Browsing Theses (MU) by Thesis Department "Mathematics"
Now showing items 111 of 11

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 ... 
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 ... 
Groupoids and semigroupoids
(University of MissouriColumbia, 2013)The theory of semigroupoids and groupoids makes the transition between arbitrary sets and groups. The usefulness of developing theory stems from various applications where a group structure is lacking, yet there exists ... 
The implicit function theorem for Lipschitz functions and applications
(University of MissouriColumbia, 2008)The subject matter of this thesis is the classical Implicit Function Theorem and its generalizations. Dictated by practical applications, it is of interest to relax the hypothesis of the standard Implicit Function Theorem ... 
Incorporation of directionally dependent diffusion with polymer composite flow theory
(University of MissouriColumbia, 2006)The extensive industrial use of shortfiber reinforced polymer composites demands an accurate understanding of fiber orientation kinematics. There is a growing concern in recent literature with the popular Folgar and Tucker ... 
A priori estimates for solutions of elliptic partial differential equations on surfaces
(University of MissouriColumbia, 2009)Let S be an (n1)dimensional bounded surface of class C² in R[real number] [superscript n] and let [set theory][subscript s] be the LaplaceBeltrami operator on S. In this thesis, under suitable geometric assumptions, we ... 
Quasimetric geometry: smoothness and convergence results
(University of MissouriColumbia, 2011)This thesis has two distinct yet related parts, the first pertaining to geometry on quasimetric spaces with emphasis on the Hausdorff outermeasure, the natural extension of the GromovPompeiuHausdorff distance to ... 
Results in analytic and algebraic number theory
(University of MissouriColumbia, 2012)The thesis begins with proving some theorems about Gauss sums and Jacobi sums. Using theorems the first chapter ends with a proof that if p is a prime such that p ≡ 1 (mod 4), then there are integers a and b such that p ... 
Surface to surface changes of variables and applications
(University of MissouriColumbia, 2008)The present thesis addresses a number of basic problems in relation to integration over surfaces in the Euclidean space, such as how the surface measure and unit normal changes under a smooth diffeomorphism how the integration ... 
Topics in harmonic analysis and partial differential equations: extension theorems and geometric maximum principles
(University of MissouriColumbia, 2011)The present thesis consists of two main parts. In the first part, we prove that a function defined on a closed subset of a geometrically doubling quasimetric space which satisfies a Höldertype condition may be extended ... 
Topics in LittlewoodPaley theory and BMO
(University of MissouriColumbia, 2012)In this thesis we discuss some important results in LittlewoodPaley theory and the space of BoundedMean Oscillation functions, henceforth called BMO. LittlewoodPaley Theory has its roots in the LittlewoodPaley Theorem, ...