With the development of low-orbit satellite Internet systems (NSIS), issues of ensuring effective operation in conditions of intentional interference come to the fore. One of the solutions is related to the use of systems using both OFDM methods and generators implementing frequency hopping (HF). Obviously, the more complex the algorithm for selecting operating frequencies, the more efficient the operation of the microwave. In the article, it is proposed to use the SPN cipher "Grasshopper" as a generator for selecting operating frequencies. As a result, the CCF system will have a high resistance to calculating operating frequency numbers by electronic warfare systems. However, failures and failures may occur during the operation of the SSC. To prevent their consequences, it is proposed to implement an SPN cipher using polynomial modular codes of residue classes (PMCC). One of the transformations in the "Grasshopper" is a nonlinear transformation that performs the substitution operation. It is obvious that the creation of a new mathematical model for performing a nonlinear transformation using MCCS will ensure the operation of the SPN-cipher-based RF generator in conditions of failures and failures.

Keywords: low-orbit satellite Internet systems, the Grasshopper SPN cipher, nonlinear transformations, modular codes of residue classes, mathematical model, fault tolerance, frequency hopping, polynomial modular code of residue classes

Optimization of the composition of heavy cement concretes modified with a complex additive based on industrial waste (alumina-containing component - aluminum slag (ASH), spent molding mixture (OFS) using the PlanExp B-D13 software package is a three-factor planned experiment, according to the criteria: compressive strength on the 2nd and 28th days of hardening.

Keywords: heavy cement concretes, fast-hardening concretes, optimization, experiment planning, strength indicators, industrial waste, spent molding mixture, aluminum slag

When evaluating student work, the analysis of written assignments, particularly the analysis of source code, becomes particularly relevant. This article discusses an approach for evaluating the dynamics of feature changes in students' source code. Various metrics of source code are analyzed and key metrics are identified, including quantitative metrics, program control flow complexity metrics, and the TIOBE quality indicator. A set of text data containing program source codes from a website dedicated to practical programming, was used to determine threshold values for each metric and categorize them. The obtained results were used to conduct an analysis of students' source code using a developed service that allows for the evaluation of work based on key features, the observation of dynamics in code indicators, and the understanding of a student's position within the group based on the obtained values.

Keywords: machine learning, text data analysis, program code analysis, digital footprint, data visualization

In the article, based on the estimate of the Euclidean norm of the deviation of the coordinates of the transition and stationary states of the dynamic system, the compression condition of the generalized projection operator of the dynamic system with restrictions is derived. From the principle of contracting mappings, taking into account the derived compression condition of the projection operator, estimates are obtained for the sufficient condition for the stability of the dynamic system of stabilization of the equilibrium position and program motions. The obtained estimates generalize the previously obtained results. Ensuring the stability of the operator of a limited dynamic system is demonstrated experimentally.

Keywords: sufficient condition for stability, projection operator, stabilization of equilibrium position. stabilization of program motions, SimInTech

This article discusses two of the most popular algorithms for constructing dominator trees in the context of static code analysis in the Solidity programming language. Both algorithms, the Cooper, Harvey, Kennedy iterative algorithm and the Lengauer-Tarjan algorithm, are considered effective and widely used in practice. The article compares these algorithms, evaluates their complexity, and selects the most preferable option in the context of Solidity. Criteria such as execution time and memory usage were used for comparison. The Cooper, Harvey, Kennedy iterative algorithm showed higher performance when working with small projects, while the Lengauer-Tarjan algorithm performed better when analyzing larger projects. However, overall, the Cooper, Harvey, Kennedy iterative algorithm was found to be more preferable in the context of Solidity as it showed higher efficiency and accuracy when analyzing smart contracts in this programming language. In conclusion, this article may be useful for developers and researchers who are involved in static code analysis in the Solidity language, and who can use the results and conclusions of this study in their work.

Keywords: dominator tree, Solidity, algorithm comparison

A characteristic feature of urban construction is an increase in the density of buildings and, accordingly, the tightness of working conditions. The need to ensure the safety of existing buildings and reduce negative impacts on the urban environment requires the development of rational solutions at the stage of organizational and technological design during construction in conditions of dense development. The factors of constraint affect already at the stage of preparation of the construction site. The purpose of the study is to select and justify the methods of work during the removal of engineering networks from the construction site. The existing methods of network re-routing and technology comparison are considered. An example of a construction object shows a variant of an organizational and technological solution for the removal of networks using trenchless technologies.

Keywords: engineering training, construction site, dense buildings, cramped conditions, trenchless laying of networks

The purpose of the article is a software implementation of a module for analyzing the activity of site users based on a heat map of clicks, compatible with domestic web services, for example, combining the functionality of correlation and regression analysis and visualization in the form of dashboards before and after making changes to site elements. All functionality is carried out directly in the web analytics service. Based on the data obtained on the analyzed site element, a decision is made to adjust the design and/or content to increase the click rate. Thus, the proposed solution allows us to expand the functionality of the web analytics service and reduce labor costs. The software module has been successfully tested. As a result of the analysis and making the necessary adjustments to the site, the click rate increased

Keywords: user activity, correlation and regression analysis, dashboard, program module, trend line, coefficient of determination

The article considers the possibility of modeling the random forest machine learning algorithm using the mathematical apparatus of Petri net theory. The proposed approach is based on the use of three types of Petri net extensions: classical, colored nets, and nested nets. For this purpose, the paper considers the general structure of decision trees and the rules for constructing models based on a bipartite directed graph with a subsequent transition to the random forest machine learning algorithm. The article provides examples of modeling this algorithm using Petri nets with the formation of a tree of reachable markings, which corresponds to the operation of both decision trees and a random forest.

Keywords: Petri net, decision tree, random forest, machine learning, Petri net theory, bipartite directed graph, intelligent systems, evolutionary algorithms, decision support systems, mathematical modeling, graph theory, simulation modeling

The article presents a system research of the factors of formation of architectural and typological models of a medium-rise dwelling. The research was conducted in two stages. At the first stage, the main internal and external factors of building architectural and typological models based on the study and processing of literary sources, analysis of modern domestic and foreign experience in designing medium-rise housing are collected and systematized. The structural elements of the factors are systematized according to well-established architectural concepts. At the second stage of the study, a matrix of dependencies between external and internal factors was formed, and the number of dependencies between internal and external factors was calculated. Based on the data obtained, the internal factors were grouped by the number of links with external factors. The obtained results of the system research provide the basis for further construction of a limited number of the most versatile and flexible architectural and typological models that take into account the greatest number of environmental conditions.

Keywords: architectural and typological models, urban planning conditions, cultural conditions, national and ethnographic conditions, natural and climatic conditions, socio-demographic conditions, medium-rise housing

This article analyzes the main causes of fatal injuries in the construction industry of the Russian Federation and a number of other foreign countries, including falls from heights, electric shock, injuries associated with the use of construction machinery and mechanisms, as well as exposure to harmful substances. In conclusion, the article highlights the importance of joint efforts by employers, employees and regulators to create a safer and healthier work environment in the construction industry. The implementation of the preventive measures described in the article can significantly reduce the risk of accidents and improve the well-being of employees.

Keywords: construction industry, industrial injuries, accidents, causes of injuries, working conditions, occupational risks, working at height, occupational safety, environmental factors, workplace organization, training

The work presents the review of modern log trucks under the recent sanctions imposed. The author states that the problem of renewing the existing log trucks becomes urgent for forest transporting and logging companies nowadays. There is a wide range of new basic chassis and trucks at the market to build log trucks with a wheel formula 6x4 and 6x6 produced by Russian, Belorussian and Chinese factories. A great number of trailer links is produced to build log trucks. There is an opportunity to buy used trucks of other companies. For the first stage of the technical and economic analysis and preliminary selection of the optimal type and composition of a logging truck, a comparative assessment of the effectiveness of logging trucks was carried out. The analysis shows that Russian log trucks with engine power more than 400 HP (horsepower) can compete with the best foreign models. Nevertheless, the problem of reliability of Russian, Belorussian and Chinese log trucks needs further research.

Keywords: log trucks, trailer links, productivity, effectiveness

 the modification of a thermally cured epoxy binder is considered due to the introduction of a plasticizer and a latent component digital and statistical methods of experimental research are used digital models linking the basic properties with changes in variable factors are obtained and an analytical technique for predicting the properties of products as well as the selection of their composition is developed a composite epoxy binder is obtained and studied.

Keywords: digital model, synthetic binder, latent component, regression equation, analytical optimization

The article presents the calculation of reinforced concrete column reinforcement using a metal cage made of angles, taking into account the physical nonlinearity of materials within the framework of the Lira CAD software package. The use of a nonlinear approach is due to the inability of linear methods to adequately reflect the real behavior of concrete and steel under load, in particular, their destruction and gradual loss of rigidity. This paper presents a model that takes into account the nonlinear stiffness characteristics of concrete and steel in accordance with regulatory documents. Taking into account the physical nonlinearity of materials when calculating column reinforcement is critically important for reliable modeling of the structure's behavior and preventing underestimation of the risks of destruction. It is necessary to check the structure for local destruction at each stage of loading to ensure the reliability of calculations and the safety of the structure. The use of specialized software with the ability to stage-by-stage loading and checking for local destruction allows you to obtain accurate results and justify optimal design solutions.

Keywords: columns, reinforced concrete, steel, strengthening, jacket, calculation, physical nonlinearity, software package, stresses, strains

In operational diagnostics and recognition of states of complex technical systems, an important task is to identify small time-determined changes in complex measured diagnostic signals of the controlled object. For these purposes, the signal is transformed into a small-sized image in the diagnostic feature space, moving along trajectories of different shapes, depending on the nature and magnitude of the changes. It is important to identify stable and deterministic patterns of changes in these complex-shaped diagnostic signals. Identification of such patterns largely depends on the principles of constructing a small-sized feature space. In the article, the space of decomposition coefficients of the measured signal in the adaptive orthonormal basis of canonical transformations is considered as such a space. In this case, the basis is constructed based on a representative sample of realizations of the controlled signal for various states of the system using the proposed algorithm. The identified shapes of the trajectories of the images correspond to specific types of deterministic changes in the signal. Analytical functional dependencies were discovered linking a specific type of signal change with the shape of the trajectory of the image in the feature space. The proposed approach, when used, simplifies modeling, operational diagnostics and condition monitoring during the implementation of, for example, low-frequency diagnostics and defectoscopy of structures, vibration diagnostics, monitoring of the stress state of an object by analyzing the time characteristics of response functions to impact.

Keywords: modeling, functional dependencies, state recognition, diagnostic image, image movement trajectories, small changes in diagnostic signals, canonical decomposition basis, analytical description of image trajectory

The research aimed to investigate the properties of glass-basalt composite tubes, specifically examining the relationship between structural fractal dimensions, composition, and mechanical properties. Physical experiments were carried out to assess the properties of glass and glass-basalt composite tubes. These tests included measurements of tensile strength, modulus of elasticity, fracture resistance, flexural strength, and additional mechanical characteristics. Fractal analysis of rovings and epoxy binder was performed at the microstructural level to evaluate the impact of structure on mechanical performance. Through predictive modeling of the physical and mechanical properties of glass-basalt composite tubes, an optimal range of properties was identified. This range is defined by specific technological parameters: rovings content of 68–74%, basalt fiber diameter of 7–12 μm, and epoxy binder content of 21–27%. Within this framework, the production of tubes with the following target properties was predicted: tensile strength, compressive strength , and modulus of elasticity.

Keywords: fractal modeling, microstructure, matrix fibers, glass-basalt plastic, composite material, forecasting, strength, fractal dimension, heterogeneity, mechanical properties, composite pipe, glass fiber, basalt, correlation analysis