This paper is devoted to the development of a unified alphabet of Ancient Turkic dialects for solving the problems of automated recognition of Orkhon–Yenisei runic inscriptions. The relevance of the study is determined by the fragmentation of existing rune classifications and the absence of a unified system for correlating symbols across different sources and regions, which complicates the formation of compatible datasets and reduces the efficiency of computer vision models.

The research is to create a unified alphabet that ensures correct image annotation and enables the training of multi alphabet neural network models for the recognition and comparative analysis of runic symbols.

The methodology is based on a comprehensive analysis of visual, phonetic, and historical-philological characteristics of runes from four sources: the Kül Tegin monument, the Irk Bitig manuscript, Orkhon inscriptions, and Yenisei inscriptions. During the study, structurally stable symbols, stylistic variations, and unique dialect markers were identified, on the basis of which a consolidated set of rune classes was formed.

The obtained results provide a foundation for the standardization of image annotation, improvement of recognition robustness, and further development of multi-alphabet computer vision systems in the study of Ancient Turkic writing.

This article is devoted to the analysis of current trends and practices of the application of artificial intelligence (AI) in agriculture based on peer-reviewed scientific sources of 2022–2026. The purpose of the work is a comprehensive study of the problems and key trends of the development of AI in the agricultural sector, as well as the systematization of quantitative data confirming the effectiveness of the implemented technologies. The article discusses the main areas of AI use: crop yield forecasting based on neural network algorithms (LSTM, CNN), plant health monitoring and precise resource application using computer vision (ResNet, YOLO), robotization of production processes, and the introduction of intelligent systems into the economy and management of the agro-industrial complex. Based on the analysis of empirical studies, the article systematizes performance indicators: the accuracy of plant disease diagnosis reaches 99.2%, the reduction of pesticide use is up to 90%, water resources are saved by up to 46%, and farm income increases by 15–20%. Special attention is paid to a comparative analysis of the barriers to the implementation of AI in different groups of countries. In developed countries, the main problems are technological fragmentation and a shortage of qualified personnel. In BRICS countries, there are infrastructure limitations and a gap between science and production. In developing countries, the key obstacles are the lack of basic infrastructure, the low solvency of small farms, and a lack of digital literacy. The final part identifies understudied aspects that require further research, such as socio-psychological barriers to technology adoption, the environmental impact of AI solutions, issues related to data sovereignty and monetization, economic efficiency for small-scale farmers, cybersecurity, and ethical dilemmas in breeding.

This article examines the pressing issue of personal data anonymization in credit and financial institutions (CFIs) in the context of tightening regulatory requirements, in particular, Roskomnadzor Order No. 140. It analyzes classic and modern anonymization methods (masking, pseudonymization, synthetic data generation, etc.) for their applicability in a banking environment where preserving data formats, referential integrity, and high performance are critical. A comparative assessment of three modern domestic solutions is provided: DataMask, Garda Data Masking, and N1 AI. Their systemic limitations are identified, including potential non-compliance with new regulations, insufficient flexibility for unique banking entities, and high cost of ownership. Based on this analysis, the strategic feasibility of developing a specialized internal anonymization tool is substantiated. This tool guarantees full regulatory compliance, maximum adaptability to the bank’s business processes, and long-term economic efficiency. A credit and financial institution is characterized by processing an extensive array of structured personal data (PD), which combines the features of general, other data, and information that constitutes bank secrecy. This information is typically stored in relational databases in a formalized format (separate fields for passport number, phone number, account number, etc.), which, on the one hand, simplifies their automated search, but on the other hand, requires strict protection measures, including secure anonymization for use in non-production environments. This determines the key requirements for the system under consideration: the need to accurately detect fields of various categories of financial and identifying information, and the use of masking algorithms that ensure irreversible conversion while preserving the structural integrity and data format for the correct operation of test systems.

The introduction of the digital ruble poses challenges for credit and financial institutions (CFIs) driven by the need to integrate external trust infrastructure into internal automated banking systems (ABS). The problem lies in the absence of standardized solutions regulating the secure interconnection of two heterogeneous security domains. The novelty of this work consists in the development of a holistic approach synthesizing technological protection measures and organizational procedures into a unified mechanism implemented on the CFI side. The objective of the article is to develop this mechanism, ensuring the minimization of risks of unauthorized access, information leakage, and disruption of business process continuity. The methodological framework is based on a systematic analysis of architectural solutions, a synthesis of threat modeling methods, and a risk-oriented approach. As a result, a two-circuit protection mechanism is substantiated, comprising a technological core (hardware cryptography, unidirectional gateway) and an organizational framework (zero-trust policy, in-line compliance). It has been proven that the proposed mechanism reduces the aggregate criticality of attack vectors at the integration stage by 35–40% according to the CVSS scale and forms the basis for a replicable standard solution.

The use of machine learning in solving direct forecasting problems is becoming an alternative to the use of comprehensive finite element modeling. However, the solutions of inverse problem by means of machine learning is conventionally not considered in the literature. Traditional approaches are based on iterative calculations that require multiple runs of models and do not work in real time, which limits the creation of digital doubles.

The objective of this study is to solve the inverse problem by developing and verifying a Gaussian regression (GPR) model for determining the strain rate sensitivity index of superplastic material from the results of bulge tests based on the results of finite element calculations. The results of finite element modeling of the superplastic forming process in the ANSYS CAE package were used as a data source. 120 finite element simulations were performed, 40 for each of the three pressure modes. Two GPR models have been developed. One is for defining K with the Matern kernel, the second is for m with the RBF kernel. It is shown that replacing the RBF kernel with the Matern kernel (ν = 2,5) reduces the median relative uncertainty of the forecast for parameter K from 50 to 16%. The following quality metrics were obtained on the test sample: R² = 0.91 for K and R² = 0.92 for m, the relative RMS error is 20% for K and 7% for m.

The developed model can be used for non-destructive quality control, integration into digital twins, and optimization of superplastic forming processes.

The article studies a discrete equation in natural numbers of the form x = count (d, x) + n, where n is a natural number; count(d, x) is the number of occurrences of the digit d ∈ {0, 1, …, 9} in the decimal notation of the number x. The objective of the work is to obtain a priori estimates of solutions to the equation and to analyze the dependence of the number of solutions on the parameters d and n. The main result of the study is the establishment of a two-sided a priori estimate for solutions to the equation: n ≤ x ≤ n + ⌊lgn⌋ + 2. It follows from this estimate that for fixed d and n, the number of natural solutions is limited; the equation is not solvable for all values of n. For digits d ∈ {9, 8, …, 2} and any natural n, it is proved that the number of solutions does not exceed 2. For d = 1 and any natural n, it is shown that the number of solutions does not exceed 3. For d = 0, it is constructively substantiated that with increasing n, the number of natural solutions, each of which can be represented in decimal notation using only four digits, can increase indefinitely. Theoretical and practical significance. The results are of a theoretical-mathematical nature and can be applied in the study of similar discrete equations in natural numbers; in the analysis of mathematical puzzle games described by similar equations; they also complement known results in the field of Diophantine equations.

This article analyzes intelligent energy consumption control systems as a tool for improving energy efficiency in the implementation of energy service projects. The aim of the study is to identify the role and capabilities of such systems and to substantiate the need for adapting existing solutions to create a unified digital management framework. The methodological basis of the research consists of the principles of system analysis, methods for classifying information systems, and analysis of the regulatory framework for energy service activities. The empirical base includes data from the State Report on the State of Energy Saving in the Russian Federation for 2023 and analytical reviews of the ASKUE market. The study reveals that none of the existing classes of systems individually possesses the full functionality necessary for end-to-end management of an energy service project. The share of intelligent metering devices in Russia reaches 72%. The results of energy service contracts implementation in 2023 are analyzed. The findings indicate that the key direction of development is the adaptation and integration of existing systems to form a unified digital management framework for energy service projects. The technological base for digitalization has already been formed, but existing solutions require adaptation for complex business tasks.

Digital transformation in all areas of life has accelerated significantly since COVID-19. Significant progress in the field of professional skills in digital technologies has been observed throughout the world and in Russia, in particular, in the last five years. It is a challenge and an opportunity when issues of integration and growth coincide with each other. Digitalization in the field of public services is developing rapidly in our country. Russia needs educational systems appropriate to the digital age, as well as additional programs for the education and retraining of that part of the adult population that has long abandoned their studies. This is a two-pronged task, dealing with both basic digital skills and a modern understanding of literacy. The goal of developing digital educational services for the population is to create an accessible and effective learning system for all categories of citizens. The paper uses clustering and classification methods to group homogeneous objects based on a wide range of socio-economic and financial indicators that are important for studying the development of digitalization in the services provided to the population. The objective of the study is to identify, using objective methods of mathematical data analysis (without any use of subjective assessments), the presence or absence of a relationship between the socio-economic parameters of a region’s development in the Russian Federation and paid educational services provided to the population. The regions are clearly divided into two large, almost equal groups based on this set of indicators. A comparative analysis of hierarchical clustering and classical clustering using the K-means method is presented. Hierarchical clustering is preferred over classical clustering. Consistent results were obtained using both methods. The importance of the geographical factor and homogeneity in the economic development of regions grouped into clusters was concluded. Moscow stands out for its digitalization development compared to other regions, as evidenced by both clustering methods.