一个新的基于口令的密钥协商协议

以不经意多项式计算作为核心组件,提出了一个基于口令的密钥协商协议PSKA-I,该协议能够抵抗字典攻击但只能工作于认证模型。为解决协议PSKA-I这一缺陷,根据BCK安全模型设计了消息传输认证器,将协议PSKA-I转换为非认证模型中的安全协议PSKA-Ⅱ。上述协议口令的安全性由不经意多项式计算予以保证。与GL协议相比,该协议的通信及计算复杂度明显降低。     

软BCK代数

提出了软BCK代数的概念,研究了软BCK代数的并,交和乘积运算,讨论了这些运算的代数性质。     

关于(i,j;m,n)型拟可换BCK-代数的"一点扩张"

证明了BCK-代数通过"一点扩张"可生成真BCI-代数,(i,j;m,n)型拟可换BCK-代数通过"一点扩张"可生成真BCI-代数并保持同型拟可换性.给出了实现"一点扩张"应满足的条件.     

Iséki algebras. Connection with BL algebras

We introduce Iséki algebras as a special class of BCK algebras and we prove they are categorically equivalent with BL algebras. Other connections are established.I thank very much Professor Antonio Di Nola for his kind suggestions that helped me to improve the final form of the paper.     

Fuzzy蕴涵代数的一些性质

Fuzzy蕴涵代数,简称FI代数,是一个新的代数系统。本文讨论了FI代数的一些新性质,简化了有界关联BCK代数系统,将Fuzzy代数与有界关联BCK代数联系起来,从而发展了Fuzzy代数系统理论。     

软BCK代数再研究

给出了软BCK代数的广义交运算和广义并运算,证明了一个集合X上的一族软BCK代数{(F_i,A_i)}_#em/em#∈I的广义交和一族软BCK代数{(F_i,A_i)}_#em/em#∈I（对任意#em/em#,j∈I,#em/em#≠j有A_i∩A_j=?)的广义并仍然是X上的软BCK代数,集合X上的软BCK代数(G,B)的一族软子代数的交、广义交和广义并仍是(G,B)的软子代数。     

On BCK algebras: Part II: New algebras. The ordinal sum (product) of two bounded BCK algebras

Since all the algebras connected to logic have, more or less explicitly, an associated order relation, it follows, by duality principle, that they have two presentations, dual to each other. We classify these dual presentations in “left” and “right” ones and we consider that, when dealing with several algebras in the same research, it is useful to present them unitarily, either as “left” algebras or as “right” algebras. In some circumstances, this choice is essential, for instance if we want to build the ordinal sum (product) between a BL algebra and an MV algebra. We have chosen the “left” presentation and several algebras of logic have been redefined as particular cases of BCK algebras. We introduce several new properties of algebras of logic, besides those usually existing in the literature, which generate a more refined classification, depending on the properties satisfied. In this work (Parts I–V) we make an exhaustive study of these algebras—with two bounds and with one bound—and we present classes of finite examples, in bounded case. In Part II, we continue to present new properties, and consequently new algebras; among them, bounded α γ algebra is a common generalization of MTL algebra and divisible bounded residuated lattice (bounded commutative Rl-monoid). We introduce and study the ordinal sum (product) of two bounded BCK algebras. Dedicated to Grigore C. Moisil (1906–1973).     

Soft ideals of BCK/BCI-algebras based on fuzzy set theory

Characterizations of a (?, ? ∨ q?)-fuzzy subalgebra (ideal) are considered. Given an ∈-soft set, an (?, ? ∨ q?)-fuzzy subalgebra is established. Using the notion of (t, s)-fuzzy subalgebras, characterizations for an∈-soft set to be a (idealistic) soft BCK/BCI-algebra are provided. Using the notion of fuzzy p-ideals, a characterization of an∈-soft set to be a p-idealistic soft BCI-algebra is constructed. An equivalent condition for a q-soft set to be a p-ideal is given. Characterizations of a (∈,∈ ∨ q)-fuzzy p-ideal are initiated. Conditions for a (∈,∈∨ q)-fuzzy ideal to be a (∈,∈∨ q)-fuzzy p-ideal are stated.     

粗糙集与BCK代数

粗糙集的代数刻画是粗糙集理论中研究的一个重要方向,在偶序对[R(X),R(X)]构成的集合中定义了二元运算[*],证明了序偶对构成的集合构成了一个有界BCK代数,给出了基本的性质,为粗糙逻辑和粗糙推理奠定了基础。     

X. Yeast sequencing reports. Sequence and function analysis of a 9·46 kb fragment of Saccharomyces cerevisiae chromosome X

In the framework of the European yeast genome sequencing project, we have determined the nucleotide sequence of the cosmid clone 233 provided by F. Galibert (Rennes Cedex, France). We present here 9464 base pairs of this cosmid located on the left arm of Saccharomyces cerevisiae chromosome X. This sequence contains two new open reading frames and includes the published sequences of the RADH gene (also identified as SRS2/HPR5) and the 3′-end of the gene BCK1/SLK1/SSP31. Deletion mutants of the two unknown genes J0909 and J0911 are viable. The sequence has been deposited in the EMBL data library under accession number X77087.