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Generalizations of Various Results in Quantum Computation Theory to Mixed-Dimensional Quantum Systems
(2021-04-05)
The majority of the research in quantum computation theory is based on quantum mechanical systems consisting of quantum subsystems that are all of the same dimension. Following and expanding on the research conducted by ...
Slow Coloring Cyclic Permutation Graphs
(2021-04-12)
The slow coloring game is played by two players, Lister and Painter, on a graph \(G\). In round \(i\), Lister marks a nonempty subset of \(V(G)\), which we'll call \(M\). By doing this he scores \(|M|\) points. Painter ...
Maximal L1 Regularity for a Class of Parabolic Systems and Applications to Navier-Stokes Equations
(2021-07-14)
This dissertation is devoted to the maximal L1-in-time regularity for a class of linear parabolic systems with variable coefficients. This theory can be applied to investigate the global-in-time well-posedness and stability ...
Computational Design of Random Rough Surfaces in Thin-film Solar Cells by Stochastic Gradient Methods
(2021-07-21)
We present an efficient numerical algorithm to solve for the optimal random structure in
maximizing the absorptance for thin-film solar cells. Random rough texture can increase the
absorbing efficiency of solar cells by ...
Scattering Resonances for Three-dimensional Subwavelength Holes
(2021-07-19)
This thesis aims to investigate scattering resonances and the field amplification at resonant frequencies for two different subwavelength structures: The first structure is a cavity with a closed bottom and width $\varepsilon$ ...
Applications of Stochastic Gradient Descent for Optimization of Complex Systems with Uncertainty
(2021-07-27)
The Stochastic Gradient Descent (SGD) method in all its variations has gained popularity with the recent progress in Machine learning. In this dissertation we implement and analyze two modifications of the SGD method. In ...
Global existence, persistence, spreading speeds, and forced waves in chemotaxis models
(2021-07-29)
Chemotaxis models are widely used to describe the movements of biological species or living organisms in response to certain chemicals in their environments. This dissertation is devoted to the study of various dynamical ...
Efficient and Robust Classification for Positive Definite Matrices with Wasserstein Metric
(2021-04-16)
Riemannian geometry methods are widely used to classify SPD (Symmetric Positives-Definite) matrices, such as covariances matrices of brain-computer interfaces. Common Riemannian geometry classification methods are based ...
Single Index Model for Tensor Data: Theory and Application
(2021-09-09)
Modern scientific applications are frequently producing data sets where the data are not in the form of vectors but instead higher order tensors. For instance, multi-channel MEG signals in biomedical engineering, gene ...
Adjoint Orbits of Borel Subgroup on Maximal Nilpotent Subalgebra of Types A and C.
(2021-11-18)
We describe the adjoint orbits of a Borel subgroup on a maximal nilpotent algebra of Types A and C.
In Chapter 1, we provide a historical background and motivation behind the study. We highlight the
important works in ...