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Численное исследование скорости сходимости черновских аппроксимаций к решениям уравнения теплопроводности
Журнал Средневолжского математического общества. 2023. Т. 25. № 4. С. 255–272.
Chernoff approximations are a flexible and powerful tool of functional analysis, which can be used, in particular, to find numerically approximate solutions of some differential equations with variable coefficients. Such approximations have already been constructed for many classes of equations, however, the question of the rate of convergence of approximations has not even been raised until recently. The present work is devoted to the construction of examples illustrating (by means of computer calculation) the convergence rate of Chernoff approximations to the solution of the Cauchy problem for the heat conduction equation, considering two Chernoff functions and several initial conditions of different smoothness.
Publication based on the results of:
Шиманогов И. Н., Vyalyi M., Дискретный анализ и исследование операций 2025 Т. 32 № 4 С. 213–230
A well-studied class of algorithmic problems is that of regular realizability: checking the non-emptiness of the intersection of a regular language with a given language. This problem has a natural algebraic interpretation: verifying whether an element of a Boolean algebra belongs to the kernel of a certain homomorphism. This motivates the consideration of an analogous ...
Added: July 12, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Springer, 2027.
The series Lecture Notes in Computer Science (LNCS), including its subseries Lecture Notes in Artificial Intelligence (LNAI) and Lecture Notes in Bioinformatics (LNBI), has established itself as a medium for the publication of new developments in computer science and information technology research, teaching, and education. LNCS enjoys close cooperation with the computer science R & ...
Added: July 8, 2026
Маликов М. А., Монахова Э. А., Rzaev E. et al., Ученые записки Казанского университета. Серия: Физико-математические науки 2026 Т. 168 № 2 С. 269–286
This article examines series of families of two-dimensional circulant networks with rectangular
L -shapes, optimal in diameter, as network-on-chip topologies with a minimal number of crossings
between the links and a bounded length of the maximum link that does not depend on the network
size. New network-on-chip routing algorithms, which use the coordinates of three adjacent zeros in
the ...
Added: July 8, 2026
Pilé I., Shchur L., Deng Y., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 Article 014101
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Swendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for models in different universality classes: Ising model, Potts model with three components, and four-state Potts model. The overlap of two ...
Added: July 6, 2026
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. ...
Added: July 5, 2026
М.: Наука и технологии, 2026.
«Телекоммуникации» ежемесячный рецензируемый производственный, информационно-аналитический и учебно-методический журнал выходит в свет с июля 2000 г.
Для руководителей и работников промышленности, научно-исследовательских и проектно-конструкторских институтов, высших учебных заведений, аспирантов и студентов, а также для специалистов, разрабатывающих, выпускающих и эксплуатирующих средства телекоммуникаций.
Новости разработок и производства, прогнозы развития, защита информации, Нормативные, справочные, аналитические и учебно-методические материалы.
Переход к глобальному информационному ...
Added: July 4, 2026
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.
Журнал «Труды МФТИ» входит в базу данных РИНЦ (Российский Индекс Научного Цитирования) и доступен в электронной ...
Added: July 4, 2026
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 ...
Added: June 30, 2026
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 ...
Added: June 30, 2026
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 ...
Added: June 29, 2026
Remizov I., Владикавказский математический журнал 2025 Vol. 27 No. 4 P. 124–135
The Chernoff approximation method is a powerful and flexible tool of functional analysis, which allows in many cases to express exp(tL) in terms of variable coefficients of a linear differential operator L. In this paper, we prove a theorem that allows us to apply this method to find the resolvent of L. Our theorem states ...
Added: February 19, 2026
Ivan D. Remizov, Working papers by Cornell University. Series math "arxiv.org" 2023 Article 1
Abstract. The method of Chernoff approximation is a powerful and flexible tool of functional analysis that in many cases allows expressing exp(tL) in terms of variable coefficients of linear differential operator L. In this paper we prove a theorem that allows us to apply this method to find the resolvent of operator L. We demonstrate ...
Added: November 10, 2023
Mazzucchi S., Moretti V., Remizov I. et al., Mathematische Nachrichten 2023 Vol. 296 No. 3 P. 1244–1284
Chernoff approximations of Feller semigroups and the associated diffusion pro-cesses in Riemannian manifolds are studied. The manifolds are assumed to beof bounded geometry, thus including all compact manifolds and also a widerange of non-compact manifolds. Sufficient conditions are established for a classof second order elliptic operators to generate a Feller semigroup on a (gener-ally non-compact) ...
Added: October 23, 2022
Vedenin A., Voevodkin V., Galkin V. et al., Mathematical notes 2020 Vol. 108 No. 3 P. 451–456
Short communication is presented without abstract ...
Added: December 29, 2021
Dragunova K., Гаращенкова А. А., Remizov I., / Series arXiv "math". 2021.
Chernoff approximations are a flexible and powerful tool of functional analysis, which can be used, in particular, to find numerically approximate solutions of some differential equations with variable coefficients. For many classes of equations such approximations have already been constructed, however, the speed of their convergence to the exact solution has not been properly studied. ...
Added: December 16, 2021
Galkin O., Remizov I., Математические заметки 2022 Т. 111 № 2 С. 297–299
Despite the fact that Chernoff's theorem has been published for more than 50 years ago and since then it has been actively used (including, for example, for building of the Smolyanov surface measure), only a small number of results are known on the rate of convergence of Chernoff approximations. In this message we announce some ...
Added: October 14, 2021
Pavel S. Prudnikov, / Series math "arxiv.org". 2020.
Paul Chernoff in 1968 proposed his approach to approximations of one-parameter operator semigroups while trying to give a rigorous mathematical meaning to Feynman's path integral formulation of quantum mechanics. In early 2000's Oleg Smolyanov noticed that Chernoff's theorem may be used to obtain approximations to solutions of initial-value problems for linear partial differential equations (LPDEs) ...
Added: December 16, 2020
Vedenin A., Remizov I., / Series math "arxiv.org". 2020.
Abstract. The method of Chernoff approximation was discovered by Paul Chernoff in 1968 and now is a powerful and flexible tool of contemporary functional analysis. This method is different from grid-based approach and helps to solve numerically the Cauchy problem for evolution equations, e.g., for heat equation and for more general parabolic second-order partial differential equations ...
Added: December 14, 2020
Vedenin A., Воеводкин В. С., Galkin V. et al., Математические заметки 2020 Т. 108 № 3 С. 463–468
This communication is devoted to establishing the very first steps in study of the speed at which the error decreases while dealing with the based on the Chernoff theorem approximations to one-parameter semigroups that provide solutions to evolution equations. ...
Added: October 21, 2019
Vedenin A., Galkin V., Karatetskaia E. et al., / Series arXiv "math". 2020.
This communication is devoted to establishing the very first steps in study of the speed at which the error decreases while dealing with the based on the Chernoff theorem approximations to one-parameter semigroups that provide solutions to evolution equations. ...
Added: October 12, 2019