The Capital Sculpture of Wells Cathedral, c. 1184-1210

The understudied capital sculpture of Wells Cathedral in Somerset, England (c. 1184-1210) provides ample opportunity of expanding the current scholarship and understanding of interior ecclesiastical sculpture in a West Country cathedral. While the Gothic style of architecture is typically understood as, according to Paul Binski (2014), rational in execution and reception, the capital sculpture at Wells Cathedral has been considered illogical in terms of both its iconography and location within the nave, transepts, and north porch. Utilizing Michael Camille’s post/anti-iconographical approach, this project examines the Wells figural capitals in five case studies: labour, Old and New Testament Scenes, animals and beast fables, busts, and monsters and hybrids. Each group of capitals will be approached with an understanding that this type of art was viewed by people of different classes and professions, with each viewer bringing their own personal experiences and abilities into how they could have read and understood these types of images. Therefore, the capitals at Wells must be read through layers of meaning and interpretation while also considering their locations within the cathedral and how they react and respond to surrounding figural capitals.

Geometry of Dirac Operators

Let $M$ be a compact, oriented, even dimensional Riemannian manifold and let $S$ be a Clifford bundle over $M$ with Dirac operator $D$. Then \[ \textsc{Atiyah Singer: } \quad \text{Ind } \mathsf{D}= \int_M \hat{\mathcal{A}}(TM)\wedge \text{ch}(\mathcal{V}) \] where $\mathcal{V} =\text{Hom}_{\mathbb{C}l(TM)}(\slashed{\mathsf{S}},S)$. We prove the above statement with the means of the heat kernel of the heat semigroup $e^{-tD^2}$. The first outstanding result is the McKean-Singer theorem that describes the index in terms of the supertrace of the heat kernel. The trace of heat kernel is obtained from local geometric information. Moreover, if we use the asymptotic expansion of the kernel we will see that in the computation of the index only one term matters. The Berezin formula tells us that the supertrace is nothing but the coefficient of the Clifford top part, and at the end, Getzler calculus enables us to find the integral of these top parts in terms of characteristic classes.

QUADRUPOLE CENTRAL TRANSITION NMR SPECTROSCOPY OF QUADRUPOLAR NUCLEI IN SOLUTION

This thesis reports on 17O (I = 5/2) and 59Co (I = 7/2) quadrupole central transition (QCT) NMR studies of three classes of biologically important molecules: glucose, nicotinamide and Vitamin B12 derivatives. Extensive QCT NMR experiments were performed over a wide range of molecular motion by changing solvent viscosity and temperature. 17O-labels were introduced at the 5- and 6-positions respectively: D-[5-17O]-glucose and D-[6-17O]-glucose following the literature method. QCT NMR greatly increased the molecular size limit obtained by ordinary solution NMR. It requires much lower temperatures to get the optimal spectral resolution, which are preferable for biological molecules. In addition, quadrupolar product parameter (PQ) and shielding anisotropy product parameter (PSA) were obtained for hydroxide group and amide group for the first time. For conventional NMR studies of quadrupolar nuclei, only PQ is accessible while QCT NMR obtained both PQ and PSA simultaneously. Our experiments also suggest the resolution of QCT NMR can be even better than that obtained by conventional NMR. We observed for the first time that the second-order quadrupolar interaction becomes a dominant relaxation mechanism under ultraslow motion. All these observations suggest that QCT NMR can become a standard technique for studying quadrupolar nuclei in solution.