Emile Borel's difficult days in 1941

The German forces occupying Paris arrested Emile Borel and three other members of the Acad\'emie des Sciences in October 1941 and released them about five weeks later. Why? We examine some relevant German and French archives and other sources and propose some hypotheses. In the process, we review how the Occupation was structured and how it dealt with French higher education and some French mathematicians

The emergence of French statistics. How mathematics entered the world of statistics in France during the 1920s

This paper concerns the emergence of modern mathematical statistics in France after the First World War. Emile Borel's achievements are presented, and especially his creation of two institutions where mathematical statistics was developed: the {\it Statistical Institute of Paris University}, (ISUP) in 1922 and above all the {\it Henri Poincar\'e Institute} (IHP) in 1928. At the IHP, a new journal {\it Annales de l'Institut Henri Poincar\'e} was created in 1931. We discuss the first papers in that journal dealing with mathematical statistics

Optimal control for rough differential equations

In this note, we consider an optimal control problem associated to a differential equation driven by a H\"{o}lder continuous function g of index greater than 1/2. We split our study in two cases. If the coefficient of dg\_t does not depend on the control process, we prove an existence theorem for a slightly generalized control problem, that is we obtain a literal extension of the corresponding deterministic situation. If the coefficient of dg\_t depends on the control process, we also prove an existence theorem but we are here obliged to restrict the set of controls to sufficiently regular functions.Comment: 13 page

Biosynthesis of α-Tocopherol and Plastoquinone-9 in spinach chloroplasts

Prenylation and methylation reaction in al biosynthesis is localized in the envelope membranes of the chloroplasts, while PQ-9 biosynthesis takes place in the envelope membranes and also in the thylakoid membranes. The sequence in a-T biosynthesis in spinach is (see also Figure 1): Homogentisate + Phytyl-PP —> Me-6-PQH?—> 2,3-Me2PQH?—>γ J ->a T ; for the PQ-9 biosynthesis it is: Homogentisate + Solanesyf-PP4-> Me-6-SQH2—> PQH2

The ghosts of the Ecole Normale. Life, death and legacy of Ren\'e Gateaux

The present paper deals with the life and some aspects of the scientific contributions of the mathematician Ren\'e Gateaux, killed during World War 1 at the age of 25. Though he died very young, he left interesting results in functional analysis. In particular, he was among the first to try to construct an integral over an infinite dimensional space. His ideas were extensively developed later by Paul L\'evy. Among other things, L\'evy interpreted Gateaux's integral in a probabilistic framework that later contributed to the construction of the Wiener measure. This article tries to explain this singular personal and professional destiny in pre- and postwar France

Au delà des réels. Borel et l'approche probabiliste de la réalité

Nous examinons dans cet article la manière singulière dont Emile Borel, à partir de ses études sur la structure des nombres réels et un certain rejet de la vision abstraite de Cantor, a trouvé dans le calcul des probabilités un outil adéquat pour formuler une nouvelle approche des problèmes, en même temps prenait conscience de son utilité pour l'approche des phénomènes de la physique et de la société