Quaternionic Brownian Windings

Journal of Theoretical Probability - We define and study the three-dimensional windings along Brownian paths in the quaternionic Euclidean, projective and hyperbolic spaces. In particular, the...     

Bayesian Inference of a Parametric Random Spheroid from its Orthogonal Projections

Methodology and Computing in Applied Probability - The paper focuses on a new method for the inference of a parametric random spheroid from the observations of its 2D orthogonal projections. Such a...     

Stationary Analysis of a Fluid Queue Driven by Some Countable State Space Markov Chain

Motivated by queueing systems playing a key role in the performance evaluation of telecommunication networks, we analyze in this paper the stationary behavior of a fluid queue, when the instantaneous input rate is driven by a continuous-time Markov chain with finite or infinite state space. In the case of an infinite state space and for particular classes of Markov chains with a countable state space, such as quasi birth and death processes or Markov chains of the G/M/1 type, we develop an algorithm to compute the stationary probability distribution function of the buffer level in the fluid queue. This algorithm relies on simple recurrence relations satisfied by key characteristics of an auxiliary queueing system with normalized input rates.      

Smoothing and dispersive estimates for 1D Schrödinger equations with BV coefficients and applications

We prove smoothing estimates for Schrödinger equations it_∂?+x_∂(a(x)x_∂?)=0 with a(x)∈BV, real and bounded from below. We then bootstrap these estimates to obtain optimal Strichartz and maximal function estimates, all of which turn out to be identical to the constant coefficient case. We also provide counterexamples showing a∈BV to be in a sense a minimal requirement. Finally, we provide an application to sharp well-posedness for a generalized Benjamin-Ono equation.     

Skew-product decompositions of Brownian motions on manifolds: A probabilistic aspect of the Lichnerowicz-Szabo theorem

We show that the only compact simply connected manifolds for which the radial part of Brownian motion enjoys the Markov property are compact two points homogeneous spaces, i.e. rank one symmetric spaces.     

Numerical spectral analysis of a grid: Application to strain measurements

We present a nondestructive and noncontact extensometry technique, which has been developed in order to study the behavior of different materials such as polycarbonate, araldite, urethane, etc. A spectral analysis of a crossed grating marked on the surface of a specimen and recorded by a charge coupled device camera is presented. The procedure is based on the use of a bidimensional fast Fourier transform algorithm coupled with an interpolation process. It leads to the accurate determination of frequencies. Numerical simulations have been made to evaluate the strain sensitivity; it depends on both the initial phase and the number of cycles characterizing the grid. Theoretically, the strain sensitivity can reach 10^-5 in best cases, but practically it is notbetter than 10^-4. Several applications on different materials are presented: polyurethane, paper and cloth.     

Test d'indépendance nonparametrique

We consider the minimax problem of testing the independence of the components of a d-dimensional random vector against a set of alternatives defined by L₂-norm. We are interested in finding the minimax rate of testing and a test that attains this rate. The bound of the error of the first kind is a positive sequence which can decrease to zero as the number of observations increases. To cite this article: A.F. Yode, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Non-explosion en temps grand et stabilité de solutions globales des équations de Navier–StokesNon-blowup at large times and stability for global solutions to the Navier–Stokes equations

Suppose there exists a global solution u to the incompressible Navier–Stokes equations, such that $\text{u∈}\text{C}{}_{\mathrm{t}}\text{(}\text{H}\text{?}{}^{\mathrm{1/2}}\text{)}$. We prove that its $\text{H}\text{?}{}^{\mathrm{1/2}}$ norm goes to 0 at infinity. We next use this fact to control the $\text{L}{}^2{}_{\mathrm{t}}\text{(}\text{H}\text{?}{}^{\mathrm{3/2}}\text{)}$ norm of u, and finally we prove that such a solution is stable. To cite this article: I. Gallagher et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 289–292.     

Monolayers as models for supported catalysts: zirconium phosphonate films containing manganese(III) porphyrins

Organized monolayer films of a manganese tetraphenylporphyrin have been prepared and used as supported oxidation catalysts. Manganese 5,10,15,20-tetrakis(tetrafluorophenyl-4'-octadecyloxyphosphonic acid) porphyrin (1) has been immobilized as a monolayer film by a combination of Langmuir-Blodgett (LB) and self-assembled monolayer techniques that use zirconium phosphonate linkages to bind the molecule to the surface. Analysis by FTIR, XPS, UV-vis and polarized optical spectroscopy show that the films consist of noninteracting molecules effectively anchored and oriented nearly parallel to the surface. The monolayer films are stable to the solvent and temperature conditions needed to explore organic oxidations. The activity of films of 1 toward the epoxidation of cyclooctene using iodosylbenzene as the oxidant was compared to that of Manganese 5,10,15,20-tetrakis(pentafluorophenyl) porphyrin (2) and 1 under equivalent homogeneous conditions. The immobilized porphyrin 1 shows an enhanced activity relative to either homogeneous reaction. The main difference between 1 and 2 is the four alkyl phosphonate arms in 1 designed to incorporate the porphyrin within the films. The increased activity of immobilized 1 is a combination of the porphyrin structure, which prohibits the formation of mu-oxo dimers even in solution, and a change in conformation when anchored to the surface. The study demonstrates that careful monolayer studies can provide useful models for the design and study of supported molecular catalyst systems.     

Diasteroselective synthesis of new spiropiperidine scaffolds from the CN(R,S) building block

A methodology allowing the construction of spiropiperidine scaffolds similar to those found in naturally occurring alkaloids has been developed. This approach begins with the well-established CN(R,S) strategy, the spiro-center being built by way of an intramolecular attack of a nitrile function by an organolithium species obtained by a halogen/lithium exchange reaction mediated by either t-BuLi or lithium naphthalenide.