实数与超实数

本文对实数如何扩充到超实数作了探讨，并证明了超实数的5个重要性质。     

杨辉三角中被素数整除的组合数及其个数

设n为素数,t∈N,a=∑ti=0aini,这里ai∈N,0≤ai≤n-1,0≤i≤t,推出了杨辉三角第a行的组合数被n整除的有a+1-∏ti=0(ai+1)个,第0行至第nt-1行的组合数中,被n整除的有nt+12-n+12t个,斜列a+rr:r=0,1,…,bnt+1-1,(b＞0)中被n整除的有bnt+1-∏ti=0(n-ai)个,得到了ar≡0(modn)和a+rr≡0(modn)成立的充要条件.     

关于Euler数和Bernoulli数的推广

本文利用下标算子ｌ及偏下标算子ｌ（ｉ）对Ｅｕｌｅｒ和Ｂｅｒｎｏｕｌｌｉ数进行了推广，给出了ｎ元Ｅｕｌｅｒ数和ｎ元Ｂｅｒｎｏｌｌｉ数的定义，通过导出ｎ元Ｅｕｌｅｒ数和ｎ元Ｂｅｒｎｏｕｌｌｉ数的母函数，从而得到ｎ元Ｅｕｌｅｒ数和ｎ元Ｂｅｒｎｏｕｌｌｉ数的关系式。     

回文数与镜反数

回文数与镜反数是两种有趣的数字现象,但通过研究发现．相当一部分回文数与镜反数有一种特定的数字联系或规律。寻找平方镜反数、立方镜反数,对镜反数进行分割或组合时可以得到多少种镜反数等式、等幂和数组?还待进一步研究探索。     

高阶Bernoulli数、Euler数和Genocchi数的几个恒等式

用初等方法研究Euler数、Bernoulli数、Genocchi数,揭示了高阶Euler数、Bernoulli数、Genocchi数之间内在联系,得到了包含高阶Euler数、Bernoulli数、Genocchi数的几个有趣的恒等式。     

孩子眼中的数字——课改实验区学生习作一则评析

前不久，笔者到南宁市课改实验区新民中学与教师座谈，饶桂芳老师从学生的成长记录袋中拿出学生的习作给我看，阅毕内心久久不能平静，喜悦之情油然而生。现从中选取一篇“原著”，以飧读者。美妙的数字——１００万南宁市新民中学初一（４）班金璐美是什么？是绿叶丛中的一朵花，还是河堤岸旁的一株柳？是中秋之夜的一轮皓月，还是西山之巅的一抹夕阳？只要你仔细地去观察、体验生活，美是无处不在的。在初一上册的数学中，有一个题目叫“１００万有多大？”我对它产生了兴趣：是啊！１００万到底有多大？这也让我认为１００万是个美妙的数…     

英语听力中的数字听记训练

英语数字是听力训练中的要点和难点．能否正确记下英语听力材料中的数字，直接影响听力理解的效果。在听力课中有针对性地训练学生对英语数字的听记能力，能提高学生的听力效率，增强其理解力。     

关于素数的孪生素数的注记

利用Sundcaram筛法，给出素数的表示，在此基础上得到了关于素和的判别定理和相应筛法。     

数字摭谈

论述了数字是科学决策与管理的依据,是统计工作的基础.     

图K_(3,3)的Zarankiewicz数和Bipartite Ramsey数

在对完全二部图Kn,n进行k-边着色中,记brk(Kt,t)为能够诱导出单色Kt,t的最小的正整数n,另外,记z(n;t)为Kn,n中不含子图Kt,t最大的边数。对t=2,3情形,分别证明了以下两个渐近公式:brk(Kt,t)■kt(k→∞),z(n;t)■n2-1/t(k→∞)。     

k角形数化为平方数问题

讨论了把k角形数化为平方数问题,用Pell方程方法把k角形数化为平方数,例子说明了方法的正确性。     

Semantic relationships between contextual synonyms

Contextual synonym is a linguistic phenomenon often applied but rarely discussed. This paper is to discuss the semantic relationships between contextual synonyms and the requirements under which words can be used as contextual synonyms between each other. The three basic relationships are embedment, intersection and non-coherence. The requirements are discussed in the course of the discussion on the three relationships.     

Factors governing one-trial contextual conditioning

When a rat was placed in a chamber and shortly thereafter received a single footshock, it showed conditional freezing upon re-exposure to that chamber but not a different one (Experiment 1). Experiments 2–4 showed that the probability of this freezing decreased linearly with decreases in the delay between placement in the chamber and shock delivery. With very short delays (e.g., less than 27 sec), there was no freezing. Experiments 2 and 3 demonstrated that a 2-mm pre-exposure to the chamber, 24 h prior to shock delivery, reduced the minimum delay necessary to successfully condition freezing. Experiment 4 demonstrated that shorter delays were successful in conditioning freezing if a salient tone was a component of the contextual stimulus. The changes in freezing caused by delay interval and preexposure did not simply reflect the total time in the context, suggesting that there may be two requirements that place temporal restrictions on the conditioning of the freezing response. One is satisfied by sufficient exposure, whether or not that exposure is contiguous with shock. The second requirement is for a small amount of context exposure that is contiguous with shock.     

自生数、超级数及其有关问题

从“以数字 0、 1、 5、 6为结尾的数 ,平方后仍以这些数字为其结尾”这一常识出发 ,研究自生数、超级数 同时还与方程x2 =x紧密联系起来 ,从而推广了文 [1]的结果