Reflection Talbot Effect and Application

The reflection Talbot effect under the illumination of Gaussian spherical wave and plane wave is observed on 1D and 2D photonic crystal of silicon prepared by nanosecond laser. It is found that the distance between two adjacent Talbot images increases lineally with increasing of image distance as well as amplification of Talbot images under the illumination of Gaussian spherical wave. The result of theory is coincident with that of experiment, which shows that selecting suitable wavefront shape of input field can enlarge the amplification rate and improve the resolution of Talbot imaging. The reflection Talbot effect will have a lot of good application in microscopy of micro-fabrication on silicon, such as detecting period structures of plasma on line of PLD fabricating.     

ECO方法在Fine数中的应用

利用ECO方法研究了Fine数的组合对象,得到了相应的生成规则和生成树.     

关于平方三角数及相关定理的证明

研究的对象为既是三角数，又是平方数的“三角平方数”．利用Ferma的无穷下降法证明了平方三角数定理，从而说明了平方三角数存在无穷多个这一事实，并且给出了平方三角数的表示方法．     

ρ~-混合随机变量序列加权和的完全收敛性质

应用ρ-混合随机变量序列截断法、Hlder不等式、Markov不等式、Jensen不等式、Cr不等式及ρ-混合随机变量的Rosenthal型矩不等式,考察在没有同分布假设条件下,ρ-混合随机变量序列加权和的完全收敛性质,并利用Borel-Cantelli引理,给出ρ-混合随机变量序列加权和的Marcinkiewicz-Zygmund型强大数定律.     

秩2对称(a,b)矩阵中元素a的可能个数

设a和b是两个不同的实数,如果一个矩阵的元素为a或b,我们称这样的矩阵为(a,b),根据a、b的不同取值,分四种情形分析了秩2对称(a,b)矩阵的结构,给出了秩2对称(a,b)矩阵中元素a的可能个数。     

Pell方程x2-[(mn)2±4n]y2=1的最小解

运用计算连分数的方法,给出Pell方程x2-Dy2=1当D=(mn)2±4n(m,n)为正整数)时的最小解的计算公式.     

一些特殊第二类Stirling数的p-adic赋值

设k和n为非负整数.第二类Stirling数表示将n个元素划分为恰好k个非空集合的个数,记为S（n,k）.对任意给定的素数p和正整数n,存在惟一的整数a和m≥0使得n=ap^m,其中（a,p）=1（a与p互素）.称m为n的p-adic赋值,并记v_p（n）=m.第二类Stirling数的p-adic赋值是数论和代数拓扑领域的重要问题.本文研究了一些特殊第二类Stirling数S（pⁿ,2^tp）的p-adic赋值,其中p为奇素数,t和n为正整数.本文证明当n≥2,2≤2^tp(S（pⁿ,2^tp）)≥n+2-2^t,推广了Zhao和Qiu最近的结果.     

希托夫法测定离子迁移数实验的改进

希托夫法是测定离子迁移数的一种常用方法,为适应学生实验对时间和评测的要求,对希托夫法测定离子迁移数的实验设备、实验和计算过程进行了一定的改进和完善,在阴阳极和中间区域增加了三通活塞,方便赶除气泡,选择滴定阴极或者阳极其中一个极区的溶液以保证实验时间安排的合理性,并在初步实验过程中取得了良好的实际效果。     

“号码”投资的法律容纳度

当"号码"成为不可重复的有限公共资源时就具备了寻租和投资的潜质,一旦法律容纳,就会按一级市场、二级市场的逻辑演绎下去,并且市场会失控、法律会失灵,"号码"资源也在动荡中寻求其应有的归属。为此,探讨"号码"资源在行政领域、公用事业领域经有偿寻租后的法律属性和法律适用,分析公权力在与私权利对接时的利益放养与制衡尤为重要。     

State feedback control of network-based systems with packet disordering

A new method that stabilizes network-based systems with both bounded delay and packet disordering is discussed under the state feedback controller. A novel model, fully describing the dynamic characteristic of network-based systems with packet disordering, is constructed. Different from the existing models of network-based systems, the number of delay items is time-varying in the model proposed. Further, this model is converted into a parameter-uncertain discrete-time system with time-varying delay item numbers in terms of matrix theory. Moreover, the less conservative stability condition is obtained by avoiding utilisation of Moon et al.’ inequality and bounding inequalities for quadratic functional terms. By solving a minization problem based on linear matrix inequalities, the state feedback controller is presented. A numerical example is given to illustrate the effectiveness of the proposed method.