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The transform formula of partially polarized GSM beam in dispersive and absorbing media as well as in anomalously dispersive media is derived.

利用张量方法导出了部分偏振GSM光束在色散吸收介质和负色散介质中的传输公式。

Three are three major actions that Mn effects fracture behavior in the alloy at room temperature, as follow: One is that Mn fines grains, antiphase domains and weakens dislocation clog, which retain formation of cleavage crackle. The second is that Mn decreases APB energy and promotes slop and cross slip, in particular, a large number of cross slip make deformed APBs transform from line type into zigzag type and the APBs interact and cross each other, resulting in propagation of cleavage cracks. The last is that Mn raises the relative proportion of cleavage strength to grain-boundary strength and then restrains formation and propagation of cleavage crack.

Mn对合金室温断裂行为的影响主要反映在三个方面，一是Mn的存在细化晶粒和反相畴，使得位错塞积程度减小，从而阻碍解理裂纹源的生成；二是Mn的存在提高解理强度与晶界强度的相对比值，从而抑制了解理裂纹的形成和扩展；三是Mn降低反相畴界能量、促进超位错的滑移、交滑移，特别是断裂前位错大量的交滑移使形变反相畴由直线型变为折线"Z"字型，反相畴界间的相互作用、相互交错阻碍了解理裂纹的扩展。

Convolutional differentiator is obtained by inverse Fourier transform of bandlimited Fourier spectra of partial derivative operator. CD is symmetric or antisymmetric and decays rapidly.

褶积微分算子是将偏导数算子的带限傅氏谱进行反傅氏变换得到的，具有对称或反对称和衰减速度快的特点。

A new Contoutlet transform, it is apparent frequency localized.

一种新的Contoutlet变换，它具有明显频率局部性。

And then there was the small matter of the Swift Boat Veterans for Truth: the shocking efficiency with which a few well-placed ads and the chants of conservative media could transform a decorated Vietnam War hero into a weak-kneed appeaser.

于是，《快艇老兵的真相》书中的一个小事件，几个安置适当的广告和保守派媒体的口号发挥了惊人的效率，使获得不少荣誉的越南战争英雄变成一个没骨气的和事佬。

An approximate nth derivative of an analytical signal can be obtained by applying n times of the wavelet transform to the signal.

用Haar小波对信号进行n次连续小波变换，可得到信号的近似n阶导数。

Two new functions based on the property of bubble wavelet are proposed. An approximate 2nd derivative of an analytical signal can be obtained by applying n times of the wavelet transform to the signal, the signal-to-noise ratio can be enhanced greatly.

根据小波的定义和墨西哥帽小波的一些特点提出了两种简单的窗口函数，利用它们对模拟高斯信号求2n阶近似导数的同时滤除了噪声，同时还可分离重叠峰，并讨论了尺度因子对变换结果的影响。

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。

In this thesis, The theory and advantages of JPEG2000 and wavelet transform theory ara briefly presented firstly.

本文首先简要介绍了JPEG2000标准的原理和优越性，以及小波变换原理。

Clams as well as many other species of mollusk produce aragonite first and then transform the crystal to calcite.

我们要研究的文蛤及大部分的软体动物会先制造霰石，再将霰石转成方解石结晶。

Chimborazo and Cotopaxi, took me by the hand.

越过琴博腊索山和科托帕克西山。

This car is in a good condition.

这辆车的状况很好。