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132 articles for “Mathematics studies”
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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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Comparing Results of a Study on Mathematics Instruction in English at Diploma College in Solapur District
Abstract: Study programmes at the Diploma College in Solapur include mathematics courses, which are instructed in English. Comparing the educational outcomes in the Mathematics study course with the English language of instruction is the primary objective of the paper. We concentrated on the students' proficiency in solving specific linear algebra and mathematical analysis problems. The first-year students in the Diploma study programme in Diploma College, Solapur made up the research sample. …
Published in Recent Trends in Mathematics · Vol. 2, Issue 2, 2025 · pp. 12–18 Read article
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Studies of Mathematics: A Review of Research Trends, Themes and Implications
Abstract: This review examines contemporary research trends, thematic developments, and emerging implications within the field of mathematics education and mathematical studies. Drawing on a synthesis of recent scholarly literature, it explores how mathematics as both a discipline and a pedagogical practice continues to evolve in response to technological advancements, interdisciplinary applications, and changing educational paradigms. Major research trends reveal a growing emphasis on problem-based learning, mathematical modeling, and the integration of …
Published in Recent Trends in Mathematics · Vol. 2, Issue 2, 2025 · pp. 19–24 Read article
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Analyzing The Electromagnetic Transients and Corona Performance of Long Overhead Lines with Multiple Tower Spans
Abstract: This paper addresses the simulation of the electromagnetic transients developed in an important class of non-uniform high voltage power lines. The resulting information is of paramount importance for the proper planning, design, operation and protection of electric power networks. It deals particularly with long overhead high voltage transmission lines composed of several tower spans which are connected in cascade. The presented approach considers eventually existing localized corona discharges at some …
Published in International Journal of Electrical and Communication Engineering Technology · Vol. 3, Issue 1, 2025 · pp. 35–44 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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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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Mathematical Approaches to Nonlinear Oscillatory Systems with Damping: Exact and Approximate Solutions
Abstract: The study of nonlinear oscillatory systems with damping is a key area of research in applied mathematics, particularly in the context of dynamical systems, stability analysis, and bifurcation theory. These systems, described by second-order nonlinear differential equations, exhibit a rich variety of behaviors, including periodic, quasi-periodic, and chaotic motions. The introduction of damping—representing energy dissipation—adds a layer of complexity, making the analytical and numerical solution of such systems a challenging …
Published in Recent Trends in Mathematics · Vol. 2, Issue 2, 2025 · pp. 7–11 Read article
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Exploring the Influence of Machining Parameters on Geometric Form and Orientation Controls (23 Design)
Abstract: This work explores the influence of machining parameters using on geometric form controls flatness and straightness as well as orientation control parallelism using an aluminum 6061 workpiece. Due to its good strength, machinability and cost- effectiveness, aluminum 6061 is widely used. In this experimental work, full factorial design is used and each factor has two levels. The response parameters chosen include flatness, straightness, and parallelism, which govern the form and …
Published in Journal of Experimental & Applied Mechanics · Vol. 16, Issue 1, 2025 · pp. 10–16 Read article
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Experimental and Statical Analysis of Glass Fibre Reinforced Concrete
Abstract: During the most recent couple of decades, with the chance of fortifying the solid with fiber support to an incredible preferred position, the solid development field has encountered an expanded consideration. Various strands utilized are steel, manufactured, glass and common filaments, a portion of the planned advantages of filaments in concrete are improved split control and the chance of planning progressively thin structures. Glass fibre is a vital ingredient used …
Published in Journal of Polymer & Composites · Vol. 12, Issue 3, 2024 · pp. 266–273 Read article
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Electromagnetic Transients in Compensated Overhead Lines with Multiple Tower Spans
Abstract: This paper addresses the analysis of the electromagnetic transients developed in an important class of non-uniform high-voltage power lines. It deals particularly with compensated long overhead high- voltage transmission lines composed of several tower spans, which are connected in cascade. The derived mathematical model leads to a system composed of simultaneous partial differential and algebraic equations, which can be solved numerically in terms of parametric functions using the software Mathematica’s …
Published in Trends in Electrical Engineering · Vol. 15, Issue 2, 2025 · pp. 1–9 Read article
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Electromagnetic Transients in Compensated Power Lines- Revisited: New Approach and Case Studies
Abstract: This paper addresses the simulation of the electromagnetic transients developed in high voltage power lines, which are initiated by lightning discharges. The analysis can handle both individual and simultaneous series inductive and shunt capacitive compensation types. The sizes and locations of the compensating elements are included in the analysis. The derived Laplace s-domain mathematical model applies the concept of the ABCD transmission constants representing equivalent two-port networks. The resulting currents …
Published in International Journal of Electrical and Communication Engineering Technology · Vol. 2, Issue 1, 2024 · pp. 19–26 Read article
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A Study of Fixed-Point and Best Proximity Point
Abstract: Fixed-point theory plays a fundamental role in nonlinear analysis and has significant applications in optimization, differential equations, and applied mathematics. This study investigates the existence and properties of fixed points and best proximity points for various classes of mappings defined on metric and normed spaces. While fixed-point results guarantee the existence of a point that remains invariant under a given mapping, such points may not exist when the mapping is …
Published in Recent Trends in Mathematics · Vol. 3, Issue 1, 2026 · pp. 28–39 Read article
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The Role of Mathematical Reasoning in Legal Analysis: Bridging Two Disciplines
Abstract: This research paper explores the integration of mathematical reasoning into legal analysis, emphasizing the inherent similarities between the two disciplines. Both fields rely on logical structures, such as deductive reasoning, inductive reasoning, and other formal methods of thought. By examining these parallels, the paper reveals the nascent but growing interaction between mathematics and law, uncovering how the organizational schemes that underpin mathematical principles can enhance legal argumentation, decision-making, and analysis. …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 3, 2024 · pp. 1–5 Read article
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Novel Laplace-domain Approach to the Electromagnetic Transients in Compensated High Voltage Power Lines
Abstract: This paper addresses the simulation of the electromagnetic transients developed in high voltage power lines, which are initiated by lightning discharges. The analysis can handle both individual and simultaneous series inductive and shunt capacitive compensation types. The sizes and locations of the compensating elements are included in the analysis. The derived Laplace s-domain mathematical model applies the concept of the ABCD transmission constants representing equivalent two-port networks. Applying the relations …
Published in International Journal of Electrical Machine Analysis and Design · Vol. 2, Issue 1, 2024 · pp. 15–21 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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The Contribution of Mathematics to Make Developed India
Abstract: This research paper explores the significant contributions of mathematics to the development of India, tracing its influence from ancient innovations to modern applications across diverse sectors. India has a long-standing mathematical tradition, with foundational achievements such as the invention of zero, the decimal system, and advancements in algebra, trigonometry, and geometry, which profoundly shaped global knowledge systems. These early contributions established India as a pioneering hub of mathematical thought and …
Published in Research & Reviews : Journal of Statistics · Vol. 14, Issue 3, 2025 · pp. 08–15 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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Advancements in Windmill Technology: Comprehensive Research on Conventional and Piezoelectric Windmills
Abstract: This research delves into the structural components and mechanisms of conventional wind turbines, emphasizing blade material considerations for optimal performance. It introduces a paradigm shift by exploring the use of epoxy resin and piezoelectric materials, specifically zinc oxide, in wind turbine blades. The study presents mathematical models and conducts a comparative analysis between conventional and piezoelectric turbines, evaluating efficiency, cost-effectiveness, environmental impact, and energy output differences. While awaiting experimental data, …
Published in Journal of Aerospace Engineering & Technology · Vol. 14, Issue 3, 2024 · pp. 31–42 Read article
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Quantifying Damage Evolution in Fiber-reinforced Composites Using Fracture Mechanics
Abstract: By evaluating the evolution of damage, such as cracks or delamination, within the material over time or under various loading situations, damage evolution in fiber-reinforced composites can be characterized using fracture mechanics. Fracture mechanics offers a framework for understanding and projecting the behavior of materials that already have damage or flaws. Since they have a high strength-to-weight ratio and unique mechanical qualities, fiber-reinforced composites are essential in many branches of …
Published in International Journal of Fracture Mechanics and Damage Science · Vol. 1, Issue 1, 2023 · pp. 26–32 Read article
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Unveiling Patterns in Complexity: The Role of Simple Statistics and Fuzzy Mathematics in Data Analysis
Abstract: In this study, statistical methods must be integrated with fuzzy mathematics to solve complex data. Statistical methods offer clear, unbiased, and computationally feasible tools for analysing numerical data. whereas fuzzy mathematics excels in describing the vagueness and ambiguity of human feeling by way of linguistic variables, membership functions, and inference systems. Giving it an apparent advantage when modelling complex conditions. Hybrid frameworks offer fine-grained decision-making and resilient adaptability to real-world …
Published in Research & Reviews : Journal of Statistics · Vol. 14, Issue 1, 2025 · pp. 01–10 Read article