Group Theory
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Group-Theoretic Symmetry Indices for Modular Building Layouts under Seismic Load Redistribution
Abstract: Symmetry in modular buildings operates simultaneously as an architectural language, a structural regularizer, and a computational design variable. This paper develops a group-theoretic framework for evaluating and optimizing plan symmetry in modular buildings subjected to seismic load redistribution. The building layout is modeled as a finite occupancy–stiffness field defined on a rectangular lattice, where each module encodes both mass and stiffness contributions. Planar reflections and quarter-turn rotations are represented as …
Published in Emerging Trends in Symmetry · Vol. 2, Issue 1, 2026 · pp. 01–07 Read article
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Algebraic Foundations of AES (Advanced Encryption Standard): Group Theory and Finite Field Applications in Symmetric Cryptography
Abstract: This paper presents a mathematical study of symmetric cryptographic algorithms, with a particular emphasis on the Advanced Encryption Standard (AES), which is one of the most widely used encryption schemes in modern security applications. The study highlights how abstract mathematical frameworks such as group theory, finite fields, and vector space concepts provide the foundation for the design, implementation, and analysis of AES. By approaching the algorithm from a mathematical perspective, …
Published in Recent Trends in Mathematics · Vol. 2, Issue 1, 2025 · pp. 12–16 Read article
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Study of Algebraic Structures in Discrete Mathematics and Its Applications
Abstract: Algebraic structures such as groups, rings, fields, semi groups, and lattices form the foundational framework of discrete mathematics. These structures are defined by specific sets and operations that follow algebraic laws, enabling a systematic approach to problem-solving in various domains. This paper explores the theoretical principles of these algebraic systems and highlights their vital role in computer science, cryptography, automata theory, coding theory, and software engineering. By examining their properties …
Published in Emerging Trends in Symmetry · Vol. 1, Issue 1, 2025 · pp. 35–40 Read article
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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