序列连续性与拓扑连续性

首先在线性空间中给出一个序列收敛关系,然后利用列邻域得到了由绝对凸吸收集构成的可加滤子基,进而构成了局部凸空间－LCL空间,文中证明了LCL空间的重要特征是序列连续性等价于拓扑连续性,并讨论了LCL空间的拓扑结构。     

延迟离散Hopfield型网络的异步收剑性

延迟离散Hopfield型网络是离散Hopfield网络的一种推广,研究了非对称的延迟离散Hopfield型神经网络的异步收剑性,并给出了相应的收剑性定理,所获结果推广了已有的结论。     

Computational uncertainty principle in nonlinear ordinary differential equations——Ⅱ.Theoretical analysis

The error propagation for general numerical method in ordinary differential equations ODEs is studied. Three kinds of convergence, theoretical, numerical and actual convergences, are presented. The various components of round-off error occurring in floating-point computation are fully detailed. By introducing a new kind of recurrent inequality, the classical error bounds for linear multi-step methods are essentially improved, and joining probabilistic theory the "normal" growth of accumulated round-off error is derived. Moreover, a unified estimate for the total error of general method is given. On the basis of these results, we rationally interpret the various phenomena found in the numerical experiments in part I of this paper and derive two universal relations which are independent of types of ODEs, initial values and numerical schemes and are consistent with the numerical results. Furthermore , we give the explicitly mathematical expression of the computational uncertainty principle and expound the i     

Robot path planning in globally unknown environments based on rolling windows

In this paper, robot path planning in globally unknown environments is studied. Using the rolling optimization concept in predictive control for reference, a new strategy of path planning for a mobile robot, based on rolling windows, is proposed. The method makes full use of the real-time local environmental information detected by the robot and the on-line path planning is carried on in a rolling style. Optimization and feedback are combined in a reasonable way. The convergence of the planning algorithm is also discussed.     

一类迭代序列Cesaro平均收敛的条件

给出了帐篷映射产生的迭代序列Ｃｅｓａｒｏ平均收敛的条件，研究了它与实数二进展式度量性质之间的联系。     

复域中 Hermite-Fejer 插值多项式的一致收敛性

设Ｄ是复平面上的Ｊｏｒｄａｎ区域，证明了设Ｄ的边界是某些光滑的，又ｆ∈Ｂ（Ｄ），则在Ｆｅｊｅｒ点上ｆ（ｚ）的Ｈｅｒｍｉｔｅ—Ｆｅｊｅｒ插值多项式在Ｄ上一致收敛。     

判别无穷级数敛散性的一种方法

讨论了级数与广义积分的内在联系，通过例题给出了由此产生的一种级数敛散性的判别法。     

一类大范围收敛的迭代法

给出了三种新的计算整函数实零点的大范围收敛迭坐代法。该类迭代法只需计算函数值及函数的一阶导数值。文中讨论了该类迭代法的收敛性及收敛阶的估计式。三个计算实例说明了文中给出的迭代法的有效性。     

正项级数的审敛法

本文给出正项级数的一种审敛法，此审敛法可以概括常见的柯西审敛法。且由此方法还可以推出比柯西审剑法更为细致的结论。     

一种可用于线性动态延迟系统控制的开环比例型一阶给定超前迭代学习控制算法

本文讨论了迭代学习控制的基本概念，并给出了一种可用于线性动态延迟系统的比例型一阶给定超前迭代学习控制算法。理论分析证明，这种控制算法对于跟踪重复运动的轨迹具有良好的效果。