Abstract A two-dimensional axisymmetric problem of pressure wave propagation in a porous medium of a layered structure is considered. The wave initiated by a pressure pulse in a cavity with a liquid enters and propagates in a layered porous medium. The problem is solved numerically in the framework of the two-velocity, two-stress model of a porous medium. The features of the evolution of elastic waves

Abstract We consider an initial-boundary value problem for the heat equation with an inhomogeneous initial condition and boundary conditions. One of the boundary conditions contains a mixed derivative. When solving this problem by the method of separation of variables, a spectral problem arises. A system of eigenfunctions of this spectral problem and a biorthogonally conjugate system, are constructed

Abstract This paper is dedicated to the solution of a coupled problem on creep and viscoplastic flow in a flat heavy layer. The layer is on an inclined surface and subject to heating and cooling. The problem has been solved in the framework of the large elastoplastic strain mathematical model, which generalized for the case of taking into account rheological and thermophysical material properties.

Abstract Direct numerical simulation is employed to study the complex vortical flow in the wake of a circular cylinder in a rectangular channel at \(\textrm{{Re}}\approx 10^{2}\). Formation and development of vortices behind bodies are governed by two phenomena: Karman street in the central part of the channel and a pair of spiral peripheral vortices near the channel sidewalls. Both of these phenomena

Abstract New probability density functions in the MWDP (Multiple-Wave with Diffuse Power) model is derived for signal fadings description in wireless communication systems.

Abstract The paper addresses the issue of filling the gaps in the semantic library based on the distributional semantics of the terms of its thesaurus and the ontology relations. The goal of the study is to fully reflect the actual structure of relations between mathematical subject domains. This is done through identifying context-sensitive semantic relations, and with the use of an algorithm that

Abstract The problem of the passage of a monoharmonic plane sound wave through a thin composite rectangular plate hingly supported in the aperture of an absolutely rigid partition has been considered. In this work, two-dimensional equations of motion constructed by reduction of three-dimensional equations were used. These equations were based on a discrete structural model of multilayer plates deformation

Abstract We study the properties of generalized solutions in unbounded domains and the asymptotic behavior of solutions of elliptic boundary value problems at infinity. Namely, we study the unique solvability of the mixed biharmonic problem with the Steklov and Steklov-type conditions on the boundary in the exterior of a compact set under the assumption that generalized solutions of this problem has

Abstract We consider generalized variational models of media with fields of defects and assume that the tensor of free distortions is interpreted as a dilatation associated with changing of temperature. A variational model of coupled thermoelasticity and stationary thermal conductivity is considered. The model is consistent with the thermodynamics and based parameters of the model are identified from

Abstract In this work boundary value problem for a circular plate under the action of two-sided gas pressure is considered. The problem relations use a refined expression for the transverse distributed force. The force consists of the average overpressure and the difference of pressures acting on both surfaces of the plate as well as in the curvature that arises during bending. The effect of the boundary

Abstract Trefftz approximation scheme on the structure of subdomains-blocks for the problems of the gradient elasticity is proposed. This scheme based on the analytical representation for the gradient elasticity solutions of Papkovich–Neuber type. Independent in blocks, complete systems of functions are used for approximation, that analytically exact satisfy the initial fourth-order equations. It is

Abstract The modified multiplicative representation of the deformation gradient tensor at a mesoscale that used in multilevel mathematical models to describe the behavior of polycrystals has been considered. In the decomposition, an orthogonal tensor characterizing the motion of a rigid moving coordinate system is explicitly distinguished. The rigid moving coordinate system is associated with the symmetry

Abstract The speed up of numerical modeling of the oil reservoir waterflooding on high-resolution grids is possible by reducing the dimension of the two-phase flow problem. This problem is posed in fixed streamtubes connecting injection and production wells. The article describes an algorithm for constructing an effective streamtube between a pair of wells in a homogeneous oil reservoir, which guarantees

Abstract Using the basic recurrence formulas for Chebyshev polynomials of the second kind, the several additional relationships have been obtained which play an important role in the construction of various variants of the theory of thin bodies. The moments of the tensor functions, as well as the moments of their derivatives and the moments of the repeated derivatives are determined, too. The moments

Abstract The subject of the present paper is a material connection that describes the sources of incompatibility in growing solids. There are several possibilities to introduce such a connection on the body manifold, which provides formal description of a body as a continuous collection of material particles. Two of them are discussed in detail. The first sets the geometry of Riemannian manifold, while

Abstract In this paper, the unsteady vibrations of an ortotropic rectangular Kirchhoff–Love plate are studied. In general formulation, the plate is under the action of longitudinal and transverse forces, bending and torque moments. It also set a diffusion fluxes density and a diffusion fluxes relaxation. The coupled elastic diffusion orthotropic multicomponent continuum model has been used to formulate

Abstract The paper is dedicated to the construction of a computational algorithm for the investigation of solids, taking into account the material and geometric nonlinearity and contact interaction. In the framework of the previously developed algorithm for the investigation of large elastoplastic deformations of solids the solutions of contact problems are derived. The algorithm has been based on

Abstract The linear statement of the theory of elasticity of a three-dimensional body was used. Issues related to the elimination of unnecessary functions from the known solutions of the theory of elasticity for isotropic and orthotropic materials were examined. A system of three second order partial differential equations was written down. Linear operators have been introduced, and the original system

Abstract The solution of a spatial non-steady problem of the influence of a moving heat flow source (laser heating) on the surface of half-space using superposition principle and transient functions method is presented, and a numerical analytical algorithm based on discretization in time and space coordinates is developed and realized.

Abstract The paper describes the approaches and methods to create a semantic library within the ‘‘Mathematics’’ subject domain. The theoretical background of the research involves the approach based on ontologies used when creating semantic libraries. The paper suggests a step-by-step description of the general ontology within the subject domain. The results obtained are well-grounded and contribute

Abstract A quasilinear parabolic problem with a time fractional derivative of the Caputo type and mixed boundary conditions is considered. The coefficients of the elliptic operator depend on the gradient of the solution, and this operator is uniformly monotone and Lipschitz-continuous. For this problem, unconditionally stable linear regularized semi-discrete scheme is constructed based on the \(L1\)-approximation

Abstract We construct and investigate the high-order symmetric explicit and implicit methods to solve the systems of second-order ordinary differential equations. The methods were selected according to size of the interval of periodicity, an error constant, behaviour of the roots of the stability polynomial, and accuracy of numerical solution of tests problem including simulation of disturbed orbital

Abstract This article discusses advantages and disadvantages of various computational platforms in application to problems of wave propagation simulation. Modern SIMD processors, such as multi-core ARM and Intel CPUs, as well as NVidia GPUs are considered. Wave propagation simulation is the main element of algorithms for solving inverse problems of wave tomography as coefficient inverse problems for

Abstract We perform a comparison study of different subgrid scale closures in large-eddy simulations (LES) of the non-stationary boundary layer dynamics during the evening transition. In particular, we consider LES models supplemented with the dynamic procedure, which allows the variation of subgrid closure parameters (Smagorinsky coefficient and subgrid Prandtl number) in space and time and a recently

Abstract In this paper we discuss the usefulness of applying semi-automatic checking procedures to existing thesauri for natural language processing—large manually-created lexical-semantic resources. The procedure is based on computation of word vector representations and word semantic similarities on large text collections. The first procedure analyses discrepancies between corpus-based and thesaurus-based

Abstract Distributed computing environments execute great amount of various computing jobs that can fail or break for some reason. The analysis of the error messages describing the reasons of failures has become one of the most crucial parts of the existing monitoring systems. This analysis is complicated by the presence of a large number of messages, especially in the case of the retrospective analysis

Abstract We present a modification of the Ramsey model that describes the consumer behavior of the households. We assume that the salary of the households is a stochastic process, defined by the stochastic differential equation (SDE). The impact of the large amount of the households can be modelled by a mean field term. This leads to a Kolmogorov–Fokker–Planck equation, evolving forward in time that

Abstract Most of the problems of theoretical quantum physics are characterized by a high complexity. Practically, this means that solution of such a problem demands computational effort and resources that often scale exponentially with the size of the quantum model and the solution can be obtained—even for relatively small models—only by resorting to high performance computing (HPC) technologies. Here

Abstract In this paper, we consider mixed-integer global optimization problems and propose a parallel algorithm for solving problems of this class based on information-statistical approach for solving continuous global optimization problems. Within this algorithm, we suggest using a local tuning scheme based on the assumption that the multiextremality of the discussed problem is weak. We also compare

Abstract Physical experiment and direct numerical simulation are employed to study a transitional flow of viscous fluid past a spanwise circular cylinder mounted near the wall of a rectangular channel. The Reynolds number varies in the range of 60 to 480. Spiraling tornado-like motion of fluid directed from the sidewalls toward the center of the channel behind the cylinder is discovered. The evolution

Abstract Numerical integration is a classical problem emerging in many fields of science. Multivariate integration cannot be approached with classical methods due to the exponential growth of the number of quadrature nodes. We propose a method to overcome this problem. Tensor-train decomposition of a tensor approximating the integrand is constructed and used to evaluate a multivariate quadrature formula

Abstract In this paper, we study the third boundary value problem for the convection-diffusion equation with a time fractional derivative and variable coefficients in a multidimensional domain. For an approximate solution in a rectangular parallelepiped of the problem set, in the same area, the third boundary value problem for a differential equation with a small parameter is considered. An a priori

Abstract The differential eigenvalue problem governing eigenvibrations of an elastic bar with fixed first end and mechanical resonator attached to second end is investigated. This problem has an increasing sequence of positive simple eigenvalues with limit point at infinity. To the sequence of eigenvalues, there corresponds a complete orthonormal system of eigenfunctions. We introduce limit differential

Abstract We give a relatively complete analysis of the penalty methods for one-sided parabolic problems with piecewise smooth obstacles, which include an important subclass of polyhedra. It is shown that the original variational inequality can be equivalently formulated as unconstrained variational inequality with a locally Lipschitz functional, which has a different form for convex and non-convex

Abstract This paper analyzes the problem of optimal control of two work-stealing deques in two-level memory (for example, registers—random access memory), where probabilities of parallel operations with deques are known. The classic sequential cyclic method for representing a deque in memory is considered. In the case of the deque overflowing in fast memory or emptying the FIFO-part or LIFO-part the

Abstract The architecture of modern supercomputers is extremely complex, so it is exceedingly difficult to monitor and maintain the efficiency of their functioning. And even if it is possible to collect the necessary data on the operation of all important supercomputer components, how not to drown in this ‘‘sea of information’’ and not miss the onset of a critical situation? This requires the automation

Abstract This article is devoted to solving the inverse problems of exploration seismology of fractures and their uniformly oriented systems using convolutional neural networks. The use of convolutional neural networks is optimal due to the multidimensionality of the studied data object. A training sample was formed using mathematical modeling. In the numerical solution of direct problems, a grid-characteristic

Abstract Dark states of atomic ensembles do not interact with light (can neither emit nor absorb a single photon due to destructive interference). Being free of decoherence, they can be widely used in quantum computing (particularly as a mechanism for creating quantum memory). To date, the structure of dark states of two-level atoms has been sufficiently well studied; meanwhile, this problem remains

Abstract In this article, we present a study on constructing a second order local approximation monotone difference schemes on spatial non-uniform grids for the parabolic equation of convection-diffusion type with a third kind boundary condition without using the basic differential equation at the boundary of the domain. The goal is a combination of the differential inequality, the regularization principle

Abstract The paper presents a computational algorithm for solving problem formulated in terms of Mean Field Game theory with limited management resource. The Mean Field equilibrium leads to a coupled system of two parabolic partial differential equations: Fokker–Planck–Kolmogorov and Hamilton–Jacobi–Bellman ones with an additional constraint in the form of the inequality. The article is devoted to

Abstract The paper focuses on the problem of normal surface waves in an open metal-dielectric inhomogeneous waveguide of arbitrary cross-section with losses. The medium filling the waveguide is characterized by a isotropic inhomogeneous complex permittivity. The setting is reduced to a boundary eigenvalue problem for longitudinal components of the electromagnetic field in Sobolev spaces. Variational

Abstract Different variants of the problem of diffraction of spherical electromagnetic wave by axial-symmetric bodies are researched in the work. These problems are reduced to infinite sets of linear algebraic equations. The joining method is used. The conductive bodies, dielectric bodies and spherical conductive screens on the coordinate and non-coordinate boundaries are considered. The results of

Abstract The current paper clarifies the connection between the generalized complex-frequency eigenvalue problem and the corresponding nonlinear eigenvalue problem for the set of Muller integral equations posed on two disjoint closed curves. It is proved that the last problem has no solutions if the original problem and a specially tailored eigenvalue problem do not have solutions. This result is important

Abstract We investigate a family of Schrödinger operators \(H(K)\), \(K\in(-\pi,\pi]^{d}\) associated with a system of three quantum particles on the \(d\)-dimensional lattice \({\mathbb{Z}}^{d}\) interacting via short-range pair potentials. It’s shown that the essential spectrum of the three-particle discrete Schrödinger operator \(H(K)\), \(K\in(-\pi,\pi]^{d}\) consists of a finitely many bounded

Abstract The two-dimensional problem of the diffraction of an electromagnetic wave by a metal diaphragm of finite thickness in an infinite rectangular waveguide is solved and investigated. Using the method of the integral-series identity, the problem is reduced to an infinite system of linear algebraic equations. Through computational experiments, it was shown that the expansion coefficients of the

Abstract In this work we consider the weight spaces of integrable functions \(L_{p}^{\omega}\) \((p\geq 1)\) and continuous functions \(C^{\omega}\) on the real line. Let \(\Lambda=\{\lambda_{k},n_{k}\}\) be an unbounded increasing sequence of positive numbers \(\lambda_{k}\) and their multiplicities \(n_{k}\), \(\mathcal{E}(\Lambda)=\{t^{n}e^{\lambda_{k}t}\}\) be a system of exponential monomials

Abstract A three-dimensional problem of viscous fluid filtration in domain containing homogeneous porous medium is considered. Filtration flow is described by Darcy–Brinkman law. The boundary of the medium is divided into parts with either impermeability condition or condition on velocity vector flux or pressure. Integral representation for velocity and pressure of fluid is constructed with methods

Abstract For an equation of mixed parabolic-hyperbolic type in a rectangular parallelepiped, the inverse problem of finding the factors of the right-hand side that depend on spatial variables is investigated. A criterion for the uniqueness of a solution is established. The solution is constructed as a sum of orthogonal series. When justifying the convergence of the series, the problem of small denominators

Abstract In this article we construct a special class of the generalized functions for the rigorous justification of joining method of solving some diffraction problems of electromagnetic waves by thin conducting screens. Linear functionals on a set of linear combinations of Hermit functions are considered as the generalized functions. The traces of the solutions of Helmholtz equation on the plane

Abstract In this paper we study zero sets of entire functions in the Schwartz algebra. This algebra is defined as the Fourier–Laplace transform image of the space of all distributions compactly supported on the real line. We obtain the conditions under which given complex sequence forms zero set of some invertible in the sense of Ehrenpreis element of the Schwartz algebra (slowly decreasing function)

Abstract We study solvability for a model elliptic pseudo-differential equation with an additional integral condition in Sobolev–Slobodetskii spaces in certain conical domains in Euclidean space. . Using the wave factorization for an elliptic symbol we construct a solution for this boundary value problem and study the behavior of the solution when parameters of cones tend to their extremal values.

Abstract The problem on normal TE-waves in an inhomogeneous partially shielded dielectric layer is reduced to eigenvalue problem for the component of the electromagnetic field in Sobolev space. We formulate the definition of solution using variational relation. The variational problem is reduced to the study of an operator pencil. We investigate properties of the operators of the pencil for the analysis

Abstract The maximum of the modulus of a meromorphic function cannot be restricted from above by the Nevanlinna characteristic of this meromorphic function. But integrals from the logarithm of the module of a meromorphic function allow similar restrictions from above. This is illustrated by one of the important theorems of Rolf Nevanlinna in the classical monograph by A. A. Goldberg and I. V. Ostrovskii

Abstract The problem of electromagnetic wave diffraction by a flat convex screen of arbitrary shape is considered. The numerical solution for the problem is obtained by the method of moments using the parallel programming technology CUDA. As basic and testing functions RWG functions are used. To construct the corresponding RWG elements on CUDA, a simple and fast algorithm of triangulation for a convex

Abstract The family of boundary value problems for a system of integro-differential equations of mixed type is considered. First, considered problem is reduced to the family of boundary value problems for the Fredholm integro-differential equations with an unknown function and the integral relation. Further, based on the introduction of an additional parameter as a value of the solution at the beginning

Abstract In this paper, we consider the questions of the unique solvability of a boundary value problem for a third-order partial integro-differential equation with a degenerate kernel and multiple characteristics. An explicit solution of the boundary value problem is constructed. In this case, a combination of three methods was used: the method for constructing Green’s function, the method of Fourier

Abstract We study Sturm–Liouville operators on closed sets of a special structure, which are sometimes referred to as time scales and often appear in modelling various real-world processes. Depending on the set structure, such operators unify both differential and difference operators. The time scales under consideration consist of a finite number of non-intersecting segments. We obtain properties

Abstract The problem on normal waves in an open regular waveguide of arbitrary cross-section is considered. The permittivity and permeability of the waveguide are described by tensors. The determination of normal waves is reduced to a boundary eigenvalue problem for longitudinal components of the electromagnetic field in Sobolev spaces. A variational formulation corresponding to this problem is obtained

Abstract In this article, a non-classical problem with an integral condition for a parabolic-hyperbolic equation of the third order, has been formulated and investigated. By the method of integral equations, the unique solvability of the considered problem has been proved. The problem is equivalently reduced to a problem for a second order parabolic-hyperbolic equation with unknown right-hand side

Abstract Let \(\Omega\) be a simple-connected domain, \(Z=\{z_{k}\in\Omega,\ k=\overline{1,N}\}\ (N\leq\infty)\), and let \(TM(\Omega,Z)\) be a set of functions meromorphic in \(\Omega\) and satisfying at each its pole \(z_{k}\) the trivial monodromy condition. The criterion for trivial monodromy is well known (it was established by Duistermaat and Grünbaum in 1987). However, this criterion is of a