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Vol. 16 (55), No. 2. 2003
Mathematics. Mechanics. Informatics and Cybernetics.

Mathematics.

Zakora D.A.
Оn Some Quasilinear Nonstationary Equation
Some quasilinear nonstationary equation with hounded operator coefficients depending of time and specific quadratic nonlinearitv is investigated. The theorem on global solvability of the Cauchy problem is proved. Conditions for boundedness of solutions are obtained.

Karpenko І.I., Omel'chenko P.V.
Structure of a Linear Operator in a Finite-Dimensional Quaternionic Hilbert Space
In this paper the structure of a linear operator acting in a finite-dimensional quaternionic Hilbert space is studied. The main result is that an analogue of decomposition of complex linear space in the direct sum of the algebraic eigenspaces has place for such operators. The method of the construction of minimal invariant cyclic subspaces is suggested. Other results concern the spectral decomposition of normal operators in a finite-dimensional quaternionic space.

Krivoruchko А.I.
On the Groups Generated by Reflections with Respect to the Skew Straight Lines
The basic polynomial invariants of a transformation group H of the affine space V are found in the case when H satisfies the following conditions: a) H acts on some non-cylindrical algebraic surface F ⊂ V; b) H is generated by affine reflections with respect, to straight lines, some two of which are skew.

Muratov М.А., Pashkova Yu.S., Rubshtein В.A.
Dominated Ergodic Theorem for Sequence Positive Contraction in Rearrangement Invariant Spaces of Measurable Functions
We study conditions under which Dominated Ergodic Theorems hold in rearrangement invariant spaces for sequence positive contraction.

Orlov I.V.
Theorems on Homomorphism, Open Mappings and Closed Graph in Inductive Scales of Spaces
Banach theorems on homomorphism, open mappings and closed graph are transferred to linear operators in inductive scales of spaces. The results are applied to the operators acting in inductive limits.

Orlov I.V., Tolstopyatov Ya.V.
Operators in the Double Scales of Spaces and Regularity Condition
In the work linear continuous operators in double scales of spaces are investigated. The extension conditions for operators in unary scales up to the operators in double scales are obtained. In particular, new regularity conditions for classical linear operators are obtained.

Starkov P.A.
Exclusive Values of the Fixed Parameter for Transmition Problems
Given article finishes studying properties of decisions of an abstract spectral problem, which was obtained during researching the transmition problem. Last case of values of the fixed parameter λ unexplored earlier by the author, namely its exclusive values is considered. In work theorems of a spectrum and basis of eigen elements of a researched abstract spectral problem are formulated and proved.

Tikhonov A.S.
An Extreme Factorizations of J-Contractive-Valued Functions
Using the notion of abstract weak subspace, unified approach to extreme factorizations of J-contractive-valued functions is presented.

Tyshkevich D.L.
Nonorthoextendable Subspaces of Indefinite Inner Product Spaces
In this paper we study structure and properties of so-called nonorthoextendable subspaces of indefinite inner product spaces, i.e. subspaces ӿ1 satisfying relation ӿ 1[⊥]⊆ ӿ1. Subspaces of such type naturally appear in study of maximal orthogonal systems in indefinite inner product spaces.

Tsvetkov D.О.
Problem on Normal Oscillations of a Partially Dissipative Hydrosystem
There was investigated the problem on normal oscillations of some partially dissipative hydrosystem. The spectrum of normal oscillations and other questions are studied.

Yakovlev А.V.
Small Movements of a Rigid Body with a Cavity Fulfilled by a Visco-Elastic Fluid
In the paper, there was investigated two-dimentional initial boundary value problem on small movements of a rigid body with a cavity fulfilled by a visco- elastic fluid. Under some assumptions/ the theorem on strong solvability of the problem on arbitrary interval of time is proved.

Kruglyak S.A., Popovych S.V., Samoilenko Yu.S.
Representations of *-Algebras Associated with Dynkin Graphs and Horn's Problem
The connection between *-representations of *-algebras associated with graphs locally scalar graph representations and algebraic Horn's problem is studied. The solution of algebraic Horn's problem for Dynkin graph D4 is given.

Informatics.

Donskoy V.l.
On Metrical Properties of the Shortest Empirical Conjunctive Regularities
In this paper, it is shown that utilization of the shortest empirical conjunctive regularities as elementary classifier for Pattern Recognition problem, satisfying the compactness hypothesis, can reduce to considerable errors.