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.

Use of fibrolytic enzymes to improve the nutritive value of ruminant diets - A biochemical and in vitro rumen degradation assessment

Two commercial enzyme products, Depol 40 (D) and Liquicell 2500 (L), were characterised from a biochemical standpoint and their potential to improve rumen degradation of forages was evaluated in vitro. Enzyme activities were determined at pH 5.5 and 39 degreesC. Analysis of the enzyme activities indicated that L contained higher xylanase and endoglucanase, but lower exoglucanase, pectinase and alpha-amylase activities than D. The Reading Pressure Technique (RPT) was used to investigate the effect of enzyme addition on the in vitro gas production (GP) and organic matter degradation (OMD) of alfalfa (Medicago sativa L.) stems and leaves. A completely randomised design with factorial arrangement of treatments was used. Both alfalfa fractions were untreated or treated with each enzyme at four levels, 20 h before incubation with rumen fluid. Each level of enzyme provided similar amounts of filter paper (D1, L1), endoglucanase (D2, L2), alpha-L-arabinofuranosidase (D3, L3) and xylanase units (D4, L4) per gram forage DM. Enzymes increased the initial OMD in both fractions, with improvements of up to 15% in leaves (D4) and 8% in stems (L2) after 12 h incubation. All enzyme treatments increased the extent of degradation (96 h incubation) in the leaf fractions, but only L2 increased final OMD in the stems. Direct hydrolysis of forage fractions during the pre-treatment period did not fully account for the magnitude of the increases in OMD, suggesting that the increase in rate of degradation was achieved through a combined effect of direct enzyme hydrolysis and synergistic action between the exogenous (applied) and endogenous (rumen) enzymes. (C) 2003 Elsevier Science B.V. All rights reserved.

Whole crop cereals 2. Prediction of apparent digestibility and energy value from in vitro digestion techniques and near infrared reflectance spectroscopy and of chemical composition by near infrared reflectance spectroscopy

Samples of whole crop wheat (WCW, n = 134) and whole crop barley (WCB, n = 16) were collected from commercial farms in the UK over a 2-year period (2003/2004 and 2004/2005). Near infrared reflectance spectroscopy (NIRS) was compared with laboratory and in vitro digestibility measures to predict digestible organic matter in the dry matter (DOMD) and metabolisable energy (ME) contents measured in vivo using sheep. Spectral models using the mean spectra of two scans were compared with those using individual spectra (duplicate spectra). Overall NIRS accurately predicted the concentration of chemical components in whole crop cereals apart from crude protein. ammonia-nitrogen, water-soluble carbohydrates, fermentation acids and solubility values. In addition. the spectral models had higher prediction power for in vivo DOMD and ME than chemical components or in vitro digestion methods. Overall there Was a benefit from the use of duplicate spectra rather than mean spectra and this was especially so for predicting in vivo DOMD and ME where the sample population size was smaller. The spectral models derived deal equally well with WCW and WCB and Would he of considerable practical value allowing rapid determination of nutritive value of these forages before their use in diets of productive animals. (C) 2008 Elsevier B.V. All rights reserved.

Effect of variety, nitrogen fertiliser and various agronomic factors on the nutritive value of husked and naked oats grain

The effect of variety, agronomic and environmental factors on the chemical composition and energy value for ruminants and non-ruminants of husked and naked oats grain was studied. Winter oats were grown as experimental plots in each of 2 years on three sites in England. At each site two conventional husked oat cultivars (Gerald and Image) and two naked cultivars (Kynon and Pendragon) were grown. At each site, crops were sown on two dates and all crops were grown with the application of either zero or optimum fertiliser nitrogen. Variety and factors contained within the site + year effect had the greatest influence on the chemical composition and nutritive value of oats, followed by nitrogen ferfiliser treatment. For example, compared with zero nitrogen, the optimum nitrogen fertiliser treatment resulted in a consistent and significant (P < 0.001) increase in crude protein for all varieties at all sites from an average of 95 to 118 g kg(-1) DM, increased the potassium concentration in all varieties from an average of 4.9 to 5.1 g kg(-1) DM (P < 0.01) and reduced total lipid by a small but significant (P < 0.001) amount. Optimum nitrogen increased (P < 0.001) the NDF concentration in the two husked varieties and in the naked variety Pendragon. Naked cultivars were lower in fibre, had considerably higher energy, total lipid, linoleic acid, protein, starch and essential amino acids than the husked cultivars. Thus nutritionists need to be selective in their choice of naked or husked oat depending on the intended dietary use. (C) 2004 Elsevier B.V. All rights reserved.

Whole crop cereals 1. Effect of method of harvest and preservation on chemical composition, apparent digestibility and energy value

A total of 133 samples (53 fermented unprocessed, 19 fermented processed. 62 urea-treated processed) of whole crop wheat (WCW) and 16 samples (five fermented unprocessed, six fermented processed, five urea-treated processed) of whole crop barley (WCB) were collected from commercial farms over two consecutive years (2003/2004 and 2004/2005). Disruption of the maize grains to increase starch availability was achieved at the point of harvest by processors fitted to the forage harvesters. All samples were subjected to laboratory analysis whilst 50 of the samples (24 front Year 1, 26 front Year 2 all WCW except four WCB in Year 2) were subjected to in vivo digestibility and energy value measurements using mature wether sheep. Urea-treated WCW had higher (P<0.05) pH, and dry matter (DM) and crude protein contents and lower concentrations of fermentation products than fermented WCW. Starch was generally lower in fermented, unprocessed WCW and no effect of crop maturity at harvest (as indicated by DM content) on starch concentrations was seen. Urea-treated WCW had higher (P<0.05) in vivo digestible organic matter contents in the DM (DOMD) in Year 1 although this was not recorded in Year 2. There was a close relationship between the digestibility values of organic matter and gross energy thus aiding the use of DOMD to predict metabolisable energy (ME) content. A wide range of ME values was observed (WCW. 8.7-11.8 MJ/kg DM; WCB 7.9-11.2 MJ/kg DM) with the overall ME/DOMD ratio (ME = 0.0156 DOMD) in line With Studies in other forages. There was no evidence that a separate ME/DOMD relationship was needed for WCB which is helpful for practical application. This ratio and other parameters were affected by year of harvest (P<0.05) highlighting the influence of environmental and Other undefined factors. The variability in the composition and nutritive value of WCW and WCB highlights the need for reliable and accurate evaluation methods to be available to assess the Value of these forages before they are included in diets for dairy cows. (C) 2008 Elsevier B.V. All rights reserved.

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.

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.

Seeds of change: The value of using Rhinanthus minor in grassland restoration

Question: What is the value of using Rhinanthus minor in grassland restoration and can restrictions on its establishment be overcome? Location: England (United Kingdom). Methods: Two experiments were established to determine the efficacy of inoculating R. minor on a suite of four agriculturally improved grasslands and the efficacy of using R. minor in grassland restoration. In Experiment 1, the effect of herbicide gap creation on the establishment and persistence of R. minor in grasslands ranging in productivity was investigated with respect to sward management. In Exp. 2, R. minor was sown at 1000 seeds/m(2) in conjunction with a standard meadow mix over a randomized plot design into Lolium perenne grassland of moderate productivity. The treatment of scarification was investigated as a treatment to promote R. minor. Results: Gap size had a significant role in the establishment and performance of R. minor, especially the 30 cm diameter gaps (Exp. 1). However, R. minor failed to establish long-term persistent populations in all of the agriculturally improved grasslands. In Exp. 2, establishment of R. minor was increased by scarification and its presence was associated with a significant increase in Shannon diversity and the number of sown and unsown species. Values of grass above-ground biomass were significantly lower in plots sown with R. minor, but values of total above-ground biomass (including R. minor) and forb biomass (not including R. minor) were not affected. Conclusions: The value of introducing R. minor into species-poor grassland to increase diversity has been demonstrated, but successful establishment was dependent on grassland type. The scope for using R. minor in grassland restoration schemes is therefore conditional, although establishment can be enhanced through disturbance such as sward scarification.

A new RBF neural network with boundary value constraints

We present a novel topology of the radial basis function (RBF) neural network, referred to as the boundary value constraints (BVC)-RBF, which is able to automatically satisfy a set of BVC. Unlike most existing neural networks whereby the model is identified via learning from observational data only, the proposed BVC-RBF offers a generic framework by taking into account both the deterministic prior knowledge and the stochastic data in an intelligent manner. Like a conventional RBF, the proposed BVC-RBF has a linear-in-the-parameter structure, such that it is advantageous that many of the existing algorithms for linear-in-the-parameters models are directly applicable. The BVC satisfaction properties of the proposed BVC-RBF are discussed. Finally, numerical examples based on the combined D-optimality-based orthogonal least squares algorithm are utilized to illustrate the performance of the proposed BVC-RBF for completeness.