Indice d'un hérisson : étude et applications

Hedgehogs are a natural generalization of convex bodies of class C2+. After recalling some basic facts concerning this generalization, we use the notion of index to study differential and integral geometries of hedgehogs. As applications, we prove a particular case of the Tennis Ball Theorem and a property of normals to a plane convex body of constant width

Tout chemin générique de hérissons réalisant un retournement de la sphère dans comprend un hérisson porteur de queues d’aronde positives

Hedgehogs are (possibly singular and self-intersecting) hypersurfaces that describe Minkowski differences of convex bodies in Rn+1. They are the natural geometrical objects when one seeks to extend parts of the Brunn–Minkowski theory to a vector space which contains convex bodies. In this paper, we prove that in every generic path of hedgehogs performing the eversion of the sphere in R3, there exists a hedgehog that has positive swallowtails. This study was motivated by an open problem raised in 1985 by Langevin, Levitt, and Rosenberg

Courbes planes : rappels et exercices

Maste

Analysis of wear mechanism in TPU-steel contact pair by means of long stroke tribometer tests

A complete wear characterisation of a thermoplastic polyurethane (TPU) sliding against steel is presented. Wear tests were performed using a long stroke tribometer under sliding reciprocating movement and dry conditions. The dependence of some of the most significant parameters was studied. Before and after wear tests, complementary observations, analyses and measurements were also performed on both contacting materials. These various characterisations involved weight loss of TPU, physico-chemical and thermo- mechanical analyses of TPU, included topographical measurements and morphological observations of worn surfaces of contacting pairs and calculations of the temperature rise generated by friction