Time-hopping patterns can be constructed from simple difference sets. By studying such constructions, we prove that whenever n 2, n, n 1, or n + 1 is a prime power, then we can construct timehopping patterns that have n terms, and are of length less than n2. We show by computation that such patterns can have length less then n2 n’ for all n 5 150. We also show that time-hopping patterns of n te...

In this paper we consider the Anderson type model and show that the density of states is analytic in an interval for large disorder. The examples we have allow for the single site distributions to have some singular components. We also allow non-nearest neighbour hopping terms.

From a hopping rate equation for disordered materials we derive a macroscopic drift{di usion equation. For this purposes two space{time scales are simultaneously considered. The microscopic dynamics is characterized by the distribution of localized states and the hopping rate. On the macroscopic space scale both the hopping rate and the disordered material are allowed to be inhomogeneous.