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Introduction. The relevance of the study is related to the problem of increasing soil fertility. The value of soil as the main means of agricultural production in a specific economic infrastructure is determined by its fertility that is its ability to satisfy the needs of specific plants for nutrients, water, and to provide the root system of plants with air and heat. The effectiveness of increasing soil fertility depends on objective soil assessments and forecasting. Therefore, mathematical modeling for the fertility level of soils for the agricultural production is an urgent task for agroengineering studies. Aim of the Study. The study is aimed at developing a mathematical model for an integrated assessment of soil fertility levels. Materials and Methods. When conducting the study, analytical methods were used and the results obtained by various authors on this problem were summarized. The object of the study was the published results of scientific researches by the authors from other scientific institutions obtained on the problem under consideration. Results. Based on an analysis of the literature references, there was made a scientifically-based list of the most significant indicators for assessing soil fertility, which includes the content of organic matter (humus), acidity, humidity, soil porosity, presence of microorganisms and clay particles, content of mobile forms of nitrogen, phosphorus and exchangeable potassium. A mathematical model has been developed based on the criterion of maximum soil fertility, which makes it possible to assess the level of soil fertility using the proposed indicators. Discussion and Conclusion. The examples of calculations based on average and basic values of indicators with the use of the proposed mathematical model are presented. They give an idea of the most typical procedures for generating indicators and assessing the process under consideration. The value of the fertility probabilistic coefficient 1 indicates soil depletion (degradation), which will not ensure an economically sound harvest. In this case, measures must be taken to increase soil fertility. When 1, the soil is fertile and is able to supply plants with nutrients, water and air for their growth and development. The soil fertility level is an important criterion for assessing the impact of agricultural technologies on environmental safety and the environment state.

Introduction. Environmental pollution prevention, including prevention of water bodies, with nutrients (nitrogen and phosphorus) when they are removed from agricultural lands with possible runoff is a topical problem that requires a timely solution. The studies have found that the removal of nutrients is a result of geochemical processes, fertilization, and other factors. In this regard, mathematical modeling of the process of removal of nutrients from agricultural lands and their possible entry into water bodies is an urgent task. Aim of the Study. The study is aimed at modeling and predicting the process of possible removal of nutrients from agricultural lands to water bodies. Materials and Methods. When conducting the study, there were used well-known modeling methods. They are the methods for calculating the removal of nutrients from agricultural objects into water bodies, based on the minimum amount of initial information for predicting the eutrophication of water bodies and agrochemical methods taking into account the structure and size of field and agricultural areas, crop yields, and removal nutrients with the harvest. Results. Based on an analysis of the literature and expert judgment, a list of the most significant indicators influencing the process of nitrogen and phosphorus removal was justified. There have been developed mathematical models to determine and predict the input of nutrients from agricultural lands to water bodies. There have been found significant indicators influencing the amount of input of nutrients, such as the amount of applied fertilizers, the volume of moisture, soil water capacity, field area, depth of cultivation, etc. There is given an example of calculating the amount of input of nutrients into water bodies with a rainfall intensity of 50 mm per hour. Discussion and Conclusion. The essence of the proposed mathematical models comes down to the synthesis of numerous indicators in the complex process of removal of nutrients and their impact on water quality. The proposed mathematical models make it possible to predict the removal of nutrients from agricultural lands and to develop and implement technical and technological solutions to prevent environmental pollution.

Introduction. Tillage is the most important part of the agricultural crops cultivation technology. Currently, tillage accounts for 35‒40% of the energy consumption of the total volume of field work and up to 20% of the energy consumed in the agriculture sector. Tillage allows regulating the water-air regime and the intensity of biological processes, maintaining the necessary phytosanitary condition of the soil and crops. The energy intensity and quality of tillage depends on the degree of excellence of technical means. Mathematical modeling of the tillage process by various soil-cultivating working bodies is an urgent task to develop more advanced energy-efficient technical means. Aim of the Article. The purpose of the research is to develop mathematical models for determining and analyzing the indicators of tilling the soil by the bracket-shaped working body. Materials and Methods. In the process of theoretical studies of the bracket-shaped tillage working body for continuous surface tillage, there were used the methods of analysis, generalization and systematization, theoretical mechanics, mathematical statistics and modeling, probability theory, differential calculation, and the theory of interaction of working bodies with soil and their movement over the field surface. Results. The analytical models for determining the pressure, traction resistance, the total force of the soil layer compression, the time of passage of the working body, the required power and the quantity of energy expended on compression of the soil layer depending on the speed of the working body movement are obtained. Graphic dependencies of the investigated parameters of the bracket-shaped tillage working body are presented. The dynamics of parameter changes is identified. Discussion and Conclusion. The proposed mathematical models and the revealed regularities of changing the parameters of tilling the soil by the closed-cycle working body a will make it possible to develop new effective working bodies and optimize the design, technological parameters and modes of their operation.