The nonlinear oscillator model allows a basic understanding of all nonlinear processes and can be adopted to analyse optical vibrational modes and electronic transitions in molecules and crystals, in order to derive general properties of harmonic generation to all orders. In particular, we obtain Kramers-Krönig relations and sum rules referred to all momenta of the susceptibility, and Miller’s ...

The relationships between crude oil prices and exchange rates have always been of interest to academics policy analysts. There are theoretical transmission channels that justify such links; however, the empirical evidence is not clear. Most studies on causal in this area restricted a linear framework, which can omit important properties investigated dependencies could be exploited for forecasti...

In this paper we show that regularization methods form a scale-space where the regularization parameter serves as scale. In analogy to nonlinear diiusion ltering we establish continuity with respect to scale, causality in terms of a maximum{minimum principle, simpliica-tion properties by means of Lyapunov functionals and convergence to a constant steady-state. We identify nonlinear regularizati...

A numerical study of nonlinear r-modes in isentropic, rapidly rotating relativistic stars, via 3-D general-relativistic hydrodynamical evolutions, is presented. On dynamical timescales, we find no evidence for strong coupling of r-modes to other modes at amplitudes of order one or larger. Therefore, unless nonlinear saturation sets in on longer timescales, the maximum r-mode amplitude is of ord...