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     

Phase rotation scheme of laser-produced ions for reduction of the energy spread

In order to widely spread out particle beams utilized in cancer therapy, laser-produced ions are developed as the injection beam for an ion synchrotron dedicated for cancer therapy. Such a laser ion source is expected to contribute largely to the realization of compactness of the size and low cost of the cancer therapy accelerator. The energy spectrum of the laser-produced ions, however, has no peak, but their intensities decrease exponentially according to the increase of the energy. For the purpose of modifying such a situation, we have proposed a scheme to rotate the beam in the longitudinal phase space with the use of the RF electric field, which is phase-adjusted with the pulse laser. We aim for a reduction of the energy spread of ± 5% selected by an energy analyzer and slits to ±1% by such phase rotation. For this purpose, a quarter wavelength resonator with two gaps with the same resonant frequency as the source laser has already been fabricated, together with its RF power source. The above phase rotation system and its recent experimental realization are presented.     

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.     

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.     

Thermosensitive biodegradable polydepsipeptide

A poly(N-isopropylacrylamide) (PNIPAAm)-like biodegradable thermosensitive polydepsipeptide, poly[Glc-Asn(N-isopropyl)], was synthesized by introducing an isopropyl amide group into poly[Glc-Asn]. Poly[Glc-Asn(N-isopropyl)] was degraded in vitro by cleavage of the ester bonds in the main chain in water at room temperature. The non-toxic nature of the polymer and its degradation products, coupled with a cloud point at 29 degrees C in water, make this polymer attractive for biomedical implant applications.     

Synthetic organic chemistry with 2-ethoxy-2-(phenylselenenyl)perfluoroalk-2-enenitrile: application to alpha-cyanoperfluoroacylation of aldehydes

(Z)- and (E)-2-Ethoxyperfluoro-2-(phenylselenenyl)alk-2-enenitriles 2-4 prepared by our original method underwent transmetalation on treatment with n-BuLi or EtMgBr, and the successive reaction with aldehyde and ketones afforded the corresponding allylic alcohols 10a-f, 9a, and 11a,b in good to high yields. Hydrolysis of the alcohols gave alpha-cyano-alpha,beta-unsaturated perfluoroalkyl ketones 13a-c, 13e, 12a, and 15a. alpha-Cyanoperfluoroalkyl ketones were easily converted to alpha,beta-unsaturated 3-aryl-2-cyanoallylic alcohols 18-22 having interesting biological activities and chemical reactivities.     

Conformation of drawn poly(trimethylene terephthalate) studied by solid-state 13C NMR

The change in the conformation of the flexible O-CH2-CH2-CH2-O segment of poly(trimethylene terephthalate) (PTT) monofilament caused by drawing was investigated by means of the gamma-gauche effect on the 13C solid-state NMR chemical shift of the internal methylene carbon, combined with the NMR relaxations. The conformation around the O-CH2 and CH2-O bonds for as-spun fiber was trans/trans. On drawing, followed by heat treatment, the conformation changed to gauche/gauche. The ratio of gauche/gauche to trans/trans for the drawn PTT fiber was determined quantitatively.     

In Situ Processing of Nano Crystalline Oxide Particles/Polymer Hybrid

Nano sized crystalline particles/polymer hybrids were synthesized form designed metal-organic precursors. The newly developed method is composed of the synthesis of organic matrix by polymerization and the in situ nucleation and growth of crystalline oxide particles in the organic matrix below 100°C. The design of metal-organic precursor modified with polymerizable ligand and the selection of reaction conditions does influence the size and crystallinity of ceramic particles in organic matrix. The nano-sized magnetic particle/polymer hybrid exhibits the interesting feature of superparamagnetism and quantum size effect. The crystalline particles of BaTiO₃/, PbTiO₃/, and KNbO₃/polymer hybrids behave to be dielectric and show the typical electro-rheological behavior.