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).     

Formation of metallic NbSe2 nanotubes and nanofibers

We succeed in synthesizing NbSe₂ nanotubes along with nanofibers by chemical vapor transportation. They are stable crystalline systems and can be synthesized reproducibly in a nearly equilibrium reacting process. We have investigated these nanosize structures of NbSe₂ by transmission electron microscopy and electron diffraction. Both of the structures have a similar size of 100–200 nm in diameter. While nanotubes consist of rolled-up NbSe₂ layers, nanofibers are a pile of thin flat layers. We propose a mechanism of the formation of NbSe₂ nanotubes and nanofibers on the basis of deseleniditive transition from a NbSe₃ fiber-shaped crystal. We also measured electrical resistance of the nanofibers with conductive atomic force microscopy and demonstrated that the material show metallic behavior at room temperature.     

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.     

Ab initio calculations of isomerization reaction of diphosphene 1-sulfide to thiadiphosphirane

Ab initio Calculations of the isomerization reaction of diphosphene 1-sulfide (2′) to thiadiphosphirane (3′) suggest that the energy barrier of the reaction in the ground state is 25 kcal/mol and that 2′ lies 21 kcal/mol above 3′, while the calculations show that there exists one local minimum on the lowest triplet energy surface.     

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.