Microstructure and Strength of Laser Welds of Sub-micron Particulate-reinforced Aluminum Matrix Composite Al_2O_(3p)/6061Al

The microstructure of laser welds of sub-micron particulate-reinforced aluminum matrix composite Al_2O_(3p)/6061Al and the weldability of the material were studied. Experimental results indicated that because of the huge specific surface area of the reinforcement, the interfacial reaction between the matrix and the reinforcement was re- strained intenslvely at elevated temperature and pulsed laser beam. The main factor affecting the weldability of the com- posite was the reinforcement segregation in the weld resulting from the push of the liquid/solid interface during the soli- dification of the molten pool. The laser pulse frequency directly affected the reinforcement segregation and the reinfor- cement distribution in the weld, so that the weldability of the composite could be improved by increasing the laser pulse frequency. On the basis of this, a satisfactory welded joint of sub-micron paniculate-reinforced aluminum matrix com- posite Al_2O_(3p)/6061Al was obtained by using appopriate welding parameters.

Applications of AuNRs@SiO₂Matrix Nanocomposites

Gold nanorods (AuNRs/GNR) have unique, controllable and anisotropic local surface plasmon resonance (SPR) properties, which have been widely used in biochemistry, electronics and catalysis. It is of great value and significance to study the synthesis, properties, surface modification and structural regulation of AuNRs. This paper introduces AuNRs and AuNRs@SiO2. The synthesis of AuNRs@SiO2 composite nanomaterials with quantum dots, graphene, rare earth materials and magnetic materials is described. The applications of nanocomposites in optics, biomedicine and biosensors are also discussed. The future development of nanocomposites is proposed.

Effects of Mg content on aging behavior of sub-micron Al_2O_(3p)/Al-Cu-Mg composites

30%Al2O3p/Al-Cu-2.0Mg composite and Al2O3p/Al-Cu-2.5Mg composite with 0.3μm-Al2O3 particles were fabricated. Age-hardening behaviors of two composites and the related matrix alloys were studied by means of Brinell-hardness measurement, DSC and TEM. The results show that the hardness of the composite is improved obviously because of the addition of sub-micron Al2O3 particles. But the hardness increment of Al2O3p/Al composite after aging is lower than that of the related matrix alloy. Moreover, the formation of GP region is suppressed by the addition of sub-micron Al2O3 particles, which broadens the exothermic peak of S' phase. The increment of Mg content has a different influence on accelerating the aging processes of aluminum alloys and the composites, and the hardness also increases.

Optimal Management of the Pension Contribution Rate Using the H∞-Control Theory

In this paper, we construct a general model for a pension fund when there are time delays in the valuation process. Actually, we use the standard structure of the basic reserve equation in order to rebuild a more sophisticated approach based on the theory of H∞ control. Our model evaluates the incomplete information from the delayed fund valuations—due to the oscillatory pattern for benefit claims and investment experience of the past years—within the context of uncertainty additionally to the randomness which certainly exists. So, we construct estimations for the optimal proposed contribution rates based on a feedback mechanism which is a robust stabilization controller, using typical linear matrix inequalities. Finally, a numerical application is fully investigated to obtain further insight into the problem.

Delay-Dependent Robust H∞ Control for Uncertain 2-D Discrete State Delay Systems Described by the General Model

This paper considers the problem of delay-dependent robust optimal H∞ control for a class of uncertain two-dimensional (2-D) discrete state delay systems described by the general model (GM). The parameter uncertainties are assumed to be norm-bounded. A linear matrix inequality (LMI)-based sufficient condition for the existence of delay-dependent g-suboptimal state feedback robust H∞ controllers which guarantees not only the asymptotic stability of the closed-loop system, but also the H∞ noise attenuation g over all admissible parameter uncertainties is established. Furthermore, a convex optimization problem is formulated to design a delay-dependent state feedback robust optimal H∞ controller which minimizes the H∞ noise attenuation g of the closed-loop system. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.

Robust Optimal H∞ Control for Uncertain 2-D Discrete State-Delayed Systems Described by the General Model

This paper investigates the problem of robust optimal H∞ control for uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model (GM) with norm-bounded uncertainties. A sufficient condition for the existence of g-suboptimal robust H∞ state feedback controllers is established, based on linear matrix inequality (LMI) approach. Moreover, a convex optimization problem is developed to design a robust optimal state feedback controller which minimizes the H∞ noise attenuation level of the resulting closed-loop system. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed method.

Robust Finite-Time H∞ Filtering for ItôStochastic Systems

This paper investigates the problem of robust finite-time H∞ filter design for Itô stochastic systems. Based on linear matrix inequalities (LMIS) techniques and stability theory of stochastic differential equations, stochastic Lyapunov function method is adopted to design a finite-time H∞ filter such that, for all admissible uncertainties, the filtering error system is stochastic finite-time stable (SFTS). A sufficient condition for the existence of a finite-time H∞ filter for the stochastic system under consideration is achieved in terms of LMIS. Moreover, the explicit expression of the desired filter parameters is given. A numerical example is provided to illustrate the effectiveness of the proposed method.

H∞ Control for Externally Excited Building Structures with Active Mass Damper under Actuator Saturation

This paper investigates the application of active mass dampers to mitigate the vibrations of building structures subjected to unknown external excitations under controller saturation conditions. By utilizing an H∞ control strategy, the optimal state feedback controller is derived by solving the linear matrix inequality problem for controller saturation. Case studies show that the proposed controller is capable of stabilizing the closed-loop system with good control performance and effectively suppressing vibrations in building structures under unknown external excitation. When compared to controllers that do not consider saturation, the proposed controller requires lower gain and results in reduced energy consumption. The research findings provide valuable insights for addressing real-world building structure control problems, contributing to both theoretical significance and practical applications.

基于特征值的动态数字信道化子带检测算法

动态数字信道化接收结构通过检测所有子带,判断信号是否存在,为综合滤波器组处理提供依据,因此子带检测在接收结构中起着关键作用。针对传统检测算法存在低信噪比(signal-to-noise ratio,SNR)下检测性能不高的问题,依据随机矩阵理论,提出了基于最大最小特征值之差与平均特征值之比的检测算法,利用平均特征值和最小特征值的极限分布规律来推导算法的检测门限。其次,根据所有子带数据获取的特征值信息对所提算法进行了优化。最后,在动态数字信道化接收结构中,分析不同因素下算法的性能,表明了所提算法能够克服低SNR的影响,子带检测的性能更好。

液晶调控下的亚波长金光栅反射相位

空间光调制器(Spatial Light Modulator,SLM)是实现光场调控的关键器件。本文研究了一种将亚波长金光栅嵌入硅基液晶(Liquid Crystal on Silicon,LCoS)构成的SLM(G-LCoS)器件模型的反射相位特性,该器件模型以ITO透明导电层和液晶构成G-LCoS中亚波长金光栅的非对称边界。首先运用散射矩阵原理给出了亚波长金光栅反射相位的计算表达式,其次给出了下表面液晶的有效折射率计算公式。在此基础上,利用TechWiz 3D软件模拟加电情况下金光栅下表面液晶指向矢的变化,给出金光栅下表面液晶有效折射率的变化值。将得到的有效折射率数据导入到FDTD Solutions软件,对该器件结构开展了相关的仿真实验和结果分析。综合考虑了上表面的ITO色散情况、金光栅高度变化以及不同电压下液晶有效折射率值,实现了可见光范围内多波长的近2π相位调制。本文研究的器件也为AR/VR显示系统以及全息视频显示的优化提供了一种新思路。

不同对角矩阵的特征值求解

利用分块矩阵的性质,结合分块上三角矩阵,给出了次对角矩阵的特征值求解公式;利用迭代递推的方法给出了三对角矩阵的特征值求解公式;证明了2 n+1阶三对角矩阵与n阶三对角矩阵的特征值的关系,并应用降低行列式阶数的办法求出了高阶矩阵的部分特征值。

Optimal Estimation of High-Dimensional Covariance Matrices with Missing and Noisy Data

The estimation of covariance matrices is very important in many fields, such as statistics. In real applications, data are frequently influenced by high dimensions and noise. However, most relevant studies are based on complete data. This paper studies the optimal estimation of high-dimensional covariance matrices based on missing and noisy sample under the norm. First, the model with sub-Gaussian additive noise is presented. The generalized sample covariance is then modified to define a hard thresholding estimator , and the minimax upper bound is derived. After that, the minimax lower bound is derived, and it is concluded that the estimator presented in this article is rate-optimal. Finally, numerical simulation analysis is performed. The result shows that for missing samples with sub-Gaussian noise, if the true covariance matrix is sparse, the hard thresholding estimator outperforms the traditional estimate method.

伴随矩阵性质证明的一种新方法

定义了矩阵的旋转运算和矩阵的加符号因子运算,证明这两种运算的若干性质。利用这些性质定理研究了伴随矩阵,得到了伴随矩阵的一些重要性质。推广和改进了关于伴随矩阵的已有结论,丰富和完善了伴随矩阵的相关理论。

基于旋转子矩阵正交的6R机器人运动学逆解研究

以机器人运动学方程为基础,基于变换矩阵中旋转子矩阵正交的特性,提出一种6R机器人运动学逆解算法.通过矢量运算,得到含有4个未知变量的4个常系数非线性方程,辅以其它方程,最终得到8组封闭解.通过对钱江一号焊接机器人的实例求解,验证了该算法解决逆解问题仅需0.087 ms,比传统的反变换法具有更优的实时性能;平面工况的运动仿真验证了该算法的有效性.该算法可应用于6R机器人的强实时在线控制系统.

电压稳定分析中降阶潮流雅可比矩阵的研究

基于降阶潮流雅可比矩阵的V-Q灵敏度、模态分析等静态分析方法在分析电压稳定方面得到了广泛应用,但降阶雅可比矩阵涉及到系统潮流雅可比矩阵的子矩阵Pθ可逆的问题,针对此问题,该文首先结合数学矩阵理论及电力系统的实际情况就矩阵Pθ是可逆矩阵给出明确的证明,为基于降阶雅可比矩阵的应用提供理论支持。最后以新英格兰39节点系统作为算例,通过分析计算矩阵Pθ的行列式、模最小特征值及条件数来验证矩阵Pθ的可逆性,为电压稳定分析提供理论基础。

利用等差数列构造大围长准循环低密度奇偶校验码

针对准循环低密度奇偶校验(QC-LDPC)码中准循环基矩阵的移位系数确定问题,该文提出基于等差数列(AP)的确定方法。该方法构造的校验矩阵的围长至少为8,移位系数由简单的数学表达式确定,节省了编解码存储空间。研究结果表明,该方法对码长和码率参数的设计具有较好的灵活性。同时表明在加性高斯白噪声(AWGN)信道和置信传播(BP)译码算法下,该方法构造的码字在码长为1008、误比特率为510-时,信噪比优于渐进边增长(PEG)码近0.3 d B。

计入轴瓦弹性变形的滑动轴承润滑分析的快速近似算法

建立变形矩阵人工处理数据量大和润滑分析计算耗时较长是研究计入轴瓦弹性变形的滑动轴承润滑分析2个主要问题。采用APDL语言编写专门的计算程序来自动求取变形矩阵,并根据变形矩阵的特点,提出了一种在轴承承载区油膜压力对应节点位置处动态截取子矩阵的快速近似新算法。计算结果表明在内燃机一个工作循环内,快速算法得到的最大油膜压力、最小油膜厚度和轴承反力的计算误差在3.2%以内,润滑分析计算时间下降了2个数量级。

关于行对称矩阵

复数域上n阶方阵A称为行对称的,若JA=AJ,其中J=0 0…0 10 0…1 00 1…0 01 0…0 0.定义了行对称阵的次特征值、次特征向量,并研究了该类矩阵的Hermite性、酉性和正规性.

r-广义次正交矩阵

给出r广义次正交矩阵的概念,并研究了它的性质.

任意列重大围长QC-LDPC码的确定性构造

针对准循环低密度奇偶校验(Quasi-Cyclic Low-Density Parity-Check,QC-LDPC)码中准循环基矩阵的移位系数确定问题,提出基于等差数列的确定方法.该方法构造的校验矩阵围长为8,列重可任意选取,移位系数由简单的数学表达式确定,编码复杂度与码长呈线性关系,节省了编解码存储空间.研究结果表明,列重和围长是影响码字性能的重要因素.在加性高斯白噪声(Additive White Gauss Noise,AWGN)信道和置信传播(Belief Propagation,BP)译码算法下,该方法构造的码字在短码时可以获得与IEEE 802.11n、802.16e码相一致的性能,在长码时误比特率性能接近DVB-S2码.同时表明该方法对码长和码率参数的设计具有较好的灵活性.