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Moreover, the quasi-analytical expressions of the relative concentrations at the mobile region and the immobile region are deduced respectively by using Bessel equation, Bessel function and the method of Laplace transform under the initial concentration zero and the first or second boundary condition of a semi-infinite one-dimensional space.

并分别在初始浓度为零，半无限一维空间内第一类边界条件和第二类边界条件下，利用Bessel方程、Bessel函数和Laplace变换法推导出了可动区和不动区溶质相对浓度的准解析表达式。

In chapter 1, firstly, by using classical analysis methods, such as the introduction of Bessel function and semigroup theory, we transform the pseudo-parabolic equation into an abstract operator equation and achieve the existence and uniqueness of the local solution.

在第一章中，利用经典的分析方法，引入Bessel势函数，将伪抛物型方程转化为抽象算子方程，首先，利用算子半群理论，论证了局部解的存在唯一性。

Inspired by the wavelets,we introduce the concept of geometric wavelets.We transform the compression into a best uniform approximation which is familiar to us in mathematic,we approximate the signal with polynomials.

受小波方法的启发，我们引入了几何小波的概念，将压缩问题转化为逼近理论中熟知的最佳一致逼近问题。

Tubbs firstly used a regularized Beta function to fit the contrast transform of an input image.

不同对比度分布的图像应采用不同的对比度变换函数。

Tubbs redefined the several common nonlinear functions of gray transform as a normalized Incomplete Beta Function, in order to realize image enhancement processing.

传统的图像增强处理是针对图像灰度分布的不同情况，来定义相应的灰度变换函数。

In order to solve this problem, the paper presents a so - called Bi - watermarking Algorithm Based on Wavelet Packet and DCT transform.

针对这一问题，该文在结合小波包变换和离散余弦变换的同时，在图像小波包分解后的低频和高频部分选取适当系数分别嵌入同一个水印。

In this paper,three dimensional wavelet transform based on bidirectional motion compensation was presented.

但是仍然需要新的视频编码方案，以尽可能地提高视频编码的效率和质量。

Transform your favorite jewelry pieces into a dazzling display by storing them on a Polished Chrome Bijou Jewelry Tree.

改变你成为一个耀眼的显示器件最喜欢的首饰存储在一个珠宝抛光铬愉景树他们。

Parameter identification Markov method for continuous stochastic linear system and bilinear system via wavelet transform The statistical properties of continuous Wiener process are studied.

基于小波变换的离散随机线性和双线性系统参数辨识Markov方法分析了由白噪声驱动的有理滤波器输出随机信号在小波变换下的滤波和去相关特性，提出一种在线估计噪声协方差矩阵及其Cholesky分解因子的方法。

Abstraction :This paper analyzes the principle of Butterworth digital filter,discuss bilinear transformation method of filter design;record a piece of voice by Microsoft voice recorders, carry on its a time-domain analysis, spectral analysis;then design a specified Butterworth band-stop filter based on the theory of bilinear transform,analyze the filter by the tool named Fvtool;and filter the voice signal acquired by voice recorder.finally compare its characteristics of frequency domain and time domain,study the applications of Butterworth filter in digital signal processing ,in particular in signal denoising.

本文分析了巴特沃思数字滤波器的原理，探讨了双线性变换法设计滤波器的方法；用微软录音机采集一段语音，对其进行了时域分析，频谱分析；然后使用双线性变换法设计了一个的巴特沃思带阻滤波器，并且使用fvtool对设计的滤波器进行分析；然后利用该滤波器对采集的语音信号进行滤波。最后对比滤波前后的语音信号的时域和频域特性，研究了巴特沃思滤波器在信号处理尤其是信号滤波去噪方面的特性和应用。

Don not attempt to do something which you can not to do.

不要企图做那些办不到的事情。

The expression of CTGF and TNF-αweredetected by immunochemistry and the number of Clara Cells was calculated.

光镜下观察肺组织的病理变化，采用免疫组化染色观察肺组织中结缔组织生长因子和肿瘤坏死因子-α的表达和Clara细胞的数量。