An Investigation of the Electronic and Catalytic Properties of Ceria Nanocubes

The focus of this thesis was on the synthesis, characterization and application of ceria nanocubes. This thesis is divided into two main sections; the first section investigates the electronic properties of ceria nanocubes, and the second explores their catalytic applications towards alcohol oxidation reactions. The first project of this thesis consisted of the X-ray characterization of hydrothermally synthesized ceria nanocubes of various sizes. For the first time, the electronic properties of such nanocubes were systematically studied using high resolution XPS and XANES. It was found that the concentration of Ce3+ present within the nanocubes was independent of the particle size, as well as the Ce precursor used during synthesis. Throughout the analysis of the Ce 3d and 4d XPS spectra, it was observed that the surface of the ceria nanocube samples was undergoing photoreduction/damage over time. This damage was attributed to the samples’ exposure to high intensity X-ray radiation. This was confirmed through examination of the Ce M4,5- and N4,5-edge XANES spectra. From these results, it was clear that the concentration of Ce3+ on the surface of the ceria nanocubes was independent of particle size. This fact may become important when investigating their potential catalytic activity. The second project of this thesis concentrated on the analysis of the catalytic activity of a variety of CeO2, Au and Au/CeO2 catalysts towards the oxidation of benzyl alcohol. The low temperature oxidation reactions were studied using 1H NMR spectroscopy. It was observed that Au NPs, Au/bulk CeO2, and Au/CeO2 nanocubes in water and K2CO3 were active catalysts for this oxidation reaction at 60°C in both air and O2 (g) atmospheres. Surprisingly, however, the Au/bulk CeO2 and Au/CeO2 nanocube catalysts showed very similar activities. It was also found that ceria nanocubes alone, and Au25(SR)18/bulk CeO2 showed no activity for this reaction under similar conditions. It was determined that below a substrate to catalyst ratio of ~ 1500:1, the Au/CeO2 catalysts, which showed the highest activities, were mass-transport limited with respect to the O2 in the system. The turnover frequencies of the supported catalysts were approximately double those of the unsupported NPs. Furthermore, these reactions have indicated that activating Au25(SR)18/CeO2 for catalysis is a non-trivial task, and more work needs to be done to understand the activation of such clusters

Fractional Supersymmetry and Fth-Roots of Representations

A generalization of super-Lie algebras is presented. It is then shown that all known examples of fractional supersymmetry can be understood in this formulation. However, the incorporation of three dimensional fractional supersymmetry in this framework needs some care. The proposed solutions lead naturally to a formulation of a fractional supersymmetry starting from any representation D of any Lie algebra g. This involves taking the Fth-roots of D in an appropriate sense. A fractional supersymmetry in any space-time dimension is then possible. This formalism finally leads to an infinite dimensional extension of g, reducing to the centerless Virasoro algebra when g=sl(2,R).Comment: 23 pages, 1 figure, LaTex file with epsf.st

Funerary Stela of Heni

Offered symbolically, the images and hieroglyphics depicted on the right of this funerary stela ensured that Heni, a local high official, would never experience hunger or thirst in the afterlife. The slightly awkward proportions of Heni’s figure are typical of monuments of the First Intermediate period, when there was no centralized government in Egypt. The lack of royal control over artistic production during this time allowed artists to experiment, as seen in the multiple levels of relief on Heni’s kilt, the particular green of the hieroglyphs, and the striped border. 2134-2040 BCEhttps://digitalcommons.risd.edu/risdmuseum_channel/1015/thumbnail.jp

Unexpected Features of Supersymmetry with Central Charges

It is shown that N=2 supersymmetric theories with central charges present some hidden quartic symmetry. This enables us to construct representations of the quartic structure induced by superalgebra representations.Comment: 14 pages, more details have been given, to appear in J. Phys.

Hypermatrix factors for string and membrane junctions

The adjoint representations of the Lie algebras of the classical groups SU(n), SO(n), and Sp(n) are, respectively, tensor, antisymmetric, and symmetric products of two vector spaces, and hence are matrix representations. We consider the analogous products of three vector spaces and study when they appear as summands in Lie algebra decompositions. The Z3-grading of the exceptional Lie algebras provide such summands and provides representations of classical groups on hypermatrices. The main natural application is a formal study of three-junctions of strings and membranes. Generalizations are also considered.Comment: 25 pages, 4 figures, presentation improved, minor correction

Gr\"obner-Shirshov bases for Lie algebras over a commutative algebra

In this paper we establish a Gr\"{o}bner-Shirshov bases theory for Lie algebras over commutative rings. As applications we give some new examples of special Lie algebras (those embeddable in associative algebras over the same ring) and non-special Lie algebras (following a suggestion of P.M. Cohn (1963) \cite{Conh}). In particular, Cohn's Lie algebras over the characteristic $p$ are non-special when $p=2,\ 3,\ 5$. We present an algorithm that one can check for any $p$, whether Cohn's Lie algebras is non-special. Also we prove that any finitely or countably generated Lie algebra is embeddable in a two-generated Lie algebra