The basis for this thesis is H. S. Wall's book, Creative Mathematics, with particular emphasis on the chapter in that book entitled "More About Linear Spaces."

Thesis (Ph. D.)--University of Oklahoma, 1996. / Includes bibliographical references.

La supraconductivité est intensément étudiée en physique de la matière condensée pour ses éventuelles applications. En effet, ce phénomène est caractérisé macroscopiquement par des propriétés remarquables, mais pour le moment, son exploitation est limitée par la nécessité de refroidir ces matériaux à des températures cryogéniques. Après la découverte de H₃S, dont la température de transition est de 200 K, un renouveau d’intérêt est apparu pour les matériaux supraconducteurs conventionnels. Pour ce composé, le couplage entre électrons et phonons est à l’origine de l’appariement électronique, une condition nécessaire à la supraconductivité. L’énergie associée à ce couplage se trouve généralement dans la gamme des infrarouges lointains, voire des THz, faisant de la spectroscopie infrarouge un outil idéal pour étudier ce mécanisme. Cette thèse présente les études de deux matériaux supraconducteurs dans des conditions expérimentales extrêmes de pression ou de température, permise grâce à la forte brillance du rayonnement synchrotron. Pour la phase supraconductrice H₃S à des pressions supérieures à 150 GPa, l’environnement en cellule à enclumes de diamant exclut la plupart des techniques pour déterminer la nature du mécanisme mais les études optiques restent adaptées. Les résultats spectroscopiques présentés ici démontrent un fort couplage entre électrons et phonons, qui explique l’origine d’une si haute température de transition. Des mesures complémentaires visant à caractériser NaCl sous pression sont également décrites car ce matériau est couramment utilisé comme transmetteur de pression dans les cellules `a haute pression, notamment pour le supraconducteur H₃S. La deuxième étude rapporte des résultats spectroscopiques dans le THz sur des couches nanométriques de Nb, dont les températures de transition supraconductrice sont de 4,5 K et 6,8 K. Ces mesures confirment que la nature conventionnelle du mécanisme subsiste au sein de ces films minces quasi-bidimensionnels. Pour ce travail, un ensemble instrumental permettant la mesure spectroscopique de matériaux jusqu’à des températures de 200 mK a été entièrement développé autour d’un cryostat à démagnétisation adiabatique. / Superconductivity is highly studied in condensed matter physics for its potential applications. Indeed, this phenomenon is macroscopically characterized by remarkable properties, but generally occurs in materials at cryogenic temperature thus limitating their exploitation. Recently, renewed interest has appeared for conventional superconducting materials with the discovery of H₃S, whose transition temperature is at 200 K. For this compound, the coupling between electrons and phonons is at the origin of the electronic pairing, a necessary condition for superconductivity. The associated energy for this coupling belongs to the far infrared range, even THz, making infrared spectroscopy an ideal tool to study the mechanism. This thesis presents the studies of two superconducting materials in extreme experimental conditions of pressure and temperature, allowed by the high brilliance of synchrotron radiation. For the superconducting phase H₃S under pressures superior to 150 GPa, the environment of diamond anvil cell excludes most of the techniques to determine the nature of the mechanism but the optical studies remain adapted. The spectroscopic results presented here demonstrate a strong coupling between electrons and phonons, which explains the origin of such a high transition temperature. Complementary measurements aiming at characterizing NaCl under pressure is also described because this material is often used as a pressure transmitting medium in high pressure cells, in particular for the superconducting H₃S. The second study reports spectroscopic results in the THz on nanometric layers of Nb, whose superconducting transition temperatures are 4,5 K and 6,8 K. These measurements confirm that the conventional nature of the mechanism subsists within these quasi-bidimensional thin films. For this work, an instrumental ensemble allowing the spectroscopic measurements of materials down to 200 mK has been entirely developed based on an adiabatic demagnetization cryostat.

Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2013. / Submitted by Luiza Silva Almeida (luizaalmeida@bce.unb.br) on 2013-07-16T16:36:56Z No. of bitstreams: 1 2013_OttoAugustodeMoraisCosta.pdf: 643449 bytes, checksum: 5c1dc30e495fb393e98796175549d80d (MD5) / Approved for entry into archive by Leandro Silva Borges(leandroborges@bce.unb.br) on 2013-07-16T20:28:44Z (GMT) No. of bitstreams: 1 2013_OttoAugustodeMoraisCosta.pdf: 643449 bytes, checksum: 5c1dc30e495fb393e98796175549d80d (MD5) / Made available in DSpace on 2013-07-16T20:28:44Z (GMT). No. of bitstreams: 1 2013_OttoAugustodeMoraisCosta.pdf: 643449 bytes, checksum: 5c1dc30e495fb393e98796175549d80d (MD5) / Neste trabalho, fazemos um breve estudo a respeito dos grupos de reflexões finitos, para os quais associamos sistemas de raízes, matrizes de Cartan e grafos, a fim de classificarmos todos os tais grupos. Em seguida, estudamos uma generalização desses grupos para os denominados grupos de Coxeter. Utilizando a função comprimento como ferramenta fundamental, mencionamos diversos resultados acerca dos subgrupos parabólicos. No último capítulo, determinamos a estrutura dos centralizadores dos elementos de um grupo de Coxeter finito, seguindo o artigo: M. Konvalinka, G. Pfeiffer, C.E. Röver, ‘A note on element centralizers in finite Coxeter groups', J. Group Theory, 14 (2011) 727-745. Como aplicação final, apresentamos uma demonstração alternativa de um importante teorema de Solomon, conhecido como a fórmula de Solomon. _______________________________________________________________________________________ ABSTRACT / This work is a brief study about the finite reflections groups, to which we associate root systems, Cartan matrices and Coxeter graphs, in order to classicate such groups. After that, we study a generalisation of these groups to Coxeter groups. By using the lenght function as fundamental tool, we mention various results about the parabolic subgroups. In the last chapter we determinate the structure of the element centralisers of a finite Coxeter group, following the paper: M. Konvalinka, G. Pfeiffer, C.E. Röver, ‘A note on element centralizers in finite Coxeter groups', J. Group Theory, 14 (2011) 727-745. As final application we present an alternative proof of an important theorem of Solomon, known as the Solomon formula.

Hydrogen sulfide (H₂S) was recognized as a critical signaling molecule in mammals nearly two decades ago. Since this discovery biologists and chemists have worked in concert to demonstrate the physiological roles of H₂S as well as the therapeutic benefit of exogenous H₂S delivery. As the understanding of H₂S physiology has increased, the role(s) of other sulfur-containing molecules as potential players in cellular signaling and redox homeostasis has begun to emerge. This creates new and exciting challenges for chemists to synthesize compounds that release a signaling compound in response to specific, biologically relevant stimuli. Preparation of these signaling compound donor molecules will facilitate further elucidation of the complex chemical interplay within mammalian cells. To this end we report on two systems for the sustained release of H₂S, as well as other sulfur signaling molecules. The first system discussed is based on the N-thiocarboxyanhydride (NTA) motif. NTAs were demonstrated to release carbonyl sulfide (COS), a potential sulfur signaling molecule, in response to biologically available nucleophiles. The released COS is shown to be rapidly converted to H₂S in the presence of the ubiquitous enzyme carbonic anhydrase (CA). A synthetic route that affords NTAs with reactive functionalities was devised and the functional "parent" NTAs were successfully conjugated to a variety of substrates, ranging from small molecules to polymers. These functional NTAs provide a platform from which a library of NTA-based COS/H₂S may be readily prepared convergently in an effort to move towards H₂S-releasing drug and polymer conjugates. Additionally, preliminary in vitro cytotoxicity studies indicate that NTAs are noncytotoxic at concentrations above 100 µM. The second system discussed in this dissertation leverages the 1,6-benzyl elimination reaction (or self-immolative reaction) to facilitate the release of a persulfide (R–SSH) from a small molecule prodrug platform as well as a separate system that releases COS/H₂S from a polymer. The self-immolative persulfide prodrug was designed to be responsive to reactive oxygen species (ROS) and demonstrates efficacy as an antioxidant in vitro. Furthermore, the polymeric COS/H₂S self-immolative system was designed to respond to reducing agents, including H₂S itself, and shows promise as a H₂S signal amplification platform. / Doctor of Philosophy / Hydrogen sulfide (H₂S) has long been recognized as a malodorous and toxic byproduct of industrial chemical processes. However, the discovery of H₂S as a key signaling molecule in mammals has drastically shifted the paradigm of H₂S research over the last two decades. Research into the production and roles of H₂S in the body is ongoing, but has pointed to the implication of changes in H₂S production to the onset of a variety of disease states, including cardiovascular disease and Alzheimer’s. As alterations in the body’s production of H₂S have been correlated to certain disease states, collaborative research efforts among biologists and chemists have demonstrated the utility of H₂S-based therapeutics in helping to alleviate these disease states. Our understanding of the roles of H₂S in the body, and potential benefits derived from H₂S-releasing drugs, can only continue to advance with the development and improvement of H₂S releasing compounds. The first portion of this dissertation focuses on the synthesis of a new class of H₂S-releasing compounds, termed N-thiocarboxyanhydrides (NTAs). NTAs release H₂S through an intermediate sulfur-containing molecule, carbonyl sulfide (COS), which may have signaling properties independent of H₂S. The COS that is released from the NTAs is rapidly converted to H₂S by the action of the ubiquitous enzyme carbonic anhydrase. A variety of functional NTAs were synthesized, which in turn were used to prepare a small library of NTA-based COS/H₂S releasing compounds. This work informs the preparation of H₂S-drug or H₂S-polymer conjugates. The second portion of this dissertation examines a class of compounds broadly termed self-immolative prodrugs. The self-immolative prodrug platform was leveraged to release H₂S, or persulfides (R–SSH), another class of sulfur-containing molecules of biological interest. The self-immolative persulfide prodrug system was designed to be responsive to reactive oxygen species (ROS), a harmful cellular byproduct. The persulfide donor was successful in mitigating the harmful effects of ROS in heart cells. Independently, a polymeric self-immolative H₂S releasing system was designed to depolymerize in the presence of H₂S, resulting in the generation of 6-8-fold excess of H₂S upon depolymerization. We envision the self-immolative H₂S-releasing polymer will show promise in biological applications where a vast excess of H₂S is needed rapidly.

Over the past decade, membrane based gas separations have gained traction in industry as an attractive alternative to traditional thermally based separations due to their potential to offer lower operational and capital expenditures, greater ease of operation and lower environmental impact. As membrane research evolves, new state-of-the-art membrane materials as well as processes utilizing membranes will likely be developed. Therefore, their incorporation into existing thermally based units as a debottlenecking step or as a stand-alone separation unit is expected to become increasingly more common. Specifically for natural gas, utilization of smaller, more remote natural gas wells will require the use of less equipment intensive and more flexible separation technologies, which precludes the use of traditional, more capital and equipment intensive thermally based units. The use of membranes is, however, not without challenges. Perhaps the most important hurdle to overcome in membrane development for natural gas purification is the ability to maintain high efficiency in the presence of harsh feed components such as CO₂ and H₂S, both of which can swell and plasticize polymer membranes. Additionally, as this project demonstrates, achievement of similarly high selectivity for both CO₂ and H₂S is challenged by the different governing factors that control their transport through polymeric membranes. However, as others have suggested and shown, as well as what is demonstrated in this project, when CO₂ is the primary contaminant of interest, maintaining high CO₂/CH₄ efficiency appears to be more important in relation to product loss in the downstream. This work focuses on a class of fluorinated, glassy polyamide-imides which show high plasticization resistance without the need for covalent crosslinking. Membranes formed from various polyamide-imide materials show high mixed gas selectivities with adequate productivities when subjected to feed conditions that more closely resemble those that may be encountered in a real natural gas well. The results of this project highlight the polyamide-imide family as a promising platform for future membrane material development for materials aimed at aggressive natural gas purifications due to their ability to maintain high selectivities under aggressive feed conditions without the need for extensive stabilization methods.

In der vorliegenden Arbeit wurden Strömungen räumlich begrenzter Strahlen untersucht. Zum einen wurde die Ausströmung eines runden Strahls in ein Rohr betrachtet, der sog. begrenzte Strahl. Zum anderen wurde die Ausströmung von 7 hexagonal angeordneten runden Strahlen in ein Rohr betrachtet, das sog. hexagonale Strahlbündel. Die Motivation zur vorliegenden Arbeit ergab sich aus der Entwicklung von Durchflussmessgeräten, die als Bypassapparaturen ausgeführt sind und stromabwärts des Staudruckkörpers ein Strömungsgebiet mit begrenzten Strahlen aufweisen. Dafür wurden mit Hilfe der Ähnlichkeitstheorie die zugrundeliegenden Kennzahlen bestimmt. Besonderes Augenmerk lag auf der Charakterisierung der instationären bzw. turbulenten Strömungseigenschaften für Reynolds-Zahlen zwischen 1.000 und 20.000. Es wurden die selbstähnlichen Eigenschaften der Strömungen untersucht, wobei sich insbesondere für den begrenzten Strahl wichtige Erkenntnisse ergaben. Für das hexagonale Strahlbündel wurden mit Hilfe der numerischen Strömungssimulation die grundlegenden Eigenschaften des Strömungsfeldes untersucht. Dabei weisen die Geometriekennzahlen einen dominierenden Einfluss auf. So konnten in Abhängigkeit zum Durchmesserverhältnis und Strahlabstand drei Strömungsformen identifiziert und experimentell mittels Laser-Doppler Anemometrie nachgewiesen werden. Eine wesentliche Fragestellung bestand in der Anwendung der numerischen Strömungssimulation, des RANS-Ansatzes und des SST-Turbulenzmodells. Dazu wurde die Anpassung der Modellkoeffizienten untersucht, wobei für den begrenzten Strahl ein allgemein gültiger Satz gefunden wurde. / In the present work flows of spatially limited radiation were investigated. On the one hand, the outflow of a round jet into a pipe was considered, the so-called confined jet. On the other hand, the outflow of 7 hexagonal arranged round jets into a pipe was con-sidered, the so-called hexagonal jet array. The motivation for the present work arose from the development of flowmeters which are designed as bypass apparatures that have a jet array flow downstream of the dynamic pressure body. For this purpose the underlying similarity parameters were determined. Special attention was paid to the cha-racterization of transient and turbulent flow properties for Reynolds numbers between 1,000 and 20,000. The self-similar properties of the flows were investigated with im-portant findings in particular for the confined jet. For the hexagonal jet array the basic properties of the flow field were investigated by using computational fluid dynamics. The geometric similarity parameters have a dominant influence. Thus, depending on the di-ameter ratio and jet distance ratio, three flow patterns could be identified and experimen-tally detected by the use of laser Doppler anemometry. An important question was the application of the computational fluid dynamic method, the RANS approach and the SST turbulence model. For this purpose a generally valid set of model coefficients was found for the confined jet flow.