关于不定方程4x^2-py^2=1的一个注记

利用连分数理论证明了不定方程4x^2-py^2=1（p=19,31,43,59,67,71）分别有最小正整数解（x,y）=（85,39）;（x,y）=（760,273）;（x,y）=（1741,531）;（x,y）=（530,69）;（x,y）=（24421,5967）;（x,y）=（1740,413）从而获得不定方程4x^2-py^2=1（p=19,31,43,59,67,71）的全部正整数解．     

函数y=[x]及y=(x)的若干性质及应用

取整函数与小数部分函数既相互联系又有区别,各有一些独特的性质,在数学及生活中有着较广泛的应用。     

SiC颗粒粒度对高体积分数复合材料力学性能的影响

研究体积分数为55％的高体积分数SiCp/Al复合材料的硬度、强度及韧性随SiC颗粒粒度的变化规律．结果表明：高体积分数复合材料的抗拉强度随粒度变化出现一峰值,在粒度为10μm时最高;当颗粒粒度在5μm到20μm之间时,复合材料断裂韧性随颗粒粒度增加而增大,且颗粒粒度越大增加的幅度越小．     

二次无理数的连分数

给出了以下几个结果：1.给出了√n（1/2）的连分数展式的简便算法.2.证明了√n（1/2）连分数循环节结构的中心对称性.3.给出了一般二次无理数（a＋√n（1/2））/b的连分数算法.     

二次无理数的连分数及其应用

给出了二次无理数（a＋√n）／b展为连分数的简便算法,并将该算法用于有理数的连分数展开及某些定理的证明．     

气泡对声传播影响的研究

以气泡壁处声压和径向振动速度为边界条件,研究气泡对声传播的影响;给出了含气泡介质内声速的表达式,得到了声速随气泡体积分数及声波频率的变化图。表明：声波频率一定时,声速随着气泡体积分数增大而减小;气泡体积分数一定时,频率增大对声速的影响较小。     

等价连分式的若干性质

该文研究了等价连分式的性质,得到若干新的结论。     

浅析分式函数不定积分问题

本文针对部分分式函数积分问题概括了四种特殊的积分方法，熟练掌握和应用这四种方法对于解决部分类型的分式函数的不定积分问题非常方便快捷，从而有利于进一步拓宽思路，大炎提高不定积分的运算能力。     

MODIS亚像元积雪覆盖率提取方法

积雪覆盖区域,在全球能量平衡中发挥着重要作用.目前较常用的积雪覆盖率算法主要是利用雪盖率与雪盖指数(NDSI)间的关系建立统一的回归模型,但这种方法在完全雪盖区及稀疏雪盖区的反演精度较差.尝试通过分段建立模型反演雪盖率,并利用ETM+数据对模型估算结果进行验证.结果表明,分段模型可以有效提取亚像元尺度的信息,并且对NDSI高值区的雪盖率反演有一定的改善.     

Young children's partitioning strategies

Taxonomies for classifying children's partitioning strategies have generally focused on the contexts in which the strategies occur and whether the strategies generate fair shares. Therefore, the overall aim of this study was to increase our knowledge about young children's partitioning strategies by setting out not only to identify new partitioning strategies but also to develop a taxonomy for classifying young children's partitioning strategies in terms of their ability to facilitate the abstraction of the partitive quotient fraction construct from the concrete activity of partitioning objects and/or sets of objects. Clinical interviews were conducted with twelve purposely-selected Year Three students. Each student was presented with a unique set of realistic partitioning tasks. The paper concludes with a taxonomy for: (i) qualitatively evaluating a child's progress towards the abstraction of the partitive quotient fraction construct, and (ii) planning and implementing teaching interventions commensurate with the child's level of progress towards the abstraction of the partitive quotient fraction construct. This taxonomy provides researchers and teachers with means of better utilising children's informal partitioning strategies as the foundation upon which to further develop their understandings of the partitive quotient fraction construct. This revised version was published online in July 2006 with corrections to the Cover Date.