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06 October 2001, Volume 21 Issue 4 Previous Issue    Next Issue

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WEAK CONVERGENCE OF SOME DIRICHLET SERIES DING Xia-Qi, LUO Pei-Zhu Acta mathematica scientia,Series B. 2001, 21 (4):  433-439.  Abstract ( 656 )   RICH HTML PDF (106KB) ( 837 )   Save This paper treats Dirichlet series from the point of view developed in [1],[2].Especially it is found that the kernal function is closely related with the Riemann Zetafunction. References | Related Articles | Metrics

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INFINITE ELEMENT METHOD FOR PROBLEMS ON UNBOUNDED AND MULTIPLY CONNECTED DOMAINS YING Long-An Acta mathematica scientia,Series B. 2001, 21 (4):  440-452.  Abstract ( 620 )   RICH HTML PDF (147KB) ( 1488 )   Save The author studies the infinite element method for the boundary value prob-lems of second order elliptic equations on unbounded and multiply connected domains.The author makes a partition of the domain into infinite number of elements. Without dividing the domain, as usual, into a bounded one and an exterior one, he derives an ini-tial value problem of an ordinary differential equation for the combined stiffness matrix, then obtains the approximate solution with a small amount of computer work. Numerical examples are given. References | Related Articles | Metrics

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STATIONARY STRUCTURES FOR A WEAKLY COUPLED ELLIPTIC SYSTEM ARISING IN TWO-PREDATOR, TWO-PREY MODELS YAN Ping, LIN Zhi-Gui Acta mathematica scientia,Series B. 2001, 21 (4):  453-459.  Abstract ( 689 )   RICH HTML PDF (101KB) ( 917 )   Save Weakly-coupled elliptic system arising in the two-predator, two-prey model is discussed. It is proved that there is no non-constant solution if diffusions or inter-specific competitions are strong, or if the intrinsic growths of the prey are slow and the intrinsic drop rates of predator are fast. References | Related Articles | Metrics

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GLOBALLY SMOOTH SOLUTIONS TO CAUCHY PROBLEM OF A QUASILINEAR HYPERBOLIC SYSTEM ARISING IN BIOLOGY ZHENG Yong-Shu Acta mathematica scientia,Series B. 2001, 21 (4):  460-468.  Abstract ( 762 )   RICH HTML PDF (114KB) ( 1026 )   Save This article considers Cauchy problem ut − (uv)x = 0, vt − ux = 0, (E) u(x, 0) = u0(x) > 0, v(x, 0) = v0(x). (I) A necessary and sufficient condition in guaranteeing that Cauchy problem admits a global C1-solution on t  0 is obtained. References | Related Articles | Metrics

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THE EXISTENCE OF SOLUTIONS OF QUASILINEAR ELLIPTIC EQUATIONS WITH CHANGE OF SIGN LI Gong-Bao, YU Chun Acta mathematica scientia,Series B. 2001, 21 (4):  469-482.  Abstract ( 804 )   RICH HTML PDF (168KB) ( 952 )   Save This paper considers the following quasilinear elliptic problem( −div(|∇u|p−2∇u) = a(x)g(u) in u = 0 on @ where  is a bounded regular domain in RN(N≥3), N > p > 1. When g(u) satisfies suitable conditions and g(u)u − R u 0g(s)ds is unbounded, a(x) is a H¨older continuous function which changes sign on   and R − |a(x)|dx is suitably small. The authors prove the existence of a nonnegative nontrivial solution for N > p > 1, in particular, the existence of a positive solution to the problem for N > p≥2. Our main theorem generalizes a recent result of Samia Khanfir and Leila Lassoued (see [1]) concerning the case where p = 2.They prove also that if g(u) = |u|q−2u with p < q < p and + = {x∈|a(x) > 0} is a nonempty open set, then the above problem possesses infinitely many solutions. References | Related Articles | Metrics

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PRICING AND HEDGING OPTION UNDER PORTFOLIO CONSTRAINED WEI Gang, CHEN Shi-Ping Acta mathematica scientia,Series B. 2001, 21 (4):  483-494.  Abstract ( 651 )   RICH HTML PDF (145KB) ( 1149 )   Save The authors employ convex analysis and stochastic control approach to study the question of hedging contingent claims with portfolio constrained to take value in a given closed, convex subset of RK, and extend the results of Gianmario Tessitore and Jerzy Zabczyk[6] on pricing options in multiasset and multinominal model. References | Related Articles | Metrics

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STRONG LAW OF LARGE NUMBERS AND SHANNON-MCMILLAN THEOREM FOR MARKOV CHAINS FIELD ON CAYLEY TREE YANG Wei-Guo, LIU Wen Acta mathematica scientia,Series B. 2001, 21 (4):  495-502.  Abstract ( 772 )   RICH HTML PDF (130KB) ( 1115 )   Save This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and orderd couples of states for Markov chains field on Cayley tree. Then they prove the Shannon-McMillan theorem with a.e. conver-gence for Markov chains field on Cayley tree. In the proof, a new technique in the study the strong limit theorem in probability theory is applied. References | Related Articles | Metrics

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APPROXIMATION OF SOLUTION OF LINEAR DIFFERENTIAL EQUATION WITH ALMOST PERIOD FUNCTION COEFFICIENTS CA Hai-Tao, HUANG Bo-Yun Acta mathematica scientia,Series B. 2001, 21 (4):  503-508.  Abstract ( 627 )   RICH HTML PDF (91KB) ( 843 )   Save This paper is devoted to the study of approximation of the solution for the differential equation whose coefficients are almost period functions. To this end the authors establish the estimation of the solution of general linear differential equation for infinite interval case. For finite interval case, this equation was investigated by G. Tamarkin[1] applying the Picard method of successive approximation. References | Related Articles | Metrics

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OPTIMAL CONTROL PROBLEM FOR PARABOLIC VARIATIONAL INEQUALITIES WONG Geng-Sheng Acta mathematica scientia,Series B. 2001, 21 (4):  509-525.  Abstract ( 715 )   RICH HTML PDF (163KB) ( 1102 )   Save This paper deals with the optimal control problems of systems governed by a parabolic variational inequality coupled with a semilinear parabolic differential equations.The maximum principle and some kind of approximate controllability are studied. References | Related Articles | Metrics

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THE TWO FUNCTORS IN THE FUZZY MODULAR CATEGORY Pan Fu-Zheng Acta mathematica scientia,Series B. 2001, 21 (4):  526-530.  Abstract ( 712 )   RICH HTML PDF (98KB) ( 1186 )   Save After defining Hom(A, B) and A  B in the fuzzy modular category Fm, the sufficient conditions of the existence for exact Hom functors Hom(M, ), and Hom(, M), as well as exact Tensor functors M  and  M are given in this paper. Fi-nally the weak isomorphisms relations between Hom functors and Tensor functors are displayed. References | Related Articles | Metrics

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CONVERGENCE RATES FOR A CLASS OF EVOLUTIONARY ALGORITHMS WITH ELITIST STRATEGY DING Li-Xin, KANG Li-Shan Acta mathematica scientia,Series B. 2001, 21 (4):  531-540.  Abstract ( 710 )   RICH HTML PDF (131KB) ( 1049 )   Save This paper discusses the convergence rates about a class of evolutionary algorithms in general search spaces by means of the ergodic theory in Markov chain and some techniques in Banach algebra. Under certain conditions that transition probability functions of Markov chains corresponding to evolutionary algorithms satisfy, the authors obtain the convergence rates of the exponential order. Furthermore, they also analyze the characteristics of the conditions which can be met by genetic operators and selection strategies. References | Related Articles | Metrics

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FRACTIONAL (g, f)-FACTORS OF GRAPHS LIU Gui-Zhen, ZHANG Lan-Ju Acta mathematica scientia,Series B. 2001, 21 (4):  541-545.  Abstract ( 578 )   RICH HTML PDF (100KB) ( 1483 )   Save This paper presents a new proof of a charaterization of fractional (g, f)-factors of a graph in which multiple edges are allowed. From the proof a polynomial algorithm for finding the fractional (g, f)-factor can be induced. References | Related Articles | Metrics

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THE UNCONDITIONAL STABILITY FOR THE HYPERNEUTRAL TYPE CONSTANT LINEAR CONTROL SYSTEM WITH DELAYS LI Ye-Ping, ZHANG Shao-Hua Acta mathematica scientia,Series B. 2001, 21 (4):  546-552.  Abstract ( 761 )   RICH HTML PDF (96KB) ( 984 )   Save In this paper, by means of the frequency domain method and the inequality analysis, unconditional stability problem for the hyperneutral type constant linear control system with delays are discussed, and some precise sufficient, sufficient and necessary conditions are obtained. References | Related Articles | Metrics

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EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR VOLTERRA INTERGO-DIFFERENTIAL EQUATIONS JIANG Da-Qing, WEI Jun-Jie Acta mathematica scientia,Series B. 2001, 21 (4):  553-560.  Abstract ( 860 )   RICH HTML PDF (108KB) ( 1239 )   Save This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results. References | Related Articles | Metrics

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THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR THE NONLINEAR HEAT-CONDUCTION EQUATION AND ITS APPLICATION CHEN Fang-Nian, DUAN Zhi-Wen Acta mathematica scientia,Series B. 2001, 21 (4):  561-571.  Abstract ( 686 )   RICH HTML PDF (138KB) ( 927 )   Save In this paper the nonlinear heat-conduction equations with Dirichlet boundary condition and the nonlinear boundary condition are studied. The asymptotic behavior of the global of solution are analyzed by using Lyapuunov function.As its application, the approximate solutions are constructed. References | Related Articles | Metrics

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THE OPIAL INEQUALITY IN RN DENG Yin-Bin Acta mathematica scientia,Series B. 2001, 21 (4):  572-576.  Abstract ( 726 )   RICH HTML PDF (108KB) ( 1026 )   Save This paper discusses the minimal eigenvalue 1(p, q,) and its best estimate of the following nonlinear eigenvalue problem − pu = |u|q−2 u, u|@  = 0. Where   is a bounded smooth domain in RN, p is the p-laplace operator, p  2, q 2 [p, Np N−p ). By this result, the famous Opial inequality in RN are deduced References | Related Articles | Metrics