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14 articles for “Algebraic Structures”
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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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Algebraic Foundations of Generalized Signal Processing: A Unified Approach Across Domains
Abstract: Using the techniques of algebra, notably polynomial algebras and modules, algebraic signal processing (ASP) is a contemporary, abstract framework that generalizes conventional signal processing— including Fourier analysis, filtering, and convolution. The notion is to use algebraic structures to explain signals, systems, and transformations such that ideas may be understood and generalized across many domains, including time, space, graph, or group. A unifying theoretical framework called ASP generalizes classical signal processing …
Published in Current Trends in Signal Processing · Vol. 15, Issue 3, 2025 · pp. 33–44 Read article
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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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Algebraic Geometry and Mathematical Physics: An Interdisciplinary Exploration
Abstract: Algebraic geometry, a branch of mathematics that studies solutions to systems of polynomial equations, has profound implications in mathematical physics. This paper delves into the intersection of algebraic geometry and mathematical physics, exploring how concepts from algebraic geometry illuminate various physical phenomena. We examine applications in string theory, quantum field theory, and positive geometry, highlighting the role of algebraic structures in understanding the fabric of the universe.
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 3, 2025 · pp. 26–29 Read article
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Intuitionistic Fuzzy Hypergraph Laplacians and Dominating Transversals for Resilient Discrete Network Design
Abstract: This manuscript develops a discrete mathematical framework for resilience analysis on networks whose interactions are polyadic, uncertain, and partially conflicting. Classical graphs compress multi-way coordination into pairwise edges, while ordinary fuzzy graphs often ignore the non-membership information that becomes critical in emergency logistics, infrastructure interdependence, and cyberphysical coordination. We therefore formulate an intuitionistic fuzzy hypergraph in which each vertex hyperedge incidence carries membership, non-membership, and hesitation, and we construct a …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 13, Issue 2, 2026 · pp. 15–21 Read article
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Spectral Intuitionistic Fuzzy Hypergraph Operators and Dominance Kernels for Resilient Discrete Network Design
Abstract: A new discrete-mathematical framework is developed for resilient network design on intuitionistic fuzzy hypergraphs, where uncertainty is explicitly represented through membership, non-membership, and hesitation degrees associated with both vertices and hyperedges. These three components are systematically integrated into an effective incidence operator that captures the underlying uncertain relationships within complex hypergraph structures. Based on this operator, both un-normalised and normalized Laplacian matrices are formulated to characterize the spectral properties and …
Published in Recent Trends in Mathematics · Vol. 3, Issue 2, 2026 · pp. 41–48 Read article
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Idempotent Semiring Path Algebras and Fuzzy Dominance Automata for Multi-State Communication Reliability
Abstract: A semiring-based theory is proposed for multi-state communication reliability with fuzzy dominance constraints. Links are weighted in the max-product semiring, while nodes carry dominance coefficients and operating states that modulate admissible transitions in a weighted automaton. The paper derives semiring matrix products, Kleene closures, fixed point equations, congestion-regularized path scores, and reliability inequalities. A fuzzy dominance automaton is introduced so that route selection depends not only on link reliability but …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 13, Issue 2, 2026 · pp. 07–14 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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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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Microvita as a Fermi-Boson Hybrid Quantum Excitation: A Statistical Pathway Toward Unified Physics, Chemistry, and Biological Organization
Abstract: This article reformulates Microvita as a hybrid quantum excitation that interpolates continuously between fermionic and bosonic statistical behavior. A generalized operator algebra, a dynamical statistical order parameter, and a Lorentz-covariant field equation are used to frame Microvita as an effective unification scheme rather than a mere philosophical construct. The formalism predicts renormalization-group flow between infrared fermionic and ultraviolet bosonic limits, while numerical profiles suggest vacuum-energy smoothing and topological-defect suppression in …
Published in Journal of Modern Chemistry & Chemical Technology · Vol. 17, Issue 1, 2026 · pp. 115–122 Read article
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The Evolution and Impact of Numbers: From Ancient Tallies to Quantum Computing: Review Article on Numbers
Abstract: Numbers are among the most fundamental constructs in human civilization, serving as the backbone of mathematics, science, technology, and virtually every aspect of daily life. They represent not only quantities and measures but also relationships, structures, and patterns that underpin the fabric of human understanding. From the earliest tallies etched on bones by prehistoric humans to the sophisticated numerical systems embedded in today’s artificial intelligence and quantum computing, the evolution …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 3, 2025 · pp. 15–19 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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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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A Method of Mesh Deformation for Flow Analysis Around Oscillating Bodies
Abstract: In general, high-speed rotating machines are subjected to complex phenomena due to various reasons, such as increased noise and strong vibration due to dynamic unbalance, which affect the dynamic motion of rotating machines and are necessarily a problem to overcome. Therefore, it is necessary to have a mathematical model to simulate it, and a strong tool to solve the constructed model. Using fluid-structure coupling techniques, which are currently a powerful …
Published in Journal of Experimental & Applied Mechanics · Vol. 16, Issue 2, 2025 · pp. 35–42 Read article