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On the Enumeration of Labeled SeriesParallel $$k $$ Cyclic $$2 $$ Connected Graphs J. Appl. Ind. Math. Pub Date : 20210422
V. A. VoblyiAbstract We deduce an explicit formula for the number of labeled seriesparallel \(k \)cyclic \(n \)vertex \(2 \)connected graphs and find the corresponding asymptotics for a large number of vertices and a fixed \(k \). Under the uniform probability distribution, an asymptotic formula is obtained for the probability that a random \(n \)vertex \(k \)cyclic \(2 \)connected graph with a large number

About Elastic Torsion around Three Axes J. Appl. Ind. Math. Pub Date : 20210422
S. I. Senashov, I. L. SavostyanovaAbstract We consider the equations of nonlinear elasticity assuming that the components of the deformation vector depend only on the two space coordinates each of which has the two corresponding coordinates. Some system of the three differential equations for three tangent components of the stress tensor is obtained in result of this study. This system can be used to describe the elastic torsion of

Regularization of the Solution of a Cauchy Problem for a Hyperbolic Equation J. Appl. Ind. Math. Pub Date : 20210422
V. G. Romanov, T. V. Bugueva, V. A. DedokAbstract Given a hyperbolic equation with variable coefficients, we construct a regularizing algorithm to solve the problem of continuation of the wave field from the boundary of the halfplane inside it. We introduce some \(N\)approximate solutions and establish their convergence to the exact solution. Under consideration is the case when the problem data have an error of \(\delta \). We find an

Method of Commutators for Integration of a Matrix Riccati Equation J. Appl. Ind. Math. Pub Date : 20210422
M. V. Neshchadim, A. P. ChupakhinAbstract Complete integration is carried out of the matrix Riccati equation arising in continuum mechanics in the twodimensional case. The method of commutators is used to obtain some compatibility conditions.

Connected Boolean Functions with a Locally Extremal Number of Prime Implicants J. Appl. Ind. Math. Pub Date : 20210422
I. P. ChukhrovAbstract The wellknown lower bound for the maximum number of prime implicants of a Boolean function (the length of the reduced DNF) differs by \(\Theta (\sqrt {n}) \) times from the upper bound and is asymptotically attained at a symmetric belt function with belt width \(n/3 \). To study the properties of connected Boolean functions with many prime implicants, we introduce the notion of a locally

Asymptotic Justification of the Models of Thin Inclusions in an Elastic Body in the Antiplane Shear Problem J. Appl. Ind. Math. Pub Date : 20210422
E. M. Rudoy, H. Itou, N. P. LazarevAbstract The equilibrium problem for an elastic body having an inhomogeneous inclusion with curvilinear boundaries is considered within the framework of antiplane shear. We assume that there is a powerlaw dependence of the shear modulus of the inclusion on a small parameter characterizing its width. We justify passage to the limit as the parameter vanishes and construct an asymptotic model of an elastic

Global Solvability of OneDimensional AxiallySymmetric Micropolar Fluid Equations J. Appl. Ind. Math. Pub Date : 20210422
V. V. NeverovAbstract We prove the theorem of global existence of a weak solution to an onedimensional initialboundary value problem for the micropolar fluid equations under the condition of axial symmetry. The micropolar fluid model is a wellknown generalization of the classical Navier–Stokes equations for the case when the rotation of the continuum particles is taken into account.

Efficient Solvability of the Weighted Vertex Coloring Problem for Some Two Hereditary Graph Classes J. Appl. Ind. Math. Pub Date : 20210422
O. O. Razvenskaya, D. S. MalyshevAbstract The weighted vertex coloring problem for a given weighted graph is to minimize the number of colors so that for each vertex the number of the colors that are assigned to this vertex is equal to its weight and the assigned sets of vertices are disjoint for any adjacent vertices. For all but four hereditary classes that are defined by two connected \(5 \)vertex induced prohibitions, the computational

Global Unique Solvability of an InitialBoundary Value Problem for the OneDimensional Barotropic Equations of Binary Mixtures of Viscous Compressible Fluids J. Appl. Ind. Math. Pub Date : 20210422
A. E. Mamontov, D. A. ProkudinAbstract We consider the equations of a multivelocity model of a binary mixture of viscous compressible fluids (the twofluid medium) in the case of onedimensional barotropic motions. We prove the time global existence and uniqueness of a strong solution to the initialboundary value problem describing the motion in a bounded space domain.

The Distinguishing Numbers and the Distinguishing Indexes of Cayley Graphs J. Appl. Ind. Math. Pub Date : 20210422
S. Alikhani, S. SoltaniAbstract The distinguishing number (index) \(D(G)\) ( \(D^{\prime }(G) \)) of a graph \(G \) is the least integer \(d \) such that \(G \) has a vertex labeling (edge labeling) with \(d \) labels which is preserved only by a trivial automorphism. In this paper, we investigate the distinguishing numbers and the distinguishing indexes of Cayley graphs. In particular, we obtain an upper bound for the distinguishing

The Affine Hull of the Schedule Polytope for Servicing Identical Requests by Parallel Devices J. Appl. Ind. Math. Pub Date : 20210422
R. Yu. Simanchev, P. V. Solovieva, I. V. UrazovaAbstract Under consideration are some polyhedral properties of the set of schedules for servicing identical requests by parallel devices. The requests satisfy some precedence conditions. Any service interruptions are prohibited. We propose some formalization of the set of schedules as a family of subsets of a finite set, define the polytope of schedules, and find the affine hull and dimension of this

Existence of a Solution to a System of Equations in Variations in an Optimal Control Problem J. Appl. Ind. Math. Pub Date : 20210422
K. S. MusabekovAbstract We consider an optimal control problem for some mathematical problem of a chemical reactor. We prove the existence of a solution to the system in variations which arises in deriving a necessary optimality condition in the form of the Pontryagin Maximum Principle.

Magnetohydrodynamic Vortex Motion of an Incompressible Polymeric Fluid J. Appl. Ind. Math. Pub Date : 20210422
A. M. Blokhin, R. E. Semenko, A. S. RudometovaAbstract Under consideration is some mathematical model describing magnetohydrodynamic motion of viscoelastic polymeric fluid in the cylindrical nearaxial zone of a swirl chamber. The absence of steadystate solutions is proved for the cylindrical zone with a fixed lateral boundary. The solutions are also considered in the case of nearaxial zone with a free lateral boundary.

Dynamics of Plane Strains in Heteromodular Isotropic Elastic Media J. Appl. Ind. Math. Pub Date : 20210422
O. V. Dudko, A. A. MantsyboraAbstract Under consideration are the features of nonlinear dynamics of a heteromodular elastic medium under the plane strain. Some mathematical model of the heteromodular isotropic elastic medium is given by a stressstrain relation with variable elastic moduli that are nonanalytic functions of deformation invariants. In this case, we show that the two planepolarized combined shock waves called quasilongitudinal

Trajectory and Global Attractors for a Modified Kelvin–Voigt Model J. Appl. Ind. Math. Pub Date : 20210422
A. S. Ustiuzhaninova, M. V. TurbinAbstract We study the qualitative behavior of weak solutions to an autonomous modified Kelvin–Voigt model on the base of the theory of attractors for noninvariant trajectory spaces. For the model under consideration, we determine the trajectory space, introduce the notions of a trajectory attractor and a global attractor, and prove the existence of these attractors.

Families of Portraits of Some PendulumLike Systems in Dynamics J. Appl. Ind. Math. Pub Date : 20210129
M. V. ShamolinAbstract The socalled pendulumlike systems arise in dynamics of a rigid body in a nonconservative field, in the theory of oscillations, and in theoretical physics. In this article, the methods of analysis are described which allow us to generalize the previous results. Herewith, we deal with some qualitative questions of the theory of ordinary differential equations whose solution facilitates studying

Asymptotic Expansion of the Solution of the Equation of a Slow Axisymmetric Electrovortex Flow Between Two Planes J. Appl. Ind. Math. Pub Date : 20210129
E. A. Mikhailov, A. Yu. ChudnovskyAbstract Electrovortex flows are of great interest both from the viewpoints of theoretical magnetohydrodynamics and applications. They arise when the electric current of variable density passes through a conducting medium (such as a liquid metal). The interaction between the current and self magnetic field of the current induces a nonpotential electromagnetic force that causes a vortex flow of the

A Maximum Dicut in a Digraph Induced by a Minimal Dominating Set J. Appl. Ind. Math. Pub Date : 20210129
V. V. VoroshilovAbstract Let \(G = (V,A)\) be a simple directed graph and let \(S\subseteq V \) be a subset of the vertex set \(V \). The set \(S \) is called dominating if for each vertex \(j\in V\setminus S\) there exist at least one \(i\in S \) and an edge from \(i \) to \(j\). A dominating set is called (inclusion) minimal if it contains no smaller dominating set. A dicut \(\{S\rightarrow \overline {S}\} \) is

Numerical Methods for Constructing Suboptimal Packings of Nonconvex Domains with Curved Boundary J. Appl. Ind. Math. Pub Date : 20210129
P. D. Lebedev, V. N. Ushakov, A. A. UspenskiiAbstract We study the problem of constructing some optimal packings of simplyconnected nonconvex plane domains with a union of congruent circles. We consider the minimization of the radius of circles if the number of the circles is fixed. Using subdifferential calculus, we develop theoretical methods for solution of the problem and propose an approach for constructing some suboptimal packings close

A Mathematical Model of Aseptic Inflammation Dynamics J. Appl. Ind. Math. Pub Date : 20210129
O. F. Voropaeva, T. V. BayadilovAbstract We present a new mathematical model of the aseptic inflammation dynamics. The adequacy of the model is confirmed by a qualitative and quantitative agreement with the laboratory data on the dynamics of the inflammatory process factors in the central zone of wound damage. We show that the model adequately describes not only the classical version of this process but also the available scenarios

On the Sixth International Olympiad in Cryptography NSUCRYPTO J. Appl. Ind. Math. Pub Date : 20210129
A. A. Gorodilova, N. N. Tokareva, S. V. Agievich, C. Carlet, E. V. Gorkunov, V. A. Idrisova, N. A. Kolomeec, A. V. Kutsenko, R. K. Lebedev, S. Nikova, A. K. Oblaukhov, I. A. Pankratova, M. A. Pudovkina, V. Rijmen, A. N. UdovenkoAbstract NSUCRYPTO is the unique cryptographic Olympiad containing scientific mathematical problems for professionals, school and university students from any country. Its aim is to involve young researchers in solving curious and tough scientific problems of modern cryptography. From the very beginning, the concept of the Olympiad was not to focus on solving olympic tasks but on including unsolved

On Integration of a Matrix Riccati Equation J. Appl. Ind. Math. Pub Date : 20210129
M. V. Neshchadim, A. P. ChupakhinAbstract We execute the complete integration of the simplest matrix Riccati equation in the two and threedimensional cases for an arbitrary linear differential operator. The solution is constructed in terms of the Jordan form of an unknown matrix and the corresponding similarity matrix. We show that a similarity matrix is always representable as the product of two matrices one of which is an invariant

Variable Neighborhood Search Algorithms for a Competitive Location Problem with Elastic Demand J. Appl. Ind. Math. Pub Date : 20210129
T. V. Levanova, A. Yu. GnusarevAbstract Under consideration is the situation in a competitive market when a new Company plans to make profit from opening its own facilities that offer goods or services. The Company have to take it into account that there are several projects for opening each facility, and similar facilities of the Competitor are already placed on the market. Moreover, customers themselves choose the places to meet

Analytical Solutions to the Differential Equation of Transverse Vibrations of a Piecewise Homogeneous Beam in the Frequency Domain for the Boundary Conditions of Various Types J. Appl. Ind. Math. Pub Date : 20210129
A. L. KarchevskyAbstract We obtain an analytical solution for the differential equation of transverse vibrations of a piecewise homogeneous beam in the frequency domain for various types of boundary conditions. All calculations use only addition, multiplication, and inversion of square matrices of second order. The formulas are such that, when using them for layerbylayer recalculation, the rounding error does not

Estimating Nonlinearity Characteristics for Iterative Transformations of a Vector Space J. Appl. Ind. Math. Pub Date : 20210129
V. M. FomichevAbstract We present theoretical foundations for the matrixgraphic approach (MGA) to the estimation of characteristics of the sets of essential and nonlinear variables of the composition of transformations of an \(n \)dimensional vector space over a field. The ternary nonlinearity matrix corresponds to a transformation, where the \(i \)th row and the \(j \)th column of the matrix contain \(0 \), \(1\)

A Parametrization of the General Lorentz Group J. Appl. Ind. Math. Pub Date : 20210129
N. I. OstrosablinAbstract We obtain the two new variants of an explicit parametrization for the general Lorentz group. Formulas are given for the direct and inverse fourdimensional Lorentz transformations. These formulas use the orthogonal three or fourdimensional matrices. We find the infinitesimal operators of the proper Lorentz group and the multiplication formulas (commutators) of the infinitesimal operators

Complete Complexity Dichotomy for $$\boldsymbol 7 $$ Edge Forbidden Subgraphs in the Edge Coloring Problem J. Appl. Ind. Math. Pub Date : 20210129
D. S. MalyshevAbstract The edge coloring problem for a graph is to minimize the number of colors that are sufficient to color all edges of the graph so that all adjacent edges receive distinct colors. The computational complexity of the problem is known for all graph classes defined by forbidden subgraphs with at most \(6\) edges. We improve this result and obtain a complete complexity classification of the edge

On Invariant Surfaces in Gene Network Models J. Appl. Ind. Math. Pub Date : 20210129
N. E. KirillovaAbstract We construct an invariant twodimensional surface in the phase portrait of a certain sixdimensional dynamical system considered as a model for the circular gene network functioning. This invariant surface contains an equilibrium point \(S_0 \) of the system, and if \(S_0 \) is hyperbolic then this surface contains a cycle of the system. The conditions for the existence of a cycle of this

Optimization Analysis of Electrostatic Cloaking Problems J. Appl. Ind. Math. Pub Date : 20210129
G. V. Alekseev, A. V. LobanovAbstract Under consideration are the inverse problems of electrostatics which arise in designing twodimensional multilayer shielding and cloaking devices. Using optimization, we reduce these inverse problems to the finitedimensional extremal problems in which the roles of control parameters are played by the constant dielectric permittivities of the layers. Basing on particle swarm optimization,

On Phase Correction in Tomographic Research J. Appl. Ind. Math. Pub Date : 20210129
Ya. Wang, A. S. Leonov, D. V. Lukyanenko, V. D. Shinkarev, A. G. YagolaAbstract Under consideration is the problem of improving the contrast of the image obtained by processing tomographic projections with phase distortion. The study is based on the wellknown intensity transfer equation. Unlike other works, this equation is solved in a bounded region of variation of the tomographic parameters. In a domain, a boundary value problem is posed for the intensity transfer

Some Approximate Solutions of the Dynamic Problem of Axisymmetric Shock Deformation of a Previously Unstressed Incompressible Elastic Medium J. Appl. Ind. Math. Pub Date : 20210129
V. E. Ragozina, Yu. E. IvanovaAbstract Approximate theoretical solutions are presented for the boundary value problem of the shock load on the boundary of a circular cylindrical cavity in the space occupied by an incompressible elastic medium undeformed previously. We assume that the shock load causes the movement of the medium particles along helical trajectories. Data on the types and velocities of shock waves are based on the

Application of Geodesic Grids for Modeling the Hydrodynamic Processes in Spherical Objects J. Appl. Ind. Math. Pub Date : 20210129
I. M. Kulikov, E. I. Vorobyov, I. G. Chernykh, V. G. ElbakyanAbstract We propose a new numerical method that bases on the mathematical apparatus of geodesic grids. This approach allows us to simulate spherical objects without any singularities that occur in using spherical or cylindrical coordinates. Solution of hyperbolic equations is described in detail. The method is expanded to solve the equations of hydrodynamics and tested on the Sedov point explosion

On Convergence of Computational Algorithms for a Variational Problem of Identifying the Coefficients of Difference Equations J. Appl. Ind. Math. Pub Date : 20201016
A. A. LomovAbstract Under consideration is the variational problem of identifying the coefficients of difference equations which the modified Prony method of extracting the sinusoids and exponentials from observations reduces to. We study the convergence of computational algorithms that are based on inverse iterations in a variable metric.

A Comprehensive Mathematical Model of the Hydrodynamic and Thermodynamic Processes in the Lower Pool of a Hydraulic Power Station J. Appl. Ind. Math. Pub Date : 20201016
A. A. Atavin, A. T. Zinoviev, A. V. Kudishin, T. E. OvchinnikovaAbstract Given the observations at the section of the Ob river below the dam location of the Novosibirsk Hydropower Station, the calculations of water level dependence on water discharge and ice hole length in winter are carried out by the model of nonstationary hydrodynamic and icethermal processes. Some algorithm is developed that uses the dependence and allows us to determine the optimum discharge

On a Routing Open Shop Problem on Two Nodes with Unit Processing Times J. Appl. Ind. Math. Pub Date : 20201016
M. O. Golovachev, A. V. PyatkinAbstract The Routing Open Shop Problem deals with \(n \) jobs located in the nodes of an edgeweighted graph \(G=(V,E) \) and \(m \) machines that are initially in a special node calleddepot. The machines must process all jobs in arbitrary order so that each machine processes at most one job at any one time and each job is processed by at most one machine at any one time. The goal is to minimize the

Planning a Defense That Minimizes a Resource Deficit in the WorstCase Scenario of Supply Network Destruction J. Appl. Ind. Math. Pub Date : 20201016
V. L. Beresnev, A. A. MelnikovAbstract We consider same model of planning the defense of edges of a supply network. The vertices of the network represent the consumers and the providers of a resource, while the edges allow us to transmit the resource without delays and capacity constraints. The Defender commits a bounded budget to protect some of the edges, aiming to minimize the damage that is caused by the destruction of the

Some Model of a Suspension Filtration in a Porous Media That Accounts for the TwoZone and Multistage Character of Deposition Kinetics J. Appl. Ind. Math. Pub Date : 20201016
B. Kh. Khuzhayorov, J. M. Makhmudov, B. M. Fayziev, T. I. BegmatovAbstract The problem of suspension filtration in a porous medium consisting of active and passive zones is posed and numerically solved in the case of a multistage kinetics of particle deposition. Some mathematical model of the process is proposed that is based on the general conservation laws and additional phenomenological assumptions. The influence of the multistage kinetics of particle deposition

Efficient Solvability of the Weighted Vertex Coloring Problem for Some Hereditary Class of Graphs with $$\boldsymbol {5}$$ Vertex Prohibitions J. Appl. Ind. Math. Pub Date : 20201016
D. V. Gribanov, D. S. Malyshev, D. B. MokeevAbstract We consider the problem of minimizing the number of colors in the colorings of the vertices of a given graph so that, to each vertex there is assigned some set of colors whose number is equal to the given weight of the vertex; and adjacent vertices receive disjoint sets. For all hereditary classes defined by a pair of forbidden induced connected subgraphs on \(5 \) vertices but four cases

An MHD Model of an Incompressible Polymeric Fluid: Linear Instability of a Steady State J. Appl. Ind. Math. Pub Date : 20201016
A. M. Blokhin, A. S. Rudometova, D. L. TkachevAbstract We study linear stability of a steady state for a generalization of the basic rheological Pokrovskii–Vinogradov model which describes the flows of melts and solutions of an incompressible viscoelastic polymeric medium in the nonisothermal case under the influence of a magnetic field. We prove that the corresponding linearized problem describing magnetohydrodynamic flows of polymers in an infinite

Analysis of a StageDependent Epidemic Model Based on a NonMarkov Random Process J. Appl. Ind. Math. Pub Date : 20201016
N. V. Pertsev, K. K. Loginov, V. A. TopchiiAbstract We present some stochastic model of an infection spread among the adult population of a certain region. The model bases on a random birth and death process supplemented by the point distributions that reflect the durations of stay of individuals at various stages of the disease. The durations of some stages of the disease are assumed constant. The model is a stochastic analog of a system of

On a Modification of the Rusanov Solver for the Equations of Special Relativistic Magnetic Hydrodynamics J. Appl. Ind. Math. Pub Date : 20201016
I. M. KulikovAbstract We describe the implementation of a modification of the Rusanov solver for the equations of special relativistic magnetic hydrodynamics. The particularity of the relativistic hydrodynamics equations, including a magnetic field, is a natural constraint on the admissible wave propagation velocity, which allows us to construct a fairly simple modification of the Rusanov solver using the maximum

2Approximation Algorithms for Two Graph Clustering Problems J. Appl. Ind. Math. Pub Date : 20201016
V. P. Il’ev, S. D. Il’eva, A. V. MorshininAbstract We study a version of the graph \(2\)clustering problem and the related semisupervised problem. In these problems, given an undirected graph, we have to find a nearest \(2 \)cluster graph, i.e. a graph on the same vertex set with exactly two nonempty connected components each of which is a complete graph. The distance between two graphs is the number of noncoinciding edges. The problems

Nonlinear Oscillations in the Clock Frequency Generator Excited by a Sequence of Concentrated Electrostatic Pulses Coordinated with the Oscillations J. Appl. Ind. Math. Pub Date : 20201016
S. I. FadeevAbstract Under consideration is the mathematical model of a clock frequency generator in which some highfrequency oscillations of a movable electrode are excited by a sequence of concentrated electrostatic pulses; wherein the times of pulse action are coordinated with the oscillations of the movable electrode by analogy with the wellknown theory of a trigger clock. The results of studying the mathematical

On the Approximation of Random Variables on a Finite Chain J. Appl. Ind. Math. Pub Date : 20201016
A. D. YashunskyAbstract We consider the transformations of independent random variables over a linearly ordered finite set (a chain) by the join and meet operations. We investigate the possibility of approximating an arbitrary probability distribution on a chain by means of a (possibly iterated) application of the join and meet operations to independent random variables with distributions from a given set. We establish

Equilibrium Problem for a Timoshenko Plate with a Geometrically Nonlinear Condition of Nonpenetration for a Vertical Crack J. Appl. Ind. Math. Pub Date : 20201016
N. P. Lazarev, G. M. SemenovaAbstract Under consideration are the variational problems concerning the equilibrium of plates containing a crack. Two new mathematical models are proposed in which the nonpenetration conditions define the corresponding nonconvex sets of admissible functions. The first model describes the equilibrium of a Timoshenko plate with a crack, and the second corresponds to a composite plate containing a crack

Estimation of the Calculation Accuracy in the Problem of Partial Identification of a Substance J. Appl. Ind. Math. Pub Date : 20201016
V. G. NazarovAbstract Under consideration is the problem of estimating the accuracy of calculations in the problem of partial identification of the chemical composition of an unknown medium from the results of repeated irradiation of this medium by collimated Xray fluxes at various energies. The mathematical formulation of the identification problem is presented together with its comparison with a similar problem

Solution of the Convolution Type Volterra Integral Equations of the First Kind by the QuadratureSum Method J. Appl. Ind. Math. Pub Date : 20201016
A. L. KarchevskyAbstract Some algorithm is presented for solving the convolution type Volterra integral equation of the first kind by the quadraturesum method. We assume that the integral equation of the first kind cannot be reduced to an integral equation of the second kind but we do not assume that either the kernel or some of its derivatives at zero are unequal to zero. For the relations we propose there is given

A Polynomial Algorithm with Asymptotic Ratio $$\boldsymbol {2/3}$$ for the Asymmetric Maximization Version of the $$\boldsymbol m $$ PSP J. Appl. Ind. Math. Pub Date : 20201016
A. N. Glebov, S. G. ToktokhoevaAbstract In 2005, Kaplan et al. presented a polynomialtime algorithm with guaranteed approximation ratio \(2/3\) for the maximization version of the asymmetric TSP. In 2014, Glebov, Skretneva, and Zambalaeva constructed a similar algorithm with approximation ratio \(2/3 \) and cubic runtime for the maximization version of the asymmetric \(2 \)PSP (\(2 \)APSPmax), where it is required to find two

The D’Alembert–Lagrange Principle: a Geometrical Aspect J. Appl. Ind. Math. Pub Date : 20201016
O. E. ZubelevichAbstract The d’Alembert–Lagrange Principle and the theory of ideal connections are considered from the viewpoint of modern differential geometry and tensor analysis.

Mathematical and Numerical Models of the Central Regulatory Circuit of the Morphogenesis System of Drosophila J. Appl. Ind. Math. Pub Date : 20200710
T. A. Bukharina, A. A. Akinshin, V. P. Golubyatnikov, D. P. FurmanAbstractThe results are presented of mathematical and computer simulation of the functioning of the central regulatory circuit (CRC) which is the system integrator of the gene networks of morphogenesis of Drosophila mechanoreceptors. The main element of the CRC is represented by the complex of AchaeteScute (ASC) genes, the main genes of the mechanoreceptor morphogenesis. The content level of the

On the Angular Moment Operators of Attenuated Ray Transforms of Scalar $$\boldsymbol {3D}$$ Fields J. Appl. Ind. Math. Pub Date : 20200710
E. Yu. DerevtsovAbstractUnder consideration are the operators of angular moments which map the values of generalized attenuated ray transforms (ART) into the set of symmetric \(p \)tensor fields. The differential relations between the values of ARTs of various orders, acting on stationary or dynamic source distributions \(f \), serve as the basis for establishing the differential connections between the tensor fields

SymbolicNumerical Analysis of the Necessary Stability Conditions for the Relative Equilibria of an Orbital Gyrostat J. Appl. Ind. Math. Pub Date : 20200710
A. V. BanshchikovAbstractUsing the software developed on the basis of the computer algebra system Mathematica, we study the rotational motion along the circular orbit of a satellitegyrostat in a Newtonian central field of forces. The linearized equations of a perturbed motion in the vicinity of the relative equilibrium of the system are constructed on a computer in symbolic form, and the necessary stability conditions

NPCompleteness of the Independent Dominating Set Problem in the Class of Cubic Planar Bipartite Graphs J. Appl. Ind. Math. Pub Date : 20200710
Ya. A. Loverov, Yu. L. OrlovichAbstractIt is known that the independent dominating set problem is NPcomplete both in the class of cubic planar graphs and in the class of cubic bipartite graphs. Still open is the question about the computational complexity of the problem in the intersection of these graph classes. In this article, we prove that the independent dominating set problem is NPcomplete in the class of cubic planar bipartite

A GraphTheoretical Method for Decoding Some Group MLDCodes J. Appl. Ind. Math. Pub Date : 20200710
V. M. Deundyak, E. A. LelyukAbstractWe construct the class of majoritylogical decodable group codes using a method for combining the codes that are based on the tensor product and the sum of codes. The construction of this class rests on the Kasami–Lin technique, which allows us to consider not only individual codes but also families of codes and utilizes the \(M\)orthogonality construction presented by Massey that is important

Simulation of the Stationary Nonisothermal MHD Flows of Polymeric Fluids in Channels with Interior Heating Elements J. Appl. Ind. Math. Pub Date : 20200710
A. M. Blokhin, B. V. SemisalovAbstractBasing on the rheological mesoscopic Pokrovskii–Vinogradov model, the equations of nonrelativistic magnetohydrodynamics, and the heat conduction equation with dissipative terms, we obtain a closed coupled system of nonlinear partial differential equations that describes the flow of solutions and melts of linear polymers. We take into account the rheology and induced anisotropy of a polymeric

On the König Graphs for a $$\boldsymbol 5 $$ Path and Its Spanning Supergraphs J. Appl. Ind. Math. Pub Date : 20200710
D. B. Mokeev, D. S. MalyshevAbstractWe describe the hereditary class of graphs whose every subgraph has the property that the maximum number of disjoint \(5\)paths (paths on \(5 \) vertices) is equal to the minimum size of the sets of vertices having nonempty intersection with the vertex set of each \(5 \)path. We describe this class in terms of the “forbidden subgraphs” and give an alternative description, using some operations

Reconstruction of the Lambert Curve in a Scattering Medium by Using Pulsed Sounding J. Appl. Ind. Math. Pub Date : 20200710
V. A. Kan, I. V. ProkhorovAbstractUnder study is some mathematical model of the radiation transfer process in a scattering medium initiated by a pulsed point isotropic source. We inspect the inverse problem of finding a diffusely reflecting curve by using the two integral overdetermination conditions on the solution of the radiative transfer equation. Some nonlinear differential equation is obtained for the function that describes

A Hybrid Local Search Algorithm for the Consistent Periodic Vehicle Routing Problem J. Appl. Ind. Math. Pub Date : 20200710
I. N. Kulachenko, P. A. KononovaAbstractUnder consideration is some new realworld application of vehicle routing planning in a finite time horizon. Let a company have a set of capacitated vehicles in some depots and serve some set of customers. There is a frequency for each customer which describes how often the customer should be visited. Time intervals between two consecutive visits are fixed, but the visiting schedule is flexible

The Problem of Determining the 2D Kernel in a System of IntegroDifferential Equations of a Viscoelastic Porous Medium J. Appl. Ind. Math. Pub Date : 20200710
D. K. Durdiev, A. A. RakhmonovAbstractUnder consideration is the system of integrodifferential equations of a viscoelastic porous medium. The direct problem is to define the \(y\)component of the displacement vectors of the elastic porous body and the liquid from the initial boundary value problem for these equations. We assume that the kernel of the integral term of the first equation depends on time and one of the spatial variables

Computational Complexity of the Problem of Choosing Typical Representatives in a $$\boldsymbol 2$$ Clustering of a Finite Set of Points in a Metric Space J. Appl. Ind. Math. Pub Date : 20200710
I. A. BorisovaAbstractWe consider the computational complexity of one extremal problem of choosing a subset of \(p \) points from some given \(2 \)clustering of a finite set in a metric space. The chosen subset of points has to describe the given clusters in the best way from the viewpoint of some geometric criterion. This is a formalization of an applied problem of data mining which consists in finding a subset