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U-max-Statistics and limit Theorems for perimeters and areas of random polygons
Journal of Multivariate Analysis. 2014. Vol. 127. No. 5. P. 98–111.
Koroleva E. V., Nikitin Y. Y.
Recently Lao and Mayer (2008) considered U-max-statistics, where the maximum of kernels over the set of indices is studied instead of the usual sums. Such statistics emerge frequently in stochastic geometry. The examples include the largest distance between random points in a ball, the maximal diameter of a random polygon, the largest scalar product within a sample of points, etc. Their limit distributions are related to the distributions of extreme values. Among the results obtained by Lao and Mayer, the limit theorems for the maximal perimeter and the maximal area of random triangles inscribed in a circumference are of great interest. In the present paper, we generalize these theorems to the case of convex m-polygons, m ≥ 3, with random vertices on the circumference. In addition, a similar problem for the minimal perimeter and the minimal area of circumscribed m-polygons is solved in this paper. This problem has not been studied in the literature so far.
Irkutsk: ISDCT SB RAS, 2026.
We study a model problem on the filtration of a conducting fluid through a
porous layer. A porous medium is presented as an assemblage of identical spherical
cells. Each cell consists of a porous core and liquid shell. We derive apriori estimates
for flow characteristics which show the specific behavior of the fluid. Our estimates
are validated numerically. ...
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М.: Наука и технологии, 2026.
«Телекоммуникации» ежемесячный рецензируемый производственный, информационно-аналитический и учебно-методический журнал выходит в свет с июля 2000 г.
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МФТИ, 2025.
абота редакции научного журнала «Труды Московского физико-технического института» (кратко «Труды МФТИ»), редакционной коллегии и редакционного совета осуществляется в соответствии с Положением, утвержденным ректором института. В состав редакционной коллегии входят руководители института, факультетов, институтских и факультетских кафедр. Главный редактор журнала —президент МФТИ, член-корр. РАН Кудрявцев Н.Н.
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Springer, 2026.
This book presents established and new research on the close connections between graph games and systems of logic, particularly existing and newly designed modal logics. The volume utilizes two graph games – the sabotage game and the hide-and-seek game – to demonstrate the natural interplay between designing new graph games and exploring new kinds of ...
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Pochinka O., Barinova M., Journal of Geometry and Physics 2026 Vol. 228 P. 1–8
In the present paper we consider an Ω-stable 3-diffeomorphism with a solid or thickened surfaced non-trivial basic set. Such basic sets include, for instance, all one-dimensional expanding attractors and those two-dimensional basic sets that are not expanding. We prove that the chain recurrent set of every such a diffeomorphism necessarily contains at least two non-trivial ...
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German O., Illarionov A., Известия РАН. Серия математическая 2026 Т. 90 № 3 С. 3–18
Пусть симплекс с целочисленными вершинами - содержащий ровно одну целочисленную точку, отличную от своих вершин. В работе доказывается, что если точка находится во внутренности симплекса или в относительной внутренности некоторой гиперграни симплекса, то объем симплекса ограничен величиной, зависящей только от размерности, в противном случае объем симплекса может быть сколь угодно большим. Этот результат применяется для вывода асимптотической формулы для среднего числа вершин полиэдров ...
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Ivchenko A., Nigmatullin R. R., Dorokhin S. V., Mathematics 2021 Vol. 9 No. 4 Article 381
n this paper, we focus on the generalization of the Hurst empirical law and suggest a set of reduced parameters for quantitative description of long-time series. These series are usually considered as a specific response of a complex system (economic, geophysical, electromagnetic and other systems), where successive fixations of external factors become impossible. We consider ...
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Ivchenko A., Shestoperov A. I., Fomina E. V., Microgravity Science and Technology 2025 Vol. 37 No. 19 P. 1–19
The paper is dedicated to the analysis of medico-biological data obtained during locomotor testing of astronauts. Accurate data interpretation plays a crucial role in locomotion system monitoring, prophylaxis of long-duration spaceflight negative effects and thus in the development of an autonomous medical support system for deep space expeditions. During the locomotor testing the astronaut changes ...
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Gadzhimirzaev S., Хельвас А. В., 2023 3rd International Conference on Innovative Research in Applied Science, Engineering and Technology (IRASET) Mohammedia, Morocco 2023 P. 1–6
The article proposes the architecture for eventdriven Emergency Operation Center with Machine Vision Component. Sources of information are analyzed and approaches to machine vision events for tactical situations detection and estimation are discussed. Messages from Machine Vision Components are converted to Common Alerting Protocol and processed by Operation Center environment for tactical situations recognition. ...
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Gadzhimirzaev S., Хельвас А. В., Лукьянченко П. П., Computer Research and Modeling 2023 Vol. 15 No. 1 P. 129–140
In this article we propose a new approach to the analysis of econometric industry parameters for the industry consolidation level. The research is based on the simple industry automatic control model. The state of the industry is measured by quarterly obtained econometric parameters from each industry’s company provided by the tax control regulator. An approach ...
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Бестолкова Г. В., Теория языка и межкультурная коммуникация 2022 № 4(47) С. 25–35
The article is aimed at considering Franco-Provençal and Occitan languages in order to delimit these languages’ areas and to eliminate erroneous use of the terms “Provençal language” and “Franco-Provençal language” in Russian linguistics. Material contained in the article can serve as basis for fundamental scientific works as well as be of interest to linguists, philologists ...
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Бестолкова Г. В., Теория языка и межкультурная коммуникация 2023 № 2 (49) С. 1–12
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Kulya M., Pusev R., Moskvitin D., , in: 2025 International Russian Smart Industry Conference (SmartIndustryCon).: Sochi: IEEE, 2025. P. 83–88.
We claim the method to obtain a reliable queuing one-way delay metric for the wireless computer networking systems. The method requires only a measurement of the timestamp series between packet departure and arrival events. These timestamps are included inside the packets with stream frames. Thus, the method does not need to involve any additional probe ...
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Simarova E., Journal of Mathematical Sciences 2023 Vol. 273 P. 844–860
The convex hull of several i.i.d. beta distributed random vectors in ℝd is called the random beta polytope. Recently, the expected values of their intrinsic volumes, number of faces, normal and tangent angles and other quantities have been calculated, explicitly and asymptotically. In the present paper, we aim to investigate the asymptotic behavior of the ...
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Yakov Nikitin, Simarova E., Journal of Applied Probability 2022 Vol. 59 No. 3 P. 825–848
U-max statistics were introduced by Lao and Mayer in 2008. Such statistics are natural
in stochastic geometry. Examples are the maximal perimeters and areas of polygons and
polyhedra formed by random points on a circle, ellipse, etc. The main method to study
limit theorems for U-max statistics is via a Poisson approximation. In this paper we
consider a general ...
Added: November 15, 2024
Ya. Yu. Nikitin, Metrika 2018 Vol. 81 No. 6 P. 609–618
We consider two scale-free tests of normality based on the characterization of the symmetric normal law by
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We studied the information basis for the assessment of wind power potential on the territory of Russia. We described the methodology to determine the parameters of the Weibull function, which reflects the density of distribution of probabilities of wind flow speeds at a defined basic height above the surface of the earth using the available ...
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