Now showing items 1-6 of 6
Interval exchange transformations: Applications of Keane's construction and disjointness
This thesis is divided into two parts. The first part uses a family of Interval Exchange Transformations constructed by Michael Keane to show that IETs can have some particular behavior including: (1) IETs can be topologically ...
Optimization governed by stochastic partial differential equations
This thesis provides a rigorous framework for the solution of stochastic elliptic partial differential equation (SPDE) constrained optimization problems. In modeling physical processes with differential equations, much of ...
Young tableaux with applications to representation theory and flag manifolds
We outline the use of Young tableaux to describe geometric and algebraic objects using combinatorial methods. In particular, we discuss applications to representations of the symmetric group and the general linear group, ...
Optimization of shell structure acoustics
This thesis analyzes a mathematical model for shell structure acoustics, and develops and implements the adjoint equations for this model. The adjoint equations allow the computation of derivatives with respect to large ...
Complex flow and transport phenomena in porous media
This thesis analyzes partial differential equations related to the coupled surface and subsurface flows and develops efficient high order discontinuous Galerkin (DG) methods to solve them numerically. Specifically, the ...
Branch-decomposition heuristics for linear matroids
This thesis present two new heuristics which utilize classification and max-flow algorithm respectively to derive near-optimal branch-decompositions for linear matroids. In the literature, there are already excellent ...