Browsing by Department "Mathematics"
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Applications of calculus : summary of Dr. Stephen McAdam’s summer course Mathematics Department at the University of Texas at Austin
(201008)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
(201208)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
(201205)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
(201212)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
(200905)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
(201205)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 ... 
Aspects of derived Koszul duality
(201605)This thesis comprises two distinct chapters. In the first, we rigidify constructions of generalized string topology Thom spectra due to GruherSalvatore into lax symmetric monoidal functors from spaces parametrized by a ... 
Asset liability management in a life insurance company
(201005)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 ... 
Asymptotic limits in the Hitchin moduli space
(201605)Given a Higgs bundle ([Higgs bundle symbol]), Hitchin's equations are equations for a Hermitian metric on the underlying vector bundle. Hitchin's equations are a coupled system of nonlinear PDEs, and as such are difficult ... 
Asymptotics for optimal investment with highwater mark fee
(201508)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
(2007)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 ... 
Bayesian Estimation of the Discrepancy with Misspecified Parametric Models
(2013)We study a Bayesian model where we have made specific requests about the parameter values to be estimated. The aim is to find the parameter of a parametric family which minimizes a distance to the data generating density ... 
Bayesian Mixture Models for Assessment of Gene Differential Behaviour and Prediction of pCR through the Integration of Copy Number and Gene Expression Data
(PLOS One, 20130712)We consider modeling jointly microarray RNA expression and DNA copy number data. We propose Bayesian mixture models that define latent Gaussian probit scores for the DNA and RNA, and integrate between the two platforms via ... 
Behavior of knot Floer homology under conway and genus two mutation
(201305)In this dissertation we prove that if an nstranded pretzel knot K has an essential Conway sphere, then there exists an Alexander grading s such that the rank of knot Floer homology in this grading, [mathematical equation], ... 
The Bianchi Groups Are Separable On Geometrically Finite Subgroups
(200105)Let d be a square free positive integer and Od the ring of integers in Q(root d). The main result of this paper is that the groups PSL(2,Od) are subgroup separable on geometrically finite subgroups. 
BMBC: a Bayesian method of base calling for Solexa sequence data
(BMC Bioinformatics, 20120829)Base calling is a critical step in the Solexa nextgeneration sequencing procedure. It compares the positionspecific intensity measurements that reflect the signal strength of four possible bases (A, C, G, T) at each ... 
The Boltzmann equation : sharp Povzner inequalities applied to regularity theory and Kaniel & Shinbrot techniques applied to inelastic existence
(200808)This work consists of three chapters. In the first chapter, a brief overview is made on the history of the modern kinetic theory of elastic and dilute gases since the early stages of Maxwell and Boltzmann. In addition, I ... 
Boundaries of Siegel Disks: Numerical Studies of their Dynamics and Regularity
(200809)Siegel disks are domains around fixed points of holomorphic maps in which the maps are locally linearizable (i.e., become a rotation under an appropriate change of coordinates which is analytic in a neighborhood of the ...