No abstract

A mathematical model of a travelling wave in a matrix form is constructed. A degree of discreteness of the travelling wave and corresponding steps in phase and length are introduced. Asymmetric, unified matrices are compiled, which represent a generalized travelling wave, depending on a degree of discreteness. A generalized, dimensionless travelling wave is transformed into a required one with dimensions by specified technical parameters: amplitude and wavelength that is realized. A dependency of coordinates of points of a plane discrete travelling wave and discrete phase angles is established. A dependency of angular (phase) velocity and velocity of the travelling wave, which corresponds to the known results, is established. The presented matrix mathematical model is considered as an initial stage of technical possibility to realize a continuous travelling wave in a discrete form when developing a new type of transportation – wave transport.

The increase in the share of electric transport in mining and municipal enterprises in the short term may lead to changes in the structure of the transport fleet of enterprises and can affect the technology of work, in particular, surface mining operations. Changes in technology relate to the need for charging batteries, as well as the appropriate economic and technological planning. Having implemented the combinatorial representation and using the chain diagrams, a new method has been developed for determining the optimal plan of the vehicles flow distribution at the charging station of industrial enterprises, which provides the greatest enterprise profit. The developed mathematical model of vehicle flow at the charging station is compiled taking into account the objective constraints related to the cyclicality of the station loading capacity. The optimal plan for the vehicles flow distribution at the charging station is, based on geometric representations, as the greatest distance from the beginning of the reference to the plane (hyperplane), which passes through the vertex of the polyhedron of the area of admissible solutions and is oriented by the gradient of the target function (enterprise profit). The task becomes urgent in the light of the electrification of industrial transport and the improvement of batteries for them.

It has been demonstrated that vibratory impact mineral loading results in the formation of solid solutions. A technique to determine concentration dependence of inversion degree of solid binary solutions according to the known values of their components activity has been proposed. Values of thermodynamic functions of the solutions mixing in terms of statistic formulas as well as by means of immediate processing of the experiment have been determined.