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Properties of an aggregated quasi-gasdynamic system of equations for a homogeneous gas mixture
Doklady Mathematics . 2021. Vol. 104. No. 3. P. 340–346.
For an aggregated quasi-gasdynamic system of equations for a homogeneous gas mixture, we give an entropy balance equation with a nonnegative entropy production in the presence of diffusion fluxes. We also derive the existence, uniqueness, and L^2 -dissipativity of weak solutions to an initial-boundary value problem for the system linearized at a constant solution. Additionally, the Petrovskii parabolicity and local-in-time classical unique solvability of the Cauchy problem for the quasi-gasdynamic system itself are established.
Kupavskii A., Noskov F., Forum of Mathematics, Sigma 2026 Vol. 14 Article 124
We call a family of $s$ sets $\{F_1, \ldots, F_s\}$ a sunflower with $s$ petals if, for any distinct $i, j \in [s]$, one has $F_i \cap F_j = \cap_{u = 1}^s F_u$. The set $C = \cap_{u = 1}^s F_u$ is called the {\it core} of the sunflower. It is a classical result of ...
Added: October 8, 2026
Flamarion M. V., Pelinovsky E., Chaos, Solitons and Fractals 2026 Vol. 213 No. 2 Article 119245
This article concerns the study of modulational instability in the rotated-modified Gardner–Whitham (rmGW) equation. This model incorporates both quadratic and cubic nonlinearities, similarly to the Gardner equation, while also retaining the fully dispersive character of the Whitham equation together with a large-scale dispersive term analogous to that in the Ostrovsky equation. Using a classical multiple-scale asymptotic expansion, we ...
Added: October 8, 2026
Люксембург А. А., УРСС, 2005.
Изучается возможность автоматизированного построения математических теорий. Рассматривается дедуктивная система, основанная на языке логики предикатов первого порядка, объектами системы являются математические выражения или формулы, которые описывают математические объекты или их свойства. В дедуктивной системе выводятся математические определения и теоремы. Для доказательства теорем используются методы автоматического доказательства. Разработан алгоритм, выводящий часть формул системы. Для решения задачи используется аппарат математической ...
Added: October 7, 2026
Bernardin C., Gonçalves P., Olla S., Mathematical Physics Analysis and Geometry 2024 Vol. 27 No. 7
We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit. We prove that the distribution of these fluctuations converge to a gaussian space-time field that is delta correlated in time but with long-range correlations in space. ...
Added: October 6, 2026
Bernardin C., Chhaibi R., Najnudel J. et al., Probability Theory and Related Fields 2026 Vol. 195 P. 1823–1875
We study the celebrated Shiryaev-Wonham filter (Wonham, W.M., in J. Soc. Ind. Appl. Math. 347–369, 1964) in its historical setup, where the hidden Markov jump process has two states. We are interested in the weak noise regime for the observation equation. Interestingly, this becomes a strong noise regime for the filtering equations. Earlier results of ...
Added: October 5, 2026
Ismailov A., Spiridonov V., Успехи математических наук 2026 Т. 81 № 5 С. 183–184
Получена новая формула для цепной дроби Аски–Вильсона в форме отношения двух q-гипер-геометрических рядов. ...
Added: October 5, 2026
Abdulkhaev K., Shirokov D., Advances in Applied Clifford Algebras 2026 Vol. 36 P. 1–21
In this paper, we present explicit formulas for the inverse and determinant in geometric (Clifford) algebras over vector spaces of dimension n = 7. The derivation of these formulas is made possible by generalizing the concept of conjugation to basis conjugation operations. We further develop a general method for constructing such formulas over odd-dimensional spaces ...
Added: October 4, 2026
Kuninets A., IEEE Transactions on Information Theory 2026 P. 1–1
In this work we study the applicability of Quasi-Cyclic Subfield Subcodes of Dual Elliptic (QC-SSDE) codes for integration into code-based cryptographic schemes. Detailed algorithms are provided for constructing parity-check matrices as well as block-circulant parity-check matrices for this family of codes, accompanied by empirical results that enable the construction of QC-SSDE codes with predetermined dimensions. ...
Added: October 3, 2026
Medvedev G., Alexandrov Artem, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2026 Vol. 114 Article 044102
Graphons are measurable functions used to describe the asymptotic behavior of convergent graph families. Originally motivated by problems in combinatorics and graph theory, graphons have found numerous applications in the modeling and analysis of dynamical processes on networks. In this work, we use graphons to formulate the Ising model on convergent graph sequences, which include ...
Added: October 2, 2026
Pochinka O., Baranov D., Nozdrinova E., Теоретическая и математическая физика 2026 Т. 229 № 1 С. 3–14
The Birman–Williams problem on describing the planetary link of a fibered knot K in S^3 has been partially solved. Using Nielsen's theory for the classification of periodic surface homeomorphisms and its close relationship with the theory of gradient-like diffeomorphisms, it is proved that the planetary link of the trefoil (the unique periodic fibered knot of genus ...
Added: October 2, 2026
Lubashevsky I., Lubashevskiy V., Physica D: Nonlinear Phenomena 2026 Vol. 498 Article 135441
We develop a novel cloud-function formalism describing the dynamical relationship between sensory-information processing in large-scale brain networks (supraliminal processing) and the content of the mental representation of an observed object. The formalism combines elements of neural field theory for large-scale neural activity with the spatial characteristics of perceived objects and their embedding in the environment ...
Added: October 2, 2026
Zlotnik A., Математические заметки 2026 Т. 120 № 6 С. 1005–1009
Численным методам решения систем газодинамических уравнений посвящена обширная литература. Ранее было разработано и успешно апробировано специальное семейство симметричных по пространству консервативных разностных методов, основанных на предварительной кинетической, точнее, квазигазодинамической (КГД), регуляризации этих уравнений. Актуальной задачей является построение численных методов, которые обладают не только свойством консервативности по массе, импульсу и полной энергии, но и удовлетворяют условиям энтропийной ...
Added: October 1, 2026
Vyugin I. V., Sashadhar D., Algebra and Number Theory 2026 P. 1–10
We study the K-Fibonacci sequence Fp modulo prime p. Cardinalities of sets |Fp+Fp| and |Fp⋅Fp| are estimated. We present the method of estimating doubling constant of some m-dimensional recurrent sets in Fp. ...
Added: October 1, 2026
Kuksin S., Dynamical Systems 2026
We study the mixing properties of discrete-time and continuous-time dissipative dynamical systems driven by bounded mixing random forces. The continuous-time systems are
reduced to discrete-time random dynamical systems generated by time-one maps, so that
the main analysis is carried out in the discrete setting. We introduce a class of mixing random forcings whose regular conditional distributions with ...
Added: October 1, 2026
Kuksin S., Shirikyan A., Journal of Dynamics and Differential Equations 2026 P. 1098–1100
The paper deals with the problem of large-time behaviour of trajectories for discrete-time dynamical systems driven by a random noise. Assuming that the phase space is finite-dimensional and compact, and the noise is a Markov process with a transition probability satisfying some regularity hypotheses, we prove that all the trajectories converge to a unique measure ...
Added: October 1, 2026
Potanin B., Dolgikh S., Statistics and Probability Letters 2027 Article 110984
We derive bounds on the gradient and Hessian of the log-CDF, ln F(x), of the multivariate normal distribution. These bounds scale linearly and quadratically in ‖x‖ , respectively, with constants depending only on the covariance matrix. We demonstrate the usefulness of these bounds by proving asymptotic normality of the maximum-likelihood estimator of the multivariate probit ...
Added: October 1, 2026
A. V. Pereskokov, Journal of Mathematical Sciences 2026 Vol. 302 No. 4 P. 531–545
We consider the Zeeman effect problem for the hydrogen atom in a magnetic field using
irreducible representations of the Karasev–Novikova algebra with quadratic commutation
relations. We find the asymptotics of a series of eigenvalues and the corresponding
asymptotic eigenfunctions near the upper boundaries of spectral clusters. ...
Added: October 1, 2026
Fedchenko A., Journal of Mathematical Sciences 2023 Vol. 270 No. 6 P. 815–826
We consider regularizations of systems of equations for a multicomponent gas mixture dynamics in the barotropic multi-velocity and one-velocity cases. Energy balance equations are derived for them.
For the system of equations in the one-velocity case, the system linearized on a constant solution is studied, and, for the weak solutions to the initial-boundary value problem with ...
Added: May 11, 2023
A. A. Zlotnik, T. A. Lomonosov, Computational Mathematics and Mathematical Physics (Germany) 2022 Vol. 62 No. 11 P. 1817–1837
We study an explicit two-level finite difference scheme on staggered meshes, with a quasi-hydrodynamic regularization, for 1D barotropic gas dynamics equations. We derive both necessary conditions and sufficient conditions close to them, for $L^2$-dissipativity of solutions to the Cauchy problem linearized on a constant solution, for any background Mach number $M$. We apply the spectral approach and analyze matrix ...
Added: October 18, 2022
Zlotnik A.A., Fedchenko A.S., Differential Equations 2022 Vol. 58 No. 3 P. 341–356
We study a quasihydrodynamic system of equations for a homogeneous (with common velocity and temperature) multicomponent gas mixture in the absence of chemical reactions with a common regularizing velocity. For this system, we derive an entropy balance equation with nonnegative entropy production in the presence of diffusion flows of the mixture components. In the absence of diffusion ...
Added: May 13, 2022
Zlotnik A., Fedchenko A., Mathematical Methods in the Applied Sciences 2022 Vol. 45 No. 15 P. 8906–8927
Two aggregated regularized systems of equations for a multicomponent homogeneous gas mixture are considered.
An entropy balance equation with a non-negative entropy production is derived for them in the presence of diffusion fluxes. The existence, uniqueness and $L^2$-dissipativity of weak solutions to an initial-boundary value problem for the systems linearized on a constant solution are established. The Petrovskii ...
Added: January 12, 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
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
Zlotnik A., Lomonosov T., Математическое моделирование 2021 Т. 33 № 5 С. 16–34
We study explicit two-level finite-difference schemes on staggered meshes for two known regularizations of 1D barotropic gas dynamics equations including schemes with discretizations in x that possess the dissipativity property with respect to the total energy. We derive criterions of L^2-dissipativity in the Cauchy problem for their linearizations at a constant solution with zero background ...
Added: April 1, 2021