Search
Now showing items 21-40 of 178
Mathematical and computational modeling of fluid flow with applications in ophthalmology and geoscience
(University of Missouri--Columbia, 2020)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Complex systems in our life can be translated to mathematical models whose solutions can help us to predict the behavior of the system. Disease in eye ...
Adams inequalities with exact growth condition : on Rn and the Heisenberg group
(University of Missouri--Columbia, 2020)
In this thesis we prove sharp Adams inequality with exact growth condition for the Riesz potential as well as the more general strictly Riesz-like potentials on R[superscript n]. Then we derive the Moser-Trudinger type ...
Applied problems in frame theory
(University of Missouri--Columbia, 2019)
This thesis is a study of two applied problems in frame theory: phase retrieval and quantum detection. These problems are inspired by engineering applications in signal processing and information theory. ... The goal of ...
Capillary-gravity water waves with vorticity : steady wind-driven waves and waves with a submerged dipole
(University of Missouri--Columbia, 2019)
In this thesis, we study two mathematical problems on water waves in the setting of the incompressible Euler equations with vorticity, gravity, and surface tension. We investigate the existence of small-amplitude steady ...
Phase retrieval in frame theory
(University of Missouri--Columbia, 2020)
This dissertation is the study of phase retrieval in frame theory. The first part is concerned with the analysis of phase retrieval and the complete classification of norm retrieval. Norm retrieval is essential to transfer ...
Structural features of persistent homology and their algorithmic transformations
(University of Missouri--Columbia, 2021)
We re-examine the theory and orthodox methods that underlie the study of persistent homology, particularly in its calculation of homological cycle representatives that are associated to persistence diagrams. A common ...
Global bifurcation and stability of solitary waves in two-layer water
(University of Missouri--Columbia, 2022)
The present work concerns two mathematical problems on wave in a stratified body of water governed by the incompressible Euler equations. In the first part, we present a large-amplitude existence theory for two-dimensional ...
Elliptic curves and their applications in cryptography
(University of Missouri--Columbia, 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 ...
A class of Gorenstein Artin algebras of embedding dimension four
(University of Missouri--Columbia, 2007)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Let R be a polynomial ring in n variables and I be a homogeneous ideal in R. Such an ideal I is called Gorenstein if the quotient R/I has a free ...
Applications of the fourier transform to convex geometry
(University of Missouri--Columbia, 2006)
The thesis is devoted to the study of various problems arising from Convex Geometry and Geometric Functional Analysis using tools of Fourier Analysis. In chapters two through four we consider the Busemann-Petty problem and ...
Complex and almost-complex structures on six dimensional manifolds
(University of Missouri--Columbia, 2006)
We investigate the properties of hypothetical exotic complex structures on three dimensional complex projective space CP³. This is motivated by the long standing question in differential geometry of whether or not the six ...
Trace formulae in finite von Neumann algebras
(University of Missouri--Columbia, 2007)
The dissertation is devoted to some aspects of spectral perturbation theory in the context of finite Von Neumann algebras. The central results are analogs of the Birman-Schwinger principle and the Birman-Krein formula for ...
Quasi-metric geometry : smoothness and convergence results
(University of Missouri--Columbia, 2011)
This thesis has two distinct yet related parts, the first pertaining to geometry on quasi-metric spaces with emphasis on the Hausdorff outer-measure, the natural extension of the Gromov-Pompeiu-Hausdorff distance to ...
Surface to surface changes of variables and applications
(University of Missouri--Columbia, 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 ...
Asymptotic unconditionality in Banach spaces
(University of Missouri--Columbia, 2009)
We show that a separable real Banach space embeds almost isometrically in a space [Upsilon] with a shrinking 1-unconditional basis if and only if lim [subscript n] [subscript arrow] [subscript infinity] [norms] [chi] [group ...
Oscillators : resonances and excitations
(University of Missouri--Columbia, 2009)
This thesis is a compilation of work done in the field of oscillators. One topic is an investigation into impact oscillators and their properties. The second topic is concerned with excitation of oscillators. The thesis ...
Approximate isometries and distortion energy functionals
(University of Missouri--Columbia, 2009)
A fundamental problem in Riemannian Geometry and related areas is to determine whether two diffeomorphic compact Riemannian manifolds (M, [subscript g][subscript M]) and (N, [subscript g][subscript N]) are isometric; that ...
Topics in geometric analysis with applications to partial differential equations
(University of Missouri--Columbia, 2009)
The main aim of the current thesis is to investigate the mathematical tools and methods used to study problems which bridge between analysis and geometry. Such an undertaking is particularly useful in situations in which ...
Seiberg-Witten invariants on 3-manifolds with an orientation reversing involution
(University of Missouri--Columbia, 2009)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] This work is devoted to the study of Seiberg-Witten theory for three dimensional manifolds in the presence of involutions. G. Tian and S.Wang explored ...
A transition matrix for two bases of the integral cohomology of the Hilbert scheme of points in the projective plane
(University of Missouri--Columbia, 2010)
This work is devoted to comparing two integral bases for the integral cohomology of the Hilbert scheme of points in the projective plane. Let X be a smooth complex projective surface. One of the more interesting moduli ...