THEORETICAL AND PRACTICAL STUDIES OF EFFECTIVE PHYSICAL AND MATHEMATICAL MODELS OF DESIGNING EDUCATIONAL RESOURCES IN AGRARIAN INSTITUTIONS OF HIGHER EDUCATION
Authors:   Vinnytsya National Agrarian University, Ukraine, Dubchak Viktor , Manzhos Elvira ,   National Pirogov Memorial Medical University, Ukraine
Published: May 2023

The purpose of this paper to investigate the issue of optimal, extreme (minimum) coverage of the area of one flat figure, namely, a square (rectangle) of the area of another flat geometric figure, such as a circle (ellipse). The value of a certain function that determines the difference in the areas of the mismatch of the given geometric figures at the intersection has been obtained, in the first case the function is dependent on one variable argument, in the second case – on two arguments, in both cases the study of the extreme of this function has been carried out, it is shown that in the found extremum point, the function that determines the mismatch of the areas of the figures acquires a minimum value. Methodology. The conditions of such extremely minimal covering of one area with another area are established, drawings are provided for a better understanding of the formulation and solution of the given problem. Results. The conclusions have been made, in which the values of the sought arguments are given, when the corresponding function will acquire minimum values. Also, as an alternative criterion for the optimality of such a mutual placement of one figure relative to another, this paper proposes such a criterion as an effective assessment of the length of the set of lines along which the specified figures diverge. The value of a certain function that determines the length of such a sum of the lines of divergence of the figures in both cases has been obtained, a study has been carried out on the extremity of this function, it has been shown that at the found extremum point the function that determines the total length of the line of divergence of the figures acquires a minimum value. The issue of body movement under the influence of gravitational field forces and environmental resistance has been considered in these studies, the obtained solutions and their practical use in the field of agro-industrial complex of the economic sphere have been analyzed. Practical implcations. As a result of the conducting research using a fundamental analytical and mathematical apparatus, an algorithmic model has been developed. It describes the movement of seeds or mineral fertilizers on the path of movement from sowing machines to the grooves that are formed in the soil after the passage of coulters of seeders; the movement of grain, which moves from top to bottom in the cleaning systems of grain harvesters or during unloading from the hopper, etc. Such processes and phenomena occur during the production operation of planters and planters, machines for post-harvest processing of grain, harvesting of root vegetables, fruits, berries, etc. Value/originality. Drawings are provided for a better understanding of the formulation and solution of the set problems, conclusions are drawn, as the meaning of the sought arguments, when the corresponding function acquires minimum values, the corresponding differential equations of body motion are drawn up and the directions of using their solutions are indicated, particularly in the agro-industrial sector of the economy.