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We consider motion in a periodic potential in a classical, quantum, and semiclassical context. Various results on the distribution of asymptotic velocities are proven.

- Firas W. Obeidat, Reinhold A. Lang, +5 authors Thomas P. Hüttl
- Surgical Endoscopy
- 2010

Treatment of type 4 hiatal hernia using a minimally invasive approach is challenging and requires good familiarity with this technique. From October 1992 to August 2010, 40 patients with a median age of 68 years underwent laparoscopic anterior hemifundoplication surgery for upside-down stomach and were included in our prospective study. The median symptoms… (More)

- Andreas Knauf
- 2008

We consider the classical three-dimensional motion in a potential which is the sum of n attracting or repelling Coulombic potentials. Assuming a non-collinear configuration of the n centres, we find a universal behaviour for all energies E above a positive threshold. Whereas for n = 1 there are no bounded orbits, and for n = 2 there is just one closed… (More)

It is known that for n ≥ 3 centres and positive energies the ncentre problem of celestial mechanics leads to a flow with a strange repellor and positive topological entropy. Here we consider the energies above some threshold and show: Whereas for arbitrary g > 1 independent integrals of Gevrey class g exist, no real-analytic (that is, Gevrey class 1)… (More)

- Nihat Ay, Andreas Knauf
- Kybernetika
- 2006

Stochastic interdependence of a probablility distribution on a product space is measured by its Kullback-Leibler distance from the exponential family of product distributions (called multi-information). Here we investigate lowdimensional exponential families that contain the maximizers of stochastic interdependence in their closure. Based on a detailed… (More)

- Andreas Knauf
- 1998

We derive criteria for the existence of trapped orbits (orbits which are scattering in the past and bounded in the future). Such orbits exist if the boundary of Hill's region is non-empty and not homeomorphic to a sphere. For non-trapping energies we introduce a topological degree which can be non-trivial for low energies, and for Coulombic and other… (More)

Consider the Schrödinger operator with semiclassical parameter h, in the limit where h goes to zero. When the involved long-range potential is smooth, it is well known that the boundary values of the operator’s resolvent at a positive energy λ are bounded by O(h−1) if and only if the associated Hamilton flow is non-trapping at energy λ. In the present… (More)

- Jean-Marc Biannic, Clement Roos, Andreas Knauf
- Eur. J. Control
- 2006

- Andreas Knauf
- 2007

It is an empirical observation that the Riemann zeta function can be well approximated in its critical strip using the Number-Theoretical Spin Chain. A proof of this would imply the Riemann Hypothesis. Here we relate that question to the one of spectral radii of a family of Markov chains. This in turn leads to the question whether certain graphs are… (More)

- Andreas Knauf
- 1998

It is an empirical observation that the Riemann zeta function can be well approximated in its critical strip using the Number-Theoretical Spin Chain. A proof of this would imply the Riemann Hypothesis. Here we relate that question to the one of spectral radii of a family of Markov chains. This in turn leads to the question whether certain graphs are… (More)