Now showing items 49-68 of 82

• #### On numerics and inverse problems ﻿

In this thesis, two projects in inverse problems are described. The first concerns a simple mathematical model of synthetic aperture radar with undirected beam, modeled as a 2D circular Radon transform with centers restricted ...
• #### On Particle Interaction Models ﻿

(2014-02-24)
This dissertation deals with three problems in Stochastic Analysis which broadly involve interactions, either between particles (Chapters 1 and 2), or between particles and the boundary of a C2 domain (Chapter 3). In Chapter ...
• #### On singularities of generic projection hypersurfaces ﻿

(2006)
The present work studies singularities of hypersurfaces arising from generic projections of smooth projective varieties, in the context of Du Bois and semi log canonical singularities. It is demonstrated that Du Bois ...
• #### On special Lagrangian equations ﻿

(2014-02-24)
In this paper we study the special Lagrangian equation and related equations. Special Lagrangian equation originates in the special Lagrangian geometry by Harvey-Lawson [HL1]. In subcritical phases, we construct singular ...
• #### On the mod 2 general linear group homology of totally real number rings ﻿

(1997)
We study the mod 2 homology of the general linear group of rings of integers in totally real number fields. In particular, for certain such rings R, we construct a space JKR and show that the mod 2 homology of JKR is a ...
• #### The Ornstein-Uhlenbeck Process In Neural Decision-Making: Mathematical Foundations And Simulations Suggesting The Adaptiveness Of Robustly Integrating Stochastic Neural Evidence ﻿

(2013-02-25)
This master's thesis reviews the concepts behind a stochastic process known as the Ornstein-Uhlenbeck Process, and then uses that process as a way to investigate neural decision making. In particular, MATLAB simulations ...
• #### Path algebras and monomial algebras of finite GK-dimension as noncommutative homogeneous coordinate rings ﻿

This thesis sets out to understand the categories QGr A where A is either a monomial algebra or a path algebra of finite Gelfand-Kirillov dimension. The principle questions are: \begin{enumerate} \item What is the structure ...
• #### Permutation diagrams in symmetric function theory and Schubert calculus ﻿

A fundamental invariant of a permutation is its inversion set, or diagram. Natural machinery in the representation theory of symmetric groups produces a symmetric function from any finite subset of <bold>N</bold><super>2</super>, ...
• #### Polynomials in Multiview Geometry ﻿

(2013-04-17)
We study multiview geometry and some of its applications through the use of polynomials. A three-dimensional world point gives rise to n ≥ 2 two-dimensional projections in n given cameras. The object of focus in this ...
• #### The Positive Semidefinite Rank of Matrices and Polytopes ﻿

The positive semidefinite (psd) rank of a nonnegative <italic>p</italic> × <italic>q</italic> matrix <italic>M</italic> is defined to be the smallest integer <italic>k</italic> such that there exist <italic>k</italic> × ...
• #### Problems in computational algebra and integer programming ﻿

(2007)
This thesis is a compendium of several projects that span the gap between commutative algebra and geometric combinatorics: one in tropical geometry, one in computational algebra, and two in discrete geometry and integer ...
• #### Qualitative stability properties of matrices ﻿

(1985)
A matrix A is sign stable if some matrix with the same sign pattern of positive, negative, and zero entries has all eigenvalues with negative real parts. It is potentially stable if it is not sign unstable. The system A x ...
• #### The Radiative Transfer Equation in Photoacoustic Imaging ﻿

(2013-07-25)
Photoacoustic tomography is a rapidly developing medical imaging technique that combines optical and ultrasound imaging to exploit the high contrast and high resolution of the respective individual modalities. Mathematically, ...
• #### The regularity of Loewner curves ﻿

The Loewner differential equation, a classical tool that has attracted recent attention due to Schramm-Loewner evolution (SLE), provides a unique way of encoding a simple 2-dimensional curve into a continuous 1-dimensional ...
• #### Self-shrinking Solutions to Mean Curvature Flow ﻿

We construct new examples of self-shrinking solutions to mean curvature flow. We first construct an immersed and non-embedded sphere self-shrinker. This result verifies numerical evidence dating back to the 1980's and shows ...
• #### Selmer groups for elliptic curves with isogenies of prime degree ﻿

(2003)
The Mordell-Weil theorem states that the points of an elliptic curve defined over a number field form a finitely generated, abelian group. The rank of this group, generally referred to as the rank of the elliptic curve, ...
• #### Sheaves on support varieties and varieties of elementary subalgebras ﻿

We present several results about two closely related types of objects: the projectivized scheme $\PG$ of one parameter subgroups of an infinitesimal group scheme $G$ and the variety $\bE(\fg)$ of maximal elementary subalgebras ...
• #### Shimura Degrees for Elliptic Curves over Number Fields ﻿

A crowning achievement of Number theory in the 20th century is a theorem of Wiles which states that for an elliptic curve E over <bold>Q</bold> of conductor N, there is a non-constant map from the modular curve of level N ...
• #### Smoothness of Loewner Slits ﻿

(2013-02-25)
In this dissertation, we show that the chordal Loewner differential equation with C^{beta} driving function generates a C^{beta + 1/2} slit for 1/2 < beta <= 2, except when beta = 3/2 the slit is only proved to be weakly C^{1,1}.
• #### Some cohomology of finite general linear groups ﻿

We prove that the degree r(2p − 3) cohomology of any (untwisted) finite group of Lie type over F_(p^r), with coefficients in characteristic p, is nonzero as long as its Coxeter number is at most p. We do this by providing ...