Groupes Moyennables, Dimension Topologique Moyenne et sous-décalages

Let G be an infinite countable residually finite amenable group. In this paper we construct a continuous action of G on a compact metrisable space X such that the dynamical system (X, G) cannot be embedded in the G-shift on [0,1] ^G . This result generalizes a construction due to E. Lindenstrauss and B. Weiss (Mean topological dimension, Israel J. Math. 115 (2000), 1–24) for .     

The Jacobian, the square root and the set ∞

In these notes, we wish to present a new approach to the problem of prescribing Jacobian determinants in dimension two: we restrict ourselves to the case the datum is a finite sum of Dirac masses. The main point is to show that we may relate this problem to the search of harmonic maps into a singular space shaped as the symbol ∞. The later problem in turn is closely linked to questions in complex analysis. A large part of the paper is devoted to a presentation of these mathematical objects and their connections.     

Sojourn Times in the <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">PH</Emphasis>/1 Processor Sharing Queue

We give in this paper an algorithm to compute the sojourn time distribution in the processor sharing, single server queue with Poisson arrivals and phase type distributed service times. In a first step, we establish the differential system governing the conditional sojourn times probability distributions in this queue, given the number of customers in the different phases of the PH distribution at the arrival instant of a customer. This differential system is then solved by using a uniformization procedure and an exponential of matrix. The proposed algorithm precisely consists of computing this exponential with a controlled accuracy. This algorithm is then used in practical cases to investigate the impact of the variability of service times on sojourn times and the validity of the so-called reduced service rate (RSR) approximation, when service times in the different phases are highly dissymmetrical. For two-stage PH distributions, we give conjectures on the limiting behavior in terms of an M/M/1 PS queue and provide numerical illustrative examples.This revised version was published online in June 2005 with corrected coverdate     

Perelman’s Entropy and Doubling Property on Riemannian Manifolds

The purpose of this work is to study some monotone functionals of the heat kernel on a complete Riemannian manifold with nonnegative Ricci curvature. In particular, we show that on these manifolds, the gradient estimate of Li and Yau (Acta Math. 156, 153–201, 1986), the gradient estimate of Ni (J. Geom. Anal. 14(1), 87–100, 2004), the monotonicity of the Perelman’s entropy and the volume doubling property are all consequences of an entropy inequality recently discovered by Baudoin and Garofalo, , 2009. The latter is a linearized version of a logarithmic Sobolev inequality that is due to D. Bakry and M. Ledoux (Rev. Mat. Iberoam. 22, 683–702, 2006).     

Strong Solutions To The Incompressible Navier Stokes Equations In The Half Space

We derive an exact formula for solutions to the Stokes equations in the half space with an external forcing term. This formula is used to establish local and global existence and uniqueness in a suitable Besov space for solutions to the Navier Stokes equations. In particular, wellposedness is proved for initial data in L³(R³ ₊).     

Asymptotic results for the superposition of a large number of data connections on an ATM link

The M/PH/∞ system is introduced in this paper to analyze the superposition of a large number of data connections on an ATM link. In this model, information is transmitted in bursts of data arriving at the link as a Poisson process of rate λ and burst durations are PH distributed with unit mean. Some transient characteristics of the M/PH/∞ system, namely the duration θ of an excursion by the occupation process {X_t} above the link transmission capacity C, the area V swept under process {X_t} above C and the number of customers arriving in such an excursion period, are introduced as performance measures. Explicit methods of computing their distributions are described. It is then shown that, as conjectured in earlier studies, random variables Cθ,CV and N converge in distribution as C tends to infinity while the utilization factor of the link defined by γ = λ/C is fixed in (0,1), towards some transient characteristics of an M/M/1 queue with input rate γ and unit service rate. Further simulation results show that after adjustment of the load of the M/M/1 queue, a similar convergence result holds for the superposition of a large number of On/Off sources with various On and Off period distributions. This shows that some transient quantities associated with an M/M/1 queue can be used in the characterization of open loop multiplexing of a large number of On/Off sources on an ATM link. This revised version was published online in June 2006 with corrections to the Cover Date.     

Electrolytic electrospray ionization mass spectrometry of quaterthiophene-bridged bisporphyrins: beyond the identification tool

Several quaterthiophene-bridged bisporphyrins were analyzed by electrospray ionization mass spectrometry (ESI-MS). The active centers of these molecular assemblies are two porphyrins moieties complexed (Z) or not (H) with a metal ion, typically Zn(2+), and the spacer is a quaterthiophene. The two end-groups were chemically linked to the quaterthiophene spacers by (i) a C--C single bond, (ii) a trans double bond or (iii) a triple bond. The formation of charged species either by protonation ([M + H](+) and [M + 2H](2+)) or electron(s) loss (M(+) and M(2+)), account for the occurrence of electrochemical processes in the basic operation of an electrospray source acting in a non-aqueous solvent. The nature of the observed charged species is correlated with the electro-oxidation properties and proton production by electro-oxidation of residual water. The occurence of these electrochemical reaction is proposed when the electroactivity of the electrosprayed substrates is not sufficient to support the current demand of the ESI source. In this way, the results obtained from the analysed series suggest the occurrence of such a process when the interfacial potential of the metal capillary reaches a value of 0.75 V vs Ag/AgCl. The results of theoretical calculations confirm the importance of the ionization energy with regard to the protonation energy in the course of the ionization reaction. The structural differences at the porphyrin-linker junctions lead to significantly smaller ionization energy in the case of the trans double bond. The MS observation of discharged dimers from molecular assemblies, including two complexed porphyrins ZZ or two free bases HH as end-group and a triple bond as the quaterthiophene-bisporphyrin junction, indicates together with molecular modelling (carried out at the semi-empirical PM3 level), that the planar and symmetric structures favour stacking.     

Multidimensional gas chromatography for the detailed PIONA analysis of heavy naphtha: hyphenation of an olefin trap to comprehensive two-dimensional gas chromatography

A multidimensional method providing the composition of a heavy naphtha in paraffins, isoparaffins, olefins, naphthenes, and aromatics (PIONA) in the C8-C14 range is presented. The analytical set-up consists in a silver modified silica olefin trap on-line coupled to comprehensive two-dimensional gas chromatography (GC x GC). In this configuration, hydrocarbons are separated, in gaseous state, in two fractions, saturate and unsaturate, each fraction being subsequently analysed by GC or by GC x GC. The resolution between saturates and olefins was found to be improved compared to a single GC x GC run. The characterisation of the olefin trap highlights the benefits and the limits related to the use of that stationary phase as a double bond selective fractionation medium.     

Backward stochastic differential equations on manifolds II

In [1], we have studied a generalization of the problem of finding a martingale on a manifold whose terminal value is known. This article completes the results obtained in the first article by providing uniqueness and existence theorems in a general framework (in particular if positive curvatures are allowed), still using differential geometry tools.     

On the Optical Diagnosis and Sizing of Spherical Coated and Multilayered Particles with phase-Doppler anemometry

After having recalled basic theoretical results concerning the extension of generalized Lorenz-Mie theory to the case of multilayered spheres, results connected with phase-Doppler anemometry are considered, showing the influence of Gaussian beam intensity profiles on the light scattering properties of these particles. Particular emphasis is placed on the case of water-coated carbon core particles, for which the possibility of obtaining simultaneous size measurements of the core and outer diameters is discussed. The sensitivity of the technique to particles with a refractive index profile is also considered, showing that this technique is more sensitive to changes in the average refractive index of the particles than to refractive index profiles, such as produced by high pressure and temperature stresses, at least for the studied geometry.