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.

Studying the impact of ubiquitous monitoring technology on office worker behaviours: the value of sharing research data

Pervasive computing is a continually, and rapidly, growing field, although still remains in relative infancy. The possible applications for the technology are numerous, and stand to fundamentally change the way users interact with technology. However, alongside these are equally numerous potential undesirable effects and risks. The lack of empirical naturalistic data in the real world makes studying the true impacts of this technology difficult. This paper describes how two independent research projects shared such valuable empirical data on the relationship between pervasive technologies and users. Each project had different aims and adopted different methods, but successfully used the same data and arrived at the same conclusions. This paper demonstrates the benefit of sharing research data in multidisciplinary pervasive computing research where real world implementations are not widely available.

The National Audit Office uses OR to assess the value for money of public services

Supreme audit institutions (SAIs) have an important role in assessing value for money in the delivery of public services. Assessing value for money necessarily involves assessing counterfactuals: good value for money has been achieved if a policy could not reasonably have been delivered more efficiently, effectively, or economically. Operations research modelling has the potential to help in the assessment of these counterfactuals. However, is such modelling too arcane, complex, and technically burdensome for organisations that, like SAIs, operate in a time- and resource-constrained and politically charged environment? We report on three applications of modelling at the UK's SAI, the National Audit Office, in the context of studies on demand management in tax collection, end-of-life care, and health-care associated infections. In all cases, the models have featured in the audit reports and helped study teams come to a value-for-money judgment. We conclude that OR modelling is indeed a valuable addition to the value-for-money auditor's methodological tool box.

Estimating regional benefits of reducing targeted pollutants: An application to agricultural effects on water quality and the value of recreational fishing

The general focus of this paper is the regional estimation of marginal benefits of targeted water pollution abatement to instream uses. Benefit estimates are derived from actual consumer choices of recreational fishing activities and the implied expenditures for various levels of water quality. The methodology is applied to measuring the benefits accruing to recreational anglers in Indiana from the abatement of pollutants that are by-products of agricultural crop production.