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9 articles for “Applications of algebraic equations”
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Numerical Solution of Ordinary Differential Equation and Solution of Partial Differential Equation
Abstract: This research paper explores the fundamental role of various mathematical concepts in engineering and scientific fields like aerospace engineering, materials science, software development, and the energy sector. We delve into the applications of solving algebraic and transcendental equations, finite difference interpolation, numerical methods, solutions to ordinary differential equations (ODEs), and numerical solutions to partial differential equations (PDEs). By examining their applications in these diverse fields, we illustrate the critical importance …
Published in Journal of Aerospace Engineering & Technology · Vol. 14, Issue 3, 2024 · pp. 12–20 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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Time and Frequency Response of Non-uniform Overhead Lines Under Corona
Abstract: This study presents an efficient and direct technique for determining both the time and frequency responses of non-uniform overhead power transmission lines operating under corona conditions. The assumed-line's non-uniformity is due to the conductors’ sag. Expressions will be presented for the location-dependent line surge impedance and the unevenly distributed lines’ electrical parameters. The analysis starts with solving the relevant system of differential and algebraic equations, subject to the boundary conditions. …
Published in International Journal of Electrical Machine Analysis and Design · Vol. 2, Issue 2, 2024 · pp. 25–33 Read article
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Electromagnetic Transients in Strongly Non-Uniform Overhead High Voltage Lines
Abstract: This paper addresses the electromagnetic transients in high strongly non-uniform overhead voltage lines. For their simulation, a novel Laplace-domain approach has been introduced. The voltage and current patterns in terms of location and complex frequency are determined by a set of simultaneous algebraic and partial differential equations. To solve them numerically, an effective Mathematica code is proposed. By contrasting the outcomes of their application to multiple case studies with those …
Published in Journal of Power Electronics and Power Systems · Vol. 15, Issue 1, 2025 · pp. 30–36 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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Microvita: A New Hybrid Particle Bridging the Fermionic and Bosonic Domains in Particle Physics
Abstract: In particle physics, the established classification of particles into fermions and bosons—obeying Fermi-Dirac and Bose-Einstein statistics, respectively—has shaped theoretical and experimental frameworks for nearly a century. This study introduces 'Microvita', a novel theoretical particle that exhibits hybrid characteristics modulated by a continuous parameter α ∈ [0,1]. Through this parameter, Microvita interpolates between bosonic and fermionic behavior in terms of spin, statistical distributions, and operator algebra. We explore the foundational algebra …
Published in Research & Reviews : Journal of Physics · Vol. 15, Issue 1, 2026 · pp. 14–27 Read article
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Strategic Solutions: How Mathematics Reshapes Industrial Landscapes
Abstract: One of the earliest and most fundamental fields of the physical sciences is mathematics. It has a significant impact on industrial enterprises' bottom lines and enhances their performance in the current data-driven market. One subfield of applied mathematics is industrial mathematics. It concentrates on issues that arise in the industry and seeks answers that are pertinent to the sector. The use of mathematical models and techniques to diverse industry difficulties …
Published in International Journal of Industrial and Product Design Engineering · Vol. 2, Issue 1, 2024 · pp. 16–23 Read article
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Direct Determination of the Frequency-Dependent Transmission Constants of Non-Uniform Two-Port Networks
Abstract: Due to space constraints and the expansion of electricity networks, transmission lines that cross close to one another are now commonplace. Power networks also commonly install higher operational voltage lines that share transmission corridors with lower voltage lines. Overhead transmission lines are the primary method for transmitting electrical energy across vast distances. This paper presents an efficient and direct technique for identifying the four frequency-dependent ABCD transmission constants of arbitrary …
Published in Journal of Power Electronics and Power Systems · Vol. 14, Issue 3, 2024 · pp. 1–8 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