Abhyankar's Affine Arithmetic Conjecture for the Symmetric and Alternating Groups

A Entin, N Pirani - arXiv preprint arXiv:2205.03879, 2022 - arxiv.org
We prove that for any prime $p>2$, $q=p^\nu$ a power of $p$, $n\ge p$ and $G=S_n$ or $G=A_n$
(symmetric or alternating group) there exists a Galois extension $K/\mathbb F_q(T)$ …

Affine arithmetic in matrix form for polynomial evaluation and algebraic curve drawing

R MARTIN, I VOICULESCU, A BOWYER - Progress in Natural Science, 2002 - cnki.com.cn
正 This paper shows how tight bounds for the range of a bivariate polynomial can be found
using a matrix method based on affine arithmetic. Then, this method is applied to drawing an …

[PDF][PDF] Cue integration using affine arithmetic and gaussians

S Goldenstein, C Vogler… - Technical Reports (CIS), 2002 - repository.upenn.edu
In this paper we describe how the connections between affine forms, zonotopes, and
Gaussian distributions help us devise an automated cue integration technique for tracking …

Error analysis and precision estimation for floating-point dot-products using affine arithmetic

TV Huynh, M Mücke - The 2011 International Conference on …, 2011 - ieeexplore.ieee.org
… We apply affine arithmetic, an extension to interval arithmetic, to estimate the rounding error
… range of parameters and show that affine arithmetic with a probabilistic bounding operator is …

A Novel Approach to Describe and Aggregate Multi-Energy Flexibility in Cellular Energy Systems Using Affine Arithmetic

SJ Rasti, P Schegner - ETG Congress 2021, 2021 - ieeexplore.ieee.org
… This paper presents a flexibility model based on Affine Arithmetic which specifies allowed
power and energy ranges while considering relations between time steps and energy forms. …

Affine arithmetic and Bernstein hull methods for algebraic curve drawing

H Shou, R Martin, G Wang, I Voiculescu… - Uncertainty in Geometric …, 2002 - Springer
… than using the power basis, and that affine arithmetic in the power basis is better than using …
using affine arithmetic with the Bernstein basis gives no advantage over affine arithmetic

Three-Phase Optimal Power Flow based on Affine Arithmetic

JP Morán, JC López, AP Feltrin - 2021 IEEE PES Innovative …, 2021 - ieeexplore.ieee.org
… self-validation method called Affine Arithmetic. The affine shapes for tree-phase variables
was performed using the theoretical approach of Reduced Affine Arithmetic together with the …

[PDF][PDF] Load flow analysis of a power system network in the presence of uncertainty using complex affine arithmetic

YM Abebe, PM Rao, MG Nak - International Journal of Engineering …, 2017 - mecs-press.net
… On this paper, a novel complex affine arithmetic (AA) based load flow analysis in the presence
of generation and load uncertainties is proposed. The proposed approach is tested on an …

Affine Arithmetic Based Methods for Power Systems Analysis Considering Intermittent Sources of Power

JC Munoz Guerrero - 2014 - uwspace.uwaterloo.ca
… Thus, this thesis proposes computationally efficient Affine Arithmetic (AA)-based approaches
for voltage and transient stability assessment of power systems, considering uncertainties …

Approximating parametric curves with strip trees using affine arithmetic

LH De Figueiredo, J Stolfi… - Proceedings. XV Brazilian …, 2002 - ieeexplore.ieee.org
… We show how to use affine arithmetic to represent a parametric curve with a strip tree. The …
by exploiting the linear correlation information given by affine arithmetic. As an application, we …