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25 June 2003, Volume 23 Issue 3 Previous Issue    Next Issue

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The Existence of Positive Solutions of Singular Boundary Value Problems with p-Laplacian LI Bi-Wen Acta mathematica scientia,Series A. 2003, 23 (3):  257-264.  Abstract ( 1709 )   RICH HTML PDF (349KB) ( 1134 )   Save In this paper, the authors discuss the existence of positive solu tions for a singular boundary value problems with p-Laplacian (Φp(x′) )′+a(t)f(x(t))=0,x(0)-βx′(0)=0,x(1)+δx′(1)=0,where Φp(x)=|x|p-2 ,p>1. By using the fixed point index theorem the authors established the sufficient conditions of the existence of positive solutions for this boundary value problem s under some conditions.These results can be applied to study the existence of the radial solutions for the elliptic boundary value problems.  References | Related Articles | Metrics

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Implicit Iterative Methods Based on Some Orthogonal Polynomials for Ill Posed Operator Equations TANG Jian-Guo Acta mathematica scientia,Series A. 2003, 23 (3):  265-275.  Abstract ( 1678 )   RICH HTML PDF (405KB) ( 1333 )   Save In this paper, implicit iterative methods (IIMs) based on Chebyshev and Jacobi polynomials for ill posed operator equations are investigated. The relation between IIMs and the explicit iterative methods (EIMs) developed by Hanke is established. An important lemma about residual rational formula of the iterative schemes related to the first and the second Chebyshev polynomials is presented. For nonperturbed and perturbed data, the convergence properties and convergence rate are studied. An implementable algorithm is given by using Moro zov's discrepancy principle, which is a robust regularization algorithm.Finally, numerical examples are also given, which coincide well with theoretical results.  References | Related Articles | Metrics

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Existence of Random Solutions for a Class of Random Operator Equations ZHU Chuan-Xi Acta mathematica scientia,Series A. 2003, 23 (3):  276-279.  Abstract ( 1297 )   RICH HTML PDF (282KB) ( 1443 )   Save In this paper, the authors study random solutions for a class of random operator  equation s,and generalize several important theorems. Meanwhile, the authors obtain some  new results.  References | Related Articles | Metrics

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On the Stability of Linear Time Change Differential Algebraic System XIONG Ge, ZHENG Lu-Zhou Acta mathematica scientia,Series A. 2003, 23 (3):  280-286.  Abstract ( 1635 )   RICH HTML PDF (342KB) ( 1378 )   Save In this paper, the stability of linear time change differential algebraic system is disscussed.Some conditions of stability are given directly by coefficients of equations. References | Related Articles | Metrics

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On the Roots on Orientable Embeddings of Graph MAO Lin-Fan, LIU Yan-Pei Acta mathematica scientia,Series A. 2003, 23 (3):  287-293.  Abstract ( 1556 )   RICH HTML PDF (376KB) ( 1198 )   Save For a given family G of graphs, how many rooted maps on surfaces with underlying graph in G?  The authors obtain an answer for th is problem in orientable case and a new method to get the enufunction f^r(M) by using the  automorphism groups of these graphs in this paper. References | Related Articles | Metrics

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Congruence Permutable Stone Algebras LUO Cong-Wen Acta mathematica scientia,Series A. 2003, 23 (3):  294-297.  Abstract ( 1080 )   RICH HTML PDF (288KB) ( 1136 )   Save In this paper the author characterizes congruence permutable Stone  algebras by means of dual space theory of Stone algebras References | Related Articles | Metrics

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A Hierarchy of Discrete Generalized Hamiltonian Systems and a New Integrable Symplectic Map XU Xi-Xiang, WANG Shi-Fan Acta mathematica scientia,Series A. 2003, 23 (3):  298-305.  Abstract ( 1666 )   RICH HTML PDF (338KB) ( 1131 )   Save A new discrete eigenvalue  problem is discussed, the corresponding isospectra l hierarchy of discrete Hamiltonian system is presented. It is shown that this h ierarchy are all integrable in Liouville  sense. A new integrable symplectic map  is derived by means of nonlinearization of the eigenvalue problem. References | Related Articles | Metrics

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The Classification of States for Skew Product Markov Chains XIAO Zheng-Yan, HU Di-He Acta mathematica scientia,Series A. 2003, 23 (3):  306-313.  Abstract ( 1418 )   RICH HTML PDF (370KB) ( 1477 )   Save The main result of this paper is the classification of states on skew  product Markov chains. First of all, the authors introduce some basic concepts o n the sta tes, such as recurrent state, strongly recurrent state, and strongly transient s tate, essential state, and then give some criteria. At last, the paper provides  the necessary and  sufficient conditions for proper essential state where joint space is indecompo sable and proper essential. References | Related Articles | Metrics

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Quantum Corrects to the Entropy of the Barriola Vilenkin Black Hole Due to Spin Fields LI Gu-Qiang, LI Zhong-Heng Acta mathematica scientia,Series A. 2003, 23 (3):  314-319.  Abstract ( 1708 )   RICH HTML PDF (331KB) ( 1112 )   Save The quantum corrections to the entropy of the Barriola Vilenkin black  hole due to the gravitation electromagnetic and neutrino fields are calculated b y using the  brick wall model. It is shown that the quantum corrects consist in two parts :  One is aquadratic divergent term at event horizon and is proportional to t he s urface area of the event horizon. The other is two logarithmically divergent terms which not only depend on the characteristics of the black hole but also on th e spin of fields. The whole expression does not take the form of the scalar field.   References | Related Articles | Metrics

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The Markov Approximation of the Random Fields on Cayley Trees and a Class of Small Deviation Theorems LIU Wen, WANG Li-Ying Acta mathematica scientia,Series A. 2003, 23 (3):  320-326.  Abstract ( 1732 )   RICH HTML PDF (375KB) ( 1154 )   Save  By introducing the sample relative entropy rate as a measure of the deviation bewteen the arbitrary random fields and the Markov chain fields on Cayley trees, a class of small deviation theorems  for the frequencies of state ordered couples  are established. In the proof a new analytic technique in the study of the strong limit theorems for Markov chains is applied. References | Related Articles | Metrics

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Additional Remarks on a Superiority Problem in Misspecified Re stricted Singular Linear Models ZHANG Bao-Xue Acta mathematica scientia,Series A. 2003, 23 (3):  327-332.  Abstract ( 1523 )   RICH HTML PDF (317KB) ( 1220 )   Save When the covariance matrix of the disturbance vector in t he general linear model is misspecified, Gross, Trenkler and Liski (1998) showed  Razzaghi's (1987) result that sufficient condition for nonnegative definitness  of the covariance matrix difference of competing estimators is also necessary by  applying a result of Kabe and Gupta (1989). Further, Zhang and Liu (2000) exten ded the Theorem 1 of Gross, Trenkler and Liski to the singular linear model usin g matrix inequality and subspace relations. The aim of this paper is to prove th e conjecture which Razzaghi (1987) made is true in misspecified restricted singu lar linear model and strengthen Theorem 2 of Gross, Trenkler and Liski by giving  the necessary and sufficient conditions for nonnegative definiteness of the cov ariance matrix difference in the singular linear model.  References | Related Articles | Metrics

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Oscillation of Nonlinear Delay Difference Equations JIANG Jian-Chu, LI Xiao-Ping Acta mathematica scientia,Series A. 2003, 23 (3):  333-340.  Abstract ( 1924 )   RICH HTML PDF (330KB) ( 1134 )   Save Consider the nonlinear delay difference equation of the form x_{n+1}-x_n+p_nf(x_{n-l_1},x_{n-l_2}x_{n-l_m})=0,   n=0,1,2, This paper obtain sufficient conditions for the oscillation of all solutions of this equation. Which  extend and improve  some well known results in the literature. References | Related Articles | Metrics

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On Fast Points of l^P Valued Gaussian Processes WANG Wen-Sheng Acta mathematica scientia,Series A. 2003, 23 (3):  341-348.  Abstract ( 1309 )   RICH HTML PDF (358KB) ( 1108 )   Save The author proves that the set of points where exceptional oscillations of l^p valued Gaussian processes occur infinitely often is a random fractal, and give a hitting criterion for this set. References | Related Articles | Metrics

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Some Results on Stochastic Comparison in Likelihood Ratio Order JIAO Gui-Mei, LIU Ke Acta mathematica scientia,Series A. 2003, 23 (3):  349-356.  Abstract ( 1793 )   RICH HTML PDF (336KB) ( 1354 )   Save It is established the conditions to ensure the stochastic comparison of the Likelihood ratio order between the groups of random variables. The results obtained in the paper generalize the some works developed by Shaked and Shanthikumar in a sence. References | Related Articles | Metrics

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Stability of Some Epidemic Models |with Passive Immunity LOU Jie, MA Zhi-En Acta mathematica scientia,Series A. 2003, 23 (3):  357-368.  Abstract ( 1782 )   RICH HTML PDF (411KB) ( 1374 )   Save Some epidemic models with passive immunity for the spread  of infection diseases in populations have been analyzed  mathematically and dis cussed. The basic repouduction number R_0 is obtained for these models, global asymptotical stability have been got for some  models. Vaccinations are considered on the MSIR model.  References | Related Articles | Metrics

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Singular Perturbation for a Class of Reaction Diffusion Equation XIE Feng Acta mathematica scientia,Series A. 2003, 23 (3):  369-373.  Abstract ( 1793 )   RICH HTML PDF (301KB) ( 2149 )   Save The singularly perturbed initial boundary value problem for a class of semiline ar reaction diffusion equation is considered. Under the appropriate conditions a nd by using the fixedpoint theorem the existence, uniqueness and asymptotic be havior of solution for the original problem are showed. References | Related Articles | Metrics

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The Nonlinear Singularly Perturbed Problems for Reaction Diffusion Equations MO Jia-Qi Acta mathematica scientia,Series A. 2003, 23 (3):  374-378.  Abstract ( 1637 )   RICH HTML PDF (302KB) ( 1427 )   Save The nonlinear singularly perturbed problems for the reaction diffusio n equations are considered. Under suitable conditions, using the theory of diffe rential inequalities the asymptotic behavior of solution for the initial boundar y value problems are studied, which reduced problems possess two intersecting so lutions. References | Related Articles | Metrics

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A Single Step Scheme for Ordinary Differential Initial Problem of Second Order  LI Tian-Ran, CHEN Chuan-Miao Acta mathematica scientia,Series A. 2003, 23 (3):  379-384.  Abstract ( 1718 )   RICH HTML PDF (332KB) ( 1372 )   Save  A single step scheme for ordinary differential initi al problem of seco nd order, utt+au=f,u(0)=u 0,ut(0)=v0, is discussed, in which both  u  and ut are used as two unknowns and the ir computation is simpler. The stability and second order high accuracy for both  u and u t is proved. The scheme can be applied to hyperbolic problem.  References | Related Articles | Metrics