scholarly journals An effective proof of the hyperelliptic Shafarevich conjecture

2014 ◽  
Vol 26 (2) ◽  
pp. 507-530 ◽  
Author(s):  
Rafael von Känel
Keyword(s):  
Shafarevich Conjecture ◽  
Effective Proof

scholarly journals No Singular Modulus Is a Unit

2018 ◽  
Vol 2020 (24) ◽  
pp. 10005-10041 ◽  
Author(s):  
Yuri Bilu ◽  
Philipp Habegger ◽  
Lars Kühne
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Endomorphism Ring ◽  
Complex Multiplication ◽  
Computer Assisted ◽  
Algebraic Unit ◽  
Special Points ◽  
Effective Proof ◽  
Rule Out

Abstract A result of the 2nd-named author states that there are only finitely many complex multiplication (CM)-elliptic curves over $\mathbb{C}$ whose $j$-invariant is an algebraic unit. His proof depends on Duke’s equidistribution theorem and is hence noneffective. In this article, we give a completely effective proof of this result. To be precise, we show that every singular modulus that is an algebraic unit is associated with a CM-elliptic curve whose endomorphism ring has discriminant less than $10^{15}$. Through further refinements and computer-assisted arguments, we eventually rule out all remaining cases, showing that no singular modulus is an algebraic unit. This allows us to exhibit classes of subvarieties in ${\mathbb{C}}^n$ not containing any special points.

Theory and Manufacturing Processes of Solar Nanoantenna Electromagnetic Collectors

2010 ◽  
Vol 132 (1) ◽  
Author(s):  
D. K. Kotter ◽  
S. D. Novack ◽  
W. D. Slafer ◽  
P. J. Pinhero
Keyword(s):  
Large Scale ◽  
Low Cost ◽  
Cost Effective ◽  
Optical Antenna ◽  
Technological Barriers ◽  
Large Scale Manufacture ◽  
Future Work ◽  
Optical Behavior ◽  
Effective Proof ◽  
Selection Of

The research described in this paper explores a new and efficient approach for producing electricity from the abundant energy of the sun, using nanoantenna (nantenna) electromagnetic collectors (NECs). NEC devices target midinfrared wavelengths, where conventional photovoltaic (PV) solar cells are inefficient and where there is an abundance of solar energy. The initial concept of designing NECs was based on scaling of radio frequency antenna theory to the infrared and visible regions. This approach initially proved unsuccessful because the optical behavior of materials in the terahertz (THz) region was overlooked and, in addition, economical nanofabrication methods were not previously available to produce the optical antenna elements. This paper demonstrates progress in addressing significant technological barriers including: (1) development of frequency-dependent modeling of double-feedpoint square spiral nantenna elements, (2) selection of materials with proper THz properties, and (3) development of novel manufacturing methods that could potentially enable economical large-scale manufacturing. We have shown that nantennas can collect infrared energy and induce THz currents and we have also developed cost-effective proof-of-concept fabrication techniques for the large-scale manufacture of simple square-loop nantenna arrays. Future work is planned to embed rectifiers into the double-feedpoint antenna structures. This work represents an important first step toward the ultimate realization of a low-cost device that will collect as well as convert this radiation into electricity. This could lead to a broadband, high conversion efficiency low-cost solution to complement conventional PV devices.

scholarly journals Recent advances in managing gastrointestinal stromal tumor

F1000Research ◽  
2017 ◽  
Vol 6 ◽  
pp. 1689 ◽  
Author(s):  
Florence Duffaud ◽  
Axel Le Cesne
Keyword(s):  
Gastrointestinal Stromal Tumors ◽  
Growth Factor Receptor ◽  
Standard Of Care ◽  
Platelet Derived Growth Factor ◽  
Proof Of Concept ◽  
Current Standard ◽  
Stromal Tumors ◽  
Concept Model ◽  
Activating Mutations ◽  
Effective Proof

Constitutive activating mutations inKITand platelet-derived growth factor receptor α (PDGFRα) are heavily involved in the pathobiology of gastrointestinal stromal tumors (GISTs). This disease has served as an effective “proof-of-concept” model for targeting gain-of-function kinase mutations in cancer. This review discusses the current standard of care in terms of pharmacotherapy in the management of localized and metastatic GISTs.

scholarly journals An effective proof of the Cartan formula: The even prime

2020 ◽  
Vol 224 (12) ◽  
pp. 106444
Author(s):  
Anibal M. Medina-Mardones
Keyword(s):  
Effective Proof

scholarly journals Représentations linéaires des groupes kählériens : factorisations et conjecture de Shafarevich linéaire

2014 ◽  
Vol 151 (2) ◽  
pp. 351-376 ◽  
Author(s):  
Fréderic Campana ◽  
Benoît Claudon ◽  
Philippe Eyssidieux
Keyword(s):  
General Type ◽  
Linear Representation ◽  
Kähler Manifolds ◽  
Fundamental Groups ◽  
Kahler Manifolds ◽  
Shafarevich Conjecture ◽  
Classical Work ◽  
Projective Manifolds ◽  
Complex Projective ◽  
Holomorphic Convexity

AbstractWe extend to compact Kähler manifolds some classical results on linear representation of fundamental groups of complex projective manifolds. Our approach, based on an interversion lemma for fibrations with tori versus general type manifolds as fibers, gives a refinement of the classical work of Zuo. We extend to the Kähler case some general results on holomorphic convexity of coverings such as the linear Shafarevich conjecture.

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