Organosilanols: The structure of 1,1,3,3-tetraphenyldisiloxane-1,3-diol

The title compound is triclinic, space groupP¯1, witha=13.468(2),b=20.289(2),c=14.247(1) Å,=98.92(1),=113.42(1),=99.52(1)°,V _c=3416(1) ų, andZ=6. The structure was solved by direct methods and refined by full-matrix least squares toR=0.078,R _w=0.089, for 6511 observed data. The molecules hydrogen-bond into helical chains parallel to [111], each oxygen being involved in one donor and one acceptor hydrogen bond. The geometry of the siloxane link is different in the three independent molecules present, with Si-O-Si angles of 147.8(3), 157.0(3), and 162.5(3)°.     

The crystal and molecular structure of hexadecaphenyloctasiloxyspiro(9,9)titanate(IV)

The crystal and molecular structures of the title compound have been determined by single crystal X-ray diffraction methods. In the spiro molecule, the metal atom has a geometry very close to tetrahedral, with OTiO angles of 107.9–111.0(2)° and very short TiO bonds of length 1.777–1.791(5)Å. The two TiO₅Si₄ rings have different, ill-defined conformations; the SiO bond lengths and SiOSi angles are similar to those in (SiO)_n rings.     

Encapsulated sulfates: insight to binding propensities

Two crystal structures of sulfate inclusion complexes in an aza- and amido-cryptand represent the first examples of encapsulated sulfate in synthetic cryptand receptors and indicate penta- and octa-coordination, respectively.     

Cluster structure of <Superscript>16</Superscript>O

A folding potential describing the -scattering on ¹⁶O over a broad energy range 25.8-146.0 MeV is constructed on the basis of -like cluster and unclustered-nucleon configurations of ¹⁶O. The resulting potential does not need any renormalization to fit the angular distribution of elastic cross-sections. The effects of the repulsive part of - and -nucleon interactions are investigated. The analysis suggests that both the - repulsive potential and the unclustered nucleonic configuration in the target are important to describe the scattering data over a broad range of incident energies. The root-mean-square radius for the ¹⁶O nucleus is deduced.Received: 5 December 2002, Published online: 9 October 2003PACS: 25.55.Ci Elastic and inelastic scattering - 24.10.Ht Optical and diffraction models - 21.60.Gx Cluster models     

Superradiance of dyonic black holes

The Klein-Gordon equation is applied to investigate superradiance around a dilatonic variant of dyonic black holes, a type of black holes whose extremal limits are justified for the S-wave approximation. The result is: The dilaton field boosts the superradiance.     

Positive shrinkage, improved pretest and absolute penalty estimators in partially linear models

Shrinkage estimators of a partially linear regression parameter vector are constructed by shrinking estimators in the direction of the estimate which is appropriate when the regression parameters are restricted to a linear subspace. We investigate the asymptotic properties of positive Stein-type and improved pretest semiparametric estimators under quadratic loss. Under an asymptotic distributional quadratic risk criterion, their relative dominance picture is explored analytically. It is shown that positive Stein-type semiparametric estimators perform better than the usual Stein-type and least square semiparametric estimators and that an improved pretest semiparametric estimator is superior to the usual pretest semiparametric estimator. We also consider an absolute penalty type estimator for partially linear models and give a Monte Carlo simulation comparisons of positive shrinkage, improved pretest and the absolute penalty type estimators. The comparison shows that the shrinkage method performs better than the absolute penalty type estimation method when the dimension of the parameter space is much larger than that of the linear subspace.