RSS 1.0Mathematics 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 Missouri-Columbia. Click on one of the browse buttons above for a complete listing of the works.
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Counting theorems and inverse function theorems for analytic functions
(University of Missouri--Columbia, 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 a-Euler equations
(University of Missouri--Columbia, 2017)We study stability and instability of time independent solutions of the two dimensional a-Euler equations and Euler equations; the a-Euler equations are obtained by replacing the nonlinear term (u · ?)u in the classical ... -
Large-amplitude solitary water waves with discontinuous vorticity
(University of Missouri--Columbia, 2017)Consider a two-dimensional 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 Missouri--Columbia, 2017)This dissertation is devoted to two eigenvalue counting problems: Determining the asymptotic behavior of large eigenvalues of self-adjoint extensions of partial differential operators, and computing the number of negative ... -
A sublinear version of the Schur Test and weighted norm inequalities
(University of Missouri--Columbia, 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 Missouri--Columbia, 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 Missouri--Columbia, 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 Schwarz-Christoffel transformation
(University of Missouri--Columbia, 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 f-finite rings and their applications
(University of Missouri--Columbia, 2017)This dissertation establishes uniform bounds in characteristic p rings which are either F-finite or essentially of finite type over an excellent local ring. These uniform bounds are then used to show that the Hilbert-Kunz ... -
Perinormality in Polynomial and Module-Finite Ring Extensions
(University of Missouri--Columbia, 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 Missouri--Columbia, 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 Missouri--Columbia, 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, ... -
Locally semi-simple representations of quivers
(University of Missouri--Columbia, 2016)In this dissertation, we solve a conjecture raised by Victor Kac in 1982 concerning the so-called locally semi-simple representations of quivers. -
Calderon-Zygmund theory for singular integral operators associated with second-order elliptic partial differential systems on rough subdomains of Riemannian manifolds
(University of Missouri--Columbia, 2016)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] This dissertation is a treatise on the theory of Calderon-Zygmund type singular integral operators capable of handling boundary layer potentials arising ... -
Properties of frames and relationships between them with emphasis on subframes and unconditional convergence
(University of Missouri--Columbia, 2016)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] -
Stability of planar fronts for a class of reaction diffusion systems
(University of Missouri--Columbia, 2016)The purpose of this thesis is to study stability of one-dimensional traveling waves and multidimensional planar fronts as well as space-independent steady states for a class of reaction diffusion systems that arise in ... -
Maximal Fourier integrals and multilinear multiplier operators
(University of Missouri--Columbia, 2016)The first topic of this dissertation is concerned with the L^2 boundedness of a maximal Fourier integral operator which arises by transferring the spherical maximal operator on the sphere S^n to a Euclidean space of the ... -
The Dirichlet problem for elliptic and degenerate elliptic equations, and related results
(University of Missouri--Columbia, 2016)In this thesis, we first prove the solvability of Dirichlet problem with Lp data on the boundary for degenerate elliptic equations. Second, We obtain Lp bounds semi-groups and their gradients, and then we get Lp bounds for ... -
Weak Hardy spaces and paraproducts
(University of Missouri--Columbia, 2016)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] The purpose of this dissertation is to provide a new square function characterization of weak Hardy spaces in the full range of exponents possible and ... -
Some results in convex geometry
(University of Missouri--Columbia, 2016)This thesis is divided into four parts. The first part is about proving that the unit ball of the Lorentz space is not an intersection body for dimension greater than or equal to 5 and q > 2. We go on to explain the ...