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Conditions for L² -dissipativity of an explicit symmetric finite-difference scheme for linearized 2D and 3D gas dynamics equations with a regularization
Discrete and Continuous Dynamical Systems - Series B. 2023. Vol. 28. No. 3. P. 1571–1589.
We study an explicit two-level in time and symmetric in space finite-difference scheme for a linearized 2D and 3D gas dynamic system of equations with a kinetic-type regularization. For an initial-boundary value problem on any nonuniform rectangular mesh, sufficient Courant-type conditions for the $L^2$-dissipativity are derived for the first time by the energy method. For the Cauchy problem on the uniform mesh, recent both necessary conditions and sufficient conditions for the $L^2$-dissipativity in the spectral method are improved. A new form for the relaxation parameter is suggested which guarantees that the Courant-type number is uniformly bounded from above and below with respect to the mesh and the Mach number.
Ivchenko A., Nigmatullin R. R., Dorokhin S. V., Mathematics 2026 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 ...
Added: June 27, 2026
Ivchenko A., Шестопёров А. И., Фомина Е. В., 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 ...
Added: June 26, 2026
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. ...
Added: June 26, 2026
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 ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., International Frequency Sensor Association (IFSA) Publishing, 19-21 February 2025 Granada, Spain 2025 P. 172–176
The paper presents models for an innovative fully robotic warehouse for storing boxed goods. A discrete multiagent simulation of the movement of shuttles in a warehouse for a given sequence of pallet shipments has been implemented. Different strategies for placement of boxes in various areas of a warehouse are evaluated, as well as optimal routing ...
Added: June 26, 2026
Fedorov Timofey, Moscow Mathematical Journal 2026 Vol. 26 No. 1 P. 73–85
We obtain a complete list of smooth projective threefolds over C for which the dimension of the space of vanishing cycles (in H2(Y,Q) of the smooth hyperplane section Y) equals 2. We also obtain a complete list of rank 2 very ample vector bundles E on smooth projective surfaces with c2(E)=3. ...
Added: June 25, 2026
Воронеж: Издательский дом ВГУ, 2026.
В сборнике представлены материалы докладов и лекций, включенных в программу весенней математической школы. ...
Added: June 25, 2026
Воронеж: Издательский дом ВГУ, 2026.
В сборнике представлены материалы докладов и лекций,
включенных в программу Воронежской зимней матаматической школы С. Г. Крейна - 2026. ...
Added: June 25, 2026
Gadzhimirzaev S., Хельвас А. В., Computer Research and Modeling 2026 Vol. 18 No. 2 P. 423–438
This article presents a model of a fully automated warehouse with deep storage racks designed
for boxed goods storage. The study focuses on optimizing warehouse operations through discrete
multiagent simulation of shuttle movements for pallet loading and unloading tasks. The authors
investigate various product placement strategies, including the Nearest Channel Positioning Algorithm
(NCPA), Most Empty ChannelGroup Placement (MECGP), and ...
Added: June 24, 2026
Gaianov N., Parusnikova A., Уфимский математический журнал 2026 Т. 18 № 2 С. 14–22
We consider an algebraic 𝑞–difference equation. We propose a sufficient condition for the existence of a formal power–logarithmic expansion in the vicinity of zero of the solution to such an equation. We apply this sufficient condition to construct the formal expansion of a solution to a certain 𝑞–difference analogue of the fifth Painlevé equation for
particular ...
Added: June 24, 2026
Buryak A., Clader E., Tessler R., Journal of Differential Geometry 2024 Vol. 128 No. 1 P. 1–75
We conclude the construction of $r$-spin theory in genus zero for Riemann surfaces with boundary. In particular, we define open $r$-spin intersection numbers, and we prove that their generating function is closely related to the wave function of the $r$th Gelfand--Dickey integrable hierarchy. This provides an analogue of Witten's $r$-spin conjecture in the open setting ...
Added: June 23, 2026
Buryak A., Shadrin S., Epijournal de Geometrie Algebrique 2024 Vol. 8
We present a family of conjectural relations in the tautological cohomology of the moduli spaces of stable algebraic curves of genus g with n marked points. A large part of these relations has a surprisingly simple form: the tautological classes involved in the relations are given by stable graphs that are trees and that are decorated only by powers ...
Added: June 23, 2026
A. Zlotnik, T. Lomonosov, Lobachevskii Journal of Mathematics 2025 Vol. 46 No. 11 P. 5718–5731
We deal with the 1D quasi-gasdynamic (QGD) system of equations and a two-level explicit in time and three-point symmetric in space conservative difference scheme that approximates it, in the case of general equations of state.
Both the QGD system and scheme are linearized at any constant background solution (with non-zero or zero velocity). Matrices of their convective ...
Added: October 18, 2025
Dubnov Y. A., Bulychev A., Информационные технологии и вычислительные системы 2023 № 1 С. 71–81
In this paper, we investigate a method of approximate entropy estimation, designed to speed up the classical method of maximum entropy estimation due to the use of regularization in the optimization problem. This method is compared with the method of maximum likelihood and Bayesian estimation, both experimentally and in terms of theoretical calculations for some ...
Added: June 16, 2023
Zlotnik A., Lomonosov T., / Series arXiv "math". 2023. No. 2305.10522.
We deal with the reduced four-equation model for dynamics of the heterogeneous compressible binary mixtures with the stiffened gas equations of state. We study its further reduced form, with the excluded volume concentrations and a quadratic equation for the common pressure of the components, that can be called a quasi-homogeneous form. We prove new properties of ...
Added: May 28, 2023
Zlotnik A., Lomonosov T., Entropy 2023 Vol. 25 No. 1 Article 158
We deal with multidimensional regularized systems of equations for the one-velocity and one-temperature inert gas mixture dynamics consisting of the balance equations for the mass of components and the momentum and total energy of the mixture, with diffusion fluxes between the components as well as the viscosity and heat conductivity terms. The regularizations are kinetically motivated and aimed at ...
Added: January 10, 2023
Zlotnik A.A., Doklady Mathematics 2022 Vol. 106 No. 2 P. 380–385
A regularization of two types and aggregation are performed for the system of equations of motion for a multivelocity mixture of viscous incompressible fluids, and new multivelocity and single-velocity systems are constructed. For all of them, elliptic equations for the pressure and dissipative balance equations for the total energy of the mixture (the sum of its kinetic ...
Added: November 11, 2022
Salnikov A., Stepanova I., Gudkova T. et al., , in: 2021 14th International Conference Management of large-scale system development (MLSD).: IEEE, 2021. P. 1–3.
We have constructed an analytical model of the magnetic field over a region of the Martian surface using satellite raw data and S-approximations within the modified structural-parametric approach. The method mentioned above implies considering the environment features as a function included in an integral. We approximated the anomalous field by the sum of simple and ...
Added: October 30, 2022
Gudkova T. V., Stepanova I. E., Batov A. et al., Inverse Problems in Science and Engineering 2021 Vol. 29 No. 6 P. 790–804
The connection of different modifications of the method of linear integral representation is studied. Solutions of the related inverse problems based upon a ‘hybrid version of two approximations’ of the topography and geopotential fields enable more refined tuning of the method in solving the inverse problems of geophysics and geomorphology and more complete allowance for ...
Added: October 29, 2022
Stepanova I. E., Gudkova T. V., Salnikov A. M. et al., Inverse Problems in Science and Engineering 2022 Vol. 30 No. 1 P. 41–60
A new three-staged technique based on various versions of the linear integral representation method (S-, F- and R-approximations) is applied to solve the problem of analytical modelling of the magnetic field on the surface of Mars. At the first step, we build an analytical approximation from the given data set (in local or regional cases). ...
Added: October 28, 2022
Zlotnik A.A., Doklady Mathematics 2022 Vol. 106 No. 1 P. 236–242
We study an explicit two-level finite-difference scheme for a linearized multidimensional quasigasdynamic system of equations. For an initial-boundary value problem on a nonuniform rectangular mesh,
sufficient conditions of Courant-type for L^2-dissipativity are derived for the first time by applying the energy
method. For the Cauchy problem on a uniform mesh, both necessary and sufficient conditions for L^2-dissipativity ...
Added: September 7, 2022
Zlotnik A., Discrete and Continuous Dynamical Systems - Series B (США) 2023 Vol. 28 No. 3 P. 1571–1589
We study an explicit two-level in time and symmetric in space finite-difference scheme for a linearized 2D and 3D gas dynamic system of equations with a kinetic-type regularization. For an initial-boundary value problem on any nonuniform rectangular mesh, sufficient Courant-type conditions for the $L^2$-dissipativity are derived for the first time by the energy method. For the Cauchy ...
Added: June 20, 2022
Zlotnik A., Symmetry 2021 Vol. 13 No. 11 Article 2184
We deal with 2D and 3D barotropic gas dynamics system of equations with two viscous regularizations: so-called quasi-gas dynamics (QGD) and quasi-hydrodynamics (QHD) ones. The system is linearized on a constant solution with any velocity, and an explicit two-level in time and symmetric three-point in each spatial direction finite-difference scheme on the uniform rectangular mesh is ...
Added: November 12, 2021
Lomonosov T., Journal of Mathematical Sciences 2021 Vol. 255 No. 4 P. 459–466
We propose an algorithm for linearizing systems of partial differential equations at constant solutions. The algorithm is based on an isomorphism constructed between the ring of linearized functions and the ring of special matrices, which makes it possible to simplify calculations in the process of linearization. The algorithm is illustrated by applying it to the ...
Added: May 9, 2021