Diophantine vectors in analytic submanifolds of Euclidean spaces

Let M be an m-dimensional analytic manifold in R~n.In this paper,we prove that almost all vectors in M (in the sense of Lebesgue measure) are Diophantine if there exists one Diophantine vector in M.     

Convergence and stability of the semi-implicit Euler method for a linear stochastic differential delay equation

The paper deals with convergence and stability of the semi-implicit Euler method for a linear stochastic differential delay equation. It is proved that the semi-implicit Euler method is convergent with strong order . The conditions under which the method is MS-stable and GMS-stable are determined and the numerical experiments are given.     

大功率高温超导滤波器的设计与功率测试

本文在双面YBCO高温超导薄膜上设计并制备了两节大功率超导滤波器,根据滤波器功率承载能力与最大电流密度之间的关系,减小电流密度和分散电流密度的分布是提高功率承载能力的关键.本文采用增加超导谐振器尺寸、优化几何结构及改进馈线耦合方式的方法,设计了两节2 GHz频段梭型谐振器结构的滤波器.设计及测量结果显示了馈线结构及谐振器几何尺寸优化程度对超导滤波器功率承载能力有不同程度的影响,说明了在大功率超导滤波器设计中应选用无结点间隙耦合式馈线以抑制电流密度的聚集.采用优化后的谐振器结构制备的梭型两节超导滤波器经测试功率承载能力为2 W.超导滤波器的尺寸为25×12 mm LaAlO3基片,中心频率2.022 GHz,相对带宽为2.4%.同时给出了超导滤波器功率测试的结构和方法.     

实四元数矩阵的数值半径

本文定义了实四元数矩阵的数值半径,并讨论了它与矩阵迹、谱范数的关系,得到了一些等式与不等式.     

Study on hypochlorite degradation of aromatic polyamide reverse osmosis membrane

A serious limitation of most commercial polyamide reverse osmosis (RO) membranes is their sensitivity to chlorine attack. By studying the hypochlorite degradation of aromatic polyamide RO membrane, this work was to get some understandings in the prevention of membrane depreciation and develop membranes with improved chlorine resistance. Membrane performances, including water flux and salt rejection, were evaluated before and after hypochlorite exposure under different pH and concentration conditions. The results showed that chlorination destroyed hydrogen bonds in polyamide chains, causing a notable decline of membrane flux especially in acid environment; however, membrane performance was slightly improved after the treatment of alkaline hypochlorite solution for a certain time, which was probably due to the effect of amine groups in barrier layer. Based on the attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR) characterizations and performance measurements, the results indicated that N-chlorination reaction of aromatic polyamide was also reversible, in other words, the N-chlorinated intermediate could be regenerated to initial amide with the alkaline treatment before ring-chlorination reaction. This conclusion provided several relative suggestions for membrane cleaning procedures. Finally, a method adopting surface coating was proposed to develop membranes with good chlorine resistance, and the preliminary results showed its potential for applications.     

Distributed optical fiber surface plasmon resonance sensors

The relationships of the resonant wavelength of optical fiber surface plasmon resonance (SPR) sensors to the modulation layer refractive index, thickness and the refractive index of the bulk medium are obtained by using theoretical calculation model of optical fiber SPR sensors under certain conditions, which indicates that resonant wavelength of the sensors is approximately linear with modulation layer thickness. Based on the linear relationship, multiple SPR sensors with different resonant wavelengths can be fabricated in a single optical fiber named as distributed optical fiber surface plasmon resonance sensors (DOFSPRSs).Experimental results are presented, showing that it is practical to fabricate more than one SPR sensors in a single optical fiber.     

Trivial stationary solutions to the Kuramoto-Sivashinsky and certain nonlinear elliptic equations

We show that the only locally integrable stationary solutions to the integrated Kuramoto-Sivashinsky equation in R and R² are the trivial constant solutions. We extend our technique and prove similar results to other nonlinear elliptic problems in RN.     

Raman spectra of samarium-fullerene intercalation compounds

Samarium-fullerene intercalation compounds of nominal composition Sm_xC₆₀ (x=1,2,…,6) have been synthesized by a solid-state reaction method. We obtain a Sm_2.75C₆₀ superconducting phase with orthogonal structure and a Sm₆C₆₀ phase with body-centered cubic structure. The broadening and weakening of Raman peaks of the Sm_xC₆₀ compounds are due to the distortion of C₆₀ and electron-phonon interaction. The Raman measurements reveal that the distortion of C₆₀ decrease in Sm_xC₆₀ (x=3,4,5) exposed to air, although the fulleride solids have transformed into an amorphous state. The Raman results also show that the distortion of C₆₀ is still very large in the Sm₆C₆₀ exposed to air, or the C₆₀ molecules have been destroyed and become some amorphous carbide.     

皮秒脉冲在色散缓变光纤中的孤子效应压缩

本文给出了描述皮秒脉冲在色散缓变单模光纤中孤子效应压缩过程的数学模型。通过数值求解，首次对该孤子效应压缩进行了全面的计算和分析。结果表明，与常规光纤相比，采用色散缓变程度合适的光纤压缩皮秒脉冲，不仅能显著地提高压缩后脉冲的峰值功率和脉冲压缩比，而且能有效地消除压缩后脉冲的次峰和脉座。对于确定的脉冲输入，发现，当光纤的色散缓变程度取某一最佳值时，能获得最佳的压缩效果。进一步研究表明，色散的这一最佳变