The Asymptotic Behavior of the Takhtajan-Zograf Metric

We obtain the asymptotic behavior of the Takhtajan-Zograf metric on the Teichmüller space of punctured Riemann surfaces. The first author is partially supported by JSPS Grant-in-Aid for Exploratory Research 2005-2007. The second author is partially supported by the research grant R-146-000-106-112 from the National University of Singapore and the Ministry of Education.     

Carbon multi-walled nanotubes grown by HWCVD on a pyroelectric detector

Carbon multi-wall nanotubes (MWNTs) were grown on a lithium niobate (LiNbO₃) pyroelectric detector with a nickel film as the catalyst by hot-wire chemical vapor deposition (HWCVD). Two detectors are documented, each with slightly different deposition conditions. The absolute spectral responsivity of each device was measured from 600 nm to 1800 nm and indicates that the MWNT-coating absorptance is spectrally uniform, with variations of only a few percent. We also discuss growth of MWNTs on LiTaO₃ by CVD and the limitations presented by the Curie temperature of the pyroelectric material.     

Effect of the Water Quenched Slag‐epoxy Resin Composite on Microwave Absorbing Properties

Although in recent years, the ash residues produced from municipal solid waste incinerators (MSWI) in Taiwan have been decreased gradually due to the public awareness of waste classification, it is still necessary to find a suitable landfill site to dispose these wastes safely and economically. For this reason, the plasma melting technology was selected to convert the unwanted ash residues into harmless water quenched slag. More importantly, the effect of the dielectric and magnetic properties of microwave absorber composed of water quenched slag‐epoxy resin composite was studied. The absorbing performance of water quenched slag‐epoxy composites at same sample thickness and at various sample thickness were also studied by measuring complex permittivity, complex permeability and reflection loss in the 2–18 and 18–40 GHz microwave frequency range using the free space method. It was found that the optimum thickness of absorber needed to yield the best reflection loss could be obtained and an absorption frequency range shifting at the frequency range of 2–18 and 18–40 GHz.     

Nanoparticle mixing through rapid expansion of high pressure and supercritical suspensions

Mixing of binary mixtures of nanopowders afforded by rapid expansion of high pressure and supercritical suspensions (REHPS) is investigated to examine the roles of two previously reported deagglomeration mechanisms. The quality of mixing was characterized through intensity and scale of segregation using concentration data obtained through energy dispersive X-ray spectroscopy; the corresponding deagglomeration was quantified using differential mobility and image analyses in conjunction with electron microscopy. Increasing the pressure from which expansion was carried out, and decreasing the nozzle diameter led to improved deagglomeration. However, increased pressure alone did not influence the mixture quality, which was found to also depend on the scale of mixedness of the constituents before transport through the nozzle, establishing that the REHPS mixing is significantly improved by improving the quality of the premix. The scale of segregation correlated with the size of the most energetic eddies present during flow through the nozzle, both of which increased with nozzle diameter, corroborating the importance of previously reported shear-induced deagglomeration mechanism. Finally, REHPS was also shown to be capable of deagglomerating carbon nanotube bundles and mix them well with alumina, silica, and titania at submicron scale.     

Enzyme-catalyzed synthesis of (R)- and (S)-3-hydroxy-3-(10-alkyl-10H-phenothiazin-3-yl)propanoic acids

Starting from the racemic ethyl 3-hydroxy-3-(10-alkyl-10H-phenothiazin-3-yl)propanoates as substrates, a multienzymatic procedure was developed for the efficient synthesis of the corresponding highly enantiomerically enriched (R)- and (S)-3-heteroaryl-3-hydroxypropanoic acids.     

金刚石车削表面微纳织构的气囊抛光改进

单点金刚石车削技术被广泛应用于光学表面的超精密加工。然而,车削表面固有的周期性残留刀痕结构将增强表面散射效应,恶化元件光学性能。为了抑制散射以获得高质量光学表面,采用气囊抛光技术主动改变车削表面周期性刀痕结构。基于Taguchi正交试验,以表面粗糙度及功率谱密度的改善率为设计指标,分析获得了最优抛光参数。采用该最优参数对一精车表面进行了抛光试验,抛光后表面粗糙度Ra由3.81 nm降到1.42 nm,各空间频率功率谱密度大幅降低,同时表面的衍射条纹消失。试验结果验证了所采用的抛光及相应优化方法的有效性,具有重要的工程应用价值。     

Proton transport properties in hybrid membranes investigated by ac-electrogravimetry

In this paper, a hybrid organic/inorganic membrane, based on poly(VDF-co-HFP) polymer associated to mesostructured modified silica and made through sol–gel techniques, was characterized by using ac-electrogravimetry. In order to perform experiments, a polypyrrole–heteropolyanion doped mediator film was inserted between the working electrode of the microbalance and the hybrid membrane. This mediator film, which is characterized by mixed conducting properties, is necessary to provide proton transfer between the different interfaces and in that way, the proton transport inside the hybrid film which is only an ionic conducting material. Proton transfer and transport was characterized through ac-electrogravimetry and an original theoretical approach was developed for extracting the attractive parameters. The change of the exchanged species concentration and the diffusion coefficient of the protons in the hybrid membrane, were estimated, for the first time, according to the applied potential. These studies pointed out that the low conductivity value in this hybrid membrane is related to i) the low diffusion coefficient of proton (10^? 7 cm² s^? 1) in this membrane associated, ii) the low concentration of proton in the membrane (0.4 meq g^? 1).     

A NEW FINITE ELEMENT APPROXIMATION OF A STATE-CONSTRAINED OPTIMAL CONTROL PROBLEM

In this paper, we study numerical methods for an optimal control problem with pointwise state constraints. The traditional approaches often need to deal with the deltasingularity in the dual equation, which causes many difficulties in its theoretical analysis and numerical approximation. In our new approach we reformulate the state-constrained optimal control as a constrained minimization problems only involving the state, whose optimality condition is characterized by a fourth order elliptic variational inequality. Then direct numerical algorithms （nonconforming finite element approximation） are proposed for the inequality, and error estimates of the finite element approximation are derived. Numerical experiments illustrate the effectiveness of the new approach.     

On intersections of conjugacy classes and bruhat cells

For a connected semisimple algebraic group G over an algebraically closed field k and a fixed pair (B, B ^– ) of opposite Borel subgroups of G, we determine when the intersection of a conjugacy class C in G and a double coset BwB ^– is nonempty, where w is in the Weyl group W of G. The question comes from Poisson geometry, and our answer is in terms of the Bruhat order on W and an involution m _C ∈ 2 W associated to C. We prove that the element m _C is the unique maximal length element in its conjugacy class in W, and we classify all such elements in W. For G = SL(n + 1; k), we describe m _C explicitly for every conjugacy class C, and when w ∈ W ≌ S_n+1 is an involution, we give an explicit answer to when C ∩ (BwB) is nonempty.