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10 articles for “nonlinear systems”
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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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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
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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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(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
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The Role of Adaptive Filters in Enhancing Acoustic Echo Cancellation Efficiency in Noisy Environments
Abstract: The novel approach that this work discusses is a DCD-based iterative learning filter approach improved with deep learning methodologies, designed to improve the efficiency of acoustic echo cancellation. The proposed system can really manage both linear and nonlinear echo scenarios, dynamically adapting to fluctuating acoustic environments. The above comparative evaluations with standard filter, the standard RLS filter, indicate that the mean square error, and the standard deviation of the correlation …
Published in International Journal of Radio Frequency Innovations · Vol. 2, Issue 2, 2024 · pp. 9–24 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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Land surface dynamics: A Multiphysics Approach to Modeling Mass Transport
Abstract: Land surface dynamics are governed by complex interactions among hydrological, atmospheric, and geomorphological processes that collectively drive the transport of mass across terrestrial environments. Traditional modeling approaches often isolate individual mechanisms, limiting their ability to capture the coupled feedbacks that shape landscape evolution. This study presents a multiphysics framework for modeling mass transport on land surfaces, integrating fluid flow, sediment transport, heat exchange, and chemical reactions within a unified computational …
Published in International Journal of Land · Vol. 2, Issue 2, 2025 · pp. 31–36 Read article
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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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Comprehensive Review of the Fundamental and Functional Properties of Crystalline Materials
Abstract: Crystalline materials, characterized by their highly ordered atomic arrangements, serve as the backbone of modern engineering and technology. This review provides a detailed examination of their diverse properties, categorized into mechanical, thermal, electrical, and optical domains. We analyze fundamental mechanical parameters such as the elastic modulus, yield strength, and fracture toughness, alongside functional behaviors like fatigue and creep. The discussion extends to thermal transport and expansion, electrical conductivity and resistivity, …
Published in International Journal of Crystalline Materials · Vol. 3, Issue 1, 2026 · pp. 20–24 Read article
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A Machine Learning Approach to Forecasting Outcomes in Limited Overs Cricket
Abstract: This study explores the application of machine learning techniques to forecasting outcomes in limited overs cricket matches, with a particular focus on One Day Internationals (ODIs). The research investigates how classification algorithms can be effectively utilized to analyze both contextual and dynamic factors that influence match results, including venue details, toss decisions, team strength, and historical performance records. By employing a structured methodology encompassing feature selection, data preprocessing, model training, …
Published in Recent Trends in Sports · Vol. 2, Issue 2, 2025 · pp. 09–19 Read article