Results 31 to 40 of about 81,722 (194)
, 2023 The equation $f^n+g^n=1$, $n\in\mathbb{N}$ can be regarded as the Fermat Diophantine equation over the function field. In this paper we study the characterization of entire solutions of some system of Fermat type functional equations by taking $e^{g_1(z)}
Haldar, Goutam
core
Properties of meromorphic solutions to certain differential-difference equations
Electronic Journal of Differential Equations, 2013 We consider the properties of meromorphic solutions to certain type of non-linear difference equations. Also we show the existence of meromorphic solutions with finite order for differential-difference equations related to the Fermat type functional ...
Xiaoguang Qi, Lianzhong Yang
doaj
Generalized free wreath products and their operator algebras
Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.Abstract We develop a new approach on free wreath products, generalizing the constructions of Bichon and of Fima‐Pittau. We show stability properties for certain approximation properties such as exactness, Haagerup property, hyperlinearity, and K‐amenability. We study qualitative properties of the associated von Neumann algebra: factoriality, primeness,
Pierre Fima, Arthur Troupel
wiley +1 more source
Photon‐Sphere Modes in Curved Optical Microcavities: A Black‐Hole Analogue Laser
Advanced Science, Volume 13, Issue 28, 18 May 2026.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
Chenni Xu +9 more
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Journal of Synchrotron Radiation, Volume 33, Issue 3, Page 829-840, May 2026.The 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 ...
Darren Thompson +2 more
wiley +1 more source
A necessary and sufficient condition for the primality of Fermat numbers [PDF]
, 2001 summary:We examine primitive roots modulo the Fermat number $F_m=2^{2^m}+1$. We show that an odd integer $n\ge 3$ is a Fermat prime if and only if the set of primitive roots modulo $n$ is equal to the set of quadratic non-residues modulo $n$. This result
Somer, Lawrence, Křížek, Michal
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The hard X‐ray ptychography endstation at the Taiwan Photon Source
Journal of Synchrotron Radiation, Volume 33, Issue 3, Page 841-847, May 2026.The newly commissioned hard X‐ray ptychography endstation at the Taiwan Photon Source, TPS 25A2, is introduced, detailing the instrumental specifications and demonstrating a benchmark spatial resolution of 6.9 nm in 2D, showcased through the imaging of a standard test pattern, inorganic nanoparticles and a complex biological structure.Following our ...
Yi-Wei Tsai +9 more
wiley +1 more source
A new class of modular equation for Weber functions [PDF]
, 2007 We describe the construction of a new type of modular equation for Weber functions. These bear some relationship to Weber's modular equations of the irrational kind. Numerous examples of these equations are explicitly computed.
Hart, William B.
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On solutions of several Fermat-type partial differential-difference equations in C2
Demonstratio MathematicaIn this paper, we study entire solutions of several Fermat-type partial differential-difference equations in C2 ${\mathbb{C}}^{2}$ by applying Nevanlinna theory of meromorphic functions in several complex variables.
Tang Caoqiang, Huang Zhigang
doaj +1 more source
Counting 5‐isogenies of elliptic curves over Q$\mathbb {Q}$
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract We show that the number of 5‐isogenies of elliptic curves defined over Q$\mathbb {Q}$ with naive height bounded by H>0$H > 0$ is asymptotic to C5·H1/6(logH)2$C_5\cdot H^{1/6} (\log H)^2$ for some explicitly computable constant C5>0$C_5 > 0$. This settles the asymptotic count of rational points on the genus zero modular curves X0(m)$\mathcal {X}
Santiago Arango‐Piñeros +3 more
wiley +1 more source