No 3 (2011)

We present new results connecting the number of focal points of a conjoined basis of а 2n × 2n symplectic difference system and the negative inertia index of the Schur complement in a symmetric matrix of the same size. The proved result makes it possible to reduce the problem of calculating of focal points for discrete symplectic systems to a saddle point spectral problem for a symmetric indefinite block matrix.

The aim of this paper is to continue study of simply-open sets, and we give some properties of simply-open sets. And we investigate the relations between simply-open sets and other forms of generalized open sets in a topological space like semi-open sets α-sets δ-sets preopen sets semi-preopen sets, and we give some properties of the class of all simply-open sets.

In this paper we consider a redundant system with reduced reserve and investigate the rate of convergence of the distribution of its failure-free time to the exponential law under the fast recovery of its elements. The results for systems with loaded and unloaded reserve are presented as particular cases.

In this paper the model of P2P live streaming network with peer churn (peers joining and leaving) providing the closed-form expressions was developed. The approximation of a universal streaming probability with the normal (or Gaussian) distribution for large P2P live streaming networks was obtained.

The work is dedicated to analysis of photonic band gaps of one-dimensional photonic crystal and simulating diffraction on one-dimensional binary diffraction grating using RCWA method. The results of simulating diffraction using RCWA are compared with spectrophotometrical data.

In this paper we propose the CGE-model of economic sector. This model represents the system of differential equations. The analysis of trajectories in the points corresponding to equilibrium of investigated economic system is introduced and studied. We also try to get the dicision of the system in a some special case.

The article discusses the problem of organizing different levels of access to data within information systems. These are based on a relational database designed to automate the management of the enterprise. Here we introduce the necessary definitions and concepts to build a model that allows us to make the mechanism of restricting access to data at the level of the relational model.

In view of development of unary relational approach to description of physical interactions theories of direct interparticle action are discussed, that include the Fokker-Feynman-Wheeler electrodynamics, the theory of direct interparticle gravitational interaction, and the Hoyle-Narlikar theory of gravitation. These theories have several resemblances, main of which is implication of Machs principle in them, according to which there is a relation between distribution of particles in the universe, their masses and gravitation constant. In the Hoyle-Narlikar theory and in the unary relational approach free action of a chosen particle is represented in the form of its interaction with the rest part of the whole universe. In present work correspondence between the Hoyle-Narlikar theory and the relational theory is set up, relation between their parameters is found, differences between these theories are pointed out, and relation between Machs principle and cosmological coincidences is discussed.