A moment inequality of the Marcinkiewicz–Zygmund type for some weakly dependent random fields

The goal of this note is to give a new moment inequality for sums of some weakly dependent random fields. Our result extends moment bounds given by Wu (2007) or Liu and Lin (2009) for causal autoregressive processes and follows by using recursive applications of the Burkhölder inequality for martingales.     

Well-posedness of a degenernate parabolic equation issuing from two-dimensional perfect fluid dynamics

A degenerate parabolic equation of convection-diffusion type has been proposed by Robert and Sommeria in [12] to describe the relaxation towards statistical equilibrium states in 2D incompressible perfect fluid dynamics. The paper is concerned with the Cauchy problem for this equation. The local existence of a variational soluation is obtained in using the decrease of the (negative) mixing entropy and Schauder theorem. A smoothing effect is used when proving the uniqueness of the variational solutions by youdovitch's method. Finally, global existence of solutions and their asymptotic convergence towards Gibbs states are shown for a large class of initial data.     

Einstein-Weyl structures on lightlike hypersurfaces

We study Weyl structures on lightlike hypersurfaces endowed with a conformal structure of certain type and specific screen distribution: the Weyl screen structures. We investigate various differential geometric properties of Einstein-Weyl screen structures on lightlike hypersurfaces and show that, for ambient Lorentzian space ? ₁ ⁿ⁺² and a totally umbilical screen foliation, there is a strong interplay with the induced (Riemannian) Weyl-structure on the leaves.     

A spatial scan statistic for case event data based on connected components

We propose a new spatial scan statistic based on graph theory as a method for detecting irregularly-shaped clusters of events over space. A graph-based method is proposed for identifying potential clusters in spatial point processes. It relies on linking the events closest than a given distance and thus defining a graph associated to the point process. The set of possible clusters is then restricted to windows including the connected components of the graph. The concentration in each of these possible clusters is measured through classical concentration indices based on likelihood ratio and also through a new concentration index which does not depend on any alternative hypothesis. These graph-based spatial scan tests seem to be very powerful against any arbitrarily-shaped cluster alternative, whatever the dimension of the data. These results have applications in various fields, such as the epidemiological study of rare diseases or the analysis of astrophysical data.     

Structure and properties of potassium niobato-borophosphate glasses

Bulk glasses of the series (1 ? x)[0.5K₂O–0.1B₂O₃–0.4P₂O₅]–xNb₂O₅ with x = 0–45.7 mol% Nb₂O₅ were prepared by slow cooling in air and investigated by Raman, ³¹P, and ¹¹B MAS NMR spectroscopy. The incorporation of Nb₂O₅ into the parent borophosphate glass results in a substantial increase in the glass transition temperature and chemical durability of glasses. Raman spectra showed that Nb atoms form distorted NbO₆ octahedra, which are isolated at low Nb₂O₅ content, whereas at higher Nb₂O₅ content they form clusters. ¹¹B NMR spectra of the glasses revealed the interaction between Nb₂O₅ and BO₄ tetrahedral units, which results in a partial transformation of tetrahedral BO₄ units to trigonal BO₃ units and the formation of mixed B(OP)_4?n(ONb)_n units.     

Excited State Dynamics of Isolated 6- and 8-Hydroxyquinoline Molecules

The photoinduced dynamics of isolated n-hydroxyquinoline (nHQ) molecules (n=6,8) was investigated in femtosecond pump-probe experiments. A qualitative difference was found between 8HQ and 6HQ. After an initial rapid decay corresponding to the departure of the initial wavepacket out of the Franck-Condon region of the excitation, the 8HQ probe signal decays to zero in 0.37 ps whereas a much longer time constant of 10.4 ps is observed in 6HQ. This interrogates on the role played by the intramolecular H-bond N HO which is at play the 8HQ molecule. Ab-initio were performed at the MCSCF/aug-cc-pVDZ level on the 8HQ molecule to help the discussion. A complex energy landscape was found, which includes a conical intersection.