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25 December 2007, Volume 27 Issue 6 Previous Issue    Next Issue

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Unbounded Solutions of Boundary Value Problems on the Half-Line with Countable Impulses Yan Baoqiang; Liu Yansheng Acta mathematica scientia,Series A. 2007, 27 (6):  961-976.  Abstract ( 2136 )   RICH HTML PDF (315KB) ( 1107 )   Save This paper presents some results on the existence of at least one and multiple unbounded solutions for boundary value problems on the half line with countable impulses. Related Articles | Metrics

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A Two-Level Method with Backtracking for the Conduction-Convection Problems Luo Zhendong;Chen Jing\quad ;Tian Xiangjun Acta mathematica scientia,Series A. 2007, 27 (6):  977-986.  Abstract ( 2125 )   RICH HTML PDF (380KB) ( 1125 )   Save In this paper, a two-level method for resolving the nonlinearity in finite element approximation of the stationary conduction-convection problems is presented. The two-level method involves solving one small, nonlinear coarse mesh system, one Oseen problem on the fine mesh and one linear correction problem on the coarse mesh. Meanwhile, the existence and convergence of approximate solutions are shown. Related Articles | Metrics

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The Obstacle Problem for the Pricing of the Fixed Rate Mortgages Jian Xiongfei;Yi Fahuai Acta mathematica scientia,Series A. 2007, 27 (6):  987-995.  Abstract ( 1645 )   RICH HTML PDF (381KB) ( 1039 )   Save The authors consider the mortgages with the constant market enviroment and the constant contract rate.Suppose that the asset price moved as a geometric Brownian motion, an one-dimensional parabolic variational inequality which arises from the fixed mortgages is studied, the existence and uniquencess of the solution are obtained. Moreover, the monotonicity and the regularity of the free boundary are proved as well. Related Articles | Metrics

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Existence of Solutions of Nonlinear Eigenvalue Problems Laplacian and Weights Lin Lishan;Li Yongqing Acta mathematica scientia,Series A. 2007, 27 (6):  996-1005.  Abstract ( 1973 )   RICH HTML PDF (294KB) ( 1141 )   Save In the paper, by using the variational methods, the authors consider the solvability ofthe equation -△pu=λ a(x)(u^{+})q-1-μ a(x)(u-)q-1+f(x,u), u∈W01,p(Ω), (Ω) in the case of p≠ q, where Ω is a bounded domain in RN(N≥ 3), the weight function (x)∈ Lr(Ω), (r≥Np/Np-Nq+pq) with a(x)>0, a.e.in Ω, and f satisfies some conditions. Related Articles | Metrics

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Distribution of Characteristic Roots and Exponential Stability of Singular Differential Delay Systems Jang Wei Acta mathematica scientia,Series A. 2007, 27 (6):  1006-1012.  Abstract ( 1876 )   RICH HTML PDF (249KB) ( 1059 )   Save This paper firstly investigates the distribution of the characteristic roots of singular differential systems with delay. It is pointed out that if all the characteristic roots have negative real parts, under a condition, the maximal value of real parts of the characteristic roots is negative. This result shows that if all the characteristic roots have negative real parts, under a condition, the solution of singular differential systems with delay is exponentially stable. And finally, as an example, for the neutral differential systems, the conditions are given under which the solution is exponentially stable. Related Articles | Metrics

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The Growth of An Entire Function Represented by Dirichlet Series with Complex Exponents Ning Juhong;Deng Guantie Acta mathematica scientia,Series A. 2007, 27 (6):  1013-1020.  Abstract ( 2222 )   RICH HTML PDF (258KB) ( 1175 )   Save Let f be an entire function represented by Dirichlet series,which is bounded in a horizontal stirp, its coefficients {an} and exponents {λn}(n=1,2,... )are sequences of complex numbers. The authors introduce φ-order and lower φ-order and study the conditions for f having φ-order and lower φ-order respectively. Related Articles | Metrics

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The Supremum of Lp -integrability Exponent on Quasiconformal Mappings Chu Yuming;Zhang Xiaohui\quad ;Wang Gendi Acta mathematica scientia,Series A. 2007, 27 (6):  1021-1024.  Abstract ( 1916 )   RICH HTML PDF (216KB) ( 1077 )   Save \noindent{\bf Abstract:} Let $f$ be a $K$-quasiconformal mapping in the unit disk $B^2$ of $R^2$. In this paper, the authors prove $$\sup_{0<R<1}\int_0^{2\pi}|f(R\e^{i\theta})|^p\mbox{d}\theta<+\infty,$$ for any $ 0<p<\frac1{2K},$ and the supremum $\frac1{2K}$ of $p$ is the best possible. Related Articles | Metrics

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The Existence of Infinitely Many Solutions for an Elliptic Equation Involving Critical Sobolev-Hardy Exponent with Neumann Boundary Condition Hu Ailian;Zhang Zhengjie Acta mathematica scientia,Series A. 2007, 27 (6):  1025-1034.  Abstract ( 1688 )   RICH HTML PDF (323KB) ( 1119 )   Save This paper deals with the Neumann problem for an elliptic equation $$ \left\{ \begin{array}{ll} \disp -\Delta u-\frac{\mu u}{|x|^2}=\frac{|u|^{2^{*}(s)-2}u}{|x|^s}+\lambda|u|^{q-2}u, \ \ &x\in\Omega,\\ D_\gamma{u}+\alpha(x)u=0, &x\in\partial\Omega\backslash\{0\}, \end{array} \right. $$ where $\Omega $ is a bounded domain in $ R^N$ with $ C^1$ boundary, $ 0\in\partial\Omega$, $N\ge5$. $2^{*}(s)=\frac{2(N-s)}{N-2}$ ($0\leq s\leq 2$) is the critical Sobolev-Hardy exponent, $1<q<2$, $0<\mu<\mu^{*}$, $\gamma$ denotes the unit outward normal to boundary $\partial\Omega$. By variational method and the dual fountain theorem, the existence of infinitely many solutions with negative energy is proved. Related Articles | Metrics

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The Growth of Entire Functions of Infinte Order Represented by Laplace-Stieltjes Transformation Shang Lina; Gao Zongsheng Acta mathematica scientia,Series A. 2007, 27 (6):  1035-1043.  Abstract ( 1903 )   RICH HTML PDF (262KB) ( 1234 )   Save In this paper, the authors investigate the growth of entire functions of infinite order represented by Laplace-Stieltjes transformation; the authors obtain two necessary and sufficient conditions and extend some results of Dirichlet series in the whole plane. Related Articles | Metrics

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Isochronous Center for a Class of Quintic System Wang Qinlong; Liu Yirong Acta mathematica scientia,Series A. 2007, 27 (6):  1044-1053.  Abstract ( 1681 )   RICH HTML PDF (319KB) ( 1363 )   Save The complex isochronous centers for a class of quintic systems are discussed. This article, following a new algorithm to compute periodic constants, then mainly finding a proper change of coordinates to judge the origin as complex isochronous center, obtains all real isochronous centers and saddle point linearizable conditions. Related Articles | Metrics

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Statistical Entropy of Dirac Field in Schwarzschild-anti-de Sitter Space-time Li Guqiang; Acta mathematica scientia,Series A. 2007, 27 (6):  1054-1058.  Abstract ( 1746 )   RICH HTML PDF (284KB) ( 1067 )   Save By using brick-wall method, the statistical entropy of Dirac field in Schwarzschild-anti-de Sitter spacetime is calculated and the effect of the spins of the Dirac particles on the entropy is investigated. It is shown that if the author ignores the usual contribution from the vacuum surrounding the system, then the statistical entropy consists of a quadratically divergent term which is proportional to the horizon area of the black hole and two logarithmically divergent terms, the structure of the whole expression is different from that of the black hole entropy. The logarithmically divergent term may be positive, zero, or negative for different values of |∧|r2h . Related Articles | Metrics

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The Shock Behavior of the Solution for a Class of Nonlinear Boundary Value Problems Tang Rongrong Acta mathematica scientia,Series A. 2007, 27 (6):  1059-1064.  Abstract ( 1778 )   RICH HTML PDF (311KB) ( 1053 )   Save By using the shock theory and the matching principle, under appropriate conditions, the shock problems for a class of nonlinear equations are considered. The expressions of the shock solutions and the shock locations are obtained. The result is applied to the model for a class of compressible fluid flow. And the shock behavior of the solution for the model is obtained separately. Related Articles | Metrics

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Existence of Positive Solutions for Fourth-Order Boundary Value Problem with Variable Coefficients Chai Guoqing;Huang Chaoyan Acta mathematica scientia,Series A. 2007, 27 (6):  1065-1073.  Abstract ( 1791 )   RICH HTML PDF (293KB) ( 1148 )   Save In this paper, by use of the fixed point theorem, combining spectral theory of operator, the authors establish the theorem on existence of positive solutions for fourth-order boundary value problem with variable coefficient as follows \[\left\{ {\begin{array}{l} u^{(4)} + B(t){u}'' - A(t)u = f(t,u),0 < t < 1 ,\\ u(0) = u(1) = {u}''(0) = {u}''(1) = 0 \end{array}} \right.\] \noindent where $A(t),B(t) \in C[0,1]$ and $f(t,u):[0,1]\times [0,\infty ) \to[0,\infty )$ is continuous. Related Articles | Metrics

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The Real Compact n-Lie Algebras and Invariant Bilinear Forms Bai Ruipu;Jia Peipei Acta mathematica scientia,Series A. 2007, 27 (6):  1074-1081.  Abstract ( 1529 )   RICH HTML PDF (266KB) ( 969 )   Save In this paper, the authors study the nondegenerate invariant bilinear forms on n-Lie algebras. The authors propose the definition of compact n -Lie algebra over the real field R and study its structural properties Related Articles | Metrics

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Existence and Exponential Stability of Almost Periodic Solutions for Cellular Neural Networks with Delays Liu Bingwen;Hunang Lihong Acta mathematica scientia,Series A. 2007, 27 (6):  1082-1088.  Abstract ( 2177 )   RICH HTML PDF (266KB) ( 1089 )   Save In this paper cellular neural networks with delays are Sconsidered. Sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using a fixed-point theorem and Lyapunov functional method. The results of this paper are new and they complement previously known results. Related Articles | Metrics

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Global Existence for Semilinear wave Equations in Exterior Domain Wu haigen;Yang han\quad ;Liu Juan Acta mathematica scientia,Series A. 2007, 27 (6):  1089-1097.  Abstract ( 1511 )   RICH HTML PDF (302KB) ( 1031 )   Save We consider the problems for linear and semilinear wave equations in exterior domain. The authors first derive total energy decay for linear damped wave equation. This result can be applied to the proof of the global existence for semilinear wave equation with nonlinear term |u|psatisfies 2<p≤ N/[N-4]+. For this purpose the authors deal with a radially symmetric solution in the N-D (3≤ N≤ 7) exterior domain Related Articles | Metrics

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The Existence of Weak Solutions and the Trajectory Attractors to the Model of Climate Dynamics Huang Haiyang;Guo Boling Acta mathematica scientia,Series A. 2007, 27 (6):  1098-1110.  Abstract ( 1902 )   RICH HTML PDF (486KB) ( 1368 )   Save In this paper, the model of climate for weather forecast is studied, in which the pressing force of topography on atmosphere and the divergent effect of airflow are included.The suitable space of functions and the reasonable operators are selected to represent the complex atmosphere dynamical equations by the simple abstract operator equation, such that the weak solution can be defined. Then the existence of the weak solution is proved by Galerkin method, and the asymptotic behaviors of the weak solution is described by the trajectory attractors. Related Articles | Metrics

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A Numerical Simulation Method of Nonlinear Schrodinger equation Zhang Jing;Zhang Luming;Chen Juan Acta mathematica scientia,Series A. 2007, 27 (6):  1111-1117.  Abstract ( 2242 )   RICH HTML PDF (290KB) ( 1154 )   Save In this paper, the authors propose a three-level and linear difference scheme through adding a dissipation term to the nonlinear Schr\"{o}dinger equation. It is proved that the scheme preserves two conservative quantities that the continuous equation owns. Comparing it with the known schemes by the numerical examples, the authors get the conclusion that the scheme is computed easily and has higher precision. Related Articles | Metrics

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Influence Diagnostics In Simplex Distribution Models Zhang Chunli;Wei Bocheng Acta mathematica scientia,Series A. 2007, 27 (6):  1118-1132.  Abstract ( 1677 )   RICH HTML PDF (439KB) ( 1092 )   Save In this paper, by introducing a specific linear model, several influence measures are proposed for simplex distribution models (SDM), based on Barndorff-Nielsen and Jorgensen (1991), Jorgensen (1997), and Song and Tan (2000). The equivalency of case-deletion models and mean-shift outlier models in SDM is presented. The diagnostic test for varying dispersion in SDM is investigated and the score statistics are obtained. The proposed diagnostic measures are illustrated with examples. Related Articles | Metrics

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Singular Perturbation of Boundary Value Problems for Vector Second Order Nonlinear Integro-Differential Equations Lin Surong Acta mathematica scientia,Series A. 2007, 27 (6):  1133-1140.  Abstract ( 1882 )   RICH HTML PDF (306KB) ( 1120 )   Save The present paper covers the singularly perturbed boundary value problems for vector second order nonlinear integro-differential equations. Under suitable conditions, the existence of the solution is proved by the diagonalization method, the asymptotic expansion of the solution is constructed, and its uniformly valid estimate of remainder term is given as well. Related Articles | Metrics

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Embeddings of Circular Graphs Ren Han; Deng Mo Acta mathematica scientia,Series A. 2007, 27 (6):  1148-1154.  Abstract ( 1857 )   RICH HTML PDF (413KB) ( 1012 )   Save In this paper the authors investigate the embeddings of the circular graphs. The authors determine the minimum orientable genus and the minimum nonorientable genus and show that all the circular graphs are up-embeddable. The authors show that for a fixed integer $l (\geq 3)$ and large enough $n$, there is only one way to embed a 4-regular circular graph $C(n,l)$ into the torus such that each face is a quadrilateral. In particular, the authors find that both the torus and the Klein bottle may be quadrangulated by the circular graph $C(2l+2,l)$ which, by introducing some new edges, may also triangulate both of the two surfaces. Related Articles | Metrics

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The Inverse Laplace Transform Theorem of Henstock-Kurzweil Integrable Function Su Feng ;Peng Zhigang Acta mathematica scientia,Series A. 2007, 27 (6):  1155-1163.  Abstract ( 1700 )   RICH HTML PDF (241KB) ( 1155 )   Save In this paper, the Laplace transform ofHenstock-Kurzweil integrable function has been defined. Its analyticity and some of its basic properties have been discussed. The inverse formula in the sense of the Henstock-Kurzweil integrable is obtained. The authors also give a example to show that the result can not been improved. Related Articles | Metrics