766 research outputs found
Pluricomplex Green and Lempert functions for equally weighted poles
For a domain in , the pluricomplex Green function with
poles is defined as .
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 by . It is known
that we always have . In the more general case where we
allow weighted poles, there is a counterexample to equality due to Carlehed and
Wiegerinck, with 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 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
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
Convergence and multiplicities for the Lempert function
Given a domain , the Lempert function is a
functional on the space Hol (\D,\Omega) of analytic disks with values in
, depending on a set of poles in . We generalize its definition
to the case where poles have multiplicities given by local indicators (in the
sense of Rashkovskii's work) to obtain a function which still dominates the
corresponding Green function, behaves relatively well under limits, and is
monotonic with respect to the indicators. In particular, this is an improvement
over the previous generalization used by the same authors to find an example of
a set of poles in the bidisk so that the (usual) Green and Lempert functions
differ.Comment: 24 pages; many typos corrected thanks to the referee of Arkiv for
Matemati
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
On Vector Bundles of Finite Order
We study growth of holomorphic vector bundles E over smooth affine manifolds.
We define Finsler metrics of finite order on E by estimates on the holomorphic
bisectional curvature. These estimates are very similar to the ones used by
Griffiths and Cornalba to define Hermitian metrics of finite order. We then
generalize the Vanishing Theorem of Griffiths and Cornalba to the Finsler
context. We develop a value distribution theory for holomorphic maps from the
projectivization of E to projective space. We show that the projectivization of
E can be immersed into a projective space of sufficiently large dimension via a
map of finite order.Comment: version 2 has some typos corrected; to appear in Manuscripta
Mathematic
Physical and optical properties of sol-gel nano-silver doped silica film on glass substrate as a function of heat-treatment temperature
Nano-silver doped silica films were deposited on glass slides using a sol-gel process and heat-treated at different temperatures. The films were characterized by ultraviolet-visible spectroscopy, x-ray photoelectron spectroscopy (XPS), atomic force microscopy (AFM), Rutherford backscattering spectrometry (RBS), and transmission electron microscopy for their optical, chemical, and structural properties. The absorption peak of silver colloids (wavelength from 400 to 460 nm) was present and a blueshift and intensity reduction of the absorption peak was observed during heat-treatment. Particle size reduction and surface morphology changes in the films were observed by AFM as a function of varying heat treatment temperatures. Silver nanoparticles were formed through spontaneous reduction of silver ions. The oxidation of silver occurs during heat-treatment, causing a reduction of absorption intensity. An interdiffusion between the Ag in the film and Na in the substrate glass was observed by XPS and RBS. Sodium in the coating likely increased the stability of silver oxide at high temperature treated samples
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