An analytic model of long used systems functioning is considered. A set of systems’ possible states is partitioned into two subsets and the functioning of the system is represented by transitions between the subsets. The transitions inside the subsets and between the subsets are described by Markov processes in discrete and continuous time. The transitions between the subsets are considered under transient and stationary conditions. The approach considered in this paper allows to simulate the functioning of different systems and its equipment.

In this paper, we consider the problem of finding integral Cayley graphs for the alternating groups A_n for n = 4,5,6 . For this purpose, we provide different representations for the alternating groups A_n of arbitrary degree in terms of generating and defining relations.

To solve a number of text analysis problems, especially cryptographic, the known values of some frequency characteristics of natural language texts are required. The paper provides measuring results, depending on Russian language texts sizes: the number of alphabetic bigrams and digrams used in texts, as well as connected characteristics named as scatter index and conjunction index. Measurements were taken for two samples: the first sample includes nonfiction and fiction, the second one consists of university study guides. This paper represents alphabetic bigrams and digrams to form different but mathematically strictly related texts elements. Based on this relationship, the scatter index and the conjunction index are introduced enabling to distinguish texts in natural language from random texts, to determine misrepresentations in texts and the size of letter encoding. Bigrams frequency characteristics are submitted to be the most balanced characteristics according to stability, informativity, and computing efficiency.

Constructions of perfect imitation resistant ciphers and authentication codes resistant to imitation and substitution messages are considered in this paper. Finite fields and orthogonal tables are applied in these constructions.

In this article, correlation of complex currents in mutually perpendicular vibrators, forming circularly polarized turnstile antenna, which is located near superconductive screen or is irradiated by another antenna's circularly polarized field is considered. Correlations of amplitude and current phases differences in vibrators with the distance between the antenna and the screen or between active and passive antennas are presented. On the basis of this model, the mechanism of distortion of circularly polarized antenna (helical antennas in particular) characteristics in the presence of the screen is found out. It is shown that the characteristics are distorted as a result of the currents redistribution on antenna's conductors because of the wave being reflected from the screen.

An analytic model of relay protection system functioning of power systems is presented. Different types of failures are considered in the model taking into account regular periodical checking conditions. The model is based on the theory of semimarkov processes using matrix methods for mathematical operations. Some reliability and functioning measures can be calculated using the model e.g. mean down time, steady state unavailability, mean frequency of check-out operations.

A model of distributed computer systems functioning with group restorations of failed machines is considered. The model is formalized in the form of differential equations systems, where unknown quantity is probability distribution. To assess the effectiveness of CS functioning, mathematic expectation and variance of the number of working machines in the model are accepted. Analytical solutions are obtained.

In the paper, the six types of the coplanar transmission lines have been analyzed: single-layer and multilayer conventional coplanar waveguide, single-layer and multilayer conductor-backed coplanar waveguide, single-layer and multilayer coplanar strip. Strips analysis has been based on conformal-mapping and partial capacitance techniques. Formulas of the effective dielectric constant and characteristic impedance for each coplanar transmission lines have been given.

This paper deals with the information technology for educational competency parameter assessment by an expert panel to structure competencies of optimal structure for developing professional degree programs. Experts’ competency assessment based on their self-esteem and objective professional characteristics has been modelled. The data base and software for meeting this challenge have been developed.

The results of estimating statistical characteristics of events flow of application level in operating information system of telecommunications operator, allowing to draw a conclusion about the presence of fractal properties in the process are given.

The test results for shot-range UAVs with multi-functional radar complex are presented. The promise of using radar in small avionics, including shot-range UAVs, are shown. Such UAVs are all-weather and can be used to solve economic and special tasks in the presence of dust and smoke screens.