This article examines transportation network modeling using the Ford–Fulkerson algorithm. It describes the process of finding a minimum cut using a graphical editor and library developed in the C# programming language. Key concepts of graph and network theory are presented to clarify the problem statement. An example of solving a transportation problem using the developed software is shown, and the program's results are compared with a control example.

Keywords: transportation network, maximum flow problem, Ford–Fulkerson algorithm, minimum cut in the network, software library, graphical editor, C# programming language

The article is devoted to the development of an innovative neural network decision support system for firefighting in conditions of limited visibility. A comprehensive approach based on the integration of data from multispectral sensors (lidar, ultrasonic phased array, temperature and hygrometric sensors) is presented. The architecture includes a hybrid network that combines three-dimensional convolutional and bidirectional LSTM neurons. To improve the quality of processing, a cross-modal attention mechanism is used to evaluate the physical nature and reliability of incoming signals. A Bayesian approach is used to account for the uncertainty of forecasts using the Monte Carlo dropout method. Adaptive routing algorithms allow for quick response to changing situations. This solution significantly improves the efficiency of firefighting operations and reduces the risk to personnel.

Keywords: mathematical model, intelligence, organizational model, gas and smoke protection service, neural networks, limited visibility, fire department, management, intelligent systems, decision support

The article discusses the differences and uniformity of architectural structures from different times and nations, the shapes of houses and roofs, and the structural design of buildings. The article provides a clear understanding of the shapes of the circle, its semantics, and significance. Using examples from contemporary architects, the article explores the concepts of creating ideological projects and the complexities involved in their implementation. The ideological solutions for the shape of the circle in modern buildings are slightly modified through the creative designs of the architects.
Architectural forms are based on basic geometric shapes such as circles, squares, and triangles. Without knowing the beginning of the stories of the creation of houses and settlements, we do not come to a solution of a new, completely unaccepted for us one century ago, building and houses. The main research material affects the round forms of not only houses (mansion, estate, manor) and buildings, but also settlements, estates of different peoples. If earlier built houses of the same type, now, thanks to high technologies and productions.

Keywords: circle, architecture, building, texture, shape, material, construction, project, structures, house

Methods of increasing the efficiency of data analysis based on topology and analytical geometry are becoming increasingly popular in modern information systems. However, due to the high degree of complexity of topological structures, the solution of the main tasks of processing and storing information is provided by spatial geometry in combination with modular arithmetic and analytical assignment of geometric structures, the description of which is involved in the development of new methods for solving optimization problems. The practical application of elliptic cryptography, including in network protocols, is based on the use of interpolation methods for approximating graphs of functions, since a loss of accuracy may occur when performing many sequential mathematical operations. This problem is related to the features of the computing architecture of modern devices. It is known that an error can have a cumulative effect, so data approximation methods must be used sequentially as calculations are performed.

Keywords: elliptic curve, information system, data analysis, discrete logarithm, point order, scalar, subexponential algorithm

The article discusses the conceptual foundations of the transformation of the fire extinguishing management system based on the theory of complex organizational systems. The author substantiates the need to move from linear-hierarchical models to adaptive and networked structures capable of providing high stability and efficiency of response in conditions of uncertainty and dynamics of emergency situations. The analysis of the compliance of the fire extinguishing system with the characteristics of a complex organizational system has been carried out, contradictions between its complex nature and primitive control mechanisms have been identified, the causes and consequences of this paradox have been identified. Multi-agent digital platforms, the use of digital twins, situation centers, as well as the use of game theory methods to optimize resource allocation and decision support are proposed as ways to solve the identified problems.

Keywords: system approach, organizational system, firefighting, network structures, management, digitalization, transformation, game theory, optimization, criteria

The paper provides a comparative analysis of the accuracy of determining the coordinates of an aircraft using the classical correlation extreme algorithm (CEA) and the machine irradiation method based on a fully convolutional neural network (FCN) based on terrain maps. Two-dimensional correlated random functions are used as relief models.  It has been shown that CEA is effective with small amounts of data, whereas FCN demonstrates high noise immunity after training on representative samples. Both methods showed the dependence of the accuracy of determining the coordinates of the aircraft on the size of the reference area, the number of standards, entropy, and the correlation coefficient of the random relief.

Keywords: correlation-extreme algorithm, deep learning, convolutional neural network, aircraft guidance, digital terrain model, Fourier filtering, spatial correlation, noise immunity, algorithm comparison, autonomous navigation, hybrid systems, terrain entropy

The article forms the task of hierarchical classification of texts, describes approaches to hierarchical classification and metrics for evaluating their work, examines in detail the local approach to hierarchical classification, describes different approaches to local hierarchical classification, conducts a series of experiments on training local hierarchical classifiers with various vectorization methods, compares the results of evaluating the work of trained classifiers.

Keywords: classification, hierarchical classification, local classification, hierarchical presicion, hierarchical recall, hierarchical F-measure, natural language processing, vectorization

The work is devoted to the application of a linear Kalman filter (KF) for estimating the roll angle of a quadcopter with structural asymmetry, under which the control input contains a nonzero constant component. This violates the standard assumption of zero mathematical expectation and reduces the efficiency of traditional KF implementations. A filter synthesis method is proposed based on the optimization of the covariance matrices ratio using a criterion that accounts for both the mean square error and the transient response time. The effectiveness of the approach is confirmed by simulation and experimental studies conducted on a setup with an IMU-6050 and an Arduino Nano. The obtained results demonstrated that the proposed Kalman filter provides improved accuracy in estimating the angle and angular velocity, thereby simplifying its tuning for asymmetric dynamic systems.

Keywords: Kalman filter, quadcopter with asymmetry, optimization of covariance matrices, functional with mean square error and process time, complementary filter, roll and pitch control

The article is devoted to the analysis of the typological features of Orthodox churches. This topic is related to the spread of Orthodoxy throughout the world, which prompted the authors to analyze and systematize some of the features of decorative and artistic techniques of temple construction, as well as the canons of Orthodoxy in time, originating from Byzantine architecture.

Keywords: orthodox architecture, temple architecture, typological analysis, semantics of temples, Byzantine style, cross‑domed structure, tent temples, Russian patterned, Naryshkin style, architectural styles, sacred meaning, three-part division, domed completion

The article explores the application of the residue number system in text information processing. The residue number system, based on the principles of modular arithmetic, represents numbers as sets of residues relative to pairwise coprime moduli. This approach enables parallel computation, potential data compression, and increased noise immunity. The study addresses issues such as character encoding, parallel information processing, error detection and correction, computational advantages in implementing polynomial hash functions, as well as practical limitations of the residue number system.

Keywords: residue number system, modular arithmetic, text processing, parallel computing, data compression, noise immunity, Chinese remainder theorem, polynomial hashing, error correction, computational linguistics

This article examines the results of computer simulations of adhesive bond tear testing. Simulation models of adhesive bond tearing were constructed taking into account two stages of sample testing, the geometric structure, and the physical and mechanical properties of the materials and adhesive. The modeling took into account the statistical dispersion of parameters at the micro-level of the process. The article describes the algorithm for the sample testing process and evaluates its behavior depending on the values ​​and variations of the material parameters.

Keywords: Computer simulation, model, tear test, adhesive bond, material strength, simulation results, stress concentration

This article discusses numerical modeling of a plywood roof panel based on a finite element model. The modeling of the panel skins was performed taking into account the orthotropy of the plywood. When calculating the roof panel's deformability, it is necessary to account for the reduction in structural rigidity during operation by introducing a reduction factor. A computational study of the roof structure's deformability allowed us to establish a coefficient for the utilization of the roof panel's cross-section rigidity.

Keywords: plywood roofing board, glued laminated board element, modulus of elasticity, volumetric density, Poisson's ratio, design span, standard load, four-node finite element, section moment of inertia

The article focuses on the development of a web portal for monitoring and forecasting atmospheric air quality in the Khabarovsk Territory. The study analyzes existing solutions in the field of environmental monitoring, identifying their key shortcomings, such as the lack of real-time data, limited functionality, and outdated interfaces. The authors propose a modern solution based on the Python/Django and PostgreSQL technology stack, which enables the collection, processing, and visualization of air quality sensor data. Special attention is given to the implementation of harmful gas concentration forecasting using a recurrent neural network, as well as the creation of an intuitive user interface with an interactive map based on OpenStreetMap. The article provides a detailed description of the system architecture, including the backend, database, and frontend implementation, along with the methods used to ensure performance and security. The result of this work is a functional web portal that provides up-to-date information on atmospheric air conditions, forecast data, and user-friendly visualization tools. The developed solution demonstrates high efficiency and can be scaled for use in other regions.

Keywords: environmental monitoring, air quality, web portal, forecasting, Django, Python, PostgreSQL, neural networks, OpenStreetMap

A comprehensive approach is proposed for automated diagnostics and condition monitoring of steel hoisting wire ropes, implemented by integrating two independent methods—optical and magnetometric—into a single synchronized monitoring system. In the optical channel, two analysis mechanisms are implemented: defect classification based on evaluating characteristic patterns of changes in the cross-sectional dimensions, and classification using a convolutional neural network trained on annotated images of real damage. The magnetometric channel applies the magnetic flux leakage principle, detecting internal anomalies using a sensor array whose signals are converted into a numerical feature vector. Temporal and spatial synchronization of the data using correlation algorithms provides unified defect mapping and minimizes false alarms. Experimental validation was conducted on ropes with defects such as bending, kinking, and breakage, as well as on undamaged ropes, under conditions close to real operation. The results confirm high sensitivity, noise robustness, and the potential suitability of the proposed solution for continuous industrial monitoring.

Keywords: automation of monitoring, steel wire ropes, non-destructive testing, integrated monitoring, computer vision, defect classification, neural networks, gradient boosting, convolutional neural networks

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