做一个“善于举例”的数学教师——来自一线教师的认识、实践与思考

一、缘起 近期再读郑毓信教授在《中学数学月刊》2010年第3、4期关于“三项基本功”的文章[1][2]并链接阅读了郑教授在《人民教育》2008年的系列文章《善于提问》、《善于举例》、《善于优化》,读后颇有感触恰逢学校备课组一月活动日,备课组成员就“善于举例”这一论题展开充分的讨论与交流下面我们从一线教师的角度谈谈“善于举例”的认识与实践.     

Difference systems of sets based on cosets partitions

Difference systems of sets （DSS） are combinatorial configurations that arise in connection with code synchronization. This paper proposes a new method to construct DSSs, which uses known DSSs to partition some of the cosets of Zv relative to subgroup of order k, where v = km is a composite number. As applications, we obtain some new optimal DSSs.     

追踪问题轨迹的解析解

关于追踪目标问题,一般文献仅计算了追上所用的时间,或者在给定位置追上的条件下,追踪者与目标的速度比的取值.而获得追踪者运动轨迹的解析解,显然更重要也更困难.本文在追踪问题一般表述的基础上,通过建立并求解追踪者运动的二阶微分方程,得到追踪轨迹的解析解,最后顺便简捷地推导了追上的地点、时间以及在给定位置追上时二者的速度比.     

New tetraphenylpyridinium-baseci luminogens with aggregation-induced emission characteristics

The research on aggregation-induced emission （AIE） has drawn increasing interests in the past decade. With the efforts scientists paid, a variety of AIE systems have been developed, among which the tetraphenylethelene and silole derivatives are the most studied. Development of new AIE systems could further enrich the AIE molecules and promote the development of AIE area. In this communication, we prepared a new AIE system based on 1,2,4,6-tetraphenylpyridinium ions according to the restriction of intramolecular rotation mechanism. These molecules could be facilely synthesized via one-step and one-pot reaction. The ionic AIE-active molecules could find wide application in sensing and optoelectronic areas.     

One-pot synthesis of N-aryl propargylamine from aromatic boronic acid,aqueous ammonia,and propargyl bromide under microwave-assisted conditions

A facile,one-pot synthesis of N-aryl propargylamine from aromatic boronic acid,aqueous ammonia,and propargyl bromide has been achieved under microwave-assisted conditions.The reactions can be smoothly completed within a total 10 min through a two-step procedure,including copper-catalyzed coupling of aromatic boronic acids with aqueous ammonia and following propargylation by propargyl bromide.     

Some Remarks on One-dimensional Functions and Their Riemann–Liouville Fractional Calculus

A one-dimensional continuous function of unbounded variation on [0,1] has been constructed.The length of its graph is infnite,while part of this function displays fractal features.The Box dimension of its Riemann–Liouville fractional integral has been calculated.     

Facile,one-pot synthesis of new phenanthridine derivatives through 1,4-dipolar cycloaddition of phenantridine,activated acetylenes,and aromatic aldehydes

A facile, one-pot synthesis of new phenanthridine derivatives by a three-component reaction between phenantridine, dialkyl acetylenedicarboxylates（DAADs）, and aromatic aldehydes is described. The reaction is characterized by mild conditions, high selectivity, and tolerance to various functional groups.     

2,4-二甲基吡咯-3,5-二羧酸二乙酯的合成——推荐一个大学有机化学实验

采用Knorr吡咯合成法，以乙酰乙酸乙酯和亚硝酸钠为原料，在醋酸和锌粉作用下采用“一锅法”得到2,4-二甲基吡咯-3,5-二羧酸二乙酯。本实验涉及到控温、回流、重结晶、熔点测定、红外光谱及核磁共振等实验操作和分析检测方法。该实验原料简单易得、产物收率高，结合波谱解析方法，可以培养和提高学生合成实验的能力，加强学生对杂环合成和波谱解析的理解与分析。     

中国XRF历史发展的相关资料征集启事

X射线荧光光谱(XRF)技术是当今最重要的无机分析技术之一,拥有无污染的独特优势,使得它在未来的"环境友好"分析实验室建设中具有广阔的发展前景。XRF仪器自1948年问世以来,已有66年的发展历史,在我国的应用研究也已经历了50多年。为记载我国XRF的历史发展,国内多家XRF实验室提议共同编写一本记载我国XRF发展历程及成果的专著。     

6×n阶矩形网络等效电阻猜想的证明

任意k×n阶电阻网络等效电阻的公式研究属于科学难题,到目前为止已经获得了当k=1,2,…,5时的5种情形下的等效电阻公式,但对k≥6时的等效电阻的普适公式仅仅作为猜想给出.本文根据建立的任意k×n阶电阻网络等效电阻研究的方法,证明了k=6时的等效电阻公式的正确性,并且给出了其无穷网络的等效电阻公式,在对比验证时得到了一些新的三角恒等式.