Relation Word Problems

Let N={0,1,2,…} be the set of all natural numbers, and let R and S be any two (binary) relations on N. The product (referring to the relation theoretic product) of R and S is the relation T on N:     

A Property of N-ary Relation Ring

In paper [1], Professor Xie Bangjie discussed the ring with left zero factor ideals having the condition of rising chain. Qiu Qichang also has work on the aspect [2]. By using T-ary relation Professor Wu Xuemou investigated body-shadow relation, whole-parts relation, etc, [3]. In this paper, the conception of n-ary relation ring is introduced, and a necessary and sufficient condition of a ring R being a right Noether ring is given.     

The K2-groups over Fimite Commutative Rings

The present note determines the structure of the K2-group and of itssubgroup over a finite commutative ring R by considering relations between R andfinite commutative local ring Ri (1 ≤ i ≤ m), where R ≌ m i=1 Ri and K2(R) ≌ m i=1 K2(Ri). We show that if charKi = p (Ki denotes the residual field of Ri), then K2(Ri) and its subgroups must be p-groups.     

The K_2-groups over Finaite Commutative Rings

The present note determines the structure of the K2-group and of its subgroup over a finite commutative ring R by considering relations between R and finite commutative local ring Ri (1 < i < m), where R Ri and K2(R) = K2(Ri). We show that if charKi= p (Ki denotes the residual field of Ri), then K2(Ri) and its subgroups must be p-groups.     

FUNCTIONS(Ⅰ)

<正>As we all know that a relation is a cor- respondence between two variables x and y. When relations are written as ordered pairs (x,y),we say that x is related to y.Often, we are interested in specifying the type of re- lation (such as an equation) that might exist between the two variables. For example,the relation between the revenue R resulting from the sale of x items     

A remark on the generalized second order Toda system

In this paper, we establish a priori estimates to the generalized second order Toda system{-Δu1(x)=2R1(x)eu1-R2eu2,-Δu2(x)=R1(x)eu1+2R2eu2 in R2 , and discuss the convergence and asymptotic behavior of its solutions, where Ri(x), i=1, 2, is bounded function in R2 . Consequently, we prove that all the solutions satisfy an identity, which is somewhat a generalization of the well-known Kazdan-Warner condition.     

η-INVARIANT AND CHERN-SIMONS CURRENT

The author presents an alternate proof of the Bismut-Zhang localization formula of ηinvariants, when the target manifold is a sphere, by using ideas of mod k index theory instead of the difficult analytic localization techniques of Bismut-Lebeau. As a consequence, it is shown that the R/Z part of the analytically defined ηinvariant of Atiyah-Patodi-Singer for a Dirac operator on an odd dimensional closed spin manifold can be expressed purely geometrically through a stable Chern-Simons current on a higher dimensional sphere. As a preliminary application, the author discusses the relation with the Atiyah-Patodi-Singer R/Z index theorem for unitary flat vector bundles, and proves an R refinement in the case where the Dirac operator is replaced by the Signature operator.     

Mean Index for Non-periodic Orbits in Hamiltonian Systems

In this paper, we define mean index for non-periodic orbits in Hamiltonian systems and study its properties. In general, the mean index is an interval in R which is uniformly continuous on the systems. We show that the index interval is a point for a quasi-periodic orbit. The mean index can be considered as a generalization of rotation number defined by Johnson and Moser in the study of almost periodic Schr?dinger operators. Motivated by their works, we study the relation of Fredholm property of...     

Dispersion Analysis of Multi-symplectic Scheme for the Nonlinear Schrodinger Equations

In this paper,we study the dispersive properties of multi-symplectic discretizations for the nonlinear Schrodinger equations.The numerical dispersion relation and group velocity are investigated.It is found that the numerical dispersion relation is relevant when resolving the nonlinear Schrodinger equations.     

A Half—Power Trace Formulas for the Generalized Jaulent—Miodek Equation

A new dispersive relation is found and a half-pow tormulas for the generalizeMiodek equation under the deeaying conditions at infinity are obtained.     

可拓集合上的关系

本文给出可拓集合Ｘ到Ｙ上的关系Ｒ的概念，并讨论了可拓集合关系Ｒ的一般性质。     

等价关系的判定及性质

设R是集合A上的二元关系,要判定R在A上是否是等价关系,一般来讲,只能从定义出发,当R包含的序偶较多时,从定义出发又比较难于判定.从关系矩阵出发,给出一种判定方法,并讨论等价关系的矩阵性质.     

几种模糊传递关系的收敛性

本文对几种模糊传递关系进行比较 ,从一个侧面说明了用于构造偏好关系的模糊关系应是互逆关系 .文中证明了对任意的 n阶互逆传递模糊关系 R,必有 Rn=Rn+1 .     

离散数学教材中传递闭包的两个问题

设R和F是有限集合X上的两个关系.借助关系图的概念,本文确定了分别满足t(R∪F)=t(R)∪t(F),t(s(R))=s(t(R))的R和F的充分必要条件,解决了耿素云、曲婉玲和王捍贫2002年编著的《离散数学教程》第40页和44页中的两个遗留问题.     

R0-代数上的Fuzzy同余关系

在R0-代数中引入Fuzzy同余关系的概念,讨论了Fuzzy同余关系的一些基本性质,并通过对R0-代数中的Fuzzy MP滤子,特别是生成Fuzzy MP滤子的讨论建立了Fuzzy MP滤子与Fuzzy同余关系之间的联系。     

Valued preference-based instantiation of argumentation frameworks with varied strength defeats

A Dung-style argumentation framework aims at representing conflicts among elements called arguments. The basic ingredients of this framework is a set of arguments and a Boolean abstract (i.e., its origin is not known) binary defeat relation. Preference-based argumentation frameworks are instantiations of Dung's framework in which the defeat relation is derived from an attack relation and a preference relation over the arguments. Recently, Dung's framework has been extended in order to consider the strength of the defeat relation, i.e., to quantify the degree to which an argument defeats another argument. In this paper, we instantiate this extended framework by a preference-based argumentation framework with a valued preference relation. As particular cases, the latter can be derived from a weight function over the arguments or a Boolean preference relation. We show under some reasonable conditions that there are “less situations” in which a defense between arguments holds with a valued preference relation compared to a Boolean preference relation. Finally, we provide some conditions that the valued preference relation shall satisfy when it is derived from a weight function.     

有限集合上偏序关系的矩阵判别方法

要从定义出发去判断集合X上的二元关系R是否是偏序关系比较困难,从关系矩阵出发,给出了偏序关系的矩阵判别方法,并对此方法进行了证明.     

Twisted Extensions of Spin Models

A spin model is one of the statistical mechanical models which were introduced by V.F.R. Jones to construct invariants of links. In this paper, we give a new construction of spin models of size 4n from a given spin model of size n. The process is similar to taking tensor product with a spin model of size four, but we add some sign exchange. This construction also gives symmetric four-weight spin models of the type introduced by E. Bannai and E. Bannai.     

序半群的滤子与Green关系

给出了半格同余N分别为Green关系L，R，Z和H之一的序半群的刻画。