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.     

Macromolecular synthesis from saccharic lactones. Ring-opening polyaddition of D-glucaro- and D-mannaro-1,4:6,3-dilactones with alkylenediamines

Ring-opening polyaddition of a saccharic acid dilactone prepared from D-glucose, D-glucaro-1,4 : 6,3-dilactone, with several alkylenediamines proceeded at room temperature with no catalyst. The resulting new polyamides carrying many pendant hydroxyl groups, poly(alkylene D-glucaramide)s, were more amorphous and hydrophilic than the corresponding nylons having no hydroxyl groups, and were hydrolyzed more easily than the latter in an acidic condition. The ring-opening ability of D-mannaro-1,4:6,3-dilactone, which was another saccharic acid dilactone obtained from D-mannitol, was found to be lower than that of the D-glucaric analogue. © 1993 John Wiley & Sons, Inc.     

Microlocal study of topological Radon transforms and real projective duality

Various topological properties of projective duality between real projective varieties and their duals are obtained by making use of the microlocal theory of (subanalytically) constructible sheaves developed by Kashiwara [M. Kashiwara, Index theorem for constructible sheaves, Astérisque 130 (1985) 193-209] and Kashiwara-Schapira [M. Kashiwara, P. Schapira, Sheaves on Manifolds, Grundlehren Math. Wiss., vol. 292, Springer, Berlin-Heidelberg-New York, 1990]. In particular, we prove in the real setting some results similar to the ones proved by Ernström in the complex case [L. Ernström, Topological Radon transforms and the local Euler obstruction, Duke Math. J. 76 (1994) 1-21]. For this purpose, we describe the characteristic cycles of topological Radon transforms of constructible functions in terms of curvatures of strata in real projective spaces.     

Pressure and temperature effects on the excess deuteron and proton conductance

The limiting molar conductances ° of deuterium chloride DCl in D₂O were determined as a function of pressure and temperature in order to examine the proton-jump mechanism in detail. The excess deuteron conductances °_E(D ⁺), as estimated by the equation [°_E(D ⁺) = °(DCl/D ₂ O) – °(KCl/D ₂ O)], increases with an increase in the pressure and temperature as well as the excess proton conductance [°_E(H ⁺) = °(HCl/H ₂ O) – °(KCl/H ₂ O)]. The isotope effect on the excess conductances, however, depends on the pressure and temperature contrary to the model proposed by Conway et al.: °_E(H ⁺)/°_E(D ⁺) decreases with increasing pressure and temperature. The magnitude of the decrease with pressure becomes more prominent at lower temperature. These results are discussed in terms of the pre-rotation of adjacent water molecules, the bending of hydrogen bonds with pressure, and the difference in strength of hydrogen bonds between D₂O and H₂O.     

Pressure response of Raman spectra of water and its implication to the change in hydrogen bond interaction

In situ Raman spectroscopic measurements of water in the region of OH vibration were conducted up to 0.4 GPa at 23 and 52 degrees C. The frequencies of the decomposed OH stretching bands initially decreased with increasing pressure, reached a minimum at 0.15 GPa and increased up to 0.3 GPa and then decreased, which corresponds to the variations of the strength of hydrogen bonding. This variation was observed at 23 degrees C, but not at 52 degrees C, which suggests a change in pressure dependence on the hydrogen bond interaction between these two temperatures. Based on the equilibration model between hydrogen-bonded and nonhydrogen-bonded molecules, the present experimental results indicate that the pressure variation of the viscosity depends on the ratio of hydrogen-bonded molecules, rather than the strength of hydrogen bonding between molecules.     

Complexation of a hydrophobic thiazorylazophenol with Ni2+ at sodium dodecylsulfate micellar surface

Complexation of thiazorylazododecylphenol (TADP) with Ni2+ at the surface of sodium dodecylsulfate (SDS) micelles has been spectrophotometrically studied. Complicated spectral changes are analyzed by a factor and multivariate analysis, which implies the formation of [TDAP(OH-)Ni]0 as well as a simple 1:1 complex of Ni2+ with TDAP at the micellar interface. All of the equilibrium constants required to describe this system are substantially affected by electrolyte concentrations. Coexistent electrolytes vary the surface potential of the micelle, and in turn influence the equilibria taking place on the micellar surface. The electrostatic potential estimated based on the equilibrium shifts is more negative than that calculated according to Poisson-Boltzmann theory, which simply involves electrostatic effects. This disagreement is possibly caused by different aqueous environments around the micelle from bulk solution, which also facilitate the formation of unusual complex such as [TDAP(OH-)Ni]0.     

Gas-stirred solvent extraction with propylene carbonate for separation and direct polarographic determination of thallium (III)

Gas-stirred propylene carbonate (PC) extraction can be performed by bubbling nitrogen without loss of volume. This extraction technique has proved to be highly useful for the separation and subsequent direct polarographic estimation of Tl(III) in the recovered PC phase. Tl(III) can be determined by differential-pulse polarography over the concentration range of 0.4 10 g ml^–1 without any interferences due to most metal ions such as Pb(II), Bi(III), Cu(II), Sb(III) and As(III). This proposed technique would be possible to use as a simple extraction step prior to the final estimation by instrumental method of analysis such as atomic absorption spectrometry or spectrophtometry.