Mathematics electronic theses and dissertations (MU): Recent submissions
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Weak phase retrieval and phaseless reconstruction
(2019)Phase retrieval and phaseless reconstruction for Hilbert space frames is a very active area of research. Recently, it was shown that these concepts are equivalent. In this thesis, we make a detailed study of a weakening ... 
Capillarygravity water waves with vorticity : steady winddriven waves and waves with a submerged dipole
(2019)In this thesis, we study two mathematical problems on water waves in the setting of the incompressible Euler equations with vorticity, gravity, and surface tension. We investigate the existence of smallamplitude steady ... 
Applied problems in frame theory
(2019)This thesis is a study of two applied problems in frame theory: phase retrieval and quantum detection. These problems are inspired by engineering applications in signal processing and information theory. ... The goal of ... 
The vanishing of the chow cohomology ring for affine toric varieties and additional results
(2019)From the recent work of Edidin and Satriano, given a good moduli space morphism between a smooth Artin stack and its good moduli space X, they prove that the Chow cohomology ring of X embeds into the Chow ring of the stack. ... 
Absolute continuity of parabolic measure and the initialdirichlet problem
(2019)This thesis is devoted to the study of parabolic measure corresponding to a divergence form parabolic operator. We first extend to the parabolic setting a number of basic results that are well known in the elliptic case. ... 
Shapleylike values without symmetry
(2019)Following the work of Shapley on the Shapley value [16], and further work of Owen [14], we offer an alternative formulation of and path to and through the work of Weber in his paper on efficient but not symmetric cooperative ... 
Potential theory methods for some nonlinear elliptic equations
(University of MissouriColumbia, 2018)This dissertation presents a unified approach via potential theory for solvability of a class of nonlinear elliptic equations. 
Effective numerical methods to model dynamic behavior of springs with torsion
(University of MissouriColumbia, 2018)The purpose of this thesis is to find effective algorithms to numerically solve certain systems of differential equations that arise from standard Newtonian mechanics. Numerical models of elastica has already been well ... 
Frames and subspaces
(University of MissouriColumbia, 2018)This thesis will consist of three parts. In the first part we find the closest probabilistic Parseval frame to a given probabilistic frame in the 2 Wasserstein Distance. It is known that in the traditional [symbol]2 distance ... 
Asymptotic properties of deep water solitary waves with compactly supported vorticity
(University of MissouriColumbia, 2018)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] In this thesis, we consider twoand threedimensional gravity and capillarygravity solitary waves propagating along the surface of a body of water ... 
Persistent homology : categorical structural theorem and stability through representations of quivers
(University of MissouriColumbia, 2018)The purpose of this thesis is to advance the study and application of the field of persistent homology through both categorical and quiver theoretic viewpoints. While persistent homology has its roots in these topics, there ... 
Generating sequences and semigroups of valuations on 2 dimensional normal local rings
(University of MissouriColumbia, 2018)In this thesis we develop a method for constructing generating sequences for valuations dominating the ring of a two dimensional quotient singularity. Suppose that K is an algebraically closed field of characteristic zero, ... 
Generalized littlewoodrichardson coefficients for branching rules of GL(n) and extremal weight crystals
(University of MissouriColumbia, 2018)This thesis is devoted to the combinatorial and geometric study of certain multiplicities, which we call generalized LittlewoodRichardson coefficients. These are sums of products of single LittlewoodRichardson coefficients, ... 
On the global GanGrossPrasad conjecture for general spin groups
(University of MissouriColumbia, 2018)In the 1990s, Benedict Gross and Dipendra Prasad formulated an intriguing conjecture connected with restriction laws for automorphic representations of a particular group. More recently, Gan, Gross, and Prasad extended ... 
Radiation conditions and integral representations for Clifford algebravalued null solutions of the iterated perturbed Dirac operator
(University of MissouriColumbia, 2017)In 1912 Arnold Sommerfeld introduced a special decay condition at infinity to address uniqueness issues for certain boundary value problems involving the Helmholtz operator in an exterior domain. Examples of such boundary ... 
Sequences of rank1 projections and Gabor tight fusion frames
(University of MissouriColumbia, 2017)This dissertation provides new results in two areas. The first part concerns the particular properties that are inherited by a sequence of rank1 projections from the inducing sequence of unitnorm vectors. The second part ... 
On hydrodynamic equations and their relation to kinetic theory and statistical mechanics
(University of MissouriColumbia, 2017)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] We establish conditions on the Hamiltonian evolution of interacting molecules that imply hydrodynamic equations at the limit of infinitely many molecules ... 
On the Euler characteristics of certain moduli spaces of 1dimensional subschemes
(University of MissouriColumbia, 2017)Generalizing the ideas in [LQ] and using virtual Hodge polynomials as well as torus actions, we compute the Euler characteristics of some moduli spaces of 1dimensional closed subschemes when the ambient smooth projective ... 
Counting theorems and inverse function theorems for analytic functions
(University of MissouriColumbia, 2017)In this master's thesis, we discuss the counting and Rouche's theorems. These theorems are used to find the roots of complex analytic functions.Also, we investigate the existence of the inverse function of an analytic ... 
Stability and instability results for the 2D [alpha]Euler equations
(University of MissouriColumbia, 2017)We study stability and instability of time independent solutions of the two dimensional aEuler equations and Euler equations; the aEuler equations are obtained by replacing the nonlinear term (u [times] [del.])u in the ...