A topological approach to the theory of groups acting on trees

Bass and Serre recast the foundations of combinatorial group theory in [7]. Here we apply the allied notions of fundamental group and covering space to redevelop their theory in a less combinatorial fashion; for example the Bass—Serre Structure Theorem is proved with no a priori knowledge of the group theoretic structure of the fundamental group of a graph of groups. Van Kampen's Theorem is used only once, in its simplest form (in the proof of Theorem 7). Cancellation arguments and normal form theorems, such as Britton's Lemma, are completely avoided; indeed they are incidental corollaries from our viewpoint. The tree which plays a central role in [7] appears in Theorem 2 as the natural analogue of the “strecken komplexe” introduced by A. Speiser [8], and subsequently also employed by R. Nevanlinna [5], to describe certain simply connected Riemann surfaces occurring in value distribution theory.     

A remark on compatibility of strain

Résumé On montre que les relations de compatibilité de Saint-Venant peuvent être déduites de la théorie des grandes déformations sans aucune approximation.     

The structural nature of amorphous Se and Te

We present new photoemission measurements on amorphous and trigonal Te. These results and other recent photoemission experiments on amorphous and trigonal Se are interpreted using density of states and charge density calculations. These studies result in new insights into the possible structural nature of the amorphous phase.     

Valence charge distribution and electric field gradients in GaAsAlAs mixed crystals

Electric field gradients at the arsenic sites in the GaAsAlAs mixed compounds are calculated using the self-consistent pseudo-potential method. The result is in good agreement with recent nuclear quadrupole resonance (NQR) experiments and supports the interpretation that the NQR splittings arise from an Al ion relacing one of the four Ga ions near an As site.     

Collective properties of polyatomic gases in a magnetic field: Effects on light scattering spectrum

The effect of magnetic fields on collective properties of polyatomic gases has been extended outside the hydrodynamic regime. The calculations are based on a linearized Waldmann-Snider equation. The Waldmann-Snider collision operator is truncated yielding a finite matrix equation. The resulting matrix equation is solved on a computer to yield the polarized and depolarized light scattering spectra. These spectra are calculated in the absence and presence of a magnetic field. For long wavelengths it is found that the magnetic effects are of the same order of magnitude as in the Senftleben-Beenakker effects. For shorter wavelengths the effects disappear due to Doppler effects.This work was supported by NSF GP22881.Alfred P. Sloan Foundation Fellow.NIH Predoctoral Fellow.