Results 31 to 40 of about 651 (161)
Journal of Synchrotron Radiation, EarlyView.We present the analytic equations for a new grazing‐incidence mirror surface, a sagittal collimating diaboloid, and illustrate its advantages for higher‐throughput soft X‐ray spectrometer design.A major challenge in soft X‐ray spectroscopy is the efficient collection of the emitted X‐rays by grazing‐incidence mirrors.
Joseph Dvorak, Lei Huang, Mourad Idir
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
core +1 more source
The Role of Dice in the Emergence of the Probability Calculus
International Statistical Review, EarlyView.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
Rational points on even‐dimensional Fermat cubics
Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.Abstract We show that even‐dimensional Fermat cubic hypersurfaces are rational over any field of characteristic not equal to three, by constructing explicit rational parameterizations with polynomials of low degree. As a byproduct of our rationality constructions, we obtain estimates for the number of their rational points over a number field and ...
Alex Massarenti
wiley +1 more source
Fermat Index and Newton Polygon Calculator for Extended Fermat Equation
, 2019 <p>This app calculates the Fermat Index of a triangles, the sides of which are given as inputs. It also calculates and plots the p-adic values of the Fermat-Pythagoras polynomial which enables the easy inference of the corresponding Newton polygon,
Prabhakar, Giri (5455286) +1 more
core +1 more source
Protein Science, Volume 35, Issue 7, July 2026.Abstract Cellulosomes are multi‐enzyme assemblies whose catalytic efficiency depends on the spatial organization of their components. However, their pronounced conformational flexibility has precluded quantitative characterization of inter‐enzyme distances and overall topology.
Iker Pardo Larrabeiti +11 more
wiley +1 more source
Approximate Ricci‐Flat Metrics for Calabi–Yau Manifolds
Fortschritte der Physik, Volume 74, Issue 7, July 2026.ABSTRACT We outline a method to determine analytic Kähler potentials with associated approximately Ricci‐flat Kähler metrics on Calabi–Yau manifolds. Key ingredients are numerically calculating Ricci‐flat Kähler potentials via machine learning techniques and fitting the numerical results to Donaldson's ansatz.
Seung‐Joo Lee, Andre Lukas
wiley +1 more source
Sylow subgroups and the number of irreducible characters of degrees divisible by a prime p$p$
Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.Abstract Let G$G$ be a finite group and p$p$ be a prime. We establish an upper bound for the derived length of a Sylow p$p$‐subgroup of G$G$ in terms of the number of irreducible characters of G$G$ whose degrees are divisible by p$p$. We also prove that if B$B$ is a p$p$‐block of a finite p$p$‐solvable group G$G$ with defect group D$D$, then the ...
James P. Cossey +3 more
wiley +1 more source
Random Diophantine equations in the primes
Mathematika, Volume 72, Issue 3, July 2026.Abstract We consider equations of the form a1x1k+⋯+asxsk=0$a_{1}x_{1}^{k}+\cdots +a_{s}x_{s}^{k}=0$ where the variables xi$x_{i}$ are all taken to be primes. We define an analogue of the Hasse principle for solubility in the primes (which we call the prime Hasse principle), and prove that, whenever k⩾2$k\geqslant 2$, s⩾3k+2$s\geqslant 3k+2$, this holds
Philippa Holdridge
wiley +1 more source
Seismic imaging of the critical zone of dolerite dykes at Cap Fréhel in Brittany (France)
Near Surface Geophysics, Volume 24, Issue 3, Page 262-288, June 2026.Abstract In June 2023, we measured ten near‐surface seismic profiles to image the critical zone of dolerite (diabase) dykes that cut the sandstone at Cap Fréhel in Brittany (France). Seismic ray tracing and inversion are used to determine the thickness of the regolith layer from first‐arrival P‐wave traveltimes.
M. Zillmer +4 more
wiley +1 more source