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38 articles
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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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Fuzzy Mathematics in Decision-Making: A Quantitative Perspective
Abstract: Fuzzy mathematics plays an increasingly generalized role in decision-making, and thus, this paper details different types of fuzzy mathematics and highlights other possible alternatives alongside fuzzy methodologies. Fuzzy models offer a versatile and precise approach to assessing complex and uncertain situations using fuzzy sets, membership functions, linguistic variables, and aggregation methods. Through the lenses of time, cost, and quality, the project management case study illustrates how fuzzy logic effectively evaluates …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 1, 2025 · pp. 6–12 Read article
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Expanding Hicks Contraction Theory, Multi-Valued Mappings in Generalized b-Menger Spaces
Abstract: This paper extends the Hicks contraction theory to multi-valued mappings within generalized b-Manger spaces, a class of metric-like structures that accommodate more flexible distance functions. By introducing new definitions, such as generalized admissibility conditions and weak compatibility in the multivalued sense, we provide a comprehensive analysis of how these contractions behave in broader topological and metric contexts. Our approach systematically generalizes classical contraction principles by relaxing conventional constraints, thereby broadening …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 1, 2025 · pp. 1–05 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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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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Encoding-Decoding Algorithm Using the Catalan Transform of Weighted Tribonacci Sequence
Abstract: In order to improve information security, this paper presents a unique algorithm for encoding and decoding messages utilizing the Catalan Transform of a Weighted Tribonacci Sequence. Utilizing the Catalan and Tribonacci sequences, the methodology combines the concepts of number theory and combinatorics to create an effective encryption and decryption process. First, an array is created by mapping each character in the plaintext message to its corresponding ASCII value. The ASCII-weighted …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 3, 2024 · pp. 12–16 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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Key Generation Algorithms Using Difference Equations with Multi-Precision Arithmetic: A Review
Abstract: Modern cryptographic systems rely on robust key generation to secure data and communication. This review explores the integration of difference equations and multi-precision arithmetic for cryptographic key generation, addressing limitations in traditional methods like pseudorandom number generators and chaotic systems. Difference equations produce deterministic yet chaotic sequences ideal for cryptography due to their sensitivity to initial conditions and nonlinearity. However, finite precision arithmetic can lead to periodicity and loss of …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 3, 2024 · pp. 23–36 Read article
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Exact Solutions of Kuramoto–Sivashinsky Equation Using Modified Sub-equation Method
Abstract: Equations for non-linear evolution are mathematical representations of physical phenomena. The physical interpretation of the solution functions of these equations enhances the viewpoint of many natural processes. Numerous scientists who acknowledge this truth have focused on this area. These mathematical models are even more important since they provide light on a multitude of events when their solutions take on a physical significance. Through their research, numerous scientists create methods and …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 2, 2024 · pp. 25–33 Read article
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Human Skin Abnormality Detection with Process Similarity Criteria Fit Machine Learning Method
Abstract: This method presents a machine learning method that satisfies the defined conditions for healthy waterside beach activities. The boundary conditions of the normal and abnormal radiation spaces were formulated. The objectives of using a Regression Polynomial with Process Similarity Criteria Fit for skin temperature prediction are justified by the analysis of the existing analytical and machine learning approaches. An algorithm for skin temperature prediction using the theories of similarity criteria …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 2, 2024 · pp. 17–24 Read article
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Comprehensive Analysis of Counting by Sorting
Abstract: Sorting algorithms play an important role in computer science, as they facilitate the effective organization and retrieval of data. Counting sort is a non-comparative integer sorting algorithm that works well with a limited number of integers known beforehand. The process, advantages, and limitations of this sorting algorithm were investigated in this study. Unlike other comparison-based sorting algorithms, counting sort achieves a time complexity of O(n+k), which depends on the input …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 2, 2024 · pp. 1–6 Read article
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Analysis of Gold Price Trend Using the Hidden Markov Model
Abstract: This study aims to analyze the behavior of gold prices in India through a two-state Hidden Markov Model (HMM). We first formulated crucial parameters, such as the Transition Probability Matrix (TPM), Initial Probability Vector (IPV), and Emission Probability Matrix (EPM). Subsequently, we constructed a hidden Markov probability distribution and evaluated Pearson’s coefficients to gauge the correlations separately for each state. The goodness of fit of the developed model was assessed …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 2, 2024 · pp. 7–16 Read article
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Optimal Homotopy Analysis Method (OHAM) For the Approximate Series Solution of Non-linear Partial Differential Equation
Abstract: In this article, we have used the Optimal Homotopy Analysis Method (OHAM), which is a basically semi-analytic method to solve differential equations. The ability for the user to choose the convergence control parameter, auxiliary linear operator, auxiliary function, and starting approximation is what sets apart the OHAM technique. We guaranteed the efficacy and efficiency of the procedure by fine-tuning the convergence control parameter. We solved a non-linear partial differential equation …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 1, 2024 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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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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Context of Different Graph Operations: Fibonacci Product Cordial Labeling of Herschel Graph
Abstract: The function φ: V (G) → {F1, F2,..., Fn}, where Fj is the jth Fibonacci number (j = 1,..., n), is said to be Fibonacci product cordial labeling if the induced function φ*: E (G) → {0, 1} defined by 𝜑∗ (𝑢𝑣) = (𝜑(𝑢)𝜑 (𝑣))(𝑚𝑜𝑑 2) meets the criterion |𝑒𝜑∗(0) – � �𝜑∗(1)| ≤ 1. A graph known as the Fibonacci product cordial graph is one that permits Fibonacci product …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 1, 2024 Read article
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A novel similarity measure for interval value picture fuzzy Environment and extended TOPSIS
Abstract: Correct decision-making is the most arduous task in our daily life. The decisions are hard to make in the multi-criteria decision-making (MCDM) problems due to ambiguous and unexpected information. In order to cope with such uncertainties in the data, a new decision-making approach has been developed using a newly defined similarity measure under the framework of interval-valued picture fuzzy set (IVPFS), as an extension of picture fuzzy sets (PFS). In …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 1, 2024 · pp. 1–10 Read article
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Image Compression via Non-separable Discrete Fractional Fourier Transform
Abstract: The main idea behind image compression is to reduce the bandwidth for transmission and required space for storage. Thus, image compression is of great importance. In this paper we present the image compression technique using Non-Separable Discrete Fractional Fourier Transform (NSDFrFT). Numerical simulation results suggested that image compression method using NSDFrFT as transform technique gives better performance for images when compression ratio is high in comparison to DFrFT and JPEG. …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 2, Issue 3, 2015 · pp. 1–9 Read article