Ja n 20 06 On Seneta ’ s Constants for the Supercritical

On Seneta’s Constants for the Supercritical Bellman-Harris Process with E(Z+ log Z+) = ∞

For a finite mean supercriticial Bellman-Harris process, let Zt be the number of particles at time t. There exist numbers χt (the Seneta constants) such that χtZt converges almost surely to a non-degenerate limit. Furthermore, χt ∝ e −βt L(e), where β is the Malthusian parameter, and L is slowly varying at zero. We obtain a characterisation of the slowly varying part of the Seneta constants und...

Ja n 20 06 WKB ANALYSIS FOR NONLINEAR SCHRÖDINGER EQUATIONS WITH POTENTIAL RÉMI

We justify the WKB analysis for the semiclassical nonlinear Schrödinger equation with a subquadratic potential. This concerns subcritical, critical, and supercritical cases as far as the geometrical optics method is concerned. In the supercritical case, this extends a previous result by E. Grenier; we also have to restrict to nonlinearities which are defocusing and cubic at the origin, but besi...

The supercritical Galton-Watson process in varying environments - Seneta-Heyde norming

A natural sufficient condition is given for a Galton-Watson process in a varying environment to have a single rate of growth that obtains throughout the survival set of the process. In the homogeneous process the growth rate is provided by the usual Seneta-Heyde norming.

Ja n 20 06 Constraints on new interactions from neutron scattering experiments

Constraints for the constants of hypothetical Yukawa-type corrections to the Newtonian gravitational potential are obtained from analysis of neutron scattering experiments. Restrictions are obtained for the interaction range between 10 −12 and 10 −7 cm, where Casimir force experiments and atomic force microscopy are not sensitive. Experimental limits are obtained also for non-electromagnetic in...

Ja n 20 06 Adding high powered relations to large groups : A short proof of Lackenby ’ s result