直线型动态几何

中考要求 把全等、相似的计算和证明通过运动变化,使之转化为探究和开放性问题,主要考查学生的猜想、探究和逻辑推理能力,培养学生的分析问题和解决问题的能力.直线型动态几何是近几年各地中考命题的热点和亮点.     

Intermediate Self-similar Solutions of the Nonlinear Schrodinger Equation with an Arbitrary Longitudinal Gain Profile

We study pulse propagation in a normal-dispersion optical fibre amplifier with an arbitrary longitudinal gain profile by self-similarity techniques. We show the functional form of the development of low-amplitude wings on the parabolic pulse, which are associated with the evolution of an arbitrary input pulse to the asymptotic parabolic pulse solution. It is found that for the increasing gain the amplifier output corresponding to the input Gaussian pulse converges to the asymptotic parabolic pulse solution more quickly than the output obtained with the input hyperbolic secant pulse, whereas for the decreasing gain the input pulse profiles have nearly no effect on the speed of convergence to the parabolic pulse solution. These theoretical results are confirmed by numerical simulations.     

探究镜框上的相似问题

老师:"小刚,你平时照镜子吗?"小刚:"那当然啦!我还是比较讲卫生的."老师:"有一个如图1所示的镜框,它是用等宽的木条制作而成的,你认为镜框和相框是相似形吗?"小刚:"那是一定的.因为镜框和相框的三条边分别平行,可推出三个角分别相等,即可判定这两个三角形相     

Structure properties and Noether symmetries for super-long elastic slender rod

DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural model of DNA and other long-train molecules, is a useful tool in analysing the symmetrical properties and the stabilities of DNA. This paper studies the structural properties of a super-long elastic slender rod as a structural model of DNA by using Kirchhoff＇s analogue technique and presents the Noether symmetries of the model by using the method of infinitesimal transformation. Baaed on Kirchhoff＇s analogue it analyses the generalized Hamilton canonical equations. The infinitesimal transfornaationa with rcspect to the radial coordinnte, the gonarnlizod coordinates, and the Cluasi-momenta of 5he model are introduced. The Noether gymmetries and conserved qugntities of the model are obtained.     

关于多指标变量大数律尾概率级数的完全收敛性

本文对ｉｄ多指标随机变量序列｛Ｘｋ;ｋ∈Ｎｄ｝（ｄ≥２）的部分和Ｓｎ＝∑ｋ≤ｎＸｋ及Ｈ（ｔ）↑＋∞,（ｔ→＋∞）,提出并讨论了Порохоров的３个问题（ｄ≥２）,并讨论了多指标随机变量和的完全收敛性．     

高电荷态氪离子双电子复合过程的理论研究

本文采用相对论的Flexible Atomic Code (FAC) 程序计算类氦Kr34+离子双电子复合的截面及速率系数,其中用n-3标度律对速率系数作了外推.文中我们还讨论了辐射分支比随不同共振峰的变化以及级联辐射的影响.     

拟相似算子近似点谱的连通分支

讨论了Banach空间X上两个算子T，S拟相似时，近似点谱σα(T)的每一个连通分支与σα（S）以及σs(S)的相交关系，证明了σα(T)的每一个连通分支与σs(S)的交非空，并且给出了σα（T）的连通分支与σα（S）交非空的充要条件。     

非时齐Poisson过程MLE的重对数律

在时间区间（０，Ｔ）上，我们观察到Ｘ（Ｔ）＝（Ｘ（ｔ，θ）０≤ｔ≤Ｔ），其中θ∈⊙为参数，且未知，Ｋｕｔｏｙａｎｔｓ讨论了非时齐过程参数θ的最大似然估计（ＭＬＥ）的性质，他给出了极限分布，并且得到了弱收敛及矩收敛等结果，但他要求参数空间为有限区间（α，β）。本文讨论了非时齐Ｐｏｉｓｓｏｎ过程ＭＬＥ的性质，我们允许参数空间随时间而不渐增大，即θｔ是θ在Ｔ＝（α，βＴ）上的最大似然估计，其中ｌｉｍβＴ     

分位点函数的光滑非参数估计的BAHADUR表示

文中对分位函数给出了具有更广泛应用的光滑分位估计,证明了该光滑分位估计的逐点和一致的Bahadur强表示定理;并由此结果推导了估计的重对数律,强逼近等深刻结果。     

Lacunary Measures and Self-similar Probability Measuresin Function Spaces

The paper deals with multifractal quantities for some types of Radon measures, especially self-similar probability measures, and their relations to Besov spaces.