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25 December 2003, Volume 23 Issue 6 Previous Issue    Next Issue

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Antiperiodic and Nonlinear Boundary Problemsfor First Order Differential Equations withPiecewise Constant Arguments ZHANG Feng-Qin, MA Zhi-En Acta mathematica scientia,Series A. 2003, 23 (6):  641-649.  Abstract ( 1504 )   RICH HTML PDF (351KB) ( 1215 )   Save The authors employ the method of upper and lower solutions coupled with  the monotone iterative technique to obtain results of existence and  uniqueness for anti periodic  and nonlinear boundary problems of  differential equations with piecewise constant arguments x′(t)=f(t,x(t),x(［t-k］)), x(0)+h(x(T))=0$, where $h(θ)∈C^1(R),h′(θ)>0. References | Related Articles | Metrics

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3 Restricted Edge Connectivity and Regular Factor OU Jian-Beng, ZHANG Fu-Ji- Acta mathematica scientia,Series A. 2003, 23 (6):  650-654.  Abstract ( 1473 )   RICH HTML PDF (314KB) ( 1495 )   Save Let G be a connected k regular vertex transitive graph of order at least 6. If G is triangle free, then either G is maximal 3 restricted edge connected, or G  has a (k_1)regular factor with components isomorphic to a same vertex transitive graph of order h such that 2k_2≤h≤3k_5.The only exception is that G is a cubic graph with girth 4. References | Related Articles | Metrics

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The Nernst Theorem and the Entropy of\= the A Torus like Black Hole HAN Fu-Long, ZHANG Li-Chun, ZHAO Ren Acta mathematica scientia,Series A. 2003, 23 (6):  655-659.  Abstract ( 1580 )   RICH HTML PDF (314KB) ( 1285 )   Save Using brick wall method, the authors calculate the free energy and entropy o f the scalar  field on the background of non asympotic flat torus like black hole under the  sphere coordinates. The results show that the entropy not only is related to th e area of an outer horizon but also is the function of a inner horizon. Furtherm ore, the entropy expressed by inner and outer horizon will approach zero when th e radiation temperature of the black hole approaches zero. It satisfies the Nern st theorem. It can be taken as Planck absolute entropy. References | Related Articles | Metrics

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Multiple Solutions for a Singular Elliptic Equation with Critical SobolevHardy Exponent and Inhomogeneous Term TAO Yang-Xin, CHEN Yao-Tian Acta mathematica scientia,Series A. 2003, 23 (6):  660-666.  Abstract ( 1559 )   RICH HTML PDF (321KB) ( 1247 )   Save In this paper, the authors study the multiple problem for  a semilinear singular elliptic equation with critical Sobolev Hardy exponent and inhomogeneous term. The authors prove that if the parameter in the equation is  less then a known constant,  the problem concerned has two solutions.  References | Related Articles | Metrics

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Critical Superprocess Dependent |on Population Size YAN Guo-Jun Acta mathematica scientia,Series A. 2003, 23 (6):  667-678.  Abstract ( 1583 )   RICH HTML PDF (411KB) ( 1492 )   Save In this paper, the authors study the limiting behavior of large branching part icle systems whose branching mechanism depends on  population size. These systems wea kly converge to a superprocess and it can be characterized as the unique soluti on of a martingale problem. The proof of the uniqueness for the martingale problem requi res  “randomization” of culminant semigroup of superprocesses. References | Related Articles | Metrics

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Explicit Exact Solutions for Generalized Ginzburg Landau Equation and Rangwala Rao Equation ZHANG Wei-Guo Acta mathematica scientia,Series A. 2003, 23 (6):  679-691.  Abstract ( 1782 )   RICH HTML PDF (401KB) ( 1618 )   Save In this paper, the authors first obtain three kinds of explicit exact solution  for the liénard equation a″(ξ)+la(ξ)+ma^{2p+1}(ξ)+na^{4p+1}(ξ)=0 by proper transformation and undetermined assumption  method. By means of these solutions, the authors obtain solitary wave solutions  and perio dic wave solutions of triangle function type for generalized GinzburgLandau eq u ation and RangwalaRao equation and several nonlinear derivation Schr[AKo¨D]di nger type equations. References | Related Articles | Metrics

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Laurent Expansion and Residue Theorems in Universal Clifford Analysis ZHANG Zhong-Xiang, DU Jin-Yuan Acta mathematica scientia,Series A. 2003, 23 (6):  692-703.  Abstract ( 1387 )   RICH HTML PDF (412KB) ( 1281 )   Save  In this paper, by using the Cauchy integral formula on certain distinguished boundary for functions with values in a universal Clifford algebra,  the Laurent expansion for LR regular functions with isolated  singular points is obtained in the corresponding Laurent domain. After that, the concept of residue and the residue theo rem is obtained. References | Related Articles | Metrics

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The Cauchy Problems of a class of Equations |for the Tension of Extensible Beam ZHANG Quan-Ju Acta mathematica scientia,Series A. 2003, 23 (6):  704-710.  Abstract ( 1582 )   RICH HTML PDF (338KB) ( 1441 )   Save  This paper deals with the hyperbolic equation in the form of utt+A2u+M(x，‖A1/2u‖22)Au=0，which comes from the mathematical description of the tension of a extensible bea m, and the existence and uniqueness of Cauchy problems for this equation are pre sented here. An existence and uniqueness theorem of local solvability is proven  for this equation, and compared with the existing results, the author's conditio ns restri cted to the nonlinear term of this equation are much general. In fact, the resul ts given here are obtained by breaking all the former restrictions on the nonlin ear term.   References | Related Articles | Metrics

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Quadrilaterals and Paths of Order 4 in Graphs YAN Jin, LIU Gui-Zhen Acta mathematica scientia,Series A. 2003, 23 (6):  711-718.  Abstract ( 1481 )   RICH HTML PDF (352KB) ( 1693 )   Save Let k be a positive integer. Let G be a graph with |G|=4k. Supposeing σ\-2(G)≥4k-1, then G has a spanning subgra ph consisting of k-1quadrilaterals and a path of order 4 such that all of them are  independent. Let G=(V\-1,V\-2;E) be a bipartite graph with |V\-1|=|V\-2|=2 k. If d(x)+d(y)≥2k+1 for each pair of nonadjacent vertices x and y of G with x∈V\-1and y∈V\-2, then G contains k-1 quadri laterals and a path of order 4 such that all of them are independent. Moreover,the condition on degrees is sharp. References | Related Articles | Metrics

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Uniform Stabilization of Timoshenko Beams with Boundary Feedba ck Control HU Gen-Qi, FENG De-Xin Acta mathematica scientia,Series A. 2003, 23 (6):  719-728.  Abstract ( 1739 )   RICH HTML PDF (396KB) ( 1301 )   Save The uniform stabilization of Timoshenko beams with boundary feedback control is  investigated in the present paper. Under some linear boundary feedback controls,   by spectral analysis of the operator determined by the closed loop system, the a smptotes of spectrum of the operator are gigen. Moreover, the spectral determine d growth assumption for the closed loop system is proved. Furthermore, it is sho wed that there is no spectrum of the operator on the imaginary axis, and hence t he exponential stability of the closed loop system is obtained, and the rate of  exponential decaying is given by the supremum of the real part of spectrum. Fina lly, the distribution of the spectra of the closed loop system is discussed.  References | Related Articles | Metrics

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The |Positive |Entire |Solutions |of a |Class |of Singular |Semilinear |Biharmonic |Equations XIE Chang-Qing Acta mathematica scientia,Series A. 2003, 23 (6):  729-734.  Abstract ( 1697 )   RICH HTML PDF (324KB) ( 1417 )   Save In the paper, the author's aims are to establish the theorems of existence of po sitive radial symmetric entire solutions for a class of singular semilinear biha rmonic equations, to present the properties of the solutions,  and to extend the result of paper ［7］. References | Related Articles | Metrics

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Entire Functions Represented by Dirichlet Series of Complex Exponents DENG Guan-Tie Acta mathematica scientia,Series A. 2003, 23 (6):  735-738.  Abstract ( 1569 )   RICH HTML PDF (282KB) ( 1357 )   Save A necessary and sufficient condition is given for the existence of an entire function whose Dirichlet coefficients are dominated by an appropriate function, being not identicall to zero, bounded in a  horizontal strip and to be able represented  by Dirichlet series of complex exponents. References | Related Articles | Metrics

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Existence of Feasible Solutions of Bilevel Programming FAN Li-Ya, LIU San-Yang Acta mathematica scientia,Series A. 2003, 23 (6):  739-744.  Abstract ( 1560 )   RICH HTML PDF (337KB) ( 1438 )   Save Bilevel programming is usually formulated with two optimization problems  where  the constraint set of the first one (upper level problem) is partially det ermined by the  optimal reactions of the second one (lower level problem). The paper is devoted to study the existence of feasible solutions, which plays a fun damental and important role in bilevel programming, by means of the w pseu do mo notonicity of the Clarke's subdifferential mapping of the lower level objective  function.   References | Related Articles | Metrics

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The Global Attractors for the Periodic Initial Value Problem for Dissipative Generalized Symmetric Regularized Long Wave Equations SHANG Ya-Dong, GUO Bo-Ling Acta mathematica scientia,Series A. 2003, 23 (6):  745-757.  Abstract ( 2036 )   RICH HTML PDF (433KB) ( 1477 )   Save The long time behavior of solutions of the generalized  symmetric regularized long wave equations with dissipation term is considered. The existence of global attractors of the periodic initial value problem is proved, and the estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors are obtained by means of uniform a priori estimates for time. References | Related Articles | Metrics

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Potential Well Method for a Class of Nonlinear Wave Equations of FourthOrder  ZHANG Hong-Wei, CHEN Guo-Wang Acta mathematica scientia,Series A. 2003, 23 (6):  758-768.  Abstract ( 1767 )   RICH HTML PDF (406KB) ( 1160 )   Save  In this paper the initial boundary value problem for the nonlinear wave equation u_{tt}+u_{xxxx}=σ(u_x)_x+f(x,t)  is  considered.  The existence  of  global  weak  solution  is  proved.  Also  the existence and uniqueness of the  generalized  global  solution  and  the classical global solution are proved. References | Related Articles | Metrics