On the Patterson–Sullivan Measure for Geometrically Finite Groups Acting on Complex or Quaternionic Hyperbolic Space

The goal of this paper is to provide a tool, the Global Measure Formula, that will facilitate the study of the limit set of discrete geometrically finite groups of isometries of the rank one symmetric spaces. We consider the shadow of a ball from a fixed reference point onto the boundary, and prove a formula that describes the measure of the shadow in terms of the center of the shadowed ball, generalizing a result from real hyperbolic geometry.     

Discrete duality finite volume schemes for Leray−Lions−type elliptic problems on general 2D meshes

Discrete duality finite volume schemes on general meshes, introduced by Hermeline and Domelevo and Omnès for the Laplace equation, are proposed for nonlinear diffusion problems in 2D with nonhomogeneous Dirichlet boundary condition. This approach allows the discretization of non linear fluxes in such a way that the discrete operator inherits the key properties of the continuous one. Furthermore, it is well adapted to very general meshes including the case of nonconformal locally refined meshes. We show that the approximate solution exists and is unique, which is not obvious since the scheme is nonlinear. We prove that, for general W^?1,p′(Ω) source term and W^1‐(1/p),p(?Ω) boundary data, the approximate solution and its discrete gradient converge strongly towards the exact solution and its gradient, respectively, in appropriate Lebesgue spaces. Finally, error estimates are given in the case where the solution is assumed to be in W^2,p(Ω). Numerical examples are given, including those on locally refined meshes. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Task Specific Onium Salts and Ionic Liquids as Soluble Supports in Grieco ’s Multicomponent Synthesis of Tetrahydroquinolines

In this work was presented an application of the use of task specific onium salts (TSOSs) as soluble supports in Grieco’s multicomponent synthesis of tetrahydroquinolines. These soluble supports are of wide applicability and combine advantages of solid phase synthesis without its limitations with those of solution phase chemistry. After a simple washing step, products were cleaved from the supports and obtained in pure form and good yields.     

A large deviation principle for 2D stochastic Navier–Stokes equation

In this paper one specifies the ergodic behavior of the 2D-stochastic Navier–Stokes equation by giving a Large Deviation Principle for the occupation measure for large time. It describes the exact rate of exponential convergence. The considered random force is non-degenerate and compatible with the strong Feller property.     

On the Weak Invariance Principle for Stationary Sequences under Projective Criteria

In this paper, we study the central limit theorem and its weak invariance principle for sums of a stationary sequence of random variables, via a martingale decomposition. Our conditions involve the conditional expectation of sums of random variables with respect to the distant past. The results contribute to the clarification of the central limit question for stationary sequences. Magda Peligrad is supported in part by a Charles Phelps Taft research support grant at the Univeristy of Cincinnati and the NSA grant H98230-05-1-0066.     

Graded parafermions: standard and quasiparticle bases

Two bases of states are presented for modules of the graded parafermionic conformal field theory associated to the coset . The first one is formulated in terms of the two fundamental (i.e., lowest-dimensional) parafermionic modes. In that basis, one can identify the completely reducible representations, i.e., those whose modules contain an infinite number of singular vectors; the explicit form of these vectors is also given. The second basis is a quasiparticle basis, determined in terms of a modified version of the exclusion principle. A novel feature of this model is that none of its bases are fully ordered and this reflects a hidden structural exclusion principle.     

Study of the spontaneous formation of organic layers on carbon and metal surfaces from diazonium salts

This study investigates the spontaneous grafting of different para-substituted phenyl groups on carbon and metallic surfaces from diazonium salts solutions. Glassy carbon, nickel, zinc and iron plates were allowed to react with an acetonitrile solution of aryldiazonium tetrafluoroborate salt by simple dipping. The surfaces were characterized before and after their immersion by XPS and AFM to evidence the formation of a coating on the different materials. The results are indicative of the presence of substituted phenyl groups on all the investigated surfaces. This study also aims at correlating grafting efficiency with metal reactivities and diazonium salt electronic properties by means of AFM and FT-IRRAS. For this purpose, zinc and nickel were chosen due to their opposite reducing properties and two diazonium salts were selected with electron-donor or -withdrawing para-substituents. The results tend to indicate that redox properties of both partners (diazonium + metal) are of prime importance for grafting to occur.