Global classical solution of the Cauchy problem to 1D compressible Navier–Stokes equations with large initial data

In this paper, we prove that the 1D Cauchy problem of the compressible Navier–Stokes equations admits a unique global classical solution (ρ,u)$(\rho ,\mathrm{u})$ if the viscosity μ(ρ)=1+ρ^β$\mu (\rho )=1+{\rho }^{\beta }$ with β?0$\beta ?0$. The initial data can be arbitrarily large and may contain vacuum. Some new weighted estimates of the density and velocity are obtained when deriving higher order estimates of the solution.     

Perturbation of systems of linear algebraic equations ∗

A classical perturbation result for nonsingular systems of linear algebraic equations is extended to general consistent systems under any norm. An optimal perturbation result is also obtained for general linear least squares problems under a Euclidean norm.     

Simple synthesis of zwitterionic diblock copolymers for the application on metal nanoparticles preparation

AB diblock copolymers of poly(2-(dimethylamino)ethyl metharylate-block-potassiurn acrylate) were prepared via reversible addition-fragmentation chain transfer (RAFT) polymerization. The structure of the block polymer was determined by the nuclear magnetic resonance (NMR) spectroscopy and the gel permeation chromatography. Moreover, it has also been shown that the diblock copolymers exhibit aggregate as function of the pH according to the result of ¹H-NMR spectroscopy, FT-IR absorption spectra, UV-vis transmittance spectroscopy, transmission electron microscopy and ultrasonic particle size analyzer. The result was attributed that such AB diblock copolymers were tailored to undergo pH-induced self-assembly. Furthermore, the aggregate can be as template of metal nanoparticles preparation, and the sizes of the aggregate, in turn, strongly control nanoparticle sizes.     

Copper‐catalyzed one‐pot synthesis of propargylamines via C?H activation in PEG

An efficient and convenient three‐component A³ coupling reaction of aldehyde, amine and alkyne via C? H activation with CuI alone as the catalyst in PEG is developed, providing a wide range of propargylamines with yields ranging from moderate to excellent. Additionally, the catalyst system was recovered and reused several times without evident loss in activity. Copyright © 2010 John Wiley & Sons, Ltd.     

激波风洞信号测量仪

本文叙述了一种用于激波风洞实验研究中的以微机为基础的多功能智能测量仪表,叙述了其构成部分和性能、硬件结构和原理、软件编制以及将BASIC程序写入EPROM的过程。     

Dye-sensitized solar cells based on a single-crystalline TiO2 nanorod film

Highly crystalline TiO2 nanorods with lengths of 100-300 nm and diameters of 20-30 nm have been synthesized by a hydrothermal process in a cetyltrimethylammonium bromide surfactant solution. The microstructure measured by X-ray diffraction and high-resolution transmission electron microscopy was a pure highly crystalline anatase phase with a long nanorod shape. The addition of a triblock copolymer poly(ethylene oxide)100-poly(propylene oxide) 65-poly(ethylene oxide)100 (F127) decreased the length of the nanorods and kept the rod shape of the particles even after sintering at high temperatures. The rod shape kept under high calcination temperatures contributed to the achievement of the high conversion efficiency of light-to-electricity as discussed in the paper. A high conversion efficiency of light-to-electricity of 7.29% was obtained with the TiO2 single-crystalline anatase nanorod cell.     

Rectification of excitation with bathochromic shift induced by intense absorption of organic ligands during emission measurement of Eu(III) complex

Bathochromic shift in excitation spectrum was observed during emission measurement of Eu(DBM)(3)Phen containing dilute solution in methyl methacrylate (MMA). Detailed analysis shows that the reason of bathochromic shift is not the formation of molecule aggregation. It is caused by the intense absorption of ligands in the complex. Based on this model, a new method has been established to rectify excitation spectra before emission measurement of systems with different concentration. There exists a critical value of the absorption strength, which is 0.87 from calculation. Higher absorption than this value will cause the bathochromic shift of excitation peak. The wavelength whose absorbance is 0.87 will be the position of the strongest excitation peak. With 200 ppm and 500 ppm Eu(DBM)(3)Phen as the standard sample, relations between relative concentration and wavelength of excitation peak in Eu(DBM)(3)Phen system were deduced and plotted. Theoretical curves are in good agreement with experiment data except extra-dilute concentration, for partial decomplexation of the beta-diketonate and phenanthroline ligands.     

On strong convergence to 3-D axisymmetric vortex sheets

We consider the 3-D axisymmetric incompressible Euler equations without swirls with vortex-sheets initial data. It is proved that the approximate solutions, generated by smoothing the initial data, converge strongly in provided that they have strong convergence in the region away from the symmetry axis. This implies that if there would appear singularity or energy lost in the process of limit for the approximate solutions, it then must happen in the region away from the symmetry axis. There is no restriction on the signs of initial vorticity here. In order to exclude the possible concentrations on the symmetry axis, we use the special structure of the equations for axisymmetric flows and careful choice of test functions.