A Natural Basis of States for the Noncommutative Sphere and its Moyal bracket

An infinite dimensional algebra which is a non-decomposable reducible representation of $su(2)$ is given. This algebra is defined with respect to two real parameters. If one of these parameters is zero the algebra is the commutative algebra of functions on the sphere, otherwise it is a noncommutative analogue. This is an extension of the algebra normally refered to as the (Berezin) quantum sphere or ``fuzzy'' sphere. A natural indefinite ``inner'' product and a basis of the algebra orthogonal with respect to it are given. The basis elements are homogenious polynomials, eigenvectors of a Laplacian, and related to the Hahn polynomials. It is shown that these elements tend to the spherical harmonics for the sphere. A Moyal bracket is constructed and shown to be the standard Moyal bracket for the sphere.Comment: 18 pages Latex, No figures, Submitted to Journal of Mathematical Physics, March 199

Non Commutative Differential Geometry, and the Matrix Representations of Generalised Algebras

The underlying algebra for a noncommutative geometry is taken to be a matrix algebra, and the set of derivatives the adjoint of a subset of traceless matrices. This is sufficient to calculate the dual 1-forms, and show that the space of 1-forms is a free module over the algebra of matrices. The concept of a generalised algebra is defined and it is shown that this is required in order for the space of 2-forms to exist. The exterior derivative is generalised for higher order forms and these are also shown to be free modules over the matrix algebra. Examples of mappings that preserve the differential structure are given. Also given are four examples of matrix generalised algebras, and the corresponding noncommutative geometries, including the cases where the generalised algebra corresponds to a representation of a Lie algebra or a $q$-deformed algebra.Comment: 16 pages Latex, No figures. Accepted for publication: Journal of Physics and Geometry, March 199

A kinetic model of radiating electrons

A kinetic theory is developed to describe radiating electrons whose motion is governed by the Lorentz-Dirac equation. This gives rise to a generalized Vlasov equation coupled to an equation for the evolution of the physical submanifold of phase space. The pathological solutions of the 1-particle theory may be removed by expanding the latter equation in powers of τ ≔ q 2/6πm. The radiation-induced change in entropy is explored and its physical origin is discussed. As a simple demonstration of the theory, the radiative damping rate of longitudinal plasma waves is calculated

Weakly coupled states on branching graphs

We consider a Schr\"odinger particle on a graph consisting of $\,N\,$ links joined at a single point. Each link supports a real locally integrable potential $\,V_j\,$; the self--adjointness is ensured by the $\,\delta\,$ type boundary condition at the vertex. If all the links are semiinfinite and ideally coupled, the potential decays as $\,x^{-1-\epsilon}$ along each of them, is non--repulsive in the mean and weak enough, the corresponding Schr\"odinger operator has a single negative eigenvalue; we find its asymptotic behavior. We also derive a bound on the number of bound states and explain how the $\,\delta\,$ coupling constant may be interpreted in terms of a family of squeezed potentials.Comment: LaTeX file, 7 pages, no figure

Electromagnetic Fields Produced by Moving Sources in a Curved Beam Pipe

A new geometrical perturbation scheme is developed in order to calculate the electromagnetic fields produced by charged sources in prescribed motion moving in a non-straight perfectly conducting beam pipe. The pipe is regarded as a perturbed infinitely long hollow right-circular cylinder. The perturbation maintains the pipe's circular cross-section while deforming its axis into a planar space-curve with, in general, non-constant curvature. Various charged source models are considered including a charged bunch and an off-axis point particle. In the ultra-relativistic limit this permits a calculation of the longitudinal wake potential in terms of powers of the product of the pipe radius and the arbitrarily varying curvature of the axial space-curve. Analytic expressions to leading order are presented for beam pipes with piecewise defined constant curvature modelling pipes with straight segments linked by circular arcs of finite length. The language of differential forms is used throughout and to illustrate the power of this formalism a pedagogical introduction is developed by deriving the theory ab-initio from Maxwell's equations expressed intrinsically as a differential system on (Minkowski) spacetime.Comment: 43pages, 7figure

Eigenstate Structure in Graphs and Disordered Lattices

We study wave function structure for quantum graphs in the chaotic and disordered regime, using measures such as the wave function intensity distribution and the inverse participation ratio. The result is much less ergodicity than expected from random matrix theory, even though the spectral statistics are in agreement with random matrix predictions. Instead, analytical calculations based on short-time semiclassical behavior correctly describe the eigenstate structure.Comment: 4 pages, including 2 figure

The use of herbal medicines by people with cancer: a cross-sectional survey

BACKGROUND: A large proportion of cancer patients are estimated to use herbal medicines, but data to substantiate this are lacking. This study aimed to investigate the prevalence of herbal medicine use among cancer patients in the West Midlands, and determine the characteristics predicting herbal medicine use. METHODS: A cross-sectional survey of oncology patients (n=1498) being followed up at a hospital in Coventry was undertaken. Recipients were asked about herbal medicine use since their cancer diagnosis, and the association between sociodemographic and cancer-related characteristics and herbal medicine use was evaluated. RESULTS: A total of 1134 responses were received (75.7%). The prevalence of herbal medicine use was 19.7% (95% CI: 17.4-22.1; n=223). Users were more likely to be affluent, female, and aged under 50 years. Usage increased with time since cancer diagnosis (X(2) for trend=4.63; P=0.031). A validation data set, derived from a survey of oncology patients in Birmingham (n=541) with differing socioeconomic characteristics showed no significant difference in estimated prevalence (16.6%; 95% CI: 11.9-22.2). CONCLUSION: A substantial number of people with cancer are likely to be taking herbal medicines. Understanding the self-medication behaviours of these individuals is essential if health-care professionals are to support treatment adherence and avoid unwanted pharmacological interactions

Band spectra of rectangular graph superlattices

We consider rectangular graph superlattices of sides l1, l2 with the wavefunction coupling at the junctions either of the delta type, when they are continuous and the sum of their derivatives is proportional to the common value at the junction with a coupling constant alpha, or the "delta-prime-S" type with the roles of functions and derivatives reversed; the latter corresponds to the situations where the junctions are realized by complicated geometric scatterers. We show that the band spectra have a hidden fractal structure with respect to the ratio theta := l1/l2. If the latter is an irrational badly approximable by rationals, delta lattices have no gaps in the weak-coupling case. We show that there is a quantization for the asymptotic critical values of alpha at which new gap series open, and explain it in terms of number-theoretic properties of theta. We also show how the irregularity is manifested in terms of Fermi-surface dependence on energy, and possible localization properties under influence of an external electric field. KEYWORDS: Schroedinger operators, graphs, band spectra, fractals, quasiperiodic systems, number-theoretic properties, contact interactions, delta coupling, delta-prime coupling.Comment: 16 pages, LaTe

Use of AUDIT-C alcohol screening tool in NHS general dental practices in North London

Background: The numerous health risks of excessive alcohol consumption are well documented. Individuals at risk of harm from alcohol consumption can be identified through alcohol screening tools; however, there is limited research regarding their use in general dental practices. Methods: Data were collected as part of a feasibility trial evaluating delivery of brief alcohol advice in general dental practices in North London. Patient demographics and health-related behaviours were collected, and the Alcohol Use Disorders Identification Test-Consumption (AUDIT-C) tool was used to assess alcohol consumption patterns. Results: The analytical sample comprised 552 dental patients, of whom approximately half (46%) were drinking alcohol at hazardous levels. Males, younger adults, those who consumed red meat weekly and smokers all had significantly increased risks of excessive alcohol consumption. Smokers were more likely to consume excessive levels of alcohol irrespective of smoking frequency. Notable sex differences in alcohol consumption were identified, with males being more likely to consume alcohol frequently and in larger quantities than females. Conclusion: The AUDIT-C tool can be used in general dental practice to screen for harmful levels of alcohol consumption. Clear associations exist between patient demographics, health behaviours and excessive alcohol consumption