PERSISTENCE OF POPULATIONS IN ENVIRONMENTS WITH AN INTERFACE
Mathematics

Human activity and climate change are putting increasing pressure on ecosystems and endangering an ever-increasing number of species. Careful management of natural resources is necessary to protect biodiversity for both moral and economic reasons. Ideas from ecology and mathematics can inform policy... Continue Reading

NONUNIFORM SAMPLING OF BAND-LIMITED FUNCTIONS
Mathematics

In this thesis we consider extensions of the well-known Whittaker-Kotelnikov-Shannon (WKS) sampling theorem. In its original form, this theorem allows the reconstruction of a band-limited function from its sampled values and reads as follows: If a function f is band-limited to [ ⇡,⇡], i.e., it is re... Continue Reading

HOMOGENEITY GROUPS OF ENDS OF OPEN 3-MANIFOLDS
Mathematics

Each Cantor set C in S3 has for complement an open 3-manifold M3 with end set C. Properties of the embedding of the Cantor set give rise to properties of the corresponding complementary 3-manifold M3. See [Souto and Stover 2013], [Garity and Repovš 2013], and [Garity et al. 2014] for examples of thi... Continue Reading

EINSTEIN’S EQUATIONS IN THE PRESENCE OF SIGNATURE CHANGE
Mathematics

INTRODUCTION Classical cosmological models containing an initial region of Euclidean signature joined to a final region with the usual Lorentzian signature were introduced by Ellis et al.1,2 A basic feature of this work is the use of the Darmois junction conditions at the surface where the signatur... Continue Reading

A POLYNOMIAL CHAOS METHOD FOR DISPERSIVE ELECTROMAGNETICS
Mathematics

Electromagnetic wave propagation in complex dispersive media is governed by the time dependent Maxwell’s equations coupled to equations that describe the evolution of the induced macroscopic polarization. We consider “polydispersive” materials represented by distributions of dielectric parameters in... Continue Reading

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