Results 1 to 10 of about 307 (115)
Photon-Sphere Modes in Curved Optical Microcavities: A Black-Hole Analogue Laser. [PDF]
Adv Sci (Weinh)An optical analogue of a Schwarzschild black hole is realized using curved microcavities that preserve light‐like geodesics. A new family of laser modes confined around the photon sphere is identified alongside conventional whispering‐gallery modes. Analytical theory, numerical simulations, and experiments reveal curvature‐induced confinement, enabling
Xu C +9 more
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Micro-Computed Tomography beamline at the Australian Synchrotron: data acquisition and processing pipeline. [PDF]
J Synchrotron RadiatThe Micro‐Computed Tomography (MCT) beamline at the Australian Synchrotron has undergone significant advancements in data acquisition and processing infrastructure to support the growing diversity of user needs and experimental techniques. Recent developments in data acquisition and processing infrastructure at the beamline are presented.The Micro ...
Thompson D, Arhatari BD, Stevenson A.
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Local criteria for the unit equation and the asymptotic Fermat’s Last Theorem [PDF]
Proceedings of the National Academy of Sciences of the United States of America, 2021 Nuno Freitas +2 more
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Fermat and Mersenne numbers in $k$-Pell sequence
Математичні Студії, 2021 For an integer $k\geq 2$, let $(P_n^{(k)})_{n\geq 2-k}$ be the $k$-generalized Pell sequence, which starts with $0,\ldots,0,1$ ($k$ terms) and each term afterwards is defined by the recurrence $ P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots +P_{n-k}^{(k)}
B. Normenyo, S. Rihane, A. Togbe
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On the equation fn + (f″)m ≡ 1
Demonstratio Mathematica, 2023 Let nn and mm be two positive integers, and the second-order Fermat-type functional equation fn+(f″)m≡1{f}^{n}+{({f}^{^{\prime\prime} })}^{m}\equiv 1 does not have a nonconstant meromorphic solution in the complex plane, except (n,m)∈{(1,1),(1,2),(1,3 ...
Dang Guoqiang
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Demonstratio Mathematica, 2023 In this article, we investigate the existence and the precise form of finite-order transcendental entire solutions of some system of Fermat-type quadratic binomial and trinomial shift equations in Cn{{\mathbb{C}}}^{n}. Our results are the generalizations
Haldar Goutam, Banerjee Abhijit
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On the ESQ Property of Certain Representations of Metacyclic Groups [PDF]
Advances in Group Theory and Applications, 2017 A group representation is said to have the ESQ property if it is isomorphic to a quotient of its own exterior square. Let us denote the semidirect product of cyclic groups $Z_p\rtimes Z_q$ by $F_{p,q}$, where p is a prime and $q | p − 1$.
János Wolosz
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Les tables de réfraction astronomique
Comptes Rendus. Physique, 2023 The paper investigates the refraction as it concerns position astronomy and the attempts of generations of astronomers since Tycho Brahe to estimate its size as a function of the apparent zenith distance of the sources.
Mignard, François
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RETRACTED: On the Nature of Some Euler’s Double Equations Equivalent to Fermat’s Last Theorem
Mathematics, 2022 In this work, I provide a new rephrasing of Fermat’s Last Theorem, based on an earlier work by Euler on the ternary quadratic forms. Effectively, Fermat’s Last Theorem can be derived from an appropriate use of the concordant forms of Euler and from an ...
Andrea Ossicini
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A note on the ternary Diophantine equation x2 − y2m = zn
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 Let ℕ be the set of all positive integers. In this paper, using some known results on various types of Diophantine equations, we solve a couple of special cases of the ternary equation x2 − y2m = zn, x, y, z, m, n ∈ ℕ, gcd(x, y) = 1, m ≥ 2, n ≥ 3.
Bérczes Attila +3 more
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