by Sin Yu Tsang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 40-42). / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Two-level structural equation model --- p.5 / Chapter Chapter 3. --- Estimation of the model under general constraints --- p.11 / Chapter Chapter 4. --- Estimation of the model under linear constraints --- p.22 / Chapter Chapter 5. --- Simulation results --- p.27 / Chapter 5.1 --- "Artificial examples for ""modified"" EM algorithm" --- p.27 / Chapter 5.2 --- "Artificial examples for ""restricted"" EM algorithm" --- p.34 / Chapter Chapter 6. --- Discussion and conclusion --- p.38 / References --- p.40 / Tables --- p.43

Thesis (M. Sc.)--University of Canterbury, 2009. / Typescript (photocopy). "5th February 2009." Includes bibliographical references (leaves 66-69). Also available via the World Wide Web.

Thesis (Ph. D.)--Ohio University, August, 2004. / Includes bibliographical references (p. 74-77).

Thesis (Ph.D.)--Ohio University, August, 2004. / Title from PDF t.p. Includes bibliographical references (p. 74-77)

Typescript. / Thesis (Ph. D.)--University of Hawaii at Manoa, 1990. / Includes bibliographical references. / Microfiche. / vi, 96 leaves, bound ill. 29 cm

The purpose of this thesis is to investigate a class of four left-invariant optimal control problems on the special orthogonal group SO(3). The set of all control-affine left-invariant control systems on SO(3) can, without loss, be reduced to a class of four typical controllable left-invariant control systems on SO(3) . The left-invariant optimal control problem on SO(3) involves finding a trajectory-control pair on SO (3), which minimizes a cost functional, and satisfies the given dynamical constraints and boundary conditions in a fixed time. The problem is lifted to the cotangent bundle T*SO(3) = SO(3) x so (3)* using the optimal Hamiltonian on so(3)*, where the maximum principle yields the optimal control. In a contribution to the study of this class of optimal control problems on SO(3), the extremal equations on so(3)* (ident ified with JR3) are integrated via elliptic functions to obtain explicit expressions for the solution curves in each typical case. The energy-Casimir method is used to give sufficient conditions for non-linear stability of the equilibrium states. / KMBT_363 / Adobe Acrobat 9.54 Paper Capture Plug-in

The aim of this thesis is to study a class of left-invariant optimal control problems on the matrix Lie group SE(2). We classify, under detached feedback equivalence, all controllable (left-invariant) control affine systems on SE(2). This result produces six types of control affine systems on SE(2). Hence, we study six associated left-invariant optimal control problems on SE(2). A left-invariant optimal control problem consists of minimizing a cost functional over the trajectory-control pairs of a left-invariant control system subject to appropriate boundary conditions. Each control problem is lifted from SE(2) to T*SE(2) ≅ SE(2) x se (2)*and then reduced to a problem on se (2)*. The maximum principle is used to obtain the optimal control and Hamiltonian corresponding to the normal extremals. Then we derive the (reduced) extremal equations on se (2)*. These equations are explicitly integrated by trigonometric and Jacobi elliptic functions. Finally, we fully classify, under Lyapunov stability, the equilibrium states of the normal extremal equations for each of the six types under consideration.

This thesis focuses on the formulation and numerical implementation of a fully coupled continuum model for deformation-diffusion in linearized elastic solids. The mathematical model takes into account the affect of the deformation on the diffusion process, and the effect of the transport of an inert chemical species on the deformation of the solid. A robust computational framework is presented for solving the proposed mathematical model, which consists of coupled non-linear partial differential equations. It should be noted that many popular numerical formulations may produce unphysical negative values for the concentration, particularly, when the diffusion process is anisotropic. The violation of the non-negative constraint by these numerical formulations is not mere numerical noise. In the proposed computational framework we employ a novel numerical formulation that will ensure that the concentration of the diffusant be always non-negative, which is one of the main contributions of this thesis. Representative numerical examples are presented to show the robustness, convergence, and performance of the proposed computational framework. Another contribution is to systematically study the affect of transport of the diffusant on the deformation of the solid and vice-versa, and their implication in modeling degradation/healing of materials. It is shown that the coupled response is both qualitatively and quantitatively different from the uncoupled response.

The topic of this thesis is the convex hull property for systems of partial differential equations, which is a natural generalisation of the maximum principle for scalar equations. The main result of this thesis is a theorem asserting the convex hull property for the solutions of a certain class of parabolic systems of nonlinear partial differential equations. It also investigates the coefficients of linear systems. The respective results are sharp which is demonstrated by counterexamples to the convex hull property for solutions of linear elliptic and parabolic systems. The general theme is that the coupling of the system is what breaks the convex hull property, not necessarily the non-linearity.

M. Tech. Electrical Engineering. / Discusses MIMO systems have been hailed for the benefits of enhancing the reliability of the wireless communication link and increasing of the channel capacity, however the complexity of MIMO encoding and decoding algorithms increases considerably with the number of antennas. This research aims to suggest an optimisation approach to a reduced complexity implementation of the Alamouti 4×2 STBC. This is achieved by considering the FPGA parallelisation of the conditionally optimised ML decoding algorithm. The above problem can be divided into two subproblems. 1. The ML decoding of the Double Alamouti 4×2 STBC has a high computational cost when an exhaustive search is performed on the signal constellation for M-ary QAM. 2. Though the conditionally optimised ML decoding leads to less computational complexity compared to the full generic ML detection algorithm, the practical implementation remains unattractive for wireless systems.