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07 January 2000, Volume 20 Issue 1 Previous Issue    Next Issue

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On Dual Gap of Semi-infinite Programming LI Shi-Zheng Acta mathematica scientia,Series A. 2000, 20 (1):  1-5.  Abstract ( 800 )   RICH HTML PDF (305KB) ( 961 )   Save Ｔｈｉｓｐａｐｅｒｐｒｏｐｏｓｅｓａｄｕａｌｐｒｏｂｌｅｍ （Ｄ１）ｆｏｒａｓｅｍｉｉｎｆｉｎｉｔｅｃｏｎｖｅｘｐｒｏｇｒａｍｍｉｎｇｐｒｏｂｌｅｍ （Ｐ）．Ｉｔｉｓｐｒｏｖｅｄｔｈａｔａｓｕｆｆｉｃｉｅｎｔａｎｄｎｅｃｅｓｓａｒｙｃｏｎｄｉｔｉｏｎｏｆｎｏｄｕａｌｇａｐｂｅｔｗｅｅｎ （Ｄ１）ａｎｄ （Ｐ）ｉｓｎｏｄｕａｌｇａｐｂｅｔｗｅｅｎ （Ｐ）ａｎｄＬａｇｒａｎｇｅ＇ｓｄｕａｌｐｒｏｂｌｅｍ（Ｄ）ｏｆ（Ｐ）．Ｔｈｅｓａｄｄｌｅｐｏｉｎｔｃｒｉｔｅｒｉｏｎｏｆ（Ｐ）ｉｓａｃｈａｒａｃｔｅｒｉｚｅｄｂｙｕｓｉｎｇｔｈｅｄｉｒｅｃｔｉｏｎａｌｄｅｒｉｖａｔｉｖｅ．Ｓｅｍｉｉｎｆｉｎｉｔｅｐｒｏｇｒａｍｍｉｎｇ，Ｄｕａｌｐｒｏｂｌｅｍ，Ｄｕａｌｇａｐ，Ｄｉｒｅｃｔｉｏｎａｌｄｅｒｉｖａｔｉｖｅ，Ｓｕｂｄｉｆｆｅｒｅｎｔｉａｌ． References | Related Articles | Metrics

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Global semitability for Generalize Lienard Planar stystem YANG Qi-Gui Acta mathematica scientia,Series A. 2000, 20 (1):  6-13.  Abstract ( 796 )   RICH HTML PDF (345KB) ( 684 )   Save ＴｈｉｓｐａｐｅｒｄｅａｌｗｉｔｈｇｌｏｂａｌｓｅｍｉｓｔａｂｉｌｉｔｙｆｏｒｇｅｎｅｒａｌｉｚｅｄＬｉéｎａｒｄｐｌａｎａｒｓｙｓｔｅｍX＝ （Y），y＝－f（x）（y）－g（x），（Ｅ）ｓｏｍｅｓｕｆｆｉｃｉｅｎｔａｎｄｎｅｃｅｓｓａｒｙｃｏｎｄｉｔｉｏｎｓａｒｅｅｓｔａｂｉｓｈｅｄｔｏｅｎｓｕｒｅｔｈａｔｔｈｅｓｙｓｔｅｍ （Ｅ）ｉｓｇｌｏｂａｌｌｙｓｅｍｉｓｔａｂｌｅ． References | Related Articles | Metrics

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THE oscillatory waves of semilear wave equations ZHENG Qin, YIN Hui-Cheng, CHOU Qiang-Jiu Acta mathematica scientia,Series A. 2000, 20 (1):  14-24.  Abstract ( 936 )   RICH HTML PDF (426KB) ( 678 )   Save Ｆｏｒａｃｌａｓｓｏｆｓｅｍｉｌｉｎｅａｒｗａｖｅｅｑｕａｔｉｏｎｓｉｎｔｗｏｏｒｔｈｒｅｅｓｐａｃｅｄｉｍｅｎｔｉｏｎｓ，ｉｆｔｈｅＯｓｃｉｌｌａｔｏｒｙＣａｕｃｈｙｉｎｉｔｉａｌｄａｔａｈａｖｅｏｎｅｎｏｎｄｅｇｅｎｅｒａｔｅｐｈａｓｅ，ｗｅｃｏｎｓｔｒｕｃｔａｎｄｊｕｓｔｉｆｙｔｈｅｇｅｏｍｅｔｒｉｃｏｐｔｉｃｓｅｘｐａｎｓｉｏｎｓｏｆａｎｙｏｒｄｅｒｏｆｔｈｅｏｓｃｉｌｌａｔｏｒｙｓｏｌｕｔｉｏｎｓｗｉｔｈｔｗｏｐｈａｓｅｓ． Related Articles | Metrics

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The first two order moments of sample of UDS MA Chang-Xin Acta mathematica scientia,Series A. 2000, 20 (1):  25-30.  Abstract ( 1274 )   RICH HTML PDF (301KB) ( 701 )   Save Ｉｎ［７］ｕｎｉｆｏｒｍｄｅｓｉｇｎｓａｍｐｌｉｎｇ（ＵＤＳ）ａｎｄｒａｎｄｏｍｕｎｉｆｏｒｍｄｅｓｉｇｎ（ＲＵＤ）ｗｅｒｅｇｉｖｅｎ．ＴｈｉｓｐａｐｅｒｇｉｖｅｓｔｈｅｆｉｒｓｔｔｗｏｏｒｄｅｒｍｏｍｅｎｔｓｏｆｓａｍｐｌｅｓｏｆＵＤＳａｎｄＲＵＤ． References | Related Articles | Metrics

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The sample path optimality for nonstationary MDP with Average criterion GUO Xian-Beng Acta mathematica scientia,Series A. 2000, 20 (1):  31-35.  Abstract ( 828 )   RICH HTML PDF (317KB) ( 692 )   Save Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｃｏｎｓｉｄｅｒｔｈｅｓａｍｐｌｅｐａｔｈｏｐｔｉｍａｌｉｔｙｆｏｒｎｏｎｓｔａｔｉｏｎａｒｙ ＭＤＰｗｉｔｈａｒｂｉｔｒａｒｙｓｔａｔｅａｎｄａｃｔｉｏｎｓｐａｃｅｓｕｎｄｅｒａｖｅｒａｇｅｃｒｉｔｅｒｉｏｎ．Ｂｙｔｈｅｍａｒｔｉｎｇａｌｅｔｈｅｏｒｙ，ｗｅｐｒｏｖｅｔｈｅｅｘｉｓｔｅｎｃｅｏｆｏｐｔｉｍａｌＭａｒｋｏｖｐｏｌｉｃｉｅｓｕｎｄｅｒｔｈｅｗｅａｋｅｒｇｏｄｉｃｃｏｎｄｉｔｉｏｎｓ，ａｎｄｔｈｅｎｅｘｔｅｎｄｔｈｅｍａｉｎｒｅｓｕｌｔｓｏｂｔａｉｎｅｄｂｙＡ．Ａｒｏｐｏｓｔａｔｈｉｓ，Ｖ．Ｂｏｒｋａｒ，Ｅ．Ｆ．Ｇａｕｃｈｅｒａｎｄ，Ｍ．ＧｈｏｓｈａｎｄＳ．Ｍａｒｃｕｓ［１］（１９９３） References | Related Articles | Metrics

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Lower Bound of Topological Entropy of Coordinate Self-maps on k-Dimension Torus JIA Da-Feng, XU Sen-Lin Acta mathematica scientia,Series A. 2000, 20 (1):  36-40.  Abstract ( 791 )   RICH HTML PDF (330KB) ( 732 )   Save Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｇｉｖｅａｌｏｗｅｒｂｏｕｎｄｏｆｔｏｐｏｌｏｇｉｃａｌｅｎｔｒｏｐｙｏｆｃｏｏｒｄｉｎａｔｅｓｅｌｆｍａｐｓｏｎｄｉｍｅｎｓｉｏｎｔｏｒｕｓ．Ｔｈｅｌａｓｔｏｆｔｈｉｓｐａｐｅｒ，ｗｅｓｋｏｗｔｈｅａｎｄ ｐｒｏｖｅｄｔｈａｔｌｅｍｍａ１ｉｎ ［３］ｉｓａｓｐｅｃｉａｌｃａｓｅｉｎｔｈｉｓｐａｐｅｒ． 　 References | Related Articles | Metrics

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The Chaaracterization of the Essential Norm of the Hankel Operators on Bergman Spaces GAO Jin-Shou Acta mathematica scientia,Series A. 2000, 20 (1):  41-47.  Abstract ( 821 )   RICH HTML PDF (332KB) ( 672 )   Save ＬｅｔΩｂｅａｓｔｒｏｎｇｌｙｐｓｅｕｄｏｃｏｎｖｅｘ ｄｏｍａｉｎｉｎ Cｎ ．Ｈａｎｋｅｌｏｐｅｒａｔｏｒ Hf（f∈L２（Ω，ｄv）ｉｓ ｄｅｆｉｎｅｄ ｏｎ ＢｅｒｇｍａｎｓｐａｃｅA２（Ω）,Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｏｂｔａｉｎｓｅｖｅｒａｌｅｑｕｖａｌｅｎｔｑｕａｎｔｉｔｉｅｓｏｆ‖Hf‖ｅｓｓ （ｔｈｅｅｓｓｅｎｔｉａｌｎｏｒｍｏｆHf）． References | Related Articles | Metrics

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existence of the nonlinear heat source in an inverse problem arising from heat conduction phenmena  LI Gong-Qing, MA Yi-Chen Acta mathematica scientia,Series A. 2000, 20 (1):  48-57.  Abstract ( 1174 )   RICH HTML PDF (379KB) ( 910 )   Save Ｔｈｉｓｐａｐｅｒｓｔｕｄｉｅｓｔｈｅｉｎｖｅｒｓｉｏｎｏｆｔｈｅｎｏｎｌｉｎｅａｒｈｅａｔｓｏｕｒｃｅｆｏｒｈｅａｔｃｏｎｄｕｃｔｉｏｎ ｅｑｕａｔｉｏｎｗｉｔｈａｃｌａｓｓｏｆｎｏｎｌｏｃａｌｂｏｕｎｄａｒｙｆｏｒｔｉｍｅ．ＡｐｐｌｙｉｎｇＳｏｂｏｌｅｖｃｏｍｐａｃｔｍｅｔｈｏｄｓ，ｗｅ＇ｖｅｐｒｏｖｅｄｔｈｅｅｘｉｓｔｅｎｃｅｏｆｔｈｅｈｅａｔｓｏｕｒｃｅｉｎＨ¨ｏｌｄｅｒｓｐａｃｅ． References | Related Articles | Metrics

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The relations Between Orlicz F-norm ‖ ·|‖ρ |and its parental modular &rho|and the inverting problem WANG Jian, WANG Jian-Yong Acta mathematica scientia,Series A. 2000, 20 (1):  58-62.  Abstract ( 835 )   RICH HTML PDF (310KB) ( 720 )   Save Ｉｎｔｈｉｓｐａｐｅｒ，ｔｈｅｒｅｌａｔｉｏｎｓｂｅｔｗｅｅｎＯｒｌｉｃｚＦｎｏｒｍ ‖·‖ρａｎｄｉｔｓｐａｒｅｎｔａｌｍｏｄｕｌａｒρａｒｅｄｉｓｃｕｓｓｅｄａｎｄｓｉｘｐｒｏｐｏｓｉｔｉｏｎｓｏｆｓｕｃｈｒｅｌａｔｉｏｎｓａｒｅｇｉｖｅｎ．Ｔｈｅａｕｔｈｏｒｓａｌｓｏｐｒｏｐｏｓｅｄｔｈｅｉｎｖｅｒｔｉｎｇｐｒｏｂｌｅｍ ｏｆＦｎｏｒｍ ａｎｄｇａｖｅｔｗｏｉｍｐｏｒｔａｎｔｒｅｓｕｌｔｓ：ｉｎｅｖｅｒｙｌｉｎｅａｒ ｓｐａｃｅ，ｅａｃｈβｎｏｒｍ （０＜β＜１）ｃａｎｂｅｉｎｖｅｒｔｅｄ，ｂｕｔａｎｙｎｏｒｍ （β＝１）ｃａｎｎ＇ｔｂｅｉｎｖｅｒｔｅｄ References | Related Articles | Metrics

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Lie Symmetries and conservd Quantilities of Nonholonomic Mechanical System in term of Quasi-coordinate FU Jing-Li, LIU Rong-Mo Acta mathematica scientia,Series A. 2000, 20 (1):  63-69.  Abstract ( 981 )   RICH HTML PDF (351KB) ( 745 )   Save ＴｈｉｓｐａｐｅｒｉｎｖｏｌｖｅｓＬｉｅｓｙｍｍｅｔｒｉｅｓａｎｄｃｏｎｓｅｒｖａｔｉｏｎｌａｗｓｏｆｎｏｎｈｏｌｎｏｍｉｃｓｙｓｔｅｍｓｉｎｔｅｒｍｓｏｆｑｕａｓｉｃｏｏｒｄｉｎａｔｅｓ．ＷｅｓｔｕｄｉｅｄｔｗｏｋｉｎｄｓｏｆｐｒｏｂｌｅｍｓｏｎＬｉｅｓｙｍｍｅｔｒｉｅｓａｎｄｃｏｎｓｅｒｖｅｄｑｕａｎｔｉｔｉｅｓ．ＯｎｅｉｓｔｈｅｄｉｒｅｃｔｐｒｏｂｌｅｍｏｆＬｉｅｓｙｍｍｅｔｒｉｅｓ：ｆｉｎｄｉｎｇｏｕｔｔｈｅｃｏｒｒｅｓｐｏｎｄｉｎｇｃｏｎｓｅｒｖｅｄｑｕａｎｔｉｔｙａｃｃｏｒｄｉｎｇｔｏａｇｉｖｅｎＬｉｅｓｙｍｍｅｔｒｙ．Ｗｅｇｉｖｅｓｔｈｅｄｅｆｉｎｉｔｉｏｎｏｆｔｈｅｉｎｆｉｎｉｔｅｓｈｍａｌｇｅｎｅｒａｔｏｒｆｏｒｔｈｅｎｏｎｈｏｌｏｎｏｍｉｃｓｙｓｔｅｍｓｉｎｔｅｒｍｓｏｆｑｕａｓｉｃｏｏｒｄｉｎａｔｅｓ．Ｕｓｉｎｇｔｈｅｉｎｖａｒｉａｎｃｅｏｆｔｈｅｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｕｎｄｅｒｔｈｅｉｎｆｉｎｉｔｅｓｉｍａｌｔｒａｎｓｆｏｒｍａｔｉｏｎｓ，ｅｓｔａｂｌｉｓｈｅｓｔｈｅｄｅｔｅｒｍｉｎｉｎｇｅｑｕａｔｉｏｎｓｏｆｔｈｅＬｉｅｓｙｍｍｅｔｒｉｅｓ．Ｏｂｔａｉｎｓｔｈｅｓｔｒｕｃｔｕｒｅｅｑｕａｔｉｏｎａｎｄｃｏｎｓｅｒｖｅｄｑｕａｎｔｉｔｉｅｓ．ＴｈｅａｎｏｔｈｅｒｋｉｎｄｓｏｆｐｒｏｂｌｅｍｉｓｃａｌｌｅｄｔｈｅｉｎｖｅｒｓｅｐｒｏｂｌｅｍｏｆＬｉｅｓｙｍｍｅｔｒｉｅｓ：ｆｉｎｄｏｕｔｔｈｅｃｏｒｒｅｓｐｏｎｄｉｎｇＬｉｅｓｙｍｍｅｔｒｙａｃｃｏｒｄｉｎｇｔｏａｋｎｏｗｎｃｏｎｓｅｒｖｅｄｑｕａｎｔｉｔｙ．Ｇｉｖｅｓａｎｅｘａｍｐｌｅｔｏｉｌｌｕｓｔｒａｔｅｔｈｅａｐｐｌｉｃａｔｉｏｎｏｆｔｈｅｒｅｓｕｌｔ． References | Related Articles | Metrics

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Lagrange Formalism of Plasticity about St.Venant-Levy-Mises Materials Shen Hui-Chuan Acta mathematica scientia,Series A. 2000, 20 (1):  70-73.  Abstract ( 1207 )   RICH HTML PDF (315KB) ( 722 )   Save The plasticity mechanics problems of St.Venant-Levy-Mises materials be bring into the theoretical system of Lagrangian mechanics,the basic differential equations of plasticity mechanics about above materials on three-dimensional problem,on small deflection problems ,and on finite-deformation (large deflection) problem be discussed in this paper. References | Related Articles | Metrics

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Extremal Solutions of Nonlinear Impulsive Integrodifferential Equation in Banach Space Chai Guo-qing Acta mathematica scientia,Series A. 2000, 20 (1):  74-80.  Abstract ( 886 )   RICH HTML PDF (338KB) ( 677 )   Save In this paper, the author combine the monotone iterative method with some new technique to investigate the extremal solutions of first order initial value problem of nonlinear impulsive integrodifferential equations in Banach space, under simpler and weaker conditions, establish the new existence theorem, essentially improve and generalize the corresponding results in [3] when L3=0. References | Related Articles | Metrics

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A Strong Limit Theorem for the Harmonic Mean of the Random Transition Probabilities of Finite Nonhomogeneous Markov Chains   Liu Wen Acta mathematica scientia,Series A. 2000, 20 (1):  81-84.  Abstract ( 1046 )   RICH HTML PDF (286KB) ( 877 )   Save  Let {Xn, n≥0} be a nonhomogeneous Markov chain with state space I = {1, 2, …, N} and transition probabilities pn(i, j) = P(X n =j|Xn-1 = i). In this paper the conditions that the harmonic mean of random transition probabilities p1(X0,X1),…, pn (Xn-1,Xn) converges to 1/N a.s. are investigated, and the differentiation technique on a net together with the tool of generating function for the study of strong limit theorems of Markov chains is presented. References | Related Articles | Metrics

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The Jeep-Fuel Station Problems Fan Wentao Ding Yiming Acta mathematica scientia,Series A. 2000, 20 (1):  85-94.  Abstract ( 999 )   RICH HTML PDF (402KB) ( 831 )   Save  The Jeep-Fuel Station problems are studied by the Optimal Sequence method. The Optimal Sequences of the oneway trip JeepFuel Station problem and the round trip Jeep-Fuel station problem are determined. References | Related Articles | Metrics

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Lie Symmetries and Conserved Quantities of Nonholonomic Mechanical Systems with Unilateral Constraints Zhang Yi | Mei Fengxiang Acta mathematica scientia,Series A. 2000, 20 (1):  95-100.  Abstract ( 873 )   RICH HTML PDF (323KB) ( 689 )   Save This paper studies the Lie symmetries of nonholonomic mechanical systems with unilateral constraints. It gives the conditions and the form of conserved quantities due to the Lie symmetries of the systems, and presents the inverse problem of the above problem, i.e., finding the corresponding Lie symmetry transformation according to a given integral of the systems. Finally, it gives an example to illustrate the application of the results. References | Related Articles | Metrics

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Existence Theorems of Solutions for Nonlinear Impulsive Volterra Integral Equations in Banach Spaces and Applications Lu Huiqin Liu Lishan Acta mathematica scientia,Series A. 2000, 20 (1):  101-108.  Abstract ( 916 )   RICH HTML PDF (347KB) ( 692 )   Save In this paper, we use a new comparison result and the Monch fixed-point theorem to prove some existence theorems of global solutions for the nonlinear impulsive Volterra integral equations in Banach spaces that   improve the results in [1-3]. Then, we give some applications to initial value problems for first order impulsive differential equations in Banach spaces. References | Related Articles | Metrics

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On a Class of Singular Two-point Boundary Value Problems Cheng Jiangang Acta mathematica scientia,Series A. 2000, 20 (1):  109-114.  Abstract ( 1151 )   RICH HTML PDF (314KB) ( 799 )   Save  This paper deals with the existence of positive solutions for a class singular two point boundary value problems. The relations between the perturbed problems and the original problems have been established in the very general conditions. As an application, the sufficient and necessary conditions of the existence of positive solutions have been given for some special cases. References | Related Articles | Metrics

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Wormhole solution of Higgs field Buhe Acta mathematica scientia,Series A. 2000, 20 (1):  115-120.  Abstract ( 854 )   RICH HTML PDF (298KB) ( 687 )   Save Many experts has discussed and studied the wormhole solution under the coupling condition of both gravitation field and all kinds of substantial field. Due to the significance of the Higgs field in the modern field theory, the research into the issues whether there exist a wormhole solution under the coupling condition of gravitation field and Higgs field will be a very meaningful problem. The article points out that there is a wormhole solution under a certain condition. References | Related Articles | Metrics

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A Nonlinear Boundary Value Problem for Biregular Function Vectors with Values in Real Clifford Chai Zhiming, Huang Sha, Qiao Yuying Acta mathematica scientia,Series A. 2000, 20 (1):  121-129.  Abstract ( 854 )   RICH HTML PDF (386KB) ( 729 )   Save In this paper we discuss a nonlinear boundary value problem for biregular function vectors with values in real Clifford analysis:           A(t1,t2) Φ++(t1,t2)+B(t1,t2) Φ+- (t1,t2)           +C(t1,t2) Φ-+ (t1,t2)+D(t1,t2) Φ-- (t1,t2)           =G(t1,t2) F*[t1,t2,Φ++(t1,t2),Φ+-(t1,t2),Φ-+(t1,t2),Φ--(t1,t2)], Applying the method of integral equations and Schauder's fixedpoint theorem, we proved the existence of the solution for the above problem. And applying contract mapping theorem, we proved the existence and uniqueness for corresponding linear boundary value problems. References | Related Articles | Metrics

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On Stability of Two Order Linear Differential Equations with Periodic Coefficient Shi Jinlin Acta mathematica scientia,Series A. 2000, 20 (1):  130-139.  Abstract ( 1201 )   RICH HTML PDF (347KB) ( 971 )   Save  In this paper, we discuss stability of two order linear differential equations with periodic coefficient and obtain some criteria for recogniting stability. References | Related Articles | Metrics

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The Limit Theorem on a Mean Operator Markov Chain Liu Jiakun Zhang Lianfang Wang Lei Shu Yantai Acta mathematica scientia,Series A. 2000, 20 (1):  140-144.  Abstract ( 972 )   RICH HTML PDF (326KB) ( 567 )   Save  In this paper we present a mean operator Markov chain and give its law of large numbers, central limit theorem, law of iterated logarithm.   References | Related Articles | Metrics