The fixed energy scattering matrix is defined on a perturbed stratified medium, and for a class of perturbations, its main part is shown to be a Fourier integral operator on the sphere at infinity. This is facilitated by developing a refined limiting absorption principle. The symbol of the scattering matrix is shown to determine the asymptotics of a large class of perturbations.

In this work we compare two different approaches to calculation of the three-body resonances on the basis of Faddeev differential equations. The first one is the complex scaling approach. The second method is based on an immediate calculation of resonances as zeros of the three-body scattering matrix continued to the physical sheet.

BACKGROUND Omeprazole is metabolized predominantly by CYP2C19, a polymorphically expressed enzymes that show marked interindividual and interethnic variation. These variations cause a substantial differences that have been reported in the pharmacokinetics of omeprazole. The aim of the present study was to evaluate the pharmacokinetic parameters of omeprazole in a random Iranian population. ME...

We consider the 1D massless Dirac operator on the real line with compactly supported potentials. We study resonances as the poles of scattering matrix or equivalently as the zeros of modified Fredholm determinant. We obtain the following properties of the resonances: 1) asymptotics of counting function, 2) estimates on the resonances and the forbidden domain, 3) the trace formula in terms of re...

Stochastic Petri nets (SPNs) have been widely used to model randomness which is an inherent feature of biological systems. However, for many biological systems, some kinetic parameters may be uncertain due to incomplete, vague or missing kinetic data (often called fuzzy uncertainty), or naturally vary, e.g., between different individuals, experimental conditions, etc. (often called variability)...

In this paper, we compute the scattering matrix for the Hilbert modular group over any number field K. We then express the determinant of the scattering matrix as a ratio of completed Dedekind zeta functions associated to the Hilbert class field of K. This generalizes work of Efrat and Sarnak [ES] in the imaginary quadratic case.