We consider discrete Schrödinger operators on the line with potentials generated by a minimal homeomorphism on a compact metric space and a continuous sampling function. We introduce the concepts of topological and metric repetition property. Assuming that the underlying dynamical system satisfies one of these repetition properties, we show using Gordon’s Lemma that for a generic continuous sam...

We give new examples of discrete Schrδdinger operators with potentials taking finitely many values that have purely singular continuous spectrum. If the hull X of the potential is strictly ergodic, then the existence of just one potential x in X for which the operator has no eigenvalues implies that there is a generic set in X for which the operator has purely singular continuous spectrum. A su...

In this paper, we study the stability of the absolutely continuous spectrum of onedimensional Stark operators under various classes of perturbations. Stark Schrödinger operators describe behavior of the charged particle in the constant electric field. The absolutely continuous spectrum is a manifestation of the fact that the particle described by the operator propagates to infinity at a rather ...

Paul Garrett [email protected] http://www.math.umn.edu/ g̃arrett/ [This document is http://www.math.umn.edu/ ̃garrett/m/mfms/notes 2013-14/13 1 cont afc spec.pdf] 1. Pseudo-Eisenstein series adjunction to constant term 2. Decomposition of pseudo-Eisenstein series: beginning 3. Eisenstein series 4. Decomposition of pseudo-Eisenstein series: conclusion 5. Plancherel theorem We prove that the ort...

the reflectance spectrum of green leaves is considerably affected by their biochemical and biophysical properties. it is possible to extract biochemical information from a continuous vegetation spectrum produced using hyperspectral sensors. the numerous absorption features present in the vegetation spectrum carry a considerable amount of information related to the content and the structure of t...

abstractbackground: an electron beam generated x-ray spectrum consists of characteristic x-ray and continuous bermsstrahlung. the aim of this research is calculating and comparing x-ray spectra for different target filter of mammograms. materials and methods: monte carlo is a very powerful tool to simulate a series of different target-filter assembly in order to calculate the x-ray spectra. mcn...

Cylindrical vector beams, such as radially or azimuthally polarized doughnut beams, are combined with topography studies of pentacene thin films, allowing us to correlate Raman spectroscopy with intermolecular interactions depending on the particular pentacene polymorph. Polarization-dependent Raman spectra of the C-H bending vibrations are resolved layer by layer within a thin film of ∼20 nm t...

A technique called Time Hopping is proposed for speeding up reinforcement learning algorithms. It is applicable to continuous optimization problems running in computer simulations. Making shortcuts in time by hopping between distant states combined with off-policy reinforcement learning allows the technique to maintain higher learning rate. Experiments on a simulated biped crawling robot confir...

We consider Schödinger operators on the half-line, both discrete and continuous, and show that the absence of bound states implies the absence of embedded singular spectrum. More precisely, in the discrete case we prove that if ∆+V has no spectrum outside of the interval [−2, 2], then it has purely absolutely continuous spectrum. In the continuum case we show that if both −∆+V and −∆−V have no ...