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Speed of Convergence of Chernoff Approximations to Solutions of Evolution Equations
Mathematical notes. 2020. Vol. 108. No. 3. P. 451–456.
Short communication is presented without abstract
Kh. Kh. Abdullin, D. B. Mokeev, D. S. Taletskii, Mathematical notes 2026 Vol. 119 No. 1 P. 3–7
By the Ramsey number R(K1,s,Pt) one means the least positive integer n such that, for every n-vertex graph G, the following condition holds: either G contains a vertex of degree at least s or the complement of G contains a simple t-path. In this paper, we fi nd precise values of R(K1,s,Pt) for certain values ...
Added: June 10, 2026
Springer, 2026.
The book presents the proceedings of the 13th International Conference on Frontiers of Intelligent Computing: Theory and Applications (FICTA 2024), held at Intelligent Systems Research Group (ISRG), London Metropolitan University, London, United Kingdom, during June 6–7, 2025. Researchers, scientists, engineers and practitioners exchange new ideas and experiences in the domain of intelligent computing theories with ...
Added: June 8, 2026
Flamarion M. V., Pelinovsky E., Nonlinear Dynamics 2026 Vol. 114 Article 784
In this article, we investigate wave packet and solitary wave dynamics in the Whitham–Ostrovsky (WO) equation. By means of a multiple-scales expansion, we formally derive a nonlinear Schrödinger (NLS) equation governing the envelope evolution.The corresponding modulational stability diagram is then obtained using the Lighthill criterion. We show that sufficiently large values of the low-frequency dispersive term render ...
Added: June 5, 2026
Medvedev T. V., Pochinka O., Chaos 2026 Vol. 36 No. 6 Article 063107
We consider 3-diffeomorphisms with source–sink dynamics where Smale solenoids play the role of the source and the sink (NSSS-diffeomorphisms). It is known that such diffeomorphisms exist only on lens spaces. On the 3-sphere, every NSSS-diffeomorphism is associated with an exchangeable braid. An exchangeable braid with the strand number n was constructed for each n 3 in such a way ...
Added: June 4, 2026
Kazakov A., Mints D., Petrova I. et al., Chaos 2026 Vol. 36 No. 6 Article 063112
We study hyperbolic chaotic dynamics for maps of a two-dimensional torus. We introduce a two-parameter family of diffeomorphisms which, as we show, demonstrates all types of hyperbolic chaotic dynamics that can appear in the two-dimensional case. In addition, we describe all the bifurcations responsible for the transitions between these chaotic regimes. ...
Added: June 4, 2026
Nozdrinova E., Pochinka O., Shmukler V., Математический сборник 2026 Т. 217 № 6 С. 71–89
Гомеоморфизмы топологических пространств называются эквивалентными по надстройке, если надстройки над ними топологически эквивалентны. В частности, топологически сопряженные гомеоморфизмы эквивалентны по надстройке. Известно, что для гомологически неприводимых гомеоморфизмов их топологическая сопряженность является необходимым и достаточным условием их эквивалентности по надстройке. Тогда как инварианты топологической сопряженности гомологически приводимых гомеоморфизмов во многих случаях являются избыточными для эквивалентности по ...
Added: June 3, 2026
Gnetov F., Konakov V., Успехи математических наук 2026 Т. 81 № 3 (489) С. 161–162
Пусть M обозначает симметрическое пространство некомпактного типа ранга 1. Опираясь на фундаментальную работу [1], в [2] было показано, что плотность соответствующим образом нормированной суммы независимых Hn-значных случайных величин, определенная через сложение Мёбиуса в модели шара Пуанкаре, сходится к фундаментальному решению соответствующего уравнения теплопроводности. Пределом являлся нормальный закон на Hn, соответствующий ядру теплопроводности, определяемому оператором Лапласа–Бельтрами. ...
Added: June 2, 2026
Gorbounov Vassily, Kazakov A., Data Analytics and Topology 2025 Vol. 1 No. 1 P. 33–45
A classic problem in data analysis is studying the systems of subsets defined by either a similarity or a dissimilarity function on X which is either observed directly or derived from a data set.
For an electrical network there are two functions on the set of the nodes defined by the resistance matrix and the response ...
Added: May 28, 2026
Kazimirov D., Rybakova E., Vitalii V. Gulevskii et al., IEEE Access 2025 Vol. 13 P. 20101–20132
The Hough (discrete Radon) transform (HT/DRT) is a digital image processing tool that has become indispensable in many application areas, ranging from general image processing to neural networks and X-ray computed tomography. The utilization of the HT in applied problems demands its computational efficiency and increased accuracy. The de facto standard algorithm for the fast ...
Added: May 28, 2026
Kazimirov D., Vitalii Gulevskii, Kroshnin A. et al., Mathematics 2026 Article 1136
The Hough transform (HT) is widely used in computer vision, tomography, and neural networks. Numerous algorithms for HT computation have been proposed, making their systematic comparison essential. However, existing comparative methodologies are either non-universal and limited to certain HT formulations, or task-oriented, relying on application-specific criteria that do not fully capture algorithmic properties. This paper ...
Added: May 28, 2026
Degtyarev A., Bakhurin S., Yudin N., DSPA 2026 P. 1–6
This paper investigates one possible solution to the problem of self-interference cancellation (SIC) arising in the design of in-band full-duplex (IBFD) communication systems. Self-interference cancellation is performed in the digital domain using multilayer nonlinear models adapted via gradient-based optimization. The presence of local minima and saddle points during the adaptation of multilayer models limits the ...
Added: May 26, 2026
Dymov A. V., Kuksin S., Труды Математического института им. В.А. Стеклова РАН 2024 Т. 327 С. 79–86
Предложена конструктивная форма метода Ньютона–Канторовича для построения решений эволюционных уравнений с малыми нелинейностями, применимая к уравнениям в линейных пространствах, не являющихся банаховыми. Описано лишь основное содержание метода без конкретизации используемых норм и необходимых ε–δ-деталей. ...
Added: May 8, 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
Oleg E. Galkin, Ivan D. Remizov, Israel Journal of Mathematics 2025 Vol. 265 P. 929–943
This paper studies the rates of convergence of Chernoff approximations to operator semigroups. We show that the convergence, in general, can be arbitrarily fast or arbitrarily slow. Under natural assumptions, the main result provides an upper estimate for the convergence rates. As an illustration, the result is applied to the study of Chernoff approximations for ...
Added: November 23, 2024
M. V. Kukushkin, Lobachevskii Journal of Mathematics 2023 Vol. 44 No. 8 P. 3411–3429
This paper is partly a historical survey of various approaches and methods in the
fractional calculus, partly a description of the Kipriyanov extraordinary theory in comparisonwith the
classical one. The significance and outstanding methods in constructing the independent Kipriyanov
fractional calculus theory are convexly stressed, also we represent modern results involving the
Kipriyanov operator and corresponding generalization under the ...
Added: November 27, 2023
Maksim V. Kukushkin, Mathematics 2022 Vol. 10 No. 13 Article 2237
Our first aim is to clarify the results obtained by Lidskii devoted to the decomposition on
the root vector system of the non-selfadjoint operator. We use a technique of the entire function theory
and introduce a so-called Schatten–von Neumann class of the convergence exponent. Considering
strictly accretive operators satisfying special conditions formulated in terms of the norm, we ...
Added: November 26, 2023
Maksim V. Kukushkin, Fractal and Fractional 2022 Vol. 6 No. 5 Article 229
In this paper, we consider evolution equations in the abstract Hilbert space under the
special conditions imposed on the operator at the right-hand side of the equation. We establish the
method that allows us to formulate the existence and uniqueness theorem and find a solution in
the form of a series on the root vectors of the right-hand ...
Added: November 26, 2023
Maksim V. Kukushkin, Axioms 2022 Vol. 11 No. 9 Article 434
In this paper, having introduced a convergence of a series on the root vectors in the AbelLidskii sense, we present a valuable application to the evolution equations. The main issue of the
paper is an approach allowing us to principally broaden conditions imposed upon the second term of
the evolution equation in the abstract Hilbert space. In ...
Added: November 26, 2023
Maksim V. Kukushkin, Fractal and Fractional 2023 Vol. 7 No. 2 Article 111
In this paper, we define an operator function as a series of operators corresponding to the
Taylor series representing the function of the complex variable. In previous papers, we considered
the case when a function has a decomposition in the Laurent series with the infinite principal part
and finite regular part. Our central challenge is to improve this ...
Added: November 26, 2023
Драгунова К. А., Никбахт Н., Remizov I., 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 ...
Added: November 10, 2023
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
Vedenin A., Журнал Средневолжского математического общества 2022 Т. 24 № 3 С. 280–288
This paper is devoted to a new method for constructing approximations to the solution of a parabolic partial differential equation. The Cauchy problem for the heat equation on a straight line with a variable heat conduction coefficient is considered. In this paper, a sequence of functions is constructed that converges to the solution of the ...
Added: May 18, 2023
A. E. Rassadin, Журнал Средневолжского математического общества 2023 Vol. 25 No. 1 P. 542–533
In the present paper, a nonlinear countable-dimensional system of integrodifferential equations is investigated, whose vector of unknowns is a countable set of functions of two variables. These variables are interpreted as spatial coordinate and time. The nonlinearity of this system is constructed from two simultaneous convolutions: first convolution is in the sense of functional analysis ...
Added: April 4, 2023
Алексеева Е. С., Рассадин А. Э., Вестник Дагестанского государственного университета 2020 Т. 35 № 3 С. 7–11
Approximate conformal mapping of the exterior of the domain on phase plane restricted by phase trajectory of the weakly nonlinear oscillator on the exterior of the unit disk is calculated in the paper. The aim of this consideration is to clarify the interrelation of Hamiltonian systems on plane with discovered at the beginning of our ...
Added: December 16, 2022