A new type of analytic expansion for use in stability calculations is presented and applied to the question of the stability of laminar solutions of the Navier-Stokes equation. This leads in a natural way to a model of the transition from laminar...
Let K be the function field over a finite field of odd order, and let H be a definite quaternion algebra over K. If Î‘ is an order of level M in H , we define theta series for each ideal I of Î‘ using the reduced norm on H. Using harmonic analysis...
In this thesis, we characterize and enumerate the permutations which are realized by the orbits of signed shifts, a family of discrete dynamical systems on words. The permutations, which are called patterns of the signed shifts, are given by the...
We prove the existence of nontrivial multiparameter isospectral deformations of metrics on the classical compact simple Lie groups SO (n) (n = 9, n â‰¥11), Spin(n) (n = 9, n â‰¥11), SU (n) (n â‰¥7), and Sp (n) (n â‰¥5). The proof breaks into three...
In this thesis we look at several problems that lie in the intersection between combinatorial and multiplicative number theory. A common theme of many of these problems are estimates for and properties of the smooth numbers, those integers not...
In this thesis we study 1=k-geodesics, those closed geodesics that minimize on any subinterval of length L=k, where L is the length of the geodesic. These curves arise as critical points of the uniform energy, a function introduced in Morse theory...
A polynomial is a product of distinct cyclotomic polynomials if and only if it is a divisor over [Special characters omitted.] [x ] of xn - 1 for some positive integer n. In this thesis, we will examine two natural questions concerning the divisors...
This thesis investigates the embedding theory of orders in central simple algebras, placing a particular emphasis on the role that the phenomenon known as selectivity plays in the theory. Although the notion of selectivity is completely algebraic,...