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Dynamic Bayesian Networks as a Testing Tool for Fuzzing Web Applications Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210822
Azarnova, T. V., Polukhin, P. V.Abstract Simulation of testing web applications using fuzzing and dynamic Bayesian networks is considered. The basic principles of optimizing the structure of dynamic Bayesian networks are formulated, and hybrid algorithms for learning and probabilistic inference using quasiNewtonian algorithms and elements of the theory of sufficient statistics are proposed.

Method for Modeling of Ionospheric Parameters and Detection of Ionospheric Disturbances Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210822
Mandrikova, O. V., Fetisova, N. V., Polozov, Yu. A.Abstract The paper proposes an automated method for analyzing ionospheric parameters and detecting ionospheric anomalies. The method is based on a generalized multicomponent model of ionospheric parameters (GMCM) developed by the authors. The model identification is based on an integrated approach combining the wavelettransform methods with the autoregressiveintegrated moving average models (ARIMA

Approximation of the Capacitated Vehicle Routing Problem with a Limited Number of Routes in Metric Spaces of Fixed Doubling Dimension Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210822
Ogorodnikov, Yu. Yu., Khachay, M. Yu.Abstract The capacitated vehicle routing problem (CVRP) is a classical combinatorial optimization problem having a wide range of practically important applications in operations research. As most combinatorial problems, CVRP is strongly NPhard (even on the Euclidean plane). A metric instance of CVRP is APXcomplete, so it cannot be approximated to arbitrary prescribed accuracy in the class of polynomial

Local OneDimensional Scheme for the First InitialBoundary Value Problem for the Multidimensional FractionalOrder Convection–Diffusion Equation Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210822
Alikhanov, A. A., Beshtokov, M. Kh., ShkhanukovLafishev, M. Kh.Abstract The first boundary value problem for the fractionalorder convection–diffusion equation is studied. A locally onedimensional difference scheme is constructed. Using the maximum principle, a prior estimate is obtained in the uniform metric. The stability and convergence of the difference scheme are proved. An algorithm for the approximate solution of a locally onedimensional difference scheme

Neural Network with Smooth Activation Functions and without Bottlenecks Is Almost Surely a Morse Function Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210822
Kurochkin, S. V.Abstract It is proved that a neural network with sigmoidal activation functions is a Morse function for almost all, with respect to the Lebesgue measure, sets of parameters (weights) in the case when the network architecture has no bottlenecks, i.e., layers with fewer neurons than in the adjacent layers. It is shown by examples that the requirement for no bottlenecks is essential.

Prior Distribution Selection for a Mixture of Experts Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210822
Grabovoy, A. V., Strijov, V. V.Abstract The paper investigates a mixture of expert models. The mixture of experts is a combination of experts, local approximation model, and a gate function, which weighs these experts and forms their ensemble. In this work, each expert is a linear model. The gate function is a neural network with softmax on the last layer. The paper analyzes various prior distributions for each expert. The authors

Numerical Study of HighDimensional Optimization Problems Using a Modification of Polyak’s Method Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210822
Gornov, A. Yu., Anikin, A. S., Andrianov, A. N.Abstract A modification of Polyak’s special method of convex optimization is proposed. The properties of the corresponding algorithm are studied by computational experiments for convex separable and nonseparable optimization problems, nonconvex optimization problems for the potentials of atomicmolecular clusters, and a model optimal control problem. Sequential and parallel versions of the algorithm

An Approach to Statistical Simulation of Traffic Flows Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210822
Starozhilets, V. M., Chekhovich, Yu. V.Abstract A statistical model of traffic flows designed for modeling the motion of vehicles on long highways is proposed. The model simulates the motion of groups of vehicles on the road using the fundamental flow–density diagram on a selected segment of the road with the purpose of calculating the speed of the group; it is assumed that the group size linearly depends on its speed. The proposed approach

Tradeoff Relation between Mutual Information and Error Probability in Data Classification Problem Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210822
Lange, A. M., Lange, M. M., Paramonov, S. V.Abstract A data classification model in which the average mutual information between source objects and made decisions is a function of the error probability is investigated. Optimization of the model consists in finding a tradeoff “mutual information–error probability” (MIEP) relation between the minimal average mutual information and the error probability, which is analogous to the wellknown rate

Corporate Dynamics in Chains of Coupled Logistic Equations with Delay Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210822
Kashchenko, S. A.Abstract The local dynamics of coupled chains of identical oscillators are considered. As a basic model of an oscillator, the wellknown logistic equation with delay is proposed. The transition to studying a spatially distributed model is made. Two types of coupling of major interest are treated: diffusive coupling and unidirectional coupling. Critical cases are distinguished in the stability problem

Morphological and Other Research Techniques for Almost Cyclic Time Series as Applied to СО2 Concentration Series Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210822
Avilov, V. K., Aleshnovskii, V. S., Bezrukova, A. V., Gazaryan, V. A., Zyuzina, N. A., Kurbatova, Yu. A., Tarbaev, D. A., Chulichkov, A. I., Shapkina, N. E.Abstract Based on the morphological analysis techniques developed under the guidance of Yu.P. Pyt’ev, a method for filtering time series is proposed that is capable of detecting an almost cyclic component with a varying cycle length and varying series members within cycles. The effectiveness of the approach is illustrated as applied to decomposition of time series of atmospheric СО2 concentrations

Automated Method for Cosmic Ray Data Analysis and Detection of Sporadic Effects Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210822
Geppener, V. V., Mandrikova, B. S.Abstract An automated method for detecting multiscale sporadic effects in data from groundbased neutron monitors is proposed. The method is based on the wavelet transform and neural networks of learning vector quantization type (LVQ neural networks). The choice of Daubechies wavelets and Coiflets at the data preprocessing stage is justified. An algorithm for choosing the “best” approximating wavelet

Metric Approach for Finding Approximate Solutions of Scheduling Problems Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210822
Lazarev, A. A., Lemtyuzhnikova, D. V., Pravdivets, N. A.Abstract Metric functions are introduced for various classes of singlemachine scheduling problems. It is shown how approximate solutions of NPhard problems can be found using these functions. The metric value is determined by solving a linear programming problem with constraints being systems of linear inequalities for polynomial or pseudopolynomial solvable instances of the problem under study.

Recognition of a QuasiPeriodic Sequence Containing an Unknown Number of Nonlinearly Extended Reference Subsequences Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210822
Kel’manov, A. V., Mikhailova, L. V., Ruzankin, P. S., Khamidullin, S. A.Abstract A previously unstudied optimization problem induced by noiseproof recognition of a quasiperiodic sequence, namely, by the recognition of a sequence \(Y\) of length \(N\) generated by a sequence \(U\) belonging to a given finite set \(W\) (alphabet) of sequences is considered. Each sequence \(U\) from \(W\) generates an exponentially sized set \(\mathcal{X}(U)\) consisting of all sequences

Biharmonic Problem with Dirichlet and SteklovType Boundary Conditions in Weighted Spaces Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210726
H. A. MatevossianAbstract The uniqueness of solutions of a biharmonic problem with Dirichlet and Steklovtype boundary conditions in the exterior of a compact set are studied under the assumption that the generalized solution of this problem has a finite Dirichlet integral with a weight \({{\left x \right}^{a}}\). Depending on the parameter \(a\), uniqueness (nonuniqueness) theorems are proved and exact formulas

Numerical Method for Solving Volume Integral Equations on a Nonuniform Grid Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210701
A. B. Samokhin, E. E. TyrtyshnikovAbstract Numerical methods for solving volume integral equations describing the problems of wave scattering by transparent obstacles are considered. The equations are approximated using the collocation method on a nonuniform grid, and the problem is reduced to solving a system of linear algebraic equations. An efficient method is proposed for the approximate multiplication of the matrix of this system

An Accurate Restarting for ShiftandInvert Krylov Subspaces Computing Matrix Exponential Actions of Nonsymmetric Matrices Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210701
M. A. BotchevAbstract An accurate residualtime (AccuRT) restarting for computing matrix exponential actions of nonsymmetric matrices by the shiftandinvert (SAI) Krylov subspace method is proposed. The proposed restarting method is an extension of the recently proposed RT (residualtime) restarting and it is designed to avoid a possible accuracy loss in the conventional RT restarting. An expensive part of the

Prospects of TensorBased Numerical Modeling of the Collective Electrostatics in ManyParticle Systems Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210701
V. Khoromskaia, B. N. KhoromskijAbstract Recently the rankstructured tensor approach suggested a progress in the numerical treatment of the longrange electrostatics in manyparticle systems and the respective interaction energy and forces. In this paper, we outline the prospects for tensorbased numerical modeling of the collective electrostatic potential on lattices and in manyparticle systems of general type. Our approach, initially

Computing the Eigenvectors of Nonsymmetric Tridiagonal Matrices Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210701
P. Van Dooren, T. Laudadio, N. MastronardiAbstract The computation of the eigenvalue decomposition of matrices is one of the most investigated problems in numerical linear algebra. In particular, real nonsymmetric tridiagonal eigenvalue problems arise in a variety of applications. In this paper the problem of computing an eigenvector corresponding to a known eigenvalue of a real nonsymmetric tridiagonal matrix is considered, developing an

TTQI: Faster Value Iteration in Tensor Train Format for Stochastic Optimal Control Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210701
A. I. Boyko, I. V. Oseledets, G. FerrerAbstract The problem of general nonlinear stochastic optimal control with small Wiener noise is studied. The problem is approximated by a Markov Decision Process. Bellman Equation is solved using Value Iteration (VI) algorithm in the low rank Tensor Train format (TTVI). In this paper a modification of the TTVI algorithm called TTQIteration (TTQI) is proposed by authors. In it, the nonlinear Bellman

Extraction of Inductances and Spatial Distributions of Currents in a Model of Superconducting Neuron Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210701
S. V. Bakurskiy, N. V. Klenov, M. Yu. Kupriyanov, I. I. Soloviev, M. M. KhapaevAbstract A mathematical model and a computational method for extracting the inductances and spatial distributions of supercurrents in an adiabatic artificial neuron are proposed. This neuron is a multilayer structure containing Josephson junctions. The computational method is based on the simultaneous solution of the London equations for the currents in the superconductor layers and Maxwell’s equations

LowRank Approximation Algorithms for Matrix Completion with Random Sampling Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210701
O. S. Lebedeva, A. I. Osinsky, S. V. PetrovAbstract The possibility of accelerating a projection algorithm onto dominant singular spaces in the problem of recovering a lowrank matrix from a small number of its entries is explored. The underlying idea is to replace best approximation procedures in the Frobenius norm by fast approximation algorithms. Two methods for computing such approximations are considered: (a) projection onto random subspaces

New Algorithms for Solving Nonlinear Eigenvalue Problems Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210701
W. GanderAbstract To solve a nonlinear eigenvalue problem we develop algorithms which compute zeros of \(\det A(\lambda ) = 0\). We show how to apply third order iteration methods for that purpose. The necessary derivatives of the determinant are computed by algorithmic differentiation. Since many nonlinear eigenvalue problems have banded matrices we also present an algorithm which makes use of their structure

Algebras Closed by JHermitianity in Displacement Formulas Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210701
E. Bozzo, P. Deidda, C. Di FioreAbstract We introduce the notion of \(J\)Hermitianity of a matrix, as a generalization of Hermitianity, and, more generally, of closure by \(J\)Hermitianity of a set of matrices. Many well known algebras, like upper and lower triangular Toeplitz, Circulants and \(\tau \) matrices, as well as certain algebras that have dimension higher than the matrix order, turn out to be closed by \(J\)Hermitianity

On the Accuracy of Cross and Column LowRank Maxvol Approximations in Average Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210701
N. L. Zamarashkin, A. I. OsinskyAbstract The article considers the problem of lowrank column and cross (\(CGR\), \(CUR\)) approximation of matrices in the Frobenius norm up to a fixed factor \(1 + \varepsilon \). It is proved that, for random matrices, in average, an estimate of the form \(1 + \varepsilon \leqslant \tfrac{{m + 1}}{{m  r + 1}}\tfrac{{n + 1}}{{n  r + 1}}\) holds, where \(m\) and \(n\) are the number of rows and

Overview of Visualization Methods for Artificial Neural Networks Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210701
S. A. Matveev, I. V. Oseledets, E. S. Ponomarev, A. V. ChertkovAbstract Modern algorithms based on artificial neural networks (ANNs) are extremely useful in solving a variety of complicated problems in computer vision, robust control, and natural language analysis of sound and texts as applied to data processing, robotics, etc. However, for the ANN approach to be successfully incorporated into critically important systems, for example, in medicine or jurisprudence

A Survey of Shanks’ Extrapolation Methods and Their Applications Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210701
C. Brezinski, M. RedivoZagliaAbstract When a sequence or a series of scalars, vectors, matrices, tensors, is converging slowly to its limit, it can be transformed, by a sequence transformation, into a new sequence or a set of new sequences, which under some assumptions converges faster to the same limit. Such a transformation can even be applied to diverging sequences or series, thus providing its analytic continuation. Shanks’

New Applications of Matrix Methods Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210701
N. L. Zamarashkin, I. V. Oseledets, E. E. TyrtyshnikovAbstract Modern directions in the development of matrix methods and their applications described in the present issue are overviewed. Special attention is given to methods associated with separation of variables, special decompositions of matrices and tensors implementing this technique, related algorithms, and their applications to multidimensional problems in computational mathematics, data analysis

Structuring Data with Block Term Decomposition: Decomposition of Joint Tensors and Variational Block Term Decomposition as a Parametrized Mixture Distribution Model Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210701
I. V. Oseledets, P. V. KharyukAbstract The idea of using tensor decompositions as a parametric model for group data analysis is developed. Two models (deterministic and probabilistic) based on block term decomposition are presented using various formats of terms. The relationship between block term decomposition and mixtures of continuous latent probabilistic models is established; specifically, a mixture distribution model with

ReducedOrder Modeling of Deep Neural Networks Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210701
J. Gusak, T. Daulbaev, E. Ponomarev, A. Cichocki, I. OseledetsAbstract We introduce a new method for speeding up the inference of deep neural networks. It is somewhat inspired by the reducedorder modeling techniques for dynamical systems. The cornerstone of the proposed method is the maximum volume algorithm. We demonstrate efficiency on neural networks pretrained on different datasets. We show that in many practical cases it is possible to replace convolutional

TT Ranks of Approximate Tensorizations of Some Smooth Functions Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210701
L. I. VysotskyAbstract Tensorizations of functions are studied, that is, tensors with elements \(A({{i}_{1}}, \ldots ,{{i}_{d}}) = f(x({{i}_{1}}, \ldots ,{{i}_{d}}))\) \(A({{i}_{1}}, \ldots ,{{i}_{d}}) = f(x({{i}_{1}}, \ldots ,{{i}_{d}}))\), where \(f(x)\) is some function defined on an interval and \(\{ x({{i}_{1}}, \ldots ,{{i}_{d}})\} \) is a grid on this interval. For tensors of this type, the problem of approximation

Inductive Matrix Completion with Feature Selection Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210701
M. Burkina, I. Nazarov, M. Panov, G. Fedonin, B. ShirokikhAbstract We consider the problem of inductive matrix completion, i.e., the reconstruction of a matrix using side features of its rows and columns. In numerous applications, however, side information of this kind includes redundant or uninformative features, so feature selection is required. An approach based on matrix factorization with group LASSO regularization on the coefficients of the side features

Vortex Phantoms in the Stationary Kochin–Yudovich Flow Problem Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210530
O. V. TroshkinAbstract The dynamics of a continuous medium in a pipe is not exhausted by spontaneous unsteady turbulence vortices (first seen in flashes of light and generated at high Reynolds numbers), which permanently level the parabolic velocity profile in the pipe. The ambient space also includes steady swirls and curls, which are usually approximated by analytical dependences decomposable in power series.

An Approach for Solving ThreeDimensional Fluid Dynamics Problems with Allowance for Elastic Processes Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210530
A. Yu. Krukovskii, Yu. A. Poveshchenko, V. O. Podryga, P. I. RahimlyAbstract A finitedifference approximation of elastic forces on Lagrangian grids is constructed by applying the support operator method. For displacement vectors on unstructured grids with minimal reasonable constraints imposed on their topological and geometric structure, approximations of vector analysis operations are constructed as applied to difference schemes for elasticity problems. Taking into

Bicompact Schemes for the Multidimensional Convection–Diffusion Equation Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210530
M. D. Bragin, B. V. RogovAbstract Bicompact schemes are generalized for the first time to the linear multidimensional convection–diffusion equation. Schemes are constructed using the method of lines, the finitevolume method, and bi and tricubic Hermite interpolation of the sought function in a cell. Time stepping is based on diagonally implicit Runge–Kutta methods. The proposed bicompact schemes are unconditionally stable

A Modified Trapezoidal Broyden’s Method for Nonlinear Equations Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210530
Song Wu, Hai Jun WangAbstract A modified Trapezoidal Broyden’s method for nonlinear equations is presented. We design and implement an alternative approximation to Jacobian matrix of Trapezoidal Broyden’s method. This method improve the efficiency by reducing the number of iterations required by the Broyden’s method, and solve the problem that the approximate matrix almost singular or singular at some points. The local

On a Method for Solving a Local Boundary Value Problem for a Nonlinear Stationary Controlled System in the Class of Differentiable Controls Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210530
A. N. KvitkoAbstract An algorithm, quite convenient for numerical implementation, is proposed for constructing a differentiable control function that guarantees the transfer of a wide class of nonlinear stationary systems of ordinary differential equations from the initial state to a given final state of the phase space, taking into account control constraints and external perturbations. A constructive criterion

Analytical Solutions of the Equation Describing Internal Gravity Waves Generated by a Moving Nonlocal Source of Perturbations Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210530
V. V. Bulatov, Yu. V. VladimirovAbstract The problem of constructing analytical solutions describing internal gravity wave fields generated by a nonlocal source of perturbations moving on the surface of a stratified medium of finite depth is considered. For a radially symmetric model source, analytical solutions expressed in terms of eigenfunctions of the basic vertical spectral problem for internal waves are obtained in the linear

Boundary Element Method for Solving an Inhomogeneous Biharmonic Equation with a RightHand Side Containing the Unknown Function and Its Derivatives Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210530
R. F. Mardanov, A. E. MardanovaAbstract A boundary element method is proposed for solving an inhomogeneous biharmonic equation with a righthand side containing the sought function and its derivatives. The accuracy of numerical results obtained for a test problem is analyzed by comparing them with its analytical solution. The flow through a porous medium with a nonuniform permeability distribution based on the Brinkman model is

SemiClassical Models of Quantum Nanoplasmonics Based on the Discrete Source Method (Review) Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210530
Yu. A. Eremin, A. G. SveshnikovAbstract Works concerning the quantum effect of nonlocal screening on field characteristics in the problem of scattering a plane wave by nanoscale structures, including ones located near a transparent substrate, are reviewed. Efficient computer models for analyzing such structures are constructed by applying the discrete source method. The nonlocality effect is studied using the generalized nonlocal

Finding Root Spaces for a Linear Algebraic Spectral Problem Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210530
L. F. YukhnoAbstract For an algebraic spectral problem that is linear with respect to the spectral parameter, some numerical methods are considered to find the root space corresponding to a chosen eigenvalue. These methods make it possible to construct the root space as a whole without calculating the corresponding eigenvectors and associated vectors. The proposed algorithms are numerically stable.

Anomalies of Acoustic Wave Propagation in Two SemiInfinite Cylinders Connected by a Flattened Ligament Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210530
S. A. Nazarov, L. ChesnelAbstract We study the propagation of waves in a waveguide which is the union of two semiinfinite cylinders connected by a thin rectangular ligament. It is shown that almost complete or even complete transmission of the piston mode at a prescribed frequency can be achieved via fine tuning of the plate sizes, although, of course, almost complete wave reflection occurs in the generic case. The result

Optimization of Source Parameters in Multipoint Nonseparated Conditions for Linear Dynamical Systems Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210530
V. M. Abdullayev, K. R. AidazadeAbstract The problem of optimizing the righthand sides of linear nonlocal multipoint conditions for a linear system of differential equations is considered. Necessary optimality conditions of the first order are obtained, which allow the use of efficient firstorder methods for the numerical solution of the problem under consideration. Solutions of test problems are presented and analyzed.

Elaboration of the Fast Boundary Element Method for 3D Simulation of the Dynamics of a Bubble Cluster with Solid Particles in an Acoustic Field Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210530
I. A. Zarafutdinov, Yu. A. Pityuk, O. A. SolnyshkinaAbstract An efficient numerical approach to the study of the dynamics of a cluster containing bubbles and solid particles under the action of an acoustic field in the 3D case is presented. The numerical method is a combination of the boundary element method (BEM) and the fast multipole method (FMM) for the Laplace equation. The hardware acceleration of the computation of a bubble cluster doped with

Exact Solutions of the KdV Equation with DualPower Law Nonlinearity Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210429
Fibay Urbain, N. A. Kudryashov, E. TalaTebue, Malwe Boudoue Hubert, S. Y. Doka, Kofane Timoleon CrepinAbstract In this paper, we investigate the KdV equation with dualpower law nonlinearity. As a result, we have obtained general exact travelling wave soliton solutions such as bright soliton solution, dark soliton solution and periodic solution. These solutions have many free parameters in such away that they may be used to simulate many experimental situations. The main contribution in this work is

On the Calculation of the T Congruence Centralizer Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210429
Kh. D. IkramovAbstract Let \(A\) be a complex \(n \times n\) matrix. The set \(\mathcal{L}\) of matrices \(X\) satisfying the relation \({{X}^{T}}AX = A\) is called the \(T\)congruence centralizer of \(A\). It is shown that the calculation of matrices from the nonlinear variety \(\mathcal{L}\) can be reduced to solving a linear matrix equation.

Analytical Inversion of the Operator Matrix for the Problem of Diffraction by a Cylindrical Segment in Sobolev Spaces Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210429
S. I. EminovAbstract A vector problem of electromagneticwave diffraction by a cylinder is described by a system of two twodimensional integrodifferential equations. After expanding the unknown functions and the righthand sides in Fourier series, the problem reduces to systems of onedimensional equations. Analytical inversion of the principal operator of onedimensional systems in Sobolev spaces is considered

Difference Schemes Based on the Laguerre Transform Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210429
A. F. MastryukovAbstract Optimal difference schemes based on the Laguerre transform are proposed for solving the wave equation. Additional parameters are introduced into the difference scheme used for the equations of harmonics. Numerical values of these parameters are obtained by minimizing the error in the difference approximation of the Helmholtz equation. The optimal parameter values thus obtained are used to

The Effect of Weak Mutual Diffusion on Transport Processes in a Multiphase Medium Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210429
A. V. NesterovAbstract The Cauchy problem for a singularly perturbed system of equations describing a transport process with diffusion in a multiphase medium is considered. A formal asymptotic expansion of its solution is constructed in the case when exchange between the phases proceeds much more rapidly than the transport and diffusion processes. The case when the diffusion fluxes of the components have a mutual

Analysis of TwoFluid Plasma in the Electromagnetic Hydrodynamics Approximation and Discontinuous Structures in Their Solutions Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210429
I. B. BakholdinAbstract Various versions of equations of twofluid plasma called the equations of electromagnetic hydrodynamics are considered. They are a generalization of the classical magnetic hydrodynamics equations obtained by adding dispersive terms. Application of finitedifference methods for solving these equations is analyzed. The Riemann problem is solved numerically, and various types of discontinuity

Inverse Problem of Determining the Absorption Coefficient in a Degenerate Parabolic Equation in the Class L ∞ Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210429
V. L. KamyninAbstract Existence and uniqueness theorems for solutions of inverse problems of determining the timedependent absorption coefficient in a degenerate parabolic equation with two independent variables are proved. An integral observation condition is additionally imposed. The unknown absorption coefficient is sought in the class of bounded functions on \([0,T]\). Examples of the inverse problems are

Gradient Projection Method for a Class of Optimization Problems with a Constraint in the Form of a Subset of Points of a Smooth Surface Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210429
Yu. A. ChernyaevAbstract The gradient projection method is generalized to nonconvex sets of constraints representing the settheoretic difference of a set of points of a smooth surface and the union of a finite number of convex open sets. Necessary optimality conditions are examined, and the convergence of the method is analyzed.

Numerical Simulation of TwoDimensional Gas Flows through Granular Phase Change Materials Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210429
N. A. Lutsenko, S. S. FetsovAbstract A mathematical model and a numerical method for studying twodimensional plane gas flows through thermal accumulators based on granular or capsular phase change materials (PCMs) are proposed. The considered objects are modeled as porous media with phase transitions occurring in the condensed component. The study is based on methods of heterogeneous continuum mechanics without detailing the

On the Interaction of Relativistic Colliding Jets of Neutral Dense Plasma Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210429
S. L. Ginzburg, V. F. Dyachenko, L. I. Mikhailova, V. M. Chechetkin, N. N. FiminAbstract A threedimensional numerical model describing the interaction of a plasma with an electromagnetic field based on the Vlasov–Maxwell equations is used to compute relativistic colliding jets of a dense neutral electron–proton plasma in a vacuum. The influence exerted by the initial velocity of plasma particles and their concentration on the interaction of the jets is investigated.

Reduced SIR Model of COVID19 Pandemic Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210429
S. I. Vinitsky, A. A. Gusev, V. L. Derbov, P. M. Krassovitskiy, F. M. Pen’kov, G. ChuluunbaatarAbstract We propose a mathematical model of COVID19 pandemic preserving an optimal balance between the adequate description of a pandemic by SIR model and simplicity of practical estimates. As base model equations, we derive twoparameter nonlinear firstorder ordinary differential equations with retarded time argument, applicable to any community (country, city, etc.).The presented examples of modeling

Bifurcations of SelfOscillatory Solutions to a Nonlinear Parabolic Equation with a Rotating Spatial Argument and Time Delay Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210429
E. P. Kubyshkin, V. A. KulikovAbstract For a problem arising in nonlinear optics, namely, for an initialboundary value problem in a disk for a nonlinear parabolic equation with time delay and rotation of spatial argument by a given angle, bifurcations of selfoscillatory solutions from homogeneous equilibrium states are studied. In the plane of basic parameters of the equation, domains of stability (instability) of homogeneous

Inviscid Suspension Flow along a Flat Boundary Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210429
O. B. Gus’kovAbstract A previously developed selfconsistent field method is used to study an arbitrary finite set of identical spherical particles of arbitrary density moving in a uniform inviscid incompressible flow specified at infinity in the presence of a flat wall. For a given initial particle distribution in space, expressions for the particle and fluid velocities are derived taking into account the collective

Dynamic Discrepancy Method in the Problem of Reconstructing the Input of a System with Time Delay Control Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210429
M. S. Blizorukova, V. I. MaksimovAbstract The problem of reconstructing the unknown input disturbance for a system of nonlinear differential equations with time delay control is considered. A solution algorithm based on constructions of guaranteed control theory is presented. The algorithm is robust to information noise and computational errors.

On the Upper Bound of the Complexity of Sorting Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210407
I. S. SergeevAbstract It is shown that \({{\log}_{2}}(n!) + o(n)\) pairwise comparisons is sufficient for sorting any subset of \(n\) elements of a linearly ordered set.

Approximation of Weak Solutions of the Laplace Equation by Harmonic Polynomials Comput. Math. Math. Phys. (IF 0.675) Pub Date : 20210407
M. E. BogovskiiAbstract A new proof based on F. Browder’s ideology is given for the theorem on the approximation of weak solutions of the Laplace equation in a bounded domain \(\Omega \subset {{\mathbb{R}}^{n}}\), \(n \geqslant 2\), with a connected Lipschitz boundary by harmonic polynomials in the Lebesgue space \({{L}_{p}}(\Omega )\) and the Sobolev space \(W_{p}^{1}(\Omega )\).