A Type of Triangular Ball Surface and its Properties

1IntroductionIntheCONSURFsystemll--3]developedbyA.A.Ball,thebasisfunctionsforcubicpolynomialsweredefinedbyandhencecubicBallcurveswithcontrolpointsPi(i=0,1,2,3)canberepresentedasp(u)=Z?=.B!(u)Pi,0Su51.TwotypesofhigherdegreegeneralizedBallbasisfunctionsandcorrespondingcurveshavebeenderivedbyWangl4]andSaidls]independently.InWang'spaper,generalizedBailbasisfunctionsofarbitrarydegreeweredefinedasfollows'.ifnisanevennumber.ifnisanoddnumberwherew~2u(1--u),05u51.Aparametriccurveofdegreentcall…     

快速计算抛物线的一种新算法

分析了孙家广先生于１９８６年提出的计算抛物线的方法，提出了一种新的快速计算方法，使常数计算量减少了６６％，循环体计算量减少２Ｎ（Ｎ是一条抛物线的采样点数）．如果Ｎ很大（一般采样上百个点或几百个点），调用次数多，则减少很多计算量．新的计算方法简单，软件实现容易，实用价值较大．     

The Complete Solution of the Competitive Rank Selection Problem

Two decision-makers A and B observe sequentially a given permutation of n uniquely rankable options. A and B have one choice each (without recall) and both must make a choice. At each step only the relative ranks are known, and A has the priority of choice. At the end the (absolute) ranks are compared and the winner is the one who has chosen the better rank. Extending results by Enns and Ferenstein [6] and Berry et al. [1] this article gives, for both A and B , the optimal strategy and the corresponding winning probabilities. We show in particular that the limiting winning probabilities for A and B do exist, which closes a most important gap in the work of previous authors. This also provides an algorithm for numerically computing the limiting value of these probabilities. Although our proof is analytic in a strong sense, it is interesting to see that it would have been very hard to assemble it without the help of computer algebra. The reason is that the functions we have to investigate display subranges of indices which contrast considerably with respect to error terms when certain terms are replaced by approximations, and that computations were very helpful to locate those ranges where a particularly fine tuning of error estimates turned out to be indispensable. Received October 1997; revised March 15, 1998.     

AR估计滤波误差能量最小二乘递推法

利用滤波误差能量给出了一个新的最小二乘快速递推算法。数值试验表明，该算法计算稳定性好，对噪声不敏感，能快速递推到高阶模型，并将该算法同Ｍａｒｐｌｅ算法等作了比较。     

一种新的谱随机有限元方法

提出了一种新的谱随机有限元分析方法——递推求解方法。讨论了已有的几种随机场的谱展式，提出将随机结构的随机响应表示成非正交多项式混沌展式，并证明了这个展式的收敛性。在此基础上将随机微分方程表示成了和摄动法类似的一系列确定的递推方程，这些递推方程可用确定性有限元方法求解。该方法比在正交多项式混沌基上投影并取期望的方法更简洁实用，更适合大规模有限元的求解。该方法同样能解决有较大随机涨落的力学问题。     

The implementation of generic smart pointers for advanced defensive programming

Smart pointers denote a well‐known technique for collective resource ownership, e.g. sharing dynamic object instances, while usually supporting automatic garbage collection based on reference counting. The original method has been retargeted to serve as a generic defensive programming method for ‘exhaustive tracking’ of erroneous pointer use in C++. Automatic bug tracking is supported in a unified manner both for pointers to heap memory, i.e. free storage, as well as for pointers to stack or global memory, i.e. auto or static storage. Overall, the presented technique (a) offers a simple contract for memory allocation and use; (b) supports type and indirection depth genericity; (c) implements most operators supported for built‐in pointers with embedded bug defense; (d) offers an alternative way of employing a garbage collection facility for memory leak detection; and (e) provides an appropriate collection of utility macros, through which defensive pointers should be used, with an alternative version re‐targeted to normal native pointers. Copyright © 2004 John Wiley & Sons, Ltd.     

系统辨识(7)：递阶辨识原理与方法

递阶辨识是系统辨识的一个重要分支.递阶辨识原理是在大系统递阶控制的“分解-协调原理”基础上发展起来的,它不仅能够解决参数数目多、维数高、大规模系统辨识算法计算量大的问题,而且能够解决结构复杂的双线性参数系统、多线性参数系统以及非线性系统的辨识问题.首先介绍递阶辨识原理和线性方程组Ax=b的著名雅可比迭代和高斯-赛德尔迭代,给出了线性方程组的迭代方法族;其次将雅可比迭代思想和递阶辨识原理用于研究一般矩阵方程和耦合矩阵方程的递阶梯度迭代求解方法和递阶最小二乘迭代求解方法;再次介绍了方程误差模型的两阶段最小二乘辨识方法(一个简单的递阶辨识方法)和线性回归模型的递阶最小二乘辨识方法;最后研究了类多变量CARMA系统的递阶辨识方法.     

对多项式的欧几里德算法的改进

本文对用于求两个多项式的最大公约多项式的欧几里德算法作了改进，主要改进了决定该算法计算复杂性的ＥＭＧＣＤ的递归过程。通过计算复杂性的分析，改进算法比原算法快了一倍，而且提高了计算精度。     

高速列车电空联合制动控制研究

由于轮轨黏着状态受车轮和轨道的表面状况、外部环境以及车辆速度等因素变化的影响,为了保证车辆在高速阶段制动的有效性和安全性,并获得最大的黏着利用,防止车轮因打滑而损伤轮轨,控制系统必须提供稳定有效的制动力.为此建立了新的制动气缸压力模型、鼠笼型异步电机模型和90个自由度的动车多刚体模型,采用Oldrich Polach的黏着力计算模型,并加人轨道激扰.开关信号控制气缸的冲排气,直接转矩策略控制电机,改进的递归最小二乘法判别车轮粘滑状态,滑模控制算法计算最佳制动力.当电机输出的制动力不足时,空气制动加以补充.仿真结果表明,基于上述方法的防滑控制系统具有良好的性能,达到了期望的控制效果.     

多元系统耦合多新息随机梯度类辨识方法

针对多元线性回归系统,利用耦合辨识概念和多新息辨识理论,讨论了多元随机梯度算法、多元多新息随机梯度算法,以及变递推间隔多元多新息梯度算法,进一步分解多元系统为一些子系统,给出了耦合子系统随机梯度算法、耦合随机梯度算法、耦合子系统多新息随机梯度算法、耦合多新息随机梯度算法,并将这些方法推广到多元伪线性滑动平均系统和多元伪线性自回归滑动平均系统.文中给出了几个典型耦合随机梯度算法、耦合多新息随机梯度算法的计算步骤和示意图.