Overview of Thesis. In this thesis we will focus on two aspects of scattering in absorbing cavities, namely the zeros of the S matrix for cavities with broken time reversal invariance and the behaviour of the reflection coefficient in single-channel cavities near its minima. As we observed above, the S matrix zeros are given by eigenvalues of J = H + iΓˆ, where H is from a Gaussian ensemble and Γˆ is a rank M Hermitian matrix with L < M negative eigenvalues. Therefore from an abstract point of view we are interested in low rank non-Hermitian perturbations of Gaussian ensembles. In the next chapter we will first obtain a perturbative expression for the distribution of the imaginary parts of the S matrix zeros, which will be used in the fourth chapter to study the tails of the RTD distribution. We then derive an expression for the joint distribution of the zeros, using a slight modification of the approach of [33] which considered positive Γˆ. In the simplest non-trivial case of M = 2, L = 1, we use this expression to calculate the probability that all eigenvalues are in the upper half-plane, and the distribution of the smallest imaginary part conditioned on this event. In the third chapter we study the k-point correlation functions in the bulk and at the edge by using a partial Xxxxx decomposition to obtain an integral representation for the k-point function and then relating this to the expectation value of a product of characteristic polynomials. The k-point functions in the bulk for positive Γˆ and finite rank M were obtained in [33]; our main aim in this section is to give a rigorous treatment of both the bulk and the edge and extend the bulk result to arbitrary indefinite Γˆ with rank M = o(√N ). At the edge, where we take the rank to grow as M = O(N 2/3), we restrict ourselves to Γˆ with two distinct eigenvalues for technical reasons. In the fourth chapter we study the statistics of the reflection time difference (RTD), using both perturbation theory and the non-perturbative two-point function derived in the previous chapter. The possibility of estimating S matrix zeros from measurements of the S matrix along the real axis via harmonic inversion is investigated, and we compare the use of the RTD and the determinant of the S matrix for this purpose. In the fifth chapter we relate the reflection coefficient of a single-channel cavity with uniform absorption to the overlap of the eigenvectors of the effective Hamiltonian. The joint distribution of an eigenvalue and the di...
Overview of Thesis. As explained above, this research is undertaken within the broader framework of the Indonesia-Netherlands Study on Environmental Law and Administration in Indonesia (INSELA), the aim of which was to analyse environmental law and management in Indonesia from both a empirical and normative perspective and to make recommendations on the basis of that analysis. The central research problem addressed by the INSELA project was as follows: 12 Followup interviews in November 2003 were conducted by phone from Perth, Australia. In addressing this broad research agenda, the project was further divided into four sections: Part A focussing on national environmental and sectoral legislation and policy, Part B on decentralisation and local management institutions, Part C on environmental law enforcement and dispute settlement and Part D on diagnosis, comparative research, recommendations and interventions. Whilst this thesis addresses research questions within all of these parts, our particular focus is on Part C, relating to legal mechanisms for environmental dispute resolution. Specifically, this thesis examines the legal framework and legally prescribed mechanisms for environmental dispute resolution in Indonesia, namely litigation and mediation. We shall examine the extent to which such mechanisms have been effective in resolving environmental disputes and the factors (both legal and non-legal) influencing the outcomes of litigation and mediation in environmental disputes. Finally, we shall make recommendations based on our analysis for the further development and improvement of environmental dispute resolution in Indonesia. Chapter 1 begins with a discussion of theoretical perspectives on environmental disputes and environmental dispute resolution, particularly litigation and mediation, illustrated in parts with references to the Indonesian context. The discussion of litigation and mediation defines the functions, objectives and necessary conditions of these two approaches to environmental dispute resolution. This theoretical discussion provides an evaluative framework that is referred to in subsequent chapters, particularly the conclusion (chapter 6).
Overview of Thesis. In this thesis we investigate questions (P1-P2) stated in the previous section for three problems. We give an overview of each type of problem below. The k-Means Minimization Problem (Chapter 3 and Chapter 4). The first problem we consider is a k-means type problem where we generalize the k-means framework [105] to allow for cluster centers in different spaces to the data. This is motivated by the following smoothing-
i=1 data association problem. We are given data {(ti, zi)}n sampled from k unknown curves µj, and in particular the association of data point to curve is unknown. The problem is then to
