多美“概率”

概率密切联系生活与现实世界，使数学问题情景新颖别致，丰富多彩．纵观近几年各省、市高考和模拟题，概率好题不胜枚举，俯拾皆是，它们像一颗颗璀璨的珍珠在数学题海中闪闪发光．本文特精选举例予以分类解析，旨在探究题型规律，揭示解题方法、提供解题规律，供读者参考．     

Analytic Solution for Magnetohydrodynamic Stagnation Point Flow towards a Stretching Sheet

A steady two-dimensional magnetohydrodynamic stagnation point flow towards a stretching sheet with variable surface temperature is investigated. The analytic solution is obtained by homotopy analysis method. The convergence region is computed and the feature of the solution is discussed.     

Rayleigh Scattering for An Electromagnetic Anisotropic Medium Sphere

Based on the scales theory of electromagnetic waves, the analytical expression of electrical fields inside an anisotropic medium sphere is studied. Differential scattering cross section and radar cross section （RCS） for an anisotropic spherical target are presented. The correctness of the obtained results is tested. The simulation results show that the scattering of an anisotropic sphere has the property of a dipole radiation under the condition of Rayleigh scattering. The larger the dielectric constant is, the stronger the dipole scattering is. Anisotropy in magnetism only has an effect on differential RCS. These results provide a theoretical base for the identification of anisotropic targets.     

Effective Action for Noncommutative U（1） Gauge Theory with Higher Dimensional Terms

In this paper we apply the assumption of our recent work in noncommutative scalar models to the noncommutative U（1） gauge theories. This assumption is that the noneommutative effects start to be visible continuously from a scale ANC and that below this scale the theory is a commutative one. Based on this assumption and using background field method and loop calculations, an effective action is derived for noncommutative U（1） gauge theory. It will be shown that the corresponding low energy effective theory is asymptotically free and that under this condition the noncommutative quadratic IR divergences will not appear. The effective theory contains higher dimensional terms, which become more important at high energies. These terms predict an elastic photon-photon scattering due to the noncommutativity of space. The coefficients of these higher dimensional terms also satisfy a positivity constraint indicating that in this theory the related diseases of superluminal signal propagating and bad analytic properties of S-matrix do not exist. In the last section, we will apply our method to the noncommutative extra dimension theories.     

解析二次函数的零点分布问题

已知二次函数的零点分布，求参数范围问题是函数与方程的重要应用问题，也是高考中的热点题型．一般情况下，可通过画函数图象、判断特殊点的函数值的情况，布列不等式（组）来解决问题，请看题例分析．     

双动点中的分类思想

分类是一种重要的数学思想方法,平面图形中双点运动时,常有某个元素不能确定,需作分类处理.     

收缩喷嘴中的湍流Ⅰ——边界层解

应用边界层积分法,研究锥形喷嘴入口区域中湍动涡流的发展.球面坐标系中的控制方程,通过边界层的假定得到简化,并对边界层进行了积分.应用4阶Adams预测校正法求解该微分方程组.入口区域的切向和轴向速度,分别应用自由涡流和均匀速度分布来表示.由于缺乏收缩喷嘴中涡流的实验数据,需要用数值模拟对该发展模式进行逆向验证.数值模拟的结果证明,该解析模型在预测边界层参数中的能力,例如边界层的生长、剪切率和边界层厚度,以及不同锥度角时的涡流强度衰减率等.为所提出的方法引进一个简明而有效的程序,用以研究几何形状收缩设备内的边界层参数.     

Approximate wφ - Ωφ Relations in Quintessence Models

Quintessence field is a widely-studied candidate of dark energy. There is ＂tracker solution＂ in quintessence models, in which evolution of the field φ at present times is not sensitive to its initial conditions. When the energy density of dark energy is negleetable （Ωφ 〈〈 1）, evolution of the tracker solution can be well analysed from ＂tracker equation＂. In this paper, we try to study evolution of the quintessence field from ＂full tracker equation＂, which is valid for all spans of Ωφ. We get stable fixed points of we and wφ （noted as wφ and Ωφ） from the ＂full tracker equation＂, i.e., we and ωφ will always approach ωφ and Ωφ respectively. Since wφ and Ωφ are analytic functions of φ, analytic relation of φ can be obtained, which is a good approximation for the we φ relation and can be obtained for the most type of quintessence potentials. By using this approximation, we find that inequalities ωφ 〈 we and 〈ωφ are statisfied if the we （or ωφ） decreases with time. In this way, the potentiai U（φ） can be constrained directly from observations, by no need of solving the equations of motion numerically.     

《中学教学原创题集》2010年1月出版

本书最大的特色是所选问题均为原创,每个问题独立成篇,设置了问题的由来、问题、解析、教育价值、问题拓展等栏目。全书基本按知识内容编排,最后一节介绍了命题的细