In ZF, the existence of a Hamel basis does not yield a well–ordering of R. Throughout this paper, by a Hamel basis we always mean a basis for R, construed as a vector space over Q. We denote by E the Vitali equivalence relation, xEy iff x− y ∈ Q for x, y ∈ R. We also write [x]E = {y : yEx} for the E–equivalence class of x. A transversal for the set of all E–equivalence classes picks exactly one...

This paper seeks to provide clues as to why experimental evidence for the alignment of fibers in semi-dilute suspensions under shear flows does not match theoretical predictions. This paper posits that it is the coupling between Jeffery’s equation and Stokes’ equation that causes the deviation from theory. It is proposed that if the initial data is slightly non-uniform, then there is feedback v...

Nous étudions le maximum du mouvement Brownian branchant (BBM) avec des taux de branchement qui varient en l’espace, via une fonction périodique. Ceci correspond à variante l’équation F-KPP milieu périodique, largement étudiée au cours 15 dernière années, admet fronts pulsés comme solutions. Les progrès récents sur cette EDP Hamel, Nolen, Roquejoffre and Ryzhik (’16) impliquent la tension centr...