mathematical modeling

Solving inverse problem of the potential theory by the cascade algorithm and the near-boundary element method

The effectiveness of the indirect method of near-boundary elements (as a variant of the method of boundary integral equations) for constructing numerical solutions of direct and inverse problems of potential theory in a limited piecewise homogeneous object of arbitrary shape whose components are in ideal contact is substantiated.  The integral representation of the solution of the direct problem is constructed using the fundamental solution of the Laplace equation for the plane.  To find the intensities of unknown sources introduced in the near-boundary elements, the co

Kinetostatic Analysis of the Propulsion System for a Mobile in-pipe Inspection Robot

Problem statement. The structural integrity of extensive pipeline networks is critical for economic and environmental safety, demanding reliable inspection methods. Mobile In-Pipe Inspection Robots (IPIRs) offer a non- disruptive solution; however, the design of their propulsion systems for confined and complex environments remains challenging. Existing analytical frameworks often exhibit a disconnect between kinematic modeling (motion planning) and force analysis (stability and traction), particularly for advanced hybrid locomotion strategies.

TECHNICAL ASSESSMENT OF DISTRICT HEATING PIPELINES UNDER VARIABLE THERMAL LOADS WITH CONSIDERATION OF INSTALLATION DEFORMATIONS

This study presents a methodology for assessing the technical condition of district heating pipelines under high wear, variable thermal loads, and limited modernization resources. Emphasis is placed on installation defects, cyclic temperature and pressure fluctuations, and corrosion-induced degradation. A case study of a return water pipeline in Kremenchuk, featuring a 3° installation misalignment and 10 cm flange displacement, demonstrated stresses of 220–250 MPa, exceeding the steel’s yield strength in critical zones.

Consideration of induced polarization effects in solving inverse problems of geoelectrical sounding

The paper aims to develop an algorithm for identifying the physical (polarizability and resistivity) and geometric (center of mass, orientation, and dimensions) characteristics of local heterogeneities. This is achieved by analyzing induced polarization (IP) potential field data measured at the boundary of the object, using the indirect near-boundary element method. Methodology. A piecewise homogeneous half-plane was chosen as a model of the Earth's crust, where the components are in non-ideal contact.

Mathematical Modeling of Hardware-Optical Distortions in Aerial Image Data

This study presents the formalization of mathematical models of hardware-optical distortions in digital images captured during aerial photography from onboard systems of Unmanned Aerial Vehicles (UAVs). These distortions significantly affect the accuracy and reliability of automated object detection and classification algorithms in complex outdoor environments.

Employing Discrete Wavelet Transform Methods and Python Libraries to Derive Mathematical Models Of Environmental Data

The article addresses the urgent problem of computer modeling of large-scale environmental monitoring datasets using discrete wavelet transforms. The research object consists of time series of harmful pollutant concentrations in the atmosphere, including nitrogen oxides, benzene, and sulfur dioxide, collected from automated stations in Central and Eastern Europe. The input data are characterized by high stochasticity, noise, missing values, and temporal shifts, which significantly com- plicate the extraction of trends and patterns required for forecasting.

Self-supervised contrastive learning for fall detection using 3D vision-based body articulation

This paper presents a mathematical modeling approach for fall detection using a 3D vision-based contrastive learning framework.  Traditional models struggle with high false positives and poor generalization across environments.  To address this, we propose a self-supervised contrastive learning model that maps 3D skeletal motion sequences into a low-dimensional embedding space, optimizing feature separation between falls and non-falls.  Our method employs spatial-temporal modeling and a contrastive loss function based on cosine similarity to enhance discrimination.  By

MATHEMATICAL FORECASTING OF SPATIO-TEMPORAL DYNAMICS OF HYDROECOLOGICAL PARAMETERS OF RIVER ECOSYSTEMS USING INTEGRALLY-MODIFIED STREETER-PHELPS MODEL

This study presents a comprehensive mathematical forecasting approach for hydroecological parameters in small urban river systems using an integrally-modified Streeter-Phelps model. The research focuses on the Kamyanka River, a small tributary within Zhytomyr city, Ukraine, which experiences significant anthropogenic influence from urban development. The modified model incorporates advanced computational algorithms implemented in Python programming environment to predict dissolved oxygen concentration and biochemical oxygen demand dynamics over a 25-year period (2020-2045).

Mathematical modeling of multi-label classification of job descriptions using transformer-based neural networks

This article presents the mathematical modeling of the multi-label classification task of job description texts aimed at the automatic detection of working conditions and social benefits, which can enhance communication efficiency between employers and job seekers.  The proposed approach is based on the use of the transformer-based BERT neural network, pre-trained on a multilingual corpus.  The dataset was constructed by collecting job postings from the three largest Ukrainian job search platforms: Work.ua, Robota.ua, and Jooble.org.  The collected texts were augmented

Drying of cappilary-porous materials in an external constant electric field

In the article, the mathematical model for the drying process of a porous layer subjected to an external electric field is developed considering the coupled effects of heat, mass, and charge transport.  A system of algebraic equations is obtained to describe the drying dynamics, incorporating key physical parameters such as boundary layer thickness, temperature, and electric field intensity.  The model is validated against experimental data, demonstrating its accuracy in predicting moisture distribution over time in a porous materials under the action of constant electr