RESEARCH ANNOUNCEMENTS——Einstein—Kahler Metric on Cartan—Hartogs Domain of the First Type

S. Y. Cheng and S. T. Yau showed in [CY] that any C2 bounded pseudoconvex domain in Cnhas a complete Einstein-Kahler metric with constant negative Ricci curvature. N. Mok and S. T.Yau[MY] have extended this result to arbitrary bounded pseudoconvex domain in Cn. CompleteEinstein-Kahler metric with Explicit form, however, is only known in the case of homogeneousdomain.     

STRONG LIMIT THEOREMS FOR EXTENDED INDEPENDENT RANDOM VARIABLES AND EXTENDED NEGATIVELY DEPENDENT RANDOM VARIABLES UNDER SUB-LINEAR EXPECTATIONS

Limit theorems for non-additive probabilities or non-linear expectations are challenging issues which have attracted a lot of interest recently.The purpose of this paper is to study the strong law of large numbers and the law of the iterated logarithm for a sequence of random variables in a sub-linear expectation space under a concept of extended independence which is much weaker and easier to verify than the independence proposed by Peng [20].We introduce a concept of extended negative dependen...     

拓扑分子格C.T.Yang定理与K.Fan定理的推广

C_1 T. Yang's theorem concerning derived sets and K. Fan's theorem concerning connectivity in general topology have been extended to fuzzy topological spaces and to the theory of topological molecular lattices and generalized topological molecular lattices. In this paper, they will be further extended to the more general theory of POINTWISE TOPOLOGY ON COMPLETELY DISTRIBUTIVB LATTICES.     

RESEARCH ANNOUNCEMENTS Einstein-Khler Metric on Cartan-Hartogs Domain of the First Type

S. Y. Cheng and S. T. Yau showed in [CY] that any C2 bounded pseudoconvex domain in C?has a complete Einstein-Kahler metric with constant negative Ricci curvature. N. Mok and S. T. Yau[MY] have extended this result to arbitrary bounded pseudoconvex domain in Cn. Complete Einstein-Kahler metric with Explicit form, however, is only known in the case of homogeneous domain.     

LIPSCHITZ SEMISTABILITY OF GENERAL CONTROL SYSTEMS

1 IntroductionThe notion of semistability was introduced to study dynamical systems byBhatia [11. Indeed, it is a kind of stability behavior under some constraints.And the considerations of this notion have been extended to semistability ofdynamic41 systems in terms of two measures[9]. AlIn this paper) the notions of (Lipschitz) semistability of general controlsystems (g.c.s.) are introducea. And the necessary and sufficient conditions for(weak) semistability, Lipschitz (locally weak) semist…     

ON SINGULAR INTEGRALS WITH SINGULARITIES OF HIGH FRACTIONAL ORDER AND THEIR APPLICATIONS

§1 Introduction Singular integrals of high order in complex integration were firts introduced in [1] and investigated in [2,3,4]. Using this concept, the classical residue theorem was extended to such cases and was applied to solving certain class of singular integral equations. [3,4]     

半覆盖远离性质与有限群的结构

In this paper,the so-called π-cover-avoiding properties of subgroups are defined and investigated.In terms of this property,we characterize the π-solvability of finite groups.Some other new results are also obtained based on the assumption that some subgroups have the semi cover-avoiding properties in a finite group.     

On the edge-binding number of some plane graphs

1. IntroductionSince WOodall gave out the concept of biIldi11g Ilu1lJber in 1973[l] ! the bil1ding nunlber fOrsome specia1 classes have beeIl studied by Kane and WaIlg Jianfang[']. Mirolawa Skowronskahave studied the binding number of Halin-graph[']. ZI1ang Zhongfu, Liu Li1lzhong andZhang Jianxun have extended the bil1di11g nuInber to the edges and studied tlle edge-bindingnumber of path, cycle, coInplete grapl1. I1l this paper, we study the edge-binding number ofouter plane graph, Ha…     

LIPSCHITZ SEMISTABILITY OF GENERAL CONTROL SYSTEMS IN TERMS OF TWO MEASURES

1 IntroductionLipschitz semistability of dynamical systems in terms of two measures andLipschitz semistability of general control systems have already been,t.di.d[llt12].In this papers semistability considerations will be extended to a variety of nonlinear systems utilizing the same versatile tools, namely, Liapunov--like functions. The notions of (ho, h)-Lipschitz (weak) semistability of general controlsystems are introduced, and the necessary and sufficient conditions are given.2 Prelimina…     

MBIUS INVARIANT GRADIENT AND LITTLE α-BLOCH FUNCTIONS

In this paper, the authors get the characterizations of the integral and Car-leson type measure both associated with the invariant gradient for little a-Bloch functions in the unit ball of Cn. As a consequence, some results of Ouyang C H, Yang W S and Zhao R H in [4] and a result of Yang W S in [10] are extended.     

THE EXTENSION OPERATOR IN BANACH SPACES FOR LOCALLY BIHOLOMORPHIC MAPPINGS

In this article, the generalized Roper-Suffridge extension operator in Banach spaces for locally biholomorphic mappings is introduced. It is proved that this operator preserves the starlikeness on some domains in Banach spaces but does not preserves convexity for some cases. Moreover, the growth theorem, covering theorem, and the radius of starlikeness are discussed. Some results of Roper and Suffridge, Gong and Liu, Graham et al in C^n are extended to Hilbert spaces or Banach spaces.     

UNIQUENESS OF MEROMORPHIC FUNCTIONS WHOSE NONLINEAR DIFFERENTIAL POLYNOMIALS SHARE ONE VALUE OR HAVE THE SAME FIXED POINTS IN AN ANGULAR DOMAIN

In this article, we study the uniqueness question of nonconstant meromorphic functions whose nonlinear differential polynomials share 1 or have the same fixed points in an angular domain. The results in this article improve Theorem 1 of Yang and Hua [26], and improve Theorem 1 of Fang and Qiu [6].     

Some Properties of the Optimal Preconditioner and the Generalized Superoptimal Preconditioner

<正>The optimal preconditioner and the superoptimal preconditioner were proposed in 1988 and 1992 respectively.They have been studied widely since then.Recently, Chen and Jin[6]extend the superoptimal preconditioner to a more general case by using the Moore-Penrose inverse.In this paper,we further study some useful properties of the optimal and the generalized superoptimal preconditioners.Several existing results are extended and new properties are developed.     

多元性相依回归系统的两步估计及其协差阵

Multivariate seemingly unrelated regression system is raised first and the two stage estimation and its covariance matrix are given. The results of the literatures[1-5] are extended in this paper.     

REFINEMENTS OF THE FAN－TODD‘S INEQUALITIES

51. IntroductionIn recent years, refinements or interpolations have played an important role on severaltypes of inequalities with new results deduced as a consequence. Please refer to the papers[2, 8, 9, 12], etc. The aim of this paper is to furnish refinements of the Cauchy's and Bessel'sinequalties as shown in Section 2, and also refinements of the Fan-Todd's inequality and theFan-Todd's determinantal inequality in Sections 3 and 4, with an improved condition forequality derived.First of…     

关于Reissner厚板模型的解——对“关于简支厚板与薄板的关系”的讨论

In this paper, the method proposed in [2] is extended to the case of thickplate, the problem in the solution of Reissner model of thick plate is reduced to a solution oftwo displacement functions ω and f, and the general form of the solution of this model isderived. For a simply supported polygonal thick plate, f vanishes identically, and hence therelation between the solution of thick plate and that of similar thin plate can be established.According to this relation, the solutions of a class of thick plates may be derived from thecorresponding solutions of thin plates.     

曲指数族的欧氏几何方法及其对置信域的应用

Efron and Amari presented a Riemannian geometric framework for qurved exponential families and studied the information loss and the variance of the estimate using this framilies. In this pap propose a relatively rumple geometric frame work in Euclidean space. Based on this new framework, we study eonfidence regiods for curved exponential families which have not been studied by Efron and Amari. The results obtained by Hamilton et al. are extended to curved exponential families.     

关于Г-半环

Just as Nobusawa has extended the concept of ring to the concept of Γ-ring. we introduce in this paper a new concept of Γ-hemiring based on the concept of abelian additive hemigroup. And then, we extend the foundamental results associated with hemiring which are developed by Bourne and Zassenhaus to some analogous results associated with Γ-hemiring, such as the notions of ideal, zeroid, homomorphism and Jacobsonian radical and semi-radical in the case of Γ-hemiring. Finally, we have given some conditions for a Γ-hemiring being a Γ-ring.     

高阶泛函微分方程解的振动性

In this paper we study the oscillation of the solutions of higher-order functional differential equations, and have given the new integral conditions when equation (1) is oscillatory and extended some known results.     

Standardness and Standard Automorphisms of Chevalley Groups, I: the Case of Rank at Least Two

The author studies the linkage between the standardness and the standard automorphisms of Chevalley groups over rings.It is proved that if H is any standard subgroup of G(R),then each of its automorphisms can be extended to an automorphism of G(R,I),restricted to an automorphism of E(R,I),and an automorphism of E(R,I) can be extended to one of G(R,I).The case of Chevalley groups of rank at least two is treated in this paper.Further results about the case of Chevalley groups of rank one,the case of non-commutative ground ring and some others exceptions will appear elsewhere.