scholarly journals A Mordell–Weil theorem for cubic hypersurfaces of high dimension

2017 ◽  
Vol 11 (8) ◽  
pp. 1953-1965 ◽  
Author(s):  
Stefanos Papanikolopoulos ◽  
Samir Siksek
Keyword(s):  
High Dimension ◽  
Weil Theorem ◽  
Cubic Hypersurfaces

scholarly journals A hybrid Feature Selection Optimization Model for High Dimension Data Classification

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Mohammed Qaraad ◽  
Souad Amjad ◽  
Ibrahim I.M. Manhrawy ◽  
Hanaa Fathi ◽  
Bayoumi A. Hassan ◽  
...  
Keyword(s):  
Feature Selection ◽  
High Dimension ◽  
Optimization Model ◽  
Data Classification ◽  
High Dimension Data

scholarly journals Maps from Feigin and Odesskii's elliptic algebras to twisted homogeneous coordinate rings

2021 ◽  
Vol 9 ◽  
Author(s):  
Alex Chirvasitu ◽  
Ryo Kanda ◽  
S. Paul Smith
Keyword(s):  
Elliptic Curve ◽  
Symmetric Power ◽  
Canonical Homomorphism ◽  
Coordinate Ring ◽  
Characteristic Variety ◽  
Closed Subvariety ◽  
Coordinate Rings ◽  
Cubic Hypersurfaces ◽  
Elliptic Algebras ◽  
Twisted Homogeneous Coordinate Ring

Abstract The elliptic algebras in the title are connected graded $\mathbb {C}$ -algebras, denoted $Q_{n,k}(E,\tau )$ , depending on a pair of relatively prime integers $n>k\ge 1$ , an elliptic curve E and a point $\tau \in E$ . This paper examines a canonical homomorphism from $Q_{n,k}(E,\tau )$ to the twisted homogeneous coordinate ring $B(X_{n/k},\sigma ',\mathcal {L}^{\prime }_{n/k})$ on the characteristic variety $X_{n/k}$ for $Q_{n,k}(E,\tau )$ . When $X_{n/k}$ is isomorphic to $E^g$ or the symmetric power $S^gE$ , we show that the homomorphism $Q_{n,k}(E,\tau ) \to B(X_{n/k},\sigma ',\mathcal {L}^{\prime }_{n/k})$ is surjective, the relations for $B(X_{n/k},\sigma ',\mathcal {L}^{\prime }_{n/k})$ are generated in degrees $\le 3$ and the noncommutative scheme $\mathrm {Proj}_{nc}(Q_{n,k}(E,\tau ))$ has a closed subvariety that is isomorphic to $E^g$ or $S^gE$ , respectively. When $X_{n/k}=E^g$ and $\tau =0$ , the results about $B(X_{n/k},\sigma ',\mathcal {L}^{\prime }_{n/k})$ show that the morphism $\Phi _{|\mathcal {L}_{n/k}|}:E^g \to \mathbb {P}^{n-1}$ embeds $E^g$ as a projectively normal subvariety that is a scheme-theoretic intersection of quadric and cubic hypersurfaces.

A Secure High-dimension Consensus Mechanism against Adversaries

2021 ◽  
Author(s):  
Xiaoyu Luo ◽  
Chengcheng Zhao ◽  
Jianping He
Keyword(s):  
High Dimension

scholarly journals Testing covariates in high dimension linear regression with latent factors

2016 ◽  
Vol 144 ◽  
pp. 25-37 ◽  
Author(s):  
Wei Lan ◽  
Yue Ding ◽  
Zheng Fang ◽  
Kuangnan Fang
Keyword(s):  
Linear Regression ◽  
High Dimension ◽  
Latent Factors

Flutter of high-dimension nonlinear system for a FGM truncated conical shell

2017 ◽  
Vol 25 (1) ◽  
pp. 47-61 ◽  
Author(s):  
Y. X. Hao ◽  
S. W. Yang ◽  
W. Zhang ◽  
M. H. Yao ◽  
A. W. Wang
Keyword(s):  
Nonlinear System ◽  
High Dimension ◽  
Conical Shell ◽  
Truncated Conical Shell

scholarly journals GBUO: “The Good, the Bad, and the Ugly” Optimizer

2021 ◽  
Vol 11 (5) ◽  
pp. 2042
Author(s):  
Hadi Givi ◽  
Mohammad Dehghani ◽  
Zeinab Montazeri ◽  
Ruben Morales-Menendez ◽  
Ricardo A. Ramirez-Mendoza ◽  
...  
Keyword(s):  
High Dimension ◽  
Essential Role ◽  
Optimization Problems ◽  
Optimization Algorithms ◽  
Stochastic Search ◽  
Objective Functions ◽  
Science And Engineering ◽  
Fixed Dimension ◽  
Dimension Functions ◽  
Simulation Results

Optimization problems in various fields of science and engineering should be solved using appropriate methods. Stochastic search-based optimization algorithms are a widely used approach for solving optimization problems. In this paper, a new optimization algorithm called “the good, the bad, and the ugly” optimizer (GBUO) is introduced, based on the effect of three members of the population on the population updates. In the proposed GBUO, the algorithm population moves towards the good member and avoids the bad member. In the proposed algorithm, a new member called ugly member is also introduced, which plays an essential role in updating the population. In a challenging move, the ugly member leads the population to situations contrary to society’s movement. GBUO is mathematically modeled, and its equations are presented. GBUO is implemented on a set of twenty-three standard objective functions to evaluate the proposed optimizer’s performance for solving optimization problems. The mentioned standard objective functions can be classified into three groups: unimodal, multimodal with high-dimension, and multimodal with fixed dimension functions. There was a further analysis carried-out for eight well-known optimization algorithms. The simulation results show that the proposed algorithm has a good performance in solving different optimization problems models and is superior to the mentioned optimization algorithms.

scholarly journals There are genus one curves of every index over every infinite, finitely generated field

2019 ◽  
Vol 2019 (749) ◽  
pp. 65-86
Author(s):  
Pete L. Clark ◽  
Allan Lacy
Keyword(s):  
Elliptic Curve ◽  
Abelian Variety ◽  
Finitely Generated ◽  
Weil Theorem ◽  
Genus One

Abstract We show that a nontrivial abelian variety over a Hilbertian field in which the weak Mordell–Weil theorem holds admits infinitely many torsors with period any given n>1 that is not divisible by the characteristic. The corresponding statement with “period” replaced by “index” is plausible but open, and it seems much more challenging. We show that for every infinite, finitely generated field K, there is an elliptic curve E_{/K} which admits infinitely many torsors with index any given n>1 .

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