一类包含高阶Bernoulli数和高阶Euler数的积分计算公式

给出了一类包含高阶Bernoulli数和高阶Euler数的积分计算公式．     

上临界渗流转角问题研究(英文)

研究二维上临界边渗流,主要关注开路旋转角度的一些性质.假设从原点到边长为n的盒子边界存在一条开路,在此条件下,证明这些路的旋转角度的最大值满足大数律.此外,还证明对于任意δ0,当n充分大时,大概率地有相邻左右贯穿开路的2个相邻接触点的距离小于log1+δn.     

自然数分拆成若干个连续奇数之和的分拆种数

本文给出了自然数分拆成若干个连续奇数之和的分拆种数的计算公式 ,并就其应用进行了举例     

大数定律应用问题分析与概率直觉思维培养

为指导人们正确地认识随机事件,引导人们适当抑制盲目应对随机事件的冲动。该文选取一个独特的视角,讨论概率统计中的小概率事件,拆解概率理论,分析中奖概率,并就概率论联系实际,培养统计思维,提高学生的应用能力等方面,探讨了通过生活中的数学问题增强对实际事物中随机性的敏感,培养学生概率直觉思维,提高学生的应用能力,培养创新人才的途径。     

Young Children'S Notations For Fractions

This paper focuses on the kinds of notations young children make for fractional numbers. The extant literature in the area of fractional numbers acknowledges children's difficulties in conceptualizing fractional numbers. Some of the research suggests possibly delaying an introduction to conventional notations for algorithms and fractions until children have developed a better understanding of fractional numbers (e.g., Hunting, 1987; Sáenz-Ludlow, 1994, 1995). Other research (e.g., Empson, 1999), however, acknowledges the interaction between conceptual understandings and the representations for those understandings. Following the latter line of thinking, this paper argues that children's notational competencies and conceptual understandings are intertwined, addressing the following research questions: (a) What kinds of notations do five and six-year-old children make for fractional numbers?; and (b) What can be learned about young children's learning of fractional numbers by analyzing the notations they make? This paper presents data from interviews carried out with twenty-four children in Kindergarten and first grade (five and six-year-old children), exploring the nuances of their notations and the meanings that they attach to fractions.     

郑板桥的奇论怪理与他的思维之妙

郑板桥是我国历史上著名的思想家、文学家、艺术家。他的作品创新根植于他超乎寻常的思维方式。郑板桥善于联想,由此及彼、睹物思人、思前想后是他思维的首要特征。他提出了乱丑为妙、宜少宜短、兰不排棘等观念,倡导开放思维、动态思维、多维思维等系统思维方式,并运用于文学与艺术的创作实践。郑板桥的成就不仅归结于他的文化艺术水平,更归结于他的思维创新。     

关于Diophantine方程x^3-1=3py^2

设p是6k＋1型的奇素数,探讨了Diophantine方程x^3 -1=3 py^2的正整数解的情况。运用Pell方程px^2 -3 y^2=1的最小解、同余式、平方剩余、勒让德符号等初等方法证明了两个结论。     

关于不定方程x2＋y2＋p=xyz解的探讨

运用无穷递降法研究了不定方程x2＋y2＋p=xyz（p为奇素数）,获得了该方程的全部正整数解。     

Theresa A. Strottman Responds

No abstract available for this article.     

矩阵与Fibonacci数

Fibonacci数是一个古老的问题,它有很多有趣的性质,在组合数学中这些性质是从数列递推公式中得出的,本文用矩阵这个工具导出了这些性质。