Now showing items 1-20 of 43

• #### A COMPREHENSIVE OVERVIEW OF MINIMAL-SURFACE THEORY, WITH A THOROUGH MATHEMATICAL TREATMENT OF BERNSTEIN'S THEOREM, THE WEIERSTRASS-ENNEPER REPRESENTATIONS, AND PROPERTIES OF THE GAUSS MAP ﻿

(2014-08)
Notable results in minimal-surface theory include Bernstein's Theorem, the Weierstrass-Enneper representations, and properties of the Gauss map of a minimal surface. For a solution f(x_1, x_2) of the minimal-surface ...
• #### A FLUID-STRUCTURE INTERACTION MODEL CAPTURING LONGITUDINAL DISPLACEMENT IN ARTERIES: MODELING, COMPUTATIONAL METHOD, AND COMPARISON WITH EXPERIMENTAL DATA ﻿

(2012-05)
The focus of this thesis is on numerical modeling of fluid-structure interaction (FSI) problems with application to hemodynamics. Recent in vivo studies, utilizing ultrasound contour and speckle tracking methods, have ...
• #### A Primal-Dual Active-Set Method and Algorithm for Chemical Equilibrium Problem Related To Modeling of Atmospheric Inorganic Aerosols ﻿

(2014-12)
In this dissertation, we studied a general equilibrium model for multiphase multicomponent inorganic atmospheric aerosols. We developed the thermodynamic model to predict the phase transition and multistage growth phenomena ...
• #### A Second Order Variational Approach For Diffeomorphic Matching Of 3D Surfaces ﻿

(2013-08)
In medical 3D-imaging, one of the main goals of image registration is to accurately compare two observed 3D-shapes. In this dissertation, we consider optimal matching of surfaces by a variational approach based on Hilbert ...
• #### CLASSIFICATION OF LEAVITT PATH ALGEBRAS USING ALGEBRAIC K-THEORY ﻿

(2015-05)
We show that the long exact sequence for the $K$-theory of Leavitt path algebras over row-finite graphs, discovered by Ara, Brustenga, and Corti{\~n}as, extends to Leavitt path algebras of arbitrary countable graphs. Using ...
• #### Combining Diffeomorphic Matching with Image Sequence Intensity Registration ﻿

(2014-05)
This thesis presents the research work completed over the past 4 years in the context of a collaborative project between The Methodist Hospital (TMH) and the University of Houston. We have developed and implemented novel ...
• #### Data-driven Techniques For Estimation And Stochastic Reduction Of Multiscale Systems ﻿

(2012-12)
Parametric estimation of stochastic processes is one of the most widely used techniques for obtaining effective models, given a discrete dataset. Often, the experimental or observational datasets are not explicitly generated ...
• #### DIRECTIONAL MULTISCALE ANALYSIS USING SHEARLET THEORY AND APPLICATIONS ﻿

(2012-08)
Shearlets emerged in recent years in applied harmonic analysis as a general framework to provide sparse representations of multidimensional data. This construction was motivated by the need to provide more efficient ...
• #### Extensions of Approximately Unital Operator Algebras ﻿

(2013-08)
Extension theory in the study of C*-algebras has been important in many aspects. For that reason, a theory of extensions of operator algebras, with as direct a link as possible to the C*-algebras theory, will be developed. ...
• #### EXTERIOR REGULARIZED HARMONIC AND HARMONIC FUNCTIONS ﻿

(2012-08)
This thesis mainly studies harmonic functions on exterior regions, having compact, Lipschitz boundaries, in our new finite energy function space, via the sequence of exterior harmonic Steklov eigenvalues and associated ...
• #### FRAMES AS CODES FOR STRUCTURED ERASURES ﻿

(2012-12)
This dissertation studies the role of frames as codes. Frames are families of vectors that give rise to embeddings of Hilbert spaces. These embeddings can be interpreted as codes, because possible linear dependencies among ...
• #### Global Existence of solutions to Reaction-Diffusion Systems with Mass Transport type Boundary Conditions ﻿

(2013-08)
We consider coupled reaction-diffusion models, where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. ...
• #### High-Order Numerical Methods for Time-Dependent Problems with Applications ﻿

(2015-08)
In this dissertation, several high-order numerical methods for solving time dependent problems are studied. In the first part, a maximum principle preserving (MPP) finite-volume (FV) weighted essentially non-oscillatory ...
• #### Image Analysis Using Directional Multiscale Representations and Applications for Characterization of Neuronal Morphology ﻿

(2015-12)
Recent advances in high-resolution fluorescence microscopy have enabled the system- atic study of morphological changes in large populations of cells induced by chemical and genetic perturbations, facilitating the discovery ...
• #### Large Deviations Approach for Stochastic Genetic Evolution ﻿

(2013-08)
Theoretical ecologists have long strived to explain how the persistence of populations depends on biotic and abiotic factors and have proposed various models to predict the long time behavior of biological populations. We ...
• #### Large Time Step and Overlapping Grids for Conservation Laws ﻿

(2014-05)
One focus of this dissertation is to construct a large time step Finite Volume Method for computing numerical solutions to hyperbolic systems of conservation laws. We also consider a method of overlapping spatial grids for ...
• #### Mass spectrometry data mining for cancer detection ﻿

(2013-12)
Early detection of cancer is crucial for successful intervention strategies. Mass spectrometry-based high throughput proteomics is recognized as a major breakthrough in cancer detection. Many machine learning methods have ...
• #### Mixed Finite Element Methods with Piece-Wise Constant Fluxes ﻿

(2015-05)
In this dissertation, we consider a new mixed finite element discretization, its error estimation, monotonicity and the approaches to implement local refinement. We also do some numerical experiments to verify error estimates ...
• #### Mixed-Finite-Element Method on Hexahedral Meshes ﻿

(2014-08)
In this dissertation, we have three goals. The first goal is to investigate the accuracy behavior due to lumping procedure. The second goal is to investigate the effects of different boundary partitions of macro-cells. The ...
• #### Modeling, analysis and numerical simulation of reactive solute transport problems in moving domains ﻿

(2014-05)
In this thesis, we study mathematical models and numerical schemes for reactive transport of a soluble substance in deformable media. The medium is a cylindrical channel with compliant adsorbing walls. The solutes are ...