The article describes the problem of calculation of Hadamard matrices of high orders. Definitions of twin matrices, Propus, Propus-M, Propus-E, is given. A method for their calculation via Mersenne and Euler matrices and modified Williamson array, based on two basic matrices, is described. A path of approximation of a Hadamard matrix of order 668 through Propus-M, based on a known Mersenne matrix of order 167, is shown, and definitions of matrices levels and their portraits are given. Equations of connection of Propus-M and Propus-E matrices levels are presented; their properties, numerical examples and portraits of Propus-M and Propus-E matrices calculated via modified Williamson array are analyzed.

The article analyzes the T. Saati analytic hierarchy process in terms of its correctness and efficiency, presents the relation of its solutions with the vector optimization problem providing that initial estimates of alternatives are measured in a quantitative ratio scale. Inconsistency of statements on incorrection of the analytic hierarchy process published by some authors is substantiated. The estimation of the approximate solution of the analytic hierarchy process with optimum solution obtained by the approximation matrix method for weights formation of objects in multicriteria selection problems is carried out.

The article is devoted to the evaluation of radio waves propagation for the LTE standard in the 1 800 to 2 600 MHz band. The attenuation is calculated for the highway with a difficult terrain in a coniferous forest. Simulated modeling is carried out using MatLab environment to compare theoretical and practical results.

The article analyzes a current problem of maintaining a service of automated deposit machines and ATMs of credit institutions. Solution of the forecasting problem will help in automating the process of cash collection management and organizing an efficient planned load of a self-service machine in order to minimize time when the machine is unavailable for service. To solve the forecasting problem, the comparative analysis of existing mathematical methods of time series forecasting (such as exponential smoothing models, seasonal autoregressive integrated models (moving average) and models based on the neural networks (single-layer neural network and neural-fuzzy
network)) is obtained. The analysis is carried out based on the data of the amount of cash withdrawn from the ATM in a closed area of the business center. As a result, the most efficient forecasting method (neural-fuzzy network) is determined and the forecast of cash withdrawal for the selfservice machine is obtained. Management of a planned load of ATMs based on the obtained forecast minimizes time of technical delay of the machine in case of cash assets excess or shortage as well as allows optimizing the collector’s work.

The article describes testing of computer shogi programs and criteria for their selection. The dependence of time of thinking about a move on the search depth limitations with consideration of an average number of moves in the game is determined. A time-limited competition is hold to identify the strongest program out of selected ones. The dependence of game duration on the search
depth is determined.

The article presents an algorithm of data clustering based on the construction of linear regression model with application of method of antirobust estimation of parameters. The algorithm has a property of equity of the number of maximum module approximation errors to the number of parameters plus one. Three clusters of data selecting, with modeling of loading volumes at the Russian Federation railways, are formulated based on the statistical data for the period of 2005–2018.

The article analyzes the process of development and gives the description of subject area of the formalized ontological representation of the concept “basic educational program”, distinguishes the most important objects, their properties and relations, introduces the indicators to control the compliance of time requirements for the educational program, establishes the ontology graph “basic educational program”.

The article presents the architecture of the developed automated information system “Student”, which includes functionality to provide online and offline university events, hackathons, competitions with team and one-person participation, to manage project activity of student groups, to calculate ratings, etc., with the full-text search technology Elasticsearch implemented in it. Different approaches to implement search algorithms developed on relational database management system are described. The article provides the main information about the search engine, the Elasticsearch search algorithm and the process of its setup on the example of search inquiry.