On the compositum of all degree d extensions of a number field

Let k be a number field, and denote by k^[d] the compositum of all degree d extensions of k in a fixed algebraic closure. We first consider the question of whether all algebraic extensions of k of degree less than d lie in k^[d]. We show that this occurs if and only if d < 5. Secondly, we consider the question of whether there exists a constant c such that if K/k is a finite subextension of k^[d], then K is generated over k by elements of degree at most c. This was previously considered by Checcoli. We show that such a constant exists if and only if d < 3. This question becomes more interesting when one restricts attention to Galois extensions K/k. In this setting, we derive certain divisibility conditions on d under which such a constant does not exist. If d is prime, we prove that all finite Galois subextensions of k^[d] are generated over k by elements of degree at most d.Comment: 14 pages, 2 figure

On the Effects of Estimation Error and Jitter in Ultra-Wideband Communication

The opening of the 3.6 - 10.1 GHz frequency spectrum below the \u27noise-floor\u27 by the FCC in 2002 has made possible the prospect of reusing this frequency spectrum through ultra-wideband (UWB) communication. In this thesis, we compare the performance of several UWB systems in the presence of estimation error and jitter. We then develop two alternative decision schemes to combat the effect of jitter in the UWB system. Numerical results show that one of the schemes provides significantly better performance in the presence of severe jitter than maximal ratio combining and minimal degradation of performance if jitter is not present. A generalized maximal ratio combining decision scheme to combat the presence of estimation error is also proposed. It is shown that the generalized scheme outperforms traditional maximal ratio combining

Using Macroinvertebrates to Assess the Effects of Nutrient Input Between the Nolichucky and Pigeon Rivers

Previous work found significant differences in growth rates of native mussels at locations downstream from the regulated Walter’s Dam and the out-of-service, free-flowing Davy Crockett Dam. The purpose of this study is to investigate differences within the macroinvertebrate communities related to factors driving the differences in mussel growth between rivers. Macroinvertebrate samples were collected following the Tennessee Department of Environment and Conservation protocol for SQKICK collection and analyzed using the Tennessee Macroinvertebrate Index (TMI). There were no significant differences in TMI scores between the downstream sites of the rivers, but there were significant increases in chlorophylla, dissolved oxygen, and specific conductance downstream compared to upstream in both rivers. This suggests that these indices are suitable to identify pollution changes, but potentially not the productivity differences that impacted mussel growth

The Singing Revolution: Chamber Singers in Concert

Kemp Recital Hall October 25, 2018 Thursday Evening 7:00 p.m