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线性置换
相关语句
  linear permutation
     TWO PROBLEMS OF LINEAR PERMUTATION STATISTICS
     线性置换统计量的两个问题
短句来源
     Linear permutation and orthomorphic permutation
     线性置换与正形置换
短句来源
     A class of maximal closed sets in the set of the unary many-valued logic functions:The maximality of the linear permutation group in the symmetric group
     一元多值逻辑函数集中的一类极大封闭集——线性置换群在对称群中的极大性
短句来源
     In this paper,we discuss the linear permutation of cipher on self-dual MDS codes,which can lead to many good permutations.
     本文讨论了线性码中的自对偶MDS码,基于这种码,我们可以设计出性质比一般MDS码更好的P线性置换
短句来源
     The properties of irreducible linear permutations are studied by using linear algebra theory,An characterization for maximal linear orthomorphism is shown using properties above obtained. Furthermore,the result that the length of rotation of any nonzero element in F~n_2 for an irreducible linear permutation σ is equal to the peromid of characteristic polynomial of σ is obtained. Finally,the counting formula for irreducible linear permutations is given.
     提出了不可约线性置换的概念,利用线性代数理论研究了不可约线性置换σ的性质,利用这些性质给出了最大线性置换的一个刻画,进而证明了不可约线性置换σ关于Fn2中任意非零元素的轮换长度一定等于σ的特征多项式的周期,最后利用群在集合上作用的有关结果给出了不可约线性置换的一个计数公式.
短句来源
  “线性置换”译为未确定词的双语例句
     Irreducible linear permutations and their counting
     不可约线性置换及其计数
短句来源
     the normalizer in S_p, Ns_p (P) of every p-Sylow subgroup;
     本文主要讨论线性置换群在S_k或A_k中的极大性问题。
短句来源
     and the alternating group A_p. The number of all the maximal subgroups are equal to 2~(p-1)+(p-2)!
     由[8]之结论和有限单群分类的成果,作者定出了线性置换群在S_k和A_k中的全部极大子群。
短句来源
     Considering the given target displacement and ductility demand, the seismic design can be done easily without linear elastic substitute structure and iterative procedures.
     从结构的目标位移和位移延性需求出发 ,使用该方法不需线性置换结构和迭代过程即可完成结构的抗震设计。
短句来源
  相似匹配句对
     TWO PROBLEMS OF LINEAR PERMUTATION STATISTICS
     线性置换统计量的两个问题
短句来源
     Linear permutation and orthomorphic permutation
     线性置换与正形置换
短句来源
     PERMUTATION OF SEQUENCES
     序列的置换
短句来源
     Quick Trickle Permutation
     全距置换
短句来源
     Linear-fitting Method
     线性拟合法
短句来源
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  linear permutation
Asymptotic normality of double-indexed linear permutation statistics
      
Further, knowledge of the rate of convergence is equivalent to knowledge of the second largest value of the character of the linear permutation representation.
      
As a consequence bounds for the index of primitive and linear permutation groups can be obtained.
      


In the many-valued logic theory and the automaton theory, it is an essential and imporant problem to determine the completeness of the systems of the unary many-valued logie functions. The complete solution of the problem has been reduced to the determination of all the maximal subgroups of the symmetric group S_k on the set E_k={0, 1, …, k-1}.Based on the study of the basic groups in the k-valued logic, we can classify permutation groups into four mutully distinct classes as follows:(1) intransitive groups...

In the many-valued logic theory and the automaton theory, it is an essential and imporant problem to determine the completeness of the systems of the unary many-valued logie functions. The complete solution of the problem has been reduced to the determination of all the maximal subgroups of the symmetric group S_k on the set E_k={0, 1, …, k-1}.Based on the study of the basic groups in the k-valued logic, we can classify permutation groups into four mutully distinct classes as follows:(1) intransitive groups and imprimitive groups:(2) the permutation groups Preserving regular binary relation, then k=h~m, h≥5, m≥2;(3) linear permutation groups;(4) basic permutation groups.Thus, all the maximal subgroups of S_k can be obtained as soon as all the maximal subgroups of above four classes in S_k are found out.All the maximal subgroups of the 1st class in S_k has been determined by R. A. Bairamov, and those of the 2nd class in S_k, by Lou Zhukai(except for K=5~2). The author finds out all the maximal subgroups of the linear permutation group in S_K in this paper.Definition: Let E_K be an addition group with k elements, σ∈S_K is said to be a linear permutation, if for any x, y∈E_k, following equation holds: σ(x+y)+σ(O)=σ(x)+σ(y). The group consisting of all the linear p crmutations is called the linear permutation group, and denoted by L(E_k).It is easy to prove that if k(?)3, then L(E_k)=S_k.The author proved the following 3 theorems in this paper.Theorem 1: Let E_k be an addition group with k elements. Then:(1) If k>4, then L(E_k)is a maximal subgroup of A_k if and only if the period of every element (except for 0) of E_k is 2.(2) Let k=4.If E_4 is a cyclic group with 4 elements, then L(E_4) is a maximal subgroup of S_4, otherwise L(E_4)=S_4.Theorem 2: Let E_k be an addition group with k elements. and k≥5. L(E_k) is a maximal subgroup of S_k if and only if the period of e very elemnt (except for 0) of E_k is a same prime number p, p≠2.Theorem 3: Let k=p be a prime number and p≥5, Then, all the maximal subgroups of S_p are all the infransitive permutation groups with the form S(D_1)·S(D_2) (where E_p=D_1+D_2 and |D_1|≠|D_2|, S(D_2), S(D_2) are the symmetric groups on D_2, D_2 respectively); the normalizer in S_p, Ns_p (P) of every p-Sylow subgroup; and the alternating group A_p. The number of all the maximal subgroups are equal to 2~(p-1)+(p-2)!Corllary: Let k be a prime number and k≥5. The number of all the maximal closed sets of P_k~(1) are equal to 2~(k-1)+(k-2)!+1.

在多值逻辑理论和自动机理论中,一元多值逻辑函数系完备性之判断问题是一个基本而重要的问题。此问题的彻底解决依赖于定出集合E_k={0,1,…,k-1}上全体一元多值逻辑函数集P_k~(1)的所有极大封闭集。Bairamov对有限对称半群中完备性问题进行了研究,据其结果,我们可把P_k~(1)的所有极大封闭集的确定归结为定出E_k上K次对称群S_k的全部极大子群。但在有限群论中,定出S_k的所有极大子群至今还是一个尚待解决的困难问题。由K值逻辑中基本群之研究,我们将E_k上的置换群分为下列互不相同的四类: 一、非可迁群和非本原群; 二、保正则二项关系的置换群,此时K=h~m,h≥5,m≥2; 三、线性置换群; 四、基本置换群,即它与一个真多元取K个不同值的函数构成P_k的一个完备集,这里P_k是由E_k上全部多值逻辑函数所作成的集合。这样,只要定出上述四类置换群在S_k中的极大子群,就定出了S_k的全部极大子群Bairamovc和Balll分别定出了第一类置换群在S_k中的全部极大子群。罗铸楷根据多位逻辑函数之特性,简捷地确定了S_k中保正则二项关系置换群的具体表示,并定出了其在S_k和工A_k(K次...

在多值逻辑理论和自动机理论中,一元多值逻辑函数系完备性之判断问题是一个基本而重要的问题。此问题的彻底解决依赖于定出集合E_k={0,1,…,k-1}上全体一元多值逻辑函数集P_k~(1)的所有极大封闭集。Bairamov对有限对称半群中完备性问题进行了研究,据其结果,我们可把P_k~(1)的所有极大封闭集的确定归结为定出E_k上K次对称群S_k的全部极大子群。但在有限群论中,定出S_k的所有极大子群至今还是一个尚待解决的困难问题。由K值逻辑中基本群之研究,我们将E_k上的置换群分为下列互不相同的四类: 一、非可迁群和非本原群; 二、保正则二项关系的置换群,此时K=h~m,h≥5,m≥2; 三、线性置换群; 四、基本置换群,即它与一个真多元取K个不同值的函数构成P_k的一个完备集,这里P_k是由E_k上全部多值逻辑函数所作成的集合。这样,只要定出上述四类置换群在S_k中的极大子群,就定出了S_k的全部极大子群Bairamovc和Balll分别定出了第一类置换群在S_k中的全部极大子群。罗铸楷根据多位逻辑函数之特性,简捷地确定了S_k中保正则二项关系置换群的具体表示,并定出了其在S_k和工A_k(K次交代群)中的全部极大子群(除K=5~2外)。目前,关于第四类置换群在S_k中的极大子群还只有一些零星结果。由于基本置换群与多值逻辑函数紧密相关,可以预见,在其极大性之研究中,多值逻辑函数的结构理论必将成为有力的工具。本文主要讨论线性置换群在S_k或A_k中的极大性问题。由[8]之结论和有限单群分类的成果,作者定出了线性置换群在S_k和A_k中的全部极大子群。此外,当K为质数时,作者还定出了S_k的全部极大子群,从而定出了P_k~(1)的所有极大封闭集。

Theorem. If f(x) is a nonlinear permutation, then f(x), ax, x+ 1 are complete system over Sp, where the degree of a (a∈Rp) is p- 1.Theorem: Let f(x) be a non-generalized linear permutation. If f(x) is an odd (even)permutation, then f(x), x+ 1 are complete system over Sp(Ap).

首次提出了广义线性置换,并定出其划定的充要条件,同时还定出了几类新的一元多值逻辑函数的完备集.

This paper deals with the relation between linear permutation and orthomorphic permutation. In addition, based on linear permutation, we have investigated the construction of orthomorphic permutation.

论述了线性置换与正形置换的关系,研究了线性置换对正形置换的构造问题,并获得了有意义的结果.

 
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