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The large sieve method has been used extensively, beginning with Bombieri in 1965, to provide bounds on the number of zeros of Dirichlet L-functions near the line σ = 1. Using the Kuznetsov trace formula and the work of Deshouillers and Iwaniec on Kloosterman sums, it is possible to derive large sieve inequalities for the Fourier coefficients of Maass cusp forms, which may then similarly be used to study the corresponding Hecke-Maass L-functions. Following an approach developed by Gallagher for Dirichlet L-functions, this thesis shows how the large sieve method may be used to prove a zero density estimate, averaged over the Laplace eigenvalues, for Maass cusp forms of weight zero for the congruence subgroup Γ₀(q) for any positive integer q.

A liquid chromatographic technique using ultrastable-Y (US-Y) molecular sieve as the stationary phase and n-pentane as the mobile phase has been developed to fractionate and enrich pentacyclic triterpanes from petroleum. The sieve provides a shape-selective window which distinguishes between the various pentacyclic components, thus fractionating them on the basis of molecular shape differences. This sieving technique has been applied to isolate various pentacyclic triterpanes from sedimentary organic matter to enable better analysis of these biomarkers to be carried out.Biodegraded crude oils from three Australian basins were analysed to assess the geochemistry of their rearranged hopanes. Enhanced abundances of 25-norhopanes, 18(alpha)-30-norneohopane and diahopanes relative to the regular hopanes were observed in the most severely biodegraded samples. Geochemical interpretation of these results suggests that the enhanced abundances are due to the greater resistance of rearranged hopanes to biodegradation compared to regular hopanes. These studies also indicate that enhanced relative abundances of 25-norhopanes in these samples is most likely due to selective bacterial demethylation of (alpha beta)-hopane precursors.A branched and cyclic alkane fraction from a higher plant-derived crude oil was subjected to the US-Y chromatography procedure and the fractions eluted from the column were analysed using GC-MS. The compositions of the first two eluted fractions were markedly different from the initial branched and cyclic alkane mixture in that they were enriched in higher plant-derived triterpanes, such as bicadinanes, spirotriterpane and the oleananes and other, previously unreported, C(subscript)29 and C(subscript)30 triterpanes. A comparison of mass spectral data, GC retention and molecular sieve sorption characteristics of these compounds with those of known ++ / triterpanes of known molecular structure was used to suggest structures for the unknown compounds.Isolation of crude oil fractions enriched in pentacyclic alkanes using the sieving procedure enabled lower concentrations of bicadinanes to be detected than was previously possible by applying selective ion detection GC-MS to branched and cyclic alkane fractions. Application of this technique to a higher-plant derived Jurassic crude oil and two Jurassic sediments from the Eromanga Basin, Australia has revealed the presence of bicadinanes. The occurrence of the cis-cis-trans and trans-trans-trans bicadinane biomarkers that have previously only been reported from angiosperms may indicate an early evolution of flowering plant like species in this basin.The molecular sieving technique has also been used to isolate three pentacyclic triterpanes from low rank coals in order to obtain unambiguous structural identification and to determine their geochemical significance. A major hopanoid component isolated from a Victorian brown coal was characterised by single crystal X-ray diffraction and (subscript)13C NMR spectroscopy as 22R 17(alpha),21(beta)(H)-homohopane. This compound was shown to correspond to the later eluting 17(alpha),21(beta)(H)-homohopane and hence, for the first time, confirmed the common practice of assigning the higher retention time peak in gas chromatograms of (alpha beta) homohopanes as the 22R diastereomer. Heating of the isolated 22R (alpha beta)-homohopane on anthracite produced a mixture of the 22S and 22R diastereomers which implied a product-reactant relationship between the two epimers. Furthermore, a C(subscript)29 and a C(subscript)30 triterpane present in the hydrous pyrolysate of a Bremer Basin coal were also isolated using the molecular sieving procedure. 28 Nor-18(alpha)-oleanane was characterised by single crystal X-ray analysis while lupane was ++ / characterised by (subscript)13C NMR spectroscopy and by co-chromatography with an authentic standard on four different GC phase columns. The unusual occurrence of these triterpanes was attributed to the high sulphur content of the coal.Finally, laboratory isomerisation and reduction of an isomeric mixture of oleanenes was carried out to investigate the origin of oleanane (18(beta)-oleanane) and 18(alpha)-oleanane. Laboratory results indicated that oleanane was mainly derived from olean-18-ene, while 18(alpha)-oleanane was derived from 18(alpha)-olean-12-ene. Analysis of oleanene/oleanane abundances in a sedimentary sequence from Indonesia provided results consistent with laboratory evidence showing that 18(alpha)- olean-12-ene, rather than oleanane, is the main sedimentary precursor of 18(alpha)- oleanane.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 31-32).

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Thesis (Ph. D.)--Michigan State University. Dept. of Chemistry, 2008. / Title from PDF t.p. (viewed Aug. 14, 2009). Includes bibliographical references (p. 149-151). Also issued in print.

Thesis (Ph.D.) - University of Queensland, 2004. / Includes bibliography.

Thesis (Ph. D.)--Chemical and Biomolecular Engineering, Georgia Institute of Technology, 2008. / Koros, William J., Committee Chair ; Breedveld, Victor, Committee Member ; Jones, Christopher W., Committee Member ; Kumar, Satish, Committee Member ; Nair, Sankar, Committee Member.