Approximation orders for natural splines in arbitrary dimensions

Based on variational properties, we generalize the approximation properties of the univariate natural cubic spline to splines in arbitrary dimensions.

     

Possible Link between the Distribution of Atomic Spectral Lines and the Radiation–Matter-Equilibrium in the Early Universe

The uncanny resemblance of the global distribution of all experimentally known atomic spectral lines to the Planckian spectral distribution associated with black body radiation at a temperature of $T\approx 9000\mathrm{K}$ is reported. This value coincides with the critical temperature of equilibrium between the respective densities of radiation and matter in the early universe.     

Two-Character Sets Arising from Gluings of Orbits

In this paper we construct two infinite families of transitive two-character sets and hence two infinite families of symmetric strongly regular graphs. We also construct infinite families of quasi-quadrics.     

An elementary proof of Schmüdgen's theorem on the moment problem of closed semi-algebraic sets

We prove the main result from Schmüdgen's 2003 article in a more elementary way. The result states that the question of whether a finitely generated preordering has the so-called strong moment property can be reduced to the same question for preorderings corresponding to fiber sets of bounded polynomials.

     

Improving the reliability of peak-evaluation results in gamma-ray spectrometry

In gamma-ray spectrometry the activities present in the samples are calculated from the areas of the peaks occurring in the spectra. Therefore, the utmost reliability of these input data must be maintained. To avoid systematic manual checks of the peak areas, the spectrum is analyzed consecutively by three peak-analysis programs. A comparative study was performed in which these peak-evaluation programs were tested to determine whether they yielded unbiased results. Only these programs can be used in a combined application. A consistency test of peak areas calculated by use of the three programs, for the same peak, was performed. Outlying results were discarded and the uncertainty of the best estimate for the area of a peak was calculated taking into account the dispersion of the peak-area results for this peak. The reliability of the computerized procedure has made manual checks of the peak areas unnecessary.     

Planes in which every quadrangle lies on a unique Baer subplane

Desarguesian projective planes of square order are characterized by the property that every quadrangle lies on a unique Baer subplane.     

Carbonyl Activation by Selenium- and Tellurium-Based Chalcogen Bonding in a Michael Addition Reaction

In the last years the use of chalcogen bonding—the noncovalent interaction involving electrophilic chalcogen centers—in noncovalent organocatalysis has received increased interest, particularly regarding the use of intermolecular Lewis acids. Herein, we present the first use of tellurium-based catalysts for the activation of a carbonyl compound (and only the second such activation by chalcogen bonding in general). As benchmark reaction, the Michael-type addition between trans-crotonophenone and 1-methylindole (and its derivatives) was investigated in the presence of various catalyst candidates. Whereas non-chalcogen-bonding reference compounds were inactive, strong rate accelerations of up to 1000 could be achieved by bidentate triazolium-based chalcogen bond donors, with product yields of >90 % within 2 h of reaction time. Organotellurium derivatives were markedly more active than their selenium and sulphur analogues and non-coordinating counterions like BAr^F₄ provide the strongest dicationic catalysts.