• Conjugate operator on variable harmonic Bergman space 

  Wang, Xuan (University of Alabama Libraries, 2020)

  Complex analytic functions have astonishing and amazing properties. Their real parts and imaginary parts are deeply connected by the Cauchy-Riemann equations. It is natural to ask if we obtain some information about the ...
• A case-study of using tensors in multi-way electroencephalograme (EEG) data analysis 

  Milligan-Williams, Essence (University of Alabama Libraries, 2020)

  Tensors are multi-dimensional arrays that can represent large datasets. Acquiring large data sets has its pros and cons; a pro being the bigger the data set, the more information could potentially be generated. A con would ...
• Bounds on the number of generators of a module 

  Morris, Peyton (University of Alabama Libraries, 2019)

  The aim of this work is to present the Forster-Swan bound on the number of generators of a module. It is not our intention to present a novel finding or research discovery. Instead, we will develop the commutative algebra ...
• A combinatorial proof of the invariance of tangle floer homology 

  Homan, Timothy Adam (University of Alabama Libraries, 2019)

  The aim of this work is to take the combinatorial construction put forward by Petkova and Vértesi for tangle Floer homology and show that many of the arguments that apply to grid diagrams for knots can be applied to grid ...
• Pseudo-transient ghost fluid methods for the Poisson-Boltzmann equation with a two-component regularization 

  Ahmed Ullah, Sheik (University of Alabama Libraries, 2019)

  The Poisson Boltzmann equation (PBE) is a well-established implicit solvent continuum model for the electrostatic analysis of solvated biomolecules. The numerical solution of the nonlinear PBE is still a challenge due to ...
• Matrix groups and Lie algebras: an algebraic treatment 

  Ervin, Tucker Jerome (University of Alabama Libraries, 2019)

  There exist two correspondences between groups and Lie algebras. One occurs between matrix Lie groups and Lie algebras. The other concerns itself with complete groups of unitriangular matrices and Lie algebras. Titled the ...
• Parallel stochastic simulation of biochemical reaction systems 

  Cook, Keisha (University of Alabama Libraries, 2019)

  Chemical reactions of various scales occur in nature and in our bodies. As technology has improved, researchers have gained access to in-depth knowledge about the relationships between the moving parts of a chemical reaction ...
• Efficient approximation of the stationary solution to the chemical master equation 

  Reid, Brandon M. (University of Alabama Libraries, 2019)

  When studying chemical reactions on the cellular level, it is often helpful to model the system using the continuous-time Markov chain (CTMC) that results from the chemical master equation (CME). It is frequently instructive ...
• Efficient algorithms for solving three dimensional parabolic interface problem with variable coefficients 

  Wei, Zhihan (University of Alabama Libraries, 2018)

  The dissertation consists of two parts, in the first part, a new matched alternating direction implicit (ADI) method is proposed for solving three-dimensional (3D) parabolic interface problems with discontinuous jumps, ...
• Sparse regression of textual analysis 

  Carter, Phylisicia N. (University of Alabama Libraries, 2018)

  We consider sparse regression techniques as tools for classification of sentiment within Twitter posts. Analysis of Twitter usage suffers from several unique challenges. For example, the 140-character limit severely limits ...
• A super-Gaussian Poisson-Boltzmann model for electrostatic solvation energy calculation: smooth dielectric distributions for protein cavities and in both water and vacuum states 

  Hazra, Tania (University of Alabama Libraries, 2018)

  Calculations of electrostatic potential and solvation energy of macromolecules are essential for understanding the mechanism of many biological processes. In the classical implicit solvent Poisson-Boltzmann (PB) model, the ...
• Regression models with a universal penalized function and applications in economics and finance 

  Sun, Mingwei (University of Alabama Libraries, 2018)

  Variable selection is an important topic in linear regression analysis and attracts considerable research in this era of big data. It is fundamental to high-dimensional statistical modeling, including nonparametric regression. ...
• Heuristics for large-scale semidefiniite programming for the K disjoint clique problem 

  Barnes, Alexander Putnam (University of Alabama Libraries, 2018)

  Large-scale semidefinite programming has many applications, including optimal control, computer vision, and machine learning. However, current algorithms for solving semidefinite programs (SDPs) can be time consuming and ...
• Development of interval and non-interval methods for solving multi-objective optimization problems 

  Liu, Sijie (University of Alabama Libraries, 2018)

  Multi-objective optimization problems are pervasive across many diverse disciplines in engineering, economics, management and design where optimal decisions need to be made in the presence of tradeoffs between two or more ...
• Inexact methods for the chemical master equation with constant or time-varying propensities, and application to parameter inference 

  Dinh, Khanh Ngoc (University of Alabama Libraries, 2018)

  Complex reaction networks arise in molecular biology and many other different fields of science such as ecology and social study. A familiar approach to modeling such problems is to find their master equation. In systems ...
• Variational models with elastica energies: a comparison, a new model and new algorithms 

  He, Xuan (University of Alabama Libraries, 2018)

  This work comprises two parts. In the first part, we propose novel ALM based algorithms for the ECV-L1 and ECV-L2 segmentation models in order to compare their performance. By imposing one extra constraint, we develop novel ...
• Curved surfaces of right cones 

  Milner, Robert Toombs (University of Alabama Libraries, 1919)

  It is the purpose of this article to derive a formula for finding the curved surface of a right cone with any plain curve as a base.
• Development of modal interval algorithm for solving continuous minimax problems 

  Luo, Xin (University of Alabama Libraries, 2017)

  While there are a large variety of effective methods developed for solving more traditional minimization problems, much less success has been reported in solving the minimax problem $\displaystyle\min_{u \in U}\displaystyle\max_{v ...
• Sparse technology in weighted harmonic analysis 

  Hoang, Cong Quoc (University of Alabama Libraries, 2017)

  This dissertation is the union of two major results that we discovered during my graduate time. Both of the results involve what are called sparse families of cubes. There will also be some partial results included though ...
• Structural validity and reliability of two observation protocols in college mathematics 

  Watley, Laura Erin (University of Alabama Libraries, 2017)

  Undergraduate mathematics education is being challenged to improve, with peer evaluation, student evaluations, and portfolio assessments as the primary methods of formative and summative assessment used by instructors. ...

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