On a problem proposed by H. Braß concerning the remainder term in quadrature for convex functions

Summary We prove that the error inn-point Gaussian quadrature, with respect to the standard weight functionw1, is of best possible orderO(n ^–2) for every bounded convex function. This result solves an open problem proposed by H. Braß and published in the problem section of the proceedings of the 2. Conference on Numerical Integration held in 1981 at the Mathematisches Forschungsinstitut Oberwolfach (Hämmerlin 1982; Problem 2). Furthermore, we investigate this problem for positive quadrature rules and for general product quadrature. In particular, for the special class of Jacobian weight functionsw _, (x)=(1–x)(1+x), we show that the above result for Gaussian quadrature is not valid precisely ifw _, is unbounded.Dedicated to Prof. H. Braß on the occasion of his 55th birthday     

CdSe and CdSe/CdS nanorod solids

We demonstrate the self-organization of CdSe nanorods into nematic, smectic, and crystalline solids. Layered colloidal crystals of CdSe nanorods grow by slow destabilization of a nanocrystal solution upon allowing the diffusion of a nonsolvent into the colloidal solution of nanocrystals. The colloidal crystals of nanorods show characteristic birefringence, which we assign to specific spherulite-like texture of each nanorod assembly. To demonstrate the general character of nanorod self-assembly technique, CdSe/CdS heterostructure nanorods were organized into highly luminescent superlattices.     

Publication activity on radioanalytical chemistry in the German Democratic Republic

The growth of the number of papers on radioanalytical methods and activation analysis, the distribution of the authorship and papers published in various periodicals are determined in the course of a scientometric analysis using the first complete National Bibliography of GDR on Radioanalytical Chemistry as a database.     

Temperature measurements in CO2-laser-induced pyrolysis flames for SiC and ternary SiC/C/B powder synthesis by means of CARS

The hot luminescent reaction zones of CO₂-laser-induced pyrolysis flames using SiH₄/C₂H₂ gas mixtures with different silane to acetylene ratios and with and without diborane additives were investigated by means of H₂ Q-branch CARS spectroscopy, leading to spatial temperature profiles in gas flow direction. In the case of B₂H₆ additive to the stoichiometric SiH₄/C₂H₂ mixture a high temperature plateau ( 800–1000 K) of the reactant gas volume develops already several millimetres before reaching the CO₂-laser focus line. This precursor preheating zone could be explained by the catalytic effect of boron atoms or boron-containing intermediate species in the flame. A similar behaviour for acetylene-rich flames operating at half laser power was not observed.     

UV-VIS spectroscopic study of interaction and transformation of allyl alcohol on zeolites HZSM-5

Formation of alkenylcarbenium ions has been proved during transformation of allyl alcohol on zeolite HZSM-5.

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HZSM-5.

     

Use of FTIR spectroscopy in the investigation of catalytic reactions in zeolites—Possibilities and limitations

FTIR-spectroscopic investigations of catalytic reactions yield detailed information about the interaction of adsorbed molecules with the catalyst and kinetic data of the surface reaction, if the participating molecules show vibrations whose position and intensity in the IR-spectrum depend on the sorption state and the quantity adsorbed. In this paper, the possibilities and limitations of the method are represented by two examples.