Results 31 to 40 of about 5,254 (156)
All solutions of consecutive natural numbers sum equation and their closed forms
Al-JabarPurpose: This study aims to find a closed-form solution for all ordered pairs of natural numbers (?,?) satisfying the consecutive natural number sum equation 1 + 2 + ⋯ + ? sama dengan (? + 1) + (? + 2) + ⋯ + ?. This research contributes to number theory,
Sofihara Al Hazmy +3 more
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Levels of Distribution and the Affine Sieve
, 2014 This article is an expanded version of the author's lecture in the Basic Notions Seminar at Harvard, September 2013. Our goal is a brief and introductory exposition of aspects of two topics in sieve theory which have received attention recently: (1) the ...
Kontorovich, Alex
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On the structure of graphs with integer Sombor indices [PDF]
Discrete Mathematics Letters, 2021 Tomislav Doslic, Tamas Reti, Akbar Ali
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Mordell-Weil ranks of families of elliptic curves associated to Pythagorean triples
, 2013 We study the family of elliptic curves $y^2=x(x-a^2)(x-b^2)$ parametrized by Pythagorean triples $(a,b,c)$. We prove that for a generic triple the lower bound of the rank of the Mordell-Weil group over $\mathbb{Q}$ is 1, and for some explicitly given ...
Naskręcki, Bartosz
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Journal of Mathematics Research, 2021 Given a leg of a right-angled triangle a, this formula gives the other leg b and the hypotenuse c by the usage of a pattern observed in Pythagorean triples. This is different as compared to Euclids method since Euclids method takes two arbitrary numbers as the input while this uses the side of the right-angled triangle as the input.
openaire +2 more sources
An Interval‐Valued Fermatean Neutrosophic Framework for Sustainable Transportation Under Uncertainty
Journal of Mathematics, Volume 2026, Issue 1, 2026.Transportation planning is facing heightened complexity because the dynamic parameters influenced by globalization and unpredictable technological disruptions. Traditional models are not capable to handle interval‐based uncertainties related to supply, demand, and costs, especially as the scale of suppliers and customers expands.
Muhammad Kamran +4 more
wiley +1 more source
Plane integral drawings of the platonic solid graphs with triangle faces [PDF]
Discrete Mathematics Letters, 2021 Alewyn P. Burger +2 more
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Journal of Mathematics, Volume 2026, Issue 1, 2026.This paper advances the theory of bipolar Pythagorean neutrosophic fuzzy (BPNF) sets by establishing their formalization within a topological and metric framework, while also demonstrating their role in decision‐making under uncertainty. The main contributions are as follows: (1) definition and characterization of BPNF topological spaces, providing a ...
Akiladevi Natarajan +5 more
wiley +1 more source
Poka: A Necro‐Robot Beetle with a Measured Payload Ratio of 6847%
Advanced Robotics Research, Volume 1, Issue 2, August 2025.Here, Poka, a necro‐robot beetle with the ability to carry more than 68 times its own weight, is introduced, making it also a walking robot with the highest payload ratio measured to date. This paper is concerned with the design, manufacture and validation of ‘Poka', a novel millimetre‐scale necro‐robot aimed at bridging the performance gap between ...
Yordan Tsvetkov, Parvez Alam
wiley +1 more source
The Hofstadter butterfly: bridging condensed matter, topology, and number theory
Frontiers in PhysicsCelebrating its golden jubilee, the Hofstadter butterfly fractal is a remarkable fusion of art and science. This iconic “X”-shaped fractal captivates physicists, mathematicians, and enthusiasts alike by elegantly illustrating the energy spectrum of ...
Indubala I. Satija
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