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     

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).     

Hydrogel‐like elastic membrane consisting of semi‐interpenetrating polymer networks based on a phosphorylcholine polymer and a segmented polyurethane

To obtain a hydrogel‐like elastic membrane, we prepared semi‐interpenetrating polymer networks (IPNs) by the radical polymerization of methacrylates such as 2‐methacryloyloxyethyl phosphorylcholine (MPC), 2‐hydroxyethylmethacrylate, and triethyleneglycol dimethacrylate diffused into segmented polyurethane (SPU) membranes swollen with a monomer mixture. The values of Young's modulus for the hydrated semi‐IPN membranes were less than that for an SPU membrane because of higher hydration, but they were much higher than that for a hydrated MPC polymer gel (non‐SPU). According to a thermal analysis, the MPC polymer influenced the segment association of SPU. The diffusion coefficient of 8‐anilino‐1‐naphthalenesulfonic acid sodium salt from the semi‐IPN membrane could be controlled with different MPC unit concentrations in the membrane, and it was about 7 × 10² times higher than that of the SPU membrane. Fibroblast cell adhesion on the semi‐IPN membrane was effectively reduced by the MPC units. We concluded that semi‐IPNs composed of the MPC polymer and SPU may be novel polymer materials possessing attractive mechanical, diffusive‐release, and nonbiofouling properties. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 68–75, 2003     

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.     

HCN laser scattering on the JIPP T-IIU tokamak

A 4-channel HCN laser scattering system has been developed and applied to the JIPP T-IIU tokamak. Main aim of this system is to study microturbulence excited in the plasma, especially in the high power ICRF heating experiment. The observed density fluctuations are in a frequency range of the electron diamagnetic drift wave and have broad frequency spectra. The main part of the wavenumber is found to satisfy the condition of . In the heating experiments, deterioration of the energy confinement time is observed, and the density fluctuation level increases with the increase of the heating power.     

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.