The thesis is concerned with techniques for realizing optimum control that are suited for analogue computers. The first half of the thesis develops an iterative scheme for the solution of the two point boundary value problem. The theory of the iterative scheme is covered in detail and the scheme is implemented on an analogue computer. Studies of the scheme have also been made using a digital computer. The iterative scheme can be modified to cope with constraints on the control law. These modifications have been tested on a digital computer. The latter half of the thesis is concerned with approximation techniques which produce, very simple controllers. These techniques require a large digital computer, such as the IBM 7040, to do the design calculations. The first approximation technique developed from the calculus of variations is covered in detail including a complete controller designed and simulated. The second approximation technique based on dynamic programming is discussed and a few points are made about the features of the controller. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

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A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, February 15, 2015. / In this thesis, the forward and inverse Spectral Theory for first order Hermitian systems with complex potentials and periodic boundary conditions are studied. The aim of this work is to prove two inverse periodicity Theorems and two uniqueness results for determinants of quasiperiodic boundary value problems.

The bending of thin flat plates has occupied the interests of mechanicians and applied mathematicians since J. L. Lagrange discovered the differential equation characterizing the behavior of such structural members. One particular phase of investigation in this field concerns itself with the solution of the differential equation subject to given boundary conditions. Indeed, it may be safely stated that the bulk of the literature on the subject of flat plates is concerned with the solution of problems involving the specification of the transverse loading on the plate and the conditions at the boundary of the plate. Various mathematical techniques are available for the solution of such problems. Among these, the most prominent are, a.) the method of series, b) the method of singularities, and c) the complex variable techniques. A survey of the literature in this area has revealed a paucity of solutions of certain types of problems; notably, those problems in which boundary conditions are mixed a.long a portion of the edge of the plate which ha.s a continuously turning tangent. By mixed boundary conditions, we mean a. change in condition from prescription of bending moment and vertical shear to assignment of slope and deflection along a portion of the edge which has a continuously turning tangent. In the first section of this thesis, a number of problems are considered for the half-plane. The attendant boundary conditions considered a.re combinations of clamping and simple support. The second portion consists of a number of problems associated with the quarter-plane. Solutions for these problems are obtained by utilizing the method of images in conjunction with the solutions presented in the first section. After this, we examine some problems connected with the circular plate. In particular, a numerical solution is given for a uniformly loaded circular plate simply-supported over half of its boundary and clamped over the remaining portion. The last chapter is a brief discussion of plates in the form of rectangles. Here, a closed solution is presented for the bending moments in terms of Weierstrassian elliptic functions. Another numerical example is included for a uniformly loaded plate clamped over a portion of one edge and simply- supported over the remainder of its boundary. / Doctor of Philosophy

M.S.

M.S.

We study the linear abstract kinetic equation T𝜑(x)′=-A𝜑(x) in the half space {x≥0} with partial range boundary conditions. The function <i>ψ</i> takes values in a Hilbert space H, T is a self adjoint injective operator on H and A is an accretive operator. The first step in the analysis of this boundary value problem is to show that T⁻¹A generates a holomorphic bisemigroup. We prove two theorems about perturbation of bisemigroups that are interesting in their own right. The second step is to obtain a special decomposition of H which is equivalent to a Wiener-Hopf factorization. The accretivity of A is crucial in this step. When A is of the form "identity plus a compact operator", we work in the original Hilbert space. For unbounded A’s we consider weak solutions in a larger space H_T, which has a natural Krein space structure. Using the Krein space geometry considerably simplifies the analysis of the question of unique solvability. / Ph. D. / incomplete_metadata

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

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