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.     

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.     

Synthesis of diazepinoquinoxalines and imidazolobenzopteridines

Diazepinoquinoxalines 3, 4 and imidazolobenzopteridines 5, 6a-d, 7a-d, 8, 9 were synthesized from 3-allylamino-6,7-dimethyl-2-quinoxalinecarboxamide ( 1 ) and 2-allylamino-6,7-dimethyl-3,4-dihydrobenzo[g]pteridin-4-one ( 2 ) by the intramolecular cyclization using phenylselenenyl chloride.     

Large-scale separation of metallic and semiconducting single-walled carbon nanotubes

In the applications of single-walled carbon nanotubes (SWNTs), it is extremely important to separate semiconducting and metallic SWNTs. Although several methods have been reported for the separation, only low yields have been achieved at great expense. We show a separation method involving a dispersion-centrifugation process in a tetrahydrofuran solution of amine, which makes metallic SWNTs highly concentrated to 87% in a simple way.     

Processing and characterization of Pb(Mg,Nb)O3-PbTiO3 thin films from metal alkoxide-derived gels

The sol-gel processing is one of promising methods to fabricate well-derived integrated thin films at relatively low temperature. Ferroelectric niobates films do afford the possibilities for adding the values by the hybridization with semiconductor and/or electro-optic systems. The molecular level designing of the precursor solution was stressed as well as the control of key processing factors. The advantages of this sol-gel have been extended to prepare the ferroelectric Pb(Mg, Nb)O₃-PbTiO₃ solid solution films integrated on Si wafers. The crystallization of the films with desired crystal structure could be promoted by the controlled partial hydrolysis of designed alkoxide solution in the intermediate state and the pre-heated treatment of alkoxide-derived films in flow of water vapor and oxygen gas mixture.     

Finding of remarkable synergistic effect on the aroxyl-radical-scavenging rates under the coexistence of α-tocopherol and catechins

Measurements of aroxyl radical (ArO^•)-scavenging rate constants () of antioxidants (AOHs) (α-tocopherol (α-TocH) and three catechins (CatHs) (ie, epicatechin (EC), epigallocatechin (EGC), and epigallocatechin gallate (EGCG)) were performed in ethanol solution, using stopped-flow spectrophotometry. values were measured not only for each AOH, but also for the mixtures of two AOHs (α-TocH and CatH). A notable synergistic effect that the value of α-TocH increases 1.29, 1.84, and 1.65 times under the coexistence of constant concentrations of EC, EGC, and EGCG, respectively, was observed for the solutions including α-TocH and CatH. Similarly, values of CatHs (EC, EGC, and EGCG) increased 1.72, 2.25, and 2.34 times under the coexistence of constant concentrations of α-TocH, respectively. UV-Vis absorption of α-tocopheroxyl radical (α-Toc^•) (λ_max = 428 nm), which had been produced by reaction of α-TocH with ArO^•, decreased remarkably under the coexistence of α-TocH and CatHs due to the fast α-TocH-regeneration reaction by CatHs. The result suggests that the prooxidant reaction due to α-Toc^• is suppressed by the coexistence of CatHs. By analyzing the formation and decay curves of α-Toc^•, it has been ascertained that one molecule of EGCG having three OH groups at B-ring may rapidly regenerate three molecules of α-Toc^• to α-TocH.