A bilinear approach to cone multipliers II. Applications

This paper is a continuation of [TV], in which new bilinear estimates for surfaces in were proven. We give a concrete improvement to the square function estimate of Mockenhaupt [M]. We apply these estimates to give new progress on several open problems concerning the wave and Schr?dinger equation in , and convolution with curves in . Submitted: September 1998, Revised version: January 1999.     

Lognormal {star} -scale invariant random measures

In this article, we consider the continuous analog of the celebrated Mandelbrot star equation with lognormal weights. Mandelbrot introduced this equation to characterize the law of multiplicative cascades. We show existence and uniqueness of measures satisfying the aforementioned continuous equation; these measures fall under the scope of the Gaussian multiplicative chaos theory developed by Kahane in 1985 (or possibly extensions of this theory). As a by product, we also obtain an explicit characterization of the covariance structure of these measures. We also prove that qualitative properties such as long-range independence or isotropy can be read off the equation.     

Fast development of separation methods for the chiral analysis of amino acid derivatives using capillary electrophoresis and experimental designs

The use of experimental design in method development was studied for the chiral separation of several amino acid derivatives with capillary electrophoresis. The aim of this study was to define rapidly experimental conditions under which the enantiomers can be sufficiently separated for quantification and to derive a methodology for the separation of new compounds. Three modified cyclodextrins (CDs) were used as chiral selectors: hydroxypropyl-beta-cyclodextrin, carboxymethyl-beta-CD and sulfobutylether-beta-CD. The following factors were examined: the type of cyclodextrin, the CD concentration, the pH and the % of organic modifier (methanol) of the electrolyte. Two types of fractional factorial design were used depending on the type of analyte and on the number of factors selected: a 3(4-2) fractional factorial design (4 factors studied at 3 different levels) and a 2(3-1) fractional factorial design (3 factors at 2 different levels). From the 14 compounds investigated, 12 could be separated with one or another CD and not more than 9 experiments were required. No generalisation of the best analysis conditions was possible within this family of compounds. Specific analysis conditions must be defined for each analyte. Experimental designs have shown to be very useful to determine rapidly conditions under which each enantiomer can be separated with an acceptable resolution.     

A spectral quadrilateral multidomain penalty method model for high Reynolds number incompressible stratified flows

A two‐dimensional quadrilateral spectral multidomain penalty method (SMPM) model has been developed for the simulation of high Reynolds number incompressible stratified flows. The implementation of higher‐order quadrilateral subdomains renders this model a nontrivial extension of a one‐dimensional subdomain SMPM model built for the simulation of the same type of flows in vertically nonperiodic domains (Diamessis et al., J. Comp. Phys, 202 :298‐322, 2005). The nontrivial aspects of this extension consist of the implementation of subdomain corners, the penalty formulation of the pressure Poisson equation (PPE), and, most importantly, the treatment of specific challenges that arise in the iterative solution of the SMPM‐discretized PPE. The two primary challenges within the framework of the iterative solution of the PPE are its regularization to ensure the consistency of the associated linear system of equations and the design of an appropriate two‐level preconditioner. A qualitative and quantitative assessment of the accuracy, efficiency, and stability of the quadrilateral SMPM solver is provided through its application to the standard benchmarks of the Taylor vortex, lid‐driven cavity, and double shear layer. The capacity of the flow solver for the study of environmental stratified flow processes is shown through the simulation of long‐distance propagation of an internal solitary wave of depression in a manner that is free of numerical dispersion and dissipation. The methods and results presented in this paper make it a point of reference for future studies oriented toward the reliable application of the quadrilateral SMPM model to more complex environmental stratified flow process studies. Copyright © 2014 John Wiley & Sons, Ltd.     

ALFITeX: a new code for the deconvolution of complex alpha-particle spectra

A new code for the deconvolution of complex alpha-particle spectra has been developed. The ALFITeX code is written in Visual Basic for Microsoft Office Excel 2010 spreadsheets, incorporating several features aimed at making it a fast, robust and useful tool with a user-friendly interface. The deconvolution procedure is based on the Levenberg–Marquardt algorithm, with the curve fitting the experimental data being the mathematical function formed by the convolution of a Gaussian with two left-handed exponentials in the low-energy-tail region. The code also includes the capability of fitting a possible constant background contribution. The application of the singular value decomposition method for matrix inversion permits the fit of any kind of alpha-particle spectra, even those presenting singularities or an ill-conditioned curvature matrix. ALFITeX has been checked with its application to the deconvolution and the calculation of the alpha-particle emission probabilities of ²³⁹Pu, ²⁴¹Am and ²³⁵U.