METHOD OF PROCESSING, ANALYZING, AND PREDICTING CHARACTERISTICS OF RADIATION FLUXES FROM SMALL-VOLUME SAMPLES
https://doi.org/10.56304/S2079562924060290
EDN: MMXJJG
Abstract
A method has been proposed to process and analyze the proximity by type-defining characteristics of large aggregations M > 104 of various types Q > 102 of empirical discrete random frequency vectors ν(⋅) = ν0, …, νl, obtained from samples of a small volume 10 ≥ n = ∑i=1lνi(k=i) of random counts k = 0, 1, …, l with averages over all samples kˉ < 5. The method is based on a bijection between the random frequency vectors and its type-defining identifier I(ν, a) > 0, which is a linear statistics in the form of the scalar product of ν and the non-random frequency vector a. Discrete multimodal empirical distributions C(I(ν, a)) representing sequences of arranged and grouped peaks enable us to analyze and forecast the characteristics of peaks and random frequency vectors forming them with low frequencies of their occurrences at the given M value.
About the Authors
V. A. Rabotkin
Voronezh State University
Russian Federation
Russian Federation
N. M. Blizniakov
Voronezh State University
Russian Federation
Russian Federation
V. M. Vahtel
Voronezh State University
Russian Federation
Russian Federation
D. E. Kostomakha
Voronezh State University
Russian Federation
Russian Federation
References
1. Риордан Дж. Введение в комбинаторный анализ. 1963. Москва: Изд. ин. лит-ры.
2. Айвазян С.А. и др. Прикладная статистика. Исследование зависимостей: Справ. изд. 1985. Москва: Финансы и статистика. 3. Петров А.А. // Теория вероятностей и ее применения. 1956. Т. 1 (2). С. 223–245.
3. Бабенко А.Г., Вахтель В.М., Муратов И.В., Работкин В.А. // Ядерн. физ. инжинир. 2022. Т. 13 (2). С. 200. https://doi.org/10.56304/S2079562922010055 [Babenko A.G., Vakhtel V.M., Muratov I.V., Rabotkin V.A. // Phys. At. Nucl. 2021. V. 84 (12). P. 2041–2047. https://doi.org/10.1134/S1063778821090076].
4. Blizniakov N.M., Vahtel V.M., Kostomakha D.E., Rabotkin V.A. // Voronezh Winter Math. School S.G. Crane. Mater. Int. Conf. 2022. P. 30–36.
5. Akindinova E.V., Babenko A.G., Vakhtel V.M., Evseev N.A., Rabotkin V.A. Kharitonova D.D. Proc. Int. Symp. Exotic Nuclei (EXON-2014). 2014. P. 651–658.
6. Кляцкин В.И. Стохастические уравнения и волны в случайно-неоднородных средах. 1980. Москва: Наука.
7. Большев Л.Н. // Теория вероятностей и ее применения. 1965. Т. 10 (3). С. 446–456.
8. Akindinova E.V., Babenko A.G., Vakhtel, Rabotkin V.A., Kharitonova D.D., Muratov I.V. // Voronezh Winter Math. School S.G. Crane. Mater. Int. Conf. 2018. P. 115–117.
9. Большев Л.Н., Смирнов Н.В. Таблицы математической статистики. 1965. Москва: Наука.
10. Ивченко Г.И., Медведев Ю.И. Дискретные распределения. Вероятностно-статистический справочник. Многомерные распределения. 2016. Москва: УРСС.
11. Потапов А.В., Чернявский А.Ф. Статистические методы измерений в экспериментальной ядерной физике. 1980. Москва: Атомиздат.
12. Rabotkin V.A., Bliznyakov N.M., Vakhtel V.M., Kostomakha D.E. // NUCLEUS-2022: Fundamental Problems and Applications. Book of Abstracts. 2022. Moscow. P. 302–304.
Review
For citations:
Rabotkin V.A., Blizniakov N.M., Vahtel V.M., Kostomakha D.E. METHOD OF PROCESSING, ANALYZING, AND PREDICTING CHARACTERISTICS OF RADIATION FLUXES FROM SMALL-VOLUME SAMPLES. Nuclear Physics and Engineering. 2025;16(4):472-482. (In Russ.) https://doi.org/10.56304/S2079562924060290. EDN: MMXJJG
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