Menelaus relation and Fay's trisecant formula are associativity equations

It is shown that the celebrated Menelaus relation and Fay's trisecant formula similar to the WDVV equation are associativity conditions for structure constants of certain three-dimensional algebra.Comment: Talk given at the Conference " Mathematics and Physics of Solitons and Integrable Systems", Dijon, 28.6-2.7, 2009. Minor misprints correcte

Magnetic Properties of MBE Grown La0.6Sr0.4MnO3 Thin Films

Honorable Mention Winner This project investigates the magnetic properties of a La1-xSrxMnO3 (x = 0.40) sample of high quality. This sample was grown one atomic layer at a time by Prof. Warusawithana using UNF’s Molecular Beam Epitaxy (MBE) machine. These magnetic properties are investigated over a range of temperatures from 5 to 400 K in fields up to 7 T. We make use of the techniques to analyze the sample to determine to a high degree of precision the critical temperature of the sample, we determined it to be 252 K. We further identified the saturated magnetization, remnant magnetization, and coercive field at 5 K to be 0.00733 emu/g, 0.00563 emu/g and 0.0090 T respectivel

Closed Universes, de Sitter Space and Inflation

We present a new approach to constructing inflationary models in closed universes. Conformal embedding of closed-universe models in a de Sitter background suggests a quantisation condition on the available conformal time. This condition implies that the universe is closed at no greater than the 10% level. When a massive scalar field is introduced to drive an inflationary phase this figure is reduced to closure at nearer the 1% level. In order to enforce the constraint on the available conformal time we need to consider conditions in the universe before the onset of inflation. A formal series around the initial singularity is constructed, which rests on a pair of dimensionless, scale-invariant parameters. For physically-acceptable models we find that both parameters are of order unity, so no fine tuning is required, except in the mass of the scalar field. For typical values of the input parameters we predict the observed values of the cosmological parameters, including the magnitude of the cosmological constant. The model produces a very good fit to the most recent CMBR data. The primordial curvature spectrum predicts the low-l fall-off in the CMB power spectrum observed by WMAP. The spectrum also predicts a fall-off in the matter spectrum at high k, relative to a power law. A further prediction of our model is a large tensor mode component, with r~0.2.Comment: 38 pages, 25 figure

Menelaus' theorem, Clifford configurations and inversive geometry of the Schwarzian KP hierarchy

It is shown that the integrable discrete Schwarzian KP (dSKP) equation which constitutes an algebraic superposition formula associated with, for instance, the Schwarzian KP hierarchy, the classical Darboux transformation and quasi-conformal mappings encapsulates nothing but a fundamental theorem of ancient Greek geometry. Thus, it is demonstrated that the connection with Menelaus' theorem and, more generally, Clifford configurations renders the dSKP equation a natural object of inversive geometry on the plane. The geometric and algebraic integrability of dSKP lattices and their reductions to lattices of Menelaus-Darboux, Schwarzian KdV, Schwarzian Boussinesq and Schramm type is discussed. The dSKP and discrete Schwarzian Boussinesq equations are shown to represent discretizations of families of quasi-conformal mappings.Comment: 26 pages, 9 figure

Quantum Symmetries and Strong Haagerup Inequalities

In this paper, we consider families of operators $\{x_r\}_{r \in \Lambda}$ in a tracial C$^\ast$-probability space $(\mathcal A, \phi)$, whose joint $\ast$-distribution is invariant under free complexification and the action of the hyperoctahedral quantum groups $\{H_n^+\}_{n \in \N}$. We prove a strong form of Haagerup's inequality for the non-self-adjoint operator algebra $\mathcal B$ generated by $\{x_r\}_{r \in \Lambda}$, which generalizes the strong Haagerup inequalities for $\ast$-free R-diagonal families obtained by Kemp-Speicher \cite{KeSp}. As an application of our result, we show that $\mathcal B$ always has the metric approximation property (MAP). We also apply our techniques to study the reduced C$^\ast$-algebra of the free unitary quantum group $U_n^+$. We show that the non-self-adjoint subalgebra $\mathcal B_n$ generated by the matrix elements of the fundamental corepresentation of $U_n^+$ has the MAP. Additionally, we prove a strong Haagerup inequality for $\mathcal B_n$, which improves on the estimates given by Vergnioux's property RD \cite{Ve}

Revalidation and electronic cataract surgery audit: a Scottish survey on current practice and opinion

PURPOSE: To determine current knowledge and opinion on revalidation, and methods of cataract surgery audit in Scotland and to outline the current and future possibilities for electronic cataract surgery audit. METHODS: In 2010 we conducted a prospective, cross-sectional, Scottish-wide survey on revalidation knowledge and opinion, and cataract audit practice among all senior NHS ophthalmologists. Results were anonymised and recorded manually for analysis. RESULTS: In all, 61% of the ophthalmologists surveyed took part. Only 33% felt ready to take part in revalidation, whereas 76% felt they did not have adequate information about the process. Also, 71% did not feel revalidation would improve patient care, but 85% agreed that cataract surgery audit is essential for ophthalmic practice. In addition, 91% audit their cataract outcomes; 52% do so continuously. Further, 63% audit their subspecialist surgical results. Only 25% audit their cataract surgery practice electronically, and only 12% collect clinical data using a hospital PAS system. Funding and system incompatibility were the main reasons cited for the lack of electronic audit setup. Currently, eight separate hospital IT patient administration systems are used across 14 health boards in Scotland. CONCLUSION: Revalidation is set to commence in 2012. The Royal College of Ophthalmologists will use cataract outcome audit as a tool to ensure surgical competency for the process. Retrospective manual auditing of cataract outcome is time consuming, and can be avoided with an electronic system. Scottish ophthalmologists view revalidation with scepticism and appear to have inadequate knowledge of the process. However, they strongly agree with the concept of cataract surgery audit. The existing and future electronic applications that may support surgical audit are commercial electronic records, web-based applications, centrally funded software applications, and robust NHS connections between community and hospital

Prostaglandin E2 Prevents Hyperosmolar-Induced Human Mast Cell Activation through Prostanoid Receptors EP2 and EP4

Background: Mast cells play a critical role in allergic and inflammatory diseases, including exercise-induced bronchoconstriction (EIB) in asthma. The mechanism underlying EIB is probably related to increased airway fluid osmolarity that activates mast cells to the release inflammatory mediators. These mediators then act on bronchial smooth muscle to cause bronchoconstriction. In parallel, protective substances such as prostaglandin E2 (PGE2) are probably also released and could explain the refractory period observed in patients with EIB. Objective: This study aimed to evaluate the protective effect of PGE2 on osmotically activated mast cells, as a model of exercise-induced bronchoconstriction. Methods: We used LAD2, HMC-1, CD34-positive, and human lung mast cell lines. Cells underwent a mannitol challenge, and the effects of PGE2 and prostanoid receptor (EP) antagonists for EP1-4 were assayed on the activated mast cells. Beta-hexosaminidase release, protein phosphorylation, and calcium mobilization were assessed. Results: Mannitol both induced mast cell degranulation and activated phosphatidyl inositide 3-kinase and mitogen-activated protein kinase (MAPK) pathways, thereby causing de novo eicosanoid and cytokine synthesis. The addition of PGE2 significantly reduced mannitol-induced degranulation through EP2 and EP4 receptors, as measured by beta-hexosaminidase release, and consequently calcium influx. Extracellular-signal-regulated kinase 1/2, c-Jun N-terminal kinase, and p38 phosphorylation were diminished when compared with mannitol activation alone. Conclusions:Our data show a protective role for the PGE2 receptors EP2 and EP4 following osmotic changes, through the reduction of human mast cell activity caused by calcium influx impairment and MAP kinase inhibition

Curvature line parametrized surfaces and orthogonal coordinate systems. Discretization with Dupin cyclides

Cyclidic nets are introduced as discrete analogs of curvature line parametrized surfaces and orthogonal coordinate systems. A 2-dimensional cyclidic net is a piecewise smooth $C^1$-surface built from surface patches of Dupin cyclides, each patch being bounded by curvature lines of the supporting cyclide. An explicit description of cyclidic nets is given and their relation to the established discretizations of curvature line parametrized surfaces as circular, conical and principal contact element nets is explained. We introduce 3-dimensional cyclidic nets as discrete analogs of triply-orthogonal coordinate systems and investigate them in detail. Our considerations are based on the Lie geometric description of Dupin cyclides. Explicit formulas are derived and implemented in a computer program.Comment: 39 pages, 30 figures; Theorem 2.7 has been reformulated, as a normalization factor in formula (2.4) was missing. The corresponding formulations have been adjusted and a few typos have been correcte

An evaluation of the effectiveness of PROMPT therapy in improving speech production accuracy in six children with cerebral palsy

This study evaluates perceptual changes in speech production accuracy in six children (3 – 11 years) with moderate-to-severe speech impairment associated with cerebral palsy before, during, and after participation in a motor-speech intervention program (Prompts for Restructuring Oral Muscular Phonetic Targets). An A1BCA2 single subject research design was implemented. Subsequent to the baseline phase (phase A1), phase B targeted each participant’s first intervention priority on the PROMPT motor-speech hierarchy. Phase C then targeted one level higher. Weekly speech probes were administered, containing trained and untrained words at the two levels of intervention, plus an additional level that served as a control goal. The speech probes were analysed for motor-speech-movement-parameters and perceptual accuracy. Analysis of the speech probe data showed all participants recorded a statistically significant change. Between phases A1 – B and B – C 6/6 and 4/6participants, respectively, recorded a statistically significant increase in performance level on the motor speech movement patterns targeted during the training of that intervention. The preliminary data presented in this study make a contribution to providing evidence that supports the use of a treatment approach aligned with dynamic systems theory to improve the motor-speech movement patterns and speech production accuracy in children with cerebral palsy