The main purpose of this paper is to better understand groups that do not have the unique product property. In particular, the goal is to better understand Promislow's example, G, of such a group. In doing so, we will develop methods for generating examples of other sets that do not have the unique product property. With these methods we can show that there exists other distinct 14 element, square, non-unique product sets in G that are not inversions or translations. Also, this paper answers the question as to whether every non-unique product set can have only 14 elements in the negative by producing a 17 element square n.u.p. set. The secondary purpose of this paper is to demonstrate that in the group ring K[G], there are no units of support size 3. / Master of Science

The investigation presented is in two parts: a study of the mixed dimerizations of halogenated ketenes with non-halogenated ketenes and a study of the rearrangements of 8-chloro-8-methylbicyclo {4.2.0} oct-2-en-7-ones.

Student Number : 0410864E - MSc dissertation - School of Chemistry - Faculty of Science / The aim of the project described in this dissertation is to explore the application of ring closing metathesis (RCM) to the synthesis of 6-, 7-, 8- and 9-membered N,N-, N,O- and O,O-benzo-fused heterocyclic compounds which are interesting structural motifs in medicinal chemistry. In recent times, their structures have been widely used as molecular scaffolds. Some of these heterocycles have been identified as antitumour agents, antibiotics and anti-HIV agents. In our laboratories, a variety of 6-, 7- and 8-membered nitrogen- and oxygen- containing benzo-fused rings have been synthesized through ruthenium-mediated isomerisation and RCM in moderate to good yields. The first step in the present project was N-protection of suitable 2-aminophenols or o-phenylenediamines followed by allylation. Rutheniummediated isomerisation followed by RCM was then used for the synthesis of the 6- membered ring system tert-butyl 4H-1,4-benzoxazine-4-carboxylate 91 and the 7- membered ring system tert-butyl 1,5-benzoxazepine-5(4H)-carboxylate 103 while only RCM was used for the 8-membered ring systems, di(tert-butyl) 2,3,4,5-tetrahydro-1,6- benzodiazocine-1,6-carboxylate 130, di(tert-butyl) 2,5-dihydro-1,6-benzodiazocine-1,6- dicarboxylate 129, 1,6-dibenzoyl-1,2,5,6-tetrahydro-1,6-benzodiazocine 132, 7-methoxy- 2,5-dihydro-1,6-benzodioxocine 137 and the 9-membered ring system 1,6-bis[(4- methylphenyl)sulfonyl]-2,5,6,7-tetrahydro-1H-1,6-benzodiazonine 159. In the synthesis of the 7-membered ring systems, based on established methodology, we encountered problems with the RCM from suitable benzylamine or benzyl alcohol precursors. The reasons for this are not clear but we suspect this could be as a result of electronic and kinetic factors. Nevertheless, we were able to synthesize a 7-membered ring system, tert-butyl 1,5-benzoxazepine-5(4H)-carboxylate 103, from a readily available precursor using a different methodology. Approaches to the synthesis of the 8-membered ring systems, di(tert-butyl) 2,3,4,5- tetrahydro-1,6-benzodiazocine-1,6-carboxylate 130, di(tert-butyl) 2,5-dihydro-1,6- benzodiazocine-1,6-dicarboxylate 129, 1,6-dibenzoyl-1,2,5,6-tetrahydro-1,6- benzodiazocine 132 and 7-methoxy-2,5-dihydro-1,6-benzodioxocine 137, as described in this dissertation, made extensive use of RCM in moderate to good yields, but the deprotection of the Boc group after hydrogenation proved to be a problem. The synthesis of the 9-membered nitrogen containing benzo-fused compounds, 1,6- bis[(4-methylphenyl)sulfonyl]-2,5,6,7-tetrahydro-1H-1,6-benzodiazonine 159 by RCM was successful but in the synthesis of the N,O-benzo-fused compound by RCM, we suspect that polymerization, which is a side reaction in RCM reactions that are slow, occurred. In the synthesis of the 9-membered O,O-benzo-fused compounds, we only isolated the starting material. The final approach in this dissertation involved the use of ruthenium-mediated isomerisation to afford internal isomerisation of the double bond within the heterocyclic rings of the 8-membered and 9-membered benzo-fused compounds previously prepared in our laboratory. This gave a mixture of regioisomers of 10-methoxy-2,3-dihydro-1,6- benzodioxocine 163 and 7-methoxy-2,3-dihydro-1,6-benzodiazocine 164, 1,6-bis[(4- Methylphenyl)sulfonyl]-1,2,3,6-tetrahydro-1,6-benzodiazocine 166, a regioisomeric mixture of 6-[(4-methylphenyl)sulfonyl]-3,6-dihydro-2H-1,6,-benzoxazocine 161 and 6-[(4-methylphenyl)sulfonyl]-5,6-dihydro-4H-1,6,-benzoxazocine 162, and the 9- membered benzo-fused ring system, 1,6-bis[(4-methylphenyl)sulfonyl]-2,3,6,7- tetrahydro-1H-1,6-benzodiazonine 170. The yields were good and the solid state structures of these isomerised compounds were examined by X-ray crystallography. Xray diffraction was also performed on the solid state 8- and 9-membered benzo-fused ring systems. We also compared the crystal structures of the 8- and 9-membered benzo-fused compounds with their isomerised compounds.

Thesis (M.S.)--Brigham Young University. Dept. of Plant and Wildlife Sciences, 2007. / Includes bibliographical references.

No description available.

In this research we attempted several modifications to microstrip ring/loop antennas to design multi-frequency antennas through systematic approaches. Such multi-frequency antennas can be useful while building compact terminals to operate at multiple wireless standards. One of the primary contributions was the use of a capacitive feed arrangement that enables simultaneous excitation of multiple concentric rings from an underlying transmission line. The combined antenna operates in the same resonant bands as the individual rings and avoids some of the bands at harmonic frequencies. A similar feeding arrangement is used to obtain dual band characteristics from just one ring, with improved bandwidth. This is made possible by widening two adjacent sides of a square ring antenna symmetrically, and attaching an open stub to the inner edge of the side opposite to the feed line. Use of fractal segments replacing the side with the stub also results in a similar performance. Use of fractal geometries has been widely associated with multi-functional antennas. It has been observed from the parametric studies that, the ratio of the resonant frequencies can range from 1.5 to 2.0. This shows some flexibility in systematically designing dual-band antennas with a desired pair of resonant frequencies. An analysis technique based on multi-port network modeling (MNM) has been proposed to accurately predict the input characteristics of these antennas. This approach can make use of the ordered nature of fractal geometries to simplify computations. Several prototype antennas have been fabricated and tested successfully to validate simulation and analytical results.

L’objectif de cette thèse est d’élargir la gamme des composés issus des aziridine-2-carboxylates, obtenues par leur utilisation comme matière première pour la synthèse d’azahétérocycles ciblés diversement substitués, via des réactions d’ouvertures nucléophiles et d’expansions de cycle. La synthèse d’hétérocycles azotés fluorés originaux sera abordée à partir d’aziridines-2-carboxylates trifluorométhylées ainsi que d’aminoalcools et aminoacides trifluorométhylés enantiopures. Les aziridines-2-carboxylates trifluorométhylées dont la synthèse à déjà été décrite dans la littérature conduiront à des hétérocycles fluorés variés selon des réactions d’ouverture et d’agrandissement de cycles faisant intervenir les méthodologies mise au point en série non fluorée par le partenaire Tunisien. Les aminoalcools et aminoacides trifluorométhylés conduiront également à des hétérocycles de type oxazolidinones. Les nouveaux hétérocycles synthétisés trouveront des applications en tant qu’unités pseudo-peptidiques utiles en chimie des peptides. / Our purpose in this thesis is to widen the range of compounds from aziridine-2-carboxylate, which obtained by its use as a feedstock for the synthesis of new hétérocycles through nucleophilic reactions openings and expansions cycle.The synthesis of fluorinated heterocycles will be approached from aziridine-2-carboxylate trifluorométhylées and amino alcohols and amino acids trifluoromethylated enantiopure.Fluorinated aziridines whose synthesis has already been described in the literature will lead to various fluorinated heterocycles according reactions and opening cycles of expansion methodologies involving setting the nonfluorinated series developed by the Tunisian partner.The new synthesized heterocycles find applications as chiral pseudo-peptide units useful in peptide chemistry.

This dissertation presents an in-depth analysis of Gotterdammerung. It provides information concerning: form, tonality, cadence, motive, text, harmony, meter, rhythm, tempo, and dynamics. This information is clearly detailed on a series of charts; the accompanying prose summarizes the charts and highlights selected topics and events. Tonality is the primary formal determinant in Gotterdammerung. The tonal plan operates at three hierarchical levels: foreground, middleground, and background. These terms are not employed in the linear/Schenkerian sense rather, they reflect harmonic/tonal implications within given structural parameters: foregound--the details of the surface level progressions; middleground--the tonal organization within the subdivisions of individual scenes; and background--the keys which govern entire scenes and the beginnings and endings of acts. Tonally, four distinct procedural techniques are employed at all three structural levels: traditional/tonic-dominant tonality, associative tonality, expressive tonality, and directional tonality. At the very core of the tonal process is associative tonality. Through its ability to represent characters, objects, events, emotions, and underlying dramatic themes it elevates the purely functional aspects of traditional/tonic-dominant, expressive, and directional tonalities to new heights. The musical forms of Gotterdammerung fall into four basic categories: traditional, symmetrical, form-within-form or "nested," and sectional. Forms and procedures from each of these categories are employed in some way at every structural level; frequently two or more are drawn upon simultaneously in the shaping of a musical unit. The one element that binds these diverse forms and procedures is tonality. Cadence, motive, and text are also consistent form-defining elements. Their affects are felt most frequently at the subsection and section levels but they also assist in the formal articulation of scenes and acts. The other musical elements play important roles in creating the superstructure but it is tonality which provides the framework and foundation throughout the music-drama.

Networks of tree-ring data are commonly applied in statistical reconstruction of spatial fields of climate variables. The importance of elevation to the climatic interpretation of tree-ring networks is addressed using 281 station precipitation records, and a network of 79 tree-ring chronologies from different species and a range of elevations in the eastern Mediterranean. Cluster analysis of chronologies identifies 6 tree-ring groups, delineated principally by site elevation. Correlation analysis suggests several of the clusters are linked to homogenous elevational moisture regimes. Results imply that climate stations close to the elevations of the tree-ring sites are essential for assessing the seasonal climatic signal in tree-ring chronologies from this region. A broader implication is that the elevations of stations contributing to gridded climate networks should be considered in the design and interpretation of field reconstructions of climate from tree rings. Finally, results suggest elevation-stratified tree-ring networks as a strategy for seasonal climate reconstruction.

published_or_final_version / Chemistry / Doctoral / Doctor of Philosophy