关于奇Euler相关数对

设a,b是正整数.t是大于1的正整数.本文证明了:当a和b都是奇数时,(a,b)不是t-Euler相关数对.     

论数字在电视新闻报道中的作用

指出电视新闻是用事实说话的 ,而电视新闻报道的很多事实 ,又都是以数字形式表现出来的 ,用数字进行新闻报道 ,可以避免人为的主观因素 ,使电视新闻报道更显客观、公正 ,更具有说服力 ;有的数字中隐含着新闻 ,这就要求记者要善于分析、研究数字 ,并能从数字变动的轨迹中找出新闻所在 ;在电视新闻报道中 ,如果数字运用得当 ,就能收到令人满意的效果。最后提出了运用数字进行报道的几种方法 ,以使新闻报道更加直观、具体和形象     

强大数定律收敛速度的一个推广

文献［１］在文献［２］的基础上讨论了Ｂａｎａｃｈ空间中随机变元列｛Ｘｉ｝满足一定条件时的完全收敛性，但收敛速度问题未得到圆满解决。文中进一步指出Ｂａｎａｃｈ空间中独立非同分布随机变元列的收敛速度，将薜留根的结果推广，得到了满意的结果     

关于自然数的方幂和

设,借助于母函数与微积分的方法,获得了S_r(n)的一些重要性质,从这些性质出发给出了求S_r(n)与Bernolli数的新方法.     

制造企业服务化转型的风险评价

在国际市场竞争日益激烈的情况下,制造企业纷纷向价值链的高端发展,由此形成了制造企业服务化转型的趋势。然而,制造企业服务化转型中不可避免地面临着法律、经济、技术、质量、社会等方面风险因素的影响和制约。在分析和识别风险因素的基础上,提出熵权法和三角模糊数集成的风险评价方法,并给出数值算例,为制造企业服务化转型风险评价提供参考。     

考虑后悔规避的灰色群体偏离靶心度决策方法

针对指标值、指标权重以及状态概率均为区间灰数的风险型多指标群决策问题，考虑决策者的后悔规避的心理行为，提出基于后悔理论和区间灰数信息的群体偏离靶心度决策方法。该方法将后悔理论融入到群决策过程中，建立了各决策者的综合灰色感知效用矩阵，由此定义了群体灰色正负靶心以及灰色群体偏离靶心度；以灰色群体偏离靶心度综合值最大化为目标、同时结合极大熵原理构建优化模型并解出最优专家权重向量，利用灰色群体偏离靶心度大小对方案进行排序；最后，通过具体算例验证了该方法的有效性和实用性。     

The strong law of large numbers for non homogeneous M-bifurcating Markov chains indexed by a M-branch Cayley tree

This article is devoted to the strong law of large numbers and the entropy ergodic theorem for non homogeneous M-bifurcating Markov chains indexed by a M-branch Cayley tree, which generalizes the relevant results of tree-indexed nonhomogeneous bifurcating Markov chains. Meanwhile, our proof is quite different from the traditional method.     

Strong law of large numbers of the delayed sums for Markov Chains indexed by a Cayley tree

Abstract

In this paper, we will study the strong law of large numbers of the delayed sums for Markov chains indexed by a Cayley tree with countable state spaces. Firstly, we prove a strong limit theorem for the delayed sums of the bivariate functions for Markov chains indexed by a Cayley tree. Secondly, the strong law of large numbers for the frequencies of occurrence of states of the delayed sums is obtained. As a corollary, we obtain the strong law of large numbers for the frequencies of occurrence of states for countable Markov chains indexed by a Cayley tree.     

Random number generators for microcomputers

This paper presents the results of comparative tests of several random number generators to generate uniform [0,1] pseudo-random numbers. Tests were run on two different kinds of microcomputers with similar results. The computers used were a Tandy Model 4D (an 8 bit machine) and a Zenith model 150 (a 16 bit IBM compatible machine operating under MS DOS 2.11 and 3.1) withouta math coprocessor chip. All programming was done in FORTRAN using the Microsoft FORTRAN compilers available for the two machines (two MS DOS compilers were used; Microsoft's FORTRAN 77, versions 3.2 and 4.0).     

A Note on the Convergence Rate of Strong Law of Large Numbers for Positively Associated Sequences

By the inequalities established in this article, we obtain the convergence rate of strong law of large numbers for positively associated sequences. The results derived extend and improve the corresponding ones in Vronskii (1999 Vronskii , M. A. ( 1999 ). Rate of convergence in the slln for associated sequences and fields . Theory Probab. Appl. 43 ( 3 ): 449 – 462 .[Crossref], [Web of Science ®] , [Google Scholar]).