Boundary singularities of positive solutions of some nonlinear elliptic equations

We study the behaviour near a boundary point a of any positive solution of a nonlinear elliptic equations with forcing term which vanishes on the boundary except at a. Our results are based upon a priori estimates for solutions and existence or non existence and uniqueness results for solutions of some nonlinear elliptic equations on the half unit sphere.Comment: 6 page

Sen, Sraffa and the revival of classical political economy

Copyright © 2012 Taylor & Francis.In his new book The Idea of Justice, Amartya Sen argues that political theory should not consist only in the characterisation of ideal situations of perfect justice. In so doing, Sen is making, within the context of political theory, a similar argument to another he also made in economic theory, when crtiticising what he called the ‘rational fool’ of mainstream economics. Sen criticised the ideal and fictitious agent of mainstream economics, while advocating for a return to an integrated view of ethics and economics, which characterised many classical political economists who inspired Sen's theory of justice, from Adam Smith to Karl Marx. I will examine Sen's revival of classical political economy, and argue that a revival of classical political economy, which was undertaken earlier by Piero Sraffa, has much potential for bringing a more plural and realist perspective to economics

Isolated Boundary Singularities of Semilinear Elliptic Equations

Given a smooth domain \Omega\subset\RR^N such that $0 \in \partial\Omega$ and given a nonnegative smooth function $\zeta$ on $\partial\Omega$, we study the behavior near 0 of positive solutions of $-\Delta u=u^q$ in $\Omega$ such that $u = \zeta$ on $\partial\Omega\setminus\{0\}$. We prove that if $\frac{N+1}{N-1} < q < \frac{N+2}{N-2}$, then u(x)\leq C \abs{x}^{-\frac{2}{q-1}} and we compute the limit of \abs{x}^{\frac{2}{q-1}} u(x) as $x \to 0$. We also investigate the case $q= \frac{N+1}{N-1}$. The proofs rely on the existence and uniqueness of solutions of related equations on spherical domains

VLBI observations of seven BL Lac objects from RGB sample

We present EVN observations of seven BL Lac objects selected from the RGB sample. To investigate the intrinsic radiation property of BL Lac objects, we estimated the Doppler factor with the VLA or MERLIN core and the total 408 MHz luminosity for a sample of 170 BL Lac objects. The intrinsic (comoving) synchrotron peak frequency was then calculated by using the estimated Doppler factor. Assuming a Lorentz factor of 5, the viewing angle of jets was constrained. The high-resolution VLBI images of seven sources all show a core-jet structure. We estimated the proper motions of three sources with the VLBI archive data, and find that the apparent speed increases with the distance of components to the core for all of them. In our BL Lacs sample, the Doppler factor of LBLs is systematically larger than that of IBLs and HBLs. We find a significant anti-correlation between the total 408 MHz luminosity and the intrinsic synchrotron peak frequency. However, the scatter is much larger than for the blazar sequence. Moreover, we find a significant positive correlation between the viewing angle and the intrinsic synchrotron peak frequency. The BL Lac objects show a continuous distribution on the viewing angle. While LBLs have a smaller viewing angle than that of IBLs and HBLs, IBLs are comparable to HBLs. We conclude that the intrinsic synchrotron peak frequency is not only related to the intrinsic radio power (though with a large scatter), but also to the viewing angle for the present sample.Comment: 22 pages,15figures, published by A&

Diversity and P-solubilizing ability of mycorrhizosphere bacteria associated with Pinus pinaster in the Landes forest ecosystem

Ectomycorrhizal fungi (ECM) and their associated mycorrhizosphere bacteria (MB) play a major role in phosphorous (P) nutrition of maritime pine, particularly in the Landes forest ecosystem considering the low bioavailability of P in its sandy-acidic soils. In order to characterize the MB associated to ECM, three collection campaigns of ECM root tips were performed from autumn 2005 to autumn 2006 throughout three forest stations. Five MB and nine ECM genera were identified overall through sequencing of 16S rDNA and mitochondrial large subunit rDNA fragment respectively. Dramatic seasonal changes were observed in the different MB-ECM associations especially in Burkholderia-Lactarius and Bacillus-Russula that were the most abundant ones. P-solubilizing ability of MB was shown to be taxon-dependent with a large majority of P-solubilizing isolates among Burkholderia, Pseudomonas and Paenibacillus contrary to Bacillus. Relationships between functional diversity of the MB-ECM associations and bioavailability of soil P remain to be investigated. (Résumé d'auteur)

Fertilité chimique des sols forestiers : concepts de base

Les diagnostics de fertilité chimique en forêt assimilent généralement le sol à un réservoir de nutriments disponibles pour les végétaux, quantifié à un instant donné puis comparé à des normes de nutrition établies par essence. Ce concept hérité de l’agronomie est régulièrement mis en défaut et de nombreux écosystèmes forestiers développés sur sols très pauvres chimiquement (notamment en Ca, Mg, K) affichent une production remarquable. L’objectif de cet article est d’illustrer les limites du concept « fertilité = réservoir sol » et de proposer les bases d’un nouveau concept rendant compte de la spécificité de la fertilité chimique des écosystèmes forestiers. Une base de données regroupant les résultats acquis sur 11 sites expérimentaux depuis les années 1970 a été utilisée. Les résultats démontrent que le concept de fertilité chimique des écosystèmes forestiers ne doit pas se limiter à la seule prise en compte des stocks de nutriments disponibles dans les sols mais doit également intégrer la circulation et le recyclage d’éléments propres aux cycles biogéochimiques