UDC 539.2; 535
M. K. Galinsky, V. V. Rumyantsev. GROUP VELOCITY OF LIGHT IN LINEAR ISOTROPIC OPTICAL MEDIUM
The paper is devoted to researching of fundamental connection between distribution of group velocity in space and parameters of a beam. For checking of correctness of equations were obtained in this work, numerical calculations of group velocity distribution in space were made for Bessel, Gaussian and Laguerre-Gaussian beams. In this work were also found the solution of inverse problem – searching of parameters of the beam, knowing the distribution of group velocity of the beam. Results of this work are applicable to information technologies.
Keywords: group velocity, amplitude distribution, phase distribution, Bessel beam, Gaussian Beam, Laguerre-Gaussian beam.

UDC 681.5.09
V. I. Levin. CONTINUOUS-LOGICAL METHODS OF CALCULATING OF RELIABILITY OF COMPLEX SYSTEMS. I. MATHEMATIC MODELS OF RELIABILITY
The article describes the mathematical apparatus of ordinal logic and logical determinants, which is an adequate tool for modeling the reliability of complex systems. The problem of reliability analysis of complex systems is formulated. Classification of complex systems is given. The general methodology for constructing the reliability model of a complex system based on the apparatus of logical determinants is outlined.
Keywords: logical determinants, dimensionality problem, classes of complex systems, formal reliability modeling, equivalent circuit method, reliability process, logical theory of reliability.

UDC 681.518.9; 621.384.3
S. S. Antsyferov, K. N. Fazilova, K. E. Rusanov. EVALUATION ALGORITHM OF COGNITIVE SYSTEMS NON-EQUILIBRIUM STABILITY
Development and practical approbation of non-equilibrium stability evaluation algorithm of cognitive systems is carried out. Algorithm is based on operations of formation the initial database of properties and knowledge base about possible states of the system, identification of the system state and, if necessary, transformation the initial system database.
Keywords: cognitive system, stability of effective functioning, structural element, entropy indicators, database, knowledge base, transformation, identification.

UDC 004.75:004.021
А. А. Koibash, T. V. Zavadskaya, S. V. Kryvosheev. MODIFICATION ALGORITHM A* FOR PREDICTION OF MOBILE OBJECT MOTION TRAJECTORY AT DISTRIBUTED SYSTEMS
The paper the algorithm A * is considered and the analysis of the basic places of falling of productivity of algorithm is conducted. To improve the speed of searching for the shortest route, the use of a sorting tree and hash tables was proposed. The study of the algorithm with the use of these structures. The test results showed a significant increase in the speed of the calculations that will be used later in the module for a distributed system.
Keywords: search for the shortest route, A * algorithm, sorting tree, hash table.

UDC 517.9
A. S. Minenko, A. V. Levkina. THE STUDY OF CONVECTIVE STEFAN PROBLEM IN THE PLANE
The work is devoted to the study of crystallization processes, which occurs in nature and is accompanied by convective mixing in the liquid phase. We will also consider the formulation of the problem in which the convection is caused by the presence of a given vortex. An approximate analysis of the free boundary depending on the intensity of the vortex will be made.
Keywords: crystallization, convection, vortex, equation, variational method, phase transition.

UDC 004.928; 004.93
A. S. Minenko, A. P. Semenova. FORMAL EMOTION MODEL
The work is devoted to the task of modeling facial expressions of emotions. Described the classification of emotions, depending on the situation in which they arise. A formal model of emotions is presented as a convex combination of two emotions. There were offered general formal model of facial expressions of emotional states in a feature space and defined basis of this space.
Keywords: mimic expression, classification of emotions, characteristic feature of emotion, algorithm, emotion vector.

UDC 004.89:004.93
A. V. Nicenko, S. A. Bolshakova, V. Ju. Shelepov. SPLITTING A SOLID TEXT INTO WORDS
The paper proposes a method for splitting continuous (without spaces) line of Russian-language text into separate words. The method uses work with a dictionary containing a large number of Russian word forms along with their morphological information. The array of word forms represented as a tree that provides a quick search. Selecting the first word starts with a character input from the beginning to the moment when the search result in the tree matches the entered substring. If you continue input to the end, additional variants of the first word may arise. Each variant is removed from the text and the second word is similarly searched. Choosing the correct variant among the arising splitting variants based on the principle of word count minimization and the deletion of variants that does not conform to the rules of Russian grammar.
Keywords: prefix tree, word division, morphological information.

UDC 518.51:005; 622
V. N. Pavlysh, I. V. Tarabayeva. THE MATHEMATICAL MODELING OF GAS-AIR MIX MOVING PROCESS IN CONTINUOUS ENVIRONMENT (WITH COAL STRATUM AS EXAMPLE)
The results of the gas-air mix moving process in continuous environment mathematical model construction using example of air pumping technology in coal stratum for reducing of its dangerous properties during underground mining. As the base of mathematical model used the mathematical physics equations, attracts Darsey low includes unbroken stream equations for every component. The border conditions are given corresponding to technologic scheme, the solution of border problems provides by numerical algorithm of modified ending-difference metods.
Keywords: process, moving, equation, mathematical model, numerical methods.

UDC 681.518
I. A. Tarasova, A. V. Drobitko. IMPROVEMENT OF THE AUTOMATIC PROCESS CONTROL SYSTEM IN FOOD INDUSTRY PRODUCTION
In article the analysis of the automatic bottling line is carried out. The elimination of identified deficiencies was made by selecting a microprocessor control unit, as well as choosing a complex of technical means. The introduction of an improved automatic bottling system will reduce the number of line outages and reduce the number of rejected products in the food industry.
Keywords: automatic process control system, microprocessor unit, complex of technical means.

UDC 371.693
N. Yu. Tarasov, V. V. Bondarchuk, S. I. Ulanov. SIMULATION SYSTEM FOR A SPECIAL PURPOSE TRAINER
The basic procedures that the simulation virtual system of a special purpose simulator should perform are determined. The inputs and outputs of the system, its control elements and mechanisms are defined. A functional model of the simulation system for a special purpose simulator has been compiled. The algorithm of the program operation and user interface is considered. The levels and the conditions that limit the simulation time are defined. The compression ratio for archiving data is determined. The results of experimental studies were obtained.
Keywords: simulator, imitation, control elements, system mechanisms, functional model.

UDC 62-5; 681.5.015; 004.942
O. Yu. Cherednikova, Yu. S. Dostlev. SYNTHESIS AND MATHEMATICAL MODELING OF GAS-SAFE CONTROL SYSTEMS FOR VENTILATION OF COAL MINE SITES
A methodology has been developed for analytical studies of transient processes in ventilation control systems for areas that have differentiating properties, forcing a change in the ventilation regime. The stability of the proposed closed ventilation control system for non-minimal phase-type sections is substantiated, and the range of optimal regulator settings is determined. Efficiency and correctness of the proposed solutions is justified by the mathematical modeling of control systems for ventilating areas in typical operating modes.
Keywords: modeling, minimal-phase object, ventilation control system.