多项式的倒数对可微函数的逼近

设非线性函数,f(x)∈C[-1,1]是非负的,f′(x)∈C[-1,1],f■(x)=f(x) ε,其中ε<0,C■是与ε无关的常数,当,f(x)满足[f'(x)]~2/f_■(x)≤C■时,存在次数不超过n的代数多项式P_n(x),使得f(x)-1/P_n(x)1≤C_f~″·1/nω(f′,1/n)(C_f~■仅与C■有关)。根据这个定理,得到多项式f(x)=x~2或x_ ~2的倒数的逼近阶是0(2/n~2)。     

切比雪夫多项式回归分析方法在测量数据处理中的应用

在进行动态和静态测试时,经常需要对测试所得的数据进行处理,以使受干扰的一组数据“回归”其原有(排除这种干扰后)的变化规律。介绍一种实际应用中准确度较高的代数多项式回归分析方法,即切比雪夫(Tchebyshev)多项式回归分析方法。     

关于第二类Chebyshev多项式的一组恒等式

利用初等方法研究了第2类Chebyshev多项式的性质,得到了一组关于第2类Chebyshev多项式的卷积公式,作为应用,给出了关于Fibonacci多项式和Pell多项式的2个结论．     

用计算机模拟整数竖式乘除法计算排列组合

用计算机模拟整数竖式乘除法给出了排列组合的算法,并用Turbo C写出程序.     

模的不动点集与置换模

令FG为有限群的群代数。本文利用模的不动点集引入了Green代数A(FG)到有理数域Q的一类线性函数δ_c,证明了当C跑遍G的循环子群时δ_c构成A(FG)的由Ic↑~G生成的子代数的对偶空间的一个基底,并且讨论了在δ_c之下p—置换模的性态。     

关于Pell多项式的一些恒等式

利用初等方法研究了Pell多项式的性质,得到了一组关于Pell多项式的卷积公式和几个有趣的结论.     

九宫重排问题的代数解决

九宫重排问题是一个经典的问题,目前国内尚有人尝试用计算机去解决它.本文将该问题代数化,用置换群的方法彻底地解决了这一难题.     

An investigation of three-matrix permutation tests

Several methods have recently been introduced for investigating relations between three interpoint proximity matricesA, B, C, each of which furnishes a different type of distance between the same objects. Smouse, Long, and Sokal (1986) investigate the partial correlation betweenA andB conditional onC. Dow and Cheverud (1985) ask whethercorr (A, C), equalscorr (B, C). Manly (1986) investigates regression-like models for predicting one matrix as a function of others. We have investigated rejection rates of these methods when their null hypotheses are true, but data are spatially autocorrelated (SA). That is,A, andB are distance matrices from independent realizations of the same SA generating process, andC is a matrix of geographic connections. SA causes all the models to be liberal because the hypothesis of equally likely row/column permutations invoked, by all these methods, is untrue when data are SA. Consequently, we cannot unreservedly recommend the use of any of these methods with SA data. However, if SA is weak, the Smouse-Long-Sokal method, used with a conservative critical value, is unlikely to reject falsely.     

The New Concept of Path Contributing to the Cryptographic Strength Exceeding 2^N

0 IntroductionIn the end of the 20th century, data encryption standard(DES) was cracked and then Advanced encryption stand-ard (AES) was established. While no new concepts or newtheory wasincludedin AES,and the enhancement of the en-cryption strength only depends ontheincreasing blocklength.Inthis paper ,a newconcept of the block cipher is presented.There are mainly two kinds of modern encryption mode:the symmetric algorithmand the asymmetric algorithm. Theasymmetric algorithm uses a publ…     

与(--K3∪Um)有相同色分划的图

应用图的伴随多项式理论完整地刻画了与K3∪Um^-的补图有相同色分划的图，其中K3表示3个顶点的圈，Um表示由Pm-4的两个1度点分别与两个P3的2度点粘接得到的图．