Reconstruction of Sparse Polynomials via Quasi-Orthogonal Matching Pursuit Method

In this paper, we propose a Quasi-Orthogonal Matching Pursuit (QOMP) algorithm for constructing a sparse approximation of functions in terms of expansion by orthonormal polynomials. For the two kinds of sampled data, data with noises and without noises, we apply the mutual coherence of measurement matrix to establish the convergence of the QOMP algorithm which can reconstruct $s$-sparse Legendre polynomials, Chebyshev polynomials and trigonometric polynomials in $s$ step iterations. The results are also extended to general bounded orthogonal system including tensor product of these three univariate orthogonal polynomials. Finally, numerical experiments will be presented to verify the effectiveness of the QOMP method.     

n × n 上三角算子矩阵的单值扩张性以及应用*

设X_i是无穷维复Banach空间, L(X_j,X_i)是X_j到X_i上的有界线性算子全体.考虑 n × n 上三角算子矩阵T=(T_ij)_1≤j≤n, 其中T_ij L(X_j,X_i),1≤j≤n; T_ij=0, i>j.本文研究了T的单值扩张性, 通过考察集合S(T)={λ∈C}: T在点λ没有SVEP},证明了S(T)在i=1 ? nS(T_i)中退化,进而给出等式S(T)=i=1 ? n S(T_i)成立的条件. 同时, 考察了T的单值扩张性扰动,得到了S(T)保持对角稳定时T_i所需的条件并予以证明, 同时举例说明这些条件的合理性.最后, 给出单值扩张性关于谱σ(T)和局部谱σT (x)的应用, 得到了谱扰动和局部谱扰动不变的新条件.     

超声全矩阵数据联合稀疏重构的多测量向量模型应用

针对单测量向量模型(Single Measurement Vector,SMV)等传统压缩感知方法处理超声全矩阵数据时,存在重构精度低和重构耗时长等问题,本文研究了多测量向量模型(Multiple Measurement Vectors,MMV)应用的可行性。针对铝合金试块中不同深度的φ2 mm横通孔,分别使用MMV模型中的多测量稀疏贝叶斯(Multiple Sparse Bayesian Learning,MSBL)算法和SMV模型中的稀疏贝叶斯(Sparse Bayesian Learning,SBL)算法进行超声全矩阵数据重构,并实施全聚焦成像。随后,引入归一化均方误差和阵列性能因子评价图像和信号的重构效果。实验结果表明,SBL算法在25%采样率时的归一化均方误差为1.9%,而MSBL算法仅需15%采样率即可达到相似效果且耗时更少。     

Finite-time stabilization of state dependent impulsive dynamical linear systems

The problem of finite-time stabilizing control design for state-dependent impulsive dynamical linear systems (SD-IDLS) is tackled in this paper. Such systems are characterized by continuous-time, linear, possibly time-varying, dynamics coupled with discrete-time, linear, possibly time-varying, dynamics. The continuous-time part determines the system evolution in any time interval between two consecutive resetting events, while the discrete-time part governs its instantaneous state jump whenever the system trajectory intersects a resetting set, i.e. a region of the state space assumed to be time-independent. By making use of a quadratic control Lyapunov function, the finite-time stabilization of SD-IDLS through a static output feedback control design is specifically discussed in this paper. A sufficient and constructive result is provided based on the conical hulls of the resetting set subregions and on some cone copositivity properties of the chosen control Lyapunov function. Such a result is based on the solution of a feasibility problem that involves a set of coupled Difference/Differential Linear Matrix Inequalities (D/DLMI), which is shown to be less conservative and more numerically amenable with respect to other results available in the literature. An example illustrates the effectiveness of the proposed approach.     

一种非对称大型有限元方程组的有效分块波前解法

提出分块波前法求解非对称大型有限元方程组，该方法综合分块解法和波前法的优点，根据计算机容量和方程的阶数优化计算过程，以在经济效率和存储效率之间达到平衡。本文利用该方法求解了轮胎稳态滚动有限元方程组，表明该方法是有效、可靠的。     

基体开裂的正交复合材料对称层合板的粘弹性力学行为

本文讨论了含有均匀基体裂纹的正交复合材料对称层合板的线性粘弹性力学行为.采用二维剪切滞后模型并对其层间剪应力在厚度方向进行线性假设分布,求得层合板的平均应力应变的线弹性解,利用等效约束模型和经典层合理论可得到层合板因为含有基体裂纹而所引起的刚度退化现象.在弹性-粘弹性对应原理的基础上对其层合板的线粘弹性进行了讨论和研究.结果表明:层合板的松弛模量和蠕变泊松比随着时间的增加而减少,到达稳态后其值基本上是恒值.并跟Zocher的解析解和有限元数值解作了比较,发现结果非常吻合.     

非协调四结点平面等参位移元新列式方法

本文导出一种等参协调元位移函数的新的表示方法,在此基础上建立起了构造等参非协调元的新方法。作为实例,构造出两个可以给出单刚显式的四结点平面非协调新单元。     

La_2O_3和WSi_2增强MoSi_2基复合材料的摩擦磨损性能研究

选用MRH-5A型环-块摩擦磨损试验机测定了3种载荷和2种转速条件下La2O3和WSi2增强MoSi2基复合材料在滑动干摩擦时的摩擦磨损性能,采用扫描电子显微镜分析了复合材料磨损表面形貌.结果表明:La2O3和WSi2增强MoSi2基复合材料的抗磨性能优于MoSi2及WSi2/MoSi2材料;当载荷与速度乘积(pv)值小于183.04N·m/s时,La2O3和WSi2增强MoSi2基复合材料的磨损质量损失仅为相同条件下MoSi2的1/4～1/6和WSi2/MoSi2的1/2;这是由于La2O3和WSi2复合增强相存在硬化和韧化协同作用所致;随着pv值增加,La2O3和WSi2增强MoSi2基复合材料依次呈现犁削、粘着磨损和疲劳磨损特征.     

基于复模态的控制力矩陀螺配置优化

由于陀螺耦合效应,系统动力学方程的特征值和特征向量皆为复数形式,不便于进行控制力矩陀螺的配置优化和控制律设计。本文基于复模态理论,构造出一种实数域上的伪模态矩阵,从而实现方程解耦。综合考虑结构模态、控制输入能量和传感器接收能量的复合优化准则,获得了控制力矩陀螺的最优配置。结果表明,采用线性二次型最优控制,能够快速将结构的响应振幅降至5%以内,验证了使用伪模态矩阵进行方程解耦的可行性及控制的有效性。     

非线性动力系统的规范形和余维3退化分叉

本文里我们利用矩阵表示法计算了具有Z_(2~-)对称性时非线性动力系统的高阶规范形,求出了余维2退化和余维3退化情况下相应规范形的普适开折。最后利用所得到的规范形和普适开折讨论了非线性动力系统的余维3退化分叉。