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Abstract. Spectral theory and classical approximation theory are used to give a new proof of the exponential decay of the entries of the inverse of band matrices. The rate of decay oí A'1 can be bounded in terms of the (essential) spectrum of A A* for general A and in terms of the (essential) spectrum of A for positive definite A. In the positive definite case the bound can be attained. These results are used to establish the exponential decay for a class of generalized eigenvalue problems and to establish exponential decay for certain sparse but nonbanded matrices. We also establish decay rates for certain generalized inverses.1. Introduction. The exponential decay of the entries of inverse of band matrices has been of some use in establishing local rates of convergence of spline approximations [12], [11], [6] and in bounding the L^-norm of the orthogonal projection onto spline spaces [4] and [15]. Kershaw proved a result of this nature for tridiagonal matrices and Descloux's paper [7] contains such a result for Grammian matrices arising in finite element approximations although exponential decay is not explicitly mentioned. For general banded invertible matrices the first proof appeared in [6]. A later proof in [3], [5] gave explicit estimates for the rate of decay. In this paper we use spectral theory and a result of Chebyshev on the best approximation of (x -a)~l by polynomials to give a new proof. The bounds on the rate of decay obtained from this proof appear to be sharper than those previously known and are actually attained in some cases. In addition, the method of proof easily extends to certain generalized inverses and certain nonbanded matrices. We show that the rate of decay for A ~l given by our method depends on only the essential spectrum of AA* and is, thus, stable under banded compact perturbations. This fact is used to establish the exponential decay of the eigenvectors of certain generalized eigenvalue

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The aim of this study was to determine the microbiological origin of plaque fluorescence observed during quantitative light-induced fluorescence (QLF) analysis. Plaque was sampled from dentures, because of easy accessibility and the homogeneous background provided by the denture tooth during imaging, and the acknowledged comparability to occlusal plaque. Forty removable poly(methyl methacrylate) dentures were screened for the presence of fluorescent plaque deposits during QLF analysis. Dentures were photographed, QLF images were recorded and samples of fluorescent plaque were taken. Plaque samples were cultured on fastidious anaerobe agar, Wilkins Chalgren agar and Sabourauds dextrose agar. Plates were screened under QLF and fluorescent colonies were subcultured and identified. Areas of red, orange and green fluorescence were detected on the fitting and non-fitting surfaces of dentures. The red and orange fluorescing species were Prevotella melaninogenica, Actinomyces israelii and Candida albicans, which are generally acknowledged to be secondary colonisers, present in more mature plaque. Green fluorescence was observed in streptococcal species (early colonisers) and Fusobacterium nucleatum (important organism in plaque development). Non-fluorescent colonies were also cultured. Plaque which accumulates on susceptible surfaces tends to be associated with caries, but it may be its maturity, rather than the presence of cariogenic streptococci, that is more likely to provide a microbiological link between red fluorescence and caries.

Corn, rice and potato flour were extruded with sweet whey solids (SWS) or whey protein concentrate (WPC) using low and high shear extrusion processing conditions. WPC added at product content of 25% had minimal effect on the texture of extruded products. Expansion and breaking strength were improved in some processes through changes in extrusion shear and moisture. Whey product incorporation resulted in reduced specific mechanical energy input to the process. Increasing whey product concentration beyond 25% reduced expansion and water absorption indices significantly, affecting textural hardness. Product quality characteristics were directly related to the whey product content.

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