关于复对称矩阵特征根的补注

This note investigates the relationship of eigenvalues of Hermitian matrices P and UPU+ with UU+ = Ik and k ≤ n. We present several equivalent conditions for λi(UPU+) = λi(P) (i ≤ k ≤ n).     

On ANOVA expansions and strategies for choosing the anchor point

The classic Lebesgue ANOVA expansion offers an elegant way to represent functions that depend on a high-dimensional set of parameters and it often enables a substantial reduction in the evaluation cost of such functions once the ANOVA representation is constructed. Unfortunately, the construction of the expansion itself is expensive due to the need to evaluate high-dimensional integrals. A way around this is to consider an alternative formulation, known as the anchored ANOVA expansion. This formulation requires no integrals but has an accuracy that depends sensitively on the choice of a special parameter, known as the anchor point.We present a comparative study of several strategies for the choice of this anchor point and argue that the optimal choice of this anchor point is the center point of a sparse grid quadrature. This choice induces no additional cost and, as we shall show, results in a natural truncation of the ANOVA expansion. The efficiency and accuracy is illustrated through several standard benchmarks and this choice is shown to outperform the alternatives over a range of applications.     

Discrete Jacobi sub‐equation method for nonlinear differential–difference equations

We will propose a unified algebraic method to construct Jacobi elliptic function solutions to differential–difference equations (DDEs). The solutions to DDEs in terms of Jacobi elliptic functions sn, cn and dn have a unified form and can be presented through solving the associated algebraic equations. To illustrate the effectiveness of this method, we apply the algorithm to some physically significant DDEs, including the discrete hybrid equation, semi‐discrete coupled modified Korteweg–de Vries and the discrete Klein–Gordon equation, thereby generating some new exact travelling periodic solutions to the discrete Klein–Gordon equation. A procedure is also given to determine the polynomial expansion order of Jacobi elliptic function solutions to DDEs. Copyright © 2010 John Wiley & Sons, Ltd.     

Limit relations for three simple hyperbolic systems of conservation laws

This paper is concerned with the limit relations from the Euler equations of one‐dimensional compressible fluid flow and the magnetohydrodynamics equations to the simplified transport equations, where the δ‐shock waves occur in their Riemann solutions of the latter two equations. The objective is to prove that the Riemann solutions of the perturbed equations coming from the one‐dimensional simplified Euler equations and the magnetohydrodynamics equations converge to the corresponding Riemann solutions of the simplified transport equations as the perturbation parameterx ε tends to zero. Furthermore, the result can also be generalized to more general situations. Copyright © 2009 John Wiley & Sons, Ltd.     

Acyclic edge chromatic number of outerplanar graphs

A proper edge coloring of a graph G is called acyclic if there is no 2‐colored cycle in G. The acyclic edge chromatic number of G, denoted by χ(G), is the least number of colors in an acyclic edge coloring of G. In this paper, we determine completely the acyclic edge chromatic number of outerplanar graphs. The proof is constructive and supplies a polynomial time algorithm to acyclically color the edges of any outerplanar graph G using χ(G) colors. © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 22–36, 2010     

5-羧基-3-氨基-1,2,4-三氮唑芳香醛席夫碱的合成与表征

利用氨基胍碳酸氢盐与草酸反应合成5-羧基-3-氨基-1,2,4-三氮唑,然后用5-羧基-3-氨基-1,2,4-三氮唑与芳香醛反应,合成了2种5-羧基-3-氨基-1,2,4-三氮唑芳香醛席夫碱,通过元素分析,红外光谱和紫外光谱对产物的结构进行了表征.     

落球法测液体粘滞系数实验的理论分析

分析了斯托克斯定律及其修正项的适用范围,讨论了落球法测液体粘滞系数实验中液体粘滞系数和落球直径对雷诺数的影响,从理论上给出了实验中落球进入液体后匀速运动的判据.     

基于STC89C51的新型液氮低温微创冷冻控制系统设计

设计了一种新型液氮低温微创冷冻控制系统,详述了系统的控制原理及各功能模块的实现.采用热流平衡原理、PID技术与STC89C51单片机及外围控制电路对冷冻冻结面范围、液氮瓶压力及冷刀刀头温度进行实时控制和显示.应用结果表明:该系统运行稳定,可靠性高,操作简单.     

ZnMgO/ZnO异质结构中二维电子气的研究

论文根据ZnMgO/ZnO异质结构二维电子气的能带结构及相关理论模型, 采用一维Poisson-Schrodinger方程的自洽求解, 模拟计算了ZnMgO/ZnO异质结构中二维电子气的分布及其对ZnMgO势垒层厚度及Mg组分的依赖关系. 研究发现该异质结构中ZnMgO势垒层厚度存在一最小临界值: 当垒层厚度小于该临界值时, 二维电子气消失, 当垒层厚度大于该临界值时, 其二维电子气密度随着该垒层厚度的增加而增大; 同时研究发现ZnMgO势垒层中Mg组分的增加将显著增强其二维电子气的行为, 导致二维电子气密度的明显增大; 论文对模拟计算获得的结果与相关文献报道的实验结果进行了比较, 并从极化效应和能带结构的角度进行了分析和讨论, 给出了合理的解释. 关键词： 氧化锌 二维电子气 异质结构 理论计算