Vol. 43 No. 3 (220) (2009)

We consider the linear bounded operator in infinite dimensional separable Hilbert space satisfying some conditions. We prove formulas that can be used to calculate the index of this operator.

We consider the Dirichlet problem in a bounded domain $Q\subset R_n, \partial Q\in C^l$, for the second order linear elliptic equation $$-\sum\limits_{i ,j=1}^n (a_i, j(x)u_{x_i})_{x_j}+\sum\limits_{i=1}^n b_i(x) u_{x_i}+\sum\limits_{i=1}^n (c_i(x)u)_ {x_i}+d(x)u=$$ $$=f(x)- div F(x), x\in Q,$$ $$u|_{\partial Q}=u_0.$$

For the solution we prove boundedness of the Dirichlet integral with the weight $r( x)$ , i.e. the function $r(x)|\bigtriangledown u(x)|^2$ is integrable over $Q$ , where $r(x)$ is the distance from a point $x\in Q$ to the boundary $\partial Q$ .

In the present paper the construction of the approximate solution to the initialboundary value problem for the pseudoparabolic equation using finite-element method is considered. It is proved that the costructed sequence converges to the exact solution and error estimate is obtained.

In the present paper the $BMAP(t)|G|\infty$ model with non-stationary input stream of customers is considered. The distribution of customers’ number served during time t and its mean value are obtained. Estimates for characteristics of $MAP(t)|G|\infty$ and $M^x(t)|G|\infty$ models are obtained as well.

In the present paper we describe the polynomial space, corresponding to the multiple intersection point of two curves that are given as products of correspondingly m and n different lines, passing through that point. The main result gives the basis of that space, using polynomials, which correspond to the derivatives with respect to the directions of those lines.

In the present paper the invertible {2,3}-algebras with a binary group operation and with balanced first sort {2,3}-hyperidentities having length 4 are characterized.

In this paper polymorphic lambda terms are considered, where no type information is provided for the variables. The aim of this work is to extend the algorithm of typification [1] of such terms introducing type constants and term constants.

Optical-electronic measuring complex is described, intended for the operative measurement of atmosphere’s transparency in the wavelengths region of 0.35-1.03 μ and of the meteorological optical range in the different climatically conditions from 0.1 to 300 km. The technique of realization of full-scale measurement of a parameter of atmospheric easing for seen beams (on λ = 0.55 μ ) with sensitivity not worse 3,4⋅10^–5 km^–1⋅mV^–1 is stated.

The goal of this article is to clarify contribution of the chain entropy in stability of RNA secondary and tertiary structures. The Hamiltonian of the model includes relevant interactions explicitly. We show that different stability of secondary and tertiary structures governed by chain entropy rather than energy of interaction.

Symmetric subalgebras of a complex Banach algebra are studied with the help of von Neiman–Fuglede Theorem. The result is closely related to the problems of approximation theory.

In the present paper the game models of information security are considered. A few formulations of information security problems are introduced and quite simple game models are built. Specific solutions of several matrix games and a duel type games are derived.

The results on development of an original method of atmosphere’s transparency determination in the infrared region are presented. The method is a halfempirical and based on the direct nephelometric and meteorological measurements of the atmosphere’s transparency in the visual region (on λ = 0.55 μ ) with following recalculation to the other spectrum region in diapason from 1 μ to 14 μ . The proposed method provides the possibility of the operative valuation “optical weather” in the atmosphere, especially in full-scale tests thermovision equipment and devices of night vision.