MATH Theses and Dissertations
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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 ... 
Forty two problems of first degree from Diophantus’ Arithmetica
(Wichita State University, 201012)This work brings to the audience Diophantus' problems of first degree in a literal word for word English translation from Ver Eecke's French translation of Arithmetica. In addition, these problems are accompanied by ... 
Order restricted Abasis and Bbasis values
(Wichita State University, 201205)In this thesis, the concept of Abasis and Bbasis as it relates to the aviation industry is studied. The rst assumption that will be made in order to help with the formulation of the Abasis and Bbasis values is that ... 
Numerical computation of SchwarzChristoffel transformations and slit maps for multiply connected domains
(Wichita State University, 201205)Two methods for the numerical conformal mapping of domains with m < ∞ separated circular holes to domains with m polygonal holes are presented; bounded and unbounded domains are both considered. The methods are based on ... 
Stability estimates for inverse problems of some elliptic equations
(Wichita State University, 201112)In this dissertation we obtain new Carleman formulas for the solution of the Cauchy problem for equations P u = h, in Ω, uE = f , where E ⊂ ∂Ω and  E  > 0. Our elliptic operator is of the form P = [ [2∂¯ 0 ; ... 
Testing homogeneity of a parameter matrix some of the rows of which are under synchronized order restrictions
(Wichita State University, 201112)This research considers a multiple multivariate linear regression model with a parameter matrix some of the rows of which are constrained by synchronized order restrictions. The test on the homogeneity of the parameter ... 
Conformal deformation of a conic metric
(Wichita State University, 201105)The problem studied here focuses on a compact manifold M without boundary in which the Riemannian metric g is on Λ = M – {p1, p2,…,pκ}. Near the pi 's, g has a particular type of singularity in which locally M = (0, δ)x ... 
A study of particular coordinate systems
(Wichita State University, 201105)This thesis is a study of the properties and relationships between isothermal, harmonic and characteristic coordinate systems. The proof of the existence of isothermal and characteristic coordinates on a manifold which ... 
A historical overview of connections in geometry
(Wichita State University, 201105)This thesis is an attempt to untangle/clarify the modern theory of connections in Geometry. Towards this end a historical approach was taken and original as well as secondary sources were used. An overview of the most ...