MATH Theses and Dissertations
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A capillary surface with no radial limits
(Wichita State University, 201705)We begin by discussing the circumstances of capillary surfaces in regions with a corner, both concave and convex. These circumstances led to the (since proved) ConcusFinn Conjecture, which gives the requirements for a ... 
Unbiasedness of homogeneity test of normal mean vectors under multivariate order restrictions
(Wichita State University, 201705)This dissertation considers homogeneity test for comparing multivariate normal populations with generalized order restricted alternative hypothesis. The framework in this dissertation presents a generalized multivariate ... 
Composite optimal control for interconnected singularly perturbed systems
(Wichita State University, 201705)This dissertation deals with the design of a decentralized control and estimators for large scale interconnected singularly perturbed stochastic systems for system stabilization and cost minimization. Singular perturbation ... 
Classification of simply connected cohomogeneity one manifolds in lower dimensions
(Wichita State University, 201705)A cohomogeneity one manifold is a topological manifold with an effective topological action of a compact Lie group whose quotient is one dimensional. Cohomogeneity one manifolds were introduced by Mostert in 1957, however ... 
Torus actions on simply connected 4manifolds
(Wichita State University, 201705)In this paper, we study smooth effective actions of the 2dimensional torus group T 2 ~= SO(2)xSO(2) on simply connected, closed 4dimensional manifolds. Using the conical orbit space of the quotient, a crosssectioning ... 
A comparison of some numerical conformal mapping methods for simply and multiply connected domains
(Wichita State University, 201605)This dissertation compares several methods for computing conformal maps from simply and multiply connected domains bounded by circles to target domains bounded by smooth curves and curves with corners. We discuss the use ... 
Isotonic regression through the Merge and Chop Algorithm for application in statistical inference
(Wichita State University, 201605)In this paper, the theory for the application of the Merge and Chop Algorithm are defined and proven. The algorithm is used to find isotonic regressions in more situations than comparable methods. A program is included ... 
Computation of Stokes waves using conformal mapping
(Wichita State University, 201605)In this paper we study the time dependent water wave problem for Stokes waves on water of infinite and finite depth using numerical conformal mapping techniques. We begin by briefly reviewing Fornberg's numerical conformal ... 
Increasing stability in the inverse problem for the Schrödinger equation
(Wichita State University, 201512)The Schrödinger equation is a partial differential equation that describes how the quantum state of a physical system changes with time. It was formulated in late 1925 by the Austrian physicist Erwin Schrödinger. The study ... 
Pellet ablation in Tokamak reactors
(Wichita State University, 201507)We implemented a rotational cloud model for the simulation of pellet ablation in a Tokamak reactor. We have shown that the ablation rate in the rotational cloud model converges quickly to a steady state value independent ... 
A multiple decision procedure for testing with ordered alternatives
(Wichita State University, 201507)In testing hypotheses with ordered alternatives, the conclusion of an order restriction when rejecting the null hypothesis is very sensitive to the correctness of the assumed model. In other words, when the null hypothesis ... 
Modules for the investigation of the central fan question through numerical computation
(Wichita State University, 201505)In this thesis, we continue the research of investigating the central fan question through numerical computation of minimal surfaces and the author develops a new conformal map in hopes of producing a more accurate and ... 
Applications of the hCobordism Theorem
(Wichita State University, 201405)We provide an exposition of J. Milnor's proof of the hCobordism Theorem. This theorem states that a smooth, compact, simply connected ndimensional manifold W with n greater than or equal to 6, whose boundary boundaryW ... 
Geometry of horizontal bundles and connections
(Wichita State University, 201405)An Ehresmann connection on a fiber bundle pi: E > M is defined by prescribing a suitable horizontal subbundle H of the tangent bundle piT: TE > E. For a horizontal bundle to be suitable, it must have a property called ... 
Examples of discontinuity for the variational solution of the minimal surface equation with Dirichlet data on a domain with a nonconvex corner and locally negative mean curvature
(Wichita State University, 201312)The purpose of this thesis is to investigate the role of smoothness, specifically the smoothness of the boundary ∂Ω, in the behavior of the variational solution f on a domain Ω to the Dirichlet problem for the Minimal ... 
On convergence sets of formal power series
(Wichita State University, 201312)In this thesis we consider the convergence sets of formal power series of the form f(z, t)=sigma infinity j=0 pj(z)tj, where pj(z) are polynomials. A subset E of the complex plane C is said to be a convergence set if there ... 
Derivation and regularization of corrections to propagators and vertices for cubically interacting scalar field theories
(Wichita State University, 201305)This thesis, a mainly expository work, attempts to give all the calculational details for some popular models in scalar quantum eld theory that serve a mostly pedagogical purpose. Starting with a real scalar eld with ... 
Stationary time series resulting from certain positive definite kernels and simulation via highorder vector autoregressive models
(Wichita State University, 201305)Vector autoregressive models have traditionally been used to model and forecast multivariate time series data, predicting future values based on previous observations. In this thesis, we introduce some multivariate time ... 
On the existence of central fans of capillary surfaces
(Wichita State University, 201305)We prove that under some conditions, the central fans of capillary surfaces exist and are stable. We perturb the contact angle of a capillary surface for a bounded domain which is not necessarily symmetric, that has a ... 
Covariance structures of Gaussian and logGaussian vector stochastic processes
(Wichita State University, 201212)Although the covariance structures of univariate Gaussian and log Gaussian stochastic processes have been extensively studied in the past few decades, the development of covariance structures for Gaussian and logGaussian ...