Boundary behavior in Hilbert spaces of vector-valued analytic functions

In this paper we study the boundary behavior of functions in Hilbert spaces of vector-valued analytic functions on the unit disc D. More specifically, we give operator-theoretic conditions on Mz, where Mz denotes the operator of multiplication by the identity function on D, that imply that all functions in the space have non-tangential limits a.e., at least on some subset of the boundary. The main part of the article concerns the extension of a theorem by Aleman, Richter and Sundberg in [A. Aleman, S. Richter, C. Sundberg, Analytic contractions and non-tangential limits, Trans. Amer. Math. Soc. 359 (2007)] to the case of vector-valued functions.     

Spreading of a smectic A liquid crystal on a rotating disc

We describe the dynamics of spreading of a smectic A liquid crystal deposited on a rotating disc. We show the existence of several regimes according to the film thickness. If it is thick enough, the thinning is controlled by bulk permeation; at intermediate thicknesses the surface dissipation dominates, whereas viscous effects begin to be felt only at very small thickness.     

Calculating Gibbs free energies of transfer from Gibbs ensemble Monte Carlo simulations

The partitioning of the ternary systems n-pentane/n-heptane/(helium or argon) at ambient conditions is investigated using configurational-bias Monte Carlo simulations in the Gibbs ensemble. The results demonstrate that this approach yields very precise partition constants and free energies of transfer. Simulations are carried out to study the dependence of the n-pentane partitioning with respect to the carrier gas, the system size, and the overall solute concentrations. None of the changes of variables, within the ranges used here, has a significant effect on the alkane partitioning. However, chemical potentials calculated via Widom's ghost particle insertions show a strong number dependence for phases containing relatively few molecules of a given type. This problem originates from the fact that the chemical potential is calculated for a concentration of real particles plus one ghost particle that is systematically larger than the equilibrium concentration. A simple correction term is suggested to account for this problem. Received: 13 May 1998 / Accepted: 18 June 1998 / Published online: 4 September 1998     

Measurement ofD(\vec p,p)D elastic scattering at 10.0, 12.0, 14.1 and 16.5 MeV especially for small forward and extreme backward scattering angles

The elastic scattering was investigated especially in the Coulomb sensitive scattering regions. Angular distributions of the differential cross section and of the analyzing powerA _y, with emphasis on small scattering angles, were measured at 10.0 and 14.1 MeV. For extreme backward angles up toJ _c.m.=179° the differential cross section was measured at 12.0, 14.1 and 16.5 MeV. The data have been compared with recent Faddeev calculations based on the realistic meson-exchange Paris potential and including an approximate Coulomb correction. There are discrepancies between the data and the calculations especially for the analyzing power. This indicates that the approximate treatment of Coulomb effects and possibly also the purely nuclear part of the calculations need to be improved.     

The 6Li,6Li-INADEQUATE Experiment: A New Tool for 1D- and 2D-NMR Studies of Organolithium Compounds

The 1D- and 2D-⁶Li, ⁶Li-INADEQUATE experiments are described as new tools for the detection of scalar coupled nonequivalent ⁶Li nuclei in organolithium clusters. Practical applications of these sequences are demonstrated for the ⁶Li-NMR spectra of (E)-1-lithio-2-(2-lithiophenyl)-1-phenylhex-1-ene ( 1 ) and (E)-2-lithio-1-(2-lithiophenyl)-1-phenylpent-1-ene ( 2 ), where signals due to dimers and monomers can be distinguished. The performance of the 2D-⁶Li, ⁶Li-INADEQUATE and the ⁶Li, ⁶Li-COSY-45-LR experiment are compared. The ⁶Li chemical shifts of 1 and 2 are discussed.     

Über Blei (II)-oxidhydrat der Zusammensetzung 3PbO·H2O

Lead oxide hydrate mentioned in the earlier literature with several formulas between PbO · H₂O and PbO · 0.33 H₂O has been synthesized and investigated by high resolution X-ray powder methods, thermogravimetry and infrared spectroscopy. The unit cell was found from 62 powder reflections to be tetragonal with a = 8.009 ± 0.003 Å, c = 9.312 ± 0.005 Å, Z = 12 [PbO · 0.33 H₂O]. These data were confirmed by WEISSENBERG and Precession photographs of single crystals grown as a corrosion product on metallic lead. The space group is D–P4/mnc or C–P4 nc. Thermogravimetric measurements, corrected for a slight content of superficially bound carbon dioxide detected by infrared spectroscopy, lead to the most probable formula 3 PbO · H₂O or PbO · 0.33 H₂O. As infrared spectra show the presence of a HOH deformation vibration, the compound is considered to be an oxide hydrate and not an oxide hydroxide of lead.     

The effectivity of solvents as electron pair donors

The effectivity of solvents as electron pair donors, their donicity as expressed by their donor numbers DN, is reexamined. The linear dependence of the enthalpy and the Gibbs free energy for the reaction of donor solvents with antimony pentachloride is affirmed. Extension of the DN scale by other measured quantities, via their linear correlations for sets of solvents where both kinds of data are known is applied to Drago's E-C scale, Kamlet's scale, and Koppel's B scale. This extension, added to previous extensions employing Selbin's D_{I, II} and Popov's ²³Na, produces a DN scale for 170 solvents. The relation of DN measured for isolated solvent molecules in 1,2-dichloroethane to DN values measured for bulk solvents is examined by means of the scaled particle theory and solute-solvent interaction terms. A scale of normalized donor numbers DN ^N is presented. These values are practically the same as the scale, and for those solvents for which DN values are presented here and values are lacking, they can serve in their place for those preferring to use the scale for donor solvents.     

Calculated vibrational structure of the first band of the photoelectron spectrum of HO 2 − and the electron affinity of HO2

The vibrational structure of the first band of the photoelectron (PE) spectrum of HO ₂ ^? and DO ₂ ^? has been calculated on the basis of (slightly modified) ab initio potentials. The best agreement with the experimental spectrum of HO ₂ ^? is obtained for a vibrational temperature of ca. 600 K. “Peak D”, which has been under debate in earlier work, is composed of two transitions, with the “hot” transition 3 ₁ ¹ being more intense than the adiabatic transition. Since thev ₂ bending mode of DO₂ has significant OO stretching character, the vibrational structure of the PE spectrum of DO ₂ ^? is more complex than that of HO ₂ ^? . Large-scale RCCSD(T) calculations of the equilibrium electron affinity of HO₂ yield 1.058 eV which agrees with the experimental value of 1.044 ± 0.020 eV.     

Surface characterization of three marine bacterial strains by Fourier transform IR, X-ray photoelectron spectroscopy, and time-of-flight secondary-ion mass spectrometry, correlation with adhesion on stainless steel surfaces

Adhesion of bacterial strains on solid substrates is likely related to the properties of the outer shell of the micro-organisms. Aiming at a better understanding and control of the biofilm formation in seawater, the surface chemical composition of three marine bacterial strains was investigated by combining Fourier transform IR spectroscopy, X-ray photoelectron spectroscopy (XPS), and time-of-flight secondary-ion mass spectrometry (ToF-SIMS). The D41 strain surface showed evidence of proteins, as deduced from the NH2 and NCO XPS and ToF-SIMS fingerprints; this strain was found to adhere to stainless steel, glass, or Teflon surfaces in a much higher quantity (2 orders of magnitude) than the two other ones, DA and D01. The latter are either enriched in COOH or sulfates, and this makes them more hydrophilic and less adherent to all substrates. Correlations with physicochemical properties and adhesion seem to demonstrate the role of the external layer composition, in particular the role of proteins more than that of hydrophobicity, on their adhesion abilities.