No 3 (2012)

We obtain unique solvability for the inverse problem of determination of the unknown righthand side in multidimensional nondivergent parabolic equation. The additional information is included in the integral ∫︀ 0 (, )()d, where () is a given weight function. We adduce the examples of the inverse problems satisfying the conditions imposed.

Using the anagy method we study the structure of solutions to some regugar and singular perturbed model systems of ODE, the problems with power behavior of boundary layer being included.

Rapid progress in telecommunications which started in the end of 20th century raises new teletraffic problems. The result of the convergence of different networks stems that set of different traffic types should be served by the system. These types differ by their characteristics, in network bandwidth and Quality of Service (QoS) requirements. Diverse consumer needs, variety of on-line services and high-speed Internet access joined in the same system generate large amount of traffic most part of which includes elastic traffic. Multi-rate communication systems, developed at the beginning of 21th century as a result of engineering progress, are able to serve elastic traffic with variable rate depending on the number of prioritized streaming requests being processed in parallel. Specific characteristics of elastic traffic do not allow us to use Erlang multi-rate loss model for simulation of modern telecommunication systems. This paper concerns Erlang-like multi-service loss model of an adaptive multi-rate system for streaming and elastic traffic, where a set of bandwidth requirements corresponds to each type of elastic traffic. A bandwidth requirement is assigned to an entered elastic request depending on occupied bandwidth. The results obtained in the paper are applied to calculation of QoS parameters of the Closs network topology which is widely used in modern switching networks.

The present investigation is devoted to the analysis of non-linear deformation waves propagation in physically non-linear elastic cylinder shell, containing viscous incompressible liquid. Wave processes in elastic cylinder shell without interaction with liquid were investigated earlier on the basis of soliton theory. The presence of liquid needs development of a new mathematical model and computer modeling of the processes, taking place in the system.

In this paper we consider a mechanism to obtain stochastic differential equation with a consistent stochastic and deterministic parts.

The paper addresses three topics: the adjoint Runge-Kutta methods, the composition of several Runge - Kutta methods and symplectic partitioned Runge-Kutta methods. A connection between the explicitness or diagonal implicitness for adjoint Runge-Kutta methods and conditions of a partitioned symplectic Runge-Kutta methods.

The procedure of constructing the controls algorithm of the nonimpact reduction of the mechanics systems to holonomic programmed set in finite time under indeterminancy is proposed.

The well-known model of the Earth standard atmosphere becomes unsatisfactory when altitudes are higher than 150 km. That is why in the paper a new model of the atmosphere is proposed. In this model strong electric fields in the Earth atmosphere are taken into account and described by means of the SU(2) Yang-Mills nonlinear generalization of the Maxwell equations. It is shown that the proposed nonlinear model is in a good balance with experimental data in the considered range of altitudes from zero to 1000 km.

By means of the method of singular sources it is possible to construct a generalization of gravitational magnetic dipole.