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This thesis exhibits skeins based on the Homfly polynomial and their relations to Schur functions. The closures of skein-theoretic idempotents of the Hecke algebra are shown to be specializations of Schur functions. This result is applied to the calculation of the Homfly polynomial of the decorated Hopf link. A closed formula for these Homfly polynomials is given. Furthermore, the specialization of the variables to roots of unity is considered. The techniques are skein theory on the one side, and the theory of symmetric functions in the formulation of Schur functions on the other side. Many previously known results have been proved here by only using skein theory and without using knowledge about quantum groups.
Epstein and Penner constructed in [EP88] the Euclidean decomposition of a non-compact hyperbolic n-manifold of finite volume for a choice of cusps, n >= 2. The manifold is cut along geodesic hyperplanes into hyperbolic ideal convex polyhedra. The intersection of the cusps with the Euclidean decomposition determined by them turns out to be rather simple as stated in Theorem 2.2. A dual decomposition resulting from the expansion of the cusps was already mentioned in [EP88]. These two dual hyperbolic decompositions of the manifold induce two dual decompositions in the Euclidean structure of the cusp sections. This observation leads in Theorems 5.1 and 5.2 to easily computable, necessary conditions for an arbitrary ideal polyhedral decomposition of the manifold to be a Euclidean decomposition.
Anomalous monism and mental causality : on the debate of Donald Davidson’s philosophy of the mental
(2004)
The English version of the first chapter of Erwin Rogler and Gerhard Preyer: Materialismus, anomaler Monismus und mentale Kausalität. Zur gegenwärtigen Philosophie des Mentalen bei Donald Davidson und David Lewis (2001) "Anomaler Monismus und Mentale Kausalität. Ein Beitrag zur Debatte über Donald Davidsons Philosophie des Mentalen" is a contribution to the current debates on the philosophy of the mental and mental causality initiated from Donald Davidson's philosophy with his article "Mental Events" (1970). It is the intent of the English version to give a response to the controversy among American, British and Australian philosophers in the context of a global exchange of ideas on problems understanding the mental. Contents 1. Preliminary Remarks 2. The Critique of Property-Epiphenomenalism and Counterarguments (a) The Enlargement of Nomological Reasoning (b) The Counterfactual Analysis (c) Supervenient Causality 3. Are Mental Properties real or unreal (fictive)? Abstract Things and events are fundamental entities in Davidson's ontology. Less distinct is the ontological status of properties, especially of mental types. Despite of some eliminative allusions there are weighty reasons to understand Davidson's philosophy of mind as including intentional realism. With it, the question of mental causality arises. There are two striking solutions to this problem: the epiphenomenalism of mental properties and the downward causation of mental events. Davidson cannot accept either. He claims to justify the mental as supervenient causality in order to thus integrate it into physicalism (his version of monism). But his argument at best proves the explanatory, not the causal relevance of mental properties. For this and for other reasons, Davidson fails the aspired synthesis of a sufficiently strong physicalism and the autonomy of the mental; a project whose realization is anyhow hard to achieve.
By most Western Europeans Cyprus is probably perceived as a tourist resort rather than a technologically highly developed country. Interested German visitors are informed by the travel brochure published by the Republic of Cyprus' tourist office that "in the villages old customs and traditions still exist" (Zypern. 9000 Jahre Geschichte und Kultur 1997, 11). Pictures of places of antiquity, churches, monasteries, fortresses, archaic villages and of people engaged in agricultural work and crafts convey the image of a traditional Mediterranean society. However, the Republic of Cyprus is a rapidly modernising country. It has developed recently "from a poor agrarian into a high-income service economy" (Christodoulou 1995, 11) and "radical transformation processes" are observed (cf. ibid., 18). The forthcoming accession to the European Union additionally accelerates the pace of these transformation processes. Due to its position on the extreme rim of Europe in the Eastern Mediterranean region at the crossroads of three continents, the island is perceived both as marginal (cf. Pace 1999) and as a link between Europe and the Asian and African continents (cf. Kasoulides 1999). Cyprus is conceptualised for the future as a centre and intersection: as regional hub of the modern capital market, as communications and trade centre in the Eastern Mediterranean, as "telecommunications hub for the Eastern Mediterranean and Middle East region", as "international services centre". The Republic of Cyprus has a highly developed telecommunications infrastructure, which is the basic prerequisite for the conversion into such a centre and is one of the most important factors for the economic competitiveness of Cyprus. The global nature of communication platforms today, especially the Internet, is regarded as the key to the integration of Cyprus into the world economy. By implementing information technologies and promoting necessary expertise, economic progress and modernisation of the country as well as its global competitiveness is assumed to be guaranteed. Investments in the information technology infrastructure are regarded as essential for the development of Cyprus, fostering the implementation of the information society. This aim and the necessary implementation measures feature increasingly on the agendas of scientific and economic conferences and symposia in Cyprus.