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.     

Properties of holomorphic Wiener functions —skeleton,contraction, and local Taylor expansion

Summary We show that each holomorphic Wiener function has a skeleton which is intrinsic from several viewpoints. In particular, we study the topological aspects of the skeletons by using the local Taylor expansion for holomorphic Wiener functions.Supported in part by the Grant-in-Aid for Science Research 03740120 Min. Education     

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.     

Synthesis of poly(benzoxazole)s by direct polycondensation of dicarboxylic acids with 3,3′-dihydroxybenzidine dihydrochloride using phosphorus pentoxide/methanesulfonic acid as condensing agent and solvent

A convenient method for the synthesis of poly(benzoxazole)s of high molecular weights has been developed. These polymers were prepared readily by direct polycondensation of aromatic dicarboxylic acids containing phenyl either structure with 3,3′-dihydroxybenzidine dihydrochloride using phosphorus pentoxide/methanesulfonic acid (PPMA) as condensing agent and solvent. Polycondensations proceeded fast and was completed within 5 h at 140°C and produced poly(benzoxazole)s with inherent viscosities up to 4.6 dL/g. Model compound work was performed in detail to demonstrate the feasibility of the reaction for polymer formation. The thermogravimetry of the aromatic poly(benzoxazole)s showed 10% weight loss in air and nitrogen at 450–505°C and 465–535°C, respectively.     

Detection of bilayer packing stress and its release in lamellar-cubic phase transition by time-resolved fluorescence anisotropy

An introduction of nonlamellar-forming lipids into planar bilayers generates packing stress, which is important for the biological functions of plasma membranes and is a driving force for the lamellar-nonlamellar phase transition. We have investigated the phase behavior of a binary system consisting of egg yolk phosphatidylcholine and monoolein (MO) and the changes in the local orientation order of lipids in a lamellar-bicontinuous cubic phase transition. Small-angle X-ray scattering has revealed that the lamellar-bicontinuous cubic phase transition occurs at an MO molar fraction (X(MO)) between 0.6 and 0.7. These phases were dispersed to form liposomes and cubosomes to monitor the anisotropy of the incorporated fluorescence probe, in which Pluronic F127, used as a dispersion stabilizer of the cubic phase, has been proven not to alter the cubic structure and the location of the probes. Time-resolved fluorescence anisotropy measurements on these dispersions have revealed that the order parameter of the probe in the lamellar phase increases with increasing X(MO), and that it decreases during the transition to the cubic phase. This observation suggests that packing stress generated by the addition of the nonlamellar-forming lipid is released by the phase transition.     

Upward temperature shift of the intrinsic phase lag of the magnetization of Bis(phthalocyaninato)terbium by ligand oxidation creating an S = 1/2 spin

An alternating-current (ac) magnetic susceptibility measurement for the [(Pc)(2)Tb(III)](0) complex (Pc = phthalocyaninato) has shown that ligand oxidation of the anionic [(Pc)(2)Tb(III)](-) complex gives rise to a significant upward shift of the temperature range where the magnetization response shows a phase lag behind the time-varying external magnetic field. The peaks of the out-of-phase component of the ac susceptibility of the pi-radical [(Pc)(2)Tb(III)](0) were observed at 50, 43, and 36 K with ac magnetic fields of 10(3), 10(2), and 10 Hz, respectively, which were more than 10 K higher than the corresponding values of the anionic complex with a closed-shell pi-system. The ac susceptibility measurements on the complex with octa(dodecoxy)-substituted Pc ligand, which is readily dilutable in diamagnetic media, proved that the significant rise of the temperatures occurs as an intrinsic single-molecular property of the complex possessing both J = 6 and S = (1)/(2) systems, and is not due to long-range magnetic order or interactions between adjacent unpaired pi-electrons.     

Synthesis of 21-nor-22-oxa-1α,25-dihydroxyvitamin D3 derivatives in quest of a drug with low calcemic activity

Two 21-nor-22-oxa-1α,25-dihydroxyvitamin D₃ derivatives have been synthesized in quest of a drug with lower calcemic activity than Maxacalcitol, 22-oxa-1α,25-dihydroxyvitamin D₃, being used as antihyperparathyroidism and antipsoriatic drug. Of two 21-nor products obtained, the product carrying one carbon elongated side chain with diethylcarbinol moiety has been found to exhibit comparable differentiation-inducing activity to Maxacalcitol with much lower exhibition of calcemic activity.