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25 April 2007, Volume 27 Issue 2 Previous Issue    Next Issue

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Additive Maps Preserving Rank-1 Nilpotency on Nest Algebras Cui Jianlian; Hou Jinchuan Acta mathematica scientia,Series A. 2007, 27 (2):  193-203.  Abstract ( 1837 )   RICH HTML PDF (405KB) ( 1253 )   Save Let ${\cal N}$ and ${\cal M}$ be two nests on real or complex Banach spaces X and Y, respectively, and $\Phi$ be an additive map between ideals Alg$_{\cal F}{\cal N}$ and Alg$_{\cal F}{\cal M}$ of finite rank operators in nest algebras Alg${\cal N}$ and Alg${\cal M}$, of which the range contains all rank-1 nilpotent operators in Alg${\cal M}$. The authors show that if $\Phi$ is rank-1 nilpotency preserving in both directions, then $\Phi$ has the form either $\Phi(x\otimes f)=Ax\otimes Cf$ for every rank-1 nilpotent operator $x\otimes {\rm Alg}_{\cal F}{\cal N}$ or $\Phi(x\otimes f)=Af\otimes Cx$ for every rank-1 nilpotent operator $x\otimes f\in {\rm Alg}_{\cal F}{\cal N}$, where $A$ and $C$ are certain $\tau$-linear operators with an automorphism $\tau$ of the underlying field. And the authors obtain particularly a characterization of such $\Phi$ if it is continuous, $X$ and $Y$ are Hilbert spaces with dimX≥ 6. Related Articles | Metrics

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Multipliers Between Hardy Spaces on the Unit Ball Luo Luo Acta mathematica scientia,Series A. 2007, 27 (2):  204-207.  Abstract ( 1706 )   RICH HTML PDF (203KB) ( 1144 )   Save In this paper, the author studies the multipliers between Hardy spaces on the unit ball in CN. The author gets the characterizations of the bounded multipliers Mg: Hp(B) → Hq(B). Related Articles | Metrics

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Non-triviality of an Elementα1β1βsin the Stable Homotopy Liu Xiugui Acta mathematica scientia,Series A. 2007, 27 (2):  208-214.  Abstract ( 2145 )   RICH HTML PDF (264KB) ( 1250 )   Save To determine the stable homotopy groups of spheres π*S is one of the central problems in homotopy theory. In this paper, it is proved that, for p≥ 5 to be an arbitrary odd prime number and 1≤ s1β1βs is nontrivial and of order p in the stable homotopy groups of spheres π*S$. Related Articles | Metrics

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A New Projection Algorithm for Mixed Variational Inequalities He Yiran Acta mathematica scientia,Series A. 2007, 27 (2):  215-220.  Abstract ( 1992 )   RICH HTML PDF (298KB) ( 1226 )   Save A new projection algorithm is proposed for mixed variational inequalities. Mixed variational inequalities are more general than classical variational inequalities and have rather practical applications in elastoplastic problems. Assuming that the underlying mapping F is pseudo-monotone with respect to the underlying function $\varphi$, the author proves that this new method is globally convergent. In addition, when a certain error bound holds locally, the author analyzes the convergence rate of the iteration sequence. Related Articles | Metrics

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Holomorphically Extendability of Proper Holomorphic Maps and Proper Holomorphic Map of Generalized Hartogs Triangle Han Jing; Chen Zhihua Acta mathematica scientia,Series A. 2007, 27 (2):  221-228.  Abstract ( 1624 )   RICH HTML PDF (282KB) ( 1268 )   Save The purpose of this paper is to prove a theorem about the local holomorphically extendability of the proper holomorphic maps between non-smooth bounded domains under some condition. At the same time the proper holomorphic maps between generalized Hartogs triangle are also discussed. Related Articles | Metrics

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Bound of Parametric Functions and Its Applications Yan Xia; Yu Dan; Li Guoying Acta mathematica scientia,Series A. 2007, 27 (2):  229-239.  Abstract ( 1719 )   RICH HTML PDF (411KB) ( 1207 )   Save This paper generalizes WCF method to the cases of parameters' estimators being not independent. Based on this result, the lower bound of confidences of the reliability is obtained for the components with weibull distributed life, and the systems involve this kind of components. Simulation studies show that the inference results given by WCF method are better than those provided by the asymptotic method. Related Articles | Metrics

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Eternal Solutions of the Boltzmann Equation Wei Jinbo; Zhang Xianwen Acta mathematica scientia,Series A. 2007, 27 (2):  240-247.  Abstract ( 2046 )   RICH HTML PDF (300KB) ( 1202 )   Save In this paper, the authors discuss the following spatially inhomogeneous Boltzmann equation \frac{\partial f}{\partial t} + \xi\cdot \nabla_{x}f(t, x, \xi) = Q(f, f). By means of a new iteration method, the existence of a positive eternal solution with initial data close to a travelling Maxwellian is proved in the case of hard potentials with angular cut-off. Hence, the authors give a negative answer to the conjecture of Villani [12, 13] in the case of unbounded space domain. Related Articles | Metrics

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Existence of Positive Stationary Solutions for a Prey-predator Model with the Third Boundary Value to the Prey Gu Yonggeng; Zeng Xianzhong Acta mathematica scientia,Series A. 2007, 27 (2):  248-262.  Abstract ( 2228 )   RICH HTML PDF (417KB) ( 1304 )   Save This paper deals with a prey-predator model with the third boundary value to the prey. First, the authors obtain that the model has positive stationary solutions if and only if a>mb+d1λ1. Secondly, the authors prove the local stability and uniqueness of its positive stationary solution. Thirdly, the authors study the change of existence of its positive stationary solution when the coefficients of its diffusion terms approach infinity. Related Articles | Metrics

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Stability in Total Variation for a Mean-Field Model of Cooperative Behavior Xi Fubao Acta mathematica scientia,Series A. 2007, 27 (2):  263-268.  Abstract ( 2252 )   RICH HTML PDF (287KB) ( 1174 )   Save In this paper the author considers the stability problem for a mean-field model of cooperative behavior. Applying the coupling methods, the author establishes the stability in total variation for the diffusion process corresponding to the mean-field model. Related Articles | Metrics

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Transience for Markov Chains in Double Infinite Random Environments Li Yingqiu Acta mathematica scientia,Series A. 2007, 27 (2):  269-276.  Abstract ( 1805 )   RICH HTML PDF (316KB) ( 1230 )   Save Various concepts of transience are introduced into the research field of Markov chains in random environments. Their connections and basic properties are discussed. Some criteria for states and chains to be transient are given. Related Articles | Metrics

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A Class of Quasilinear Elliptic Equations with Weights Liu Xiangqing; Huang Yisheng Acta mathematica scientia,Series A. 2007, 27 (2):  277-287.  Abstract ( 2139 )   RICH HTML PDF (325KB) ( 1158 )   Save In this paper, by using the variational methods, the authors consider the solvability of the equation -△p u=λa(x)(u+)p-1-μa(x)(u-)p-1+f(x, u), u∈ W01,p(\Omega) in the cases of (λ, μ)\not\in ∑p and (λ, μ) ∈ ∑p, where \Omega is a bounded domain in RN(N≥3) with smooth boundary $\partial\Omega$, ∑p is the Fucik spectrum of the equation -△p u=α a(x)(u+)p-1-βa(x)(u-)p-1, u∈ W01,p(\Omega), the weight function a(x) ∈ Lr(\Omega)(r≥ N/p) with a(x)> 0 a.e. in \Omega, f satisfies some conditions to be specified. Related Articles | Metrics

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The Existence and Expressions for the Generalized Inverse A(2)T,S of Linear Operator in Hilbert Space Zheng Bing; Zhong Chengkui Acta mathematica scientia,Series A. 2007, 27 (2):  288-295.  Abstract ( 1908 )   RICH HTML PDF (266KB) ( 1225 )   Save Let H1 and H2 be Hilbert spaces. In this paper, the authors present some equivalent conditions for the existence of generalized inverse A(2)T,S of a bounded linear operator A ∈ B(H1,H2), which is a bounded linear operator X ∈ B(H2,H1) satisfying XAX=X, R(X)=T, N(X)=S. The basic properties and some expressions of the generalized inverse A(2)T,S are also investigated. Related Articles | Metrics

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The Asymptotic Behavior of Solution for the Reaction Diffusion Equations Mo Jiaqi; Tang Rongrong Acta mathematica scientia,Series A. 2007, 27 (2):  296-301.  Abstract ( 1846 )   RICH HTML PDF (254KB) ( 1268 )   Save The initial boundary value problems for the reaction diffusion equations are considered. And the asymptotic behavior of solution for the problem is obtained by using the theory of differential inequality. Related Articles | Metrics

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Integral Formulas for Compact Space-like Hypersurfaces in anti-de Sitter Spacetime: Applications to the Case of Constant Higher Order Mean Curvature Xu Senlin; Hu Zisheng Acta mathematica scientia,Series A. 2007, 27 (2):  302-308.  Abstract ( 1887 )   RICH HTML PDF (275KB) ( 1368 )   Save In this paper, the authors develop some integral formulas for compact space-like hypersurfaces in anti-de Sitter spacetime H1n+1 and apply them to characterize the totally umbilical ones in H1n+1 as the only compact space-like hypersurfaces with constant higher order mean curvature under some appropriate hypothesis. Related Articles | Metrics

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Strong Approximations of Linear Processes Lu Chuanrong; Qiu Jin Acta mathematica scientia,Series A. 2007, 27 (2):  309-313.  Abstract ( 1704 )   RICH HTML PDF (224KB) ( 1138 )   Save In this paper, the authors establish a functional law of iterated logarithm and strong approximations for linear processes generated by a sequence of i.i.d. random variables. Related Articles | Metrics

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Limit Shadowing Property of Linear Systems Zhu Yujun; He Lianfa Acta mathematica scientia,Series A. 2007, 27 (2):  314-321.  Abstract ( 1635 )   RICH HTML PDF (285KB) ( 1020 )   Save In this paper, the authors give the characterization of both linear automorphisms and linear flows on Rn with the limit shadowing property. That is, an automorphism defined by a matrix has the limit shadowing property if and only if this matrix is hyperbolic, and a linear flow induced by a matrix has the limit shadowing property if and only if all eigenvalues of this matrix have nonzero real parts. Related Articles | Metrics

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An Analytic Characterization of B-Valued Generalized Functionals of White Noise Wang Caishi; Chen Jinshu; Qu Mingshuang Acta mathematica scientia,Series A. 2007, 27 (2):  322-330.  Abstract ( 2204 )   RICH HTML PDF (319KB) ( 1356 )   Save Banach space-valued generalized functionals of white noise form an important part of vector-valued generalized functionals of white noise. In this paper, an analytic characterization theorem is established for Banach space-valued generalized functionals of white noise. Applications of the result are also given. Related Articles | Metrics

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The Changes of F Distribution Density Curve Liu Xiaopeng; Liu Kunhui Acta mathematica scientia,Series A. 2007, 27 (2):  331-342.  Abstract ( 1786 )   RICH HTML PDF (371KB) ( 1208 )   Save This paper analyses deeply certain properties of special function, and uses these properties to discuss the relation between the positions of F distribution density curves with different parameters. Besides, this paper discusses certain asymptotic properties of density curve and builds some related equations. As the application and verifications of conclusions, this paper gives some representative examples. The analytic methods of this paper can also be used to discuss certain properties about density curves of other distributions. Related Articles | Metrics

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Periodic Solutions for Nonlinear n-th Order Differential Equations with Delays Liu Bingwen; Huang Lihong; Zhang Zhengqiu Acta mathematica scientia,Series A. 2007, 27 (2):  343-350.  Abstract ( 2166 )   RICH HTML PDF (262KB) ( 1247 )   Save By applying the continuation theorem of coincidence degree theory, the authors establish the existence of 2π-periodic solutions for a class of nonlinear n-th order differential equations with delays. Related Articles | Metrics

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On Generalized Transversality Fang Zheng; Ma Jipu Acta mathematica scientia,Series A. 2007, 27 (2):  351-358.  Abstract ( 1793 )   RICH HTML PDF (292KB) ( 1243 )   Save In this paper, the authors generalize the classical transversality by using the perturbation theory of generalized inverse of linear bounded operator, get the new concept of generalized transversality. The authors also discuss some basic properties of the generalized transversality and the relations between generalized transversality and generalized regular point. Related Articles | Metrics

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Robust Stabilization for Delay Differential Systems Based on SLQ Control Bao Jundong; Deng Feiqi; Luo Qi Acta mathematica scientia,Series A. 2007, 27 (2):  359-367.  Abstract ( 1933 )   RICH HTML PDF (335KB) ( 1154 )   Save This paper is based on the stochastic linear quadratic control problem. The robustness of stabilizability of optimal controller for stochastic multi-time delay systems with Markovian jumping parameters is investigated. Lyapunov--Krasovskii like functional, stochastic analysis, Ito formula and Schur complement are employed to analyze the exponential stability in mean square for stochastic multi-time delay differential systems with Markovian jumping parameters. The delay dependent and delay independent algebric criteria are established. Related Articles | Metrics

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The Comparison Theorem for Solutions of Forward-backward Stochastic Differential Equations Guo Zijun; Wu Rangquan Acta mathematica scientia,Series A. 2007, 27 (2):  368-373.  Abstract ( 2574 )   RICH HTML PDF (271KB) ( 1498 )   Save The comparison theorems for solutions of FBSDEs are discussed. The FBSDEs's applications in stochastic optimal control and modern financial theory are introduced. By using the tools of Ito's formula and stopping time, a comparison theorem for FBSDEs is acquired by introducing helping linear FBSDEs. Related Articles | Metrics

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The Part Hermitian Solutions of Matrix Equation AHXA=B on Subspace Peng Xiangyang; Hu Xiyan Acta mathematica scientia,Series A. 2007, 27 (2):  374-384.  Abstract ( 1881 )   RICH HTML PDF (301KB) ( 1198 )   Save In this paper, the following two problems are considered: Problem I Given M∈ Cn×e, A∈Cn×m, B∈ Cm×m, find X∈ HCM,n such that AHXA=B, where HCM,n={ X∈ Cn×n}|αH(X-XH)=0, for all α∈ C(M) }. Problem II Given X* ∈Cn×n, find $\hat{X}\in H_E$ such that ||\hat{X}-X*||=\min\limits_{X∈ HE}||X-X*||, where HE is the solution set of Problem I. The necessary and sufficient condition for the solvability and the general form of the solutions Problem I are given. For Problem II, the expression for the solution, a numerical algorithm and a numerical example are illustrated. Related Articles | Metrics