中国科学院数学与系统科学研究院期刊网

Acta Mathematica Sinica, Chinese Series 1998 Vol.41

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The Axisymmetric H 1(R 3) Solution for 3 D Incompressible Euler Equation
HuiCheng Yin,QingJiu Qiu
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0021
Abstract （2506）      PDF（pc） （413KB）（812）       Save
Under some conditions, we prove the existence of H 1(R 3) solutions for the 3 D incompressible Euler equations with axisymmetric initial data.
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Estimate of Exponential Convergence Rate in Total Variation by Spectral Gap

MuFa Chen

Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0001
Abstract （2837）      PDF（pc） （480KB）（876）       Save
This note is devoted to study the exponential convergence rate in the total variation for reversible Markov processes by comparing it with the spectral gap. It is proved that in a quite general setup, with a suitable restriction on the initial distributions, the rate is bounded from below by the spectral gap. Furthermore, in the compact case or for birth death processes or half line diffusions, the rate is shown to be equal to the spectral gap.
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Graded Rings and Localizations
ShengGui Zhang
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0002
Abstract （2131）      PDF（pc） （298KB）（765）       Save
Suppose G is a finite group, R is a graded ring of type G with identity and S is a multiplicatively closed subset of the set consisting of all homogeneous elements of R. Let =x∈Gae(gx,x)a∈S, Deg (a)=g∈G] and S==x∈ G ae (gx,xh)a ∈S, Deg (a)=g∈ G, h∈ G. M G(R) denotes the matrices over R with the rows columns indexed by elements of G. In this paper, we prove that R satisfies the left Ore condition with S if and only if R# G satisfies the left Ore condition with  if and only if M G(R) satisfies the left Ore condition with S=. Inaddition, we obtained the following results:  -1 (R# G) is isomorphic to (S -1 R)# G and S=, -1 (M G(R)) is isomorphic to M G(S -1 R) as rings.
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Strong Approximation Theorems with Applications for Strongly Mixing Random Variables Sequence
Bing Xu
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0003
Abstract （2772）      PDF（pc） （405KB）（780）       Save
This paper provides a “independent identically copy” way to establish the strong approximation theorems for strongly mixing random variables by using a special result of Sakhanenko(1984) for independent random variables. Application to increments of partial sums isdiscussed.
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Strongly Singular Convolution Operators on the Weighted Herz type Hardy Spaces
XiaoChun Li,ShanZhen Lu
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0007
Abstract （3372）      PDF（pc） （409KB）（998）       Save
In this paper the authors prove that the strongly singular integral operators are bounded from the homogeneous weighted Herz type Hardy spaces to the homogeneous weighted Herz spaces.
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The Series of Convex Functions on a Banach Space
XiYin Zheng
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0008
Abstract （2847）      PDF（pc） （394KB）（907）       Save
The series of convex functions on a Banach space is studied. The generalizations of the Moreau Rockafellar theorem are given. As an application, the partial generalization of the Kuhn Tucker theorem is obtained.
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On Limit Cycles of Type I Equation of Quadratic Differential Systems
XiaoGui Li
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0009
Abstract （3623）      PDF（pc） （404KB）（986）       Save
In this paper, the problem on limit cycles of Type I equation of quadratic differential systems dx/dt=-y+δx+lx 2+mxy+ny 2,dy/dt=x has been researched. It obtained the existential condition of limit cycles on large range when l=0 .Furthermore, the paper also discussed the existence problem of boundary line cycles (strange limit cycles) and bifurcation curve.
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Basic Connected Representation finite Algebras having Normed Multiplicative Bases with 1 Relations
HaiLou Yao(1),HaiXiao Liu(2)
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0010
Abstract （3273）      PDF（pc） （414KB）（973）       Save
In this paper we determine all basic connected, finite dimensional algebras with finite representation type over an algebraically closed field which have normed multiplicative bases with 1 relations.
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A Generalization for Estimation Theorem on Modulus of Convexity
ChangSen Yang(1),JunFeng Zhao(
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0004
Abstract （2857）      PDF（pc） （284KB）（800）       Save
In this paper, we prove that the modulus of convexity for Banach spaces X and L p(X) satisfy the following inequalities: aδ X(bε p/2 )δ L p(X) (ε)δ X (ε), p2); cδ X(dε)δ L p(X) (ε)δ X (ε),(1
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Finite Rank Operators in Some Ideals of Nest Algebras
FangYan Lu,ShiJie Lu
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0005
Abstract （5643）      PDF（pc） （362KB）（964）       Save
In this paper, we investigate finite rank operators in ideals of nest algebras.And then we use properties of finite rank operators to characterize such ideals.
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Quenching Phenomenon for Quasilinear Parabolic Equation
QiuYi Dai
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0006
Abstract （3015）      PDF（pc） （509KB）（918）       Save
In this paper, we investigate initial bound ary value problem of a class of quasilinear parabolic equation. The quenching phenomenon is obtained, and the asymptotic behavior of quenching solution is analyzed. The results which we obtain include the correspond conclusions of .
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On Strictly Real Hilbert Rings
GuangXing Zeng
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0011
Abstract （2463）      PDF（pc） （334KB）（878）       Save
In this paper, strictly real Hilbert rings are further investigated. In order to characterize strictly real Hilbert rings, we prove the following results: Let A be a commutative ring with 1, and let A be the polynomial ring over A in one variable X . Then (1) A is a strictly real Hilbert ring if and only if every real maximal ideal of A contracts in A to a maximal ideal;(2) A is a strictly real Hilbert ring if and only if A is a real Hilbert ring, and every real maximal ideal of A is maximal.
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Multiple Positive Solutions of Some Nonlinear Operator Equations and Applications
FuYi Li(1),ZhaoLi Liu(2)
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0012
Abstract （3884）      PDF（pc） （403KB）（1063）       Save
In this paper, several existence theorems on multiple positive solutions of some nonlinear operator equations are obtained. The results are applied to nonlinear Hammerstein integral equations and Sturm Liouville two point boundary value problems, moreover, some new conclusions are given.
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Poincaré-Bertrand Transformation Formulae of the Singular Integrals in Clifford Analysis
Sha Huang
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0013
Abstract （3504）      PDF（pc） （444KB）（776）       Save
In this paper, by thinking of the complex analysis in several variables, we prove the Poincaré-Bertrand transformation formulae of the singular integrals in Clifford analysis.
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The Spectral Multiplier Theorem for the Generalized Sublaplacian
ZhenQiu Zhang(1),PeiCai Xuan(2
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0014
Abstract （3170）      PDF（pc） （406KB）（745）       Save
In this paper, by establishing Littlewood-Paley theory associated with the generalized Sublaplacian L, we obtain the spectral multipliers theorem for L. As a consequence, the multipliers for a certain kind of Laguerre expansions are given.
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Analytic Solutions for a Class Second Order Interative Functional Differential Equations
WenRong Li
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0015
Abstract （3505）      PDF（pc） （362KB）（854）       Save
In this paper, by the method of majorant to give some existence theorems of the analytic solutions of a class second order iterative functional differential equations x″(z)=mj=0 p j x j(z) (where z∈ C, m 2 is a positive integer, and x j(z) denotes the m-th iterate of the unknown function x(z)).
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The Isometric Approximation Problems from Finite-dimensional Normed Space into C( Ω )
DaPeng Zhan
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0016
Abstract （2691）      PDF（pc） （411KB）（752）       Save
This paper discusses the isometric approximation problem from a finite dimensional normed space X into an infinite dimensional space C( Ω ). And it shows that the answer of the problem is negative if and only if X is not a subspace of any l ∞ n (n∈N) and Ω has infinite isolated points.
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Three Dimensional Compact Minimal Submanifolds in a Sphere
BaoQiang Wu(1),HongZao Song(2)
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0017
Abstract （3077）      PDF（pc） （395KB）（931）       Save
In this paper, we give some rigidity theorems which concern with 3-dim compact minimal submanifolds in a hight-dim sphere. Under a global pinching condition, the pinching constant on the scalar curvature is improved. We also study the problem of rigidity of Ricci curvature.
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Small Random Perturbations of One-dimensional Diffusion Processes
FuBao Xi
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0018
Abstract （2777）      PDF（pc） （355KB）（772）       Save
In the present paper we consider the small random perturbations of one-dimensional diffusion processes. By virtue of stochastic analysis methods, we investigate the asymptotics of the mean exit times and probabilistical estimates of the exit times as the perturbations tend to zero.
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The Lower Type and the Proximate Lower Order of the Analytic Function Defined by Laplace-Stieltjes Transform
XiuYing You
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0019
Abstract （2556）      PDF（pc） （378KB）（839）       Save
The defined lower type and proximate lower order for the analytic function defined by Laplace-Stieltjes transform in the half plane σ>0; we establish the relations between the proximate lower order and lower type of the transform and “coefficients” and “exponent”. It is the lower type′s sufficient and necessary conditions, extending the corresponding results of Dirichlet series.
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Oscillation of Solutions of Impulsive Neutral Delay Differential Equations
YuZhu Zhang(1),XinYi Dang(2)
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0020
Abstract （3999）      PDF（pc） （374KB）（963）       Save
Consider the impulsive neutral delay differential equation [y(t)+Py(t-τ)]′ +Q(t) y(t-σ)=0,t 0, t≠ t k, k=1,2,…, y(t + k) -y(t - k)=b k y(t k), k=1,2,…, (E)where τ,σ and P are constants, τ>0, σ>0, Q(t)∈ C([0,∞), R +), b k >-1, k=1,2,…. Sufficient conditions are given to insure that all solutions of Eq. (E) are oscillatory for the respective cases P -1, -1

<0 and P>0.

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Bifurcation of Nonlinear Problems Modeling Flows through Porous Media
Xi Yu LIU
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0027
Abstract （2615）            Save
This paper deals with a class of nonlinear boundary value problems which appears in the study of models of flows through porous media. Existence results of asymptotic bifurcation and continua are reported both for operator equations and for boundary value problems.
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Z Automata and Partition Logics
Rong Fang BIE,En Shao SHEN
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0022
Abstract （1866）            Save
This paper divides Z automata into pairs of ω automata, develops the L(MP) theory of Z . Using the technique of Z automata, it proves that the L (MP) theory of Z is decidable. As an application it also proves that the correctness problem for the finite state process is decidable.
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Study of a Class of Stationary Optimal Stochastic Controls of Impulse Type
Shi Liang SUN,Kun Hui LIU
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): null-.   DOI: 10.12386/A1998sxxb0025
Abstract （2681）            Save
This paper studies a class of stationary impulse control models, not only proves the existence of optimal impulse control but also constructs an optimal control.
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Estimate of Exponential Conver
Mufa Chen
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): 1-6.   DOI: 10.12386/A1998sxxb0030
Abstract （2436）            Save
This note is devoted to study
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Strongly Singular Convolution
,Shan Zhen LU
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): 7-18.   DOI: 10.12386/A1998sxxb0031
Abstract （2811）            Save
In this paper the authors prov
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The Axisymmetric $H^1(\BR^3)$
,
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): 29-38.   DOI: 10.12386/A1998sxxb0033
Abstract （1643）            Save
Under some conditions, we prov
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An Infinite Matrix Converge

JunDe Wu(1),RongLu Li(2),WenBo
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): 39-004.   DOI: 10.12386/A1998sxxb0034
Abstract （2584）      PDF（pc） （376KB）（734）       Save
In this paper, an infinite mat
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Basic Connected Representation
Hai Lou YAO,Hai Xia LIU
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): 55-66.   DOI: 10.12386/A1998sxxb0036
Abstract （10021）            Save
In this paper we determine all
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$Z$-Automata and Partition

RongFang Bie,EnShao Shen
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): 67-007.   DOI: 10.12386/A1998sxxb0037
Abstract （2182）      PDF（pc） （521KB）（720）       Save
This paper divides $Z$-automat
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On Limit Cycles of Type I Equa
Xiao Gui LI
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): 75-80.   DOI: 10.12386/A1998sxxb0038
Abstract （7258）            Save
In this paper, the problem on
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Quenching Phenomenon for Quasi
Qiu Yi DAI
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): 87-96.   DOI: 10.12386/A1998sxxb0040
Abstract （2836）            Save
In this paper, we investigate
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Multiple Positive Solutions of
Fu Yi LI,Zhao Li LIU
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): 97-102.   DOI: 10.12386/A1998sxxb0041
Abstract （3533）            Save
In this paper, several existen
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Bifurcation of Nonlinear Pr

XiYu Liu
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): 107-011.   DOI: 10.12386/A1998sxxb0043
Abstract （2189）      PDF（pc） （377KB）（371）       Save
This paper deals with a class
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Poincar\'e-Bertrand Transforma
Sha HUANG
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): 119-126.   DOI: 10.12386/A1998sxxb0045
Abstract （3712）            Save
In this paper, by thinking of
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An Approach to the Superpro

YongJin Wang
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): 127-013.   DOI: 10.12386/A1998sxxb0046
Abstract （1953）      PDF（pc） （518KB）（248）       Save
In this paper, we consider the
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Asymptotic Expansions of He

FaEn Wu
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): 145-015.   DOI: 10.12386/A1998sxxb0048
Abstract （3605）      PDF（pc） （401KB）（288）       Save
We calculated the first five t
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Toeplitz Operators on Discr

QingXiang Xu(1),XiaoMan Chen(2
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): 161-016.   DOI: 10.12386/A1998sxxb0050
Abstract （2629）      PDF（pc） （376KB）（270）       Save
In this paper, the finitely li
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Analytic Solutions for a Cl

WenRong Li
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): 167-017.   DOI: 10.12386/A1998sxxb0051
Abstract （4608）      PDF（pc） （362KB）（235）       Save
In this paper, by the method o
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The Isometric Approximation Pr
Da Peng ZHAN
Acta Mathematica Sinica, Chinese Series    1998, 41 (1): 177-184.   DOI: 10.12386/A1998sxxb0053
Abstract （1971）            Save
This paper discusses the isome
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