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25 December 2011, Volume 31 Issue 6 Previous Issue    Next Issue

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Study on a Free Boundary Value Problem Arising from Peeling Phenomenon ZHAO Wei-Xia Acta mathematica scientia,Series A. 2011, 31 (6):  1461-1469.  Abstract ( 935 )   RICH HTML PDF (324KB) ( 726 )   Save In this paper the following free boundary problem {utt-∂x(ux/√1+ux2)=0,    in{(t, x)|t>0, x>-l0}∩{u>0}, 1/2ut2+1/√1+ux2-1+Q=0,   in{(t, x)|t>0, x>-l0}∩∂{u>0}  is considered. The problem describes the peeling phenomenon. Different from the problem studied by K. Kikuchi and S. Omata,  the nonlinear effects in the vibrating string is also considered. Under some reasonable assumptions, the local existence and uniqueness of classical solution for the free boundary problem is proved. References | Related Articles | Metrics

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Existence of Solutions for Elliptic Equations Involving Hardy Potential under Natural Growth Condition LI Zhou-Xin, SHEN Yao-Tian Acta mathematica scientia,Series A. 2011, 31 (6):  1470-1478.  Abstract ( 1041 )   RICH HTML PDF (329KB) ( 741 )   Save In this paper, the authors study a quasilinear elliptic equation with Hardy potential under natural growth condition. The authors extend the sign condition from nonnegative to a minus part, prove that at this time the corresponding functional of the equation still satisfies the (PS) condition, and then prove the existence of two nontrivial weak solutions via the nonsmooth critical point theory. References | Related Articles | Metrics

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A Nonlinear Multigrid-FEM Inversion Algorithm for Reconstruction of a Mountain Surface DOU Yi-Xin, HAN Bo Acta mathematica scientia,Series A. 2011, 31 (6):  1479-1489.  Abstract ( 1110 )   RICH HTML PDF (646KB) ( 849 )   Save The modeling of reconstruction of a mountain surface is made  of two processes: a thermal convection diffusion process inside a mountain and a mountain surface moving process. The former one describes the change of temperature of rocks in three dimensional spatial domain, and the latter one explains the evolution of a mountain surface in two dimensional spatial domain. The reconstruction of a mountain surface comes down to solving the inverse problem for this coupled system. From the point of view of numerical computation, the authors  shall experience some difficulties,  for example, solving optimization of a non-convex cost functional and huge computational cost. In order to circumvent the difficulties above, the authors  propose a nonlinear multigrid-FEM inversion algorithm to reconstruct a mountain surface. Numerical experiments show that this algorithm is efficient for this coupled system. References | Related Articles | Metrics

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Oscillatory Behavior for a Simplified n-neuron BAM Neural Networks Model with Time Delays FENG Chun-Hua Acta mathematica scientia,Series A. 2011, 31 (6):  1490-1501.  Abstract ( 1389 )   RICH HTML PDF (817KB) ( 808 )   Save In this paper, the existence of oscillations for a simplified n-neuron BAM neural network with time delays between neural interconnections is investigated. By using the Chafee's criterion, we prove that a simplified n-neuron BAM neural network has a unique equilibrium point which is unstable. This particular type of instability, combined with the boundedness of the solutions of the system, forces the network to generate a permanent oscillation. Two sufficient conditions for these oscillations are obtained. Typical simulation examples are presented. References | Related Articles | Metrics

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Homotopic Mapping Solution for a Class of Generalized Canard Systems MO Jia-Qi Acta mathematica scientia,Series A. 2011, 31 (6):  1502-1506.  Abstract ( 841 )   RICH HTML PDF (271KB) ( 855 )   Save Using the homotopic mapping theory, the approximations of the solution for generalized canard systems are obtained. Firstly, introducing a set of homotopic mapping. Then the iteration expressions of solution for original system are constructed. Finally, the analytic expressions of the canard solution for problem are obtained. References | Related Articles | Metrics

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A Sufficient Condition on Bp Groups CHEN Song-Liang Acta mathematica scientia,Series A. 2011, 31 (6):  1507-1511.  Abstract ( 879 )   RICH HTML PDF (296KB) ( 761 )   Save Let P be a Sylow p-subgroup of a finite group G. We say G is a Bp group if the p-nilpotency of NG(P) implies the p-nilpotency of G. In this paper, we give a sufficient condition of Bp groups. References | Related Articles | Metrics

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On the Borel Points of Algebroid Functions in the Unit Circle ZHANG Hong-Shen, SUN Dao-Chun Acta mathematica scientia,Series A. 2011, 31 (6):  1512-1520.  Abstract ( 1394 )   RICH HTML PDF (305KB) ( 681 )   Save By using type-function, the existences of the Borel points of algebroid functions in the unit circle are studied. Under the same condition, the results of this paper improve the results obtained by an other paper. References | Related Articles | Metrics

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Jordan (θ, Φ)-derivations of Triangular Algebras YU Wei-Yan, ZHANG Jian-Hua Acta mathematica scientia,Series A. 2011, 31 (6):  1521-1525.  Abstract ( 1267 )   RICH HTML PDF (213KB) ( 812 )   Save Suppose that θ, Φ are automorphisms of triangular algebras U=Tri(A, M, B). In this paper, the authors  prove that every Jordan (θ, Φ)-derivation of triangular algebras is a (θ, Φ)-derivation when triangular algebras Tri(A, M, B) contain only trivial idempotents. References | Related Articles | Metrics

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Iterative Method for Centro-symmetric Solution of the Linear Matrix Equations TIAN Xiao-Hong, ZHANG Kai-Yuan Acta mathematica scientia,Series A. 2011, 31 (6):  1526-1536.  Abstract ( 1030 )   RICH HTML PDF (313KB) ( 713 )   Save An iterative method is presented to find the centro-symmetric solutions of the general linear matrix equations. By this iterative method, the solvability of the matrix equations over centro-symmetric solution can be determined, and  its least-norm centro-symmetric solution can be got by choosing a special initial centro-symmetric matrix. In addition, its optimal approximation matrix to a given matrix can be obtained. References | Related Articles | Metrics

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Solution to Problems of Symmetric Relation between Br and Wr CHEN Peng Acta mathematica scientia,Series A. 2011, 31 (6):  1537-1542.  Abstract ( 1274 )   RICH HTML PDF (284KB) ( 605 )   Save In this paper, in order to solve the problems of symmetric relation between Br and Wr, we put forward a kind of new pointwise metric on L, and show the relation between it and Erceg's metric. Finally we prove L-real line satisfies the kind of metric. References | Related Articles | Metrics

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The Relaxation Limit of Bipolar Euler-Maxwell Equations Arising from Plasma WANG Shu, YANG Jian-Wei, WANG Wei Acta mathematica scientia,Series A. 2011, 31 (6):  1543-1549.  Abstract ( 1053 )   RICH HTML PDF (289KB) ( 672 )   Save This work is concerned with multi-dimensional bipolar Euler-Maxwell equations for plasmas with short momentum relaxation time. With the help of the Maxwell iteration, the convergence for the smooth solutions to the bipolar Euler-Maxwell equations towards the solutions to the smooth solutions to the bipolar drift-diffusion equations is proved, as the relaxation time tends to zero. Meanwhile, the formal derivation of the latter from the former is justified. References | Related Articles | Metrics

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Toeplitz Products on Vector-valued Bergman Spaces of the Unit Ball YU Thao, ZHU Ruo-Wei Acta mathematica scientia,Series A. 2011, 31 (6):  1550-1558.  Abstract ( 1201 )   RICH HTML PDF (297KB) ( 715 )   Save In this paper the authors  obtain a sufficient condition and a necessary condition for the Toeplitz product TFTG* on vector-valued Bergman spaces of the unit ball to be bounded respectively, where F and G are matrices which entries are square-integrable and analytic functions on the unit ball. References | Related Articles | Metrics

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The Convergence or Divergence for Eigenfunction Expansion of Infinite Dimensional Hamiltonian Operator WU De-Yu, Alatancang Acta mathematica scientia,Series A. 2011, 31 (6):  1559-1566.  Abstract ( 1224 )   RICH HTML PDF (350KB) ( 778 )   Save In this paper, we study the eigenfunction systems of infinite dimensional Hamiltonian operator and obtain a class of infinite dimensional Hamiltonian operators whose eigenfunction systems are not complete in Hilbert space X×X, which is helpful to solve the problems that the method of separation of variable whether can be used in a class of Hamiltonian systems. In the end, concrete examples are constructed to justify the effectiveness of the criterion. References | Related Articles | Metrics

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Optimal Dividend Strategy in |the Perturbed Compound Poisson Risk Model with Investment WANG Chun-Wei, YIN Chuan-Cun Acta mathematica scientia,Series A. 2011, 31 (6):  1567-1578.  Abstract ( 1343 )   RICH HTML PDF (382KB) ( 823 )   Save In this paper, we consider the optimal dividend strategy in the perturbed compound Poisson risk model with ivestment interest. Our aim is to find an optimal dividend strategy that maximizes the cumulative expected discounted dividend payments. We characterize the optimal value function as the viscosity solution of the associated Hamilton-Jacobi-Bellman (HJB) equation and prove that there exists an optimal barrier strategy which  is optimal among all admissible dividend strategies  in some special cases. References | Related Articles | Metrics

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Singular Perturbation of a Class of Third Order |Partial Differential Equations under Limit Equation to be Mixed Type LIN Su-Rong Acta mathematica scientia,Series A. 2011, 31 (6):  1579-1585.  Abstract ( 1061 )   RICH HTML PDF (308KB) ( 769 )   Save In this paper the singular perturbation of a class of third order  partial differential equations degenerating to parabolic type at partial boundary is considered. Under appropriate conditions, a sufficient condition of solvability is derived, the existence of solution is proved and the uniformly valid asymptotic expansion of arbitray order is given as well. References | Related Articles | Metrics

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On a Multiple Hardy-type Integral Inequality with a Best Constant Factor and Its Application HONG Yong Acta mathematica scientia,Series A. 2011, 31 (6):  1586-1591.  Abstract ( 1544 )   RICH HTML PDF (237KB) ( 792 )   Save In this paper, a multiple Hardy-type integral inequality with some parameters and a best constant factor are given. References | Related Articles | Metrics

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Improved Hardy Inequality on the Heisenberg Group JIN Yong-Yang, HAN Ya-Zhou Acta mathematica scientia,Series A. 2011, 31 (6):  1592-1600.  Abstract ( 1006 )   RICH HTML PDF (300KB) ( 661 )   Save In this paper the authors prove some weighted Hardy  inequalities with remainder term on the Heisenberg group, following the ideas of Abdellaoui-Colorado-Peral in [1]. References | Related Articles | Metrics

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Regularity of Weak Solutions to the Generalized Navier-Stokes Equations BIAN Dong-Fen, YUAN Bao-Quan Acta mathematica scientia,Series A. 2011, 31 (6):  1601-1609.  Abstract ( 1582 )   RICH HTML PDF (335KB) ( 923 )   Save This paper discusses the regularity of weak solutions to the generalized Navier-Stokes equations with symbol m(ξ). Assume that m(ξ)≥|ξ|α/g(|ξ|), where  α≥1/2+n/4, g≥1, is radially symmetric, nondecreasing and satisfies ∫+ ∞1ds/sg2(s)=+∞, If ∫t0||u(s)||2Bα2, ∞ds<+∞, then  the generalized Navier-Stokes equation has a unique global smooth solution. References | Related Articles | Metrics

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The Relation Between Meromorphic Solutions of Second Order Differential Equations and Functions of Small Growth HUANG Zhi-Gang Acta mathematica scientia,Series A. 2011, 31 (6):  1610-1618.  Abstract ( 1238 )   RICH HTML PDF (307KB) ( 746 )   Save This article is devoted to studying the second order differential equation f''+A(z)f=0, where A(z) is a meromorphic function with at most finitely many poles. The relation between functions of small growth and meromorphic solutions, their 1st and 2nd derivatives of the above equation are obtained. References | Related Articles | Metrics

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A1 Weights on Doubling Measure Space FU Yu-Xia Acta mathematica scientia,Series A. 2011, 31 (6):  1619-1625.  Abstract ( 1117 )   RICH HTML PDF (268KB) ( 734 )   Save Some properties and applications of A1 weights on doubling measure space are discussed in the paper. References | Related Articles | Metrics

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Generic Submanifolds with Flat Normal Bundle in a Complex Projective Space YIN Song-Ting, SONG Wei-Dong Acta mathematica scientia,Series A. 2011, 31 (6):  1626-1632.  Abstract ( 1011 )   RICH HTML PDF (323KB) ( 795 )   Save In this paper, the authors study the relation  between properties on curvature and geometry of generic submanifolds with flat normal bundle in a complex projective space. By using the moving-frame method, the rigidity theorems on sectional curvature, Ricci curvature and the length of second fundamental form are obtained, which generalize and improve some results in the relevant literatures. References | Related Articles | Metrics

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A Generalization of Wigner's Theorem HE Kan, HOU Jin-Chuan Acta mathematica scientia,Series A. 2011, 31 (6):  1633-1636.  Abstract ( 964 )   RICH HTML PDF (249KB) ( 730 )   Save Certain operator structures play a fundamental role in the theory of quantum mechanics, such as the quantum state space. In this paper, we give an analogue of Wigner's theorem  on such operator structures for the monotone inner product. References | Related Articles | Metrics

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Gap Functions and Existence of Solutions to System of Generalized Vector Mixed Quasi-Equilibrium Problems XIE Jing, HE Zhong-Quan Acta mathematica scientia,Series A. 2011, 31 (6):  1637-1646.  Abstract ( 1165 )   RICH HTML PDF (286KB) ( 665 )   Save In this paper, we introduce four new types of the system of generalized vector mixed quasi-equilibrium problems with set-valued maps and establish their existence theorems. Then, by virtue of a nonlinear scalarization function, the gap functions for these problems are obtained. References | Related Articles | Metrics

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The Relation between the Orders of Algebroid Functions and their Coefficients II WANG Song-Min Acta mathematica scientia,Series A. 2011, 31 (6):  1647-1653.  Abstract ( 1306 )   RICH HTML PDF (304KB) ( 965 )   Save In this paper, we study the relation between the order of algebroid functions, determined by ν+1 entire functions {Aj(z)}νj=0 without common zeros, and the order of Aj(z)(0≤j≤ν), and improve some related results of Sun and Kong[6] and Wang and Gao[7]. References | Related Articles | Metrics

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Singular Integrals on the Real Hyperplane |in Cn GONG Ding-Dong Acta mathematica scientia,Series A. 2011, 31 (6):  1654-1661.  Abstract ( 976 )   RICH HTML PDF (308KB) ( 719 )   Save The upper space in Cn is an unbounded domain which cannot be biholomorphically equivalent to any bounded domain, and its boundary is the real hyperplane in Cn. The Cauchy type integral with Bochner-Martinelli kernel in the  upper space in Cn can be defined in some sense. In this paper, by using this Cauchy type integral, the Bochner-Martinelli type singular integral  on the real hyperplane in Cn is studied, and the Cauchy principal value and the Plemelj formula are obtained. References | Related Articles | Metrics

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Regularity of the Solution to the Dissipative Linear Boltzmann Equation JIN Shou-Bo, CHEN Pan-Feng, SUN Shan-Hui Acta mathematica scientia,Series A. 2011, 31 (6):  1662-1668.  Abstract ( 1074 )   RICH HTML PDF (312KB) ( 763 )   Save This paper discusses a linear Boltzmann equation describing dissipative interactions of a gas of test particles with a fixed background. For a pseudo-Maxwellian collision kernel, it is proved that, if the initial distribution has finite  temperature and f0(v)∈H∞(R3),  the solution f(v, t)  of Boltzmann equation belongs to Sobolev space H∞(R3). References | Related Articles | Metrics

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Uniqueness and Bifurcation of Limit Cycles for a Class of Polynomical System JIN Shan, LU Shi-Ping Acta mathematica scientia,Series A. 2011, 31 (6):  1669-1673.  Abstract ( 1046 )   RICH HTML PDF (269KB) ( 695 )   Save In this paper, a class of polynomical systems: dx/dt=-y+δ x+lx2+mxy+ax3, dy/dt=x(1+b1y+b2y2+… +bnxn) is studied. It gives the succesive focal values, and proves that the system has at most one limit cycle when δma=0.  References | Related Articles | Metrics

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Dynamic Below-Target Semi-Variance Risk Measure in a Fractional |Black-Scholes Market ZHANG Hua-Yue, CHEN Wan-Hua, QU Li-An Acta mathematica scientia,Series A. 2011, 31 (6):  1674-1682.  Abstract ( 1544 )   RICH HTML PDF (972KB) ( 1014 )   Save The paper is concerned with continuous time portfolio selection model in a complete Black-Scholes market driven by fractional Brownian motion with Hurst parameter H>1/2. The objective is to find an admissible portfolio π to minimize the risk measured by below target semi-variance. By the martingale method in Cox and Huang, we derive the optimal terminal wealth and the corresponding optimal investment strategy. Finally, we numerically analyze the properties of Downside risk measure, the result shows that Hurst index H must not be lost sight. References | Related Articles | Metrics

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The Second Fluctuation-Dissipation Theorem and Entropy Production Rate of a Nonequilibrium Open System YU Ming-Bao Acta mathematica scientia,Series A. 2011, 31 (6):  1683-1696.  Abstract ( 1238 )   RICH HTML PDF (401KB) ( 695 )   Save A nonequilibrium open system is studied in  the time-dependent projection operator formalism. Its environment is not a reservoir and may linearly deviate from its initial state under the influence of the system. By assuming the relevant statistical operator of the open system to be a generalized canonical one, the transport equation, the second Fluctuation-Dissipation theorem and the entropy production rate of the open system are derived and expressed in terms of correlation functions of fluctuations of inner random forces and interaction random forces. If the environment is a reservoir,  then they can be cast into the Volterra equation formalism. References | Related Articles | Metrics

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The Properties of Solutions to Higher-order Homogeneous Linear Differential Equations with Coefficient of Fabry Gap CHEN Mei-Ru, CHEN Zong-Xuan Acta mathematica scientia,Series A. 2011, 31 (6):  1697-1707.  Abstract ( 1381 )   RICH HTML PDF (355KB) ( 844 )   Save In the paper, the authors investigate the exponent of convergence of the zero-sequence of meromorphic solutions to homogeneous linear differential equation f(k)+Ak-2f(k-2)+…+A1f'+A0f=0  when its  coefficients are meromorphic functions possessing only a finite number of poles and dominant coefficient As(s∈{2, …, k-2})  is fabry gap. The  minimum number of linear independent transcendental solutions and the maximum number of linear independ ent transcendental solutions with finite exponents of convergence of the zero-sequence are obtained. References | Related Articles | Metrics

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Half Inverse Problem for a Quadratic Pencil of |Schr\"{o}dinger Operators WANG Wu-Ping, YANG Chuan-Fu, HUANG Zhen-You Acta mathematica scientia,Series A. 2011, 31 (6):  1708-1717.  Abstract ( 1469 )   RICH HTML PDF (298KB) ( 806 )   Save In this paper, the authors discuss the half inverse problem for a quadratic pencil of the Schr\"{o}dinger operator on the finite interval [0, π]. Improving the Koyunbakan and Panakhov's method[12], it is showed that  if the potentials (q(x), p(x)) are prescribed on [π/2, π ], then only one spectrum is sufficient to determine  the potentials (q(x), p(x)) on the interval [0, π/2) for the quadratic pencil of the Schr\"{o}dinger operator on the finite interval [0, π] and coefficient h of the boundary condition. References | Related Articles | Metrics

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Global Stability of Periodic Solution and Almost Periodic Solution of Price Cooperating Model with Time Lag CUI Cheng, WANG Xiao, GAO Fei, LIU An-Ping Acta mathematica scientia,Series A. 2011, 31 (6):  1718-1729.  Abstract ( 1275 )   RICH HTML PDF (385KB) ( 900 )   Save Mathematical model is an important method in study of produce price in economics. Under the economic parameters satisfying some conditions, the existence and uniqueness of periodic solution as well as  almost periodic solution of model is proved by using upper and lower solution method. The global stability of periodic solution as well as almost periodic solution is obtained through constructed Liapunov function. References | Related Articles | Metrics