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48 articles for “Mathematical problem”
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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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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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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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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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History and Applications of Kalman Filter: A Review
Abstract: The Kalman filter is a powerful algorithm that is used to estimate the dynamic system states with noisy measurements and uncertain behaviors. It is an optimal estimator that minimizes the average squared error between the estimated states and the true states, given the noisy data and a model of the system. The recursive algorithm is highly effective in tracking and predicting the state of complex systems over time. Kalman filters …
Published in International Journal of Electrical Power and Machine Systems · Vol. 2, Issue 1, 2024 · pp. 14–23 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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A Constraint-Driven Generative Design Methodology for Modular Actuated Robotic Components in Decentralized Manufacturing
Abstract: This work formalizes a constraint-driven generative design framework for actuator-integrated robotic components intended for decentralized additive manufacturing. Conventional topology optimization typically prioritizes structural efficiency while treating actuator integration, modular interfaces, and fabrication constraints as secondary considerations. In contrast, the proposed methodology encodes these requirements as first-order geometric and mechanical constraints prior to automated material redistribution. The framework defines preserved actuator geometry, bounded design envelopes, representative loading abstractions, and manufacturability-aware domains …
Published in International Journal of Robotics and Automation in Mechanics · Vol. 4, Issue 1, 2026 Read article
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Assistive Technology Advancements: Revolutionising Support for Individuals with Specific Learning Disabilities
Abstract: Assistive Technology (AT) has become an offer to revolutionise the provision of people with specific Learning Disabilities (SLD), making the learning process more inclusive and equal. In this paper, the current developments in AT will be discussed that cater to fundamental learning issues in reading, writing and mathematics. Text-to-speech and speech-to-text innovations, mind-mapping tools, and others are important innovations that improve reading comprehension and written expression, as well as strength …
Published in International Journal of Trends in Humanities · Vol. 3, Issue 1, 2026 · pp. 1–7 Read article
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Modelling of Large Elasto-plastic Deformations by EFGM
Abstract: Current work reports modelling and simulation of geometric and material nonlinearities arising due large elasto-plastic displacements in structural specimens by invoking enriched element free Galerkin method (EFGM). The displacement approximations are constructed by using moving least square approach. Standard displacement based approximations are modified by incorporating suitable enrichment functions depending on the nature of interfaces present in the components. Large deformations give rise to geometric nonlinearities which have been modelled …
Published in Journal of Polymer & Composites · Vol. 12, Issue 2, 2024 · pp. 130–143 Read article
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The Scientific Foundations of Programming Languages: Bridging Theory and Practical Application
Abstract: The study of programming languages within computer science is fundamental to the development of efficient, reliable, and scalable software systems. However, the degree to which these languages adhere to scientific principles remains a topic of debate. This paper explores the scientific nature of computer science languages by examining their theoretical foundations, design principles, and practical applications. It evaluates how programming languages are grounded in mathematical logic, formal semantics, and computational …
Published in International Journal of Computer Science Languages · Vol. 3, Issue 1, 2025 · pp. 32–41 Read article
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Mathematical Modeling Analysis of India's Accident &Use of Fly Ash and Polymers in Road Safety
Abstract: Accident predicting models (APMs) are exceptionally strong tools for adaptation and mitigation strategies because they have the ability to predict both the severity and frequency of crashes. Road accidents are a major problem all throughout the world, especially in developing countries. Understanding the key variables that contribute can assist in reducing the frequency of traffic collisions. This study also discovered recent developments on fly ash, green composites, other polymer materials …
Published in Journal of Polymer & Composites · Vol. 13, Issue 1, 2025 · pp. 488–499 Read article
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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
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Mathematical Modeling and CFD Analysis for Protype Model Development of a Low-cost Hybrid Power Operated Mini Kitchen Chimney for Rural Households
Abstract: Home chimneys remove pollution by products of fossil fuels from the atmosphere. Today's environmental problems are worsening rapidly due to technology and population growth. Thus, researchers developed a hybrid micro kitchen chimney to help rural residents at a low cost. This small hybrid chimney simplifies rural cooking. A kitchen chimney is the best way to remove smoke, grease, stink, stains, oil droplets, and more from the kitchen. It helps ventilate …
Published in International Journal of Energy and Thermal Applications · Vol. 1, Issue 1, 2023 · pp. 14–28 Read article
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Inverse Model for Predicting Thermal Abnormality of the Transient Process Triggered by Defective Electronics Element
Abstract: The paper presents a model for predicting thermal abnormalities in Printed Circuit Boards (PCBs) by approximating the thermal process of electric elements with heating from point sources. Circuit board heat sources are defined as point and non-point. The point heat source is a small electronic heating element that can be approximated as having originated from one point on the circuit board. A non-point source is one with heat distributed over …
Published in International Journal of Energy and Thermal Applications · Vol. 3, Issue 2, 2025 · pp. 24–31 Read article
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Complex Space-Time and the Structure of Relativistic Quantum Theory
Abstract: Relativistic quantum mechanics was developed to reconcile the principles of quantum mechanics with Einstein’s theory of relativity. Despite its success in describing high-energy particles, the theory continues to face unresolved conceptual and mathematical difficulties, particularly in relation to the nature of time, causality, and relativistic consistency. In recent years, the idea of extending space-time into the complex domain has emerged as a useful and potentially meaningful approach to these problems. …
Published in Recent Trends in Mathematics · Vol. 3, Issue 1, 2026 · pp. 22–27 Read article
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A Survey on the Evolution of AI (Artificial Intelligence) and Robotics
Abstract: This is the age of new technology and gadgets to improve the livelihood of human beings in aspects of every manner while arranging the host of facilities for every task related to our daily lifestyle. To improve the machine and their working manner smartly only programming is not enough it takes a lot more than just programming and here the implementation of AI tools takes place to improve the quality, …
Published in Journal of Advancements in Robotics · Vol. 11, Issue 3, 2024 · pp. 10–17 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
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A Thorough Examination of the Chemical Engineering Process: Fundamentals, Design, and Application
Abstract: This article gives a full picture of the chemical engineering process, focusing on the basic ideas, methods, and tools that make up the profession. It looks at how chemical, physical, and biological processes change raw materials into useful goods, with a focus on how design, optimization, and control work together in industrial systems. Some of the main topics talked about are process design, thermodynamics, reaction engineering, transport phenomena, and sustainability. …
Published in Journal of Modern Chemistry & Chemical Technology · Vol. 16, Issue 3, 2025 · pp. 14–25 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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A Review on Evolution of Medicine After and During Corona
Abstract: As of the beginning of 2023, 6.7 million people had perished from COVID-19, according to the World Health Organization. However, there have also been some positive developments, such as the notable decline in influenza-related deaths in the first year of the pandemic as a result of masking and social isolation, as well as the quick adoption of vaccines utilizing cutting-edge technologies like mRNA vaccines, which hold out great promise for …
Published in Research and Reviews: A Journal of Pharmacology · Vol. 14, Issue 1, 2024 · pp. 1–9 Read article