Browsing MATH Theses and Dissertations by Title
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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 ... 
A computing method for multivariate isotonic regression
(Wichita State University, 201012) 
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 ... 
Construction and solution of an inverse problem posed by "Piekara’s Chair"
(Wichita State University, 200805)The article "Piekara's Chair: Mechanical Model for Atomic Energy Levels" by Zofia GolabMeyer presents a model of the realworld problem of determining classical energy states suitable for high school or undergraduate ... 
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 ... 
Crack detection in a three dimensional body
(200605)We propose a method of analyzing a crack in a three dimensional body. We treat the problem as an inverse problem and apply Green’s Theorem, Trace Theorem, and the Fredholm Alternative. We model the problem using Helmholtz ... 
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 ... 
Equivalence testing for mean vectors of multivariate normal populations
(Wichita State University, 201005)This dissertation examines the problem of comparing samples of multivariate normal data from two populations and concluding whether the populations are equivalent; equivalence is defined as the distance between the mean ... 
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 ... 
The existence of MorseSmale diffeomorphisms in the family of Hénon maps
(Wichita State University, 200905)We consider Hénon maps on ℝ² of the form fa,c(x,y)=(y,y2+c+ax) with real parameters (a, c). Due to the work of S. Hayes and C. Wolf [8], we provide a detailed investigation of the parameters 0 < a < 1 and c = 0. For each ... 
A Fornberglike method for the numerical conformal mapping of bounded multiply connected domains
(Wichita State University, 200905)A new Fornberglike method is presented for computing conformal maps from the interior of the unit disk with m1 circular holes to the interior of a smooth closed curve with m1 holes bounded by smooth curves. The method ... 
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 ... 
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 ... 
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 ... 
Increased stability of solutions to the Helmholtz equation
(200512)Study of the Cauchy problem for Helmholtz equation is stimulated by the inverse scattering theory and more generally by remote sensing. This thesis explains the increased stability of the Cauchy problem for Helmholtz ... 
Inverse doping profile analysis for semiconductor quality control
(Wichita State University, 200912)Inverse doping pro le problems are linked to inverse conductivity problems under the assumptions of zero space charge and low injection. Unipolar inverse conductivity problems are analyzed theoretically via three uniqueness ... 
An investigation of capillary surfaces at nonconvex corners
(Wichita State University, 200912)In this thesis we take a close look at the paper CMC Capillary Surfaces at Reentrant Corners [33] a central feature of which is the question of when does the "central fan" of radial limits exist for a capillary graph in a ... 
Investigations in single layer gravitational potential
(Wichita State University, 201005) 
Multivariate isotonic regression and its algorithms
(Wichita State University, 200905)We use regression functions, which are the means of random variables, to interpret statistical inference. Often an order is imposed on the values of the regression function. Thus, we refer to the regression as an order ... 
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 ...