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）．     

学珠算 三字文（经）

学珠算，意义深，古文化，要继承，为四化。方向明。打算盘，并不难，明算理，懂算法，经常练。     

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．     

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。”     

关于方程xy+yz+zx=n的正整数解

本文在广义Ｒｉｅｍａｎｎ猜想成立的条件下证明了：当且仅当正整数ｎ＝１，２，４，６，１０，１８，２２，３０，４２，５８，７０，７８，１０２，１３０，１９０，２１０，３３０，４６２时，方程ｘｙ＋ｙｚ＋ｚｘ＝ｎ无正整数解（ｘ，ｙ，ｚ）．     

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．     

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。     

斐波那契数列研究性学习一例

新教材数学第五册P32阅读材料介绍了斐波那契数列：1，1，2，3，5，8，13，21，34，55，89，…．     

巧用柯西不等式的变式解一类分式问题

我们知道柯西不等式：设a1，a2，a3，…，an和b1，b2，b3，…，bn是给定的实数，则     

如何上好数学基础课

本文就如何上好数学基础课，谈一些个人感受，欢迎批评指正．1教学目标教学的目标至少应包含以下三个．第一，传授知识．教师应将书本知识讲活，讲透，使学生易于接受，便于掌握，使学生兴趣盎然，乐于接受；第二，培养学生的学习能力．授人以鱼，不如授人以渔．教师应培养学生的读书能力，动手能力，使他们善于获取新的知识；第三，培养学生的探索未知的方法和能力，     

矩阵乘法的推广及运用

利用矩阵的Kronecker积定义了一种矩阵乘积"*积",并且对这种乘积的性质进行了研究,发现它对于任意两个矩阵都有意义而且具有通常矩阵乘积的所有性质,并且在一些特殊情况下它比通常的矩阵乘积更和谐对称,而且当在"合适维数"下它就是通常的矩阵乘积,所以可以把这种"*积"看作是对通常矩阵乘积的推广.     

Comparative study of Mixed product and quaternion product

Mixed number is the sum of a scalar and a vector. The quaternion can also be written as the sum of a scalar and a vector but the product of mixed numbers and the product of quaternions are different. Here we studied the Mixed product which is derived from the product of mixed numbers and the quaternion product which is derived from the product of quaternions. It was observed that Mixed product is more consistent with Physics than that of quaternion product.     

The generalized hierarchical product of graphs

A generalization of both the hierarchical product and the Cartesian product of graphs is introduced and some of its properties are studied. We call it the generalized hierarchical product. In fact, the obtained graphs turn out to be subgraphs of the Cartesian product of the corresponding factors. Thus, some well-known properties of this product, such as a good connectivity, reduced mean distance, radius and diameter, simple routing algorithms and some optimal communication protocols, are inherited by the generalized hierarchical product. Besides some of these properties, in this paper we study the spectrum, the existence of Hamiltonian cycles, the chromatic number and index, and the connectivity of the generalized hierarchical product.     

Certain free products of operator spaces

Certain free products are introduced for operator spaces and dual operator spaces. It is shown that the free product of operator spaces does not preserve the injectivity. The linking C*-algebra of the full free product of two ternary rings of operators (simply, TRO's) is *-isomorphic to the full free product of the linking C*-algebras of the two TRO's. The operator space-reduced free product of the preduals of von Neumann algebras agrees with the predual of the reduced free product of the von Neumann algebras. Each of two operator spaces can be embedded completely isometrically into the reduced free product of the operator spaces. Finally, an example is presented to show that the C*-algebra-reduced free product of two C*-algebras may be contractively isomorphic to a proper subspace of their reduced free product as operator spaces.     

技术不确定环境下新产品策略的设计应用

技术的动态发展和企业间的竞争对企业新产品策略有很大影响,直接决定新产品的引进周期。本文在产业技术动态变化的随机环境下构建随机动态规划模型,关注产业技术进步、投资成本和产品市场竞争等影响因素,探讨企业进行新产品引进的周期选择,对新产品引进的周期和质量决策进行方法设计和应用举例。利用随机动态规划模型得出新产品引进的最优时间周期,用算例分析技术进步和产品研发成本对企业引进周期策略的影响,采取策略迭代的方法进行求解,发现技术进步较快时企业的新产品引进步伐也较快,研发成本的提高使企业的新产品引入步伐降低。     

Understanding the impacts of product knowledge and product type on the accuracy of intentions-based new product predictions

New product development involves several critical decisions. A key decision making area in new product development is the evaluation of the viability and the market potentials of a new product. In the absence of any relevant historical data, companies ask the potential buyers of their products about their intentions to buy those products when assessing their viability. Despite the popularity of the use of behavioral intentions in predicting the market acceptance of new product ideas, both survey and empirical studies suggest that the accuracy of such predictions is usually very low. Although earlier case-based studies suggest that a number of factors can affect the quality of new product decisions, it is still empirically unclear how product knowledge and the type of new products might impact the predictive accuracy of intentions-based new product forecasting. This study utilized a longitudinal research design and empirically tested the hypotheses across two new products. The study first collected purchase intentions data about the new products. Second, it collected subsequent actual purchase data about the new products. The results of series of hierarchical regression analyses comparing the initial purchase intentions and subsequent actual behaviors showed that while product knowledge is positively related to the predictive accuracy and consistency of intentions-based new product forecasting, product type is negatively related to them.     

Function spaces and product topologies on powers of spaces

A study is made of two classes of product topologies on powers of spaces: the general box product topologies, and the general uniform product topologies. Some examples are given and some results are shown about the properties of these general product spaces. This is applied to show that certain spaces of continuous functions with the fine topology are homeomorphic to box product spaces, and certain spaces of continuous functions with the uniform topology are homeomorphic to uniform product spaces.     

基于产品平台的多目标供应商预选方法研究

由于供应商选择问题直接影响着企业的最终收益, 所以它对企业来说一直是一个重要的决策问题. 在以往的研究中, 供应商选择仅仅是从产品零部件的角度去考虑而没有从产品的整体出发. 此外, 传统的供应商选择都是发生在产品设计阶段之后的产品生产阶段. 然而, 在产品设计初期考虑供应商选择问题可以有效地避免合适供应商的短缺问题. 提出了一个基于产品平台的多目标供应商预选方法, 并在产品设计初期从产品整体角度建立了一个以最小化产品族外包成本、最小化产品族生产风险以及最小化供应商供应时间为多目标的优化模型, 从而有助于决策者在产品开发的早期对产品整体设计方案进行改善. 此外, 由于产品平台存在部件共享问题, 因此在优化模型中也考虑了部件共享对供应商预选结果的影响. 采用非支配排序遗传算法(NSGA-II)对优化模型进行求解, 并通过实际案例来说明提出的优化方法以及求解算法的合理性和有效性.     

成品油调合优化模型及其应用研究

为了提高炼油厂制定成品油调合方案的科学性。研究建立成品油调合优化问题的非线性规划模型。首先从不同的层次，分析提出炼油厂成品油调舍工作的三类优化问题；其次，研究给出三类成品油调合优化问题的非线性规划模型形式；再次，针对成品油调合优化模型形式的特点，提出相应的求解技术；最后，通过在某炼油厂的一个应用实例验证上述成品油调合优化模型的有效性。     

On optimizing edge connectivity of product graphs

This work studies the super edge connectivity and super restricted edge connectivity of direct product graphs, Cartesian product graphs, strong product graphs and lexicographic product graphs. As a result, sufficient conditions for optimizing the edge connectivity and restricted edge connectivity of these graphs are presented.