An optical measurement of vortex shape at a free surface

We have proposed an optical method of vortex shape measurement based on Fourier transform profilometry (FTP) and verified it by experiment. The results of our experiment proposed in this paper show that FTP can efficiently reconstruct the vortex shape at a free surface and this method is suitable for wide use in studying such problems as liquid shear flow, wake of an object, flow behind a bluff body, and wetting angle.     

一类相空间中的准几率分布函数系

定义了一类相空间中的准几率分布函数系，这个准几率分布函数系直接建立在具有更加广泛意义的量子相空间Schr?dinger方程解的基础之上，其中定义_α=αp-i?q和_α=(1-α)q+i?p.发现了两个有趣的关系.(1)建立的量子相空间Schr?dinger方程的解实际上是对函数φ(λ)exp［i(1-α)qp］做窗口Fourier变换.(2)这个窗口函数g(λ)起着选择窗口形式的作用，而且不同的窗口对应着不同的分布函数.当g(λ)是一个代表Gauss窗的Gauss函数的时候，准几率分布函数就是一个类似于Husimi的分布函数f^HL_α(q,p)；当g(λ)是一个表示椭圆的复函数时，准几率分布函数就是一个椭圆分布函数f^E_α(q,p)；再在g(λ)为复函数的基础上附加α=0，就可得到标准序分布函数f^S(q,p)、反标准序分布函数f^AS(q,p)和Wigner分布函数f^W(q,p)，此时g(λ)表示高度为1/12π?而长度为λ的矩形窗. 关键词： 窗口Fourier变换 相空间 Wigner分布函数     

Laguerre expansion on the Heisenberg group and Fourier-Bessel transform on C~n Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

Given a principal value convolution on the Heisenberg group Hn = Cn×R, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on Cn. We also calculate the Dirichlet kernel for the Laguerre expansion on the group Hn.     

一类混合型微分差分方程的周期解

利用Fenchel变换,我们推出一类微分差分方程存在周期解等价于某泛函具有临界点,并求出方程具有周期解的充分条件.     

On the counting function of the lattice profile of periodic sequences

The lattice profile analyzes the intrinsic structure of pseudorandom number sequences with applications in Monte Carlo methods and cryptology. In this paper, using the discrete Fourier transform for periodic sequences and the relation between the lattice profile and the linear complexity, we give general formulas for the expected value, variance, and counting function of the lattice profile of periodic sequences with fixed period. Moreover, we determine in a more explicit form the expected value, variance, and counting function of the lattice profile of periodic sequences for special values of the period.     

一种小波域音频信息隐藏方法

提出了一种基于量化的小波域音频隐藏算法，将保密语音隐藏到载体音频中．为提高隐藏重和保密语音传输的安全性，对保密语音进行了小波域压缩编码和m序列的扩频调制，生成待隐藏的比特序列；通过量化方法，将编码和调制后的保密语音隐藏到载体音频的小波系数中；保密语音的恢复过程不需要使用原始音频、仿真结果表明，隐藏有保密语音的载体音频听觉质量没有明显下降，提取的保密语音感知质量较好；该算法对重量化、加噪、低通滤波等攻击均有良好的鲁棒性．     

A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature

We consider the discretization in time of an inhomogeneous parabolicequation in a Banach space setting, using a representation ofthe solution as an integral along a smooth curve in the complexleft half-plane which, after transformation to a finite interval,is then evaluated to high accuracy by a quadrature rule. Thisreduces the problem to a finite set of elliptic equations withcomplex coefficients, which may be solved in parallel. The paperis a further development of earlier work by the authors, wherewe treated the homogeneous equation in a Hilbert space framework.Special attention is given here to the treatment of the forcingterm. The method is combined with finite-element discretizationin spatial variables.     

小波提升算法及其在图像处理中的应用

小波提升算法是一种新的双正交小波构造方法，通过预测算子，确定高频信息，并初步确定低频信息，然后通过更新算子，对初步确定的低频信息进行修正，从而确定低频信息。它在空域对信号进行变换，完成了对信号频域的分析。在图像处理中，基于离散小波变换的提升算法比传统的卷积算法运算简单，实时性好，易于实现，因而被新一代图像压缩标准JPEG2000所采用。文中简要介绍了小波提升算法的原理，分析了其特点，并介绍了JPEG2000标准中采用的W5／3、D9／7两种小波的提升格式和实现算法。     

Quasi-Chun-Ching Shih''''s Fractional Fourier Transform with Periodicity of 2,3 and M

Based on Chun-Ching Shih's idea, the basic transform was substituted and the quasi-ChunChing Shih's fractional Fourier transform with periodicity of 2, 3 and M was deduced. The two former transforms and the Chun-Ching Shih's fractional Fourier transform were only the particular cases of quasiChun-Ching Shih's fractional Fourier transform with periodicity of M.     

Fourier-Feynman transform, convolution and first variation

We examine several interesting relationships and expressions involving Fourier-Feynman transform, convolution product and first variation for functionals in the Fresnel class F(B) of an abstract Wiener space B. We also prove a translation theorem and Parseval's identity for the analytic Feynman integral. This revised version was published online in June 2006 with corrections to the Cover Date.