Effect of molecule branching and glycosidic linkage on the degradation of polydextrose by gut microbiota.

Polydextrose is a randomly linked complex glucose oligomer that is widely used as a sugar replacer, bulking agent, dietary fiber and prebiotic. Polydextrose is poorly utilized by the host and, during gastrointestinal transit, it is slowly degraded by intestinal microbes, although it is not known which parts of the complex molecule are preferred by the microbes. The microbial degradation of polydextrose was assessed by using a simulated model of colonic fermentation. The degradation products and their glycosidic linkages were measured by combined gas chromatography and mass spectrometry, and compared to those of intact polydextrose. Fermentation resulted in an increase in the relative abundance of non-branched molecules with a concomitant decrease in single-branched glucose molecules and a reduced total number of branching points. A detailed analysis showed a preponderance of 1,6 pyranose linkages. The results of this study demonstrate how intestinal microbes selectively degrade polydextrose, and provide an insight into the preferences of gut microbiota in the presence of different glycosidic linkages.

A simple method of calculating eigenvalues and resonances in domains with infinite regular ends

A new approach is presented for the solution of spectral problems on infinite domains with regular ends, which avoids the need to solve boundary-value problems for many trial values of the spectral parameter. We present numerical results both for eigenvalues and for resonances, comparing with results reported by Aslanyan, Parnovski and Vassiliev.

A study of the ethene-ozone reaction with photoelectron spectroscopy: measurement of product branching ratios and atmospheric implications

The ozone-ethene reaction has been investigated at low pressure in a flow-tube interfaced to a u.v. photoelectron spectrometer. Photoelectron spectra recorded as a function of reaction time have been used to estimate partial pressures of the reagents and products, using photoionization cross-sections for selected photoelectron bands of the reagents and products, which have been measured separately. Product yields compare favourably with results of other studies, and the production of oxygen and acetaldehyde have been measured as a function of time for the first time. A reaction scheme developed for the ozone-ethene reaction has been used to simulate the reagents and products as a function of time. The results obtained are in good agreement with the experimental measurements. For each of the observed products, the simulations allow the main reaction (or reactions) for production of that product to be established. The product yields have been used in a global model to estimate their global annual emissions in the atmosphere. Of particular interest are the calculated global annual emissions of formaldehyde (0.96 ± 0.10 Tg) and formic acid, (0.05 ± 0.01 Tg) which are estimated as 0.04% and 0.7% of the total annual emission respectively.

Limit operators, collective compactness, and the spectral theory of infinite matrices

In the first half of this memoir we explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). We build up to results obtained by applying this generalised collectively compact operator theory to the set of limit operators of an operator (its operator spectrum). In the second half of this memoir we study bounded linear operators on the generalised sequence space , where and is some complex Banach space. We make what seems to be a more complete study than hitherto of the connections between Fredholmness, invertibility, invertibility at infinity, and invertibility or injectivity of the set of limit operators, with some emphasis on the case when the operator is a locally compact perturbation of the identity. Especially, we obtain stronger results than previously known for the subtle limiting cases of and . Our tools in this study are the results from the first half of the memoir and an exploitation of the partial duality between and and its implications for bounded linear operators which are also continuous with respect to the weaker topology (the strict topology) introduced in the first half of the memoir. Results in this second half of the memoir include a new proof that injectivity of all limit operators (the classic Favard condition) implies invertibility for a general class of almost periodic operators, and characterisations of invertibility at infinity and Fredholmness for operators in the so-called Wiener algebra. In two final chapters our results are illustrated by and applied to concrete examples. Firstly, we study the spectra and essential spectra of discrete Schrödinger operators (both self-adjoint and non-self-adjoint), including operators with almost periodic and random potentials. In the final chapter we apply our results to integral operators on .

Oligomeric pseudorotaxanes adopting infinite-chain lattice superstructures

Above a critical chain length, where oligomers contain five or more recognition units, apparently infinite donor–acceptor polypseudorotaxanes are formed in the solid state. X-ray crystallographic analyses of three different examples have shown that although the oligomeric chains are undoubtedly discrete and monodisperse, they nevertheless appear to be infinite in the crystal.

Scattering by infinite one-dimensional rough surfaces

We consider the Dirichlet boundary-value problem for the Helmholtz equation in a non-locally perturbed half-plane. This problem models time-harmonic electromagnetic scattering by a one-dimensional, infinite, rough, perfectly conducting surface; the same problem arises in acoustic scattering by a sound-soft surface. ChandlerWilde & Zhang have suggested a radiation condition for this problem, a generalization of the Rayleigh expansion condition for diffraction gratings, and uniqueness of solution has been established. Recently, an integral equation formulation of the problem has also been proposed and, in the special case when the whole boundary is both Lyapunov and a small perturbation of a flat boundary, the unique solvability of this integral equation has been shown by Chandler-Wilde & Ross by operator perturbation arguments. In this paper we study the general case, with no limit on surface amplitudes or slopes, and show that the same integral equation has exactly one solution in the space of bounded and continuous functions for all wavenumbers. As an important corollary we prove that, for a variety of incident fields including the incident plane wave, the Dirichlet boundary-value problem for the scattered field has a unique solution.

A uniqueness result for scattering by infinite rough surfaces

Consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane with an unbounded, piecewise Lyapunov boundary. This problem models time-harmonic electromagnetic scattering in transverse magnetic polarization by one-dimensional rough, perfectly conducting surfaces. A radiation condition is introduced for the problem, which is a generalization of the usual one used in the study of diffraction by gratings when the solution is quasi-periodic, and allows a variety of incident fields including an incident plane wave to be included in the results obtained. We show in this paper that the boundary value problem for the scattered field has at most one solution. For the case when the whole boundary is Lyapunov and is a small perturbation of a flat boundary we also prove existence of solution and show a limiting absorption principle.

Uniqueness results for direct and inverse scattering by infinite surfaces in a lossy medium

We consider the Dirichlet boundary-value problem for the Helmholtz equation, Au + x2u = 0, with Imx > 0. in an hrbitrary bounded or unbounded open set C c W. Assuming continuity of the solution up to the boundary and a bound on growth a infinity, that lu(x)l < Cexp (Slxl), for some C > 0 and S~< Imx, we prove that the homogeneous problem has only the trivial salution. With this resnlt we prove uniqueness results for direct and inverse problems of scattering by a bounded or infinite obstacle.

Approximate solution of second kind integral equations on infinite cylindrical surfaces

The paper considers second kind integral equations of the form $\phi (x) = g(x) + \int_S {k(x,y)} \phi (y)ds(y)$ (abbreviated $\phi = g + K\phi $), in which S is an infinite cylindrical surface of arbitrary smooth cross section. The “truncated equation” (abbreviated $\phi _a = E_a g + K_a \phi _a $), obtained by replacing S by $S_a $, a closed bounded surface of class $C^2 $, the boundary of a section of the interior of S of length $2a$, is also discussed. Conditions on k are obtained (in particular, implying that K commutes with the operation of translation in the direction of the cylinder axis) which ensure that $I - K$ is invertible, that $I - K_a $ is invertible and $(I - K_a )^{ - 1} $ is uniformly bounded for all sufficiently large a, and that $\phi _a $ converges to $\phi $ in an appropriate sense as $a \to \infty $. Uniform stability and convergence results for a piecewise constant boundary element collocation method for the truncated equations are also obtained. A boundary integral equation, which models three-dimensional acoustic scattering from an infinite rigid cylinder, illustrates the application of the above results to prove existence of solution (of the integral equation and the corresponding boundary value problem) and convergence of a particular collocation method.