A versatile semiclassical approximation for intense laser-atom processes is presented. This uniform approximation is no more complicated than the frequently used multidimensional saddle-point approximation and far superior, since it applies for all energies, both close to as well as away from the classical cutoffs. In the latter case, it reduces to the standard saddle-point approximation. The u...

With increasing energy the diamagnetic hydrogen atom undergoes a transition from regular to chaotic classical dynamics, and the closed orbits pass through various cascades of bifurcations. Closed orbit theory allows for the semiclassical calculation of photoabsorption spectra of the diamagnetic hydrogen atom. However, at the bifurcations the closed orbit contributions diverge. The singularities...

We consider the problem of uniform asymptotics in kernel functional estimation where the bandwidth can depend on the data. In a unified approach we investigate kernel estimates of the density and the hazard rate for uncensored and right-censored observations. The model allows for the fixed bandwidth as well as for various variable bandwidths, e.g. the nearest neighbor bandwidth. An elementary p...

In this paper, we present a study to understand the relation among spectra of speakers enunciating the same sound and investigate the issue of uniform versus non-uniform scaling. There is a lot of interest in understanding this relation as speaker variability is a major source of concern in many applications including Automatic Speech Recognition (ASR). Using dynamic programming, we find mappin...

The energy losses and spectra of Ultra High Energy Cosmic Rays (UHECR) are calculated for protons as primary particles. The attention is given to the energy losses due to electron-positron production in collisions with the microwave 2.73 K photons. The energy spectra are calculated for several models, which differ by production spectra and by source distribution, namely: (i) Uniform distributio...

Thomson scattering of laser light is one of the most fundamental diagnostics of plasma density, temperature and magnetic fields. It relies on the assumption that the properties in the probed volume are homogeneous and constant during the probing time. On the other hand, laboratory plasmas are seldom uniform and homogeneous on the temporal and spatial dimensions over which data is collected. Thi...

The energy losses and spectra of Ultra High Energy Cosmic Rays (UHECR) are calculated for protons as primary particles. The attention is given to the energy losses due to electron-positron production in collisions with the microwave 2.73 K photons. The energy spectra are calculated for several models, which differ by production spectra and by source distribution, namely: (i) Uniform distributio...