Browsing by Thesis Department "Mathematics (MU)"
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Convergence of an infinite series
(University of Missouri, 1902)This thesis gives some of the more important tests for the convergence of an infinite series; also the conditions that must be fulfilled in order that certain operations and transformations may be applied to an infinite series. 
Convergence of infinite series
(University of Missouri, 1900)We shall define an infinite series as a succession of series formed after sum definite law. Most generally the series are actual numbers or are at least regarded as constraints, and we are concerned with their sum. There ... 
Counterexamples to Strichartz Type Inequalities
(University of MissouriColumbia, 2013)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] The study of Strichartz s inequality is very important in the theory of nonlinear Shrodinger equations. The inequalities do not hold for all choice of ... 
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 ... 
Definition of improper groups by means of axioms : a dissertation
(University of Missouri, 1906)Essentially, a group is an associative field, in which the inverse combinations are uniquely possible. This is a concise statement of the classical definition of a group. The conditions which it connotes will be used here ... 
Dichotomy theorems for evolution equations
(University of MissouriColumbia, 2008)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] In the first part of this work, under minimal assumptions, we characterize the Fredholm property and compute the Fredholm index of abstract differential ... 
Directional timefrequency analysis with applications
(University of MissouriColumbia, 2006)The purpose of this dissertation is to introduce a new directionallysensitive time frequency representation of a function. It is shown that we may break up a function (or signal) into individual timefrequencydirection ... 
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 ... 
Distributional estimates for multilinear operators
(University of MissouriColumbia, 2005)We prove that if a multilinear operator and all its adjoints map L1 x x L1 to L1/m,oo, then the distribution function of the operator applied to characteristic functions of sets of finite measure has exponential decay at ... 
Elliptic curves and their applications in cryptography
(University of MissouriColumbia, 2009)In 1985, Koblitz and Miller proposed elliptic curves to be used for public key cryptosystems. This present thesis examines the role of elliptic curves on cryptography and basic problems involving implementation and security ... 
Endpoint solvability results for divergence form, complex elliptic equations
(University of MissouriColumbia, 2011)We consider divergence form elliptic equations Lu := ∇ • (A∇u) = 0 in the half space ℝn+1+ := {(x,t)∈ ℝn x (0,∞)}, whose coeffi cient matrix A is complex elliptic, bounded and measurable. In addition, we suppose that A ... 
Erdős distance problem in the hyperbolic halfplane
(University of MissouriColumbia, 2009)The Erd̋os distance problem asks for the minimum number of distinct distances determined by large finite point sets in the plane. The aim of this work is to investigate how the classical techniques employed in the study ... 
Errors in graphical methods
(University of Missouri, 1914)The author suggests methods for determining errors in graphical computations and discusses errors in the graphical methods in the infinitesimal calculus. 
The Evans function, the WeylTitchmarsh function, and the BirmanSchwinger operators
(University of MissouriColumbia, 2012)We focus on the spectral stability of travelling wave solutions of partial differential equations. First, we use the GohbergRouche Theorem to prove equality of the algebraic multiplicity of an isolated eigenvalue of an ... 
Existence and construction of realvalued equiangular tight frames
(University of MissouriColumbia, 2009)This paper presents results on realvalued equiangular tight frames (ETFs) and related topics. Some geometric theorems are developed, and aspects of frame theory are used to gain insight into ETFs. We develop a projection ... 
Expectation of pnorm of random matrices with heavy tails
([University of MissouriColumbia], 2014)The pnorm (p > 2) of a random matrix whose entries are gaussian, subgaussian and log concave have been studied previously. We conjecture the following generalization of the above results for heavy tailed random matrices: ... 
Explorations of geometric combinatorics in vector spaces over finite fields
(University of MissouriColumbia, 2008)We study how large a set of points needs to be in a vector space over a finite field in order for the points to determine all of a certain type of geometric structure. In addition we show that there are key differences ... 
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 ... 
An extension of Green's theorem with application
(University of MissouriColumbia, 2008)The main result of this thesis is a generalization of Green's Theorem. Green' s Theorem states: If Omega is an open subset of R[logical and]2 containing a compact subset K with smooth boundary. Let P and Q be two real ... 
Extension theorems in vector spaces over finite fields
(University of MissouriColumbia, 2008)We study the L[superscript p]  L[superscript r] boundedness of the extension operator associated with algebraic varieties such as nondegenerate quadratic surfaces, paraboloids, and cones in vector spaces over finite fields. ...