No 4 (2011)

A connection between Rational homotopy theory of T2 category of 1-connected spaces and homotopy theory of certain algebraic categories is established. Quillens approach is mainlybased upon functoriality. This enables one to extend the theory to the category of inverse systems. In the present paper a notion of Rational homotopy type of inverse systems of 1-connectedspaces is introduced. Its equivalence to Rational homotopy theories of certain algebraic categories is proved.

We consider a model of two-dimensional random vector with dependent binomial marginals.The distribution for constructed model is determined.

In this paper a discrete Markov chain for analyzing the process of content distribution inP2P streaming network was introduced, the steady state probabilities were derived and the probability of continuous playback was analyzed.

This review deals with the research of load control mechanisms in signaling networks that use three types of thresholds for congestion control. The main objective of this paper is toanalyze the congestion control mechanisms and mathematical models for SIP-servers. Thestudy is based on hysteresial techniques of flow control, which originally was developed forSignaling System 7. We propose general methods for describing hysteresis signaling flow control techniques. We study the current situation and problems of SIP built-in overloadcontrol mechanism, proposed by IETF. Our approaches to mathematical models constructionin the form of queuing systems with hysteresis control are presented.

The 3D spin glass is represented as an ensemble of disordered 1D spatial spin-chains (SSC) where interactions are random between spin-chains. It is proved that at the limit of Birkhoffs ergodic hypothesis performance 3D spin glasses can be generated by Hamiltonian of disordered 1D SSC with random environment. Disordered 1D SSC is defined on a regular lattice where one randomly oriented spin is put on each node of lattice. Also it is supposed that each spin randomly interacts with six nearest-neighboring spins (two spins on lattice and four in the environment). The recurrent transcendental equations are obtained on the nodes of spin-chain lattice. These equations combined with the Silvester conditions allow step by step construct spin-chain in the ground state of energy where all spins are in minimal energy of classical Hamiltonian. On the basis of these equations an original high-performance parallel algorithm is developed for 3D spin glasses simulation.

A numerical description of turbulent motion of a pipe localized fluid is given in the paper. The description is based on multiscale turbulent fluid motion model developed by the author. Comparison of numerical results and experimental data is given.

Experimental implementation of optical image coding method with time integration using commercial camera and liquid crystal display is described. Results of image optical coding andcoded images numerical restoration are presented. This method could be used for accessiblequality estimation of optical image coding using diffractive optical elements or as independentoptical coding method.

In this paper we consider the problem of diffraction of obliquely incident plane wave byan inhomogeneous cylinder. To simulate the two-dimensional inhomogeneities, we proposethe method of stepwise approximation of a radial dependence of the refractive index. This allows us to obtain expressions for the fields of diffraction, both inside and outside the areaof inhomogeneity, in the form of a series of the cylindrical harmonics.

This article deals with the research of enterprise modeling instrument's disadvantages and its ways of possible development. There is an example of an integrated notation, containing such notions as "Event" and "Condition", and also an example of using the formal level of application domain to estimate the completeness and the consistency of the models mentioned.