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Vol. 14 (53), No. 1. 2001
Mathematics.

Anashkin О.V.
Lyapumov-Krasovskii Functions in the Theory of Stability for Differential Equations with a Finite Delay
Sufficient conditions for the stability of the zero solution of a retarded functional differential equation are obtained. Theorems on stability are given in the form of conditions for existence of the auxiliary functional of Lyapunov-Krasovskii type. The functional are non-monotone alone the solutions.

Baygozina J.Yu.
Auxiliary Operators Tμλ and Bα in Space with Indefinite Metric
In the proposed article the auxiliary operators playing the important role in the construction of the characteristic function of regular extensions of Hermite operators in the space with in definite metric, have been sdudied, and their basic properties have been proved.

Batyr El'dar
Small Movements of a Double Pendulum with the Cavities Containing an Ideal Incompressible Fluid
In this paper we considered a linear problem of hydrodynamics connected with small movements of a double pendulum with cavities containing an ideal incompressible fluid. 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 movement of a double pendulum.

Вelan Е.P.
Bifurcation of Periodic Solutions in Parabolic Problem with Transformed Argument Nonlinear parabolic equations on the circle with a rotation transformation of the angle variable is considered. The problem of stability and quantity of the running waves in the neighborhood of a stationary solution is solved.

Wronsky В.М.
On Proper Oscillations of Compressible Stratified Fluid
In the article the problem on small motions and proper oscillations of stratified fluid in the bounded region. It was shown that the spectre consists of a countable set of eigenvalues and a part of continuous spectre. Asymptotic formulas for eigenvalues were obtained. Correct solvability of Cauchy problem has been proven.

Donskoy V.I.
The Asymptotic Estimation of a Number of Binary Decision Trees
The asymptotic estimation d(n, k, μ) ≡ (μ — 1 )![k(k — 1)]μ-1n(n — 1) μ-2, n — ∞ is found, where d(n, к, μ) is a number of Binary Decision Trees'with μ leaf, n Boolean variables, and k classes of decisions.

Zakora D.A.
Problem on Normal Oscillations of a Partially Dissipative Hydrosystem
Some statements on p-basis property. Riesz' basis, property, multiple completeness of part оf root elements, asymptotic behavior for eigenvalues are obtained.

Ivanov Yu.B.
Generalized Solutions of a Spectral Boundary Problem for the Differential System in the Shallow Water Theory
A spectral differential boundary problem of Tree oscillations in rotating ideal liquid is considered. With relation to the differential system a selfadjoint operator polynomial pencil of the third degree with unbounded opertor coefficients is derived. The generalized solutions of the boundary differential problem are regarded as solutions of the spectral problem for that operator pencil.

Karpenko I.I.
Characteristic Functions of Hermitian Operators
In the present paper it's investigated properties of dissipative and accumulative extensions of hermitian operators with a noncleuse domain, which have finite and equal defect numbers. On this class of hermitian operators we generalize the notion of characteristic function, suggested by A.N.Kochubey for symmetric operators with dense domain. It's proved the criterion of unitary equivalence of hermitian operators.

Krivoruchko А.I.
On a Cross-Ratio of a Quadruple of Linear Spans of Orbits of Directions of Simmetries of Infinite Reflection Group
Let G be an infinite reflection group acting on a non-cylindrical algebraic suface in n-dimensional real vector space and having four linear spans of G-orbits of directions of sym-metries. All possible values of the cross-ratio of these linear spans as well as corresponding groups G and their rings of invariants are obtained.

Kuzhel А.V.
Boundary Value Space of Symmetric Operator
The work is deviced the viewing of the main results, relays to the theory of boundary value spaces with the equal defect numbers.

Moskaleva Yu.P.
Generalization of Trace Formula for Case of K r+ (M)-Operators
In this paper, the formula of trace is generalized by case of unbounded nonself-adjoint dissipative operators.

Orlov I.V.
Almost Everywhere Convergence as a Convergence in Nonlinear Inductive Scale of Locally Convex Spaces
It is shown that, almost everywhere convergence may be considered as a convergence in the inductive scale of locally convex spaces. The properties of the created scale are studied.

Papkov S.О., Chekhov V.N.
Regular Infinite Systems of the Algebraic Equations in Case Long Period of Strains of a Prism
In a paper we offer the theorem about, sufficient condition of existence of a. nonzero limit of solution of a, infinite system of the linear algebraic equations with noil-negative matrix. With help of this theorem, the stress condition of an elastic prism is investigated in the field of low frequencies.

Persidskii S.K., Zhuravlev V.V.
Some Theorems On Uniform Asymptotic Stability of Solutions of System of Finite Difference Equations
In this article two new theorems on a uniform asymptotic stability for finite difference system are considered. In these theorems the first finite differences of appropriate Lyapunov functions satisfy the condition Δ Vm≤0.

Rudenko L.I.
On Development of Approaches to Decision Making with Incomplete Information
Decision making linear models with incomplete information and their classification by types of primary information are described. Approaches to solving of such problems based on synthesis algorithmes are considered.