Introduced by S.A. Lomov, the concept of a pseudoanalytic (pseudoholomorphic) solution laid the foundation for the development of the singular perturbation analytical theory. In order for this concept to work in case of linear problems, an apparatus for the theory of exponential type vector spaces was developed. When considering nonlinear singularly perturbed problems, an algebraic approach is currently used. This approval is based on the properties of algebra homomorphisms for holomorphic functions with various numbers of variables, as a result of which it is possible to obtain pseudoholomorphic solutions. In this paper, formally singularly perturbed equations are considered in topological algebras, which allows the authors to formulate the main concepts of the singular perturbation analytical theory from the standpoint of maximal generality.
It is proved that the solutions of Tikhonov systems, in addition to having the property of a limiting transition, are pseudoholomorphic under certain conditions additional to the conditions of A.N. Tikhonov’s theorem. At the same time, the number of fast and slow variables can be anything. Both initial and boundary value problems for systems of this type are considered.
An Navier-Stokes type equation is considered for which a generalized solution is constructed in the form of a series in powers of a specially introduced parameter and its convergence is proved. An example of a mixed problem for the Burgers equation is given.
The article actualizes the problem of creativity in modern culture and education; the question about the importance of a creative component in the process of a person's establishment as an individual. The necessity of the creative interactive methods' application in training and education is shown in this paper; the examples of some gaming interactions inside the social group. Various games and psychological testing methods are offered as methods of developing communication skills among pupils and students. For each psychological game described in this article the authors hold the analysis of its general peculiarities which help to reveal the creative potential of university students and schoolchildren and to espy the individual traits of character which need to be developed and improved or refined. The description of the games' and psychological tests' practical application in the student groups of National Research University 'Moscow Power Engineering Institute' is given; and on the base of this experiment the authors come to the conclusion about the development of students' creative capabilities and making a creative environment with the use of psychological games during the classes.
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