Mathematics Dissertations and Theses
Browse by
Recent Submissions

Certain plane configurations
(University of Kansas, 1930) 
Multiplicities in Commutative Algebra
(University of Kansas, 20160831)This dissertation explores the notion of multiplicity and its generalizations within the theory of commutative algebra. Chapter 2 is dedicated to calculating the limits which give rise to BuchsbaumRim multiplicities. We ... 
On summation of finite series
(University of Kansas, 1929) 
Application of stochastic differential equations to option pricing
(University of Kansas, 20160531)The financial world is a world of random things and unpredictable events. Along with the innovative development of diversity and complexity in modern financial market, there are more and more financial derivative emerged ... 
Some Studies on Parameter Estimations
(University of Kansas, 20160531)Parameter estimation has wide applications in such fields as finance, biological science, weather prediction, oil deposit detection, etc. Researchers are particularly interested in reconstructing some unknown parameters ... 
Depth and Associated Primes of Modules over a Ring
(University of Kansas, 20160531)This thesis consists of three main topics. In the first topic, we let $R$ be a commutative Noetherian ring, $I,J$ ideals of $R$, $M$ a finitely generated $R$module and $F$ an $R$linear covariant functor. We ask whether ... 
Convergence Properties of Hausdorff Closed Spaces
(University of Kansas, 20160531)The purpose of this work is to study the topological property of Hausdorff closedness as a purely convergence theoretic property. It is the author's opinion that this perspective proves to be a natural one from which to ... 
Numerical solutions of rough differential equations and stochastic differential equations
(University of Kansas, 20160531)In this dissertation, we investigate timediscrete numerical approximation schemes for rough differential equations and stochastic differential equations (SDE) driven by fractional Brownian motions (fBm). The dissertation ... 
Generalized FixedPoint Algebras for Twisted C*Dynamical Systems
(University of Kansas, 20160531)In his paper “Generalized Fixed Point Algebras and SquareIntegrable Group Actions,” Ralf Meyer showed how to construct generalized fixedpoint algebras for C*dynamical systems via their squareintegrable representations ... 
Three Dimensional Jacobian Derivations And Divisor Class Groups
(University of Kansas, 20160531)In this thesis, we use P. Samuel's purely inseparable descent methods to investigate the divisor class groups of the intersections of pairs of hypersurfaces of the form $w_1^p=f$, $w_2^p=g$ in affine $5$space with $f$, ... 
The Lattice of Compactifications of a Locally Compact Space
(University of Kansas, 20160531)This is an expanded version of [5] by Magill. The results of [5] are proven with greater detail and any result stated in [5] but not proven is proven here. Let K (X) and K (Y) be used to indicate the lattice of Hausdorff ... 
Analytical line geometry of the plane
(University of Kansas, 1927) 
Dynamics of A Degenerate FokkerPlanck Equation and Its Application
(University of Kansas, 20151231)In this project, a FokkerPlanck equation with two singular points is studied. The equation is derived from a stochastic evolution equation, LMMSABR model, which is widely used in financial industry. It is difficult to ... 
Reflected diffusions and applications to finance and operations management
(University of Kansas, 20151231)This dissertation provides explicit solutions to four special stochastic optimal control problems for reflected diffusions and Markov modulated reflected diffusions. The main mathematical tool that we use is the ergodic ... 
Fractional Diffusion in Gaussian Noisy Environment
(University of Kansas, 20151231)Three types of stochastic partial differential equations are studied in this dissertation. We prove the existence and uniqueness of the solutions and obtain some properties of the solutions. Chapter 3 studies the linear ... 
Envelopes
(University of Kansas, 1928) 
On algebraic curves having variable eccentricity
(University of Kansas, 1926) 
Duality in Euclidean geometry
(University of Kansas, 1928) 
The classification of conics in modular geometries
(University of Kansas, 1927) 
Points uniquely associated with a point on a curved surface
(University of Kansas, 1928)