New Relaxation Method for Mathematical Programs with Complementarity Constraints

In this paper, we present a new relaxation method for mathematical programs with complementarity constraints. Based on the fact that a variational inequality problem defined on a simplex can be represented by a finite number of inequalities, we use an expansive simplex instead of the nonnegative orthant involved in the complementarity constraints. We then remove some inequalities and obtain a standard nonlinear program. We show that the linear independence constraint qualification or the Mangasarian–Fromovitz constraint qualification holds for the relaxed problem under some mild conditions. We consider also a limiting behavior of the relaxed problem. We prove that any accumulation point of stationary points of the relaxed problems is a weakly stationary point of the original problem and that, if the function involved in the complementarity constraints does not vanish at this point, it is C-stationary. We obtain also some sufficient conditions of B-stationarity for a feasible point of the original problem. In particular, some conditions described by the eigenvalues of the Hessian matrices of the Lagrangian functions of the relaxed problems are new and can be verified easily. Our limited numerical experience indicates that the proposed approach is promising.     

软X射线激光偏折法测量激光等离子体电子密度分布

利用脉宽约为50ps的类镍银139nm软X射线激光作为探针,探测由脉宽80ps的驱动激光打C8H8靶产生的等离子体在1ns后的电子密度分布信息,获得了清晰的莫尔条纹图像.对结果的处理,给出了峰值电子密度为11×1021cm-3,并对在靶面附近莫尔条纹的消失现象作了初步解释 关键词： 软X射线激光探针 莫尔条纹 等离子体电子密度     

Volumes and diophantine inequalities associated with decomposable forms

For homogeneous decomposable forms in n variables with real coefficients, we consider the associated volume of all real solutions to the inequality . We relate this to the number of integral solutions to the Diophantine inequality in the case where F has rational coefficients. We find quantities which bound the volume and which yield good upper bounds on the number of solutions to the Diophantine inequality in the rational case.     

Vibration characteristics of aluminum surface subjected to ultrasonic waves and their effect on wetting behavior of solder droplets

The vibration characteristics of an aluminum surface subjected to ultrasonic waves were investigated with a combination of numerical simulation and experimental testing. The wetting behavior of solder droplets on the vibrating aluminum surface was also examined. The results show that the vibration pattern of the aluminum surface is inhomogeneous. The amplitude of the aluminum surface exceeds the excitation amplitude in some zones, while the amplitude decreases nearly to zero in other zones. The distribution of the zero-amplitude zones is much less dependent on the strength of the vibration than on the location of the vibration source. The surface of the liquid solder vibrates at an ultrasonic frequency that is higher than the vibration source, and the amplitude of the liquid solder is almost twice that of the aluminum surface. The vibration of the surface of the base metal (liquid solder) correlates with the oxide film removal effect. Significant removal of the oxide film can be achieved within 2 s when the amplitude of the aluminum surface is higher than 5.4 μm or when the amplitude of the liquid solder surface is higher than 10.2 μm.     

Enhancement of the electric field threshold for microwave breakdown by crossed magnetic field

The enhancement of breakdown threshold is of benefit to the high power microwave transmission. We propose a magnetic field in the transverse direction to the electric field to enhance the breakdown threshold. A theory of electric field threshold with crossed magnetic field for short pulse is developed, and verified by particle-in-cell/Monte Carlo collision (PIC/MCC) simulations. The result shows that the crossed magnetic field can enhance the breakdown threshold significantly.     

用自制仪器演示光通信

介绍一种新的小型演示仪器.该仪器用于普通物理光通信实验教学,能形象生动地演示光信号的耦合、传输、解调以及还原。仪器结构简单,思路清晰,可操作性强,对学生有很强的演示性。     

650 kV/2 ns高压脉冲发生器研制

研制了一套峰值650 kV、脉宽2 ns的窄脉冲发生器,具有结构紧凑、体积小巧、便于移动和产生优质的纳秒高压脉冲等优点。该发生器基于三谐振脉冲变压器原理和脉冲形成压缩实现窄脉冲输出,采用紧凑双锥形绕组铁芯变压器、LC调谐回路和27 pF,30 脉冲形成线组成三谐振回路,油介质自击穿开关导通后在负载上获得高压脉冲。实验结果表明,该窄脉冲发生器可在80 电阻负载上输出脉冲峰值约650 kV,脉宽约2 ns,与理论分析的结果相吻合。     

On Clique-Transversals and Clique-Independent Sets

A clique-transversal of a graph G is a subset of vertices intersecting all the cliques of G. A clique-independent set is a subset of pairwise disjoint cliques of G. Denote by _C (G) and _C (G) the cardinalities of the minimum clique-transversal and maximum clique-independent set of G, respectively. Say that G is clique-perfect when _C (H)= _C (H), for every induced subgraph H of G. In this paper, we prove that every graph not containing a 4-wheel nor a 3-fan as induced subgraphs and such that every odd cycle of length greater than 3 has a short chord is clique-perfect. The proof leads to polynomial time algorithms for finding the parameters _C (G) and _C (G), for graphs belonging to this class. In addition, we prove that to decide whether or not a given subset of vertices of a graph is a clique-transversal is Co-NP-Complete. The complexity of this problem has been mentioned as unknown in the literature. Finally, we describe a family of highly clique-imperfect graphs, that is, a family of graphs G whose difference _C (G)– _C (G) is arbitrarily large.     

基于简单透镜列阵的可调焦激光均匀辐照光学系统研究

本文对基于简单透镜列阵的大口径激光均匀辐照光学系统的调焦能力进行了研究, 结果表明, 改变透镜列阵与靶镜之间的距离即可方便地改变靶面上光斑的大小. 文中详细分析了相关参数对调焦能力的影响, 并在此基础上设计出一个实用的光学系统. 用数值方法模拟了激光束通过光学系统后的传输, 发现尺寸不同的靶面光斑具有基本一致的强度结构特征. 定量地分析了光斑内部散斑间隔、调制对比度、顶部不均匀度及能量集中度等描述光斑均匀辐照质量的指标, 并研究了它们随靶面离焦量的变化关系.     

一种新的卫星钟差Kalman滤波噪声协方差估计方法

采用Kalman滤波方法进行钟差参数计算和预报时, 需确定Kalman滤波噪声协方差矩阵. 针对这一问题, 提出了一种新的卫星钟差Kalman滤波噪声协方差估计方法, 通过建立新息的相关函数序列与未知的噪声参数间的线性函数模型, 采用最小二乘法进行噪声参数估计. 采用精密钟差数据进行钟差参数估计和预报分析, 结果表明, 该方法具有较好的收敛性, 并与顾及随机噪声模型的开窗分类因子自适应抗差估计方法进行对比分析, 验证了新方法的正确性和有效性.