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pro vyhledávání: '"Galligo, A."'
Let $(Z^{(n)}_k)_{1 \leq k \leq n}$ be a random set of points and let $\mu_n$ be its \emph{empirical measure}: $$\mu_n = \frac{1}{n} \sum_{k=1}^n \delta_{Z^{(n)}_k}. $$ Let $$P_n(z) := (z - Z^{(n)}_1)\cdots (z - Z^{(n)}_n)\quad \text{and}\quad Q_n (z
Externí odkaz:
http://arxiv.org/abs/2404.12472
Autor:
Galligo, André
Publikováno v:
ISSAC 2022, Jul 2022, Lille, France
In this paper, we consider nonlocal, nonlinear partial differential equations to model anisotropic dynamics of complex root sets of random polynomials under differentiation. These equations aim to generalise the recent PDE obtained by Stefan Steinerb
Externí odkaz:
http://arxiv.org/abs/2205.08747
Publikováno v:
LION15 - Learning and Intelligent Optimization Conference, Jun 2021, Athens, Greece
The purpose of this study is to provide means to physicians for automated and fast recognition of airways diseases. In this work, we mainly focus on measures that can be easily recorded using a spirometer. The signals used in this framework are simul
Externí odkaz:
http://arxiv.org/abs/2111.04315
Publikováno v:
Proc. R. Soc. A (2016), Vol. 472, Issue 2191, p. 20160194
This article describes the use of algebraic methods in a phase plane analysis of ordinary differential equations. The method is illustrated by the study of capillary-gravity steady surface waves propagating in shallow water. We consider the (fully no
Externí odkaz:
http://arxiv.org/abs/1603.07472
Publikováno v:
Graphical Models, Elsevier, 2016, 86, pp.1-12
We propose new algebraic methods for extracting cylinders and cones from minimal point sets, including oriented points. More precisely, we are interested in computing efficiently cylinders through a set of three points, one of them being oriented, or
Externí odkaz:
http://arxiv.org/abs/1603.04582
Autor:
Galligo, Andre, Jelonek, Zbigniew
Publikováno v:
In Journal of Algebra 15 November 2020 562:621-626
For a system of Laurent polynomials f_1,..., f_n \in C[x_1^{\pm1},..., x_n^{\pm1}] whose coefficients are not too big with respect to its directional resultants, we show that the solutions in the algebraic n-th dimensional complex torus of the system
Externí odkaz:
http://arxiv.org/abs/1203.1843
Publikováno v:
International Symposium on Symbolic and Algebraic Computation (ISSAC), Munich : Germany (2010)
Our probabilistic analysis sheds light to the following questions: Why do random polynomials seem to have few, and well separated real roots, on the average? Why do exact algorithms for real root isolation may perform comparatively well or even bette
Externí odkaz:
http://arxiv.org/abs/1005.2001
Let $f(X,Y) \in \ZZ[X,Y]$ be an irreducible polynomial over $\QQ$. We give a Las Vegas absolute irreducibility test based on a property of the Newton polytope of $f$, or more precisely, of $f$ modulo some prime integer $p$. The same idea of choosing
Externí odkaz:
http://arxiv.org/abs/0911.5024
Autor:
Buse, Laurent, Galligo, Andre
Given two curves in $\PP^3$, either implicitly or by a parameterization, we want to check if they intersect. For that purpose, we present and further develop generalized resultant techniques. Our aim is to provide a closed formula in the inputs which
Externí odkaz:
http://arxiv.org/abs/math/0301088