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25 April 2003, Volume 23 Issue 2 Previous Issue    Next Issue

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On the Existence of Solutions for PBVP of First Order Differential Equations CHEN Ji Acta mathematica scientia,Series A. 2003, 23 (2):  129-134.  Abstract ( 1618 )   RICH HTML PDF (321KB) ( 1372 )   Save Using the topological degree theory, the author  proves several existence theorems of solutions between lower and upper solutions for periodic boundary value problems of first order differential equations, where the lower and upper solutions  \$α(t)\$ and  \$β(t)\$ need not satisfy relations \$α(0)≤α(2π)，β(0)≥β(2π).\$ References | Related Articles | Metrics

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Quality for Very Weak Solutions to a Class\=of NonHomogeneous Aharmonic Systems ZHOU Shu-Qing, WEN Hai-Yang, FANG Hua-Jiang- Acta mathematica scientia,Series A. 2003, 23 (2):  135-144.  Abstract ( 1400 )   RICH HTML PDF (403KB) ( 1250 )   Save Using Hodge decomposition theorem, the authors obtained that the very weak solutions to nonhomogeneous Aharmonic systems -D\-i(A\+\{ij\}(x,Du))+D\-if\-j\+i(x)=0, j=1, \:, mare weak solutions, furthermore, using Morrey space and Campanato  space method and homogenizationmethod, the authors obtained the very weak solutions to the systems are locally H[AKo¨D]lder continuous, and obtained the relationbetween the H[AKo¨D]lder continuous exponent μ and λ. References | Related Articles | Metrics

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Gateaux Differentiable Points and Frechet Differentiable \=Points in MusielakOrlicz Sequence Spaces Endowed \=with the Orlicz Norm WANG Ting-Fu-[, HAO Cui-Xia, LIU Chi-Fang- Acta mathematica scientia,Series A. 2003, 23 (2):  145-153.  Abstract ( 1467 )   RICH HTML PDF (362KB) ( 1286 )   Save The criteria of Gateaux (Frechet) differentiable point and Gateaux (Frechet) diffentiability in MusielakOrlicz sequences spaces endowed with Orlicz norm are given. References | Related Articles | Metrics

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Some Properties of Matrices over Division Ring LI Tao-Sheng Acta mathematica scientia,Series A. 2003, 23 (2):  154-160.  Abstract ( 1447 )   RICH HTML PDF (319KB) ( 1280 )   Save In the paper the auther studies the matrix category over division ring, the corenilpotent decomposition of matrices and the properties forpower of matrices over division ring. References | Related Articles | Metrics

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On Well Posedness of Generalized Mutually Approximation Problem NI Ren-Xin- Acta mathematica scientia,Series A. 2003, 23 (2):  161-168.  Abstract ( 1313 )   RICH HTML PDF (354KB) ( 1214 )   Save Let C be a closed bounded convex subset of a realBanachspace X with 0 being an interior point of C. Let G be a nonempty closed, boundedly relatively weakly compact subset of X. Let K(X) denote the space ofall nonempty compact convex subset of X endowed with the Hausdorff distance. Moreover, Let KG(X) denote the closure of the set ｛A∈K(X);A∩G=｝. A generalized mutually approximation problem minC(A,G) is said to be well posed if it hasa uniquesolution (x0,z0) and every minimizing sequence converges strongly to (x0,z0). Under the assumption that C is strictly convex and (sequentially) Kadec, that the set ｛A∈KG(X);minC(A,G) is well posed｝ contains a dense Gδsubset of KG(X) is proved. The results generalize and extend the recent corresponding results due to De Blasi, Myjak and Papini［1］,Li［2］,De Blasi andMyjak［3］ and other authors. References | Related Articles | Metrics

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The Entropy of Thermal Nonequilibrium |Schwarzschildde Sitter Spacetime LIU Wen-Biao, DIAO Zheng- Acta mathematica scientia,Series A. 2003, 23 (2):  169-174.  Abstract ( 1521 )   RICH HTML PDF (358KB) ( 1576 )   Save Thinking of KleinGordon equation in Schwarzschildde Sitter spacetime, the authors  calculate the free energy and entropy of this kind of black hole via brickwall method. It is difficult to calculate the free energy because there are twohorizons whose temperature is different from one another. Taking improved brickwall model, which means that the free energy and entropy are mainly from a thinlayer close to the horizon, the authors overcame the problem successfully and got a goodresult. It is found that the entropy of this system is 1/4 of the sum of the areas of the two event horizons. This is coincided to the result expected. The entropy of this system not only includes the contribution of the black hole horizon,but also includes the contribution of the cosmological horizon. It is found that there is an internal relation between the event horizon and the entropy. The authors also understand more about what is the brickwall model. References | Related Articles | Metrics

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The Positive Entire Solutions for a Class Nonlinear Polyharmonic Equations with Singular on R^2 XU Xing-Ye Acta mathematica scientia,Series A. 2003, 23 (2):  175-182.  Abstract ( 1697 )   RICH HTML PDF (346KB) ( 1247 )   Save In this paper, author's aim is to establish the theorems of  existence  of positive radially symmetric entire solutions for a class singular nonlinear  polyharmonic on R^2  with the Schaudertychonoff fixed point theorem as  the principal ,and presents about the properties of the solutions. It enrichs and develops  the theory and apply of paper [1][4] References | Related Articles | Metrics

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A Reaction Diffusion's Free Boundary Problem SHEN Jian-Zhong, YI Fa-Huai Acta mathematica scientia,Series A. 2003, 23 (2):  183-192.  Abstract ( 1682 )   RICH HTML PDF (395KB) ( 1316 )   Save In this paper, a reaction diffusion's free boundary problem which is used to describle the original cell growth is studied. It is prove d that the problem has locally classical solution uniquely by the linearization  method in the nonlinear analysis and the estimate theory in the partial differential equations. References | Related Articles | Metrics

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Global Structure Analysis of the Plane Five Order System with the Stellar Node YAO Wei-Hong, SHANG De-Sheng, YU Min-Jie Acta mathematica scientia,Series A. 2003, 23 (2):  193-207.  Abstract ( 1449 )   RICH HTML PDF (1616KB) ( 1403 )   Save This paper deals with the topological classifications of global structures of th e plane five order system with the stellar node. Using the region of type ⅠⅣ , (see [2]), we can take the topological classifications for global structures  of the plane five order system(1) and give the ninetythree global structures  and criteria with the righthand side polynomial coefficients of the system.  References | Related Articles | Metrics

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A Kind of Optimal Design in Urn Models CHEN Gui-Jing, CHEN Yu-MIng, BAI Zhi-Dong, HU Fei-Fang Acta mathematica scientia,Series A. 2003, 23 (2):  208-214.  Abstract ( 1959 )   RICH HTML PDF (355KB) ( 1400 )   Save The ethical motivation comes the criterion that expects m ore patients to be allocated in the superior treatment in the clinical trials. B ased on minimization of error probability, a kind of asymptotic optimal design i n urn models has been constructed. By this design, not only more patients may ex pect to be assignned in the superior treatment, but also the estimates of succes s probabilites posses asymptotical statistical efficiency in some sence. References | Related Articles | Metrics

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The Cauchy Problem of the Schrodinger Poisson Systems |with |Dissipation XING Jia-Sheng Acta mathematica scientia,Series A. 2003, 23 (2):  215-223.  Abstract ( 1412 )   RICH HTML PDF (360KB) ( 1176 )   Save This paper consideres the Cauchy problem of the SP  systems with dissipation. The global existence and uniqueness of the strong solutions for the problems are proved. References | Related Articles | Metrics

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An Oscillation Result for Higher Order Linear Differential Equations with One Dominant Coefficient YUAN Wen-Jun Acta mathematica scientia,Series A. 2003, 23 (2):  224-230.  Abstract ( 1577 )   RICH HTML PDF (359KB) ( 1181 )   Save  The following theorem is known result, if the coefficients are entire (e.g. Bank  and Laine for k=2,ρ(A_0)<1/2; Rossi for k=2,ρ(A_0)=1/2; Langley and Hellers tein and coworkers for k≥2,ρ(A_0)≤1/2 In this paper the author will use some new method to  prove.Theorem Suppose that A_j(j=1,2,,k-2) are meromorphic functions  with finite poles. If the order ρ(A_0) of A_0 is not greater than 1/2, and ρ(A_j)<ρ(A_0) for j=1,2,,k-2, then Eq.(1.1) wi th k≥2 cannot have two linearly independent solutions each with zero sequen ce having finite exponent of convergence.  References | Related Articles | Metrics

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Shift Operators of Map Family and Its Application to Stochastic Processes YANG Xiang-Qun, QIU De-Hua Acta mathematica scientia,Series A. 2003, 23 (2):  231-244.  Abstract ( 1775 )   RICH HTML PDF (437KB) ( 1406 )   Save The authors researched the shift operators of map family in vague ge neralizati on. Given a parameter set T=［0，+∞) or T=｛0，1，2，…｝,and two arbit rary non empty sets Ω and E,which are not disposed any measurable σ algebra and  any measure.The set of all maps φ： T∩［0，β)→E,where β∈T∪｛＋∞｝, is deno ted by  Ω (E). The map X:   Ω→Ω(E) is a map family X=｛X(t),t∈T∩［0， σ)｝ in fact. It is followed that the necessary and sufficient condition of existence for shift  operators of a map family X=｛X(t),t∈T∩［0，σ)｝.  Some properties  of shift operators and some applications to stochastic processes for shift opera tors are discussed. References | Related Articles | Metrics

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Existence and Method of Lower and Upper Solutions for Fourth Order Nonlinear Boundary Value Problems LI Yong-Xiang Acta mathematica scientia,Series A. 2003, 23 (2):  245-252.  Abstract ( 1569 )   RICH HTML PDF (366KB) ( 2159 )   Save This paper studies the existence of solutions for the fou rthorder boundary value problem u^(4)(t) = f(t,u(t),u″(t)), t∈［0,1］,u(0)=u(1)=u″(0)=u″(1)=0,where  f: ［0,1］×R×R→R is  a  Carathéodory  function. In the general case without restriction for growth condition of f and assumption of monotonicity  on f, the author obtains the existence results of solution by using the met hod of lower and upper solutions. The validity  of finding solutions with the mo notone iterative method is also discussed.  References | Related Articles | Metrics

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The Shock Solution for a Class of Nonlinear Equation HAN Xiang-Lin Acta mathematica scientia,Series A. 2003, 23 (2):  253-256.  Abstract ( 1635 )   RICH HTML PDF (292KB) ( 2379 )   Save By using the matching asymptotic expanding method, the shock solutions  and their locations of a nonlinear equation are considered. And the relation of  them with the boundary conditions is obtained. References | Related Articles | Metrics