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In the fourth chapter, firstly it introduces the Boolean functions algebraic expressions of the 2-value clock-controlled stop-and-go generator and Gunther generator. It reveals the balanced property of the two kinds of Boolean functions, and studies the Walsh cycle spectrum and the autocorrelation function. It also obtains the coincidence rate of their output sequences with affine sum of some bits of input sequences, and analyzes their ability of resisting the best affine approximation cryptanalysis and differential cryptanalysis. Secondly, we properly present a new definition of the Best Affine Approximation, namely BAA on the Boolean vector functions, followed by the spectral characteristic of such defined BAA attacks through using the decomposition formula of the union distribution for random variables. A lower bound of such BAA attacks is proposed. Finally, we also study the spectral characteristic of the second kind of nonlinearity of Boolean vector functions, followed by a higher bound of such nonlinearity. Furthermore, the limited relationship between the second kind of nonlinearity of Boolean vector functions and the linear structure of the linear combination of every component is analyzed.

在第四章中，首先给出了2值密钥流"停走生成器"和"衮特生成器"中实际存在的布尔函数的代数表示，揭示了这两类布尔函数的平衡性，随后研究了它们的Walsh循环谱和自相关函数等，得到了它们的输出序列与输入序列中的某些bit的仿射项的符合率，分析了它们抵抗最佳仿射逼近攻击和差分攻击的能力；其次，我们合理地给出了布尔向量函数最佳仿射逼近的新定义，利用布尔随机变量联合分布的分解式考察了相应的谱特征，并给出了布尔向量函数与其最佳仿射逼近的符合率的一个下界；最后，我们还考察了布尔向量函数第二类非线性度的谱特征，给出了布尔向量函数第二类非线性度的一个上界，并揭示了布尔向量函数第二类非线性度与其各个分量的线性和的线性结构之间存在的制约关系。

Using the theories of probability, algebra and spectral theory comprehensively, we investigate some related characteristics of logic functions in cryptography: Firstly, we introduce m order generalized s - correlation immunity of Boolean vector functions and prove that the higher order generalized ε- correlation immunity can guarantee the lower order generalized ε- correlation immunity. Then by applying decomposition formula of joint distribution of Boolean random vectors, we give a spectrum criterion of m order generalized e - correlation immunity of Boolean vector functions. Furthermore, we show that the algebraic degree of m order generalized e - correlation immune Boolean vector functions is not restricted by the correlation immune orders.

本文主要运用概率论的思想和方法，并结合代数学和频谱理论的相关知识，对密码学中逻辑函数的有关性质进行了研究，主要包括以下三个方面的内容：首先，对布尔向量函数的相关免疫性进行了拓展，给出了k维布尔向量函数m阶广义ε-相关免疫的概念，证明了布尔向量函数的高阶广义ε-相关免疫性蕴含低阶广义ε-相关免疫性，并根据布尔随机向量联合分布分解式得到了布尔向量函数m阶广义ε-相关免疫的一个谱判别条件，还说明了m阶广义ε-相关免疫布尔向量函数的代数次数不受相关免疫阶数的制约。

The proof is given that the category of linear fuzzy neighborhood spaces in the sense of Katsaras is isomorphic to that of co-towers of topological vector spaces and the intersection of the category of linear fuzzy neighborhood spaces with the category of type fuzzy topological vector spaces is the extract category of induced fuzzy topological vector spaces.

证明了Katsaras的线性fuzzy邻域空间范畴与分明线性拓扑空间的余塔空间范畴同构，而Katsaras的线性fuzzy邻域空间范畴与型fuzzy拓扑线性空间范畴的交集恰为诱导的fuzzy拓扑线性空间范畴。

Research emphasis is put on thefollowing aspects:First,study of multiwavelet basis(e.g.periodic vector,interpolation vector,multi-dimensional vector)suitable for different practical demands.Second,from perspective of operatorapproximation order,study of normal function approximation operator,contrast and comparison ofwavelet operator and multiwavelet operator and their respective applicable fields.And further,onbasis of the above,exploration of approaches of multiwavelet analysis application in function spacetheoretical research,and higher-lever,more convenient approaches for multi-function spaceapproximation theoretical research.Third,by fully employing unique features of multiwavelet,research action of multiwavelet analysis in the construction of L〓space non-conditionalbasis.Fourth,research such as transient signal analysis,image edge extraction,datacompression,fractal signal analysis.

其一，研究适宜于不同实际问题需要的向量小波基（如周期向量小波、插值向量小波、高维向量小波等）；其二，从算子逼近阶的角度研究一般函数逼近算子、小波算子和向量小波算子的异同点以及较优适用领域；在此基础上，探索将向量小波分析应用于函数空间理论研究的途径，寻找更高层次、更便捷地研究多元函数空间逼近理论的方法；其三，充分利用向量小波所独具的完美性质，探索在〓空间〓无条件基的构造中，向量小波分析的价值；其四，对向量小波适用的信号瞬态分析、图像边缘分析、数据压缩保真、分形信号分析等领域应给予特别的重视。

The accurate solution of linear equations could be expressed linearly by the conjugate vector base, and the iterative strategy was used to construct the conjugate vector base groups and the corresponding coefficient. The constructed conjugate vector base groups were proved to be conjugated.

线性方程组的精确解能够由共轭向量基线性表示，利用迭代的方式给出了构造共轭向量基以及对应系数的方法，证明了算法所构造的向量基的共轭性。

As the current and voltage have the same basic frequency, the unit voltage Park vector and its conjugate are used to rotate the current Park vector. During the course of rotation, the fundamental positive sequence component in the current Park vector can be filtered out but the others remain.

利用电压与电流基波频率相等，用单位电压Park矢量及其共轭对电流Park矢量进行旋转变换，从而将电流Park矢量的基波正序分量完全滤除而不影响其他的谐波分量。

In this research we obtained the banana ACO gene with about 1.2kb length by cuffing from the cloning vector pUCm-ACO with restriction endonucleases Xba Ⅰ and Sac Ⅰ, and then directionally linked the gene to the plasmid vector pBⅠ-121 in the same endonucleases digestion sites, finally we got the construct of plant expression vector pBI-aACO.

用限制性内切酶Xba Ⅰ和sac Ⅰ从克隆载体pUCm-ACO上切下约1.2kb的香蕉ACO基因，将其定向连接在经相同酶切的质粒载体pBⅠ-121上，构建成植物表达载体pBⅠ-aACO。

First,image structure vector field is derived from source luminance orthonormal vector sets. Andusing neighbor vectors to improve the weak gradient fields produces the structure vectorfield that is needed by LIC rendering. Then, LIC convolution step-length is adjustedaccording to local curvature in the structure vector field. LIC convolution length iscalculated according to the local statistical characteristics of the texture image. Finally, thealgorithm transfers the reference image\'s color characteristics to the rendering result tomake it full of rich color like oil paintings.

该算法通过计算源图像亮度分量的切矢量产生图像的结构矢量场，并对弱矢量区域进行邻域填充处理，获得LIC绘制所需的结构矢量场；然后，根据结构矢量场的局部曲率特征调整LIC的积分步长，并根据纹理参考图像的局部统计特征，自适应地改变LIC的积分长度；最后，将颜色传输算法引入LIC绘制结果，对绘制效果颜色进行渲染。

Introduction, Reviews and Concepts of Functions, Differentiation, Vector Algebra, Vector differetiation, Vector Integral, Orthogonal Curvilinear Coordinates.

课程介绍及授课计划、函数观念及复习、微分、向量代数、向量微分、矢量积分、正交曲线坐标、微分方程式。

The brief decision rules according with the demands of threshold is directly mined from decision tables based on rough information vector.In this process,decision support ability of condition vector to decision vector is used,and the concrete decision support ability of condition attribute value is not losing.

基于粗糙信息向量，利用条件向量对决策向量的决策支持能力，直接从决策表中挖掘出符合阈值要求的尽可能简洁的决策规则，且不损失条件属性值的决策支持能力。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。