Browsing MATH Theses and Dissertations by Issue Date
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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 ... 
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 ... 
Theoretical results in inverse problems for size, solvability, and uniqueness in the pn junction and doping profile of semiconductors
(200605)We present an overview of mathematical models for electrons and holes in semiconductors. We use these to pose some inverse problems for determining the doping profile of a semiconductor. We establish the solvability of ... 
Typical points, invariant measures, and dimension for rational maps on the Riemann sphere
(200605)We present three original results for the dynamics of rational maps on the Riemann sphere. Using methods from dimension and ergodic theory, we discuss generalized physical measures and prove their existence for hyperbolic ... 
Some remarks on constructive Yukawa theory in four dimensions
(Wichita State University, 200805)We have found an exact solution to the nonlinear Yukawa system in four dimensions, and used it to derive the time development of the system. Theorems are stated and proved regarding the essential selfadjointness of the ... 
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 ... 
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 ... 
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 ... 
Spectral methods solution of the NavierStokes equations for steady viscous flows
(Wichita State University, 200905)A combination of Spectral Methods and Finite Differences will be used to solve the NavierStokes equations for a viscous flow past a circular cylinder and past symmetric Joukowski airfoils. Different discretizations of ... 
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 ... 
Order restricted inferences about lifetimes under censoring
(Wichita State University, 200907)In survival analysis and in the analysis of the life tables an important biometric function of interest is the mean residual life function (MRLF) M whose value at age t is the average future life time given that a subject ... 
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 ... 
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 ... 
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 ... 
Investigations in single layer gravitational potential
(Wichita State University, 201005) 
A pair of stationary stochastic processes with application to Wichita temperature data
(Wichita State University, 201008)The thesis investigates a pair of stationary stochastic process models whose domains are the set of integers and the set of real numbers respectively. The stationary processes with our specific correlation functions ... 
A computing method for multivariate isotonic regression
(Wichita State University, 201012) 
Stability of continuation and obstacle problems in acoustic and electromagnetic scattering
(Wichita State University, 201012)Study of the Cauchy problem for Helmholtz equation is motivated by the inverse scattering theory and more generally by remote sensing. In this dissertation the increased stability of the Cauchy problem for Helmholtz ... 
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 ... 
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 ...