Vol. 37 No. 1 (200) (2003)

The present paper, consisting of two parts, is devoted to constructing an algebraic multigrid preconditioner for stiffness matrices arising in second-order finite element approximation of elliptic boundary value problems. In the first part a two-level preconditioner, on the base of which the multigrid preconditioner will be constructed, is described.

This paper is devoted to the investigation from the point of group analysis and group classificationthird order  of some class of nonlinear partial differential equation. The whole groups of symmetry, concerning which equations are invariant, are obtained, the corresponding basis vectors of the Lee algebra are pointed.

In present paper one Volterian type integral equation with stochastic kernel is considered. Special factorization allows to reduce it to new equation with contracted operator, as well as to find asymptotic behavior of the solution depending on properties of free term. It was shown that obtained estimation is exact. The results for Volterian type equation with variable lower limit are applied.

For the double linked manipulator with three degrees of mobility game problems of approach-evasion with the given target set are investigated at different restrictions on controlling influences and on a minimax square-law functional. The received optimal decisions for linear model are used for control of nonlinear model with the help of an additional regulator.

The differential game of rapprochement-deviation for several target sets is considered with the collection of stochastic and partially programmable strategies in the homogeneous central field, when the game takes place in thin spherical stratums. The strategies of players are formed on the basis of random variables that appear in the process of measurements of the position. The strategies of the first and second players are constructed in an exact form. The bound for the distance between the true phase state of the system and the guide is obtained for every time moment.

In this paper monotonic models of typed $\lambda$-calculus are examined. Formal definition of concept of a $\delta$-reduction is given. Strong $\delta$-normalization and strong $\beta\delta$-normalization of terms are proved. The concept of a natural $\delta$-reduction is defined and the necessary and sufficient condition for uniqueness of a $\beta\delta$-normal form for such concept of a $\delta$-reduction is resulted.

Many algorithms for very large scale integration placement improvement require fast calculation of the linear wire-length depending on the position of given cell and assuming other cells fixed. Particularly it is required to find optimal locations of the cell. This paper suggests a fast algorithm for this problem. Complexity of the algorithm is $O(n \log n)$, where $n$ is the number of nets of this cell.

The temperature dependence of the polyethilentereftalat supermolecular structure is investigated. It is shown, that the most crystalline phase is formed at 80°C temperature (1 hour) inlike the literature data, according to which the most crystalline phase is formed at 110°C. Crystalline formations size $10^{–5} cm$ are formed in polyethilentereftalat at the magnetic field influence. $\alpha$-  and $\gamma$-radiation influences destroy the crystalline phase and increase the amorphous phase.