Research & Reviews: Discrete Mathematical Structures
Volume 12, Issue 1 (2025)
Table of contents
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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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Leak Location Detection in Underground Pipeline Using Transient Pollutant Propagation Concentration Signature Analysis with Theory of Hypernumbers
Abstract: The paper introduces a new analytical method of detecting leakage locations in underground pipe systems. For the first time, the phenomenon of pollutant backflush through leaks in liquid transport systems is used for algorithmic leak location identification. The paper compares the proposed concept with known monitoring methods. The theoretical analysis of the method's capability to increase leak localization distance and detect the location of tiny holes in pipelines is provided. …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 1, 2025 · pp. 13–22 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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Optimizing Sampling Techniques Using Fuzzy Set Theory: A Comprehensive Approach
Abstract: Sampling is a critical process in statistics, used to estimate population parameters without needing to examine the entire population. Traditional sampling methods, such as simple random sampling, stratified sampling, and cluster sampling, face limitations when applied to complex or heterogeneous populations with imprecise boundaries. These methods often fail to accurately represent populations with overlapping characteristics or missing data, resulting in sampling bias and reduced accuracy. To address these challenges, this …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 1, 2025 · pp. 29–43 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