Applied Mathematics and Control Sciences

Given certain restrictions on the number axis complex- periodic function. These are almost all periodic functions encountered in technical applications. It is proved that in spite of appropriate conditions expandability via Fourier integral such functions can not be decomposed into a continuous spectrum of harmonics. It is shown that a periodic function on the real axis can not be represented as a Fourier integral. It is proved that bounded on the axis of a periodic function has no harmonics in its zero values. It is shown that a rectangular pulse function can be represented as a quasi-periodic and therefore not subject to degradation by the Fourier integral, and its spectrum (if it exists) does not depend on the size of the virtual period, this conclusion, in particular, apply to the step Hevisayt function. It is proved that a rectangular pulse function is decomposed into harmonics, not counting the zero harmonic, equal to the value itself rectangular pulse function, which consequently can not be decomposed by harmonic step Hevisayt function and d-Dirac function. It is shown that bounded on the real axis harmonic function can not be decomposed into a continuous spectrum of harmonics by the Fourier integral.

The task of the deformation description at phase transformation is a part of a problem involving creation of two-level model of steel inelastic deformation at thermomechanical treatment based on approaches of the physical plasticity theory. The gradient of transformational deformation of representative mesovolume is constructed on the basis of the crystallographic theory of martensitic transformation and describes deformation with the invariant plane. It is expressed through a vector of a normal to the invariant plane and a shear vector which set transformational system (by analogy with system of crystallographic shear for dislocation sliding). According to the Kurdyumov - Sachs’s orientation relationships, there are 24 transformational systems, expressions for which component are given in the article. Features associated with application of a measure of inelastic deformation of mesolevel (crystallite) representative volume at martensitic transformation are considered. In particular conditions of activation of these systems at different types of loading are defined.

The matrix integrated assessment mechanisms are widely used for solving multi-criteria selection task. The functionality of these methods significantly enhanced by convolution interpolation function on a continuous domain of the editor boxes arguments that could be achieved, including through the procedure of fuzzy comprehensive evaluation. The possibility of use in the procedure of fuzzy comprehensive evaluation multi-parameter objects serve as an alternative to the known maxmin, probabilistic, including additive-multiplicative approaches to set-theoretic operations of union and intersection of fuzzy sets. It is shown that using the presented in this paper approaches fail to make the convolution matrix monotone and smooth, resulting in a comprehensive estimation error and unfounded decisions made in the problems of multi-criteria selection, optimization and control.

An approach knowledge engineering in problems of physical-mechanical metal properties identification when creating functional materials is considered. Also describes developed method of image recognition in thin metal section classification problems.

The method of a consumer assessment of quality of house management organizations is presented in article. Estimation is based on criteria of quality of the business processes of service in management provided by the housing legislation, standards and consumer preferences. Authors offered the concept of assessment of quality of house management organizations, and also a form of the questionnaire for monitoring of quality management of a real estate object for the Apartment House Councils and other interested persons. In article the main stages of estimation on the basis of the developed method of a consumer assessment of quality of services of managing organization are opened.

The concept of intelligent decision support at the pre-investment phase of the project management is discussed. This concept is a methodological basis of expertise of investment projects requires in grows of level of confidence in the results of expertise. Shows the algorithm of investment decisions support system, where each project manager can find everything he need in the context of the circumstances. Methodological basis is formed by the convolution matrix, inductive production functions and formal output systems.