Trace Theorems for Anisotropic Weighted SOBOLEV Spaces in a Corner

In this paper, we prove a trace theorem for anisotropic weighted Sobolev spaces in a cube Q naturally associated to a class of degenerate elliptic operators. The fundamental property of this class is the existence of a suitable metric d which is “natural” for the operators. The basic tool of the proof is a representation formula obtained via suitable non-euclidean translations closely fitting the geometry of the d-balls. In a more particular situation, we construct a right inverse of the trace operator and we describe the compatibility conditions on the edges of Q.     

Characterizing electric fields in (111)B InGaAs quantum wells using electric field modulated photoluminescence and reflectance techniques

We have performed a series of electroreflectance, photoluminescence, and electric-field-modulated photoluminescence experiments to characterize the strain-induced electric fields in (111)B InGaAs/AlGaAs quantum well p-i-n diode structures. A 180° phase change in the lineshapes of electroreflectance spectra of these samples determines when the quantum well is biased to flatband. Using this bias and a depletion model for the diode, the polarization field in the quantum well can be determined. Contrary to expectations, this polarization field increases significantly with increasing temperature. In addition, at fixed temperature, the quantum well transition energies red-shift with increasing excitation intensity when excited by photons of energy higher than the lowest quantum well transition but lower than the AlGaAs diode's bandgap. When excited with photons of energy greater than the AlGaAs bandgap, the transition energy first red shifts then blue shifts with increasing excitation intensity.     

Chaînes alternées

Résumé Je caractérise les combinaisons booléennes de parties finales d'un ordre partiel P au moyen d'une limitation de la façon dont elles peuvent alterner sur les chaînes de P.

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I characterize the Boolean combinations of final segments of an ordered set by restricting the way they alternate on the chains of P.

     

Remarks on the role of conditional probability in data exploration

A careful discussion of the concept of conditional event leads to a sensible use of frequency data as conditional probabilities: as a by-product, the well-known ‘paradoxes’ arising from the so-called confounding effect are avoided.     

Polygones

We study the class of structures formed by all the polygons over a given monoid, which is equivalent to the study of the varieties in a language containing only unary functions. We collect and amplify previous results concerning their stability and superstability. Then we characterize the regular monoids for which all these polygons are ω-stable; the question about the existence of a non regular monoid with this property is left open.     

Detection of reentry currents in atrial flutter bymagnetocardiography

We discuss the use of magnetocardiography to detect reentry currents in cardiac flutter and fibrillation. The magnetic field produced by induced atrial flutter was measured in isolated rabbit hearts. A moving dipole model is proposed to treat the experimental data and to locate the reentry path.     

Zero-flee regions for a rational function with applications

In this paper, we study a rational function which plays an important role in several problems of interest (eigenvalue problems, linear control theory, ... ). Our main interest is to determine zero-free regions. We also derive upper and lower bounds for this function.     

Possible Tests of Curvature Effects in Weak Gravitational Fields

The possibility of performing in proximity of the Earth experiments to test the predictions of general relativity for the trajectories of particles and photons in weak gravitational fields is studied. Three experiments are analyzed, all based on optical detection methods. The first experiment would allow to detect the tidal acceleration using a freely-falling Michelson interferometer. In a second experiment, based on laser-ranging methods, the relativistic correction to the classical gravity acceleration could be detected. Finally, the possibility of detecting light deflection induced by space curvature in an optical cavity with high-reflectivity mirrors is discussed.     

Derivate von 4,5-dihydroxypyridonen durch ringerweiterung

The epimeric bromoghydrins 13/14 as well as their ethers 5/6 rearrange in the presence of silver ions to the 5-hydroxypyridones 15 or their ketals 9 respectively. with the bromohydrin ethers 5/6a and b this transformation is effected also with sodium methoxide. Under these reaction conditions the ring expansion is presumend ot proceed via bicyclic aziridines of which 7 could be issolated, The N-methylated compounds 5c/6c which cannot react likewise, form with sodium methoxide the 6-methoxypyridone 12 .     

A CONTIN-Based Approach Towards the Data Analysis of Particle Sizing Experiments by Centrifugal Photosedimentometry

In order to analyse the output data of centrifugal photosedimentation experiments using CONTIN software, a mathematical model has been derived. This model is based on Fick's second law and describes the sedimentation behaviour of monomodal particles in a centrifugal field: it predicts that the extinction at the detection point decays exponentially until the particles are sedimented past the detection point, which gives a sharp drop of the curves to the baseline. In practice, however, a more fluently decaying profile was obtained. Simulations revealed that the polydispersity of the sample was responsible for this behaviour. When centrifugal photosedimentation data for effective monomodal and bimodal samples of fairly monodispersed PMMA lattices were analysed with CONTIN, using the model proposed, accurate particle size distributions were obtained, provided that the sample cell was completely filled. This was imperative in order to minimize the deviations of the practical application as compared with the theoretical model.