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8 articles for “mathematical principle”
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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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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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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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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 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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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
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Role of Fatigue and Creep in Structural Damage: A Comprehensive Review
Abstract: Fatigue and creep are two critical degradation mechanisms that significantly influence the structural integrity and longevity of engineering materials. These phenomena arise due to different loading and environmental conditions but often coexist in various industrial applications, leading to severe material degradation over time. Fatigue primarily results from cyclic loading, where repeated stress variations induce microstructural damage and crack initiation, ultimately causing catastrophic failure. Conversely, creep occurs under sustained stress at …
Published in International Journal of Fracture Mechanics and Damage Science · Vol. 3, Issue 1, 2025 · pp. 22–26 Read article
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Introduction to Biological Networks and their Contributions to Systems Biology
Abstract: Biological networks provide a conceptual framework to represent and analyze the intricate interconnections among the numerous components that make up living systems. This review paper elucidates the foundational principles of networks and their diverse applications in systems biology, highlighting their crucial role in understanding the inherent complexity of biological processes. Utilizing graph theory, these networks represent entities like genes, proteins, and metabolites as nodes, with their interactions depicted as edges. …
Published in International Journal of Bioinformatics and Computational Biology · Vol. 2, Issue 1, 2024 · pp. 53–70 Read article