Some Estimates for the Derivative of a Quasiconformal Reflection Spiral-Shaped Domains

Some estimates of derivatives are sharpened for quasiconformal reflections of a special class of simply connected plane domains. Bibliography: 2 titles.     

Complete ideals and singularities of space curves

We consider complete ideals supported on finite sequences of infinitely near points, in regular local rings with dimensions greater than two. We study properties of factorizations in Lipman special *-simple complete ideals. We relate it to a type of proximity, linear proximity, of the points, and give conditions in order to have unique factorization. Several examples are presented. Received: 2 February 2000 / in final form: 14 March 2001 / Published online: 18 January 2002     

An interior–exterior Schwarz algorithm and its convergenceUn algorithme de Schwarz intérieur–extérieur et sa convergence

In this work we study the solution of Laplace's equation in a domain with holes by an iteration consisting of splitting the problem in an exterior one, around the holes, plus an interior problem in the unholed domain. We show the existence of a decomposition of the solution when the exterior problem is represented by means of a single-layer protential. Also, for the three-dimensional case and with some adjustments for the two-dimensional case, we prove convergence of the method by writing the iteration as a Jacobi iteration for an operator equation and studying the spectrum of the iteration operator. To cite this article: R. Celorrio et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 923–926.     

CMS physics overview

The principal physics goals of the Compact Muon Solenoid experiment under construction at the Large Hadron Collider at CERN in Geneva are reviewed. Procedures to search for the Standard Model Higgs boson, supersymmetric Higgses and other supersymmetric particles are described.     

Magnetic properties of oxygenated carbon nitride films from RF-discharge in an acetylene, nitrogen, and oxygen mixture environments

Properties of oxygenated carbon nitride films have attracted the attention of physics researchers due to their magnetic and physical properties, as well as for their usefulness in the industry. The free radicals were investigated using electron paramagnetic resonance applied in the study of spin concentration due to the different mechanism of preparation of carbon nitride films by RF-discharge with different kinds of plasma. Unpaired spin concentrations, in the order of 10²⁰ per cm³, were measured and their time recombination dependency was important in those films. The films were grown by plasma enhanced chemical vapor deposition using mixtures of hydrocarbons, N₂ and O₂ in different proportions.     

Three-dimensional radiative transfer in an anisotropically scattering, semi-infinite medium: generalized reflection function

Three-dimensional radiative transfer in an anisotropic scattering medium exposed to spatially varying, collimated radiation is studied. The generalized reflection function for a semi-infinite medium with a very general scattering phase function is the focus of this investigation. An integral transform is used to reduce the three-dimensional transport equation to a one-dimensional form, and a modified Ambarzumian's method is applied to formulate a nonlinear integral equation for the generalized reflection function. The integration is over both the polar and azimuthal angles; hence, the integral equation is said to be in the double-integral form. The double-integral, reflection function formulation can handle a variety of anisotropic phase functions and does not require an expansion of the phase function in a Legendre polynomial series. Complicated kernel transformations of previous single-integral studies are eliminated. Single and double scattering approximations are developed. Numerical results are presented for a Rayleigh phase function to illustrate the computational characteristics of the method and are compared to results obtained with the single-integral method. Agreement between the two approaches is excellent; however, as the transform variable increases beyond five the number of quadrature points required for the double-integral method to produce accurate solutions significantly increases. A new interpolation scheme produces accurate results when the transform variable is large.     

Comparisons between model equations for long waves

Summary Considered here are model equations for weakly nonlinear and dispersive long waves, which feature general forms of dispersion and pure power nonlinearity. Two variants of such equations are introduced, one of Korteweg-de Vries type and one of regularized long-wave type. It is proven that solutions of the pure initial-value problem for these two types of model equations are the same, to within the order of accuracy attributable to either, on the long time scale during which nonlinear and dispersive effects may accumulate to make an order-one relative difference to the wave profiles.This research was supported in part by the National Science Foundation. A considerable portion of the project was completed while the first author was resident at the Institute for Mathematics and Its Applications, University of Minnesota.