On Liu Yi's positive-negative root extraction algorithm

Liu Yi (c. 1080), the Northern Song Dynasty mathematician, was the first who annulled the restriction that the coefficients of an equation must be positive and the leading coefficient be 1. It is commonly recognized that with the learning of four arithmetic operations for negative numbers thezeng cheng method for root extraction can be extended to the general method for solving an algebraic equation of any high degree with numerical coefficients arbitrarily positive, negative or zero, and because of that many of praises have been put on thezeng cheng method but the significance of Liu's work is not given enough attention. In order to argue about the above view, the present paper points out that conceptive innovation has occured in Liu's positive-negative algorithm and that Liu's work is a key in the field of ancient Chinese mathematician's research for solving higher numerical equations. Supported by China Postdoctoral Science Foundation Wang Rongbin: born in March, 1964, Ph. D     

Local to unity,long‐horizon forecasting thresholds for model selection in the AR(1)

This article introduces a novel framework for analysing long‐horizon forecasting of the near non‐stationary AR(1) model. Using the local to unity specification of the autoregressive parameter, I derive the asymptotic distributions of long‐horizon forecast errors both for the unrestricted AR(1), estimated using an ordinary least squares (OLS) regression, and for the random walk (RW). I then identify functions, relating local to unity ‘drift’ to forecast horizon, such that OLS and RW forecasts share the same expected square error. OLS forecasts are preferred on one side of these ‘forecasting thresholds’, while RW forecasts are preferred on the other. In addition to explaining the relative performance of forecasts from these two models, these thresholds prove useful in developing model selection criteria that help a forecaster reduce error. Copyright © 2004 John Wiley & Sons, Ltd.     

n阶方阵的任意m次方根

给出了复数域内n阶方阵任意m次方根存在的充分条件(m≥2),从而推广了文献[1]中复数域内n阶方阵的平方根(m=2)存在的充分条件。     

有限域GF(P~m)(P≥3)上3p~1、p~(l+l)、p 3次方程的根

提出了GF（3m）上3次方程根的判别方法，讨论了有限域GF（pm）（p＞-3）上3p1次方程根的状况，给出了GF（pm）上p次和pl+1次方程根的判别方法．     

Modeling Trusted Computing

0 IntroductionThe purpose of trusted computingis to solve some of to-day’s security problems through hardware changes topersonal computer . The trusted property can be extendedfromroot of trust to entire PC platformthrough the chain oftrust[1].Root of trustis a small hardware device calledtrustedplatform module (TPM) addedto PC.A well-known project of trusted computing is trustedcomputing platformalliance(TCPA) .It is calledtrusted com-puting group (TCG) now[2 ,3]. Besides this , other…     

基于密钥交换中离散对数生成元的研究

从离散对数的生成元的选择问题出发，根据欧拉定理和拉格朗日定理提出加快寻找生成元的简便算法，该算法的重要思想是：如果我们选择安全素数P=2＊Q＋1，则判断集合ZP中的元素是否是生成元的次数达到最少．该算法加快了生成元的寻找速度，节约了计算时间和计算空间．     

图Q(2,n)∪(∪i∈ACi)的匹配等价图类

刻画了Q（2,n)∪（∪i∈ACi)和它的补图的匹配等价图类，其中A是大于等于3的一些整数组成的可重集。     

ARMA模型的平方根超定递推辅助变量定阶方法

提出了自回归滑动平均(ARMA)模型的平方根超定递推辅助变量定价方法.该方法避免了计算逆协方差阵失去正定性的问题,改进了超定递推辅助变量定阶方法的数值稳定性.模拟计算与实验数据处理表明,该方法数值稳定性好,收敛速度快,抗噪能力强.是一种高性能的定阶方法。     

牛顿(Newton)求根公式的改进

对牛顿 (Newton)求根公式作了改进 ,使其对重根情况仍有效 ,并保持原有的收敛性质