基于交替投影算法求解单变量线性约束矩阵方程问题

研究如下线性约束矩阵方程求解问题:给定A∈R~(m×n),B∈R~(n×p)和C∈R~(m×p),求矩阵X∈R(?)R~(n×n)"使得A×B=C以及相应的最佳逼近问题,其中集合R为如对称阵,Toeplitz阵等构成的线性子空间,或者对称半(ε)正定阵,(对称)非负阵等构成的闭凸集.给出了在相容条件下求解该问题的交替投影算法及算法收敛性分析.通过大量数值算例说明该算法的可行性和高效性,以及该算法较传统的矩阵形式的Krylov子空间方法(可行前提下)在迭代效率上的明显优势,本文也通过寻求加速技巧进一步提高算法的收敛速度.     

Maximal saddle solution of a nonlinear elliptic equation involving the p-Laplacian

A saddle solution is called maximal saddle solution if its absolute value is not smaller than those absolute values of any solutions that vanish on the Simons cone $\mathcal{C}=\{s=t\}$ and have the same sign as s???t. We prove the existence of a maximal saddle solution of the nonlinear elliptic equation involving the p-Laplacian, by using the method of monotone iteration, $$ \Delta_{p}u=f(u) \quad \text{in} \quad R^{2m}, $$ where 2m?≥?p?>?2.     

变时滞随机模糊细胞神经网络稳定性分析(英文)

本文旨在研究一类带变时滞的随机模糊细胞神经网络的稳定性.通过构造恰当的Lyapunov泛函并运用线性矩阵不等式(LMI)理论,作者给出了保证这类神经网络全局渐近稳定的充分条件.本文推导出两个定理:一个用以判定文中模型的全局渐进稳定性,一个用以判定该模型在均方意义下的全局渐近稳定性.     

A meshfree-based local Galerkin method with condensation of degree of freedom for elastic dynamic analysis简

Condensation technique of degree of freedom is first proposed to improve the computational efficiency of meshfree method with Galerkin weak form for elastic dy- namic analysis. In the present method, scattered nodes with- out connectivity are divided into several subsets by cells with arbitrary shape. Local discrete equation is established over each cell by using moving Kriging interpolation, in which the nodes that located in the cell are used for approxima- tion. Then local discrete equations can be simplified by con- densation of degree of freedom, which transfers equations of inner nodes to equations of boundary nodes based on cells. The global dynamic system equations are obtained by as- sembling all local discrete equations and are solved by using the standard implicit Newmark＇s time integration scheme. In the scheme of present method, the calculation of each cell is carried out by meshfree method, and local search is imple- mented in interpolation. Numerical examples show that the present method has high computational efficiency and good accuracy in solving elastic dynamic problems.     

Notes on random vibration of a vehicle model and other discrete systems possessing repeated natural frequencies

In this study, we investigate random vibration of vehicle model exhibiting repeated natural frequencies. It is shown that the cross-correlations have crucial effect, and their neglect may lead to considerable error in the evaluation of mean-square values of the response. In addition, we revisit some discrete systems with coinciding natural frequencies.     

Development of an inverse heat conduction model and its application to determination of heat transfer coefficient during casting solidification

The interfacial heat transfer coefficient (IHTC) is required for the accurate simulation of heat transfer in castings especially for near net-shape processes. The large number of factors influencing heat transfer renders quantification by theoretical means a challenge. Likewise experimental methods applied directly to temperature data collected from castings are also a challenge to interpret because of the transient nature of many casting processes. Inverse methods offer a solution and have been applied successfully to predict the IHTC in many cases. However, most inverse approaches thus far focus on use of in-mold temperature data, which may be a challenge to obtain in cases where the molds are water-cooled. Methods based on temperature data from the casting have the potential to be used however; the latent heat released during the solidification of the molten metal complicates the associated IHTC calculations. Furthermore, there are limits on the maximum distance the thermocouples can be placed from the interface under analysis. An inverse conduction based method have been developed, verified and applied successfully to temperature data collected from within an aluminum casting in proximity to the mold. A modified specific heat method was used to account for latent heat evolution in which the rate of change of fraction solid with temperature was held constant. An analysis conducted with the inverse model suggests that the thermocouples must be placed no more than 2 mm from the interface. The IHTC values calculated for an aluminum alloy casting were shown to vary from 1,200 to 6,200 Wm^?2 K^?1. Additionally, the characteristics of the time-varying IHTC have also been discussed.     

Elastic interaction between edge dislocation,concentrated force,point heat source and edge crack in a semi-infinite plane

We investigate the interaction between edge crack and edge dislocation as well as concentrated force and point heat source. The stress intensity factors at the edge crack tip and the image forces acting on the edge dislocation are calculated. The influence of the concentrated force, point heat source and edge dislocation on the shielding and anti-shielding effects to edge crack as well as the glide and climb forces acting on the edge dislocation is examined in detail. The results indicate that the shielding and anti-shielding effects increase acutely with the increment of concentrated force and point heat source. In addition, the glide and climb forces increase acutely with the decrement of the distance between dislocation and crack tip.     

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

In this paper, Hermitian positive definite solutions of the nonlinear matrix equation X ＋ A^＊X^-qA = Q （q≥1） are studied. Some new necessary and sufficient conditions for the existence of solutions are obtained. Two iterative methods are presented to compute the smallest and the quasi largest positive definite solutions, and the convergence analysis is also given. The theoretical results are illustrated by numerical examples.     

碳源对SBR单级好氧工艺中微生物摄磷能力的影响及其机理研究

以两种典型基质：葡萄糖（R1）和乙酸钠（R2）作为单一碳源,考察了SBR单级好氧工艺在R1和R2中的除磷效果,并通过比较各自微生物体内储能物质的变化,探讨了SBR单级好氧工艺以不同基质作为碳源时影响其微生物摄磷能力的根本原因．结果表明：R1和R2中均观察到明显的超量摄磷现象,但在运行条件完全相同的情况下,两系统中微生物摄磷能力以及体内储能物质有很大的差别．稳定运行后,R1和R2中单位混合液挥发性悬浮固体（MLVSS）的总磷（TP）去除量分别为6．7～7．4、2．7～3．2mg·g^-1．R1中微生物体内储能物质多β羟基烷酸盐（PHA）含量没有明显的变化,另一储能物质糖原质在好氧段外碳源（葡萄糖）存在时有明显的积累现象（糖原质的最大积累量为3．21mmol-C·g^-1）,在好氧段外碳源消耗完后呈下降趋势,并在好氧结束时下降到好氧前水平;R2中PHA与糖原质在好氧段外碳源（乙酸钠）存在时均有明显的积累现象（外碳源消耗完时PHA与糖原质积累量分别为2．1,0．55mmol—C·g^-1）,PHA在好氧段外碳源消耗完后呈下降趋势,并在好氧结束时也几平下降到好氧前水平,而糖原质却在外碳源消耗完后继续积累,并在好氧2h左右时达到最大值（糖原质最大积累量为0．88mmol—C·g^-1）,此后下降明显,在好氧结束时也几乎恢复到原始水平．在整个好氧过程中,R1中内碳源（PHA与糖原质）的积累／转化量大于R2系统．在闲置期内,R1与R2中PHA与糖原质均没有明显变化,但却观察到明显的释磷现象,且R1释磷量多于R2系统．此研究显示,由于R1与R2中进水碳源不同,在其反应系统内碳源的好氧代谢途径有所差别,使各自微生物在好氧段体内储能物质的类型与积累／转化量也有所不同,各自微生物在好氧摄磷时得到的可利用的能量也不同,因而各自微生物的摄磷能力亦有所差别．