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20 April 2008, Volume 28 Issue 2 Previous Issue    Next Issue

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THE CONSTRUCTION OF DENUMERABLE q-PROCESSES IN RANDOM ENVIRONMENTS-THE EXISTENCE AND UNIQUENESS Hu Dihe; Hu Xiaoyu Acta mathematica scientia,Series B. 2008, 28 (2):  225-235.  DOI: 10.1016/S0252-9602(08)60024-7 Abstract ( 1269 )   RICH HTML PDF (174KB) ( 1526 )   Save The concepts of Markov process in random environment, q-matrix in random environment, and q-process in random environment are introduced. The minimal q-process in random environment is constructed and the necessary and sufficient conditions for the uniqueness of q-process in random environment are given. Related Articles | Metrics

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NUMERICAL SIMULATION FOR CONVECTION-DIFFUSION PROBLEM WITH PERIODIC MICRO-STRUCTURE Wu Zhihua; Yan Ningning Acta mathematica scientia,Series B. 2008, 28 (2):  236-252.  DOI: 10.1016/S0252-9602(08)60025-9 Abstract ( 1308 )   RICH HTML PDF (311KB) ( 1473 )   Save In this article, the convection dominated convection-diffusion problems with the periodic micro-structure are discussed. A two-scale finite element scheme based on the homogenization technique for this kind of problems is provided. The error estimates between the exact solution and the approximation solution of the homogenized equation or the two-scale finite element scheme are analyzed. It is shown that the scheme provided in this article is convergent for any fixed diffusion coefficient δ, and it may be convergent independent of δ under some conditions. The numerical results demonstrating the theoretical results are presented in this article. Related Articles | Metrics

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CONCEPTUAL ANALYSIS AND RANDOM ATTRACTOR FOR DISSIPATIVE RANDOM DYNAMICAL SYSTEMS Li Yuhong; Zdzislaw Brzezniak; Zhou Jianzhong Acta mathematica scientia,Series B. 2008, 28 (2):  253-268.  DOI: 10.1016/S0252-9602(08)60026-0 Abstract ( 1483 )   RICH HTML PDF (224KB) ( 1732 )   Save The aim of this work is to understand better the long time behaviour of asymptotically compact random dynamical systems (RDS), which can be generated by solutions of some stochastic partial differential equations on unbounded domains. The conceptual analysis for the long time behavior of RDS will be done through some examples. An application of those analysis will be demonstrated through the proof of the existence of random attractors for asymptotically compact dissipative RDS. Related Articles | Metrics

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SOME LIMIT THEOREMS FOR SEQUENCES OF PAIRWISE NQD RANDOM VARIABLES Gan Shixin; Chen Pingyan Acta mathematica scientia,Series B. 2008, 28 (2):  269-281.  DOI: 10.1016/S0252-9602(08)60027-2 Abstract ( 1454 )   RICH HTML PDF (171KB) ( 2093 )   Save In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong stability of Jamison's weighted sums for pairwise NQD random variables, which may have different distributions. Some well-known results are improved and extended. Related Articles | Metrics

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POWERS OF AN INVERTIBLE (s,p)-w-HYPONORMAL OPERATOR Li Haiying Acta mathematica scientia,Series B. 2008, 28 (2):  282-288.  DOI: 10.1016/S0252-9602(08)60028-4 Abstract ( 1083 )   RICH HTML PDF (153KB) ( 1620 )   Save It is known that the square of a w-hyponormal operator is also w-hyponormal. For any 00, 0characterization of (s,p)-w-hyponormal operators; the author shows that all integer powers of special (s,p)-w-hyponormal operators are (s,p)-w-hyponormal. Related Articles | Metrics

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ON SOME FEASIBILITY CONDITIONS IN MPEC Zhou Shuzi; Bai Minru Acta mathematica scientia,Series B. 2008, 28 (2):  289-294.  DOI: 10.1016/S0252-9602(08)60029-6 Abstract ( 1128 )   RICH HTML PDF (120KB) ( 1315 )   Save This article discusses feasibility conditions in mathematical programs with equilibrium constraints (MPECs). The authors prove that two sufficient conditions guarantee the feasibility of these MPECs. The authors show that the two feasibility conditions are different from the feasibility condition in [2, 3], and show that the sufficient condition in [3] is stronger than that in [2]. Related Articles | Metrics

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LARGE DEVIATIONS FOR SOME DEPENDENT SEQUENCES Hu Shuhe; Wang Xuejun Acta mathematica scientia,Series B. 2008, 28 (2):  295-300.  DOI: 10.1016/S0252-9602(08)60030-2 Abstract ( 1051 )   RICH HTML PDF (137KB) ( 1770 )   Save Let (Xi) be a martingale difference sequence and Sn=∑i=1nXi. Suppose (Xi) is bounded in Lp. In the case p≥ 2, Lesigne and Volny (Stochastic Process. Appl. 96 (2001) 143) obtained the estimation μ(Sn>n)≤ cn-p/2, Yulin Li (Statist. Probab. Lett. 62 (2003) 317) generalized the result to the case when p∈(1,2] and obtained μ(Sn>n)≤cn1-p, these are optimal in a certain sense. In this article, the authors study the large deviation of Sn for some dependent sequences and obtain the same order optimal upper bounds for μ(Sn>n) as those for martingale difference sequence. Related Articles | Metrics

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HOMOMORPHISMS BETWEEN MULTIPLICATIVE SEMIGROUPS OF MATRICES OVER FIELDS Zhang Xian; Cao Chongguang Acta mathematica scientia,Series B. 2008, 28 (2):  301-306.  DOI: 10.1016/S0252-9602(08)60031-4 Abstract ( 1105 )   RICH HTML PDF (149KB) ( 1778 )   Save Suppose <b>F</b> is a field, and n,p are integers with 1≤ p<n. Let Mn(<b> F</b>) be the multiplicative semigroup of all n× n matrices over <b> F</b>, and let Mnp(<b> F</b>) be its subsemigroup consisting of all matrices with rank p at most. Assume that F and R are subsemigroups of Mn(<b> F</b>) such that F\supseteq Mnp(<b> F</b>). A map f:F \rightarrow R is called a homomorphism if f(AB)=f(A)f(B) for any A,B∈ F. In particular, f is called an endomorphism if F= R. The structure of all homomorphisms from F to R (respectively, all endomorphisms of Mn(<b> F</b>)) is described. Related Articles | Metrics

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SMALL INTO ISOMORPHISM FROM (c0) INTO C(\Omega) TYPE Ding Guanggui Acta mathematica scientia,Series B. 2008, 28 (2):  307-314.  DOI: 10.1016/S0252-9602(08)60032-6 Abstract ( 1084 )   RICH HTML PDF (160KB) ( 1138 )   Save If T is an isomorphism of (c0) into C(\Omega) (where \Omega is a sequentially compact and paracompact space, or a compact metric space in particular), which satisfies the condition ||T||●||T-1||≤1+ε for some ε∈ (0, 1/5), then T /||T|| is close to an isometry with an error less than 9ε. The proof of this article is simple without using the dual space or adjoint operator. Related Articles | Metrics

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A SPECIAL KIND OF PRINCIPAL CONGRUENCES ON MS-ALGEBRAS Luo Congwen Acta mathematica scientia,Series B. 2008, 28 (2):  315-320.  DOI: 10.1016/S0252-9602(08)60033-8 Abstract ( 975 )   RICH HTML PDF (135KB) ( 1179 )   Save In this article, for any a in the MS-algebra L, the author considers the congruence of the form defined by (x,y)∈θa \Leftrightarrow x∧a^\circ =y∧a^\circ and x∨a^{\circ\circ}=y∨a^{\circ\circ} . A characterization of subdirectly irreducible MS-algebras is given and it is also proved that the union of two principal congruences having this form is a principal congruence if and only if L∈K2∨K3. Related Articles | Metrics

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A NEW FAMILY OF FILTRATION S+5 IN THE STABLE HOMOTOPY GROUPS OF SPHERES Wang Yuyu Acta mathematica scientia,Series B. 2008, 28 (2):  321-332.  DOI: 10.1016/S0252-9602(08)60034-X Abstract ( 1201 )   RICH HTML PDF (187KB) ( 1067 )   Save In this article, by the algebraic method, the author proves the existence of a new nontrivial family of filtration s+5 in the stable homotopy groups of spheres $\pi_rS$, which is represented by 0 ≠\widetilde{\gamma}_{s+3}h_nh_m\in {\rm Ex}t_A^{s+5,\ t}(Z_p, Z_p)$ in the Adams spectral sequence, where r=q(pm+pn+(s+3)p2+(s+2)p+(s+1))-5}, t=pmq+pnq+(s+3)p2q+(s+2)pq+(s+1)q+s, p≥7, m≥n+2>5, 0≤s<p-3, q=2(p-1). Related Articles | Metrics

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ROBUST ESTIMATION IN PARTIAL LINEAR MIXED MODEL FOR LONGITUDINAL DATA Qin Guoyou; Zhu Zhongyi Acta mathematica scientia,Series B. 2008, 28 (2):  333-347.  DOI: 10.1016/S0252-9602(08)60035-1 Abstract ( 1383 )   RICH HTML PDF (217KB) ( 1784 )   Save In this article, robust generalized estimating equation for the analysis of partial linear mixed model for longitudinal data is used. The authors approximate the nonparametric function by a regression spline. Under some regular conditions, the asymptotic properties of the estimators are obtained. To avoid the computation of high-dimensional integral, a robust Monte Carlo Newton-Raphson algorithm is used. Some simulations are carried out to study the performance of the proposed robust estimators. In addition, the authors also study the robustness and the efficiency of the proposed estimators by simulation. Finally, two real longitudinal data sets are analyzed. Related Articles | Metrics

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ON THE STABILITY OF THE POSITIVE RADIAL STEADY STATES FOR A SEMILINEAR CAUCHY PROBLEM INVOLVING CRITICAL EXPONENTS Deng Yinbin; Yang Fen Acta mathematica scientia,Series B. 2008, 28 (2):  348-354.  DOI: 10.1016/S0252-9602(08)60036-3 Abstract ( 1222 )   RICH HTML PDF (165KB) ( 1416 )   Save This article is contributed to the Cauchy problem $$ \left\{\begin{array}{ll} \D \frac{\partial u}{\partial t}= \Delta u+K( |x|)u^p \ \ \mbox{in} \ R^n \times(0,T),\\ u(x,0)=\varphi(x) \ \ \mbox{in} \ R^n ; \end{array} \right. $$ with initial function $\varphi \not \equiv 0$. The stability of positive radial steady state, which are positive solutions of △u+K( | x|)up=0, is obtained when p is critical for general K(|x|). Related Articles | Metrics

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CLASSICAL RISK MODEL WITH THRESHOLD DIVIDEND STRATEGY Zhou Ming; Guo Junyi Acta mathematica scientia,Series B. 2008, 28 (2):  355-362.  DOI: 10.1016/S0252-9602(08)60037-5 Abstract ( 1442 )   RICH HTML PDF (154KB) ( 2344 )   Save In this article, a threshold dividend strategy is used for classical risk model. Under this dividend strategy, certain probability of ruin, which occurs in case of constant barrier strategy, is avoided. Using the strong Markov property of the surplus process and the distribution of the deficit in classical risk model, the survival probability for this model is derived, which is more direct than that in Asmussen (2000, P195, Proposition 1.10). The occupation time of non-dividend of this model is also discussed by means of Martingale method. Related Articles | Metrics

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COSET DIAGRAMS FOR A HOMOMORPHIC IMAGE OF △(3,3,k) M. Ashiq; Q. Mushtaq Acta mathematica scientia,Series B. 2008, 28 (2):  363-370.  DOI: 10.1016/S0252-9602(08)60038-7 Abstract ( 1043 )   RICH HTML PDF (160KB) ( 1480 )   Save Let q be a prime power. By PL(Fq) the authors mean a projective line over the finite field Fq with the additional point ∞. In this article, the authors parametrize the conjugacy classes of nondegenerate homomorphisms which represent actions of △(3,3,k)=〈u,v:u3=v3=(uv)k=1〉on PL(Fq), where q≡±1(mod k). Also, for various values of k, they find the conditions for the existence of coset diagrams depicting the permutation actions of △(3,3,k) on PL(Fq). The conditions are polynomials with integer coefficients and the diagrams are such that every vertex in them is fixed by $(\overline{u}\,\overline{v})^{k}.$ In this way, they get △(3,3,k) as permutation groups on PL(Fq). Related Articles | Metrics

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BOUNDEDNESS OF RIESZ POTENTIALS IN NONHOMOGENEOUS SPACES Hu Guoen; Meng Yan; Yang Dachun Acta mathematica scientia,Series B. 2008, 28 (2):  371-382.  DOI: 10.1016/S0252-9602(08)60039-9 Abstract ( 1116 )   RICH HTML PDF (200KB) ( 1382 )   Save For a class of linear operators including Riesz potentials on Rd with a non-negative Radon measure μ, which only satisfies some growth condition, the authors prove that their boundedness in Lebesgue spaces is equivalent to their boundedness in the Hardy space or certain weak type endpoint estimates, respectively. As an application, the authors obtain several new end estimates. Related Articles | Metrics

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FORMULAS OF GAUSS-OSTROGRADSKII TYPE ON REAL FINSLER MANIFOLDS Li Zhiwei; Zhong Chunping Acta mathematica scientia,Series B. 2008, 28 (2):  383-392.  DOI: 10.1016/S0252-9602(08)60040-5 Abstract ( 914 )   RICH HTML PDF (165KB) ( 1050 )   Save This article generalizes the formulas of Gauss-Ostrogradskii type for semibasic vector fields from Riemannian manifolds to real Finsler manifolds and obtains some formulas of Gauss-Ostrogradskii type for Finsler vector fields which are expressed in terms of the vertical and horizontal derivatives of the Cartan connection in real Finsler manifolds. Related Articles | Metrics

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ESTIMATES FOR THE HYPER-ORDER OF SOLUTIONS OF CERTAIN LINEAR DIFFERENTIAL EQUATIONS Jiang Liangying; Chen Zongxuan Acta mathematica scientia,Series B. 2008, 28 (2):  393-400.  DOI: 10.1016/S0252-9602(08)60041-7 Abstract ( 1076 )   RICH HTML PDF (152KB) ( 1027 )   Save In this article, the authors study the growth of certain second order linear differential equation f''+A(z)f'+B(z)f=0 and give precise estimates for the hyper-order of solutions of infinite order. Under similar conditions, higher order differential equations will be considered. Related Articles | Metrics

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A SEMI-CONJUGATE MATRIX BOUNDARY VALUE PROBLEM FOR GENERAL ORTHOGONAL POLYNOMIALS ON AN ARBITRARY SMOOTH JORDAN CURVE Du Zhihua Acta mathematica scientia,Series B. 2008, 28 (2):  401-407.  DOI: 10.1016/S0252-9602(08)60042-9 Abstract ( 1016 )   RICH HTML PDF (144KB) ( 1260 )   Save In this article, the author characterizes orthogonal polynomials on an arbitrary smooth Jordan curve by a semi-conjugate matrix boundary value problem, which is different from the Riemann-Hilbert problems that appear in the theory of Riemann -Hilbert approach to asymptotic analysis for orthogonal polynomials on a real interval introduced by Fokas, Its, and Kitaev and on the unit circle introduced by Baik, Deift, and Johansson. The author hopes that their characterization may be applied to asymptotic analysis for general orthogonal polynomials by combining with a new extension of steepest descent method which we are looking for. Related Articles | Metrics

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CHARACTERIZATION OF SOLID CONES Qiu Jinghui Acta mathematica scientia,Series B. 2008, 28 (2):  408-416.  DOI: 10.1016/S0252-9602(08)60043-0 Abstract ( 1165 )   RICH HTML PDF (159KB) ( 1894 )   Save The author gives a dual characterization of solid cones in locally convex spaces. From this the author obtains some criteria for judging convex cones to be solid in various kinds of locally convex spaces. Using a general expression of the interior of a solid cone, the author obtains a number of necessary and sufficient conditions for convex cones to be solid in the framework of Banach spaces. In particular, the author gives a dual relationship between solid cones and generalized sharp cones. The related known results are improved and extended. Related Articles | Metrics

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SOME DISCRETE NONLINEAR INEQUALITIES AND APPLICATIONS TO DIFFERENCE EQUATIONS Cheung Wing-Sum; Ma Qing-Hua; Josip Pecaric Acta mathematica scientia,Series B. 2008, 28 (2):  417-430.  DOI: 10.1016/S0252-9602(08)60044-2 Abstract ( 993 )   RICH HTML PDF (184KB) ( 1674 )   Save In this article, the authors establish some new nonlinear difference inequalities in two independent variables, which generalize some existing results and can be used as handy tools in the study of qualitative as well as quantitative properties of solutions of certain classes of difference equations. Related Articles | Metrics

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ON THE GROWTH OF ZERO ORDER LAPLACE-STIELTJES TRANSFORM CONVERGENT IN THE RIGHT HALF-PLANE Kong Yinying; Sun Daochun Acta mathematica scientia,Series B. 2008, 28 (2):  431-440.  DOI: 10.1016/S0252-9602(08)60045-4 Abstract ( 1168 )   RICH HTML PDF (160KB) ( 1905 )   Save In this article, authors study the growth of Laplace-Stieltjes transform with zero order convergent in the right half-plane, define the exponential order and the exponential low order, and find the relations between them. Some results similar to Dirichlet series are obtained. Related Articles | Metrics

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UNIFORM ESTIMATES OF SOLUTIONS OF \overline{\partial}-EQUATION ON STEIN MANIFOLDS Tang Dongmei; Qiu Chunhui; Zhong Chunping Acta mathematica scientia,Series B. 2008, 28 (2):  441-448.  DOI: 10.1016/S0252-9602(08)60046-6 Abstract ( 1248 )   RICH HTML PDF (173KB) ( 1141 )   Save By means of the Hermitian metric and Chern connection, Qiu [4] obtained the Koppelman--Leray--Norguet formula for (p,q) differential forms on an open set with C1 piecewise smooth boundary on a Stein manifold, and under suitable conditions gave the solutions of \overline{\partial}-equation on a Stein manifold. In this article, using the method of Range and Siu [5], under suitable conditions, the authors complicatedly calculate to give the uniform estimates of solutions of \overline{\partial}-equation for (p,q) differential forms on a Stein manifold. Related Articles | Metrics