No abstract

One of the main problems in the theory of partial differential equations is the study of equations of mixed type. the modified Cauchy problem for some values of α is stated and investigated. The equations of the mixed type began to be studied systematically, after FI Frankl indicated their applications to the problems of transonic and supersonic gas dynamics. In this regard, the purpose of this work was to find out whether it is possible to find a more convenient form of representation of the solution of the Cauchy problem for a differential equation, with the help of which it would be possible to solve boundary value problems for a mixed type equation of both parabolic-hyperbolic and elliptic-hyperbolic types. The modified Cauchy problem for some values of α is stated and investigated. A convenient representation of the generalized solution of the modified Cauchy problem is obtained.

The purpose of the study is to substantiate the relative position of the working bodies of a combined machine for non-fall tillage of winter crops. The design scheme and the principle of operation of the combined machine are given. The basic principles and methods of classical mechanics, mathematical analysis and statistics were used in this study. It is established that the most optimal design scheme of a combined machine for non-tillage of the soil and its preparation for sowing of repeated crops is considered to be a scheme consisting of non-tillage cases with crushers, a battery with cut-out spherical disks and a roller. According to the results of theoretical and experimental studies, it was found that with a longitudinal distance between the shaft-free bodies of 40 cm and a transverse distance of 90 cm, a longitudinal distance from the toe of the ploughshare to the center of the support wheel of 50 cm and a longitudinal distance from the toe of the ploughshare of the shaft-free body to the axis of rotation of the cut-out spherical disk of 120 cm, a longitudinal distance from the axis of rotation of the cut-out spherical disk to the center of the roller of 75 cm, high-quality tillage with minimal energy costs is provided.

The article presents a method for calculating the parameters of treatment facilities to bring the level of precipitation and wastewater from small enterprises, shops, and services of the Republic to the level of sewage and irrigation trays. The aim is to improve the design parameters of resource-efficient wastewater treatment plants and their widespread use, increase the production capacity of local wastewater treatment plants, improve the level of wastewater treatment and prevent environmental degradation. Hydraulic calculation of the design parameters of the settling tank was carried out at the local treatment plant. The precipitator works by precipitating suspended solids and separating petroleum products from the liquid surface. At the local treatment plant, the content of petroleum products in industrial and precipitation effluents was reduced to 3 mg/l, and the number of suspended solids to 1-1.5 mg/l.

Modeling the movement of moisture in the soil is of great importance for assessing the impact of agricultural land on surface water bodies and, consequently, on the natural environment and humans. This is because huge volumes of pollutants from the fields (pesticides, mineral fertilizers, nitrates, and nutrients contained in them) are transferred to reservoirs by filtering moisture. Different methods solve all these tasks. The method of natural analogies is based on the analysis of graphs of fluctuations in groundwater level. To apply this method on irrigated lands, it is necessary to have a sufficiently studied irrigated area with similar natural, organizational and economic conditions. The successful application of this method, based on the fundamental theory of physical similarity, mainly depends on the availability of a sufficiently close comparison object, which is quite rare in practice. Physical modeling is often used to construct dams and other hydraulic structures. Previously, the method of electrical modeling was also widely used. It was further found that nonlocal boundary conditions arise in the problems of predicting soil moisture, modeling fluid filtration in porous media, mathematical modeling of laser radiation processes, and plasma physics problems, as well as mathematical biology.