2003年普通高等学校招生全国统一考试数学（理工农医类）（北京卷）

参考公式与文科相同一 选择题 :本大题共 1 0小题 ,每小题 5分 ,共 5 0分 .在每小题给出的四个选项中 ,只有一项是符合题目要求的 .( 1 ) ,( 2 )与文科 ( 1 ) ,( 2 )相同( 3)“cos2α=- 32 ”是“α=kπ+ 5π1 2 ,k∈Z”的(A)必要非充分条件(B)充分非必要条件(C)充分必要条件(D)既非充分又非必要条件( 4 )与文科 ( 4 )相同( 5 )极坐标方程 ρ2 cos2θ- 2 ρcosθ =1表示的曲线是(A)圆 (B)椭圆(C)抛物线 (D)双曲线( 6) ,( 7) ,( 8)分别与文科 ( 6) ,( 7) ,( 9)相同( 9)若数列 {an}的通项公式是an =3-n+ 2 -n+ ( - 1 ) n( 3-n- 2 -n)2 ,n…     

匹配问题实例空间和解空间结构

本文通过研究匹配问题的实例空间，匈牙利算法和解空间三者之间的关系，指出S实例空间的数目与问题复杂度之间的关系既不是充分也不是必要的，而如何对问题的解空间进行合理的分解才能是问题的关键。     

有界对称域上的Dp乘子

设Ω是Cn中包含原点的有界对称域.本文在Ω上得到了关于Dp空间的两个乘子定理.     

两个回归函数相等的Bootstrap检验

两个回归参数相等性检验一直是统计界感兴趣的问题之一．在这篇文章中，四个检验统计量被用于度量两曲线的差异，在原假设下统计量的分布采用向量数据的重复抽样来逼近，并给出了—些模拟结果．     

如何在大学数学课堂教学中培养学生创新思维

论述了在大学数学课堂教学中传授数学思想与数学方法的必要性与重要性 ,重点介绍了作者从大学数学教学中总结出来的一些数学思想与教学方法 .     

拟议中的21世纪光学望远镜

 不论天文爱好者还是职业天文学家都渴望有一台大的反射镜或透镜,因为它能聚集更多的光,具有显示天体细节的潜能。特别是专业工作者,大仪器是研究宇宙中的暗星系和现代天文学中许多重要问题不可或缺的。可以说望远镜越大越好。现在,大地基望远镜主要是口径8～10米的反射镜,它们代表了自伽利略将望远镜用于夜空研究400年以来光学望远镜发展的巅峰。其中有建在智利的欧洲空间局的甚大望远镜(由4台8米望远镜构成),位于夏威夷的两台10米凯克望远镜和8.3米昴星望远镜,双子望远镜(两台望远镜分别装在南半球和北半球),以及德克萨斯州麦克唐纳天文台的9米大型拼镶镜面望远镜。     

Additive Maps Preserving Nilpotent Operators or Spectral Radius

Let X be a （real or complex） Banach space with dimension greater than 2 and let B0（X） be the subspace of B（X） spanned by all nilpotent operators on X. We get a complete classification of surjective additive maps Ф on B0（X） which preserve nilpotent operators in both directions. In particular, if X is infinite-dimensional, we prove that Ф has the form either Ф（T） = cATA^-1 or Ф（T） = cAT＇A^-1, where A is an invertible bounded linear or conjugate linear operator, c is a scalar, T＇ denotes the adjoint of T. As an application of these results, we show that every additive surjective map on B（X） preserving spectral radius has a similar form to the above with ｜c｜ = 1.     

Multiple Scattering Effects of Ag Particles in Random Ag-SiN Film

A layer of 40nm-thick Ag-SiN film with Ag nano-particles embedded and distributed randomly in the SiN thin film were deposited by the method of radiant-frequency magnetron sputtering. Specimens orderly comprising a random Ag-SiN film and an optical phase change recording layer were exposed to a focused laser beam with wavelength of 69Ohm. It is shown that, with a random Ag-SiN layer deposited above the recording layer. Calculation by the finite difference time domain method of a 4Ohm-thick SiN film under a Gaussian beam irradiation has been carried out to simulate the near-field distribution in the film, which showed a huge local near-field intensity enhancement of about 200 times if small Ag particles with diameter of 6 nm were modelled inthe SiN film in the central region of the in cident laser spot.     

A Continuation Method of Parameter Inversion for Non-Equilibrium Convection-Dispersion Equation

Based on the homotopy mapping, a globally convergent method of parameter inversion for non-equilibrium convection-dispersion equations （CDEs） is developed. Moreover, in order to further improve the computational efficiency of the algorithm, a properly smooth function, which is derived from the sigmoid function, is employed to update the homotopy parameter during iteration. Numerical results show the feature of global convergence and high performance of this method. In addition, even the measurement quantities are heavily contaminated by noises, and a good solution can be found.     

NECESSARY CONDITIONS FOR OPTIMAL CONTROLS OF SEMILINEAR ELLIPTIC VARIATIONAL INEQUALITIES INVOLVING STATE CONSTRAINT

This paper deals with maximum principle for some optimal control problem governed by some elliptic variational inequalities. Some state constraints are discussed. The basic techniques used here are based on those in [1] and a new penalty functional defined in this paper.