Results 31 to 40 of about 865 (232)

Root numbers and parity of ranks of elliptic curves

, 2011
The purpose of the paper is to complete several global and local results concerning parity of ranks of elliptic curves. Primarily, we show that the Shafarevich–Tate conjecture implies the parity conjecture for all elliptic curves over number fields, we ...
Tim Dokchitser, Dokchitser, TY, Vladimir Dokchitser, Dokchitser, V   +3 more
core   +1 more source

Twin Crystal Moiré Metasurfaces for Crossing Flat‐Band Transport

Advanced Functional Materials, EarlyView.
This study introduces twin crystal moiré metasurfaces, breaking in‐plane symmetry to enable reconfigurable acoustic wave manipulation. By adjusting the twin angle and interlayer twist angle, various combinations of hyperbolic, flat bands, and elliptic states can be synthesized in the system.
Shida Fan, Chenglin Han, Kuan He, Chadi Ellouzi, Yunlong Wang, Li‐Qun Chen, Jie Sun, Zhaodong Xu, Chen Shen, Tianzhi Yang   +9 more
wiley   +1 more source

Natural Biomaterials for Osteochondral Repair: From Source to Strategy

Advanced Healthcare Materials, EarlyView.
Biological origin‐guided overview of natural biomaterials and therapeutic strategies for osteochondral tissue engineering. The circular diagram categorizes representative materials and strategies into plant/algae‐derived, microbial‐derived, animal‐derived, and human‐derived sources, centered on an osteochondral defect repair model.
Hengyu Liu, Hanyang Zhang, Wenbo Yang, Hao Chen, Jincheng Wang, Fei Chang   +5 more
wiley   +1 more source

Opportunities of Semiconducting Oxide Nanostructures as Advanced Luminescent Materials in Photonics

Advanced Materials, EarlyView.
The review discusses the challenges of wide and ultrawide bandgap semiconducting oxides as a suitable material platform for photonics. They offer great versatility in terms of tuning microstructure, native defects, doping, anisotropy, and micro‐ and nano‐structuring. The review focuses on their light emission, light‐confinement in optical cavities, and
Ana Cremades, Pedro Hidalgo, David Maestre, Ruth Martínez‐Casado, Emilio Nogales, Beatriz Rodríguez, G. Cristian Vásquez, Bianchi Méndez   +7 more
wiley   +1 more source

A heuristic for boundedness of ranks of elliptic curves

, 2019
We present a heuristic that suggests that ranks of elliptic curves E over Q are bounded. In fact, it suggests that there are only finitely many E of rank greater than 21.
Voight, John, Park, Jennifer, Poonen, Bjorn, Wood, Melanie Matchett   +3 more
core   +1 more source

Some remarks concerning points of finite order on elliptic curves over global fields

Arkiv för Matematik, 1977
Using the reduction theory of Nrron we give necessary conditions for the existence of points of order q on elliptic curves E rational over global fields. An application is the determination of all elliptic cu rves /Q with integer j and torsion points, generalizing Olson [8]. Another application is a theorem about semistable reduction whose consequences
openaire   +3 more sources

3D Anodic Alumina Nanoarchitectures: A Decade of Progress from Foundational Science to Functional Metamaterials

Advanced Materials, EarlyView.
Ordered three‐dimensional anodic aluminum oxide (3D‐AAO) nanoarchitectures with longitudinal and transverse pores enable architecture‐driven metamaterials. The review maps fabrication advances, including hybrid pulse anodization, and shows how 3D‐AAO templates tailor properties across magnetism, energy, catalysis, and sensing.
Marisol Martín‐González
wiley   +1 more source

Torsion points on elliptic curves over function fields and a theorem of Igusa

, 2009
If F is a global function field of characteristic p>3, we employ Tate's theory of analytic uniformization to give an alternative proof of a theorem of Igusa describing the image of the natural Galois representation on torsion points of non-isotrivial ...
Vigni, Stefano, S. Vigni, Longhi, Ignazio, Bandini, Andrea, A. Bandini, I. Longhi   +5 more
core   +1 more source

Stable Protein‐Based G‐Quadruplex‐Derived Supramolecular Bioinks as Tunable ECM‐Mimetic Constructs Assembled by Combining Non‐Covalent and Covalent Strategies

Advanced Materials, EarlyView.
Harnessing the synergistic interplay of supramolecular self‐assembly, under macromolecular crowding conditions, and enzymatic‐mediated covalent crosslinking toward a stable protein‐based G‐quadruplex‐derived supramolecular bioink. This bioinspired strategy enables the biofabrication of complex and tunable ECM‐mimetic constructs, providing a platform ...
Vera Sousa, Rita Sobreiro‐Almeida, Bart W. L. van den Bersselaar, E. W. Meijer, Ghislaine Vantomme, João Borges, João F. Mano   +6 more
wiley   +1 more source

Rationality of Darmon points over genus fields of non-maximal orders [PDF]

, 2020
Stark–Heegner points, also known as Darmon points, were introduced by Darmon in [5] as certain local points on rational elliptic curves, conjecturally defined over abelian extensions of real quadratic fields.
Martin Kimball, Longo M., Hu Yan
core   +1 more source