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23 articles for “Algebraic Method”
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Comparing Graphical and Algebraic Methods in Solving Linear Programming Problems
Abstract: Linear Programming (LP) is a fundamental optimization technique widely employed across engineering, manufacturing, transportation, finance, healthcare, and other industrial sectors to support effective resource allocation and informed decision- making. Among the various solution techniques, the graphical and algebraic methods remain the two most fundamental approaches, each offering distinct advantages depending on the complexity and dimensionality of the optimization problem. This paper presents a comprehensive comparative study of these methods by …
Published in Journal of Production Research & Management · Vol. 16, Issue 2, 2026 · pp. 33–43 Read article
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Parameter Identification of Vibrating MIMO Mass-Spring-Damper Mechanical Systems with Coulomb Friction
Abstract: This study presents a time-domain method for identifying parameters in multi-degree-of-freedom (DOF) linear mass-spring-damper systems that include Coulomb friction, where the friction coefficient varies within a limited range, using measurements of position and control force. For mass identification in single-degree-of-freedom (DOF) vibrating mechanical systems with stiffness and no damping but Coulomb friction, the friction term is eliminated by first derivative processing. In addition, the identification of the coefficient of friction …
Published in International Journal of Mechanical Dynamics and Systems Analysis · Vol. 3, Issue 1, 2025 · pp. 20–34 Read article
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Implementation of CDM Based PID Controller for a Stable and Double Integrating Process
Abstract: In this paper an attempt has been made to design a PID controller for a double integrating process and shell and tube heat exchanger process based on coefficient diagram method (CDM). Ball and beam system (Linear process) and the heat exchanger systems (Non-linear process) are widely used as a bench mark control setup for evaluating various control strategies. Many PID controller designs are developed for stable system, however it is …
Published in Journal of Mechatronics and Automation · Vol. 2, Issue 2, 2015 · pp. 15–22 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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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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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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Stream Cipher Based Modified Espresso Algorithm for 5G Communication
Abstract: AbstractTo meet the requirement of 5G communication, Dubrova and Hell design Espresso, which is a stream cipher. Espresso uses 128-bit key, 96-bit initial vector (IV) and a 6-degree Boolean function as its output function. Jia-Min and Wen-Feng showed that algebraic attack is possible with time complexity being O(2(66.86)). In this paper, we present a methodology for the modification of Espresso with reformed Galois configuration of 256-bit Nonlinear Feedback Shift Registers …
Published in Journal of Computer Technology & Applications · Vol. 10, Issue 1, 2019 · pp. 32–40 Read article
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Exploring the Studies of Mathematics: Foundations, Evolution, Pedagogy and Prospects
Abstract: Mathematics, often regarded as the universal language of science and logic, has evolved through centuries as both a tool for understanding the natural world and a discipline of abstract reasoning. This study explores the multifaceted dimensions of mathematics by examining its foundations, historical evolution, pedagogical approaches, and future prospects. The foundational aspects trace back to ancient civilizations—Babylonian arithmetic, Greek geometry, and Indian and Arabic contributions to algebra— highlighting how early …
Published in Recent Trends in Mathematics · Vol. 2, Issue 2, 2025 · pp. 25–31 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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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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On The Time-Domain Analysis of the Electromagnetic Transients in High-Voltage Line Towers
Abstract: This paper presents an efficient and direct method for the time-domain transient analysis of high voltage power line towers. A Mathematica-based numerical solution of the governing set of simultaneous partial differential and algebraic equations is proposed. The results of a corresponding computer code are presented and discussed. A comparison with other more sophisticated analytical time-and Laplace-domain approaches is presented. In addition to the possible use of the EMTP transients’ program, …
Published in Journal of Nuclear Engineering & Technology · Vol. 13, Issue 2, 2023 · pp. 12–20 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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Modelling & Simulation Of Fuzzy Logic Based Controller For Energy Storage System
Abstract: AbstractThe problem of transient stability in multimachine model is a semi-infinite optimization problem for nonlinear phenomenon in network of energy storage system. As this involves several sets of differential equations and algebraic constraints; therefore the application of several mathematical programming techniques won’t be enough to solve the problem. In the past several ad hoc algorithms had been proposed. This study presents a new methodology to restore the transient stability by …
Published in Journal of Electronic Design Technology · Vol. 8, Issue 2, 2017 · pp. 9–15 Read article
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A Review Study on CPU-Optimized Parameter-Efficient Fine-Tuning for Large Language Models to Increase Accuracy Using LoRA
Abstract: The fast proliferation of large language models (LLMs) has increased the need to optimize the process of fine-tuning, but the existing workflows that require a graphics processing unit (GPU) are still expensive, intensive, and unavailable to most researchers. This paper is driven by the desire to have a more cost-efficient and democratized version by examining a CPU-efficient implementation of parameter-efficient fine-tuning (PEFT) based on low-rank adaptation (LoRA). The major purpose …
Published in Recent Trends in Parallel Computing · Vol. 13, Issue 1, 2026 · pp. 32–38 Read article
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Analysis of Six-Pulse Bridge Circuits Including Zener and Semiconductor Diodes – Part Two
Abstract: The present study offers a generic method for simulating and modelling six-pulse rectifier bridge circuits in the time domain. These circuits can include Zener and/or semi-conductor type diodes or even a mixture of them. The governing system of simultaneous algebraic and differential equations are listed and solved numerically using a computer code written in Mathematica. The flexibly written program can handle voltage sources of any time waveform, frequency or internal …
Published in Journal of VLSI Design Tools and Technology · Vol. 12, Issue 2, 2022 · pp. 13–21 Read article
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Vedic Mathematics in Algebra Techniques, and Problem-Solving Benefits
Abstract: The sixteen Sutras and thirteen Sub-Sutras form the foundation of Vedic algebraic mathematics. This article discusses the Buddha's teachings and shows how to use them to solve algebra problems. Unified mathematics is defined as a state where processes can refer to and understand each other. Vedic formulas, which can be utilized for addition, subtraction, division, and other mathematical operations, are taught with examples. Vedic mathematics not only saves time, but …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 1, 2025 · pp. 23–28 Read article
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A Contribution to the Frequency and Transient Analysis of High Voltage Bushings
Abstract: The paper suggests a method for determining the frequency characteristics and transient response of capacitively graded high voltage bushings. It is based on an s-domain circuit model that describes the grading conducting foils and the insulating layers. In most cases, they are of different axial lengths. A system of simultaneous differential and algebraic equations is derived taking these differences into account. Its closed-form solution, subject to the boundary conditions, can …
Published in Journal of Power Electronics and Power Systems · Vol. 9, Issue 1, 2019 · pp. 15–26 Read article
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Spice Circuits for Optic Cellular Receiver Simulations
Abstract: A circuit-theoretic approach to the generation of equivalent circuit models of optoelectronic and integrated photonic receiver applications is presented, especially optical cellular receiver systems. In a conventional circuit, the parameters of nano-inductance, nano-capacitance, impedance and scattering (S) parameters can be effectively applied to the analog equivalent representation of a conventional circuit. In a fiber-optic system, those parameters can be used in an integrated photonics and optoelectronic and nanoelectronic circuit as …
Published in Trends in Opto-electro & Optical Communication · Vol. 16, Issue 2, 2026 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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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