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We use scattering theoretic methods to prove strong dynamical and exponential localization for one-dimensional, continuum, Anderson-type models with singular distributions; in particular, the case of a Bernoulli distribution is covered. The operators we consider model alloys composed of at least two distinct types of randomly dispersed atoms. Our main tools(More)
We use scattering theoretic methods to prove exponential local-ization for random displacement models in one dimension. The operators we consider model both quantum and classical wave propagation. Our main tools are the reeection and transmission coeecients for compactly supported single site perturbations. We show that randomly displaced, non-reeectionless(More)
An electromechanical model for a circular piezoelectric actuator is developed and analyzed. A critical challenge in certain applications employing piezoceramic actuators is to maximize the displacement provided by the actuator while minimizing it power consumption. This problem is addressed here by developing an electromechanical model which can be used to(More)
  • Robert Sims
  • Journal of embryology and experimental morphology
  • 1962
INTRODUCTION T H E literature on regeneration in the central nervous system of vertebrates has been reviewed exhaustively by Windle (1955, 1956). Adult fish and urodeles reestablish physiological and anatomical continuity of the spinal cord after it has been completely transected while adult anurans (Piatt & Piatt, 1958) and mammals on the whole do not. In(More)
(1.1) i∂tψ(t) = Hψ(t) . For all initial conditions ψ(0) ∈ H, the unique solution is given by ψ(t) = e−itHψ(0), for all t ∈ R. Due to Stone’s Theorem e−itH is a strongly continuous one-parameter group of unitary operators on H, and the self-adjointness of H is the necessary and sufficient condition for the existence of a unique continuous solution for all(More)
Abstract. For a large class of finite-range quantum spin models with half-integer spins, we prove that uniqueness of the ground state implies the existence of a low-lying excited state. For systems of linear size L, with arbitrary finite dimension, we obtain an upper bound on the excitation energy (i.e., the gap above the ground state) of the form (C(More)