Protonic Conduction and O-H Bonding State in Phosphate Glasses

Abstract

Protons in alkaline-earth phosphate glasses give much higher mobility than those in silicate glasses. This is caused by the difference in O-H bonding state. Protons in P-OH form a strong hydrogen bonding with oxygen anion, resulting in formation of weak O-H bond.

The electrical conductivity of the glasses is proportional to the square of the proton concentration. The activation energy for the conduction is related to ν_OH, peak wavenumber of infrared absorption band (around～3000 cm^?1), due to fundamental O-H stretching vibration. The mobility of protons increases with decreasing ν_OH, which depends on the species of ions included in the phosphate glasses.     

Linear expansions, strictly ergodic homogeneous cocycles and fractals

We consider a compact space Θ on whichR acts additively andR ₊ acts multiplicatively satisfying the distributive law. Moreover,R-action is strictly ergodic. Such Θ is constructed as a space of colored tilings corresponding to a weighted substitution, which is a kind of natural extension of thef-expansion for a piecewise linearf. We define a homogeneous cocycleF on Θ, which was called a cocycle with the scaling property in [2]. This is a realization of fractal functions which admit the continuous scalings. This also defines a self-similar process with strictly ergodic, stationary increments which has 0 entropy.     

Corrigendum

Corrigendum

Corrigendum     

A simple proof of the ergodic theorem using nonstandard analysis

A simple proof of the individual ergodic theorem is given. The essential tool is the nonstandard measure theory developed by P. Loeb. Any dynamical system on an abstract Lebesgue space can be represented as a factor of a “cyclic” system with a hyperfinite cycle. The ergodic theorem for such a “cyclic” system is almost trivial because of its simple structure. The general case follows from this special case.     

The reactions 6, 7Li, 9Be, 10B(e,e′p) at 700 MeV and DWIA analysis

The proton spectral functions of ⁶Li, ⁷Li, ⁹Be and ¹⁰B obtained from the (e, e′p) reactions at 700 MeV are presented. The results were analyzed in the distorted-wave impulse approximation, using the shell-model single-particle wave functions consistent with the elastic electron scattering results. The observed Ip proton momentum distributions for the nuclei ⁶Li, ⁷Li and ⁹Be show significant disagreement with the shell-model momentum distributions. The occupation probabilities of the proton single-particle states are around 0.7, with a few exceptions.     

Modeling traffic flow correlation using DFA and DCCA

An electrical analogue model has been developed based on main leaf hydraulics characteristics and intrinsic geometry. The simulations show good qualitative agreements with specialized literature reports. The constant-phase behavior and the variation with ambient temperature of the frequency response of the leaf impedance are assessed by means of simulation studies.     

Language structure of pattern Sturmian words

Pattern Sturmian words introduced by Kamae and Zamboni [Sequence entropy and the maximal pattern complexity of infinite words, Ergodic Theory Dynamical Systems 22 (2002) 1191-1199; Maximal pattern complexity for discrete systems, Ergodic Theory Dynamical Systems 22 (2002) 1201-1214] are an analogy of Sturmian words for the maximal pattern complexity instead of the block complexity. So far, two kinds of recurrent pattern Sturmian words are known, namely, rotation words and Toeplitz words. But neither a structural characterization nor a reasonable classification of the recurrent pattern Sturmian words is known. In this paper, we introduce a new notion, pattern Sturmian sets, which are used to study the language structure of pattern Sturmian words. We prove that there are exactly two primitive structures for pattern Sturmian words. Consequently, we suggest a classification of pattern Sturmian words according to structures of pattern Sturmian sets and prove that there are at most three classes in this classification. Rotation words and Toeplitz words fall into two different classes, but no examples of words from the third class are known.