精彩无限，尽在智力快车

1．请问哪里的佛像最少？A．南半球B．北半球C．赤道.2．3个人3天用3桶水,9个人9天用几桶水？A．3桶B．9桶C．27桶.3．什么动物的牙齿最好？A．狼B．老虎C．老鼠.4．读完北京大学需要多久？A．一秒钟B．4年C．一辈子.5．关羽为什么比张飞死得早？A．身体虚弱B．奋战沙场C．红颜薄命。     

数学基础课是通向数学主流的门户

2007年．作者翻译T．Needham所写的《可视的复分析》（Visual Complex Analysis．Oxford Univ．Press．2006）一书．以为这是一本很好的教本．值得许多同志花一点时间读一下．译后有一些感想．因此写了一篇较长的译后记．主要思想即认为数学基础课是通向数学主流的门户．译本将由人民邮电出版社出版．现在征得出版社的同意,将这篇译后记发表于此．在发表时又作了一点补充．补写的文字放在方括号内．     

贝卡的历险日记

担心着．担心着．北风来了,冰雪的脚步近了。一切都像没睡醒的样子．昏昏然紧闭着喉。山冷冻起来了．水凉起来了太阳在地平线下躲起来了．海豹偷偷地从水里钻出来．傻傻的．胖胖的．海洋里．浮冰上．瞧去．一大片一大片满是的．坐着．漂着．打两个滚．踢几块．水．赛几趟泳．捉几回迷藏。     

CFO式经典旅游线路

财务经理人经常考虑的问题：成本，现金流．公司治理．与老板的关系．组织结构．与银行的关系．工作流程，资产管理／投资回报．上市公司．Measurement体系，财务理念．价格体系．效率，品质，产品战略．会计信息和ERP系统。而以下旅游线路为CFO量身打造。     

同分布的NA序列加权和的强大数律

讨论了同分布NA随机变量序列加权和的强大数律,所得结果推广了Z．D．Bai和P．E．Cheng及S．H．Sung的结果．     

微积分赏析漫谈

顾名思义．微积分（Calculus）是一种无穷小的算法．但是．学习微积分。除了求导数和不定积分的大量计算之外．还应该学会欣赏．本文通过lO个案例．结合中国人文情景．提供了一些欣赏微积分的角度．     

非线性摄动电报方程解的渐近理论及应用

该文研究一类具初值问题的半线性电报方程解的渐近理论，在Sobolev空间中回答了VanHorssenW．T．与VanBurghA．H．P．[1]提出的问题．     

排球的发球问题

实际问题：在排球比赛中,地运动员站在后场发球．已知：排球的直径为0．21米（规定在20．69cm至21．327cm之间）,排球场总长为18米,网高2．5米,女子网高为2．24米;为计算方便不妨取2．5米）．运动员采用跳发球的方式以水平方向发球,为了使发出的球落在界内．     

关于Fuzzy度量点式刻画的一点注记

本文中重新定义由一个点式Ｆｕｚｚｙｐ．ｑ．度量ｄ所诱导的Ｆｕｚｚｙｐ．ｑ．度量｛Ｄｒ｜ｒ＞０｝（代替［１］中的相关重域映射族）．在新的定义下，点式Ｆｕｚｚｙｐ．ｑ．（ｐ．）度量与Ｆｕｚｚｙｐ．ｐ．（ｐ．）度量之间有令人满意的──对应关系．     

Dickson多项式与差集

1998年,Maschietti用超卵形线构造了几个循环差集．R．Evans,H．D．L．Holloman, C．Krattnthaler与Qing Xiang等给出了其对应的二元序列具有良好自相关函数的简单代数证明．在本文中,证明了超卵形线与二对一映射有着紧密的联系,并且推广了Maschietti的结果．     

Creep of polymer concrete in the nonlinear region

Two polyester-based polymer concretes with various volume content of diabase as an extender and aggregate are tested in creep under compression at different stress levels. The phenomenological and structural approaches are both used to analyze the experimental data. Common features of changes in the instantaneous and creep compliances are clarified, and a phenomenological creep model which accounts for the changes in the instantaneous compliance and in the retardation spectrum depending on the stress level is developed. It is shown that the model can be used to describe the experimental results of stress relaxation and creep under repeated loading. Modeling of the composite structure and subsequent solution of the optimization problem confirm the possibility of the existence of an interphase layer more compliant than the binder. A direct correlation between the interphase volume content and the instantaneous compliance of the composite is revealed. It is found that the distinction in nonlinearity of the viscoelastic behavior of the two polymer concretes under investigation can be due to the difference in their porosity. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000.) Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 147–164, 2000.     

乡村绿色生态旅游适宜等级VIKOR评估方法

针对乡村绿色生态旅游特征,并考虑旅游者个体感受与群体效益,本文从乡村绿色生态旅游开发与适宜评级概念出发,提出乡村绿色生态旅游适宜等级VIKOR评估模型与方法。首先,从等级评估的概念与内涵出发,刻画乡村绿色生态旅游适宜评级问题,避免混淆旅游适宜评级和排序两个本质不同的问题。然后,构建乡村绿色生态旅游适宜等级评估指标及隶属函数,提出评估指标的熵权确定方法。其次,提出乡村绿色生态旅游适宜等级VIKOR评估模型与二元语义等级评估方法。最后,通过案例研究和比较分析,说明本文所提模型与方法的合理性、可行性与实用性。     

On the use of history of mathematics: an introduction to Galileo's study of free fall motion

In this paper, we report on an experimental activity for discussing the concepts of speed, instantaneous speed and acceleration, generally introduced in first year university courses of calculus or physics. Rather than developing the ideas of calculus and using them to explain these basic concepts for the study of motion, we led 82 first year university students through Galileo's experiments designed to investigate the motion of falling bodies, and his geometrical explanation of his results, via simple dynamic geometric applets designed with GeoGebra. Our goal was to enhance the students’ development of mathematical thinking. Through a scholarship of teaching and learning study design, we captured data from students before, during and after the activity. Findings suggest that the historical development presented to the students helped to show the growth and evolution of the ideas and made visible authentic ways of thinking mathematically. Importantly, the activity prompted students to question and rethink what they knew about speed and acceleration, and also to appreciate the novel concepts of instantaneous speed and acceleration at which Galileo arrived.     

不确定环境下再制造生产调度研究

针对再制造过程中存在的再制造件质量状况和加工时间不确定性调度问题,分别采用随机数和三角模糊数表示质量状况和加工时间的不确定性。在满足工序顺序、机器等限制下,将各自带有权重系数的最大完工时间和总成本之和最小值当做目标函数,构造不确定环境下再制造生产调度模糊模型且转换成确定的单目标非线性规划模型。应用多层编码遗传算法求解某个再制造子系统算例得到,决策者对于最大完工时间和总成本的重视程度不同,调度方案不同,其需要根据自身关注的重点做出决策,选择合适的调度方案。并且调度结果会受到决策者消极或积极态度的影响,态度越积极,结果越好,反之,态度越消极,结果越差,从而检验了再制造生产调度模型的正确性。希望为再制造实现产业化,规模化提供相关参考意见。     

Interpreting linear systems of equalities and inequalities. Application to the water supply problem

This paper shows how the mathematical and the engineering points of view are complementary and help to model real problems that can be stated as systems of linear equations and inequalities. The paper is devoted to point out these relations and making them explicit for the readers to realize about the new possibilities that arise when contemplating the compatibility conditions or the set of general solutions from the dual perspective. After reviewing an orthogonally based powerful algorithm to analyse the compatibility of linear systems of equations and solving them, a water supply problem is used to illustrate its mathematical and engineering multiple aspects, including the optimal statement of the problem in terms of an adequate selection and numbering of equations and unknowns, an analysis of the compatibility conditions and a physical interpretation of the general solution, together with that of each individual generators of the affine space. The possibilities of removing unknowns without altering the compatibility of the problem is also analysed. Next, the Γ‐algorithm to analyse the compatibility of linear systems of inequalities and solving them is described and then, the water supply problem is revisited adding some constraints, such as capacity limits for the pipes and retention valves, and discussed as to how they affect the resulting general solution and other aspects. Finally, some conclusions are derived. Copyright © 2005 John Wiley & Sons, Ltd.     

复杂装备研制协调超网络均衡与实现路径

复杂装备研制主体间呈现社会关系、合作关系、协调关系等网络关系,并且相互影响相互作用,其影响复杂装备研制的重要参数。为有效描述在资源环境约束下制造商和供应商的关系,探讨复杂装备研制协调机理与实现路径,本文利用超网络方法,设计了相互影响、相互作用的社会关系网络、协调网络和合作网络的复杂装备研制协调超网络,并将社会关系水平、协调度和合作水平作为超网络的3个决策变量,建立基于关系价值最大、协调成本最低、协调风险最小、合作收益最大、合作风险最小和成本最小等不同偏好下的多目标最优决策模型,构建了复杂装备研制超网络均衡模型,并利用其探讨超网络均衡和实现路径。     

网络团购环境下基于电子中介的商品交易优化模型

在网络团购环境下,如何考虑顾客、商家和电子中介三方主体的利益并实现商品交易最优化,这是一个值得关注的研究问题。本文针对基于电子中介的网络团购商品交易问题,依据商家与电子中介事先商定的团购商品的交易数量区间、交易数量折扣以及顾客和商家分别提交的商品的报价和保留价,在考虑顾客、商家和电子中介三方利益最大化的前提下,构建了多目标商品交易优化模型;进一步地,将多目标优化模型转化为单目标优化模型,并给出了求解优化模型的遗传算法。最后,通过一个算例说明了本文构建的模型及其求解算法的可行性和有效性。     

Magneto-Compound Reaction of Convective Flow via a Porous Inclined Plate with Heat Energy Absorption

The current study is concerned with the unsteady heat and mass transfer of MHD free convection flow via a porous inclined plate that accelerates exponentially with temperature and concentration. Heat emission, source/sink, radiation absorption, and reaction are taken into account in the energy and species equations. The innovative part of the work is the analysis of the flow phenomenon with a heat source or sink and radiation absorption along the chemical reaction. The governing PDEs are reduced into ODEs via the non-dimensional variables and afterward solved analytically utilizing the perturbation strategy. Graphical representations of liquid temperature, speed, and concentration as well as the Sherwood \& Nusselt quantities and the skin friction factor are displayed in tabular form for different combinations of appropriate stream quantities. The analysis of a resistance quantum grows with the size of the magnetic, whereas the rates of mass and heat transfer decline with increasing radiation, reaction, and Schmidt number. Thermal-velocity and concentration-velocity profiles interact reciprocally with the accelerating radiation, heat source, and compound reaction. The growth of speed and thermal profiles is clearly visible due to the absorption and Prandtl values. The present results are in strongly consistent with the earlier published results. There are numerous applications for this research in many sectors and material processing for understanding drag in seepage flows on heated/cooled and inclined surfaces.     

激光辐照下圆薄板的动态屈曲研究

对强激光辐照下薄板（铜片）的动态热失稳过程进行了分析，得出了简支圆薄板在热冲击下发生的屈曲及后屈曲过程，并给出了临界激光功率密度与薄板厚径比的关系曲线，方法计入了温度分布、惯性项和缺陷大小对于失稳过程的影响。这一工作有利于人们对强激光引起的硬目标破坏机理的认识。     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].