The paper considers the effect of particle size on the dynamics of suspended sediments in a riverbed. The EcoGIS-Simulation computing complex is used to simulate the joint dynamics of surface waters and sediments in the Volga River model below the Volga hydroelectric dam. The most important factor in the variability of the riverbed is the spring releases of water from the Volgograd reservoir, when water consumption increases fivefold. Some integral and local characteristics of the riverbed are calculated depending on the particle size coefficient.

Keywords: suspended sediment, soil particle size, sediment dynamics, diffusion, bottom sediments, channel morphology, relief, particle gravitational settling velocity, EcoGIS-Simulation software and hardware complex, Wexler formula, water flow

The article examines the influence of the data processing direction on the results of the discrete cosine transform (DCT). Based on the theory of groups, the symmetries of the basic functions of the DCT are considered, and the changes that occur when the direction of signal processing is changed are analyzed. It is shown that the antisymmetric components of the basis change sign in the reverse order of counts, while the symmetric ones remain unchanged. Modified expressions for block PREP are proposed, taking into account the change in the processing direction. The invariance of the frequency composition of the transform to the data processing direction has been experimentally confirmed. The results demonstrate the possibility of applying the proposed approach to the analysis of arbitrary signals, including image processing and data compression.

Keywords: discrete transforms, basic functions, invariance, symmetry, processing direction, matrix representation, correlation

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 application, multidimensional elliptical paraboloid

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 invention related to the field of construction is proposed, which can be used for trenchless linear laying of oil, gas and other pipelines under natural and artificial obstacles, linear and extended structures (highways, railroads, etc.) located, including in monolithic rocky soils with simultaneous formation of a case, development and arrangement of a pre-drilled well.

Keywords: pilot well, diamond wire rope, foundation pit, encasement, working body, circular sector

The relevance of this study is determined by the widespread use of digitalization in many economic sectors and the significant lag in the cement industry in this area. This paper provides an overview of modern approaches to studying digital twins and assesses the status of their implementation in cement production. The purpose of this study is to identify the specific features of digitalization processes, as well as barriers and prospects for the development of digital twins in the cement industry. It is demonstrated that the implementation of digital technologies can become an effective tool for transforming the cement industry, provided that digital twins are implemented within the product value chain. Authors indicate the need for a new model for the long-term sustainable development of the cement industry based on modern digital technologies within the structure of the industry balance of building materials. management. The authors conducted a study of activities that had a negative impact on the environment and local population during project implementation. These activities were examined across the three main phases of project implementation: construction, operation, and liquidation. The results were used to determine factors and categories of impact on the economy and employment, the safety and well-being of the local population, social tensions, land ownership and land use.

Keywords: enterprise digitalization, digital modeling, digital twin, digital technologies, optimization of production processes, typology of digital twins, cement industry, value chains, sustainable development model, management efficiency

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 discusses the surface-active properties of casein and its potential for use as a bioorganic additive in repair and restoration compounds (RRC). An analysis of literary sources confirming the amphiphilic nature of casein, its ability to stabilize interfacial systems and form stable micelles is carried out. The results of an experimental study of the dependence of the surface tension of aqueous solutions of casein on its concentration, carried out by the hanging drop method on a DSA-100 tensiometer, are presented. It is shown that casein effectively reduces the surface tension of an aqueous solution, especially at concentrations of up to 4–5%, which confirms its active adsorption at the phase boundary. Based on the obtained surface tension isotherm, the predicted wettability is considered based on the Young equation. The data obtained emphasize the prospects of using casein as a natural surfactant for creating environmentally friendly and authentic restoration materials that meet the requirements of construction and restoration.

Keywords: casein, surfactants, repair and restoration compounds, surface tension, wettability.

The problem of ensuring the reliability and durability of the restored pipelines is an urgent task, especially in connection with the use of new materials in repair practice. In recent years, polymer materials have been widely used in pipeline repair and restoration work. Research in this area is mainly focused on technological processes, the development of equipment and structural elements made of composite materials. In our study, we set ourselves the task of using mathematical modeling to evaluate the operation of the steel+polymer shell structure after repair work on the gas pipeline, namely, the dynamics of changes in reactive pressure and maximum stresses in pitting corrosion zones depending on ground conditions. The results were obtained that allow us to predict the service life of this structure in soils with different corrosion activity. A significant increase in the bearing capacity of a worn pipeline repaired with polymer inserts in soils with high activity of corrosion processes has been proven.

Keywords: gas pipeline, metal corrosion, repair and restoration work, polymer materials, corrosive soil, durability, forecasting the service life

The relevance of the research is driven by the critical state of a significant portion of the historical building stock in Russia, where interfloor slabs are the most vulnerable elements. The problem lies in the need to replace them with structures that meet modern standards for load-bearing capacity and fire safety, without increasing the load on the weakened foundations and walls.

Keywords: reconstruction, cultural heritage site, monolithic floor slab, void former, lightweight structure, load-bearing capacity, work procedure statement

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 experience of a pilot project on the integration of calendar-network planning, BIM-modeling and virtual reality technology for the management of a construction organization. For this purpose, a sequence of steps for integrating technologies is presented and a combination of technologies is performed on the basis of a single digital platform; fragments of the developed calendar-network schedule and BIM model and the results of their combined display in VR glasses are presented.

Keywords: calendar-network planning, calendar-network schedule, BIM-modeling, virtual reality technology, VR-glasses, unified digital platform, TrinusVR