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Vol. 19 (58), No. 1. 2006
Mathematics.

Karpenko I.I, Sukhtaev A.I., Tyshkevich D.L.
Spectral Decomposition of a Normal Operator in a Quaternionic Hilbert Bimodule
Using the new approach to the definition of quaternionic analytic functions we received the analogue of Cauchy's formulae. The theorem about the partition of a quaternionic Hilbert bimodule into the direct sum of the invariant submodules for the continuous linear operator is proved, and also the spectral decomposition of a normal (bounded) operator in a quaternionic bimodule is constructed.

Lukjanova E.A., Mosentsova A.B.
About Solution's of Some Classes Integral Equation Best Accuracy
There is some method of approximated solution of Fredgolm's equations of 2 class with kernel from Sobolev's сlasses described in this article. Proposed method consists in substitution kernel for its special Furje's sum with numbers harmonyk choosed in special way. There was proved that this method have the best precision among all methods with fixing informational vector's length.

Rudnitskiy O.I., Romanenko I.A.
About the Special Invariants of the Tetrahedral Groups, Generated by Reflections on the Unitary Plane
Let. PG be algebra, generated by Pogorelov polynomials of the finite unitary reflection group G. The degrees of generators of the algebra PG are found in the case when G is the tetrahedral group, generated by reflections on the unitary plane.

Starkov P.A.
Interior Problem for Stocks Equation
An interior problem for linear hydrodynamics equation is studied (the Stocks equations). Before this the problem was not investigated. By the methods of orthogonal projectors and auxiliary problems a problem is taken to the abstract operator pencil which was researched in previous author's works.

Tsvetkov D.O.
About One Initial Boundary Value Problem, Contected with Motions of System Stratifieds Fluids
There was investigated the problem on small motions. The theorem on strong solvability of initial boundary value; problem is proved.