Characteristic values of the integral equation satisfied by the Mathieu functions and its application to a system with chirality-pair interaction on a one-dimensional lattice

We investigate low-temperature behaviors of a system with chirality-pair interaction on a one-dimensional lattice. In the course of the investigation, we evaluate asymptotic forms of the characteristic values of the integral equation satisfied by the Mathieu functions. It turns out that the low-temperature behavior of correlation length of the chirality-pair correlation function is different from the one for the Ising model of spin ±1 but akin to the one for the Ising model of infinite spin.     

Synthesis of polyamides by the polyaddition of bisimidazoline with dicarboxylic acids

N,N′-Dipropionylethylenediamine was synthesized by the ring-opening addition reaction of 2-ethyl-2-imidazoline with propionic acid at 220°C. By applying this reaction to polymerization, polyamides were synthesized by the ring-opening polyaddition reaction at 220°C. of 1,4-bis(imidazoline-2-yl)butane with adipic acid, succinic acid, sebacic acid, and terephthalic acid. The reaction product of 1,4-bis(imidazoline-2-yl)butane with adipic acid, which was proposed to be nylon 26, was compared with an authentic sample of nylon 26 and shown to possess a very similar infrared spectrum and melting point.     

Analysis of the release process of phenylpropanolamine hydrochloride from ethylcellulose matrix granules

The release properties of phenylpropanolamine hydrochloride (PPA) from ethylcellulose (EC, ethylcellulose 10 cps (EC#10) and/or 100 cps (EC#100)) matrix granules prepared by the extrusion granulation method were examined. The release process could be divided into two parts, and was well analyzed by applying square-root time law and cube root law equations, respectively. The validity of the treatments was confirmed by the fitness of the simulation curve with the measured curve. At the initial stage, PPA was released from the gel layer of swollen EC in the matrix granules. At the second stage, the drug existing below the gel layer dissolved, and was released through the gel layer. Also, the time and release ratio at the connection point of the simulation curves was examined to determine the validity of the analysis. Comparing the release properties of PPA from the two types of EC matrix granules, EC#100 showed more effective sustained release than EC#10. On the other hand, changes in the release property of the EC#10 matrix granule were relatively more clear than that of the EC#100 matrix granule. Thus, it was supposed that EC#10 is more available for controlled and sustained release formulations than EC#100.     

Preparation of crystalline polyamides by the alternating copolymerization of aziridines and cyclic imides

The copolymerization of aziridines and cyclic imides was studied. Aziridines copolymerized alternately with cyclic imides to give crystalline polyamides. Ethylenimine and succinimide copolymerized to nylon 2,4, melting near 300°C., without any catalyst. Similarly, the corresponding crystalline polyamides were obtained from the systems of 1,2-propylenimine–succinimide, ethylenimine–glutarimide, and ethylenimine–phthalimide. The copolymerization of aziridines and cyclic imides in the presence of BF₃OEt₂ gave a copolymer which was rich in aziridine units, whereas, the addition of triethylamine had no influence on the copolymer composition. A mechanism of copolymerization was proposed based on the facts that N-tetramethylenesuccinamide was obtained by the reaction of pyrrolidine and succinimide, N-acetylethylenimine reacted with acetamide to yield N,N′-diacetylethylenediamine and that the rate of this copolymerization was dependent on the electrophilicity of imide.     

Kinetics of γ-ray polymerization of formaldehyde in the presence of carbon dioxide

A kinetic study of the γ-ray polymerization of formaldehyde in toluene solution in the presence of carbon dioxide was carried out at temperatures of + 13 to ?17°C. Two modes of the polymerization, spontaneous and γ-ray polymerization, occur in this system. The γ-ray polymerization, experimentally separated from the spontaneous polymerization, was investigated. The rate of γ-ray polymerization increased slightly with the square root of carbon dioxide concentration. The rate of polymerization was also found to be proportional to the dose rate and the square of monomer concentration. The molecular weight of polymer formed was independent of the reaction condition. The apparent activation energy was estimated to be 10.3 kcal./mole. The kinetics of the γ-ray polymerization in the presence of carbon dioxide are explained quantitatively by a cationic mechanism, and the role of carbon dioxide is as an action of retardation for neutralization of the cationic initiating species, which was produced by γ-radiation, by means of a reverse reaction with an electron. Physical and mechanical properties of the polymer obtained by γ-ray polymerization were also investigated.     

Cationic polymerization of formaldehyde in liquid carbon dioxide. Part I

A cationic polymerization of formaldehyde which gave a high molecular weight polymer was studied in liquid carbon dioxide at 20–50°C. In the polymerization without any catalyst both the rate of polymerization and the molecular weight of the resulting polymer increased rapidly with a decrease in the loading density of the monomer solution to the reaction vessel, and also increased with an increase in the initial monomer concentration. From these results it was concluded that the initiating species could be ascribed to an impurity contained in the monomer solution. Both the rate of polymerization and the degree of polymerization of the polymer also increased with rising temperature. The carboxylic acid added acted as a catalyst in the polymerization because of increase in the polymer yield, the molecular weight of polymer formed, and the number of moles of polymer chain with increasing dissociation constant of acid used. It was concluded that the polymerization in liquid carbon dioxide proceeded by a cationic mechanism. Methyl formate had no influence on the polymerization, but methanol and water acted as a chain-transfer agent.     

Lax表示的变形与Hamilton方程族的Lax表示

本文首先给出了构造演化方程族的Ｌａｘ表示的马文秀方法的一种变形，后对这一方法作了改进，使之适用于Ｈａｍｉｌｔｏｎ形式的方程族．作为应用，得到了具有非等谱Ｌａｘ表示的杨方程族．     

Fundamental constants and higher-dimensional universe

In order to study the origin of the fundamental constants and Dirac's large number, a cosmological solution in vacuum is presented in a seven-dimensional universe which is defined by adding extra three coordinates (e ² G/c ⁴)^1/2, (hG/c ³)^1/2 and (Gm/c ²) to the four-dimensional spacetime coordinates. It has common features with Chodos-Detweiler's solution. The parameters appearing in this theory are estimated to meet the conditions required by the cosmological first-order phase transition and Dirac's large number hypothesis.     

The electronic structures of cis-polyacetylene

The electronic structures of two possible forms of the so-called $\text{cis}$-skeletal polyacetylene ($\text{cis}$-polyacetylene) are investigated on the basis of the tight-binding LCAO-SCF-MO method under the CNDO/2 version. The analyses of the total energies per unit cell, the π bond orders and the interatomic interaction energies as to the both forms predict the $\text{cis}$-transoid backbone for the $\text{cis}$-polyacetylene. The examination of the patterns of particular molecular orbitals of the hypothetical $\text{cis}$-polymer with equal C-C bond lengths also supports the $\text{cis}$-transoid form.