɬ݅௮൞ܺ௮ୈܹୈǶɎ ɰɬɷʈɹɱɵʄɱɸ ɺɭɺɳɹɬʃɴɸ Qijɮʇʃɴɽɷʋɱɸɿʊ ɮɱɼɺʋɾɹɺɽɾʈ ɰɷʋ iÃɺɯɺ ɿɳɷɬ ɹɬ jÃɺɸ ʄɬɯɱ. əɬɵɰɱɹɹɬʋ ɮɱɼɺʋɾɹɺɽɾʈ ɻɺɳɮɺɷʋɱɾ ɮʇʃɴɽɷɴɾʈ ɾɼɴ ɹɺɮʇʁ ɮɱɼɺʋɾɹɺɽɾɴ, ɻɺʋɮɷʋʊʅɴʁɽʋ ɹɬ ɾɼɱɾʈɱɸ ɿɼɺɮɹɱ ɴɱɼɬɼʁɴɴ ɮ ɰɱɼɱɮɱ ɮɱɼɺʋɾɹɺɽɾɱɵ ɹɬ ɼɴɽɿɹɶɱ 4.
ɜɴɽɿɹɺɶ 4ɫɽɹɺ, ʃɾɺPi൞݅௮πPiୈୈǴ
Piୈ൞݅௮πPiୈେ+(΅−݅௮)πPiୈୈǴPiେ൞(΅−݅௮)πPiୈେ.ɝɷɱɰɺɮɬɾɱɷʈɹɺ,ܺ௮൞݄iݛ௮+Piୈݛ௮ୈ+Piେݛ௮େǴ
ܹ൞ෟܺ௮Ƕ௰iେɚɻɴɼɬʋɽʈ ɴ ɺɭɺɭʅɬʋ ʃɱɾɮʌɼɾʇɵ ɿɼɺɮɱɹʈ ɴɱɼɬɼʁɴɴ, ɳɬɰɬʊʅɴɵ ʃɱɾʇɼɱ ɽɺɽɾɺʋɹɴʋ, ɹɬ ɼɴɽɿɹɶɱ 4, ɳɬɻɴʄɱɸ ɽɷɱɰɿʊʅɴɱ ʀɺɼɸɿɷʇ ɰɷʋjÃɺɯɺ ʄɬɯɬ iÃɺɯɺ ɿɳɷɬ, ɹɬʁɺɰʋʅɱɯɺɽʋ ɮ ɽɺɽɾɺʋɹɴɴ s. ɩɾɴ ʀɺɼɸɿɷʇ ɴɸɱʊɾ ɮɴɰQ௮௯൞ܺ௮dzjେܹ௯େǴPijେ൞ൽ΅−Q௮௯ඁπPidzjେdzେǴPijஃ൞Q௮௯πPidzjେdzஃେ+ൽ΅−Q௮௯ඁπPidzjେdzஃǴPijj൞QπPidzjେdzjେǴܺ௮௯൞ෟPijஃ௯௸େݛ௮௸Ǵܹ௯൞ෟܺ௮௯௰iେǶɐɷʋ ɮʇʃɴɽɷɱɹɴʋ ɮɱɼɺʋɾɹɺɽɾɱɵ ɴɳɮɷɱʃɱɹɴʋ ɶɼɬɽɹʇʁ ʄɬɼɺɮ ɴɳ ɴɽʁɺɰɹɺɯɺ ɿɳɷɬ (ɶɺɾɺɼʇɵ, ɮɺɺɭʅɱ ɯɺɮɺɼʋ, ɹɱ ʋɮɷʋɱɾɽʋ ɷɴɽɾɺɮʇɸ) ɹɬ jÃɺɸ ʄɬɯɱ ɴɽɻɺɷʈɳɿɱɸ jÃɿʊ ɶɺɺɼɰɴɹɬɾɿ ɮɱɶɾɺɼɬ E.ɔɽɶɺɸɬʋ jÃɬʋ ɮɱɼɺʋɾɹɺɽɾʈ ɮʇʃɴɽɷʋɱɾɽʋ ɻɺ ʀɺɼɸɿɷɱ݄௯൞ܹ௯ݑ−(ݘ−΅)Ƕɓɰɱɽʈ cÃɺɭʅɱɱ ʃɴɽɷɺ ʄɬɼɺɮ ɮ ɴɽʁɺɰɹɺɸ ɿɳɷɱ ɻɺɽɷɱ ɰɺɭɬɮɷɱɹɴʋ ɮ ɹɱɯɺ ʄɬɼɺɮ, ɴɳɮɷɱʃʌɹɹʇʁ ɴɳ ɽɺɺɾɮɱɾɽɾɮɿʊʅɴʁ ɱɸɿ ɰɺʃɱɼɹɴʁ ɿɳɷɺɮ.Ɏɱɶɾɺɼ Pɴɸɱɱɾ nɶɺɺɼɰɴɹɬɾ, ɶɬɲɰɬʋ ɴɳ ɶɺɾɺɼʇʁ Pjɻɼɱɰɽɾɬɮɷʋɱɾ ɽɺɭɺɵ ɮɱɼɺʋɾɹɺɽɾʈ ɴɳɮɷɱʃɱɹɴʋ ɶɼɬɽɹɺɯɺ ʄɬɼɬ ɹɬ jÃɺɸ ʄɬɯɱ ɻɼɴ ɿɽɷɺɮɴɴ, ʃɾɺ ɹɬ ɮɽɱʁ ɻɼɱɰʇɰɿʅɴʁ ʄɬɯɬʁ ɭʇɷɴ ɴɳɮɷɱʃɱɹʇ ɾɺɷʈɶɺ ɶɼɬɽɹʇɱ ʄɬɼʇ.ɑɽɷɴ ʉɾɺɾ ɿɳɱɷ ɹɱ ʋɮɷʋɱɾɽʋ ɶɺɼɹɱɮʇɸ, ɾɺ ɿɸɹɺɲɴɮ ɻɺɷɿʃɱɹɹʇɱ ɮɱɼɺʋɾɹɺɽɾɴ ɹɬ ɶɺɷɴʃɱɽɾɮɺ ɴɳɮɷɱɶɬɱɸʇʁ ʄɬɼɺɮ tɹɬ jÃɺɸ ʄɬɯɱ, ɻɺɷɿʃɴɸ ɸɬɾɱɸɬɾɴʃɱɽɶɺɱ ɺɲɴɰɬɹɴɱ݁௯൞݄௯ൽݢ−(ݘ−΅)ඁǶɘɬɾɼɴʂɬ Mɼɺɰɴɾɱɷʈɽɶɺɯɺ ɿɳɷɬ, ɰɷʋ ɶɺɾɺɼɺɯɺ ɴɽʁɺɰɹʇɵ ɿɳɱɷ ʋɮɷʋɱɾɽʋ iÃʇɸ ɰɺʃɱɼɹɴɸ, ʀɺɼɸɴɼɿɱɾɽʋ ɴɳ ݛ௮େdz௯൞݁௯, ɯɰɱ j=΅dzݜശശശശശ.ɛɼɺɯɼɬɸɸɹɬʋ ɼɱɬɷɴɳɬʂɴʋ ɰɬɹɹɺɯɺ ɬɷɯɺɼɴɾɸɬ ɻɼɱɰɽɾɬɮɷɱɹɬ ɹɬ ɼɴɽɿɹɶɬʁ5.1, 5.2.ɜɴɽɿɹɺɶ 5.1
ɜɴɽɿɹɺɶ 5.2
Ɏɱɼɺʋɾɹɺɽɾʈ Pɺɭʅɾɺɯɺ, ʃɾɺ ɴɳ ɶɺɼɹɱɮɺɯɺ ɿɳɷɬ, ɶɺɾɺɼɺɸɿ ɻɼɱɰʄɱɽɾɮɺɮɬɷɴN1ɿɳɷɺɮ ɮɱɾɮɷɱɹɴʋ ɴ ɷɴɽɾʈɱɮ, ɮɽɱ ɴɳɮɷɱʃʌɹɹʇɱ nʄɬɼɺɮ ɺɶɬɲɿɾɽʋ ɶɼɬɽɹʇɸɴ ɮʇʃɴɽɷʋɱɾɽʋ ɻɺ ʀɺɼɸɿɷɱ݄ˣ˖ˮ൞݄௯Ƕ௳௯େɓɬɸɱɾɴɸ, ʃɾɺ ɰɬɹɹʇɵ ɬɷɯɺɼɴɾɸ ɺɭɷɬɰɬɱɾ ɽɷɱɰɿʊʅɴɸ ɮɬɲɹʇɸ ɽɮɺɵɽɾɮɺɸ »ɽɿɲɬɱɸɺɽɾɴ¼. ɛɼɴ ɰɮɴɲɱɹɴɴ ɺɾ ɶɺɼɹɱɮɺɯɺ ɿɳɷɬ ɶ ɷɴɽɾʈʋɸ ɹɱɾ ɹɱɺɭʁɺɰɴɸɺɽɾɴ ɹɬʁɺɰɴɾʈ ɮɽɱ nɸɬɾɱɸɬɾɴʃɱɽɶɴʁ ɺɲɴɰɬɹɴɵ ɮ ɽɷɿʃɬɱ, ɱɽɷɴ ʃɴɽɷɺ ʄɬɼɺɮ, ɻɱɼɱɶɷɬɰʇɮɬɱɸʇʁ ɴɳ ɰɺʃɱɼɹɱɯɺ ɿɳɷɬ ɮ ɼɺɰɴɾɱɷʈɽɶɴɵ, ɸɱɹʈʄɱ, ʃɱɸ ʃɴɽɷɺ ʄɬɼɺɮ, ɴɳɮɷɱɶɬɱɸʇʁ ɴɳɼɺɰɴɾɱɷʈɽɶɺɯɺ ɿɳɷɬ. əɬɻɼɴɸɱɼ, ɱɽɷɴ ʃɴɽɷɺ ɴɳɮɷɱɶɬɱɸʇʁ ɴɳ ɼɺɰɴɾɱɷʈɽɶɺɯɺ ɿɳɷɬ ʄɬɼɺɮ ɼɬɮɹɺ ɻʋɾɴ, ɬ ɴɳ ɰɺʃɱɼɹɱɯɺ ɾɼʌɸ, ɾɺ ɸɬɾɱɸɬɾɴʃɱɽɶɺɱ ɺɲɴɰɬɹɴɱ ɾɺɯɺ, ʃɾɺ ɴɳ ɰɺʃɱɼɹɱɯɺ ɿɳɷɬ ɭɿɰɱɾ ɴɳɮɷɱʃɱɹɺ ʃɱɾʇɼɱ ɴɷɴ ɻʋɾʈ ʄɬɼɺɮ ɼɬɮɹɺ ɹɿɷʊ. Ɏ ɽɮɺʊ ɺʃɱɼɱɰʈ, ɰɷʋ ɱɯɺ ɰɺʃɱɼɹɴʁ ɿɳɷɺɮ ɸɬɾɱɸɬɾɴʃɱɽɶɺɱ ɺɲɴɰɬɹɴɱ ɻɺɻɼɱɲɹɱɸɿ ɮʇʃɴɽɷʋɱɾɽʋ ɾɺɷʈɶɺ ɰɷʋ ɾɼʌʁ ʄɬɼɺɮ, ɱɽɷɴ ɹɱ ɻɼɺʋɮɴɾɽʋ ɮɹɺɮʈ ɽɮɺɵɽɾɮɺ »ɽɿɲɬɱɸɺɽɾɴ¼.
Ɏʇɮɺɰ.Ɏ ɼɬɭɺɾɬʁ P3,4R ɼɬɽɽɸɬɾɼɴɮɬɷɴɽʈ ɽɷɱɰɿʊʅɴɱ ɻɺɽɾɬɹɺɮɶɴ ɳɬɰɬʃɴ.ɛɿɽɾʈ ɮ ɶɬɲɰɺɵ ɴɳN 2 ɿɼɹ ɴɸɱɱɾɽʋ ɽɮɺɵ ɹɬɭɺɼ ɶɼɬɽɹʇʁ rɴ ɽɴɹɴʁ bʄɬɼɺɮ. ɔɳ ɻɱɼɮɺɵ ɿɼɹʇ, ɽɺɰɱɼɲɬʅɱɵ r1ɶɼɬɽɹʇʁ ɴ b1ɽɴɹɴʁ ʄɬɼɺɮ,ɹɬɿɰɬʃɿɴɳɮɷɱɶɬʊɾɽʋ t1ʄɬɼɺɮɴ ɻɱɼɱɶɷɬɰʇɮɬʊɾɽʋɮɺ ɮɾɺɼɿʊ ɿɼɹɿ. ɔɳ ɮɾɺɼɺɵ ɿɼɹʇ, ɽɺɰɱɼɲɬʅɱɵ r2ɶɼɬɽɹʇʁ ɴ b2ɽɴɹɴʁ ʄɬɼɺɮ, ɴɳɮɷɱɶɬʊɾɽʋ t2ʄɬɼɺɮ ɴ ɾ. ɰ. Ɏ ɼɬɭɺɾɱ P3R ɻɼɺʂɱɰɿɼɬ ɳɬɶɬɹʃɴɮɬɱɾɽʋ ɴɳɮɷɱʃɱɹɴɱɸ ɺɰɹɺɯɺ ʄɬɼɬ ɴɳ Nɺɵ ɿɼɹʇ. Ɍ ɮ ɼɬɭɺɾɱ P4R ɴɳɮɷɱʃɱɹɴɱɸ nʄɬɼɺɮ. əɬɽ ɴɹɾɱɼɱɽɺɮɬɷɬ ɮɱɼɺʋɾɹɺɽɾʈ ɴɳɮɷɱʃɱɹɴʋ n ɶɼɬɽɹʇʁ ʄɬɼɺɮ ɴɳɻɺɽɷɱɰɹɱɵ ɿɼɹʇ. ɛɺɷɿʃɱɹʇ ʀɺɼɸɿɷʇ ɴ ɻɼɴɮɱɰɱɹʇ ɬɷɯɺɼɴɾɸʇ ɰɷʋ ɮʇʃɴɽɷɱɹɴʋ ɮɱɼɺʋɾɹɺɽɾɱɵ ɮ ɼɬɭɺɾɱ P3R ɴɳɮɷɱʃɱɹɴʋ ɺɰɹɺɯɺ ɶɼɬɽɹɺɯɺʄɬɼɬ, ɬ ɮ ɼɬɭɺɾɱ P4R ɮɽɱʁ nɶɼɬɽɹʇʁ ʄɬɼɺɮ.ɝɶɺɼɺɽɾʈ ɼɺɽɾɬɼɱɬɷɴɳɬʂɴɴɬɷɯɺɼɴɾɸɬ, ɴɳɷɺɲɱɹɹɺɯɺ ɮ [3],݃(݂).ɝɶɺɼɺɽɾʈ ɼɺɽɾɬ ɼɱɬɷɴɳɬʂɴɴ ɬɷɯɺɼɴɾɸɬ, ɴɳɷɺɲɱɹɹɺɯɺ ɮ P4R, ݃(݂௳). Ɏ ɰɬɹɹɺɵ ɼɬɭɺɾɱ ɮ ɼɱɳɿɷʈɾɬɾɱ ɸɺɰɴʀɴɶɬʂɴɴ ɬɷɯɺɼɴɾɸɬɽɶɺɼɺɽɾʈ ɱɯɺ ɼɺɽɾɬ ݃(݂ݜୈ).ɑɽɷɴ ɼɬɳɭɴɾʈ ɰɱɼɱɮɺ ɹɬ ʀɼɬɯɸɱɹɾʇ, ɶɬɲɰʇɵɴɳɶɺɾɺɼʇʁ ɽɺɽɾɺɴɾ ɴɳɿɳɷɬ ɴ ɱɯɺ ɰɺʃɱɼɹɴʁ ɿɳɷɺɮ, ɾɺ ɻɼɴ ʃɴɽɷɱɰɺʃɱɼɹɴʁ ɿɳɷɺɮ ɭɺɷʈʄɱ ɰɮɿʁ, ɹɬɴɭɺɷɱɱ ʉʀʀɱɶɾɴɮɹʇɸ ɹɬ ʉɾɺɸ ɿʃɬɽɾɶɱ ʋɮɷʋɱɾɽʋ ɬɷɯɺɼɴɾɸ,ɼɬɳɼɬɭɺɾɬɹɹʇɵ ɽ ɴɽɻɺɷʈɳɺɮɬɹɴɱɸ ɸɬɾɱɸɬɾɴʃɱɽɶɺɯɺ ɺɲɴɰɬɹɴʋ, ɻɺ ɽɼɬɮɹɱɹɴʊ ɽ ɶɺɸɭɴɹɬɾɺɼɹʇɸ ɻɺɰʁɺɰɺɸ.ɛɼɴ ʃɴɽɷɱɰɺʃɱɼɹɴʁ ɿɳɷɺɮ ɸɱɹʈʄɱ ɰɮɿʁ,ɹɺɻɼɴ ɭɺɷʈʄɺɸ ɶɺɷɴʃɱɽɾɮɱ ɴɳɮɷɱɶɬɱɸʇʁ ʄɬɼɺɮ ɴɳ ɰɺʃɱɼɹɴʁ ɿɳɷɺɮɻɺ ɽɼɬɮɹɱɹɴʊ ɽ ɼɺɰɴɾɱɷʈɽɶɴɸ,ɾɬɶɲɱ ʉʀʀɱɶɾɴɮɹʇɸɺɽɾɬʌɾɽʋ ɹɱɽɾɬɹɰɬɼɾɹʇɵ ɬɷɯɺɼɴɾɸ ɴ ɴɽɻɺɷʈɳɺɮɬɹɴɱɸ ɸɬɾɱɸɬɾɴʃɱɽɶɴʁ ɺɲɴɰɬɹɴɵ. əɬ ɼɬɳɹʇʁ ɿʃɬɽɾɶɬʁ ɰɱɼɱɮɬ ɽ ɿʃʌɾɺɸ ɿɶɬɳɬɹɹʇʁ ɺɽɺɭɱɹɹɺɽɾɱɵ ɸɺɲɹɺ ʉʀʀɱɶɾɴɮɹɺ ɻɼɴɸɱɹʋɾʈ ɬɷɯɺɼɴɾɸʇ, ɼɬɳɼɬɭɺɾɬɹɹʇɱ ɽ ɴɽɻɺɷʈɳɺɮɬɹɴɱɸ ɶɬɶ ɸɬɾɱɸɬɾɴʃɱɽɶɺɯɺ ɺɲɴɰɬɹɴʋ, ɾɬɶ ɴ ɶɺɸɭɴɹɬɾɺɼɹʇʁ ʀɺɼɸɿɷ.
ɝɽʇɷɶɴ ɹɬ ɴɽɾɺʃɹɴɶɴ1.ɍɱɼɹʄɾɱɵɹ ɝ.ə. ɞɱɺɼɴʋ ɮɱɼɺʋɾɹɺɽɾɱɵ. ɘ. Ãɗ.: ɚəɞɔ, Q934. 4Q2 ɽ.2.ɘɬɼɶɴɹɬ ɘ.ɝ., ɚɼɷɴɶ ɗ.ɖ. ɚɻʇɾ ʀɺɼɸɴɼɺɮɬɹɴʋ ɻɼɴɸɱɼɺɮ ɼɱʄɱɹɴʋ ɹɱɽɾɬɹɰɬɼɾɹʇʁ ɳɬɰɬʃ ɻɼɴ ɴɳɿʃɱɹɴɴ ɶɿɼɽɬ ɮʇɽʄɱɵ ɸɬɾɱɸɬɾɴɶɴ//Ɏ ɽɭɺɼɹɴɶɱ: ɘɬɾɱɸɬɾɴʃɱɽɶɺɱ ɸɺɰɱɷɴɼɺɮɬɹɴɱ ɽɺʂɴɬɷʈɹʇʁ ɻɼɺʂɱɽɽɺɮ ɴ ɽɺɮɼɱɸɱɹɹʇɱ ɺɭɼɬɳɺɮɬɾɱɷʈɹʇɱ ɾɱʁɹɺɷɺɯɴɴ 2PP7. ɝ. 2Q2218.3.Ɍɷɱɶɽɬɹɰɼɺɮ ɛ.ɚ., ɘɬɼɾʇɹɺɮ ɝ.ɗ., ɚɼɷɴɶ ɗ.ɖ. ɖɺɷɴʃɱɽɾɮɱɹɹɬʋ ɺʂɱɹɶɬ ɮʇʃɴɽɷɴɾɱɷʈɹʇʁ ɳɬɾɼɬɾ ɻɼɴ ɺɻɾɴɸɴɳɬʂɴɴ ɬɷɯɺɼɴɾɸɺɮ ɼɱʄɱɹɴʋ ɽɾɬɹɰɬɼɾɹʇʁ ɳɬɰɬʃ ɾɱɺɼɴɴ ɮɱɼɺʋɾɹɺɽɾɱɵ //əɬɿɶɬ ɴ ɽɺɮɼɱɸɱɹɹɺɽɾʈ. 2PQ5. ʝ 36. ɝ. Q34140.4.Ɍɷɱɶɽɬɹɰɼɺɮ ɛ.ɚ. ɜɱʄɱɹɴɱ ɳɬɰɬʃɴ ɻɺ ɮʇɭɺɼɶɱ ʄɬɼɺɮ ɴɳ ɽɴɽɾɱɸʇ ɿɼɹ ɻɼɴ ɻɺɸɺʅɴ ɸɬɾɱɸɬɾɴʃɱɽɶɺɯɺ ɺɲɴɰɬɹɴʋ.https://ekoncept.ru/best_article/young2016/participants.html. . ÃPɐɬɾɬ ɺɭɼɬʅɱɹɴʋ Q8.P3.2PQ6R.
ɚɼɷɴɶɗʊɭɺɮʈ ɖɺɹɽɾɬɹɾɴɹɺɮɹɬ,ɻɼɺʀɱɽɽɺɼ, ɶɬɹɰɴɰɬɾ ʀɴɳɴɶɺÃɸɬɾɱɸɬɾɴʃɱɽɶɴʁ ɹɬɿɶ, ɻɼɺʀɱɽɽɺɼ ɶɬʀɱɰɼʇ ɻɼɴɶɷɬɰɹɺɵ ɸɬɾɱɸɬɾɴɶɴ. ɜɺɽɽɴɵɽɶɴɵ ɏɺɽɿɰɬɼɽɾɮɱɹɹʇɵ ɝɺʂɴɬɷʈɹʇɵ ɟɹɴɮɱɼɽɴɾɱɾ. ɯ. ɘɺɽɶɮɬLubov.orlik@gmail.com
ɚɼɴɯɴɹɬɷʈɹɺɱ ɻɼɴɸɱɹɱɹɴɱ ɸɬɾɱɸɬɾɴʃɱɽɶɺɯɺ ɺɲɴɰɬɹɴʋ ɶ ɮʇʃɴɽɷɱɹɴʊ ɮɱɼɺʋɾɹɺɽɾɱɵ: ɸɺɰɱɷʈɹɬʋ ɳɬɰɬʃɬ, ɻɼɺɯɼɬɸɸɹɬʋ ɼɱɬɷɴɳɬʂɴʋ, ɺɽɺɭɱɹɹɺɽɾɴ ɬɷɯɺɼɴɾɸɬ
Ɍɹɹɺɾɬʂɴʋ. Ɏ ɽɾɬɾʈɱ ɴɳɷɺɲɱɹɺɺɼɴɯɴɹɬɷʈɹɺɱ ɼɱʄɱɹɴɱ ɮɱɼɺʋɾɹɺɽɾɹɺɵ ɳɬɰɬʃɴ ɹɬ ɶɷɬɽɽɴʃɱɽɶɿʊ ɽʁɱɸɿ ɭɱɳ ɴɽɻɺɷʈɳɺɮɬɹɴʋ ɶɺɸɭɴɹɬɾɺɼɹʇʁ ʀɺɼɸɿɷ, ɺɽɹɺɮɬɹɹɺɱ ɹɬ ɻɼɴɸɱɹɱɹɴɴ ɸɬɾɱɸɬɾɴʃɱɽɶɺɯɺ ɺɲɴɰɬɹɴʋ. ɛɼɱɰɽɾɬɮɷɱɹʇ ɹɱɽɾɬɹɰɬɼɾɹʇɱ ɮʇʃɴɽɷɴɾɱɷʈɹʇɱ ɬɷɯɺɼɴɾɸʇ ɽ ɻɼɺɯɼɬɸɸɹɺɵ ɼɱɬɷɴɳɬʂɴɱɵ ɴ ɻɺɷɿʃɱɹʇɺʂɱɹɶɴ ɴʁ ɽɶɺɼɺɽɾɴ ɼɺɽɾɬ. ɛɼɺɬɹɬɷɴɳɴɼɺɮɬɹʇ ʀɬɶɾɺɼʇ, ɿɽɶɺɼʋʊʅɴɱ ɻɼɺʂɱɽɽ ɮʇʃɴɽɷɱɹɴɵ.ɖɷʊʃɱɮʇɱ ɽɷɺɮɬ: ɾɱɺɼɴʋ ɮɱɼɺʋɾɹɺɽɾɱɵ, ɸɬɾɱɸɬɾɴʃɱɽɶɺɱ ɺɲɴɰɬɹɴɱ, ɯɼɬʀɰɱɼɱɮɺ, ɺɻɾɴɸɴɳɬʂɴʋ ɮʇʃɴɽɷɱɹɴɵ
ɐɬɹɹɬʋ ɼɬɭɺɾɬ ʋɮɷʋɱɾɽʋ ɻɼɺɰɺɷɲɱɹɴɱɸ ʂɴɶɷɬ ɽɾɬɾʈɱɵ, ɻɺɽɮʋʅʌɹɹʇʁ ɽɼɬɮɹɴɾɱɷʈɹɺɸɿ ɬɹɬɷɴɳɿ ɮʇʃɴɽɷɴɾɱɷʈɹʇʁ ɳɬɾɼɬɾ ɻɼɴ ɼɱɬɷɴɳɬʂɴɴ ɽɾɬɹɰɬɼɾɹɺɯɺ ɴ ɺɼɴɯɴɹɬɷʈɹɺɯɺ ɬɷɯɺɼɴɾɸɺɮ ɼɱʄɱɹɴʋ ɺɭɺɭʅʌɹɹɺɵ ɳɬɰɬʃɴ ɍɱɼɹʄɾɱɵɹɬ ɝ.ə.PQ,ɽ. 91].ɝɾɬɹɰɬɼɾɹʇɵ ɸɱɾɺɰ ɻɼɱɰɻɺɷɬɯɬɱɾ ɴɽɻɺɷʈɳɺɮɬɹɴɱ ɶɺɸɭɴɹɬɾɺɼɹʇʁ ʀɺɼɸɿɷ, ɺɼɴɯɴɹɬɷʈɹʇɵ Ãɻɼɴɸɱɹɱɹɴɱ ɸɬɾɱɸɬɾɴʃɱɽɶɺɯɺ ɺɲɴɰɬɹɴʋP2,3R.Ɏɬɲɹɺ ɺɾɸɱɾɴɾʈ ɻɼɴɶɷɬɰɹɺɱ ɳɹɬʃɱɹɴɱ ɰɬɹɹʇʁ ɾɱɺɼɱɾɴʃɱɽɶɴʁ ɴɳʇɽɶɬɹɴɵ. ɛɼɴɮɱɰʌɸ ɻɼɴɸɱɼ ɳɬɰɬʃɴ, ɮ ɶɺɾɺɼɺɵ ɼɱɬɷɴɳɺɮɬɹ ɺɼɴɯɴɹɬɷʈɹʇɵ ɻɺɰʁɺɰ ɶ ɼɱʄɱɹɴʊ, ɬ ɴɸɱɹɹɺ: ɸɬɾɱɸɬɾɴʃɱɽɶɺɱ ɸɺɰɱɷɴɼɺɮɬɹɴɱ ɮʇɭɺɼɺʃɹɺɯɺ ɾɬɸɺɲɱɹɹɺɯɺ ɶɺɹɾɼɺɷʋ.ɠɿɼʇ ɽ ɶɺɹɾɼɬɭɬɹɰɹʇɸɴ ɯɼɿɳɬɸɴ ɼɱɯɿɷʋɼɹɺ ɳɬɰɱɼɲɴɮɬʊɾɽʋ ɹɬ ɾɬɸɺɲɹɱ ɳɬ ɹɬɼɿʄɱɹɴɱ ɼɱɲɴɸɬ ɽɬɹɶʂɴɵ ɴ ɬɹɾɴɽɬɹɶʂɴɵ. Ɏ ɽɮʋɳɴ ɽ ʉɾɴɸ ɬɶɾɿɬɷʈɹʇɸ ʋɮɷʋɱɾɽʋ ɮɺɻɼɺɽ ɺɭ ʉʀʀɱɶɾɴɮɹɺɽɾɴ ɮʇɭɺɼɺʃɹɺɯɺ ɾɬɸɺɲɱɹɹɺɯɺ ɶɺɹɾɼɺɷʋ. əɱ ɮ ɿʅɱɼɭ ɺɭʅɹɺɽɾɴ ɼɬɽɽɿɲɰɱɹɴɵ ɰɷʋ ɻɼɺɽɾɺɾʇ ɴɳɷɺɲɱɹɴʋ ɼɬɽɽɸɺɾɼɴɸ ɸɬɾɱɸɬɾɴʃɱɽɶɿʊ ɸɺɰɱɷʈ ɮʇɭɺɼɺʃɹɺɯɺ ɰɺɽɸɺɾɼɬʀɿɼ ɮ N(N= 11) ɼɱɯɴɺɹɬʁ.ɛɺ ɺɻɱɼɬɾɴɮɹʇɸ ɰɬɹɹʇɸ ɴɳɮɱɽɾɹɺ ɶɺɷɴʃɱɽɾɮɺ ʀɿɼ ɮ ɼɱɯɴɺɹɱ ɽ ɶɺɹɾɼɬɭɬɹɰɹʇɸɴ ɯɼɿɳɬɸɴ ɴ ɹɱ ɹɬɼɿʄɬʊʅɴɸɴ ɼɱɲɴɸ ɽɬɹɶʂɴɵ/ɬɹɾɴɽɬɹɶʂɴɵ, ɬ ɾɬɶɲɱ ʃɴɽɷɺ ɮɹɺɮʈ ɻɼɴɭʇɮʄɴʁ.Ɏ ʃɱɾʇɼʌʁ ɿɼɺɮɹɱɮɺɵ ɴɱɼɬɼʁɴɴ ɶɺɼɹɱɮʇɸ ɿɳɷɺɸ ʋɮɷʋɱɾɽʋ Customs(ɞɬɸɺɲɹʋ). ɚɹɬ ɽɮʋɳɬɹɬ ɽ ɻʋɾʈʊ ɼɱɯɴɺɹɬɸɴAthenaeum, Sanctury, Blackquarter, Middleheim, Elfwind, ɶɬɲɰʇɵ ɴɳ ɶɺɾɺɼʇʁ, ɽɮʋɳɬɹ ɽ ɼɱɯɴɺɹɬɸɴɴɳ ɻɱɼɱʃɴɽɷɱɹɴʋEquinox, DragoBreach, Silverwing, Rainhaven(0, 1, 1, 2, 0
ʃɴɽɷɺ ɽɮʋɳɱɵ ɽɺɺɾɮɱɾɽɾɮɱɹɹɺ), ɴ ɰɬɷɱɱ ɹɬ ɻɺɽɷɱɰɹɱɸ ɿɼɺɮɹɱ ɴɱɼɬɼʁɴɴDragoBreachɽɮʋɳɬɹ ɽ Rockwarren(ɼɴɽɿɹɺɶ Q).ɠɿɼʇ ɻɱɼɱɸɱʅɬʊɾɽʋ ɺɾ ɰɺʃɱɼɹɴʁ ɿɳɷɺɮ ɶ ɼɺɰɴɾɱɷʈɽɶɴɸ.ɖɬɶɺɮɬ ɮɱɼɺʋɾɹɺɽɾʈ ɾɺɯɺ, ʃɾɺ ɹɬɿɯɬɰ ɺɽɾɬɹɺɮɷɱɹɹɬʋ ɰɷʋ ɰɺɽɸɺɾɼɬ ʀɿɼɬ, ɻɱɼɱɮɺɳɴɾ ɶɺɹɾɼɬɭɬɹɰɹʇɱ ɯɼɿɳʇ.ɐɷʋ ɼɱʄɱɹɴʋ ɳɬɰɬʃɴ ɴɽɻɺɷʈɳɺɮɬɹ ɸɱɾɺɰ, ɺɻɿɭɷɴɶɺɮɬɹɹʇɵ ɮ ɼɬɭɺɾɱ[3].Ɏ ɹɱɵ ɻɼɱɰɷɬɯɬɱɾɽʋ ɬɷɯɺɼɴɾɸ ɻɺɴɽɶɬ ɮɱɼɺʋɾɹɺɽɾɴ ʃɱɼɱɳ ɸɬɾɱɸɬɾɴʃɱɽɶɺɱ ɺɲɴɰɬɹɴɱ ɴ ɰɺɶɬɳʇɮɱɾɽʋ ɱɯɺ ʉʀʀɱɶɾɴɮɹɺɽɾʈ ɻɱɼɱɰ ɸɱɾɺɰɺɸ ɶɺɸɭɴɹɬɾɺɼɹɺɯɺ ɻɱɼɱɭɺɼɬ ɮɽɱʁ ɮɺɳɸɺɲɹʇʁ ɮɬɼɴɬɹɾɺɮ. ɛɼɴɮɱɰɱɹɬ ɶɺɷɴʃɱɽɾɮɱɹɹɬʋɺʂɱɹɶɬ ɮʇʃɴɽɷɴɾɱɷʈɹʇʁ ɳɬɾɼɬɾ ɻɼɴ ɺɻɾɴɸɴɳɬʂɴɴ ɬɷɯɺɼɴɾɸɺɮ ɻɼɺɯɹɺɳɴɼɺɮɬɹɴʋ.
ɜɴɽɿɹɺɶ 1
ɍɿɰɱɸ ɻɺɹɴɸɬɾʈ ɻɺɰ ɿɼɹɬɸɴ Ãɼɱɯɴɺɹʇ, ɻɺɰ ɶɼɬɽɹʇɸɴ ʄɬɼɬɸɴ Ãʀɿɼʇ ɽ ɶɺɹɾɼɬɭɬɹɰɹʇɸɴ ɯɼɿɳɬɸɴ, ɻɺɰ ɽɴɹɴɸɴ Ãʀɿɼʇ, ɹɱ ɹɬɼɿʄɬʊʅɴɱ ɽɬɹɶʂɴɺɹɹʇɵ ɼɱɲɴɸ.Ɏɮɱɰɱɸ ɽɷɱɰɿʊʅɴɱ ɺɭɺɳɹɬʃɱɹɴʋ ɰɷʋ iÃɺɵ ɿɼɹʇ: red[i]Ãɶɺɷɴʃɱɽɾɮɺ ɶɼɬɽɹʇʁ ʄɬɼɺɮ, blue[i]Ãɶɺɷɴʃɱɽɾɮɺ ɽɴɹɴʁ, takeOut[i]Ãɶɺɷɴʃɱɽɾɮɺ ɴɳɮɷɱɶɬɱɸʇʁ ɴɳ iÃɺɵɿɼɹʇ ʄɬɼɺɮ. i=΅dzݙശശശശശ, k2, ɯɰɱ kÃʃɴɽɷɺ ɿɼɹ.ɜɬɽɽɸɺɾɼɴɸ ɽʁɱɸɿ ɴɳ ɻɺɽɷɱɰɺɮɬɾɱɷʈɹɺɵ ʂɱɻɺʃɶɴ ɿɼɹ. ɔɳ ɻɱɼɮɺɵ ɿɼɹʇ ɹɬɿɰɬʃɿ ɴɳɮɷɱɶɬɱɾɽʋ ɹɱɽɶɺɷʈɶɺ ʄɬɼɺɮ ɴ ɻɱɼɱɶɷɬɰʇɮɬɱɾɽʋ ɮɺ ɮɾɺɼɿʊ. Ɏ ɽɮɺʊ ɺʃɱɼɱɰʈ, ɴɳ ɮɾɺɼɺɵ ɮ ɾɼɱɾʈʊ ɻɱɼɱɶɷɬɰʇɮɬɱɾɽʋ ɶɬɶɺɱÃɾɺ ɶɺɷɴʃɱɽɾɮɺ ʄɬɼɺɮ ɴ ɾɬɶ ɰɬɷɱɱ. ɔ ɰɷʋɹɬʁɺɲɰɱɹɴʋ ɮɱɼɺʋɾɹɺɽɾɴ ɴɳɮɷɱʃɱɹɴʋɶɼɬɽɹʇɵ ʄɬɼ ɴɳ ɻɺɽɷɱɰɹɱɵ ɿɼɹʇ ɴɽɻɺɷʈɳɺɮɬɷɽʋ ɽɷɱɰɿʊʅɴɵ ɬɷɯɺɼɴɾɸ(ɼɴɽɿɹɺɶ 2).
ɜɴɽɿɹɺɶ 2
ɝɹɬʃɬɷɬɹɬʁɺɰɴɸɸɬɾɱɸɬɾɴʃɱɽɶɺɱɺɲɴɰɬɹɴɱɴɳɮɷɱʃɱɹɴʋɶɼɬɽɹɺɯɺʄɬɼɬɰɷʋɻɱɼɮɺɵɿɼɹʇ. ɛɺɾɺɸɮʂɴɶɷɱɴʅɱɾɽʋɸɬɾɱɸɬɾɴʃɱɽɶɺɱɺɲɴɰɬɹɴɱ ɰɷʋ ɻɺɽɷɱɰɿʊʅɴʁ ɿɼɹ ɽ ɿʃʌɾɺɸ ɸɬɾɱɸɬɾɴʃɱɽɶɺɯɺ ɺɲɴɰɬɹɴʋ ɰɷʋ ɻɼɱɰʇɰɿʅɴʁ. ɓɬɾɱɸ ɹɬʁɺɰɴɸ ɮɱɼɺʋɾɹɺɽɾʈ ɴɳɮɷɱʃɱɹɴʋ ɶɼɬɽɹɺɯɺ ʄɬɼɬ ɴɳ ɻɺɽɷɱɰɹɱɵ ɿɼɹʇ. ɓɹɬʃɱɹɴɱ ɮɱɼɺʋɾɹɺɽɾɴ ɮɺɳɮɼɬʅɬɱɾɽʋ ɮ ɻɼɺɯɼɬɸɸɿ.Ɏ ɽɷɿʃɬɱ ɻɱɼɱʁɺɰɬ ɺɾ ɻɺɽɷɱɰɺɮɬɾɱɷʈɹɺɯɺ ɼɬɽɻɺɷɺɲɱɹɴʋ ɿɼɹ ɶ ɸɺɰɱɷɴɼɿɱɸɺɵ ɽɾɼɿɶɾɿɼɱ ɰɱɼɱɮɬ ɽ ɶɺɼɹɱɮʇɸ ɿɳɷɺɸ Customs, ɽ ɿɳɷɬɸɴ ɮɱɾɮɷɱɹɴʋ Sanctury, Blackquarter, Middleheim,DragoBreachɴ ɷɴɽɾʈʋɸɴ Athenaeum, Elfwind, Equinox, Silverwing, Rainhaven, Rockwarrenɬɷɯɺɼɴɾɸ ɾɼɱɭɿɱɾ ɸɺɰɴʀɴɶɬʂɴɴ ɴɳɳɬ ɾɺɯɺ, ʃɾɺ ɾɱɻɱɼʈ ɿɳɱɷ ɸɺɲɱɾ ɴɸɱɾʈ ɭɺɷɱɱ ɺɰɹɺɯɺ ɰɺʃɱɼɹɱɯɺ ɿɳɷɬ.ɔɽɻɺɷʈɳɺɮɬɹɴɱ ɸɬɽɽɴɮɺɮ ɹɱ ɻɼɱɰɽɾɬɮɷʋɱɾɽʋ ɮɺɳɸɺɲɹʇɸ, ɻɺʉɾɺɸɿ,ʃɾɺɭʇ ɴɳɭɬɮɴɾʈɽʋ ɺɾ ɹɱɺɭʁɺɰɴɸɺɽɾɴ ɮ ɹɴʁ,ɭɿɰɱɸ ɴɽɻɺɷʈɳɺɮɬɾʈ ɼɱɶɿɼɽɴʊ (ɼɴɽɿɹɺɶ 3).
ɜɴɽɿɹɺɶ 3
ɛɼɴɹɬɲɬɾɴɴɶɹɺɻɶɴ"count" ɹɬɶɬɶɺɸɷɴɭɺɿɳɷɱɳɬɻɿɽɶɬɱɾɽʋʉɾɬʀɿɹɶʂɴʋɽɻɬɼɬɸɱɾɼɺɸisRoot= true. ɩɾɺɾɿɳɱɷɽʃɴɾɬɱɾ ɽɿɸɸɿ ɸɬɾɱɸɬɾɴʃɱɽɶɴʁ ɺɲɴɰɬɹɴɵ ɰɺʃɱɼɹɴʁ ɿɳɷɺɮ, ɳɬɻɼɬʄɴɮɬʋ ɱɯɺ ɿ ɹɴʁ ɽ ɻɬɼɬɸɱɾɼɺɸ isRoot( [VahZ, ɴ, ɴɽɻɺɷʈɳɿʋ ʉɾɺ ɳɹɬʃɱɹɴɱ,ɻɺɰɽʃɴɾʇɮɬɱɾ ɮɱɼɺʋɾɹɺɽɾʈ ɺɭɹɬɼɿɲɱɹɴʋ ʀɿɼʇ ɽ ɽɬɹɶʂɴɺɹɹʇɸ ɯɼɿɳɺɸ. ɐɺʃɱɼɹɴɱ ɿɳɷʇ, ɮ ɽɮɺʊ ɺʃɱɼɱɰʈ, ɾɺʃɹɺ ɾɬɶɲɱ ɽʃɴɾɬʊɾ ɽɿɸɸɿ ɸɬɾɱɸɬɾɴʃɱɽɶɴʁ ɺɲɴɰɬɹɴɵ ɽɮɺɴʁ ɰɺʃɱɼɹɴʁ ɿɳɷɺɮ, ɹɺ ɾɬɶ ɶɬɶ ɴɸ ɻɱɼɱɰɬɹ ɻɬɼɬɸɱɾɼ isRoot( [VahZ, ɾɺɺɹɴɮɺɳɮɼɬɾʋɾ ɹɱ ɮɱɼɺʋɾɹɺɽɾʈɺɭɹɬɼɿɲɱɹɴʋ, ɬ ɸɬɾɱɸɬɾɴʃɱɽɶɺɱ ɺɲɴɰɬɹɴɱ.
ɛɺɷɿʃɱɹ ɮɴɳɿɬɷɴɳɴɼɺɮɬɹɹʇɵ ɰɴɹɬɸɴʃɱɽɶɴɵ ɮɬɼɴɬɹɾ ɼɬɭɺɾʇ ɾɬɸɺɲɹɴ Customs. ɛɼɺɯɼɬɸɸɬ ɮɴɳɿɬɷɴɳɬʂɴɴ ɼɱɬɷɴɳɺɮɬɹɬ ɹɬ ʋɳʇɶɱ ɻɼɺɯɼɬɸɸɴɼɺɮɬɹɴʋ Java.ɚɭɺɭʅɴɸ ɻɺɽɾɬɹɺɮɶɿ ɻɼɱɰʇɰɿʅɱɵ ɳɬɰɬʃɴ. ɑɽɷɴ ɮ ɭɬɳɺɮɺɵ ɽʁɱɸɱɿɼɹ ɴɳ ɻɺɽɷɱɰɹɱɵ ɿɼɹʇ ɴɳɮɷɱɶɬɷɽʋ ɺɰɴɹ ʄɬɼ, ɾɱɻɱɼʈ Ãnʄɬɼɺɮ ɺɰɹɺɯɺ ʂɮɱɾɬ.ɛɼɱɰʇɰɿʅɴɵ ɬɷɯɺɼɴɾɸ ɻɺɳɮɺɷʋɱɾ ɮʇʃɴɽɷɴɾʈɮɱɼɺʋɾɹɺɽɾʈ ɾɺɯɺ, ʃɾɺ ɻɱɼɮʇɵ ɴɳɮɷɱʃʌɹɹʇɵ ɴɳ ɶɺɼɹɱɮɺɯɺ ɿɳɷɬʄɬɼ ɶɼɬɽɹʇɵ.Ɏɺɳɹɴɶɬɱɾɮɺɻɼɺɽ:ɶɬɶ ɸɱɹʋɱɾɽʋ ɮɱɼɺʋɾɹɺɽɾʈ ɴɳɮɷɱʃɱɹɴʋ ɮɾɺɼɺɯɺ ɶɼɬɽɹɺɯɺ ʄɬɼɬ ɮ ɳɬɮɴɽɴɸɺɽɾɴ ɺɾ ɶɺɹɶɼɱɾɹɺɯɺ ɿɳɷɬ, ɴɳ ɶɺɾɺɼɺɯɺ ɭʇɷ ɴɳɮɷɱʃʌɹɻɱɼɮʇɵ ʄɬɼ. ɐɷʋ ɶɬɲɰɺɯɺ ɿɳɷɬ ɴɸɱɱɾ ɸɱɽɾɺ ɹɺɮɺɱ ɳɹɬʃɱɹɴɱ ɮɱɼɺʋɾɹɺɽɾɴ.ɚɾɮɱɾ ɹɬ ɻɺɽɾɬɮɷɱɹɹʇɵ ɮɺɻɼɺɽ ɽɺɽɾɺɴɾ ɴɳ ɹɱɽɶɺɷʈɶɴʁʉɾɬɻɺɮ. ɚɽɺɭɱɹɹɺɽɾʈ ɮʇɭɼɬɹɹɺɵ ɾɼɬɱɶɾɺɼɴɴ ɰɮɴɲɱɹɴʋɻɺ ɰɱɼɱɮɿ ɽɺɽɾɺɴɾ ɮ ɹɬɻɼɬɮɷɱɹɴɴɺɾ ɷɴɽɾʈɱɮ ɶ ɶɺɼɹʊ. ɛɼɱɰɻɺʃɾɴɾɱɷʈɹɺɽɾʈ ɾɬɶɺɯɺ ɬɷɯɺɼɴɾɸɬ ɺɭɿɽɷɺɮɷɱɹɬ ɺɾɽɿɾɽɾɮɴɱɸ ɻɺɾɺɸɶɺɮ ɿ ɷɴɽɾʈɱɮ. ɐɷʋ ɺɻɼɱɰɱɷɱɹɴʋ ɮɱɼɺʋɾɹɺɽɾɴɾɺɯɺ, ʃɾɺ ɻɱɼɮʇɵ ʄɬɼ Ãɶɼɬɽɹʇɵ, ɰɱɷɴɸ ɶɺɷɴʃɱɽɾɮɺ ɶɼɬɽɹʇʁ ʄɬɼɺɮrɹɬ ɶɺɷɴʃɱɽɾɮɺ ʄɬɼɺɮr+bɮ ɿɳɷɱ. Ɏʇʃɴɽɷɱɹɴɱ ɸɬɾɱɸɬɾɴʃɱɽɶɺɯɺ ɺɲɴɰɬɹɴʋ Mɮɶɷʊʃɬɱɾɽʋ ɮ ɽɱɭʋ ɿɸɹɺɲɱɹɴɱ ɻɺɷɿʃɱɹɹɺɯɺ ɼɱɳɿɷʈɾɬɾɬ ɹɬ ɶɺɷɴʃɱɽɾɮɺ ɴɳɮɷɱɶɬɱɸʇʁʄɬɼɺɮt.ɞɺ ɱɽɾʈ ɰɷʋ ɻɱɼɮɺɯɺ ʄɬɼɬPେ൞௷௷௧, Mେ൞݄େݢ,ɾɺɯɰɬ ɰɷʋjÃɺɯɺ ʄɬɼɬ݄௯൞௷(௯େ)௷௧(௯େ), ݁௯൞݄௯(ݢ−(ݘ−΅)).ɝʀɺɼɸɴɼɿɱɸ ɮɱɶɾɺɼ ɰɷʋ iÃɺɯɺ ɿɳɷɬ݁௮൞(ݛ௮େdzݛ௮ୈdzǷdzݛ௮௳), ݛ௮௯൞݁௯Ƕɐɷʋ ɹɱ ɷɴɽɾɺɮɺɯɺ ɿɳɷɬ, ɴɸɱʊʅɱɯɺ k
1ɰɺʃɱɼɹɴʁ ɿɳɷɺɮ Ãɷɴɽɾʈɱɮ, ɼɬɽɽɸɺɾɼɴɸ ɸɬɾɼɴʂɿMɼɬɳɸɱɼɹɺɽɾʈʊ kĀ n, ɻɺɷɺɲɴɮ ݠ௯൞ݠ−(ݘ−΅)൞ݛେ௯ÃjÃɺɱ ɸɬɾɱɸɬɾɴʃɱɽɶɺɱ ɺɲɴɰɬɹɴɱ ɼɬɽɽɸɬɾɼɴɮɬɱɸɺɯɺ ɿɳɷɬ, ݛ௮େdz௯Ã jÃɺɱ ɸɬɾɱɸɬɾɴʃɱɽɶɺɱ ɺɲɴɰɬɹɴɱiÃɺɯɺ ɰɺʃɱɼɹɱɯɺ ɿɳɷɬɰɷʋ ɼɬɽɽɸɬɾɼɴɮɬɱɸɺɯɺ, ɾɺ ɱɽɾʈ jÃɬʋ ɶɺɺɼɰɴɹɬɾɬ ɮɱɶɾɺɼɬ Mi.ɩɾɬ ɸɬɾɼɴʂɬ ɴɸɱɱɾ ɮɴɰ݁൞ۛۚۙݠେǷݠ௳ݛୈେǷݛୈ௳ݛେǷݛ௳ǷǷǷݛ௰େǷݛ௰௳۞ۜǶɎɮɱɰʌɸ ɮ ɼɬɽɽɸɺɾɼɱɹɴɱ ɮɱɶɾɺɼ ܹ൞(ܹେǴܹୈǴǷǴܹ௳),ɬɾɬɶɲɱ sÃɺɱ ɽɺɽɾɺʋɹɴɱjÃɺɯɺ ʄɬɯɬ ɰɷʋ iÃɺɯɺ ɿɳɷɬ Ãʃɴɽɷɺ ɶɼɬɽɹʇʁ ݠ௯௸, ɽɴɹɴʁ ݐ௯௸, ɴ ɴɳɮɷɱɶɬɱɸʇʁ ݢ௯௸ʄɬɼɺɮ.ɛɼɴʃʌɸ jÃʇɵ ʄɬɯ ɻɼɱɰɻɺɷɬɯɬɱɾ ɹɬɷɴʃɴɱ jɽɺɽɾɺʋɹɴɵ s.ɛɼɴ ɽɺɽɾɺʋɹɴɴ s=1ɹɬ
jÃɺɸ ʄɬɯɱɴɸɱɱɸݠ௯େ൞ݠ௯dzݐ௯େ൞ݐ௯dzݢ௯େ൞ݢ௯Ƕɛɼɴ ɽɺɽɾɺʋɹɴɴ s=2ɹɬ jɺɸ ʄɬɯɱ ɴɸɱɱɸ ݠ௯ୈ൞ݠ௯େdzݐ௯ୈ൞ݐ௯େdzݢ௯ୈ൞ݢ௯େǶɛɼɴ ɽɺɽɾɺʋɹɴɴ s=lɹɬ jÃɺɸ ʄɬɯɱ ɴɸɱɱɸ ݠ௯௱൞ݠ௯(௱େ)dzݐ௯௱൞ݐ௯(௱େ)dzݢ௯௱൞ݢ௯(௱େ)Ƕɛɼɴ ɽɺɽɾɺʋɹɴɴ s=j ɽɺɺɾɮɱɾɽɾɮɱɹɹɺ ɴɸɱɱɸ ݠ௯௯൞ݠେdzݐ௯௯൞ݐେdzݢ௯௯൞ݢେǶɚɭɺɳɹɬʃɴɸ ɮɱɼɺʋɾɹɺɽɾʈ ɹɬɽɾɿɻɷɱɹɴʋ sÃɺɯɺ ɽɺɽɾɺʋɹɴʋ ɰɷʋ jÃɺɯɺ ʄɬɯɬ iÃɺɯɺ ɿɳɷɬ ݄௮௯௸. ɡɬɼɬɶɾɱɼɴɽɾɴɶɺɵ ɶɬɲɰɺɯɺ jÃɺɯɺ ʄɬɯɬiÃɺɯɺ ɿɳɷɬ ʋɮɷʋɱɾɽʋ ܺ௮௯൞ෟPijஃ௯௸େݛ௮௸dzɬ ɽɿɸɸɬ ʉɾɴʁ ʁɬɼɬɶɾɱɼɴɽɾɴɶ ɹɬ jÃɺɸ ʄɬɯɱ ɰɷʋ ɮɽɱʁ ɿɳɷɺɮ ɺɭɼɬɳɿɱɾ jÃɿʊ ɶɺɺɼɰɴɹɬɾɿ Ejɮɱɶɾɺɼɬ E.ܹ௯൞ෟܺ௮௯௰iେǶəɬ ɻɱɼɮɺɸ ʄɬɯɱ ɰɷʋ ɶɬɲɰɺɯɺ ɿɳɷɬ ɽɿʅɱɽɾɮɿɱɾ ɱɰɴɹɽɾɮɱɹɹɺɱ ɽɺɽɾɺʋɹɴɱ, ɴ ɻɺʉɾɺɸɿ ɮɱɼɺʋɾɹɺɽɾʈ ɹɬɽɾɿɻɷɱɹɴʋ ʉɾɺɯɺ ɽɺɽɾɺʋɹɴɱ ɼɬɮɹɬ Q. ɡɬɼɬɶɾɱɼɴɽɾɴɶɬ ɻɱɼɮɺɯɺ ʄɬɯɬ iɺɯɺ ɿɳɷɬܺ௮େ൞݄௮େେπݛ௮େ൞ݛ௮େəɬɻɺɸɹɴɸ, ʃɾɺ ݛ௮େÃʉɷɱɸɱɹɾʇ ɻɱɼɮɺɯɺ ɽɾɺɷɭʂɬ ɸɬɾɼɴʂʇ M. ɑʌ ɻɱɼɮʇɵ ɽɾɺɷɭɱʂ, ɴ ɾɺɷʈɶɺ ɻɱɼɮʇɵ, ɽɺɮɻɬɰɬɱɾ ɽ ʁɬɼɬɶɾɱɼɴɽɾɴɶɬɸɴ ɻɱɼɮɺɯɺ ʄɬɯɬ ɰɷʋ ɮɽɱʁ ɿɳɷɺɮ. ɞɬɶɴɸ ɺɭɼɬɳɺɸ, ɻɱɼɮɬʋ ɶɺɺɼɰɴɹɬɾɬ ܹେɮɱɶɾɺɼɬ Eɼɬɮɹɬ ɽɿɸɸɱɶɺɺɼɰɴɹɬɾ ɻɱɼɮɺɯɺ ɽɾɺɷɭʂɬ ɸɬɾɼɴʂʇ M.ܹେ൞ෟܺ௮େ௰iେ൞ෟݛ௮େ௰iେǶ
əɬ ɶɬɲɰɺɸ ɻɺɽɷɱɰɿʊʅɱɸ ʄɬɯɱ, ɮ ɺɾɷɴʃɴɱ ɺɾ ɻɱɼɮɺɯɺ, ɴɸɱɱɸ ɶɺɷɴʃɱɽɾɮɺ ɽɺɽɾɺʋɹɴɵ ݡ൞΅dzଦശശശശ,ɭɺɷɱɱ ɺɰɹɺɯɺ.ɣɴɽɷɺ ɽɷɬɯɬɱɸʇʁ ɮ ʁɬɼɬɶɾɱɼɴɽɾɴɶɱ ʄɬɯɬ ɺɻɼɱɰɱɷʋɱɾɽʋ ɶɺɷɴʃɱɽɾɮɺɸ ɽɺɽɾɺʋɹɴɵ ɹɬ ʉɾɺɸ ʄɬɯɱ.əɬ ɮɾɺɼɺɸ ʄɬɯɱ ɴɸɱɱɸ ɰɮɬ ɽɺɽɾɺʋɹɴʋ, ɮɱɼɺʋɾɹɺɽɾɴ ɶɺɾɺɼʇʁ ɰɷʋ iÃɺɯɺ ɿɳɷɬ ɮʇʃɴɽɷʋʊɾɽʋ ɻɺ ʀɺɼɸɿɷɬɸPiୈୈ൞ܺ௮େܹେdzPiୈେ൞΅−PiୈୈǶɞɬɶɴɸ ɺɭɼɬɳɺɸ, ʁɬɼɬɶɾɱɼɴɽɾɴɶɬ ɮɾɺɼɺɯɺ ʄɬɯɬ ɰɷʋ iÃɺɯɺ ɿɳɷɬ ɳɬɰɬʌɾɽʋ ʀɺɼɸɿɷɺɵܺ௮ୈ൞݄iୈୈݛ௮ୈ+Piୈେݛ௮େǶɝɷɱɰɺɮɬɾɱɷʈɹɺ,ܹୈ൞ෟܺ௮ୈ௰iେǶɝ ɴɳɮɷɱʃɱɹɴɱɸ ɾɼɱɾʈɱɯɺ ʄɬɼɬ ɽɮʋɳɬɹɺ ɾɼɴ ɼɬɳɹʇʁ ɽɺɽɾɺʋɹɴʋ ɰɷʋ ɶɬɲɰɺɯɺ ɿɳɷɬ. əɬ ʉɾɺɸ ʉɾɬɻɱ ɺɻɼɱɰɱɷɱɹɴɱ ɮɱɼɺʋɾɹɺɽɾɱɵ ɹɬɽɾɿɻɷɱɹɴɵ ɹɺɮʇʁ ɽɺɽɾɺʋɹɴɵ ɺɻɼɱɰɱɷʋɱɾɽʋ ɻɺ ɹɺɮɺɵ ɽʁɱɸɱ. Ɍ ɴɸɱɹɹɺ, ɮ ɹɬʃɬɷɱ,ɹɬɵɰʌɸ ɮɱɼɺʋɾɹɺɽɾʈ Qɾɺɯɺ, ʃɾɺ ɻɼɱɰʇɰɿʅɴɵ ʄɬɼ ɭʇɷ ɴɳɮɷɱʃʌɹ ɴɳ iɺɯɺ ɿɳɷɬ. ɜɬɹʈʄɱ ɮ ʉɾɺɸ ɹɱ ɭʇɷɺ ɹɱɺɭʁɺɰɴɸɺɽɾɴ.ɞɬɶɴɸ ɺɭɼɬɳɺɸ, ɰɷʋ ɶɬɲɰɺɯɺ iɺɯɺ ɿɳɷɬ݅௮൞ܺ௮ୈܹୈǶɎ ɰɬɷʈɹɱɵʄɱɸ ɺɭɺɳɹɬʃɴɸ Qijɮʇʃɴɽɷʋɱɸɿʊ ɮɱɼɺʋɾɹɺɽɾʈ ɰɷʋ iÃɺɯɺ ɿɳɷɬ ɹɬ jÃɺɸ ʄɬɯɱ. əɬɵɰɱɹɹɬʋ ɮɱɼɺʋɾɹɺɽɾʈ ɻɺɳɮɺɷʋɱɾ ɮʇʃɴɽɷɴɾʈ ɾɼɴ ɹɺɮʇʁ ɮɱɼɺʋɾɹɺɽɾɴ, ɻɺʋɮɷʋʊʅɴʁɽʋ ɹɬ ɾɼɱɾʈɱɸ ɿɼɺɮɹɱ ɴɱɼɬɼʁɴɴ ɮ ɰɱɼɱɮɱ ɮɱɼɺʋɾɹɺɽɾɱɵ ɹɬ ɼɴɽɿɹɶɱ 4.
ɜɴɽɿɹɺɶ 4ɫɽɹɺ, ʃɾɺPi൞݅௮πPiୈୈǴ
Piୈ൞݅௮πPiୈେ+(΅−݅௮)πPiୈୈǴPiେ൞(΅−݅௮)πPiୈେ.ɝɷɱɰɺɮɬɾɱɷʈɹɺ,ܺ௮൞݄iݛ௮+Piୈݛ௮ୈ+Piେݛ௮େǴ
ܹ൞ෟܺ௮Ƕ௰iେɚɻɴɼɬʋɽʈ ɴ ɺɭɺɭʅɬʋ ʃɱɾɮʌɼɾʇɵ ɿɼɺɮɱɹʈ ɴɱɼɬɼʁɴɴ, ɳɬɰɬʊʅɴɵ ʃɱɾʇɼɱ ɽɺɽɾɺʋɹɴʋ, ɹɬ ɼɴɽɿɹɶɱ 4, ɳɬɻɴʄɱɸ ɽɷɱɰɿʊʅɴɱ ʀɺɼɸɿɷʇ ɰɷʋjÃɺɯɺ ʄɬɯɬ iÃɺɯɺ ɿɳɷɬ, ɹɬʁɺɰʋʅɱɯɺɽʋ ɮ ɽɺɽɾɺʋɹɴɴ s. ɩɾɴ ʀɺɼɸɿɷʇ ɴɸɱʊɾ ɮɴɰQ௮௯൞ܺ௮dzjେܹ௯େǴPijେ൞ൽ΅−Q௮௯ඁπPidzjେdzେǴPijஃ൞Q௮௯πPidzjେdzஃେ+ൽ΅−Q௮௯ඁπPidzjେdzஃǴPijj൞QπPidzjେdzjେǴܺ௮௯൞ෟPijஃ௯௸େݛ௮௸Ǵܹ௯൞ෟܺ௮௯௰iେǶɐɷʋ ɮʇʃɴɽɷɱɹɴʋ ɮɱɼɺʋɾɹɺɽɾɱɵ ɴɳɮɷɱʃɱɹɴʋ ɶɼɬɽɹʇʁ ʄɬɼɺɮ ɴɳ ɴɽʁɺɰɹɺɯɺ ɿɳɷɬ (ɶɺɾɺɼʇɵ, ɮɺɺɭʅɱ ɯɺɮɺɼʋ, ɹɱ ʋɮɷʋɱɾɽʋ ɷɴɽɾɺɮʇɸ) ɹɬ jÃɺɸ ʄɬɯɱ ɴɽɻɺɷʈɳɿɱɸ jÃɿʊ ɶɺɺɼɰɴɹɬɾɿ ɮɱɶɾɺɼɬ E.ɔɽɶɺɸɬʋ jÃɬʋ ɮɱɼɺʋɾɹɺɽɾʈ ɮʇʃɴɽɷʋɱɾɽʋ ɻɺ ʀɺɼɸɿɷɱ݄௯൞ܹ௯ݑ−(ݘ−΅)Ƕɓɰɱɽʈ cÃɺɭʅɱɱ ʃɴɽɷɺ ʄɬɼɺɮ ɮ ɴɽʁɺɰɹɺɸ ɿɳɷɱ ɻɺɽɷɱ ɰɺɭɬɮɷɱɹɴʋ ɮ ɹɱɯɺ ʄɬɼɺɮ, ɴɳɮɷɱʃʌɹɹʇʁ ɴɳ ɽɺɺɾɮɱɾɽɾɮɿʊʅɴʁ ɱɸɿ ɰɺʃɱɼɹɴʁ ɿɳɷɺɮ.Ɏɱɶɾɺɼ Pɴɸɱɱɾ nɶɺɺɼɰɴɹɬɾ, ɶɬɲɰɬʋ ɴɳ ɶɺɾɺɼʇʁ Pjɻɼɱɰɽɾɬɮɷʋɱɾ ɽɺɭɺɵ ɮɱɼɺʋɾɹɺɽɾʈ ɴɳɮɷɱʃɱɹɴʋ ɶɼɬɽɹɺɯɺ ʄɬɼɬ ɹɬ jÃɺɸ ʄɬɯɱ ɻɼɴ ɿɽɷɺɮɴɴ, ʃɾɺ ɹɬ ɮɽɱʁ ɻɼɱɰʇɰɿʅɴʁ ʄɬɯɬʁ ɭʇɷɴ ɴɳɮɷɱʃɱɹʇ ɾɺɷʈɶɺ ɶɼɬɽɹʇɱ ʄɬɼʇ.ɑɽɷɴ ʉɾɺɾ ɿɳɱɷ ɹɱ ʋɮɷʋɱɾɽʋ ɶɺɼɹɱɮʇɸ, ɾɺ ɿɸɹɺɲɴɮ ɻɺɷɿʃɱɹɹʇɱ ɮɱɼɺʋɾɹɺɽɾɴ ɹɬ ɶɺɷɴʃɱɽɾɮɺ ɴɳɮɷɱɶɬɱɸʇʁ ʄɬɼɺɮ tɹɬ jÃɺɸ ʄɬɯɱ, ɻɺɷɿʃɴɸ ɸɬɾɱɸɬɾɴʃɱɽɶɺɱ ɺɲɴɰɬɹɴɱ݁௯൞݄௯ൽݢ−(ݘ−΅)ඁǶɘɬɾɼɴʂɬ Mɼɺɰɴɾɱɷʈɽɶɺɯɺ ɿɳɷɬ, ɰɷʋ ɶɺɾɺɼɺɯɺ ɴɽʁɺɰɹʇɵ ɿɳɱɷ ʋɮɷʋɱɾɽʋ iÃʇɸ ɰɺʃɱɼɹɴɸ, ʀɺɼɸɴɼɿɱɾɽʋ ɴɳ ݛ௮େdz௯൞݁௯, ɯɰɱ j=΅dzݜശശശശശ.ɛɼɺɯɼɬɸɸɹɬʋ ɼɱɬɷɴɳɬʂɴʋ ɰɬɹɹɺɯɺ ɬɷɯɺɼɴɾɸɬ ɻɼɱɰɽɾɬɮɷɱɹɬ ɹɬ ɼɴɽɿɹɶɬʁ5.1, 5.2.ɜɴɽɿɹɺɶ 5.1
ɜɴɽɿɹɺɶ 5.2
Ɏɱɼɺʋɾɹɺɽɾʈ Pɺɭʅɾɺɯɺ, ʃɾɺ ɴɳ ɶɺɼɹɱɮɺɯɺ ɿɳɷɬ, ɶɺɾɺɼɺɸɿ ɻɼɱɰʄɱɽɾɮɺɮɬɷɴN1ɿɳɷɺɮ ɮɱɾɮɷɱɹɴʋ ɴ ɷɴɽɾʈɱɮ, ɮɽɱ ɴɳɮɷɱʃʌɹɹʇɱ nʄɬɼɺɮ ɺɶɬɲɿɾɽʋ ɶɼɬɽɹʇɸɴ ɮʇʃɴɽɷʋɱɾɽʋ ɻɺ ʀɺɼɸɿɷɱ݄ˣ˖ˮ൞݄௯Ƕ௳௯େɓɬɸɱɾɴɸ, ʃɾɺ ɰɬɹɹʇɵ ɬɷɯɺɼɴɾɸ ɺɭɷɬɰɬɱɾ ɽɷɱɰɿʊʅɴɸ ɮɬɲɹʇɸ ɽɮɺɵɽɾɮɺɸ »ɽɿɲɬɱɸɺɽɾɴ¼. ɛɼɴ ɰɮɴɲɱɹɴɴ ɺɾ ɶɺɼɹɱɮɺɯɺ ɿɳɷɬ ɶ ɷɴɽɾʈʋɸ ɹɱɾ ɹɱɺɭʁɺɰɴɸɺɽɾɴ ɹɬʁɺɰɴɾʈ ɮɽɱ nɸɬɾɱɸɬɾɴʃɱɽɶɴʁ ɺɲɴɰɬɹɴɵ ɮ ɽɷɿʃɬɱ, ɱɽɷɴ ʃɴɽɷɺ ʄɬɼɺɮ, ɻɱɼɱɶɷɬɰʇɮɬɱɸʇʁ ɴɳ ɰɺʃɱɼɹɱɯɺ ɿɳɷɬ ɮ ɼɺɰɴɾɱɷʈɽɶɴɵ, ɸɱɹʈʄɱ, ʃɱɸ ʃɴɽɷɺ ʄɬɼɺɮ, ɴɳɮɷɱɶɬɱɸʇʁ ɴɳɼɺɰɴɾɱɷʈɽɶɺɯɺ ɿɳɷɬ. əɬɻɼɴɸɱɼ, ɱɽɷɴ ʃɴɽɷɺ ɴɳɮɷɱɶɬɱɸʇʁ ɴɳ ɼɺɰɴɾɱɷʈɽɶɺɯɺ ɿɳɷɬ ʄɬɼɺɮ ɼɬɮɹɺ ɻʋɾɴ, ɬ ɴɳ ɰɺʃɱɼɹɱɯɺ ɾɼʌɸ, ɾɺ ɸɬɾɱɸɬɾɴʃɱɽɶɺɱ ɺɲɴɰɬɹɴɱ ɾɺɯɺ, ʃɾɺ ɴɳ ɰɺʃɱɼɹɱɯɺ ɿɳɷɬ ɭɿɰɱɾ ɴɳɮɷɱʃɱɹɺ ʃɱɾʇɼɱ ɴɷɴ ɻʋɾʈ ʄɬɼɺɮ ɼɬɮɹɺ ɹɿɷʊ. Ɏ ɽɮɺʊ ɺʃɱɼɱɰʈ, ɰɷʋ ɱɯɺ ɰɺʃɱɼɹɴʁ ɿɳɷɺɮ ɸɬɾɱɸɬɾɴʃɱɽɶɺɱ ɺɲɴɰɬɹɴɱ ɻɺɻɼɱɲɹɱɸɿ ɮʇʃɴɽɷʋɱɾɽʋ ɾɺɷʈɶɺ ɰɷʋ ɾɼʌʁ ʄɬɼɺɮ, ɱɽɷɴ ɹɱ ɻɼɺʋɮɴɾɽʋ ɮɹɺɮʈ ɽɮɺɵɽɾɮɺ »ɽɿɲɬɱɸɺɽɾɴ¼.
Ɏʇɮɺɰ.Ɏ ɼɬɭɺɾɬʁ P3,4R ɼɬɽɽɸɬɾɼɴɮɬɷɴɽʈ ɽɷɱɰɿʊʅɴɱ ɻɺɽɾɬɹɺɮɶɴ ɳɬɰɬʃɴ.ɛɿɽɾʈ ɮ ɶɬɲɰɺɵ ɴɳN 2 ɿɼɹ ɴɸɱɱɾɽʋ ɽɮɺɵ ɹɬɭɺɼ ɶɼɬɽɹʇʁ rɴ ɽɴɹɴʁ bʄɬɼɺɮ. ɔɳ ɻɱɼɮɺɵ ɿɼɹʇ, ɽɺɰɱɼɲɬʅɱɵ r1ɶɼɬɽɹʇʁ ɴ b1ɽɴɹɴʁ ʄɬɼɺɮ,ɹɬɿɰɬʃɿɴɳɮɷɱɶɬʊɾɽʋ t1ʄɬɼɺɮɴ ɻɱɼɱɶɷɬɰʇɮɬʊɾɽʋɮɺ ɮɾɺɼɿʊ ɿɼɹɿ. ɔɳ ɮɾɺɼɺɵ ɿɼɹʇ, ɽɺɰɱɼɲɬʅɱɵ r2ɶɼɬɽɹʇʁ ɴ b2ɽɴɹɴʁ ʄɬɼɺɮ, ɴɳɮɷɱɶɬʊɾɽʋ t2ʄɬɼɺɮ ɴ ɾ. ɰ. Ɏ ɼɬɭɺɾɱ P3R ɻɼɺʂɱɰɿɼɬ ɳɬɶɬɹʃɴɮɬɱɾɽʋ ɴɳɮɷɱʃɱɹɴɱɸ ɺɰɹɺɯɺ ʄɬɼɬ ɴɳ Nɺɵ ɿɼɹʇ. Ɍ ɮ ɼɬɭɺɾɱ P4R ɴɳɮɷɱʃɱɹɴɱɸ nʄɬɼɺɮ. əɬɽ ɴɹɾɱɼɱɽɺɮɬɷɬ ɮɱɼɺʋɾɹɺɽɾʈ ɴɳɮɷɱʃɱɹɴʋ n ɶɼɬɽɹʇʁ ʄɬɼɺɮ ɴɳɻɺɽɷɱɰɹɱɵ ɿɼɹʇ. ɛɺɷɿʃɱɹʇ ʀɺɼɸɿɷʇ ɴ ɻɼɴɮɱɰɱɹʇ ɬɷɯɺɼɴɾɸʇ ɰɷʋ ɮʇʃɴɽɷɱɹɴʋ ɮɱɼɺʋɾɹɺɽɾɱɵ ɮ ɼɬɭɺɾɱ P3R ɴɳɮɷɱʃɱɹɴʋ ɺɰɹɺɯɺ ɶɼɬɽɹɺɯɺʄɬɼɬ, ɬ ɮ ɼɬɭɺɾɱ P4R ɮɽɱʁ nɶɼɬɽɹʇʁ ʄɬɼɺɮ.ɝɶɺɼɺɽɾʈ ɼɺɽɾɬɼɱɬɷɴɳɬʂɴɴɬɷɯɺɼɴɾɸɬ, ɴɳɷɺɲɱɹɹɺɯɺ ɮ [3],݃(݂).ɝɶɺɼɺɽɾʈ ɼɺɽɾɬ ɼɱɬɷɴɳɬʂɴɴ ɬɷɯɺɼɴɾɸɬ, ɴɳɷɺɲɱɹɹɺɯɺ ɮ P4R, ݃(݂௳). Ɏ ɰɬɹɹɺɵ ɼɬɭɺɾɱ ɮ ɼɱɳɿɷʈɾɬɾɱ ɸɺɰɴʀɴɶɬʂɴɴ ɬɷɯɺɼɴɾɸɬɽɶɺɼɺɽɾʈ ɱɯɺ ɼɺɽɾɬ ݃(݂ݜୈ).ɑɽɷɴ ɼɬɳɭɴɾʈ ɰɱɼɱɮɺ ɹɬ ʀɼɬɯɸɱɹɾʇ, ɶɬɲɰʇɵɴɳɶɺɾɺɼʇʁ ɽɺɽɾɺɴɾ ɴɳɿɳɷɬ ɴ ɱɯɺ ɰɺʃɱɼɹɴʁ ɿɳɷɺɮ, ɾɺ ɻɼɴ ʃɴɽɷɱɰɺʃɱɼɹɴʁ ɿɳɷɺɮ ɭɺɷʈʄɱ ɰɮɿʁ, ɹɬɴɭɺɷɱɱ ʉʀʀɱɶɾɴɮɹʇɸ ɹɬ ʉɾɺɸ ɿʃɬɽɾɶɱ ʋɮɷʋɱɾɽʋ ɬɷɯɺɼɴɾɸ,ɼɬɳɼɬɭɺɾɬɹɹʇɵ ɽ ɴɽɻɺɷʈɳɺɮɬɹɴɱɸ ɸɬɾɱɸɬɾɴʃɱɽɶɺɯɺ ɺɲɴɰɬɹɴʋ, ɻɺ ɽɼɬɮɹɱɹɴʊ ɽ ɶɺɸɭɴɹɬɾɺɼɹʇɸ ɻɺɰʁɺɰɺɸ.ɛɼɴ ʃɴɽɷɱɰɺʃɱɼɹɴʁ ɿɳɷɺɮ ɸɱɹʈʄɱ ɰɮɿʁ,ɹɺɻɼɴ ɭɺɷʈʄɺɸ ɶɺɷɴʃɱɽɾɮɱ ɴɳɮɷɱɶɬɱɸʇʁ ʄɬɼɺɮ ɴɳ ɰɺʃɱɼɹɴʁ ɿɳɷɺɮɻɺ ɽɼɬɮɹɱɹɴʊ ɽ ɼɺɰɴɾɱɷʈɽɶɴɸ,ɾɬɶɲɱ ʉʀʀɱɶɾɴɮɹʇɸɺɽɾɬʌɾɽʋ ɹɱɽɾɬɹɰɬɼɾɹʇɵ ɬɷɯɺɼɴɾɸ ɴ ɴɽɻɺɷʈɳɺɮɬɹɴɱɸ ɸɬɾɱɸɬɾɴʃɱɽɶɴʁ ɺɲɴɰɬɹɴɵ. əɬ ɼɬɳɹʇʁ ɿʃɬɽɾɶɬʁ ɰɱɼɱɮɬ ɽ ɿʃʌɾɺɸ ɿɶɬɳɬɹɹʇʁ ɺɽɺɭɱɹɹɺɽɾɱɵ ɸɺɲɹɺ ʉʀʀɱɶɾɴɮɹɺ ɻɼɴɸɱɹʋɾʈ ɬɷɯɺɼɴɾɸʇ, ɼɬɳɼɬɭɺɾɬɹɹʇɱ ɽ ɴɽɻɺɷʈɳɺɮɬɹɴɱɸ ɶɬɶ ɸɬɾɱɸɬɾɴʃɱɽɶɺɯɺ ɺɲɴɰɬɹɴʋ, ɾɬɶ ɴ ɶɺɸɭɴɹɬɾɺɼɹʇʁ ʀɺɼɸɿɷ.
ɝɽʇɷɶɴ ɹɬ ɴɽɾɺʃɹɴɶɴ1.ɍɱɼɹʄɾɱɵɹ ɝ.ə. ɞɱɺɼɴʋ ɮɱɼɺʋɾɹɺɽɾɱɵ. ɘ. Ãɗ.: ɚəɞɔ, Q934. 4Q2 ɽ.2.ɘɬɼɶɴɹɬ ɘ.ɝ., ɚɼɷɴɶ ɗ.ɖ. ɚɻʇɾ ʀɺɼɸɴɼɺɮɬɹɴʋ ɻɼɴɸɱɼɺɮ ɼɱʄɱɹɴʋ ɹɱɽɾɬɹɰɬɼɾɹʇʁ ɳɬɰɬʃ ɻɼɴ ɴɳɿʃɱɹɴɴ ɶɿɼɽɬ ɮʇɽʄɱɵ ɸɬɾɱɸɬɾɴɶɴ//Ɏ ɽɭɺɼɹɴɶɱ: ɘɬɾɱɸɬɾɴʃɱɽɶɺɱ ɸɺɰɱɷɴɼɺɮɬɹɴɱ ɽɺʂɴɬɷʈɹʇʁ ɻɼɺʂɱɽɽɺɮ ɴ ɽɺɮɼɱɸɱɹɹʇɱ ɺɭɼɬɳɺɮɬɾɱɷʈɹʇɱ ɾɱʁɹɺɷɺɯɴɴ 2PP7. ɝ. 2Q2218.3.Ɍɷɱɶɽɬɹɰɼɺɮ ɛ.ɚ., ɘɬɼɾʇɹɺɮ ɝ.ɗ., ɚɼɷɴɶ ɗ.ɖ. ɖɺɷɴʃɱɽɾɮɱɹɹɬʋ ɺʂɱɹɶɬ ɮʇʃɴɽɷɴɾɱɷʈɹʇʁ ɳɬɾɼɬɾ ɻɼɴ ɺɻɾɴɸɴɳɬʂɴɴ ɬɷɯɺɼɴɾɸɺɮ ɼɱʄɱɹɴʋ ɽɾɬɹɰɬɼɾɹʇʁ ɳɬɰɬʃ ɾɱɺɼɴɴ ɮɱɼɺʋɾɹɺɽɾɱɵ //əɬɿɶɬ ɴ ɽɺɮɼɱɸɱɹɹɺɽɾʈ. 2PQ5. ʝ 36. ɝ. Q34140.4.Ɍɷɱɶɽɬɹɰɼɺɮ ɛ.ɚ. ɜɱʄɱɹɴɱ ɳɬɰɬʃɴ ɻɺ ɮʇɭɺɼɶɱ ʄɬɼɺɮ ɴɳ ɽɴɽɾɱɸʇ ɿɼɹ ɻɼɴ ɻɺɸɺʅɴ ɸɬɾɱɸɬɾɴʃɱɽɶɺɯɺ ɺɲɴɰɬɹɴʋ.https://ekoncept.ru/best_article/young2016/participants.html. . ÃPɐɬɾɬ ɺɭɼɬʅɱɹɴʋ Q8.P3.2PQ6R.