Results 41 to 50 of about 7,755,587 (178)

Fermat-type equations of signature $$(13,13,p)$$ via Hilbert cuspforms [PDF]

Mathematische Annalen, 2013
In this paper we prove that equations of the form $x^{13} + y^{13} = Cz^{p}$ have no non-trivial primitive solutions (a,b,c) such that $13 \nmid c$ if $p > 4992539$ for an infinite family of values for $C$. Our method consists in relating a solution (a,b,c) to the previous equation to a solution (a,b,c_1) of another Diophantine equation with ...
Dieulefait, Luis, Freitas, Nuno
openaire   +2 more sources

The Impact of ChatGPT on Higher Education: A Systematic Review of Global Opportunities, Perceptions, and Challenges

Journal of Computer Assisted Learning, Volume 42, Issue 5, October 2026.
ABSTRACT Background The advent of artificial intelligence (AI) has fundamentally changed how education is delivered and how students perform. Since its launch, ChatGPT, a popular generative AI tool, has generated mixed reactions. Objectives This research systematically reviews the opportunities, perceptions, and challenges of using ChatGPT among ...
Olukayode Emmanuel Apata, Oi‐Man Kwok, Segun Timothy Ajose   +2 more
wiley   +1 more source

Shorter X‐ray refractive lens design: a large‐aperture single‐lens dual‐focus kinoform lens based on an oval curved surface

Journal of Synchrotron Radiation, Volume 33, Issue 5, Page 1364-1371, September 2026.
This paper presents a novel kinoform refractive lens and utilizes the beam propagation method to simulate the focusing performance of the lens. The results demonstrate that this lens not only enhances the gain and reduces the FWHM but also reduces the lens length.At synchrotron radiation facilities, X‐ray focusing elements play a crucial role. To solve
Yaowu Zhang, Yuanze Xu, Tianchong Zhang, Bo Wang, Longlong Wu, Futing Yi, He Lin, Jing Liu   +7 more
wiley   +1 more source

Surface subgroups for cocompact lattices of isometries of H2n$\mathbb {H}^{2n}$

Journal of Topology, Volume 19, Issue 3, September 2026.
Abstract We prove the existence of surface subgroups within any cocompact lattice Γ$\Gamma$ in SO(2n,1)$\mathrm{SO}(2n,1)$ for n⩾2$n\geqslant 2$. This result addresses the cases missing from the work of Hamenstädt in 2015, who constructed surface subgroups in cocompact lattices for all other rank‐1 simple Lie groups of noncompact type.
Jeremy Kahn, Zhenghao Rao
wiley   +1 more source

Boundary‐Only Weak Deflection by Regular Black Holes, Black‐Bounces, Wormholes, and Static Quadrupolar Spacetimes

Fortschritte der Physik, Volume 74, Issue 8, August 2026.
ABSTRACT We apply the boundary‐only isothermal formulation of finite‐distance weak gravitational deflection to regular black holes, black‐bounces, traversable wormholes, non‐asymptotically flat backgrounds, and static quadrupolar spacetimes. The methodological advance is not a new value for a known bending angle.
Reggie C. Pantig, Ali Övgün
wiley   +1 more source

The Role of Dice in the Emergence of the Probability Calculus

International Statistical Review, Volume 94, Issue 2, Page 464-483, August 2026.
Summary The early development of the probability calculus was clearly influenced by the roll of dice. However, while dice have been cast since time immemorial, documented calculations on the frequency of various dice throws date back only to the mid‐13th century.
David R. Bellhouse, Christian Genest
wiley   +1 more source

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  

Derivations as algebras

Journal of the London Mathematical Society, Volume 114, Issue 2, August 2026.
Abstract Differential categories provide the categorical foundations for the algebraic approaches to differentiation. They have been successful in formalizing various important concepts related to differentiation, such as, in particular, derivations. In this paper, we show that the differential modality of a differential category lifts to a monad on ...
Jean‐Simon Pacaud Lemay, Chiara Sava
wiley   +1 more source

On 7‐adic Galois representations for elliptic curves over Q$\mathbb {Q}$

Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.
Abstract In recent years, significant progress has been made on Mazur's Program B, with many authors beginning a systematic classification of all possible images of p$p$‐adic Galois representations attached to elliptic curves over Q$\mathbb {Q}$. Currently, the classification is only complete for p∈{2,3,13,17}$p \in \lbrace 2,3,13,17\rbrace$.
Lorenzo Furio, Davide Lombardo
wiley   +1 more source

Guiding and Manipulating Light Fields in Microstructured Liquid Crystals

Advanced Physics Research, Volume 5, Issue 7, July 2026.
This review summarizes recent advances in guided‐wave optics enabled by microstructured liquid crystal (LC) devices, covering their fundamental material properties, key degree of freedom for dynamic light field manipulations. The advances of linear guided‐wave optics, nonlinear‐optics with spatial optical solitons, and microlasers in LC‐based devices ...
Shan‐shan Chang, Yong‐shuai Li, Jin‐hui Chen   +2 more
wiley   +1 more source