Results 101 to 110 of about 713,469 (282)
Sharp bounds on the number of solutions of $X^{2}-\left( a^{2}+b^{2} \right) Y^{4}=-b^{2}$
, 2018 We generalise and improve a result of Stoll, Walsh and Yuan by showing that there are at most two solutions in coprime positive integers of the equation in the title when $b=p^{m}$ where $m$ is a non-negative integer, $p$ is prime, $(a,p)=1$, $a^{2}+p ...
Voutier, Paul M
core
Perspective: Hollow Core Optical Fibres for Ultraviolet and Visible Wavelengths
Advanced Science, EarlyView.Hollow core optical fibres bypass material constraints that limit optical fibres at ultraviolet and visible wavelengths. However, their challenging fabrication has limited their development, and significant gains in performance remain possible. In this perspective we outline approaches to enable the next generation of fibres for shorter wavelengths ...
Robbie Mears +5 more
wiley +1 more source
A Novel Reduced-Order Analytical Fault Diagnosis Model for Power Grid
IEEE AccessPower grid fault diagnosis methods based on analytical models possess advantages such as logical rigor, strong interpretability, and high applicability.
Zhuonan Lin +3 more
doaj +1 more source
The Periodic Solution of Fractional Oscillation Equation with Periodic Input
Advances in Mathematical Physics, 2013 The periodic solution of fractional oscillation equation with periodic input is considered in this work. The fractional derivative operator is taken as -∞Dtα, where the initial time is -∞; hence, initial conditions are not needed in the model of the ...
Jun-Sheng Duan
doaj +1 more source
A note on the integer solutions ofhyperelliptic equations [PDF]
Colloquium Mathematicum, 1995 The following interesting theorem is proved: Let \(f(x)= x^ m+ a_ 1 x^{m-1}+ \cdots+ a_ m\in \mathbb{Z} [x]\) with \(m\geq 2\) and not all \(a_ i\)'s equal to zero and the first non-zero coefficient coprime to some integer \(n\geq 2\). If \(mn\geq 6\) and \(m\equiv 0\pmod n\) then all integer solutions \((x,y)\) of \(y^ n= f(x)\) satisfy \(| x|< (4m H)^
openaire +2 more sources
Advanced Science, EarlyView.Laser‐induced graphene (LIG) provides a scalable, laser‐direct‐written route to porous graphene architecture with tunable chemistry and defect density. Through heterojunction engineering, catalytic functionalization, and intrinsic self‐heating, LIG achieves highly sensitive and selective detection of NOX, NH3, H2, and humidity, supporting next ...
Md Abu Sayeed Biswas +6 more
wiley +1 more source
Integer solutions to x2+ y2= z2−k for a fixed integer value k
Involve, a Journal of Mathematics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Boyer, Wanda +4 more
openaire +3 more sources
Advanced Science, EarlyView.BiSCALE: A pathology‐driven deep learning framework for multi‐scale gene expression prediction from whole‐slide images. It accurately infers bulk and near‐cellular spot‐level expression, links predictions to clinical phenotypes, identifies disease‐associated niches, and enables applications in risk stratification and cell‐identity annotation, providing
Hailong Zheng +8 more
wiley +1 more source
DNA Replication Errors Drive Genome‐Wide Small Inverted Triplication Dynamics
Advanced Science, EarlyView.This study provides insight into the dynamic equilibrium mechanism of a novel structural variant, small inverted triplication (SIT), which is generated by misalignment of the 3’ flap generated under DNA replication stress with palindromic sequence. Alternatively, the end sequence may fold back on itself to form an inverted fragment.
Yi Lei +12 more
wiley +1 more source
Diffusion–Model–Driven Discovery of Ferroelectrics for Photocurrent Applications
Advanced Science, EarlyView.We developed a diffusion model–based generative AI and high‐throughput screening framework that accelerates the discovery of photovoltaic ferroelectrics. By coupling AI driven crystal generation with machine learning and DFT screening, we identified Ca3P2 and LiCdP as new ferroelectric materials exhibiting strong polarization, feasible switching ...
Byung Chul Yeo +3 more
wiley +1 more source