数与形

通过几个例子阐述了数与形的密切联系,“形”给出了“数”的几何直观,“数”揭示了“形”的本质特征,用数形结合的方法去解决一些数学问题,可使问题很快得到解决,有的数学问题,只有通过形才能得到解决。     

复数中模的应用

本文通过具体实例说明复数中模性质的应用.     

关于单位分数问题的一些新结论

用初等的方法研究了某些分数的第一类好表法与奇数强表法,得出了一些有用的新结论,并回答了文献[5]中由RonHardin和NeilSoane提出的一个问题.     

关于Ramsey数的下界问题

对一般的Ｒａｍｓｅｙ数的下界给出了一个加强结果，并指出用概率方法进一步研究了Ｒｍａｓｅｙ数的下界的关键之处。     

奇、偶函数概念的拓广

指出了传统奇、偶函数概念的不足，并给出奇、偶函数新概念，消除了一些不合理的现象，从而拓广了奇、偶函数的范围，同时，证明了新旧概念下的奇、偶函数在对称性、导数和积分等方面具有相同的性质。     

Curious consequences of simple sequences

Simple sequences and series of natural numbers, their reciprocals, integer powers of natural numbers and their reciprocals are considered. Some interesting physical and mathematical consequences of these are discussed. A K Mallik is a professor at IIT, Kanpur. His research interests are mechanical vibration, vibration control, nonlinear vibration and chaos in mechanical systems, kinematics and dynamics of machinery.     

关于Lucas数的高次恒等变换

本文用母函数方法研究Lucas数高次乘积和恒等变换 ,并给出了一些恒等式     

Weierstrass逼近定理的应用

应用Weierstrass逼近定理对于连续奇函数和连续偶函数的性质做了进一步的刻划.     

Variability in the natural number bias: Who,when, how,and why

When reasoning about rational numbers, people sometimes incorrectly apply principles or rules for natural numbers. Many factors affect whether participants display this natural number bias, including their age and experience, the affordances and constraints of the given task, and even the specific numbers in the given problem. In this paper, we argue that this variability can be conceptualized in terms of dynamic choices among problem-solving strategies. People's strategy choices vary as a function of their repertoire of available strategies and as a function of the specifics of the tasks, problems, and context. Further, we argue that the specific profiles of variability in strategy use that are observed in different participant groups can be conceptualized in terms of the strength and precision of the representations of numbers and operations that people in those groups possess. In our view, the natural number bias arises when people's representations of rational number magnitudes or rational number operations are not sufficiently strongly activated or sufficiently precise to guide performance on a specific task in a specific context. In these cases, participants' more highly activated or more precise representations for natural numbers may underlie and guide their performance. This account suggests that contexts and experiences (including instructional experiences) that help build, strengthen, and activate rational number representations should lead to improvements in performance.     

PA随机变量序列Wittman型强大数律

文章根据独立随机变量序列的Wittmann型强大数律,推广到PA序列的Wittmann型强大数律,并且由此得到一些相关的推论。