代数学的

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。

Our studies mainly focus on the free groups with finite ranks . Free groups with finite ranks are the fundamental subjects of combinatorial group theory, and they have central importance for the studies of both topology and algebra.

我们研究比较多的是有限秩的自由群，有限秩自由群是组合群论的中心课题，是一个在拓扑学及代数学上都具有重要意义的研究对象，获取有关这些自由群的结构的信息的一个主要方法是研究其上的各种自同构作用。

The notion of a triangulated category was first introduced and studied by Grothendieck-Verdier in early sixties of the last century, which marks a new starting point of the development of modern algebras.

由Grothendick-Verdier在上个世纪60年代提出的三角范畴的概念和建立的理论体系，标志着代数学发展的一个新的里程碑，它架设了代数与几何联系的—座桥梁。

Secondly, what Glossematical School wants is to establish the linguistic typology, namely metatheory, helping to compare different theoretical pattern, sign systems, linguistic signs, and levels of linguistic symbol theoretical pattern, on the basis of which the study objects of glossematics are finite as relation among the previous statement, defined as function.

因为语言符号的形式和意义之间的关系是任意性的，不存在普遍意义的范畴。语言学的所有范畴都要从具体语篇中演算出来，这就要建立语言代数学，即语符学。其二是用纯理语言构建的语言模型，必须拿具体的语言去检验。模型反映出的是人类所有语篇，包括未出现的和已经消亡的语篇的各种可能性，利用语符学的经验原则和推导条件帮助识别出哪些是现实中存在的形式，哪些是潜在的形式。

Objective To investigate the effects of interleukin-1 β converting enzyme gene on the biologic characteristics of ovarian cancer cells.

目的 探讨白细胞介素-1 β转换酶的表达，对卵巢癌细胞生物学特性的影响。

Campylobacter: This illness is the most commonly identified cause of diarrheal illness in the world.

弯曲：这种病是最常见的原因查明腹泻病，在世界上。