波函数

Combining the definition of CWT and the derivative property of convolution, we constructed a general method to calculate the approximate derivative of signal through CWT by using the first and second derivative of Gaussian function, Haar, and the first derivative of three-order-Spline function as wavelets. As compared with the other approaches of calculating derivative, which include the numerical differentiation, polynomial filters, Fourier transform, and the recently proposed DWT method, fast calculation and simple mathematical operation were remarkable advantages of CWT method. For the signal corrupted by severe noise (Signal-toNoise Ratio=5), the satisfactory results could also obtained via CWT method through appropriately adiusting the dilations.

在此基础上，(1)结合连续小波变换的特点和卷积的微分性质，提出了使用Gaussian函数的一阶和二阶导数，Haar和三次样条函数的一阶导数作为小波函数的连续小波变换计算信号近似导数的一般性方法，与其他导数计算方法(包括数字微分法，多项式滤波法，Fourier变换法和离散小波变换法)相比，本法简单便捷，计算速度快，对于噪声含量较高的信号(S/N为5)，只要适当调节尺度即可获得比较满意的结果。

Any function on an interval will be expanded as the sum of finite items of the scaling functions and wavelets. It plays an important role for numerical analysis of partial differential equations, signal processes, and other similar problems.

于是，任何有限区间上的函数皆可表示为该区间上的尺度函数和小波函数的有限和，即小波级数，这克服了用无穷区间上的小波进行有限信号处理时，在边界上误差较大的不足，同时将该小波用于偏微分方程具有同样重要的意义。

We find the most contributions of form factors come fromΨπ,K andΨB, but the contributions ofΨσfrom the pion and the kaon meson, the contribution ofΔfrom B meson are very small, and can be neglected in most of the calculations.

结果发现π、K介子波函数中的Ψπ，K，B介子波函数中的ΨB对形状因子的贡献最大，而π、K介子波函数中的Ψσ，B介子波函数中的Δ对形状因子的影响很小，可以忽略。

Iterative process of error-reduction algorithm is anlyzed, the phase-only object function is obtained when the amplitude of object function and the amplitude of its Fourier transformation are known, and the amplitude and phase of object function are retained as much as possible.

分析了采用错误减算法的迭代过程，在已知物波函数傅里叶谱的振幅和物波函数振幅的情况下恢复出纯相位的物波函数，最大限度地保留物波的振幅及相位信息。

We all know that mother wavelet function can create waveletframe, and the kernel function with wavelet frame can build a group of basis insquare integral space only by translation.

由于母小波函数可以生成小波框架，我们用小波框架来构造核函数，而采用该核函数的SVM，能够逼近平方可积空间中的任意函数。

The multi-wavelets functions are supported on [-1, 1], and one wavelet function is symmetric, the other is anti-symmetric.

所以，可以由这两个尺度函数构造一类多小波函数，这类多小波函数不但在[-1，1]上具有紧支撑性，而且一个小波函数具有对称性，另一个小波函数具有反对称性，因此这种紧支撑多小波函数适用于区间[0，1]。

So, in this paper, a circular cavity witha large radius is used to replace the straight boundary of thehalf space, then the half space problem can be changed tothe scattering problem of two circular cavities to the steadyincident P-wave . Having the aid of the mature cylinderfunction theory, the general solutions of the wave functionscan be given, and an infinite linear algebraic equations ofthe unknown coefficients in the wave functions can be gottenwith the boundary conditions and the Fourier complex seriesexpansion technology, the infinite linear algebraic equationscan be approximately solved by the finite trunction withsatisfying some definite precision, at the basis of thissolution of the equation, the variations and the lay-outs ofthe DSCF at the circular cavity boundary vs. the differentincident angles, the different embedded depths of thecircular cavity as well as the different dimensionless wavenumber of the incident P-wave.

为此，本文采用一个半径很大的圆孔来代替半空间的直边界，将该半空间问题转化为一无限大空间中两个圆孔对稳态P波的共同散射问题，借助于成熟的柱函数理论，通过写出问题波函数的一般形式解，利用问题的边界条件，并采用复数傅立叶级数展开技术将其化为一个仅包含问题波函数中未知系数的一无穷线性代数方程组，在满足一定计算精度的前提下，通过有限项截断进行近似求解，进而讨论了圆孔边界处的动应力集中系数随不同入射角、不同的圆孔掩埋深度、入射波的不同无量纲波数以及介质的泊松比变化和分布情况。

It is found thatthe fractal dimension D=1.25 corresponds to the lowest criticalcoupling constant αc=1.9,D=1.73 corresponds to the highest criticalratio of dielectric constants ηc=0.163,and when D≤1.145 bipolaronscan not exist at any rate.In chap,4,we will propose a novelapproach to the calculation of the exciton ground-state energy for thestrong-coupling case.Different from all previous methods,the wavefunction of the phonon part is assumed to take a form related to thewave function of the relative motion.We obtain the exciton energy bysolving the derived integrodifferential equation rather than select ahydrogen-like form to minimize the energy expectation.

结果发现，分数维的维数D＝1.25对应最小的临界的电-声耦合常数(αo＝1.9)，D＝1.73对应最大的临界的介电常数比(ηc＝0.163)，当分数维的维数D≤1.145时，双极化子无论如何也不可能存在，在第四章中，我们将提出一种新颖的变分方法来计算强耦合的激子-声子系统的基态能，不同于以前所有的方法，我们取声子的波函数与相对运动波函数有关的形式，而不是假定一个固定的关于相对运动坐标r的函数形式，得到相对运动波函数所满足的非线性的微分积分方程，我们数值求解这个微分积分方程得到系统基态能，而不是选择一个类氢原子的波函数变分使得能量的期待值最小。

Second, based on the spherical vector wave function in uniaxial anisotropic medium, and the first, second, third and fourth spherical Bessel functions satisfy the same differential equation and recursive formula. The scattering fields in terms of spherical vector wave function from a uniaxial anisotropic spherical shell and an anisotropic uniaxial-coated conducting sphere by a plane wave are derived. The electromagnetic fields in uniaxial anisotropic medium and free space can be expressed in terms of spherical vector wave functions in uniaxial anisotropic media and isotropic medium.

二、在建立均匀各向异性单轴介质球矢量波函数理论的基础上，利用二阶线性偏微分方程的性质和第一、第二、第三和第四类球Bessel函数满足相同的微分方程和递推关系，我们分别研究了单轴介质球壳和单轴介质涂覆导体球对平面波的电磁散射特性，首先给出了各个区域的电磁场用球矢量波函数来表示的解析表达式，进而利用电磁场在边界上满足电磁场切向连续的边界条件和球谐函数的正交性，得出了各向异性单轴介质球结构中电磁场用球矢量波函数表示的系数所满足的矩阵方程。

The contributions ofΨp from the pion and the kaon meson, the contribution ofΨB from B meson are not very small, and can not be safely neglected for giving more resonable results of form factors.The B meson wavefunction is a major source of uncertainty in the study of B meson decays. The B→πand B→K transition form factors provide a good platform to determine the possible regions for the two typical phenomenological parametersΛandδ.

但π、K介子波函数中的Ψp和B介子波函数中的ΨB对形状因子的贡献比较大，为了获得更加合理的形状因子的结果，一般不能忽略π、K介子波函数中的Ψp和B介子波函数中的ΨB项的贡献。B介子波函数是B介子衰变中不确定性的一个主要的来源。B→π和B→K跃迁形状因子为确定两个典型的唯象参数Λ和δ提供了一个很好的平台。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。