The article uses the mathematical apparatus of the theory of linear-quadratic differential games, as well as the method of qualitatively representative scenarios to build a mathematical model of interaction between the university and its industrial partner. The analytical solution of the game (Nash equilibrium) is obtained and the numerical solution of the problem is demonstrated.

Keywords: linear-quadratic differential games, optimization, mathematical modeling, method of qualitatively representative scenarios, game theory

The paper considers the problem of personnel training. The first part describes a mathematical model that describes staff training through scheduling theory. The second part of the article describes a numerical solution using MS Excel and provides several examples of scheduling, the results obtained show how it is necessary to schedule classes to minimize teacher downtime. At the end of the work, practical conclusions and shortcomings of the model are described. This model allows you to reduce the time for scheduling teachers, thereby reducing the possible costs of the enterprise.

Keywords: theory of schedules, discrete mathematics, optimization, training, mathematical modeling, linear programming

The paper presents the theoretical and methodological bases of research in the social partnership system of additional vocational education through building dynamic game-theoretic models of interaction.

Keywords: social partnership, additional professional education, game theory, simulation

The mathematical model formalizes the solution of a problem of optimum control and it is meaningful to minimization of number of regional extremist system (bandit underground) taking into account relative importance of parts making it at the restrictions caused by "will" of the state to fight against extremism and objective dynamics of number of groups of extremists, an ethnosociocultural protestnost defined by factors (protest potential of society). The task was solved by means of imitating modeling on a method of scenarios.

Keywords: Mathematical model, method of scenarios, extremism, dynamics of number of groups of extremists, problem region, North Caucasus.

The mathematical model formalizes the solution of a problem of optimum control and  the minimization of regional extremist system’s number (bandit underground) is meaningful taking into account the relative importance of its parts with the restrictions caused by "will" of the state to fight against extremism and the objective dynamics of the extremist groups number, defined by the ethno-and-sociocultural protest potential factors. The problem was solved by means of imitating modeling basing on scenarios method. The results of scenery modeling of republican bandit underground dynamics are obtained depending on different variants of the power influence, in conjunction with different options of republican community development. The results of modeling calculations on fixing of a range of scenarios of quantitative dynamics of separate groups layers of a republican bandit underground are given. The identification of modeling parameters according to scenarios is executed and interpretation of the received results and practical recommendations on optimization of combating regional terrorist underground is presented.

Keywords: Mathematical model, scenery modeling, extremism, bandit underground, dynamics of number of groups layers of extremists, problem region, North Caucasus.