The article developed a mathematical model of simple and complex words and phrases of the Uzbek language, which belongs to the family of Turkic languages. On the basis of the developed mathematical model, an algorithm is presented that generates simple and complex words and sentences.

The paper considers a two-dimensional mathematical model of the filtration of a viscous, incompressible fluid in a deformable porous medium. The article describes a mathematical model of the problem at the “oil-water” interface with a system of parabolic differential equations. The problem posed is solved numerically using the differential-difference method based on the longitudinal-transverse scheme and the differential sweep method to determine the unknown boundary. To obtain a differential-difference problem, an algorithmic representation of a hidden scheme of alternating directions (longitudinal-transverse scheme) is used. The resulting system of differential-difference equations with initial conditions is known for each time layer along straight lines along the x axis, and then along each y axis it is solved by a differential sweep along a straight line, where the values just found correspond to time, i.e., the layer is taken as initial conditions. By approximating the differential equations in time, the position of the interface is determined for each time layer.

This article presents based on a mathematical model of a one- and two-dimensional problem of a two-phase non-stationary filtration process in an oil and gas sys This article presents based on a mathematical model of a one- and two-dimensional problem of a two-phase non-stationary filtration process in an oil and gas sys