Quasi-free divisors and duality

We prove a duality theorem for some logarithmic $\text{D}$-modules associated with a class of divisors. We also give some results for the locally quasi-homogeneous case. To cite this article: F.J. Castro-Jiménez, J.M. Ucha-Enr??quez, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Stable boundary layers in a diffusion problem with nonlinear reaction at the boundary

We prove the existence of nonconstant stable stationary solutions of an evolution problem with a nonlinear reaction acting on the boundary. These solutions present layers at certain points of the boundary. We also study the behavior of these solutions as the small parameter appearing in the equation approaches zero and show some stability properties of the profiles given by these equilibrium solutions.     

Comparison of Several Calibration Procedures for Glass Electrodes in Proton Concentration

Several reported procedures for calibrating glass electrodes in proton concentration are compared. Some recommendations for non-experts are also given. The examined procedures can be classified into two broad categories, namely: those based on direct potential difference measurements of solutions of known proton concentration and those that use one or several pH standards to calibrate the electrode and subsequently measure the pH of solutions containing known proton concentrations. With a single buffer, the two types of procedures lead to equivalent results. However, if two pH buffers are used, the slope of the calibration graph in proton concentration will differ from the real electrode slope to an extent proportional to the difference between the liquid junction potentials of the two buffers. Therefore, any other method is preferable under these circumstances.     

Principes de grandes déviations pour des processus de « coarse graining »

We improve the Large Deviations Principle satisfied by a Coarse Grained process already analyzed by Boucher, Ellis and Turkington [Ann. Probab. 27 (1999) 297–324]. To cite this article: J. Trashorras, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

A simple Markov chain structure for the evolution of credit ratings

We focus on continuous Markov chains as a model to describe the evolution of credit ratings. In this work it is checked whether a simple, tridiagonal type of generator provides a good approximation to a general one. Three different tridiagonal approximations are proposed and their performance is checked against two generators, corresponding to a volatile and a stable period, respectively. Copyright © 2007 John Wiley & Sons, Ltd.     

57Fe Mössbauer Spectroscopy Study of LaFe1−x Co x O3 (x=0 and 0.5) Formed by Mechanical Milling

Hyperfine Interactions - Perovskite-related phases of the type LaFe1?x Co x O3 (x=0 and 0.5) have been synthesised by milling techniques. The materials are of smaller particle size and more...     

Characterization of the behaviour of flavour microcapsules in cotton fabrics

Nanotechnology processes have recently been introduced into the textile field. One of these processes involves encapsulated nanoparticles or nanoproducts, known as microcapsules. They are available with a wide range of products which confer different properties related to the nature of the encapsulated product. The composition of the wall material determines the release of the product into the fabric and is the object of study in the present work. The behaviour of microencapsulated peppermint was analyzed on cotton fabrics.Different application methods have been tested, impregnation versus bath exhaustion. As impregnation turned out to be the most efficient, some recipes were assayed and the effect of microcapsules on maintenance conditions was evaluated in order to determine the most suitable method with the longest lasting effect on fabrics.The effect of microcapsules is usually measured by the presence of a property such as odour measurements when flavours are encapsulated. The aim of this work is to explain the behaviour of the cotton fabrics with microcapsules bound to their fibers, to determine the relationship between their macroscopic properties and microscopic characteristics. A procedure based in FTIR spectroscopy is also proposed to quantify the presence of microcapsules in the fabrics.IR spectra of the textiles were obtained to determine the presence of microcapsules, which was corroborated by SEM techniques.     

Newtonian limits of warp drive spacetimes

We find a class of warp drive spacetimes possessing Newtonian limits, which we then determine. The same method is used to compute Newtonian limits of the Schwarzschild solution and spatially flat Friedmann-Robertson-Walker cosmological models. This work was partially supported by FCT/POCTI/FEDER.     

On the Cartan–Jacobson Theorem

The well-known Cartan–Jacobson theorem claims that the Lie algebra of derivations of a Cayley algebra is central simple if the characteristic is not 2 or 3. In this paper we have studied these two cases, with the following results: if the characteristic is 2, the theorem is also true, but, if the characteristic is 3, the derivation algebra is not simple. We have also proved that in this last case, there is a unique nonzero proper seven-dimensional ideal, which is a central simple Lie algebra of type A₂, and the quotient of the derivation algebra modulo this ideal turns out to be isomorphic, as a Lie algebra, to the ideal itself. The original motivation of this work was a series of computer-aided calculations which proved the simplicity of derivation algebras of Cayley algebras in the case of characteristic not 3. These computations also proved the existence of a unique nonzero proper ideal (which turns out to be seven-dimensional) in the algebra of derivations of split Cayley algebras in characteristic 3.     

Geometric Algebra in Linear Algebra and Geometry

This article explores the use of geometric algebra in linear and multilinear algebra, and in affine, projective and conformal geometries. Our principal objective is to show how the rich algebraic tools of geometric algebra are fully compatible with and augment the more traditional tools of matrix algebra. The novel concept of an h-twistor makes possible a simple new proof of the striking relationship between conformal transformations in a pseudo-Euclidean space to isometries in a pseudo-Euclidean space of two higher dimensions. The utility of the h-twistor concept, which is a generalization of the idea of a Penrose twistor to a pseudo-Euclidean space of arbitrary signature, is amply demonstrated in a new treatment of the Schwarzian derivative.