A direct independence proof of Buchholz's Hydra Game on finite labeled trees

We shall give a direct proof of the independence result of a Buchholz style-Hydra Game on labeled finite trees. We shall show that Takeuti-Arai's cut-elimination procedure of and of the iterated inductive definition systems can be directly expressed by the reduction rules of Buchholz's Hydra Game. As a direct corollary the independence result of the Hydra Game follows. Received: August 23, 1994 / Revised: July 24, 1995 and May 9, 1996     

Optical properties of impurity atoms in pressurized superfluid helium

We report on the optical properties of alkali atoms (Cs and Rb) in the pressurized superfluid helium. We observed excitation and emission spectra at various pressures from the saturated vapor pressure to about 25 atm. The theoretical calculations on the basis of the atomic bubble model have also been worked out. The qualitative agreement between the theoretical and experimental results with respect to the peak shift, the linewidth, and their pressure dependence is achieved in the framework of the spherical atomic bubble model. TheD ₂ excitation spectra with the double peaks are interpreted qualitatively in terms of the Jahn-Teller effect, indicating the existence of the nontotally symmetrical density distribution of the surrounding helium atoms.     

Temperature dependence of aluminum nitride reflectance spectra in vacuum ultraviolet region

Temperature dependence of optical reflectance spectra in vacuum ultraviolet region for aluminum nitride has been measured on high-quality single crystal with synchrotron radiation. The dominant structure due to the interband transition is observed at photon energy around 7.7 eV. With decreasing temperature, the energy position of the dominant structure in the reflectance spectra shifts towards higher energy. The experimental data has been fitted to the Bose-Einstein expression and the obtained parameter related to the strength of the electron-phonon interactions is much smaller than that for the peak at 6.2 eV, suggesting that the higher-lying interband transition energy decreases more slowly with increasing temperature in aluminum nitride (AlN).     

A Relationship Among Gentzen's Proof-Reduction,Kirby-Paris' Hydra Game and Buchholz's Hydra Game

We first note that Gentzen's proof-reduction for his consistency proof of PA can be directly interpreted as moves of Kirby-Paris' Hydra Game, which implies a direct independence proof of the game (Section 1 and Appendix). Buchholz's Hydra Game for labeled hydras is known to be much stronger than PA. However, we show that the one-dimensional version of Buchholz's Game can be exactly identified to Kirby-Paris' Game (which is two-dimensional but without labels), by a simple and natural interpretation (Section 2). Jervell proposed another type of a combinatorial game, by abstracting Gentzen's proof-reductions and showed that his game is independent of PA. We show (Section 3) that this Jervell's game is actually much stronger than PA, by showing that the critical ordinal of Jervell's game is φ_ω (0) (while that of PA or of Kirby-Paris' Game is φ₁ (0) = ?₀) in the Veblen hierarchy of ordinals.     

Preparation of chiral stationary phase via activated carbamate intermediate for liquid chromatographic optical resolution

Summary Chiral stationary phases (CSPs) for liquid chromatography were prepared by the way of an activated carbamate intermediate. The amino group of aminopropylsilyl silica gel was first activated by carbamylation with disuccinimido carbonate (DSC). The obtained activated carbamate silica gel (ACsil) proved useful as an intermediate for the preparation of urea-type CSPs. The reaction of ACsil with (S)- of (R)-1-(α-naphthyl)-ethylamine gave naphthylethylurea type CSPs. These CSPs were also obtained directly from aminopropylsilyl silica gel by its reaction with optically active (S)- or (R)-succinimido 1-(α-naphthyl)ethyl carbamate (SINEC). Several phenylthiohydantoin amino acid enantiomers and p-bromophenylcarbamyl amino acid enantiomers were resolved on the CSPs by elution with aqueous mobile phase.     

Total synthesis of tylosin

Tylosin has been synthesized byregio- and stereoselective introduction of the amino disaccharide moiety and D-mycinose onto the previously synthesized 16-membered-ring aglycone.     

Surface Modification of Fine Particles with a SnO<Subscript>2</Subscript> Film by Using a Polyhedral-Barrel Sputtering System

Fine particles were modified with a thin film of SnO₂ by using a barrel sputtering system that is a dry process. The conditions for the preparation of SnO₂ were studied by reactive sputtering onto a glass plate substrate. The optimal conditions for the preparation of tetragonal SnO₂ were identified as 60% partial oxygen pressure and 1.0 Pa total gas pressure with the substrate at room temperature. Under the optimized conditions, the surfaces of Al flake particles were modified with a thin film of SnO₂. XRD and SEM/EDS analysis of the prepared samples showed that the Al particle surfaces were uniformly modified by a thin film of SnO₂ in all cases. The film thicknesses were 80, 130, and 180 nm at RF outputs of 195, 350, and 490 W. These measured thicknesses coincided with the values estimated from the interference colors of the samples.