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03 June 1999, Volume 19 Issue 2 Previous Issue    Next Issue

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Some Central Limit Theroy for Super Brownian Motion LI Ceng-Hu Acta mathematica scientia,Series B. 1999, 19 (2):  121-126.  Abstract ( 805 )   RICH HTML   PDF (769KB) ( 1129 )   Save The aurhot proves a central limt theory for the critical super Brown Motions,which leads to a Gaussisan random field.In the transent case the limit filed  is the same as that obtained by Dawson(1977).In the recurrent case it is a spatial uniforn field. The author also give a central limit theory for the weighed occupation time of the supper Brownian motion with underlying dimension nimber d<=3.completing the results of Iscoe(1986). References | Related Articles | Metrics

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Asymptotic Expansion of Dirac-type Distribution Associates with a class of Hypersurfaces with Degenerated Critical Points JI Min-You, ZHANG Guan-Beng Acta mathematica scientia,Series B. 1999, 19 (2):  127-137.  Abstract ( 934 )   RICH HTML   PDF (1530KB) ( 956 )   Save In order to generalize Hadamard's theory of fundamental solutions to the case of degenerate holomorphic PDE, this paper studies the asymtotic expansion of Dirac-type distribution associated with a class of hypersurfaces F(x) with degenerate criticak points and proves that [F(x)]+ is   a distribution-valued meromorphc of \lamda ( -C under some assunotion on F(x).Next,the  authors use the Normal form theory of Arnold and prove that for a hypersuface F(x)=0 with A_\mu type degenerate critical point at x=0, F_+  is a distribution-valued mermorphic function of \lamda References | Related Articles | Metrics

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Optimal Control problem of Parabolic Differential Equation with Two Point Boundary Condition  HONG Geng-Sheng, lLiu-Chang-Liang Acta mathematica scientia,Series B. 1999, 19 (2):  138-147.  Abstract ( 769 )   RICH HTML   PDF (1156KB) ( 879 )   Save This paper deals with optimal control problem of parabolic differential equation with two points boundary conditions(in the time varialbe). The results here extend those in [3] on optimal control of the heat equations. Morover,the technique used in this paper is based on some smooth approximations of  "tangent cones" in the sense of Clarke and some maximal monotone operators. References | Related Articles | Metrics

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New Method for Effective Viscosity of |Colloidal Dispersions with Periodic Microstructures GU Guo-Qiang, TU Jian-Hua Acta mathematica scientia,Series B. 1999, 19 (2):  148-157.  Abstract ( 754 )   RICH HTML   PDF (1256KB) ( 967 )   Save One of the central theoretical problems in the colloid field is to determine the rheological relation between tile macroscopic properties of colloidal suspensions and the microstructures of the systems. In this work, the authors develop a method of transformation field by which one can calculate the effective viscosity of an incompressible viscous fluid containing colloidal particles (either solid particles or liquid drops) fixed at the points of a periodic lattice. The effective viscosity of a colloidal dispersion of spherical particles is calculated. The predictions of the theory are in good agreement with the Einstein's formula for suspensions and the Taylor's formula for emulsions at low particle concentrations. At higher particle concentrations, the theory reproduces the results of Nunan and Keller. The method is also applicable to tile viscosity of colloidal systems with non-spherical particles. the Research Grants Council of the Hong Kong Government under Project Number CUHK 461/95P. G.Q .G.acknowledges the support of t References | Related Articles | Metrics

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MULTIPLICITY RESULTS FOR AN INHOMOGENEOUS NONLINEAR ELLIPTIC PROBLEM XIE Zi-Qing Acta mathematica scientia,Series B. 1999, 19 (2):  158-167.  Abstract ( 933 )   RICH HTML   PDF (1204KB) ( 957 )   Save The author proves that there exist three solutions u0, u1 and u2 in the following problem where some conditions are imposed on Q and f. Here, 0 < u0 < u1 , u2 changes sign. References | Related Articles | Metrics

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THE EXTENDED SOLUTIONS OF PLURIHARMONIC MAPS INTO COMPLEX GRASSMANNIAN MANIFOLDS CHAO Xiao-Li Acta mathematica scientia,Series B. 1999, 19 (2):  168-174.  Abstract ( 687 )   RICH HTML   PDF (819KB) ( 937 )   Save In this paper , the extended solutions of some pluriharmonic maps into complex Grassmannian manifolds will be given. References | Related Articles | Metrics

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IDENTIFICATION OF PARAMETERS IN SEMILINEAR PARABOLIC EQUATIONS LIU Zhen-Hai Acta mathematica scientia,Series B. 1999, 19 (2):  175-180.  Abstract ( 727 )   RICH HTML   PDF (745KB) ( 1050 )   Save An optimization theoretic approach of coefficients in semilinear parabolic equation is presented. It is based on convex analysis techniques. General theorems on existence are proved in L1 setting. A necessary condition is given for the solutions of the parameter estimatioll problem. the post-doctoral funds of China and funds of State Educational Commission of China for returned scholars from abroad References | Related Articles | Metrics

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THE SUPPORT POINTS AND EXTREME POINTS OF THE UNIT BALL OF H'_P~ 1 BANG Zhi-Gang Acta mathematica scientia,Series B. 1999, 19 (2):  181-189.  Abstract ( 735 )   RICH HTML   PDF (1080KB) ( 944 )   Save By the author denotes the areal measure on the unit disk . Let H'p = {f(z): f(z) is analytic in D and . Let B H 'p and. This article researches the support points and extreme points of B(H'p). References | Related Articles | Metrics

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Multi-dimensional Riemann problem of scalar conservation law YANG Xiao-Zhou Acta mathematica scientia,Series B. 1999, 19 (2):  190-200.  DOI: cnki:ISSN:0252-9602.0.1999-02- Abstract ( 759 )   RICH HTML   PDF (1310KB) ( 901 )   Save This paper considers multi-dimensional Riemann problem in another kind of view. The author gets solution of (1.1)(1.2) in Theorem 3.4 and proves its uniqueness. A new method of solution constructing is applied, which is different from the usual self-similar transformation. The author also discusses some generalized concepts in multi-dimensional situation (such as "convex condition", "left value" and "right value", etc). An example is finally given to demonstrate that rarefaction wave solution of (1 .1)(1 .2) is not self-similar. Related Articles | Metrics

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Local C-semigroups and Local C-cosine Functions GAO Meng-Chu Acta mathematica scientia,Series B. 1999, 19 (2):  201-213.  Abstract ( 743 )   RICH HTML   PDF (1546KB) ( 867 )   Save This paper is concered with the local C-semigroups and local C-coscine functions without the assumption that the image of  C is dense in a Banach space X. First, the sufficient and necessary conditions for  a local C-semiproup and a C-cosine function to be the restriction of a global C-semigroup and a  global C-cosine function to an interval are given,respectively.Secondaly, it is characterized for a closed operator to be the generator of a global  C-semigroup and a local C-cosine function,respectively. Related Articles | Metrics

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Intersection of translations of cantor triadic set LI Wen-Xia, XIAO Dong-Mei Acta mathematica scientia,Series B. 1999, 19 (2):  214-219.  Abstract ( 717 )   RICH HTML   PDF (779KB) ( 829 )   Save Let C be the Cantor triadic set and let C_\alpha=C+\alpha={\beta+\alpha:\beta(-C} for  -1<=\alpha<=1.Let Hp={\alpha(-C:dim|H(C_\alpha \intersection C)=(1-p)log2/log3},0<p<1.The author give the dimesions of C_\aplha intersection C and H_p. In addition the characteristic of H_p is describled by means of some measure \mu surrported on C. Related Articles | Metrics

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Some results about RCK model with endogenouse fertility CA Dong-Han Acta mathematica scientia,Series B. 1999, 19 (2):  220-225.  Abstract ( 1216 )   RICH HTML   PDF (772KB) ( 899 )   Save In this paer. incorporating the fertility in the utility function and the production function, an improved Ramsey-Cass-Koopmans(RCK) model with engenous fertility is obtained. In this model ,the fertility can be expressed as a function of per capita and per capital consumption.It has been proved that at least one equilibruim point exists and the equilibrium point is unique under a condition. The author discusses the possibility of existing multiple equilibria.their geometrical relationship and explains the economical sense of the main results. Related Articles | Metrics

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On the Hitting Probability and Polarity for a Class of Self-similar Markov Processes XIONG Shuang-Beng, LIU Lu-Qi Acta mathematica scientia,Series B. 1999, 19 (2):  226-233.  Abstract ( 753 )   RICH HTML   PDF (964KB) ( 1055 )   Save The author investigate the hitting probility,polarity and the relationship between the polarity and Hausdorff dimension for self-similar Markov process with state space(0,∞) and increasing path. Related Articles | Metrics

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THE VALUE DISTRIBUTION OF RANDOM ANALYTIC DIRICHLET SERIES OF NEUTRAL GROWTH(Ⅰ) DING Xiao-Qiang Acta mathematica scientia,Series B. 1999, 19 (2):  234-240.  Abstract ( 692 )   RICH HTML   PDF (775KB) ( 890 )   Save This paper deals with the value distribution of random Dirichlet series whose coefficients are martingale difference sequece, and which is of  neutral growth. Related Articles | Metrics