On a theorem by Hsiang and Yu

In 1841, Delaunay classified surfaces of revolution with constant mean curvature in the Euclidean three space. As a byproduct of his result, one obtains: A surface of revolution has a periodic generating curve if and only if its mean curvature is non-zero. One hundred and forty years after Delaunay’s work, Hsiang and Yu extended this result to higher dimensions, by extending Delaunay’s idea of tracing the locus of a focus by rolling a given conic section along a line. In this paper, we give a new proof of their result using elementary ODE theory to obtain the periodicity of the solutions under consideration.      

Syntheses of the 47 electron clusters [(Cp*Fe)3(mu3-X)2] (X = S, Se) and the First Fe/Sn/Se Heterocubane Cluster [(CpFe)3(SnCl3)(mu3-Se)4] x DME by the use of chalcogenostannate salts

By reacting 1-aminoethylammonium (H2NCH2CH2NH3+ = enH+) salts of [Sn2E6]4- anions (E = S, Se), [enH]4[Sn2S6] (1) and [enH]4[Sn2Se6] x en (2), with FeCl2/LiCp, three novel (partly) oxidized, Cp* ligated iron chalcogenide clusters were synthesized. Two of them, [(CpFe)3(mu3-S)2] (3) and [(Cp*Fe)3(mu3-Se)2] (4), contain formally 47 valence electrons. [(Cp*Fe)3(SnCl3)(mu3-Se)4] x DME (5) represents the first known mixed metal Fe/Sn/Se heterocubane type cluster. Compounds 3-5 were structurally characterized by single-crystal X-ray diffraction, and the odd valence electron number of the [Fe3E2] clusters (E = S, Se) was confirmed by density functional (DFT) investigations, mass spectrometry, cyclic voltammetry and a susceptibility measurement of 3.     

Development of High NIR-Reflective Red Li2MnO3 Pigments

In this work, the development of a novel class of eco-friendly red pigments based on doped Li₂MnO₃ is reported. These new compounds offer red color values of a* > 34, which are recognizably higher than the red value provided by the commonly used red pigment iron oxide Bayferrox 4130. However, the real outstanding attribute of these novel substances is their strikingly high NIR-reflectance that gives promise for a new class of materials for the practical utilization as cool pigments in building components and ceramics. We have synthesized the inorganic pigments by conventional solid-state reactions at 900 °C and subsequently carried out the structural characterizations by X-ray powder diffraction (XRPD) and Rietveld analysis. We recorded the diffuse reflectance spectra of the obtained powders and determined the color properties by means of CIE L*a*b* coordinates. Finally, we measured the NIR reflectance and calculated the NIR solar reflection of these compounds affording values above 85 % in the range from 700 to 2500 nm.     

Minimax optimal procedures for testing the structure of multidimensional functions

We present a novel method for detecting some structural characteristics of multidimensional functions. We consider the multidimensional Gaussian white noise model with an anisotropic estimand. Using the relation between the Sobol decomposition and the geometry of multidimensional wavelet basis we can build test statistics for any of the Sobol functional components. We assess the asymptotical minimax optimality of these test statistics and show that they are optimal in presence of anisotropy with respect to the newly determined minimax rates of separation. An appropriate combination of these test statistics allows to test some general structural characteristics such as the atomic dimension or the presence of some variables. Numerical experiments show the potential of our method for studying spatio-temporal processes.     

Static Moments of Neutron-Rich Ground States and Isomers Produced by Projectile Fragmentation

New achievements in nuclear moment measurements on nuclei produced and spin-oriented in intermediate energy (50–80 MeV/u) projectile fragmentation reactions are presented. By combining different types of spin-orientation with different experimental techniques, we show that the magnetic dipole moments and electric quadrupole moments of exotic neutron rich nuclei in their ground state as well as in their excited isomeric states can be measured. A selection of recent experiments performed at the LISE spectrometer at GANIL (Caen, France) is described. This revised version was published online in September 2006 with corrections to the Cover Date.     

NDDO quantum chemical calculations of molecules. A comparison between the modified version and the AM1 method

Advantages and disadvantages of two approaches to electronic structure calculations of molecules using the NDDO approximation are revealed.     

Bootstrapping Pseudolikelihood Models for Clustered Binary Data

Asymptotic properties of the parametric bootstrap procedure for maximum pseudolikelihood estimators and hypothesis tests are studied in the general framework of associated populations. The technique is applied to the analysis of toxicological experiments which, based on pseudolikelihood inference for clustered binary data, fits into this framework. It is shown that the bootstrap approximation can be used as an interesting alternative to the classical asymptotic distribution of estimators and test statistics. Finite sample simulations for clustered binary data models confirm the asymptotic theory and indicate some substantial improvements.     

Ion bombardment-induced charge state effects CaO single crystals: F+ and F centers

The effects of heavy-and light-ion bombardment on defect formation in CaO have been investigated by UV-absorption spectroscopy and volume measurements. While 500 keV Ar or Ca implantation produces only F⁺ centers, 240 keVH produces both F⁺ and F centers at a F⁺ to F ratio of 5.6 to 1. On the other hand, when an argon implanted sample is subsequently bombarded with hydrogen, about 30% of the F⁺ centers anneal during 1 ×10¹⁴ H/cm²; at higher H fluences, new F⁺ and F centers are produced. An effect of energy partition between ionization and nuclear/atomic collision processes for the incident ions on the charge state of the resulting defect is thus clearly demonstrated.

The formation and annealing of these defects are accompanied by volume changes in the ion implanted surface layer which can be monitored in sltu with a cantilever beam technique. The measurements show volume expansion of the order of 1.5% following 10¹⁶ 500 keV Ar implantation; subsequent implantation of 10¹⁸ 240 keV H compacts the previously expanded material by 25 %. These results are in qualitative agreement with the optical data and seem to indicate that volume changes are associated with the formation and annealing of F⁺ centers.