The paper addresses an initial boundary value problem for a partial differential-algebraic equation involving a parameter. An integral condition with respect to the time derivative of the unknown function is provided ...
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The paper addresses an initial boundary value problem for a partial differential-algebraic equation involving a parameter. An integral condition with respect to the time derivative of the unknown function is provided as an additional condition to determine this parameter. The Dzhumabaev parameterization method is employed to solve the problem. The domain is subdivided, and functional parameters are defined as the values of the solution along the internal lines of the subdomains. This reformulates the original problem into an equivalent initial boundary value problem for a system of hyperbolic equations with parameters and associated functional relations. The paper develops algorithms to solve the problem, demonstrating their applicability. Furthermore, conditions for the existence and uniqueness of a solution to the initial boundary value problem, involving the partial differential-algebraic equation with a parameter and discrete memory, are established.
The goal of this research is to propose a new modification of a non-equilibrium effect in the k-omega$$ k-\omega $$ turbulence model to better predict high-speed turbulent flows. For that, the two local compressibilit...
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The goal of this research is to propose a new modification of a non-equilibrium effect in the k-omega$$ k-\omega $$ turbulence model to better predict high-speed turbulent flows. For that, the two local compressibility coefficients are included in the balance production/dissipation terms in a specific dissipation rate equation. The specific dissipation rate reacts to changes in the local Mach number and density through these local coefficients. The developed model is applied to the numerical simulation of the spatial supersonic turbulent airflow with round hydrogen injection. In that, the effects of the proposed turbulence model on the flow field behavior (shock wave and vortex formations, shock wave/boundary layer interaction, and mixture layer) are studied via the solution of three-dimensional Favre-averaged Navier-Stokes equations with a third-order Essentially Non-Oscillatory scheme. A series of numerical experiments are performed, in which an allowable range of local constants by comparing results with experimental data is obtained. The non-equilibrium modification by simultaneous decrease of the turbulence kinetic energy and increase of the specific dissipation rate gives a good agreement of the hydrogen depth penetration with experimental data. Also, the numerical experiment of the supersonic airflow with a nitrogen jet shows wall pressure distribution is consistent well with experimental data.
We study the class of all strongly constructivizable models having omega-stable theories in a fixed finite rich signature. It is proved that the Tarski-Lindenbaum algebra of this class considered together with a Godel...
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We study the class of all strongly constructivizable models having omega-stable theories in a fixed finite rich signature. It is proved that the Tarski-Lindenbaum algebra of this class considered together with a Godel numbering of the sentences is a Boolean Sigma(1)(1)-algebra whose computable ultrafilters form a dense subset in the set of all ultrafilters;moreover, this algebra is universal with respect to the class of all Boolean Sigma(1)(1)-algebras. This gives a characterization to the Tarski-Lindenbaum algebra of the class of all strongly constructivizable models with omega-stable theories.
This study concentrates on achieving quasi-bipartite synchronization within signed coupled inertial neural networks featuring time-varying delays. The pinning controller technique addresses this problem within a struc...
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This study concentrates on achieving quasi-bipartite synchronization within signed coupled inertial neural networks featuring time-varying delays. The pinning controller technique addresses this problem within a structure incorporating cooperative and competitive interaction among the nodes. With the structurally balanced networks, some linear matrix inequality based sufficient conditions are derived for both reduced and non-reduced order methods with the help of Lyapunov-Krasovskii functional to achieve the quasi-bipartite pinning synchronization criterion. Further, the error bound is derived analytically for the leader-follower representation of the signed coupled inertial neural network model. At last, a numerical simulation result is provided to verify the correctness of the established theoretical results.
We conjecture unimodality for some sequences of generalized Kronecker coefficients and prove it for partitions with at most two columns. The proof is based on a hard Lefschetz property for corresponding highest weight...
We conjecture unimodality for some sequences of generalized Kronecker coefficients and prove it for partitions with at most two columns. The proof is based on a hard Lefschetz property for corresponding highest weight spaces. We also study more general Lefschetz properties, show implications to a higher-dimensional analogue of the Alon-Tarsi conjecture on Latin squares and give related positivity results.
The main aim of this paper is to show that the first singular number of the generalized Cauchy-Dirichlet heat operator is minimized by a circular cylinder among all domains of the same measures with the circular cylin...
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The main aim of this paper is to show that the first singular number of the generalized Cauchy-Dirichlet heat operator is minimized by a circular cylinder among all domains of the same measures with the circular cylinder in Euclidean space. This result gives us an analogue of the celebrated Rayleigh-Faber-Krahn inequality for the absolute value of the heat operator. Further, we obtain an analogue of the Hong-Krahn-Szego inequality for the same operator.
The paper considers an inverse problem and a direct problem for the Burgers equation in a domain with movable boundaries. With the help of an additional condition, a formula is obtained for determining the desired fun...
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The paper considers an inverse problem and a direct problem for the Burgers equation in a domain with movable boundaries. With the help of an additional condition, a formula is obtained for determining the desired function from a direct problem for the loaded Burgers equation for the solvability of which we require a condition on the functions according to which the boundaries of the domain change. The solvability of direct problems is proved using a priori estimates and the methods of Faedo-Galerkin and functional analysis.
In this paper, we present a refined version of the (classical) Stein inequality for the Fourier transform, elevating it to a new level of accuracy. Furthermore, we establish extended analogues of a more precise versio...
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In this paper, we present a refined version of the (classical) Stein inequality for the Fourier transform, elevating it to a new level of accuracy. Furthermore, we establish extended analogues of a more precise version of the Stein inequality for the Fourier transform, broadening its applicability from the range 1 2 to 2 <= p < infinity. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
We present two new compactness criteria in non-commutative quasi-Banach symmetric spaces associated to a finite von Neumann algebra, with focus on the non-commutative torus. The first result is novel, even in the comm...
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We present two new compactness criteria in non-commutative quasi-Banach symmetric spaces associated to a finite von Neumann algebra, with focus on the non-commutative torus. The first result is novel, even in the commutative setting;while the second resembles the Kolmogorov-Riesz compactness theorem (see Theorems 4.1 and 5.7, respectively). The work contributes to understanding a conjecture of Brudnyi, adapted here for the non-commutative torus. (c) 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// ***/licenses/by/4.0/).
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