The article proposes the development of a mathematical model that includes an integrated approach to modeling the interaction of surfaces, taking into account the geometric features of the groove. An important aspect of the novelty of the work is its validation based on experimental data. To describe the movement of the lubricant in the working gap, a model is used that describes the movement of a truly viscous lubricant, including the continuity equation. The calculations and experiments performed have confirmed the adequacy of the proposed model, which indicates the possibility of its practical application for engineering analysis and design. The results of this work made it possible to improve the understanding of the mechanism of movement of the lubricant in radial sliding bearings having a polymer coating with an axial groove on the shaft surface. Studies have also shown that the presence of a groove on the shaft surface affects the pressure distribution, which, in turn, affects the tribotechnical parameters of the bearing. The introduction of the groove helps to distribute the lubricant more efficiently over the working gap, increase the bearing capacity of the bearing, reduce the coefficient of friction and reduce wear on the contact surfaces.

Keywords: radial bearing, wear resistance assessment, antifriction polymer coating, groove, hydrodynamic mode, verification

This paper proposes a mathematical model of the laminar flow of a truly viscous lubricant in the clearance of a radial plain bearing with a nonstandard support profile. The influence of a fluoroplastic-containing polymer coating and a groove on the shaft surface is considered, taking into account nonlinear effects, which improves the accuracy of the description of hydrodynamic processes. Thin-film approximations and continuity equations are used to determine the hydrodynamic pressure, load capacity, and friction coefficient. A comparison with existing calculation models demonstrated improved performance prediction. The results demonstrate the feasibility of ensuring stable shaft floatation, confirming the applicability of the developed model for engineering calculations of bearings with a polymer coating and a groove.

Keywords: radial plain bearing, mathematical modeling, true viscous lubricant, polymer composite coating, hydrodynamic regime, tribotechnical characteristics

This article presents the development of a combined method for summarizing Russian-language texts, integrating extractive and abstractive approaches to overcome the limitations of existing methods. The proposed method is preceded by the following stages: text preprocessing, comprehensive linguistic analysis using RuBERT, and semantic similarity-based clustering. The method involves extractive summarization via the TextRank algorithm and abstractive refinement using the RuT5 neural network model. Experiments conducted on the Gazeta.Ru news corpus confirmed the method's superiority in terms of precision, recall, F-score, and ROUGE metrics. The results demonstrated the superiority of the combined approach over purely extractive methods (such as TF-IDF and statistical methods) and abstractive methods (such as RuT5 and mBART).

Keywords: combined method, summarization, Russian-language texts, TextRank, RuT5

The paper considers a stochastic model of the operation of an automatic information processing system, which is described by a system of differential equations of the Kolmogorov distribution of state probabilities, assuming that the flow of requests is Poisson, including the simplest one. A scheme for solving a system of differential equations of high dimensionality with slowly changing initial data is proposed, and the parameters of the presented model are compared with the parameters of the simulation model of the Apache HTTP Server. To compare the simulation and stochastic models, a test server was used to generate requests and simulate their processing using the Apache JMeter program, which was used to estimate the parameters of the incoming and processed request flows. The presented model does not contradict the simulation model and allows us to evaluate the system's states under different operating conditions and calculate the load on the web server when there is a large amount of data.

Keywords: stochastic modeling, simulation model, Kolmogorov equations, sweep method, queuing system, performance characteristics, test server, request flow, service channels, queue

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

The study addresses the problem of short-term forecasting of ice temperature in engineering systems with high sensitivity to thermal loads. A transformer-based architecture is proposed, enhanced with a physics-informed loss function derived from the heat balance equation. This approach accounts for the inertial properties of the system and aligns the predicted temperature dynamics with the supplied power and external conditions. The model is tested on data from an ice rink, sampled at one-minute intervals. A comparative analysis is conducted against baseline architectures including LSTM, GRU, and Transformer using MSE, MAE, and MAPE metrics. The results demonstrate a significant improvement in accuracy during transitional regimes, as well as robustness to sharp temperature fluctuations—particularly following ice resurfacing. The proposed method can be integrated into intelligent control loops for engineering systems, providing not only high predictive accuracy but also physical interpretability. The study confirms the effectiveness of incorporating physical knowledge into neural forecasting models.

Keywords: short-term forecasting, time series analysis, transformer architecture, machine learning, physics-informed modeling, predictive control

The article presents the results of an analysis of the stress-strain state and the failure mode of a frame joint connecting a monolithic reinforced concrete crossbar with a column in a frame structural system. The distinctive feature of the considered joint is that part or all of the tensioned (top) reinforcement of the crossbar, bending with a certain radius R, continues into the column.
The research was conducted through a computational experiment. The modeling was performed in the LIRA-SAPR software package. The issue of calculating the normal sections of the joint from the standpoint of SP 63.13330 (Russian Building Code) using the formulas for eccentric compression is considered. An analysis of the joint failure modes during a physical experiment is performed. The dependence of the radial pressure exerted by the curved reinforcement on the concrete on the stress in the reinforcement and its bend radius is determined. The bisectoral section of the joint, represented as a rectangular plate of unit thickness cut by two planes perpendicular to the mid-surface of the joint, was adopted as the calculation object. The calculations were performed using a nonlinear formulation. Recommendations are made for limiting stresses in the reinforcement when calculating the joint according to SP 63.13330. A model for calculating joint failure due to spalling of the side faces from the radial pressure of the curved bars is proposed.

Keywords: reinforced concrete frame joint; curved reinforcement; stress-strain state; joint failure; finite element analysis; LIRA-SAPR; concrete spalling; bisectoral section; normal section; bend radius

This paper is devoted to the theoretical analysis of the methods used in verifying the dynamics of a signature obtained from a graphic tablet. A classification of three fundamental approaches to solving this problem is carried out: matching with a standard; stochastic modeling and discriminative classification. Each approach in this paper is considered using a specific method as an example: dynamic transformation of the time scale; hidden Markov models; support vector machine. For each method, the theoretical foundations are disclosed, the mathematical apparatus is presented, the main advantages and disadvantages are identified. The results of the comparative analysis can be used as the necessary theoretical basis for developing modern signature dynamics verification systems.

Keywords: verification, biometric authentication, signature dynamics, graphic tablet, classification of methods, matching with a standard, stochastic modeling, discriminative classification, hidden Markov models, dynamic transformation of the time scale

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 is devoted to the study of the possibilities of automatic transcription and analysis of audio recordings of telephone conversations of sales department employees with clients. The relevance of the study is associated with the growth of the volume of voice data and the need for their rapid processing in organizations whose activities are closely related to the sale of their products or services to clients. Automatic processing of audio recordings will allow checking the quality of work of call center employees, identifying violations in the scripts of conversations with clients. The proposed software solution is based on the use of the Whisper model for speech recognition, the pyannote.audio library for speaker diarization, and the RapidFuzz library for organizing fuzzy search when analyzing strings. In the course of an experimental study conducted on the basis of the developed software solution, it was confirmed that the use of modern language models and algorithms allows achieving a high degree of automation of audio recordings processing and can be used as a preliminary control tool without the participation of a specialist. The results confirm the practical applicability of the approach used by the authors for solving quality control problems in sales departments or call centers.

Keywords: call center, audio file, speech recognition, transcription, speaker diarization, replica classification, audio recording processing, Whisper, pyannote.audio, RapidFuzz

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 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 article presents a novel approach for adaptive control of genetic algorithm parameters using reinforcement learning methods. The use of the Q-learning algorithm enables dynamic adjustment of mutation and crossover probabilities based on the current population state and the evolutionary process progress. Experimental results demonstrate that this method offers a more efficient solution for optimization problems compared to the classical genetic algorithm and previously developed approaches employing artificial neural networks. Tests conducted on the Rastrigin and Shaffer functions confirm the advantages of the new method in problems characterized by a large number of local extrema and high dimensionality. The article details the theoretical foundations, describes the implementation of the proposed hybrid model, and thoroughly analyzes experimental results. Conclusions highlight the method's adaptability, efficiency, and potential for application in complex optimization scenarios.

Keywords: genetic algorithm, reinforcement learning, adaptive control, Q-learning, global optimization, Rastrigin function, Shaffer function

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

Traditional marketing methods of promoting goods and services are aimed at a wide audience and do not take into account the individual characteristics of consumers, which can lead to a small percentage of positive responses and even to negative responses (loss of customers). Wide audience coverage leads to an increase in the cost of marketing interactions and does not guarantee the achievement of the goals of marketing campaigns. In such a situation, the task is to minimize excess costs through a more rational organization of marketing interactions aimed at obtaining maximum profit from each target client. To implement such a strategy, tools are needed that can identify customer segments, marketing interaction with which will lead to a positive response. One of the technologies for building such tools is uplift modeling, which is a section of machine learning and is considered a promising direction in data-driven marketing. In this article, based on the open data X5 RetailHero Uplift Modeling Dataset, provided by X5 Retail Group, a comparative analysis of the effectiveness of various uplift modeling approaches is conducted to identify the segment of customers who are most susceptible to target impact. Various uplift metrics and visual technologies are used to conduct the comparative analysis.

Keywords: effective marketing communications with customers, customer segmentation, machine learning methods, uplift modeling, uplift quality metrics

The article studies possibilities for analyzing geopolitical processes within the framework of situational analysis methodology using cognitive modeling. Situational analysis description is given, and scenario for developing events is presented where two stages are distinguished: a preparatory stage (a pre-scenario stage) which is essential for performing descriptive and explanatory functions of predictive research, and a scenario stage intended for substantive and formal research as well as for description of predicted processes, construction of system models and preparation of all significant information for scenario synthesis. Furthermore, a method for applying situational analysis is proposed to be used within the framework of the cognitive modeling toolkit of a “future scenario” option and its analysis with account of new “main” factors, relationships, feedbacks and dynamics of their alterations. When forming a scenario for a specific geopolitical situation within the framework of cognitive modeling, this method can be presented by causal (functional) and logical-semantic relation between the elements/agents of actions and counteractions. By interpreting the logical-semantic as structural, and the causal as dynamic, we obtain a structural-dynamic systemic description of geopolitical confrontation using the language of cognitive graphs, i.e. presenting a graphical expression of causal relationships between the concepts (factors) that characterize a particular geopolitical process. Thus, within the framework of a scenario stage the following procedures are conducted: analyzing the initial geopolitical situation, namely: determining key factors that build up the scheme of internal connections and external relationships, and their structuring; defining factors that make an impact; determining impact directions and force (positive and negative effect); choosing basic stereotypes or generalized models of interactions that correspond to the initial situation; constructing cognitive models of the current state of a situation; studying trends for the situation’s development and its dynamics analysis; transferring a scenario onto a practical basis. 

Keywords: geopolitical processes, situational analysis, cognitive modeling, and forecasting scenario

A study was conducted to examine the influence of anode material on heat dissipation efficiency in a plasma torch cooling system. Computer modeling was used to calculate thermal and hydrodynamic processes for anodes made of M1 copper, L63 brass, and BrO8Ts4 bronze. Copper achieved the highest heat dissipation efficiency due to its high thermal conductivity, as confirmed by a full-scale experiment. The results demonstrate that the choice of anode material is a key factor in improving the reliability and service life of a plasma torch.

Keywords: plasma torch, anode unit, copper, brass, bronze, heat sink, thermal conductivity, computer modeling, finite element method, cooling efficiency, thermal conditions

The article is devoted to the problem of verification of distributed algorithms using formal methods. The classical leader selection algorithm in ring topology, the ring algorithm, is chosen as the object of research. For its analysis, the specification language of the Temporal Logic of Actions (TLA+) is used. The paper presents a detailed formal model of the algorithm, describing its states and transitions, taking into account the features of distributed systems, such as the lack of shared memory. The key properties of correctness are formulated and proved: the uniqueness of the leader (the property of security), the finality of elections (the property of liveliness) and consent. The correctness of the specification was confirmed using the model model verifier of the language of temporal logic of actions, which exhaustively checked all achievable states for the model with three processes. The results demonstrate the effectiveness of the Time Logic Specification language (TLA+) for providing a high degree of confidence in the reliability of distributed systems.

Keywords: formal verification, distributed systems, ring algorithm, leader selection, specification language for temporal logic of actions, model verification, security properties, vivacity properties.formal verification, distributed systems, ring algorithm

This study presents a method for preprocessing data sequences aimed at identifying and grouping different data files for subsequent use in training neural networks. An algorithm for file comparison based on the relative deviation of feature values ​​is proposed, taking into account boundary cases (zero and near-zero values). The implementation includes parallel processing to improve performance and the generation of detailed reports. The method is tested on a dataset containing 10,000 files with parameters of a chemical process in a laboratory reactor. The results demonstrate the method's effectiveness in identifying stationary regions and generating balanced training sets.

Keywords: вata preprocessing, relative deviation, machine learning, parallel computing, file grouping, computational fluid dynamics, chemical reactor

A vectorial diffraction model is presented for the focusing of a Gaussian laser beam with a wavelength of 800 nm by a parabolic metallic mirror with a diameter of 15 mm and a focal length of 150 mm. The model is based on a rigorous calculation of the reflected electromagnetic field using s- and p-polarization basis functions, complex Fresnel coefficients, and the Kirchhoff–Rayleigh surface integral. The reflective coating is characterized by a complex refractive index n = 0.145 + 4.5i, corresponding to silver in the near-infrared spectral range. The incident beam has a waist radius of 3 mm at the mirror’s vertex plane. The field distribution in the focal plane is numerically computed on a 300×300 grid over a ±30 μm region. Focus quality is evaluated using three criteria: total intensity, radial intensity distribution, and the full width at half maximum (FWHM) of the focal spot. A focal spot with FWHM ≈ 8.56 μm is obtained, in close agreement with the theoretical diffraction-limited estimate. The results demonstrate that accounting for the vectorial nature of the field and the dissipative properties of the metal enables accurate prediction of polarization distortions and energy losses in practical mirror-based focusing systems.

Keywords: vectorial diffraction model, parabolic metallic mirror, Gaussian laser beam, Fresnel coefficients, complex refractive index

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

An integrated approach to the numerical study of forced oscillations of a vehicle moving over an uneven road surface is proposed. The method combines 3D parametric modeling in SolidWorks with spectral-correlation analysis in MATLAB/Simulink. A multibody CAD model of a vehicle with independent suspension for all wheels was developed, including the main frame, lever suspensions with nonlinear elastic-damping elements, wheels, and the powertrain. The road microprofile was formalized using a correlation function implemented as a random process in MATLAB and imported into SolidWorks as a spatial profile. Dynamic analysis was performed using the SolidWorks Motion module. The results show that the vehicle's suspension exhibits a filtering effect, attenuating high-frequency disturbances from the road and shifting the dominant frequency of the center of mass oscillations to a lower range (~0.4 Hz). The rapid decay of the autocorrelation function indicates effective damping. This approach allows for efficient virtual testing without costly physical experiments.

Keywords: vehicle dynamics, road microprofile, multibody modeling, SolidWorks Motion, MATLAB/Simulink, spectral analysis, autocorrelation function, suspension filtering effect, forced oscillations

The paper investigates the improvement of methods for computing the concentration of nanoparticles in transparent liquids under the action of laser radiation. The exact solution of the third boundary value problem for the Einstein–Fokker–Planck equation is analyzed, the direct use of which in the Maple computer algebra system leads to computational instabilities at large values of the transfer parameter. A solution to the problem of unstable numerical calculations at high values of dimensionless parameters, leading to significant distortions of the result, is presented. The key result is to expand the working range of the transfer parameter and ensure the correct asymptotic behavior of the solution. Numerical experiments have confirmed the effectiveness of the proposed approach, which makes it a valuable tool for modeling and optimizing the processes of laser separation of nanoparticles.

Keywords: nanosuspension, laser radiation, concentration of nanoparticles, continuity equation, third boundary value problem, computer calculations, Maple