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

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

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.

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

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 +

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

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.

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

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

Abstract— Analogues of the Heath-Brown and Selberg identities for three-dimensional Kloosterman sums are proved.

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.

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

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

Abstract— A characterization of bilinear inequalities with two-dimensional rectangular Hardy operators in weighted Lebesgue spaces is given.

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.

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

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

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

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 (\({\text{SU}}(2)\)

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

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,

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

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.

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

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

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

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

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.

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

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.

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.

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.

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

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.

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

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

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

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

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

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.

The statistical kernel estimator in the Monte Carlo method is usually optimized based on the preliminary construction of a “microgrouped” sample of values of the variable under study. Even for the two-dimensional case, such optimization is very difficult. Accordingly, we propose a combined (kernel-projection) statistical estimator of the two-dimensional distribution density: a kernel estimator is constructed

According to the well-knows Heyde theorem the Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form of independent random variables given the other. We study analogues of this theorem for some locally compact Abelian groups that contain an element of order 2. While coefficients of linear forms are topological automorphisms of a group

Abstract A quasilinear system of hyperbolic equations describing plane one-dimensional relativistic oscillations of electrons in a cold plasma is considered. For a simplified formulation, a criterion for the existence of a global-in-time smooth solution is obtained. For the original system, a sufficient condition for singularity formation is found, and a sufficient condition for the smoothness of the

Abstract Spectral problems for the Dirac operator specified on a finite interval with regular, but not strongly regular boundary conditions and a complex-valued integrable potential are studied. This work is aimed at finding the conditions under which the root function system forms a common Riesz basis rather than a Riesz basis with parentheses.

Abstract Two results concerning the number \(P(2,n)\) of threshold functions and the singularity probability \({{\mathbb{P}}_{n}}\) of random (\(n \times n\)) \({\text{\{ }} \pm 1{\text{\} }}\)-matrices are established. The following asymptotics are obtained: \(P(2,n)\sim 2\left( {\begin{array}{*{20}{c}} {{{2}^{n}} - 1} \\ n \end{array}} \right)\quad {\text{and}}\quad {{P}_{n}}\sim {{n}^{2}} \times

Abstract A new approach to the problems of estimating the global maximum point and the integral of a continuous function on a compact set is proposed. The approach combines a simple Monte Carlo method and the ideas of the Lebesgue theory of measure and integration. Quality estimates for the proposed methods are given.

Abstract In this paper we extend Y. Eliashberg’s theorem on the maps with fold type singularities to arbitrary Thom-Boardman singularities. Namely, we state a necessary and sufficient condition for a continuous map of smooth manifolds of the same dimension to be homotopic to a generic map with a prescribed Thom-Boardman singularity ΣI at each point. In dimensions 2 and 3 we rephrase this condition

Abstract An antipodal nonbipartite distance-regular graph Γ of diameter 3 has an intersection array \(\{ k,(r - 1){{c}_{2}},\;1;\;1,\;{{c}_{2}},\;k\} \) (\({{c}_{2}} < k - 1\)) and eigenvalues k, n, –1, and –m, where n and –m are the roots of the quadratic equation \({{x}^{2}} - ({{a}_{1}} - {{c}_{2}})x - k = 0\). The Krein bound \(q_{{33}}^{3} \geqslant 0\) gives \(m \leqslant {{n}^{2}}\) if \(r \ne

Abstract For two-step free nilpotent Lie algebras, we describe symplectic foliations and Casimir functions. A left-invariant time-optimal problem is considered in which the set of admissible controls is given by a strictly convex compact set in the first layer of the Lie algebra that contains the origin in its interior. We describe integrals for the vertical subsystem of the Hamiltonian system of the

Abstract The classical Pólya–Schur inequality for the logarithmic energy of a point charge distributed on a circle is generalized to the Green energy with respect to the concentric circular ring.

Abstract Let 0 < α, σ < 1 be arbitrary fixed constants, let \({{q}_{1}} < {{q}_{2}} < \ldots < {{q}_{n}} < {{q}_{{n + 1}}}\) < … be the set of primes satisfying the condition \(\{ q_{n}^{\alpha }\} < \sigma \) and indexed in ascending order, and let \(m \geqslant 1\) be any fixed integer. Using an analogue of the Bombieri–Vinogradov theorem for the above set of primes, upper bounds are obtained for

Abstract In the paper, the Cauchy problem for wave equations with constant and variable coefficients is considered. We assume that the initial data are a random function with finite mean energy density and study the convergence of distributions of the solutions to a limiting Gaussian measure for large times. We derive the formulas for the limiting energy current density (in mean) and find a new class

Abstract The problem of seismic wave propagation from a source located in a well is considered. Acoustic equations are used to describe the dynamic behavior of the fluid. The damaged zone is described as a porous fluid-saturated medium by applying the Dorovsky model. The elastic approximation is used to describe the dynamic behavior of the surrounding rock. A unified algorithm based on the grid-characteristic

Abstract The minimax-maximin relations for vector-valued functionals over the real field are studied. An increase in the dimensionality of criteria may result in a violation of some basic relations, for example, in an inequality between maximin and minimax that is always true for classic problems. Accordingly, the conditions for its correctness or violation need to be established. This paper introduces

Abstract In layered media, the solution of Maxwell’s equations suffers a strong or weak discontinuity at the layer boundaries. Finite-difference schemes providing convergence on strong discontinuities have been proposed for the first time. These are conservative bicompact two-point schemes with mesh nodes lying on the layer boundaries. A fundamentally new technique for taking into account the medium

Abstract We propose a new way of justifying the accelerated gradient sliding of G. Lan, which allows one to extend the sliding technique to a combination of an accelerated gradient method with an accelerated variance reduction method. New optimal estimates for the solution of the problem of minimizing a sum of smooth strongly convex functions with a smooth regularizer are obtained.

Abstract The concept of stability of continuous extension of mappings with respect to a Nemytskii superposition operator is studied. Sufficient conditions of such stability with respect to a Nemytskii superposition operator are obtained. The essentiality of the corresponding assumptions is illustrated by examples.

Abstract An approach is proposed to consider heuristic metrics introduced and used in data analysis problems. In the approach, the entire information on pairwise distances expressed by numerical values is reduced to information on a metric belonging as a point of a semi-metric cone to corresponding subcones, which are elements of factor sets for proposed relations of kernel equivalences for mappings

Abstract The central-difference Nessyahu–Tadmor (NT) scheme is considered, which is built using second-order MUSCL reconstruction of fluxes. The accuracy of the NT scheme is studied as applied to calculating shock waves propagating with a variable velocity. It is shown that this scheme has the first order of integral convergence on intervals with one of the boundaries lying in the region of influence

Abstract According to a theorem of Andre Weil, there does not exist a standard Lebesgue measure on any infinite-dimensional locally convex space. Because of that, Schrödinger quantization of an infinite-dimensional Hamiltonian system is often defined using a sigma-additive measure, which is not translation-invariant. In the present paper, a completely different approach is applied: we use the generalized