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Теоретико-числовые методы в приближенном анализе
MCCME, 2004.
Коробов Н. М.
Ustinov A., Быковский В. А., Известия РАН. Серия математическая 2009 Т. 73 № 4 С. 17–36
In connection with the two-dimensional model known as the ‘periodic Lorentz gas’, we study the asymptotic behaviour of statistical characteristics of a free path interval of a point particle before its first occurrence in an h-neighbourhood (a circle of radius h) of a non-zero integer point as h→0 given that the particle starts from the h-neighbourhood of the origin. We evaluate the limit distribution ...
Added: October 10, 2025
German O., Успехи математических наук 2023 Т. 78 № 2(470) С. 71–148
Diophantine exponents are some of the simplest quantitative characteristics responsible for the approximation properties of linear subspaces of a Euclidean space. This survey is aimed at describing the current state of the area of Diophantine approximation that studies Diophantine exponents and relations they satisfy. We discuss classical Diophantine exponents arising in the problem of approximating zero ...
Added: February 18, 2024
Oleg N. German, Monatshefte fur Mathematik 2022 Vol. 197 No. 4 P. 579–606
In this paper we consider a multiparametric version of Wolfgang Schmidt and Leonard Summerer’s parametric geometry of numbers. We apply this approach in two settings: the first one concerns weighted Diophantine approximation, the second one concerns Diophantine exponents of lattices. In both settings we use multiparametric approach to define intermediate exponents. Then we split the ...
Added: October 28, 2022
Высоцкий Л. И., Смирнов А. В., Тыртышников Е. Е., Lobachevskii Journal of Mathematics 2021 Vol. 42 P. 1608–1621
Numerical integration is a classical problem emerging in many fields of science. Multivariate integration cannot be approached with classical methods due to the exponential growth of the number of quadrature nodes. We propose a method to overcome this problem. Tensor-train decomposition of a tensor approximating the integrand is constructed and used to evaluate a multivariate ...
Added: October 31, 2021
Belomestny D., Iosipoi L., Mathematics and Computers in Simulation 2021 No. 181 P. 351–363
Markov Chain Monte Carlo methods become increasingly popular in applied mathematics as a tool for numerical integration with respect to complex and high-dimensional distributions. However, application of MCMC methods to heavy-tailed distributions and distributions with analytically intractable densities turns out to be rather problematic. In this paper, we propose a novel approach towards the use ...
Added: October 31, 2020
Grabchak M., Molchanov S., Theory of Probability and Its Applications 2019 Vol. 63 No. 4 P. 634–647
In this paper we study the asymptotic distributions, under appropriate normalization, of the sum $S_t = \sum_{i=1}^{N_t} e^{t X_i}$, the maximum $M_t = \max_{i\in\{1,2,\dots,N_t\}} e^{tX_i}$, and the $l_t$ norm $R_t=S_t^{1/t}$, when $N_t\to\infty$ as $t\to\infty$ and $X_1,X_2,\dots$ are independent and identically distributed random variables in the maximum domain of attraction of the reverse-Weibull distribution. ...
Added: November 15, 2019
Kalmynin A. B., Современные проблемы математики 2017 № 24 С. 7–45
Статья содержит обзор докладов международной Конференции памяти А.А. Карацубы по теории чисел и приложениям, прошедшей с 28 по 30 января 2016 года в Математическом институте им. В.А. Стеклова и на механико-математическом факультете МГУ. ...
Added: November 23, 2017
Ismagilov R. S., Filippova L., Вестник Московского государственного технического университета им. Н.Э. Баумана. Серия Естественные науки 2017 № 2 С. 12–21
The study examines the problem of approximate integration of multivariable functions. These functions are taken from a space with Gaussian measure. According to it, we calculated the average value of the integral standard deviation from theintegral sum. The paper gives the vanishing order for the standard deviation depending on the parameters that define the integral ...
Added: June 5, 2017
Aksenov S. A., Bober S. A., Nikolaeva Y. A. et al., / ЦНИИмаш. 2015.
В работе предлагается методика расчета ограниченных орбит вокруг точки либрации L2 системы Солнце-Земля. Движение космического аппарата (КА) в окрестности точки либрации рассматривается как суперпозиция трех компонент: убывающей (устойчивой), возрастающей (неустойчивой) и ограниченной. Предлагаемая методика позволяет скорректировать вектор состояния КА, таким образом, чтобы нейтрализовать неустойчивую компоненту движения. На основе численных расчетов, выполненных с помощью данной методики, произведено ...
Added: October 12, 2015
Frolenkov D., Известия РАН. Серия математическая 2012 Т. 76 № 4 С. 125–184
We get an asymptotic formula for the mean value of Frobenius numbers wiyh three arguments when averaged with respect to three parameters ...
Added: November 1, 2014
Frolenkov D., Kan I. D., Moscow Journal of Combinatorics and Number Theory 2014 Vol. 4 No. 1 P. 78–117
Zaremba's conjecture (1971) states that every positive integer number can be represented as a denominator (continuant) of a finite continued fraction with all partial quotients being bounded by an absolute constant A. Recently (in 2011) several new theorems concerning this conjecture were proved by Bourgain and Kontorovich. The easiest of them states that the set of ...
Added: November 1, 2014
Norman G., Stegailov V., Mathematical Models and Computer Simulations 2013 Vol. 5 No. 4 P. 305–333
The work is devoted to fundamental aspects of the classical molecular dynamics method, which was developed half a century ago as a means of solving computational problems in statistical physics and has now become one of the most important numerical methods in the theory of condensed state. At the same time, the molecular dynamics method ...
Added: March 19, 2014
Morozenko V. V., Pleshkova I. Y., Information Theories & Applications 2013 Vol. 20 No. 3 P. 252–262
It is shown that genetic algorithms can be used successfully in problems of definite integral calculation especially when an integrand has a primitive which can't be expressed analytically through elementary functions. A testing of the program, which uses the genetic algorithm developed by authors, showed that the best results are reached if the size of ...
Added: March 5, 2014
Makarov I., / Математические заметки. 2012. № -.
Выпуклая оболочка всех целых точек в некомпактном полиэдре замкнута и является обобщенным полиэдром лишь при некоторых условиях. В работе доказывается, что если ограничиться целыми точками во внутренности полиэдра, большинство условий можно опустить. При этом получается объект со схожими свойствами, который совпадает с полиэдром Клейна в случае иррационального симплициального конуса. ...
Added: September 28, 2012