Fr\'echet completions of moderate growth old and (somewhat) new results

This article has two objectives. The first is to give a guide to the proof of the (so-called) Casselman-Wallach theorem as it appears in Real Reductive Groups II. The emphasis will be on one aspect of the original proof that leads to the new result in this paper which is the second objective. We show how a theorem of van der Noort combined with a clarification of the original argument in my book lead to a theorem with parameters (an alternative is one announced by Berstein and Kr\"otz). This result gives a new proof of the meromorphic continulation of the smooth Eisenstein series

MeMBL: Ring-Opening a Pathway to a Renewable, Chemically Customizable Plastic

The Tower is an official publication of the Georgia Tech Board of Student Publications and is sponsored by the Undergraduate Research Opportunities Program and the Price Gilbert Memorial Library System. This article is from Volume 1, Issue 1.MeMBL (α-methylene-γ-methyl-γ-butyrolactone) is a biomass-derived compound known to be polymerizable to make an acrylic material with a high glass transition temperature. Presence of a lactone ring in the structure of MeMBL can be opened to create a pathway to modification of a MeMBL polymer. This would expand the range of uses for poly(MeMBL) as a plastic. A polymer composed of pure MeMBL and a polymer composed of MeMBL and styrene (the main component of Styrofoam) were prepared, and subjected to reactions with sodium hydroxide in alcohols, water, or dimethyl sulfoxide (DMSO). Evidence of ring-opening was determined either by observation of a change in the polymer’s solubility or by NMR analysis. Both the pure MeMBL polymer and MeMBL/styrene copolymer showed evidence of ring-opening when exposed to sodium hydroxide in water, while no reaction was observed with the same treatment in alcohols. The poly(MeMBL) ring was observed to close over time. Ring-opening was found to be achievable, but ring-opening with hydroxide was found to be an ineffective pathway to further work on the opened ring.Undergraduate Research Opportunities Program ; Price Gilbert Memorial Library System

Evolutionary helium and CNO anomalies in the atmospheres and winds of massive hot stars

The ubiquitous evidence for processed materials in the atmospheres, winds, and circumstellar ejecta of massive stars is reviewed. A broad array of normal and peculiar evolutionary stages is considered, up to and including Type II supernova progenitors. The quantitative analysis of these spectra is difficult, and until recently for the most part only qualitative or approximate results have been available. However, several important current programs promise reliable abundance calculations. A significant emerging result is that the morphologically normal majority of both hot and cold supergiants may already display an admixture of CNO-cycle products in their atmospheres. It may become possible in this way to identify blue supergiants returning from the red supergiant region, as appears to have been the case for the SN 1987A progenitor