Modern engineering equipment operation necessitates solving optimal control problems based on measurement data from numerous physical and technological process parameters. The analysis of multidimensional data arrays for their approximation with analytical dependencies represents both current and practically significant challenges. Existing software solutions demonstrate limitations when working with multidimensional data or provide only fixed sets of basis functions.
Objectives. The aim of this study is to develop software for multidimensional regression based on the least squares method and a library of constructible basis functions, enabling users to create and utilize diverse basis functions for approximating multidimensional data.
Methods. The development employs a generalized least squares method model with loss function minimization in the form of a multidimensional elliptical paraboloid. LASSO (L1), ridge regression (L2), and Elastic Net regularization mechanisms enhance model generalization and numerical stability. A precomputation strategy reduces asymptotic complexity from O(b²·N·f·log₂(p)) to O(b·N·(b+f·log₂(p))). The software architecture includes recursive algorithms for basis function generation, WebAssembly for computationally intensive operations, and modern web technologies including Vue3, TypeScript, and visualization libraries.
Results. The developed web application provides efficient approximation of multidimensional data with 2D and 3D visualization capabilities. Quality assessment employs MSE, R², and AIC metrics. The software supports XLSX data loading and intuitive basis function construction through a user-friendly interface.
Conclusion. The practical value lies in creating a publicly accessible tool at https://datapprox.com for analyzing and modeling complex multidimensional dependencies without requiring additional software installation.

Keywords: approximation, least squares method, basic functions, multidimensional regression, L1/L2 regularization, web-based

A two-level hierarchically organized model of managing the interaction of the director with the personnel in a company related to the development of projects in the construction sector is presented. The director acts as the leader, and the company's employees act as followers. Both management entities strive to maximize their target functions, reflecting their income and expenses. The study of the model was conducted taking into account its hierarchical structure.  An algorithm for constructing a Stackelberg solution under inducement has been developed. A numerical study of the model has been conducted using the scenario method by partially enumerating the areas of admissible controls of subjects with a certain step. When conducting simulation experiments, all input parameters of the model varied in a fairly wide range. The results of the simulation experiments have been analyzed, and some patterns of system development have been identified.

Keywords: hierarchy, incentive, control system, solution algorithm, Stackelberg equilibrium, leader, follower, imitation, experiment, investment project

This article proposes a new concept of production management of a chemical industry holding as the basis for mathematical support of an automated control system. The concept is based on the use of both traditional methods of proactive management (preventive and predictive) and new generation proactive management, which not only prevents the occurrence of undesirable events, but also ensures a decrease in the frequency of occurrence of such events in the future. A system of basic concepts and principles of proactive production management has been developed. The proposed concept will allow developing the existing mathematical support of an automated production control system and increasing its efficiency.

Keywords: production, automated production control system, mathematical support, concept, proactivity, strategies, proactive management

In this paper, methods for estimating one's own position from a video image are considered. A robust two-stage algorithm for reconstructing the scene structure from its observed video images is proposed. In the proposed algorithm, at the feature extraction and matching stage, a random sample based on the neighborhood graph cuts is used to select the most probable matching feature pairs. At the nonlinear optimization stage, an improved optimization algorithm with an adaptive attenuation coefficient and dynamic adjustment of the trust region is used. Compared with the classical Levenberg-Marquard (LM) algorithm, global and local convergence can be better balanced. To simplify the system's decisions, the Schur complement method is used at the group tuning stage, which allows for a significant reduction in the amount of computation. The experiments confirmed the operability and effectiveness of the proposed algorithm.

Keywords: 3D reconstruction, graph-cut, Structure-from-Motion (SfM)，RANSAC，Bundle Adjustment optimization，Levenberg-Marquardt algorithm，Robust feature matching

The paper considers a lightweight modified version of the YOLO-v5 neural network, which is used to recognize road scene objects in the task of controlling an unmanned vehicle. In the proposed model, the pooling layer is replaced by the ADown module in order to reduce the complexity of the model. The C2f module is added as a feature extraction module to improve accuracy by combining features. Experiments using snowy road scenes are presented and the effectiveness of the proposed model for object recognition is demonstrated.

Keywords: Bobkov A. V., Du K., Dai I., Wang Z., Chen H.

The characteristics of a submersible induction motor are described with sufficient reliability for practice by the theory of multi-motor electric drive. In this case, the classical circuit of a submersible induction motor is a coupled system of several equivalent-T circuits. In turn, this significantly increases its computational complexity and reduces the speed of ACS. It is proposed to construct a mathematical model of the submersible electric motor in the form of polynomials with significantly higher speed using the methods of experiment planning. In the area of applicability, the differences in the estimation of energy performance do not exceed 1.1%, between the proposed models and classical equivalent-T circuits.

Keywords: automated control system, mathematical model, polynomial, mean absolute percentage error, computational complexity, design of experiment, scatter diagram, modal interval, submersible electrical motor, rotor package

The article presents a mathematical model that formalizes the process of managing the scientific activities of an organization. The model based on the theory of queuing. The principle of death - reproduction used in the construction. For a special case, a graph of states and a system of Kolmogorov differential equations are given. The intensity of the input and output streams are time-dependent non-stationary streams. The model allows us to consider various structures and schemes of interaction between scientific departments and various sce-narios for setting scientific tasks and the intensity of their solution by employees of the organization. A software package for decision-making has developed for the model for optimal management of the scientific activities of the department. The article presents one of the results of an experimental and model study of the influence of the motivational component and the level of competence of employees. Graphs of the system states given for the resulting solution. The research can used for comprehensive evaluation of results, planning, resource allocation and management of scientific activities.

Keywords: scientific activity, mathematical model, queuing system, death-reproduction principle, graph of states, system of differential equations

The article presents the results of a study on the effectiveness of the hashing algorithms Argon2, Scrypt, and Bcrypt in the context of developing web applications with user registration and authentication features. The main focus of this research is on analyzing the algorithms' resilience to brute-force attacks, hardware attacks (GPU/ASIC), as well as evaluating their computational performance. The results of the experiments demonstrate the advantages of Scrypt in terms of balancing execution time and security. Recommendations for selecting algorithms based on security and performance requirements are also provided.

Keywords: hashing algorithm, user registration interface, user authentication interface, privacy protection

The article discusses the structure and principle of operation of an improved centrifugal unit for mixing bulk materials. A special feature of which is the ability to control mixing modes. Due to its design, the selection of a rational position of the bump makes it possible to provide such conditions for the impact interaction of particle flows, in which a high-quality homogeneous mixture of components is formed, the particles of which have different sizes, shapes and other parameters. To characterize the resulting mixture, the coefficient of heterogeneity was used, the conclusion of which is based on a probabilistic approach. A computational scheme of the rarefied flow formation process is given. An expression is derived for calculating the coefficient of heterogeneity when mixing bulk media, the particles of which have different sizes, shapes and other parameters. The research conducted in the article allows not only to predict the quality of the resulting mixture, but also to identify the factors that have the greatest impact on achieving the required uniformity.

Keywords: aggregate, bulk media, mixing, coefficient of heterogeneity, concentration, design scheme, particle size

The problem of substantiating the grid step of an electronic map used to establish the fact that a vehicle, whose coordinates are read from an on-board GPS sensor, enters the control area is considered. The proposed decision support system determines the maximum allowable step for marking a geographical area for subsequent information processing, in which the amount of resulting data is close to the minimum, taking into account the preservation of processing time and acceptable the level of error of the data for analytics. To solve the problem, it is proposed to use the regression analysis apparatus to determine the dependence of the expected verdict error on the grid step of the electronic map. The analysis of residual variances was used to prove the applicability of the proposed device. The Laplace formula was used to estimate the confidence interval of erroneous verdicts.

Keywords: grid step, confidence probability, percentage of erroneous verdicts, regression analysis, coefficient of determination

The article discusses a software module developed by the authors for automatic generation of program code based on UML diagrams. The relevance of developing this module is due to the limitations of existing foreign code generation tools related to functionality, ease of use, support for modern technologies, as well as their unavailability in Russian Federation. The module analyzes JSON files obtained by exporting UML diagrams from the draw.io online service and converts them into code in a selected programming language (Python, C++, Java) or DDL scripts for DBMS (PostgreSQL, Oracle, MySQL). The Python language and the Jinja2 template engine were used as the main development tools. The operation of the software module is demonstrated using the example of a small project "Library Management System". During the study, a series of tests were conducted on automatic code generation based on the architectures of software information systems developed by students of the Software Engineering bachelor's degree program in the discipline "Design and Architecture of Software Systems". The test results showed that the code generated using the developed module fully complies with the original UML diagrams, including the structure of classes, relationships between them, as well as the configuration of the database and infrastructure (Docker Compose). The practical significance of the investigation is that the proposed concept of generating program code based on visual models of UML diagrams built in the popular online editor draw.io significantly simplifies the development of software information systems, and can be used for educational purposes.

Keywords: code generation, automation, python, jinja2, uml diagram, json, template engine, parsing, class diagram, database, deployment diagram

Differential-algebraic equations for describing the motion of a plane-parallel robot-manipulator are investigated. The dynamic model is constructed using the Lagrange equation and the substructure method. The design of a control system regulator using the sliding mode method is considered. The control accuracy is tested on a model of a 3-RRR plane-parallel robot . It consists of three kinematic chains, each of which has two links with three rotational joints. To study the efficiency of the controller, a circular trajectory is used as the target motion for the multibody system. The considered control system for a plane-parallel robot is capable of solving problems of movement and ensuring high positioning accuracy.

Keywords: control, plane-parallel robot, kinematic characteristics, dynamic model, differential-algebraic equations, constraint equation, controller, sliding mode, Lyapunov function, program trajectory

This article presents a structured approach to deploying and integrating Grafana, Loki, and Alloy in Kubernetes environments. The work was performed using a cluster managed via Kubespray. The architecture is focused on ensuring external availability, high fault tolerance, and universality of use.

Keywords: monitoring, ocestration, containerization, Grafana, Loki, Kubernetes, Alloy

The article considers the issue of forming a system of public spaces on university campuses as a key factor in educational, social and innovative activities. The functions, typology and principles of organizing campus public spaces are analyzed in the context of modern educational paradigms and urban trends. The scientific novelty lies in the systematization of the principles of organizing public spaces of various types as a single system that responds to the challenges of digitalization and the actualization of social interaction. A conclusion is made about the need to move from designing individual spaces to creating a holistic, flexible and multifunctional system that serves as the framework for university life.

Keywords: university campus, public space, educational environment, social interaction, innovation ecosystem, campus urbanism

Changes in external conditions, parameters of object functioning, relationships between system elements and system connections with the supersystem lead to a decrease in the accuracy of the artificial intelligence models results, which is called model degradation. Reducing the risk of model degradation is relevant for electric power engineering tasks, the peculiarity of which is multifactor dependencies in complex technical systems and the influence of meteorological parameters. Therefore, automatic updating of models over time is a necessary condition for building user confidence in forecasting systems in  power engineering tasks and industry implementations of such systems. There are various methods used to prevent degradation, including an algorithm for detecting data drift, an algorithm for updating models, their retraining, additional training, and fine-tuning. This article presents the results of a study of drift types, their systematization and classification by various features. The solution options that developers need to make when creating intelligent forecasting systems to determine a strategy for updating forecast models are formalized, including update trigger criteria, model selection, hyperparameter optimization, and the choice of an update method and data set formation. An algorithm for forming a strategy for automatic updating of artificial intelligence models is proposed and practical recommendations are given for developers of models in problems of forecasting time series in the  power industry, such as forecasting electricity consumption, forecasting the output of solar, wind and hydroelectric power plants.

Keywords: time series forecasting, artificial intelligence, machine learning, trusted AI system, model degradation, data drift, concept drift