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The Partitionability Conjecture
(American Mathematical Society, 201702)In 1979 Richard Stanley made the following conjecture: Every CohenMacaulay simplicial complex is partitionable. Motivated by questions in the theory of face numbers of simplicial complexes, the Partitionability Conjecture ... 
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 ... 
Composing Scalable Nonlinear Algebraic Solvers
(Society for Industrial and Applied Mathematics (SIAM), 20151105)Most efficient linear solvers use composable algorithmic components, with the most common model being the combination of a Krylov accelerator and one or more preconditioners. A similar set of concepts may be used for ... 
A FETIDP TYPE DOMAIN DECOMPOSITION ALGORITHM FOR THREEDIMENSIONAL INCOMPRESSIBLE STOKES EQUATIONS
(Society for Industrial and Applied Mathematics, 20150303)The FETIDP (dualprimal finite element tearing and interconnecting) algorithms, proposed by the authors in [SIAM J. Numer. Anal., 51 (2013), pp. 1235–1253] and [Internat. J. Numer. Methods Engrg., 94 (2013), pp. 128–149] ... 
Nonexistence of solitonlike solutions for defocusing generalized KdV equations
(Texas State University, Department of Mathematics, 20150224)We consider the global dynamics of the defocusing generalized KdV equation $$ \partial_t u + \partial_x^3 u = \partial_x(u^{p1}u). $$ We use Tao's theorem [5] that the energy moves faster than the mass to prove a ... 
On L2 modulus of continuity of Brownian local times and Riesz potentials
(Institute of Mathematical Statistics, 20150505)This article is concerned with modulus of continuity of Brownian local times. Specifically, we focus on three closely related problems: (a) Limit theorem for a Brownian modulus of continuity involving Riesz potentials, ... 
Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency
(Institute of Mathematical Statistics, 20160604)This paper studies the stochastic heat equation with multiplicative noises of the form uW, where W is a mean zero Gaussian noise and the differential element uW is interpreted both in the sense of Skorohod and Stratonovich. ... 
Density convergence in the BreuerMajor theorem for Gaussian stationary sequences
(Bernoulli Society for Mathematical Statistics and Probability, 2015)Consider a Gaussian stationary sequence with unit variance X={Xk;k∈N∪{0}}. Assume that the central limit theorem holds for a weighted sum of the form Vn=n−1/2∑n−1k=0f(Xk), where f designates a finite sum of Hermite ... 
Effects of (Small) Permanent Charge and Channel Geometry on Ionic Flows via Classical PoissonNernstPlanck Models
(Society for Industrial and Applied Mathematics, 20150115)In this work, we examine effects of permanent charges on ionic flows through ion channels via a quasionedimensional classical PoissonNernstPlanck (PNP) model. The geometry of the threedimensional channel is presented ... 
Stability of Periodic Traveling Waves for Nonlinear Dispersive Equations
(Society for Industrial and Applied Mathematics, 20150917)We study the stability and instability of periodic traveling waves for Kortewegde Vriestype equations with fractional dispersion and related, nonlinear dispersive equations. We show that a local constrained minimizer ... 
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 ...