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。     

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。     

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．     

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．     

面积法解题例说

二、基本性质 1．同(等)底等(同)高的两个三角形面积相等．2．同(等)底的两个三角形面积的比等于高的比．3．同(等)高的两个三角形面积比等于底的比．4．两个相似三角形面积的比等于相似比的平方．     

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．     

白骨化尸体死亡时间的推断

本文分析了15具白骨化尸体标本的股骨汞(Hg),铅(Pb),镉(Cd)元素含量数据,在三年的时间内采集了3次,一共收集到45个数据。首先将这组数据看着纵向数据,利用线性随机效应混合模型、Cox随机混合效应模型进行分析,结果显示,如果对每个白骨化尸体标本建立线性模型,可以精确预测出死亡时间,而且不需要采集铅元素含量数据。混合效应模型的预测效果也很好,最大误差不会超过1个月。其次我们对数据不作任何假设,利用机器学习中随机森林方法分析数据,并利用5折交叉验证方法来判断结果的可靠性,训练集和测试集的NMSE分别为0.1205944,0.5604286,因此可以用训练出的模型来预测死亡时间。     

有资格限制的指派问题的求解方法

在实际的指派工作中，常会遇到某个人有没有资格去承担某项工作的问题，因此，本建立了有资格限制的指派问题的数学模型。在此数学模型中，将效益矩阵转化为判定矩阵，由此给出了判定此种指派问题是否有解的方法；在有解的情况下，进一步将效益矩阵转化为求解矩阵，从而将有资格限制的指派问题化为传统的指派问题来求解。最后给出了一个数值例子来说明这样的处理方法是有效的。     

Modelling and analysis of dynamics of viral infection of cells and of interferon resistance

Interferons are active biomolecules, which help fight viral infections by spreading from infected to uninfected cells and activate effector molecules, which confer resistance from the virus on cells. We propose a new model of dynamics of viral infection, including endocytosis, cell death, production of interferon and development of resistance. The novel element is a specific biologically justified mechanism of interferon action, which results in dynamics different from other infection models. The model reflects conditions prevailing in liquid cultures (ideal mixing), and the absence of cells or virus influx from outside. The basic model is a nonlinear system of five ordinary differential equations. For this variant, it is possible to characterise global behaviour, using a conservation law. Analytic results are supplemented by computational studies. The second variant of the model includes age-of-infection structure of infected cells, which is described by a transport-type partial differential equation for infected cells. The conclusions are: (i) If virus mortality is included, the virus becomes eventually extinct and subpopulations of uninfected and resistant cells are established. (ii) If virus mortality is not included, the dynamics may lead to extinction of uninfected cells. (iii) Switching off the interferon defense results in a decrease of the sum total of uninfected and resistant cells. (iv) Infection-age structure of infected cells may result in stabilisation or destabilisation of the system, depending on detailed assumptions. Our work seems to constitute the first comprehensive mathematical analysis of the cell-virus-interferon system based on biologically plausible hypotheses.     

Convergence of densities of some functionals of Gaussian processes

The aim of this paper is to establish the uniform convergence of the densities of a sequence of random variables, which are functionals of an underlying Gaussian process, to a normal density. Precise estimates for the uniform distance are derived by using the techniques of Malliavin calculus, combined with Stein?s method for normal approximation. We need to assume some non-degeneracy conditions. First, the study is focused on random variables in a fixed Wiener chaos, and later, the results are extended to the uniform convergence of the derivatives of the densities and to the case of random vectors in some fixed chaos, which are uniformly non-degenerate in the sense of Malliavin calculus. Explicit upper bounds for the uniform norm are obtained for random variables in the second Wiener chaos, and an application to the convergence of densities of the least square estimator for the drift parameter in Ornstein–Uhlenbeck processes is discussed.     

碾压混凝土坝施工层面变形分析模型

针对碾压混凝土坝施工层面对大坝变形产生显著影响的问题,深入研究了施工层面的变化性质及规律,提出了层面不同阶段变形的模拟方法,建立了施工层面有厚度和无厚度分析模型,提出的模型能反映层面的弹性变形、衰减蠕变、不可逆变形以及加速蠕变等变形状态．实例分析表明:所提出的碾压混凝土坝施工层面有厚度和无厚度分析模型能较客观地模拟大坝的结构变化形态,尤其是施工层面有厚度分析模型较完整地模拟了层面的渐变规律,其计算结果与原位监测成果吻合较好．同时,提出的方法和建立的分析模型可推广应用于常规混凝土坝,特别是坝基内断层和夹层等变形规律的分析．     

Variational analysis of functions of the roots of polynomials

The Gauss-Lucas Theorem on the roots of polynomials nicely simplifies the computation of the subderivative and regular subdifferential of the abscissa mapping on polynomials (the maximum of the real parts of the roots). This paper extends this approach to more general functions of the roots. By combining the Gauss-Lucas methodology with an analysis of the splitting behavior of the roots, we obtain characterizations of the subderivative and regular subdifferential for these functions as well. In particular, we completely characterize the subderivative and regular subdifferential of the radius mapping (the maximum of the moduli of the roots). The abscissa and radius mappings are important for the study of continuous and discrete time linear dynamical systems. Dedicated to R. Tyrrell Rockafellar on the occasion of his 70th birthday. Terry is one of those rare individuals who combine a broad vision, deep insight, and the outstanding writing and lecturing skills crucial for engaging others in his subject. With these qualities he has won universal respect as a founding father of our discipline. We, and the broader mathematical community, owe Terry a great deal. But most of all we are personally thankful to Terry for his friendship and guidance. Research supported in part by the National Science Foundation Grant DMS-0203175. Research supported in part by the Natural Sciences and Engineering Research Council of Canada. Research supported in part by the National Science Foundation Grant DMS-0412049.     

On Sums of Coefficients of Products of Polynomials

We study the nilpotency of the sums of all coefficients of some sorts of products of polynomials over reversible, IFP, and NI rings, and introduce an SCN ring as a generalization. We characterize SCN rings in relation with related ring properties, and also provide several useful properties and ring extensions of SCN rings.     

Analytic description of statistics of spectra of quantum graphs

We discuss how to obtain exact and approximate distributions for various statistical characteristics of the spectra of quantum graphs using previously found exact solutions of the spectral problem. We indicate the relation between the appearing spectral decompositions and the theory of weakly dependent random variables and indicate the relation between the known limit theorems for trigonometric sums and the universal statistical properties of the spectra of quantum chaotic systems. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 1, pp. 38–66, July, 2008.     

Classification of pairs of natural quadrics from the point of view of Laguerre geometry

The problem of classification of pairs of natural quadrics (spheres, circular cones and circular cylinders) arises in problems such as the blending of two or more natural quadrics using canal surfaces. In this paper, considering this problem from the point of view of Laguerre geometry, we reduce it to the classification of point/line and line/line pairs in the pseudo-Euclidean space with Lorenz metrics. We establish equations of the surfaces of centers for all canonical positions and their projective equivalence with toric surfaces.__________Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 1, pp. 64–83, January–March, 2005.Translated by M. Kazakeviit     

一类柔性臂机器人的稳定性

本文研究了一类柔性臂机器人的控制问题,且柔性臂的弯曲振动与扭转振动的耦合作用表现在边界方程中。本文运用算子谱理论、算子半群理论等,得到系统的主算子生成的C0-半群的具体表示式,并证明了半群的解析性、非紧性及非一致指数稳定性。