Now showing items 48-67 of 152

• #### Geometric Jacobian Linearization ﻿

(2007-12-21)
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: second-order 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 ﻿

(2016-07-05)
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 Gibbs-Appell equations and Gauss's Principle of Least Constraint ﻿

(1995)
We present a generalisation of the Gibbs-Appell equations which is valid for general Lagrangians. The general form of the Gibbs-Appell 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 second-order differential equation whose right-hand side ...
• #### Global Fluctuations of Random Matrices and the Second-Order Cauchy Transform ﻿

In this thesis we study the global fluctuations of random matrices (i.e., the covariance of two traces) from a second-order 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 edge-weighted bipartite graphs ﻿

(2010-07-28)
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 ﻿

(2010-12-23)
We study the Hamiltonian structure of an important class of nonlinear partial differential equations: the so-called systems of hydrodynamic type, which are first-order in tempo-spatial variables, and quasi-linear. Chapters ...
• #### High-order variations for families of vector fields ﻿

(2002)
Sufficient conditions involving Lie brackets of arbitrarily high-order are obtained for local controllability of families of vector fields. After providing a general framework for the generation of high-order ...
• #### High-Q Spectral Peaks and Nonstationarity in the Deep Ocean Infragravity Wave Band: Tidal Harmonics and Solar Normal Modes ﻿

(Wiley, 2019-02-20)
Infragravity waves have received the least study of any class of waves in the deep ocean. This paper analyzes a 389-day-long deep ocean pressure record from the Hawaii Ocean Mixing Experiment for the presence of narrowband ...
• #### Higher rank sieves and applications ﻿

(2016-04-25)
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 ﻿

(2013-09-17)
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 Digital-Analog Source-Channel Coding and Information Hiding: Information-Theoretic Perspectives ﻿

(2007-10-02)
Joint source-channel coding (JSCC) has been acknowledged to have superior performance over separate source-channel 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 ﻿

(2016-09-22)
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 ﻿

(2012-10-04)
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 ...
• #### Information and Estimation Theoretic Approaches to Data Privacy ﻿

Warner [145] in 1960s proposed a simple mechanism, now referred to as the randomized response model, as a remedy for what he termed “evasive answer bias” in survey sampling. The randomized response setting is as follows: ...
• #### Instability of Periodic Orbits of Some Rhombus and Parallelogram Four Body Problems ﻿

(2012-11-27)
The rhombus and parallelogram orbits are interesting families of periodic solutions, which come from celestial mechanics and the N-body problem. Variational methods with finite order symmetry group are used to construct ...
• #### Invariants of Modular Two-Row Groups ﻿

(2009-10-06)
It is known that the ring of invariants of any two-row group is Cohen-Macaulay. This result inspired the conjecture that the ring of invariants of any two-row group is a complete intersection. In this thesis, we study ...