The symmetric Radon-Nikod\'ym property for tensor norms

We introduce the symmetric-Radon-Nikod\'ym property (sRN property) for finitely generated s-tensor norms $\beta$ of order $n$ and prove a Lewis type theorem for s-tensor norms with this property. As a consequence, if $\beta$ is a projective s-tensor norm with the sRN property, then for every Asplund space $E$, the canonical map $\widetilde{\otimes}_{\beta}^{n,s} E' \to \Big(\widetilde{\otimes}_{\beta'}^{n,s} E \Big)'$ is a metric surjection. This can be rephrased as the isometric isomorphism $\mathcal{Q}^{min}(E) = \mathcal{Q}(E)$ for certain polynomial ideal \Q. We also relate the sRN property of an s-tensor norm with the Asplund or Radon-Nikod\'{y}m properties of different tensor products. Similar results for full tensor products are also given. As an application, results concerning the ideal of $n$-homogeneous extendible polynomials are obtained, as well as a new proof of the well known isometric isomorphism between nuclear and integral polynomials on Asplund spaces.Comment: 17 page

Nosocomial transmission of hepatitis B from an infected healthcare worker to a patient, France, 2005

International audienceIn 2005, following seroconversion by hepatitis B virus in a patient who underwent surgery, an investigation was carried out to identify the origin of the contamination. Evidence collected through this investigation strongly suggests a likely nosocomial transmission from a healthcare worker to a patient. An observational workplace practice review disclosed a certain number of malfunctions that could have played a role in the transmission, even if the exact route of transmission could not be established retrospectively. This case report underlines the importance of standard precautions and good practices of care

Natural norms on symmetric tensor products of normed spaces

The basics of the theory of symmetric tensor products of normed spaces and some applications are presented

An initial study of fallow periods on the nematode community in the Soudanese-Sahelian zone of Senegal

Les observations ont été réalisées sur des jachères naturelles, sur sols ferrugineux peu profonds, dans la région de Nioro du Rip au Sud du Sénégal. Sur l'ensemble du site, 12 espèces de nématodes phytoparasites ont été identifiées. Dans les jachères anthropisées, l'effectif du peuplement ainsi que le nombre d'espèces observées diminuent lorsque l'âge de la jachère augmente de 1 à 17 ans. La mise en défens pendant 5 ans d'une jachère de 17 ans modifie ces tendances : le peuplement diminue moins vite et le nombre d'espèces est plus élevé que dans les zones anthropisées. Au plan qualitatif, seuls #Helicotylenchus dihystera et #Tylenchorhynchus gladiolatus se développent quelle que soit la situation de la jachère. Parmi les autres espèces, #Xiphinema parasetariae est plus particulièrement présent sur les jachères âgées et inversement pour #Scutellonema cavenessi. La mise en défens fait pratiquement disparaître cette espèce considérée comme très dangereuse pour les cultures de cette région. Le peuplement de nématodes saprophages reste pratiquement stable sur les jachères anthropisées. Il augmente sur la jachère en défens, notamment à proximité des ligneux. Parmi les espèces végétales, #Andropogon pseudapricus, contrairement à #Pennisetum pedicellatum, est généralement associé à des populations importantes de nématodes. (Résumé d'auteur

Geometry of integral polynomials, MM-ideals and unique norm preserving extensions

We use the Aron-Berner extension to prove that the set of extreme points of the unit ball of the space of integral polynomials over a real Banach space $X$ is $\{\pm \phi^k: \phi \in X^*, \| \phi\|=1\}$. With this description we show that, for real Banach spaces $X$ and $Y$, if $X$ is a non trivial $M$-ideal in $Y$, then $\hat\bigotimes^{k,s}_{\epsilon_{k,s}} X$ (the $k$-th symmetric tensor product of $X$ endowed with the injective symmetric tensor norm) is \emph{never} an $M$-ideal in $\hat\bigotimes^{k,s}_{\epsilon_{k,s}} Y$. This result marks up a difference with the behavior of non-symmetric tensors since, when $X$ is an $M$-ideal in $Y$, it is known that $\hat\bigotimes^k_{\epsilon_k} X$ (the $k$-th tensor product of $X$ endowed with the injective tensor norm) is an $M$-ideal in $\hat\bigotimes^k_{\epsilon_k} Y$. Nevertheless, if $X$ is Asplund, we prove that every integral $k$-homogeneous polynomial in $X$ has a unique extension to $Y$ that preserves the integral norm. We explicitly describe this extension. We also give necessary and sufficient conditions (related with the continuity of the Aron-Berner extension morphism) for a fixed $k$-homogeneous polynomial $P$ belonging to a maximal polynomial ideal \Q(^kX) to have a unique norm preserving extension to \Q(^kX^{**}). To this end, we study the relationship between the bidual of the symmetric tensor product of a Banach space and the symmetric tensor product of its bidual and show (in the presence of the BAP) that both spaces have `the same local structure'. Other applications to the metric and isomorphic theory of symmetric tensor products and polynomial ideals are also given.Comment: 25 page

Plant phenology in relation to water availability : herbaceous and woody species in the savannas of northern Cameroon

Phenological patterns of herbaceous and woody plants well represented in the Sudano-Sahelian savannas of northern Cameroon were studied in relation to water availability in three contrasted soil types. Mean annual precipitation in this region is 800 mm, entirely restricted to the period May-June to September-October, but redistribution of rainwater by varying soil substrates leads to considerable heterogeneity in available water resources fo plants. Results are discussed in terms of probable competition for water resources among co-occurring plants and the adaptations shown by observed patterns to prevailing environmental conditions. Water stress is seen to be a limiting factor to plant growth but does not constitute the sole trigger for the phenological phases observed, nor is it the principal factor responsible for the preponderance of annual species in the herbaceous stratum. (Résumé d'auteur