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。     

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．     

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．     

学校体育的困局与破局——在天津市学校体育工作会议上的报告

一、缘起我校2009届高三有20个班级,笔者连续三年施教（20）班的数学．2009年高考,我班文科数学均分127．8,理科数学均分112．6（2009届学校实行高三“加一”学科走班制,数学在同一个班级文理并存）,均为全区第一,分别超校平均18．8和11．6分,超市平均33．1和19．9分;超市实验性示范性高中平均分12．7和7．8分．个中原因,值得回味．     

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．     

HERM ITE-FEJR TYPE INTERPOLATION OF HIGHER ORDER

§１ＬｅｔＸｖ＝｛ｘｎｋ,ｙｎμ｝ｂｅａｍａｔｒｉｘｏｆｎｏｄｅｓｓａｔｉｓｆｙｉｎｇ－１≤ｘｎ１＜ｘｎ２＜．．．＜ｘｎｎ≤１,　－１≤ｙｎ１＜ｙｎ２＜．．．＜ｙｎｌ≤１,ｘｎｋ≠ｙｎμ,ｋ＝１,．．．,ｎ,μ＝１,．．．,ｌ,ｎ≥１,ｌｖ＝ｌ（ｎ）≥０（１）　　Ｆｏｒｓｉｍｐｌｉｃｉｔｙｗｅｓｈａｌｌｏｆｔｅｎｏｍｉｔｔｈｅｓｕｐｅｒｆｌｕｏｕｓｎｏｔａｔｉｏｎｓ．ＤｅｆｉｎｅｂｙＰｎｔｈｅｓｅｔｏｆｐｏｌｙｎｏｍｉａｌｓｏｆｄｅｇｒｅｅ≤ｎ．Ｎｏｗｆｏｒａｎａｒｂｉｔｒａｒｙｆｉｘｅｄｉｎｔ…     

到复Grassmann流形的多重调和映照的构造

本文给出了一些到复Ｇｒａｓｓｍａｎｎ流形的多重调和映照的构造定理,从而推广了莫小欢,Ｂｕｒｓｔａｌｌ　Ｆ． Ｅ．,Ｗｏｏｄ Ｊ． Ｃ．和 Ｕｄａｇａｗａ Ｓ．的结果．     

关于矩阵特征值问题向后误差分析的注记

本文研究实矩阵关于复近似特征对的范数型向后误差．在复扰动情形,这个问题已被Higham 等学者解决．本文研究实扰动情形．结果表明,通常情况下,两种情形差别不大,但在某些情形,二者可以相差很大．作为推广,我们还讨论了矩阵多项式的相应问题．文中的一个结果部分地解决了D．J．Higham和N．J．Higham 1999年提出的一个待解决的问题．     

极大η-单调集值映射的一个性质

本文着重研究了在什么条件下集值映射I λT的值域是全空间Rn这一问题,其中I是恒等映射,λ>0是任意给定的常数,T是一个极大η-单调的集值映射．文中主要结果部分地解决了C．-H．Lee,Q．H．Ansari和J．-C．Yao在2000年提出的一个公开问题．此外,针对真下半连续泛函的η-次微分映射,也讨论了上述问题．     

Wave parameter identification problem for ocean test structure data,part 2, discrete formulation

This paper deals with the solution of the wave parameter identification problem for ocean test structure data. A discrete formulation is assumed. An ocean test structure is considered, and wave elevation and velocities are assumed to be measured with a number of sensors. Within the frame of linear wave theory, a Fourier series model is chosen for the wave elevation and velocities. Then, the following problem is posed: Find the amplitudes of the various wave components of specified frequency and direction, so that the assumed model of wave elevation and velocities provides the best fit to the measured data. Here, the term best fit is employed in the least-square sense over a given time interval.At each time instant, the wave representation involves four indexes (frequency, direction, instrument, time); hence, four-dimensional arrays are required. This formal difficulty can be avoided by switching to an alternative representation involving only two indexes (frequency-direction, instrument-time); hence, standard vector-matrix notation can be used. Within this frame, optimality conditions are derived for the amplitudes of the assumed wave model.A characteristic of the wave parameter identification problem is that the condition number of the system matrix can be large. Therefore, the numerical solution is not an easy task and special procedures must be employed. Specifically, Gaussian elimination is avoided and advantageous use is made of the Householder transformation, in the light of the least-square nature of the problem and the discretized approach to the problem.Numerical results are presented. The effect of various system parameters (number of frequencies, number of directions, sampling time, number of sensors, and location of sensors) is investigated in connection with global or strong accuracy, local or weak accuracy, integral accuracy, and condition number of the system matrix.From the numerical experiments, it appears that the wave parameter identification problem has a unique solution if the number of directions is smaller than or equal to the number of sensors; it has an infinite number of solutions otherwise. In the case where a unique solution exists, the condition number of the system matrix increases as the size of the system increases, and this has a detrimental effect on the accuracy. However, the accuracy can be improved by proper selection of the sampling time and by proper choice of the number and location of the sensors.Generally speaking, the computations done for the discrete case exhibit better accuracy than the computations done for the continuous case (Ref. 5). This improved accuracy is a direct consequence of having used advantageously the Householder transformation and is obtained at the expense of increased memory requirements and increased CPU time.This work was supported by Exxon Production Research Company, Houston, Texas. This paper is based partly on Refs. 1–4.     

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。     

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.     

A double-stage piecewise recursive filter for real-time applications

This paper examines the basic problem of estimating the state of a system described by a set of dynamical equations. The state estimation is performed by means of optimal filtering techniques in which the state observation is given by a set of nonlinear equations.The basic issue encountered in most engineering problems is the availability of more observable information than the processor can effectively process in real-time, while performing full optimal filtering on all available observable data. To alleviate this deficiency, an algorithm is developed in which the rate of information processing is kept at a high value, while the system statistics are evaluated at a much slower rate.The method utilizes a combination of fast and slow filtering loops, in which the observable data are processed at a high rate during the fast loop, while the system error covariance, gain computations, and all other system statistics are processed at a lower rate in the slow loop. Methods are provided to resolve any incompatibility in the system statistics resulting from this fast-loop/slow-loop processing combination.Applications describing problems pertaining to aircraft navigation are presented. Specifically, applications to aircraft navigation through a satellite network are studied. Appropriate simulation results from the above studies are shown.This work was performed under contract with the Department of the Air Force, Space and Missile Organization (SAMSO), Los Angeles, California, Contract No. F04-701-75-C-0180.The authors are indebted to Dr. C. Johnson, GPS System Engineer, Mr. G. Consolver, GPS Software Manager, and Mr. W. Riley, Communications/Navigation Department, Texas Instruments for their continuous encouragement in the course of this work. Also, they are indebted to Major M. Birnbaum, SAMSO, for his constructive criticism on the conceptual design of this work, and to Mr. A. Bierman, Aerospace Corporation, for kindly providing simulation data of aircraft trajectories. Finally, the authors would like to express their gratitude to Dr. N. Carlson, Intermetrics, for valuable consultation during the progress of this work.Portions of this paper were presented by the senior author at the GSP Conference, Plan 76, IEEE Position, Location, and Navigation Symposium, San Diego, California, 1976.     

考虑成本、等待时间和安全水平的分类安检模式研究

近年来,随着民航机场旅客吞吐量快速增加,机场安检部门的工作压力正不断加大,旅客等待时间也正在逐渐增加。针对该问题,引入了分类安检模式。然而,分类安检模式通常需要额外的投资成本,可能会产生较大的财务负担。因此,以成本为目标,综合考虑旅客等待时间和安全水平的要求,研究了分类安检模式和传统安检模式的比较以及最优决策性质等相关问题。首先,考虑安全水平和旅客等待时间的约束,分别为传统安检模式和分类安检模式建立了模型,并分析了其最优运营决策性质。其次,从成本的角度,对两种安检模式做了比较研究。研究结果表明,当旅客数量多、安检犯错容忍度较高或旅客等待敏感时,分类安检模式比传统安检模式表现更优;反之,传统安检模式更优。此外,在分类安检模式中,分配到高风险安检通道的旅客比例存在一个最优值,并且其通常在20%到30%之间取到。最后,通过数值分析验证了分类安检模式的最优服务配置。     

Representation of the solution to a model problem in semiconductor physics

We study a mixed type problem for the Poisson equation arising in the modeling of charge transport in semiconductor devices [V. Romano, 2D simulation of a silicon MESFET with a non-parabolic hydrodynamical model based on the maximum entropy principle, J. Comput. Phys. 176 (2002) 70-92; A.M. Blokhin, R.S. Bushmanov, A.S. Rudometova, V. Romano, Linear asymptotic stability of the equilibrium state for the 2D MEP hydrodynamical model of charge transport in semiconductors, Nonlinear Anal. 65 (2006) 1018-1038]. Unlike well-studied elliptic boundary-value problems in domains with smooth boundaries (see, for example, [O.A. Ladyzhenskaya, N.N. Uralceva, Linear and Quasilinear Elliptic Equations, Nauka, Moscow, 1973; D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1983]), our problem has two significant features: firstly, the boundary is not a smooth curve and, secondly, the type of boundary conditions is mixed (the Dirichlet condition is satisfied on the one part of the boundary whereas the Neumann condition on the other part). The well-posedness of the problem in Hölder and Sobolev spaces is proved. The representation of the solution to the problem is obtained in an explicit form.     

公众参与视角下的央地环境规制博弈分析

本文首先构建环境规制中中央政府和地方政府的两方演化博弈模型,并在此基础上将公众作为第三方参与主体,构建中央政府、地方政府和公众三方演化博弈模型,详细比较两方和三方博弈模型的区别,探究各个主体策略行为的影响因素。研究发现:(1)未有公众参与下,地方政府策略选择主要受地方政府积极执行成本、环境收益、经济损失,消极执行的环境政绩损失,中央政府监管力度、治理补贴和对地方政府的处罚等因素影响;中央政府的监管策略主要受到严格监管的成本以及对地方政府的治理补贴和处罚等因素影响。引入公众参与后,在央地两方博弈的基础上,地方政府环境规制执行策略的影响因素还增加了地方政府被举报后所受到的追加处罚,中央政府监管策略的影响因素还增加了中央政府监管力度、对地方政府的追加处罚以及中央政府的公信力损失。(2)未有公众参与下,中央政府严格监管的概率随地方政府积极执行概率的增大而减小。引入公众参与后,中央政府严格监管率随地方政府积极执行概率的增大而增大。说明在公众参与下,地方政府积极执行环境规制对中央政府严格监管产生的抑制作用转变成了促进作用。(3)地方政府积极执行的概率、中央政府严格监管的概率都随公众举报概率的增大而增大。说明公众参与不仅对地方政府承担环保责任具有促进作用,而且有利于促使中央政府落实环境治理政策。     

Personae at play. ‘Men of Mathematics’ in commentary

Mathematical writers, above all, Euclid, tend to present their theorems as decontextualized, abstract propositions, which has become the standard modus of textual presentation in theoretical mathematics. Mathematical commentators, however, provide their readers with personal names and historical facts in order to elucidate problems, provide contexts of discovery, or construct doxographies, among other things. Modern readers have used such information for the construction of histories of science. When we look at these passages, however, we see that personal names and information about mathematicians of the past can serve quite a range of different objectives, such as the strategic self-positioning of the commentator vis-à-vis the past or present of mathematics, the education of the reader, mathematical or moral, the construction of the history of the field, etc. Not only does the commentator present a persona of himself to the reader, he can also turn colleagues and predecessors into personae. This paper attempts to elucidate the practice, by offering four examples of such plays of and with personae, in Pappus, Eutocius, al-Nayrīzī, and Proclus.     

颤振分析中的特征值排序问题

颤振分析中判断颤振临界速度的重要依据是系统V-g和V-f图,即系统特征值随参数的变化曲线.在几乎所有商用软件及自编程序的输出结果中,有时会出现所谓的"窜支"现象,这给颤振临界速度和颤振穿越分支及耦合形式的判断带来很大不便.通过隐函数定理可以证明,除重特征值点以外,系统特征值连续依赖于系统参数变化.依据多元向量值函数连续性,建立对特征值的排列算法,给出系统特征根轨迹的正确曲线,再输出V-g和V-f图数据,从而避免"窜支"现象.编制应用程序,通过几个典型算例对算法进行了验证.该工作能够有效简化颤振分析的后处理工作,提高分析效率.     

基于EGB2分布族的GAS-EGARCH模型与VaR预测

GARCH族模型是刻画资产收益率的常用工具,在风险度量领域具有广泛应用。为了更有效地描述收益率的偏斜厚尾等特征,越来越多学者对GARCH族模型的条件分布形式进行了研究。但是仅对GARCH模型条件分布进行修正是不够的,还需要对模型本身的函数形式进行修正。基于得分函数的时变参数建模思想近年来受到广泛关注,本文借助这一思想对EGARCH模型中对数标准差进行时变波动建模,并利用EGB2分布族作为模型的条件分布,进而建立GAS-EGARCH-EGB2模型。以我国10只中证行业指数为研究对象考察GAS-EGARCH-EGB2模型的风险预测效果,GAS-EGARCH-EGB2模型样本外VaR预测表现普遍优于ACM-EGARCH-EGB2模型。