The multiple regression analysis method is widely used to describe and investigate some processes of the regional economy and may be also used to solve an important problem of distinguishing the effects of various independent or partially dependent variables. The regression model considered includes the specification of its constituent relationships, the choice of variables included in each relation, and the definition of mathematical functions corresponding to these relations. Regression model of food expenditure with two independent variables - expenditure as a function of income and price is based upon the official quarterly averaged statistical information (2015 and 2016 years). All the data are presented in the interpolated monthly version. Regression analysis made it possible to specify the dependence of expenditure on food in the country's households on the disposable personal income and the relative price of foodstuffs, which must be taken into account when solving problems of the region's social and economic development.

The basic principles of organization and algorithms of information system eLab operation for accredited testing laboratories based on free software are described. The system runs under Windows and Linux. The work is carried out through the Web-interface in multi-user mode with the sharing the access rights through widely distributed browsers installed on the users' desktops. The software composition, problems of security and the enhancement of the functionality of the system, as well as the organizational chart of the software and the hierarchy of basic classes are discussed in detail. The algorithm of secure connection to the database and the algorithm for installation of the system software on the server are given.

Synthesis technique for fault-tolerant filters with redundant sensors based on recurrent least squares method (deterministic approach) is proposed. It allows to design simple filtering algorithms with failure detection and to realize filter structure reorganization providing filter functionality.

Three examples of applied systems with a speech interface are considered in the article. The first two of these provide the end user with the opportunity to ask verbally the question and to hear the response from the system, creating an addition to the traditional I / O via the keyboard and computer screen. The third example, the «IntonTrainer» system, provides the user with the possibility of voice interaction and is designed for in-depth self-learning of the intonation of oral speech.

In the paper a human body shape estimation technology based on scan data acquired from sensor controller Microsoft Kinect is described. This device includes an RGB camera and a depth sensor that provides, for each pixel of the image,a distance from the camera focus to the object. A scan session produces a triangulated high-density surface noised with oscillations, isolated fragments and holes. When scanning a human, additional noise comes from garment folds and wrinkles. An algorithm of creating a sparse and regular 3D human body model (avatar) free of these defects, which approximates shape, posture and basic metrics of the scanned body is proposed. This solution finds application in individual clothing industry and computer games, as well.

A method for multi-block parallel decomposition of a system of partial Boolean functions represented by a pair of ternary matrices is described. The method involves examining the row orthogonality graphs of those matrices. It is reduced to finding the complete bipartite subgraphs (bicliques) in one of those graphs and finding a shortest cover of the row set of the other graph by those bicliques.