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16 articles for “number theory”
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Perfect Numbers: Computational and Technical Exploration
Abstract: This paper explores perfect numbers, by getting into their historical significance and computational journey from ancient times to the present day. The discussion covers the mathematical definition of perfect numbers, their importance in number theory, and the major milestones in their discovery. Also, it elaborates how the coders are using their skillsets to identify new perfect numbers and the transforming outcome of getting more and more perfect numbers found. By …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 13, Issue 1, 2026 · pp. 9–16 Read article
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Temperature dependence of Schmidt number of composite material based liquid lithium
Abstract: This work presents a simple formalism for Schmidt number and its temperature dependence for liquid lithium. It is explained that the temperature dependence of Schmidt number (Sc = η/ ρD) can be understood through dependence of topological-short-range-order (TSRO) parameter on temperature. Expression for Schmidt number has been deduced in terms of average potential energy US of superficial core, probability of diffusional displacement (P) and the TSRO parameter (x) . Calculations …
Published in Journal of Polymer & Composites · Vol. 12, Issue 3, 2024 · pp. 206–212 Read article
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Primality Testing: A Comprehensive Analysis of Methods and Time Complexity
Abstract: This paper examines various primality testing algorithms and analyzes their time complexity. The algorithms we examine include the trial division, which is straightforward but becomes inefficient with large numbers; Fermat’s little theorem which is a probabilistic method included in Monte Carlo type of randomized algorithm; the Solovay–Strassen, based on properties from number theory, particularly those related to Euler’s criterion and Jacobi symbols; and the Miller–Rabin Probabilistic Test, which balances efficiency …
Published in International Journal of Algorithms Design and Analysis Review · Vol. 2, Issue 2, 2024 · pp. 25–31 Read article
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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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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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The Evolution and Impact of Numbers: From Ancient Tallies to Quantum Computing: Review Article on Numbers
Abstract: Numbers are among the most fundamental constructs in human civilization, serving as the backbone of mathematics, science, technology, and virtually every aspect of daily life. They represent not only quantities and measures but also relationships, structures, and patterns that underpin the fabric of human understanding. From the earliest tallies etched on bones by prehistoric humans to the sophisticated numerical systems embedded in today’s artificial intelligence and quantum computing, the evolution …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 3, 2025 · pp. 15–19 Read article
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Comparative Study Between Dashavatara (Incarnation) and Darwinian Theory of Evolution
Abstract: The word Dashavatara derives from Dasha, meaning “Ten”, and Avatara, roughly equivalent to “Incarnation”. Lord Vishnu manifested in various avatars to safeguard the universe and reinstate “peace and dharma” during the four distinct yugas, or cosmic cycles. The Hindu text Dashavatara, which describes ten forms of Lord Vishnu, has a better developed theory of evolution than the hypothesis put out by English scientist Charles Darwin in the 17th century. Objective …
Published in OmniScience: A Multi-disciplinary Journal · Vol. 14, Issue 1, 2024 · pp. 50–58 Read article
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The Anhadnaad Universe
Abstract: Current Science considers that 95% universe is made of Dark energy and Dark Matter which are completely unknown entities and can’t be detected directly. Current Science also does not believe in independent existence of Consciousness on its own. It rather consider it as an outcome of electrical interaction in brain cells which means there are as many consciousnesses as the number of brains in the entire universe. But my theory …
Published in Research & Reviews : Journal of Physics · Vol. 14, Issue 2, 2025 · pp. 19–29 Read article
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Theoretical Study of Z = 122 Nuclei
Abstract: We used atomic nuclei with proton number Z = 122 to calculate bulk properties within the relativistic mean field (RMF) theory. We utilized the force parameters recognized as NL3 in our calculations. We extend our calculation to isotopic series of Z = 122 and analyses the theoretical outcomes. A whole isotopic chain of nuclei with atomic number 𝑍 = 122 Z=122 is included in our inquiry, enabling a methodical examination …
Published in Journal of Nuclear Engineering & Technology · Vol. 16, Issue 1, 2026 · pp. 1–9 Read article
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Thevenin Impedance Networks for Spice Simulation Using Analog Behavioural Modelling
Abstract: PSPICE/OrCAD software analog behavioral modeling (FREQ) option is used to obtain equivalent circuits for Thevenin equivalent resistance to be used for three types of applications for different circuits (other different networks with these Thevenin models at DC), and Spice files are described to simulation circuits with AC analyses. Three different applications are useful in linear integrated circuits using DC Thevenin resistance of two networks are considered. Firstly, the DC Thevenin …
Published in Journal of VLSI Design Tools and Technology · Vol. 14, Issue 3, 2024 · pp. 39–46 Read article
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Modeling Galaxy Formation in a Hierarchical Universe: A Fiducial Approach and Comparison with Observational Data
Abstract: We have developed a detailed model to understand how galaxies form in the framework of hierarchical theories of structure formation. Our model accounts for key processes like the formation and merging of dark matter halos, the heating and cooling of gas inside these halos, the regulation of star formation driven by energy from evolving stars and supernovae, galaxy mergers, and the changes in star populations over time. This approach is …
Published in International Journal of Universe · Vol. 1, Issue 1, 2025 · pp. 30–36 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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Unravelling the Influence of Dimensions on the Thermoelectric Properties of AHEGNR
Abstract: The thermoelectric properties of hydrogenated edge semiconductor graphene nanoribbons (GNRs) have thus far been explored in detail. The effects of varying the sizes of zigzag hydrogenated edge graphene nanoribbons (ZHEGNRs) and armchair hydrogenated edge graphene nanoribbons (AHEGNRs) in terms of their properties were investigated in this study. This was achieved via the control of the graphene nanoribbon dimensions i.e., width and length by utilizing density functional theory in Quantum Espresso, …
Published in Journal of Nanoscience, NanoEngineering & Applications · Vol. 14, Issue 3, 2024 · pp. 45–51 Read article
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Currents, Waves, and Whirls: An Academic Exploration of Fluid Mechanics
Abstract: Fluid mechanics investigates the behavior of liquids and gases in motion and at rest, revealing the principles that control natural occurrences and engineering systems alike. This article gives an easy review of essential concepts such as fluid characteristics, pressure, flow patterns, and the contrast between laminar and turbulent flow. It explores how fundamental rules, including conservation of mass and energy, impact the transport of fluids across varied settings. Through real-world …
Published in Recent Trends in Fluid Mechanics · Vol. 13, Issue 1, 2026 · pp. 8–13 Read article
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Beyond Binary: A Holistic Exploration of Fuzzy Logic Systems in Control Theory-An Extensive Review and Future Directions
Abstract: Now a days non renewable energy or conventional energy sources are reduced due to the increased usage of energy for several purposes, for that renewable energy source are introduced for the same. This help islanded areas electrification, several methods are used for the storage and distribution of energy. one of the technique is fuzzy logic control, in this paper discuss about the usage of energy and fuzzy logic system usage …
Published in International Journal of Electrical Power and Machine Systems · Vol. 2, Issue 1, 2024 · pp. 8–13 Read article
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Deploying Fuzzy Logic for Self-Tuning Regulator Design for Motion Control in Modern Electrical Machines
Abstract: Modern electrical machines require sophisticated motion control systems capable of adapting to varying operating conditions, load disturbances, and parameter uncertainties. Traditional self-tuning regulators (STR) based on classical control theory often struggle with nonlinearities, time-varying dynamics, and complex operational environments characteristic of contemporary electric drives. This article presents a comprehensive framework for deploying fuzzy logic in self-tuning regulator design to address these challenges in motion control applications. Fuzzy logic controllers leverage …
Published in International Journal of Electrical Machine Analysis and Design · Vol. 3, Issue 2, 2025 · pp. 11–21 Read article