Pluricomplex Green and Lempert functions for equally weighted poles

For $\Omega$ a domain in $\mathbb C^n$, the pluricomplex Green function with poles $a_1, ...,a_N \in \Omega$ is defined as $G(z):=\sup \{u(z): u\in PSH_-(\Omega), u(x)\le \log \|x-a_j\|+C_j \text{when} x \to a_j, j=1,...,N \}$. When there is only one pole, or two poles in the unit ball, it turns out to be equal to the Lempert function defined from analytic disks into $\Omega$ by $L_S (z) :=\inf \{\sum^N_{j=1}\nu_j\log|\zeta_j|: \exists \phi\in \mathcal {O}(\mathbb D,\Omega), \phi(0)=z, \phi(\zeta_j)=a_j, j=1,...,N \}$. It is known that we always have $L_S (z) \ge G_S(z)$. In the more general case where we allow weighted poles, there is a counterexample to equality due to Carlehed and Wiegerinck, with $\Omega$ equal to the bidisk. Here we exhibit a counterexample using only four distinct equally weighted poles in the bidisk. In order to do so, we first define a more general notion of Lempert function "with multiplicities", analogous to the generalized Green functions of Lelong and Rashkovskii, then we show how in some examples this can be realized as a limit of regular Lempert functions when the poles tend to each other. Finally, from an example where $L_S (z) > G_S(z)$ in the case of multiple poles, we deduce that distinct (but close enough) equally weighted poles will provide an example of the same inequality. Open questions are pointed out about the limits of Green and Lempert functions when poles tend to each other.Comment: 25 page

Inverse problem and Bertrand's theorem

The Bertrand's theorem can be formulated as the solution of an inverse problem for a classical unidimensional motion. We show that the solutions of these problems, if restricted to a given class, can be obtained by solving a numerical equation. This permit a particulary compact and elegant proof of Bertrand's theorem.Comment: 11 pages, 3 figure

Effects of nanoparticles on murine macrophages

Metallic nanoparticles are more and more widely used in an increasing number of applications. Consequently, they are more and more present in the environment, and the risk that they may represent for human health must be evaluated. This requires to increase our knowledge of the cellular responses to nanoparticles. In this context, macrophages appear as an attractive system. They play a major role in eliminating foreign matter, e.g. pathogens or infectious agents, by phagocytosis and inflammatory responses, and are thus highly likely to react to nanoparticles. We have decided to study their responses to nanoparticles by a combination of classical and wide-scope approaches such as proteomics. The long term goal of this study is the better understanding of the responses of macrophages to nanoparticles, and thus to help to assess their possible impact on human health. We chose as a model system bone marrow-derived macrophages and studied the effect of commonly used nanoparticles such as TiO2 and Cu. Classical responses of macrophage were characterized and proteomic approaches based on 2D gels of whole cell extracts were used. Preliminary proteomic data resulting from whole cell extracts showed different effects for TiO2-NPs and Cu-NPs. Modifications of the expression of several proteins involved in different pathways such as, for example, signal transduction, endosome-lysosome pathway, Krebs cycle, oxidative stress response have been underscored. These first results validate our proteomics approach and open a new wide field of investigation for NPs impact on macrophagesComment: Nanosafe2010: International Conference on Safe Production and Use of Nanomaterials 16-18 November 2010, Grenoble, France, Grenoble : France (2010

Neoadjuvant chemoradiation and pancreaticoduodenectomy for initially locally advanced head pancreatic adenocarcinoma

International audienceThe most accepted treatment for locally advanced pancreatic adenocarcinoma (LAPA) is chemoradiotherapy (CRT). We sought to determine the benefit of pancreaticoduodenectomy (PD) in patients with LAPA initially treated by neoadjuvant CRT

Polya's inequalities, global uniform integrability and the size of plurisubharmonic lemniscates

First we prove a new inequality comparing uniformly the relative volume of a Borel subset with respect to any given complex euclidean ball \B \sub \C^n with its relative logarithmic capacity in \C^n with respect to the same ball \B. An analoguous comparison inequality for Borel subsets of euclidean balls of any generic real subspace of \C^n is also proved. Then we give several interesting applications of these inequalities. First we obtain sharp uniform estimates on the relative size of \psh lemniscates associated to the Lelong class of \psh functions of logarithmic singularities at infinity on \C^n as well as the Cegrell class of \psh functions of bounded Monge-Amp\`ere mass on a hyperconvex domain \W \Sub \C^n. Then we also deduce new results on the global behaviour of both the Lelong class and the Cegrell class of \psh functions.Comment: 25 page

Resonant and near-resonant internal wave interactions

Author Posting. © American Meteorological Society, 2012. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 42 (2012): 669–691, doi:10.1175/2011JPO4129.1.The spectral energy density of the internal waves in the open ocean is considered. The Garrett and Munk spectrum and the resonant kinetic equation are used as the main tools of the study. Evaluations of a resonant kinetic equation that suggest the slow time evolution of the Garrett and Munk spectrum is not in fact slow are reported. Instead, nonlinear transfers lead to evolution time scales that are smaller than one wave period at high vertical wavenumber. Such values of the transfer rates are inconsistent with the viewpoint expressed in papers by C. H. McComas and P. Müller, and by P. Müller et al., which regards the Garrett and Munk spectrum as an approximate stationary state of the resonant kinetic equation. It also puts the self-consistency of a resonant kinetic equation at a serious risk. The possible reasons for and resolutions of this paradox are explored. Inclusion of near-resonant interactions decreases the rate at which the spectrum evolves. Consequently, this inclusion shows a tendency of improving of self-consistency of the kinetic equation approach.YL is supported by NSF DMS Grant 0807871 and ONR Award N00014-09-1-0515.2012-11-0

Etude calorimétrique de la réactivité du silicate tricalcique. Influence du mode de broyage et de la dimension des particules

International audienceL'étude concertée du CERILH, de l'Ecole des Mines de Saint-Etienne et de Lafarge Coppée a porté sur le silicate tricalcique C3S. Le silicate tricalcique (C3S) est le minéral prépondérant du clinker et peut s'hydrater en système binaire C3S-eau. La phase comportant le C3S, qu'on appelle l'alite, a été choisie pour l'étude et a dû être synthétisée séparément, dans le but (1) d'observer les différences sur la morphologie des grains et leur réactivité physico-chimique (2) de caractériser les différences de réactivité des grains, en surface et en masse, en étudiant leur hydratation et l'acquisition de la résistance mécanique qui en découle (3) de réaliser ce programme en s'affranchissant de l'effet de finesse et de répartition granulométrique. Ces effets font l'objet d'essais complémentaires permettant de mesurer leur importance relative

A Renormalization Group Approach to Relativistic Cosmology

We discuss the averaging hypothesis tacitly assumed in standard cosmology. Our approach is implemented in a "3+1" formalism and invokes the coarse graining arguments, provided and supported by the real-space Renormalization Group (RG) methods. Block variables are introduced and the recursion relations written down explicitly enabling us to characterize the corresponding RG flow. To leading order, the RG flow is provided by the Ricci-Hamilton equations studied in connection with the geometry of three-manifolds. The properties of the Ricci-Hamilton flow make it possible to study a critical behaviour of cosmological models. This criticality is discussed and it is argued that it may be related to the formation of sheet-like structures in the universe. We provide an explicit expression for the renormalized Hubble constant and for the scale dependence of the matter distribution. It is shown that the Hubble constant is affected by non-trivial scale dependent shear terms, while the spatial anisotropy of the metric influences significantly the scale-dependence of the matter distribution.Comment: 57 pages, LaTeX, 15 pictures available on request from the Author