Browsing UT Electronic Theses and Dissertations by Department "Mathematics"
Now showing items 120 of 255

A brief introduction into fair division
(20120203)This report discusses the theory of fair division from its history to its uses in social sciences. Fair division goes beyond the envy free solution of the cake cutting problem to how people divide chores and rent and ... 
A compressive sensing approach to solving nonograms
(20130710)A nonogram is a logic puzzle where one shades certain cells of a 2D grid to reveal a hidden image. One uses the sequences of numbers on the left and the top of the grid to figure out how many and which cells to shade. We ... 
A criterion for toric varieties
(20130815)We consider the pair of a smooth complex projective variety together with an anticanonical simple normal crossing divisor (we call it "log Calabi Yau"). Standard examples are toric varieties together with their toric ... 
A localnonlocal transmission problem
(20150507)We consider solutions to some elliptic equations which change abruptly across a smooth interface. The main equation of interest, motivated by applications to atmospheric dynamics, is local on one side of this interface and ... 
A proposal for a semesterlong course : prime numbers at the secondary level
(20120202)Prime numbers play an integral part in many upper level mathematics courses, most notably in Number Theory. Can a course or section on prime numbers be introduced at the secondary (high school) level? This report outlines ... 
A review on computation methods for Bayesian statespace model with case studies
(20101124)Sequential Monte Carlo (SMC) and Forward Filtering Backward Sampling (FFBS) are the two most often seen algorithms for Bayesian state space models analysis. Various results regarding the applicability has been either claimed ... 
A shadowprice approach of the problem of optimal investment/consumption with proportional transaction costs and utilities of power type
(20121025)We revisit the optimal investment and consumption model of Davis and Norman (1990) and Shreve and Soner (1994), following a shadowprice approach similar to that of Kallsen and MuhleKarbe (2010). Making use of the ... 
A summary of M396C : analysis and the real line UTeach summers master's course mathematics department at the University of Texas at Austin
(20120202)The purpose of this paper is to review and summarize the topics involved in the study of real analysis. Real analysis is a branch of mathematics that studies the field of real numbers including the calculus of real numbers, ... 
Abelian ChernSimons theory with toral gauge group, modular tensor categories, and group categories
(20120906)Classical and quantum ChernSimons with gauge group U(1)N were classified by Belov and Moore in [BM05]. They studied both ordinary topological quantum field theories as well as spin theories. On the other hand a correspondence ... 
About the largest subsolution for a free boundary problem in R²
(20111221)We analyze the geometry and regularity of the largest subsolution of a Free Boundary Problem. We showed that the largest subsolution is a viscosity solution of (1) with Lipschitz and NonDegenerate properties under a very ... 
Adiabatic limits of the Hermitian YangMills equations on slicewise stable bundles
(20080828)Not available 
Agents' agreement and partial equilibrium pricing in incomplete markets
(20120925)We consider two riskaverse financial agents who negotiate the price of an illiquid indivisible contingent claim in an incomplete semimartingale market environment. Under the assumption that the agents are exponential ... 
Algebra readiness : building strong foundations through conceptual understanding
(20120203)Algebra readiness has been a topic of much research and debate. This report summarizes findings pertaining to how researchers and experts in the field of mathematics education define the term algebra readiness. The Southern ... 

Alternative estimation approaches for some common Item Response Theory models
(20110106)In this report we give a brief introduction to Item Response Theory models and multilevel models. The general assumptions of two classical Item Response Theory, 1PL and 2PL models are discussed. We follow the discussion ... 
An analogue of the KorkinZolotarev lattice reduction for vector spaces over number fields
(20101214)We show the existence of a basis for a vector space over a number field with two key properties. First, the nth basis vector has a small twisted height which is bounded above by a quantity involving the nth successive ... 
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 ...