Vol. 40 No. 1 (209) (2006)

In the paper the weighted classes $A_{\omega}^2(\mathbb{C}^n)$ t of entire functions of several complex variables are introduced. These classes depend on parameter-function $\omega(x)$ and they are arbitrarily large. For functions belonging to $A_{\omega}^2(\mathbb{C}^n)$ the integral representation is obtained.

In the space $L^2(\mathbb{R})$  the Sturm-Liouville operator L with certain behavior of potential at infinity is considered. We prove that the eigenvalues of L are simple and are finite in number.

The paper is devoted to the study of behavior of the solution of first boundary problem for biharmonik equation in the neighborhood of angular point. It is proved that the solution of the problem can be represented in a certain form, which allows constructing variation-difference schemes on non-regular grids. Exact estimations for convergence rate are obtained.

The present paper, consisting of two parts, is devoted to constructing algebraic multigrid preconditioners for stiffness matrices arising in finite element approximation of elliptic problems in rectangular domain. The Dirichlet condition is placed on one part of the boundary and third type condition on the rest of the boundary. In the first part of the paper a sequence of two-grid preconditioners is described on the base of which the multigrid preconditioner will be constructed.

In this paper the problems of optimum stabilization and optimum traffic control of rigid body rotating around a motionless point with the help of flywheels is solved. It is shown, that the system is not quite controlled only by gyroscopic forces. The dissipative forces arising from the rotation of flywheels are added to the system. Linear systems are considered and for them optimum stabilizing and controlling operations are found.

In order to maintain signal integrity and reasonable delay in high frequent designs, each critical net must undergo buffer insertion. At the same time a big number of nets in such designs create restrictions in terms of algorithms' run time. This paper studies the problem of constructing minimum cost buffered routing trees in high utilized and congested designs with possible buffer locations.

The features of propagation of light wave on a metal-coated conical tip of optical fiber is considered. During the experiment we detected an output radiation from the tip, when the tip came out from the liquid. The peak of output optical intensity is obtained. This process very essentially depends on the position of the fibre top, with the help of which it is possible to find out very weak vibrations of the surface of the liquid.

In this paper we give imbedding of group Fibonacci F(2,9), given by 9 generators and 9 defining relations in the group $G =< a, b; a^9=1, ab = b^2 a^2 >$.