An effective proof of a theorem of Coates

1975 ◽  
pp. 44-48
Author(s):  
D. W. Masser
Keyword(s):  
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 An effective proof that open sets are Ramsey

1998 ◽  
Vol 37 (4) ◽  
pp. 235-240 ◽  
Author(s):  
Jeremy Avigad
Keyword(s):  
Effective Proof

Provable Data Possession in Cloud Computing

2014 ◽  
Vol 513-517 ◽  
pp. 1406-1413
Author(s):  
Tan Shuang ◽  
Jian Feng Zhang ◽  
Zhi Kun Chen
Keyword(s):  
Cloud Computing ◽  
Data Storage ◽  
Data Centers ◽  
Large Data ◽  
Application Software ◽  
Provable Data Possession ◽  
And Performance ◽  
Opening Up ◽  
Effective Proof ◽  
Provably Secure

Several trends are opening up the era of cloud computing. It moves the application software and databases to the centralized large data centers, where the management of the data and services may not be fully trustworthy. This work studies the problem of ensuring the integrity of data storage in cloud computing. We use RSAs homomorphic property to construct the protocol of provable data possession. In our protocol, we can aggregate multiple Provable Data possession into one, and reduce the overhead of communication. While prior work on ensuring remote data integrity often lacks the specific implementations, this paper achieves an effective proof of storage protocol. Extensive security and performance analysis show that the proposed scheme is highly efficient and provably secure.

scholarly journals Reasoning Inside The Box: Deduction in Herbrand Logics

10.29007/kx2m ◽  
2018 ◽  
Author(s):  
Liron Cohen ◽  
Yoni Zohar
Keyword(s):  
Automated Reasoning ◽  
Proof System ◽  
First Order ◽  
Proof Systems ◽  
The Rich ◽  
Order Structures ◽  
Effective Proof

Herbrand structures are a subclass of standard first-order structures commonly used in logic and automated reasoning due to their strong definitional character. This paper is devoted to the logics induced by them: Herbrand and semi-Herbrand logics, with and without equality. The rich expressiveness of these logics entails that there is no adequate effective proof system for them. We therefore introduce infinitary proof systems for Herbrand logics, and prove their completeness. Natural and sound finitary approximations of the infinitary systems are also presented.

Analysis and Optimization for the Dynamic Characteristics of Drilling & Boring Machine Spindle System

2014 ◽  
Vol 1027 ◽  
pp. 320-324
Author(s):  
Ran Yao ◽  
Jian Hui Liu ◽  
Lei Ma ◽  
Bin Yao
Keyword(s):  
Fundamental Frequency ◽  
Dynamic Characteristics ◽  
Performance Optimization ◽  
Spindle System ◽  
Modeling Analysis ◽  
Machine Spindle ◽  
Optimal Span ◽  
Bearing Structure ◽  
Effective Proof

Taking the spindle system of CNC drilling and boring machine that exclusively used in the latest developed bearing cage as study subject, this paper investigates the optimization of the spindle system by improving the support bearing structure and optimizing the spindle span to get the optimal span. Through modeling analysis, the fundamental frequency of the optimized spindle increase 16.9%, which provides effective-proof performance optimization.

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