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25 June 2009, Volume 29 Issue 3 Previous Issue    Next Issue

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Necessary and Sufficient Conditions for the Global Weak Attractivity and Global Attractivity of a Class of Nonlinear Differential Equations ZHAO Li-Qin Acta mathematica scientia,Series A. 2009, 29 (3):  529-537.  Abstract ( 1672 )   RICH HTML PDF (327KB) ( 1247 )   Save This paper deals with the global weak attractivity and global attractivity for the  nonlinear differential equations x = φ（y）-F(x), {y}=- g(x)q(y). It is shown that Filippov condition (A2) cannot exclude the existence of the maximum elliptic sector  S* and it cannot exclude the possibility of  ∂S* as the ω-limit set of the orbits departing from the  exterior of S*.  The problem proposed by Jiang Jifa in  Nonlinear Analysis, 28(5), 855--870(1997) is answered by a negative answer. A series of necessary and sufficient conditions for the global weak attractivity and global attractivity are established for both the cases that  Filippov condition holds and Filippov condition  fails. Some new conditions for the global asymptotic stability are also obtained. References | Related Articles | Metrics

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The Drazin Inverse of a Sum of Morphisms CHEN Jian-Long, PENG Gui-Fen, WEI Yi-Min Acta mathematica scientia,Series A. 2009, 29 (3):  538-552.  Abstract ( 1581 )   RICH HTML PDF (255KB) ( 1073 )   Save Let C be an additive category. Suppose that φ and η: X→ X are two morphisms of C. If φ and η have the Drazin inverses such that  φη=0, then φ+η has the Drazin inverse. If φ has the Drazin inverse  φD such that 1X+φDη  is  invertible. We study the Drazin inverse (resp. group inverse) of f =φ+η and give the necessary and sufficient condition for fD(resp. f #}=(1X+φDη)-1φD. Finally, we  extend the Huylebrouck's result from the group inverse to the Drazin inverse. References | Related Articles | Metrics

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Weighted Weak Type Estimates for Commutators of |Fractional Integrals on Spaces of Homogeneous Type WANG Wei-Hong, WU Huo-Xiong Acta mathematica scientia,Series A. 2009, 29 (3):  553-563.  Abstract ( 1715 )   RICH HTML PDF (295KB) ( 1165 )   Save A weighted weak type endpoint estimate is established for the maximal operator  associated with the commutator generated by fractional integral operator and BMO function on spaces of homogeneous type. As an application, a two-weight weak type norm inequality for the commutator is obtained. References | Related Articles | Metrics

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A Class of Generalized Three Dimensional Convection-Diffusion Equations with Multi-Level Incremental Unknowns Method YANG Ai-Li, WU Yu-Jiang, SONG Lun-Ji Acta mathematica scientia,Series A. 2009, 29 (3):  564-572.  Abstract ( 1989 )   RICH HTML PDF (367KB) ( 1154 )   Save With the finite difference discretization techniques, the authors get a nonsymmetric and positive-definite linear system when considering a class of generalized three-dimensional convection-diffusion equations even if they have variable coefficients. Considering that the condition number of incremental unknowns(IU)-type coefficient matrix is much better than the matrix without IU(see [1]), the authors use the IU method in conjunction with several classical iterative methods to approximate the solution of the system. After estimating the condition number of IU-type coefficient matrix, the authors numerically confirm that these IU-type iterative methods are much more efficient. References | Related Articles | Metrics

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Weighted Composition Operators Between &mu|-Bloch Spaces on the Unit Ball of Cn ZHANG Xue-Jun, LI Ju-Xiang Acta mathematica scientia,Series A. 2009, 29 (3):  573-583.  Abstract ( 2044 )   RICH HTML PDF (313KB) ( 1166 )   Save Let μ and ν be two normal functions on [0,1). In this paper, the necessary and sufficient conditions are given for the weighted composition  operator Tψ，φ to be bounded (or compact) from  Bloch type spaces  βμ to βν on the unit ball B of Cn (n>1). References | Related Articles | Metrics

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Atomic Decompositions of B -valued Quasi-martingales with Respect to Complex Measures MA Cong-Bian, HOU You-Liang Acta mathematica scientia,Series A. 2009, 29 (3):  584-592.  Abstract ( 2124 )   RICH HTML PDF (321KB) ( 1225 )   Save  Let  P be a probability measure, ψ  a  complex valued integrable function and  dμ=ψdP  a  complex valued measure. Two theorems of atomic decompositions for the space Dα(X)  and pQα(X) of X-valued quasi-martingales with respect to the complex measure μ are obtained  when ψ ∈a1 ∩ b∝+  and the Banach space X  has suitable convexity and smoothness.  As the applications of atomic decompositions  two inequalities are proved for X-valued quasi-martingales respect to the complex measures μ by using atomic decompositions in the case of   0< α ≤ 1. References | Related Articles | Metrics

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The Calculation of One Loop Free Energy in Non-Critical Liouville String Model YA Jun, SUN Wei-Li Acta mathematica scientia,Series A. 2009, 29 (3):  593-596.  Abstract ( 1278 )   RICH HTML PDF (261KB) ( 1272 )   Save In this paper, the one loop free energy in non-critical Liouville string model is calculated by using path integral method. The result shows that critical temperature depends on the central charge of conformal matter field at D=27, and  the asymptotic expression of free energy is also obtained. References | Related Articles | Metrics

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Multiple Unsymmetrical Core Hardy-Hilbert's Integral Inequalities LU Sheng-Jie, TAO Xiang-Xing Acta mathematica scientia,Series A. 2009, 29 (3):  597-606.  Abstract ( 1426 )   RICH HTML PDF (259KB) ( 1244 )   Save In this paper, Hardy-Hilbert's integral inequalities are generalized. Hardy-Hilbert's integral inequality with optimal constant factor on unsymmetrical core function and weighted Hardy-Hilbert's integral inequality are obtained, and some special cases are also considered. References | Related Articles | Metrics

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Admissibility for Linear Estimators of the Regression Coefficients in the Growth Curve Model LIU Gang, ZHANG Shang-Li Acta mathematica scientia,Series A. 2009, 29 (3):  607-612.  Abstract ( 1436 )   RICH HTML PDF (282KB) ( 1140 )   Save In this paper, the admissibility for linear estimators of regression coefficients in the general growth curve model is discussed. Under the matrix loss function (d(Y)-KBL)(d(Y)-KBL)' , some necessary and sufficient conditions for linear estimators to be admissible are obtained, which extend some results in literature. References | Related Articles | Metrics

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Generalized Perturbation Results of Banach Frames and Atomic Decompositions on Banach Spaces LI De-Feng, YANG Li-Jun Acta mathematica scientia,Series A. 2009, 29 (3):  613-622.  Abstract ( 1714 )   RICH HTML PDF (304KB) ( 1091 )   Save Frame perturbation is one of active research contents in frame theory, but it was discussed on a Hilbert space in most literatures. This paper presents the perturbations of Banach frames and atomic decompositions on a Banach space, and obtains some more generalized perturbation results. It is shown that many known results are corollaries of our results. References | Related Articles | Metrics

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Random Meromorphic Functions in the Unit Disc SUN Dao-Chun Acta mathematica scientia,Series A. 2009, 29 (3):  623-629.  Abstract ( 1538 )   RICH HTML PDF (277KB) ( 1132 )   Save In this paper, the growth order and Borel exceptional value of random meromorphic functions are discussed firstly. Obtained are two interesting fundamental theorems. References | Related Articles | Metrics

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Littlewood-Paley Operator with Variable Kernel in Generalized Morrey Spaces CHEN Yan-Ping, DING Yong Acta mathematica scientia,Series A. 2009, 29 (3):  630-642.  Abstract ( 2184 )   RICH HTML PDF (316KB) ( 1268 )   Save In this paper the authors study the boundedness for a class of parabolic Littlewood-Paley operator gΦ with variable kernels in generalized Morrey spaces Lp, ω(Rn). As an application of the above result, the boundeness of the commutator [b, gΦ], formed by gΦ and a BMO(Rn)function b(x) in Lp, ω(Rn) is also obtained. References | Related Articles | Metrics

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The Finite Element Method with Perfectly Matched Layers for the Electromagnetic Scattering by a Chiral Obstacle GAO Tian-Ling, MA Fu-Ming Acta mathematica scientia,Series A. 2009, 29 (3):  643-650.  Abstract ( 1492 )   RICH HTML PDF (511KB) ( 1211 )   Save This paper is concerned with the electromagnetic scattering by a chiral obstacle. A two-dimensional mathematical model is established. The existence and uniqueness of the problem is discussed by a variational approach. A finite element method with perfectly matched layers(PML) is developed for solving the problem. References | Related Articles | Metrics

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Weak Monotonicity for the Component Functions of |Weak Solutions of Beltrami System GAO Hong-Ya, WANG Hong-Min, GU Guang-Ze Acta mathematica scientia,Series A. 2009, 29 (3):  651-655.  Abstract ( 1985 )   RICH HTML PDF (255KB) ( 1102 )   Save A new class of function space is introduced. The weak monotonicity of very weak solutions of  A-harmonic equation is studied by using this function class. The weak monotonicity for component functions of weak solutions of Beltrami system in space is derived. References | Related Articles | Metrics

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Solving Variational Inequality with Weak Contraction by Using Viscosity Approximation Methods SONG Yi-Sheng, YANG Chang-Sen Acta mathematica scientia,Series A. 2009, 29 (3):  656-668.  Abstract ( 1735 )   RICH HTML PDF (328KB) ( 1122 )   Save In this paper, under the framework of a strictly convex Banach space with a uniformly Gâteaux differentiable norm, we study strong convergence of two explicit viscosity approximation methods for finding a solution to the variational inequality with weakly contractive mapping A,  and give the estimate of convergence rate. References | Related Articles | Metrics

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Asymptotic Estimate for the Probability of an Exceedance over Negatively Associated Renewal Thresholds and the Ruin Probability in Dividend Barrier Models YANG Yang, WANG Yue-Bao Acta mathematica scientia,Series A. 2009, 29 (3):  669-676.  Abstract ( 1423 )   RICH HTML PDF (337KB) ( 1085 )   Save In this paper, we obtain an asymptotic estimate for the probability of an exceedance over negatively associated renewal thresholds, which extends the corresponding result of Robert (2005)[12]. Furthermore, using a new method, we also derive a more rigorous proof of the asymptotics for the ruin probability in dividend barrier models. References | Related Articles | Metrics

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The |Error |Estimates of |Approximation by Interpolatory Zonal Translation Networks on the Unit Sphere CHEN Zhi-Xiang, LI Peng Acta mathematica scientia,Series A. 2009, 29 (3):  677-684.  Abstract ( 1454 )   RICH HTML PDF (311KB) ( 1189 )   Save The spherical zonal translation networks with the property of interpolation are constructed. Furthermore, in the uniform norm, the upper bound of approximation is given for continuous functions.   References | Related Articles | Metrics

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The Properties of Statistics of the Mean-mixture of Normal Distribution XIONG Ming, XIE Min-Yu Acta mathematica scientia,Series A. 2009, 29 (3):  685-690.  Abstract ( 1846 )   RICH HTML PDF (268KB) ( 1093 )   Save Based on background in genetic analysis, this paper proposes a class of mean-mixture  of normal distribution. It is different from the variance-mixture of normal distribution,  which is discussed in several bibliographies in general. We principally consider the  properties of statistics of the mean-mixture of normal distribution. It is shown that  those statistics which are invariant under translational transformation are robust in  the class of mean-mixture of normal distribution, that is, these statistics have the   same properties as those of normal distribution. Then the   mean-mixture of normal distribution has the advantage of easily transferring properties enjoyed by  normal distribution. Besides, the distributions of several other statistics are discussed. References | Related Articles | Metrics

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An Efficient Levin-type Collocation Method for Highly Oscillatory Integrals MO Hong-Min, XIANG Shu-Huang Acta mathematica scientia,Series A. 2009, 29 (3):  691-698.  Abstract ( 2133 )   RICH HTML PDF (360KB) ( 1294 )   Save This paper presents a new efficient Levin-type method, which can get higher accuracy than the Levin's collocation method and can be easily implemented. The effectiveness and accuracy of the quadrature are tested. References | Related Articles | Metrics

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Positive Solutions of Nonlinear ∞-point Boundary Value Problems MA Ru-Yun, FAN Hong-Xia, HAN Xiao-Ling Acta mathematica scientia,Series A. 2009, 29 (3):  699-706.  Abstract ( 1958 )   RICH HTML PDF (274KB) ( 1175 )   Save Let α i ∈[0,  ∞), ξ i ∈ (0,1) and ∑∞i=1α i ξ i <1.  We study the existence of positive solutions to  the  boundary value problem u''+a(t) f(u)=0,  t  ∈(0, 1), u(0)=0,  u(1)= ∑∞i =1 α i u ( ξ i ) , where α ∈ C([0, 1], [0, ∞)), and f:[0, ∞) → [0, ∞) is continuous. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying a fixed-point theorem in cones. References | Related Articles | Metrics

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Rates of Strong Uniform Consistency for Kernel Density Estimators of Directional Data LI Li-Na, GAO Fu-Qing Acta mathematica scientia,Series A. 2009, 29 (3):  707-715.  Abstract ( 1511 )   RICH HTML PDF (297KB) ( 1124 )   Save Let fn be the non-parametric kernel density estimator of directional data based on a kernel function K and a sequence of independent and identically distributed random variables taking values in d-dimensional unit sphere  Sd-1. A rate of strong uniform consistency for the kernel density estimators is presented by the empirical process method References | Related Articles | Metrics

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Properties of k-Hypermonogenic Functions and Their Relative Functions YUAN Hong-Fen, JIAO Yu-Ying Acta mathematica scientia,Series A. 2009, 29 (3):  716-726.  Abstract ( 1766 )   RICH HTML PDF (368KB) ( 1463 )   Save In the first part of this paper, the authors show the extension theorem and uniqueness theorem of k-hypermonogenic functions. What  is more, by the uniqueness theorem, the authors prove the inner-closed uniform convergence of  sequence of hypermonogenic functions. In the second part of this paper, as P-part and Q-part of k-hypermonongenic functions satisfy  two equations, the authors discuss the relationship between these two equations and k-hypermonogenic functions and  their relative functions. References | Related Articles | Metrics

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The Existence of Nontrivial Generalized Solution of a Class of Quasilinear Elliptic Equations WANG Ji-An, DENG Xue-Mei Acta mathematica scientia,Series A. 2009, 29 (3):  727-736.  Abstract ( 1349 )   RICH HTML PDF (314KB) ( 1139 )   Save In this paper, we study the existence of nontrivial solutions of the following quasilinear elliptic Dirichlet problem in an Orlicz-Sobolev space: { -div(a(|     u(x)|)     u(x))=g(x, u),     x ∈ Ω，   u(x)=0,                                               x ∈ ∂Ω. where Ω is a bounded domain in Rn. Using the generalized mountain pass lemma, we prove, under some conditions on Φ and g, the existence of nontrivial generalized solutions for this  problem. References | Related Articles | Metrics

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Finite p}-groups in which any Two Noncommutative Elements Generate a |Subgroup of Order p3 ZHANG Qi-Hai, DENG Li-Jun, XU Ming-Yao Acta mathematica scientia,Series A. 2009, 29 (3):  737-740.  Abstract ( 1682 )   RICH HTML PDF (250KB) ( 1014 )   Save In this note we classify finite p-groups in which any two noncommutative elements generate a  subgroup of order p3. As a consequence, we solve the research problem No. 237 in [1]: Study the p-groups G such that |( x, y) | ≤ p3 for all x, y ∈ G. References | Related Articles | Metrics

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The w-weighted Drazin Inverse of Morphisms with Kernels LIU Xiao-Ji, ZHANG Shi-Guang Acta mathematica scientia,Series A. 2009, 29 (3):  741-750.  Abstract ( 1610 )   RICH HTML PDF (278KB) ( 1178 )   Save Let a: X →  Y, w:  Y →  X be morphisms in an additive category, k1: K1 →  X  be a kernel of (aw) i, k2: K2 → Y  be a kernel of (wa) i. Then the following propositions are equivalent: (1) a has a  w -weighted Drazin inverse ad,w in £ ; (2)  1: X → L1 is cokernel of (aw) i, k1 1 and (aw) i+1+ 1(k1 1) -1k1 are invertible; (3)  2 : Y →  L2 is cokernel of (wa) j, k2  2 and (wa) j+1+ 2(k2  2)-1k2 are invertible. And the Core-Nilpotent decomposition of w-weighted Drazin inverse of morphisms in the exact additive category £ with {1}-inverse is studied, the existence for the Core-Nilpotent decomposition of  w - weighted Drazin inverse of morphisms is proved. The extension of Drazin inverse of morphisms with kernels and its Core-Nilpotent decomposition are introduced and representations for its  w - weighted Drazin inverse and Core-Nilpotent decomposition are derived. References | Related Articles | Metrics

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The Compact Minimal Submanifolds in Locally Symmetric Space JI Yong-Jiang, LI Hai-Feng Acta mathematica scientia,Series A. 2009, 29 (3):  751-756.  Abstract ( 1503 )   RICH HTML PDF (257KB) ( 1161 )   Save  Let N n+p be an n+p-dimensional locally symmetric complete Riemannian manifold with sectional curvature KN satisfies 1/2 < δ ≤ KN ≤ 1  and M n be an n-dimensinal compact minimal submanifold  in N n+p. In this paper, we discuss the Pinching theorem about this sub manifold with the square of the length of the second fundamemtal form and Ricci curvature. References | Related Articles | Metrics

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Lattices Generated by Joins of Elements in Orbits of Subspaces under Finite Unitary Groups ZHANG Geng-Sheng, GUO Jun, ZHANG Jing-Xuan Acta mathematica scientia,Series A. 2009, 29 (3):  757-763.  Abstract ( 1888 )   RICH HTML PDF (298KB) ( 1111 )   Save Let Fq2(n) be the n-dimensional vector space over the finite field Fq2 and let   Un( Fq2) be  unitary group of degree n over Fq2 . Let M(m, r; n) be any orbit of subspaces under Un( Fq2}. Denote by L(m, r; n) the set of subspaces which are joins of  subspaces in M(m, r; n) . This paper discusses the relation of  inclusion between sets generated by different orbits, the condition that a subspace is an element of set generated by the given orbit, and the condition when sets generated by orbits form geometric lattices. References | Related Articles | Metrics

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A Two-weight Norm Inequality for Singular Integral Operators with Non-smooth Kernel on Spaces of Homogeneous Type HU Guo-En, ZHANG Qi-Hui Acta mathematica scientia,Series A. 2009, 29 (3):  764-772.  Abstract ( 1822 )   RICH HTML PDF (337KB) ( 1172 )   Save In this paper, a two-weight weak type norm inequality for singular integral operators with non-smooth kernel is established on spaces of homogeneous type. The authors prove that the operators in question are bounded from Lp(X, v) to Lq, ∞( X, u) with 1< p ≤  q <∞, provided that the pair of weights (u, v) verifies an Ap-type condition with an '`Orlicz-bump'' on the weight u. References | Related Articles | Metrics

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The Study of Fractal Interpolation on Rectangular Area SUN Hong-Quan Acta mathematica scientia,Series A. 2009, 29 (3):  773-783.  Abstract ( 2112 )   RICH HTML PDF (541KB) ( 1106 )   Save In this paper, the principle of   fractal  interpolation on rectangular area is introduced, interpolation functions for the fractal interpolation surface are discussed, the theorem of uniqueness of iterated function system of fractal interpolation surface is proved, the theorem of fractal  dimension of fractal interpolation surface is derived, and the case that practical data are used to interpolate fractal surface is studied. References | Related Articles | Metrics

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Positive Solutions |of Nonlinear Sturm-Liouville Boundary |Value Problems in Banach Spaces ZHANG Ling-Zhong, LI Yong-Xiang Acta mathematica scientia,Series A. 2009, 29 (3):  784-793.  Abstract ( 2152 )   RICH HTML PDF (303KB) ( 1071 )   Save The existence of the positive solutions to the Sturm-Liouville problem in Banach spaces is discussed  in the  superlinear or sublinear case by using the fixed point theory of condensing mapping and doing precise computation of measure of noncompactess and using the eigenvalues corresponding to the relevant linear equations. References | Related Articles | Metrics

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Existence of Periodic Solutions for a Type of High Order Neutral Functional Differential Equations WANG Kai Acta mathematica scientia,Series A. 2009, 29 (3):  794-799.  Abstract ( 1692 )   RICH HTML PDF (263KB) ( 1268 )   Save By employing the coincidence degree theory, the author studies a kind of higher order neutral functinal differential equation with distributed delay. Some simple conditions which guarantee the existence of periodic solutions to the equation are obtained. References | Related Articles | Metrics

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Henig Proper Efficiency in the ic-Conen-Convexlike Set-valued Optimization Problems YU Guo-Lin, LIU Wan-Li Acta mathematica scientia,Series A. 2009, 29 (3):  800-809.  Abstract ( 1816 )   RICH HTML PDF (316KB) ( 1065 )   Save In this paper, the set-valued vector optimization problems with constraint in locally convex spaces is studied. Under the assumption of the ic-cone-convexlikeness, the optimality conditions for Henig proper efficient solutions are established in terms of scalarization and Lagrange multipliers. After introducing the new concept of Henig proper saddle-point for an appropriate set-valued Lagrange map, we use it to charactertize the Henig proper efficiency. In addition, a scalar Lagrange dual model for set-valued optimization is presented, and the dual theorems are obtained in sense of Henig proper efficiency. All the results   obtained in this paper are proven under the conditions that the constraint cone need not to have a nonempty interior. References | Related Articles | Metrics

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Uniqueness of the One-bubbling Solution for a Neumann Problem Involving the Critical Sobolev Exponent DU Gang Acta mathematica scientia,Series A. 2009, 29 (3):  810-822.  Abstract ( 1885 )   RICH HTML PDF (328KB) ( 1102 )   Save In this paper, we consider a class of  Neumann problem involving critical Sobolev exponents. The uniqueness is established by using Pohozaev identity and some estimates. References | Related Articles | Metrics

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New Composite Implicit Iterative Scheme With Errors RAO Ro-Feng Acta mathematica scientia,Series A. 2009, 29 (3):  823-831.  Abstract ( 1694 )   RICH HTML PDF (294KB) ( 1106 )   Save In this paper, a new composite implicit iterative process with errors for a family of asymptotically nonexpansive mappings was reasonably introduced in view of Banach's contraction principle,  and a new theorem  for weak and strong convergence  was obtained under some suitable conditions,  which deduced a new convergent theorem for a non-implicit iterative process with errors. It is worthy to say that  this result extend the corresponding results of  S.S.Chang [1] from implicit iterative process to non-implicit algorithm without any additive assumptions. References | Related Articles | Metrics