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The Constrained Solutions of Two Matrix Equations

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Acta Mathematica Sinica,English Series 2002年第4期18卷 671-678页

作者： An Ping LIAO Zhong Zhi BAI department of mathematics. Hunan University. Changshu, 410082. P. R..china department of mathematics and Information Science, Changsha University, Changsha 410003. P. R. china Academy of mathematics and System. Sciences. Chinese Academy of Sciences. Beijing 100080. P. R. china State Key Laboratory of Scientific/Engineering Computing. Chinese Academy of Sciences. Institute of Computational mathematics and Scientific/Engineering Computing. Academy of mathematics and System Sciences. Chinese Academy of Sciences. P. O. Box 2719. Beijing 100080. P. R. china department of mathematics Hunan University Changsha 410082 P. R. China department of mathematics and Information Sciences Changsha University Changsha 410003 P. R. China Academy of mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 P. R. China State Key Laboratory of Scientific/Engineering Computing Chinese Academy of Sciences Institue of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences 2719 Beijing 100080 P. R. China

We study the symmetric positive semidefinite solution of the matrix equation AX_1A^T + BX_2B^T=C. where A is a given real m×n matrix. B is a given real m×p matrix, and C is a given real m×m matrix, with m, n, p positive integers: and the bisymmetric positive semidefinite solution of the matrix equation D^T XD=C, where D is a given real n×m matrix. C is a given real m×m matrix, with m. n positive integers. By making use of the generalized singular value decomposition, we derive general analytic formulae, and present necessary and sufficient conditions for guaranteeing the existence of these solutions.

关键词： Matrix equation Symmetric positive semidefinite matrix Bisymmetric positive semidefinite matrix

A Characterization of Homomorphisms Between Banach Algebras

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Acta Mathematicae Applicatae Sinica 2004年第4期 761-768页

作者： Jian Lian CUI department of Mathematical Sciences,Tsinghua University,Beijing 100084 P.R.china and department of mathematics,Shanxi Teachers University,Linfen 041004,P.R.china Jin Chuan HOU department of mathematics,Shanxi Teachers University,Linfen 041004,P.R.china and department of mathematics,Shanxi University,Taiyuan 030000,P.R.china

We show that every unital invertibility preserving linear map from a yon Neumann algebraonto a semi-simple Banach algebra is a Jordan homomorphism;this gives an affirmative answer to aproblem of Kaplansky for all von Neumann *** a unital linear map Φ from a semi-simplecomplex Banach algebra onto another,we also show that the following statements are equivalent:(1)Φ is an homomorphism;(2)Φ is completely invertibihty preserving;(3)Φ is 2-invertibility preserving.

关键词： Banach algebras Homomorphisms Jordan homomorphisms

WEAK TYPE(1,1)BOUNDS FOR A MARCINKIEWICZ INTEGRAL

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Analysis in Theory and Applications 1994年第2期10卷 54-66页

作者： Hu Guoen Institute of Information Engineering,.china department of mathematics Institute of Information Engineering Zhengzhou, Henan, 450002. 1. department of mathematics Institute of Information Engineering Zhengzhou 450002 Henan

In this paper, the two-dimensional Marcinkewicz integral introduced by Stein μ(f)(x)=(∫_0~x|∫_(|x-y|≤1) _(|x-y|)^(Ω(x-y))f(y)dy|~2t^(-3)dt)~2 is shown to be of weak type (1,1) and weighted weak type (1,1) with respect to power weight |x|~' if - 1< α< 0, where Ω is homogeneous of degree 0. has mean value 0 and belongs to Llog^+L(S^1).

关键词： Math Pro BOUNDS FOR A MARCINKIEWICZ INTEGRAL WEAK TYPE

EXISTENCE　OF　NONTRIVIAL　SOLUTIONS　FOR　CRITICAL　SEMILINEAR　BIHARMONIC　EQUATIONS

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Systems Science and Mathematical Sciences 1994年第2期7卷 140-152页

作者： GU Yonggeng(Institute of Systems Science, Academia Sinica, Beijing 100080, china)DENG Yinbin(department of mathematics, Huazhong Normal University ,Wuhan 430070, china)WANG Xujia(department of mathematics, Zhejiang University, Hangzhou 310027, china)

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关键词： Nontrivial solution biharmonic equations critical Sobolev exponent.

Oscillation of Solutions of Nonlinear Partial Differential Equations of Neutral Type

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Acta Mathematica Sinica,English Series 1997年第4期13卷 563-570页

作者： Yu Yuanhong Liu Bin Liu Zhengrong Institute of Applied mathematics, Academia Sinica, Beijing 100080,.china department of mathematics, Hubei Normal College, Huangshi 435002..china department of mathematics, Yunnan University. Kunming 650091. china Institute of Applied mathematics of Yunnan Province, Kunming 650091, china 中科院应用数学所北京湖北师范学院湖北黄石云南大学数学系云南昆明

In this paper. we deal with the oscillatory behavior of solutions of the neutral partial differential equation of the form /t[p(t)/t(u(x.t)+sun from i=1 to t pi(t)u(x,t-ti))]+q(x,t)u(x,t)+sun form j=1 to m qj(x,t)f_j(u(x,σ_j(t))) =a(t)△u(x,t)+sun form k=1 to n ak(t)△u(x,pk(t)), (x,t)∈Ω×R_+≡G where △ is the Laplacian in Euclidean N-space R^N, R_+=(0, ∞) and Ω is a bounded domain in R^N with a piecewise smooth boundary Ω.

关键词： Oscillation Neutral type Partial differential equation

Picard Values and Normal Families of Meromorphic Functions with Multiple Zeros

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Acta Mathematica Sinica,English Series 1998年第1期14卷 17-26页

作者： Wang Yuefei Fang Mingliang Institute of mathematics, Academia Sinica, Beijing 100080, china Institute of mathematics, Academia Sinica, Beijing 100080,.china department of mathematics, Nanjing Normal University, Nanjing 210097, china 中科院数学所北京

In this paper, general modular theorems are obtained for meromorphic functions and their derivatives. The related criteria for normality of families of meromorphic functions are proved.

关键词： Meromorphic function Critical value Normal family

THE　THRESHOLD　OF　SURVIVAL　FOR　PREDATOR－PREY　VOLTERRA　SYSTEM　OF　THREE　SPECIES　IN　A　POLLUTED　ENVIRONMENT

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Systems Science and Mathematical Sciences 1995年第4期8卷 373-382页

作者： MA Zhien LUO Zhixue department of mathematics,Xi’an Jiaotong University, Xi’an 710049,china)JIN Zhen(department of mathematics,North china Institute of Technology,Taiyuan 030051,china)ZHAO Hengbao (Nankai University,Tianjin 300071, china) 西安交通大学数学系陕西西安华北工学院数学系山西太原 030051 南开大学天津

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关键词： Population persistenceextinction toxicant threshold.

ON APPROXIMATION BY SPHERICAL ZONAL TRANSLATION NETWORKS BASED ON BOCHNER-RIESZ MEANS

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Journal of Systems Science & Complexity 2005年第3期18卷 361-374页

作者： SHENGBaohuai LIHongtao departmentofmathematics ShaoxingCollegeofArtsandSciencesShaoxing312000China departmentofmathematics BaojiCollegeofArtsandSciencesBaoji721007China

A sequence of spherical zonal translation networks based on the Bochner-Riesz means of spherical harmonics and the Riesz means of Jacobi polynomials is introduced, and its degree of approximation is achieved. The results obtained in the present paper actually imply that the approximation of zonal translation networks is convergent if the action functions have certain smoothness.

关键词： spherical harmonics zonal translation networks approximation

Variable Separation Solution for(1+1)-Dimensional Nonlinear Models Related to Schrdinger Equation

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Communications in Theoretical Physics 2004年第10期42卷 568-572页

作者： XU Chang-Zhi~(1,2) ZHANG Jie-Fang~11 Institute of Nonlinear Physics,Zhejiang Normal University,Jinhua 321004,china2 department of Physics and mathematics,Jinhua Educational College,Jinhua 321000,china department of Physics and mathematics Jinhua Educational College Jinhua 321000 China

A variable separation approach is proposed and successfully extended to the(1+1)-dimensional *** new exact solution of(1+1)-dimensional nonlinear models related to Schr(?)dinger equation by the entranceof three arbitrary functions is *** special types of soliton wave solutions such as multi-soliton wave solution,non-stable soliton solution,oscillating soliton solution,and periodic soliton solutions are discussed by selecting thearbitrary functions appropriately.

关键词： variable separation approach (1+1)-dimensional nonlinear models solution of soliton