The article discusses integrated development environments based on artificial intelligence as an innovative programming tool that provides automation of routine software development tasks. The Cursor development environment, developed by Anywhere, is the main object of research. The architectural features of the system are analyzed, including an agent-based approach to interacting with code, context management mechanisms through generation supplemented with extracted data, and code base indexing using vector representations and Merkle trees to optimize updates. The key limitations of modern integrated development environments based on artificial intelligence have been identified: problems with the size of the context window, indexing performance of large repositories, accuracy of context extraction, as well as privacy and security issues. Special attention is paid to the human factor – the lack of competence of developers in the field of effective context management and the creation of high-quality products. The article substantiates the need to create a preliminary context management agent capable of technically optimizing processes and directing users to effective practices of working with integrated development environments based on artificial intelligence.

Keywords: integrated development environment, artificial intelligence, Cursor development environment, large language models, context management, generation with addition of extracted data, code base indexing, Merkle trees, agent-based approach, software developmen

The article presents the results of calculations of the stress-strain state of the Sophie Germain-Lagrange plate obtained using approximate methods for solving differential equations: the Bubnov-Galerkin method, the finite difference method and the differential quadrature method. It is shown that the differential quadrature method using the Chebyshev grid is an effective method for solving bending problems of thin rectangular plates and allows obtaining high-precision results using a limited number of nodes.

Keywords: differential equation, approximate solution, differential quadrature method, Chebyshev grid, Sophie Germain-Lagrange plate, plate bending, stress-strain state

The article presents the architecture and implementation of an intelligent software package (ISP) for predicting the thermal resistance of semiconductor devices, in particular MOSFET transistors, at the design stage. The developed system combines physical and mathematical modeling of multilayer heat-conducting structures with machine learning methods, which allows for an accurate prediction of thermal parameters based on engineering characteristics and case design. The ISP implements a mechanism for automatically supplementing incomplete data using a knowledge base of typical parameters of domestic and foreign devices. Models were trained on a synthetically expanded sample formed taking into account the thermal conductivity of structural materials and layer geometry. Among the algorithms used are ensembles of random forests and gradient boosting, as well as neural network models. An analysis of the importance of features was carried out, key parameters that determine them were identified, and the possibility of using the ISP for early assessment of thermal conditions in CAD and CAE environments was demonstrated.

Keywords: thermal resistance, MOSFET, machine learning, intelligent software system, multilayer structure, predictive model, CAD, thermal conductivity

The paper examines the nature of exponential behavior and identifies the conditions under which the probabilistic distribution of the project completion period deviates from the exponential one. For this purpose, a model has been developed in which the evolution of the project is described as a Markov process with a transition matrix containing a constant in all elements of the first row. This structure corresponds to a situation in which the project can be restarted at any time. Project completion times can follow various statistical distributions, including normal, exponential, and more complex forms. Examples of such projects can be research, exploration, venture and other similar projects. An analysis of the dynamics shows that the model reliably reproduces the exponential distribution in cases where the probability of a restart remains moderate. This indicates the limit of applicability of the exponential description.: it is adequate for low and medium restart probabilities, but loses accuracy with a high level of uncertainty.

Keywords: Markov processes, project management, exponential distribution, project completion time, risk assessment, probabilistic forecasting, uncertainty in projects, risks of assumptions, dynamics of project evolution

Construction work often involves risks when carrying out complex sets of tasks described in the form of network schedules, in particular, risks of violating tender deadlines and project costs. One of the main reasons for increased project risks is a lack of resources. The main objective of this study is to develop a methodology for modeling network schedules under resource constraints, taking into account the stochastic influence of risks on project completion deadlines. The paper analyzes tools for modeling project schedules; describes a mathematical model for estimating project cost based on a network schedule under resource constraints; proposes a method for modeling a network schedule in the AnyLogic environment; develops an algorithm for modeling parallel branches of a project schedule under resource constraints; and describes a method for modeling a network schedule for project work. Testing was conducted based on a network schedule for a project to construct a contact line support. It has been shown that the method allows for obtaining probabilistic estimates of project deadlines and costs under conditions of risk and limited resources. The methodology can be applied to various projects described by network schedules and will allow solving a number of practical tasks: optimizing resources allocated for project implementation, taking into account the time and cost of the project, analyzing risks affecting project implementation, and developing optimal solutions for project risk management.

Keywords: network schedule, work plan, simulation modeling, risk analysis, project duration, project cost

The paper discusses issues related to the use of graph-theoretic models in text analysis. One of the tasks is to aggregate such models to identify more "simple" graphs, the vertices of which correspond to subsets of the vertices of the original model, and the edges reflect the "strong connections" between the vertices. Using the example of a Russian folk tale plot, it is shown how to build an aggregated model with a given threshold of significance and present it for further analysis. To conduct the experiments, a set of graph-theoretical models for fairy-tale plots from the collection of A.M. Afanasyev was built using the Folklore information system, where the graph aggregation module was improved.

Keywords: text analysis, graph-theoretical model, aggregation, significance threshold, storage format, folklore text, fairy tale plot, information system "Folklore"

The article deals with the problem of quantifying the security of objects of the penal correction system based on mathematical modeling. The authors propose a modified genetic algorithm in which the traditional fitness function is replaced by a mechanism of "virtual movement" of individuals in a discrete space, which allows taking into account both the individual characteristics of safety measures and their cumulative impact. A step-by-step example of applying the algorithm to choosing the optimal set of protective measures based on expert assessments based on several criteria is given. The results demonstrate the effectiveness of the proposed approach for solving multi-criteria tasks of assessing and improving security in conditions of uncertainty and the absence of an explicit analytical relationship between system parameters.

Keywords: security, vulnerability, event, penal enforcement system, genetic algorithm, mathematical modeling, optimization, expert assessment, criterion, security, security regime, discrete space, coalition, crossing, fitness function

The article presents a comparative analysis of the performance of three solver programs (based on the libraries lpSolve, Microsoft Solver Foundation and Google OR-Tools) when solving a large-dimensional linear Boolean programming problem. The study was conducted using the example of the problem of identifying the parameters of a homogeneous nested piecewise linear regression of the first type. The authors have developed a testing methodology that includes generating test data, selecting hardware platforms, and identifying key performance metrics. The results showed that Google OR-Tools (especially the SCIP solver) demonstrates the best performance, surpassing analogues by 2-3 times. The Microsoft Solver Foundation has shown stable results, while the lpSolve IDE has proven to be the least productive, but the easiest to use. All solvers provided comparable accuracy of the solution. Based on the analysis, recommendations are formulated for choosing a solver depending on performance requirements and integration conditions. The article is of practical value for specialists working with optimization problems and researchers in the field of mathematical modeling.

Keywords: regression model, homogeneous nested piecewise linear regression, parameter estimation, method of least modules, linear Boolean programming problem, index set, comparative analysis, software solvers, algorithm performance, Google OR-Tools

This research investigates the development of expert systems (ES) based on large language models (LLMs) enhanced with augmented generation techniques. The study focuses on integrating LLMs into ES architectures to enhance decision-making processes. The growing influence of LLMs in AI has opened new possibilities for expert systems. Traditional ES require extensive development of knowledge bases and inference algorithms, while LLMs offer advanced dialogue capabilities and efficient data processing. However, their reliability in specialized domains remains a challenge. The research proposes an approach combining LLMs with augmented generation, where the model utilizes external knowledge bases for specialized responses. The ES architecture is based on LLM agents implementing production rules and uncertainty handling through confidence coefficients. A specialized prompt manages system-user interaction and knowledge processing. The architecture includes agents for situation analysis, knowledge management, and decision-making, implementing multi-step inference chains. Experimental validation using YandexGPT 5 Pro demonstrates the system’s capability to perform core ES functions: user interaction, rule application, and decision generation. Combining LLMs with structured knowledge representation enhances ES performance significantly. The findings contribute to creating more efficient ES by leveraging LLM capabilities with formalized knowledge management and decision-making algorithms.

Keywords: large language model, expert system, artificial intelligence, decision support, knowledge representation, prompt engineering, uncertainty handling, decision-making algorithms, knowledge management

This paper is devoted to the theoretical analysis and comparative characteristics of methods and algorithms for automatic identity verification based on the dynamic characteristics of a handwritten signature. The processes of collecting and preprocessing dynamic characteristics are considered. An analysis of classical methods, including hidden Markov models, support vector machines, and modern neural network architectures, including recurrent, convolutional, and Siamese neural networks, is conducted. The advantages of using Siamese neural networks in verification tasks under the condition of a small volume of training data are highlighted. Key metrics for assessing the quality of biometric systems are defined. The advantages and disadvantages of the considered methods are summarized, and promising areas of research are outlined.

Keywords: verification, signature, machine learning, dynamic characteristic, hidden Markov models, support vector machine, neural network approach, recurrent neural networks, convolutional neural networks, siamese neural networks, type I error

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 discusses the principles of operation, key technologies, and prospects for the development of eye-tracking systems in virtual reality (VR) devices. It highlights the main components of such systems, including infrared cameras, computer vision algorithms, and calibration methods. Eye-tracking technologies such as Pupil Center Corneal Reflection (PCCR) are analyzed in detail, as well as their integration with rendering to implement foveal rendering, which significantly reduces the load on the GPU. Current issues, including latency and power consumption, are discussed, and solutions are proposed, such as the use of predictive algorithms and hardware acceleration. Special attention is paid to promising areas, including neurointerfaces and holographic systems. The article is based on the latest research and developments from leading companies such as Tobii, Qualcomm, and Facebook Reality Labs. The article is of interest to VR device developers, researchers in the field of human-computer interaction, and computer vision specialists.

Keywords: eye-tracking, virtual reality, foveated rendering, computer vision, human-computer interaction, PCCR

This article presents a methodology for assessing damage to railway infrastructure in emergency situations using imagery from unmanned aerial vehicles (UAVs). The study focuses on applying computer vision and machine learning techniques to process high-resolution aerial data for detecting, segmenting, and classifying structural damage.
Optimized image processing algorithms, including U-Net for segmentation and Canny edge detection, are used to automate analysis. A mathematical model based on linear programming is proposed to optimize the logistics of restoration efforts. Test results show reductions in total cost and delivery time by up to 25% when optimization is applied.
The paper also explores 3D modeling from UAV imagery using photogrammetry methods (Structure from Motion and Multi-View Stereo), enabling point cloud generation for further damage analysis. Additionally, machine learning models (Random Forest, XGBoost) are employed to predict flight parameters and resource needs under changing environmental and logistical constraints.
The combination of UAV-based imaging, algorithmic damage assessment, and predictive modeling allows for a faster and more accurate response to natural or man-made disasters affecting railway systems. The presented framework enhances decision-making and contributes to a more efficient and cost-effective restoration process.

Keywords: UAVs, image processing, LiDAR, 3D models of destroyed objects, emergencies, computer vision, convolutional neural networks, machine learning methods, infrastructure restoration, damage diagnostics, damage assessment

The article considers mathematical and computer modeling of noise characteristics of strain-resistant pressure sensors. A model has been developed that takes into account thermal, shotgun, flicker, and process noise, which form the total output signal of the sensor. Based on a numerical experiment, spectral analysis by the Welch method was performed, the slope of the 1/𝑓 region was approximated, and the integrated noise powers in various frequency ranges were calculated. It is shown that flicker noise dominates in the low-frequency range, thermal noise dominates in the medium and high-frequency ranges, and drift noise components manifest themselves near the zero frequency. Analysis of the signal-to-noise ratio revealed its decrease at low frequencies and stabilization at frequencies above 1 kHz. The results obtained confirmed the adequacy of the model and its applicability for predicting noise characteristics, manufacturing quality, and optimizing the operating conditions of pressure sensors.

Keywords: tensoresistive sensors, noise characteristics, thermal noise, flicker noise, shot noise, power spectral density, signal-to-noise ratio, computer simulation

The practice of producing optical interference coatings shows that when using new thin-film materials, obtaining optical products with specified quality function requirements depends on the accuracy of their refractive index. The results of its evaluation on large frequency crystals differ, which does not allow narrowband filters with the required technical parameters. This article proposes an approach to estimating the parameters of the refractive index of a thin film based on solving the inverse synthesis problem, which is based on the experimental determination of the thickness of sprayed films using an X-ray fluorescence coating thickness analyzer and data on the reflection coefficient spectrum obtained using a broadband spectrophotometer. The numerical modeling carried out during the study showed that even if there are 5% tolerances for estimating the thickness of coatings, a fairly accurate determination of the refractive index can be expected. The correctness of the results of using this approach was verified by using a thin film with a known refractive index, which was also determined using the proposed method of numerical modeling of the reflection spectrum of the digital twin coating.

Keywords: interference coating, numerical modeling, reflection coefficient spectrum

Modern approaches to synthetic speech recognition are in most cases based on the analysis of specific acoustic, spectral, or linguistic patterns left behind by speech synthesis algorithms. An analysis of open sources has shown that the further development of methods and algorithms for synthetic speech recognition is crucial for providing protection against emerging threats and maintaining trust in existing biometric systems.
This paper proposes an algorithm for synthetic speech detection based on the calculation of audio signal entropy. The relevance of the work is driven by the increasing number of cases involving the malicious use of synthetic speech, which is becoming almost indistinguishable from genuine human speech. The results demonstrated that the entropy of synthetic speech is significantly higher, and the algorithm is robust to data losses. The advantages of the algorithm are its interpretability and low computational complexity. Experiments were conducted on the CMU ARCTIC dataset using the XTTS v.2 model. The proposed algorithm enables making a decision on the presence of synthetic speech without the need for complex spectral analysis or machine learning methods.

Keywords: synthetic speech, spoofing, Shannon entropy, speech recognition

Разработан алгоритм и составлена программа на языке программирования Python для расчета численных значений оптимального оператора фильтрации с запаздыванием для L-марковского процесса с квазирациональной спектральной плотностью, являющегося обобщением марковского процесса с рациональным спектром. В основе построения оптимального оператора фильтрации с запаздыванием лежит спектральная теория случайных процессов. Расчетная формула оператора фильтрации была получена с использованием теории L-марковских процессов, методов вычисления стохастических интегралов, теории функций комплексного переменного и методов тригонометрической регрессии. Рассмотрен интересный с точки зрения управления сложными стохастическими системами пример L-марковского процесса (сигнала) с квазирациональным спектром. За основу при построении математической модели оптимального оператора фильтрации с запаздыванием была взята тригонометрическая модель. Показано, что значения оператора фильтрации с запаздыванием представляются линейной комбинацией значений принимаемого сигнала в определенные моменты времени и значений синусоидальных и косинусоидальных функций в те же моменты. Установлено, что числовые значения оператора фильтрации существенно зависят от параметра β совместной спектральной плотности принимаемого и передаваемого сигналов, в связи с чем в работе рассматривались три разные задачи прохождения сигнала через разные физические среды. Установлено, что абсолютная величина действительной части оператора фильтрации на всех трех интервалах изменения срока запаздывания и во всех трех средах превышает абсолютную величину мнимой части в среднем в два и более раз. Построены графики зависимости действительных и мнимых частей оператора фильтрации от срока запаздывания τ, а также трехмерные графики зависимости самого оператора фильтрации с запаздыванием от срока запаздывания. Дано физическое обоснование полученным результатам.

Keywords: random process, L-Markov process, noise, delayed filtering, spectral characteristic, filtering operator, trigonometric trend, standardized approximation error

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

In the modern world, when technology is developing at an incredible rate, computers have gained the ability to "see" and perceive the world around them like a human. This has led to a revolution in visual data analysis and processing. One of the key achievements was the use of computer vision to search for objects in photographs and videos. Thanks to these technologies, it is possible not only to find objects such as people, cars or animals, but also to accurately indicate their position using bounding boxes or masks for segmentation. This article discusses in detail modern models of deep neural networks used to detect humans in images and videos taken from a height and a long distance against a complex background. The architectures of the Faster Region-based Convolutional Neural Network (Faster R-CNN), Mask Region-based Convolutional Neural Network (Mask R-CNN), Single Shot Detector (SSD) and You Only Look Once (YOLO) are analyzed, their accuracy, speed and ability to effectively detect objects in conditions of a heterogeneous background are compared. Special attention is paid to studying the features of each model in specific practical situations, where both high-quality target object detection and image processing speed are important.

Keywords: machine learning, artificial intelligence, deep learning, convolutional neural networks, human detection, computer vision, object detection, image processing

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