Now showing items 59-78 of 107

• #### Nonholonomic Euler-Poincaré equations and stability in Chaplygin's sphere ﻿

(2000)
A method of reducing several classes of nonholonomic mechanical systems that are defined on semidirect products of Lie groups is developed. The method reduces the Lagrange-d'Alembert principle to obtain a reduced constrained ...
• #### Novel uses of the Mallows model in coloring and matching ﻿

A natural model of a highly ordered random ranking is the Mallows model. Disorder is measured by the number of inversions; these are pairs of elements whose order is reversed. The Mallows model assigns to each ranking of ...
• #### On f-vectors of polytopes and matroids ﻿

The f-vector of a simplicial complex is a fundamental invariant that counts the number of faces in each dimension. A natural question in the theory of simplicial complexes is to understand the relationship between the ...
• #### 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 Selmer groups and factoring p-adic L-functions ﻿

Samit Dasgupta has proved a formula factoring a certain restriction of a 3-variable Rankin-Selberg p-adic L-function as a product of a 2-variable p-adic L-function related to the adjoint representation of a Hida family and ...
• #### 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 T-Semisimplicity of Iwasawa Modules and Some Computations with Z3-Extensions ﻿

For certain Zp-extensions of abelian number fields, we study the Iwasawa module associated to the ideal class groups. We show that generic Zp-extensions of abelian number fields are T-semisimple. We also construct the ...
• #### On the g2-number of various classes of spheres and manifolds ﻿

For a $(d-1)$-dimensional simplicial complex $\Delta$, we let $f_i=f_i(\Delta)$ be the number of $i$-dimensional faces of $\Delta$ for $-1\leq i\leq d-1$. One classic problem in geometric combinatorics is the following: ...
• #### On the Geometry of Rectifiable Sets with Carleson and Poincare-type inequlaities ﻿

A central question in geometric measure theory is whether geometric properties of a set translate into analytical ones. In 1960, E. R. Reifenberg proved that if an $n$-dimensional subset $M$ of $\mathbb{R}^{n+d}$ is well ...
• #### 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 Algebraic Vision ﻿

This thesis studies several fundamental mathematical problems that arise from computer vision using techniques in algebraic geometry and optimization. Chapters 2 and 3 consider the fundamental question of the existence of ...
• #### 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 ...