The article describes the stages of developing a web-application for mobile phones based on an artificial neural network model trained by machine learning libraries (Tensorflow and Keras) to classify plant health with maximum accuracy. The HTML markup language, cascading style sheets, and JavaScript program-ming language were all used during the development process. All photo editing manipulations were performed using the RGB color model.

The article considers an algorithm for situational control of a quadruped dog, based on building and optimizing a regression model in Gazebo. The results of simulation experiments demonstrate the effect of step length and height as well as leg transfer time on the minimum possible decrease in the roll and pitch angles of the robot body.

The study presents the development of a simulation model for an element of the road network that consists of two adjacent intersections in Omsk using agent-based and discrete-event modeling in order to analyze traffic, forecast traffic, and propose traffic optimization measures. Based on the traffic calculations aimed at improving functionality of the selected element of the road network, an efficient scheme for traffic flows is proposed by changing the duration of traffic light phases.

The article presents a comparative analysis of two versions of the National Research Council Canada Emotion Intensity Lexicon and proposes a hypothesis regarding the difference in intensity of Russian emotional norms. Based on the use of synonym words during translation, an algorithm for compiling a Russian-language dictionary of emotions is proposed. Online multiple translation services are investigated according to their quality and variety in order to select the one that will suit the research goal and determine the quanti-tative difference of emotion intensity coefficients in Russian and English lexicons.

The study analyzes the time series of the number of new cases in the administrative courts of the Russian Federation using two methods of time series grouping according to the chaotic, stochastic, and regular structure. The first model is based on the entropy‒complexity plane, the second one is presented by the attribute‒object graph. As a result, four groups of time series were derived: regular, regular-chaotic, purely chaotic, and chaotic-stochastic. Most of the series turned out to be chaotic-stochastic, which is common for real systems. Each group of time series is assigned with a suitable prediction algorithm. For example, algo-rithms of nonlinear dynamics can be used for chaotic series, and models based on stochastic processes can be used for strongly stochastic series.

The study presents a solution to the inverse problem of approximate constants determination of response rate according to the given concentrations of initial substance and products in the framework of mathematical model of kinetics of oil refining process. In the course of the study, the finite difference method, the data interpolation method (the cubic spline), and the Tikhonov regularization method were used. Response rate approximate constants are identified. They are unique and depend on the initial data. Response rate ap-proximate constants aid in forecasting concentrations of the initial substance and products at any moment and determining indicators in oil refining process reactions, such as energy activation, temperature, and other external conditions.

The object of the study is analytical and topological methods for automatic control systems engineering. The aim of the study is to build a practice-oriented approach for applying the state space method, which is part of nonmetric mathematics, to analyze the single input single output systems. A generalized nthorder input output system is investigated. A structural scheme for such system modeling is developed according to the state space method. The scheme was tested on the example of the second order system using verifi-cation of the control modeling method. The nth-order system is transformed into “input ‒ internal state ‒ output” type. The structural scheme of its modeling is developed according to the state space method in various visual simulation systems and tested on the example of the third order system using verification of the control modeling method. The criterion of correctness is equality of graphs of output signals of the system analyzed, which were obtained by the state space method, the structural modeling method and the assignment of the transfer function. The developed universal mathematical tools make it possible to study single input single output systems of any complexity.

The simple non-elementary linear regression model contains two explanatory variables trans-formed by a minimum or maximum binary operation. One of the arguments of a binary operation in such models contains only the slope. Non-elementary linear regressions, in which the argument of a binary operation contains both the unit slope and intercept, are studied. Based on the algorithm of approximate estimation by ordinary least squares for non-elementary linear regressions, an algorithm for estimating a non-elementary linear regression, in which the argument of a binary operation contains the slope and intercept, is developed. The proposed algorithms were implemented as a program that solves the modeling problem for railway freight traffic in Tyumen Oblast using hansl, a scripting language from the gretl package. A classical linear regression and three options of non-elementary linear regression (with the slope in the argument of a
binary operation, the unit slope and intercept, and the slope and intercept) were constructed. The proposed non-elementary models with the intercept in a binary operation were found to be more efficient than their wellknown
alternatives.

The article presents a mathematical description of methods for performing non-modular oper-ations in modular arithmetic, such as transfer operations from a modular number system to a positional number system and comparison operations in a modular number system. A program for simulating algorithms on a com-puter was developed in Python. The study provides examples and results of the algorithms’ performance. The algorithms’ complexity is estimated in order to compare them and determine the most effective one.