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25 December 1997, Volume 17 Issue 4 Previous Issue    Next Issue

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THE RIEMANN PROBLEM FOR A TWO-DIMENSIONAL HYPERBOLIC SYSTEM OF CONSERVATION LAWS WITH NON-CLASSICAL WEAK SOLUTIONS: SOME ONE-J AND NON-R INITIAL DATA Hu Jiaxin Acta mathematica scientia,Series B. 1997, 17 (4):  361-375.  Abstract ( 65 )   RICH HTML PDF (706KB) ( 31 )   Save The Riemann problem for a two-dimensional 2×2 nonstrictly hyperbolic system of nonlinear conservation laws has been considered for constant initial data having discontinuities on three rays with vertex at the origin. The solutions are constructed for some one-J and non-R initial data. One kind of new discontinuity, which is labelled as the δ-shock wave, appears in some solutions. The δ-shock wave is a discontinuity plane that is the suport of a generalized function. Related Articles | Metrics

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AN EXPONENTIAL STABILITY PROBLEM ON THE SMALL DELAY LINEAR SYSTEM Song Guozhu, Shen Junhao Acta mathematica scientia,Series B. 1997, 17 (4):  376-384.  Abstract ( 57 )   RICH HTML PDF (507KB) ( 34 )   Save In this paper, we define the mild solution of the delay system, and consider the eristence and uniqueness of the mild solution of the delay system. The relationship between the solution of linear system and the one of the delay system will be considered.And we also discuss the exponential stability equivalence between the solution of the linear system and the mild solution of the delay system. Related Articles | Metrics

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LEFT INVERSES AND RIGHT INVERSES OF A STRONG ENDOMORPHISM OF A GRAPH Li Weimin Acta mathematica scientia,Series B. 1997, 17 (4):  385-391.  Abstract ( 55 )   RICH HTML PDF (417KB) ( 32 )   Save In this paper, we characterize left inverses and right inverses of a strong endomorphism of a graph under some certain Green's equivalence conditions. In addition,the number of them is also given. Related Articles | Metrics

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ON THE INFINITESIMAL ISOMETRIC DEFORMATIONS OF SUBMANIFOLDS Chen Xinyue,Yang Wenmao Acta mathematica scientia,Series B. 1997, 17 (4):  392-404.  Abstract ( 61 )   RICH HTML PDF (691KB) ( 33 )   Save In this paper, we consider the infinitesimal Ⅰ-and Ⅱ-isometry deformations of submanifolds immersed in a space form N of constant curvature. We obtain some results which are new even in the case of N being the Euclidean space. At the same time, we generalize some classical results in E3 to the submanifolds immersed in a space form of constant curvature. Related Articles | Metrics

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EXTRAPOLATION AND DEFECT CORRECTION FOR DIFFUSION EQUATIONS WITH BOUNDARY INTEGRAL CONDITIONS Lin Qun, Zhang Shuhua, Yan Ningning Acta mathematica scientia,Series B. 1997, 17 (4):  405-412.  Abstract ( 63 )   RICH HTML PDF (394KB) ( 30 )   Save In this paper we study the higher accuracy methods-the extrapolation and defect correction for the semidiscrete Galerkin approximations to the solutions of the parabolic equations with boundary integral conditions. The global extrapolation and the correction approximations, rather than the pointwise extrapolation results, are derived. Related Articles | Metrics

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BOUNDARY LAYER ESTIMATION OF THE QUASILINEAR STOKES EQUATIONS He Cheng Acta mathematica scientia,Series B. 1997, 17 (4):  413-428.  Abstract ( 64 )   RICH HTML PDF (775KB) ( 35 )   Save We first prove the existence and uniqueness of solution of quasilinear Stokes equations. Then it is shown when the viscosity vanishes, the solution of the quasilinear Stokes equations tends to the solution of the degenerate equations, in which the viscous term is omitted from the quasilinear Stokes equations and the boundary condition is weakened. In the end, we obtain the boundary layer estimation. Our result shows that the thickness of the boundary layer is proportional to ε(1)/4. Related Articles | Metrics

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GLOBAL EXISTENCE OF THE SOLUTION FOR THE LANDAU-LIFSHITZ EQUATION OF THE FERROMAGNETIC SPIN CHAIN Guo Boling, Wang Bixiang Acta mathematica scientia,Series B. 1997, 17 (4):  429-436.  Abstract ( 63 )   RICH HTML PDF (432KB) ( 35 )   Save In this paper, we establish the global existence of the solution for the Landau-Lifshitz equation of the ferromagnetic spin chain. By Galerkin method, we first show the existence of the local solution for this equation, and then by a priori estimates method, we extend the local solution to a global solution. Related Articles | Metrics

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HARNACK'S INEQUALITIES FOR ANALYTIC OPERATOR FUNCTIONS Jian Ming, Yang Changsen Acta mathematica scientia,Series B. 1997, 17 (4):  437-442.  Abstract ( 56 )   RICH HTML PDF (302KB) ( 31 )   Save Some Harnack type inequalities for analytic operator functions have been obtained in this paper. Related Articles | Metrics

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THE LSRS PROPERTY AND THE CONVERGENCE THEOREM OF HENSTOCK-KURZWEIL INTEGRAL Xu Dongfu Acta mathematica scientia,Series B. 1997, 17 (4):  443-448.  Abstract ( 107 )   RICH HTML PDF (335KB) ( 33 )   Save The well-known Controlled Convergence Theorem[5] and the equi-integrabillty theorem[9] are the main convergence theorems of the Kurzweil-Henstock integral,which is of the non-absolute type.These theorems are fundamential in the application of the KH-integral to real and functional analysis.But their conditions can be weakened to extend their applications. In this paper, using the property of Locally-Small-Riemann-Sums[7], we give all other convergence theorem (Theorem 1).By Theorem 2 we prove that Theorem 1 contains the Equi-integrability Theorem and is not equivalent to it. Therefore the Controlled Convergence Theorem and the Equi-integrabillty Theorem are all corollaries of Theorem 1. Related Articles | Metrics

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A COMPLETE CLASSIFICATION OF FINITE-DIMENSIONAL SIMPLE NOVIKOV ALGEBRAS OF CHARACTERISTIC p>2 Chen Hongji Acta mathematica scientia,Series B. 1997, 17 (4):  449-454.  Abstract ( 52 )   RICH HTML PDF (288KB) ( 36 )   Save In the paper we will give a complete classification of finite-dimemsional simple Novikov algebras over an algebraically closed field with prime characteristic p>2. Related Articles | Metrics

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FIXED POINT INDEX THEORY FOR WEAKLY INWARD MAPPINGS Han Zhiqing Acta mathematica scientia,Series B. 1997, 17 (4):  455-462.  Abstract ( 68 )   RICH HTML PDF (461KB) ( 33 )   Save In this paper we define a fixed point index theory for locally Lip., completely continuous and weakdy inward mappings defined on closed convex sets in general Banach spaces where no other artificial conditions are imposed. This makes us to deal with these kinds of mappings more easily. As obvious applications, some results in[3],[5],[7],[9],[10] are deepened and extended. Related Articles | Metrics

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QUANTITATIVE THEOREM AND SATURATION THEOREM FOR MULTIVARIATE RANDOM FUNCTIONS Zhao Jinghui Acta mathematica scientia,Series B. 1997, 17 (4):  463-470.  Abstract ( 56 )   RICH HTML PDF (427KB) ( 30 )   Save In this paper, we give the quantitative theorem and saturation theorem for random functions with compact convex parameter spaces. Related Articles | Metrics

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SOME CHARACTERIZATIONS OF α-BLOCH SPACES ON THE UNIT BALL OF Cn Yang Weisheng Acta mathematica scientia,Series B. 1997, 17 (4):  471-477.  Abstract ( 50 )   RICH HTML PDF (354KB) ( 32 )   Save In this paper,we get the invariant gradient characterizations and β-Carleson measure characterization of α-Bloch functions.Two examples are also given to show that the condition about α is the best. Related Articles | Metrics