This paper concerns a question that frequently occurs in various applications: Is any dispersal coupling of stable discrete linear systems, also stable? Although it has been known this is not the case, we shall identify a reasonably diverse class of systems for which it is true. We shall employ the...
In the 1954 John Nash [1] showed, through use of an iterative scheme of approximate embedding maps, that the sphere S² could be isometrically embedded into a ball of any radius by a C¹ map. In the 1980's M. Gromov [2] generalized Nash's work to the h-principal and convex integration....
As industries relating to science, technology, engineering, and mathematics in America continue to grow, employers will need more mathematicians and mathematically able workers than are currently graduating. Women are an underrepresented portion of these graduates, and researches say that this could be due to the difference between women’s and men’s...
A long running problem in mathematical biology is the prediction of extinction events, a specialized case of the larger global stability problem found in differential equations and dynamical systems theory. A central technical question is how to introduce the randomness observed in real ecological systems not accounted for in deterministic...
There are three chapters of manuscripts in this dissertation and all of them are talking about a specific theme: stochastic control, but with completely different perspectives.
In the first manuscript, we solve the optimal barrier strategy for dividend distribution in a complicated Lévy system. In this system, the capital of...
Teachers may be attracted to the use of a game in a learning activity under the presumption that students will find the game experience to be more “fun” than typical classroom activities. The use of a game in a learning activity should help students attain important learning outcomes and engage...
In this dissertation, we use Fourier-analytic methods to study questions of equidistribution on the compact abelian group Zp of p-adic integers. In particu- lar, we prove a LeVeque-type Fourier analytic upper bound on the discrepancy of sequences. We establish p-adic analogues of the classical Dirichlet and Fejér kernels on R/Z,...
Junior level physics students are familiar with a few types of vector field derivatives, such as divergence and curl, but are typically unfamiliar with how to take a general derivative of a vector field. Three junior-level physics students were interviewed with the open-ended prompt, “How would you think about taking...
An almost torus manifold $M$ is a closed $(2n+1)$-dimensional orientable Riemannian manifold with an effective, isometric $n$-torus action such that the fixed point set $M^T$ is non-empty. Almost torus manifolds are analogues of torus manifolds in odd dimension and share many of the characteristics of torus manifolds. For example, both...
In this thesis we study mathematical and computational models for phenomena of flow and transport in porous media in the presence of changing pore scale geometries. The differential equations for the flow and transport models at Darcy scale involve the coefficients of permeability, porosity, and tortuosity which depend on the...