A mathematical model has been constructed, an algorithm has been developed, and a program has been written in the Python programming language for calculating the numerical values of the optimal filtering operator with a forecast for an L-Markov process with a quasi-rational spectrum. The probabilistic model of the filtering operator formula has been obtained based on the spectral analysis of L-Markov processes using methods for calculating stochastic integrals, the theory of analytical functions of a complex variable, and methods for correlation and regression analysis. Considered an example of L-Markov process, the values of the optimal filtering operator with a forecast for which it was possible to express in the form of a linear combination of the values of the process at some moments of time and the sum of numerical values of cosines and sines at the same moments. The basis for obtaining the numerical values of the filtering operator was the mathematical model of trigonometric regression with 16 harmonics, which best approximates the process under study and has a minimum

Keywords: random process, L-Markov process, prediction filtering, spectral characteristics, filtering operator

The article describes the process of developing a volumetric display for information and communication interaction in the Arctic, where traditional means of visualization and communication face the challenges of extreme climate, isolation and limited infrastructure. An analysis of the main areas of using volumetric in the Arctic zone is carried out. The main disadvantages of methods for creating a volumetric image in existing 3D displays are considered. Taking into account the main tasks to be solved - creating the illusion of a three-dimensional object for a group of people (more than 2 people) at a wide viewing angle - a description and analysis of two main developed configurations of the optical system is given, the latter of which meets the requirements, ensuring stable operation in Arctic conditions and opening up prospects for implementation in remote and hard-to-reach regions of the Far North.

Keywords: volume display, arctic zone, 3D image, system analysis, lens, optical system, computer modeling

The paper considers the synthesis of a non-stationary automatic control system for braking the wheels of a heavy vehicle using the generalized Galerkin method. The research method under consideration is used to solve the problem of synthesizing a non-stationary system whose desired program motion is specified at the output of a nonlinear element. The paper presents the results of studying the impact of non-stationarity on the parameters of the fixed part of the system (object) on the deterioration of the quality of the transient process. For critical operating conditions, the parameters of the controller were recalculated, and the results of accounting for non-stationarity and re-synthesis were evaluated.

Keywords: automatic control system, regulator, braking system, unsteadiness of parameters, generalized Galerkin method

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

The article examines the features of adaptive design in construction as a fundamental component for ensuring life safety in the zone of a special military operation. The modern world is changing at an incredible pace: climate anomalies are becoming more frequent, technological paradigms are being replaced within years, and social and economic conditions are undergoing constant transformations. Nowhere are these challenges manifested as acutely and concentratedly as in the zone of a special military operation (SMO). It is precisely here that the traditional approach to construction, focused on creating static, "frozen" objects, proves not only ineffective but also dangerous. It is being replaced by adaptive design – a philosophy and methodology that views a building or infrastructure object not as a final product, but as a living, evolving organism capable of evolving in response to direct threats and changing operational conditions. Adaptive design is a strategy for creating architectural objects and urban planning systems that can be easily modified, transformed, or repurposed in response to changes in external or internal conditions. In peacetime, this is a response to changing markets and technologies. In the zone of a special military operation, it is a matter of ensuring life safety. This is not simply post-factum repair or reconstruction, but the inherent ability of an object to instantly change its function and protective properties without radical rebuilding. The experience of the special military operation zone has openly proven that adaptive design is not an abstract idea from construction textbooks, but a critically important discipline upon which people's lives and the success of the assigned task depend. The principles of flexibility, modularity, and multifunctionality that are being tested today in extreme conditions will tomorrow become the new standard for the entire construction complex of the Russian Federation. They will form the basis for the restoration of cities, the creation of sustainable civil infrastructure, and the formation of new, anti-crisis architecture capable of withstanding the challenges of both wartime and peacetime. In the zone of a special military operation, architectural heritage is being tested and created, which will remain functional, in demand, and sustainable tomorrow. The future of construction belongs to those who design not for years, but for possibilities.

Keywords: adaptive construction, modern trends, modern design technologies, construction industry, construction processes, special military operation

The article considers the parameter identification issues of linear non-stationary dynamic systems adaptive models using the example of a linearized adjustable model of a DC motor with independent excitation. A new method for estimating the parameters of adjustable models from a small number of observations is developed based on projection identification and the apparatus of linear algebra and analytical geometry. To evaluate the developed identification method, a comparison of the transient processes of the adaptive model of a DC motor with independent excitation with the obtained parameter estimates with reference characteristics was carried out. The efficiency of the proposed identification method in problems of DC electric drive control is shown.

Keywords: DC motor, projection identification, dynamic system parameter estimation, adaptive model of non-stationary dynamic system

Analysis of a digital data transmission system through a noisy communication channel based on the Huffman compression method and encoding using cyclic Bose-Chowdhury-Hockingham codes This article examines the effectiveness of a digital data transmission system through a noisy communication channel using the Huffman compression method and cyclic BCH encoding (Bose-Chowdhury-Hockingham). Huffman compression reduces data redundancy, which increases the effective transmission rate, while BCH codes detect and correct errors caused by channel noise. The analysis likely includes evaluating parameters such as compression ratio, data transmission rate, error probability after decoding, and computational complexity of the algorithms. The results demonstrate the effectiveness of this combination of techniques in improving data transmission reliability in noisy environments.

Keywords: digital transmission system, cyclic coding, compression ratio, decoding, encoding

The article examines the aspects of using bionics as a basis for adaptive architecture and construction in the conditions of the North Caucasus. Modern architecture is undergoing a shift from static and resource-intensive models to dynamic, intelligent and environmentally oriented systems. This approach is particularly relevant for regions with difficult climatic and landscape conditions, such as the North Caucasus, where traditional construction is often unable to effectively withstand the challenges of sudden temperature fluctuations, seismic activity, strong winds and high insolation. This article substantiates the thesis that the integration of bionics principles into adaptive construction offers not just innovative solutions, but a holistic design philosophy based on centuries of experience in the evolution of natural systems. It is proved that bionics is not an alien concept for the region, but, on the contrary, finds deep parallels in traditional mountain architecture, such as in tower complexes demonstrating organic integration into the landscape and effective thermoregulation, similar to natural prototypes. The paper discusses specific areas of application of bionic principles, including the development of adaptive facades inspired by plant and animal thermoregulation systems, as well as the creation of earthquake-resistant structures similar to the flexible structures of bamboo stems or trees. Special attention is paid to the design methodology that combines the analysis of local conditions, biomimicry methods and the integration of modern digital technologies such as computer modeling and 3D printing to create unique, energy-efficient facilities. The need for synergy between traditional architectural knowledge and innovative technologies is emphasized, which makes it possible to create buildings that not only adapt to the environment, but also reflect the unique cultural identity of the North Caucasus. In conclusion, it is argued that bionics is a logical and promising direction for the architectural development of the region, ensuring the creation of a sustainable, safe and comfortable living environment through harmonization with the natural context.

Keywords: construction, bionics, modern trends, modern design technologies, construction industry, biomimicry, adaptive architecture, North Caucasus

This article examines the growing threat of web scraping (parsing) as a form of automated cyberattack, particularly aimed. Although scraping publicly available data is often legal, its misuse can lead to serious consequences, including server overload, data breaches and intellectual property infringement. Recent court cases against OpenAI and ChatGPT highlight the legal uncertainty associated with unauthorized data collection.
The study presents a dual approach to combat malicious scraping. Traffic Classification Model - a machine learning based solution using Random Forest algorithms results in performance that achieves 89% accuracy in distinguishing between legitimate and malicious bot traffic, enabling early detection of scraping attempts. Data Deception Technique - the countermeasure dynamically modifies HTML content to convey false information to scrapers while maintaining the original look of the page. This technique prevents data collection without affecting the user experience.
Performance results include real-time traffic monitoring, dynamic page obfuscation, and automatic response systems.
The proposed system demonstrates effectiveness in mitigating the risks associated with scraping and emphasizes the need for adaptive cybersecurity measures in evolving digital technologies.

 

Keywords: parsing, automated attacks, data protection, bot detection, traffic classification, machine learning, attack analysis, data spoofing, web security

The article explores the experience of adaptive reuse and the redevelopment of the former Vena Plant, located within the “Gray Belt” of St. Petersburg. Using this case study, it analyzes the fundamental principles of industrial site refunctionalization, as well as the strategies employed to preserve architectural heritage while integrating it into a contemporary urban context.

Keywords: adaptive reuse, urban greening, high-quality residential environment, Gray Belt, spirit of place (genius loci), industrial facilities, Vena Plant, residential complex, cultural heritage

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