Well-posed boundary value problems for integrable evolution equations on a finite interval

We consider boundary value problems posed on an interval [0,L] for an arbitrary linear evolution equation in one space dimension with spatial derivatives of order n. We characterize a class of such problems that admit a unique solution and are well posed in this sense. Such well-posed boundary value problems are obtained by prescribing N conditions at x=0 and n–N conditions at x=L, where N depends on n and on the sign of the highest-degree coefficient n in the dispersion relation of the equation. For the problems in this class, we give a spectrally decomposed integral representation of the solution; moreover, we show that these are the only problems that admit such a representation. These results can be used to establish the well-posedness, at least locally in time, of some physically relevant nonlinear evolution equations in one space dimension.

Initial boundary value problems for the nonlinear Schrödinger equation

A new spectral method for solving initial boundary value problems for linear and integrable nonlinear partial differential equations in two independent variables is applied to the nonlinear Schrödinger equation and to its linearized version in the domain {x≥l(t), t≥0}. We show that there exist two cases: (a) if l″(t)<0, then the solution of the linear or nonlinear equations can be obtained by solving the respective scalar or matrix Riemann-Hilbert problem, which is defined on a time-dependent contour; (b) if l″(t)>0, then the Riemann-Hilbert problem is replaced by a respective scalar or matrix problem on a time-independent domain. In both cases, the solution is expressed in a spectrally decomposed form.

A Nyström method for a boundary value problem arising in unsteady water wave problems

This paper is concerned with solving numerically the Dirichlet boundary value problem for Laplace’s equation in a nonlocally perturbed half-plane. This problem arises in the simulation of classical unsteady water wave problems. The starting point for the numerical scheme is the boundary integral equation reformulation of this problem as an integral equation of the second kind on the real line in Preston et al. (2008, J. Int. Equ. Appl., 20, 121–152). We present a Nystr¨om method for numerical solution of this integral equation and show stability and convergence, and we present and analyse a numerical scheme for computing the Dirichlet-to-Neumann map, i.e., for deducing the instantaneous fluid surface velocity from the velocity potential on the surface, a key computational step in unsteady water wave simulations. In particular, we show that our numerical schemes are superalgebraically convergent if the fluid surface is infinitely smooth. The theoretical results are illustrated by numerical experiments.

The value of badger populations and control of tuberculosis in cattle in England and Wales: A note

This note reports on the results of a choice experiment survey of 400 people in England and Wales, conducted to estimate the value that society places on changes to the size of the badger population. The study was undertaken in the context of the possible need to reduce the badger population by culling to help control bovine tuberculosis in cattle. The study found that people were concerned about the problem of bovine tuberculosis in cattle, which was reflected in their willingness to pay to control the disease, and gave a relatively low value to changes in the size of the badger population (within limits). However, people did not like the idea of a policy that intentionally killed large numbers of badgers and had a relatively very high willingness to pay not to have such a policy.

The value of sown grass margins for enhancing soil macrofaunal biodiversity in arable systems

The presence of a grass strip was found to be beneficial to soil macrofauna, increasing the species densities and abundances of earthworms, woodlice and staphylinid beetles. The biodiversity of the three main feeding groups - predators, soil ingesters and litter consumers - was also significantly higher in the grass strips than in the field edges without strips, indicating that establishment of grassy margins in arable fields may enhance ecosystem services such as soil fertility and pest control. The grass strip habitat contained a large number of species of soil macrofauna, being second only to hedgerow habitat, with 10% of the total species list for the farm found only within the margins. Of the rare species recorded on the farm, five of the nine were from the grass strips, four of which were found only there. This study shows that establishing grassy strips in the margins of arable fields increases the biodiversity of the soil macrofauna, both within fields (alpha diversity) and across the farm (beta diversity). (C) 2008 Elsevier B.V. All rights reserved.

The value of arable field margins for enhancing soil macrofaunal biodiversity in agroecosystems

The presence of a grass strip was found to be beneficial to soil macrofauna, increasing the species densities and abundances of earthworms, woodlice and staphylinid beetles. The biodiversity of the three main feeding groups – predators, soil ingesters and litter consumers – was also significantly higher in the grass strips than in the field edges without strips, indicating that establishment of grassy margins in arable fields may enhance ecosystem services such as soil fertility and pest control. The grass strip habitat contained a large number of species of soil macrofauna, being second only to hedgerow habitat, with 10% of the total species list for the farm found only within the margins. Of the rare species recorded on the farm, five of the nine were from the grass strips, four of which were found only there. This study shows that establishing grassy strips in the margins of arable fields increases the biodiversity of the soil macrofauna, both within fields (alpha diversity) and across the farm (beta diversity).

Can arable field margins be managed to enhance their biodiversity, conservation and functional value for soil macrofauna?

1. The establishment of grassy strips at the margins of arable fields is an agri-environment scheme that aims to provide resources for native flora and fauna and thus increase farmland biodiversity. These margins can be managed to target certain groups, such as farmland birds and pollinators, but the impact of such management on the soil fauna has been poorly studied. This study assessed the effect of seed mix and management on the biodiversity, conservation and functional value of field margins for soil macrofauna. 2. Experimental margin plots were established in 2001 in a winter wheat field in Cambridgeshire, UK, using a factorial design of three seed mixes and three management practices [spring cut, herbicide application and soil disturbance (scarification)]. In spring and autumn 2005, soil cores taken from the margin plots and the crop were hand-sorted for soil macrofauna. The Lumbricidae, Isopoda, Chilopoda, Diplopoda, Carabidae and Staphylinidae were identified to species and classified according to feeding type. 3. Diversity in the field margins was generally higher than in the crop, with the Lumbricidae, Isopoda and Coleoptera having significantly more species and/or higher abundances in the margins. Within the margins, management had a significant effect on the soil macrofauna, with scarified plots containing lower abundances and fewer species of Isopods. The species composition of the scarified plots was similar to that of the crop. 4. Scarification also reduced soil- and litter-feeder abundances and predator species densities, although populations appeared to recover by the autumn, probably as a result of dispersal from neighbouring plots and boundary features. The implications of the responses of these feeding groups for ecosystem services are discussed. 5. Synthesis and applications. This study shows that the management of agri-environment schemes can significantly influence their value for soil macrofauna. In order to encourage the litter-dwelling invertebrates that tend to be missing from arable systems, agri-environment schemes should aim to minimize soil cultivation and develop a substantial surface litter layer. However, this may conflict with other aims of these schemes, such as enhancing floristic and pollinator diversity.

Trust and governance of global value chains: The case of a Brazilian beef processor

Purpose - The purpose of this paper is to offer an exploratory case study comparing one Brazilian beef processor's relationships supplying two different distribution channels, an EU importer and an EU retail chain operating in Brazil. Design/methodology/approach - The paper begins with a short review of global value chains and the recent literature on trust. It gives the background to the Brazilian beef chain and presents data obtained through in-depth interviews, annual reports and direct observation with the Brazilian beef processor, the EU importer and the retailer. The interviews were conducted with individual firms, but the analysis places them in a chain context, identifying the links and relationships between the agents of the chains and aiming to describe each distribution channel. Findings - Executive chain governance exercised by the domestic retailer stimulates technical upgrading and transferring of best practices to local. suppliers. Consequently, this kind of relationship results in more trust within the global value chain. Practical implications - There are difficulties and challenges facing this Brazilian beef processor that are party related to the need to comply with increasingly complex and demanding food safety and food quality standards. There is still a gap between practices adopted for the export market and practices adopted locally. The strategies of transnational retailers in offering differentiated beef should be taken in account. Originality/value - The research outlines an interdisciplinary framework able to explain chain relationships and the kind of trust that emerges in relationships between EU importer/retail and a developing country supplier.