一些新数列的偏差与伪随机性

设P为奇素数,x为整数且满足1≤x≤P-1.定义数列xn={{(n)+(n+x)/p},如果p(|)n(n+x),0,其它以及en={+1,如果p(|)n(n+x)且0≤{(n)+{(n)+(n+x)}＜1/2,-1,如果p(|)n(n+x)且1/2≤{(n)+{(n)+(n+x)}＜1,+1,如果p|n(n+x),其中瓦是(n)模p的乘法逆,满足n(n)≡1 mod p以及1≤(n)≤p-1.证明了(xn)是一致分布数列,(en)是好的伪随机数列.这表明在二进制数列与[0,1)数列之间存在某种联系.     

等分布度与伪随机性检验

本文从熵的角度探讨了伪随机性检验问题，提出了有关序列的等分布度ｒｎ（Ｋ）概念，并证明：一序列｛Ｘｎ｝（０≤ｘｎ≤１）为等分布的充分必要条件是：Ｋ＞１，ｎ→∞ｌｉｍｒｎＫ＝１。利用这一结果对几个典型伪随机序列的等分布度进行了比较，给出了它们的伪随机性优劣排序。     

合数模上的伪随机二进制数列

设m为"RSA"类型的模,即m为两个大小差不多的素数的乘积:m=pqp,q为素数,p相似文献   

相依重尾随机变量中偏差的充分必要条件

本文研究了实值扩展负相依(END)一致变尾随机变量的中偏差.在给出部分和中偏差的基础上,得到了一定条件下随机和中偏差成立的充分必要条件.     

伪抛物方程的一些研究进展

本文是关于伪抛物方程的综述,内容包括伪抛物方程的物理背景以及从黏性角度对伪抛物方程的研究,重点介绍半线性伪抛物方程解的渐近行为方面的研究成果,这是目前研究较为深入的领域.     

集合H上矩阵A的左(右)逆、伪左(右)逆

以集合 S与空集Φ的交、并运算为背景 ,定义集合 H ={ 0 ,1 }中的加法与乘法运算 0 ,并考虑 H上一个 s×n级矩阵的左逆矩阵、右逆矩阵以及伪左逆矩阵、伪右逆矩阵的定义 ,并且证明了矩阵 A有左、右逆矩阵 ,A有伪左、右逆矩阵的充分必要条件 .     

一般组合逆同余法的算法与偏差分析

本文研究了逆同余产生伪随机数的方法，给出了一般的组合逆同余法算法．将已有结果进行理论比较，得到了一个较好的伪随机数序列的产生方法．     

广义框架和算子的伪逆

运用Hilbert空间H上线性算子的伪逆，得到了关于广义框架的框架算子和综合算子的伪逆之间的关系，同时还给出了任意f∈H关于不满足广义框架上界条件的向量族（hm)m∈M的表达式。     

新序意义下集值模糊测度的伪自连续性

在m维正欧式空间的子集类上, 通过引入集合的新序和依序收敛的概念,讨论新序意义下集值模糊测度的伪自连续、一致伪自连续性,并研究它们的蕴涵关系,从而丰富集值模糊测度的理论.     

关于两个伪硬币问题的一些新结果

下面的问题被称为n个外观不可区分硬币的分组测试问题,每个硬币可以是伪硬币或是标准硬币.本文所涉及的问题是:已知一个由n个硬币组成的集合中有两个伪(较重的)硬币,用一台天平以最小的称重次数,从这n个硬币组成的集合中探测出两个伪(较重的)硬币. 我们构造了找出两个伪(较重的)硬币的两个算法,并且这两个算法是最优的.     

均匀性度量中的密集性偏差与稀疏性偏差

该文根据王元，方开泰［２］的近似偏差（discrepancy）的均匀性准则，定义了理想布点情况下的标准半径，定义了ｍ 维单位子空间Ｃｍ＝［０，１］中两点间的ｆ距离和ｇ距离，由此定义了最大空穴半径和最小空穴半径，提出了均匀性度量的密集性偏差与稀疏性偏差．给出了二维情况 下的计算结果．我们的方法计算量不大，不仅能较好地度量布点的均匀性以及布点在低维投影的均匀性，而且能指导如何调整布点使之尽可能与理想布点接近．     

The characteristic polynomial of a random permutation matrix

We establish a central limit theorem for the logarithm of the characteristic polynomial of a random permutation matrix. We relate this result to a central limit theorem of Wieand for the counting function for the eigenvalues lying in some interval on the unit circle.     

On a Global Optimization Problem in the Study of Information Discrepancy

A nonlinear function has been introduced for indexing the disagreementdegree of a group of judgment matrices (Weiwu Fang, 1994). It has many goodproperties and may be applied in decision making and information processes.In this paper, we will discuss a global optimization problem concerned withthe global maximum of this function which is constrained on some sets ofmatrices. Because the size of matrix groups in the problem is arbitrary andthe number of local maximum solutions increases exponentially, numericalmethods are not suitable and formalized results are desired for the problem.By an approach somewhat similar to the branch and bound method, we haveobtained some formulae on global maximums, a sufficient and necessarycondition of the function taking the maximums, and some maximum solutionsets.     

关于最小偏差LH设计

:本文对 LH设计编差的计算进行了研究 ,并得到了 LH设计偏差的下界 ,对寻求整体最优 LH设计进行了讨论     

Generalized explicit inversive generators of small p-weight degree

Using rational functions to generate pseudorandom number sequences is a popular research topic. In this paper, we study bounds on additive character sums of a new explicit generator based on rational functions with small p-weight degree. This extends the class of functions where a nontrivial character sum bound is known.     

On Pseudorandomness in Families of Sequences Derived from the Legendre Symbol

We construct a family of finite binary sequences which has a remarkable uniformity with respect to specification of several terms and which also has the property that every sequence in the family has small measures of normality, well distribution in arithmetical progressions and multiple correlations. We also construct a pseudorandom bit generator whose output consists of members of the family.     

Discrepancy in different numbers of colors

In this article, we investigate the interrelation between the discrepancies of a given hypergraph in different numbers of colors. Being an extreme example we determine the multi-color discrepancies of the k-balanced hypergraph on partition classes of (equal) size n. Let . Set k₀ k mod c and b_nkc (n−n/c/k)k/c. For the discrepancy in c colors we show

if k₀≠0, and , if c divides k. This shows that, in general, there is little correlation between the discrepancies of in different numbers of colors. If c divides k though, holds for any hypergraph .     

Discrepancy of random graphs and hypergraphs

Answering in a strong form a question posed by Bollobás and Scott, in this paper we determine the discrepancy between two random k‐uniform hypergraphs, up to a constant factor depending solely on k. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 47, 147–162, 2015