?
On dissipativity of linearized 1d quasi-gasdynamic system of equations and its difference approximation for general equations of state
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 and dissipative terms are the same, and after respective scaling, they both become symmetric and depend mainly on the background ``signed'' Mach number and the ratio of the specific heats as well as the QGD parameters. Moreover, their form is almost the same as in the previously studied basic particular case of the perfect polytropic gas. This allows us to extend results on $L^2$-dissipativity of the QGD system and the scheme to the general case.
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
Netherlands: ScienceDirect, 2025.
No ...
Added: June 28, 2026
Seidel A., Weske M., Montali M. et al., Information Systems 2026 Vol. 141 Article 102728
Business process management employs process models and event logs to represent the behavior of the information systems under study. Traditional case-centric notions consider the order of activities and events in isolated process instances. The emerging field of object-centric processes challenges this assumption by putting objects in the center. Object-centric process mining and modeling approaches identify ...
Added: June 27, 2026
IEEE, 2024.
A.S. Popov Russian Science and Technical Society with support from V. A. Trapeznikov Institute of Control Sciences, V.A. Kotelnikov Institute of Radio Engineering and Electronics, Autex Ltd. is leading the ХХVIII International Conference «Digital Signal Processing and its Applications — DSPA-2024» ...
Added: June 27, 2026
Ivchenko A., Дворкович А. В., Телекоммуникации 2020 Т. 12 С. 2–11
Dynamic Adaptive Streaming over HTTP (DASH) technology powers most multimedia services. Its specific features (re-buffering, quality switching, etc.) necessitate the development of specialized methods for assessing user subjective quality of experience (QoE) based on objective parameters. This article examines the impact of various metrics on QoE and presents assessment models with Spearman correlation coefficients up ...
Added: June 27, 2026
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
Zlotnik A., Applied Mathematics Letters 2026 Vol. 173 Article 109793
The system of equations for dynamics of the heterogeneous multicomponent mixtures with the common temperature, pressure and velocity of components is considered in the case of general equations of state. The phase transitions are taken into account. Recently, a kinetic (quasi gasdynamic)-type regularization of the system has been developed and verified in computer simulations in ...
Added: October 23, 2025
Zlotnik A., Lomonosov T., Mathematical Models and Computer Simulations 2025 Vol. 17 No. 3 P. 352–364
A system of four balance differential equations is used to describe dynamics of heteroge neous compressible binary mixtures with stiffened gas equations of state for the mixture’s components, including gas and liquid ones. The main points are its quasi-homogeneous form, which arises as a result of eliminating volume fractions of components from the collection of ...
Added: July 4, 2025
Zlotnik A., Lomonosov T., Doklady Mathematics 2023 Vol. 108 No. 3 P. 443–449
We consider the so-called four-equation model for dynamics of the heterogeneous compressible binary mixtures with the Noble-Abel stiffened-gas equations of state. We exploit its quasi-homogeneous form that arises after excluding the volume concentrations from the sought functions and is based on a quadratic equation for the common pressure of the components. We present new properties ...
Added: March 1, 2024
Zlotnik A., Lomonosov T., Chaos 2023 Vol. 33 No. 11 Article 113128
We deal with the reduced four-equation model for the dynamics of heterogeneous compressible binary mixtures with the stiffened gas equations of state. We study its further reduced form, with the excluded volume concentrations, and with a quadratic equation for the common pressure of the components; this form can be called a quasi-homogeneous form. We prove new properties ...
Added: October 30, 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. 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 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: August 11, 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.A., Lomonosov T.A., Mathematical Models and Computer Simulations 2021 Vol. 13 No. 6 P. 1097–1108
Explicit two-level difference schemes on staggered meshes are studied for two well-known
regularizations of 1D barotropic gas dynamics equtions, including schemes with discretization in
x with the property of total energy dissipation. The criteria of L^2-dissipativity in the Cauchy problem
are derived for their linearizations on a constant solution with zero background velocity. The criteria for
schemes on nonstaggered and staggered ...
Added: September 21, 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
Zlotnik A., , in: Differential and Difference Equations with Applications. ICDDEA 2019, Lisbon, Portugal, July 1–5Vol. 333.: Springer, 2020. P. 53–67.
We study an explicit two-level in time and three-point symmetric in space finite-difference scheme for 1D barotropic and full gas dynamics systems of equations. The scheme is a linearization at a constant background solution (with an arbitrary velocity) of finite-difference schemes with general viscous regularization. We enlarge recently proved sufficient conditions (on the Courant-like number) for $L^2$-dissipativity in ...
Added: November 1, 2020
Helminck G. F., Poberezhny V. A., Polenkova S. V., Theoretical and Mathematical Physics 2020 Vol. 204 No. 3 P. 1140–1153
We show that both the dKP hierarchy and its strict version can be extended to a wider class of deformations satisfying a larger set of Lax equations. We prove that both extended hierarchies have appropriate linearizations allowing a geometric construction of their solutions. ...
Added: October 28, 2020
Sinelshchikov D., Chaos, Solitons and Fractals 2020 Vol. 141 Article 110318
Nonlinear second-order ordinary differential equations are common in various fields of science, such as physics, mechanics and biology. Here we provide a new family of integrable second-order ordinary differential equations by considering the general case of a linearization problem via certain nonlocal transformations. In addition, we show that each equation from the linearizable family admits ...
Added: September 30, 2020