All articles
47 articles
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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
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Assessing Air Quality, Climate Change, and Migration Dynamics in Delhi NCR: A System Dynamics Approach
Abstract: As climate change accelerates and environmental degradation worsens, urban centers like Delhi NCR are under increasing pressure from internal migration. Poor air quality—especially in rural and peri-urban regions—emerges both as a driver of out-migration and a deterrent for in-migration to already burdened cities. This study develops a system dynamics (SD) model that integrates climate variables, air pollution metrics, economic indicators, governance quality, and migration behavior to simulate population flows into …
Published in Recent Trends in Mathematics · Vol. 2, Issue 1, 2025 · pp. 7–11 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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Comparative Performance Study: Deterministic vs. Probabilistic Models in Retail Chains
Abstract: The finished goods, raw materials, and product stock that a business has on hand for sale are referred to as inventory. They enable the companies to achieve their sales levels and are a chance to cost control and decision making. It is a huge asset to a manufacturing firm. Inventory model permits forecasting of quantities of raw material, inventory and spare parts of the equipment to a very high level …
Published in Recent Trends in Mathematics · Vol. 2, Issue 1, 2025 · pp. 1–6 Read article
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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
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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
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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
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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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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
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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
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Remote Sensing in Atmospheric Studies: Enhancing Understanding of Climate Dynamics and Air Quality, Atmospheric Monitoring and Analysis; Emerging Technologies and Future Directions
Abstract: Remote sensing has emerged as a transformative tool in atmospheric sciences, providing detailed and comprehensive insights into various atmospheric phenomena. Its advanced capabilities have revolutionized our understanding of climate dynamics, air quality, and atmospheric composition, enabling more accurate monitoring and analysis. This paper reviews the critical role of remote sensing technologies in enhancing knowledge of atmospheric processes and their practical applications in areas such as climate change monitoring, air pollution …
Published in International Journal of Atmosphere · Vol. 2, Issue 1, 2025 · pp. 1–5 Read article
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Environmental ethics: duties to the ordinary world
Abstract: Environmental justice is a crucial framework that ensures fair and equitable access to clean air, water, and natural resources for all, particularly for marginalized and vulnerable populations. It addresses the environmental inequalities and injustices that disproportionately impact ordinary people and communities. This research highlights the pressing need to bridge the gap between environmental protection and social equity, ensuring that no community bears an undue burden of environmental degradation while others …
Published in International Journal of Atmosphere · Vol. 2, Issue 1, 2025 · pp. 6–13 Read article
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Atmospheric Remote Sensing: Bridging Technology and Environmental Challenges
Abstract: The rapid advancements in remote sensing technologies have revolutionized the field of atmospheric studies, offering unprecedented capabilities for detailed observation, analysis, and understanding of the Earth's atmosphere. These technological innovations have proven to be instrumental in tackling critical environmental challenges, providing scientists and researchers with the tools needed to monitor and analyze atmospheric phenomena with greater precision and depth.This article delves into the historical development, current state, and diverse applications …
Published in International Journal of Atmosphere · Vol. 2, Issue 1, 2025 · pp. 14–19 Read article
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R-M and M-R Model for Interpreting Logic State of Memristor Aided NOR with Enhanced Noise Margin
Abstract: Memristive crossbar arrays are one of the fascinating subjects in the field of nanoelectronics and memory devices. The arrangement of arrays consists of grid-like structure with rows and columns of memristors which are resistive devices that can preserve their resistance state even after power is turned OFF. They have now emerged as a promising alternative to traditional memory technologies due to their high density, non-volatility and low power consumption. This …
Published in Recent Trends in Mathematics · Vol. 1, Issue 1, 2024 · pp. 35–41 Read article
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Atmospheric Boundary Layer Processes: Impacts on Weather Patterns and Climate Change
Abstract: The atmospheric boundary layer (ABL) is a vital component of the Earth's climate system, acting as the interface between the terrestrial surface and the overlying atmosphere. This layer, typically extending from the surface to a height of a few hundred meters, is characterized by strong gradients in meteorological variables such as temperature, humidity, wind speed, and atmospheric pressure. Understanding the dynamics of the ABL is essential for comprehending weather phenomena, …
Published in International Journal of Atmosphere · Vol. 1, Issue 2, 2024 · pp. 22–25 Read article
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Innovations in Atmospheric Remote Sensing: From Satellites to Lidar and Beyond
Abstract: Atmospheric remote sensing plays a vital role in monitoring and understanding the Earth's atmosphere, providing essential data for climate studies, weather forecasting, and environmental management. This review discusses various remote sensing technologies, including satellites, radiometers, lidar, radar, and GPS radio occultation, each contributing unique capabilities for atmospheric observations. Satellite remote sensing allows for global coverage and continuous monitoring of atmospheric parameters, while ground-based systems enhance localized measurements. Key applications include …
Published in International Journal of Atmosphere · Vol. 1, Issue 2, 2024 · pp. 10–15 Read article
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Atmospheric Modeling: A Comprehensive Review of Numerical Approaches and Applications
Abstract: Atmospheric modeling plays a crucial role in understanding and predicting atmospheric processes, weather patterns, and climate variability. This review synthesizes current methodologies and applications across several types of atmospheric models, including numerical weather prediction (NWP), climate models, air quality models, and chemical transport models. We explore the intricacies of data assimilation, model evaluation, parameterization, and the importance of high-performance computing in advancing model accuracy and efficiency. Special emphasis is placed …
Published in International Journal of Atmosphere · Vol. 1, Issue 2, 2024 · pp. 16–21 Read article
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Recent Advances in Atmospheric Physics and Chemistry: Composition, Dynamics, and Impacts
Abstract: The Earth's atmosphere is vital for sustaining life and regulating climate. This review explores key aspects of atmospheric physics and chemistry, including atmospheric composition, the dynamics of greenhouse gases, ozone depletion, and the effects of aerosols and atmospheric pollutants. The interaction between anthropogenic emissions and natural processes, such as the carbon and nitrogen cycles, is crucial for understanding climate feedback mechanisms. The impact of photochemistry on air quality and the …
Published in International Journal of Atmosphere · Vol. 1, Issue 2, 2024 · pp. 5–9 Read article
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Understanding the Dynamics of Biogenic and Anthropogenic Aerosols in the Atmosphere
Abstract: This study explores the complex interactions between marine aerosols, biogenic organic matter, and anthropogenic pollutants, highlighting their implications for climate and air quality. It is established that submicron-sized marine aerosols, primarily of biogenic origin, play a crucial role in cloud condensation nuclei (CCN) concentration, particularly during periods of high biological oceanic activity (HBA). The chemical composition of marine aerosols is significantly influenced by the ocean's annual biological cycle, with seasonal …
Published in International Journal of Atmosphere · Vol. 1, Issue 1, 2024 · pp. 15–22 Read article
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Integrating Atmospheric Science: Understanding Greenhouse Gases, Aerosols, and Air Quality Dynamics
Abstract: Atmospheric science investigates the Earth’s atmospheric systems to understand their composition, dynamics, and the implications for climate, weather, and air quality. This review explores five primary areas within the field: atmospheric composition, atmospheric modeling, remote sensing, air pollution, and boundary layer dynamics, highlighting critical challenges and advancements. Rising levels of greenhouse gases (GHGs), including carbon dioxide and methane, continue to drive global warming, while feedback mechanisms—like cloud interactions and surface …
Published in International Journal of Atmosphere · Vol. 1, Issue 1, 2024 · pp. 32–35 Read article