Visnyk of V.N.Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics

Contents and Abstracts

Volume 82, 2015

 

/ This page in Ukrainian



V.D. Gordevskyy, .. ukalov, The bimodal distribution with some Maxwell modes for the Bryan-Piddak equation, P. 4-18.

The approximate solution of Bryan-Piddack equation in the form of a bimodal distribution with the Maxwell modes that describe the motion of the gas type ''Accelerating-Packing'' is constructed . The sufficient conditions for minimization of inhomogeneous weighted residual for the model of rough spheres are obtained.

Keywords: Bryan-Piddak equation,rough spheres, ''Accelerating-Packing'', non-uniform weight.

2000 Mathematics Subject Classification: 76P05, 45K05, 82C40, 35Q55.   [ Full-text available (PDF) ]   Top of the page.


V.I. Sudilovskaya, Description operator C-symmetry in the case of the space C^2., P. 1926.

We describe all operators C in two-dimensional Hilbert space C^2 using Pauli matrices. The conditions for J_alpha-adjoint operator, which guarantee it the property of C-symmetry.

Keywords: Krein spaces, indefinite metrics, C-symmetry, Pauli matrices.

2000 Mathematics Subject Classification: 47A55, 47A57, 47B25.   [ Full-text available (PDF) ]   Top of the page.


S.M. Chuiko, The solution of the linear matrix equations, P. 27-33.

Linear matrix equations widely used in the theory of stability of motion, control theory and signal processing. We suggest an algorithm for finding solutions of the inhomogeneous generalized matrix equation and, in particular, the Sylvester equation in general case when the linear matrix operator L, corresponding to the homogeneous part of the linear generalized matrix equation, has no inverse.

Keywords: Lyapunov matrix equation, Sylvester matrix equation, pseudoinverse matrix.

2000 Mathematics Subject Classification: 15A24, 34A15, 34C25.   [ Full-text available (PDF) ]   Top of the page.


E.V. Oliynyk, The study of solutions of a class of nonlinear systems, P. 34-46.

We have studied and described for systems of nonlinear equations. It is a basis of the triangular model for commutative systems of non-selfadjoint bounded operators. The case of a multiple spectrum of the spectral density.

Keywords: : triangular model, commutative systems of linearnonselfadjoint, eigenvectors.

2000 Mathematics Subject Classification: 47A48, 47N20, 34G20.   [ Full-text available (PDF) ]   Top of the page.


N.A. Guk, N.I. Stepanova, Identification of rigid inclusions in the thin plate, P. 47-60.

The problem of identifying the location of the rigid inclusions in thin plate is considered. The finite element method is being used for discretization the unknown functions of the mathematical model. Geometric inverse problem is formulated in the conditional-correct statement, taking into account restrictions on the number of solutions. Parameters identification is performed via minimization of the Lagrangian.

Keywords: rigid inclusion, geometric inverse problem, finite element method, the Lagrangian.

2000 Mathematics Subject Classification: 15A24, 34A15, 34C25.   [ Full-text available (PDF) ]   Top of the page.


O.V. Zelenskiy, V.M. Darmosiuk, The sum of elements of the reduced exponent matrix, P. 61-66.

This paper investigates the possible sum of elements of the reduced exponent matrix and possible sum of elements of the reduced exponent matrix with a quiver without loops.

Keywords: exponent matrix; admissible quiver of exponent matrix.

2000 Mathematics Subject Classification: 16G20, 16G30.   [ Full-text available (PDF) ]   Top of the page.


A.F. Grishin (obituary). P. 67-68.         [ Full-text available (PDF) ]   Top of the page.



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