Heat treatment is a common operation in grain processing technology. Thermal action on grain is characterized by temperature level and duration. Also, the grain changes all its complex properties. Frequently, the temperature in grain activates the process of change in the moisture content and is accompanied by moisture loss. The processes of change in the heat and moisture are interrelated. Based on the experiments conducted on legumes (different varieties of bean, white lupin), a mathematical model of these processes has been developed and the appropriate non-linear differential equations have been used. The obtained equations cannot be solved either analytically or numerically, because some of the coefficients are unknown. The equations are solved based on certain assumptions. Based on these assumptions, the paper provides the calculation of the change in temperature and moisture content over time in legumes, such as bean and white lupin. The obtained results have been compared with experimental data.

With a view to determining the dynamics and possible trauma sustained by a disabled person in a wheelchair in the passenger compartment of a bus, a physical model has been developed. The system, as the time function, generalized in the coordinates X(t), (t), was described by second-order Lagrangian differential equations. The proposed mathematical model allows for determining the motion characteristics of disabled people in a wheelchair in a bus that can cause injuries. This paper presents the curves of the change in coordinates of the angular velocity of the head and its center of gravity, as well as the curve of the change in the angle between the femur and the wheelchaior seat, through mathematical modeling and an experiment.

Proceeding from three-dimensional formulations of initial boundary value problems of the three-dimensional linear micropolar theory of thermoelasticity, similar formulations of initial boundary value problems for the theory of multilayer thermoelastic thin bodies are obtained. The initial boundary value problems for thin bodies are also obtained in the moments with respect to systems of orthogonal polynomials. We consider some particular cases of formulations of initial boundary value problems. In particular, the statements of the initial-boundary value problems of the micropolar theory of K-layer thin prismatic bodies are considered. From here, we can easily get the statements of the initial-boundary value problems for the five-layer thin prismatic bodies.

The article considers the change in chemical and biological characteristics in some legumes grains, under conditions of high-temperature micronization with different moisture contents during heat treatment with infrared rays. The heat treatment of grains was carried out on a laboratory apparatus with a quartz radiant infrared panel. The temperature variation in the heat treatment zone occurred due to changing the distance between the panel and the surface of grains. The grain temperature was determined using a laser thermometer, and with a timer. To determine chemical and biological characteristics, we used a special optical density metering device. We have studied: 1. The dependence of starch content on the temperature in the changing initial moisture content. We found that after 30 seconds of high-temperature micronization of, “Tsanava“ beans at a grain moisture content of 12.7%, the starch content in the grain increases from 39.65% to 40.12%, then gradually decreases, and at 18.3% moisture content, it increases from 38.71% to 41.2%, with a moisture content of 28.6% it increases from 37.36% to 42.42%. Similar processes are also observed for the beans “field red“ and “white lupine“; 2. The dependence of glucose content on the temperature in the changing initial moisture content. As the mass fraction of starch decreases, the percentage of sugar (in terms of the equivalent amount of glucose) at a moisture content of 12.7% at the initial stage increases from 1.36% to 1.46%, and then the percentage of sugar increases relatively quickly to 1.64%, at a moisture content of 18.3% it increases from 1.3% to 1.38%, and then increases to 1.51, with a moisture content of 28.6%, it increases from 1.28% to 1.35% and then increases to 1.54. Similar processes are also observed for the beans “field red“ and “white lupine“.

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