Variational approach in weighted Sobolev spaces to scattering by unbounded rough surfaces

We consider the problem of scattering of time harmonic acoustic waves by an unbounded sound soft surface which is assumed to lie within a finite distance of some plane. The paper is concerned with the study of an equivalent variational formulation of this problem set in a scale of weighted Sobolev spaces. We prove well-posedness of this variational formulation in an energy space with weights which extends previous results in the unweighted setting [S. Chandler-Wilde and P. Monk, SIAM J. Math. Anal., 37 (2005), pp. 598–618] to more general inhomogeneous terms in the Helmholtz equation. In particular, in the two-dimensional case, our approach covers the problem of plane wave incidence, whereas in the three-dimensional case, incident spherical and cylindrical waves can be treated. As a further application of our results, we analyze a finite section type approximation, whereby the variational problem posed on an infinite layer is approximated by a variational problem on a bounded region.

A helmet mounted display system with active gaze control for visual telepresence

The objective of a Visual Telepresence System is to provide the operator with a high fidelity image from a remote stereo camera pair linked to a pan/tilt device such that the operator may reorient the camera position by use of head movement. Systems such as these which utilise virtual reality style helmet mounted displays have a number of limitations. The geometry of the camera positions and of the displays is generally fixed and is most suitable only for viewing elements of a scene at a particular distance. To address such limitations, a prototype system has been developed where the geometry of the displays and cameras is dynamically controlled by the eye movement of the operator. This paper explores why it is necessary to actively adjust the display system as well as the cameras and justifies the use of mechanical adjustment of the displays as an alternative to adjustment by electronic or image processing methods. The electronic and mechanical design is described including optical arrangements and control algorithms. The performance and accuracy of the system is assessed with respect to eye movement.

Marks, spaces and boundaries

Dictionary compilers and designers use punctuation to structure and clarify entries and to encode information. Dictionaries with a relatively simple structure can have simple typography, and simple punctuation; as dictionaries grew more complex, and encountered the space constraints of the printed page, complex encoding systems were developed, using punctuation and symbols. Two recent trends have emerged in dictionary design: to eliminate punctuation, and sometimes to use a larger number of fonts, so that the boundaries between elements are indicated by font change, not punctuation.

Community strategies in England: reshaping spaces of governance?

The preparation of Community Strategies (CS) has been required of LSPs and Local Authorities in England since the passing of the Local Government Act 2000. This paper examines the process and content of two Community Strategies in southern England as part of an ongoing project to understand their impact and explore ways that CSs may be carried through in a meaningful and effective manner. The paper concludes that the two CSs studied illustrate the challenge faced by LSPs in producing Strategies that are meaningful, inclusive and which follow the spirit of the government CS guidance. LAs and LSPs are also posed with a difficult challenge of seeing through an implicitly required transition from a traditional representative democratic structure/process with a more fluid participatory model. Thus we detect that at least two forms of conflict may arise – firstly with elected councillors threatened by a loss of power and secondly between communities and the LAs who are encouraged to problematise local policy and service delivery in the context of limited resource availability.

Conceptualizing change in the Portuguese footwear industry: regional voices and cognitive spaces of agency

Expanding national services sectors and global competition aggravate current and perceived future market pressures on traditional manufacturing industries. These perceptions of change have provoked a growing intensification of geo-political discourses on technological innovation and ‘learning’, and calls for competency in design among other professional skills. However, these political discourses on innovation and learning have paralleled public concerns with the apparent ‘growth pains’ from factory closures and subsequent increases in unemployment, and its debilitating social and economic implications for local and regional development. In this respect the following investigation sets out to conceptualize change through the complementary and differing perceptions of industry and regional actors’ experiences or narratives, linking these perceptions to their structure-determined spheres of agent-environment interactivity. It aims to determine whether agents’ differing perceptions of industry transformation can have a role in the legitimization of their interests in, and in sustaining their organizational influence over the process of industry-regional transformation. It argues that industry and regional agent perceptions are among the cognitive aspects of agent-environment interactivity that permeate agency. It stresses agents’ ability to reason and manipulate their work environments to preserve their self-regulating interests in, and task representative influence over the multi-jurisdictional space of industry-regional transformation. The contributions of this investigation suggest that agents’ varied perceptions of industry and regional change inform or compete for influence over the redirection of regional, industry and business strategies. This claim offers a greater appreciation for the reflexive and complex institutional dimensions of industry planning and development, and the political responsibility to socially just forms of regional development. It positions the outcomes of this investigation at the nexus of intensifying geo-political discourses on the efficiency and equity of territorial development in Europe.

Extension of explicit formulas in Poissonian white noise analysis using harmonic analysis on configuration spaces

Harmonic analysis on configuration spaces is used in order to extend explicit expressions for the images of creation, annihilation, and second quantization operators in L2-spaces with respect to Poisson point processes to a set of functions larger than the space obtained by directly using chaos expansion. This permits, in particular, to derive an explicit expression for the generator of the second quantization of a sub-Markovian contraction semigroup on a set of functions which forms a core of the generator.