Generalized weakly symmetric rings

A ring R is defined to be GWS   if abc=0$abc=0$ implies bac⊆N(R)$bac\subseteq N(R)$ for a,b,c∈R$a,b,c\in R$, where N(R)$N(R)$ stands for the set of nilpotent elements of R. Since reduced rings and central symmetric rings are GWS, we study sufficient conditions for GWS rings to be reduced and central symmetric. We prove that a ring R is GWS   if and only if the n×n$n\times n$ upper triangular matrices ring _Un(R,R)$U_n(R,R)$ is GWS for any positive integer n. It is proven that GWS rings are directly finite and left min-abel. For a GWS ring R, R is a strongly regular ring if and only if R is a von Neumann regular ring if and only if R is a left SF   ring and J(R)=0$J(R)=0$; R is an exchange ring if and only if R is a clean ring. Finally, we show that GWS exchange rings have stable range 1 and a GWS semiperiodic ring R   with N(R)≠J(R)$N(R)\ne J(R)$ is commutative.     

Generalized composition and Volterra type operators between QK spaces

Abstract

In this paper, the boundedness and compactness of the generalized composition operators and the products of Volterra type operators a nd composition operators between Q_K spaces are investigated. We also give a necessary condition for multiplication operators between Q_K spaces to be bounded or compact.     

广义Hammerstein型方程的存在定理

本文利用单调型强制映射满射性和逼近方法建立了广义Ｈａｍｍｅｒｓｔｅｉｎ型方程ｕ＋Ｋ（ｕ）Ｆ（ｕ）＝０解的存在性定理，这里对于实自反Ｂａｎａｃｈ空间Ｘ的共轭空间Ｘ^*的每个ｕ，Ｋ（ｕ）：Ｘ→Ｘ^*是线性映射，Ｆ：Ｘ^*→Ｘ是任一映射．所得结果推广了Ｓｃｈｉｌｉｎｇ，Ｓｒｉｋａｎｔｈ ａｎｄ Ｊｏｓｈｉ等相应的结果     

Generalized pseudo-Riemannian geometry

Generalized tensor analysis in the sense of Colombeau's construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving several characterizations of invertibility in the algebra of generalized functions, we define the notions of generalized pseudo-Riemannian metric, generalized connection and generalized curvature tensor. We prove a ``Fundamental Lemma of (pseudo-) Riemannian geometry' in this setting and define the notion of geodesics of a generalized metric. Finally, we present applications of the resulting theory to general relativity.

     

广义Macaulay-Northcott模与Tor-群

Let （S,≤） be a strictly totally ordered monoid which is also artinian, and R a right noetherian ring. Assume that M is a finitely generated right R-module and N is a left Rmodule. Denote by [[MS,≤]] and [NS,≤] the module of generalized power series over M, and the generalized Macaulay-Northcott module over N, respectively. Then we show that there exists an isomorphism of Abelian groups：Tori[[ RS,≤]]（[[MS,≤]],[NS,≤]）≌ s∈S ToriR （M,N）.     

一个广义Markov不等式（英）

This paper gives a generalized Markov inequality dx for every polynomial P of degree at most n provided that f′ is con tinuous and strictly increasing on [0,∞ ), where ‖?‖ denotes the uniform and T_n,stands for the n-th Chebyshev polynomial of the first kind.     

广义向量变分不等式和广义对偶模型

研究实Banach空间中带有不等式约束的非光滑向量优化问题(VP).首先,借助下方向导数引进了广义Minty型向量变分不等式,并通过变分不等式来探讨问题(VP)的最优性条件.接着,利用函数的上次微分构造了不可微向量优化问题(VP)的广义对偶模型,并且在适当的弱凸性条件下建立了弱对偶定理.     

Whiteman广义分圆序列的自相关值

Let p,q be distinct primes with gcd(p-1,q-1) = 4.In this paper,we calculate the autocorrelation values of binary sequences of generalized cyclotomic sets of order four in Z pq and get conditions of p and q such that they are four-valued.     

非负广义幂等矩阵

非负幂等矩阵在［１］中已有详细地讨论和重要地应用。［２］给出了Ａ≥０，Ａｋ＋１＝Ａ，ｋ是正整数，Ａｋ是零对称幂等矩阵的充要条件。本文给出了一般非负广义幂等矩阵的充要条件。并讨论了广义幂等矩阵的秩与其广义幂等指数的关系，推广了［２］中的部分结论。     

树的广义本原指数最大值及极图刻划

本文继续[1]的研究,给出了取得树的最大广义本原指数的极图的完全刻划。     

广义集值拟变分不等式

本文研究了一类广义集值拟变分不等式,得到了这类广义集值拟变分不等式解存在的一个充分条件,并给出了近似解的迭代算法.     

广义Schur补的广义逆

对四分块矩阵A=A(︿) A(︿,︿′)A(︿′,︿) A(︿′)来说 ,如果 A和 A(︿)都是非奇异的 ,则A- 1 (︿′) =(A/︿) - 1 ,这里 A/ ︿=A(︿′) -A(︿′,︿) A(︿) - 1 A(︿,︿′)是 A(︿)在 A中的 Schur补 .王伯英教授指出上述等式 ,对半正定的 Hermitian矩阵而言 ,一般也是不能推广到 Moore-Penrose逆上去的 .在某些限制条件下 ,我们证明了广义逆的主子矩阵与广义 Schur补的关系是密切的 ,它使经典结果成为特例     

广义鸡尾酒宴图的谱特征

In the paper, we prove that all generalized cocktail-party graphs with order at least 23 are determined by their adjacency spectra.     

广义Frame与广义Frame的商

本文将frame、frame同态、商frame与核的概念在范畴意义下作推广,并且证明Frame范畴是广义Frame范畴的反射子范畴.进而讨论了一个广义frame A的商与A上核函子之间的关系.特别地,我们证明了A上全部核函子所构成的范畴N(A)是一个广义frame.     

关于广义双拟变分不等式和拟变分不等式

研究了一类广义双拟变分不等式和广义拟变分不等式解的存在性，推广、改进、统一了一些近期的相关结果．     

具有非退化Killing型的广义李超代数

设F是特征数为零的域.本文证明了F上的有限维广义李超代数的Killing型是相容的、不变的与上对称的.进而证明了具有非退化Killing型的有限维广义李超代数的 若干性质，最后得出这种广义李超代数必为有限个典型的广义李超代数的直积.     

Holomorphic Maps of Compact Generalized Hopf Manifolds

We investigate holomorphic maps between compact generalized Hopf manifolds (i.e., locally conformal Kähler manifolds with parallel Lee form). We show that they preserve the canonical foliations. Moreover, we study compact complex submanifolds of g.H. manifolds and holomorphic submersions from compact g.H. manifolds.     

带有广义导子的素环

The concept of derivations and generalized inner derivations has been generalized as an additive function δ: R→ R satisfying δ(xy) = δ(x)y xd(y) for all x,y∈R,where d is a derivation on R.Such a function δis called a generalized derivation.Suppose that U is a Lie ideal of R such that u2 ∈ U for all u ∈U.In this paper,we prove that U(C)Z(R) when one of the following holds:(1)δ([u,v]) = uov (2)δ([u,v]) uov=O(3)δ(uov) =[u,v](4)δ(uov) [u,v]= O for all u,v ∈U.     

正交射影在广义框架理论中的应用

本文研究了可分的Hilbert空间H中的广义框架,运用算子理论方法,研究了可分的 Hilbert空间H中广义框架的性质,给出了广义框架的对偶广义框架的一些刻画,并且证明了两个广义框架是强非交的一个充分必要条件．     

Generalized Vector Equilibrium Problems in Generalized Convex Spaces

In this paper, we introduce and study a class of abstract generalized vector equilibrium problems (AGVEP) in generalized convex spaces which includes most vector equilibrium problems, vector variational inequality problems, generalized vector equilibrium problems, and generalized vector variational inequality problems as special cases. By using the generalized GKKM and generalized SKKM type theorems due to the first author, some new existence results of equilibrium points for the AGVEP are established in noncompact generalized convex spaces. As consequences, some recent results in the literature are obtained under much weaker assumptions.