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**Редакційна колегія (UA)**,*P. 2.*[ (PDF) ] **Contents / Зміст (UA)**,*P. 3.*[ (PDF) ]**V.D. Gordevskyy, O.O. Hukalov,**The bimodal distribution with some Maxwell modes for the Bryan-Piddañk equation,*P. 4-18.*[ Abstract ] [ Full-text available (PDF) ]**V.I. Sudilovskaya,**Description operator C-symmetry in the case of the space C^2,*P. 19–26.*[ Abstract ] [ Full-text available (PDF) ]**S.M. Chuiko,**The solution of the linear matrix equations,*P. 27-33.*[ Abstract ] [ Full-text available (PDF) ]**E.V. Oliynyk,**The study of solutions of a class of nonlinear systems,*P. 34-46.*[ Abstract ] [ Full-text available (PDF) ]**N.A. Guk, N.I. Stepanova,**Identification of rigid inclusions in the thin plate,*P. 47-60.*[ Abstract ] [ Full-text available (PDF) ]**O.V. Zelenskiy, V.M. Darmosiuk,**The sum of elements of the reduced exponent matrix,*P. 61-66.*[ Abstract ] [ Full-text available (PDF) ]**A.F. Grishin (obituary).***P. 67-68.*[ Full-text available (PDF) ]

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-Piddañk equation,rough spheres,
''Accelerating-Packing'', non-uniform weight.

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

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.

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.

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.

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.

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.

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