The rise of urban tourism in Havana since 1989

This article looks at the development of urban tourism in Havana, Cuba, in the period since the collapse of state socialism in the USSR and Eastern Europe. It provides an interesting case study of the adoption of an outward-oriented state development policy in the context of a socialist state. The dramatic rise of urban-based tourism in Havana since 1989 is described, followed by a review of the socio-economic impacts of such tourism. These include: income generation; job creation; the rise of the informal economy, including crime and prostitution; increased migration to the primary city, along with spatial concentration on the coastal strip, and associated environmental impacts. In conclusion, the article considers the fat that the promotion of tourism has returned Havana to some of the conditions that existed in the city Socialist Revolution in 1959.

The Victoria Falls 1900-1940: Landscape, tourism and the geographical imagination

This article is about the politics of landscape ideas, and the relationship between landscape, identity and memory. It explores these themes through the history of the Victoria Falls, and the tourist resort that developed around the waterfall after 1900. Drawing on oral and archival sources, including popular natural history writing and tourist guides, it investigates African and European ideas about the waterfall, and the ways that these interacted and changed in the course of colonial appropriations of the Falls area. The tourist experience of the resort and the landscape ideas promoted through it were linked to Edwardian notions of Britishness and empire, ideas of whiteness and settler identities that transcended new colonial borders, and to the subject identities accommodated or excluded. Cultures of colonial authority did not develop by simply overriding local ideas, they involved fusions, exchanges and selective appropriations of them. The two main African groups I am concerned with here are the Leya, who lived in small groups around the Falls under a number of separate chiefs, and the powerful Lozi rulers, to whom they paid tribute in the nineteenth century. The article highlights colonial authorities' celebration of aspects of the Lozi aristocracy's relationship with the river, and their exclusion of the Leya people who had a longer and closer relationship with the waterfall. It also touches on the politics of recent attempts to reverse this exclusion, and the controversial rewriting of history this has involved.

The rejuvenation of tourism in Barbados 1993-2003 - Reflections on the Butler model

This article examines how Barbados as a mature resort destination has set about rejuvenating its tourism product since the early 1990s, when the number of stop-over tourist arrivals showed year-on-year declines. This has been achieved in three principal ways: the extensive upgrading of existing hotel facilities, especially at the luxury end of the market: the increase of overall tourist capacity, and the development of niche markets, especially golf tourism. At both the outset and the conclusion, the rejuvenation of tourism in Barbados between 1993 and 2003 is viewed in light of Butler's (1980) model of resort-cycle development.

Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation

We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the $L^2$ condition numbers for these formulations, and also on the norms of the classical acoustic single- and double-layer potential operators. These bounds to some extent make explicit the dependence of condition numbers on the wave number $k$, the geometry of the scatterer, and the coupling parameter. For example, with the usual choice of coupling parameter they show that, while the condition number grows like $k^{1/3}$ as $k\to\infty$, when the scatterer is a circle or sphere, it can grow as fast as $k^{7/5}$ for a class of `trapping' obstacles. In this paper we prove further bounds, sharpening and extending our previous results. In particular we show that there exist trapping obstacles for which the condition numbers grow as fast as $\exp(\gamma k)$, for some $\gamma>0$, as $k\to\infty$ through some sequence. This result depends on exponential localisation bounds on Laplace eigenfunctions in an ellipse that we prove in the appendix. We also clarify the correct choice of coupling parameter in 2D for low $k$. In the second part of the paper we focus on the boundary element discretisation of these operators. We discuss the extent to which the bounds on the continuous operators are also satisfied by their discrete counterparts and, via numerical experiments, we provide supporting evidence for some of the theoretical results, both quantitative and asymptotic, indicating further which of the upper and lower bounds may be sharper.

Limit operators, collective compactness, and the spectral theory of infinite matrices

In the first half of this memoir we explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). We build up to results obtained by applying this generalised collectively compact operator theory to the set of limit operators of an operator (its operator spectrum). In the second half of this memoir we study bounded linear operators on the generalised sequence space , where and is some complex Banach space. We make what seems to be a more complete study than hitherto of the connections between Fredholmness, invertibility, invertibility at infinity, and invertibility or injectivity of the set of limit operators, with some emphasis on the case when the operator is a locally compact perturbation of the identity. Especially, we obtain stronger results than previously known for the subtle limiting cases of and . Our tools in this study are the results from the first half of the memoir and an exploitation of the partial duality between and and its implications for bounded linear operators which are also continuous with respect to the weaker topology (the strict topology) introduced in the first half of the memoir. Results in this second half of the memoir include a new proof that injectivity of all limit operators (the classic Favard condition) implies invertibility for a general class of almost periodic operators, and characterisations of invertibility at infinity and Fredholmness for operators in the so-called Wiener algebra. In two final chapters our results are illustrated by and applied to concrete examples. Firstly, we study the spectra and essential spectra of discrete Schrödinger operators (both self-adjoint and non-self-adjoint), including operators with almost periodic and random potentials. In the final chapter we apply our results to integral operators on .