AN APPLICATION OF COMPENSATED COMPACTNESS ON QUASILINEAR HYPERBOLIC SYSTEMS

ＡＮＡＰＰＬＩＣＡＴＩＯＮＯＦＣＯＭＰＥＮＳＡＴＥＤＣＯＭＰＡＣＴＮＥＳＳＯＮＱＵＡＳＩＬＩＮＥＡＲＨＹＰＥＲＢＯＬＩＣＳＹＳＴＥＭＳ￥ＬＩＵｆｕＧＵＩ（刘法贵）（ＢａｓｉｃＤｅｐａｒｔｍｅｎｔ，ＮｏｒｔｈＣｈｉｎａＩｎｓｔｉｔａｔｅｏｆＷａｔｅｒｃ...     

CLIFFORD MARTINGALES Φ-EQUIVALENCE BETWEEN S（f） AND f^＊

ＣＬＩＦＦＯＲＤＭＡＲＴＩＮＧＡＬＥＳΦ－ＥＱＵＩＶＡＬＥＮＣＥＢＥＴＷＥＥＮＳ（ｆ）ＡＮＤｆ￥ＬＯＮＧＲＵＬＩＮ；ＱＩＡＮＴＡＯ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ．）...     

USING FINITE GEOMETRIES TO CONSTRUCT 3-PBIB(2) DESIGNS AND 3-DESIGNS

ＵＳＩＮＧＦＩＮＩＴＥＧＥＯＭＥＴＲＩＥＳＴＯＣＯＮＳＴＲＵＣＴ３－ＰＢＩＢ（２）ＤＥＳＩＧＮＳＡＮＤ３－ＤＥＳＩＧＮＳ￥ＹＡＮＧＢＥＮＦＵ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＣｈｅｎｇｄｕＴｅａｃｈｅｒｓＣｏｌｌｅｇｅ，Ｃｈｅｎｇｄｕ...     

GLOBAL ANALYSIS OF AN EBENMAN＇S MODEL OF POPULATION WITH TWO COMPETING AGE CLASSES

ＧＬＯＢＡＬＡＮＡＬＹＳＩＳＯＦＡＮＥＢＥＮＭＡＮ＇ＳＭＯＤＥＬＯＦＰＯＰＵＬＡＴＩＯＮＷＩＴＨＴＷＯＣＯＭＰＥＴＩＮＧＡＧＥＣＬＡＳＳＥＳＬＩＵＷＥＩＭＩＮ（刘为民）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃａｌＳｃｉｅｎｃｅｓ，Ｉｎｄｉａｎａ...     

ON A MULTILINEAR OSCILLATORY SINGULAR INTEGRAL OPERATOR （I）

ＯＮＡＭＵＬＴＩＬＩＮＥＡＲＯＳＣＩＬＬＡＴＯＲＹＳＩＮＧＵＬＡＲＩＮＴＥＧＲＡＬＯＰＥＲＡＴＯＲ（Ｉ）ＣＨＥＮＷＥＮＧＵＨＵＧＵＯＥＮＬＵＳＨＡＮＺＨＥＮＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＯｃｔｏｂｅｒ１８，１９９４．ＲｅｖｉｓｅｄＤｅｃｅ...     

LIMIT SETS OF A CLASS OF FOUR-DIMENSIONAL COMPETITIVE SYSTEMS

ＬＩＭＩＴＳＥＴＳＯＦＡＣＬＡＳＳＯＦＦＯＵＲ－ＤＩＭＥＮＳＩＯＮＡＬＣＯＭＰＥＴＩＴＩＶＥＳＹＳＴＥＭＳＲｕａｎＪｉａｎｃｈｅｎｇ（阮建成）（ＪｉｎａｎＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ａ．Ｊ．Ｓｃｈｗａｒｔｚ［９］ｓｔｕｄｉｅｄＣ２ｄｙｎａ...     

MARKOV DECISION PROGRAMMING WITH CONSTRAINTS

ＭＡＲＫＯＶＤＥＣＩＳＩＯＮＰＲＯＧＲＡＭＭＩＮＧＷＩＴＨＣＯＮＳＴＲＡＩＮＴＳＬＩＵＪＩＡＮＹＯＮＧ（刘建庸）；ＬＩＵＫＥ（刘克）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，...     

SOME KINDS OF LIAPUNOV FUNCTIONAL IN STABILITY THEORY OF RFDE

ＳＯＭＥＫＩＮＤＳＯＦＬＩＡＰＵＮＯＶＦＵＮＣＴＩＯＮＡＬＩＮＳＴＡＢＩＬＩＴＹＴＨＥＯＲＹＯＦＲＦＤＥＤＵＸＵＥＴＡＮＧ（杜雪堂）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｕｎａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｓｈａ４１００...     

COMPLETE EXTREMAL SURFACES OF MIXED TYPE IN 3-DIMENSIONAL MINKOWSKI SPACE

ＣＯＭＰＬＥＴＥＥＸＴＲＥＭＡＬＳＵＲＦＡＣＥＳＯＦＭＩＸＥＤＴＹＰＥＩＮ３－ＤＩＭＥＮＳＩＯＮＡＬＭＩＮＫＯＷＳＫＩＳＰＡＣＥ￥ＧＵＣＨＡＯＨＡＯ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＦｕｄａｎＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈａｉ２００...     

FINITE TRAVELING WAVES FOR A REACTION-DIFFUSION SYSTEM WITH N（≥3） COMPONENTS

ＦＩＮＩＴＥＴＲＡＶＥＬＩＮＧＷＡＶＥＳＦＯＲＡＲＥＡＣＴＩＯＮ┐ＤＩＦＦＵＳＩＯＮＳＹＳＴＥＭＷＩＴＨＮ（３）ＣＯＭＰＯＮＥＮＴＳＷＡＮＧＳＨＵ,ＷＥＮＳＨＩＨＬＩＡＮＧＡＮＤＹＥＱＩＸＩＡＯＡｂｓｔｒａｃｔ．Ｉｎｔｈｉｓｐａｐｅｒ,ｔｈｅｅｘ...     

A five-dimensional Riemannian manifold with an irreducible SO(3)-structure as a model of abstract statistical manifold

In the present paper, we consider a five-dimensional Riemannian manifold with an irreducible SO(3)-structure as an example of an abstract statistical manifold. We prove that if a five-dimensional Riemannian manifold with an irreducible SO(3)-structure is a statistical manifold of constant curvature, then the metric of the Riemannian manifold is an Einstein metric. In addition, we show that a five-dimensional Euclidean sphere with an irreducible SO(3)-structure cannot be a conjugate symmetric statistical manifold. Finally, we show some results for a five-dimensional Riemannian manifold with a nearly integrable SO(3)-structure. For example, we prove that the structure tensor of a nearly integrable SO(3)-structure on a five-dimensional Riemannian manifold is a harmonic symmetric tensor and it defines the first integral of third order of the equations of geodesics. Moreover, we consider some topological properties of five-dimensional compact and conformally flat Riemannian manifolds with irreducible SO(3)-structure.     

Locally symmetric left invariant Riemannian metrics on 3‐dimensional Lie groups

In this paper, we use the powerful tool Milnor bases to determine all the locally symmetric left invariant Riemannian metrics up to automorphism, on 3‐dimensional connected and simply connected Lie groups, by solving system of polynomial equations of constants structure of each Lie algebra . Moreover, we show that E ₀(2) is the only 3‐dimensional Lie group with locally symmetric left invariant Riemannian metrics which are not symmetric.     

Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram

The local geometry of a Riemannian symmetric space is described completely by the Riemannian metric and the Riemannian curvature tensor of the space. In the present article I describe how to compute these tensors for any Riemannian symmetric space from its Satake diagram, in a way that is suited for the use with computer algebra systems; an example implementation for Maple Version 10 can be found on . As an example application, the totally geodesic submanifolds of the Riemannian symmetric space SU(3)/SO(3) are classified.      

Almost everywhere convergence of Riesz means on noncompact symmetric spaceSL(3,H)/Sp(3)

LetG/K be the noncompact Riemannian symmetric spaceSL(3,H)/Sp(3). We shall prove in this paper that forf∈L ^p(SL(3,H)/Sp(3)), 1≤p≤2, the Riesz means of orderz off with respect to the eigenfunctions expansion of Laplace operator almost everywhere converge tof for Rez >δ(n,p). The critical index δ(n,p) is the same as in the classical Stein's result for Euclidean space, and as in the noncompact symmetric spaces of rank one and of complex type. Partially supported by National Natural Science Foundation of China     

对称空间SU~*(2n)/sp(n)上的Busemann函数

Busemann函数在对完备Riemann流形上的拓扑与几何问题的研究中起作十分重要的作用。而显式求出一个域上的Busemann函数将有助于一些问题的解决。在本文中,我们显式求出了对称空间SU~*(2n)/sp(n)上的Busemann函数。     

Symmetric submanifolds associated with irreducible symmetric R-spaces

We construct examples of symmetric submanifolds in Riemannian symmetric spaces of noncompact type and obtain the classification of symmetric submanifolds in irreducible Riemannian symmetric spaces of noncompact type and rank greater than one. This finishes the classification problem of symmetric submanifolds in Riemannian symmetric spaces completely.     

Pseudo-Riemannian weakly symmetric manifolds

There is a well-developed theory of weakly symmetric Riemannian manifolds. Here it is shown that several results in the Riemannian case are also valid for weakly symmetric pseudo-Riemannian manifolds, but some require additional hypotheses. The topics discussed are homogeneity, geodesic completeness, the geodesic orbit property, weak symmetries, and the structure of the nilradical of the isometry group. Also, we give a number of examples of weakly symmetric pseudo-Riemannian manifolds, some mirroring the Riemannian case and some indicating the problems in extending Riemannian results to weakly symmetric pseudo-Riemannian spaces.     

n-Marked黎曼球面的对称性

本文讨论了n-marked黎曼球面模空间上自然的对称群作用,计算出其全部的不动点及n-marked黎曼球面的对称类型,同时讨论了黎曼球面上SL(2,C)作用的动力系统特征,得出其周期性的一个描述,并在这些基础上给出n-punctured黎曼球面模空间的奇性刻画．     

On the complete decomposition of curvature tensors of Riemannian manifolds with symmetric connection

We give a complete decomposition of the space of curvature tensors with the symmetry properties as the curvature tensor associated with a symmetric connection of Riemannian manifold. We solve the problem under the action ofS0(n). The dimensions of the factors, the projections, their norms and the quadratic invariants of a curvature tensor are determined. Several applications for Riemannian manifolds with symmetric connection are given. The group of projective transformations of a Riemannian manifold and its subgroups are considered.