MULTIPLICATION OF WEAK FUNCTIONS

This paper is a contionuation of [1] and is concerned with multiplication of weak functions. Here the weak functions are treated as generalized expansions in Hermite functions in [2].     

Imprinting by hot embossing in polymer substrates using a template of silica glass surface-structured by the ablation of LIBWE method

Laser-induced backside wet etching (LIBWE) of silica glass plates was performed to fabricate an imprinting template for hot embossing in polymer substrates such as polystyrene and silicone resin. Well-defined inverse surface-micropatterns of gratings and grid arrays on the substrates were produced by the hot embossing using a surface-structured silica glass as the template. These results indicate that the LIBWE method allows us to generate robust glass molding tools that exhibit the inverse shapes of the intended microstructures. PACS 52.38.Mf; 68.47.Mn; 81.05.Kf; 81.05.Lg; 83.50.Uv     

An enantioselective Michael addition of malonate to nitroalkenes catalyzed by low loading demethylquinine salts in water

An enantioselective Michael addition of malonate to nitroalkenes is efficiently catalyzed by low loading demethylquinine salts in water; the yield range from 49% to 93% and the ee up to 90%.     

Markov traces on cyclotomic Temperley-Lieb algebras

In this note, we use generalized Tchebychev polynomials to define a trace function which satisfies certain conditions. Such a trace will be called the Markov trace. In particular, we obtain formulae for the weights of the Markov trace. As a corollary, we get a combinatorial identity. This generalizes Jones's 1983 result on Temperley-Lieb algebras.

     

Isolation and Structure Elucidation of Nortriterpenoids from Schisandra rubriflora

Seven new highly oxygenated nortriterpenoids, rubriflorins D–J ( 1 – 7 ), were isolated from the leaves and stems of Schisandra rubriflora, and their structures were elucidated on the basis of extensive analysis of spectroscopic data. These new compounds feature the opening of ring A compared with related known nortriterpenoids isolated from the genus Schisandra and showed weak activity against HIV‐1.     

X-ray absorption spectra of plasmas

In this paper we present a theoretical method to calculate the absorption spectra of hot dense plasmas. Based on our fully relativistic treatment incorporated with the quantum defect theory to handle the huge number of transition arrays from many configurations with high principal quantum number, we can calculate the absorption spectra for any element or multi-element plasmas with little computational efforts. We calculate the absorption spectra of C10H1605 plasmas, which are in good agreement with the experimental spectra. We can then provide diagnostic analysis for plasmas in relevant inertial confinement fusion (lCF) experiments; namely not only to determine plasmas' temperatures and densities, but also to provide the population densities of various ionic stages. Our theoretical method verified by "benchmark experiments" will be a basic tool to provide "precise" opacity data for the ICF research.``     

Synthesis of TiO2–SiO2/polymer core–shell microspheres with a microphase‐inversion method

A novel microphase‐inversion method was proposed for the preparation of TiO₂–SiO₂/poly(methyl methacrylate) core–shell nanocomposite particles. The inorganic–polymer nanocomposites were first synthesized via a free‐radical copolymerization in a tetrahydrofuran solution, and the poor solvent was added slowly to induce the microphase separation of the nanocomposite and result in the formation of nanoparticles. The average particle sizes of the microspheres ranged from 70 to 1000 nm, depending on the reaction conditions. Transmission electron microscopy and scanning electron microscopy indicated a core–shell morphology for the obtained microspheres. Thermogravimetric analysis and X‐ray photoelectron spectroscopy measurements confirmed that the surface of the nanocomposite microspheres was polymer‐rich, and this was consistent with the core–shell morphology. The influence of the synthetic conditions, such as the inorganic composition and the content of the crosslinking monomer, on the particle properties was studied in detail. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3911–3920, 2006     

Positive Steady States of a Prey-predator Model with Diffusion and Non-monotone Conversion Rate

In this paper, we study the positive steady states of a prey-predator model with diffusion throughout and a non-monotone conversion rate under the homogeneous Dirichlet boundary condition. We obtain some results of the existence and non-existence of positive steady states. The stability and uniqueness of positive steady states are also discussed.     

Phase-Locked Fibre Array for Coherent Combination and Atmosphere Aberration Compensation

We report a fibre amplifier array that not only achieves coherent beam combination by compensation of phase noises of fibre amplifier, but also accomplishes correction of atmosphere aberration. It is of master-oscillatormultiple-amplifier （MOPA） configuration, which can be phase-locked by the multidither principle or heterodyne detection principle. First laboratory experiments of atmosphere aberration compensation of a three-element fibre amplifier array are reported. The atmosphere aberration is created by a phase screen in the experiment. The phase changes of the beam, which are introduced by the fibre amplifier and the phase screen, are both detected by the heterodyne detection method. Phase modulators are controlled to compensate for the phase in the three paths. No matter whether there is a phase screen producing atmosphere aberration or not, the dim dynamic interference fringes in the far field turn to a clear and stable pattern, and the peak intensity is maximized. It is indicated that the fibre amplifier array is phase-locked, and coherent combination of the three beams is achieved. It can be used not only to obtain high power fibre laser array but also in laser space communication.