The development of the modern economic system is becoming increasingly dependent on the sufficient provision of quality energy resources due to the intensification and transformation of the mechanization and automation of all industries. The growth of the energy needs of society is parallel to the awareness of the need to ensure the environmentally friendly development of society. There are a number of reasons for the search for new energy sources, including the limited reserves of traditional sources, dependence on oil-exporting countries, the greenhouse effect due to the entry of carbon dioxide into the atmosphere and air pollution by harmful gases. The biofuel sector offers the potential for both the development of national agriculture and for increasing its energy independence. Global trends in the rapid development of bioenergy in combination with the systemic crisis of the energy sector in Ukraine have necessitated a detailed study on the possibility of increasing the yield of biofuels from crops. The economic and mathematical modeling of the possibility of increasing the yield of bioethanol and vegetable oil from agricultural crops has been carried out. An economic optimization model has been formed, which made it possible to study an increase in the yield of bioethanol from sugar-containing and starch-containing crops and vegetable oil from oil crops from 1 ton per 1 hectare of area. Also, an assessment of the lost yield for the investigated crops has been carried out using the method of analysis of the functioning environment (Farrell’s method).

The article focuses on selected problems which have now appeared and fall under the ideas “industry 4.0” and “society 5.0”, namely on anthropological issues. Changes in the relationships between man and technology based on trust lead to an increase of the role of the technological factor in these relations. Other aspects of the analyzed changes concern the new requirements of the responsibility and changes of human subjectivity and rationality. The future of man appears to be an area of uncertainty related to inter alia the conditions of functioning and living in the order of the post-digital world.

The study presents the results of theoretical investigations into lateral torsional buckling (LTB) of bi-symmetric I-beams, elastically restrained against warping at supports. Beam loading schemes commonly used in practice are taken into account. The whole range of stiffness of the support joints, from free warping to warping fully restrained, is considered. To determine the critical moment, the energy method is used. The function of the beam twist angle is described with power polynomials that have simple physical interpretation. Computer programs written in symbolic language for numerical analysis are developed. General approximation formulas are devised. Detailed calculations are performed for beams with end-plate joints. Critical moments determined with programs and approximation formulas are compared with the results obtained by other researchers and with those produced by FEM. Very good accuracy of results is obtained.

Efficiency, functionality and performance of the grain grinding process are significantly influenced by phenomena that are difficult to describe and occur in the working area of the grinder. In a machine-based, multi-disc grinding of grain biomaterials, the design of the quasi-cutting unit, volumes, sections of transport/grinding holes, their motion and the design features of the discs (the grinding unit) must facilitate the functions of grinding in the inter-hole space (with minimum energy-consumption of the process and maximum efficiency) and minimising undesirable phenomena related to mixing and transport. The pre-requisite for optimisation of the quasi-cutting unit design is a mathematical model. Among many aspects of the problem, this study describes a sample procedure resulting in a filling model for a biomass grain quasi-cutting unit including an initial verification of the same under conditions of the evaluation of maize and triticale grain grinding efficiency, using an innovative multi-hole 5-disc and 7-disc grinder.