The equations of some dispersionless limit

This short article presents a table of new equations which can be regarded as the generalized equations of the dispersionless limit of several nonlinear equations. From the definition expressed in an algebraic formula, one can get an equation for any positive numbers p and q. The equations were calculated by using the computers and were examined by hand-calculation up to p=10. Relations with some dispersionless hierarchies are mentioned.Comment: AmSTeX, 6 pages, amsppt.st

Counting Arithmetical Structures on Paths and Cycles

Let G be a finite, connected graph. An arithmetical structure on G is a pair of positive integer vectors d, r such that (diag (d) - A) r=0 , where A is the adjacency matrix of G. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices (diag (d) - A)). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients ((2n-1)/(n-1)) , and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles

Meson-baryon interaction in the meson exchange picture

This is the contribution to the proceedings of the MENU 2010 conference. The recent work of Ref. [7] is summarized. Elastic piN scattering and the reaction pi^+ p --> K^+ Sigma^+ are described simultaneously in a unitary coupled-channels approach which respects analyticity. SU(3) flavor symmetry is used to relate the t- and u- channel exchanges that drive the meson-baryon interaction in the different channels. Angular distributions, polarizations, and spin-rotation parameters are compared with available experimental data. The pole structure of the amplitudes is extracted from the analytic continuation.Comment: 4 pages, contribution to the proceedings of the MENU 2010 conference, May 31- June 4, 2010, Williamsburg VA, US