1982年以来国内出版的数学建模教材、译著及竞赛辅导材料

<正> 1.E. A. Bender,数学模型引论,朱尧辰、徐伟宣译,科学普及出版社,1982.2.近藤次郎,数学模型,宫荣章等译,机械工业出版社,1985.3.姜启源,数学模型,高等教育出版社,1987.4.任善强,数学模型,重庆大学出版社,1987.5.M. Braun, C. S. Coleman, D. A. Drew,微分方程模型,朱煜民、周宇虹译,国防科技大学出版社,(本书为W. P. Lucas主编的Modules in Applied Mathematics一书的第一卷),1988.     

(伪)单调集值映射拟均衡问题

主要讨论G-凸上的广义向量拟均衡问题,推广W.O ettli,D.Sch l ger,Q.H.A nsari,I.V.K onnov,和J.C.Y ao的一些主要结果.     

2007年普通高等学校招生全国统一考试 理科数学Ⅱ

一、选择题:共12小题,共60分1.sin210°()A.23B.-23C.21D.-212.函数y=|sinx|的一个单调增区间是()A.-π4,-4πB.4π,34πC.π,32πD.32π,2π3.设复数z满足1 z2i=i,则z=()A.-2 iB.-2-iC.2-iD.2 i4.下列四个数中最大的是()A.(ln2)2B.ln(ln2)C.ln2D.ln25675.在△ABC中,已知D是AB边上一点,若AD=2DB,CD=31CA λCB则λ=()A.32B.31C.-31D.-326.不等式xx2--14>的解集是()A.(-2,1)C.(-2,1)∪(2, ∞)B.(2, ∞)D.(-∞,-2)∪(1, ∞)7.已知正三棱柱ABC-A1B1C1的侧棱长与底面边长相等,则AB1与侧面ACC1A1所成角的正弦值等于()A.46B.…     

Approximation to the expectation of a function of order statistics and its applications

ThisprojectissupportedbytheNationalNaturalScienceFoundationofChinaandDoctoralProgramFoundationofHigherEducation.1.IntroductionLetUI,U2,'bei.i.d.randomvariableswithuniformd.f.ontheinterval(0,l),andforeveryn31,writeUt,,15'5Un,.fortheorderstatisticsofUI,'tUn.SupposethatXI1X2,'arei.i.d.observationsfromanondegenerated.f.F,anddenotebyX.,l5'5X.,.theorderstatisticsofXI,'IX,,'Withoutlossofgenerality,wewillassume0相似文献   

2007年普通高等学校招生全国统一考试 (江西卷)理科数学

一、选择题:本大题共12小题,共60分.1.化简(12 4i)i2的结果是()A.2 iB.-2 iC.2-iD.-2-i2.li mx→1x3-x2x-1()A.等于0B.等于1C.等于3D.不存在3.若tan4π-α=3,则cotα等于()A.-2B.-12C.12D.24.已知x 33xn展开式中,各项系数的和与其各项二项式系数的和之比为64,则n等于()A.4B.5C.6D.75.若0π3xC.sinx<π42x2D.sinx>π42x26.若集合M={0,1,2},N={(x,y)|x-2y 1≥0,且x-2y-1≤0,x,y∈M},则N中元素的个数为()7.A如.图9,正方B.体6ACC.4D.21的棱长为1,过点A作平面A1BD的垂线,垂足为点…     

RESIDUALS DENSITY ESTIMATION IN CENSORED LINEAR REGRESSION MODEL

1.IntroductionSupposethatinthelinearregressionmodelK=XIP ei.KarenotcompletelyobserVableandtheObserVationsare(X',Zi,6i),i=l,'',n,wherePandXiarepx1vectors,Zi=adn(K,Wi),6i=I(K5Wi),theresidualei'sarei.i.d.r.v.'swithunknowncommondensityfullctionj(distributionfunctionF)andthe(Wi,Xi)'sarei.i.d.randomvectorsthatareindependentofei's.Fittingthemodelwithcensoreddatahasreceivedconsiderableattentioninthestatistical.literature.TherearetWOmaintrendsinthisbodyofliterature.OnetrendistoeXtendthecompl…     

2005年北京市中考数学试卷

一、选择题(共44分,每题4分)1.-2的相反数是()A.-12B.21C.2D.-22.下列运算中,正确的是()A.4=2B.2-3=-6C.(ab)2=ab2D.3a 2a=5a23.下列根式中,与3是同类二次根式的是()A.24B.12C.23D.184.下列图形中,不是中心称图形的是()A.圆B.菱形C.矩形D.等边三角形5.据国家环保总局通报,北京市是“十五”水污染防治计划完成最好的城市.预计今年年底,北京污水处理能力可以达到每日1684000吨.将1684000吨用科学记数法表示为()A.1.684×106吨B.1.684×105吨C.0.1684×107吨D.16.84×105吨6.如图,在半径为5的⊙O中,如果弦AB的长为8,那么它的弦心距OC…     

2005年甘肃省定西市中考数学试卷

一、选择题(本大题共10小题,每小题3分,共30分)1.方程x2-5x=0的根()A.0B.0,5C.5,5D.52.甲乙两人在相同的条件下各射靶10次,他们的环数的方差分别为S2甲=2.4,S2乙=3.2,则射击稳定程序是()A.甲高B.乙高C.两人一样D.不能确定的3.抛物线y=x2-2x 3的对称轴是直线()A.x=-2B.x=2C.x=-1D.x=14.如果α是锐角,且sinα=54,那么cos(90°-α)=()A.54B.43C.53D.515.若关于x的方程x2 2x k=0有实数根,则()A.k<1B.k≤1C.k≤-1D.k≥-16.下列命题中,假命题是()A.两条弧的长度相等,它们是等弧B.等弧所对的圆周角相等C.直径所对的圆周角是直角D.一条弧…     

代数函数的对数的线性形式

<正> 代数函数与代数数的某些性质的相似性,引起人们的兴趣.在 B.P.Gill,C.F.Osgood,W.M.Schmidt,S.Uchiyama 及 R.C.Mason 等人的文章中,就研究了关于代数函数的 Thue-Siegel 方程等问题.     

RQI DYNAMICS FOR NON-NORMAL MATRICES WITHREAL EIGENVALUES

1.IntroductionAswellknown,RQI(RayleighQuotientiteration)isapracticalalgorithmforeigen-valueproblemsofsymmetricmatrices.In1974,B.N.ParlettprovedthatthesequencegeneratedbyRQIalwaysconvergestoaneigenvectorforalmostallofinitialvectorsifthematrixinquestionisanormalone.NamelythesetofvectorsinR",forwhichRQIdiverges,hajszeromeasure.Nevertheless,healsopointedouttheconvergelitspeedbeingcubicone[1].In1989,S.BarttsonandJ.SmillieconsideredRQIforsymmetricmatrixagain.Theydiscoveredthatthedynamicsof…     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Linear problems of the stability of a type of rotation of a satellite about the centre of mass

The stability in the first approximation of the rotation of a satellite about a centre of mass is investigated. In the unperturbed motion the satellite performs, in absolute space, three rotations around the normal to the orbital plane in a time equal to two periods of rotation of its centre of mass in the orbit (Mercury-type rotation). Three cases of such rotations are considered: the rotations of a dynamically symmetrical satellite and a satellite, the central ellipsoid of inertia of which is close to a sphere, in an elliptic orbit of arbitrary eccentricity, and the rotation of a satellite with three different principal central moments of inertia in a circular orbit.     

Variational formulations of certain problems of the theory of the flow of rigid-plastic media

The mathematical content of variational problems of the mechanics of rigid-plastic media reduces to minimizing convex functionals in non-reflexive spaces of solenoidal vector fields. Different formulations are presented in /1/. Problems are examined there in which discontinuous velocity fields occur. The initial functional is undetermined in such fields. In this connection, the problem is posed of constructing that extension of the original set of kinematically allowable velocity fields as would contain all their possible discontinuities allowed by the mechanics of rigidly plastic media, and of continuing the original functional into the extension obtained. This problem is solved in this paper for the case when the velocity field is given on the whole surface of the rigid-plastic body.     

Asymptotic properties of the solutions of the equations of motion of gyroscopic systems

The motion of mechanical systems acted upon by gyroscopic and positional forces characterized by a large parameter in the corresponding equations of motion is considered. Periodic solutions of such equations were investigated earlier in [1, 2]. It is proved below that solutions of these equations exist, defined in an interval the length of which is a monotonically increasing unbounded function of the large parameter, and which transfer into the solutions of the corresponding degenerate systems as the large parameter approaches infinity. This function can be specified in more detail if additional assumptions are made regarding the properties of the system and the nature of the forces acting on it.     

Structure of genera of representations of nonsemisimple rings

The investigation of integral representations of arbitrary rings is shown to be equivalent to the case of orders in semisimple algebras. An example is constructed showing that, for an order in a nonsemisimple algebra, the number of representations in the genus may increase without limit with varying genera.Translated from Matematicheskie Zametki, Vol. 10, No. 1, pp. 63–87, July, 1971.     

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.     

Region of linearity of the deformation properties of contact-molded glass-reinforced plastic

A study was made of the creep and recovery of contact-molded glass-reinforced plastic in different directions in the plane of the sheet in uniaxial tension. On the basis of experimental data, the region of linearity of the deformation properties of the material under investigation was established. The influence functions in the relations of the theory of viscoelasticity were taken in the form proposed by Bronskii. The dependence of the parameters which determine these functions on direction was investigated. It is shown that, in practice, this dependence is inherent in only one of the parameters, and a relationship which is in satisfactory agreement with the experimental results is proposed to describe it.Moscow Institute of Chemical Machine Building. Scientific-Research Institute for Mechanics, M. V. Lomonosov State University, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 404–410, May–June, 1970.     

Smallest constant of extension of functions of Sobolev classes

The problem is posed on the class-preserving extension of functions of Sobolev class is a finite domain in the in-dimensional space) onto the whole of such that the supports of the extended functions would lie in a specified finite domain and such that the so-called constant of extension would be minimal. The existence of such an extension is proved under constraints on of the type of a certain minimal smoothness; an algorithm for the approximate computation of the minimal constant of extension is indicated forp=2. Ifp=2 andS=I while are concentric balls, then the exact value of the constant of extension has been computed under the usual definition of a norm in; it is expressed in terms of Bessel functions of an imaginary argument. The exact value mentioned permits the estimation from above and from below of the constant of extension in the case when the domain is diffeomorphic to a sphere.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 90, pp. 150–185, 1979.     

The use of splitting of the equations of motion in the numerical solution of problems of the dynamics of elastic systems

Linear elastic systems with a finite number of degrees of freedom, the initial equations of motion of which are constructed using the finite element method or other discretization methods, are considered. Since, in applied dynamics problems, the motions are usually investigated in a frequency range with an upper bound, the degrees of freedom of the initial system of equations are split into dynamic and quasi-dynamic degrees. Finally, the initial system of equations is split into a small number of differential equations for the dynamic degrees of freedom and into a system of algebraic equations for determining the quasi-static displacements, represented in the form of a matrix series. The number of terms of the series taken into account depends on the accuracy required.     

Existence of solutions of certain systems of non-linear inequalities

In recent years there has been increasing interest in the problem of the existence of solutions to systems of linear inequalities, however little has been done in the general case of non-linear inequalities. In this paper a certain class of non-linear inequalities is considered. Several existence theorems are established which generalize certain recent results in linear inequalities.