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.     

Integral representations of nonnegative solutions for parabolic equations and elliptic Martin boundaries

We consider nonnegative solutions of a parabolic equation in a cylinder D×(0,T), where D is a noncompact domain of a Riemannian manifold. Under the assumption [IU] (i.e., the associated heat kernel is intrinsically ultracontractive), we establish an integral representation theorem: any nonnegative solution is represented uniquely by an integral on (D×{0})∪(M_∂D×[0,T)), where M_∂D is the Martin boundary of D for the associated elliptic operator. We apply it in a unified way to several concrete examples to explicitly represent nonnegative solutions. We also show that [IU] implies the condition [SP] (i.e., the constant function 1 is a small perturbation of the elliptic operator on D).     

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.     

AC calorimetric study of phase transitions in phosphatidylcholine-cholesterol systems

Using an ac calorimetric method, detailed behaviour of the heat capacity in dipalmitoyl-phosphatidylcholine-cholesterol system was studied in the cholesterol concentration less than 5 mol%. It was revealed that the heat capacity near the main transition was composed of at least four anomalies, i.e., multipeak took place in the heat capacity. This fact indicates that a simple theory explaining coexistence of two phases in two component systems does not work in the multipeak region. Then, relation between the multipeak heat capacity and the change of the ripple structure with the cholesterol concentration should be taken into account, when we consider thermodynamical behaviour of the systems.

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Zusammenfassung Mittels AC-Kalorimetrie wurde bei Cholesterol-Konzentrationen von weniger als 5 mol% das Verhalten der Wärmekapazität im System Dipalmitoylphosphatidylcholin-Cholesterol untersucht. Es wurde gezeigt, daß sich die Wärmekapazität in der Nähe der Hauptumwandlung aus mindestens vier Anomalien zusammensetzt, d.h. bei der Wärmekapazität kann ein Multipeak beobachtet werden. Diese Tatsache zeigt, daß eine einfache Theorie, welche die Koexistenz zweier Phasen in einem Zweikomponenten-System erklärt, für die Multipeakregion nicht geeignet ist. Weiterhin sollte bei Überlegungen zum thermodynamischen Verhalten von Systemen eine Beziehung zwischen der Multipeak-Wärmekapazität bzw. der Welligkeitsstruktur und der Cholesterol-Konzentration berücksichtigt werden.