浅谈高中数学的类比方法

世界万物总在不断变化、完善着,数学知识亦不例外.对诸多数学知识的理解在深化,应用在优化,有诸多数学命题在延伸、拓广,在这些变化过程中“类比”有着它独特的功效.     

懂数学 明算账

1 问题来源 央行在2006年8月19日上调金融机构存款利率后,许多希望尽快享受新利率的储户,纷纷选择将仍在存期内的定期存单提前支取后办理转存.银行提醒储户,1年期存款在54天内、2年期存款在110天内、3年期存款在165天内、5年期存款在284天内提前支取,转存同期限定期存款是合算的.反之不要盲目提前支取,以免得不偿失.     

高考数学“思想实验”中的若干关键词

除有形实验(physical experi ments)外,还有在较高理智水平上使用的其他实验,即思想实验(thought experi ments).而在数学中的实验是在想象中做的,是设想着做的,是在思想中进行的实验[1].显然,这种实验乃是在头脑中进行的抽象     

数学奥林匹克讲与练（24）

例题讲解185 .在正方形场地的中心有一只狼 ,而在其四个顶点处各有一只狗 ,狼可以在整个正方形中任意奔走 ,而狗只许在正方形的边界跑动 .已知狼可以打赢每一只狗 ,但任两只狗在一起可以制服狼 .设每只狗的速度均为狼的速度的 1.5倍 .求证 :这四只狗可以看住这只狼 ,使它不能从     

几何画板在初中几何教学中的运用

以前的课堂,人们总是把黑板、粉笔或纸笔联系在一起,这样的教学方式会把学生的思维局限在有限的空间中.在科学技术高度发展的今天,多媒体的应用已经相当普及,尤其是在教师开课的时候基本上都有精美课件的展示.在数学课上,几何画板的运     

Brown运动的逗留时与首中时

设为中的标准Brown运动,对0＜α,记本文求出了X在首中球面之前逗留在Bα内的时间的Laplace变换,在首中之前逗留在Bαb内的时间的Laplace变换以及在首中之前逗留在Bαb内的时间的Laplace变换．作为推论,求出了X关于球面首中时的Laplace变换,逗留在球内总的时间的Laplace变换及逗留在球壳内的总的时间的LaPlace变换．     

探究一例

探究活动如图1,在数学实践探究活动图1中,小亮将直角三角板ABC的直角边AB在直角框DOE内滑动,其中A点在OD上滑动,B点在OE上滑动.在滑动过程中,小亮发现点C与点O的距离在不断发生变化,当点B与点O重合时,OC距离最小,那么,是否存在特定位置,能使OC距离最大呢?     

反函数连续性和可微性的若干注记

在不要求函数在区间连续的假设下,研究了其反函数存在的条件及其在一点的连续和可微的条件,给出了反函数在一点连续的本质刻画.主要结论是原函数在某点连续不是其反函数在相应点连续的必要条件,而是函数将区间映射为区间,最后用例子说明结论的直观性.     

读者心声

张老师:您好!请允许我这样称呼。听了您去年5月份在兰州和前天在西安的培训、讲座,改变了原来不切合实际的、盲目追求成绩的做法,顶着领导的质疑,我回来后一直在尝试,在我们一个农村学校,在我的班级也收效很好,学生受益匪浅,我将继续坚持下去,真的很感谢您!     

在国际学校中开展中学数学建模教育——组织参加美国高中生数学建模竞赛的启示

<正>一、数学建模在中外数学大纲中的地位在我国2007年颁布的新课程标准中,高中数学课程要求把数学建模的思想以不同的形式渗透在各个模块和专题内容之中,并在高中阶段至少安排较为完整的一次数学建模活动.这是首次在课程标准中提出数学建模的教学要求.通过设立数学建模等学习活动,为学生形成积极主动的、多样的学习方式进一步创造有利的条件,以激发学生的数学学习兴趣,鼓励学生在学习过程中,养成独立思考、积极探索的习惯.     

Conceptualizations of slope in Mexican intended curriculum

Slope is a fundamental mathematics concept in middle and high school that transcends to the university level. An understanding of slope is needed at the university level since slope plays an important role in understanding problems involving variation and change. In this study Mexican curricula documents were examined to determine which conceptualizations of slope are addressed in the intended mathematics curriculum. To explain the results, we use conceptualizations of slope identified in previous research. Our findings reveal that, to a certain extent, the conceptualizations proposed in the Mexican intended mathematics curriculum differ slightly in terms of the emphasis and timing of instruction from what others have identified in the U.S., with slope as a geometric ratio receiving less emphasis in the Mexican curriculum. There was also noted discontinuity within the Mexican curriculum in introducing slope in grade 9 and subsequently introducing of linear functions in grade 10 without explicit mention of slope. Suggestions are made for future studies, both to consider the conceptualizations of slope promoted in the Mexican textbooks and the impact they have in classroom instruction and student learning of slope.     

基于平行DEA模型的我国小学教育资源配置效率分析

小学教育是教育阶段的基础,也是我国强制教育的一部分。但如何在各省份性别比例相差较大的情况下,更加有效的提高各省份小学教育资源配置效率是一个值得思考的问题。为了避免性别带来的影响,可以通过平行结构DEA模型根据学生性别分为两个平行子系统,来衡量我国2012~2018年各省份小学教育的资源配置情况。研究发现大部分省份小学教育资源配置的总系统效率未达到有效边界,仍有需要改进的地方。男学生在小学教育阶段的效率通常优于女学生在小学教育阶段的效率,但随着近些年我国教育体制的日益完善,女学生在小学教育阶段的效率呈上升趋势。此外,我国西部地区的小学教育资源配置效率在一些年份普遍优于东部和中部地区,而中部地区和东部地区小学教育总系统效率相对稳定,西部地区小学教育总系统效率波动较大。     

On Potential Theoretic Skeletons of Polyhedra

We prove that any polyhedron in two dimensions admits a type of potential theoretic skeleton called mother body. We also show that the mother bodies of any polyhedron in any number of dimensions are in one-to-one correspondence with certain kinds of decompositions of the polyhedron into convex subpolyhedra. A consequence of this is that there can exist at most finitely many mother bodies of any given polyhedron. The main ingredient in the proof of the first mentioned result consists of showing that any polyhedron in two dimensions contains a convex subpolyhedron which sticks to it in the sense that every face of the subpolyhedron has some part in common with a face of the original polyhedron.     

Sur la détermination d'une relation binaire à partir d'informations locales

This paper deals with the problematic aspect of the reconstruction of binary relations: it includes all the questions raising the possibility or impossibility to determine a structure by gathering given substructures. It is the continuation of three studies: the first made by G. Lopez [9] in 1972 about the determination of a binary relation through the types of isomorphism of its restrictions, the second made by K. B. Reid and C. Thomassen [15] in 1976 about the strongly self-complementary tournaments (every subtournament is self-complementary), the third made by C. Thomassen [16] in 1989 about the cycle space of a tournament. In the second section, we use the notion of class of difference (which was introduced in [9]) to extend a study made in [16] to binary relations. Then, in the third section, we improve the result of this last study in the case of the tournaments. After noticing that the result of [15] inferred itself naturally from the approach developed in [9], we extend, in the fourth section, the study made in [15] to binary relations.     

火灾发生的周期性规律及其在火灾非线性组合预测模型中应用

研究火灾发生规律及发展趋势,具有实用价值.分析历年中国火灾统计数据,发现中国火灾的发生规律同时具有增长趋势性和周期波动性特征:①中国火灾从90年代开始大幅度增加,在2002年达到最大,然后逐年缓慢下降;②每年12个月呈正弦函数波动,周期为12,1、2月发生起数最大,8、9月最小.借助于M ATLAB软件,根据2000-2006年中国火灾统计数据,建立火灾的月发生起数的非线性周期性组合预测模型,预测值与实际值的平均相对误差小于0.07.研究结论为消防研究、消防部门决策提供科学依据.     

On slice hyperholomorphic fractional Hardy spaces

In this paper we introduce and study the fractional Hardy spaces of the half space and of the unit ball in the quaternionic setting. In particular, we discuss their properties of invariance and of factorization in terms of functions in the Hardy space of the half space in the first case, and in terms of a suitable reproducing kernel Hilbert space in the case of the unit ball.     

CFD simulation of gas–solid flow with a cluster structure-dependent drag coefficient model in circulating fluidized beds

To model the effect of clusters on hydrodynamics of gas and particles phases in risers, the interfacial drag coefficient is taken into account in computational fluid dynamic simulations by means of a two-fluid model. The momentum and energy balances that characterize the clusters in the dense phase and dispersed particles in the dilute phase are described by the multi-scale resolution approach. The model of cluster structure-dependent (CSD) drag coefficient is proposed on the basis of the minimization of energy dissipation by heterogeneous drag (MEDHD) in the full range of Reynolds number. The model of CSD drag coefficient is then incorporated into the two-fluid model to simulate flow behavior of gas and particles in a riser. The distributions of volume fraction and velocity of particles are predicted. Simulated results are in agreement with experimental data published in the literature.     

Exponential dispersion relation and its effects on unstable propagating pulses in unidirectionally coupled symmetric bistable elements

The propagation of pulses in unidirectionally coupled symmetric bistable elements is studied. The speeds of unstable traveling pulse waves in a ring of elements increase with pulse width in an exponential manner. This dispersion relation causes exponential increases in the duration of transient propagating pulses and the noise-sustained propagation of pulses, which are qualitatively the same as those in a reaction-diffusion-convection equation and a ring of sigmoidal neurons. However, the speeds of pulse fronts in propagating pulses depend on the backward pulse width. Properties of pulse transmission in an open chain of elements then differ from those in the above two systems qualitatively.     

A task that elicits reasoning: A dual analysis

This paper reports on the forms of reasoning elicited as fourth grade students in a suburban district and sixth grade students in an urban district worked on similar tasks involving reasoning with the use of Cuisenaire rods. Analysis of the two data sets shows similarities in the reasoning used by both groups of students on specific tasks, and the tendency of a particular task to elicit numerous forms of reasoning in both groups of students. Attributes of that task and ways that those attributes can be replicated in other domains may have implications in the teaching of early reasoning.     

Bootstrap and empirical likelihood methods in extremes

One of the major interests in extreme-value statistics is to infer the tail properties of the distribution functions in the domain of attraction of an extreme-value distribution and to predict rare events. In recent years, much effort in developing new methodologies has been made by many researchers in this area so as to diminish the impact of the bias in the estimation and achieve some asymptotic optimality in inference problems such as estimating the optimal sample fractions and constructing confidence intervals of various quantities. In particular, bootstrap and empirical likelihood methods, which have been widely used in many areas of statistics, have drawn attention. This paper reviews some novel applications of the bootstrap and the empirical likelihood techniques in extreme-value statistics. Dedicated to Professor Laurens de Haan on the occasion of his 70th birthday.