There are results of the melts of semimetals and semiconductors of various structural groups research in the article. On the example of simplified regular Bethe lattice one can model destruction and aggregation of structures in clusters and on it’s basis to substantiate the metal melts properties in the form of nanolayers. The variety of compressibility polytherms forms in electronic melts requires typing, since their analysis makes it possible to explain the mechanism of the aggregation and dissolution processes of extended objects in melts. The article contains formulas that allow explaining the mechanism of the dissolution of cluster structures and their influence on the physicochemical nature of the molten state. There is considered the process of cluster fragmentation. Larger fragments of clusters are formed in the process of crushing, and this fact leads to the compressibility that decreases more rapidly, only after passing through the extremum it begins to increase due to the thermal loosening. The study of the function's compressibility for an extremum in the compressibility's temperature dependence also indicates the changing process of the clusters decomposition mechanisms in melts with an increase in temperature and vice versa to aggregation with a decrease in the melt temperature to the melting temperature.

The article presents a mathematical model of coal self-heating in the stack in which the heat exchange and gas exchange processes are described by a system of two non-linear differential equations of the second order with respect to the temperature t of coal self-heating and the volume fraction C of oxygen in the voids of the stack with boundary and initial conditions. The differential equations took into account that self-heating of coal in the stack and appearance of spontaneous combustion are observed in a relatively small layer adjacent to the surface of its contact with the air and called the zone of oxygen influence. In the mathematical model, the influence on the process of coal self-heating of parameter F- specific heat release power was taken into account, which in addition characterises the stability of coal during storage. When compiling the differential equations, such physical parameters as thermal conductivity, diffusion coefficient, specific heat capacity of coal in the stack, bulk density, thermal effect of oxidation, stack voidness, temperature coefficient of exponential growth of heat release power were also used. For numerical implementation of the mathematical model, dimensionless variables and criteria were introduced, which allowed us to apply the net method. Analysis of the obtained results allowed to get: change in the stack temperature profiles with time; change in the stack oxygen concentration profiles with time; influence on the stack temperature profile of the specific heat release power; influence on the stack temperature profile of the parameter characterizing exponential growth of heat release intensity with temperature increase. It has been determined that the dynamics of coal self-heating in the stack is mostly influenced by the Lykov criterion, proportional to the diffusion coefficient, and the Nusselt criterion related to the effective thermal conductivity and to the effective thermal diffusivity of coal. The obtained results suggest that self-heating in the stack is due on the one hand to intensive penetration of air oxygen and on the other hand to a weakened heat transfer. Self-heating and the transition of self-heating into ignition are associated with the occurrence of turbulent diffusion in the stack, arising from increased thermal blowing, whose impact can be enhanced by directing it perpendicular to the surface of the stack.

The problem of stresses and displacements of an oblique-layered massif near a mine working, which is located entirely in one of the rock layers, is considered when the mine is tested by the effects of cleaning works in a coal seam. This effect is taken into account by specifying a system of normal and shear forces at the boundary of the lower layered half-plane with a hole. The problem is solved by imposing the complex Kolosov – Muehehelishvili potentials and Fourier integral transforms. Based on the method of Fourier integral transforms in the theory of elasticity, a system of integral with respect to normal and tangential contact forces is obtained for the case of two different layered half-surfaces. In this work, systems of integral equations are obtained in solving the problem of the reference pressure on an obliquely buried coal seam near the mine working. In this paper, the method of integral Fourier transforms in the theory of elasticity, obtained a system of integral with respect to normal and tangential contact forces for the case of two different layered half-surfaces.

Karaganda region occupies the most elevated central part of the Kazakh hillocky area - Saryarka, which is a peculiar and geomorphologically heterogeneous, highly elevated natural country. The relief is complicated by shallow hummocks, river valleys, dry watercourses, holiows with outcrops to the surface of groundwater, closed basins, lake basins. The total area of the state forest fund on the territory of the Karaganda region is 269.6 thousand hectares. High temperatures and lack of rain in summer, the presence of vast steppe zones can lead to wildfires in July-September. Karaganda region is a large industrial center. Main industries: mining (mining of coal, ferrous and non-ferrous metal ores), ferrous and non-ferrous metallurgy, chemical industry. The share of processing enterprises accounts for 80.1% of industrial production.

Б а с р е д а к т о р ы х. ғ. д., проф., ҚР ҰҒА академигі М. Ж. Жұрынов Р е д а к ц и я а л қ а с ы:Ресей) Абишев М.Е. проф., корр.-мүшесі (Қазақстан) Аврамов К.В. проф. (Украина) Аппель Юрген проф. (Германия) Баймуқанов Д.А. проф., корр.-мүшесі (Қазақстан) Байтулин И.О. проф., академик (Қазақстан) Банас Иозеф проф. (Польша) Берсимбаев Р.И. проф., академик (Қазақстан) Велесько С. проф. (Германия) Велихов Е.П. проф., РҒА академигі (Ресей) Гашимзаде Ф. проф., академик (Əзірбайжан) Гончарук В.В. проф., академик (Украина) Давлетов А.Е. проф., корр.-мүшесі (Қазақстан) Джрбашян Р.Т. проф., академик (Армения) Қалимолдаев М.Н. проф., академик (Қазақстан), бас ред. орынбасары Лаверов Н.П. проф., академик РАН (Россия) Лупашку Ф. проф., корр.-мүшесі (Молдова) Мохд Хасан Селамат проф. (Малайзия) Мырхалықов Ж.У. проф., академик (Қазақстан) Новак Изабелла проф. (Польша) Огарь Н.П. проф., корр.-мүшесі (Қазақстан) Полещук О.Х. проф. (Ресей) Поняев А.И. проф. (Ресей) Сагиян А.С. проф., академик (Армения) Сатубалдин С.С. проф., академик (Қазақстан) Таткеева Г.Г. проф., корр.-мүшесі (Қазақстан) Умбетаев И. проф., академик (Қазақстан) Хрипунов Г.С. проф. (Украина) Юлдашбаев Ю.А. проф., РҒА корр-мүшесі (Ресей) Якубова М.М. проф., академик (Тəжікстан) «Қазақстан Республикасы Ұлттық ғылым академиясының Хабаршысы».