• Weighted Norm Inequalities for the Maximal Operator on Variable Lebesgue Spaces Over Spaces of Homogeneous Type 

  Cummings, Jeremy (University of Alabama Libraries, 2020)

  Given a space of homogeneous type $(X,\mu,d)$, we prove strong-type weighted norm inequalities for the Hardy-Littlewood maximal operator over the variable exponent Lebesgue spaces $L^\pp$. We prove that the variable ...
• Topological transformation groups with a fixed end point 

  Gray, William Jesse (University of Alabama Libraries, 1965)
• A compiler for the Bama-Bell floating point interpretive system 

  Gray, William J. (University of Alabama Libraries, 1962)
• A Classifying Family of Spaces for the Cohomology of Profinite Groups 

  Lee, Evan Matthew (University of Alabama Libraries, 2021)

  In the study of homological algebra, one useful tool for studying the cohomology of a discrete group is that group's classifying space. In some sense, the classifying space captures both the group itself and a description ...
• Coordinate Descent Methods for Sparse Optimal Scoring and its Applications 

  Ford, Katie Wood (University of Alabama Libraries, 2021)

  Linear discriminant analysis (LDA) is a popular tool for performing supervised classification in a high-dimensional setting. It seeks to reduce the dimension by projecting the data to a lower dimensional space using a set ...
• Augmented matched interface and boundary (AMBI) method for solving interface and boundary value problems 

  Feng, Hongsong (University of Alabama Libraries, 2021)

  This dissertation is devoted to the development the augmented matched interface and boundary(AMIB) method and its applications for solving interface and boundary value problems. We start with a second order accurate AMIB ...
• Regularization methods on solving Poisson’s equation and Poisson Boltzmann equation with singular charge sources and diffuse interfaces 

  Wang, Siwen (University of Alabama Libraries, 2021)

  Numerical treatment of singular charges is a grand challenge in solving Poisson-Boltzmann (PB) equation for analyzing electrostatic interactions between the solute biomolecules and the surrounding solvent with ions. For ...
• Adaptive pseudo-time methods for the Poisson-Boltzmann equation with eulerian solvent excluded surface 

  Jones, Benjamin Daniel (University of Alabama Libraries, 2021)

  This work further improves the pseudo-transient approach for the Poisson Boltzmann equation (PBE) in the electrostatic analysis of solvated biomolecules. The numerical solution of the nonlinear PBE is known to involve many ...
• On the Theory of Structures in Sets 

  Hall, Japheth Jr. (University of Alabama Libraries, 1970)

  In many branches of mathematics the property of being a subspace receives considerable attention. The subspaces of a given space might be regarded as values of a structure in a set, that is, a function P on the subsets of ...
• 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 ...

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