中立双曲型时滞偏微分方程解振动的充要条件

本文讨论一类线性中立双曲型时滞微分方程解的振动性质，获得了其一切解振动的充要条件．     

矩阵方程AXB+CYD＝E的对称极小范数最小二乘解

对于任意给定的矩阵A∈Rm×n,B∈Rn×s,C∈Rm×k,D∈Rk×s,E∈Rm×s,本文利用矩阵的Kmnecker积和Moore-Penrose广义逆,研究矩阵方程AXB CYD=E的对称极小范数最小二乘解,得到了解的表达式．并由此给出了矩阵方程AXB=C的双对称极小范数最小二乘解的表达式．此外,我们还给出了求矩阵方程AXB=C的双对称极小范数最小二乘解的数值算法和数值例子．     

矩阵方程X+A*X-nA=I的正定解

In this paper we give some sufficient conditions and some necessary conditions under which the matrix equation X A^*X^-nA=I has a positive definite solution. An iterative method which converges to a positive definite solution of this equation is constructed. And an error estimate formula on this iterative method is also derived.     

OSCILLATION OF NONLINEAR IMPULSIVE PARABOLIC DIFFERENTIAL EQUATION WITH SEVERAL DELAYS

In this paper, oscillatory properties for solutions of certain nonlinear impulsive parabolic equation are investigated and a series of new sufficient conditions is established.     

叶轮机械叶片颤振研究的进展与评述

颤振一类气动弹性稳定性问题是叶轮机械设计者关心的主要问题之一. 本文对叶轮机械叶片颤振模型研究的进展进行了回顾, 包括非定常气动模型、结构模型以及颤振的预测方法等内容. 通过对颤振模型研究的介绍, 讨论了不同方法处理颤振这类气动弹性稳定性问题的优缺点. 提出了关于颤振研究目前的不足和部分难点, 认为流固耦合模型的研究值得进一步重点关注.      

航空发动机叶片气动弹性动力响应的数值方法研究进展

流动诱发振动造成的航空发动机叶片高周疲劳失效问题深受关注.对叶片的气动弹性动力响应研究的数值方法及进展进行了回顾,总结了航空发动机叶片振动响应实验研究和数值模拟研究的典型成果与特点,并对未来研究发展趋势进行展望.指出进一步的机理研究将集中于不稳定流动因素引发叶片强迫振动发作规律的探索以及更贴近流固耦合物理机制的气动弹性数值模拟方法的发展;在工程需求牵引下,建立适用于工程预测的动力响应分析模型,在设计过程中科学评价叶片气动弹性动力响应问题的潜在风险和发展流动控制基础上的气动阻尼减振技术值得进一步关注.      

矩阵方程X+A^{*}X^{-q}A=Q(q\geq 1)的Hermitian正定解

本文研究矩阵方程X A~*X~(-q)A=Q(q≥1)的Hermitian正定解,给出了存在正定解的充分条件和必要条件,构造了求解的迭代方法.最后还用数值例子验证了迭代方法的可行性和有效性.     

Establishment of an immunoaffinity chromatography for simultaneously selective extraction of Sudan I, II, III and IV from food samples

The establishment of an immunoaffinity chromatography (IAC) for simultaneously selective extraction of four illegal colorants Sudan dyes (Sudan I, II, II and IV) from food samples was described. The IAC column was constructed by covalently coupling monoclonal antibody (mAb) against Sudan I to CNBr-activated Sepharose 4B and packed into a common solid phase extraction (SPE) cartridge. It was observed that IAC column was able to separately capture Sudan I, II, III and IV with maximum capacity of 295, 156, 184 and 173ng, respectively. The extraction conditions including loading, washing and eluting solutions were carefully optimized. Under optimal conditions, the extraction recoveries of the IAC column for Sudan I-IV at two different spiked concentrations were within 95.3-106.9%. After 50 times repeated usage, 64% of the maximum capacity was still remained. Six food samples randomly collected from local supermarket without spiking Sudan dyes were extracted with IAC column and detected by high performance liquid chromatography (HPLC). It was found that there was no detectable Sudan II, III and IV in all six food samples, but Sudan I with the content of 2.7-134.5ngg(-1) was detected in three food samples. To further verify the extraction efficiency, other three negative samples were spiked with Sudan I-IV at the concentrations of 20ngg(-1) and 50ngg(-1), which were then extracted with IAC column. The extraction recoveries and relative standard deviation (RSD) were 68.6-96.0% and 4.8-15.2%, respectively, demonstrating the feasibility of the prepared IAC column for Sudan dyes extraction.     

聚焦部分相干涡旋光束作用于不同折射率瑞利粒子上的辐射力

 使用聚焦部分相干高斯谢尔涡旋光束,对不同折射率的瑞利粒子的辐射力做了分析,着重研究了相关长度和束腰宽度对辐射力和俘获稳定性的影响。结果表明：相关长度和束腰宽度分别存在临界值,相干长度小于等于其临界值或束腰宽度大于等于其临界值时,可利用其俘获相对折射率大于1的微粒;而在相关长度大于其临界值或束腰宽度小于其临界值时,可利用其俘获相对折射率小于1的微粒。对俘获稳定性的分析表明,需选择适当的相关长度和束腰宽度才能稳定俘获瑞利粒子。     

有损耗波导中非线性TE波的数值模拟

本文发展了一种以有限元技术为基础的数值方法,用它分析有损耗波导中的非线性TE模。在这种方法中,非线性有损耗波导中TE波与功率有关的复传播常数和局城电场分布,可从这种波导直接得到,没有任何近似。作为这种方法的应用,计算了非线性有损耗波导系统中TE0模的功率色散关系和电场分布。