Our main result is a description of the boundary of the parameter space of classical Schottky groups affording two parabolic generators within the larger parameter space of all Schottky groups with two parabolic generators. This boundary is surprisingly different from that of the larger space. It is analytic while the boundary of the larger space is fractal. Approaching the boundary of the smal...

A Carleman estimate for a differential operator P is a weighted energy estimate with a weight of exponential form exp(τφ) that involves a large parameter, τ > 0. The function φ and the operator P need to fulfill some sub-ellipticity properties that can be achieved for instance by choosing φ = exp(αψ), involving a second large parameter, α > 0, with ψ satisfying some geometrical conditions. The ...

This paper evaluates the suitability of Java as an implementation language for the foundations of a computer algebra library. The design of basic arithmetic and multivariate polynomial interfaces and classes have been presented in [1]. The library is type-safe due to its design with Java’s generic type parameters and thread-safe using Java’s concurrent programming facilities. We evaluate some k...

As the physical foundations can rely neither on a reduced set of deterministic-like equations (heavily truncated in order to fit the very limited size of [super-] computers and with a subsequent large number of ad-hoc parameterizations) nor on ad-hoc stochastic models (e.g., with parameters tuned up in an ad hoc way), one needs to consider stochastic models respecting the symmetries of the fund...