Mathematics electronic theses and dissertations (MU)
The items in this collection are the theses and dissertations written by students of the Department of Mathematics. Some items may be viewed only by members of the University of Missouri System and/or University of MissouriColumbia. Click on one of the browse buttons above for a complete listing of the works.
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Asymptotic properties of deep water solitary waves with compactly supported vorticity
(University of MissouriColumbia, 2018)In this thesis, we consider two and threedimensional gravity and capillarygravity solitary waves propagating along the surface of a body of water with infinite depth.The waves are acted upon by gravity and we allow the ... 
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, ... 
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)We establish conditions on the Hamiltonian evolution of interacting molecules that imply hydrodynamic equations at the limit of infinitely many molecules and show that these conditions are satisfied whenever the solutions ... 
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 aEuler 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 · ?)u in the classical ... 
Largeamplitude solitary water waves with discontinuous vorticity
(University of MissouriColumbia, 2017)Consider a twodimensional body of water with constant density which lies below a vacuum. The ocean bed is assumed to be impenetrable, while the boundary which separates the uid and the vacuum is assumed to be a free ... 
Topics in spectral theory of differential operators
(University of MissouriColumbia, 2017)This dissertation is devoted to two eigenvalue counting problems: Determining the asymptotic behavior of large eigenvalues of selfadjoint extensions of partial differential operators, and computing the number of negative ... 
A sublinear version of the Schur Test and weighted norm inequalities
(University of MissouriColumbia, 2017)In this thesis, we study the sublinear elliptic equations of the form (?u  u qs = 0 s  a.e. on ? u = 0 on ??, where 0 greater than q less than 1 and s is a positive Borel measure on ?. Our results show that, under ... 
Outer products and frame coefficients
(University of MissouriColumbia, 2017)In this dissertation, we will examine two distinct areas of frame theory. The first will be the area of outer products. In particular, we will examine the spanning and independence properties of the collection {fif * i ... 
Harmonic functions and the Dirichlet problem
(University of MissouriColumbia, 2017)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Let ? be an open and connected subset of the complex plane. A real valued function u : ? ? R is said to be harmonic if it has continuous first and ... 
Conformal mappings and the SchwarzChristoffel transformation
(University of MissouriColumbia, 2017)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Let ? be an open and connected set in the complex plane. A mapping f : ? ? C is said to be conformal at a point z0 if it preserves angles and orientation ... 
Uniform bounds in ffinite rings and their applications
(University of MissouriColumbia, 2017)This dissertation establishes uniform bounds in characteristic p rings which are either Ffinite or essentially of finite type over an excellent local ring. These uniform bounds are then used to show that the HilbertKunz ... 
Perinormality in Polynomial and ModuleFinite Ring Extensions
(University of MissouriColumbia, 2017)In this dissertation we investigate some open questions posed by Epstein and Shapiro in [9] regarding perinormal domains. More specifically, we focus on the ascent/descent property of perinormality between "canonical" ... 
Exponential sums, character sums, sieve methods and distribution of prime numbers
(University of MissouriColumbia, 2017)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] This thesis is focus on the methods of exponential sums and sieve methods applying to distribution of primes numbers in several forms, such as ... 
Integration by parts formulas for higher order operators and applications to boundary value problems
(University of MissouriColumbia, 2016)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Green formulas for differential operators are important tools in the study of Partial Differential Equations. The first such formula, published in 1828, ...