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1.
是一个比较独特的函数,因为从古典分析的观点来看,它具有下面一些不寻常的性质:(1)R(x)在[0,1]上的所有无理点连续,而在所有的有理点不连续,即几乎处处连续。证明见菲赫金哥尔茨著的《微积分学教程》一卷一分册p.146。(2)R(x)在[0 ,1]上R可积证明见上书二卷一分册p.97。(3)R(x)在[0,1]上处处不可导。证明在R(x)的不连续点自然不可导,现没ξ。为R(x)的连续点(即无理点),则必可在(0,1)内选取一无理点列{ξ_n},使ξ_n→ξ。(n→∞),这时,极限 相似文献
2.
秦德生 《数学学习与研究(教研版)》2004,(1):17-19
坐标平面上横、纵坐标都是整数的点称为格点(或整点)；坐标平面上横、纵坐标都是有理数的点称为有理点。不是有理数的点称为无理点； 相似文献
3.
一、问题的提出
等可能地在区间[0,1]上投点,所投的点落在I=[0,1]中的任意子区间A中的概率,与A的长度L成正比,而与A在I=[0,1]中的位置无关.如果记这一事件为A,那么事件A的概率P(A)=L/1=L.如果区间A的长度逐渐缩小到一个点时,那么P(A)又等于多少?
比如向区间[0,1]上等可能地投点,所投的点落在I=[0,1]中的任意子区间A=[A,b]中的概率就是几何概率. 相似文献
4.
考虑一类严格局部鞅在典范空间C[0,1]上的概率测度Q的一种特殊情形,假设P是一个由过程h(Xt^TD)确定的一个可变鞅测度,利用局部鞅变换方法证明了一个存在性结果. 相似文献
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[28—IMO—5]:试证:对于任意n(n≥3),在欧氏平面上总存在n个点,每两点间的距离为无理数,每三点构成非退化的三角形,且有有理面积. [分析]本题就是要构造欧氏平面上无三点共线的k个点,满足下述两个条件:1)每两点有“无理距离”;2)每三点有“有理面积”.所以我们抛开原题,扣住“无理距离”和“有理面积”构想它的证明, 相似文献
6.
(一)两种积分的可积性差异及原因黎曼积分存在的必要条件是被积函数有界,但有界函数不一定 R 可积。例如:狄利克雷函数:D(x)={1,x 为[0,1]内有理点 0,x 为[0,1]内无理点在[0,1]上有界,但非 R 可积。那么,函数 R 可积的充要条件是什么呢?在数学分析中已证得在闭区间上有界函数 R 可积的充分条件 相似文献
7.
本文应用文[2、4]引进的区间值泛函和Sugeno[1]意义下的Fuzzy积分,分别把文[3]的区间值Fuzzy测度扩张到可测区间值Fuzzy集空间上,并在这两种意义下研究扩张区间值Fuzzy测度的关系。 相似文献
8.
设S*={1/n：n∈N+}为一收敛数列。用K表示从区间（0,1]到[0,1]且分段点之集为S*的分段线性连续函数全体。 USC表示单位闭区间到自身的所有上半连续函数全体。对任意 f∈USC ,↓f 表示 f 的下方图形,即↓f={(x, t)|x∈I,0tf (x)}。对任意USC的子集A ,令↓A={↓f|f∈A},对↓USC赋予Hausdorff度量拓扑,并对K中的每个函数补充其在0点的函数值为其上极限使K变为USC的子集,记为L 。将证明↓L同胚于s=(0,1)∞,其中s为希尔伯特方体Q=[0,1]∞的子空间。 相似文献
9.
题目:设f(x)是定义在[0,1]上的函数,若存在x*∈(0,1),使得f(x)在[0,x*]上单调递增, 在[x*,1]上单调递减,则称f(x)为[0,1]上的单峰函数,x*为峰点,包含峰点的区间为含峰区间．对任意的[0,1]上的单峰函数f(x),下面研究缩短其含峰区间长度的方法． 相似文献
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11.
学生初次接触到负数的概念时 ,对理解负数的意义及有理数的运算法则都会产生困难。北师大新世纪版实验教材对解决这些问题的设计思路有这样几个特点 :借助问题情境、从数不够用了的角度引出“负数” ;渗透正负数是“具有相反意义的量”的数学模型的思想 ;从不同的角度表示正负数 ;经过三个层次、借助不同的素材得出正负整数的加法运算法则 ;在应用中体会有理数的作用、熟练有理数的运算 ,以及降低笔算的难度等。这将有助于帮助学生在理解的基础上掌握相关的内容。 相似文献
12.
The present study focuses on the development of two sub-concepts necessary for a complete mathematical understanding of rational numbers, a) representations of the magnitudes of rational numbers and b) the density of rational numbers. While difficulties with rational number concepts have been seen in students' of all ages, including educated adults, little is known about the developmental trajectories of the separate sub-concepts. We measured 10- to 12-year-old students' conceptual knowledge of rational numbers at three time points over a one-year period and estimated models of their conceptual knowledge using latent variable mixture models. Knowledge of magnitude representations is necessary, but not sufficient, for knowledge of density concepts. A Latent Transition Analysis indicated that few students displayed sustained understanding of rational numbers, particularly concepts of density. Results confirm difficulties with rational number conceptual change and suggest that latent variable mixture models can be useful in documenting these processes. 相似文献
13.
Charalampos Lemonidis Helen Tsakiridou Ioanna Meliopoulou 《International Journal of Science and Mathematics Education》2018,16(6):1127-1145
The purpose of the present study is to examine content knowledge (CK) and pedagogical content knowledge (PCK) of Greek teachers in number sense and specifically in mental calculations with rational numbers (fractions, decimals and percentages). Examined within the framework of CK were the type of strategies employed by teachers and the extent of the repertoire of these strategies, which provides an indication of their flexibility. Teachers’ CK performance in mental calculations with rational numbers was compared with the extent of their strategic repertoire as well as with the PCK they employed when teaching mental calculations with rational numbers. The data revealed that the teachers’ high CK performance in mental calculations with rational numbers is positively influenced by the existence of an extensive strategic repertoire. Furthermore, it was found that a high CK performance and an extensive strategic repertoire in mental calculations with rational numbers positively influence the PCK of mental calculations with rational numbers. 相似文献
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针对web社区的发现和链接分析技术的一些关键问题,基于面向主题的技术,重点研究了二分图的特征,引入了Х二分核集来更为明确地定义抽取的方法.通过扫描主题子图构造Х二分图,对该子图的（i,j）裁剪后得到Х二分核集,这也是社区的最小元素.最后,对所抽取的所有Х二分核集应用层次聚类的方法得到社区内部结构的树状图,证明了构造和裁剪方法的正确性并设计了算法.实验采用HITS（hyperlink-induced topic search）算法中的典型数据集获取方法,选择了10个主题和4个搜索引擎并综合返回的结果.采用社会网中测量社区结构强度的模块化度量来验证所提方法的有效性,实验结果表明所提方法是有效并可行的. 相似文献
16.
Many children and adults have difficulty gaining a comprehensive understanding of rational numbers. Although fractions are taught before decimals and percentages in many countries, including the USA, a number of researchers have argued that decimals are easier to learn than fractions and therefore teaching them first might mitigate children’s difficulty with rational numbers in general. We evaluate this proposal by discussing evidence regarding whether decimals are in fact easier to understand than fractions and whether teaching decimals before fractions leads to superior learning. Our review indicates that decimals are not generally easier to understand than fractions, though they are easier on some tasks. Learners have similar difficulty in understanding fraction and decimal magnitudes, arithmetic, and density, as well as with converting from either notation to the other. There was too little research on knowledge of percentages to include them in the comparisons or to establish the ideal order of instruction of the three types of rational numbers. Although existing research is insufficient to determine the best sequence for teaching the three rational number formats, we recommend several types of research that could help in addressing the issue in the future. 相似文献
17.
This report focuses on prospective secondary mathematics teachers’ understanding of irrational numbers. Various dimensions
of participants’ knowledge regarding the relation between the two sets, rational and irrational, are examined. Three issues
are addressed: richness and density of numbers, the fitting of rational and irrational numbers on the real number line, and
operations amongst the elements of the two sets. The results indicate that there are inconsistencies between participants’
intuitions and their formal and algorithmic knowledge. Explanations used by the vast majority of participants relied primarily
on considering the infinite non-repeating decimal representations of irrationals, which provided a limited access to issues
mentioned above. 相似文献
18.
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. 相似文献
19.
学生的理解水平、认知发展水平是制定课程目标的重要依据。只有厘清、界定了学生的实际理解水平,才能寻求、探查到一个多数人都能达到的目标层次,制定出适切的课程目标。以有理数乘法运算为例,学生对有理数乘法运算的理解具有层次性与有限性。由低到高,理解的三个水平为程序理解、直观理解、抽象理解。学生对有理数乘法运算的理解是非常有限的,原因在于知识的超验性与学生认知发展的层次性。对照义务教育课程标准发现,课程目标要求偏高,课程目标表述模糊。因而,课程目标需要基于学生的理解水平,具有层次性、明确性、适切性。 相似文献
20.
电力变压器常见故障及诊断 总被引：1，自引：0，他引：1
分析了电力变压器常见故障：油故障、瓦斯保护、短路、自动跳闸．提出了减少变压器故障的措施,并阐述了变压器在线监测技术：故障气体在线监测技术、局部放电在线监测技术、红外线测温在线监测技术等． 相似文献