例说建立递推关系式解题

在解某些数学问题时,若能根据问题的实质和特征,建立递推关系式,就会使问题很巧妙地得到解决.下面举例说明,供读者参考.     

带不同分布增量的随机和的局部渐近性

在Asmussen,Foss and Korshunov(J.Theoretical Probab.,2003,16(2):489-518)的基础上,讨论了支撑在(-∞,∞)上的不同分布的卷积的封闭性及带上述不同分布增量的局部渐近性.上述分布包括了常见的轻尾分布和重尾分布.     

带有相依重尾冲击的Poisson噪音过程尾的一致渐近性质

本文考虑了带有某种相依重尾冲击的Poisson噪音过程尾的一致渐近性质.当冲击是二元上尾渐近独立的非负随机变量具有长尾和控制变化尾分布且噪音函数具有正的上下界时,得到了过程尾概率的一致渐近公式.进而,当冲击具有连续的一致变化尾分布时,去除了噪音函数具有正的下界的限制.对于噪音函数不一定具有正的上界的情形,当冲击具有两两负象限相依结构时,也得到了一致渐近性结果.     

On decentralized stabilization of linear large scale systems with symmetric circulant structure

The decentralized stabilization of continuous and discrete linear large scale systems with symmetric circulant structure was studied. A few sufficient conditions on decentralized stabilization of such systems were proposed. For the continuous systems, by introducing a concept called the magnitude of interconnected structure, a very important property that the decentralized stabilization of such systems is fully determined by the structure of each isolated subsystem that is obtained when the magnitude of interconnected structure of the overall system is given. So the decentralized stabilization of such systems can be got by only appropriately designing or modifying the structure of each isolated subsystem, no matter how complicated the interconnected structure of the overall system is. A algorithm for obtaining decentralized state feedback to stabilize the overall system is given. The discrete systems were also discussed. The results show that there is a great dfference on decentralized stabilization between continuous case and discrete case.     

秦九韶算法的教学价值

人教A版<数学3>介绍了秦九韶算法:n次多项式f(x)=anxn+an-1xn-1+…+a1x+a0. 当x=x0时,令v0=an,通过公式{v0=an,vk=vk-1x0=an-k(k=1,2,…,n)可求出f(x0)的值为vn. 它是我国古代数学中的著名算法,本文将从三个方面介绍该算法的教学价值.     

一种无磁低振微型同轴脉冲管制冷机

脉冲管制冷机与超导量子干涉仪耦合进行微弱磁场测量是脉冲管制冷机的一个主要应用方向。本文系统分析了脉冲管制冷机的主要干扰源并给出其相应的解决办法,并据此设计制造了一台无磁低振微型同轴脉冲管制冷机。以实现同轴脉冲管制冷机的低振动、低电磁干扰化,并最终实现利用脉冲管制冷机有效冷却包括高温超导量子干涉仪在内的对电磁干扰要求极严格的高温超导器件。     

矩阵不可约的一个新的充要条件及判定矩阵不可约性的一个新算法

本文获得了矩阵不可约的一个新的充要条件及判定矩阵不可约性的一个新算法，这相结果优于（１－４）中的结果。     

基于FastICA的高光谱图像目标分割

针对高光谱图像目标识别与分类的应用背景,提出了一种基于快速独立成分分析的高光谱图像目标分割算法.通过引入虚拟维数对图像中的目标端元数量进行估计,利用基于非监督正交子空间投影的异常端元提取算法自动获取目标端元光谱,并将其作为快速独立成分分析的初始混合矩阵.采用最小噪声分量变换对原始数据进行降维,利用快速独立成分分析从降维后的主成分中依次提取出图像中的独立分量.最后,对各独立分量进行恒虚警率检测与形态学滤波,从而得到最终的目标分割结果.对AVIRIS型高光谱图像的实验结果表明,该方法可有效探测出图像中的目标,并可获得较好的分割结果.     

Equal-amplitude optical comb generation using multi-frequency phase modulation in optical fibers

<正>We theoretically analyze and experimentally demonstrate a method of generating equal-amplitude optical comb exploiting multi-frequency phase modulation.The theoretical analysis shows that 4n-1 equal-amplitude spectral lines can be obtained when the modulation signal comprises n frequency components including the fundamental frequency and the odd harmonic frequencies,and 2n+1 equal-amplitude spectral lines can be obtained when the modulation signal comprises n frequency components including the fundamental frequency and the even harmonic frequencies.Then,we numerically simulate the spectra of 5,7,9,and 11 equal-amplitude spectral lines,respectively,which are also obtained in experiments with frequency separation of 30 MHz and flatness of better than 0.3 dB.     

Common Features in Electronic Structure of the Oxypnictide Superconductors from Photoemission Spectroscopy

High resolution photoemission measurements are carried out on non-superconducting LaFeAsO parent com- pound and various superconducting RFeAs（O1-ZFx） （R=La, Ce and Pr） compounds. It is found that the parent LaFeAsO compound shows a metallic character. By extensive measurements, several common features are identified in the electronic structure of these Fe-based compounds： （1） 0.2 eV feature in the valence band, （2） a universal 13-16 meV feature, （3） near EF spectral weight suppression with decreasing temperature. These uni- versal features can provide important information about band structure, superconducting gap and pseudogap in these Fe-based materials.