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.
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.
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
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).
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
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
A generalized mathematical model of the process of extraction of target components from yeast biomass (carbohydrates, lipids and ribonucleic acids)has been developed on the basis of experimental studies. It is substantiated that the theoretical provisions are satisfactorily consistent with the experimental results of the research. The obtained model allows to describe with sufficient accuracy the kinetics of extraction of carbohydrates, lipids and ribonucleic acids from yeast biomass, to determine the yield of the extract and to predict the optimal time of extraction
Mobile robotic systems with vibratory drives are becoming increasingly popular in various fields of industry and medicine. This article is dedicated to the study of the dynamic behavior of a mobile capsule-type robot equipped with an imbalanced vibration exciter. The research methodology involves constructing a simplified dynamic diagram of the robot's mechanical system, using Lagrange's equations of the second kind to describe its motion, and solving the obtained system of differential equations using numerical methods integrated into the Wolfram Mathematica software
The design of a highly efficient vibrating machine for dry cleaning root vegetables of various types, shapes, and sizes has been developed. First, a schematic diagram of the machine was built, containing all the future machine's main components. A nonlinear mathematical model was constructed to describe its dynamics during its operation to determine the future machine's optimal geometric, kinematic, and power parameters. The mathematical model is based on the apparatus of asymptotic methods of nonlinear mechanics and Lagrange's equations.
Six-phase induction machines offer several advantages over traditional three-phase machines, including higher levels of electromechanical compatibility with loads, energy efficiency, and fault tolerance.
This article presents an analysis of the impact of harmonics in the winding distribution function in the stator slots and the harmonics of the machine’s supply on its electromechanical compatibility with the load during a single-phase failure.