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.     

Effect of the pore surface modification of an inorganic substrate on the plasma‐grafting behavior of pore‐filling‐type organic/inorganic composite membranes

We have investigated the effect of the surface state and surface treatment of the pores of an inorganic substrate on the plasma‐grafting behavior of pore‐filling‐type organic/inorganic composite membranes. Shirasu porous glass (SPG) was used as the inorganic substrate, and methyl acrylate was used as the grafting monomer. The grafting rate increased as the density of silanol on the SPG substrate increased. This result suggests that radicals are generated mainly at the silanol groups on the pore surface by plasma irradiation. The SPG substrates were treated with silane coupling agents used to control the mass of organic material bonded to the pore surface. The thickness of the grafted layer became thinner as the mass of organic material bonded to the pore surface of SPG increased. This decrease in the thickness of the grafted layer could be explained by the decrease in the penetration depth of vacuum ultraviolet rays contained in plasma having a wavelength of less than 160 nm that generated radicals in the pores of the substrate. The thickness of the grafted layer inside the SPG substrates could be controlled through the control of the mass of organic material bonded to the pore surface of the SPG substrate. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 846–856, 2006     

Spectrophotometric determination of anthracycline anticancer agents with aluminum(III) and chromazurol S in a nonionic surfactant micellar medium.

A simple and highly sensitive spectrophotometric method for the determination of anthracycline anticancer agents, such as Daunorubicin hydrochloride (DAU), was established by using aluminum(III) and Chromazurol S (CAS) in a nonionic surfactant micellar medium. In the case of determination of DAU, the apparent molar absorptivity was 1.3 x 10(5) dm3 mol(-1) cm(-1) at 615 nm. Beer's law was obeyed in the concentration range of 0.028 - 2.82 microg ml(-1) for DAU. Owing to no need for solvent extraction, this method could be applied to assays of DAU and related drugs in pharmaceutical preparations.     

Studies on the synthesis of condensed pyridazine derivatives. IV. Synthesis and anxiolytic activity of 2-aryl-5,6-dihydro-(1)benzothiepino[5,4- c]pyridazin-3(2H)-ones and related compound.

A series of 2-aryl-5,6-dihydro-(1)benzothiepino[5,4-c]pyridazin-3(2H)- ones and related compounds were synthesized and evaluated for their ability to displace 3H-diazepam from rat brain membranes in vitro, and to prevent bicuculline induced convulsions in mice in vivo. Compounds with a 4'-methoxyphenyl (36) or 4'-chlorophenyl group (37, 39--42) as 2-aryl substituents showed prominent activities in both the in vitro and in vivo tests. Among them, 2-(4'-chlorophenyl)-5,6-dihydro- (37) and 2-(4'-chlorophenyl)-5,6-dihydro-10-fluoro-(1)benzothiepino[5,4-c]+ ++pyridazin- 3(2H)-one 7-oxides (41) showed activity twice as potent as diazepam in an anticonflict test (Vogel type, rats) while exhibiting less muscle relaxation (rotarod test, mice) and augmentation of gamma-aminobutyric acid-induced chloride current (Icl) in isolated frog sensory neurones than diazepam. Compound 37 (Y-23684) was selected from this series as a candidate for further development. The structure-activity relationships are discussed.     

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.     

Time decay of solutions to the cauchy problem for time-dependent Schrödinger-Hartree equations

We consider the time-dependent Schrödinger-Hartree equation (1) $$iu_t + \Delta u = \left( {\frac{1}{r}*|u|^2 } \right)u + \lambda \frac{u}{r},(t, x) \in \mathbb{R} \times \mathbb{R}^3 ,$$ (2) $$u(0,x) = \phi (x) \in \Sigma ^{2,2} ,x \in \mathbb{R}^3 ,$$ where λ≧0 and \(\Sigma ^{2,2} = \{ g \in L^2 ;\parallel g\parallel _{\Sigma ^{2,2} }^2 = \sum\limits_{|a| \leqq 2} {\parallel D^a g\parallel _2^2 + \sum\limits_{|\beta | \leqq 2} {\parallel x^\beta g\parallel _2^2< \infty } } \} \) . We show that there exists a unique global solutionu of (1) and (2) such that $$u \in C(\mathbb{R};H^{1,2} ) \cap L^\infty (\mathbb{R};H^{2,2} ) \cap L_{loc}^\infty (\mathbb{R};\Sigma ^{2,2} )$$ with $$u \in L^\infty (\mathbb{R};L^2 ).$$ Furthermore, we show thatu has the following estimates: $$\parallel u(t)\parallel _{2,2} \leqq C,a.c. t \in \mathbb{R},$$ and $$\parallel u(t)\parallel _\infty \leqq C(1 + |t|)^{ - 1/2} ,a.e. t \in \mathbb{R}.$$