Search
23 articles for “theorems”
-
Density Functional Theory (DFT): Understanding and Quantifying Molecular Structure of 2-D Materials
Abstract: Density Functional Theory (DFT) has emerged as a cornerstone in computational chemistry and materials science, offering a powerful framework for predicting electronic structures and properties of atoms, molecules, and solids. By focusing on electron density rather than wave functions, DFT simplifies the many-body problem through approximations like the local density approximation (LDA) and generalized-gradient approximations (GGAs). The Hohenberg-Kohn theorems establish the theoretical foundation, proving that ground-state properties are uniquely determined …
Published in Journal of Microelectronics and Solid State Devices · Vol. 12, Issue 2, 2025 · pp. 33–40 Read article
-
An Analytical Review of Machine Learning Methodologies
Abstract: Machine Learning (ML) is a dynamic and rapidly developing area of computer science that enables the system to learn from data and improve its performance without clear programs. Rooted in statistical theory and computer algorithms, ML has become a major technology that progresses in artificial intelligence. It strengthens the detection of the recommendations and speech for extensive applications from autonomous vehicles and medical diagnoses. This paper has reviewed the basics …
Published in Recent Trends in Mathematics · Vol. 3, Issue 1, 2026 · pp. 13–21 Read article
-
Research Paper A Review of Symmetry in Mechanical Systems: Theoretical Systems Foundations and Engineering Applications
Abstract: In mechanical system analysis and design, symmetry is of mechanical systems. This article examines the idea of symmetry in mechanical systems, exploring its mathematical foundations (such as Lie algebras and group theory) and how these ideas help explain the behavior, stability, and control of the system. We explore the applications of symmetry in a range of mechanical systems, from basic mechanical connections to intricate multi-body dynamics, emphasizing the benefits of …
Published in Emerging Trends in Symmetry · Vol. 1, Issue 1, 2025 · pp. 15–19 Read article