一类任意随机变数序列的强大数律

给出了一类任意随机变数序列的强大数律。     

塞尔的隐喻理论与汉英数字文化内涵对比

数是数学符号和观念的合集,除了用来计算,表示字面意义之外,更多表达了文化内涵.塞尔的隐喻意义理论区分了语言中的字词意义和说话者所表达的意义,前者被成为字面意义,后者为隐喻意义.要正确理解汉英数字字面意义之外的隐喻意义,关键是了解数字中所蕴含的文化内涵.文章从对塞尔的隐喻理论观出发,基于数字的哲学内涵,对英汉数字的隐喻意义进行了对比分析.     

Teaching Undergraduate Mathematics on the Internet

This is Part 2 of a two-part study of how APOS theory may be used to provide cognitive explanations of how students and mathematicians might think about the concept of infinity. We discuss infinite processes, describe how the mental mechanisms of interiorization and encapsulation can be used to conceive of an infinite process as a completed totality, explain the relationship between infinite processes and the objects that may result from them, and apply our analyses to certain mathematical issues related to infinity.     

对于轮和完全图的Ramsey函数的渐近上界

给出了当n趋向于无穷时, 对于不小于4的偶数m, 有r(Wm, Kn)≤(1 o(1))C1·(n)/(logn)(2m-2)/(m-2); 对于不小于5的奇数m, 有r(Wm, Kn)≤(1 o(1))C2(n(2m)/(m 1))/(logn)(m 1)/(m-1). 这里C1=C1(m)＞0, C2=C2(m)＞0. 特别地, C2(5)=12. 该定理是在Caro等给出的r(Cm, Kn)的渐近上界的基础上利用函数fm(x)=∫10((1-t)(1)/(m)dt)/(m (x-m)t) 得到的. 当n趋向于无穷时, c(n)/(logn)(5)/(2)≤r(K4, Kn)≤(1 o(1))(n3)/((logn)2). 本文还给出了r(Kk Cm, Kn)的渐近上界.     

多重调和级数的几个同余式

通过研究∑l1＋l2＋…＋ln=p σln/l1…ln-1lkn,σ∈{-1,1}的同余式,当k=2,3时,对任意的正整数n和素数p〉n＋k-1,得到了∑l1＋l2＋…＋ln=p 1/l1l2…lkn关于模p的同余式.对任意的素数p≥7,证明了∑l1＋l2＋l3＋l4=p （-1）l1/l1l2l3l4关于模的同余式.     

自然数幂和通项公式证明的新方法

针对自然数幂和问题,利用多项式和矩阵理论,得到了一种计算自然数幂和通项公式的方法,给出了该方法的具体推导过程．此方法的优点是将自然数幂和问题转换为了线性方程组求解问题,更浅显易懂．     

Fuzzy集与Fuzzy数

定义了凸Fuzzy集、区间数及Fuzzy数,讨论了Fuzzy集的有关命题,最后给出了求Fuzzy数的方法及实例．     

非独立不同分布随机变量序列的弱大数定律

本文讨论非独立不同分布情况下随机变量序列的弱大数定律的存在条件,将I.I.D情形下的弱大数定律进行了推广.     

The emergence of the quantified child

Using document analysis, this paper examines the historical emergence of the quantified child, revealing how the collection and use of data has become normalized through legitimizing discourses. First, following in the traditions of Foucault's genealogy and studies examining the sociology of numbers, this paper traces the evolution of data collection in a range of significant education policy documents. Second, a word count analysis was used to further substantiate the claim that data collection and use has been increasingly normalized through legitimizing discourses and routine actions in educational settings. These analyses provide evidence that the need to quantify educational practices has been justified over long periods of time through a variety of documents and that the extent to which data governs educators’ thoughts, discourses, and actions has dramatically increased during the past century.