Search
15 articles for “mathematical models”
-
Mathematical Models for COVID-19 Pandemic: A Comparative Analysis
Abstract: The COVID-19 pandemic has really underlined the importance of mathematical modeling in understanding disease-spread dynamics and especially informing public health interventions. The paper aims to provide a comprehensive comparative analysis of various mathematical models used for COVID-19 studies, with a focus on assumptions underlying those models, strengths, and also the limitations in their applications as well as special focus is given to compartmental models, agent-based models, machine learning-enhanced models, and …
Published in Recent Trends in Mathematics · Vol. 1, Issue 1, 2024 · pp. 42–53 Read article
-
Mathematical Modeling of Epidemics Using Stochastic Differential Equations: A Review
Abstract: The accurate modeling of infectious disease dynamics is crucial for predicting outbreaks and informing public health interventions. While deterministic models such as the SIR (Susceptible-Infected-Recovered) framework have traditionally been used to understand disease transmission, they often fail to account for the randomness inherent in real-world scenarios. Disease spread is influenced by numerous uncertain factors, including individual behavioral changes, environmental fluctuations, and imperfect data reporting. These uncertainties can significantly impact model …
Published in Recent Trends in Mathematics · Vol. 1, Issue 2, 2024 · pp. 1–6 Read article
-
Evaluating AI-Driven Adaptive Learning Models in Mathematics: A Contemporary Perspective
Abstract: Artificial Intelligence (AI) continues to transform mathematics education through data-driven personalization and adaptive learning technologies. This study investigates how AI-enabled adaptive platforms influence student performance and engagement in mathematics classrooms. Using a quantitative approach across two institutions, pre- and post-assessment results were compared between students using AI-assisted adaptive learning tools and those receiving conventional instruction. The findings reveal that AI-driven learners demonstrated significantly higher gains in conceptual understanding and engagement …
Published in Recent Trends in Mathematics · Vol. 3, Issue 1, 2026 · pp. 8–12 Read article
-
From Differential Equations to Data Science: A Survey on Analytical Methods in Contemporary Problems
Abstract: The integration of differential equations and data science methods represents a dynamic and evolving approach to solving contemporary challenges across a wide range of disciplines, including engineering, physics, biology, economics, and finance. Differential equations have long served as fundamental tools for modeling continuous systems and processes, offering powerful insights into the behavior of natural and man-made phenomena. For example, they describe how heat diffuses through materials, how populations grow in …
Published in Recent Trends in Mathematics · Vol. 2, Issue 2, 2025 · pp. 1–6 Read article
-
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
-
Kinematic and Dynamic Modelling of a 6-DOF Robotic Manipulator for Industrial Applications
Abstract: The rapid evolution of industrial automation has intensified the need for highly accurate, flexible, and intelligent robotic systems capable of operating in dynamic and demanding environments. Among these systems, six-degree-of-freedom (6-DOF) robotic manipulators have emerged as a versatile solution due to their superior dexterity, large workspace, and human-arm-like motion capabilities. This research focuses on the comprehensive kinematic and dynamic modelling of a 6-DOF robotic manipulator designed for various industrial tasks …
Published in International Journal of Robotics and Automation in Mechanics · Vol. 3, Issue 2, 2025 · pp. 27–32 Read article
-
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
-
A Novel Mathematical Exploration of Fractal Dynamics in Hyperbolic Spaces
Abstract: This research paper presents an original study on the behavior, generation, and properties of fractal structures within hyperbolic geometry. Unlike classical Euclidean fractals, hyperbolic fractals demonstrate accelerated boundary complexity and distinct scaling symmetries due to the curvature of the underlying space. The paper proposes new iterative models, analyzes geometric invariants, and explores potential applications in data visualization, network science, and theoretical physics. This research paper conducts an in-depth investigation into …
Published in Recent Trends in Mathematics · Vol. 3, Issue 1, 2026 · pp. 1–7 Read article
-
Study of Proximity Points and Fixed Points
Abstract: This paper explores the concepts of proximity points and fixed points, which are fundamental in mathematical analysis and nonlinear functional analysis. Fixed-point theorems play a crucial role in optimization, game theory, differential equations, and dynamic systems. Proximity points, an extension of fixed points, provide a more generalized approach, allowing near-coincidence rather than exact identity. The study discusses classical fixed-point theorems, such as Banach’s contraction principle, Brouwer’s fixed-point theorem, and Schauder’s …
Published in Recent Trends in Mathematics · Vol. 1, Issue 2, 2024 · pp. 28–31 Read article
-
Multicriteria Decision Making using SR-Fuzzy Sets
Abstract: In this study, we introduce and explore square-root fuzzy sets (SR-Fuzzy sets), a novel extension within the realm of fuzzy set theory. We begin by establishing a comparative analysis between SR-Fuzzy sets and two well-known fuzzy set models: Intuitionistic Fuzzy Sets (IFS) and Pythagorean Fuzzy Sets (PFS). This comparison highlights the unique characteristics and mathematical structure of SR-Fuzzy sets. A particular focus is placed on the complement operator, which plays …
Published in Recent Trends in Mathematics · Vol. 1, Issue 2, 2024 · pp. 12–20 Read article
-
Agentic AI: Architectures, Types, Capabilities, Mathematical Equations and Governance in the Era of Autonomous Intelligence
Abstract: Agentic Artificial Intelligence (Agentic AI) represents a major advancement in the evolution of intelligent systems by enabling autonomous planning, decision-making, and action execution. Unlike traditional AI models, which are primarily reactive and designed to respond to predefined inputs, Agentic AI systems possess capabilities such as memory, reasoning, goal-oriented planning, tool integration, and dynamic adaptation to changing environments. These characteristics allow them to perform complex, multi-step tasks with minimal human intervention, …
Published in Recent Trends in Mathematics · Vol. 3, Issue 2, 2026 Read article
-
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
-
(𝛅,Ü ) Convex Structure on Partial B-Metric Space Concerning Quasi Contraction and Fixed-Point Results
Abstract: This work introduces the concept of (δ,Ü )– Convex Partial b-Metric Spaces using convex structure. Motivated by this approach, we demonstrated fixed point results and their uniqueness, as well as quasi contraction, and provided some supporting instances for the established results. Our findings expand prior fixed-point results to a novel concept (δ,Ü )– Convex Partial b-Metric Spaces. To support our theoretical findings, we provide several instances that exemplify the established …
Published in Recent Trends in Mathematics · Vol. 1, Issue 1, 2024 Read article
-
Topology and Geometry in Data Science: Persistent Homology and Beyond
Abstract: In recent years, the interplay between topology, geometry, and data science has gained substantial momentum, offering powerful frameworks to analyze and interpret complex datasets. Traditional statistical and machine learning methods often rely on linear or metric- based assumptions, which may fail to capture the intrinsic structure of high-dimensional or nonlinear data. In contrast, topological and geometric methods provide shape-oriented, scale- invariant tools that focus on the continuity, connectivity, and global …
Published in Recent Trends in Mathematics · Vol. 1, Issue 2, 2024 · pp. 21–27 Read article
-
Breaking Barriers: Overcoming Challenges for Women in STEM in India-A Conceptual Perspective
Abstract: STEM education which brings together Science, Technology, Engineering, and Mathematics has become the foundation for success in today’s fast-changing, technology-driven world. It helps students think critically, solve real-world problems, and adapt to new innovations like artificial intelligence, robotics, data science, and biotechnology. In a country like India, where digital transformation is reshaping every sector, STEM education is not just an academic choice but a key to national growth and progress. …
Published in International Journal of Education Sciences · Vol. 3, Issue 2, 2026 · pp. 8–13 Read article