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Vol. 17 (56), No. 1. 2004
Mathematics. Mechanics. Informatics and Cybernetics.

Wronsky В.М.
On Problem on Small Motions and Proper Oscillations of System "Fluid-Gas" in the Bounded Region
In the article the problem on small motions and proper oscillations of system "fluid-gas"in the bounded region is considered. It was show spectrum consists of a countable set of eigenvalues. Asymptotic formulas for eigenvalues were obtained.

Kopachevsky N.D., Zakora D.A.
On Spectral Problem Connected with the Second Order Integro-Differential Equation
The Cauchy problem
is considered. The associated spectral problem is formulated. Localization of a spectrum, asymptotic formulas for branches of eigenvalues are received. Statements on Riesz basis property and multiple completeness of a part of eigenvalues and adjoint elements are proved.

Karpenko I.I., Sukhtaev А.I., Tyshkevich D.L.
On One Approach for Differentiability of Functions of Quaternion Variables
In this paper the new approach for differentiability of functions defined on region of the real quaternion skew-field is suggested. It's proved different criteria for functions of a quaternion variable to be differentiable.

Krivoruchko А.І.
On the Non-Centroaffine Groups Generated by Reflections with Respect to the Straight Lines
The basic polynomial invariants of a transformation group H of the affine space are found in the case when H satisfies the following conditions:

  1. H is the non-centroaffine group generated by affine reflections with respect to straight lines;
  2. H acts on some non-cylindrical algebraic surface.

Lyakh A.M.
Space Deformations and their Application to Phytoplankton Shape Modeling
The theory of Bezier curves, pathes and volumes is investigated, and two methods of 3D space deformation, — Free Form Deformation and Axial Deformation, which are used for phytoplankton cells shape modeling, are considered. The method of 3D phytoplankton models building, on the basis of a photographic images, is described. These models are used for accurate calculating phytoplankton volumes and surfaces area.

Muratov М.A., Rubshtain В.A.
On One Class of Maximal Invariant Subspaces of Continuous Operator in Indefinite Inner Product Space
We study analogs of Dominated Ergodic Theorems in rearrangement invariant spaces of a measurable functions for sequence absolute contraction on the positive semiaxis.

Pavlov E.A.
On Birkof-Hinchin Theorem
In this paper Birkof-Hinchin theorem is generalized on ideal Banach functional spaces.

Orlov I.V.
Sufficient Conditions of Extremum and If-Extremum in the Product of Two Nuclear LCS (General Case)
In the work the sufficient conditions of extremum and compact extremum in the product of two nuclear LCS for the case of non-commuting second partial deri-vatives are proposed. In particular, the sufficient conditions of compact extremum for Euler-Lagrange functional are proved.

Tretyakov D.V.
On the Orthogonality Relation in Hilbert Space and Some Properties of Additive Operators
The special inner product and orthogonality relation in complex Hilbert space were defined. With the help of this product it's defined and studied involution and different classes of operators on the bimodulne of all continued additive operators. The classification of spectrum of bounded additive operator is proposed too.

Tyshkevich D.L.
On One Class of Maximal Invariant Subspaces of Continuous Operator in Indefinite Inner Product Space
In this paper we study the structure of maximal reducing subspaces of continuous linear operator in indefinite inner product space inducing unitary operator.

Tikhonov A.S.
Property of Maximality for Spectral Components (Case of Multiply Connected Domains)
The aim of this paper is to show that operators closed to normal ones with spectrum on a curve possess certain maximal invariant subspaces, which are related to the interior and the exterior of the curve. We generalize the corresponding results (for the real axis and the unit circle) established by Naboko and Makarov.