All articles
13 articles
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Representation-Theoretic Symmetry Reduction and Fuzzy-Grey Optimization of Modular Vibration Systems
Abstract: This paper presents a representation-theoretic framework for symmetry-aware vibration control in modular structural systems. Exploiting cyclic symmetry, the mass, damping, and stiffness operators are block-diagonalised into irreducible representations, reducing the full structural dynamics to a collection of lower-dimensional modal subsystems. This decomposition provides both computational efficiency and a rigorous mathematical description of symmetry-preserving dynamic behaviour. To account for imperfections arising in practical implementations, near-symmetry defects in stiffness and damping are …
Published in Emerging Trends in Symmetry · Vol. 2, Issue 1, 2026 · pp. 22–30 Read article
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Quantum-Fuzzy Tensor Operators for Multi-Qubit Conjunction, Disjunction, and Symmetry-Preserving State Discrimination
Abstract: The integration of fuzzy logic and quantum information theory raises a fundamental mathematical question: how can degrees of truth be encoded in multi-qubit amplitudes while preserving the unitary dynamics and symmetry structure of quantum state spaces? This paper develops a tensor-operator framework for implementing quantum-fuzzy logical operations on finite qubit registers. Fuzzy truth values are represented by normalized quantum amplitude pairs, enabling logical information to be embedded directly into quantum …
Published in Emerging Trends in Symmetry · Vol. 2, Issue 1, 2026 · pp. 16–21 Read article
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Quantum-Fuzzy Tensor Operators and Uncertainty-Band Bifurcation for Symmetry-Preserving State Discrimination
Abstract: A tensor-operator framework is developed for fuzzy conjunction, fuzzy disjunction, and symmetry-preserving state discrimination in multi-qubit quantum systems. In this formulation, fuzzy membership and non-membership degrees are represented through expectations of effect operators acting on density matrices, providing a natural bridge between fuzzy logic and quantum measurement theory. Conjunction and disjunction operations are extended to the quantum domain via tensorised channels, constructed using projective measurements and unitary transformations, enabling logical …
Published in Emerging Trends in Symmetry · Vol. 2, Issue 1, 2026 · pp. 08–15 Read article
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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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Entropy, Symmetry, and Data Fusion: Emerging Methods in Multi-Objective Decision- Making and Smart Systems
Abstract: In the era of intelligent technologies and data-driven systems, multi-objective decision-making (MODM) has become an essential aspect of managing complex environments such as smart cities, autonomous systems, and cyber-physical networks. As decision-making scenarios become increasingly dynamic and uncertain, there is a growing need for advanced methodologies that can handle diverse objectives, conflicting constraints, and incomplete information. This review highlights the emerging role of entropy, symmetry, and data fusion as foundational …
Published in Emerging Trends in Symmetry · Vol. 1, Issue 2, 2025 · pp. 44–49 Read article
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The Role of Symmetry in Topological Insulators and Superconductors
Abstract: Topological insulators and superconductors constitute a class of quantum materials characterized by insulating bulks and symmetry-protected conducting boundaries. Symmetry principles, notably time-reversal (TRS), particle-hole (PHS), and chiral symmetry, play a fundamental role in determining the topological phases and their classification within the Altland-Zirnbauer scheme. TRS protects gapless surface states in topological insulators, while PHS stabilizes Majorana modes in topological superconductors. Symmetry-protected topology extends this framework by considering partial symmetry breaking, …
Published in Emerging Trends in Symmetry · Vol. 1, Issue 2, 2025 · pp. 01–05 Read article
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Symmetry Breaking in Mathematical Models: Bifurcation, Chaos, and Pattern Formation
Abstract: Symmetry breaking serves as a central organizing principle in the understanding of nonlinear systems across physics, biology, chemistry, and engineering. When a system transitions from a symmetric state to an asymmetric configuration, it often signals the onset of new structures, dynamic behaviors, or even chaotic regimes. This review explores symmetry breaking from the theoretical and mathematical perspectives of bifurcation theory, chaos theory, and pattern formation. We discuss how small parameter …
Published in Emerging Trends in Symmetry · Vol. 1, Issue 2, 2025 · pp. 25–30 Read article
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Symmetry Principles in Digital Twin Systems: Modeling, Integration, and Applications
Abstract: This systematic review comprehensively examines the burgeoning field of Digital Twin (DT) technology, analyzing its current state, diverse applications, and future trajectory. Through a rigorous methodology involving a systematic search of academic databases and relevant industry literature, this review synthesizes findings across a spectrum of disciplines. We identify the core components and underlying principles of DTs, distinguishing them from traditional simulation models by their dynamic, realtime data integration and bi-directional …
Published in Emerging Trends in Symmetry · Vol. 1, Issue 2, 2025 · pp. 06–24 Read article
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Emerging Trends in Interdisciplinary Perspectives and Future Frontiers in Modern Symmetry
Abstract: Symmetry, long recognized as a cornerstone of the natural sciences, has increasingly found relevance across a variety of disciplines, from physics and mathematics to economics, architecture, and systems theory. This interdisciplinary review explores the expanding role of symmetry as a conceptual and analytical tool, highlighting its applications in diverse fields. In classical and quantum physics, symmetry principles form the foundation for conservation laws, particle interactions, and field equations. In economics …
Published in Emerging Trends in Symmetry · Vol. 1, Issue 1, 2025 · pp. 26–30 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
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Differential Equations in Quantum Mechanics and Schrödinger Equation
Abstract: In this study we investigate how differential equations play a role in quantum mechanics, focusing mainly on the role of a prominent one, Schrödinger's equation, which governs the behavior of quantum systems. In time two the mathematical picture of the wave nature of particles at quantum scales is provided, and the resulting equations are Schrödinger's equation, both in its time dependent as well as in its time independent form. The …
Published in Emerging Trends in Symmetry · Vol. 1, Issue 1, 2025 · pp. 15–25 Read article
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The Essential Importance of Tactile Experience in Universal Design
Abstract: This research paper explores the synergy between tactile experience and Universal Design, investigating how integrating tactile elements enriches inclusivity, accessibility, and usability. Through a comprehensive literature review, it examines existing studies on Universal Design, tactile perception, and touch's role in design. The paper introduces theoretical frameworks to support the crucial link between tactile experience and inclusivity. It delves into the physiological and psychological aspects of tactile perception, highlighting how tactile …
Published in Emerging Trends in Symmetry · Vol. 1, Issue 1, 2025 · pp. 01–14 Read article