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A group of bijections G acting on a set X is said with fixed points (abbreviated as gaf from the french "groupe {\`a} points fixes") if any element of G has at least one fixed point in X. The G group is said with a common fixed point (abbreviated as
Externí odkaz:
http://arxiv.org/abs/1901.08895
Autor:
Fruchard, Augustin
A set of points a 1 ,. .. , a n fixes a planar convex body K if the points are on bdK, the boundary of K, and if any small move of K brings some point of the set in intK, the interior of K. The points a 1 ,. .. , a n $\in$ bdK almost fix K if, for an
Externí odkaz:
http://arxiv.org/abs/1708.02745
A pizza is a pair of planar convex bodies $A\subseteq B$,where $B$ represents the dough and $A$ the topping of the pizza. A partition of a pizza by straight lines is a succession of double operations:a cut by a full straight line, followed by a Eucli
Externí odkaz:
http://arxiv.org/abs/1509.02090
Let $K$ be a planar convex body af area $|K|$, and take $0 \textless{} \alpha \textless{} 1$.An $\alpha$-section of $K$ is a line cutting $K$ into two parts, one of whichhas area $\alpha|K|$. This article presents a systematic study of the envelope o
Externí odkaz:
http://arxiv.org/abs/1509.02084
Akademický článek
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Autor:
Fruchard, Augustin, Schäfke, Reinhard
We develop the theory of a new type of asymptotic expansions for functions of two variables the coefficients of which contain functions of one of the variables as well as functions of the quotient of these two variables. These combined asymptotic exp
Externí odkaz:
http://arxiv.org/abs/1004.5254
Autor:
Fruchard, Augustin
A circle C holds a convex body K if C does not meet the interior of K and if there does not exist any euclidean displacement which moves C as far as desired from K, avoiding the interior of K. The purpose of this note is to explore how small can be a
Externí odkaz:
http://arxiv.org/abs/1004.5255
Publikováno v:
In Linear Algebra and Its Applications 15 July 2018 549:246-255
Autor:
Fruchard, Augustin, Schäfke, Reinhard
Publikováno v:
In Comptes rendus - Mathématique 2010 348(23):1273-1277
Autor:
MOHDEB, NADIA1 n_mohdeb@hotmail.com, FRUCHARD, AUGUSTIN2 augustin.fruchard@uha.fr, MEHIDI, NOUREDDINE1 manogha@yahoo.fr
Publikováno v:
Electronic Journal of Differential Equations. 2018, Vol. 2018 Issue 158-200, p1-14. 14p.