1. Introduction Multidimensional NMR methods have become an important tool in the 1970s. In the past years a new set of experiments has developed whose postprocessing is based on a multidimensional inverse Laplace transformation rather than a Fourier transformation which provides the capabilities to find correlations between various parameters such as diffusion coefficients D and NMR relaxation...

We define a notion of determining sets for the discrete Laplacian in a domain Ω. A set D is called determining if harmonic functions are uniquely determined by providing their values on D, and if D has the same size as the boundary of Ω. It is shown that there exist determining sets that are fairly evenly distributed in Ω. A number of basic properties of determining sets are derived.

OF THE DISSERTATION Chip-Firing Games with Dirichlet Eigenvalues and Discrete Green’s Functions