Scientific Notes of

Taurida National V.I. Vernadsky University

Taurida National V.I. Vernadsky University

Series

Physical and Mathematical Sciences

**Vol. 23 (62), No. 2. 2010****Physics and Mathematics Sciences.**

**Akhramovich M.V., Orlov I.V.
**Variant of Universal Banach-Steinhaus Type Theorem for Arbitrary Locally Convex Spaces

**Баtyr E.I.**

Small Movements and Normal Oscillations of a System of Three Connected Bodies with the Cavities, Filled by an Ideal Incompressible Fluid.batyr

*In this paper we considered an initial-boundary value and spectral problems about the**small movements of a system of three bodies. The system is a circuit of the consistently **connected hard bodies. Each of the bodies of such circuit is a gyrostat. The existence**theorem of solutions of the Cauchy problem is formulated. The properties of normal**oscillations are described. The known
N.E. Zhukovsky’s theorem is transferred on a case**of a movement of three bodies*.

**Bozhonok E.V.
**Conditions of Existence of Nonlocal Compact Extrema of Variational Functionals in Sobolev Space H

**Vronsky B.M., Kopachevsky N.D.
**Asymptotic of Some Operator-Function is Investigated

**Donskoy V.I.**

VC-Dimension Estimations of the Basic Algorithms of Empirical Generalization for Pattern Recognition Problems Obtained by the pVCD Method

*In this paper, VC-Dimension estimations for Decision Trees, Neural Networks, DNF, Function Compositions obtained by pVCD method are presented. The pVCD method is based on the Kolmogorov’ approach to complexity definition.*

**Dudik O.A.
**On Normal Oscillations of a Pendulum with a Cavity Partially Filled with a Capillary Viscous Fluid

**Karpenko I.I. **

Non-Hermitian Self-Adjoint Quaternionic Matrixes

*In this paper there considered matrices which are self-adjoint concerning the non-Hermitian involution in the real algebra of quaternions (a– self-adjoint matrices). Analog of Takagi decomposition for this matrix class is received. As applications the theorem about similarity of any quaternionic matrix and some a–self-adjoint matrix is proved and properties of the finite-dimensional quaternionic module with the inner product are investigated*.

**Muratov M.A., Pashkova Yu.S., Rubshteyin B.A.
**Order Ergodic Theorems in Orlicz Spaces

**Pogrebitskaya A.M., Smirnova S.I.
**On Estimate of Exactness of Analytical Hybrid Solution for the Heat Transfer Problem

**Rudnitsky O.I., Romanenko I.A.
**Algebras of Polynomials Pogorelov of the Octahedral Groups

**Stonyakin F.S.
**Strong Compact Properties and Limit Form of Radon-Nikodym Property for Vector Measures

**Tyshkevich D.L.
**On Commensurability of Bimodules of the Special Types