The intrinsic torsion of SU(3) and G_2 structures

We analyse the relationship between the components of the intrinsic torsion of an SU(3) structure on a 6-manifold and a G_2 structure on a 7-manifold. Various examples illustrate the type of SU(3) structure that can arise as a reduction of a metric with holonomy G_2.Comment: Proc. conf. Differential Geometry Valencia 200

A mapping from conceptual graphs to formal concept analysis

A straightforward mapping from Conceptual Graphs (CGs) to Formal Concept Analysis (FCA) is presented. It is shown that the benefits of FCA can be added to those of CGs, in, for example, formally reasoning about a system design. In the mapping, a formal attribute in FCA is formed by combining a CG source concept with its relation. The corresponding formal object in FCA is the corresponding CG target concept. It is described how a CG, represented by triples of the form source-concept, relation, target-concept, can be transformed into a set of binary relations of the form (target-concept, source-concept a relation) creating a formal context in FCA. An algorithm for the transformation is presented and for which there is a software implementation. The approach is compared to that of Wille. An example is given of a simple University Transaction Model (TM) scenario that demonstrates how FCA can be applied to CGs, combining the power of each in an integrated and intuitive way

Hamilton's theory of turns revisited

We present a new approach to Hamilton's theory of turns for the groups SO(3) and SU(2) which renders their properties, in particular their composition law, nearly trivial and immediately evident upon inspection. We show that the entire construction can be based on binary rotations rather than mirror reflections.Comment: 7 pages, 4 figure

The STAR Tracking Upgrade

The STAR experiment at the Relativistic Heavy Ion Collider RHIC studies the new state of matter produced in relativistic heavy ion collisions and the spin structure of the nucleon in collisions of polarized protons. In order to improve the capabilities for heavy flavor measurements and the reconstruction of charged vector bosons an upgrade of the tracking system both in the central and the forward region is pursued. The challenging environments of high track multiplicity in heavy ion collisions and of high luminosity in polarized proton collisions require the use of new technologies. The proposed inner tracking system, optimized for heavy flavor identification, is using active pixel sensors close to the collision point and silicon strip technology further outward. Charge sign determination for electrons and positrons from the decay of W bosons will be provide by 6 large-area triple GEM disks currently under development. A prototype of the active pixel detectors has been tested in the STAR experiment, and an extensive beam test of triple GEM detectors using GEM foils produced by Tech-Etch of Plymouth, MA has been done at Fermilab.Comment: 3 pages, 1 figure, contributed paper to EPS HEP2007, Manchester, U

Polynomials with no zeros on the bidisk

We prove a detailed sums of squares formula for two variable polynomials with no zeros on the bidisk $\mathbb{D}^2$ extending previous versions of such a formula due to Cole-Wermer and Geronimo-Woerdeman. The formula is related to the Christoffel-Darboux formula for orthogonal polynomials on the unit circle, but the extension to two variables involves issues of uniqueness in the formula and the study of ideals of two variable orthogonal polynomials with respect to a positive Borel measure on the torus which may have infinite mass. We present applications to two variable Fej\'er-Riesz factorizations, analytic extension theorems for a class of bordered curves called distinguished varieties, and Pick interpolation on the bidisk.Comment: 52 page

Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle

We prove that for any $n\times n$ matrix, $A$, and $z$ with $|z|\geq \|A\|$, we have that \|(z-A)^{-1}\|\leq\cot (\frac{\pi}{4n}) \dist (z, \spec(A))^{-1}. We apply this result to the study of random orthogonal polynomials on the unit circle.Comment: 27 page

Transient Optical Characterisation of Donor-Acceptor Block Copolymers for Use in Solar Cells

This thesis presents a study of photo-active, semiconducting block copolymers for use in molecular solar cells. Current state-of-the-art organic devices utilise blends of two (or more) materials that are co-deposited from a common solution; the resulting structures formed are determined by material properties and deposition conditions, but often result in configurations that are detrimental to device performance. An answer to this problem comes in the form of the block copolymer; using these materials, devices can be formed from a single material active layer. In addition, the counterbalance of forces within films of block copolymer can lead to nano-scale self-assembly that allows for a strong degree of control over layer equilibrium morphology. Such control will be an important step forward in the evolution of molecular solar cells. The main body of this work is concerned with the study of the photo-physics of photo-conductive block copolymers, especially the generation of free charge. First, an investigation is made into the inherent structure-function relationship in block copolymers. A varying chain length is seen to drastically affect the photoluminescence quenching and yield of long-lived charges. Photovoltaic devices made using these materials show a peak efficiency of 0.11% and correlate with the spectroscopic results, subject to a trade off between charge generation and transport/collection. In a second investigation, the effects of post-fabrication annealing on block copolymer films are considered; studies on annealed samples lead to the conclusion that domain crystallinity is a significant factor in determining the yields of long-lived charge carriers. It is found that these yields are comparable with those of a standard blend (that achieve 75% photon to electron conversion efficiency). Annealing leads to increases in photovoltaic device performance over unannealed samples, although additional control over active layer morphology is necessary for these materials to attain their potential. Following this, a comparative study is made between a block copolymer and a similarly composed blend formed from well studied polyfluorene copolymers. Further advantages of block copolymers are highlighted, including the stability of morphologies generated under different deposition conditions. Finally, a novel tool set is introduced using a block copolymer sample to emphasise the experiments potential with regard to studying interfacial photophysical effects