Nhu Nguyen

• University of Southern California

. We prove that the Heighway dragon is a countable union of closed geometrically similar disk-like planar sets which intersect each other in a linear order: any two of them intersect at no more than one cut point and for any three disks there exist at least two with an empty intersection. Consequently, the interior of the Heighway dragon is a count...

We prove that any iterated function system of nite type possesses the weak separation property.

Roberts constructed a linear metric space which contains a compact convex set without any extreme points. The space constructed by Roberts is complicated and special.We investigate the topological property of Roberts' example and demonstrate that the linear metric space constructed by Roberts is an AR, therefore is homeomorphic to Hilbert space.

For any triple of positive integers (m,N,q), the matrix F(m,N,q), called the (m,N,q)-regular Fourier matrix, is defined. The regular Fourier matrices F(m,N,q) are then applied to set up new algorithms for nonuniform fast Fourier transforms. Numerical results show that the accuracies obtained by the algorithms are much better than previously reporte...

Based on a class of regular Fourier matrices, a new nonuniform fast Fourier transform (NUFFT) algorithm is developed for unequally spaced data. With a comparable complexity of O(N log₂N), this algorithm is much more accurate than previously reported results since it is optimal in the least squares sense. The algorithm is useful for compu...