多元函数条件极值的几种求解方法

研究多元函数的条件极值问题．针对稳定点的各种不同情形．结合具体实例．给出判断条件极值中稳定点是否取得极值的几种方法．     

超实数系统及其一致连续问题

基于模型论的观点与方法介绍超实数系统的构造及其公理体系,以说明非标准分析.由于超实数系统是普通实数系统的一个真扩张,所以,实数系统中的一致连续问题可推广至超实数系统.     

基于多项式模型的混沌系统平方和算法脉冲控制

针对一大类混沌系统,提出一种新颖的基于多项式模型的脉冲控制方法.首先,建立系统的多项式模型.其状态方程由系统状态的多项式矩阵与其单项式组成列向量构成.与其他建模方法相比,该方法不必使用任何预制的假设.其次,提出基于平方和优化算法的脉冲控制方法,使得混沌系统的状态能够实现渐近稳定.基于该算法的脉冲控制与基于线性矩阵不等式凸优化算法的结果相比,能得到更大的脉冲间距,从而可以使用较少的控制能量实现同样的控制效果.最后,仿真实验结果验证了本方法的有效性.     

Exponential networked synchronization of master-slave chaotic systems with time-varying communication topologies

The networked synchronization problem of a class of master-slave chaotic systems with time-varying communication topologies is investigated in this paper. Based on algebraic graph theory and matrix theory, a simple linear state feedback controller is designed to synchronize the master chaotic system and the slave chaotic systems with a time- varying communication topology connection. The exponential stability of the closed-loop networked synchronization error system is guaranteed by applying Lyapunov stability theory. The derived novel criteria are in the form of linear matrix inequalities (LMIs), which are easy to examine and tremendously reduce the computation burden from the feedback matrices. This paper provides an alternative networked secure communication scheme which can be extended conveniently. An illustrative example is given to demonstrate the effectiveness of the proposed networked synchronization method.     

激光熔覆硬质合金强化化纤切断刀的研究

在机械压制法预置硬质合金WC/Co粉末的条形55Si2Mn弹簧钢上,用激光熔覆方法制备了化纤切断刀.调整熔覆层粉末配方中Al、TiC的加入量,结果表明加适量的Al粉能有效地抑制气孔,加TiC粉末能提高熔覆硬度.通过优化激光熔覆工艺参数,得到了无气孔缺陷、组织性能良好、硬度达到HV0.21250的激光熔覆层,达到了化纤切断刀的性能要求.     

MgB2混合态热导率的反常增强

测量了MgB2多晶样品的混合态热导率,磁场强度为0-7 T,温度范围为5-45 K.实验结果显示MgB2热导率在低场下迅速上升,高场下趋于饱和,这与MgB2的二能隙电子结构有关.对实验结果的分析指出,低温强场下MgB2多晶样品热导率的显著增强无法完全用电子热导来解释,并对此进行了讨论.     

SBN:Cr晶体的光折变四波混频相位共轭特性实验研究

从实验上研究了同成分SBN:Cr晶体在He-Ne激光照射下的四波混频相位共轭特性.首先测量了在不同泵浦光与信号光光强比m及不同光束夹角2θ的情况下,晶体的四波混频相位共轭反射率R随泵浦光强比p的变化关系.其次测量了泵浦光束与信号光束耦合方向对SBN:Cr晶体的四波混频相位共轭特性的影响,并就两种不同掺杂浓度的晶体样品进行了对比,所得实验结果与理论分析基本一致.最后,利用SBN:Cr晶体四波混频相位共轭特性进行了图象畸变消除实验.     

A unified approach to fuzzy modelling and robust synchronization of different hyperchaotic systems

In this paper, a Takagi Sugeno （T-S） fuzzy model-based method is proposed to deal with the problem of synchronization of two identical or different hyperchaotic systems. The T S fuzzy models with a small number of fuzzy IF-THEN rules are employed to represent many typical hyperchaotic systems exactly. The benefit of employing the T-S fuzzy models lies in mathematical simplicity of analysis. Based on the T-S fuzzy hyperchaotic models, two fuzzy controllers arc designed via parallel distributed compensation （PDC） and exact linearization （EL） techniques to synchronize two identical hyperchaotic systems with uncertain parameters and two different hyperchaotic systems, respectively. The sufficient conditions for the robust synchronization of two identical hyperchaotic systems with uncertain parameters and the asymptotic synchronization of two different hyperchaotic systems are derived by applying the Lyapunov stability theory. This method is a universal one of synchronizing two identical or different hyperchaotic systems. Numerical examples are given to demonstrate the validity of the proposed fuzzy model and hyperchaotic synchronization scheme.