Interpolation of Hilbert and Sobolev spaces: quantitative estimates and counterexamples

This paper provides an overview of interpolation of Banach and Hilbert spaces, with a focus on establishing when equivalence of norms is in fact equality of norms in the key results of the theory. (In brief, our conclusion for the Hilbert space case is that, with the right normalisations, all the key results hold with equality of norms.) In the final section we apply the Hilbert space results to the Sobolev spaces Hs(Ω) and tildeHs(Ω), for s in R and an open Ω in R^n. We exhibit examples in one and two dimensions of sets Ω for which these scales of Sobolev spaces are not interpolation scales. In the cases when they are interpolation scales (in particular, if Ω is Lipschitz) we exhibit examples that show that, in general, the interpolation norm does not coincide with the intrinsic Sobolev norm and, in fact, the ratio of these two norms can be arbitrarily large.

The spaces of the Wednesday Play (BBC TV 1964–1970): production, technology and style

The BBC television drama anthology The Wednesday Play, broadcast from 1964-70 on the BBC1 channel, was high-profile and often controversial in its time and has since been central to accounts of British television’s ‘golden age’. This article demonstrates that production technologies and methods were more diverse at that time than is now acknowledged, and that The Wednesday Play dramas drew both approving but also very critical responses from contemporary viewers and professional reviewers. This article analyses the ways that the physical spaces of production for different dramas in the series, and the different technologies of shooting and recording that were adopted in these production spaces, are associated with but do not determine aesthetic style. The adoption of single-camera location filming rather than the established production method of multi-camera studio videotaping in some of the dramas in the series has been important to The Wednesday Play’s significance, but each production method was used in different ways. The dramas drew their dramatic forms and aesthetic emphases from both theatre and cinema, as well as connecting with debates about the nature of drama for television. Institutional and regulatory frameworks such as control over staff working away from base, budgetary considerations and union agreements also impacted on decisions about how programmes were made. The article makes use of records from the BBC Written Archives Centre, as well as published scholarship. By placing The Wednesday Play in a range of overlapping historical contexts, its identity can be understood as transitional, differentiated and contested.

Writers' rooms: theories of contemporary authorship in portraits of creative spaces

This article analyzes two series of photographs and essays on writers’ rooms published in England and Canada in 2007 and 2008. The Guardian’s Writers Rooms series, with photographs by Eamon McCabe, ran in 2007. In the summer of 2008, The Vancouver International Writers and Readers Festival began to post its own version of The Guardian column on its website by displaying, each week leading up to the Festival in September, a different writer’s “writing space” and an accompanying paragraph. I argue that these images of writers’ rooms, which suggest a cultural fascination with authors’ private compositional practices and materials, reveal a great deal about theoretical constructions of authorship implicit in contemporary literary culture. Far from possessing the museum quality of dead authors’ spaces, rooms that are still being used, incorporating new forms of writing technology, and having drafts of manuscripts scattered around them, can offer insight into such well-worn and ineffable areas of speculation as inspiration, singular authorial genius, and literary productivity.

Accurate delay analysis in prioritised wireless sensor networks for generalized packet arrival

This letter presents an accurate delay analysis in prioritised wireless sensor networks (WSN). The analysis is an enhancement of the existing analysis proposed by Choobkar and Dilmaghani, which is only applicable to the case where the lower priority nodes always have packets to send in the empty slots of the higher priority node. The proposed analysis is applicable for any pattern of packet arrival, which includes the general case where the lower priority nodes may or may not have packets to send in the empty slots of the higher priority nodes. Evaluation of both analyses showed that the proposed delay analysis has better accuracy over the full range of loads and provides an excellent match to simulation results.

Local spaces: open minds - inspirational ideas for managing lowland commons and other green spaces

The Chiltern commons are typical of those in the south east of England: small and numerous, but with the potential to provide important natural green space whilst contributing to environmental sustainability. In order to keep commons in good heart, they need to be managed. However, as activities such as grazing and coppicing become unviable on the commons, owners need to find sustainable roles beyond traditional agricultural and silvicultural practices. This paper examines ways of making management pay. It begins by exploring the economic, social and environmental challenges of sustainable management within the context of contemporary life. Section 2 identifies the different ways in which revenue contributions might be made towards the management of commons. Section 3 examines the relevant legal and other restrictions and Section 4 offers insights into where management proposals might offer multiple positive benefits, but also where there is the potential to cause conflict with environmental and social interests. Section 5 explores alternative funding streams for commons. Finally, Section 6 concludes with practical tips for the owners and managers of commons in the Chilterns and identifies areas for further research. Full references, links and resources are provided in the footnotes and appendix.

Dynamical properties of S-gap shifts and other shift spaces

We study the dynamical properties of certain shift spaces. To help study these properties we introduce two new classes of shifts, namely boundedly supermultiplicative (BSM) shifts and balanced shifts. It turns out that any almost specified shift is both BSM and balanced, and any balanced shift is BSM. However, as we will demonstrate, there are examples of shifts which are BSM but not balanced. We also study the measure theoretic properties of balanced shifts. We show that a shift space admits a Gibbs state if and only if it is balanced. Restricting ourselves to S-gap shifts, we relate certain dynamical properties of an S-gap shift to combinatorial properties from expansions in non-integer bases. This identification allows us to use the machinery from expansions in non-integer bases to give straightforward constructions of S -gap shifts with certain desirable properties. We show that for any q∈(0,1) there is an S-gap shift which has the specification property and entropy q . We also use this identification to address the question, for a given q∈(0,1), how many S-gap shifts exist with entropy q? For certain exceptional values of q there is a unique S-gap shift with this entropy.

Promenades in Enlightenment Madrid: the tapestry cartoons and new social spaces

Discusses how the painters of the Royal Tapestry Factory of Santa Barbara in Madrid depicted the new social spaces of the capital in the cartoons designed to be turned into tapestries for Royal apartments. The cultural and sociological role of the 'paseo' or 'promenade' is also considered.

Generalized convective quasi-equilibrium principle

A generalization of Arakawa and Schubert's convective quasi-equilibrium principle is presented for a closure formulation of mass-flux convection parameterization. The original principle is based on the budget of the cloud work function. This principle is generalized by considering the budget for a vertical integral of an arbitrary convection-related quantity. The closure formulation includes Arakawa and Schubert's quasi-equilibrium, as well as both CAPE and moisture closures as special cases. The formulation also includes new possibilities for considering vertical integrals that are dependent on convective-scale variables, such as the moisture within convection. The generalized convective quasi-equilibrium is defined by a balance between large-scale forcing and convective response for a given vertically-integrated quantity. The latter takes the form of a convolution of a kernel matrix and a mass-flux spectrum, as in the original convective quasi-equilibrium. The kernel reduces to a scalar when either a bulk formulation is adopted, or only large-scale variables are considered within the vertical integral. Various physical implications of the generalized closure are discussed. These include the possibility that precipitation might be considered as a potentially-significant contribution to the large-scale forcing. Two dicta are proposed as guiding physical principles for the specifying a suitable vertically-integrated quantity.

Aspects of particle filtering in high-dimensional spaces

Nonlinear data assimilation is high on the agenda in all fields of the geosciences as with ever increasing model resolution and inclusion of more physical (biological etc.) processes, and more complex observation operators the data-assimilation problem becomes more and more nonlinear. The suitability of particle filters to solve the nonlinear data assimilation problem in high-dimensional geophysical problems will be discussed. Several existing and new schemes will be presented and it is shown that at least one of them, the Equivalent-Weights Particle Filter, does indeed beat the curse of dimensionality and provides a way forward to solve the problem of nonlinear data assimilation in high-dimensional systems.

Generalized drivers in the mammalian endangerment process

An important challenge for conservation today is to understand the endangerment process and identify any generalized patterns in how threats occur and aggregate across taxa. Here we use a global database describing main current external threats in mammals to evaluate the prevalence of distinct threatening processes, primarily of anthropogenic origin, and to identify generalized drivers of extinction and their association with vulnerability status and intrinsic species' traits. We detect several primary threat combinations that are generally associated with distinct species. In particular, large and widely distributed mammals are affected by combinations of direct exploitation and threats associated with increasing landscape modification that go from logging to intense human land-use. Meanwhile, small, narrowly distributed species are affected by intensifying levels of landscape modification but are not directly exploited. In general more vulnerable species are affected by a greater number of threats, suggesting increased extinction risk is associated with the accumulation of external threats. Overall, our findings show that endangerment in mammals is strongly associated with increasing habitat loss and degradation caused by human land-use intensification. For large and widely distributed mammals there is the additional risk of being hunted.

Toeplitz operators on Dirichlet-Besov spaces

We study Toeplitz operators on the Besov spaces in the case of the open unit disk. We prove that a symbol satisfying a weak Lipschitz type condition induces a bounded Toeplitz operator. Such symbols do not need to be bounded functions or have continuous extensions to the boundary of the open unit disk. We discuss the problem of the existence of nontrivial compact Toeplitz operators, and also consider Fredholm properties and prove an index formula.

Rossby wave propagation tracks in southern hemisphere mean basic flows associated to generalized frosts over southern South America

Based on previous observational studies on cold extreme events over southern South America, some recent studies suggest a possible relationship between Rossby wave propagation remotely triggered and the occurrence of frost. Using the concept of linear theory of Rossby wave propagation, this paper analyzes the propagation of such waves in two different basic states that correspond to austral winters with maximum and minimum generalized frost frequency of occurrence in the Wet Pampa (central-northwest Argentina). In order to determine the wave trajectories, the ray tracing technique is used in this study. Some theoretical discussion about this technique is also presented. The analysis of the basic state, from a theoretical point of view and based on the calculation of ray tracings, corroborates that remotely excited Rossby waves is the mechanism that favors the maximum occurrence of generalized frosts. The basic state in which the waves propagate is what conditions the places where they are excited. The Rossby waves are excited in determined places of the atmosphere, propagating towards South America along the jet streams that act as wave guides, favoring the generation of generalized frosts. In summary, this paper presents an overview of the ray tracing technique and how it can be used to investigate an important synoptic event, such as frost in a specific region, and its relationship with the propagation of large scale planetary waves.