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).     

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.     

WIDE RANGE DETECTOR USING PARABOLIC CYLINDRICAL MIRROR FOR THz APPLICATIONS

A new, wide-band, high-speed and high-sensitivity THz detector has been developed. The prototype detector consists of a parabolic cylindrical mirror, a long wire antenna and a Schottky barrier diode. Direct detection measurements have shown a stable sensitivity of 150 ± 50 V/W for 1–2 THz without any adjustments. The long wire antenna was fixed at the focus of parabolic cylindrical mirror then it has been realized less operation steps, easy coupling to the external THz signals and a dramatic enhancement in the practicality of this system. The optically polished mirror and frosted surface one showed comparable sensitivities, thus easy polishing and less cost mirror fabrication can be applied for this system. The radiation pattern showed a maximum radiation angle of approximately 23° with its dominant main lobe, which was attributed to the wire antenna character and confirmed good agreements with classical antenna theory.     

Non-adiabatic calculation of muonic atom-nucleus collisions

In order to calculate the cross sections of the muonic atom-nucleus collisions, we have proposed a precise numerical method, a non-adiabatic coupled-rearrangement-channel method with the use of the Jacobian coordinates for the three-body system in the whole space. The scattering boundary condition is correctly imposed along the coordinates; this method does not suffer from the well known defects of the method of adiabatic representation. We applied our method to the muonic atom-nucleus collisions for an incident c.m. energies of 0.001–100 eV.     

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.