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Approximate Methods for Solving Hypersingular Integral Equations on Fractals
Ch. 7. P. 81–95.
Boykov I., Boykova A., Potapov A., Alexander E. Rassadin
The paper consists of three parts. The first one is devoted to approximate methods for evaluating Riemann integrals, singular and hypersingular integrals on closed non-rectifiable curves and fractals in the complex plane. An integral on non-rectifiable curves or fractals is defined as a double integral over a region that bounded by a non-rectifiable curve or a fractal. To evaluate double integral cubature formulas have been constructed. The second part contains methods for solving hypersingular integral equations on prefractals. Issues of solvability of singular and hypersingular integral equations with fractal in the right-hand side have been studied in the third part. Singular and hypersingular integral equations that model aerodynamics problems have been investigated. In such cases right-hand side of equations describes the gas flow which is a fractal.
Gafurova D., Sergey Aksenov, Regular and Chaotic Dynamics 2025 Vol. 30 No. 6 P. 969–991
The circular restricted three-body problem is used as an approximate model in space mission planning. Its periodic solutions around equilibrium points, which are referred to as the libration points, are utilized for exploration of possible spacecraft trajectories in the preliminary stages of mission design. In this paper, a numerical methodology for periodic libration point orbits ...
Added: November 24, 2025
Springer, 2023.
This book constitutes the refereed proceedings of the 14th International Conference on Advances in Optimization and Applications, OPTIMA 2023, held in Petrovac, Montenegro, during September 18–22, 2023.
The 21 full papers included in this book were carefully reviewed and selected from 68 submissions. They were organized in topical sections as follows: mathematical programming; global optimization; continuous optimization; ...
Added: December 9, 2023
Dymov A. V., Теоретическая и математическая физика 2023 Т. 214 № 2 С. 179–197
We find asymptotical expansions as $\nu \to 0$ for integrals of the form $\int_{\mathbb{R}^d} F(x) / \big(\omega(x)^2 + \nu^2\big)\, dx$,
where sufficiently smooth functions $F$ and $\omega$ satisfy natural assumptions for their behaviour at infinity and all critical points of the function $\omega$ from the set $\{\omega(x) = 0\}$ are non-degenerate. ...
Added: November 29, 2023
Красавин А. В., Физматлит, 2010.
В книге рассмотрены основные численные методы моделирования квантовых физических систем: метод точной диагонализации гамильтоновой матрицы, квантовый и классический методы Монте-Карло. Объяснены способы выбора адекватного дискретного базиса волновых функций, нахождения спектра и различных корреляционных функций систем, описываемых основными типами квантовых статистик - статистиками Ферми, Бозе и спиновой. Исследованы проблемы численного анализа температурных и термодинамических характеристик различных систем; ...
Added: July 18, 2023
Springer, 2022.
This book constitutes selected and revised papers from the 22nd International Conference on Mathematical Modeling and Supercomputer Technologies, MMST 2022, held in Nizhny Novgorod, Russia, in November 2022.
The 20 full papers and 5 short papers presented in the volume were thoroughly reviewed and selected from the 48 submissions. They are organized in topical secions on computational methods ...
Added: December 26, 2022
Springer, 2022.
This book constitutes the refereed proceedings of the 16th International Conference on Parallel Computational Technologies, PCT 2022, held in Dubna, Russia, during March 29–31, 2022.
The 22 full papers included in this book were carefully reviewed and selected from 60 submissions. They were organized in topical sections as follows: high performance architectures, tools and technologies; parallel ...
Added: August 10, 2022
A semi-implicit unstructured operator-difference scheme for three-dimensional self-gravitating flows
Kondratyev I., Moiseenko S., Journal of Physics: Conference Series 2021 Vol. 2028 No. 1 Article 012007
A support operators (operator-difference) method has proven itself well for implicit simulations of different astrophysical fluid flows. Following the operator-difference approach, we construct nodal difference analogues of differential operators in Cartesian coordinates, where the conjugacy properties are the same as for original ones. Using the difference operators, we develop an Eulerian semi-implicit gas-dynamical solver with ...
Added: February 3, 2022
Gladkov N., Kolesnikov A., Zimin A., Journal of Mathematical Analysis and Applications 2022 Vol. 506 No. 2 Article 125666
The multistochastic Monge–Kantorovich problem on the product X=∏i=1nXi of n spaces is a generalization of the multimarginal Monge–Kantorovich problem. For a given integer number 1≤k<n we consider the minimization problem ∫cdπ→inf on the space of measures with fixed projections onto every Xi1×…×Xik for arbitrary set of k indices {i1,…,ik}⊂{1,…,n}. In this paper we study basic properties of the multistochastic problem, including well-posedness, existence of a dual solution, boundedness and continuity of a dual ...
Added: December 4, 2021
Switzerland: Springer, 2021.
This book constitutes the refereed proceedings of the 12th International Conference on Optimization and Applications, OPTIMA 2021, held in Petrovac, Montenegro, in September-October 2021.
The 22 full and 3 short papers presented were carefully reviewed and selected from 63 submissions. The papers are organized into the following topical sub-headings: mathematical programming, global optimization, discrete and combinatorial ...
Added: November 4, 2021
Granitsa Y.V, , in: IV International Scientific Conference "Competitiveness and the Development of Socio-Economic Systems" dedicated to the memory of Alexander Tatarkin (CDSES - 2020). EpSBS - Volume 105 - CDSES 2020.: European Proceedings of Social and Behavioural Sciences EpSBS, 2021. P. 939–946.
The purpose of the study is to assess the state and dynamics of the region's development. The research object is the production sphere of the Central Federal District - the leader in Russia in terms of socio-economic indicators. Modeling the state of the production system was carried out using stream models of economic dynamics. At ...
Added: November 2, 2021
Azhmyakov V., Fernández-Gutiérrez J. P., Pickl S., Italian Journal of Pure and Applied Mathematics 2017 Vol. 2017 No. 38 P. 653–670
Our paper discusses a novel computational approach to the extended Maximal Covering Location Problem (MCLP). We consider a fuzzy-type formulation of the generic MCLP and develop the necessary theoretical and numerical aspects of the proposed Separation Method (SM). A speciffic structure of the originally given MCLP makes it possible to reduce it to two auxiliary ...
Added: October 30, 2021
Azhmyakov V., Trujillo L. A., Italian Journal of Pure and Applied Mathematics 2017 Vol. 2017 No. 37 P. 219–237
This paper deals with a constrained LQ-type optimal control problem (OCP) in the presence of fixed levels input restrictions. We consider control processes governed by linear differential equations with a priori known control switching structure. The set of admissible inputs reflects some important natural engineering applications and moreover, can also be interpreted as a result ...
Added: October 30, 2021
Kondratyev I., Moiseenko S. G., Бисноватый-Коган Г. С. et al., Monthly Notices of the Royal Astronomical Society 2020 Vol. 497 No. 3 P. 2883–2892
Determination of a magnetic field structure on a neutron star (NS) surface is an important problem of a modern astrophysics. In a presence of strong magnetic fields, a thermal conductivity of a degenerate matter is anisotropic. In this paper, we present 3D anisotropic heat transfer simulations in outer layers of magnetized NSs, and construct synthetic ...
Added: October 14, 2021
Cham: Springer, 2021.
This book constitutes the proceedings of the 20th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2021, held in Irkutsk, Russia, in July 2021.
The 29 full papers and 1 short paper presented in this volume were carefully reviewed and selected from 102 submissions. Additionally, 2 full invited papers are presented in the volume. ...
Added: July 8, 2021
Dymov A. V., Proceedings of the Steklov Institute of Mathematics 2020 Vol. 310 P. 161–175
Added: June 30, 2021
Switzerland: Springer, 2020.
This book constitutes the refereed post-conference proceedings of the 6th Russian Supercomputing Days, RuSCDays 2020, held in Moscow, Russia, in September 2020.*
The 51 revised full and 4 revised short papers presented were carefully reviewed and selected from 106 submissions. The papers are organized in the following topical sections: parallel algorithms; supercomputer simulation; HPC, BigData, AI: ...
Added: December 10, 2020
Springer, 2020.
This edited volume gathers selected, peer-reviewed contributions presented at the fourth International Conference on Differential & Difference Equations Applications (ICDDEA), which was held in Lisbon, Portugal, in July 2019.
First organized in 2011, the ICDDEA conferences bring together mathematicians from various countries in order to promote cooperation in the field, with a particular focus on applications. ...
Added: November 1, 2020
Gladkov N., Kolesnikov A., Zimin A., Calculus of Variations and Partial Differential Equations 2019 Vol. 58 No. 173 P. 1–33
The multistochastic (n, k)-Monge–Kantorovich problem on a product space ∏ni=1Xi∏i=1nXi is an extension of the classical Monge–Kantorovich problem. This problem is considered on the space of measures with fixed projections onto Xi1×⋯×XikXi1×⋯×Xik for all k-tuples {i1,…,ik}⊂{1,…,n}{i1,…,ik}⊂{1,…,n} for a given 1≤k<n1≤k<n. In our paper we study well-posedness of the primal and the corresponding dual problem. Our central result describes a solution ππ to the following important model ...
Added: October 9, 2019
Cham: Springer, 2018.
This book constitutes the refereed proceedings of the 12th International Conference on Parallel Computational Technologies, PCT 2018, held in Rostov-on-Don, Russia, in April 2018.
The 24 revised full papers presented were carefully reviewed and selected from 167 submissions. The papers are organized in topical sections on high performance architectures, tools and technologies; parallel numerical algorithms; supercomputer simulation. ...
Added: March 11, 2019