一道MO试题的再证

在文[1]、[2]中分别给出了下面一道 MO试题的解析法证明和平几法的证明.文[2]中的证法用了梅涅劳斯定理,本文再给出一种不用梅涅劳斯定理的证法.题目,在△ABC中.AA_1为中线,AA_2     

一致L-lipschitz渐近伪压缩映象的三重迭代解

该文在一般Banach空间中研究了渐近伪压缩映象方程具误差的三重迭代解的逼近问题.把文中证明所用下确界改为下极限,保证了必有一点列收敛.本证明还改进了文献[2]中的主要结果,证明方法也不同于[2]中给出的.     

再证一道MO试题

在文[1]、[2]、[3]、[4]中分别给出了下面一道 MO 试题的证明方法.包括解析法,向量法,平面几何证法,其中平面几何证法中,有用了梅涅劳斯定理,和避开这一定理,适合初中学生,但证明时,其辅助线较多,证明也不够明快,下面再给一种证法.     

一类与自然数有关的命题的一种证法思路

贵刊文 [1]、[2 ]实际上探讨了一类可用数学归纳法证明的与自然数有关的命题的非数学归纳法的证明方法 ,文 [1]给出了二个定理 ,方法虽好 ,但却增加了记忆负担 ;文 [2 ]给出了不借助于辅助定理 ,直接证明的方法 ,虽然操作起来更容易 ,但其关键步骤(即构造相关的不等式或等式 )不易想到 .受文 [1]、[2 ]的启发 ,笔者以这类问题的数学归纳法证明中探寻出一种非数学归纳法的证明方法思路更清晰 ,操作更容易 .例 1　求证1 11 2 … 11 2 … ｎ =2 - 2ｎ 1.　　分析　用数学归纳法证明该式时 ,在第二步 ,假设对ｎ- 1时等式成立 ,即等式 1 11 2…     

三角函数求和公式的推广

本文利用尤拉公式建立了某些类型三角函数求和公式,从而使解决这些类型三角问题的过程大为简化.文中所得到的定理1、定理2,推广了文[1] 、[2]、[3]的主要结论.我们还利用尤拉公式简化了文[2]中定理的证明.     

一道猜想不等式的又一初等证明

题目 设a,b,c是正数,n是正整数,求证:a/n√an+(3n-1)bn/2cn/2+b/n√bn(3n-1)an/2cn/2c/n√cn+(3n-1)an/2bn/2≥1. 文[1]给出了该不等式的极限证明.文[2]用拉格朗日条件极值法给出了证明.这两种方法都不易理解,文[3]中我们给出一个初等证明.本文再用反证法给出一个新的证明.     

I.J.Matrix 定理的再推广

文[1]推广了I.J.Matrix定理,在文[1]的基础上,用Lagrange定理对文[1]中的定理1又作了进一步推广,并给出了文[1]中定理2的一个简捷证明。     

I.J.Matrix定理的进一步推广

文[1]将I.J.Matrix定理作了推广,本文运用Lagrange插值公式对文[1]中的定理1又作了推广,并给出了文[1]中定理2的简化证明。     

一个三元轮换不等式的手工证明

<正>题1设a、b、c是正数,求证:∑(a⁴/(a4/(a³+b3+b³))≥1/2∑a,其中∑表示轮换对称和.此题是一道已有的习题,国内流行的三本不等式专著[1]、[2]、[3]都有证明.但[1]、[2]的证明是错误的,[3]的证明利用了Vasile不等式.本文将给出此不等式的一个简洁的手工证明.供参考与欣赏.同时为我们的英才教育提供一点新鲜血液!     

关于可测空间中非负可测函数序列积分的不等式

Xie在文献[1]给出了一个关于Borel-Cantelli引理的重要的双边不等式,对Borel-Cantelli引理做了一个新的推广.胡舒合、王学军等在文献[2]中指出了在文献[1]中定理的证明及举例有错误,给出了定理的正确证明和例子的详细分析.本文在上述文献的基础之上,主要通过对文献[1]中双边不等式的研究,将Xie的结果推广到可测空间中的非负可测函数序列,得到相应的不等式.     

A Never‐Ending Painting: The Generosity of Time Spent Making and Learning with Others through Artistic Research

This article examines the role of spending time with others in and through artistic research and practice. I draw from my doctoral work which took me on a cross‐Canada journey visiting 125 artists in their studios. Following the studio visits, I made a series of paintings of artists’ studios, however a year later these same paintings were cut up and rearranged to create collaborative studio assemblages on the walls of the Tate Exchange Gallery in Liverpool. Drawing on the metaphor of a never‐ending‐painting to examine never‐ending pedagogies, this article examines the evolution of this project through three iterations of the studio paintings. With each iteration, I explore different ways of knowing others through making thus proposing the performative and relational qualities of artistic research. The first iteration allowed me to spend time with artists even in their absence, as I engaged with our conversations through painting their studios, thus blurring the lines between solitary and social art practices. The second iteration allowed me to give up my art to others through asking them to create collages with fragments of my studio paintings. And the third iteration allowed my work to merge with other arts‐based researchers. Through this process, I propose that making art allows for multiple conversations to emerge through spending time getting to know others through art making.     

敖伦苏木古城的若干问题

本文是2012年11月在包头召开的＂敖伦苏木文化研讨会＂上的发言,不是纯学术性论文,是根据我30年前研究有关问题的体会,提供建议以供敖伦苏木古城文物调查和历史考古工作参考。内容除介绍以往国内外的调查研究外,也提到自己亲历亲闻涉及此问题的前辈事迹,由于他们的探索,才得以积累今日丰富的成果。     

Towards an understanding of the role of language in the science classroom and its association with cultural identity development in the context of Mozambique

I am reflecting here my struggle to understand the issue of language in the science classroom and in our lives from three different perspectives: before and after Mozambican independence and after completion of my doctoral research. The main method used is auto|ethnographic inquiry in which I use the events in my life to question what is happening in my society. I have used Maria Rivera Maulucci’s paper, Language experience narratives and the role of autobiographical reasoning in becoming an urban science teacher as a reference. This paper helps me to show how isolated and generalized is the Mozambican situation and the value of our struggle in giving value to local languages.     

非线性方程求根的加速方法

通过对简单的迭代公式和迭代的加工公式进行改进,本文构造了四种新的迭代公式。第一个迭代公式是基于迭代公式收敛的条件构建的,另外三个迭代公式则基于迭代加工公式进一步迭代加速得到。数值实验证明第一个公式的有效性,及后三个公式确实比原来公式在非线性方程求根上加速。     

White on White: Researcher Reflexivity and the Logics of Privilege in White Schools Undertaking Reform

I use this paper to reexamine my role as a White researcher on a multi-racial research team. I reanalyze data I collected during an evaluation project to reveal how I avoided seeing race in the schools I visited and how I dodged discussions of race with members of those school communities. By analyzing my own discursive practice, I introduce a series of logics enacted through a variety of strategies that I used to manage race talk. The purpose of this paper is two-fold: (1) an analysis of the strategies I used to sustain White privilege and (2) an examination of the logics of those strategies in order to understand the power they have in reproducing inequity. Only by understanding the self-perpetuating nature of White privilege will we be able to begin to dismantle it. Jenny Gordon is an assistant professor in the Division of Education, School of Education and Human Development at Binghamton University. She teaches foundations courses for elementary education and courses on qualitative research methods. Her scholarly work includes articles on methodological issues pertaining to qualitative research methods and narratives on the impact of race on research and teaching.     

独立学院学生大学英语四级写作教学实践和思考

在独立学院教学实践中,本人深切体会到学生在四级作文写作实践中存在的问题,在实践教学中,作者根据学生作文中常出现的问题和不足,调整教学内容,向学生讲授四级作文写作要领,有效帮助学生提高写作水平,并以所授班级为研究对象,将学生一年以来的作文情况进行比较。     

Year-long Undergraduate Research Projects

Abstract

Undergraduate research has become the centerpiece of many institutions of higher education’s efforts to attract and recruit high school graduates. Since 1987, throughout my tenure at Bloomsburg University, I have involved over 20 students in my research. In my experience, there is clear evidence that students of mathematics substantially benefit if they engage in research during their undergraduate studies. Whether the student plans to apply for employment after graduation or continue with graduate studies, the undergraduate research experience has a tremendous effect on the student’s success. In this paper, I will provide some personal insight on my experience in working with undergraduate students. In most cases, my experience has been in working with one student on a long term (one semester or mostly year-long) research problems. I will discuss my approach to identifying students, the type of projects, providing guidance, and finally the challenges that we face in supervising undergraduate research. To exemplify, emphasis will be placed on the status of a recent 1-year research project, which was funded by the Pennsylvania State System of Higher Education, and a senior undergraduate student worked on it for one year.     

Adapting the boundaries in primary physical education: an account of my learning,my educational influence and improved practice

In this paper I explore how I have come to theorise my work as a critical emancipatory practice as a lecturer in primary physical education (PE). I give an account of what I understand to be the epistemological foundations and practices of practitioner research and my potential educational influence in my own and other practitioner-researchers’ learning. I explain how I have generated my living educational theory of practice and discuss the changes in my learning from a propositional approach towards a dynamic epistemology of practice that is grounded in inclusional and dialogical ways of knowing. Within my paper I position myself as a professional educator and researcher, and share the exciting and transformational experiences of teaching and learning in evolving action research cycles of practice. I view my learning to date as an active act, working with the novice teachers I support to offer improvement and change in our future practice. I celebrate my reconceptualised view of education as a learner from within my practice and explain my move from knowledge transfer to knowledge co-creation. I make an original contribution to educational knowledge by explaining how I try to inspire others to research their practice and contribute to a new scholarship of educational enquiry.