Vol. 37 No. 2 (201) (2003)

The problem of continuity of multivalued mappings plays a great role in parametrical problems of optimization and in theory of differential inclusion. The article studies the problem of continuity of some multivalued mappings, which are given by inequalities and equations. The article also provides sufficient conditions, under which the intersection of multivalued mappings is a continuous multivalued mapping too.

In this work a nonlinear equation, connected with the hyperbolic equations, satisfying the Huygens’ principle, is considered. An evolution equation for the bend of oscillations, described by the solutions of these equations, is obtained. The fact that it is a nonlinear Shrodinger equation is shown.

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 second part of the paper, being based on the two-level preconditioner described in the first part, the multigrid preconditioner is constructed. The multigrid preconditioner is proved to be spectrally equivalent to the initial stiffness matrix and its arithmetic cost is proportional to the dimensionality of the finest-grid algebraic problem.

Problem of rapprochement is considered at $m$ target sets for stage by stage varying stochastic system. Under certain conditions, based on stochastic processes, the extremal strategy is constructed by a method extremal aiming.

In this paper are studied subdirect indecomposable, partially commutative, normal and quasinormal algebras. It is proved that the cardinality of base set $\leq 3$.

The task of reusable correction of the indignant trajectory controlled of the double linked manipulator is considered provided that the information on a condition of object acts with a mistake. The algorithm of optimum control of the manipulator watching for real movement and reducing difference of real movement from desirable is constructed.

The issue of optimal stochastic control with the motion of double-link electromechanic manipulator is studied taking into account the factors of links of interaction. It is indicated under which conditions the interaction factors can be neglected and an assessment is given. The stochastic optimal control over the system is obtained and an assessment is given to the deviation of phase condition of the quide from the phase condition of the real motion.

In the present paper the structural textures of lecitin–water liquid crystal system within 40–80% concentration region are investigated by the polaroid microscope. In this system confocal domains are discovered by means of cross sectioned prism, the presence of which at the chain boarders is expressed by the “maltian crosses”.

In the present work the experiments on obtaining polychloropren Nairit films with different electroconductive fillers were made and their electroresistance is investigated. The character of the electroresistance change depending on the type of conductor filler is revealed. The electroresistance changes of these films are determined depending on the temperature and ageing.

Regular variation conditions for distribution tail of a sum of random number of independent random variables are established. It is assumed that the random index does not depend on the summands.