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26 August 1997, Volume 17 Issue 4 Previous Issue    Next Issue

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Quantization and Renormalization of 4-Derivative Gravity Shao Changgui, Chen Zhongqiu, Chen Yihan Acta mathematica scientia,Series A. 1997, 17 (4):  364-374.  Abstract ( 60 )   RICH HTML PDF (620KB) ( 30 )   Save Field equations, tree dlagram propagators and divergence degrees of loops,for 4-derivative gravity, are calculated. It is pointed out that the use of usual method for solving renormalization equation to obtain the counter-terms to cancel out divergences, used in renorrmalization scheme of higher-derivative quantum gravity. has need for clarification. Related Articles | Metrics

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A Kind of Strong Deviation Theorem for the Sequences of Nonnegative Integer-Valued Random Variable Liu Wen Acta mathematica scientia,Series A. 1997, 17 (4):  375-381.  Abstract ( 67 )   RICH HTML PDF (391KB) ( 98 )   Save Let {Xn,n ≥ 1} be a sequence of random variables taking valnes in S={0,1,2,…} with the joint distribution fn(x1,…,xn),(p(0),p(1),…) a distribution on S,m=Σk=1∞kp(k),pn(x1,…xn)=Πk=1np(xk), and ψn=(1/n)Σk=1n(Xk-m). In this paper the limit relation between ψn(ω) and the log-likelihood ratio Ln(ω)=ln[pn(X1,…,Xn)/fn(X1,…,Xn)] is investigated and a kind of strong limit theorem represented by inequalities which we call the strong deviation theorem is obtained. In the proof an approach of applying the tool of generating function together with the method of splitting intervals to the investigation of the strong limit theorem is proposed. Related Articles | Metrics

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A Nonlinear Bounary Value Problem for Analytic Functions of Several Complex Variables Huang Sha Acta mathematica scientia,Series A. 1997, 17 (4):  382-388.  Abstract ( 58 )   RICH HTML PDF (430KB) ( 228 )   Save In this paper, we discuss a nonlincar boundary value problem for analytic fucntions of several complex variables: A(t1,t2)φ++(t1,t2)+B(t1,t2)φ+-(t1,t2)+C(t1,t2)φ-+(t1,t2)+D(t1,t2)φ——(t1,t2)=g(t1,t2)f(t1,t2),φ++(t1,t2),φ+-(t1,t2),φ-+(t1,t2),φ——(t1,t2)) Applying the method of intcgral equations and Schauder fixed-point theorem, we proved existence of solution for above problem and get integral representations of solution. Related Articles | Metrics

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Non-existence and the Pohozaev Identity for the Singular Solutions of Quasilinear elliptic systems Shen Yaotian Acta mathematica scientia,Series A. 1997, 17 (4):  389-395.  Abstract ( 85 )   RICH HTML PDF (435KB) ( 332 )   Save The Pohozaev identity is obtained for the singular solutions of the elliptic systems involving super-critical sobolev exponent and natural growth condition. Related Articles | Metrics

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On Asymptotic Stability for C0 Semigroups Luo Yuehu, Feng Dexing Acta mathematica scientia,Series A. 1997, 17 (4):  396-402.  Abstract ( 55 )   RICH HTML PDF (515KB) ( 185 )   Save In this paper, properties on C0 isometric-semigroups in Banach Spaces are studied. By using these results, the asymptoic stability and the existence of trajectory for C0 semigroups in Banach Spaces are studied. Finally, a guess on the asymptotic stability possed by Huang Falung is solved. Related Articles | Metrics

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The Existence Uniqueness and Asymptotic Properties of a Class of Semilinear Elliptic Equations Yang Haitao, Wu Shaoping Acta mathematica scientia,Series A. 1997, 17 (4):  403-411.  Abstract ( 61 )   RICH HTML PDF (463KB) ( 65 )   Save In this paper, using sub and supsolution mecthods and potential estimations, we study following semilinear elliptic equation on RN with sublinear and suplinear nonlinearities: -△u=a(x)ua+λb(x)us,x∈RN The existence uniqueness and asymptotic properties of bounded positive solution are given, where 0 < α < 1,s > 1 is a constant,λ > O is a paramcter. Related Articles | Metrics

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Stationary Respones of two Clalles of Mechanical Systems With Constraints Under Whete Noise Excitations Zhu Haiping Acta mathematica scientia,Series A. 1997, 17 (4):  412-417.  Abstract ( 83 )   RICH HTML PDF (350KB) ( 80 )   Save The stationary responses of nonlinear nonholonomic systems under white noise excitations are studied the exact solutions of two classes of systems are obtained and an illustrative example is given. Related Articles | Metrics

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The Convergence of the Slaving Principle in Single-Mode Laser Model Xu Haibo Acta mathematica scientia,Series A. 1997, 17 (4):  418-426.  Abstract ( 70 )   RICH HTML PDF (460KB) ( 63 )   Save By virtue of introducing an auxiliary series of positive terms corresponding to the formal slaving series of variable terms we prove the convergence of the slaving principle in the simplified single-mode laser model and give the approximation involved in the substitution of stable mode by slaving function. Related Articles | Metrics

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The Limit of Biholomorphic Invariant on a Class of Pseudoconvex Domains Tong Wu Acta mathematica scientia,Series A. 1997, 17 (4):  427-431.  Abstract ( 56 )   RICH HTML PDF (266KB) ( 69 )   Save E=E(m,n,k)={(z,w)∈Cn+m:|z|2+|w|2k<1,z∈Cn,w∈Cm,k>0} is a class of pseudoconvex domains in Cn+m. In this note is showed it, that lim(z,w)→∂EJE((z,w))=πn+m(n+m+1)n/(n+m)!,when m>1. lim(z,w)→∂EJE((z,w))=πn+1(n+2)n+1/(n+1)!, when m=1 holds on the strongly pseudoconvex points of boundary ∂E; the limit given above not exist on the weakly pseudoconvex points of boundary ∂E. Related Articles | Metrics

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The Homogenization of Non-homogeneous Markov Decision Processes Hou Zhenting, Guo Xianping Acta mathematica scientia,Series A. 1997, 17 (4):  432-438.  Abstract ( 66 )   RICH HTML PDF (427KB) ( 83 )   Save In this paper we consider the homogenization of Non-homogneous Markov decision model with expected total reward criterion.denumerable state space and finite action spaces. We translate the non-homogeneous Markov decision processes into a homegeneous one by the method of extanding state space which is different from the usual one, and then we easily obtain the mail results obtained by usual method. Specially, the mail results obtained by K. Hinderer. Related Articles | Metrics

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On the Existence and Nonexistence of Solution,Blow-up Problem and The Infinite Growing up Problem of Solution for Initial Problem of Semilinear Parabolic Eguation With Singular Cofficient Jian Suwen, Yang Fengzao Acta mathematica scientia,Series A. 1997, 17 (4):  439-446.  Abstract ( 50 )   RICH HTML PDF (419KB) ( 17 )   Save In this paper we study that existence and nonexistence of solution, Blow-up problem and the infinite growing up problem If solution for the initial prolem of semilinear para bolic eguation with singular coefficient. Related Articles | Metrics

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The obligue Derivative Boundary Value Problem for the Generalized Regular Function with Value in Quaternions Qiao Yuying Acta mathematica scientia,Series A. 1997, 17 (4):  447-451.  Abstract ( 59 )   RICH HTML PDF (318KB) ( 88 )   Save The first part of this paper discuses the obligue derivative boundary value problem for the generalized regular function with value in Quaternions. We got the existence and uniqueness of the solution of the problem. In the second part of the paper we discuse existence of solution of the obligue derivative boundary value problem for first order degeneracy elliptic system include four variates. Related Articles | Metrics

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Existence of Nontrivial Solutions of Critical Biharmonic Equations Peng Yongdong, Deng Yinbin Acta mathematica scientia,Series A. 1997, 17 (4):  452-465.  Abstract ( 66 )   RICH HTML PDF (782KB) ( 197 )   Save With the help of the Mountain-Pass Theorem lacking Palais-Smale compactness condition and by adoption of the best attained function of Sobolev embedding, the paper sucessfully ovetcomes seria1 difficulties caused by lose of compactness due to Sobolev embedding and proves the existence of nontrivial solutions of two classes of critical biharmonic equations on boundary conditions. Related Articles | Metrics

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Quantify Behaviors of Approximation Degree to Unbounded Fuctions by Generalized Feller Operators Derived S-λ Zhao Jinghui Acta mathematica scientia,Series A. 1997, 17 (4):  466-472.  Abstract ( 69 )   RICH HTML PDF (391KB) ( 29 )   Save Applying combination of mathods from probability and fuction theory in the paper we study the quantify estimation of approximation degree to unbounded and continuouns or discontinuous fuctions by generalized Feller operators derived from original fuction S(x)and extending factor λ(x). Related Articles | Metrics

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Second-order Conservative Algorithm for Unsteady Free-Suface Flows with shocks Cai Qifu Acta mathematica scientia,Series A. 1997, 17 (4):  473-478.  Abstract ( 52 )   RICH HTML PDF (396KB) ( 77 )   Save TVD Lax-Wendroff schemes for the computation of weak solution of hyperbolic conservation law are extended to the gencral shallow-water equations with thc arbitrary variation of the section shape with distance. A second-order accurate finite difference scheme ispresented. The new scheme can be applied to simulating the dam-break flood wave propagation in the natural river courses. Numerical examples are provided to test the performance of the method. Numerical experirnents with dam-break problems in the practical natural cascade reservoirs show that the scheme is stable and robust. Related Articles | Metrics