Browsing by Department "Mathematics"
Now showing items 2140 of 305

An application of KAM theory to a model for particle channelling in crystals and some related numerical simulations
(20101130)It has been seen in physical experiments as early as the 1960’s that when a positively charged particle is injected into a crystal in certain directions and with sufficiently high energy, the particle can penetrate into ... 
An empirical investigation into the validity of the security market line
(20101116)The wellknown CAPM (capital asset pricing model) model in finance states that return is a function of risk. The more risky a stock is, the higher the return is expected to be. One way of modeling this relationship between ... 
An exploration of Diophantine equations
(20121127)This paper outlines recent research on Diophantine equations. The topics discussed include methods for generating solutions to specific equations and analysis of patterns in solutions to some specific equations 
An exploration of Fermat numbers
(20110105)This report focuses on the discovery of Fermat numbers as well as the subsequent innovations in processes for finding factors of Fermat numbers. The property of the prime factors of Fermat numbers, as well as the connections ... 
An overview of multilevel regression
(20110221)Due to the inherently hierarchical nature of many natural phenomena, data collected rests in nested entities. As an example, students are nested in schools, school are nested in districts, districts are nested in counties, ... 
Analysis of a DarcyStokes system modeling flow through vuggy porous media
(20080828)Not available 
Analysis of errors and improvements in numerical approximations and methods in secondary mathematics curriculum
(20130830)This report discusses three topics relating to errors of numerical methods and to improvements of numerical approximations. The introduction connects these topics to the secondary mathematics curriculum. The three chapters ... 
Analysis of geometric flows, with applications to optimal homogeneous geometries
(20110706)This dissertation considers several problems related to Ricci flow, including the existence and behavior of solutions. The first goal is to obtain explicit, coordinatebased descriptions of Ricci flow solutionsespecially ... 
Analysis of Ricci flow on noncompact manifolds
(20130502)In this dissertation, we present some analysis of Ricci flow on complete noncompact manifolds. The first half of the dissertation concerns the formation of TypeII singularity in Ricci flow on [mathematical equation]. For ... 
Analysis of the real line
(20120202)The purpose of this report is to describe the course, Analysis of the Real Line, taught at The University of Texas at Austin. Course materials are presented using the inquiry based learning method. Students work a series ... 
An application of the continuity method for an equation on line bundles
(20080828)Not available 
Applications of calculus : summary of Dr. Stephen McAdam’s summer course Mathematics Department at the University of Texas at Austin
(20110105)The aim of this paper is to summarize Professor McAdam’s course on the applications of calculus by showing how calculus can be applied within mathematical situations by understanding concepts in physics. Aside from using ... 
Applications of prime numbers
(20121127)This report explores the historical development of three areas of study regarding prime numbers. The attempt to find an efficient and useful function to generate primes could be a helpful tool in the improvement of encryption. ... 
Applying Classification and Regression Trees to manage financial risk
(20120816)This goal of this project is to develop a set of business rules to mitigate risk related to a specific financial decision within the prepaid debit card industry. Under certain circumstances issuers of prepaid debit cards ... 
Approximation of the 2D complex eikonal equation : analysis and simulation
(20130130)High frequency wave propagation is well described even at caustics by Gaussian beams and the complex eikonal equation. In contrast to the real eikonal equation, the complex eikonal equation is elliptic and not well posed ... 
The arithmetic and geometry of twogenerator Kleinian groups
(20100526)This thesis investigates the structure and properties of hyperbolic 3manifold groups (particularly knot and link groups) and arithmetic Kleinian groups. In Chapter 2, we establish a stronger version of a conjecture of A. ... 
Arithmetic reflection groups and congruence subgroups
(20120712)This thesis investigates the geometric and topological constraints placed on the quotient space of a Fuchsian or Kleinian group by requiring that the group admits a fundamental domain which is simultaneously a Ford domain ... 
Asset liability management in a life insurance company
(20101118)Asset Liability Management is relevant to, and critical for, the sound management of the finances of any organization that invests to meet its future cash flow needs and capital requirements. For a life insurance company ... 
Asymptotics for optimal investment with highwater mark fee
(20150731)This dissertation studies the problem of optimal investment in a fund charging highwater mark fees. We consider a market consisting of a riskless moneymarket account and a fund charging highwater mark fees at rate λ, ... 
Auxiliary polynomials and height functions
(20080828)We establish two new results in this dissertation. Recent theorems of Dubickas and Mossinghoff use auxiliary polynomials to give lower bounds on the Weil height of an algebraic number [alpha] under certain assumptions on ...