Browsing Mathematics and Statistics, Department of by Title
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Generalization of Ruderman's Problem to Imaginary Quadratic Fields
(20120413)In 1974, H. Ruderman posed the following question: If $(2^m2^n)(3^m3^n)$, then does it follow that $(2^m2^n)(x^mx^n)$ for every integer $x$? This problem is still open. However, in 2011, M. R. Murty and V. K. Murty ... 
Geodesic reduction via frame bundle geometry
(20070725)Reduction theory for systems with symmetry deals with the problem of understanding dynamics on a manifold with an action of a Lie group. In geometric mechanics, this problem can be formulated in the Lagrangian, Hamiltonian ... 
A Geometric Approach to Energy Shaping
(20090902)In this thesis is initiated a more systematic geometric exploration of energy shaping. Most of the previous results have been dealt wih particular cases and neither the existence nor the space of solutions has been discussed ... 
Geometric Jacobian Linearization
(20071221)For control systems that evolve on Euclidean spaces, Jacobian linearization is a common technique in many control applications, analysis, and controller design methodologies. However, the standard linearization method ... 
Geometric local controllability: secondorder conditions
(2002)In a geometric point of view, a nonlinear control system, affine in the controls, is thought of as an affine subbundle of the tangent bundle of the state space. In deriving conditions for local controllability from ... 
Geometric sliding mode control: The linear and linearised theory
(2002)The idea of sliding mode control for stabilisation is investigated to determine its geometric features. A geometric definition is provided for a sliding submanifold, and for various properties of a sliding submanifold. Sliding ... 
Geometry of Dirac Operators
(20160705)Let $M$ be a compact, oriented, even dimensional Riemannian manifold and let $S$ be a Clifford bundle over $M$ with Dirac operator $D$. Then \[ \textsc{Atiyah Singer: } \quad \text{Ind } \mathsf{D}= \int_M ... 
The geometry of the GibbsAppell equations and Gauss's Principle of Least Constraint
(1995)We present a generalisation of the GibbsAppell equations which is valid for general Lagrangians. The general form of the GibbsAppell equations is shown to be valid in the case when constraints and external forces ... 
The geometry of the maximum principle for affine connection control systems
(2000)The maximum principle of Pontryagin is applied to systems where the drift vector field is the geodesic spray corresponding to an affine connection. The result is a secondorder differential equation whose righthand side ... 
Global Fluctuations of Random Matrices and the SecondOrder Cauchy Transform
In this thesis we study the global fluctuations of random matrices (i.e., the covariance of two traces) from a secondorder free probability perspective, putting a particular emphasis on block Gaussian matrices. Our main ... 
Group structures in a class of control systems
(1992)We investigate two classes of control systems, one of Brockett and one of Murray and Sastry. We are able to show that these two systems may be formulated in the language of principle fibre bundles. Controllability of ... 
Hall conditions for edgeweighted bipartite graphs
(20100728)A weighted variant of Hall's condition for the existence of matchings is shown to be equivalent to the existence of a matching in a lexicographic product. This is used to introduce characterizations of those bipartite ... 
Hamiltonian Systems of Hydrodynamic Type
(20101223)We study the Hamiltonian structure of an important class of nonlinear partial differential equations: the socalled systems of hydrodynamic type, which are firstorder in tempospatial variables, and quasilinear. Chapters ... 
Highorder variations for families of vector fields
(2002)Sufficient conditions involving Lie brackets of arbitrarily highorder are obtained for local controllability of families of vector fields. After providing a general framework for the generation of highorder ... 
HighQ Spectral Peaks and Nonstationarity in the Deep Ocean Infragravity Wave Band: Tidal Harmonics and Solar Normal Modes
(Wiley, 20190220)Infragravity waves have received the least study of any class of waves in the deep ocean. This paper analyzes a 389daylong deep ocean pressure record from the Hawaii Ocean Mixing Experiment for the presence of narrowband ... 
Higher rank sieves and applications
(20160425)This thesis focuses on some of the key sieve theoretic ideas behind recent progress on bounded gaps between the primes. One such idea is the notion of higher rank sieve weights, first proposed by Atle Selberg and applied ... 
Homoclinic Points in the Composition of Two Reflections
(20130917)We examine a class of planar area preserving mappings and give a geometric condition that guarantees the existence of homoclinic points. To be more precise, let $f,g:R \to R$ be $C^1$ functions with domain all of $R$. ... 
Hybrid DigitalAnalog SourceChannel Coding and Information Hiding: InformationTheoretic Perspectives
(20071002)Joint sourcechannel coding (JSCC) has been acknowledged to have superior performance over separate sourcechannel coding in terms of coding efficiency, delay and complexity. In the first part of this thesis, we study ... 
An impulsive differential equation model for Marek's disease
(20160922)Many dynamical processes are subject to abrupt changes in state. Often these perturbations can be periodic and of short duration relative to the evolving process. These types of phenomena are described well by what are ... 
Inclusive Fitness on Evolutionary Graphs
(20121004)The evolution of cooperative behaviours has received a large amount of attention in the literature. A recurrent result is that a spatial population structure often aids the evolution of cooperation. One such possible ...