The method of compaction of subsident soils by deep explosions is widely used in civil construction of buildings and structures. It is characterized by high efficiency of soil compaction and low financial costs for the production of works. This emphasizes the undoubted advantage of the method in comparison with other analogues. In this paper, some features of constructing a mathematical model of compaction of subsident soils by deep explosions are described. The conditions for the existence and uniqueness of the solution of boundary value problems in the framework of the investigated model are given.

Keywords: subsidence soil, loess, deep explosion, concentrated charge, elongated charge, soil compaction, mathematical model, diffusion equation, boundary value problem, solvability of the model

The article deals with mathematical modeling of thin-film materials production, based on the solution of multi-criteria optimization problems by convolution criteria. The method of estimation of coefficients in linear convolution is presented. The mathematical model developed by the authors allows to calculate the maximum profit of the enterprise from the production of thin-film materials, taking into account the cost of their production.

Keywords: thin film, substrate, production, mathematical modeling, multi-criteria optimization, convolution of criteria