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11 articles for “Calculus”
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Fractional Calculus-Based Analysis of Magneto-Thermal Nanofluid Flow Over Stretching and Shrinking Surfaces
Abstract: This study presents a comprehensive investigation of magneto-thermal hybrid nanofluid flow over stretching and shrinking surfaces using a fractional calculus framework to capture the memory and hereditary characteristics of complex fluid transport phenomena. The proposed model incorporates the effects of magnetic field intensity, thermal radiation, viscous dissipation, Brownian motion, and thermophoretic diffusion on the velocity and temperature distributions within the boundary layer region. A fractional-order derivative formulation is employed to …
Published in Recent Trends in Fluid Mechanics · Vol. 13, Issue 2, 2026 Read article
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The Rise of Fractional Calculus: Novel Applications in Engineering and Biological Systems
Abstract: Fractional calculus (FC) is an advanced mathematical framework that generalizes the classical concepts of differentiation and integration to non-integer, or fractional, orders. This extension of traditional calculus allows for the modeling of complex dynamic systems that exhibit behavior not easily captured by integer-order differential equations. Over the last few decades, fractional calculus has seen a rapid rise in popularity, particularly in applied mathematics, engineering, and biological sciences, due to its …
Published in Recent Trends in Mathematics · Vol. 1, Issue 2, 2024 · pp. 7–11 Read article
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Study to evaluate and correlate the levels of heavy metals in dental calculus of burnt tobacco (Mishri) users and non-tobacco users with their periodontal status Using Atomic Absorption Spectrometry (AAS)
Abstract: The use of burnt tobacco products, such as Mishri, is associated with numerous health risks, including periodontal diseases. Heavy metals present in tobacco can accumulate in dental calculus, potentially exacerbating periodontal conditions. This study aimed to assess and establish a correlation between the levels of heavy metals present in dental calculus among burnt tobacco (Mishri) users and non-tobacco users, in relation to their periodontal health status. Utilizing Atomic Absorption Spectrometry …
Published in Journal of Polymer & Composites · Vol. 12, Issue 2, 2024 · pp. 166–174 Read article
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The Calcium Paradox – Calcium Dietary Intake and Supplementation in the Context of Calcium Oxalate Renal Calculus
Abstract: Renal Calculi, also known commonly as kidney stone is one of the most common manifestations of kidney function dysregulation causing discomfort and alterations to an individual’s life. Although kidney stones come in a variety of forms, calcium oxalate stones are the most prevalent kind. These Calcium Oxalate renal stones often arise from various issues like metabolic imbalances, dehydration and dietary imbalances. About 70–80% of kidney stones are calcium oxalate stones, …
Published in International Journal of Sustainability · Vol. 2, Issue 1, 2025 · pp. 17–25 Read article
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A Review Paper on The Mathematical Foundations of Artificial Intelligence
Abstract: Artificial Intelligence (AI) is deeply rooted in various branches of mathematics, which provide the theoretical foundation and practical tools for developing intelligent systems. This paper explores the crucial role of mathematics in AI, focusing on key areas such as Linear Algebra, Probability and Statistics, Optimization Techniques, Calculus, Graph Theory, and Fourier and Wavelet Transforms. Linear Algebra is fundamental for representing and manipulating data, with applications in dimensionality reduction and neural …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 3, 2025 · pp. 7–14 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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Advance Fixed Point Theorems and Its Application to Ordinary and Fractional Differential Equations
Abstract: In the present research, advanced results on the fixed point theorem are applied to typical boundary value problems. Finding a differential equation's solution under certain boundary conditions is the goal of typical boundary value topics. The article appears to extend new fixed point results to a new context, likely involving fractional operators with unique kernels, notably the Caputo-type fractional operator. This extension involves applying the fixed point theorem to a …
Published in Recent Trends in Mathematics · Vol. 1, Issue 1, 2024 · pp. 1–15 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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Automated Math Solver Assist with LLM RAG
Abstract: The challenges of solving complex mathematical problems often hinder efficiency in various scientific and engineering domains. This project proposes an innovative solution to these challenges by integrating automated math solvers with large language model (LLM) retrieval-augmented generation (RAG). The proposed system aims to streamline mathematical problem-solving processes, offering a robust and precise tool for real-time recognition, classification, and solution generation. This work provides a novel method of automating the solution …
Published in Current Trends in Signal Processing · Vol. 14, Issue 2, 2024 · pp. 25–30 Read article
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Effects of Bearing Design Parameter on Working Characteristics of Floating Ring Bearing
Abstract: The working stability of turbochargers supported by floating ring bearings depends on not only the structure of the rotors but also working characteristic of floating ring bearings. These working characteristics are related to working conditions and design parameters of floating ring bearings. The main goal of this research is to investigate the working characteristics of bearings by design parameters of floating ring bearings. In order to study the working characteristics …
Published in Journal of Experimental & Applied Mechanics · Vol. 15, Issue 3, 2024 · pp. 39–52 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