Leisure, consumerism and active citizenship in the UK

Since the first election victory of the Thatcher administration in 1979, Britain has witnessed a cultural transformation from the municipal socialism enshrined in the post-World War 2 development of the Welfare State to a form of post-industrial entrepreneurialism based largely on market rationality. This has had a profound effect on all aspects of civil life, not least the redefinition of the role of active leisure. Since the late 1950s the dominant policy for active leisure has been 'Sport For All', an assertion of a social right too important to be left to the market. The transformation has, therefore, signalled a shift from government support for active leisure as an element of citizen rights to the use of leisure to promote the government's interest in legitimating a new social order based not on rights but on means. Thus access to active living is no longer a societal goal for all, but a discretionary consumer good, the consumption of which signifies 'active' citizenship. It furthermore signifies differentiation from the growing mass of 'deviants' who are unwilling or unable to embrace this new construction of citizenship and are, therefore, increasingly denied access to active living and, hence, active citizenship.

Expectation versus provision in the management and use of urban open space

This paper discusses the implications of the shifting cultural significance of public open space in urban areas. In particular, it focuses on the increasing dysfunction between people's expectations of that space and its actual provision and management. In doing so, the paper applies Lefebvre's ideas of spatiality to the evident paradigm shift from 'public' to 'private' culture, with its associated commodification of previously public space. While developing the construct of paradigm shift, the paper recognises that the former political notions inherent in the provision of public space remain in evidence. So whereas public parks were formerly seen as spaces of confrontation between the 'rationality' of public order as the 'irrationality' of individual leisure pursuits, they are now increasingly seen, particularly 'out of hours', as the domain of the dispossessed, to be defined and policed as 'dangerous'. Where once people were welcomed into public open spaces as a means of 'educating' them in good, acceptable, leisure practices, therefore, they are now increasingly excluded, but for the same ostensible reasons. Building on survey work undertaken in Reading, Berkshire, the paper illustrates how communities can become separated from 'their' space, leaving them with the overriding impression that they have been 'short-changed' in terms of both the provision and the management of urban open space. Rather than the intimacy of local space for local people, therefore, the paper argues that parks have become externalised places, increasingly responding to commercial definitions of culture and what is 'public'. Central urban open spaces are therefore increasingly becoming sites of stratification, signification of a consumer-constructed citizenship and valorisation of public life as a legitimate element of the market surface of town and city centres.

Recent trends in UK Government policy on the provision and management of leisure facilities

Since the first election victory of the Thatcher administration in 1979, Britain has witnessed a cultural transformation from the municipal socialism of the post-World War 2 Welfare State to a form of post-industrial entrepreneurialism. This has had a profound effect on all aspects of civil society, not least the redefinition of the role of active leisure from the 1950s evocation of 'Sport For All' to the market rationality of the 1980s. The transformation has signalled a shift from government support for active leisure as an element of citizen rights to the use of leisure to promote the government's interest in legitimating a new social order based not on rights but on means. Thus access to active living is no longer a societal goal for all, but a discretionary consumer good, the consumption of which signifies 'active' citizenship. It furthermore signifies differentiation from the growing mass of 'deviants' who are unwilling or unable to embrace this new construction of citizenship and are, therefore, increasingly denied access to active living and, hence, active citizenship.

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 .

Robustness in partial pole placement

The robustness of state feedback solutions to the problem of partial pole placement obtained by a new projection procedure is examined. The projection procedure gives a reduced-order pole assignment problem. It is shown that the sensitivities of the assigned poles in the complete closed-loop system are bounded in terms of the sensitivities of the assigned reduced-order poles, and the sensitivities of the unaltered poles are bounded in terms of the sensitivities of the corresponding open-loop poles. If the assigned poles are well-separated from the unaltered poles, these bounds are expected to be tight. The projection procedure is described in [3], and techniques for finding robust (or insensitive) solutions to the reduced-order problem are given in [1], [2].

Stability results for the time-harmonic Maxwell equations with impedance boundary conditions

We consider the time-harmonic Maxwell equations with constant coefficients in a bounded, uniformly star-shaped polyhedron. We prove wavenumber-explicit norm bounds for weak solutions. This result is pivotal for convergence proofs in numerical analysis and may be a tool in the analysis of electromagnetic boundary integral operators.

Place making in Hellenistic Athens: beyond decline and foreign patronage

The study of cities is integral to the study of the Hellenistic Age, the period bounded by the deaths of two legendary rulers: Alexander in 323 BC and Kleopatra in 30 BC. Modern scholarship has followed in the footsteps of Johann-Gustav Droysen, who coined the term 'Hellenistic' in the nineteenth century and associated it with the diffusion of Greek culture through the founding of new cities in the East by Alexander and his successors. Hellenistic Athens, traditionally discussed under the rubric of its Classical legacy and/or in contrast with thriving cities, such as Pergamon, has been presented as a backwater exemplifying the demise of the 'polis'. My objective in this paper is to criticise these negative sentiments by exploring how the built environment of Hellenistic Athens could potentially become an indicator of city vitality.

Quasilimiting behavior for one-dimensional diffusions with killing

This paper extends and clarifies results of Steinsaltz and Evans [Trans. Amer. Math. Soc. 359 (2007) 1285–1234], which found conditions for convergence of a killed one-dimensional diffusion conditioned on survival, to a quasistationary distribution whose density is given by the principal eigenfunction of the generator. Under the assumption that the limit of the killing at infinity differs from the principal eigenvalue we prove that convergence to quasistationarity occurs if and only if the principal eigenfunction is integrable. When the killing at ∞ is larger than the principal eigenvalue, then the eigenfunction is always integrable. When the killing at ∞ is smaller, the eigenfunction is integrable only when the unkilled process is recurrent; otherwise, the process conditioned on survival converges to 0 density on any bounded interval.

Smoothness of scale functions for spectrally negative Lévy processes

Scale functions play a central role in the fluctuation theory of spectrally negative Lévy processes and often appear in the context of martingale relations. These relations are often require excursion theory rather than Itô calculus. The reason for the latter is that standard Itô calculus is only applicable to functions with a sufficient degree of smoothness and knowledge of the precise degree of smoothness of scale functions is seemingly incomplete. The aim of this article is to offer new results concerning properties of scale functions in relation to the smoothness of the underlying Lévy measure. We place particular emphasis on spectrally negative Lévy processes with a Gaussian component and processes of bounded variation. An additional motivation is the very intimate relation of scale functions to renewal functions of subordinators. The results obtained for scale functions have direct implications offering new results concerning the smoothness of such renewal functions for which there seems to be very little existing literature on this topic.

Toeplitz operators on Bergman spaces with locally integrable symbols

We study the boundedness of Toeplitz operators $T_a$ with locally integrable symbols on Bergman spaces $A^p(\mathbb{D})$, $1 < p < \infty$. Our main result gives a sufficient condition for the boundedness of $T_a$ in terms of some ``averages'' (related to hyperbolic rectangles) of its symbol. If the averages satisfy an ${o}$-type condition on the boundary of $\mathbb{D}$, we show that the corresponding Toeplitz operator is compact on $A^p$. Both conditions coincide with the known necessary conditions in the case of nonnegative symbols and $p=2$. We also show that Toeplitz operators with symbols of vanishing mean oscillation are Fredholm on $A^p$ provided that the averages are bounded away from zero, and derive an index formula for these operators.

Hankel and Toeplitz transforms on H 1: continuity, compactness and Fredholm properties

We revisit the boundedness of Hankel and Toeplitz operators acting on the Hardy space H 1 and give a new proof of the old result stating that the Hankel operator H a is bounded if and only if a has bounded logarithmic mean oscillation. We also establish a sufficient and necessary condition for H a to be compact on H 1. The Fredholm properties of Toeplitz operators on H 1 are studied for symbols in a Banach algebra similar to C + H ∞ under mild additional conditions caused by the differences in the boundedness of Toeplitz operators acting on H 1 and H 2.

Spectral theory of Toeplitz and Hankel operators on the Bergman space A1

The Fredholm properties of Toeplitz operators on the Bergman space A2 have been well-known for continuous symbols since the 1970s. We investigate the case p=1 with continuous symbols under a mild additional condition, namely that of the logarithmic vanishing mean oscillation in the Bergman metric. Most differences are related to boundedness properties of Toeplitz operators acting on Ap that arise when we no longer have 1bounded Toeplitz operators on A1 were characterized completely very recently but only for bounded symbols. We also consider compactness of Hankel operators on A1.

Boundary value problems for the elliptic sine-Gordon equation in a semi-strip

We study boundary value problems posed in a semistrip for the elliptic sine-Gordon equation, which is the paradigm of an elliptic integrable PDE in two variables. We use the method introduced by one of the authors, which provides a substantial generalization of the inverse scattering transform and can be used for the analysis of boundary as opposed to initial-value problems. We first express the solution in terms of a 2 by 2 matrix Riemann-Hilbert problem whose \jump matrix" depends on both the Dirichlet and the Neumann boundary values. For a well posed problem one of these boundary values is an unknown function. This unknown function is characterised in terms of the so-called global relation, but in general this characterisation is nonlinear. We then concentrate on the case that the prescribed boundary conditions are zero along the unbounded sides of a semistrip and constant along the bounded side. This corresponds to a case of the so-called linearisable boundary conditions, however a major difficulty for this problem is the existence of non-integrable singularities of the function q_y at the two corners of the semistrip; these singularities are generated by the discontinuities of the boundary condition at these corners. Motivated by the recent solution of the analogous problem for the modified Helmholtz equation, we introduce an appropriate regularisation which overcomes this difficulty. Furthermore, by mapping the basic Riemann-Hilbert problem to an equivalent modified Riemann-Hilbert problem, we show that the solution can be expressed in terms of a 2 by 2 matrix Riemann-Hilbert problem whose jump matrix depends explicitly on the width of the semistrip L, on the constant value d of the solution along the bounded side, and on the residues at the given poles of a certain spectral function denoted by h. The determination of the function h remains open.

A multidisciplinary literature review of low and zero carbon technologies into new housing

The UK Government is committed to all new homes being zero-carbon from 2016. The use of low and zero carbon (LZC) technologies is recognised by housing developers as being a key part of the solution to deliver against this zero-carbon target. The paper takes as its starting point that the selection of new technologies by firms is not a phenomenon which takes place within a rigid sphere of technical rationality (for example, Rip and Kemp, 1998). Rather, technology forms and diffusion trajectories are driven and shaped by myriad socio-technical structures, interests and logics. A literature review is offered to contribute to a more critical and systemic foundation for understanding the socio-technical features of the selection of LZC technologies in new housing. The problem is investigated through a multidisciplinary lens consisting of two perspectives: technological and institutional. The synthesis of the perspectives crystallises the need to understand that the selection of LZC technologies by housing developers is not solely dependent on technical or economic efficiency, but on the emergent ‘fit’ between the intrinsic properties of the technologies, institutional logics and the interests and beliefs of various actors in the housing development process.

Hankel operators on Fock spaces

We study Hankel operators on the weighted Fock spaces Fp. The boundedness and compactness of these operators are characterized in terms of BMO and VMO, respectively. Along the way, we also study Berezin transform and harmonic conjugates on the plane. Our results are analogous to Zhu's characterization of bounded and compact Hankel operators on Bergman spaces of the unit disk.