矩阵方程AXB+CYD＝E的对称极小范数最小二乘解

对于任意给定的矩阵A∈Rm×n,B∈Rn×s,C∈Rm×k,D∈Rk×s,E∈Rm×s,本文利用矩阵的Kmnecker积和Moore-Penrose广义逆,研究矩阵方程AXB CYD=E的对称极小范数最小二乘解,得到了解的表达式．并由此给出了矩阵方程AXB=C的双对称极小范数最小二乘解的表达式．此外,我们还给出了求矩阵方程AXB=C的双对称极小范数最小二乘解的数值算法和数值例子．     

The fluorescence properties of Yb3+ and Er3+ Co-doped YAl3(BO3)4 powders prepared by sol-gel method

Yb³⁺ and Er³⁺ co-doped YAB powders were prepared by sol-gel method. The structure and fluorescence properties were investigated. XRD pattern indicated that the single phase was obtained at 1150°C and the structure belonged to rhombohedral. Under 379 nm excitation, two emissions around 983 nm and 1531 nm were observed and the effect of Yb³⁺ ion concentration on the emission intensity was discussed. The energy transfer was observed under 930 nm excitation and the energy transfer efficiencies for all samples were calculated. The lifetimes of ² F _5/2 level of Yb³⁺ ion and ⁴ I _13/2 level of Er³⁺ ion were measured and the effect of Yb³⁺ ion concentration on the lifetime was also discussed. The results indicated that there was an additional mechanism for the decay of ⁴ I _13/2 level in powder samples. The Yb³⁺ and Er³⁺ co-doped YAB powders should be a potential candidate for ceramic laser materials.     

矩阵方程X+A*X-nA=I的正定解

In this paper we give some sufficient conditions and some necessary conditions under which the matrix equation X A^*X^-nA=I has a positive definite solution. An iterative method which converges to a positive definite solution of this equation is constructed. And an error estimate formula on this iterative method is also derived.     

ROBUST GLOBAL EXPONENTIAL STABILITY OF UNCERTAIN IMPULSIVE SYSTEMS

By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory.     

Unique continuation along curves and hypersurfaces for second order anisotropic hyperbolic systems with real analytic coefficients

In this paper we prove the following kind of unique continuation property. That is, the zero on each geodesic of the solution in a real analytic hypersurface for second order anisotropic hyperbolic systems with real analytic coefficients can be continued along this curve.

     

高质量等曲率物参光像面数字全息显微系统

对等曲率物参光像面数字全息显微成像系统进行研究,分析了光路配置方法,推导了系统的点扩散函数,并由此指出了决定系统成像分辨率的因素及系统的成像特点,最后讨论了再现像光场一次位相畸变校正的方法.结果表明,等曲率物参光像面数字全息具有最大的信息容量;该系统的成像分辨率取决于显微物镜的数值孔径和CCD的像元大小,与CCD的光敏面尺寸无关;物体各点中通过显微物镜的所有频率成分均能被系统完全记录与再现,样品被照亮区域的大小对记录条件和再现像质没有影响;等曲率物参光像面数字全息系统是一种优化的全息记录与再现系统,利用该系统可以实现高质量成像.实验结果验证了理论分析的正确性.     

X波段过模弯曲圆波导TM01-HE11模式变换器研究

在波束波导和反射面天线的馈源应用中, 为了产生低副瓣且方向图等化的高斯波束, 需要将高功率微波转换为准高斯模HE₁₁模辐射. 本文利用弯曲圆波导可同时从TM₀₁模产生TE₁₁模和TM₁₁模的原理, 提出了采用双弯曲过模圆波导结构直接将TM₀₁转换为HE₁₁的模式变换器, 避免了常规微波领域中首先将TM₀₁转换为TE₁₁再用波纹式或半径渐变式TE₁₁-HE₁₁转换器转换为准高斯波束功率容量不足或尺寸过长的不足. 基于模式耦合理论和Taguchi优化算法对模式变换器的弯曲半径、相移直端长度及引入位置进行了优化, 使输出的TE₁₁和TM₁₁成一定比率, 以组成HE₁₁模式, 并对设计的模式变换器进行了全电磁波仿真分析, 结果表明输出波束的标量高斯含量在9.05–9.8 GHz范围内均高于99%, 理论功率容量可达4.5 GW. 关键词： 高功率微波 模式耦合理论 Taguchi优化算法 模式变换器     

基于吸聚一体的低散射传输型透镜设计

通过传输型超表面透镜与电路模拟雷达波吸收器的集成设计,提出了一种兼具透射波前变换与带外雷达散射截面减缩特性的微波复合材料设计方法。透镜采用亚波长分布的周期性单元,由梯度相位补偿对透射波进行调节,进而获得平面波前与球面波前之间的互易变换。并且,使用透镜在波前变换频带以外低频端的反射特征,结合单个有耗层设计,构造了电路模拟吸波器。选用一副缝隙耦合馈电的微带贴片天线单元作为初级馈源天线,观察到复合材料的波前变换特性可在宽频带范围内产生主瓣增益增强效果。与透镜相比,电路模拟吸波器的引入使得复合材料针对TE与TM极化分别可在130.68%与155.11%的频率范围内获得雷达散射截面减缩效果。通过全波模拟和实验测量,验证了辐射增益增强与雷达散射截面减缩效果,表明了复合材料吸聚一体设计的有效性。     

Collider search of light dark matter model with dark sector decay

We explore the possibility that the dark matter relic density is not produced by a thermal mechanism directly, but by the decay of other heavier dark-sector particles which themselves can be produced by the thermal freeze-out mechanism. Using a concrete model with light dark matter from dark sector decay, we study the collider signature of the dark sector particles associated with Higgs production processes. We find that future lepton colliders could be a better place to probe the signature of this kind of light dark matter model than hadron colliders such as LHC. Also, we find that a Higgs factory with center-of-mass energy 250 GeV has a better potential to resolve the signature of this kind of light dark matter model than a Higgs factory with center-of-mass energy 350 GeV.     

离子注入诱导量子阱界面混合效应的光致荧光谱研究

采用多元芯片方法获得了一系列不同离子注入剂量的GaAsAlGaAs非对称耦合量子阱单元,通过光致荧光谱测量,研究了单纯的离子注入导致的界面混合效应.荧光光谱行为与有效质量理论计算研究表明,Al原子在异质结界面的扩散在离子注入过程中已基本完成,而热退火作用主要是去除无辐射复合中心. 关键词： 量子阱 离子注入 光致荧光谱 界面混合