A definable nonstandard enlargement

This article establishes the existence of a definable (over ZFC), countably saturated nonstandard enlargement of the superstructure over the reals. This nonstandard universe is obtained as the union of an inductive chain of bounded ultrapowers (i.e. bounded with respect to the superstructure hierarchy). The underlying ultrafilter is the one constructed by Kanovei and Shelah [10]. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

反向Chrystal不等式

利用控制不等式理论建立了三个反向Chrysta l不等式,并给出了若干应用.     

密立根油滴实验数据处理的一种方法

以在重力场和静电场中运动的带电油滴为研究对象,提出了一种数据处理的方法,快速、准确地求解出基本电荷的电量,验证电荷的不连续性。     

浅析量子力学中的不确定性原理

德国物理学家海森伯在1927年提出的不确定性原理,包括两力学量间的不确定性原理和能量与时间的不确定性原理,它的提出意味着量子力学不仅有了完整的数学形式,而且有了合理的理论解释.本文尝试通过对不确定性原理的创立背景、过程、应用等来对这一原理做简要介绍,特别强调了科学讨论在科学发展中的作用.     

用高中数学求解异面直线公垂线方程

用高中向量基础知识和待定法可非常方便地得出n（n≥3）维线性空间中异面直线的公垂线方程.若在大学数学教学中挖掘与中学数学的衔接和联系,则可在很大程度上降低大学数学的教学难度.     

高等数学与高中数学的衔接

从高中教材和高等数学教材的内容、高等数学和初等数学的思维模式、教师的教学方法、学生的学习方法四个方面分析学生在学习高等数学时感到困难的原因,并探讨在高等数学教学中,做好高等数学与高中数学衔接的五项具体措施：上好绪论课,帮助学生建立自主学习的观念;指导正确的学习方法,培养学生的自学能力;给出数学概念要循序渐进,注意知识的衔接;加强习题指导,加深学生对基本概念的理解;及时了解学生状况,有针对性地开展教育。     

Middle-school students’ concept images of geometric translations

This study explored sixth grade students’ concept images of geometric translations and the possible sources of their conceptions in a non-technological environment. The data were gathered through a written instrument, student and teacher interviews and document analyses. Analyses of student responses revealed two major concept images of geometric translations: (a) translation as translational motion, and (b) translation as both translational and rotational motion. Students who held these conceptions showed various levels of understanding, such as conceiving translations as undefined motion, partially-defined motion, and defined-motion of a single geometric figure on the plane. The findings of the study suggested, in general, consistencies between students’ concept images and their concept definitions. However, most of the students’ concept definitions were inconsistent with the formal concept definition of geometric translations.Data analyses also revealed five interpretations of a translation vector: (a) vector as a reference line, (b) vector as a symmetry line, (c) vector as a direction indicator, (d) vector as a parameter, and (e) vector as an abstract tool. Furthermore, classroom instruction, mathematics and science textbooks, real-life examples and everyday language were the major sources of students’ concept images of geometric translations.     

Jordan标准形定理的初等变换证明

本文对 Jordan标准形定理给出了一种使用初等变换的证明 ,直观意义明显、易于理解 ,可用于线性代数教学 .     

Lowest breathing mode of bosonic helium clusters

We analyze various microscopic calculations of vibrational frequencies for ⁴He_N clusters, N = 3-728. The lowest breathing frequency with total angular momentum J = 0 varies smoothly as a function of N, with a maximum around N = 50-120. Received 11 July 2001     

Supporting the development of algebraic thinking in middle school: a closer look at students’ informal strategies

This study investigated how 31 sixth-, seventh-, and eighth-grade middle school students who had not previously, nor were currently taking a formal Algebra course, approached word problems of an algebraic nature. Specifically, these algebraic word problems were of the form x + (x + a) + (x + b) = c or ax + bx + cx = d. An examination of students’ understanding of the relationships expressed in the problems and how they used this information to solve problems was conducted. Data included the students’ written responses to problems, field notes of researcher-student interactions while working on the problems, and follow-up interviews. Results showed that students had many informal strategies for solving the problems with systematic guess and check being the most common approach. Analysis of researcher-student interactions while working on the problems revealed ways in which students struggled to engage in the problems. Support mechanisms for students who struggle with these problems are suggested. Finally, implications are provided for drawing upon students’ informal and intuitive knowledge to support the development of algebraic thinking.