On the construction of exact solutions of the stationary axially symmetric Einstein equations

Summary For the stationary axially symmetric vacuum, field, the Einstein equations reduce to a system for the logarithmic derivatives of the unknown function. An inverse scattering formula and a Bäcklund transformation are presented for the reduced system. As the simplest case, successive uses of the Bäcklund transformation give the Kasner type solutions and their generalization starting from the Minkowski metric.     

The structure of aureothin, a nitro compound obtained from Streptomyces thioluteus

The structure of aureothin, the third nitro compound obtained from nature, has been elucidated as I. Several reactions of aureothin and its derivatives are described.     

A new calix[5]arene-based container: selective extraction of higher fullerenes

[reaction: see text] A new double calix[5]arene successfully extracts higher fullerenes from fullerene mixtures. The syn isomer of the double calix[5]arene selectively captures higher fullerenes from fullerene mixtures. The elevation of the temperature more than 100 degrees C stimulates its conformational change to the anti isomer, bringing liberation of the captured higher fullerenes.     

Asymptotic analysis for an extended discrete Lotka–Volterra system related to matrix eigenvalues

The integrable discrete hungry Lotka–Volterra (dhLV) system is easily transformed to the qd-type dhLV system, which resembles the recursion formula of the qd algorithm for computing matrix eigenvalues. Some of the qd-type dhLV variables play a role for assisting the time evolution of the others. This property does not appear in the original dhLV system. In this article, we first show the existence of a centre manifold for the qd-type dhLV system. With the help of the centre manifold theory, we next investigate the local convergence of the qd-type dhLV system, and then clarify the monotonicity related to the qd-type dhLV variables at the final phase of the convergence.     

Preparation of phenyl‐modified natural rubber in latex stage

Phenyl‐modified natural rubber was prepared in latex stage by bromination of deproteinized natural rubber followed by Suzuki‐Miyaura cross‐coupling reaction. First, the bromination of natural rubber was carried out using N‐bromosuccinimide in latex stage. The bromine atom content increased as amount of N‐bromosuccinimide increased. Second, the allylic bromine atom was replaced with a phenyl group using phenyl boronic acid in the presence of a palladium catalyst, according to the Suzuki‐Miyaura cross‐coupling reaction in latex stage. The resulting products were characterized by nuclear magnetic resonance (NMR) spectroscopy. Signal at 7.13 ppm was assigned to the phenyl group of the product, while signals at 3.98, 4.14, and 4.44 ppm were assigned to the remaining allylic brominated cis‐1,4‐isoprene units. The estimated phenyl group content and the conversion of the Suzuki‐Miyaura cross‐coupling reaction were 1.32 and 23.7 mol%, respectively. Glass transition temperature (T_g) of deproteinized natural rubber increased from ?62°C to ?46.7°C, when the phenyl group was introduced into the rubber.