构造单元刚度矩阵的双参数法

§1.引言 用位移法构造有限元单元刚度矩阵的常规方法如下:设单元为K,位移形函数空间是 ?(K)=Span{N_1,…,N_m}, (1.1)其中N_1,…,N_?是线性无关的多项式.     

Blind convolutive separation method for speech signals via joint block diagonalization

A blind speech source separation method for the overdetermined convolutive mixture model in time-domain is proposed via joint block-diagonalization based on the mutual- independence and short-time stationarity properties of the speech signals. Taking the sum of the F-norms of all off-diagonal sub-matrices as a criterion, a novel joint block-diagonalization method is proposed to estimate the whole mixture matrix through minimizing a sequence of quadratic sub-functions corresponding to mixture sub-matrices. Both theoretical analysis and simulations show that the proposed method has much lower complexity and faster convergence speed than the classical Jacobi-like method with no performance loss. In addition, there are almost no obvious impacts of the channel order and initialization values on the convergence speed.     

Spiking Behavior in Chua's Circuit

Chua ＇s circuit with a slow-fast effect is established under certain parameter conditions. The dynamics of this slow- fast system is investigated. A spiking phenomenon can be observed in the numerical simulation. By introducing slow-fast analysis and a generalized Jacobian matrix at the non-smooth boundaries, the bifurcation mechanism for the periodic spiking solution, different from the smooth case, is discussed.     

A Simple Method for Generating Discrete Multi-Component Integrable Hierarchy

For M×N spectral matrix, a kind of operation ？ which satisfies combination law （a？b）？c=a？（b？c） is introduced. The discrete multi？component zero-curvature equation is deduced by using the new operation ？, and a simple method for constructing discrete multi-component integrable hierarchy is proposed. As its application, the multi-component Toda hierarchy and its two kinds of integrable couplings are worked out.     

Cluster Consensus of Nonlinearly Coupled Multi-Agent Systems in Directed Graphs

We investigate the cluster consensus problem in directed networks of nonlinearly coupled multi-agent systems by using pinning control. Depending on the community structure generated by the group partition of the underlying digraph, various clusters can be made coherently independent by applying feedback injections to a fraction of the agents. Sufficient conditions for cluster consensus are obtained using algebraic graph theory and matrix theory and some simulations results are included to illustrate the method.     

用转移矩阵方法来研究发生在势阱内的量子反射

本文利用转移矩阵方法对两种简单的具有吸引尾的势进行了研究.我们发现反射系数在波矢k→0时R=1,反射率与波矢k在k→0时呈线性关系.这说明在发生阱内量子反射时有利于超冷原子生存,因为超冷原子是低速低能原子.此外,我们可以用一个反射时间变化量Δt来判断量子反射的延迟或者超前.     

非球形烟尘粒子后向散射场的光谱分析

在利用后向散射法测量烟尘浓度和粒径的过程中,对烟尘粒子模型的后向散射光谱特性进了计算,确定影响后向散射光谱强度的主要因素并进行分析。对实际排放的烟尘进行显微观察表明,利用椭球、圆柱和广义切比雪夫3种非球模型可以较好地模拟烟尘粒子,其等效直径约1μm。通过"T矩阵法"对这3种非球形粒子模型后向散射场的光谱特性进行了分析,结果表明:非球形粒子的可见/红外波段后向散射现象较球形粒子明显,特别是广义切比雪夫粒子的后向散射光强最高可达到前向的3.5倍;对于吸收性非球形粒子(复折射率m=1.57-0.56i),后向散射光强远大于非吸收性非球形粒子(复折射率m=1.57-0.001i);随着粒子等效半径的增大,光源波长也应随之增加。这为在实际测量时光源及方位的选择提供了理论依据。     

正则化HSS预处理鞍点矩阵的特征值估计

最近,Bai和Benzi针对鞍点问题提出了一类正则化HSS（Regularized Hermitian and skew-Hermitian splitting,RHSS）预处理子（BIT Numer.Math.,57（2017）287-311）.为了进一步分析RHSS预处理子的效果,本文重点研究了RHSS预处理鞍点矩阵特征值的估计,分析了复特征值实部和模的上下界、实特征值的上下界,还给出了特征值均为实数的充分条件.当正则化矩阵取为零矩阵时,RHSS预处理子退化为HSS预处理子,分析表明本文给出的复特征值实部的界比已有的结果更精确.数值算例验证了本文给出的理论结果.