Partial inner product spaces: Some categorical aspects

We make explicit in terms of categories a number of statements from the theory of partial inner product spaces (PIP spaces) and operators on them. In particular, we construct sheaves and cosheaves of operators on certain PIP spaces of practical interest.Comment: 21 page

Generalised Fermat Hypermaps and Galois Orbits

We consider families of quasiplatonic Riemann surfaces characterised by the fact that -- as in the case of Fermat curves of exponent $n$ -- their underlying regular (Walsh) hypermap is the complete bipartite graph $K_{n,n}$, where $n$ is an odd prime power. We will show that all these surfaces, regarded as algebraic curves, are defined over abelian number fields. We will determine the orbits under the action of the absolute Galois group, their minimal fields of definition, and in some easier cases also their defining equations. The paper relies on group-- and graph--theoretic results by G. A. Jones, R. Nedela and M.\v{S}koviera about regular embeddings of the graphs $K_{n,n}$ [JN\v{S}] and generalises the analogous question for maps treated in [JStW], partly using different methods.Comment: 14 pages, new version with extended introduction, minor corrections and updated reference

The synthesis of monomers with pendent ethynyl group for modified high performance thermoplastics

The objectives of this project were to develop synthetic schemes for the following classes of modified monomers: (1) difunctional triarylethanes with pendent acetylenic groups; and (2) tertiary aspartimides with terminal acetylene groups at the two ends. Our efforts have resulted in the successful development of high yield schemes for the syntheses of several diamino and bisphenolic analogs of difunctional triarylethanes with pendent ethynyl group. A scheme for one new tertiary aspartimide was also established. Multi-gram samples of all prepared new monomers were provided to our technical contact at NASA-LaRC and preliminary polymerization studies were encouraging. Details of the accomplished work within the last four years are described

Simulating full-sky interferometric observations

Aperture array interferometers, such as that proposed for the Square Kilometre Array (SKA), will see the entire sky, hence the standard approach to simulating visibilities will not be applicable since it relies on a tangent plane approximation that is valid only for small fields of view. We derive interferometric formulations in real, spherical harmonic and wavelet space that include contributions over the entire sky and do not rely on any tangent plane approximations. A fast wavelet method is developed to simulate the visibilities observed by an interferometer in the full-sky setting. Computing visibilities using the fast wavelet method adapts to the sparse representation of the primary beam and sky intensity in the wavelet basis. Consequently, the fast wavelet method exhibits superior computational complexity to the real and spherical harmonic space methods and may be performed at substantially lower computational cost, while introducing only negligible error to simulated visibilities. Low-resolution interferometric observations are simulated using all of the methods to compare their performance, demonstrating that the fast wavelet method is approximately three times faster that the other methods for these low-resolution simulations. The computational burden of the real and spherical harmonic space methods renders these techniques computationally infeasible for higher resolution simulations. High-resolution interferometric observations are simulated using the fast wavelet method only, demonstrating and validating the application of this method to realistic simulations. The fast wavelet method is estimated to provide a greater than ten-fold reduction in execution time compared to the other methods for these high-resolution simulations.Comment: 16 pages, 9 figures, replaced to match version accepted by MNRAS (major additions to previous version including new fast wavelet method

Origins of chemical diversity of back-arc basin basalts: a segment-scale study of the Eastern Lau Spreading Center

We report major, trace, and volatile element data on basaltic glasses from the northernmost segment of the Eastern Lau Spreading Center (ELSC1) in the Lau back-arc basin to further test and constrain models of back-arc volcanism. The zero-age samples come from 47 precisely collected stations from an 85 km length spreading center. The chemical data covary similarly to other back-arc systems but with tighter correlations and well-developed spatial systematics. We confirm a correlation between volatile content and apparent extent of melting of the mantle source but also show that the data cannot be reproduced by the model of isobaric addition of water that has been broadly applied to back-arc basins. The new data also confirm that there is no relationship between mantle temperature and the wet melting productivity. Two distinct magmatic provinces can be identified along the ELSC1 axis, a southern province influenced by a “wet component” with strong affinities to arc volcanism and a northern province influenced by a “damp component” intermediate between enriched mid-ocean ridge basalts (E-MORB) and arc basalts. High–field strength elements and rare earth elements are all mobilized to some extent by the wet component, and the detailed composition of this component is determined. It differs in significant ways from the Mariana component reported by E. Stolper and S. Newman (1994), particularly by having lower abundances of most elements relative to H_(2)O. The differences can be explained if the slab temperature is higher for the Mariana and the source from which the fluid is derived is more enriched. The ELSC1 damp component is best explained by mixing between the wet component and an E-MORB-like component. We propose that mixing between water-rich fluids and low-degree silicate melts occurs at depth in the subduction zone to generate the chemical diversity of the ELSC1 subduction components. These modified sources then rise independently to the surface and melt, and these melts mix with melts of the background mantle from the ridge melting regime to generate the linear data arrays characteristic of back-arc basalts. The major and trace element framework for ELSC1, combined with different slab temperatures and compositions for difference convergent margins, may be able to be applied to other back-arc basins around the globe