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Abstract: The logistic equation with delay and diffusion and with nonclassical boundary conditions is studied. The stability of a nontrivial equilibrium state is investigated, and the resulting bifurcations are studied numerically. PubDate: 2024-08-09 DOI: 10.1134/S1064562424702132
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Abstract: We define a divisible completion of the solvable Baumslag-Solitar group \(BS(1,n)\) and prove that under certain restrictions on n the elementary theory of this completion is decidable. PubDate: 2024-08-09 DOI: 10.1134/S1064562424601239
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Abstract: To satisfy the conditions of Jacobi’s theorem on the last multiplier, the existence of an invariant measure and a sufficient number of independent first integrals are needed. In this case, the system can be locally integrated by quadratures. There are examples of systems for which the existence of partial first integrals is sufficient for the possibility of integration by quadratures. Moreover, integration by quadratures occurs at the level of partial first integrals. In this paper, Jacobi’s theorem on the last multiplier is extended to the general situation when the first integrals include partial ones. PubDate: 2024-08-09 DOI: 10.1134/S1064562424702144
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Abstract: The concept of a conic function with operator coefficients on a conic metric space is introduced. A zero existence theorem is proved for such functions. On this basis, a fixed point theorem for a multivalued self-mapping of a conic metric space is obtained, which generalizes the recent fixed point theorem of E.S. Zhukovskiy and E.A. Panasenko for a contracting multivalued mapping of a conic metric space with an operator contracting coefficient. Coincidence theorems for two multivalued mappings of conic metric spaces are obtained, which generalize the author’s previous results on coincidences of two multivalued mappings of metric spaces. PubDate: 2024-07-31 DOI: 10.1134/S1064562424601306
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Abstract: A finite-volume algorithm with splitting over physical processes is developed to model nonstationary problems of laser thermochemistry with catalytic nanoparticles in subsonic gas flows. Two-phase flows in a heated pipe with laser radiation and radical kinetics of nonoxidative methane conversion are simulated. It is shown that the conversion of methane at the outlet of the pipe is more than 60% with predominant formation of ethylene and hydrogen. PubDate: 2024-07-31 DOI: 10.1134/S1064562424702107
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Abstract: The paper proposes a new approach to control the process of general education. Digital tools are used to form spaces of goals, tasks and learning activities, and to record the educational process of each student. Artificial intelligence tools are used when choosing a student’s personal goals and ways to achieve them, to make forecasts and recommendations to participants in the educational process. Big data from the entire education system and big linguistic models are used. The effects of the approach include ensuring the success of each student, objective assessment of the work of teachers and schools, and the adequacy of the succession process to higher education. PubDate: 2024-07-31 DOI: 10.1134/S1064562424702119
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Abstract: Volterra integro-differential equations with operator coefficients in Hilbert spaces are studied. Previously obtained results are used to establish the relationship between the spectra of operator functions that are the symbols of the specified integro-differential equations and the spectra of generators of operator semigroups. Representations of solutions for the considered integro-differential equations are obtained on the basis of spectral analysis of generators of operator semigroups and corresponding operator functions. PubDate: 2024-07-31 DOI: 10.1134/S1064562424601240
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Abstract: An original method for processing large factor models based on graph condensation using machine learning models and artificial neural networks is developed. The proposed mathematical apparatus can be used to plan and manage complex organizational and technical systems, to optimize large socioeconomic objects of national scale, and to solve problems of preserving the health of the nation (searching for compatibility of medications and optimizing health care resources). PubDate: 2024-07-31 DOI: 10.1134/S1064562424702090
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Abstract: It is proved that the coefficients of the interpolation polynomial over a parallelepipedal grid for a multidimensional function are equal to the coefficients of the interpolation polynomial over a uniform grid for a one-dimensional function. These coefficients can be obtained by applying the fast Fourier transform based on various schemes. PubDate: 2024-07-17 DOI: 10.1134/S1064562424702065
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Abstract: We consider a model of current distribution in a tungsten sample and a vapor layer produced when the surface is heated by an electron beam. The model is based on solving electrodynamic equations and a two-phase Stefan problem in cylindrical coordinates. Based on the temperature distribution in the computational domain, the electrical resistance and thermopower are calculated via an integral over the electron energy at each grid node. The electromagnetic field configuration is a possible source of rotation of the substance, which is observed in experiments. The simulation results demonstrate the role of thermionic emission and the way of model development. The model parameters are taken from experiments at the Beam of Electrons for materials Test Applications (BETA) facility created at the Budker Institute of Nuclear Physics of the Siberian Branch of the Russian Academy of Sciences. PubDate: 2024-07-17 DOI: 10.1134/S1064562424601070
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Abstract: We consider a non-self-adjoint Schrödinger operator on the unit interval with Dirichlet conditions perturbed by an operator of small translation. The main result is a three-term asymptotic expansion for the eigenvalues with respect to their index, and this asymptotics is uniform in the small translation. We also show that the system of eigenfunctions and generalized eigenfunctions of the considered operators forms a Bari basis in the space of square integrable functions on the considered unit interval. PubDate: 2024-07-17 DOI: 10.1134/S1064562424702077
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Abstract: Upwind bicompact schemes of third-order approximation in space are presented for the first time. A formula is obtained for the transition factor of an arbitrary fully discrete bicompact scheme with Runge–Kutta time stepping. Stability and monotonicity of a scheme of first order in time are investigated, and the dissipative and dispersion properties of a scheme of third order in time are analyzed. Advantages of the new schemes over their centered counterparts are demonstrated. PubDate: 2024-07-17 DOI: 10.1134/S1064562424702089
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Abstract: We present a new result on the generalisation of A.G. Postnikov’s formula to the case of powers of 2. This, together with the original work of A.G. Postnikov and some structural theorems on reduced residue systems modulo prime-power ideals, is used to obtain estimates for certain character sums in algebraic number fields. PubDate: 2024-06-20 DOI: 10.1134/S1064562424601185
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Abstract: Two problems of sub-Lorentzian geometry on the Martinet distribution are studied. For the first one, the reachable set has a nontrivial intersection with the Martinet plane, while a trivial intersection occurs for the second problem. Reachable sets, optimal trajectories, and sub-Lorentzian distances and spheres are described. PubDate: 2024-06-20 DOI: 10.1134/S1064562424702053
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Abstract: In a complex Banach algebra, under the assumptions of separateness and spectral separateness, invertibility conditions for the Vandermonde matrix are formulated and proved. Necessary and sufficient conditions for the invertibility of the Vandermonde matrix are given. Analogues of Sylvester’s theorem are formulated. PubDate: 2024-06-20 DOI: 10.1134/S1064562424702041
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Abstract: Two methods for quantitatively assessing the chirality of a set are considered. As a measure of the noncoincidence between two sets, one method uses the area of the symmetric difference between them, and the other, the Hausdorff distance between them. It is shown that these methods, generally speaking, do not provide a correct quantitative estimate for a fairly wide class of sets, such as bounded Borel sets. Using examples of flat triangles and convex quadrangles, we consider the problem of dividing geometric objects into right- and left-handed ones. For triangles, level lines of two versions of the chirality measure are calculated on the plane of angular parameters. For a spatial helix, the values of two versions of the chirality index are found by calculating the mixed product of vectors and the Hausdorff distance between two sets, respectively. PubDate: 2024-06-10 DOI: 10.1134/S106456242470203X
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Abstract: For arbitrary continuous functions on the interval [0, 1], we obtain an interpolation formula based on known values of these functions on some uniform grid. No additional assumptions about the functions are required. The construction of such a formula is connected with the properties of local Bernstein polynomials and the Riemann zeta function. Numerical results for the interpolation of functions of the Riemann, Weierstrass, Besicovitch, and Takagi types are presented. PubDate: 2024-06-10 DOI: 10.1134/S1064562424702028
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Abstract: Using the recoupling theory, we define a representation of the pure braid group and show that it is not trivial. PubDate: 2024-05-13 DOI: 10.1134/S1064562424701977
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Abstract: We prove that for any \(\varepsilon > 0\) and \({{n}^{{ - \frac{{e - 2}}{{3e - 2}} + \varepsilon }}} \leqslant p = o(1)\) the maximum size of an induced subtree of the binomial random graph \(G(n,p)\) is concentrated asymptotically almost surely at two consecutive points. PubDate: 2024-05-13 DOI: 10.1134/S1064562424701989
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