Optimal boundary control for damping the vibrations in a Mindlin-type beam is considered. Wellposedness and controllability of the system are investigated. A maximum principle is introduced and optimal control function is obtained by means of maximum principle. Also, by using maximum principle, control problem is reduced to solving a system of partial differential equations including state, adjoint variables, which are subject to initial, boundary and terminal conditions. The solution of the system is obtained by using MATLAB. Numerical results are presented in table and graphical forms.

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The choice of instructional strategies, methods and techniques used by teachers is important in terms of establishing an effective learning environment. The purpose of this study is to examine the most common methods teachers use in their lessons and the factors that influence their choice of methods by using game theory. Game theory has different applications such as social sciences, politics and economics. A questionnaire is prepared by the researchers in this study, which is conducted with forty-seven teachers working in different branches and at different levels. The two most preferred teaching methods are considered to be players: direct instruction and problem solving method. The characteristics of these methods are compared with game theoretic approach according to the survey results. Two separate game problems are revealed in the study. The first game problem is a zero-sum game representing the state of the two teaching methods, which are considered as rival to each other. With the non-zero-sum game, the characteristics of both teaching methods are analyzed. According to results, direct instruction method is superior in terms of usage properties in accordance with problem solving method. The advantages and disadvantages of the two teaching methods are discussed for further research.