Eigenvalue Comparison on Bakry-Emery Manifolds

We prove a comparison theorem on the modulus of continuity of the solution of a heat equation with a drifting term on Bakry-Emery manifolds. A direct consequence of the result is an alternate proof of an eigenvalue comparison result of Bakry-Qian. Examples are given to show that the estimate is sharp. Discussions on an explicit lower estimate for the corresponding ODE and an application to the diameter lower bound for gradient shrinking solitons are also included.     

Hölder stability estimates for some inverse pointwise source problems

In this Note we establish a Hölder stability estimate for an inverse pointwise source elliptic problem.     

Directional and Anisotropic Regularity and Irregularity Criteria in Triebel Wavelet Bases

Many natural mathematical objects, as well as many multi-dimensional signals and images from real physical problems, need to distinguish local directional behaviors (for tracking contours in image processing for example). Using some results of Jaffard and Triebel, we obtain criteria of directional and anisotropic regularities by decay conditions on Triebel anisotropic wavelet coefficients (resp. wavelet leaders).     

Methode de laplace: etude variationnelle des fluctuations de diffusions de type

This article concerns the asymptotic behaviour of diffusions consisting of various systems of mean-field type interacting particles. We specifically study the following properties: propagation of chaos; critical and non critical fluctuations, using the Laplace method which has been developed by Bolthausen in the general Banach valued random variables context; and finally the large deviations of laws of trajectorial empirical measures.

We also study Gibbs variational formula associated with this problem and show that it reduces to a finite dimensional problem     

The monotonic property of the generalized root mean square

The link between a differential equation and its initial conditions is not quite as simple as usually imagined. Several examples illustrate the complications that can arise.     

The Inorganic-free Organic Conductor α''''-(ET)_2C_6H_4(SO_3)_2 : Its Synthesis, Structure, and Conductivity

Having more than twenty years?glory, ET series still keep the most promising family in various kinds of organic conductors. Most of ET based molecular conductors consist of organic cationic ET+0.5 radical and certain anionic inorganic component such as the superconductor k-(ET)2Cu[N(CN)2]Cl (TC = 12.8K, 0.3kbar)1. Recently, the first purely organic superconductor b-(ET)2SF5CH2CF2SO3 (TC = 5.2K)2 has been reported, which aroused our interest on this kind of inorganic-free organic c…