The article is dedicated to topical questions of Russian education modernisation from the point of view of the conflict of scientific interests and educational staff of higher school, namely the analysis of adaptation strategies of lecturers in the conditions of modernisation of higher education. Main transformation trends of Russian higher school have been singled out and their influence on the position of lecturers has been revealed. Basing on the results of opinion poll, dynamics of conditions, content and character of teachers' activity has been revealed. We have also identified important behaviour strategies of teachers on the professional labour market in the conditions of significant intensification of competition and real risk of losing their jobs. Significance of academic degrees in the system of strategic guidelines of the faculty community has been studied. Most high-demand technologies of self-marketing have been identified, and their use allows increasing competitive advantage of teachers and strengthens their positions in the professional field in the modern period.

The basic branch of both discrete and continuous mathematics is Set theory, the study of which is a difficult task. Designed and developed in the Maple computer algebra system, the Maplets package–the set theory application–enables to provide assistance both in teaching (by demonstrating the performance of operations on sets, testing knowledge and skills in using operations), and in studying set theory and solving the simplest combinatorial tasks (can be used as a simulator for students). By using interactive worksheets and animated images in Maple, students are given the opportunity for numerous experiments that will contribute to the development of their math education as well as computational skills. The application will form a sustainable need for the use of computer systems by students in the study of various branches of mathematics.

The article discusses the world experience in the application of the antitrust regulation system and antitrust compliance. The concept of antitrust compliance and antitrust regulation, the history of the emergence of antitrust regulation and compliance, the foreign practice of application, the features of the use of antitrust compliance in the Russian Federation are analyzed. The system of antitrust regulation is designed to ensure the effective functioning of economic relations of economic entities and reduce the risks of offenses. Antitrust compliance is a combination of legal and organizational measures aimed at compliance with the requirements of antitrust laws and prevention of its violation.

The article reveals the problems of improving environmental impact assessment and justification of the economic investments of industrial enterprises. The existing tools for environmental impact assessment are analyzed, information on the role and place of environmental impact assessment and investment design in the justification of the planned economic activity is systematized. For this purpose, considerable attention is paid to the analysis and synthesis of existing methodological approaches to this problem. The authors propose to consider environmental impact assessment and justification of environmental investments as a process aimed at making environmentally oriented management decisions on the feasibility and economic feasibility of implementing planned economic activities, the reasonableness of capital investments, taking into account possible adverse environmental, social, economic impacts and developing measures for their reduction and prevention. Based on the study, the authors developed a classification of the causes of environmental pollution, presented in the form of a tree of systems, allowing for a clear decomposition of the causes of pollution of the environment, specifying and refining the targeting of environmental measures necessary to reduce pollution. This research direction is also complemented by the development of a strategy (decision tree) and a mathematical description of the simulation procedure, which allows real-time making an objectively reasonable choice of options for implementing the planned economic activity, taking into account the totality of known information.

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