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.     

Precise measurement of magnetic moment of short-lived β-emitting nuclei12B ( I π=1+, T 1/2=20.18 ms)

The spin polarized β-emitting nuclei¹²B (I ^π=1⁺,T _1/2=20.18 ms) were produced by the nuclear reaction¹¹B(d, p)¹²B and by the selection technique of the incident deuteron energy and the¹²B recoil angle following the nuclear reaction. The nuclear magnetic moment of the short-lived nuclei¹²B was measured by β-NMR with the β-NMR and β-NQR setup established for the first time in China. The nuclear magnetic moment of¹²B was determined to be μ=0.99993±0.00048 nm org=0.99993±0.00048 after the precise correction of the Knight shift.     

Syntheses and characterization of 16‐arm star and star diblock copolymer and AB8 9‐miktoarm star copolymer via NMRP and ROP from dendritic multifunctional macroinitiators

A dendritic macroinitiator having 16 TEMPO‐based alkoxyamines, Star‐16 , was prepared by the reaction of a dendritic macroinitiator having eight TEMPO‐based alkoxyamines, [G‐3]‐OH , with 4,4′‐bis(chlorocarbonyl)biphenyl. The nitroxide‐mediated radical polymerization (NMRP) of styrene (St) from Star‐16 gave 16‐arm star polymers with PDI of 1.19–1.47, and NMPR of 4‐vinylpyridine from the 16‐arm star polymer gave 16‐arm star diblock copolymers with PDI of 1.30–1.43. The ring‐opening polymerization of ε‐caprolactone from [G‐3]‐OH and the subsequent NMRP of St gave AB₈ 9‐miktoarm star copolymers with PDI of 1.30–1.38. The benzyl ether linkages of the 16‐arm star polymers and the AB₈ 9‐miktoarm star copolymers were cleaved by treating with Me₃SiI, and the resultant poly(St) arms were investigated by size exclusion chromatography (SEC). The SEC results showed PDIs of 1.23–1.28 and 1.18–1.22 for the star polymers and miktoarm stars copolymers, respectively, showing that they have well‐controlled poly(St) arms. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1159–1169, 2007.     

Decomposition mechanism of triethylindium (TEI) on a GaP(0 0 1)-(2×1) surface studied by LEED, AES, TPD and HREELS

Adsorption and decomposition of triethylindium (TEI: (C₂H₅)₃In) on a GaP(0 0 1)-(2×1) surface have been studied by low-energy electron diffraction (LEED), Auger electron spectroscopy (AES), temperature-programmed desorption (TPD) and high-resolution electron energy loss spectroscopy (HREELS). It is found from the TPD result that ethyl radical and ethylene are evolved at about 300–400 and 450–550 K, respectively, as decomposition products of TEI on the surface. This result is quite different from that on the GaP(0 0 1)-(2×4) surface. The activation energy of desorption of ethyl radical is estimated to be about 93 kJ/mol. It is suggested that TEI is adsorbed molecularly on the surface at 100 K and that some of TEI molecules are dissociated into C₂H₅ to form P–C₂H₅ bonds at 300 K. The vibration modes related to ethyl group are decreased in intensity at about 300–400 and 450–550 K, which is consistent with the TPD result. The TEI molecules (including mono- and di-ethylindium) are not evolved from the surface. Based on the TPD and HREELS results, the decomposition mechanism of TEI on the GaP(0 0 1)-(2×1) surface is discussed and compared with that on the (2×4) surface.     

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).     

X-ray damage characterization in BaLiF3,KMgF3 and LiCaAlF6 complex fluorides

Two-inch sized KMgF₃,BaLiF₃ and LiCaAlF₆ (LiCAF) single crystals were grown by the Czochralski method under a CF₄ atmosphere. X-ray irradiation was used to carry out a comparative study of induced optical absorption phenomena and colour centre creation in the ultra-violet and visible spectral regions. The integral of the induced absorption spectra is significantly lower in LiCAF with respect to the other studied materials. It is found that the amplitude of the F-absorption band is suppressed more than a factor of 3 by Mg-doping. For Mg-doped crystals, the optimum doping concentration is about 0.2 mol% of Mg²⁺.     

Structural and electrical properties of crystalline (1−x)Ta2O5−xTiO2 thin films fabricated by metalorganic decomposition

Polycrystalline (1−x)Ta₂O₅−xTiO₂ thin films were formed on Si by metalorganic decomposition (MOD) and annealed at various temperatures. As-deposited films were in the amorphous state and were completely transformed to crystalline after annealing above 600 °C. During crystallization, a thin interfacial SiO₂ layer was formed at the (1−x)Ta₂O₅−xTiO₂/Si interface. Thin films with 0.92Ta₂O₅–0.08TiO₂ composition exhibited superior insulating properties. The measured dielectric constant and dissipation factor at 1 MHz were 9 and 0.015, respectively, for films annealed at 900 °C. The interface trap density was 2.5×10¹¹ cm⁻² eV⁻¹, and flatband voltage was −0.38 V. A charge storage density of 22.8 fC/μm² was obtained at an applied electric field of 3 MV/cm. The leakage current density was lower than 4×10⁻⁹ A/cm² up to an applied electric field of 6 MV/cm.     

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.