Disorder-induced phonon self-energy of semiconductors with binary isotopic composition

Self-energy effects of Raman phonons in isotopically disordered semiconductors are deduced by perturbation theory and compared to experimental data. In contrast to the acoustic frequency region, higher-order terms contribute significantly to the self-energy at optical phonon frequencies. The asymmetric dependence of the self-energy of a binary isotope system $m_{1-x} M_x$ on the concentration of the heavier isotope mass x can be explained by taking into account second- and third-order perturbation terms. For elemental semiconductors, the maximum of the self-energy occurs at concentrations with $0.5<x<0.7$, depending on the strength of the third-order term. Reasonable approximations are imposed that allow us to derive explicit expressions for the ratio of successive perturbation terms of the real and the imaginary part of the self-energy. This basic theoretical approach is compatible with Raman spectroscopic results on diamond and silicon, with calculations based on the coherent potential approximation, and with theoretical results obtained using {\it ab initio} electronic theory. The extension of the formalism to binary compounds, by taking into account the eigenvectors at the individual sublattices, is straightforward. In this manner, we interpret recent experimental results on the disorder-induced broadening of the TO (folded) modes of SiC with a $^{13}{\rm C}$-enriched carbon sublattice. \cite{Rohmfeld00,Rohmfeld01}Comment: 29 pages, 9 figures, 2 tables, submitted to PR

Stability of homogeneous bundles on P^3

We study the stability of some homogeneous bundles on P^3 by using their representations of the quiver associated to the homgeneous bundles on P^3. In particular we show that homogeneous bundles on P^3 whose support of the quiver representation is a parallelepiped are stable, for instance the bundles E whose minimal free resolution is of the kind 0 --> S^{l_1, l_2, l_3} V (t) --> S^{l_1 +s, l_2, l_3} V (t+s) --> E --> 0 are stable.Comment: to appear in Geometriae Dedicata http://www.springer.com/mathematics/geometry/journal/1071

Breathe right nasal strips and the respiratory disturbance index in sleep related breathing disorders

This investigation assesses the effects of Breathe Right nasal strips on the respiratory disturbance index (RDI) measured by polysomnography in patients suffering from obstructive sleep apnea and snaring. The positive effect of these strips on nasal ventilation was shown in earlier studies. Twenty-six patients with art RDI higher than 10 in an initial measurement underwent a second preoperative polysomnography with Breathe Right nasal strips in place. Nineteen of these 26 patients showed reduction of RDI during the second night of polysomnography using the nasal strips, indicating that nasal obstruction seems to be a predominant factor in the etiology of snoring and apnea in these individuals. Demographic data, medical history, rhinoscopy, clinical assessment of pharyngeal obstruction (Mueller's maneuver), as well as anterior rhinomanometry and acoustic rhinometry were used to identify typical findings correlating with a positive effect of the Breathe Right nasal strips on the RDI: 1. Hyperplasia or hypertrophy of the lower turbinates, septal deviation, and/or allergic rhinitis. 2. None or only minor pharyngeal obstruction. 3. Age less than 55 years. if a positive effect is seen during polysomnography with the strips in place, patients will most likely profit from an improvement of nasal ventilation. This may help to target more effectively septal or turbinate surgery if applicable. In other cases, ifa significant RDI reduction is obtained by the use of the nasal strips, they could also offer a noninvasive modality of treatment, especially since the high degree of co-morbidity in this group of patients can sometimes make a surgical approach less favorable