The elliptic sine-Gordon equation in a half plane

We consider boundary value problems for the elliptic sine-Gordon equation posed in the half plane y > 0. This problem was considered in Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) using the classical inverse scattering transform approach. Given the limitations of this approach, the results obtained rely on a nonlinear constraint on the spectral data derived heuristically by analogy with the linearized case. We revisit the analysis of such problems using a recent generalization of the inverse scattering transform known as the Fokas method, and show that the nonlinear constraint of Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) is a consequence of the so-called global relation. We also show that this relation implies a stronger constraint on the spectral data, and in particular that no choice of boundary conditions can be associated with a decaying (possibly mod 2π) solution analogous to the pure soliton solutions of the usual, time-dependent sine-Gordon equation. We also briefly indicate how, in contrast to the evolutionary case, the elliptic sine-Gordon equation posed in the half plane does not admit linearisable boundary conditions.

Testing solutions in grass-dominated landscapes: a review of current research

In this paper we review the experimental development of agri-environment measures for use on grasslands. Sward structure has been shown to have a strong influence on birds' ability to forage in grasslands, but the effects of food abundance on foraging behaviour are poorly understood and this hinders development of grassland conservation measures. The experiments described have a dual purpose: to investigate the foraging ecology of birds on grasslands and to test candidate management measures. Most of the work featured focuses on increasing invertebrate food resources during the summer by increasing habitat heterogeneity. We also identify important gaps in the habitats provided by existing or experimental measures, where similar dual-purpose experiments are required.

Saturated salt solutions for humidity control and the survival of dry powder and oil formulations of Beauveria bassiana conidia

Oil-based formulated conidia sprayed on steel plates and conidia powder (control) of Beauveria bassiana isolate IMI 386243 were stored at temperatures from 10 to 40 degrees C in desiccators over saturated salt solutions providing relative humidities from 32 to 88%, or in hermetic storage at 40 degrees C, and moisture contents in equilibrium with 33 or 77% relative humidity. The negative semi-logarithmic relation (P < 0.005) between conidia longevity (at 40 degrees C) and equilibrium relative humidity did not differ (P > 0.25) between formulated conidia and conidia powder. Despite this, certain saturated salts provided consistently greater longevity (NaCl) and others consistently shorter longevity (KCl) for formulated conidia compared to conidia powder. These results, analysis of previous data, and comparison with hermetic storage, indicate that storage of conidia over saturated salt solutions provides inconsistent responses to environment and so may be problematic for bio-pesticide research. In hermetic storage, oil formulation was not deleterious to longevity and in the more moist environment enhanced survival periods. (c) 2005 Elsevier Inc. All rights reserved.

Osmotic pressure and aggregate shape in BSA/poly (ethylene glycol)-lipid/Dextran solutions

In this work we study the colloidal osmotic pressure (COP) and aggregate shape in phosphate saline buffer solutions (PH 7.4) containing bovine serum albumin (BSA), poly(ethylene glycol) lipid (PEG(2000)-PE) and Dextran (Dx). Dx was added to the BSA/PEG(2000)-PE system in order to increase the COP of the solution to levels comparable to the COP of healthy adults, with the aim of using the solution as a blood COP regulator. Dynamic light scattering and small angle X-ray scattering results shown the formation of BSA/PEG(2000)-PE/Dx aggregates in the solution. Osmometry results shown that the addition of Dx to the BSA/PE2000-PE system could successfully increase the COP, through the formation of BSA/PEG(2000)-PE/Dx aggregates. The BSA/PEG(2000)-PE/Dx solutions attained COP= 15 mm Hg, representing 60% of COP measured for healthy adults. (c) 2008 Elsevier B.V. All rights reserved.