高考数学“思想实验”中的若干关键词

除有形实验(physical experi ments)外,还有在较高理智水平上使用的其他实验,即思想实验(thought experi ments).而在数学中的实验是在想象中做的,是设想着做的,是在思想中进行的实验[1].显然,这种实验乃是在头脑中进行的抽象     

揭示问题内隐谨防以假乱真

在数学问题中,或在解决数学问题的过程中,如果包含了没有直接言明但又确实存在的事实,那么我们称这个事实为问题内隐．在教学中经常发现,同学们在解决某些数学问题时,由于忽视问题内隐的存在,从而导致解题过程的失误．本文拟例举此类失误的几种常见情形,以资同学们在学习中参考．     

Interval DEA模型中决策单元的投影问题

在传统的DEA模型中,最优相对效率模型是在不大于1的范围内研究决策单元的效率的,最差相对效率模型是在不小于1的范围内研究决策单元的效率,这两种模型在研究投影问题时,是在不同的范围内进行的,有一定的片面性.将在interval DEA模型中,研究决策单元的投影问题,该模型是在相同的约束域内研究最优和最差相对效率模型,得出的结论将更加全面,通过两个定理给出了非DEA有效的决策单元在DEA有效面上的投影表达式和非DEA无效的决策单元在DEA无效面上的投影表达式.同时,通过一个实例对决策单元在interval DEA模型中的投影结果与在传统的DEA模型的投影结果进行了比较,发现投影结果比传统模型得到的投影结果对实际的生产有更强的指导意义.     

关注数学活动 提升数学素养——以《勾股定理》应用为例

在新课程的指导下,数学教学中越来越关注学生数学综合实践能力的培养,基于此,在教学中可以开展一些拓展性课程,多让学生参加一些数学活动,让学生在活动中发现,在发现中探究,在探究中解决,在解决中积累,进而培养学生发现问题、提出问题、分析问题和解决问题的能力,以此促进学生综合能力和数学素养不断提升.     

让数学课堂教学行走在生活的道路上——《向量加法》教学案的设计示例

新课程改革的背景下,学生想要的是:自由遨游在数学的天空中,自由呼吸在数学的花园里,自由徜徉在数学的长廊里.在数学的天空里,飞翔着生动,闪烁着鲜活,蕴育着智慧,然而,数学的抽象与逻辑就像一堵墙,在定格数学的同时,也凝固了人们对数学的兴趣.怎么办?……答案无他:实现数学的生活化,让数学课堂教学行走在生活的道路上.一、导入新课要实现"生活化"很多老师在教学过程中对导入新课环节不是很重视,其实中学课堂教学的导入新课环节,是整个课堂教学中不可缺少的     

基于学科素养的思辨教学策略

数学作为基础学科,其地位不言而喻.要充分发挥其学科价值就要在数学教学中打破“照本宣科”的“灌输”式讲授,引导学生站在更高的角度去审视问题,审视数学,为此,在教学中要努力提高学生的思辨能力,以此活跃思维,发展思维,让思维在发展中优化,在优化中完善,促进数学素养全面提升.     

财务人员的“投资观”

如今,企业在市场上的竞争日趋惨烈。这样的竞争不仅仅是在商品市场层面的竞争,而是逐步渗透到企业经营活动的各个环节中。在激烈的竞争中,企业要想胜出,就需要不断提升自身的投入产出比,而财务管理在其中扮演着至关重要的角色,因此,财务人员要与时俱进,要形成与企业一致的“投资观”。     

利用位似图形解作图题一例

位似图形所有对应点的连线所在直线相交于一点,这一交点或在两图形的同侧,或在两图形之间,或在图形之内,或在图形的边上及顶点上,利用这一性质可以解决某些作图问题.     

浅谈高中数学的类比方法

世界万物总在不断变化、完善着,数学知识亦不例外.对诸多数学知识的理解在深化,应用在优化,有诸多数学命题在延伸、拓广,在这些变化过程中“类比”有着它独特的功效.     

活用课本方法解题

数学思想和方法是数学知识在更高层次上的概括和抽象 ,它蕴藏在数学知识的发生、发展和应用的过程中 ,中学数学的许多数学思想方法蕴含在课本的例题、习题中 ,蕴藏在公式、定理的推导过程中 ,蕴含在概念、定义的形成过程中 ,而我们学生常会忽视蕴含在课本中的方法 ,从而不能灵活应用课本中方法解题 ,本文试着挖掘蕴含在课本中的一些方法 ,从而引起大家的共鸣 !一、本末倒置在解决某些问题时可以变换思维视角 ,突破常规的做法 ,来个“本末倒置” .例 1　已知函数 f(x) =14 x+2 　x1 ,x2 ∈R与x1+x2 =1时 ,f(x1 ) +f(x2 ) =12 　设an=f(0 ) +…     

旋转抛物面的新定义及其性质

从点的轨迹的角度,将R<'3>中的旋转抛物面定义为:R<'3>中到一定点与到一定平面(点不在平面上)距离相等的点的轨迹.同时引入旋转抛物面的焦点、准平面、准线等概念,并在此基础上证明关于旋转抛物面的焦点弦、准平面、顶点、对称轴、切平面之间的若干重要性质.     

基于模糊FNN-ELECTRE法的国有商业银行竞争力评价

随着金融业全方位开放,国有商业银行已成为国家经济命脉的核心,其竞争力强弱关系着国家经济的繁荣与衰退。本文基于模糊FNN-ELECTRE方法建立国有商业银行竞争力评价模型,以因素神经网络理论(FNN)与ELECTRE融合方法为基础,以现有商业银行竞争力评价指标为着眼,把国有商业银行竞争力的评价体系从现实竞争力和潜在竞争力两个因素抽取为一级指标,以规模、质量、业务结构、效率、成长性五个因素设为二级指标。从实证的角度对银行A、银行B、银行C、银行D、银行E五大国有银行进行分析验证,对其属性值进行和谐性与非和谐性检验得出,银行B竞争能力最强,银行E竞争能力最弱,五大国有银行均有改进空间。     

网络优化中一个组合问题的探讨

文[4]提出了网络优化中若干有待解决的组合问题，本文围绕其中之一“减小直径问题”进行了探讨．设P（n，t）表示长为n的路径增加t条边后所得图直径的最小值，C（n，t）表示长为n的圈增加t条边后所得回直径的最小值．本文取得如下进展：1）给出P（n，2），P（n，3）及C（n，2）的精确值，并得出P（n，4）的一更精细的上界及一种更好的加边方式．上述结果均满足小极大度原则．2）在有极大度限制的条件下，分别对t为偶数和奇数给出了P（n，t）的上界．     

Moment information for probability distributions,without solving the moment problem,II: Main-mass,tails and shape approximation

How much information does a small number of moments carry about the unknown distribution function? Is it possible to explicitly obtain from these moments some useful information, e.g., about the support, the modality, the general shape, or the tails of a distribution, without going into a detailed numerical solution of the moment problem? In this, previous and subsequent papers, clear and easy to implement answers will be given to some questions of this type. First, the question of how to distinguish between the main-mass interval and the tail regions, in the case we know only a number of moments of the target distribution function, will be addressed. The answer to this question is based on a version of the Chebyshev–Stieltjes–Markov inequality, which provides us with upper and lower, moment-based, bounds for the target distribution. Then, exploiting existing asymptotic results in the main-mass region, an explicit, moment-based approximation of the target probability density function is provided. Although the latter cannot be considered, in general, as a satisfactory solution, it can always serve as an initial approximation in any iterative scheme for the numerical solution of the moment problem. Numerical results illustrating all the theoretical statements are also presented.     

Formulation of linear problems and solution by a universal machine

Using the predicate language for ordered fields a class of problems referred to aslinear problems is defined. This class contains, for example, all systems of linear equations and inequalities, all linear programming problems, all integer programming problems with bounded variables, all linear complementarity problems, the testing of whether sets that are defined by linear inequalities are semilattices, all satisfiability problems in sentenial logic, the rank-computation of matrices, the computation of row-reduced echelon forms of matrices, and all quadratic programming problems with bounded variables. A single, one, algorithm, to which we refer as theUniversal Linear Machine, is described. It solves any instance of any linear problem. The Universal Linear Machine runs in two phases. Given a linear problem, in the first phase a Compiler running on a Turing Machine generates alinear algorithm for the problem. Then, given an instance of the linear problem, in the second phase the linear algorithm solves the particular instance of the linear problem. The linear algorithm is finite, deterministic, loopless and executes only the five ordered field operations — additions, multiplications, subtractions, divisions and comparisons. Conversely, we show that for each linear algorithm there is a linear problem which the linear algorithm solves uniquely. Finally, it is shown that with a linear algorithm for a linear problem, one can solve certain parametric instances of the linear problem.Research was supported in part by the National Science Foundation Grant DMS 92-07409, by the Department of Energy Grant DE-FG03-87-ER-25028, by the United States—Israel Binational Science Foundation Grant 90-00434 and by ONR Grant N00014-92-J1142.Corresponding author.     

基于共同配送的快递企业末端服务网点定价博弈研究

在末端共同配送背景下,以快递共配联盟为研究对象,建立了分散决策和集中决策的定价博弈模型。对分散决策情景考虑了固定支付、按件支付、收益共享、服务水平补偿、收益共享与成本共担五种不同的利润分配方法。在构建模型时,考虑了快递员提成比例、同行竞争、服务水平、宣传水平对需求和成本的影响,给出了快递企业与合作企业的最佳决策。最后,分析在不同模式下联盟的服务水平、价格、利润变化。结果显示,集中决策下联盟的总利润最高,分散决策下使用收益共享与成本共担模式最佳。     

关于药物对小鼠肝脏细胞色素P-450含量的影响实验结果的分析

肝药酶诱导剂苯巴比妥能诱导细胞色素P-450的合成,而肝药酶抑制剂放线菌素D能抑制细胞色素P-450的合成,本实验应用示差光谱法对P-450含量加以测定.本文改进了传统的计算药后诱导组和抑制组P-450含量增加或减少的百分比来评价药物的方法,在M athem atica数学软件环境下,对数据进行方差分析和t检验,提高了数据处理精度和可信度.并对原方法表示怀疑.     

Sustainable SC through the complete reprocessing of end-of-life products by manufacturers: A traditional versus social responsibility company perspective

Every item produced, transported, used and discarded within a Supply Chain (SC) generates costs and creates an impact on the environment. The increase of forward flows as effects of market globalization and reverse flows due to legislation, warranty, recycling and disposal activities affect the ability of a modern SC to be economically and environmentally sustainable. In this context, the study considers an innovative sustainable closed loop SC problem. It first introduces a linear programming model that aims to minimize the total SC costs. Environmental sustainability is guaranteed by the complete reprocessing of an end-of-life product, the re-use of components, the disposal of unusable parts sent directly from the manufacturers, with a closed loop transportation system that maximizes transportation efficiency. Secondly, the authors consider the problem by means of a parametrical study, by analyzing the economical sustainability of the proposed CLSC model versus the classical Forward Supply Chain model (FWSC) from two perspectives: Case 1, the ‘traditional company perspective’, where the SC ends at the customers, and the disposal costs are not included in the SC, and Case 2, the ‘social responsibility company perspective’, where the disposal costs are considered within the SC. The relative impact of the different variables in the SC structure and the applicability of the proposed model, in terms of total costs, SC structure and social responsibility, are investigated thoroughly and the results are reported at the conclusion of the paper.     

常微分算子谱的定性分析

本文对常微分算子谱的定性分析的若干问题做一综合性的概要介绍。着重介绍研究谱的定性分析的主要途径和研究方法；讨论谱的离散性判别准则及其发展和推广，列举一些在方法上有代表性的结论。