光学干涉计量中的位相测量方法

对光学干涉计量中常用的位相测量方法进行了综述,包括时间相移法、空间相移法、空间载波相移法和Fourier变换法以及位相展开问题。     

拉普拉斯变换微分性质的若干应用

给出拉普拉斯变换微分性质在求解拉普拉斯变换和拉普拉斯逆变换时的三个应用,并分别给出相应算例.     

单调性条件在Fourier级数收敛性中的最终推广:历史、发展、应用和猜想

为了对Fourier级数进行近似计算和有效应用,必须研究其收敛性,这个课题有长久的历史,形成了数学分析中吸引包括许多著名数学家在内的学者研究的一条热烈但困难的主流.其中,在三角级数(Fourier级数)一致收敛性和平均收敛性问题中人们一直关心Fourier系数的单调递减条件最终的推广.这个开始于英国Chaundy-Jollife(1916年)和Young(1913年)的工作最近出现了突破性的进展,产生了许多完善的结果.本文将对这方面的历史、发展给出综述,并重点介绍最近的应用成果,并对以后的工作给出研究思路和线索.     

任意矩阵伸缩的正交小波包

1 引言 Coifman和Meyer引入L~2(R)中正交小波包,可以用张量积形式构造L~2(R~2)上的二维正交小波包;Chui和Li研究单变量非正交小波包和对偶小波包;Shen给出矩阵伸缩为2I时L~2(R~s)上非张量积小波包的构造算法;程正兴给出矩阵小波包的构     

Fourier变换微积特性定理的普遍公式

采用Fourier变换的极限定义式,给出并证明普遍形式的Fourier主换微积特性定理.采用所得公式计算,可从根本上防止错误的发生,并能避免复杂的极限计算,而直接写出大多数Fourier象函数.     

FRACTIONAL DIFFUSION EQUATIONS WITH INTERNAL DEGREES OF FREEDOM

We present a generalization of the linear one-dimensional diffusion equation by com-bining the fractional derivatives and the internal degrees of freedom. The solutions areconstructed from those of the scalar fractional diffusion equation. We analyze the in-terpolation between the standard diffusion and wave equations defined by the fractionalderivatives. Our main result is that we can define a diffusion process depending on theinternal degrees of freedom associated to the system.     

THE SPACE—FRACTIONAL TELEGRAPH EQUATION AND THE RELATED FRACTIONAL TELEGRAPH PROCESS

The space-fractional telegraph equation is analyzed and the Fourier transform of its fundamental solution is obtained and discussed.A symmetric process with discontinuous trajectories, whose transition function satisfies the space-fractional telegraph equation, is presented. Its limiting behaviour and the connection with symmetric stable processes is also examined.     

半圆和四分之一圆二维弹子球的量子谱分析

采用近来提出的量子谱函数,我们把闭合轨道理论应用到半圆和四分之一圆弹子球系统,这种量子谱函数的傅利叶变换包含了连接任意两点的许多经典轨道的信息.计算表明量子谱的傅立叶变换和经典轨道的长度符合的很好.从这两个体系可以看出半经典理论为经典和量子力学提供了很好的桥梁作用.     

Monitoring of Methyldopa by Fast Fourier Transform Continuous Cyclic Voltammetry at Gold Microelectrode

A continuous cyclic voltammetric study of methyldopa at gold micro electrode was carried out. The drug in phosphate buffer (pH 2.0) is adsorpted at 400 mV, giving rise to change in the current of well-defined oxidation peak of gold in the flow injection system. The proposed detection method has some of advantages, the greatest one of which are as follows: first, it is no more necessary to remove oxygen from the analyte solution and second, this is a very fast and appropriate technique for determination of the drug compound in a wide variety of chromatographic analysis methods. Signal-to-noise ratio has significantly increased by application of discrete Fast Fourier transform (FFT) method, background subtraction and two-dimensional integration of the electrode response over a selected potential range and time window. Also in this work some parameters such as sweep rate, eluent pH, and accumulation time and potential were optimized. The linear concentration range was of 1.0×10－7—1.0×10－11 mol•L－1 (r＝0.9975) with a limit of detection and quantitation 0.004 nmol•L－1 and 0.03 nmol•L－1, respectively. The method has the requisite accuracy, sensitivity, precision and selectivity to assay methyldopa in tablets. The influences of pH of eluent, accumulation potential, sweep rate, and accumulation time on the determination of the methyldopa were considered.     

一类含参数的交错巴塞尔级数的和

利用Fourier级数及其和函数给出了含参数的一类交错巴塞尔级数的和，作为应用得到了一系列的特殊级数的和，最后验证了含参数的交错巴塞尔级数的和即是交错巴塞尔级数的和的推广.