Quasi-Whittaker modules for the Schr\"odinger algebra

In this paper, we construct a new class of modules for the Schr\"{o}dinger algebra \mS, called quasi-Whittaker module. Different from \cite{[ZC]}, the quasi-Whittaker module is not induced by the Borel subalgebra of the Schr\"{o}dinger algebra related with the triangular decomposition, but its Heisenberg subalgebra \mH. We prove that, for a simple \mS-module $V$, $V$ is a quasi-Whittaker module if and only if $V$ is a locally finite \mH-module; Furthermore, we classify the simple quasi-Whittaker modules by the elements with the action similar to the center elements in U(\mS) and their quasi-Whittaker vectors. Finally, we characterize arbitrary quasi-Whittaker modules.Comment: 17 page

Ceramic composites of 3Y-TZP doped with CuO: processing, microstructure and tribology

The work described in this thesis is about processing, microstructure and tribology of CuO doped 3Y-TZP (3 mol% yttria stabilised tetragonal zirconia polycrystals) composite ceramics. This group of materials has shown attractive properties such as superplastic behaviour at elevated temperature and a low friction coefficient under dry sliding conditions.\ud \ud This thesis can be divided in two parts. The first part (chapter 2-7) describes investigations on the fabrication process, including powder preparation, compaction and sintering, and the relation between\ud processing and microstructure. Major efforts were paid on fabrication of nanostructured composite ceramic in this part. The second part (chapter 8-9) deals with the tribological properties of the coarse-grained CuO\ud doped 3Y-TZP composite ceramics under dry sliding conditions

Towards Understanding Helicase and Chaperone Activities in the RNA Degradosome

The E. coli RNA degradosome is a complex multi-enzyme machine which is central to the post-transcriptional regulation of the cell. Some of its functions include maturing and processing sRNA, rRNA, and tRNA, as well as degrading mRNA. The key components of the RNA degradosome include the endoribonuclease RNase E, the DEAD-box RNA helicase RhlB, the glycolytic enzyme enolase, and the phosphorolytic exoribonuclease PNPase. The degradosome has also been previously shown to associate with the RNA chaperone Hfq to form a small RNA guided machinery that targets defined transcripts. This thesis attempts to investigate several characteristics of the degradosome, including the importance of RhlB, the structure of a portion of the RNase E C-terminal domain that recruits enolase and helicase, and the association between Hfq, ChiX and the RNase E C-terminus. The thesis also explored structural details regarding the small domain of RNase E involved in both RNA binding and oligomerisation and its relationship to the RNA binding KH domains. Utilizing a point mutation in the DEAD box of RhlB, I have found increased RNA affinity to mutant RhlB, the potential structure of Hfq — an RNA chaperone — bound to the sRNA ChiX, and a structural correlation between the RNase E small domain and other KH domains. Preliminary models of Hfq and ChiX structure show a novel binding mode for class II sRNAs as the majority of ChiX associating with the distal face of Hfq. Bioinformatic studies reveal evolutionary roots between the KH domains and the RNase E small domain, supporting the hypothesis that the RNase E small domain may be involved in a novel mode of RNA binding and recognition