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It includes the following two major aspects:Firstly, the classification and recognition of bifurcation problems.

这些研究主要有以下两个方面的问题：第一，分歧问题的分类与识别。

This paper, firstly, after a deep study of image mathematical models, sets up two kinds of image models namely Laplace partial differential equation model and biharmonic equation model and then obtains the eigenvectors of image by the methods of eigenfunction expansion and boundary recurrence.

本文首先较深入地研究了图象的数学描述，提出图象的Laplace偏微分方程和双调和方程两种模型，继而采用特征函数展开法和边界递推法分别求得图象的特征矢量。

Firstly, we discuss the boundary value problem of one dimensional biharmonic equation in an interval and its variational problem,multiresolution analysis in the Sobolev space , then solve it with wavelet-Galerkin methods.

首先本文讨论了一维双调和方程边值问题及其相应的变分问题，定义Sobolev空间的多分辨分析，用小波–伽辽金方法进行数值求解，两组基下得到的系数矩阵为七对角阵和块状对角阵。

Firstly, the performance indices of S-box were summarized. Five properties such as nonlinearity, SAC, BIC, differential uniformity and bijection, were employed as the main indices to evaluate S-boxes.

首先对评价S盒性能的指标进行了分析，以非线性度、完全雪崩准则、输出比特间独立性、差分均匀性和双射作为主要的评价指标。

The design of digital notch filters can be achieved through three steps:firstly,the design of analog lowpass filter; secondly,it is analog lowpass to analog band stop filter conversion;at last,using the bilinear transformation make the analog notch filters change into digital notch filters.

研究一种在Matlab语言环境下设计IIR数字陷波滤波器的方法，在数字陷波滤波器设计过程中，先进行模拟低通滤波器的设计，然后进行模拟低通/模拟带阻滤波器转换，最后采用双线性变化法将模拟陷波滤波器转化成数字陷波滤波器。

along with the development of digital technology,digital filters are widely used in many fields,this paper introduces how to design a iir digital notch filters in matlab environment.the design of digital notch filters can be achieved through three steps:firstly,the design of analog lowpass filter; secondly,it is analog lowpass to analog band stop filter conversion;at last,using the bilinear transformation make the analog notch filters change into digital notch filters.the paper also introduces how to design the transfer function of the digital notch filters using all the zeros and farthest points at the same time,it also introduces the program of the digital notch filters under butterworth analog lowpass prototype.

摘 要：随着数字技术的发展，数字滤波器在许多领域得到广泛的应用。研究一种在matlab语言环境下设计iir数字陷波滤波器的方法，在数字陷波滤波器设计过程中，先进行模拟低通滤波器的设计，然后进行模拟低通/模拟带阻滤波器转换，最后采用双线性变化法将模拟陷波滤波器转化成数字陷波滤波器。提出一种用所有零点和极点来表达数字陷波器传递函数的方法，同时给出以巴特沃斯模拟低通为原型设计数字陷波滤波器的程序。关键词：无限冲激响应；巴特沃斯滤波器；数字陷波滤波器；matlab；双线性变换

Firstly, an ID-based signature scheme is proposed based on pairings. The bilinearity and non-degeneration of pairings are explored to make the verification result of the signature vary only with the identity of the signer.

基于双线性对构造了一种基于身份的签名算法，利用双线性对的双线性和非退化性，使得算法中签名矢量的验证结果相对于用户身份为一个常量。

Firstly, bilingual education is to create better environment of foreign language learning over two cultures and subjects.

首先，双语教学是为了营造更好的跨文化，跨学科的外语学习的环境。

In chapter 3, we firstly discuss the equivalence of the known APN polynomialfunctions on binary field. Moreover, we present a new family of APN polynomialfunctions and analyze their bent property.

在第三章中，首先讨论了特征为2的域中已知的几类APN多项式函数的等价性质，接着给出了一类新的APN多项式函数，并进一步分析了它的bent属性。

Firstly the function of decoder in binary translation was introduced and a decoding algorithm was designed based on instruction bundle according to the features of IA-64 instructions.

文中介绍了二进制翻译中解码器的功能，并结合IA-64的指令特点，设计出基于指令束的解码算法。

Chinese traditional virtue is humility and wariness,the compliment and praise to the others should be declination

中国人的传统美德是谦虚谨慎，对别人的恭维和夸奖应是推辞。如

We bought this house on the never-never.

我们以分期付款的方式买下这座房子。