To design the effective model of the center of excellence we must take into account that the following play an important role for them: external sources (links to the competencies sources), interaction within the business unit, the effectiveness of the center’s activities (profitability and competitiveness, innovativeness, transfer of knowledge) and the investment of the parent company. The article proves that advancing education and training at a high level of difficulty (while creating psychological and pedagogical conditions of personal growth of students) enables school leavers to win national competitions, organized by the ranked universities and, accordingly, to enter those universities out of competition. Therefore, modern lyceums for gifted children may be not for really gifted, but for more or less cable pupils. And whether or not they become talented, depends on many factors, including reasons related to the preparation special teachers for them. Moreover, daily experience shows that often they become gifted not thanks to but in spite of the education, which is considered as profile or in-depth (for gifted only).
The creation of centers of excellence as innovative structures of university science and education should include: development and support of its own structure, and then search for and justification of the idea of innovation; the creation of innovations, ready for sale; the promotion of innovation in the economy and the market of educational services. Of particular importance in this case are the mechanisms and methods of reasoning the ideas, economic evaluation of innovations, market research, evaluation of innovative projects, creativity motivation and economic incentive to stimulate the personnel initiative, the target program management, promotion of innovations. For the senior staff of universities strategic task-oriented management should be of higher priority: management should be directed at identifying and ranking specific problems, determination of scale and direction of their impact, and the possible consequences and the strategy of behavior under standard conditions.
Of great importance is the creation of conditions for the transfer of knowledge. Properly constructed educational trajectory from pre-school to university is a prerequisite for a scientific breakthrough.