Mrs. Dorothea Waley Singer

A Multiscale Region Detector ’ : DOROTHEA BLOSTEIN

A multiscale region detector is derived from properties of a v ‘G (Laplacian-of-Gaussian) scalespace. The detector finds all image regions that have small gray-level variation relative to a neighborhood of their size. These regions may he nested. Since the region detector is designed as a coarse estimator of region size and shape, it is better suited for texture element extraction than for gene...

Wolf Singer

Nilpotent Singer Groups

Let N be a nilpotent group normal in a group G. Suppose that G acts transitively upon the points of a finite non-Desarguesian projective plane P. We prove that, if P has square order, then N must act semi-regularly on P. In addition we prove that if a finite non-Desarguesian projective plane P admits more than one nilpotent group which is regular on the points of P then P has non-square order a...

The Kadison-Singer Conjecture

We are given a large integer N , and a fixed basis {ei : 1 ≤ i ≤ N} for the space H = C . We are also given an N -by-N matrix H that has all its diagonal entries zero, and has norm one. If σ ⊆ {1, 2, . . . , N}, let Pσ be the projection onto the space Hσ := ∨{ei : i ∈ σ}. Call such a projection basic, and the range of a basic projection a basic subspace. For each constant 0 < γ < 1, we want to ...

- Patodi - Singer Index Theorem ∗

In [Wu], the noncommutative Atiyah-Patodi-Singer index theorem was proved. In this paper, we extend this theorem to the equivariant case.