An infinite family of superintegrable Hamiltonians with reflection in the plane

We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schr\"odinger equations admit separation of variables in polar coordinates and are exactly solvable. The angular part of the wave function is expressed in terms of little -1 Jacobi polynomials. The spectra exhibit "accidental" degeneracies. The superintegrability of the model is proved using the recurrence relation approach. The (higher-order) constants of motion are constructed and the structure equations of the symmetry algebra obtained.Comment: 19 page

Corrections to Sirlin's Theorem in O(p6)O(p^6) Chiral Perturbation Theory

We present the results of the first two-loop calculation of a form factor in full $SU(3) \times SU(3)$ Chiral Perturbation Theory. We choose a specific linear combination of $\pi^+, K^+, K^0$ and $K\pi$ form factors (the one appearing in Sirlin's theorem) which does not get contributions from order $p^6$ operators with unknown constants. For the charge radii, the correction to the previous one-loop result turns out to be significant, but still there is no agreement with the present data due to large experimental uncertainties in the kaon charge radii.Comment: 6 pages, Latex, 2 LaTeX figure

Crohn's disease activity index and Vienna classification - Is it worthwhile to calculate before surgery?

Background: Crohn's disease (CD) patients with increased disease activity may reveal an increased risk for perioperative complications. The `Crohn's disease activity index' (CDAI) and the `Vienna classification' (VC) were developed for standardized disease activity estimations. The significance of these scores to predict extent, type and early outcome of surgery in CD patients was analyzed. Methods: In 179 surgically treated CD patients, the CDAI and VC were assessed from a prospective database. Relations of the scores with CD risk factors, type, number, location and complications of surgery were analyzed. Results: VC behavior and location subtypes were associated with distinct types of surgery (i.e. `strictureplasty' in `stricturing disease', `colon surgery' in `colon involvement'), but not with surgery type and extent or outcome. Surgery extent (i.e. with 5 vs. 3 `surgical sites' 425 +/- 25 vs. 223.3 +/- 25) and complications (357.1 +/- 36.9 (with) vs. 244.4 +/- 13 (without)) were associated with elevated CDAI levels; however, nicotine abuse remained the only significant risk factor for perioperative complications after multiple logistic regression. Conclusion: The significance of VC or CDAI for predicting the extent of surgery or complications is limited. None of the tested variables except preoperative nicotine abuse influenced the likelihood for perioperative complications. Copyright (c) 2006 S. Karger AG, Base