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16 articles for “Discrete Mathematics”
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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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Intuitionistic Fuzzy Hypergraph Laplacians and Dominating Transversals for Resilient Discrete Network Design
Abstract: This manuscript develops a discrete mathematical framework for resilience analysis on networks whose interactions are polyadic, uncertain, and partially conflicting. Classical graphs compress multi-way coordination into pairwise edges, while ordinary fuzzy graphs often ignore the non-membership information that becomes critical in emergency logistics, infrastructure interdependence, and cyberphysical coordination. We therefore formulate an intuitionistic fuzzy hypergraph in which each vertex hyperedge incidence carries membership, non-membership, and hesitation, and we construct a …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 13, Issue 2, 2026 · pp. 15–21 Read article
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Spectral Intuitionistic Fuzzy Hypergraph Operators and Dominance Kernels for Resilient Discrete Network Design
Abstract: A new discrete-mathematical framework is developed for resilient network design on intuitionistic fuzzy hypergraphs, where uncertainty is explicitly represented through membership, non-membership, and hesitation degrees associated with both vertices and hyperedges. These three components are systematically integrated into an effective incidence operator that captures the underlying uncertain relationships within complex hypergraph structures. Based on this operator, both un-normalised and normalized Laplacian matrices are formulated to characterize the spectral properties and …
Published in Recent Trends in Mathematics · Vol. 3, Issue 2, 2026 · pp. 41–48 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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Real-Time Edge Detection Camera Module Using Discrete Taylor Transform and Heat Equation (PDE): An Applied Mathematical Approach
Abstract: In modern digital signal processing, the capability for denoising and smoothing in real time is very important in scientific, engineering, and industrial applications. This paper presents an efficient hybrid framework that merges two mathematically sound methods, namely, DTT and PDE defined as the Heat Equation, to robustly denoise a signal with minimal distortion. The model addresses one of the most challenging tasks in signal restoration, which maintains the fidelity of …
Published in Current Trends in Signal Processing · Vol. 16, Issue 2, 2026 Read article
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A SEIR-Informed Stacked Fusion of Prophet, XGBoost, and LSTM for Ward-Level Epidemic Forecasting in Amravati Municipal Corporation
Abstract: Municipal epidemic preparedness depends on accurate short-horizon forecasts at fine spatial granularity. Ward-level incidence series are typically nonstationary due to changing contact patterns, interventions, reporting delays, and heterogeneous demographic and environmental factors. This paper presents a mathematically formulated hybrid forecasting architecture designed for Amravati Municipal Corporation (AMC). The method decomposes observed incidence into (i) a mechanistic SEIR baseline that enforces epidemiological structure and (ii) a data-driven residual learned using Prophet …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 13, Issue 1, 2026 · pp. 17–23 Read article
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Research on Selection Method of the Optimum Alternative Using Improved AHP Method in NSDL Environment
Abstract: In this paper, we have considered the development of a decision-making tool to optimize the design of the ship-roll fin stabilizer using improved analytical hierarchy process (AHP) in a network-oriented system description language (NSDL) environment developed by combining the advantages of Petri nets and object-oriented programming languages. First, we have considered the network-oriented system description language NSDL, a new software development tool that combines the advantages of Petri nets and …
Published in International Journal of Machine Systems and Manufacturing Technology · Vol. 3, Issue 1, 2025 · pp. 46–56 Read article
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Idempotent Semiring Path Algebras and Fuzzy Dominance Automata for Multi-State Communication Reliability
Abstract: A semiring-based theory is proposed for multi-state communication reliability with fuzzy dominance constraints. Links are weighted in the max-product semiring, while nodes carry dominance coefficients and operating states that modulate admissible transitions in a weighted automaton. The paper derives semiring matrix products, Kleene closures, fixed point equations, congestion-regularized path scores, and reliability inequalities. A fuzzy dominance automaton is introduced so that route selection depends not only on link reliability but …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 13, Issue 2, 2026 · pp. 07–14 Read article
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Differential Model of Wave Vibration on Strings and Rods
Abstract: Vibration, as a physical phenomenon, plays a multifaceted role in both natural and engineered systems. Beyond its essential contribution to communication through sound and speech, it finds critical application in various technological domains. For instance, in the design of stringed musical instruments such as violins and guitars, precise manipulation of string vibrations defines tonal quality and musical resonance. Similarly, metal rods in tuning forks exhibit vibrational properties that are finely …
Published in Research & Reviews : Journal of Physics · Vol. 14, Issue 1, 2025 · pp. 17–21 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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Effect of Sinusoidal and Inverse sinusoidal Load on the Vibration and Buckling Behaviour of Laminated Composite Symmetrical and Unsymmetrical Trapezoidal Panels
Abstract: Using finite element (FE) techniques, this work analyzes the influence of sinusoidal and invers sinusoidal stresses on the buckling behavior of trapezoidal laminated composite panels (also known as trapezoidal laminated composite panels). The discretization of the composite panel is accomplished by the use of an eight-noded iso-parametric plate element, which has five degrees of freedom for each node. Due to the incorporation of Higher Order Shear Deformation Theory (HOSDT) into …
Published in Journal of Polymer & Composites · Vol. 13, Issue 3, 2025 Read article
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Effect Of Sinusoidal and Inverse Sinusoidal Load on The Vibration and Buckling Behaviour of Laminated Composite Symmetrical and Unsymmetrical Trapezoidal Panels
Abstract: Using finite element (FE) techniques, this work analyzes the influence of sinusoidal and inverse sinusoidal stresses on the buckling behavior of trapezoidal laminated composite panels (also known as trapezoidal laminated composite panels). The discretization of the composite panel is accomplished by the use of an eight-noded iso-parametric plate element, which has five degrees of freedom for each node. Due to the incorporation of Higher Order Shear Deformation Theory (HOSDT) into …
Published in Journal of Polymer & Composites · Vol. 13, Issue 3, 2025 · pp. 72–84 Read article
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Continuous-Time Modelling of the Two-Input Fourth Order DC_DC Converter
Abstract: Two-input fourth-order integrated (TIFOI) converter is designed to process the power from two different sources Vg1 and Vg2. This converter facilitates regulation of dc-bus voltage and LVS current. In the power conversion process it performs bucking operation for first dc source Vg1, buck-boost operation for the second source Vg2. Power stage dynamics of the TIFOI converters is modeled using the state-space analysis. The system modelling plays an important role in …
Published in Journal of Control & Instrumentation 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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Optimized Design and Control of Oil Exploitation Strategies: An Assisted Approach
Abstract: Because there are so many factors and scenarios to consider, optimizing oil exploitation tactics requires complicated decision-making. Conventional approaches frequently concentrate on particular elements of the design infrastructure, which restricts their capacity to fully handle the process. In order to maximize a set of oil exploitation variables in a hierarchical fashion, this research proposes a novel assisted optimization technique that combines mathematical algorithms with engineering analysis. By grouping variables into …
Published in Journal of Petroleum Engineering & Technology · Vol. 15, Issue 1, 2025 · pp. 29–34 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