Isospectral theory of Euler equations

Isospectral problem of both 2D and 3D Euler equations of inviscid fluids, is investigated. Connections with the Clay problem are described. Spectral theorem of the Lax pair is studied.     

Effects of the H-bond donor structure on the properties of supramolecular side chain liquid crystalline polymers based on poly(3-carboxypropylmethylsiloxane-co-dimethylsiloxane)s and stilbazoles

Supramolecular side chain liquid crystalline polymers (SCLCPs) based on poly(3-carboxypropylmethylsiloxane-co-dimethylsiloxane) (PSIX, X=100, 76, 60, 41 or 23, denoting the mole percentage of 3-carboxypropylmethylsiloxane unit in the polymer) and stilbazole derivatives have been obtained through intermolecular hydrogen bonding (H-bonding) interactions between the carboxylic acid and the pyridyl moieties. The formation of H-bonding and self-assembly results in the formation of new mesogenic units, in which H-bonds function as molecular connectors. FTIR shows the existence of H-bonding in the complexes. The polymeric complexes behave as single component liquid crystalline polymers and exhibit stable and enantiotropic mesophases. The liquid crystalline properties of the supramolecular SCLCPs were studied using differential scanning calorimetry, polarizing optical microscopy and X-ray diffraction, and were found to exhibit smectic A phases with focal-conic textures. The thermal stability of the SCLCP increases on increasing the carboxylic acid content in the polysiloxane and the concentration of the stilbazole derivative in the complex. However, the thermal stability decreases on increasing the chain length of the stilbazole derivative. The crystal phase was not formed even on cooling to the glass transition temperature of the polymeric complex.     

The Spectrum of a Linearized 2D Euler Operator

We study the spectral properties of the linearized Euler operator obtained by linearizing the equations of incompressible two-dimensional fluid at a steady state with the vorticity that contains only two nonzero complex conjugate Fourier modes. We prove that the essential spectrum coincides with the imaginary axis, and give an estimate from above for the number of isolated nonimaginary eigenvalues. In addition, we prove that the spectral mapping theorem holds for the group generated by the linearized 2D Euler operator.     

A minimal pair joining to a plus cupping Turing degree

A computably enumerable (c.e.) degree a is called nonbounding, if it bounds no minimal pair, and plus cupping, if every nonzero c.e. degree x below a is cuppable. Let NB and PC be the sets of all nonbounding and plus cupping c.e. degrees, respectively. Both NB and PC are well understood, but it has not been possible so far to distinguish between the two classes. In the present paper, we investigate the relationship between the classes NB and PC , and show that there exists a minimal pair which join to a plus cupping degree, so that PC ? NB . This gives a first known difference between NB and PC . (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于网格的知识资源挖掘研究

为满足网络上不同用户群体对个性化资源的要求,文章从网格与服务网格的概念出发,引入知识挖掘技术,提出了网格环境下的个性化知识资源挖掘实现框架,并对其实现功能与应用加以分析.     

Nonlinear rheological behavior of silica filled solution‐polymerized styrene butadiene rubber

The reinforcement and nonlinear viscoelastic behavior have been investigated for silica (SiO₂) filled solution‐polymerized styrene butadiene rubber (SSBR). Experimental results reveal that the nonlinear viscoelastic behavior of the filled rubber is similar to that of unfilled SSBR, which is inconsistent with the general concept that this characteristic comes from the breakdown and reformation of the filler network. It is interesting that the curves of either dynamic storage modulus (G′) or loss tangent (tan δ) versus strain amplitude (γ) for the filled rubber can be superposed, respectively, on those for the unfilled one, suggesting that the primary mechanism for the Payne effect is mainly involved in the nature of the entanglement network in rubbery matrix. It is believed there exists a cooperation between the breakdown and reformation of the filler network and the molecular disentanglement, resulting in enhancing the Payne effect and improving the mechanical hysteresis at high strain amplitudes. Moreover, the vertical and the horizontal shift factors for constructing the master curves could be well understood on the basis of the reinforcement factor f(φ) and the strain amplification factor A(φ), respectively. The surface modification of SiO₂ causes a decrease in f(φ), which is ascribed to weakeness of the filler–filler interaction and improvement of the filler dispersion. However, the surface nature of SiO₂ hardly affects A(φ). © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2594‐2602, 2007     

铝电解电容器用橡皮塞中铁的测定

主要研究了用硫氰酸钾作显色剂，用分光光度法测定橡皮塞中铁含量的方法。并对国产和进口橡皮塞做了比较，为铝电解电容器质量水平的提高提供一条新思路。     

扫描近场光学显微镜及其在生物微结构探测上的应用

扫描近场光学显微镜（ＳＮＯＭ）可探测生物体亚波长水平的光学特性，以接近分子水平的分辨率在生物微结构成象、探测和修饰等多方面有巨大的潜力。本文对ＳＮＯＭ的技术方法及其近期的的生物学应用进行了介绍。     

坦克红外特征控制技术评述

坦克红外特征控制对于提高坦克的战场生存能力具有重要意义。控制的主要方法有遮障、表面处理、外形技术、主动冷却、总体设计等。坦克红外特征的控制必须与其他波段，特别是射频波段的特性控制兼容。遮障和低发射率涂料是现役坦克红外特征控制的主要措施。而对未来的主战坦克，设计应是减少其系统特性的重要途径。