Michael Edward Harper

Edward.

Norm Estimates of Harper Operators

n denotes the canonical orthonormal basis in l2. The study of the spectral properties of this class of operators has attracted a significant amount of interest in the past couple of decades (see [5], [3], [8], [1], [10], [14], [12], [7] for some of the most important developments). Most of this work has focused on the “Ten Martini problem” of M. Kac, concerning the possible values of the labels...

Quantum diffusion in the generalized Harper equation

We study numerically the dynamic and spectral properties of a one-dimensional quasi-periodic system, where site energies are given by k = V cos 2πf xk with xk denoting the kth quasiperiodic lattice site. When 2πf is given by the reciprocal lattice vector G(m, n) with n and m being successive Fibonacci numbers, the variance of the wavepacket is found to grow quadratically in time, regardless of ...

Harper skirts transparency on foreign aid.

Hypophysitis Edward

Hypophysitis is an uncommon inflammatory condition that may affect the pituitary gland and stalk. Patients often present with varying degrees of hypopituitarism. The diagnosis is often made presumptively based on clinical history and biochemical data but may also be supported by magnetic resonance imaging. Therapy is generally supportive in nature but may require surgery for pathological diagno...