Regularity of Harmonic Functions in Cheeger-Type Sobolev Spaces

We give a geometric approach to the study of the regularity of harmonic functions in Cheeger-type Sobolev spaces, and prove the Hölder continuity of such functions. In the proof, we give a definition of an upper curvature bound of the unit sphere of a Banach space, which seems to be of independent interest.     

Products, cones, and suspensions of spaces with the measure contraction property

This article concerns several geometric properties of metricmeasure spaces satisfying the measure contraction property (MCP),which can be considered as a generalized notion of lower Riccicurvature bounds. We prove that the MCP of spaces descends totheir products and Euclidean cones. We also show that a positivelycurved space in terms of the MCP with a maximal diameter canbe represented as the spherical suspension of some topologicalmeasure space.     

Electron spin resonance studies of plasma-induced polystyrene radicals

Plasma-induced polystyrene radicals were first studied by electron spin resonance (ESR). The room temperature ESR spectrum was compared with those obtained by γ-irradiation, UV-irradiation, and mechanical fracture. It was found that even less than a few seconds of plasma-irradiation gave rise to a large amount of polystyrene radicals and the ESR spectrum consisted of two types of spectra, a triplet and a single broad line. The spectral feature of the triplet was nearly identical with that of γ-irradiated polystyrene. Thus, it was assigned to the structure of a cyclohexadienyl-type radical formed by a nearly random addition of a hydrogen atom to the aromatic ring. The single broad line, thought to be an outline of multicomponent spectrum, was assigned to an immobilized dangling-bond sites at the plasma-induced crosslinked portion of the polystyrene surface.     

Reactions of hydropolysilanes with alcohols catalysed by tris(triphenylphosphine)chlororhodium

[RhCl(PPh₃)₃] is a very effective catalyst for the cleavage of Si-Si bonds by alcohols.     

Manganese(II) o ctacyanotungstate(V)-based magnet containing a noncoordinated aromatic molecule

We have prepared a pillared layer magnetic material containing a noncoordinated aromatic molecule, [{MnII(pyrimidine)(H2O)}2{MnII(H2O)2}{WV(CN)8}2](pyrimidine)2.2H2O. This compound has one-dimensional channels (6.2 x 2.1 A) that are occupied by noncoordinated pyrimidine. The magnetization versus temperature plots showed the magnetic phased transition temperature (TC) was 47 K. The magnetization versus external magnetic field plots showed that the saturation magnetization (MS) value was 13.0 muB at 2 K. This MS value indicates that an antiferromagnetic interaction operates between the WV (S = 1/2) and MnII (S = 5/2) ions. The magnetic hysteresis loop showed that the coercive field (HC) was 17 G at 2 K.     

Catalytic Oxidation of Dimethyl Ether to Dimethoxymethane over Cs Modified HaPW12O40/SiO2 Catalysts

The attractive utilization route for one-step catalytic oxidation of dimethyl ether to dimethoxymethane was successfully carried out over the H3PW12O40（40%）/SiO2 catalyst, modified by Cs, K, Ni, and V. The Cs modification of H3PW12O40（40%）/SiO2 gave the most promising result of 20% dimethyl ether conversion and 34.8% dimethoxymethane selectivity. Dimethoxymethane could be synthe- sized via methoxy groups decomposed from dimethyl ether through the synergistic effect between the acid sites and the redox sites of Cs modified H3PW12O40（40%）/SiO2.     

Establishment of de facto standard catalysts in the polypropylene industry

Polypropylene (PP) has become an indispensable material in our daily lives. Annual worldwide production of PP is now more than 30000000 tons and is predicted to grow at an annual rate of about 6% during the first decade of the 21st century. Commercial production of PP began in 1957 with the use of TiCl(3) catalysts established by Ziegler and Natta. However, the low activities and low stereospecificities of the catalysts resulted in large amounts of catalyst residue and atactic PP in the product, necessitating steps for their removal in commercial production. As a means of finding appropriate catalysts, we developed MgCl(2)-supported TiCl(4) catalysts, which basic concept was introduction of organic compounds onto the inorganic crystal catalyst surface. This addition led to remarkable enhancements in stereospecificity with extremely high activity. Use of the new catalysts enlarged and simplified the PP production process by eliminating the steps previously required for removal of catalyst residue and atactic PP. In addition, it greatly improved the properties of the PP, enabling a much wider range of PP applications by replacing metal and engineering plastics with the highly stereoregular PP. Therefore, these catalysts helped the rapid establishment of the current PP industry and now play a major role in production. The latest MgCl(2)-supported TiCl(4) catalyst is providing precise control of the isotactic PP structure. Future expectations for this type of catalyst are to acquire a single-site nature and to contribute to the creation of a new class of hybrid materials.