Department of Mathematics (MU)
Faculty members in MU’s Department of Mathematics are actively engaged in research in both theoretical and applied mathematics. With a wide range of research interests, they prepare students for careers in teaching, medicine, scientific research, business, finance and a host of other fields. Working side by side with students, faculty members stress learning how to learn and keep up with the future of mathematics. With 39 regular faculty members working in a variety of fields, the department provides a comprehensive understanding of mathematics. The faculty’s research and teaching are supported by postdoctoral fellows and visiting faculty.
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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, ... 
Locally semisimple representations of quivers
(University of MissouriColumbia, 2016)In this dissertation, we solve a conjecture raised by Victor Kac in 1982 concerning the socalled locally semisimple representations of quivers. 
CalderonZygmund theory for singular integral operators associated with secondorder elliptic partial differential systems on rough subdomains of Riemannian manifolds
(University of MissouriColumbia, 2016)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] This dissertation is a treatise on the theory of CalderonZygmund 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 MissouriColumbia, 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 MissouriColumbia, 2016)The purpose of this thesis is to study stability of onedimensional traveling waves and multidimensional planar fronts as well as spaceindependent steady states for a class of reaction diffusion systems that arise in ... 
Maximal Fourier integrals and multilinear multiplier operators
(University of MissouriColumbia, 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 MissouriColumbia, 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 semigroups and their gradients, and then we get Lp bounds for ... 
Weak Hardy spaces and paraproducts
(University of MissouriColumbia, 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 MissouriColumbia, 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 ...