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.     

阵列天线最大输出信干噪比下最优权重降维算法

本文研究阵列天线系统最大输出信干噪比准则下最优权重的降维算法。在求最优权重的过程中，计算复杂度是我们要关心的重要的问题，而计算复杂度与权重矢量的维数成正比。权重矢量的维数和天线阵的阵元个数相同。在期望方向和干扰方向小于天线阵元个数的情况下，完全可以通过某种变换，降低计算最优权重的实际维数，从而降低计算复杂度。     

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.     

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。     

半无限规划的一个对偶问题

本文对半无限凸规划提出一个新的对偶问题，使用扰动函数、次微分和法锥，文中证明了相应的弱对偶性及强对偶性的充要条件．     

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.     

BERNOULLI CONVOLUTIONS ASSOCIATED WITH CERTAIN NON——PISOT NUMBERS

The Bernoulli convolution Vλ measure is shown to be absolutely continuous with L^2 density for almost all 1/2＜λ＜1, and singular if λ^-1 is a Pisot number. It is an open question whether the Pisot type Bernoulli conuolutions are the only singular ones. In this paper, we construct a family of non-Pisot type Bernoulli convo-lutions Vλ such that their density functions, if they exist, are not L^2. We also construct other Bernolulli convo-lutions whose density functions if they exist, behave rather badly.     

色散渐减光纤中Ginzburg-Landau方程的自相似脉冲演化的解析解

采用对称约简的分析方法，得出了变系数Ginzburg-Landau方程的抛物渐近自相似脉冲解析解的一般表达式.给出了二阶色散系数纵向双曲型变化和纵向指数型变化的色散渐减光纤中自相似脉冲的振幅、啁啾以及脉冲宽度的具体形式，并与数值解进行了对比，其结果符合得很好.从而证实了稀土元素掺杂的色散渐减光纤中，在增益色散因子的影响下，脉冲的演化具有抛物型自相似特性.     

激光主动探测中回波信号的小波去噪方法

在分析激光主动探测中回波信号的噪声特性和小波变换去噪原理的基础上，提出了一种基于最大信噪比准则的小渡阈值去噪方法。首先用最大信噪比准则对小波变换系数进行阈值选取，然后采用软阂值方法对小波系数进行量化处理后再重构。仿真结果表明最大信噪比准则小波去噪方法改善信噪比效果十分显著，检测下限达到-16．2dB。证明了该方法在激光主动探测系统回波信号检测中的有效性。