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The article analyzes the modern researchers theoretical ideas regarding the concept of professional competencies. The problem of professional competencies formation and development is essential under the current circumstances, as competition among production organizations increases every day. Moreover, employers are interested in highly qualified workers who are ready to achieve effective production results and contribute to the prosperity of companies via the implementation of theoretical knowledge and practical skills. The purpose of the article is to analyze the process of formation of professional competencies among employees. In this article, special attention is paid to the analysis of the most important competencies and skills of employees necessary for the full functioning of labor relations in the production process. Also, in this article, the competence-based approach to the implementation of practice-oriented training at the university for the preparation of potential employees, who are able to compete and adapt to the emergence of the latest modern technologies, has been examined and analyzed. The introduction of a competence-based approach into the higher education system is a new step in the training of highly qualified personnel who has not only a set of theoretical knowledge, but is also ready to implement the practical skills to solve various production tasks. An employee, who has received a high-quality higher education, a rich theoretical set of knowledge and practical skills, will apply his / her abilities in his work, demonstrating high efficiency. The results are presented via practical recommendations for employers and educational organizations concerning the employees formation of professional competencies.

With all the regional features, it is possible to identify the main patterns that, in the authors’ opinion, were manifested in the Voronezh Region, which is a typical region of the Central Federal District. The data for 2010-2018 of the Federal State Statistics Service (Rosstat) were used as an information base to conduct the analysis. The research algorithm was presented by the following steps: application of the PEST analysis at the regional level, application of the SPACE analysis at the regional level, development of the authors’ methodology for integrating the results of SPACE and PEST analyses at the regional level. Based on the research results, an expert assessment was performed with respect to the aspects that reflected the region's potential, namely, social, economic, political, and technological. The use of methodology for integrating the results of SPACE and PEST analyses allowed combining and forming a track of the strategic state of the social and labor sphere of the Voronezh Region, reflecting the vector of its change.

We study a quasi-hydrodynamic system of equations for a homogeneous (with common velocity and temperature) multicomponent gas mixture in the absence of chemical reactions, with a regularizing velocity common for the components. We derive the entropy balance equation with a non-negative entropy production taking into account the diffusion fluxes of the mixture components. In the absence of diffusion fluxes, a system of equations linearized at a constant solution is constructed by a new technique, In the absence of diffusion fluxes, a system of equations linearized on a constant solution is constructed by a new technique. It is reduced to a symmetric form, the L^2-dissipativity of its solutions is proved, and a degeneration (with respect to the densities of the mixture components) of the parabolicity property for the original system is established. Actually, the system has the composite type. The obtained properties strictly reflect its physical correctness and dissipative nature of the quasi-hydrodynamic regularization.

The purpose of the study is to substantiate the peculiarities of the application of human resource economic analysis within a digital economy and reason the directions of use of the results obtained.

Purpose Determining the reasons for opposition to changes and methods of overcoming the opposition. Discussion A lot of socio-economic systems change slightly with time under the influence of external factors. This happens even with the systems for which changes are vitally important. The reason for such state of affairs is presence of factors that hinder the implementation of innovations, which is called opposition to changes. Opposition to changes has a systemic character and does not suppose unambiguous reaction of people and their groups to their conduct. Opposition is the first reaction to what is happening in the system of changes. Results It is shown that opposition to changes is predetermined by reasons of various qualities. The main groups of reasons for opposition to changes include: routines of organizational, reproduction, and institutional characters; political reasons, related to violation of balance of influence of various persons and groups; culturological reasons. The main provisions, which are significant for effective opposition to changes, are offered.