An integrable shallow water equation with peaked solitons

We derive a new completely integrable dispersive shallow water equation that is biHamiltonian and thus possesses an infinite number of conservation laws in involution. The equation is obtained by using an asymptotic expansion directly in the Hamiltonian for Euler's equations in the shallow water regime. The soliton solution for this equation has a limiting form that has a discontinuity in the first derivative at its peak.Comment: LaTeX file. Figure available from authors upon reques

Nerve Blood Flow Control in Health & Disease:The Effects of Type 1 Diabetes and Exercise Training

Peripheral nerve blood flow (NBF) is critical to nerve health. Impaired NBF control may contribute to the progression of diabetes peripheral neuropathy. The purposes of this dissertation were: i) to investigate the acute and chronic effects of hyperglycemia on basal sciatic NBF (measured via Doppler ultrasound), ii) to examine the potential vasodilatory effects of insulin (euglycemic hyperinsulinemic clamp; 10 mµ•kg-1•min-1) on NBF control in healthy rats and rats with insulin-treated type 1 diabetes (DS) and iii) to determine if exercise training (~75% VO2max, 60 min/day, 5 days/wk for 10 wk) improves vasa nervorum reactivity to insulin and motor nerve conduction velocity (MNCV) in rats with DS. The studies tested the overall hypotheses that i) basal NBF, the vasodilatory response to insulin, and MNCV would be attenuated in rats with DS, and ii) DS-induced deficits would be offset by concurrent exercise training. Rats with DS were hypertensive and featured reduced MNCV (P\u3c0.01). However, DS did not alter: basal NBF; the relationship between NBF and blood pressure; or the vascularization of the sciatic nerve compared to healthy controls (P≥0.50). Based on these data, hypertensive rats with DS may exhibit elevated NBF in the conscious, basal state (P=0.02). Despite similar or possibly elevated basal NBF values compared with control rats, rats with DS displayed impaired insulin-mediated vasodilation (P≤0.01). Deficits in insulin-mediated vasa nervorum dilation and MNCV were prevented by concurrent endurance exercise training in a separate group of rats with DS. Enhanced insulin-mediated vasa nervorum dilation in aerobically exercise trained rats with DS may be explained partially by the observed increase in sciatic nerve endothelial NO synthase expression (P=0.04). The degree of hyperglycemia was similar in both groups with DS, but exogenous insulin requirements were reduced in rats with DS that exercise trained (P=0.02). Perhaps increased insulin sensitivity, and not reduced hyperglycemia, is the mechanism responsible for preserving vasa nervorum and nerve function in exercise-trained rats with DS. Improved insulin signaling in the vasa nervorum may potentiate insulin signaling in the sciatic nerve and protect against diabetic peripheral neuropathy. Keywords: nerve blood flow, diabetes, hypertension, exercise training, insulin, N

Roughness in lubricated rolling contact: the dry contact limit

Published versio

A Kind of Affine Weighted Moment Invariants

A new kind of geometric invariants is proposed in this paper, which is called affine weighted moment invariant (AWMI). By combination of local affine differential invariants and a framework of global integral, they can more effectively extract features of images and help to increase the number of low-order invariants and to decrease the calculating cost. The experimental results show that AWMIs have good stability and distinguishability and achieve better results in image retrieval than traditional moment invariants. An extension to 3D is straightforward

Quasi-Normal Modes of a Schwarzschild White Hole

We investigate perturbations of the Schwarzschild geometry using a linearization of the Einstein vacuum equations within a Bondi-Sachs, or null cone, formalism. We develop a numerical method to calculate the quasi-normal modes, and present results for the case $\ell=2$. The values obtained are different to those of a Schwarzschild black hole, and we interpret them as quasi-normal modes of a Schwarzschild white hole.Comment: 5 pages, 4 Figure

Analytic linearization of nonlinear perturbations of Fuchsian systems

Nonlinear perturbation of Fuchsian systems are studied in regions including two singularities. Such systems are not necessarily analytically equivalent to their linear part (they are not linearizable). Nevertheless, it is shown that in the case when the linear part has commuting monodromy, and the eigenvalues have positive real parts, there exists a unique correction function of the nonlinear part so that the corrected system becomes analytically linearizable

On a Order Reduction Theorem in the Lagrangian Formalism

We provide a new proof of a important theorem in the Lagrangian formalism about necessary and sufficient conditions for a second-order variational system of equations to follow from a first-order Lagrangian.Comment: 9 pages, LATEX, no figures; appear in Il Nuovo Cimento

The varying role of the GP in the pathway between colonoscopy and surgery for colorectal cancer: a retrospective cohort study

Extent: 11p.Objectives: To describe general practitioner (GP) involvement in the treatment referral pathway for colorectal cancer (CRC) patients. Design: A retrospective cohort analysis of linked data. Setting: A population-based sample of CRC patients diagnosed from August 2004 to December 2007 in New South Wales, Australia, using the 45 and Up Study, cancer registry diagnosis records, inpatient hospital records and Medicare claims records. Participants: 407 CRC patients who had a colonoscopy followed by surgery. Primary outcome measures: Patterns of GP consultations between colonoscopy and surgery (ie, between diagnosis and treatment). We investigated whether consulting a GP presurgery was associated with time to surgery, postsurgical GP consultations or rectal cancer cases having surgery in a centre with radiotherapy facilities. Results: Of the 407 patients, 43% (n=175) had at least one GP consultation between colonoscopy and surgery. The median time from colonoscopy to surgery was 27 days for those with an intervening GP consultation and 15 days for those without the consultation. 55% (n=223) had a GP consultation up to 30 days postsurgery; it was more common in cases of patients who consulted a GP presurgery than for those who did not (65% and 47%, respectively, adjusted OR 2.71, 95% CI 1.50 to 4.89, p=0.001). Of the 142 rectal cancer cases, 23% (n=33) had their surgery in a centre with radiotherapy facilities, with no difference between those who did and did not consult a GP presurgery (21% and 25% respectively, adjusted OR 0.84, 95% CI 0.27 to 2.63, p=0.76). Conclusions: Consulting a GP between colonoscopy and surgery was associated with a longer interval between diagnosis and treatment, and with further GP consultations postsurgery, but for rectal cancer cases it was not associated with treatment in a centre with radiotherapy facilities. GPs might require a more defined and systematic approach to CRC management.David Goldsbury, Mark Harris, Shane Pascoe, Michael Barton, Ian Olver, Allan Spigelman, Justin Beilby, Craig Veitch, David Weller, Dianne L O'Connel

Statistical physics of power fluctuations in mode locked lasers

We present an analysis of the power fluctuations in the statistical steady state of a passively mode locked laser. We use statistical light-mode theory to map this problem to that of fluctuations in a reference equilibrium statistical physics problem, and in this way study the fluctuations non-perturbatively. The power fluctuations, being non-critical, are Gaussian and proportional in amplitude to the inverse square root of the number of degrees of freedom. We calculate explicit analytic expressions for the covariance matrix of the overall, pulse and cw power variables, providing complete information on the single-time power distribution in the laser, and derive a set of fluctuation-dissipation relations between them and the susceptibilities of the steady-state quantities.Comment: 7 pages, 1 figure, RevTe

Generalized Smarr relation for Kerr AdS black holes from improved surface integrals

By using suitably improved surface integrals, we give a unified geometric derivation of the generalized Smarr relation for higher dimensional Kerr black holes which is valid both in flat and in anti-de Sitter backgrounds. The improvement of the surface integrals, which allows one to use them simultaneously at infinity and on the horizon, consists in integrating them along a path in solution space. Path independence of the improved charges is discussed and explicitly proved for the higher dimensional Kerr AdS black holes. It is also shown that the charges for these black holes can be correctly computed from the standard Hamiltonian or Lagrangian surface integrals.Comment: 21 pages Latex file, 1 figure; discussion on integrability rectified, typo in (2.14) correcte