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On the KolmogorovArnold representation theorem for continuous functions
(Wichita State University, 201812)In 1900 at the International Congress of Mathematicians in Paris, D. Hilbert posed 23 questions that later became known as Hilbert's 23 problems. Number 13 remained unresolved for over half a century until 1956 and 1957 ... 
Coverage probability of tolerance levels
(Wichita State University, 201812)In this thesis the ideas of the tolerance limit and coverage probabilities are explored in the context of the Abasis and Bbasis for composite materials. The breaking strength of composite materials are random variables ... 
Two contributions to order restricted inferences
(Wichita State University, 201812)We are proposing two separate problems from order restricted inferences. The rst is a onesided test for stochastic ordering of two distribution functions that protects against false positive conclusions because of model ... 
The effect of small time delays on largescale systems
(Wichita State University, 201812)In this research, model reduction techniques are used to design optimal control strategies with low sensitivity in order to model uncertainty. The source of uncertainty encountered is the time delay, and the reducedorder ... 
Continuation of solutions of elliptic systems from discrete sets with application to geometry of surfaces
(Wichita State University, 201807)We obtain new estimates of stability for continuation of solutions of elliptic inequali ties  ∂u2 < = au2 from finite discrete sets. For this we use Hormander's type of Carleman estimates for ∂bar with boundary ... 
Increasing stability for the inverse scattering source problem with many frequencies
(Wichita State University, 201807)In mathematics and physics, the inverse scattering problem is the problem of determining characteristics of an object, based on data of how it scatters incoming radiation or particles. It is the inverse problem to the ... 
A comparative study of electroweak Higgs boson production at future Hadron Colliders
(Wichita State University, 201807)The discovery of the Higgs boson has opened the door to the next phase of exploration in particle physics. Since the Higgs boson was found in July 2012 at CERN's Large Hadron Collider (LHC), many researches and experiments ... 
Semiinclusive neutral current neutral pion production selection at the NOvA (numi offaxis electron neutrino appearance) near detector using prong level convolutional neural networks
(Wichita State University, 201805)The NONA neutrino experiment based in Fermilab is designed to measure ! e neutrino oscillations. This experiment will give us insight into the properties of massive neutrinos. Neutral current (NC) ;e neutral pion ... 
Monochromatic molecular absorption coefficients for use in calculations of stellar opacity
(Wichita State University, 201805)In order to fully understand stellar structure, it is necessary to know the opacity, as it influences the behavior of radiative transfer within the stellar interior. Opacity plays an important role in the onset of ... 
Strict Whitney arcs and tquasi selfsimilar arcs
(Wichita State University, 201805)A connected compact subset E of RN is said to be a strict Whitney set if there exists a realvalued C1 function f on RN with ∇f E ≡ 0 such that f is constant on no nonempty relatively open subsets of E. We prove that ... 
Computation of plane potential flow past multielement airfoils using conformal mapping, revisited
(Wichita State University, 201805)Calculations of potential ow and pressure over multielement airfoils are studied, using conformal maps. A composition of classical KarmanTre tz maps is used to smooth out the trailing edge corners successively, from ... 
Scalar and vector tomography for the weighed transport equation
(Wichita State University, 201805)This dissertation is embargoed to May 2019. 
Pluripolar hulls and convergence sets
(Wichita State University, 201805)The pluripolar hull of a pluripolar set E in Pn is the intersection of all complete pluripolar sets in Pn that contain E. We prove that the pluripolar hull of each compact pluripolar set in Pn is F . The convergence set ... 
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 ... 
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 ... 
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 ... 
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 ...