Fractional order Sobolev spaces on Wiener space

Summary Fractional order Sobolev spaces are introduced on an abstract Wiener space and Donsker's delta functions are defined as generalized Wiener functionals belonging to Sobolev spaces with negative differentiability indices. By using these notions, the regularity in the sense of Hölder continuity of a class of conditional expectations is obtained.     

Synthesis and characterization of crosslinked uniform polymeric microspheres containing a polyimide prepolymer by a new emulsification process

A highly crosslinked poly(styrene–divinyl benzene–trimethyolpropane trimethacrylate) microsphere containing a polyimide prepolymer (PIP) was prepared by a new emulsification method, Shirasu porous glass (SPG) membrane emulsification, and a subsequent radical suspension polymerization. That is, a mixture of styrene, divinyl benzene, trimethyol propane trimethacrylate (TMPTMA), and PIP containing an initiator was permeated through the uniform pores of the SPG membrane into a continuous phase containing a stabilizer to form uniform droplets. Then, the suspension polymerization was carried out at 65 °C for 24 h. The trifunctional crosslinker TMPTMA was added to enhance the destructive strength of the microsphere, and PIP was incorporated into the microsphere to provide an adhesion force by a known self‐curing reaction at 220 °C. The effects of the feed amounts of TMPTMA and PIP on the monomer conversion, size distribution, and destructive strength of the microsphere were investigated. The monomer conversion increased with an increase in TMPTMA. The particle size distribution became narrower as the TMPTMA feed amount increased, but it became broader with an increase in PIP. The destructive strength increased with increases in TMPTMA and PIP. After a heat treatment at 220 °C, the destructive strength decreased because of the heat degradation of the polymer. The addition of TMPTMA suppressed the heat degradation, and PIP could undergo self‐curing at 220 °C. The obtained highly crosslinked uniform microsphere containing PIP has potential applications in liquid‐crystal displays. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2588–2598, 2003     

Preparation of high performance nanocomposite elastomer: effect of reaction conditions on in situ silica generation of high content in natural rubber

Effect of amines on an in situ silica generation in natural rubber was investigated, and n-hexylamine, n-heptylamine and n-octylamine were found to increase the in situ silica content. The nanometer sized silica particles up to ca. 80 parts per hundred rubber by weight were generated in situ in the rubber matrix via a sol–gel reaction of tetraethoxysilane. Additionally, dispersion of the silica in the rubbery matrix was more homogeneous than that of commercial silica dispersed by a conventional mechanical mixing. In this in situ silica generation, the polarity and solubility in water of amine were influential factors for controlling the in situ silica content in the rubbery matrix. The obtained high in situ silica filled natural rubber was useful to prepare high performance nanocomposite elastomers.     

Macromolecular helicity inversion of an optically active helical poly(phenylacetylene) by chemical modification of the side groups

An optically active helical poly(phenylacetylene) was synthesized by the copolymerization of phenylacetylenes bearing optically active hydroxy or ester groups obtained by the kinetic resolution of a racemic phenylacetylene with lipase; the helix-sense was inverted from one helix to another by the further chemical modification of the hydroxy groups with achiral bulky isocyanates or an acid chloride.     

Electronic structure of BaTiO3 using resonant X-ray emission spectroscopy at the Ba-L3 and Ti-K absorption edges

We have studied the electronic properties of the ferroelectric barium titanate BaTiO₃ using two complementary bulk-sensitive spectroscopic probes, resonant X-ray emission spectroscopy (RXES) and X-ray absorption spectroscopy in the partial fluorescence mode (PFY-XAS) at the Ba-L₃ and Ti-K absorption edges. Contrary to a previous study, we found no fine structure in the pre-edge area of the PFY-XAS spectrum at the Ba-L₃ edge, and no temperature-induced spectral change was observed between room temperature and 150 °C. This result is not supportive of the possible presence of the displacement around Ba²⁺ at the Curie temperature. RXES spectra were measured at the Ti-K edge for BaTiO₃, along with SrTiO₃ and La-doped metallic SrTiO₃. The photon energy of the emission peak is found to be nearly constant throughout the absorption edge for all three compounds. We deduce the Ti 3d states to have a delocalized character, in contrast with the Ba 5d states, a property which is consistent with the proposed scenario of the formation of electric dipoles in BaTiO₃.     

Asymptotic Windings of Brownian Motion Paths on Riemann Surfaces

We study asymptotic winding properties of Brownian motion paths on Riemann surfaces by obtaining limit laws for stochastic line integrals along Brownian paths of meromorphic differential 1-forms (Abelian differentials).     

An efficient diastereoselective synthesis of 6-hydroxy-4a-[3,4-crowned(15-crown-5)phenyl]-trans-decahydroisoquinoline

A high diastereoselective synthesis of 6-hydroxy-4a-aryl-$\text{trans}$-decahydroisoquinoline derivatives was achieved by an application of N-acyliminium ion-induced polyene cyclization procedure.