The paper investigates the improvement of methods for computing the concentration of nanoparticles in transparent liquids under the action of laser radiation. The exact solution of the third boundary value problem for the Einstein–Fokker–Planck equation is analyzed, the direct use of which in the Maple computer algebra system leads to computational instabilities at large values of the transfer parameter. A solution to the problem of unstable numerical calculations at high values of dimensionless parameters, leading to significant distortions of the result, is presented. The key result is to expand the working range of the transfer parameter and ensure the correct asymptotic behavior of the solution. Numerical experiments have confirmed the effectiveness of the proposed approach, which makes it a valuable tool for modeling and optimizing the processes of laser separation of nanoparticles.

Keywords: nanosuspension, laser radiation, concentration of nanoparticles, continuity equation, third boundary value problem, computer calculations, Maple

The purpose of the work was to develop a model of maintaining balance in accordance with the parameters of the human body, which ensures the function of maintaining the body's balance in space. The key indicator of stable balance is the center of mass (CM) of the human body. The stability of the posture is ensured by the projection of the center of mass (CM) within the support area. The article describes two models that assess the displacement of the CM projection relative to the support area. The principle of operation of the models is based on pendulum motion in the sagittal plane (forward-backward movements) and the frontal plane (lateral movements). The model includes a comprehensive visualization of the CM projection on the support area in real time, as well as a quantitative assessment of stability by counting the percentage of time spent in the support area. The model provides a more comprehensive understanding of the mechanisms involved in maintaining equilibrium.

Keywords: balance maintenance mechanisms, modeling, biomechanics, and the center of mass

Ring-shaped reinforced concrete structures are widely used in construction. For example, in the form of underground pipelines. They experience a complex nonlinear deformed state (VAT), which is analytically described as a complex mathematical problem of mechanics. Therefore, numerical methods are often used to solve it. This article uses the finite element method (FEM) implemented in the Lira-CAD 2022 PC. The VAT of reinforced concrete pipelines is determined in a physically nonlinear formulation, taking into account 4 factors of influence: the inner diameter, the concrete class, the properties of the filling soil, and the properties of the foundation soil. A plan has been drawn up for a complete multifactorial numerical experiment, which includes 81 models. The values of internal force factors in all sections of the underground pipeline are obtained, taking into account the variation of each factor individually and taking into account their mutual influence. Combinations of factors giving extreme values of internal forces in the pipeline have been established. Based on this, recommendations for rational design have been developed.

Keywords: underground pipeline, reinforced concrete, computer modeling, longitudinal profile, cross section, PC "Lira-CAD"

The article presents and analyzes the algorithm for calculating bending reinforced concrete structures by normal section based on a nonlinear deformation model recommended in the standards for the design of reinforced concrete structures SP 63.13330.2018. Calculation of reinforced concrete structures based on a nonlinear deformation model is a priority, since it expands the set of controlled parameters, which leads to a more accurate description of the operation of building structures. The features of performing the calculation using this algorithm, as well as other approaches to calculating bending reinforced concrete structures by a normal section based on deformation and other models, are considered. The sequence of calculations using computer technologies is shown using the example of calculations in the engineering nonlinearity1 system of the LIRA-SAPR software package. The results of calculating a rod element of the calculation scheme are given: changes of the bending moment, stiffness, and deformation modulus for finite elements along the rod length. In this case, the calculation in the engineering nonlinearity1 system is performed with subsequent adjustment of the stiffness characteristics of the finite elements, carried out during the iterative calculation, with clarification of the stress-strain state, deflection of the element and its reinforcement. Additional capabilities of performing calculations using the engineering nonlinearity2 system are described: expanded the possibilities of assigning various laws of material deformation, describing the loading of the calculation scheme, reinforcement of structures, and the possibility of using a step processor.

Keywords: bending reinforced concrete structures, nonlinear deformation model, calculation scheme, calculation algorithm, PC LIRA-SAPR, engineering nonlinearity, system

The article is devoted to the application of modern methods of generative image compression using variational autoencoders and neural network architectures. Special attention is paid to the analysis of existing approaches to image generation and restoration, as well as a comparative assessment of compression quality in terms of visual perception and metric indicators. The aim of the study is to systematize deep image compression methods and identify the most effective solutions based on the variational Bayesian approach. The paper considers various architectures, including conditional autoencoders and hypernetwork models, as well as methods for evaluating the quality of the data obtained. The main research methods used were the analysis of scientific literature, a comparative experiment on the architectures of generative models and a computational estimation of compression based on metrics. The results of the study showed that the use of variational autoencoders in combination with recurrent and convolutional layers makes it possible to achieve high-quality image recovery with a significant reduction in data volume. The conclusion is made about the prospects of using conditional variational autoencoders in image compression tasks, especially in the presence of additional information (for example, metadata). The presented approaches can be useful for developing efficient systems for storing and transmitting visual data.

Keywords: variational autoencoders, generative models, image compression, deep learning, neural network architectures, data recovery, conditional models

The article focuses on developing data clustering algorithms using asymmetric similarity measures, which are relevant in tasks involving directed interactions. Two algorithms are proposed: stepwise cluster formation and a modified version with iterative center refinement. Experiments were conducted, including a comparison with the k-medoids method. The results showed that the fixed-center algorithm is efficient for small datasets, while the center-recalculation algorithm provides more accurate clustering. The choice of algorithm depends on the requirements for speed and quality.

Keywords: clustering, asymmetric similarity measures, clustering algorithms, iterative refinement, k-medoids, directed interactions, adaptive methods

This paper considers the modeling of user work with a multi-server database developed on the basis of microservice architecture. The subject area was analyzed, the main entities of the system were described, and the mechanisms of data transfer and service interaction using Docker and Apache Kafka were implemented. It was revealed that the development of a multi-server database allowed to achieve high scalability and fault tolerance of the system. The implementation of replication and sharding mechanisms provided even load distribution, and the use of Kafka message broker facilitated efficient data exchange between services. The testing confirmed the system's reliability under high load, as well as revealed its strengths and potential improvements.

Keywords: modeling, load balancing, Docker, Apache Kafka, microservice architecture, distributed systems, query optimization

The article is devoted to the method of calculating the effective frequency of the load impulse FWD, which allows establishing a correspondence between the laboratory-determined viscoelastic characteristics of asphalt concrete layers included in the road pavement and the modulus of elasticity calculated by backcalculation based on the deflection  bowl determined in field tests using FWD. The article proposes an algorithm for finding this frequency, presents the results of its calculations, and compares the elastic moduli obtained in the laboratory and by the results of the backcalculation. The conducted numerical experiment confirms that for the deflection cups generated within the viscoelastic calculation model, the difference in modules does not exceed 8%. At the end of the work, ways are proposed for the practical application of the calculated parameter and further improvement of the method on real deflection  bowl obtained on  road pavements.

Keywords: dynamic loading system, road surface, deflection bowl, asphalt concrete, elastic modulus, relaxation modulus, AMPT test, master curve, backcalculation, effective pulse frequency

The article presents numerical modeling of flow dividers (separators) with different hole diameters (3.5 mm, 7.0 mm, 14.0 mm) to prevent cavitation damage. The hole diameters, number, and rows in the separators have equivalent significance, as they determine the distribution of local velocities and pressures in the flow. This minimizes the risk of vapor bubble formation and subsequent collapse, which can lead to erosion of metal surfaces. For clarity, the simulation results are presented in the form of pictures of the distribution of pressure and velocities in each of the separators with different diameters. In order to prevent cavitation, the authors have presented a design of a "short-stroke" valve in which it is allowed to use flow dividers with enlarged holes.

Keywords: valve, cavitation, distribution pattern, separator, holes, rotation, simulation, flow divider

An ensemble of models for predicting the position of a mobile robot moving in an unstructured environment is presented. An architecture has been developed that integrates a kinematic motion model with trainable models utilizing elevation map data and semantic segmentation. The principles for constructing a spatial feature map are described, incorporating geometric characteristics such as the terrain roughness index and a fuzzy traversability index. A modular structure of the following blocks is proposed: data preprocessing, geometric property computation, segmentation, and decision-making. Test results demonstrate the advantage of combining kinematic and sensor-based models for autonomous navigation in complex environments.

Keywords: traversability model, elevation map, point cloud, kinematic model, segmentation, machine learning, feature map

The article is devoted to assessing the influence of possible inhomogeneities in the layers of road pavements on the results of backcalculation of elastic moduli based on testing data of falling weight deflectometres (FWD). The article discusses the influence of different locations of theoretically specified inhomogeneities of structural layers within the roadway. Additionally, the influence of the location of the edge of the pavement on the results of calculating elastic moduli by backcalculation is considered. The conducted numerical experiment confirms that possible inhomogeneities of the road pavement can significantly influence the results of reverse calculations, and as a consequence, the decision-making on the appointment of repair measures. The boundaries are also determined at which the presence of a shoulder with a pavement design that differs from the roadway significantly distorts the results obtained. At the end of the work, ways to practically take into account inhomogeneities and further improve the method of inverse calculation of the elastic moduli of non-rigid road pavements are proposed.

Keywords: dynamic loading system, road pavement,structural layers, deflection bowl, asphalt concrete, elastic modulus, backcalculation, heterogeneity of layers, roadway, roadside

The calculation of wind loads on curtain facades and their fastening elements for high-rise buildings and structures using engineering methods and various numerical techniques remains an important task to this day. The corner sections of the building, where the greatest negative wind pressure occurs, are of particular interest. Incorrect calculation of wind suction can lead to the separation of panels during strong winds. The article calculates the peak wind load using a numerical method for a rectangular building with an aspect ratio of 0.6. Numerical calculations of the two-dimensional flow around the building profile in the ANSYS Fluent program using the k-e Realizable turbulence model were used to obtain the coefficients of drag, lateral force, and the distribution of the pressure coefficient at maximum lateral force. The calculations showed that the wind suction at the edge of the building exceeds the standard value by approximately 30%. The results obtained in the article should be taken into account when designing the facade.

Keywords: peak wind load, wind suction, rectangular buildings, peak negative aerodynamic pressure coefficient

The article examines a functional-dynamic model of implementing intelligent digital platforms and solutions, whose governing role in the development of a macroeconomic system is taken into account using a feedback mechanism. The relevance of the study is demonstrated in the context of active digital transformation of industries. The mathematical form of the model under consideration is a system of nonlinear differential equations of an evolutionary type, similar to dynamic models of the development of biological communities. An analysis of a macrosystem influenced by innovative technologies is carried out. As such a system, a two-sector macrostructure is considered, simulating the impact through the implementation and use of intelligent digital platforms (IDP) of two related industries, which are the transport and logistics and manufacturing sectors. The objective of the work is to study the stable states of such a structure. The model allows for taking into account the influence of investments in IDPs based on the principle of their proportionality to the growth rates of return on assets in these industries. In the work, quantitative estimates of the parameters of the original model are adjusted. An analysis of the macrosystem is carried out under conditions of different development rates of the interacting industries. The stability of the system according to Lyapunov is studied. An asymptotic approximation ‒ a solution to the problem ‒ was constructed using A.B. Vasil’eva's boundary layer decomposition method. The results describe the process of self-organization in a stable model of interaction between two related industries, supported by integrated digital platforms.

Keywords: functional-dynamic model, intelligent digital platforms, two-sector macrostructure, transport and logistics industry, production, sustainability, inter-industry interaction, asymptotic analysis, boundary layer function method

Verification and debugging of algorithms and related software that implements the search for such dangerous phenomena for aircraft flights as wind gusts and turbulence areas can be implemented in radar signal simulators, including using the concept of accessing databases storing test wind fields by coordinate components. The practical value of this approach is to minimize the number of expensive flight tests in difficult weather conditions. After implementing database data interpolation, continuous fields can be obtained, including predicted radar parameters, the processing of which, depending on the changing parameters of the locator: beam width, probe pulse duration, leads to different estimates, including the measured parameters of the movement of air masses. This article describes an approach to simulation modeling that makes it possible, by generating radio signals, the primary source of which are continuous interpolated functions of air mass motion parameters, to obtain either averaged radial velocity values in resolution elements or its standard deviation.  As a result, it allows us to test signal processing algorithms for detecting wind shifts or turbulence in weather navigation radars. The results of verification of the procedure for processing radio signals generated using the proposed approach are presented, confirming the correctness of the formation and detection of simulated fields of turbulent regions.

Keywords: on-board radar, meteorological navigation, simulation, algorithms, parameter estimation

The article is devoted to the study of the problem of estimating unknown parameters of linear regression models using the least absolute deviations method. Two well-known approaches to identifying regression models are considered: the first is based on solving a linear programming problem; the second, known as the iterative least-squares method, allows one to obtain an approximate solution to the problem. To test this method, a special program was developed using the Gretl software package. A dataset of house prices and factors influencing them, consisting of 20640 observations, was used for computational experiments. The best results were obtained using the quantreg function built into Gretl, which implements the Frisch-Newton algorithm; the second result was obtained using an iterative method; and the third result was achieved by solving a linear program using the LPSolve software package.

Keywords: regression analysis, least absolute deviations method, linear programming, iterative least squares method, variational weighted quadratic approximation method

For accurate modeling of the stress-strain state of the lithospheric plate, it is necessary to correctly define boundary conditions that reflect the interaction with the geological environment. The Dirichlet edge problem, in this context, involves setting displacements at the boundary of the calculated region. The problem is that the true displacements at the craton boundary are generally unknown and can change over time under the influence of tectonic processes and load changes.

Keywords: boundary conditions, stress-strain state, mathematical modeling, model, lithospheric plate, finite element method, geotectonics, stretching, compression, computer modeling, asthenosphere

An oil field is a complex system the operability of which depends on the power supply reliability. The main disturbance in the electrical system is voltage sag which causes transient processes which can lead to a halt in oil production.
The article discusses the transients modeling in the oil production well electrical system, consisting of a transformer, a cable line and a submersible induction motor. The mathematical model has been compiled for calculating transient processes in such systems while each element is described as a separate module containing algebraic and differential equations which allows modeling dynamic and steady-state modes of operation. Dependences of longitudinal and transverse components of stator current and rotor speed of submersible induction motor at start-up, voltage sag and power supply disconnection are obtained.

Keywords: transient processes, electrical system, oil production, submersible induction motor, voltage sag, mathematical modeling

The use of machine learning when working with text documents significantly increases the efficiency of work and expands the range of tasks to be solved. The paper provides an analysis of the main methods of presenting data in a digital format and machine learning algorithms, and a conclusion is made about the optimal solution for generative and discriminative tasks.

Keywords: machine learning, natural language processing, transformer architecture models, gradient boosting, large language models

To evaluate the noise suppression efficiency of railway transport screens, the COMSOL Multiphysics software package (module "Pressure Acoustics, Frequency Domain") was used in this article. Using the finite element method, calculations were carried out and the sound insulation characteristics of noise protection screens were assessed, and a comparative analysis of the characteristics of various screen models was also carried out. Based on the effects of acoustic interference, an interference-type noise suppression device is proposed, in which filling the upper part with a porous material improves the diffraction sound absorption of the noise protection screen, thereby enhancing its acoustic characteristics.

Keywords: COMSOL software, finite element method, transport, noise barriers, acoustic interference, acoustic characteristics

The paper presents a technique for integrating three-dimensional solid-state models developed in the CAD SolidWorks environment into the MATLAB/Simulink dynamic modeling environment. A key element of the research is the use of the Simscape Multibody module to transform geometric data and kinematic relationships into a multi-mass dynamic model. The technique has been tested using the example of creating a virtual prototype of a steering wheel platform.

Keywords: SolidWorks, MATLAB/Simulink, Simscape Multibody, Virtual prototype, steering kinematics, end-to-end design, multi-mass dynamic modeldiversification, production and technical goals to ensure production flexibility

This article presents a comprehensive analysis of Russian-language texts utilizing neural network models based on the Bidirectional Encoder Representations from Transformers (BERT) architecture. The study employs specialized models for the Russian language: RuBERT-tiny, RuBERT-tiny2, and RuBERT-base-cased. The proposed methodology encompasses morphological, syntactic, and semantic levels of analysis, integrating lemmatization, part-of-speech tagging, morphological feature identification, syntactic dependency parsing, semantic role labeling, and relation extraction. The application of BERT-family models achieves accuracy rates exceeding 98% for lemmatization, 97% for part-of-speech tagging and morphological feature identification, 96% for syntactic parsing, and 94% for semantic analysis. The method is suitable for tasks requiring deep text comprehension and can be optimized for processing large corpora.

Keywords: BERT, Russian-language texts, morphological analysis, syntactic analysis, semantic analysis, lemmatization, RuBERT, natural language processing, NLP

The article presents an analysis of modern methods of image generation: variational autoencoders (VAE), generative adversarial networks (GAN) and diffusion models. The main attention is paid to a comparative analysis of their performance, generation quality and computational requirements. The Frechet Inception Distance (FID) metric is used to assess the image quality. Diffusion models showed the best results (FID 20.8), outperforming VAE (FID 59.75) and GAN (FID 38.9), but require significant resources. VAEs are stable, but generate blurry images. GANs provide high quality, but suffer from training instability and mode collapse. Diffusion models, due to step-by-step noise decoding, combine detail and structure, which makes them the most promising. Also considered are methods of image-to-image generation used for image modification. The results of the study are useful for specialists in the field of machine learning and computer vision, contributing to the improvement of algorithms and expansion of the areas of application of generative models.

Keywords: deepfake, deep learning, artificial intelligence, GAN, VAE, diffusion model

This paper examines methods for modeling the spread of infectious diseases. It discusses the features of the generalized compartmental approach to epidemic modeling, which divides the population into non-overlapping groups of individuals. The forecast of models built using this approach involves estimating the size of these groups over time. The paper proposes a method for estimating model parameters based on statistical data. It also introduces a method for estimating confidence intervals for the model forecast, based on a series of stochastic model runs. A computational experiment demonstrates the effectiveness of the proposed methods using data on the spread of influenza in European countries. The results show the model's efficiency in predicting the dynamics of the epidemic and estimating confidence intervals for the forecast. The paper also justifies the applicability of the described methods to modeling chronic diseases.

Keywords: epidemic modeling, computer modeling, compartmental models, SIR, stochastic modeling, parameter estimation, confidence interval, forecast, influenza

A non-stationary system of automatic speed control of a DC motor with an adaptive controller is considered. Comparative simulation modeling in Simulink of the system with and without an adapter is performed. The results of the modeling confirm the stability of the adaptive system in a larger range of change of the non-stationary parameter compared to the conventional system. At the same time, the speed and quality of transient processes are maintained at the level recommended for such systems.

Keywords: automatic control system, non-stationarity, adaptive controller, subordinate control system, electromechanical object, DC motor

Many problems related to high-speed interaction with soil represent an interesting area of ​​research. For example, the fall of heavy objects on the ground surface not only creates a dynamic impact effect, but can also serve as an effective method of soil compaction under future foundations of buildings and structures. This process, along with the penetration of objects into the soil, poses new challenges for researchers. The most accurate results in these complex scenarios can be obtained by using a nonlinear dynamic formulation, which allows for a deeper understanding of the interaction mechanisms and ensures the reliability of structures under extreme loads. This requires using appropriate modeling approaches. In addition, under such an impact, the soil exhibits the properties of a liquid or gas, so it is necessary to use special soil models. The paper presents the main basic relationships and main parameters of soil models required for dynamic calculations of soils, which can be useful in modeling the operation of a soil massif in modern software packages.

Keywords: physical nonlinearity, damping, soil, foundation of buildings and structures, dilatancy, soil compaction, pore pressure, soil density, deformation modulus, numerical soil model