Browsing Mathematics and Statistics, Department of by Title
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Smooth Complete Intersections with PositiveDefinite Intersection Form
(20121016)We classify the smooth complete intersections with positivedefinite intersection form on their middle cohomology. There are two families. The first family are quadric hypersurfaces in P(4k+1) with k a positive integer. ... 
Sobolev Gradient Flows and Image Processing
(20100825)In this thesis we study Sobolev gradient flows for PeronaMalik style energy functionals and generalizations thereof. We begin with first order isotropic flows which are shown to be regularizations of the heat equation. ... 
Some Advances in the Multitaper Method of Spectrum Estimation
(20090209)Four contributions to the multitaper method of applied spectrum estimation are presented. These are a generalization of the multitaper method of spectrum estimation to timeseries possessing irregularly spaced ... 
Special values of Lseries, periodic coefficients and related themes
This thesis is centered around the theme of special values of Lfunctions and other infinite series, which are often expected to be transcendental numbers. More specifically, we focus on the following two questions in ... 
Stability of Agreement in Statedependent Interaction Environments
(20130702)We study stochastic stability for a class of agreement dynamics and define two forms of agreement which we call stochastic agreement and stochastic absolute agreement. We identify conditions for a broad class of random, ... 
Statistical Inference for the Treatment Effect in Cancer Clinical Trials
(20110525)Randomized clinical trials provide the best evidence on the effect of treatment studied. There are different types of measures on the treatment effect, depending on the endpoints of the trials. For a given measure, based ... 
Statistical Inferences of TwoStage Phase II Cancer Clinical Trials with Two Coprimary Endpoints
In cancer research, twostage designs are usually used to assess the eﬀect of a new agent in phase II clinical trials. The optimal twostage designs with two coprimary endpoints have been proposed to assess the eﬀects ... 
Statistical Methods For Biomarker Threshold Models in Clinical Trials
In clinical trials, the main objective is to investigate the treatment effects on patients. However, many molecularly targeted drugs or treatments tend to benefit a subset of patients more, identified by a certain biomarker. ... 
Statistical Methods for Testing TreatmentCovariate Interactions in Cancer Clinical Trials
(20110927)Treatment–covariate interaction is often used in clinical trials to assess the homogeneity of treatment effects over these subgroups defined by a baseline covariate, which is frequently conducted after primary analysis ... 
Statistical Modeling and Analysis for Survival Data with a Cure Fraction
(20120126)The analysis of survival data with a possible cure fraction has attracted much interest in the last two decades. Various models and estimating methods have been proposed for such data and they have been applied in many ... 
Symmetric Gaussian Rearrangement with Applications to Gaussian Noise Stability
We introduce a new symmetric Gaussian rearrangement that applies to sets and functions which are invariant with respect to a given finite subgroup of the orthogonal group. The properties of this rearrangement are developed, ... 
Symmetry Transforms, Global Plasma Equilibria and Homotopy Analysis Method
(20100825)Magnetohydrodynamics (MHD) flows and equations have been the focus of a large number of researchers. Here a study of such flows and equations is presented. The first chapter contains a brief introduction to Homotopy ... 
The Tate Conjectures for Product and Quotient Varieties
(20130924)This thesis extends Tate’s conjectures from the smooth case to quotient varieties. It shows that two of those conjectures hold for quotient varieties if they hold for smooth projective varieties. We also consider arbitrary ... 
Tilting objects in derived categories of equivariant sheaves
(20080905)We construct classical tilting objects in derived categories of equivariant sheaves on quasiprojective varieties, which give equivalences with derived categories of modules over algebras. Our applications include a ... 
Topics in Combinatorics and Random Matrix Theory
(20090927)Motivated by the longest increasing subsequence problem, we examine sundry topics at the interface of enumerative/algebraic combinatorics and random matrix theory. We begin with an expository account of the increasing ... 
Topics related to vector bundles on abelian varieties
(20130625)This thesis is comprised of three logically independent parts. As the title suggests, each part is related to vector bundles on abelian varieties. We first use BrillNoether theory to study the geometry of a general ... 
Towards F=ma in a general setting for Lagrangian mechanics
(1998)By using a suitably general definition of a force, one may geometrically cast the EulerLagrange equations in a ``force balance'' form. The key ingredient in such a construction is the EulerLagrange 2force which is a ... 
Transcendence of Various Infinite Series and Applications of Baker's Theorem
(20091113)We consider various infinite series and examine their arithmetic nature. Series of interest are of the form $$\sum_{n =0}^{\infty} \frac{f(n)A(n)}{B(n)}, \;\;\;\; \sum_{n \in \mathbb{Z}}\frac{f(n)A(n)}{B(n)}, \;\;\;\; ... 
The twovariable Artin conjecture and elliptic analogues
In 1927, Emil Artin conjectured that for any integer a other than 1 or squares, the set of primes p for which a is a primitive root modulo p has positive density in the set of all primes. This was proven subject to the ... 
Unstable Brake Orbits in Symmetric Hamiltonian Systems
(20130925)In this thesis we investigate the existence and stability of periodic solutions of Hamiltonian systems with a discrete symmetry. The global existence of periodic motions can be proven using the classical techniques of ...