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Relevance of computer based learning and testing of students are discussed. Construction of mixed diagnostic tests that are a compromise between unconditional and conditional components is used in order to develop blended education and training. It is proposed for control, monitoring students' knowledge, professional and personal skills and abilities, and designing learning trajectory of courses for every student. We suggest a technique for construction of optimal mixed diagnostic tests that is based only on the experts' knowledge about problem area. KEY WORDS Intelligent pattern recognition, tree of mixed diagnostic tests, learning trajectory, blended education and training.

The portfolio optimization problem is a basic problem of financial analysis. In the study, an optimization model for constructing an option's portfolio with a certain payoff function has been proposed. The model is formulated as an integer linear programming problem and includes an objective payoff function and a system of constraints. In order to demonstrate the performance of the proposed model, we have constructed the portfolio on the European call and put options of Taiwan Futures Exchange. The optimum solution was obtained using the MATLAB software. Our approach is quite general and has the potential to design option's portfolios on financial markets.

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