Pages: 315 - 322
Recently, B. A. Kupershmidt have constructed a reflection symmetries of q-Bernoulli polynomials (see ). In this paper we give another construction of a q-Bernoulli polynomials, which form Barnes' multiple Bernoulli polynomials at q = 1, cf. [1, 13,14]. By using q-Volkenborn integration, we can also...
Pages: 323 - 351
We prove that, for the irreducible complex crystallographic Coxeter group W, the
following conditions are equivalent: a) W is generated by reflections;
b) the analytic variety X/W is isomorphic to a weighted projective space.
The result is of interest, for example, in application to topological conformal...
Pages: 352 - 364
We present and study bihamiltonian equations of Euler type which include a n
Pages: 365 - 376
We introduce perturbative Feynman integrals in the context of q-calculus generalizing the Gaussian q-integrals introduced by Diaz and Teruel. We provide analytic as well as combinatorial interpretations for the Feynman-Jackson integrals.
Pages: 377 - 392
The complete symmetry group of a 1 + 1 linear evolution equation has been demon-
strated to be represented by the six-dimensional Lie algebra of point symmetries
sl(2, R)?s W , where W is the three-dimensional Heisenberg-Weyl algebra. The infinite number of solution symmetries does not play a role...
Pages: 393 - 419
In this paper we employ a “direct method” to construct rank-k solutions, express-
ible in Riemann invariants, to hyperbolic system of first order quasilinear differential
equations in many dimensions. The most important feature of our approach is the
analysis of group invariance properties of these...
Pages: 420 - 440
We study the well-known Kepler’s problem by introducing a new vectorial regularization. This helps deduce Kepler’s equations by a simple and unified method. Some integral temporal means are also obtained by means of this regularization. The vectorial eccentricity plays a fundamental part in this approach.
Pages: 441 - 466
The Korteweg de Vries (KdV) equation is well known as an approximation model
for small amplitude and long waves in different physical contexts, but wave breaking phenomena related to short wavelengths are not captured in. In this work we consider a class of nonlocal dispersive wave equations which...