Inner Radius of Univalence for a Strongly Starlike Domain

 The inner radius of univalence of a domain D with Poincaré density ρ _D is the possible largest number σ such that the condition ∥ S _f ∥ _D  = sup _{w∈ D} ρ _D (w) ⁻²∥ S _f (z) ∥ ≤ σ implies univalence of f for a nonconstant meromorphic function f on D, where S _f is the Schwarzian derivative of f. In this note, we give a lower bound of the inner radius of univalence for strongly starlike domains of order α in terms of the order α. The author was partially supported by the Ministry of Education, Grant-in-Aid for Encouragement of Young Scientists, 11740088. A part of this work was carried out during his visit to the University of Helsinki under the exchange programme of scientists between the Academy of Finland and the JSPS. Received November 26, 2001; in revised form September 24, 2002 Published online May 9, 2003     

Photoluminescence properties of trace amounts of Pr and Tb in yttria-stabilized zirconia

We have investigated the photoluminescence (PL) properties of trace amounts of Pr and Tb in single-crystal samples of yttria-stabilized zironia (YSZ), and found that Pr of the order of 10⁻⁶ mass% and Tb of the order of 10⁻⁵ mass% in YSZ can be detected by the PL spectroscopy. The PL spectra of the YSZ samples for the 280 nm excitation were comprised of several peaks and a broad emission. The peaks were attributed to transitions of Pr³⁺ and Tb³⁺ in the YSZ samples, whereas the broad emission seemed to be attributed to the yttria-associated oxygen vacancies. The peak intensities corresponded to the amounts of Pr and Tb in the YSZ samples, the amounts of which were analyzed by glow discharge mass spectrometry. In the PL excitation spectra, but not in the photoabsorption spectra, small peaks at 376 and 381 nm were observed, and were attributed to the transitions of Tb³⁺ in the YSZ samples. The results of the PL excitation spectra corresponding to the Pr³⁺ line emissions suggest that the charge transfer occurs between the YSZ and Pr ion in it. The trace amounts of these lanthanoids in YSZ would disturb the decay process of the photoinduced electrons to the yttria-associated oxygen vacancies.     

Electroweak radiative corrections to the top quark decay

The top quark, once produced, should be an important window to the electroweak symmetry breaking sector. We compute electroweak radiative corrections to the decay processt→b+W ⁺ in order to extract information on the Higgs sector and to fix the background in searches for a possible new physics contribution. The large Yukawa coupling of the top quark induces a new form factor through vertex corrections and causes discrepancy from the tree-level longitudinalW-boson production fraction, but the effect is of order 1% or less form _H<1 TeV.     

Local structure analysis of smoky and colorless topaz using single crystal Al NMR

The angular dependence of the ²⁷Al NMR spectrum was measured for single crystals of smoky and colorless topaz, Al₂SiO₄(F,OH)₂. Smoky topaz was obtained by irradiating high energy neutrons to colorless topaz. The quadrupole coupling constant e²Qq/h and the asymmetry parameter η were obtained from the analysis of the angular dependences of quadrupole splitting of the ²⁷Al NMR spectrum. The local structures around the aluminum atoms in smoky and colorless topaz were discussed from the magnitude and the direction of the electric field gradient. The directions of principal axes of the EFG tensor of ²⁷Al were close to the directions of Al-O and Al-F bonds. The difference in the bond lengths between Al(1)-F(1) and Al(1)-F(2) was found to affect the x and y components of the EFG tensor.     

Evaluation of fine structure of tubular zeolite NaA membrane by FTIR-ATR and FIB-TEM.

A zeolite NaA (LTA) membrane supported by an alumina porous support tube for pervaporation (PV) dehydration of ethanol was characterized by transmission electron microscopy (TEM) using a focused ion beam (FIB) thin-layer specimen preparation technique and by Fourier transform infrared attenuated total reflectance method (FTIR-ATR) using a diamond prism as the waveguide. FIB-TEM clearly presented cross-section images up to about 15 microm depth from the membrane surface. FTIR-ATR monitored the Si-O asymmetric stretching vibration spectrum. The Si-O spectrum was compared with the TEM image and their relationships were discussed. By combining the two methods, we could study the thickness of surface LTA crystals, the grain boundary, the LTA/alumina interface structure and the crystallinity and density of materials inside of the alumina porous support. Consequently, fine structure changes of the LTA membrane corresponding to the hydrothermal synthesis condition could be sensitively detected.     

Proper action on a homogeneous space of reductive type

Partially supported by Grant-in-Aid for Scientific Research (No. 63740074)     

Synthesis of spherical and hemispherical sugar‐containing poly(ornithine) dendrimers

A novel sugar‐containing poly(ornithine) dendrimer is synthesized for possible antigen delivery and related applications. The dendrimer contains an ornithine dendron as interior scaffolding and oligosaccharides on the periphery, which provide an attachment site for a peptide antigen. Maltose or lactose is bound to both hemispherical and spherical poly(ornithine) dendrimer generation 3 (G3) by reductive amination between its reducing end and the peripheral amino group of the dendrimer using a borane‐pyridine complex in a buffer solution at 50 °C. The degree of substitution of sugar is changed by varying the molar ratio of sugar to dendrimer. When the surface of spherical poly(ornithine) dendrimer G3 is modified by binding β‐alanine to the 16 amino groups, highly substituted maltose‐ or lactose‐β‐alanine‐poly(ornithine) dendrimer G3 is obtained in high yield after 7 days of reaction. The structures of these sugar‐containing dendrimers are characterized by NMR and matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry analyses. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1400–1414, 2004