Solvability and spectral properties of integral equations on the real line: I. Weighted spaces of continuous functions

We consider in this paper the solvability of linear integral equations on the real line, in operator form (λ−K)φ=ψ, where and K is an integral operator. We impose conditions on the kernel, k, of K which ensure that K is bounded as an operator on . Let Xa denote the weighted space as |s|→∞}. Our first result is that if, additionally, |k(s,t)|⩽κ(s−t), with and κ(s)=O(|s|−b) as |s|→∞, for some b>1, then the spectrum of K is the same on Xa as on X, for 01. As an example where kernels of this latter form occur we discuss a boundary integral equation formulation of an impedance boundary value problem for the Helmholtz equation in a half-plane.

Quantifying uncertainty in remotely sensed land cover maps

Remotely sensed land cover maps are increasingly used as inputs into environmental simulation models whose outputs inform decisions and policy-making. Risks associated with these decisions are dependent on model output uncertainty, which is in turn affected by the uncertainty of land cover inputs. This article presents a method of quantifying the uncertainty that results from potential mis-classification in remotely sensed land cover maps. In addition to quantifying uncertainty in the classification of individual pixels in the map, we also address the important case where land cover maps have been upscaled to a coarser grid to suit the users’ needs and are reported as proportions of land cover type. The approach is Bayesian and incorporates several layers of modelling but is straightforward to implement. First, we incorporate data in the confusion matrix derived from an independent field survey, and discuss the appropriate way to model such data. Second, we account for spatial correlation in the true land cover map, using the remotely sensed map as a prior. Third, spatial correlation in the mis-classification characteristics is induced by modelling their variance. The result is that we are able to simulate posterior means and variances for individual sites and the entire map using a simple Monte Carlo algorithm. The method is applied to the Land Cover Map 2000 for the region of England and Wales, a map used as an input into a current dynamic carbon flux model.

In Vitro Fermentation of NUTRIOSE® FB06, a wheat dextrin soluble fibre, in a continuous culture human colonic model system

Wheat dextrin soluble fibre may have metabolic and health benefits, potentially acting via mechanisms governed by the selective modulation of the human gut microbiota. Our aim was to examine the impact of wheat dextrin on the composition and metabolic activity of the gut microbiota. We used a validated in vitro three-stage continuous culture human colonic model (gut model) system comprised of vessels simulating anatomical regions of the human colon. To mimic human ingestion, 7 g of wheat dextrin (NUTRIOSE® FB06) was administered to three gut models, twice daily at 10.00 and 15.00, for a total of 18 days. Samples were collected and analysed for microbial composition and organic acid concentrations by 16S rRNA-based fluorescence in situ hybridisation and gas chromatography approaches, respectively. Wheat dextrin mediated a significant increase in total bacteria in vessels simulating the transverse and distal colon, and a significant increase in key butyrate-producing bacteria Clostridium cluster XIVa and Roseburia genus in all vessels of the gut model. The production of principal short-chain fatty acids, acetate, propionate and butyrate, which have been purported to have protective, trophic and metabolic host benefits, were increased. Specifically, wheat dextrin fermentation had a significant butyrogenic effect in all vessels of the gut model and significantly increased production of acetate (vessels 2 and 3) and propionate (vessel 3), simulating the transverse and distal regions of the human colon, respectively. In conclusion, wheat dextrin NUTRIOSE® FB06 is selectively fermented in vitro by Clostridium cluster XIVa and Roseburia genus and beneficially alters the metabolic profile of the human gut microbiota.

Continuous-flow processing of gaseous ammonia using a Teflon AF-2400 tube-in-tube reactor: synthesis of thioureas and in-line titrations

A simple tube-in-tube reactor based on the gas-permeable membrane Teflon AF-2400 was used in the continuous flow reaction of gaseous ammonia with isothiocyanates and one isocyanate. A colourimetric in-line titration technique is also reported as a simple method to quantify the amount of ammonia taken up by the solvent in the system.