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.

Political market characteristics and the provision of educational infrastructure in North India

In this paper, we are concerned with the provision of schools in rural North India, particularly with whether such provision is determined by the demographic and economic characteristics of the region or whether local democracy also plays a role. We find that the probability that a governing party loses an election has a positive effect on the provision of schooling infrastructure, while the margin of victory of the governing party has a negative effect. Political reservation for members of the Scheduled Castes (SCs) has a positive effect on schooling infrastructure in villages with a large SC population, but a negative effect overall.

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.