Call number: LD2668 .T4 1978 K34 / Master of Science

Thesis. 1979. Ph.D.--Massachusetts Institute of Technology. Dept. of Ocean Engineering. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: leaves 154-158. / Ph.D.

Thesis. 1976. Ph.D.--Massachusetts Institute of Technology. Dept. of Ocean Engineering. / Microfiche copy available in Archives and Engineering. / Bibliography: leaves 83-84. / by Robert J. Van Houten. / Ph.D.

Thesis. 1978. Ph.D.--Massachusetts Institute of Technology. Dept. of Ocean Engineering. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: leaves 148-151. / Ph.D.

Wang Jing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 55-59). / Abstracts in English and Chinese. / Acknowledgments --- p.i / Abstract --- p.ii / Introduction --- p.3 / Chapter 1 --- Formulation of the Problem --- p.10 / Chapter 1.1 --- Reformulated Navier-Stokes Equations --- p.10 / Chapter 1.2 --- Linearized Problems --- p.15 / Chapter 2 --- Construction of the Approximate Solution --- p.19 / Chapter 2.1 --- Two-scale Asymptotic Expansions --- p.19 / Chapter 2.2 --- Determination of Each Inner and Boundary Terms --- p.22 / Chapter 2.3 --- Truncation Terms --- p.31 / Chapter 3 --- Estimates of the Error Term of the Approximate Solution and Main Results --- p.33 / Chapter 3.1 --- Error Equations --- p.33 / Chapter 3.2 --- Energy Estimates --- p.36 / Chapter 3.2.1 --- BasicL2 Estimates --- p.36 / Chapter 3.2.2 --- Tangential Derivatives Estimates --- p.38 / Chapter 3.2.3 --- Normal Derivatives Estimates --- p.49 / Chapter 3.3 --- Pointwise Estimates --- p.52 / Bibliography --- p.55

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A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, in ful llment of the requirements for the degree of Master of Science in Engineering, Johannesburg, 2016 / The aim of this research project is evaluating the application of the Crum-based transformation in solving engineering systems modelled as two-point boundary value problems. The boundary value problems were subjected to the various combinations of Dirichlet, Non-Dirichlet and Affine boundary conditions. The engineering systems that were modelled were in the elds of electrostatics, heat conduction and longitudinal vibrations. Other methods such as the Z-transforms and iterative methods have been discussed. An attractive property of the Crum-based transformation is that it can be applied to cases where the eigenparameters (function of eigenvalues) generated in the discrete case are negative and was therefore chosen to be explored further in this dissertation. An alternative matrix method was proposed and used instead of the algebraic method in the Crum- based transformation. The matrix method was tested against the algebraic method using three unit intervals. The analysis revealed, that as the number of unit intervals increase, there is a general increase in the accuracy of the approximated continuous-case eigenvalues generated for the discrete case. The other observed general trend was that the accuracy of the approximated continuous- case eigenvalues decrease as one ascends the continuous-case eigenvalue spectrum. Three cases: (Affine, Dirichlet), (Affine, Non-Dirichlet) and (Affine, Affine) generated negative eigenparameters. The approximated continuous-case eigenvalues, derived from the negative eigenparameters, were shown not to represent true physical natural frequencies since the discrete eigenvalues, derived from negative eigenparameters, do not satisfy the condition for purely oscillatory behaviour. The research has also shown that the Crum-based transformation method was useful in approximating the shifted eigenvalues of the continuous case, in cases where the generated eigenparameters were negative: since, as the number of unit intervals increase, the post-transformed approximated eigenvalues improved in accuracy. The accuracy was also found to be better in the post-transformed case than in the pre-transformed case. Furthermore, the approximated non-shifted and shifted continuous- case eigenvalues (except the approximated continuous-case eigenvalues generated from negative eigenparameters) satis ed the condition for purely oscillatory behaviour. / MT2017

We prove that the solution of the Boussinesq equation with relatively small initial data exists globally and decays exponentially under some boundary conditions. / Ph. D.

Numerical schemes for the solution of two-point boundary value problems arising from the application of optimal control theory to mathematical models of dynamic systems, are discussed. Optimal control problems are formulated for rotational maneuvers of multiple rigid body, asymmetric spacecraft configurations with both external torques and/or internal torques. Necessary conditions for optimality are derived through Pontryagin’s principle; solutions to the problems are obtained numerically. Comparison studies using competing numerical methods and various choices of performance indices are reported. / Ph. D.

Li Kin-kuen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 52-54). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.4 / Chapter 2 --- Variational Formulation --- p.10 / Chapter 3 --- The Existence Of A Mountain Pass Solution --- p.12 / Chapter 4 --- Ground States --- p.21 / Chapter 5 --- The Projections Of v And w --- p.35 / Chapter 6 --- Computation Of The Energy: An Upper Bound --- p.37 / Chapter 7 --- Convergence: The First Approximation --- p.40 / Chapter 8 --- Convergence: The Second Approximation --- p.44 / Chapter 9 --- Computation Of The Energy: A Lower Bound --- p.48 / Chapter 10 --- Comparing The Energy: Completion Of The Proof Of Theorem 1.2 --- p.51 / Bibliography --- p.52