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Exact Solutions of Incompressible Navier–Stokes Equations in the Case of Oil and Gas Industrial Problems Dokl. Math. (IF 0.548) Pub Date : 2021-03-10 V. B. Betelin, V. A. Galkin, A. O. Dubovik
Abstract Classes of exact solutions corresponding to vortex and potential flows are presented within the framework of a hydrodynamic model describing flows of a viscous incompressible fluid. The study of exact solutions is a prerequisite for creating a core simulator, which is associated with modeling fluid dynamics in a porous medium and the response of the field to dynamic influences in order to
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On Implementation of Boolean Functions by Contact Circuits with a Constant Uniform Width Dokl. Math. (IF 0.548) Pub Date : 2021-03-10 K. A. Popkov
Abstract We introduce the concept of the uniform width of a contact circuit. For each Boolean function, we find the minimal possible value of the uniform width of a contact circuit implementing this function. We prove constructively that this value does not exceed 3. We also establish that, for almost all Boolean functions on n variables, it equals 3.
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Noise-Immune Communication with Orthogonal Frequency Division Multiplexing Using Kravchenko Weight Function Processing Dokl. Math. (IF 0.548) Pub Date : 2021-03-10 V. F. Kravchenko, L. E. Nazarov, V. I. Pustovoit
Abstract Signal structures based on OFDM signals and error-correcting codes resistant to the influence of spectrum-concentrated noise are described. An algorithm for receiving such signal structures with the use of weight functions is presented. It is shown by theoretic analysis and simulations that the class of Kravchenko weight functions based on atomic functions represents nearly optimal windows
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The Kolmogorov Problem on Uniqueness of Probability Solutions of a Parabolic Equation Dokl. Math. (IF 0.548) Pub Date : 2021-03-10 V. I. Bogachev, T. I. Krasovitskii, S. V. Shaposhnikov
Abstract—We give a solution to the Kolmogorov problem on uniqueness of probability solutions to a parabolic Fokker–Planck–Kolmogorov equation.
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Stability Analysis of Artificial Ice Islands by Methods of Mathematical Modeling Dokl. Math. (IF 0.548) Pub Date : 2021-03-10 I. B. Petrov, M. V. Muratov, F. I. Sergeev
Abstract The elastic effects on an artificial ice island produced by drill impacts and the pressure of structures located on the island are numerically modeled. The problem is solved numerically by applying the grid-characteristic method with interpolation on structured and unstructured meshes. The grid-characteristic method most accurately describes dynamic processes in exploration seismology problems
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Orthogonal Elements in Nonseparable Rearrangement Invariant Spaces Dokl. Math. (IF 0.548) Pub Date : 2021-03-10 S. V. Astashkin, E. M. Semenov
Abstract Let E be a nonseparable rearrangement invariant space, and let E0 denote the closure of the set of all bounded functions in E. We study elements of E orthogonal to the subspace E0, i.e., elements \(x \in E\) such that \({{\left\| x \right\|}_{E}} \leqslant {{\left\| {x + y} \right\|}_{E}}\) for any \(y \in {{E}_{0}}\).
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Minimum Clique-Free Subgraphs of Kneser Graphs Dokl. Math. (IF 0.548) Pub Date : 2021-03-10 S. V. Vahrushev, M. E. Zhukovskii, S. G. Kiselev, A. Yu. Skorkin
Abstract The saturation and weak saturation numbers of Kneser graphs with clique patterns are estimated.
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On Dividing Sets into Parts of Smaller Diameter Dokl. Math. (IF 0.548) Pub Date : 2021-03-10 A. M. Raigorodskii
Abstract An important generalization of Borsuk’s classical problem of partitioning sets into parts of smaller diameter is studied. New upper and lower bounds for the Borsuk numbers are found.
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One Problem of Extremal Functional Interpolation and the Favard Constants Dokl. Math. (IF 0.548) Pub Date : 2021-03-10 Yu. S. Volkov
Abstract For an extremal functional interpolation problem first considered by Yu.N. Subbotin, the explicit form of the extremal interpolation constants is calculated in terms of the Favard constants in the spaces Lp, \(p = 1,3{\text{/}}2,2\). Simple efficient recurrence formulas are obtained to calculate the Favard constants, and formulas for calculating these constants in terms of the Euler numbers
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Interpolation of Spaces of Functions of Positive Smoothness on a Domain Dokl. Math. (IF 0.548) Pub Date : 2021-03-10 O. V. Besov
Abstract— An interpolation theorem for spaces of functions of positive smoothness on a domain with flexible cone condition is established.
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Mathematical Modeling of Vibrational Combustion Dokl. Math. (IF 0.548) Pub Date : 2021-03-10 E. V. Radkevich, N. N. Yakovlev, O. A. Vasilieva
Abstract A new model of laminar vibrational combustion is constructed relying on a thermodynamic analysis of the combustion process. Two combustion modes, detonation and deflagration, are modeled. The nature of their origin depending on the structure of the standard chemical potential is established, and a numerical experiment concerning the onset of these combustion modes is carried out. By controlling
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On the Existence of Focus Singularities in One Model of a Lagrange Top with a Vibrating Suspension Point Dokl. Math. (IF 0.548) Pub Date : 2021-03-10 A. V. Borisov, P. E. Ryabov, S. V. Sokolov
Abstract We consider a completely integrable Hamiltonian system with two degrees of freedom that describes the dynamics of a Lagrange top with a vibrating suspension point. The results of a stability analysis of equilibrium positions are clearly presented. It turns out that, in the case of a vibrating suspension point, both equilibrium positions can be unstable, which corresponds to the existence of
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On Moment Methods in Krylov Subspaces Dokl. Math. (IF 0.548) Pub Date : 2021-03-10 V. P. Il’in
Abstract Moment methods in Krylov subspaces for solving symmetric systems of linear algebraic equations (SLAEs) are considered. A family of iterative algorithms is proposed based on generalized Lanczos orthogonalization with an initial vector \({{v}^{0}}\) chosen regardless of the initial residual. By applying this approach, a series of SLAEs with the same matrix, but with different right-hand sides
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On the Finiteness of the Number of Expansions into a Continued Fraction of $$\sqrt f $$ for Cubic Polynomials over Algebraic Number Fields Dokl. Math. (IF 0.548) Pub Date : 2021-03-10 V. P. Platonov, M. M. Petrunin
Abstract We obtain a complete description of cubic polynomials f over algebraic number fields \(\mathbb{K}\) of degree \(3\) over \(\mathbb{Q}\) for which the continued fraction expansion of \(\sqrt f \) in the field of formal power series \(\mathbb{K}((x))\) is periodic. We also prove a finiteness theorem for cubic polynomials \(f \in K[x]\) with a periodic expansion of \(\sqrt f \) for extensions
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On Oscillation Properties of Self-Adjoint Boundary Value Problems of Fourth Order Dokl. Math. (IF 0.548) Pub Date : 2021-03-04 A. A. Vladimirov, A. A. Shkalikov
Abstract The connection between the number of internal zeros of nontrivial solutions to fourth-order self-adjoint boundary value problems and the inertia index of these problems is studied. We specify the types of problems for which such a connection can be established. In addition, we specify the types of problems for which a connection between the inertia index and the number of internal zeros of
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Force Evolutionary Billiards and Billiard Equivalence of the Euler and Lagrange Cases Dokl. Math. (IF 0.548) Pub Date : 2021-03-04 V. V. Vedyushkina, A. T. Fomenko
Abstract A class of force evolutionary billiards is discovered that realizes important integrable Hamiltonian systems on all regular isoenergy 3-surfaces simultaneously, i.e., on the phase 4-space. It is proved that the well-known Euler and Lagrange integrable systems are billiard equivalent, although the degrees of their integrals are different (two and one).
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Problem of Determining the Anisotropic Conductivity in Electrodynamic Equations Dokl. Math. (IF 0.548) Pub Date : 2021-03-04 V. G. Romanov
Abstract For a system of electrodynamic equations, the inverse problem of determining an anisotropic conductivity is considered. It is supposed that the conductivity is described by a diagonal matrix σ(x) = \({\text{diag}}({{\sigma }_{1}}(x),{{\sigma }_{2}}(x)\), σ3(x)) with \(\sigma (x) = 0\) outside of the domain Ω = \(\{ x \in {{\mathbb{R}}^{3}}|\left| x \right| < R\} \), \(R > 0\), and the permittivity
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Sub-Riemannian (2, 3, 5, 6)- Structures Dokl. Math. (IF 0.548) Pub Date : 2021-03-04 Yu. L. Sachkov, E. F. Sachkova
Abstract We describe all Carnot algebras with growth vector (2, 3, 5, 6), their normal forms, an invariant that separates them, and a change of basis that transforms such an algebra into a normal form. For each normal form, Casimir functions and symplectic foliations on the Lie coalgebra are computed. An invariant and normal forms of left-invariant (2, 3, 5, 6)-distributions are described. A classification
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Linear System of Differential Equations with a Quadratic Invariant as the Schrödinger Equation Dokl. Math. (IF 0.548) Pub Date : 2021-03-04 V. V. Kozlov
Abstract Linear systems of differential equations with an invariant in the form of a positive definite quadratic form in a real Hilbert space are considered. It is assumed that the system has a simple spectrum and the eigenvectors form a complete orthonormal system. Under these assumptions, the linear system can be represented in the form of the Schrödinger equation by introducing a suitable complex
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On Global Solvability of Nonlinear Equations with Parameters Dokl. Math. (IF 0.548) Pub Date : 2021-03-04 A. V. Arutyunov, S. E. Zhukovskiy
Abstract We consider smooth mappings acting from one Banach space to another and depending on a parameter belonging to a topological space. Under various regularity assumptions, sufficient conditions for the existence of global and semilocal continuous inverse and implicit functions are obtained. We consider applications of these results to the problem of continuous extension of implicit functions
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3D Filtering of Images Corrupted by Additive-Multiplicative Noise Dokl. Math. (IF 0.548) Pub Date : 2021-01-14 V. F. Kravchenko, V. I. Ponomaryov, V. I. Pustovoit, A. Palacios-Enriquez
Abstract A novel method for filtering images contaminated by mixed (additive-multiplicative) noise is substantiated and implemented for the first time. The method includes several stages: the formation of similar structures in 3D space, homomorphic transformation, a 3D filtering approach based on a sparse representation in the discrete cosine transform space, inverse homomorphic transformation, and
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On the Convergence of Probabilities of First-Order Sentences for Recursive Random Graph Models Dokl. Math. (IF 0.548) Pub Date : 2021-01-14 M. E. Zhukovskii, Yu. A. Malyshkin
Abstract We study first-order zero–one law and the first-order convergence law for two recursive random graph models, namely, the uniform and preferential attachment models. In the uniform attachment model, a new vertex with \(m\) edges chosen uniformly is added at every moment, while, in the preferential attachment model, the distribution of second ends of these edges is not uniform, but rather the
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Adaptive Mesh Refinement Simulations of Gas Dynamic Flows on Hybrid Meshes Dokl. Math. (IF 0.548) Pub Date : 2021-01-14 S. A. Soukov
Abstract An adaptive mesh refinement algorithm for simulations of the Navier–Stokes equations on unstructured hybrid meshes is presented. Numerical results for compressible supersonic flow around a sphere are given.
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Double Potential Method for Modeling the Internal Flow of a Viscous Incompressible Liquid Dokl. Math. (IF 0.548) Pub Date : 2021-01-14 S. V. Polyakov, T. A. Kudryashova, N. I. Tarasov
Abstract The problem of numerical modelling water purification from iron impurities is considered. The cleaning task is relevant for many industrial applications, including the development of new cleaning methods and devices for the preparation of ultrapure water. The performed mathematical study is associated with the calculations of the water flow and the transfer of contaminants in the treatment
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Arithmetic Properties of Euler-Type Series with a Liouvillian Polyadic Parameter Dokl. Math. (IF 0.548) Pub Date : 2021-01-14 V. G. Chirskii
Abstract This paper states that, for any nonzero linear form \({{h}_{0}}{{f}_{0}}(1) + {{h}_{1}}{{f}_{1}}(1)\) with integer coefficients h0, h1, there exist infinitely many p-adic fields where this form does not vanish. Here, \({{f}_{0}}(1) = \mathop \sum \limits_{n = 0}^\infty {{\left( \lambda \right)}_{n}}\) and \({{f}_{1}}\left( 1 \right) = \mathop \sum \limits_{n = 0}^\infty {{\left( {\lambda +
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Two-Stage Method for Solving Systems of Nonlinear Equations and Its Applications to the Inverse Atmospheric Sounding Problem Dokl. Math. (IF 0.548) Pub Date : 2021-01-14 V. V. Vasin, G. G. Skorik
Abstract For an overdetermined system of nonlinear equations, a two-stage method is suggested for constructing an error-stable approximate solution. The first stage consists in constructing a regularized set of approximate solutions for finding normal quasi-solutions of the original system. At the second stage, the regularized quasi-solutions are approximated using an iterative process based on square
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Deviation of an Object with a Striking Device from a Visibility Area of an Observer in $${{\mathbb{R}}^{3}}$$ Dokl. Math. (IF 0.548) Pub Date : 2021-01-14 V. I. Berdyshev
Abstract An autonomous object possessing a high-speed striking device is moving under observation conditions. Threatened by the device, a spatial observer has to hide behind convex fragments of the surrounding terrain. The paper describes the routes from a given movement corridor along which the object could pass remaining hidden from the observer by choosing a suitable velocity of motion.
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Combined Multidimensional Bicompact Scheme with Higher Order Accuracy in Domains of Influence of Nonstationary Shock Waves Dokl. Math. (IF 0.548) Pub Date : 2021-01-14 M. D. Bragin, B. V. Rogov
Abstract For the first time, a method is proposed for constructing a multidimensional combined shock-capturing scheme that monotonically localizes shock wave fronts and, at the same time, has increased accuracy in smoothness regions of calculated generalized solutions. In this method, the solution of the combined scheme is constructed using monotonic solutions of a bicompact scheme of the first order
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An Almost Exact Linear Algorithm for Transformation of Chain-Cycle Graphs with Optimization of the Sum of Operation Costs Dokl. Math. (IF 0.548) Pub Date : 2021-01-14 K. Yu. Gorbunov, V. A. Lyubetsky
Abstract For weighted directed chain-cycle graphs, an algorithm transforming one graph into another is constructed. The algorithm runs in linear time and yields a sequence of transformations with the smallest, up to an additive error, total cost. The costs of the operations of inserting and deleting an edge segment may differ from each other and from the costs of the other operations. The additive
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Three-Dimensional Analogues of the Heath-Brown and Selberg Identities Dokl. Math. (IF 0.548) Pub Date : 2021-01-14 V. A. Bykovskii, A. V. Ustinov
Abstract— Analogues of the Heath-Brown and Selberg identities for three-dimensional Kloosterman sums are proved.
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Absence of Global Periodic Solutions for a Schrödinger-Type Nonlinear Evolution Equation Dokl. Math. (IF 0.548) Pub Date : 2021-01-14 Sh. M. Nasibov
Abstract— The problem of the absence of global periodic solutions for a Schrödinger-type nonlinear evolution equation with a linear damping term is investigated. It is proved that when the damping coefficient is nonnegative, the problem does not have global periodic solutions for any initial data, while when it is negative, the same is valid for “sufficiently large values” of the initial data.
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Kirchhoff Index for Circulant Graphs and Its Asymptotics Dokl. Math. (IF 0.548) Pub Date : 2021-01-14 A. D. Mednykh, I. A. Mednykh
Abstract The aim of this paper is to find an analytical formula for the Kirchhoff index of circulant graphs \({{C}_{n}}({{s}_{1}},{{s}_{2}},\; \ldots ,\;{{s}_{k}})\) and \({{C}_{{2n}}}({{s}_{1}},{{s}_{2}},\; \ldots ,\;{{s}_{k}},n)\) with even and odd valency, respectively. The asymptotic behavior of the Kirchhoff index as n → ∞ is investigated. We proof that the Kirchhoff index of a circulant graph
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Uniqueness of Solutions to Initial Boundary Value Problems for Parabolic Systems in Plane Bounded Domains with Nonsmooth Lateral Boundaries Dokl. Math. (IF 0.548) Pub Date : 2021-01-14 E. A. Baderko, M. F. Cherepova
Abstract We consider initial boundary value problems with boundary conditions of the first or second kind for one-dimensional (with respect to a spatial variable) Petrovskii parabolic systems of the second order with variable coefficients in a bounded domain with nonsmooth lateral boundaries. The uniqueness of regular solutions to these problems in the class of functions that are continuous in the
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Bilinear Weighted Inequalities with Two-Dimensional Operators Dokl. Math. (IF 0.548) Pub Date : 2021-01-14 V. D. Stepanov, G. E. Shambilova
Abstract— A characterization of bilinear inequalities with two-dimensional rectangular Hardy operators in weighted Lebesgue spaces is given.
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On Alternating Quasipositive Links Dokl. Math. (IF 0.548) Pub Date : 2021-01-14 S. Yu. Orevkov
Abstract An effectively verifiable condition for quasipositivity of links is given. In particular, it is proven that if a quasipositive link can be represented by an alternating diagram satisfying the condition that no pair of Seifert circles is connected by a single crossing, then the diagram is positive and the link is strongly quasipositive.
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On the Chromatic Numbers of Random Hypergraphs Dokl. Math. (IF 0.548) Pub Date : 2021-01-14 Yu. A. Demidovich, D. A. Shabanov
Abstract The asymptotic behavior of the chromatic number of the binomial random hypergraph \(H(n,k,p)\) is studied in the case when \(k \geqslant 4\) is fixed, n tends to infinity, and p = p(n) is a function. If p = p(n) does not decrease too slowly, we prove that the chromatic number of \(H(n,k,p)\) is concentrated in two or three consecutive values, which can be found explicitly as functions of n
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Forecasting a Cyclical Downturn (Recession) in the US Economy Using a Mathematical Model of Hyman Minsky’s Theory of Financial Instability Dokl. Math. (IF 0.548) Pub Date : 2021-01-14 A. A. Akaev, V. A. Sadovnichii
Abstract By using the US economy as an example, the paper shows how the COVID-19 pandemic has changed its short-term dynamics, causing a deep crisis recession in 2020 rather than the expected short-term and shallow recession in 2022 caused by the inflation of the financial bubble during the credit expansion that followed the financial and economic crisis of 2008–2009. To predict the latter scenario
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Representations of $$\zeta (2n + 1)$$ and Related Numbers in the Form of Definite Integrals and Rapidly Convergent Series Dokl. Math. (IF 0.548) Pub Date : 2021-01-14 K. A. Mirzoev, T. A. Safonova
Abstract Let \(\zeta (s)\) and \(\beta (s)\) be the Riemann zeta function and the Dirichlet beta function. The formulas for calculating the values of \(\zeta (2m)\) and \(\beta (2m - 1)\) (\(m = 1,\;2,\; \ldots \)) are classical and well known. Our aim is to represent \(\zeta (2m + 1)\), \(\beta (2m)\), and related numbers in the form of definite integrals of elementary functions and rapidly converging
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Explicit Solutions for a Series of Optimization Problems with 2-Dimensional Control via Convex Trigonometry Dokl. Math. (IF 0.548) Pub Date : 2021-01-14 A. A. Ardentov, L. V. Lokutsievskiy, Yu. L. Sachkov
Abstract We consider a number of optimal control problems with 2-dimensional control lying in an arbitrary convex compact set \(\Omega \). Solutions to these problems are obtained using methods of convex trigonometry. The paper includes (1) geodesics in the Finsler problem on the Lobachevsky hyperbolic plane; (2) left-invariant sub-Finsler geodesics on all unimodular 3D Lie groups (\({\text{SU}}(2)\)
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Composition Operators on Weighted Sobolev Spaces and the Theory of $${{\mathcal{Q}}_{p}}$$ -Homeomorphisms Dokl. Math. (IF 0.548) Pub Date : 2021-01-14 S. K. Vodopyanov
Abstract We define the scale \({{\mathcal{Q}}_{p}}\), \(n - 1 < p < \infty \), of homeomorphisms of spatial domains in \({{\mathbb{R}}^{n}}\), a geometric description of which is due to the control of the behavior of the p-capacity of condensers in the image through the weighted p-capacity of the condensers in the preimage. For p = n the class \({{\mathcal{Q}}_{n}}\) of mappings contains the class
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Trajectory Optimality Conditions for Moving Object with Nonuniform Radiation Pattern Dokl. Math. (IF 0.548) Pub Date : 2020-10-19 A. A. Galyaev, P. V. Lysenko, V. P. Iakhno
Abstract The problem of optimal trajectory planning for a moving object with a nonuniform radiation pattern is considered and analytically solved as a variational problem. The object tries to evade detection by a search system consisting of a single sensor. Necessary and sufficient conditions for trajectory optimality are obtained. Analytical expressions for optimal trajectories, the velocity law,
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On Necessary Conditions of Probability Limit Theorems in Finite Algebras Dokl. Math. (IF 0.548) Pub Date : 2020-10-19 A. D. Yashunsky
Abstract We consider the conditions for a finite set with a given system of operations (a finite algebra) to be subject to a probability limit theorem, i.e., arbitrary computations with mutually independent random variables have value distributions that tend to a certain limit (limit law) as the number of random variables used in the computation grows. Such behavior may be seen as a generalization
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Asymptotic Efficiency of Maximum Entropy Estimates Dokl. Math. (IF 0.548) Pub Date : 2020-10-19 Yu. S. Popkov
Abstract The problem of entropy estimation of probability density functions with allowance for real data is posed (the maximum entropy estimation (MEE) problem). Global existence conditions for the implicit dependence of Lagrange multipliers on data collection are obtained. The asymptotic efficiency of maximum entropy estimates is proved.
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On the Dimension of the Congruence Centralizer Dokl. Math. (IF 0.548) Pub Date : 2020-10-19 Kh. D. Ikramov
Abstract Let A be a nonsingular complex (n × n) matrix. The congruence centralizer of A is the collection \(\mathcal{L}\) of matrices X satisfying the relation \(X{\kern 1pt} {\text{*}}AX = A\). The dimension of \(\mathcal{L}\)as a real variety in the matrix space \({{M}_{n}}({\mathbf{C}})\) is shown to be equal to the difference of the real dimensions of the following two sets: the conventional centralizer
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Coadjoint Orbits of Three-Step Free Nilpotent Lie Groups and Time-Optimal Control Problem Dokl. Math. (IF 0.548) Pub Date : 2020-10-19 A. V. Podobryaev
Abstract We describe coadjoint orbits for three-step free nilpotent Lie groups. It turns out that two-dimensional orbits have the same structure as coadjoint orbits of the Heisenberg group and the Engel group. We consider a time-optimal problem on three-step free nilpotent Lie groups with a set of admissible velocities in the first level of the Lie algebra. The behavior of normal extremal trajectories
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Stationary Spherically Symmetric Solutions of the Vlasov–Poisson System in the Three-Dimensional Case Dokl. Math. (IF 0.548) Pub Date : 2020-10-19 J. Batt, E. Jörn, A. L. Skubachevskii
Abstract We consider the three-dimensional stationary Vlasov–Poisson system of equations with respect to the distribution function of the gravitating matter \(f = {{f}_{q}}(r,u)\), the local density \(\rho = \rho (r)\), and the Newtonian potential \(U = U(r)\), where \(r: = {\text{|}}x{\text{|}}\), \(u: = {\text{|}}v{\text{|}}\) (\((x,v) \in {{\mathbb{R}}^{3}} \times {{\mathbb{R}}^{3}}\) are the space–velocity
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Limits for Detailed Description of Problems in Continuous Media Mechanics and Numerical Algorithm for Viscous Gas Flow Simulation Dokl. Math. (IF 0.548) Pub Date : 2020-10-19 A. E. Lutsky, B. N. Chetverushkin
Abstract A mathematical model for viscous gas flow simulation with time scales bounded by the characteristic time between molecular collisions is considered. This approach is a variant of the quasi-gasdynamic system of equations, which is based on the relationship between the kinetic and macroscopic descriptions of continuous medium motion. Based on the presented model, a numerical algorithm is constructed
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Problem of Safely Tracking an Object Avoiding Observation in $${{\mathbb{R}}^{2}}$$ Dokl. Math. (IF 0.548) Pub Date : 2020-10-19 V. I. Berdyshev
Abstract For the problem of an autonomous object moving under hostile observation, the observer’s positions are characterized in which the object following any route can choose a speed mode that allows observation evasion, and positions guaranteeing that the observer is able to track the object on the initial part of the trajectory and only on it are described.
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Terminal Invariance of Jump Diffusions Dokl. Math. (IF 0.548) Pub Date : 2020-10-19 M. M. Khrustalev, K. A. Tsarkov
Abstract— Terminal invariance sufficient conditions for nonlinear dynamical stochastic controllable systems of diffusion-jump type are proposed. These conditions have no analogues in the world literature. Both perturbation invariance conditions (for a fixed initial point) and absolute invariance conditions (ensuring that the terminal criterion takes a constant value for any initial data) are formulated
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Topological Modeling of Integrable Systems by Billiards: Realization of Numerical Invariants Dokl. Math. (IF 0.548) Pub Date : 2020-10-19 V. V. Vedyushkina, V. A. Kibkalo, A. T. Fomenko
Abstract A local version of A.T. Fomenko’s conjecture on modeling of integrable systems by billiards is formulated. It is proved that billiard systems realize arbitrary numerical marks of Fomenko–Zieschang invariants. Thus, numerical marks are not a priori a topological obstacle to the realization of the Liouville foliation of integrable systems by billiards.
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Young Duality and Aggregation of Balances Dokl. Math. (IF 0.548) Pub Date : 2020-10-19 A. A. Shananin
Abstract An operation generalizing convolution is introduced using the Young transform and Fenchel’s duality theorem. Based on this operation, an aggregation procedure for a nonlinear input–output model with concave positively homogeneous production functions is proposed.
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Geometry of Factorization Identities for Discriminants Dokl. Math. (IF 0.548) Pub Date : 2020-10-19 E. N. Mikhalkin, V. A. Stepanenko, A. K. Tsikh
Abstract Let Δn be the discriminant of a general polynomial of degree n and \(\mathcal{N}\) be the Newton polytope of Δn. We give a geometric proof of the fact that the truncations of Δn to faces of \(\mathcal{N}\) are equal to products of discriminants of lesser n degrees. The proof is based on the blow-up property of the logarithmic Gauss map for the zero set of Δn.
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Interference-Based Logic Gates Dokl. Math. (IF 0.548) Pub Date : 2020-10-19 S. A. Stepanenko
Abstract Interference-based logic gates serve as a basis for photonic computers intended (as distinct from quantum computers) for the same class of problems as electronic computers and making it possible to increase performance irrespective of the limitations inherent in electronic technologies. The proposed interference-based logic gates represent a complete basic functional set. They meet the requirement
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On the Motion, Amplification, and Blow-up of Fronts in Burgers-Type Equations with Quadratic and Modular Nonlinearity Dokl. Math. (IF 0.548) Pub Date : 2020-10-19 N. N. Nefedov, O. V. Rudenko
Abstract A singularly perturbed initial-boundary value problem for a parabolic equation, which is called in applications an equation of Burgers type, is considered. Existence conditions are obtained, and an asymptotic approximation of a new class of solutions with a moving front is constructed. The results are applied to problems with quadratic and modular nonlinearity and nonlinear amplification.
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Contact Geometry in Optimal Control of Thermodynamic Processes for Gases Dokl. Math. (IF 0.548) Pub Date : 2020-10-19 A. G. Kushner, V. V. Lychagin, M. D. Roop
Abstract We solve an optimal control problem for thermodynamic processes in an ideal gas. The thermodynamic state is given by a Legendrian manifold in a contact space. Pontryagin’s maximum principle is used to find an optimal trajectory (thermodynamic process) on this manifold that maximizes the work of the gas. In the case of ideal gases, it is shown that the corresponding Hamiltonian system is completely
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Zero Preservation for a Family of Multivalued Functionals, and Applications to the Theory of Fixed Points and Coincidences Dokl. Math. (IF 0.548) Pub Date : 2020-10-19 T. N. Fomenko, Yu. N. Zakharyan
Abstract A theorem on the zero existence preservation for a parametric family of multivalued (α, β)-search functionals on an open subset of a metric space is proved. Several corollaries on the existence preservation for preimages of a closed subspace, for coincidence points, and for common fixed points under the action of a parametric family (a number of families) of mappings are obtained. The notion
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Abductive Reasoning in Explanation Problems of an Observed Effect Dokl. Math. (IF 0.548) Pub Date : 2020-10-19 S. N. Vassilyev
Abstract The problems of artificial intelligence, as well as control and decision-making with incomplete or inaccurate information, cover a wide class of problems of abductive explanation, including tasks in terms of cause–effect. This paper is devoted to the logical formation of hypotheses that explain observed effects. Means of representing knowledge and hypothesizing are proposed. A language is
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Methods for Calculating Zero-Level Instability of Electronic Circuits under Variations in Parameters and External Disturbances Dokl. Math. (IF 0.548) Pub Date : 2020-10-19 V. I. Anisimov, V. N. Gridin
Abstract An important stage in the design of electronic circuits of various classes and purposes is the calculation of the zero-level instability of a developed device under the influence exerted on the parameters of its components by external disturbances (variations in temperature, humidity, pressure, radiation, etc.), as well as by technological variations in these parameters in the course of serial
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On the Problem of Periodicity of Continued Fraction Expansions of $$\sqrt f $$ for Cubic Polynomials over Number Fields Dokl. Math. (IF 0.548) Pub Date : 2020-10-19 V. P. Platonov, M. M. Petrunin, V. S. Zhgoon
Abstract We obtain a complete description of fields \(\mathbb{K}\) that are quadratic extensions of \(\mathbb{Q}\) and of cubic polynomials \(f \in \mathbb{K}[x]\) for which a continued fraction expansion of \(\sqrt f \) in the field of formal power series \(\mathbb{K}((x))\) is periodic. We also prove a finiteness theorem for cubic polynomials \(f \in \mathbb{K}[x]\) with a periodic expansion of \(\sqrt
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Efficient Approximation of the Capacitated Vehicle Routing Problem in a Metric Space of an Arbitrary Fixed Doubling Dimension Dokl. Math. (IF 0.548) Pub Date : 2020-10-19 M. Yu. Khachay, Yu. Yu. Ogorodnikov
Abstract In this paper, for the first time, we provide a quasi-polynomial time approximation scheme for the well-known capacitated vehicle routing problem formulated in metric spaces of an arbitrary fixed doubling dimension.
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