Research on the aromas. On the aroma of coffee. I

The analysis of a coffee concentrate is described: 202 constituents have been identified, 154 of which for the first time. Some of these compounds are new chemicals; their synthesis is described. Most identifications are based upon mass spectrometry combined in many cases with IR. spectrometry and comparison with reference compounds. MS. and IR. data are given in detail. The analysis shows that a large number of minor constituents is present, many of which could not be identified.     

Neutralizing nearby singularities in numerical quadrature

A method of “neutralization” is presented that significantly weakens, if not eliminates, a singularity close to, but outside, the interval of integration. The effectiveness of the method is illustrated by a number of examples.     

Computing the Hilbert Transform of the Generalized Laguerre and Hermite Weight Functions

Explicit formulae are given for the Hilbert transform $f_\mathbb{R} $ w(t)dt/(t ? x), where w is either the generalized Laguerre weight function w(t) = 0 if t ≤ 0, w(t) = t ^α e ^?t if 0 <#60; t <#60; ∞, and α > ?1, x > 0, or the Hermite weight function w(t) = e ^{?t 2}, ?∞ <#60; t <#60; ∞, and ?∞ <#60; x <#60; ∞. Furthermore, numerical methods of evaluation are discussed based on recursion, contour integration and saddle-point asymptotics, and series expansions. We also study the numerical stability of the three-term recurrence relation satisfied by the integrals $f_\mathbb{R} $ π _n (t;w)w(t)dt/(t ? x), n = 0 ,1 ,2 ,..., where π _n (?w) is the generalized Laguerre, resp. the Hermite, polynomial of degree n.     

Vandermonde matrices on the circle: Spectral properties and conditioning

Summary We study Vandermonde matrices whose nodes are given by a Van der Corput sequence on the unit circle. Our primary interest is in the singular values of these matrices and the respective (spectral) condition numbers. Detailed information about multiplicities and eigenvectors, however, is also obtained. Two applications are given to the theory of polynomials.Dedicated to R. S. Varga on the occasion of his sixtieth birthdayResearch of A. C. supported by the Fundación Andes, Chile, and by the German Academic Exchange Service (DAAD), Federal Republic of GermanyResearch of W. G. supported, in part, by the National Science Foundation, USA, (Grant CCR-8704404)Research of S. R. supported by the Fondo Nacional de Desarollo Cientßfico y Tecnológico (FONDECYT), Chile, (Grant 237/89), by the Universidad Técnica F. Santa Marßa, Valparaßso, Chile, (Grant 89.12.06), and by the German Academic Exchange Service (DAAD), Federal Republic of Germany