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48 articles for “Mathematical problem”
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Automated Math Solver Assist with LLM RAG
Abstract: The challenges of solving complex mathematical problems often hinder efficiency in various scientific and engineering domains. This project proposes an innovative solution to these challenges by integrating automated math solvers with large language model (LLM) retrieval-augmented generation (RAG). The proposed system aims to streamline mathematical problem-solving processes, offering a robust and precise tool for real-time recognition, classification, and solution generation. This work provides a novel method of automating the solution …
Published in Current Trends in Signal Processing · Vol. 14, Issue 2, 2024 · pp. 25–30 Read article
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Vedic Mathematics in Algebra Techniques, and Problem-Solving Benefits
Abstract: The sixteen Sutras and thirteen Sub-Sutras form the foundation of Vedic algebraic mathematics. This article discusses the Buddha's teachings and shows how to use them to solve algebra problems. Unified mathematics is defined as a state where processes can refer to and understand each other. Vedic formulas, which can be utilized for addition, subtraction, division, and other mathematical operations, are taught with examples. Vedic mathematics not only saves time, but …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 1, 2025 · pp. 23–28 Read article
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Quantum Key Distribution in Optical Fiber Communication: A Study
Abstract: The relentless march of technological advancements, particularly in the realm of quantum computing, stances a noteworthy threat to security of existing cryptographic systems. Traditional encryption methods, like RSA and AES, trust on mathematical problems considered computationally hard for computers. However, sufficiently powerful quantum computers could render these systems vulnerable to attacks, jeopardizing the confidentiality of sensitive data transmitted over optical fiber networks. This looming threat has spurred significant research and …
Published in Trends in Opto-electro & Optical Communication · Vol. 15, Issue 1, 2025 · pp. 30–40 Read article
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Novel Perspectives in Quantum Safe Crypto algorithms for Enhanced Cyber Security
Abstract: This paper explores novel perspectives in quantum-safe cryptographic algorithms to bolster cybersecurity in the face of impending quantum computing advancements. Due to the efficient resolution of intricate mathematical problems by quantum computers, posing a substantial threat to existing cryptographic systems, there is a pressing requirement to create resilient alternatives. This study delves into innovative approaches, drawing from quantum-resistant cryptographic primitives, lattice-based cryptography, code-based cryptography, and hash-based cryptography. By examining the …
Published in International Journal of Computer Science Languages · Vol. 1, Issue 2, 2023 · pp. 18–22 Read article
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First Order Sliding Mode Control of Coupled Tank System
Abstract: This paper investigates the challenging problem of liquid level control in Coupled Tank Systems (CTS). CTS, characterized by its nonlinear behaviour and sensitivity to disturbances, presents significant control challenges. This report suggests and assesses several control measures to solve these problems. Mathematical models are developed to capture the system's nonlinear dynamics, and controllers such as Proportional-Integral (PI) and Sliding Mode Controllers (SMC) are designed. The PI controller effectively regulates the …
Published in Trends in Electrical Engineering · Vol. 14, Issue 3, 2024 Read article
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Algorithmic Encryption of Natural Numbers Based on the Collatz Conjecture
Abstract: This paper creates an encryption technique based on the well-known unresolved mathematical problem known as the Collatz conjecture. This conjecture states that every natural number larger than one eventually lowers to one by a set of precise procedures called the Collatz sequence. The study’s methodology associates these sequences’ terms with the Turkish alphabet’s letters. The Collatz transformation is applied to the integer that corresponds to each letter. The words created …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 3, 2024 · pp. 6–11 Read article
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A Comprehensive Study of Quantum Cryptography
Abstract: Quantum cryptography has emerged as one of the most promising fields in modern information security, offering innovative solutions that have the potential to transform the future of global cyber-defense. Unlike classical cryptographic systems, which depend primarily on the computational difficulty of solving complex mathematical problems, quantum cryptography is grounded in the fundamental and unbreakable laws of quantum mechanics. Core principles such as superposition, entanglement, and the uncertainty principle form the …
Published in Journal of Advanced Database Management & Systems · Vol. 12, Issue 3, 2025 · pp. 12–26 Read article
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Exploration of Partial Order Structures in Menger Spaces Properties Characterizations and Applications
Abstract: Partial order structures play a crucial role in understanding the intricate relationships within mathematical spaces. In this paper, we delve into the realm of Menger spaces and investigate their properties through the lens of partial orders. Menger spaces, a generalization of metric spaces, possess unique characteristics that can be further elucidated by considering partial order structures. Through rigorous analysis, we explore various properties of partial order Menger spaces, including topological …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 3, 2024 · pp. 17–22 Read article
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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
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Comparing Results of a Study on Mathematics Instruction in English at Diploma College in Solapur District
Abstract: Study programmes at the Diploma College in Solapur include mathematics courses, which are instructed in English. Comparing the educational outcomes in the Mathematics study course with the English language of instruction is the primary objective of the paper. We concentrated on the students' proficiency in solving specific linear algebra and mathematical analysis problems. The first-year students in the Diploma study programme in Diploma College, Solapur made up the research sample. …
Published in Recent Trends in Mathematics · Vol. 2, Issue 2, 2025 · pp. 12–18 Read article
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Comparative Evaluation of Fixed-Point Theorems Investigating Differences Among Conditions in Metric Spaces
Abstract: This paper provides a concise overview of metric spaces, their fundamental properties, and the idea of continuity as it pertains to these spaces, drawing parallels to uniform continuity and convergence. Also included is a review of previous research on metric space, its generalization, and practical outcomes from studies that utilized these spaces in various applications. We introduce a fixed point theorem for mixed monotone mappings in partially ordered metric spaces, …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 1, 2024 Read article
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Strategic Solutions: How Mathematics Reshapes Industrial Landscapes
Abstract: One of the earliest and most fundamental fields of the physical sciences is mathematics. It has a significant impact on industrial enterprises' bottom lines and enhances their performance in the current data-driven market. One subfield of applied mathematics is industrial mathematics. It concentrates on issues that arise in the industry and seeks answers that are pertinent to the sector. The use of mathematical models and techniques to diverse industry difficulties …
Published in International Journal of Industrial and Product Design Engineering · Vol. 2, Issue 1, 2024 · pp. 16–23 Read article
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A Journey through Fixed Points and Non-expansive Mappings
Abstract: Fixed points in non-expansive mappings are elements that remain unchanged under the action of the mapping. Non-expansive mappings preserve or contract distances in a metric space. The rigorous proof of the Banach fixed-point theorem is presented at the outset of the paper, highlighting its fundamental significance. According to this theorem, every contraction mapping (a particular kind of non-expansive mapping that strictly reduces distances) has a single fixed point in a …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 1, 2024 Read article
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Extended Fixed Point Theorems in Menger PM-Type Spaces: Generalized Auxiliary Functions and Contractivity Conditions
Abstract: Background: Fixed point theory in probabilistic metric spaces, particularly Menger spaces, has been a subject of intensive research due to its applications in nonlinear analysis and mathematical modeling. Traditional approaches often impose restrictive constraints on the defining properties of Menger spaces and limit the class of auxiliary functions in contractivity conditions Methods: We extend recent fixed point theorems in Menger spaces by: (1) introducing the notion of Menger PM-type spaces …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 3, 2025 · pp. 1–6 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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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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Solving Optimization Problems Using the Graphical Method of Linear Programming
Abstract: Linear programming is a mathematical optimization technique used for maximizing or minimizing a linear objective function while satisfying a set of linear constraints. This method plays a crucial role in various industries, including manufacturing, finance, transportation, and supply chain management. Among the different approaches to solving linear programming problems, the graphical method provides a simple and intuitive way to visualize and solve problems involving two decision variables. By plotting constraints …
Published in Research & Reviews : Journal of Statistics · Vol. 14, Issue 2, 2025 · pp. 01–08 Read article
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Higher Order Sliding Controller Parameter Determining Method: A Research
Abstract: In this paper, it is generally believed that sliding switching surfaces should reflect the design parameters of the system in variable structure control, and the control characteristics are the way to constrain the state on sliding switching surfaces. In the literature, classical sliding (primary sliding) is considered that sliding-switching surface is the same as the characteristic equation of the closed-loop system, and the design of the control system is reflected …
Published in Trends in Electrical Engineering · Vol. 14, Issue 2, 2024 · pp. 51–66 Read article
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A Method of Mesh Deformation for Flow Analysis Around Oscillating Bodies
Abstract: In general, high-speed rotating machines are subjected to complex phenomena due to various reasons, such as increased noise and strong vibration due to dynamic unbalance, which affect the dynamic motion of rotating machines and are necessarily a problem to overcome. Therefore, it is necessary to have a mathematical model to simulate it, and a strong tool to solve the constructed model. Using fluid-structure coupling techniques, which are currently a powerful …
Published in Journal of Experimental & Applied Mechanics · Vol. 16, Issue 2, 2025 · pp. 35–42 Read article
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An Analytical Study on Learning Difficulties in Estimation Theory Among Undergraduate Engineering Students
Abstract: Estimation Theory is a critical mathematical foundation for all engineering disciplines, enabling learners to model uncertainty, analyse signals, and derive optimal estimators. However, undergraduate students frequently struggle with its abstract properties, complex derivations, and prerequisite statistical concepts. This study investigates the key learning difficulties faced by students across multiple engineering branches using diagnostic tests, structured questionnaires, and interviews. The findings reveal that students commonly experience challenges related to weak probability …
Published in Research & Reviews : Journal of Statistics · Vol. 15, Issue 1, 2026 Read article