素环中的协中心化广义导子

Let R be a prime ring with center Z and S (?) R. Two mappings D and G of R into itself are called cocentralizing on S if D(x)x-xG(x) ∈ Z for all x ∈ S. The main purpose of this paper is to describe the structure of generalized derivations which are cocentralizing on ideals, left ideals and Lie ideals of a prime ring, respectively. The semiprime case is also considered.     

导子交换子幂值的零化子条件

Let R be a prime ring with center Z(R), I a nonzero ideal of R, d a nonzero derivation of R and 0≠a∈ R. In the present paper, our object is to study the situation a[d(xk), xk]n∈ Z(R) for all x ∈ I under certain conditions, where n(≥ 1), k(≥ 1) are fixed integers.     

On Quasi-weakly Almost Periodic Points of Continuous Flows

Let X be a compact metric space, F : X ×R→ X be a continuous flow and x ∈ X a proper quasi-weakly almost periodic point, that is, x is quasi-weakly almost periodic but not weakly almost periodic. The aim of this paper is to investigate whether there exists an invariant measure generated by the orbit of x such that the support of this measure coincides with the minimal center of attraction of x? In order to solve the problem, two continuous flows are constructed. In one continuous flow,there exist a proper quasi-weakly almost periodic point and an invariant measure generated by its orbit such that the support of this measure coincides with its minimal center of attraction; and in the other,there is a proper quasi-weakly almost periodic point such that the support of any invariant measure generated by its orbit is properly contained in its minimal center of attraction. So the mentioned problem is sufficiently answered in the paper.     

素环上的导子在Lie理想上的协交换子的零化子

Let R be a prime ring of characteristic different from 2,d and g twoderivations of R at least one of which is nonzero,L a non-central Lie ideal of R,anda∈R.We prove that if a(d(u)u-ug(u))=0 for any u∈L,then either a=0,or R is an s_4-ring,d(x)=[p,x],and g(x)=-d(x)for some p in the Martindalequotient ring of R.     

On the Normal Subgroup with Exactly Two G-Conjugacy Class Sizes

Let G be a finite group with a non-central Sylow r-subgroup R, Z（G） the center of G, and N a normal subgroup of G. The purpose of this paper is to determine the structure of N under the hypotheses that N contains R and the G-conjugacy class size of every element of N is either i or m. Particularly, it is shown that N is Abelian if N ∩ Z（G）=1 and the G-conjugacy class size of every element of N is either 1 or m.     

Generalized derivations as Jordan homomorphisms on lie ideals and right ideals

Let R be a prime ring, L a non-central Lie ideal of R and g a non-zero generalized derivation of R. If g acts as a Jordan homomorphism on L, then either g（x） = x for all x ∈ R, or char（R） = 2, R satisfies the standard identity s4（x1, x2, x3, x4）, L is commutative and u2 ∈ Z（R）, for any u C L. We also examine some consequences of this result related to generalized derivations which act as Jordan homomorphisms on the set [I, I], where I is a non-zero right ideal of R.     

ISOGENOUS OF THE ELLIPTIC CURVES OVER THE RATIONALS

AbstractAn elliptic curve is a pair (E,O), where ?is a smooth projective curve of genus 1 and O is a point of E, called the point at infinity. Every elliptic curve can be given by a Weierstrass equationE:y2 a1xy a3y = x3 a2x2 a4x a6.Let Q be the set of rationals. E is said to be dinned over Q if the coefficients ai, i = 1,2,3,4,6 are rationals and O is defined over Q.Let E/Q be an elliptic curve and let E(Q)tors be the torsion group of points of E denned over Q. The theorem of Mazur asserts that E(Q)tors is one of the following 15 groupsE(Q)tors　Z/mZ, m = 1,2,..., 10,12,Z/2Z × Z/2mZ, m = 1,2,3,4.We say that an elliptic curve E'/Q is isogenous to the elliptic curve E if there is an isogeny, i.e. a morphism : E E' such that (O) = O, where O is the point at infinity.We give an explicit model of all elliptic curves for which E(Q)tors is in the form Z/mZ where m= 9,10,12 or Z/2Z × Z/2mZ where m = 4, according to Mazur's theorem. Morever, for every family of such elliptic curves, we give an explicit m     

Co-commuting Mappings of Generalized Matrix Algebras

Let G be a generalized matrix algebra over a commutative ring R and Z(G)be the center of G.Suppose that F,T:G→G are two co-commuting R-linear mappings,i.e.,F(x)x=xT(x) for all x∈G.In this note,we study the question of when co-commuting mappings on G are proper.     

Principal quasi-Baerness of formal power series rings

Let R be a ring. We consider left （or right） principal quasi-Baerness of the left skew formal power series ring R[[x;α]] over R where a is a ring automorphism of R. We give a necessary and sufficient condition under which the ring R[[x; α]] is left （or right） principally quasi-Baer. As an application we show that R[[x]] is left principally quasi-Baer if and only if R is left principally quasi- Baer and the left annihilator of the left ideal generated by any countable family of idempotents in R is generated by an idempotent.     

Derivations And Homomorphisms in Prime Rings

Let R be an associative ring, recall that an additive mapping d of R into itself is a derivation if for all x,y in R: d(xy)=d(x)y+xd(y) It is shown that structure of a ring is very tightly determined by the imposition of a special behavior on one of its derivations. analogously,we shall consider the problem: Suppose that R is a prime ring with nonzero derivation d such that the derivation d is a homomorphism (anti-     

L－fuzzy集网的R－收敛性质

本文在ＬＦ拓扑空间中建立了Ｌ－ｆｕｚｚｙ集网的弱收敛（Ｒ－收敛）概念，应用文［４］中的Ｒ－闭包，系统讨论了它们的性质，证明了等式ＲｌｉｍＡ＿ｎ＝∧（∨Ａ＿ｍ）＿Ｒ和ＲｌｉｍＡ＿ｎ＝Ａ＿ｎ＝∧（∨Ａ＿ｍ）＿Ｒ并且给出了Ｌ－ｆｕｚｚｙ集网与其子网之间的关系。     

两种图多项式根的重数的一个注记

设P1，P2，……，Pt是几乎覆盖图G的l条不相交的路，s是没有被这些路覆盖的孤立点数．本证明：(i)匹配多项式μ(G，x)的非零根的重数最多是l，零根的重数最多l s。（ii)对于不含三角形的n阶图G，伴随多项式h(G，x)的非零根的重数最多是l，零根的重数最多是1/2(n l s)．(iii)对一种含三角形的所谓A型图，（ii）也成立．     

任意矩阵的特征值的扰动估计

设A和B是两个任意的n阶方阵,其特征值分别为{λ_1,…,λ_n}和{μ_1,…,μ_n}.本文对此两组特征值的如下“距离”的界给出了若干估计: B对于A的谱改变量 A与B的特征值的改变量这里的结果包含了Bauer-Fike定理,并且优于Kahan-Parlett/Jiang定理及Chu,施和肖所得出的结果.     

Number of connected components of groups of real points of adjoint groups

We present a unified approach to compute the number of connected components in the group of real points of adjoint almost simple real algebraic groups.     

一类完全正则半群簇子簇格的性质

本文研究了完全正则半群簇的子簇格［Ｖ＋∩ＰＶ，Ｖ＋∩ＰＶ］的某些格运算性质，我们证明了簇Ｖ＋∩ＰＶ可分解为Ｖ与Ｖ＋∩ＰＶ的并；对任意完全正则半群簇Ｗ，有Ｗ∩（Ｖ∨Ｖ＋∩ＰＶ）＝（Ｗ∩Ｖ）∨（Ｗ∩Ｖ＋∩ＰＶ）．特别地，我们得到了等式Ｖ＋∩ＰＶ＝Ｖ成立的若干条件．     

On the R-Order of Convergence of a Family of Methods for Simultaneous Extraction of Part of All Roots of Algebraic Polynomials

This note deals with the R-order of convergence of Weierstrass-Durand-Kerner-Dochev type single-step methods for the simultaneous determination of only a part of all roots of algebraic polynomials.     

抛散落点的均匀性检验

讨论了抛散落点的均匀性检验，给出了一种排序法检验，并将它与传统的两种检验方法进行比较．     

Enumeration of perfect matchings of a type of Cartesian products of graphs

Let G be a graph and let Pm(G) denote the number of perfect matchings of G.We denote the path with m vertices by P_m and the Cartesian product of graphs G and H by G×H. In this paper, as the continuance of our paper [W. Yan, F. Zhang, Enumeration of perfect matchings of graphs with reflective symmetry by Pfaffians, Adv. Appl. Math. 32 (2004) 175-188], we enumerate perfect matchings in a type of Cartesian products of graphs by the Pfaffian method, which was discovered by Kasteleyn. Here are some of our results:1. Let T be a tree and let C_n denote the cycle with n vertices. Then Pm(C₄×T)=∏(2+α²), where the product ranges over all eigenvalues α of T. Moreover, we prove that Pm(C₄×T) is always a square or double a square.2. Let T be a tree. Then Pm(P₄×T)=∏(1+3α²+α⁴), where the product ranges over all non-negative eigenvalues α of T.3. Let T be a tree with a perfect matching. Then Pm(P₃×T)=∏(2+α²), where the product ranges over all positive eigenvalues α of T. Moreover, we prove that Pm(C₄×T)=[Pm(P₃×T)]².     

Distribution of Cardinalities of Row Spaces of Boolean Matrices of Order n

Let R(A) denote the row space of a Boolean matrix A of order n. We show that if n 7, then the cardinality |R(A)| (2^n–1 - 2^n–5, 2^n–1 - 2^n–6) U (2^n–1 - 2^n–6, 2^n–1). This result confirms a conjecture in [1].AMS Subject Classification (1991): 05B20 06E05 15A36Support partially by the Postdoctoral Science Foundation of China.Dedicated to Professor Chao Ko on the occasion of his 90th birthday