二棱镜系统二阶和三阶色散的理论计算

基于光的色散和棱镜光谱仪的特点,采用等光程方法推导了紧凑累加型二棱镜系统二阶和三阶色散的表达式,并分析具体实例。通过计算机模拟得出二阶和三阶色散曲线,为可调谐激光的线宽压窄提供了一定的理论依据。     

伪随机码光栅锐化光栅于涉仪条纹

本文报道了伪随机序列编码的光栅干涉仪,可以取得锐化条纹,给出了理论分析和实验结果.     

非线性发展方程的Riemann theta 函数等几种新解

为了构造非线性发展方程的复合型无穷序列精确解, 获得了第二种椭圆方程的Riemann theta 函数等几种新解.在此基础上,利用第二种椭圆方程与Riccati方程的Bäcklund变换和解的非线性叠加公式, 借助符号计算系统 Mathematica, 以mKdV方程为应用实例, 构造了该方程的复合型无穷序列新精确解.这里包括Riemann theta 函数、Jacobi椭圆函数、双曲函数、 三角函数和有理函数,通过几种形式构成的复合型无穷序列新精确解. 关键词： 第二种椭圆方程 Riccati方程 非线性发展方程 Riemann theta 函数无穷序列解     

非均匀性和彩色失真图像的同时补偿

针对CCD摄像机或扫描仪产生图像存在颜色偏差和非均匀性使图像质量下降 ,通过多元线性回归分析方法同时对图像的非均匀性和彩色失真进行补偿 ,使输出图像信号均匀且其色度值与输入信号的色度值相匹配。依据算法进行了仿真试验 ,结果表明补偿后图像与原图像相比大体相近 ,且比非均匀性校正和彩色校正分步进行方法计算量小 ,节省时间     

Sorting of bending magnets for the SSRF booster

The Shanghai Synchrotron Radiation Facility(SSRF)booster ring,a full energy injector for the storage ring,is deigned to accelerate the electron beam energy from 150MeV to 3.5GeV that demands high extraction efficiency at the extraction energy with low beam loss rate when electrons are ramping.Closed orbit distortion(COD)caused by bending magnet field uniformity errors which affects the machine performance harmfully could be effectively reduced by bending magnet location sorting.Considering the affections of random errors in measurement,both ideal sorting and realistic sorting are studied based on measured bending magnet field uniformity errors and one reasonable combination of bending magnets which can reduce the horizontal COD by a factor of 5is given as the final installation sequence of the booster bending magnets in this paper.     

The expected payoff to Internet auctions

In an Internet auction, the expected payoff acts as a benchmark of the reasonableness of the price that is paid for the purchased item. Since the number of potential bidders is not observable, the expected payoff is difficult to estimate accurately. We approach this problem by considering the bids as a record and 2-record sequence of the potential bidder’s valuation and using the Extreme Value Theory models to model the tail distribution of the bidder’s valuation and study the expected payoff. Along the discussions for three different cases regarding the extreme value index γ, we show that the observed payoff does not act as an accurate estimation of the expected payoff in all the cases except a subclass of the case γ = 0. Within this subclass and under a second order condition, the observed payoff consistently converges to the expected payoff and the corresponding asymptotic normality holds.      

On the Ehrenfeucht–Mycielski sequence

We introduce the inverted prefix tries (a variation of suffix tries) as a convenient formalism for stating and proving properties of the Ehrenfeucht–Mycielski sequence [A. Ehrenfeucht, J. Mycielski, A pseudorandom sequence—how random is it? American Mathematical Monthly 99 (1992) 373-375]. We also prove an upper bound on the position in the sequence by which all strings of a given length will have appeared; our bound is given by the Ackermann function, which, in light of experimental data, may be a gross over-estimate. Still, it is the best explicitly known upper bound at the moment. Finally, we show how to compute the next bit in the sequence in a constant number of operations.     

复合函数极限的应用

利用复合函数极限的运算法则给出收敛数列与其子列的关系、海涅定理以及数列重排的另一种证明,把三个重要的定理归结为复合函数极限的应用,将大学数学里三个重要但理解起来相对困难的定理纳入统一简单的框架.     

On almost sure max-limit theorems of complete and incomplete samples from stationary sequences

Let M _n denote the partial maximum of a strictly stationary sequence (X _n ). Suppose that some of the random variables of (X _n ) can be observed and let [(M)\tilde]_n\tilde M_n stand for the maximum of observed random variables from the set {X ₁, ..., X _n }. In this paper, the almost sure limit theorems related to random vector ([(M)\tilde]_n\tilde M_n , M _n ) are considered in terms of i.i.d. case. The related results are also extended to weakly dependent stationary Gaussian sequence as its covariance function satisfies some regular conditions.     

Examples of entropy generating sequence

We introduce the notion of entropy generating sequence for infinite words and define its dimension when it exists. We construct an entropy generating sequence for each symbolic example constructed by Cassaigne such that the dimension of the sequence is the same as its topological entropy dimension. Hence the complexity can be measured via the dimension of an entropy generating sequence. Moreover, we construct a weakly mixing example with subexponential growth rate.