The completeness property of the set of real numbers in the transition from calculus to analysis

This paper focuses on teaching and learning the set of real numbers R and its completeness property at the university level. It studies, in particular, the opportunities for understanding this property that students are offered in four undergraduate correlative courses in Calculus and Analysis. The theoretical framework used in the study draws on concepts developed in the Anthropological Theory of Didactics, especially the notions of praxeology and mathematical organization. The paper shows different expectations concerning the same notion (R and its completeness) through different school levels, and intends to bring up some reflections about the transition from Calculus to Analysis.

关于两个k进制数互素的一个定理及其推论

从k进制 (k≥ 2 )中特殊形式的数出发 ,研究了十进制数中一类数的性质     

正交多项式的零点随参数的变化

讨论了一般的正交多项式其零点随参数变化的规律。作为应用 ,对几种古典的正交多项式给出了相应的结果。     

两个长数字串全乘快速算法实现 --双向循环链表应用实例

两个长数字串(可含小数)进行快速乘法运算的C 程序，对于参加运算的两个数字串只要内存空间允许，没有长度限制，而且能够得到绝对精确的结果。对某些乘法计算精度要求高的场合可作实际应用，另可作为数据结构课程中双向循环链表的一个应用实例，供教学参考。     

一随机变数序列服从强大数定律的必要条件

本文通过对一随机变数序列的研究,给出了一随机变数序服从强大数定律的一个必要条件     

有关Bernoulli数的两个递推公式

利用函数方程，研究了函数的幂级数展开，揭示了Bernoulli数的内在联系，得到了两个有趣的关于Bernoulli数恒等式，从而得到了计算Bernoulli数的两个新的递推公式．     

4n阶幻方的一种构造方法

给出了一种4n阶幻方的构造方法，并同时给出了数学证明．     

线性交簇超图边数的上界

H是线性交簇超图，｜E∩F｜：1（∨E、F∈H），记s=s（H）：min｜E｜，A：｜E∈H：｜E｜：s｜．若｜A｜〈s^2＋1，则m（H）≤A（[H]2）＋1；若｜A｜≥s^2＋1，则当s≤2时，m（H）≤△（[H]2）＋1；当s≥3时，m（H）≤△（[H]2）-2s．     

关于由广义的Fibonacci数构成的倒数和及其交错和的若干性质

本文给出了由广义的Fibonacci数构成的倒数和及其交错和之间的某种联系.     

Congruences for finite triple harmonic sums

Zhao (2003a) first established a congruence for any odd prime p>3, S(1,1,1;p)≡-2Bp-3 (mod p), which holds when p=3 evidently. In this paper, we consider finite triple harmonic sum S(α,β,γ;p) (mod p) is considered for all positive integers α,β,γ. We refer to w=α β γ as the weight of the sum, and show that if w is even, S(α,β,γ;p)≡0 (mod p) for p≥w 3; if w is odd, S(α,β,γ;p)≡rBp≥w (mod p) for p≥w, here r is an explicit rational number independent of p. A congruence of Catalan number is obtained as a special case.