Implicit compact difference schemes for the fractional cable equation

In this paper, we propose two implicit compact difference schemes for the fractional cable equation. The first scheme is proved to be stable and convergent in l_∞-norm with the convergence order O(τ + h⁴) by the energy method, where new inner products defined in this paper gives great convenience for the theoretical analysis. Numerical experiments are presented to demonstrate the accuracy and effectiveness of the two compact schemes. The computational results show that the two new schemes proposed in this paper are more accurate and effective than the previous.     

Long TiO2 hollow fibers with mesoporous walls: sol-gel combined electrospun fabrication and photocatalytic properties

Long TiO2 hollow fibers with mesoporous walls have been fabricated with the sol-gel combined two-capillary spinneret electrospinning technique using a triblock copolymer (Pluronic, P123, (H(C2H5O)20(C3H7O)70 (C2H5O)20OH) as a pore-directing agent. The as-prepared hollow fibers were as long as 30 cm with an outer diameter of 0.1-4 microm and wall thickness of 60-500 nm. The diameters and wall thicknesses of the hollow fibers could be tuned by adjusting the electrospinning parameters. The fiber walls were composed of mesopores 6.7 nm in diameter as calculated from the N2 adsorption/desorption isotherm. The high-resolution TEM (HR-TEM) images exhibited that the mesopores were hexagonally aligned with a low order because of the curving of the pores. When comparing with other nanostructured TiO2 materials such as commercial TiO2 nanoparticles (P25, Degussa) and mesoporous TiO2 powders, the hollow fibers exhibited higher photocatalytic activities toward degradation of methylene blue and gaseous formaldehyde.     

Monoclinic structured BiVO4 nanosheets: hydrothermal preparation, formation mechanism, and coloristic and photocatalytic properties

Bismuth vanadate (BiVO(4)) nanosheets have been hydrothermally synthesized in the presence of sodium dodecyl benzene sulfonate (SDBS) as a morphology-directing template. The nanosheets were characterized by X-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM) equipped with an X-ray energy dispersive spectrometer (EDS), X-ray photoelectron spectroscopy (XPS), IR spectroscopy, transmission electron microscopy (TEM), and high-resolution TEM (HR-TEM). The BiVO(4) nanosheets had a monoclinic structure, were ca. 10-40 nm thick, and showed a preferred (010) surface orientation. The formation mechanism and the effects of reaction temperature and time on the products were investigated. UV-visible diffuse reflection spectra indicated that the BiVO(4) nanosheets had outstanding spectral selectivity and improved color properties compared with the corresponding bulk materials. Furthermore, the nanosheets showed good visible photocatalytic activities as determined by degradation of N,N,N',N'-tetraethylated rhodamine (RB) under solar irradiation.     

Comparison of alpha1-adrenergic receptor cell-membrane stationary phases prepared from expressed cell line and from rabbit hepatocytes

A G-protein-coupled receptor-cell-membrane stationary phase (CMSP) has been prepared by immobilizing cell membranes on the surface of silica, as carrier. The resulting HEK293 α _1A adrenoceptor cell-membrane stationary phase can be used for rapid on-line chromatographic determination of potential subtype-selective α ₁ -adrenoceptor ligand-binding affinities for α ₁ -adrenoceptor subtypes. The objective of the research was to study whether cell lines stably overexpressing subtype receptors could improve the sensitivity and specificity of cell-membrane chromatography (CMC) compared with use of homogenized tissue and cells in primary culture. Effects of mobile-phase ionic strength, sample concentration, and the presence of competitive agents on ligand-receptor interaction in CMSP were also evaluated. We found that cell lines stably overexpressing subtype receptors led to improved sensitivity and specificity in CMC. The technique leads to useful procedures-cell-membrane stationary phases may, for example, facilitate exploration of ligand-receptor interaction and determination of ligand-receptor binding affinity in initial screening and separation of lead compounds or active components in Chinese traditional natural medicine and herbs. This might eventually be an important contribution and an addition to our collection of techniques.     

关于遗传可遮和遗传σ-亚紧可数乘积的注记

证明了在逆序列的情形下,可遮空间、强可遮空间在假设X是可数仿紧空间的条件下可被其极限空间保持,进一步证明了遗传可遮,遗传强可遮及遗传σ-亚紧性在无需对投射及极限空间X做任何假设的情况下即可被其逆极限空间保持.作为上述两个结果的应用,分别给出了两个相关的可数Tychonoff乘积定理.     

基于金属催化C-H官能团化/脱芳构化反应的螺环构筑

螺环化合物因其在天然产物和药物分子中的广泛分布而备受化学家的青睐(图1),因此开发高效构筑含有螺环骨架的复杂分子的方法引起了合成化学家的广泛关注.基于金属催化C—H键活化反应从简单起始原料出发,以较短的合成步骤得到一些重要的杂环分子,被证明是一种通用且便捷的路径.同时,过渡金属催化去芳构化反应被认为是将平面芳香环直接转化为具有三维螺环结构的最有效、最直接的策略之一[1].     

Visible-light-promoted sulfonylmethylation of imidazopyridines

The visible light promoted C–H sulfonylmethylation of imidazopyridines with easily accessible bromomethyl sulfones under mild reaction conditions was described. This protocol provides an effective and practical access to sulfonylmethylated imidazopyridines with good functional group tolerance. The desired products were provided in moderate to excellent yields for 50 examples at room temperature. The method could also be an attractive strategy to install a methyl group on imidazopyridines.