PHYSICO-MATHEMATICAL MODELLING AND INFORMATIONAL TECHNOLOGIES

Visual localization based on images: methods, challenges, and trends (2019–2025)

Іван Ільницький, Петро Пукач (Author) — Fri, 26 Dec 2025 00:00:00 +0000

The article provides an overview of the domain of image-based localization systems, focusing on key methods, challenges, and current trends in development for the period 2019–2025. It considers the classification of approaches to visual localization, including traditional approaches based on local features and 3D structures, approaches based on image search (visual recognition of terrain), as well as the latest deep learning methods. It analyzes datasets, key industry challenges, and promising areas for further research.

Analysis of thermal regimes of an aluminium plate under the action of a quasi-steady electromagneticfield

Роман Мусій, Андрій Кунинець, Любомир Гошко, Роман Пелех (Author) — Fri, 26 Dec 2025 00:00:00 +0000

A two-dimensional initial-boundary problem of electrodynamics for an aluminium plate under the action of a quasi-steady electromagnetic field has been formulated. The defining function is chosen as the component of the magnetic field intensity vector tangent to the plate base. The action of a quasi-steady electromagnetic field causes the emergence of Joule heat sources in it. These sources create certain thermal regimes of the plate under appropriate parameters of electromagnetic action. The solution of the electrodynamics problem was found using finite integral transformations in terms of the thickness and transverse coordinates of the rectangle of the plate cross-section and Laplace integral transformations in terms of time. A numerical analysis of Joule heat was performed for two characteristic cases of surface and continuous induction heating by a quasi-steady electromagnetic field. The time variation of Joule heat in the transient mode and its distribution across the cross section of the plate in the steady state of the electromagnetic field are analysed.

Determination and analysis of Joule heat and ponderomotive forcein a solid copper cylinder under the action of anelectromagnetic impulse

Андрій Кунинець, Роман Мусій, Богдан Бандирський, Галина Івасик (Author) — Fri, 26 Dec 2025 13:11:36 +0000

The initial-boundary problem of electrodynamics for a solid electrically conductive cylinder subjected to an electromagnetic pulse has been formulated. The effect of such a impulse appears in two physical factors – Joule heat and ponderomotive force.For the purpose of determining their expressions, it is first necessary to determine the axial component of the magnetic field intensity vector from the solution of the formulated electrodynamics problem, and then to write down the expressions for the specific heat density of Joule and the ponderomotive force in the cylinder under consideration.The cubic approximation of the distribution of the axial component of the magnetic field intensity vector along the radial variable was used to find the solution to the electrodynamics problem. As a result, the initial boundary value problem for the determinant function is reduced to the Cauchy problem for the time variable for the integral characteristics of the determinant function for the radial variable. The solution of the Cauchy problem is obtained using the Laplace integral transform, and the expressions for the integral characteristics and the axial component of the magnetic field intensity vector are obtained.The expressions for the determinant function, specific heat density of Joule, and ponderomotor force in the cylinder under consideration under the action of an electromagnetic impulse are derived based on the general solutions of the initial boundary value problem obtained under non-stationary electromagnetic action. A numerical analysis was performed of the change over time and distribution along the radius of the cylinder of the axial component of the magnetic field intensity vector and physical factors – Joule heat and ponderomotor force – depending on the duration of the electromagnetic impulse.

Mathematical Modeling And Analysis Of Temperature Regimes of A Tungsten Strip Under The Action Of A Quasi-Steady Electromagnetic Field

Роман Мусій, Мирослава Клапчук, Богдан Бандирський, Оксана Орищин (Author) — Fri, 26 Dec 2025 13:28:23 +0000

A physical and mathematical model for determining the specific Joule heat density in a tungsten strip and the temperature field during its induction heat treatment by a quasi-steady electromagnetic field is considered. The initial relations of the two-dimensional initial-boundary value problems of electrodynamics and thermal conductivity for the strip under consideration are formulated. The tangential component of the magnetic field vector and the temperature vector tangent to the strip bases are chosen as the determining functions. Using the Laplace integral transform in time and double integral transforms in the thickness and transverse coordinates, expressions for the tangential component of the magnetic field vector, Joule heat, and temperature are found. The change in temperature over time at characteristic points of the cross section in the transition mode and over the entire cross section of the strip in the steady mode for two types of near-surface and in-depth induction heating by a homogeneous quasi-steady electromagnetic field is numerically analyzed.

Influence of hydrogen on the strength of metallic structures

Богдана Гайвась, Вероніка Дмитрук (Author) — Fri, 26 Dec 2025 13:33:46 +0000

The study examines the physicochemical and mechanical mechanisms of degradation of metallic structures under the action of hydrogen that adsorbs and diffuses into the region of the stress-strain field. The equations describing the influence of surface processes on the critical pressure at which unstable crack propagation occurs are presented. A macro-level criterion for hydrogen-induced fracture is constructed, combining hydrogen concentration, stress state parameters, and strain energy. It is shown that this criterion is consistent with the local conditions of hydrogen accumulation at the crack tip. A local criterion for achieving a critical concentration governed by stress intensities and plastic shear deformation is also considered. The relationship between surface adsorption processes, hydrogen diffusion transport, and the micromechanisms of microcrack initiation and growth is established. The developed model provides a unified, multiscale description of hydrogen effects on the fracture toughness of metals, ranging from surface energy changes to local and macro-fracture criteria. The proposed relations form a basis for further numerical studies and can be used to assess the residual life and predict the durability of structural components operating in hydrogen environments.

Recognition of Major Depressive Disorder Based on EEG Wavelet Coherence

Олександр Сухолейстер, Адріан Наконечний (Author) — Fri, 26 Dec 2025 00:00:00 +0000

This study investigates whether features derived from wavelet coherence between EEG channels improve the recognition of Major Depressive Disorder (MDD) compared with baseline features obtained from wavelet transforms of individual channels. A comprehensive algorithm was developed, incorporating signal preprocessing, coherence estimation using the analytic Morlet mother wavelet, and the construction of derived inter-channel and network-level features. Experimental evaluation was performed on the TDBRAIN dataset with a subject-wise split into independent training and test cohorts. Baseline spectral–energetic features (relative wavelet energy and wavelet entropy) achieved a test accuracy of 76.2%, representing the highest performance among individual feature sets. Adding pair wise wavelet-coherence features substantially improved classification performance up to 83.3%. These results indicate that features reflecting functional interactions between electrodes are complementary to spectral descriptors and enhance the system’s ability to detect patterns associated with depressive disorders. Overall, the combination of wavelet-energy features with inter-channel coherence provides a stable and reproducible approach for automated MDD recognition from EEG signals.

Hierarchical Role-Based Access Control Architecture for CRM/ERM Systems with Complex Data Topologies

Ulyana Dzelendzyak, Nazar Mashtaler (Author) — Fri, 26 Dec 2025 14:55:15 +0000

This paper proposes an advanced access management architecture designed for Customer Relationship Management (CRM) and Enterprise Resource Planning (ERM) systems that manage data within complex hierarchies. Recognizing the limitations of traditional flat RBAC models in providing object-level security, the architecture introduces dedicated entities for Groups (G), Hierarchical Nodes (O), and a specialized Permission Assignment (PA) mechanism. This extension enables dynamic access decisions based on the intersection of a user's role, group membership, and the target object's position in the hierarchy. The model is characterized by high scalability ) and relies on permission aggregation via union. Key findings highlight the model’s effective balance between fine-grained control and administrative efficiency, while acknowledging the inherent complexity in evaluation and the need for strict governance via the Privilege Escalation (PE) permission.

Study of temperature regimes of a steel rod under the action of an unsteady electromagnetic field

Наталія Мельник, Роман Мусій, Надія Тимошенко, Адріан Торський (Author) — Fri, 26 Dec 2025 15:01:35 +0000

A physical and mathematical model is proposed for determining the temperature field in a steel rod under the action of an unsteady electromagnetic field. This model is described by sequentially coupled Maxwell equations and Fourier equations of thermal conductivity. It consists of two stages: determining the axial component of the magnetic field strength vector and temperature. The initial relations of the initial-boundary problems of electrodynamics and thermal conductivity for the rod under consideration are recorded. To construct their solutions, a cubic approximation of the distribution of determining functions along the radial coordinate is used. As a result, the initial-boundary problems for determining functions are reduced to Cauchy problems with time variation for the integral characteristics of determining functions along the radial variable. General solutions of Cauchy problems are recorded using the Laplace integral transform. The coefficients of the approximation polynomials are given in the form of a linear combination of integral characteristics and determining functions on the rod surface. The expressions for Joule heat and temperature in the rod under consideration under the action of an unsteady electromagnetic field are obtained. A numerical analysis is performed to investigate the change in temperature over time and its distribution across the radius of the rod, depending on the duration of the unsteady electromagnetic field and the magnitude of the magnetic field strength.

Determination of the concentration and absorption of impurity microparticles during movement of liquid in a porous body

Богдан Гера (Author) — Fri, 26 Dec 2025 15:06:11 +0000

The formulation of the problem of determining the concentration function of impurity components during their convective transfer in a homogeneous porous body and the distribution density of absorbed microparticles until the maximum permissible limit is reached is proposed. Using operational methods, a solution to the one-dimensional initial-boundary value problem in the half-space region is obtained at a given constant concentration of microparticles at the boundary. The results of calculations of the concentration and density of microparticles absorbed by the body matrix at small values of the diffusion coefficient, as well as in its absence, are presented. The obtained results are analyzed

Study of transition times in diffusion processes using fractional order derivatives

Yaroslav Pyanylo, Anna Lyantse, Halyna Pyanylo (Author) — Fri, 26 Dec 2025 15:18:58 +0000

The paper develops a mathematical model of the diffusion process using Caputo fractional-order derivatives with
respect to time. The problem solution was obtained in an analytical form through contour integration methods. An
analytical solution provides explicit expressions for the diffusion behavior across the entire time range, including
both short- and long-time ranges. The emphasis on analytical solutions arises from the sensitivity of fractionalorder
models to variations in the derivative order, and the implementation of numerical methods does not always
allow for reducing the discretization step. Literature analysis indicates that even slight changes in the fractional
derivative order can lead to significant differences in results. Therefore, it is crucial to obtain the results in an
analytical form that will allow us to adapt and optimize them in relation to real information about the process
being modeled.