空间直线与平面

本单元的知识点主要有：平面的基本性质（三个公理及推论，空间图形的直观画法），线线关系（平行，异面，垂直，异面直线所成的角），线面关系（平行，相交，垂直，斜线在平面内的射影，直线和平面所成的角，三垂线定理），面面关系（平行，垂直，相交，二面角的平面角）．     

新教材中几点商榷之处

1．人教A版选修2-1P98A组第11题已知向量a，b，c是空间的一个单位正交基底，向量a＋b，a-b，c是空间的另一个基底，若向量p在基底口，b，c下的坐标为（1，2，3），求p在基底a＋b，a-b，c下的坐标．     

数列和式不等式的放缩策略

数列和式不等式的证明经常在竞赛题或试卷压轴题的最后一问出现，在思维能力和方法上要求很高，往往让人束手无策，其实，这类不等式的证明，是有章可循的，遵循什么章？就是要把和求出来，求出后再放缩，更多的情况下是不能直接求和的，这时就要先把通项放大或缩小，使得每一项按照相同的规律放大或缩小后，把和求出来，求和后再放缩，下面简述几个用来证明数列和式不等式的一般性策略。     

互补与对称——文学与数学的一个切合点

“人有悲欢离合，月有阴晴圆缺，此事古难全，但愿人长久，千里共婵娟”．这千古名句道出了：互相思念的亲人，在千里之外，共瞻一轮明月，体味着“宁静的夜晚你也思念我也思念”的离别的酸楚和憧憬着“却看妻子愁何在，漫卷诗书喜欲狂”的归乡的喜悦．把相距千里的亲人，在月光的映照下，纳入到一张图画中，遥相呼应，成为千告绝唱．“独在异乡为异客，每逢佳节倍思亲，遥知兄弟登高处，遍插茱萸少一人．”独居异乡的飘零游子，每逢佳节情何以堪？     

例谈数学中的一般化与特殊化

一般化与特殊化是人类认识事物的两个重要侧面，也是解题的两种基本策略，它们相辅相成，是辩证的统一．在多数场合，特殊问题简单、直观，容易认识，容易把握．但是，也有一些场合，特殊问题的个别特性可能会掩盖事物的本质属性，给解题带来困难，而直接求解相应的一般性问题，反而来得简便、明快、奇巧．     

他乡遇君分外亲

1983年深秋，一群已过而立之年的民办教师，怀着高考拼搏获胜后的欣喜，抖落掉满身的粉笔细末，从太行山麓的柿林，黄河两岸的竹乡，从九朝古都、二七煤城、中原油海，从殷墟之地、韩愈桑梓、岳鹏举家乡、朱载靖故里，沿着伏牛山的小径，追着红旗渠的浪花，跨过洪水上的小桥，汇聚到了一所高等师范专科学校。     

争鸣

本刊自2002年开办“争鸣”栏目以来，得到了广大读者的热情支持，提出了不少好的问题，本刊表示衷心感谢!为了进一步办好“争鸣”栏目，繁荣教学研究的大好局面，尽量避免在一些具体问题上因自然语言方面的歧义而导致的争论不清，本刊除了希望广大读者继续大力支持本刊，提供有关教学上的具体问题之外，还特别希望就一些大的方面也提出自己的问题，开展百家争鸣，如教学思想、理念、观点，对新课标、新教材、素质教育与高考等的不同意见，通过探讨，各抒己见，防止一种倾向掩盖另一种倾向，推动新一轮课改健康、深入地开展．     

由一道高考数学题引发的探究与思考

高考题具有很强的代表性和示范性，对高考题进行深入地探索，挖掘其潜在的价值，对其变式引伸，能有效地避免陷入“题海”战术，减负增效，也有利于调动学生学习的积极性、主动性，改善师生关系，激发创造活力，提高思维的灵活性与实效性，是习题教学中不可忽视的隐性资源．     

顾准的饭碗与理想

顾准（1915—1974），字哲云，上海人，中国当代学者，思想家，经济学家，会计学家。顾准被称为“有三个大脑的人”，用易中天的话说，“惟其思绪敏捷聪颖，才能在建国初期的大上海身兼数职，也才能在当学徒、当教授、当领导时，都先走一步，高人一筹。”     

基于巴斯卡数据成败型元件串联系统可靠性经典精确置信限

设Ａ为由Ｋ个相互独立的成败型元件组成的串联系统，第ｉ个元件的可靠性ｐｉ，ｐｉ未知，ｉ＝１，２，…，Ｋ．设对第ｉ个元件，对于给定的ｍｉ，有ｎｉ个巴斯卡试验数据：Ｘｉ１，Ｘｉ２，…，Ｘｉｎｉ，其中Ｘｉｊ表示对第ｉ个元件进行试验，试验进行到ｍｉ次成功时所需要的试验次数ｊ＝１，２，…，ｎｉ，ｉ＝１，２，…，Ｋ．记Ｔｉ＝Ｘｉ１＋Ｘｉ２＋…＋Ｘｉｎｉ，ｉ＝１，２，…，ｋ．本文研究基于统计量（Ｔ１，Ｔ２，…，Ｔｋ）求串联系统Ａ的可靠性经典精确最优置信下限．     

Algebraic Topology for Minimal Cantor Sets

It will be shown that every minimal Cantor set can be obtained as a projective limit of directed graphs. This allows to study minimal Cantor sets by algebraic topological means. In particular, homology, homotopy and cohomology are related to the dynamics of minimal Cantor sets. These techniques allow to explicitly illustrate the variety of dynamical behavior possible in minimal Cantor sets. submitted 20/07/05, accepted 18/10/05     

A recognition algorithm for the intersection graphs of directed paths in directed trees

Consider a finite family of non-empty sets. The intersection graph of this family is obtained by representing each set by a vertex, two vertices being connected by an edge if and only if the corresponding sets intersect. The intersection graph of a family of directed paths in a directed tree is called a directed path graph. In this paper we present an efficient algorithm which constructs to a given graph a representation by a family of directed paths on a directed tree, if one exists. Also, we prove that a graph is a proper directed path graph if and only if it is a directed path graph.     

On the use of binary decision diagrams for solving problems on simple games

Simple games are yes/no cooperative games which arise in many practical applications. Recently, we have used reduced ordered binary decision diagrams and quasi-reduced ordered binary decision diagrams (abbreviated as Robdds and Qobdds, respectively) for the representation of simple games and for the computation of some power indices. In the present paper, we continue this work. We show how further important computational problems on simple games can be solved using Qobdds, viz. the identification of some key players, the computation of the desirability relation on individuals, the test whether a simple game is proper and strong, respectively, and the computation of Qobdd-representations for the sets of all minimal winning coalitions, all shift-minimal winning coalitions and all blocking coalitions, respectively. Applications of these solutions include the computation of recent power indices based on shift-minimal winning coalitions and the test for linear separability of a directed simple game.     

The Prime Spectrum of an MV-Algebra

In this paper we show that the prime ideal space of an MV-algebra is the disjoint union of prime ideal spaces of suitable local MV-algebras. Some special classes of algebras are defined and their spaces are investigated. The space of minimal prime ideals is studied as well. Mathematics Subject Classification : 03B50, 06D99.     

相容连续Domain上的序同态

首先给出相客定向极小集的概念,讨论它的性质及与相客连续Domain的关系;其次蛤出相客连续Domain基的概念,得到它的等价刻画.最后,引入了相客连续Domain上的序同态,同时研究了它的性质,并得出相应的扩张定理.     

基于最小描述交的覆盖广义粗糙集

针对Bonikowski覆盖广义粗糙集模型的不足,给出了基于最小描述史的覆盖上下近似算子.通过和Pawlak经典粗糙集以及Bonikowski的覆盖广义粗糙集比较,发现给出的覆盖上、下近似算子具有了对偶关系,并得到了相关重要性质;进一步讨论了在新定义下覆盖广义粗糙集的约简和公理化问题,丰富了覆盖广义粗糙条理论,并为覆盖广义粗糙集的应用提供了更确切的理论根据.     

Minimal cubature formulae of trigonometric degree

In this paper we construct minimal cubature formulae of trigonometric degree: we obtain explicit formulae for low dimensions of arbitrary degree and for low degrees in all dimensions. A useful tool is a closed form expression for the reproducing kernels in two dimensions.

     

Constructive Order Theory

We introduce the notion of constructive suprema and of constructively directed sets. The Axiom of Choice turns out to be equivalent to the postulate that every supremum is constructive, but also to the hypothesis that every directed set admits a function assigning to each finite subset an upper bound. The Axiom of Multiple Choice (which is known to be weaker than the full Axiom of Choice in set theory without foundation) implies a simple set‐theoretical induction principle (SIP), stating that any system of sets that is closed under unions of well‐ordered subsystems and contains all finite subsets of a given set must also contain that set itself. This is not provable without choice principles but equivalent to the statement that the existence of joins for constructively directed subsets of a poset follows from the existence of joins for nonempty well‐ordered subsets. Moreover, we establish the equivalence of SIP with several other fundamental statements concerning inductivity, compactness, algebraic closure systems, and the exchange between chains and directed sets.     

The classification of minimal matrices of size 2×q

Minimal matrices were introduced to give an algebraic characterization of sets of uniqueness, a notion of interest in Discrete Tomography. They have also been used to produce minimal summands in Kronecker products of complex irreducible characters of the symmetric group. In this paper, motivated by these two applications, we classify all minimal matrices of size 2×q.     

格蕴涵代数的区间值模糊子代数

将区间值模糊集的概念应用于格蕴涵代数,引入区间值模糊格蕴涵子代数的概念并研究它们的性质.讨论了区间值模糊格蕴涵子代数与（模糊）格蕴涵子代数之间的关系;定义了区间值模糊集的象和原象,获得了区间值模糊格蕴涵子代数的象和原象成为区间值模糊格蕴涵子代数的条件.