In this paper, we give a constructive proof that a real, piecewise continuous function can be almost uniformly approximated by single hidden-layer feedforward neural networks (SLFNNs). The construction procedure avoids the Gibbs phenomenon. Computer experiments show that the resulting approximant is much more accurate than SLFNNs trained by gradient descent.
An enzymatic method for determining L-malic acid in wine based on an L-malate sensing layer with nicotinamide adenine dinucleotide (NAD+), L-malate dehydrogenase (L-MDH) and diaphorase (DI), immobilized by sol-gel technology, was constructed and evaluated. The sol-gel glass was prepared with tetramethoxysilane (TMOS), water and HCl. L-MDH catalyzes the reaction between L-malate and NAD+, producing NADH, whose fluorescence (lambdaexc=340 nm, lambdaem=430 nm) could be directly related to the amount of L-malate. NADH is converted to NAD+ by applying hexacyanoferrate(III) as oxidant in the presence of DI. Some parameters affecting sol-gel encapsulation and the pH of the enzymatic reaction were studied. The sensing layer has a dynamic range of 0.1-1.0 g/L of L-malate and a long-term storage stability of 25 days. It exhibits acceptable reproducibility [sr(%) approximately 10] and allows six regenerations. The content of L-malic acid was determined for different types of wine, and polyvinylpolypyrrolidone (PVPP) was used as a bleaching agent with red wine. The results obtained for the wine samples using the sensing layer are comparable to those obtained from a reference method based on UV-vis molecular absorption spectrometry, if the matrix effect is corrected for.
In this paper we present a new algorithm (LSABV) for determining the intersection between a ray and a convex polyhedron (RCPI) in a fast way. LSABV is based on local search and the concept of visibility. LSABV requires only the boundary description of the polyhedron and it does not need additional data structures. Numerical experiments show that LSABV is faster than Haines's algorithm in the case of polyhedra with moderate or large number of faces.
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