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

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

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

Formulas for Continued Fractions. An Automated Guess and Prove Approach

We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial conditions. This is used to generate the first few coefficients and from there a conjectured formula. This formula is then proved automatically thanks to a linear recurrence satisfied by some remainder terms. Extensive experiments show that this simple approach and its straightforward generalization to difference and $q$-difference equations capture a large part of the formulas in the literature on continued fractions.Comment: Maple worksheet attache

Jet Bundles in Quantum Field Theory: The BRST-BV method

The geometric interpretation of the Batalin-Vilkovisky antibracket as the Schouten bracket of functional multivectors is examined in detail. The identification is achieved by the process of repeated contraction of even functional multivectors with fermionic functional 1-forms. The classical master equation may then be considered as a generalisation of the Jacobi identity for Poisson brackets, and the cohomology of a nilpotent even functional multivector is identified with the BRST cohomology. As an example, the BRST-BV formulation of gauge fixing in theories with gauge symmetries is reformulated in the jet bundle formalism. (Hopefully this version will be TeXable)Comment: 26 page

The Moyal bracket and the dispersionless limit of the KP hierarchy

A new Lax equation is introduced for the KP hierarchy which avoids the use of pseudo-differential operators, as used in the Sato approach. This Lax equation is closer to that used in the study of the dispersionless KP hierarchy, and is obtained by replacing the Poisson bracket with the Moyal bracket. The dispersionless limit, underwhich the Moyal bracket collapses to the Poisson bracket, is particularly simple.Comment: 9 pages, LaTe

Properties of the Scalar Universal Equations

The variational properties of the scalar so--called ``Universal'' equations are reviewed and generalised. In particular, we note that contrary to earlier claims, each member of the Euler hierarchy may have an explicit field dependence. The Euler hierarchy itself is given a new interpretation in terms of the formal complex of variational calculus, and is shown to be related to the algebra of distinguished symmetries of the first source form.Comment: 15 pages, LaTeX articl

Lie Symmetries and Exact Solutions of First Order Difference Schemes

We show that any first order ordinary differential equation with a known Lie point symmetry group can be discretized into a difference scheme with the same symmetry group. In general, the lattices are not regular ones, but must be adapted to the symmetries considered. The invariant difference schemes can be so chosen that their solutions coincide exactly with those of the original differential equation.Comment: Minor changes and journal-re