Mathematics Dissertations and Theses
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A special Riemann surface with application to the hyperelliptic case
(University of Kansas, 1915) 
The principle of duality in a projective space of N dimensions
(University of Kansas, 1922.) 
Euclidean proofs of projective geometry theorems /
(University of Kansas, 1922.) 
The Arbelos
(University of Kansas, 19490801) 
Coordinate Systems in One and Two Dimensions
(University of Kansas, 19140601) 
On the Kalman Filter and Its Variations
(University of Kansas, 20140531)The objective of this paper is to explore the standard Kalman filter and two nonlinear variations. Additionally, we will discuss the derivation of the Kalman filter using Newton's method. Next we will consider the ... 
Limit Domains in Several Complex Variables
(University of Kansas, 20131231)In this thesis we demonstrated the existence of domains in C^2 evidencing both intrinsic phenomena of C^n, n 1, and different types of boundary smoothness. We constructed these domains by taking limits of preimages of ... 
Finding Eigenvalues of Unitary Matrices
(University of Kansas, 20131231)The study introduces methods of finding eigenvalues for unitary matrices and pencils. BunseGerstner and Elsner ([2]) proposed an algorithm of using the Schur parameter pencil to solve eigenproblems for unitary matrices ... 
Bilinear LittlewoodPaley Square Functions and Singular Integrals
(University of Kansas, 20130531)In this dissertation we further develop the bilinear theory of vector valued CalderoónZygmund operators, LittlewoodPaley square functions, and singu lar integral operators. These areas of harmonic analysis are motivated ... 
Some application of Malliavin calculus to SPDE and convergence of densities
(University of Kansas, 20130531)Some applications of Malliavin calculus to stochastic partial differential equations (SPDEs) and to normal approximation theory are studied in this dissertation. In Chapter 3, a FeynmanKac formula is established for a ... 
Dynamics of PoissonNernstPlanck systems and applications to ionic channels
(University of Kansas, 20130831)Dynamics of PoissonNernstPlanck systems and its applications to ion channels are studied in this dissertation. The PoissonNernstPlanck systems serve as basic electrodiffusion equations modeling, for example, ion flow ... 
Central Limit Theorems for Some Symmetric Stochastic Integrals
(University of Kansas, 20130831)The problem of stochastic integration with respect to fractional Brownian motion (fBm) with H 1/4, but not in general if H 1/2. This result approximates an fBm version of Spitzer's theorem for planar Brownian motion. 
Simulation Methods Comparison and Parameter Estimation for a Fractional Stochastic Volatility Model with Application in Stock Price Analysis
(University of Kansas, 20130831)This paper studies continuoustime stock pricing models with stochastic volatility driven by fractional Brownian motion. We compare two ways for simulating the paths of stochastic volatility and stock price when the Hurst ... 
The Rebate Value Process with Some Applications
(University of Kansas, 20130831)In the pricing of credit derivatives default is modelled as a stopping time and prices are typically determined by separation of cashflows before and at default. In a general riskneutral valuation setting, this technique ... 
Numerical Methods for Parameter Estimation in Stochastic Systems
(University of Kansas, 20130531)The objective of this work is to provide numerical simulations in support of a collection of existing results on estimation in two distinct types of stochastic systems. In the first chapter, we consider a linear timeinvariant ... 
Quotients of Metric Spaces
(The University of Kansas, 1968)The question of when a given property of a topological space is preserved under mappings is one of the most familiar problems of general topology. Among the properties of greatest interest for general spaces is, without ... 
Neutral Equations of Mixed Type
(University of Kansas, 20121231)In this dissertation we consider neutral equations of mixed type. In particular, we con sider the associated linear Fredholm theory and nerve fiber models that are written as systems of neutral equations of mixed type. ... 
SuperStretched and Countable CohenMacaulay Type
(University of Kansas, 20120812)This dissertation defines what it means for a CohenMacaulay ring to to be superstretched. In particular, a superstretched CohenMacaulay ring of positive dimension has hvector (1), (1,n), or (1,n,1). It is shown that ... 
Normal form approach for dispersive equations with lowregularity data
(University of Kansas, 20120101)In this dissertation, we examine applications of the normal form technique to nonlinear dispersive equations with rough initial data. Working within the framework of Bourgain spaces, the normal form method often produces ... 
Shearing Flows in Liquid Crystal Models
(University of Kansas, 20120531)The liquid crystal phase is a phase of matter between the solid and liquid phase whose flow is characterized by a velocity field and a director field which describes locally the orientation of the liquid crystal. In this ...