亥姆霍兹线圈的均匀磁场区

不少物理实验仪器应用了亥姆霍兹线圈的均匀磁场区,但缺乏必要的使用限制性。本文依毕奥—萨伐尔定律推导出该线圈区域内任意点磁感应强度的积分公式,用计算机进行了数值计算,画出等值线图。并由此确定出允许误差所对应的均匀磁场区,为使用限制性提供了依据。还通过理论分析肯定了中心点磁场的二阶均匀性。     

具有小时滞的非线性振动系统的周期振动

本文研究具有小时滞的非线性振动系统。主要结果是:当时滞充分小时,若对应的不含时滞的常微分系统的解是一致有界和一致毕竟有界的,则时滞系统存在周期振动。最后讨论了扭振问题。     

彩色体三维显示系统上基于GPU的实时均匀体素化算法

为了使基于旋转屏的彩色体三维显示设备在显示动态场景时实时且高分辨率、高质量地实现圆柱体空间彩色体素化,提出了一种基于GPU的算法.首先在长方体空间内完成对三维场景的实时彩色体素化,将生成的数据保存于多张纹理工作表中;然后采取多对多映射的方法对这些工作表进行重采样,得到该场景在圆柱体空间内均匀的彩色体素化结果.实验结果表明,该算法在GPU内完成,达到了实时性要求,并在基于LED旋转屏的体三维显示设备上获得了令人满意的三维虚拟场景再现效果.     

Low-complexity 2D coherently distributed sources decoupled DOAs estimation method

The existing directions-of-arrival (DOAs) estimation methods for two-dimensional (2D) coherently distributed sources need one- or two-dimensional search, and the computational complexities of them are high. In addition, most of them are designed for special angular signal distribution functions. As a result, their performances will degenerate when deal with different sources with different angular signal distribution functions or unknown angular signal distribution functions. In this paper, a low-complexity decoupled DOAs estimation method without searching using two parallel uniform linear arrays (ULAs) is proposed for coherently distributed sources, as well as a novel parameter matching method. It can resolve the problems mentioned above efficiently. Simulation results validate the effectiveness of our approach. Supported by the National Natural Science Foundation of China (Grant No. 60772146), and the Program for New Century Excellent Talents in University (Grant No. NCET-05-0806)     

Stability and robust stability of positive linear Volterra difference equations

We first introduce a class of positive linear Volterra difference equations. Then, we offer explicit criteria for uniform asymptotic stability of positive equations. Furthermore, we get a new Perron–Frobenius theorem for positive linear Volterra difference equations. Finally, we study robust stability of positive equations under structured perturbations and affine perturbations. Two explicit stability bounds with respect to these perturbations are given. Copyright © 2008 John Wiley & Sons, Ltd.     

三参数binary细分法

通过在曲线细分过程中引入三个参数,给出一种新的细分曲线构造的算法,并利用生成多项式等方法对细分法的一致收敛性、Ck连续性进行了分析.在给定初始控制数据的条件下,可以通过对形状参数的适当选择来实现对细分极限曲线形状的调控.该方法可以生成C4连续的细分曲线,增加了曲线造型的灵活性.数值试验表明这种算法是有效的.     

广义非线性系统的模型跟踪控制及内部状态稳定性证明

将被控对象设定成线性部分和非线性部分,提出了一种广义非线性系统模型跟踪控 制的新方法,给出了非线性代数约束方程中包含控制输入时闭环系统具有唯一解的条件,证 明了当非线性项满足范数条件以及相关的传递函数满足正实条件时,闭环系统的所有变量都 是有界的.该方法可处理代数约束为非线性,用状态空间方程无法描述的被控对象.仿真结果 验证了设计方法的有效性.     

双参数C2插值细分法

提出了一类包含两个形状参数的双参数4点ternary插值细分法，可造型C^1或C^2光滑插值曲线，且易通过对两个形状参数取值的调整来实现对细分曲线形状的调控。讨论了形状参数对细分法的收敛性及连续性的影响，给出并证明了细分法一致收敛、C^1连续、C^2连续的充分条件，并给出了一些数值算例。     

Uniform approximation of time‐invariant non‐linear systems

An Erratum has been published for this article in International Journal of Circuit Theory and Applications 2004; 32(6):633. It is shown that the elements of a large class of time‐invariant non‐linear input–output maps can be uniformly approximated arbitrarily well, over infinite time intervals, using a certain structure that can be implemented in many ways using, for example, radial basis functions, polynomial functions, piecewise linear functions, sigmoids, or combinations of these functions. For the special case in which these functions are taken to be certain polynomial functions, the input–output map of our structure is a generalized finite Volterra series. Results are given for the case in which inputs and outputs are defined on ?. The case in which inputs and outputs are defined on the half‐line ?₊ is also addressed, and in both cases inputs need not be functions that are continuous. Copyright © 2004 John Wiley & Sons, Ltd.     

关于重要极限lim from (n→∞)(1+1/n)~n=e教学的思考

对于lim from (n→∞)(1+1/n)~n=e,文章提出了与许多教材上不同的另外三种证明数列(1+1/n)~n 单调有界的方法,并对lim from (n→∞)(1+1/n)~n=e进行了推广。