循环小数几个猜想的证明及推广

1引言 为了叙述的方便，我们约定：既约分数芳q/p（p是素数，目．P≠2，5）可化成循环小数，最短循环节形式的循环小数我们称之为P-小数；最短循环节的长度称为该小数的长度．     

分配P-代数的核理想

研究了分配P-代数的核理想的构造,给出了分配P-代数的核理想的一些充要条件.     

论如何用傅立叶级数求P-级数∞∑n=1/np(P为偶数)的和

P-级数(∞↑∑↓n=1)1/n^P的求和问题，是数项级数求和中的难点问题．本文主要阐述了如何用傅立叶级数来求P-级数(∞↑∑↓n=1)1/n^P（P为偶数）的数。     

P-半单BCI-代数的几组等价公理系

本文利用BCI-代数的某些基本性质和P-半单BCI-代数的等价特性,给出了P-半单BCI-代数的四组等价公理系.它不同于目前已有的公理系.     

P-级数敛散性的简单证法

对有关文献中关于P-级数敛散性证明的处理方法，文章做了概述和利弊分析，且给出了一种证明方法．本文的方法非常初等，不依赖比较判别法，一次性整个地证明了P-级数(包括调和级数)敛散性．     

BCI-代数的伴随元与BCI-代数的根性

给出了BCI-代数的伴随元与ZTR型BCI-代数的概念,证明了一个ZTR型BCI-代数是一个P-半单BCI-代数。     

唐山市区公交系统静态网络性质的研究

以唐山市公交系统为研究对象,构建网络模型。在L空间和P空间分别研究唐山市公交系统静态网络性质,包括网络的聚类系数、平均路径长度和度分布。结果表明,唐山市的公交网络具有较大的聚类系数、较小的平均路径长度和指数形式的度分布,具有典型的小世界网络的特征。     

小木琴——音乐教学的好助手 叮咚木琴 教师之友 学生知音

瞧,照片上是哈尔滨师范附小1500名学生在为全国中小学整体改革研讨会表演我厂P-4型小木琴! 我厂P-4型小木琴已在全国中小学广泛应用,其学生学得快、在教学中能利用琴键间特殊的音程关系进行音乐创作等优点已充分     

收敛的P-级数余项的进一步估计

在文献[1]的基础上对P-级数的余项作进一步的估计。     

P-半单广群与对合亚交换广群

对P-半单广群与对合亚交换广群作了进一步的研究,探讨了它们之间的逻辑联系及其与P-半单BCI-代数的关系,指明两种广群不具有必然的逻辑联系,举出了许多有用的反例.     

纯循环小数循环节的规律

纯循环小数循环节的规律是a/b(a,b是自然数,a＜b,(a,b)=1)能表示成纯循环小数的充要条件是(b,10)=1,且对满足上述条件的任意小于b的自然数a,a/b化成小数时循环节节长都是相同的.进一步得到了对任意自然数b((b,10)=1),a/b化成小数时节长的长度规律.     

带余除法与同余对循环小数的一个应用

利用同余及带余除法解决：小数展开式最简单的分数；对任意正整数n，不用直接做小数除法，1／n的小数展开式循环节的长度的上限及相关问题．     

化分数为纯循环小数的一些简单方法

过去化分数为循环小数都是直接用除法去作，这里介绍几种简单化法。     

Developmental changes in the comparison of decimal fractions

Learning about decimal fractions is difficult because it requires an extension of the number concept built on natural numbers. The aim of the present study was to investigate developmental changes in children's misconceptions in decimal fraction processing. A large sample of children from Grades 3 to 6 performed a numerical comparison task on different categories of pairs of decimal fractions. The success rate and the type of error they made varied with age and categories. We distinguished the impact of the value of the digits from the impact of the length of the fractional part on children's pattern of responses. Although both kinds of impact affected the success rate, the digit values had a stronger impact and were mastered later than the length. Our results also showed that a zero just after the decimal point was understood better and earlier than a zero at the end of the fractional part of a number. Cluster analysis was conducted to determine groups of children who answered similarly regarding the response type across the various categories of decimal fractions. To interpret the data the conceptual change framework was used.     

改进基于均值运算的线性同余伪随机序列图像置乱算法研究

随着网络技术的迅猛发展,图像被作为一种数据信息频繁传输于世界各地的网络中。为了保证某些保密图像的安全性,提出了一种改进基于均值运算的线性同余伪随机序列图像置乱算法,先对通过均值运算获取的图像象素进行矩阵转换,将每个象素值从十进制转换成二进制,随后实现按位倒序,将其逐个转换成十进制数,最终实现对于图像的置乱。实验结果表明,该算法更加适用于图像文件的加密传输和秘密图像信息在数字水印技术中的置乱预处理,而且对图像的处理有良好的鲁棒性。     

Acquiring meaning for decimal fraction symbols: A one year follow-up

Fourth graders with differing achievement records participated in a specially designed two week unit on decimal fractions. Students were encouraged to connect meaningful referents with decimal fraction symbols and use these meanings to develop procedures for adding and subtracting decimal numbers. One year later these students and a matched set of fifth graders were interviewed and given paper-and-pencil tests. Three questions were of interest: (1) Do short term changes in the processes students use to solve problems remain stable over time; (2) Do students who have been instructed in conceptually-based processes exhibit a higher level of performance one year later than their conventionally taught peers; and (3) What is the relationship between entry achievement level and the year-long effects of conceptually-based instruction? The results suggest that: (1) If students used the meanings of written symbols as a basis for solving problems immediately after instruction, they used these processes to solve problems one year later, regardless of entering achievement; (2) Compared to their conventionally taught peers, students in the lower achievement group benefitted relatively more from the conceptually-based instruction than students in the higher achievement group; (3) However, higher achieving students were more likely to exhibit use of conceptually-oriented processes one year later than the lower achieving students.     

中国古代先哲对数学的哲学思考

笔者简要论述了古希腊哲学家毕达哥拉斯、柏拉图、亚里士多德对数学对象的存在方式和“万物的本原是一”的认识以及对“1”本身的深入研究。在此基础上,从比较的视角深入分析了中国古代思想家老子、庄子、苏轼对数的“道”—“数”—“万物”生成模式和尹文子、墨家的思想家、刘徽和朱世杰等著名数学家对数的“十进制生成模式”的辩证思想和对“1”的哲学思考。     

Children's understanding of the additive composition of number and of the decimal structure: what is the relationship?

Nunes and Bryant (Children doing mathematics, Blackwell, Oxford, 1996) proposed that an understanding of the additive composition of number could be a precursor to an understanding of the decimal structure. If this is so, children should achieve an understanding of additive composition before they can handle the decimal structure. The aim of our study was to determine the developmental timing of these two forms of mathematical understanding. 5- and 6-year-old children each completed both an addition task and Terezinha Carraher's (In: Streefland, L. (Ed.), Proceedings of the Ninth International Conference for the Psychology of Mathematics Education, vol. 1. Research Group on Mathematics Education and Computer Centre, State University of Utrecht, Utrecht, The Netherlands, 1985, pp. 288–303) shop task, with concrete materials. The addition task tested an understanding of additive composition by measuring whether children used a counting-all or counting-on strategy to add two quantities. The shop task tested an understanding of the decimal structure by investigating whether or not children could successfully combine tens and ones in producing a given amount of money. Our results suggest that learning about the decimal structure enhances children's understanding of the general principle of additive composition.     

0.01ms红外数字毫秒计的制作

利用100KHz石英晶体、红外线光电门及十进制计数/七段译码器二合一集成电路,制做了测量精度可达0.01ms的红外数字毫秒计.     

循环连分数与二次无理数关系初探

研究循环连分数与二次无理数关系问题 ,首先证明了任何循环连分数皆为二次无理数 ,并给出化循环连分数为二次无理数的一般方法