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Abstract: The second author’s name should read J. G. Ingtem In the article metadata on SpringerLink, the email icon should appear after J. G. Ingtem. PubDate: 2019-04-01 DOI: 10.1007/s10958-019-04240-x

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Abstract: We establish necessary and sufficient conditions for the solvability of a system of matrix equations AX = B and BY = A over associative rings. PubDate: 2019-04-01 DOI: 10.1007/s10958-019-04215-y

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Abstract: We prove the exponential stability of a trivial torus for a class of nonlinear extensions of dynamical systems on a torus. The obtained results can be applied to the study of stability of toroidal sets for a certain class of impulsive dynamical systems. PubDate: 2019-04-01 DOI: 10.1007/s10958-019-04234-9

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Abstract: We consider conjugate boundary-value problems of heat exchange for the cases where a viscous incompressible liquid moves through channels with noncanonical cross section flowing around a bundle of rods. The influence of the type of packing on the velocity and temperature distributions is investigated. For the solution, we use the R-functions method in combination with the Ritz variational method. We consider the cases of cyclic, staggered, and rectangular packing of fuel elements. PubDate: 2019-04-01 DOI: 10.1007/s10958-019-04225-w

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Abstract: We establish new properties of solutions of a functional-differential equation with linearly transformed argument. PubDate: 2019-04-01 DOI: 10.1007/s10958-019-04230-z

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Abstract: The problem of stability of shells compliant to shear and compression is studied by the finite-element method. On the basis of relations of the geometrically nonlinear theory of thin shells compliant to shear and compression (six-mode version), we write the key equations for the determination of their initial postcritical state and formulate the corresponding variational problem. A numerical scheme of the finite-element method is constructed for the solution of the problems of stability of these shells. The order of the rate of convergence of the scheme proposed for the numerical solution of the problems of stability is investigated. PubDate: 2019-04-01 DOI: 10.1007/s10958-019-04221-0

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Abstract: We study the conditional symmetry of a system of nonlinear reaction-diffusion equations and establish the existence of operators of conditional symmetry for systems of nonlinear reaction-diffusion equations with any number of independent variables and find these operators in the explicit form. The exact solutions of nonlinear reaction-diffusion equations with exponential nonlinearity are constructed. PubDate: 2019-04-01 DOI: 10.1007/s10958-019-04229-6

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Abstract: We establish sufficient conditions for the existence of solutions of a weakly perturbed linear boundary-value problems for a system of integrodifferential equations. We also establish conditions for the existence and uniqueness of solutions of problems of this kind and propose an iterative procedure for the construction of the required solutions. PubDate: 2019-04-01 DOI: 10.1007/s10958-019-04231-y

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Abstract: We substantiate an averaging scheme for integrodifferential inclusions on a bounded interval. PubDate: 2019-04-01 DOI: 10.1007/s10958-019-04236-7

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Abstract: We establish necessary and sufficient conditions for the existence of solutions of a linear matrix boundaryvalue problem for a system of matrix differential-algebraic equations with pulsed action. We also construct a generalized Green operator of linear boundary conditions for a system of matrix differentialalgebraic equations with pulse action. To solve the matrix differential-algebraic boundary problem with pulsed action, we use the original conditions of solvability and the structure of the general solution of the linear matrix equation. PubDate: 2019-04-01 DOI: 10.1007/s10958-019-04239-4

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Abstract: We study the random flow of admixtures in a two-phase stochastically inhomogeneous strip with the most probable arrangement of inclusions in the vicinity of the surfaces of the body. A mathematical model is formulated for the function of diffusion flow with nonzero constant initial concentration. A random diffusion flow is represented in the form of a Neumann series. The procedure of averaging of the random mass flow over the ensemble of phase configurations with arcsine distribution function is performed. The influence of the characteristics of the medium on the distribution of mass flow is analyzed. It is shown that if the diffusion coefficient of admixtures in the inclusion is higher than for the matrix, then the increase in the characteristic thickness of the layers causes a decrease in the value of the diffusion flow, whereas the mass flow in the entire body increases with the volume fraction of the inclusions. PubDate: 2019-04-01 DOI: 10.1007/s10958-019-04222-z

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Abstract: We study the problem of optimization of motion of a two-link manipulator, which performs transport operations under the action of controls (moments of forces in the hinges). The initial and the final position of the gripping device of the manipulator and the time of the operation are regarded as known. The quality of motion of the manipulator is estimated by a quadratic functional. Possible configurations of the manipulator at the beginning and at the end of the operation are taken into account. We propose an algorithm for the construction of suboptimal solutions of the problem based on the parametrization of the angular coordinates of the manipulator by the sum of a cubic polynomial and a finite trigonometric series and on the use of the methods of inverse problems of dynamics and numerical procedures of nonlinear programming. The influence of configurations of the manipulator and the parameters of the trigonometric series on the characteristics of the suboptimal process is analyzed. PubDate: 2019-04-01 DOI: 10.1007/s10958-019-04227-8

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Abstract: We consider a quasistatic problem of thermoelasticity for a cylindrical shell of finite length in a variable temperature field. The surface of the shell exchanges heat with the ambient medium of constant temperature according to Newton’s law. The problem is solved with regard for the shear strains. The asymptotic state of the shell in which the computed quantities attain their maximal values is studied in detail. We also perform the comparative analysis of the thermoelastic state of the shell of finite length and the corresponding state of a shell of infinite length. PubDate: 2019-04-01 DOI: 10.1007/s10958-019-04220-1

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Abstract: We consider a synchronization problem for genetic oscillator networks. The genetic oscillators are modeled as nonlinear systems of the Lur’e type. Simple and verifiable synchronization conditions are presented for genetic oscillator networks by using the theory of absolute stability and the matrix theory. A network composed of coupled Goodwin models is used as an example of numerical simulation to verify the efficiency of the theoretical method. PubDate: 2019-04-01 DOI: 10.1007/s10958-019-04232-x

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Abstract: We find the asymptotic distributions of stresses and displacements near the edge point of a contact zone for problems of friction contact and contact with complete adhesion of an elastic body with a die, as well as for the problems of friction contact of two elastic bodies and contact of the faces of interface cracks. The distributions of elastic fields are obtained by using one of the Kolosov–Muskhelishvili complex potentials in the form of a Cauchy-type integral whose density is given by a complex function of contact forces. PubDate: 2019-04-01 DOI: 10.1007/s10958-019-04218-9

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Abstract: We present new fixed-point theorems for mappings acting on a metric space and establish conditions for the existence of bounded solutions of difference equations. PubDate: 2019-04-01 DOI: 10.1007/s10958-019-04237-6

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Abstract: For a linearly ordered group G , we define a subset A ⊆ G to be a shift-set if, for any x, y, z ϵ A with y < x, we get x · y-1 ··z ϵ A. We describe the natural partial order and solutions of equations on the semigroup B(A) of shifts of positive cones of A . We study topologizations of the semigroup B(A). In particular, we show that, for an arbitrary countable linearly ordered group G and a nonempty shift-set A of G , every Baire shift-continuous T1-topology τ on B(A) is discrete. We also prove that, for any linearly nondensely ordered group G and a nonempty shift-set A of G , every shift-continuous Hausdorff topology τ on the semigroup B (A) is discrete. PubDate: 2019-04-01 DOI: 10.1007/s10958-019-04216-x

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Abstract: We formulate a complete system of relations of the local gradient electromagnetothermomechanics of electrically conductive nonferromagnetic polarizable solid media. The nonlocal character of the constitutive relations of the proposed mathematical model is explained by the presence of electric quadrupole moments in the polarization current. As a result of taking into account these moments, the space of parameters of the thermodynamic state of the body is expanded by including a pair of additional conjugate parameters, namely, the quadrupole moment and the gradient of the vector of electric-field intensity. It is shown that the developed model takes into account the electromechanical interaction for materials with high level of symmetry (isotropic materials) and describes the flexoelectric and thermopolarization effects. We also present the key system of equations for a physically and geometrically linear medium. PubDate: 2019-04-01 DOI: 10.1007/s10958-019-04223-y

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Abstract: We consider a nonlocal problem with integral conditions for a system of hyperbolic equations with two independent variables. We study the solvability of the considered problem and construct algorithms aimed at finding its approximate solutions by introducing additional functional parameters. The investigated problem is reduced to an equivalent problem that consists of the Goursat problem for a system of hyperbolic equations with parameters and a boundary-value problem with integral condition for a system of ordinary differential equations for the introduced parameters. We propose algorithms for finding approximate solutions of the problem based on the algorithms used for the solution of the equivalent problem and prove their convergence to the exact solution. PubDate: 2019-04-01 DOI: 10.1007/s10958-019-04228-7

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Abstract: We consider a linear parabolic boundary-value problem in a thin 3D starlike joint that consists of a finite number of thin curvilinear cylinders connected through a domain (node) with diameter O(ε). We develop a procedure for the construction of the complete asymptotic expansion of the solution as ε → 0, i.e., in the case where the starlike joint is transformed into a graph. By using the method of matching of the asymptotic series, we deduce the limit problem (ε = 0) on a graph with the corresponding Kirchhoff-type conjugation conditions at the vertex. We also prove asymptotic estimates, which enable us to trace the influence of the geometric shape of the node and the physical processes running in the node on the global asymptotic behavior of the solution. PubDate: 2019-04-01 DOI: 10.1007/s10958-019-04235-8