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Vol. 15 (54), No. 2. 2002
Mathematics. Mechanics. Informatics and Cybernetics.

Mathematics.

Anaphiyev A.S.
Delta-Boolean Functions and their Properties
In this article we consider the new class of Delta-Boolean functions. Delta-Boolean functions and their arguments may take values 0,1 or Δ. The definitions of the degree of uncertainty, relative and absolute essential variable degrees were introduced for Delta-Boolean functions. These definitions are necessary to research the problem of Boolean functions reconstruction. Also we consider some properties of Delta-Boolean functions.

Batyr El'dar
Small Movements of a System of the Consistently Connected Bodies with the Cavities Containing an Ideal Incompressible Fluid
In this paper we considered a linear problem of hydrodynamics connected with small movements of a system n bodies. The system is a circuit of the consistently connected bodies. Each of 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 movement of a system n bodies.

Belan Е.Р.
Bifurcation of Periodic Solutions for Nonlinear Parabolic Functional Differentional Equations
This paper is devoted to bifurcation of equilibria for nonlinear parabolic functional differential equations with transformation of space variables. Theorem on bifurcation of periodic solutions, stability, asymptotic form is proved by the method of center manifolds.

Donskoy V.l., Ilchenko A.V.
On Statistical Substantiation for Classes of Object Separation Possibility in Empirical Samples
The approach for substantiation of ability of classification based on the hypothesis of more than one mode existence in pair distance distribution is considered. The sufficient condition of nonrandomness of two modes is proved and statistical criterion of classification is given.

Ivanov Yu.B.
Approximate Equations for Low-Frequency Oscillating Free Surface of Rotating Two-Layer Liquid
For mathematical simulation of low-frequency oscillating free surface of rotating two-layer liquid a polinomial operator pencil is used. It is presupposed that density p1 of an upper layer close to density p2 of an underlying layer with p1 < p2. In that case the mathematical model has a small parameter. Equations for the zero and the first approximations in parameter-series expansion are derived.

Karpenko Irina
About One Approach to Constructing of Boundary Value Space of J— Hermitian Operators
In this paper we considered some properties of defect subspaces of J-Hermitian linear relations in the space with an indefinite metric. These results are used for definition and study of the boundary value space for the J-Hermitian operator with nondense domain. In particular, different properties of the boundary operators are obtained.

Kyrychenko A.A.
On Linear Combinations of Orthoprojectors
We investigate n-tiples of the projectors P1,P2...,Pn in the complex Hilbert space H satisfying the condition ∑ni=1 αiPi=IH(here IH is identity operator, αi>0) and their application to description of the self-adjoint operators having two points of the spectrum and representable as a sum of three orthoprojectors.

Kovalenko А., Маrуаnіn В., Smolich V.
Queueing Process of Type (M/G/1/1)
Stationary probabilities of system described by non-Markovian stochastic process are derived. The authors avoid the traditional technique of embedded Markov chains and suggest their own technique.

Krivoruchko А.I.
On a Mutual Disposition of Four Linear Spans of Symmetry Directions of an Infinite Reflection Group
Let G be an infinite reflection group acting on a non-cylindrical algebraic hypersuface in n-dimensional real vector space. Some new restrictions on a mutual disposition of four linear spans of symmetry directions of a group G with pairwise 0-dimensional intersections are obtained.

Makhina G.A.
Neural Network Architecture for Weekly Defined Optimization Problem with Linear Restrictions
The neural network architecture for the inequality constrained weakly defined optimization problem is introduced in this paper. The objective function is reconstructed in the form of neural network using the initial precedent information. Inclusion of inequality restrictions into the problem leads to the extended architecture of neural network, which is mathematically based on the logarithmic barrier functions approach.

Muratov М.А.
Different Kind of Convergence in the Rings of the Measurable Operators
In the paper, relation between convergence in measure, convergence almost everywhere end bilaterally convergence almost everywhere in the ring of measurable operators, affiliated to a finite von Neumann algebra is studied.

Myagkov V.l.
Characteristic Property of Mutual Transformation on the Plane
Two curves γ and γ* in a Euclidean plane are called mutual with the mutuality center at the point Q if there is mutually one-to-one correspondence between the curves, where two conditions are fulfilled. Here M and M* are corresponding points of the curves, , are vectors of normal of γ and γ* curves at the corresponding points M and M*. The transition from an original curve γ onto the mutual curve γ* is called mutuality transformation H with the mutuality center at Q point. The simpler proof of the theorem has been found: The class of real disintegrated curves of the second order is invariable concerning mutuality transformation H.

Orlov I.V.
Young Theorem for Normal Derivatives and Functional Extremums in the Products of Nuclear Spaces

The classical sufficient conditions for extremum of two variables function are generalized for the case of twice normally ditferentiable function in the product of the nuclear spaces.

Rudnitsky О.I.
About one Class of the Wild Groups of the Skew Symmetries, which have Four Orbits of Directions of Symmetry
Let G be the infinite group generated by skew reflections with respect to hyperplanes in an euclidean space and have four infinite G-orbits of the directions of symmetry. The conditions of existence of the groups G, if the linear spans of G-orbits of the directions of symmetry have three different straight lines of intersection, are obtained.

Starkov P.A.
On the Operator Pencil of the Transmission Problem for Helmholtz Equation
In the work we consider the general case for the spectral problem, which is appear in the operator approach to the transmission problem for Helmholtz equation.

Tikhonov A.S.
"Curved" Conservative Systems and their Applications
In this paper the notion of "curved"linear conservative systems is introduced. It is shown that such systems: 1) naturally appear for problems relating to functional models; 2) allow an informative definition of the transfer function; 3) have interesting applications to perturbation theory, scattering theory, and for extreme factorizations of operator- valued functions.

Tyshkevich D.L.
On Classes of Adjointable Operators in General Indefinite Inner Product Spaces
General approach for definition of operation of conjugation of linear operators in general indefinite inner product spaces (including degenerate spaces) is suggested. Some simple consequences of introduced definitions are considered.

Tsvetkov D.O.
On Small Motions of a Stratified Fluid
The problem on small motions of viscous fluid, which density in a equilibrium state has stable stratification is investigated on the base of approach connected with applications of operator matrix theory with unbounded entries. The theorem on strong solvability of initial boundary value problem is proved.

Yakovlev A.V.
Small Transverse Oscillations of a Visco-Elastic Beam with a Load at the End
The problem on small transverse oscillations of a visco-elastic beam with a load at the end is investigated by operator approach. The theorem on strong solvability of the initial boundary value problem is proved.