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24 articles for “prime numbers”
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On the Formula for Distribution of Prime Numbers
Abstract: The detailed derivation of the distribution of prime numbers, the research result originally presented in the 2013’ monograph Study of Analytic Number Theory: Riemann’s Hypothesis and Prime Number Theorem with Addendum on Integer Partitions published with Cam- bridge International Science Publishing, is once again presented in this paper with the purpose to give an insight to unfamiliar authors.
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 1, Issue 1, 2014 · pp. 16–19 Read article
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On Searching the New Chemical Element by Prime Numbers
Abstract: This paper presents a direction for searching the new chemical element by prime number. Every chemical element is defined by atomic number and weight. These comprised with the set of natural numbers. The prime number is the subset of natural number. We define the new mapping for chemical element and prime number in this paper. Beryllium is taken as an example to prove the proposed theory.Keywords: Chemical Element, Prime Number, …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 7, Issue 2, 2020 · pp. 21–23 Read article
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Dynamics of Prime Gap Sets: An Algorithmic and Set-Theoretic Approach
Abstract: In this paper, we present a theorem and an efficient algorithm for computing all prime numbers up to a given integer X. Our theorem establishes a relationship between the primes up to X and those up to (X+1)2, providing a theoretical foundation for the algorithm. The proposed method improves upon the traditional Sieve of Eratosthenes by dynamically eliminating multiples of primes using only the remaining numbers in the set, thereby …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 3, 2025 · pp. 20–25 Read article
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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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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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Artificial Neural Network and Its Application to Diagnosis
Abstract: In this paper, we are giving an excellent idea for the designing of the standard diagnosis key diagnosis systems, which security is based on the well known number theoretic problem, i.e., elliptic curve discrete logarithm problem in multiplicative group of the finite field. But now we are moving in the revolutionary idea, “The Automatic groups G converted into the multiplicative groups G’ of the finite field Zp* of the order …
Published in Journal of Advancements in Robotics · Vol. 7, Issue 2, 2020 · pp. 15–22 Read article
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Medical Applications of Artificial Neural Network
Abstract: The correspondence between the natural neurons and artificial neurons is defined in this paper. Thus, an excellent idea appears to design the standard diagnosis key diagnosis systems, which security is based on the well known number theoretic problem, i.e. elliptic curve discrete logarithm problem in multiplicative group of the finite field. But now we are moving in the revolutionary idea, “The Automatic groups G converted into the multiplicative groups G’ …
Published in Journal of Software Engineering Tools & Technology Trends · Vol. 7, Issue 2, 2020 · pp. 23–30 Read article
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Construction of Neighbour Balanced BIBRC Designs
Abstract: AbstractConstruction of a series of Balance Incomplete Block with nested Rows and Columns (BIBRC) designs having Neighbor Balanced properties has been presented in this paper. The series of BIBRC designs has been developed on the concept of mutually orthogonal mates (MOM’s) of existing BIBRC designs with v as a prime number. The designs thus constructed are found to be first order neighbor balanced with respect to rows, columns as well …
Published in Research & Reviews : Journal of Statistics · Vol. 2, Issue 3, 2013 · pp. 1–7 Read article
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Color Image Segmentation Using Optimized FCM Based on Modified Xie-Beni’s Validity Index
Abstract: AbstractColor image segmentation is an important task for image processing. There are many techniques used for segmentation; among them clustering is the most popular technique. The main issue of clustering process is to determine the number of clusters present in the image, which often is decided by the user or by cluster validity index. It is illogical to have correct or exact knowledge about the data points present in the …
Published in Journal of Image Processing & Pattern Recognition Progress · Vol. 4, Issue 2, 2017 · pp. 4–12 Read article
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Design Fabrication and Experimental Analysis of Air Conditioner by Peltier’s Module
Abstract: The modern air conditioner cools by using refrigeration gases like Freon, CFCs, etc. Although these refrigerants produce good results, one of their main drawbacks is the release of hazardous chemicals that affect the ozone molecules. Attempting to make utilisation of air conditioners that cool using thermoelectric cooling modules, which operate by the Peltier effect, becomes an option to solve this problem. These modules safeguard the ecosystem by not emitting any …
Published in Journal of Aerospace Engineering & Technology · Vol. 12, Issue 2, 2022 · pp. 9–15 Read article
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Self Driving Car Simulation Using Deep Learning
Abstract: Every year, traffic accidents account for 2.2% of worldwide deaths. That accumulates to a few millions a year. On prime of this, some individuals are seriously lacerate in auto-related accidents annually in large numbers mostly due to human error. From distracted driving to drunk driving to reckless driving to careless driving, one poor or inattentive call may be the distinction between a typical drive and a critical state of affairs. …
Published in Journal of Advancements in Robotics · Vol. 8, Issue 1, 2021 · pp. 6–13 Read article
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Review: Distribution Generation and Islandin
Abstract: The demand for distributed generation (DG) has increased in recent years and many countries across the world are adopting it due to various factors such as improvements in technologies including renewable energy sources and the efficiency it provides. However, islanding detection is of prime importance as it can be hazardous to the maintenance workers. The increasing use of distributed generation causes more number of parameters to be controlled for the …
Published in Journal of Power Electronics and Power Systems · Vol. 6, Issue 2, 2016 · pp. 45–54 Read article
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Competency of Natural Fiber Based Eco-Friendly Friction Lining Composites Over the Conventional Friction Material
Abstract: The Braking system is important system of automobiles and is responsible for providing better performance and safety. A Millions of automobiles are frequently decelerated and stopped at heavy traffic zone. Overall performance of vehicle braking system depends on braking conditions and brake material. All friction based application releases wear products; either gaseous form or particulate matter form and braking system is prime source of non exhaust particulate matter emission. The …
Published in Journal of Polymer & Composites · pp. 57–65 Read article
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Competency of Natural Fiber Based Eco-Friendly Friction Lining Composites Over the Conventional Friction Material
Abstract: The Braking system is important system of automobiles and is responsible for providing better performance and safety. A Millions of automobiles are frequently decelerated and stopped at heavy traffic zone. Overall performance of vehicle braking system depends on braking conditions and brake material. All friction based application releases wear products; either gaseous form or particulate matter form and braking system is prime source of non exhaust particulate matter emission. The …
Published in Journal of Polymer & Composites · Vol. 9, Issue 2, 2021 · pp. 57–65 Read article
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An Efficient Counter Using Modified Upper and Lower SVL Techniques and TSPCL
Abstract: Low power VLSI has emerged as the fundamental building block of the modern electronic era. This leads to a substantial paradigm shift where both power dissipation, performance and area of utmost importance. In the earlier time of fabrication, power dissipation was mainly neglected due to low device density and low operating frequency needed for computation. But in modern technological era, the need for high device density, higher operating frequency, proliferation …
Published in Research & Reviews : Journal of Physics · Vol. 13, Issue 2, 2024 · pp. 37–43 Read article
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Geospatial Analysis of Wetlands in Jharkhand Using Multi-temporal Satellite Data
Abstract: The present study was carried out to study the wetlands of Jharkhand using pre-monsoon and post-monsoon satellite data. Different indices were used to quantify the seasonal extent of wetlands, aquatic vegetation and turbidity levels of wetlands. Wetlands occupying an area smaller than 2.25 ha were identified separately as small wetlands. The total number of wetlands identified in Jharkhand was 2436 covering an area of 1568.27 sq. km. Small wetlands were …
Published in Journal of Remote Sensing & GIS · Vol. 3, Issue 3, 2012 · pp. 22–30 Read article
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Solar Charkha Retrofit
Abstract: Hand operated charkha is used to make thread from cotton. It is sensitive work and involves great deal of care and effort to spin the charkha wheel manually during thread extrusion. Charkha operation causes physical strain and fatigue in long run. Abrupt spinning creates thread knots and breakage thus results poor quality and cotton wastage. Large number of people board on this khadi profession to make their meager earnings and …
Published in Trends in Machine design · Vol. 9, Issue 3, 2022 · pp. 23–28 Read article
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Advanced Fuel Flow Measurement in Aero Engine Using Microcontroller
Abstract: AbstractThe amount of fuel that must flow in an aircraft engine is an important parameter that must be considered while designing the fuel control unit in an aircraft engine. The amount of fuel supplied must be optimised as per the speed requirement of aircraft. The basic aim of this project is to solve the major problem of measurement of fuel flow rate in an aero engine. This project fulfils the …
Published in Journal of Operating Systems Development & Trends · Vol. 6, Issue 2, 2019 · pp. 6–13 Read article
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Comparative Study of Reinforcement Learning Algorithms on Traffic Light Control System
Abstract: With the changing times, the need of upgraded and efficient state-of-the-art traffic light control system is truly required. How well do various state-of-the-art algorithms handle complex real-life situations, more technically speaking, how well the reward function operates and minimizes the waiting time, is the prime question of the hour. Here we have successfully employed three reinforcement learning agents-REINFORCE, D3QN and DDPG each of which can independently handle large volumes of …
Published in Journal of Artificial Intelligence Research & Advances · Vol. 8, Issue 3, 2021 · pp. 33–45 Read article
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Therapeutic view of Anupadeshaja vikara in Ayurveda
Abstract: Introduction: Maintenance of the health in healthy and the cure of the diseased one is the prime goal of Ayurveda science. The dosha and dhatu are responsible for the mechanism of the body. Thus, the treatment of the diseases aims at the balancing the dosha and dhatu. The spectrum of treatment of diseases includes desha, dosha, aushadha and sadhyasadhyata of the vyadhi. The term desha encompasses deha (body) and bhumi …
Published in Research and Reviews : A Journal of Ayurvedic Science, Yoga and Naturopathy · Vol. 10, Issue 2, 2023 · pp. 1–5 Read article