Random discrete groups of Möbius transformations : probabilities and limit set dimensions : a thesis presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Albany, New Zealand

This thesis addresses two areas related to the quantification of discrete groups. We study "random" groups of Möbius transformations and in particular random two-generator groups; that is, groups where the generators are selected randomly. Our intention is to estimate the likelihood that such groups are discrete and to calculate the expectation of their associated geometric and topological parameters. Computational results of the author [55] that indicate a low probability of a random group being discrete are extended and we also assess the expected Hausdorff dimension of the limit set of a discrete group. In both areas of research analytic determinations are correlated with computational results. Our results depend on the precise notion of randomness and we introduce geometrically natural probability measures on the groups of all Möbius transformations of the circle and the Riemann sphere

Art-making as a resource for the emergence of alternative personal and recovery narratives for people with an experience of psychosis

Dominant narratives about psychosis portray individuals as lonely, dangerous and unable to contribute to society. Such views may be incorporated into an individual’s personal story and are associated with negative outcomes for personal and clinical recovery. Art-making is associated with personal meaning-making and alternative forms of expression. It is therefore considered potentially relevant to narrative modification. Adult service-users with psychosis participated in a gallery-based art-making intervention. At interview, participants used their self-created images to help tell their story. Literary, experience-centred and culturally-oriented lenses were used to analyse narratives. Turning-points as modifiers of stigmatised dominant narratives were explored, as was how the intervention supported recovery. Art-making was associated with achievement, challenge and satisfaction. Story-telling using visual and verbal means opened up stories and alternative perspectives for participants. Recovery-principles including hope and aspiration were supported, identified through goals and recognition of achievement. Sharing experiences with others with similar experiences was viewed as impacting positively on mental-health. The intervention represented effective partnership working between NHS services and a gallery in overcoming barriers to accessing the arts, for people with psychosis. Achievements in art-making and narrating experience using visual and verbal means offered alternatives to personally limiting and illness-dominated narratives

Resolving the large scale spectral variability of the luminous Seyfert 1 galaxy 1H 0419-577: Evidence for a new emission component and absorption by cold dense matter

An XMM-Newton observation of the luminous Seyfert 1 galaxy 1H 0419-577 in September 2002, when the source was in an extreme low-flux state, found a very hard X-ray spectrum at 1-10 keV with a strong soft excess below ~1 keV. Comparison with an earlier XMM-Newton observation when 1H 0419-577 was `X-ray bright' indicated the dominant spectral variability was due to a steep power law or cool Comptonised thermal emission. Four further XMM-Newton observations, with 1H 0419-577 in intermediate flux states, now support that conclusion, while we also find the variable emission component in intermediate state difference spectra to be strongly modified by absorption in low ionisation matter. The variable `soft excess' then appears to be an artefact of absorption of the underlying continuum while the `core' soft emission can be attributed to recombination in an extended region of more highly ionised gas. We note the wider implications of finding substantial cold dense matter overlying (or embedded in) the X-ray continuum source in a luminous Seyfert 1 galaxy.Comment: 34 pages, 15 figures, submitted to Ap

Refugees on the High Seas: International Refugee Solutions to a Law of the Sea Problem

Following in the aftermath of the Arab Spring, Europe’s southern marine borders have been the showplace of human tragedies previously unseen on this scale and the issue of refugees on the high seas has assumed a newfound importance. This article examines the flawed system provided by the ‘Constitution of the Oceans’, the UN Convention on the Law of the Sea for the protection of the lives of migrants at sea. It submits that international refugee law is well-equipped to assume a greater responsibility in ensuring the protection of those involved. Although the concept of non-refoulement cannot be stretched ad absurdum, it may still be reasonably interpreted as providing a temporary right to disembark for the purpose of processing possible asylum applications. In the long-term, a system of burden-sharing and permanent, yet flexible, reception agreements remain the only sustainable solution

Representation in the Doctrine of Estoppel in International Law

Effective relations between international actors require that these must be able to place their trust in the representations made by others, in particular, when such representations directly or indirectly affect. More specifically, a State ought to act in such a manner so that other subjects of international law are able to rely on such acts or statements and comport themselves accordingly. Mere reliance per se does not give rise to potentially far-reaching legal consequences, however, reliance, which is legitimate and therefore worthy of legal protection, must be recognised as such and shielded. The practical promotion of consistency occurs in international law (as in several domestic legal orders) by way of the application of, inter alia, the doctrine of estoppel, the existence of which is trite law. Notwithstanding several applications of this doctrine, which in essence shields an innocent party from the detrimental consequences of reliance on the actions of another party, by international tribunals, the International Court of Justice has declined to elaborate extensively on the dogmatic basis of the doctrine, its specific elements or its application

Introduction

The costs and benefits of European Imperialism from the conquest of Ceuta, 1415, to the Treaty of Lusaka, 1974.Twelfth International Economic History Congress. Madrid, 1998.Patrick K. O'Brien and Leandro Prados de la Escosura (eds.)Editada en la Fundación Empresa PúblicaPatrick K. O'Brien and Leandro Prados de la Escosura. The Costs and Benefits for Europeans from their Empires Overseas.Publicad

Theories of Technological Progress and the British Textile Industry from Kay to Cartwright

Editada en la Fundación Empresa PúblicaLa industria textil británica continúa en el centro del debate sobre la revolución industrial. Las innovaciones técnicas en el período produjeron una aceleración extraordinaria del crecimiento del output y una considerable reducción de los precios de los tejidos. En este trabajo presentamos un estudio de la comunidad de los inventores responsables de la transformación tecnológica, lo que nos permite alcanzar una serie de conclusiones nuevas sobre el ritmo y dirección de la actividad innovadora durante la revolución industrialThe cotton textile industry remains central to all accounts of the first industrial revolution. Innovations in this period precipitated an extraordinary acceleration in the growth of output and a steep decline in the cost of producing all varieties of cloth. In this paper we outline an explanation through an analysis of the community of inventors responsible for the technological transformation, which enables us to offer some generalizations of the pace and pattern of the inventive activity in this period.Publicad

El progreso material europeo en el largo plazo

Nombrado Doctor Honoris Causa en el acto de apertura del curso 99/0