Now showing items 45-64 of 151

    • Generalization of Ruderman's Problem to Imaginary Quadratic Fields 

      Rundle, Robert John (2012-04-13)
      In 1974, H. Ruderman posed the following question: If $(2^m-2^n)|(3^m-3^n)$, then does it follow that $(2^m-2^n)|(x^m-x^n)$ 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 

      Bhand, Ajit (2007-07-25)
      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 

      Gharesifard, Bahman (2009-09-02)
      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 

      Tyner, David (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 

      Hirschorn, Ron M.; Lewis, Andrew D. (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 

      Hirschorn, Ron M.; Lewis, Andrew D. (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 

      Beheshti Vadeqan, Babak (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 

      Lewis, Andrew D. (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 

      Lewis, Andrew D. (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 

      Diaz Torres, Mario
      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 

      Lewis, Andrew D. (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 

      Gregory, David (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 

      Reynolds, A. Patrick (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 

      Hirschorn, Ron M.; Lewis, Andrew D. (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 

      Chave, Alan D.; Luther, Douglas S.; Thomson, David J. (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 

      Vatwani, Akshaa (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 

      Jensen, Erik (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 

      Wang, Yadong (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 

      Rozins, Carly (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 

      Maciejewski, Wesley (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 ...