Underground mining, including underground coal mining, is accompanied by accidents and fire hazards that pose a threat to the life safety of miners. The fire hazard increases with an increase in the mining depth. Currently, most accidents in coal mines are mine fires. The cost of eliminating mine fires is 80–95% of the cost of eliminating all accidents occurring at mining enterprises. Therefore, the problem of developing a new methodology for modeling the ventilation network parameters of the mine to increase the reliability of controlling the aerogas mode at the excavation site is very relevant. The comprehensive analysis and assessment of gas-dynamic processes in coalmines under study were carried out using the methods of probability theory and mathematical statistics. Spatial data were processed using spline interpolation in “gnuplot”. As a result, a generalized expression for the transfer functions of coalmine objects, taking into account delays, was developed, including the description of dynamic properties of mining sites under various operating modes. The principal possibility of using a graphical method for estimating additional parameters of the sections of the ventilation system branches has been proved due to the alignment of their profiles at an equivalent distance relative to an arbitrary analogue. The improved method of spatial modeling was used to determine the gas-dynamic characteristics through additive gas-dynamic processes. The studies have been carried out and the method for managing the process of changing connections between devices (controllers–switches) of the technical system was developed in order to obtain greater reliability for safe mining. In subsequent studies, there is an issue of more detailed clarification of the peculiarities concerning the interrelations between the studied parameters in several projections of the response space.

X-ray diffraction analysis is essential in studying stacking faults. Most of the techniques used for this purpose are based on theoretical studies. These studies suggest that the observed diffraction patterns are caused by random stacking faults in crystals. In reality, however, the condition of randomness for stacking faults may be violated. The purpose of the study was to develop a technique that can be used to calculate the diffraction effects of the axis of the thin plates of twin, new phases, as well as other variations in defective structures. Materials and methods. This was achieved through modern X-ray diffraction methods using differential equations (transformations and Fourier transforms) and the construction of the Ewald sphere, mathematical analysis, mathematical logic, and mathematical modeling (complex Markov chain). Conclusion. The study made it possible to develop a technique for the calculation of the diffraction effects of the axis of the thin plates of twin, new phases and other variations in defective structures. The technique makes it possible to solve several complex, urgent problems related to the calculation of X-ray diffraction for crystals with face-centered lattices containing different types of stacking faults. At the same time, special attention was paid to the correlations between the relative positions of faults. The calculations showed that the proposed method can help to determine the nature and structure of stacking faults by identifying the partial and vertex dislocations limiting them in twin crystals with a face-centered cubic structure of silicon carbide based on X-ray diffraction analysis.

The practical development of the algorithm for optimal control of mine ventilation was preceded by comprehensive studies of the specific features of mining sites in order to obtain their mathematical description. The latter includes the static and dynamic characteristics of objects, i.e. the relationship between input and output values. The purpose of the research: to develop methods and management tools aerogasdynamics processes on mining sites of coalmines. Research methods. The methodology based on the system approach; modern methods of mathematical statistics, decision theory; mathematical logic devices; factor analysis; mathematical modeling; set theory and system analysis. To determine the dynamic characteristics of aerogasodynamic processes, experimental methods were used, divided into active and passive. The active method consists in con-structing a dynamic model of airing objects by approximating the transition curve obtained because of special effects on the airing object with an analytical expression. Statistical dynamics methods were used to obtain dynamic characteristics based on normal operation data. The method of correlation analysis was used. Results of research: experimental verification showed that the maximum relative error of in determining the methane concentration from the static characteristic constructed using a modified technique does not exceed 10 %. The value of the error was determined by comparing the static characteristic obtained by the modified correlation analysis method with the exact static characteristic of the airing object. The latter were found with regard to dynamic properties of the object and additive structures aerogas dynamics processes. Conclusion. The method of correlation analysis can be used to determine the dependence of the methane flow rate on the airflow rate in the steady-state mode, i.e. the static characteristic q = f (Q) for the site and lava. To determine the static characteristics based on the data of normal operation with a limited observation interval (5-10 days), a modified method of correlation analysis is proposed. Small values of the relative error of indicate the possibility and feasibility of using a modified correlation analysis technique to construct a static characteristic of the airing object based on random processes of methane concentration and air flow obtained during normal operation of the site. The static characteristics C= f (Q) and q= f(Q) are widely used to determine the mathematical expectations of the methane concentration and flow rate of mining sites, in the modeling of ventilation facilities and in the analysis and synthesis of mine ventilation control systems.