Ω-模糊软环

将软集理论的概念应用到Ω-模糊环中,提出了Ω-模糊软环的概念,给出了Ω-模糊软环的交与并的定义;探讨了交与并的一些相关性质;讨论了Ω-模糊软环的同态的一些性质,并提出了Ω-模糊软子环和模糊软同构的概念,研究了与其相关的性质。     

概率命题逻辑是经典命题演算形式系统的随机事件语义

经典命题演算形式系统(CPC)中的公式只是一些形式符号,这些形式符号的意义是由具体的解释给出的.概率逻辑是在标准概率空间上建立的一种逻辑体系,是CPC的随机事件语义,对联结词的解释就是集合运算,对形式公式的解释就是事件函数,对逻辑蕴涵和逻辑等价的解释就是事件(集合)包含和事件相等=.由于不存在处处适用的真值函数(算子),概率逻辑不能在CPC内实现概率演算,但可在CPC内实现事件演算,CPC完全适用于概率命题演算.     

Soft groups and normalistic soft groups

Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, first we correct some of the problematic cases in a previous paper by Akta? and Çag˜man [H. Akta?, N. Çag˜man, Soft sets and soft groups, Inf. Sci. 177 (2007) 2726-2735]. Moreover, we introduce the concepts of normalistic soft group and normalistic soft group homomorphism, study their several related properties, and investigate some structures that are preserved under normalistic soft group homomorphisms.     

Soft polygroups

Soft set theory, introduced by Molodtsov, has been considered as an effective mathematical tool for modeling uncertainties. In this paper, we initiate the study of algebraic hyperstructures of soft sets. The concepts of soft polygroups, normal soft polygroups, soft subpolygroups and normal soft subpolygroups are introduced, and some related properties are investigated. Furthermore, we propose the homomorphism and isomorphism of soft polygroups, and establish three isomorphism theorems for soft polygroups.     

Intuitionistic fuzzy transformation semigroups

The idea of (faithful) intuitionistic fuzzy transformation semigroup, intuitionistic admissible relation, and intuitionistic (strong) homomorphism are introduced and their basic properties are examined.     

L-拓扑空间的θ-闭包与θ-连续序同态

在L-拓扑空间中通过引入θ-闭包的概念,定义θ-开（闭）集,讨论θ-闭包和θ-闭集的性质及其刻画.同时给出了两个有用的命题,证明了L-拓扑空间中全体θ-开集形成一个比原拓扑更粗的拓扑,进而引入并研究了θ-连续序同态,同时给出了θ-连续序同态的刻画,并举例说明θ-连续映射不必是连续映射.     

关于高斯二次反比定律的另一种证明方法

高斯利用有限体中的元都是二次的这一性质,推证了Legendre符号的二次反比定律（l/p）=（p/l）（-1）^ε（l）ε（p）.如果乘群F＊p的子集S满足F＊p是S和-S的和,那么S可取为S={1,2,...,p-1/2}的特殊形式.本文利用这一性质把Legendre符号的运算转化成S中元的三角运算,再通过三角引理的具体计算推得高斯二次反比定律,从而给出其另一种证明方法.     

Separable reversible data hiding in encrypted image based on pixel value ordering and additive homomorphism

This work proposes a separable reversible data hiding scheme in encrypted images based on pixel value ordering (PVO). After the original image is encrypted using homomorphism encryption by the content owner, the data hider embeds the secret data in encrypted domain. The PVO strategy realizes hiding data in each block. Additive homomorphism guarantees the performance of PVO in encrypted domain is close to that in plain domain. Besides, the homomorphism encryption does not cause data expansion, and the payload can be further improved. With the watermarked encrypted image, if the receiver has only the data hiding key, he can extract the additional data. If the receiver has only the encryption key, he can obtain a decrypted image similar to the original one. If the receiver has both the data hiding key and the encryption key, he can extract the additional data without any error and recover the original image losslessly.     

不可满足公式的同态证明系统

合取范式(CNF)公式H到F的同态φ是一个从H的文字集合到F的文字集合的映射,并保持补运算和子句映到子句.同态映射保持一个公式的不可满足性.一个公式是极小不可满足的是指该公式本身不可满足,而且从中删去任意一个子句后得到的公式可满足.MU(1)是子句数与变元数的差等于1的极小不可满足公式类.一个三元组(H,φ,F)称为的一个来自H的同态证明,如果φ是一个从H到F的同态.利用基础矩阵的方法证明了:一个不可满足公式F的树消解证明,可以在多项式时间内转换成一个来自MU(1)中公式的同态证明.从而,由MU(1)中的公式构成的同态证明系统是完备的,并且由MU(1)中的公式构成的同态证明系统与树消解证明系统之间是多项式等价的.     

Ω-代数遗传性的注记

探讨了Ω-代数的遗传性,即考察Ω-代数的生成元集的性质对Ω-代数自身性质的影响.证明了在一定条件下Ω-代数的交换性及从一个Ω-代数到另一个Ω-代数的同态映射都由Ω-代数的生成元集决定.