On the Asymptotics of Fekete-Type Points for Univariate Radial Basis Interpolation

Suppose that K ^d is compact and that we are given a function fC(K) together with distinct points x_iK, 1in. Radial basis interpolation consists of choosing a fixed (basis) function g : ⁺→ and looking for a linear combination of the translates g(|x−x_j|) which interpolates f at the given points. Specifically, we look for coefficients c_j such that has the property that F(x_i)=f(x_i), 1in. The Fekete-type points of this process are those for which the associated interpolation matrix [g(|x_i−x_j|)]_1i,jn has determinant as large as possible (in absolute value). In this work, we show that, in the univariate case, for a broad class of functions g, among all point sequences which are (strongly) asymptotically distributed according to a weight function, the equally spaced points give the asymptotically largest determinant. This gives strong evidence that the Fekete points themselves are indeed asymptotically equally spaced.     

Characterization of algebraic curves by Chebyshev quadrature

Complex potential theory is used to show that Chebyshev-type quadrature works particularly well on algebraic Jordan curves Γ in ℝ ^d , supplied with normalized arc length or a similar probability measure μ. Evaluating the integral ∫_Γ fdμ by the arithmetic mean of the value off on any cycle ofN equally spaced nodes on Γ (relative to μ), the quadrature error will, be bounded byAe ^−bN sup_Γ|f| for allN and all polynomialsf(x) of degree ≤cN. It is plausible that small shifts of the nodes would give quadrature error zero for such polynomials. There are related results for algebraic Jordan arcs and certain algebraic surfaces. The situation is completely different for nonalgebraic curves and surfaces, where corresponding quadrature remainders are at least of order 1/N.     

Weakly Admissible Meshes and Discrete Extremal Sets

We present a brief survey on (Weakly) Admissible Meshes and corresponding Discrete Extremal Sets, namely Approximate Fekete Points and Discrete Leja Points. These provide new computational tools for polynomial least squares and interpolation on multidimensional compact sets, with different applications such as numerical cubature, digital filtering, spectral and high-order methods for PDEs.     

Comparison of ‘blue’ and ‘infrared’ emission bands in thermoluminescence of alkali feldspars

Dating quaternary sediments by thermoluminescence (TL) or optically stimulated luminescence (OSL) calls for a detailed knowledge of the luminescence of feldspars. TL of the various alkali feldspars ((K, Na) Si₃AlO₈) display many common features, and some of these cause great difficulties for dating. After long storage following ionizing irradiation, the TL of most alkali feldspars is known to fade away by “anomalous fading”, which is incompatible with dating. This effect had been attributed to tunnel recombination. Following irradiation, a very intense tunnelling afterglow is observed at temperatures down to liquid nitrogen, in accordance with the observed rate of fading. This emission has a Gaussian spectrum entirely in the infrared (IR) with a maximum at 1.7 eV. It displays an important thermal quenching from 77 to 300 K. Its intensity is related with the ‘disorder’ of the crystal lattice. At higher temperatures, in TL proper, two emission bands can be separated. One is the well-studied complex visible emission, distributed over the spectral region from UV to orange, but mostly ‘blue’. The other is the ‘infrared’ band already observed at lower temperatures, which is attributed to Fe³⁺ ions. These two bands are clearly separated, with the spectral maxima, respectively, below and above 600 nm. They have also different kinetics, the glow peaks temperatures are different. But these two different bands are also coupled in many ways, they have parallel growth and fading. With ‘disordered’ feldspars, the ‘blue’ emission displays anomalous fading, which is stronger than that of the ‘infrared’. The infrared emission is more stable, which may be interesting for the purpose of dating.     

Copper and iron interactions with angiotensin-converting enzyme inhibitors. A study by fast-atom bombardment tandem mass spectrometry

Fast atom bombardment, combined with high-energy collision-induced tandem mass spectrometry, has been used to investigate gas-phase metal-ion interactions with captopril, enalaprilat and lisinopril, all angiotensin-converting enzyme inhibitors.Suggestions for the location of metal-binding sites are presented. For captopril, metal binding occurs most likely at both the sulphur and the nitrogen atom. For enalaprilat and lisinopril, binding preferably occurs at the amine nitrogen. Copyright 1999 John Wiley & Sons, Ltd.     

Network forming properties of various proteins adsorbed at the air/water interface in relation to foam stability

A series of proteins was studied with respect to their ability to form a network at the air/water interface and their suitability as foaming agents and foam stabilizers. Proteins were chosen with a range of structures from flexible to rigid/globular: beta-casein, beta-lactoglobulin, ovalbumin, and (soy) glycinin. Experiments were performed at neutral pH except for glycinin, which was studied at both pH 3 and pH 6.7. The adsorption process was followed with an automated drop tensiometer (ADT). Network forming properties were assessed in terms of surface dilational modulus (determined with the ADT), the critical falling film length (L(still)) and flow rate (Q(still)) below which a stagnant film exists (as measured with the overflowing cylinder technique), and the fracture stress and fracture strain measured in surface shear. It was found that glycinin (pH 3) can form an interfacial gel in a very short time, whereas beta-casein has very poor network-forming properties. Hardly any foam could be produced at the chosen conditions with glycinin (pH 6.7) and with ovalbumin, whereas beta-casein, beta-lactoglobulin, and glycinin (pH 3) were good foaming agents. It seems that adsorption and unfolding rate are most important for foam formation. Once the foam is formed, a rigid network might favor stabilizing the foam.     

A generalized approach for the calculation and automation of potentiometric titrations Part 1. Acid-Base Titrations

Fast and accurate calculation procedures for pH and redox potentials are required for optimum control of automatic titrations. The procedure suggested is based on a three-dimensional titration curve V = f(pH, redox potential). All possible interactions between species in the solution, e.g., changes in activity coefficients and influences of redox potential on pH variations, are taken into account. The number of titrant additions can be reduced considerably without loss of precision, by using the fact that the pH of a protolyte or mixture of protolytes at some fraction titrated does not depend strongly on the actual concentration.     

Systematical study of beta delayed proton emission energies

Graphs are given of the maximum proton energies in delayed proton emitters. This quantity, equal to the difference of the electron capture decay energy of the precursor and the separation energy of a proton in the daughter, has been calculated in a least squares adjustment of mass spectroscopic data and nuclear decay and reaction energies. The graphs would lead to expect a 950 keV lower maximum proton energy in⁷³Kr(?p)⁷²Se than has been reported from experiments. They can be used to predict new cases for further studies on this subject.     

Determination of valepotriates

In this paper an overview is given of qualitative and quantitative methods of analysis used for valepotriates. Methods like spectophotometry, titrimetry, TLC, GC, HPLC, MS, CE as well as p-SFC have been applied. Today HPLC is the method of choice. The usefulness of the individual methods are discussed.