PHYSICO-MATHEMATICAL MODELLING AND INFORMATIONAL TECHNOLOGIES

Modified pruning process algorithm for k-cores decomposition in a complex networks

2025-08-24T07:05:04+00:00

The most commonly used algorithm for extracting k-cores of complex networks (CNs) is analyzed. The main drawback of this algorithm is identified, which is the possibility of degenerating the k-core into an empty set even if this network contains a sufficiently large number of nodes with a degree not less than k. To eliminate this drawback, a modified pruning process algorithm is proposed and its effectiveness for extracting k-cores is shown on the examples of a number of model and real-world complex networks. k-cores are formed as groups of the most important CN elements, which can become the target of simultaneous targeted attack on the network, and a scenario of such attack is formed, which takes into account the potential capabilities of intruder. A method for evaluation the consequences of successful attack on k-core is proposed, which is based on the concept of its neighborhood domain.

Video system for determining the number of people

2025-08-24T07:11:48+00:00

The article investigates the effectiveness of using a video system to detect and track the movements of living objects, particularly people. A model for counting the number of people in a frame using the Arduino ESP_Camera hardware module and Python software has been developed. NumPy and OpenCV libraries have been used to process the video stream, which provide detection and tracking of movements in real time. The experimental results confirm that the system is able to accurately record the movements of people even in the presence of several moving objects, which indicates its practical effectiveness in real conditions. The proposed approach provides high accuracy in detecting movements in real-time video streams, which makes it promising for further application in the field of automated video surveillance.

Analysis of h-Adaptive Finite Element Method in Static Problems of Cylindrical Shells: І. Wellposedness of Axisymmetric Variational Formulation

2025-08-24T07:16:21+00:00

This article is devoted to establishing the correctness of boundary value problems in the statics of Timoshenko shells and the approximation of their solutions using the finite element method (FEM) with a priori guaranteed accuracy. In the first part of this study, the following results are established for this shell model: (i) sufficient (and entirely practical) conditions for the solvability of the variational formulation of the boundary value problem for a cylindrical shell under axisymmetric loading; (ii) the structure of the rigid displacement vectors of such shell; (iii) a criterion for the singular perturbation of the boundary value problem. In the second part, the following are proposed:(iv) an a posteriori error estimator (APE) for piecewise linear FEM approximations of the generalized displacement vector of the shell; (v) a local mesh refinement strategy for the efficient computation of FEM approximations with a predefined level of allowable error. The efficiency and reliability of the developed iterative h-adaptive approximation procedure are illustrated by numerical results from the analysis of model problem solutions, in particular, in comparison with traditional uniform mesh refinement.

The heat conduction problem for a half-space with a multilayer coating under nonstationary heating

2025-08-24T07:19:30+00:00

Based on the mathematical model with generalized boundary conditions of heat exchange of the bodies with ambient medium via thin multilayer coatings, the statement of heat conduction problem for a half-space with a multilayer coating under nonstationary heating at the arbitrary function of temperature of ambient medium is formulated. Applying the method of Laplace integral transformation with the use of Duhamel integral relation, we obtain an analytical solution of this problem and write the specific expressions for temperature in body and coating’s layers for the cases of linear, exponential, logarithmic, and periodic functions of temperature of ambient media. The influence of heat exchange condition with ambient medium on the contact temperature and temperature distribution across the spatial coordinate is analyzed

Analysis of the implementation of parallel algorithms for digital filtering of large arrays of distorted data

2025-08-24T07:23:36+00:00

Parallel algorithms for solving a one-dimensional problem of digital filtering of data arrays using a syn-chronous calculation scheme are considered. These algorithms are implemented on a multi-core computer using the high-level language C# and the Visual Studio 2022 environment with the involvement of the System and System.Threading libraries. The ThreadPool and Parallel.For tools were used when executing the aforementioned filtering algorithms. Numerical experiments were conducted for different types of distorted signals using different methods of setting weight coefficients. As a result, a significant real speed up of parallel algorithms was obtained, which confirmed their high efficiency. The results obtained can be used during the preliminary processing of large data arrays in many subject areas using modern software and hardware tools.

Modelling and investigation of the heating process of a tungsten panel under the action of a quasi-steady-state electromagnetic field

2025-08-24T07:27:07+00:00

A nonferromagnetic electroconductive panel of rectangular cross-section is considered under the action of a quasi-steady electromagnetic field. Under such an action, unsteady volumetrically distributed Joule heat sources arise in it. To investigate the regularities of its thermal modes, a two-dimensional physico-mathematical model consisting of two stages is proposed. At the first stage, the tangent component of the magnetic field intensity vector to the panel bases is determined from Maxwell's relations. At the second stage, this component is used to calculate the Joule specific heat density. The solution to the electrodynamics problem is constructed by approximating the distribution of the determining function along the thickness coordinate with a cubic polynomial. The coefficients of the approximation polynomial are represented as a linear combination of the integral characteristics of the determining function along the thickness coordinate and its specified values at the panel bases. As a result, the original two-dimensional initial-boundary value problem for the defining function is reduced to a one-dimensional initial-boundary value problem for the integral characteristics of the defining function. The solutions of the one-dimensional problem are obtained by applying a finite integral transform along the transverse coordinate of the panel using the specified boundary conditions on the determining function at the end sections of the panel and the Laplace transform in time.
Numerical studies have been performed for a tungsten panel under the homogeneous action of a quasi-steady electromagnetic field. The thermal modes of the panel are analysed depending on the parameter characterising the relative depth of induction current penetration for two typical cases of near-surface and continuous heating.

Analysis of the use of activated wavelet functions in wavelet neural networks for categorizing ECG cardiac reductions

2025-08-24T07:29:35+00:00

Accurate and automated classification of heartbeats in an electrocardiogram (ECG) is fundamental to the diagnosis and treatment of cardiovascular diseases (CVD), but it remains a challenging task due to the complexity and variability of ECG signals [1]. This study examines the effectiveness of using various wavelet functions, including Morlet, Mexican Hat, Gabor, Shannon, and Gaussian, as activation functions in a wavelet neural network (WNN) architecture for ECG heart rate classification [3]. Using a publicly available dataset obtained from the MIT-BIH Arrhythmia and PTB Diagnostic ECG databases focusing on the 5-grade arrhythmia categorization based on the Association for the Advancement of Medical Instrumentation (AAMI) standard [5]. The key findings point to differences in the performance of different wavelet activation functions, emphasizing the potential benefits of using the inherent properties of time-frequency localization of wavelets to capture discriminative morphological features in ECG rhythms [7]. This work emphasizes the prospects of using wavelet-based activation functions to improve the accuracy and reliability of deep learning models in biomedical signal processing programs, including ECG analysis.

Image upscaling using generative adversarial networks

2025-08-24T07:32:48+00:00

The purpose of this article is to develop and improve image scaling algorithms aimed at preserving details and visual appearance when changing image size. The subject of this article is image scaling algorithms, particularly their enhancement to ensure high-quality images. An analysis of artifacts arising during image scaling are conducted. Additionally, various image scaling algorithms are analyzed. Special attention is given to algorithms and methods of image scaling that use machine learning and neural networks. In this article a software implementation of the image scaling method using Generative Adversarial Networks is proposed. The architecture of GAN is described in detail and the loss functions for generator and discriminator are calculated. The results of this article demonstrate that improved algorithms based on GANs allow achieving high-quality image scaling with minimal detail loss and artifacts. The software implementation of the algorithms showed efficiency and the possibility of real-time image scaling, which is crucial for various practical applications such as medical imaging, video processing, and other fields where image quality is critical.

Analysis of the possibilities application of the Vision Grid Transformer model for document structure analysis of ukrainian accounting documents

2025-08-24T07:39:37+00:00

In the context of ongoing digital transformation, the need for automation of accounting document processing is steadily increasing, particularly in Ukraine, where a significant portion of primary documentation still exists in paper form or as scanned images. Effective information extraction from such documents requires the application of advanced artificial intelligence techniques, especially deep learning and multimodal data analysis. This paper explores the applicability of the Vision Grid Transformer (VGT) architecture for analyzing the layout structure of Ukrainian accounting documents.
The VGT model combines two information streams – a visual stream (based on the Vision Transformer, ViT) and a text-spatial stream (based on the Grid Transformer, GiT), enabling comprehensive document representation both in terms of visual layout and semantic content. The model's flexibility is further enhanced by pretraining methods such as Masked Grid Language Modeling (MGLM) and Segment Language Modeling (SLM), which help capture both local and global contextual dependencies among textual elements. The study emphasizes the specific challenges of adapting VGT to the Ukrainian language and accounting domain. These include the lack of high-quality publicly annotated Ukrainian datasets, the necessity of accurate optical character recognition (OCR) for Cyrillic scripts, issues related to handwritten text recognition (HTR), and the complexity of domain-specific terminology and abbreviations used in accounting.

Strength analysis of a bimaterial with an internal crack and sliding interface contact

2025-08-24T07:43:20+00:00

For analyzing the stress-strain state of an infinite bimaterial composed of two half-spaces containing a circular internal crack under static tensile loading, a boundary-integral approach is considered. Smooth contact conditions with slip are imposed on the interface surface of the body. The problem is reduced to solving a two-dimensional boundary integral equation of the Newtonian potential type concerning the unknown crack opening displacement function on the defect surfaces. Using the obtained solutions, stress intensity factors for mode I are computed, and their dependencies on the stiffness ratio of the bimaterial components, the distance between the defect and interface, and on the angular coordinate of the crack contour point are analyzed

Synthesis of a focusing radiation system taking into account physical constraints on optimal characteristics

2025-08-24T07:48:11+00:00

The optimization problem of the focusing transmitting system, which consists of a set of the inclined semitransparent elements is solved in the paper. The optimization parameter is a filling coefficient of arrays, which is connected with the radius of wires and distance between them. The optimization problem is solved with respect to some physical parameters defining the transparency of mirrors. Taking into account the restrictions on this parameter one can get the filling coefficient values, which does not contradict the physically justified values.

Control with delay of combined motion of the structure with the free surfaced liquid

2025-08-24T07:50:18+00:00

The problem of delay control on a combined motion of the structure with a free surfaced liquid in the nonlinear range of perturbations of surface is considered. It is assumed that the reservoir is of cylindrical shape and it is filled with an ideal homogeneous incompressible liquid. The mathematical model of the system is constructed based on the aggregate use of the Hamilton–Ostrogradsky variational principle with preliminarily elimination of all kinematical restrictions of the problem, approaches of nonlinear mechanics and the Kantorovich method. In the end this enables to get the nonlinear dynamical model of the system in the form of ordinary differential equations with respect to amplitudes of perturbations of normal modes of liquid oscillations and parameter of the reservoir translational motion. The system control is done based on the principle of compensation of the force response of the liquid on reservoir walls. We consider the case of the delayed control, when the control starts immediately, during an active loading and after completion of the active loading. Specific characters of the delayed control were ascertained.

Generalization of the Faraday problem for the mechanical system «reservoir – liquid» in the presence of a vertical periodic two-frequency disturbance

2025-08-24T07:52:20+00:00

The generalization of Faraday's classic problem about the parametric resonance of the free surface during vertical oscillations of the tank according to the periodic law of the modulus of the cosine is considered. Regions of stability and instability are designed, which are compared with similar results for the classical Faraday problem. The behavior of the system is considered on the basis of a nonlinear multimode model, which describes the combined movement of the tank and fluid under the influence of external force excitation or kinematic disturbance. It is shown that, unlike the classical case, the presence of the second frequency leads to a narrowing of the parametric resonance region with an increase in the amplitude of the second harmonic of the external vertical disturbance of the reservoir.

Logical-Graph Interpretation of Scene in the Transformer Core of an Autonomous Drone

2025-08-24T07:53:43+00:00

This paper presents the concept of an intelligent drone equipped with a semantic core designed to construct logical-graph representations of the environment based on sensory data. The main objective is to develop an adaptive system capable not only of object recognition but also of forming causal, spatial, and functional relationships between objects to enable logical reasoning. The proposed approach integrates reinforcement learning techniques with graph-based semantics within a transformer architecture, thus ensuring autonomous operation and behavioral flexibility in partially observable environments.