A NOTE FOR THE TOPOLOGICAL CLASSIFICATION OF STRUCTURALLY STABLE QUADRATIC DIFFERENTIAL SYSTEMS WITHOUT LIMIT CYCLES

ＡＮＯＴＥＦＯＲＴＨＥＴＯＰＯＬＯＧＩＣＡＬＣＬＡＳＳＩＦＩＣＡＴＩＯＮＯＦＳＴＲＵＣＴＵＲＡＬＬＹＳＴＡＢＬＥＱＵＡＤＲＡＴＩＣＤＩＦＦＥＲＥＮＴＩＡＬＳＹＳＴＥＭＳＷＩＴＨＯＵＴＬＩＭＩＴＣＹＣＬＥＳ￥ＹｅＷｅｉｙｉｎ（叶惟寅）（ＮａｎｊｉｎｇＮ...     

A NOTE ON REGULARITY AND EXISTENCE OF SOLUTIONS FOR A CLASS OF NON－UNIFORMLY DEGENERATE ELLIPTIC EQUATIONS

ＡＮＯＴＥＯＮＲＥＧＵＬＡＲＩＴＹＡＮＤＥＸＩＳＴＥＮＣＥＯＦＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＮＯＮ－ＵＮＩＦＯＲＭＬＹＤＥＧＥＮＥＲＡＴＥＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳ￥ＬＩＪＵＮＪＩＥ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＺｈｅｊｉａｎｇＵｎｉ...     

UNIFORM BOUNDEDNESS AND UNIFORM STABILITY OF A KIND OF DELAY──DIFFERENTIAL EQUATIONS

ＵＮＩＦＯＲＭＢＯＵＮＤＥＤＮＥＳＳＡＮＤＵＮＩＦＯＲＭＳＴＡＢＩＬＩＴＹＯＦＡＫＩＮＤＯＦＤＥＬＡＹ──ＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＺｈｅｎｇＢｕｎａｎ（ＧｕａｎｇｘｉＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｔｈｉｓｐａ...     

UNIFORM CONVERGENCY FOR WEIGHTED PERIODOGRAM OF STATIONARY LINEAR RANDOM FIELDS

ＵＮＩＦＯＲＭＣＯＮＶＥＲＧＥＮＣＹＦＯＲＷＥＩＧＨＴＥＤＰＥＲＩＯＤＯＧＲＡＭＯＦＳＴＡＴＩＯＮＡＲＹＬＩＮＥＡＲＲＡＮＤＯＭＦＩＥＬＤＳ￥ＨＥＳＨＵＹＵＡＮＡｂｓｔｒａｃｔ：Ｌｅｔ｛Ｘｎ；ｎ∈Ｎ２｝ｂｅａｔｗｏｄｉｍｅｎｓｉｏｎａｌｌｙｉｎｄｅｘ...     

ON THE FUNDAMENTAL PROBLEM FOR AN INFINITE ELASTIC PLANE BONDED BY DIFFERENT ANISOTROPIC MATERIALS WITH CRACKS

ＯＮＴＨＥＦＵＮＤＡＭＥＮＴＡＬＰＲＯＢＬＥＭＦＯＲＡＮＩＮＦＩＮＩＴＥＥＬＡＳＴＩＣＰＬＡＮＥＢＯＮＤＥＤＢＹＤＩＦＦＥＲＥＮＴＡＮＩＳＯＴＲＯＰＩＣＭＡＴＥＲＩＡＬＳＷＩＴＨＣＲＡＣＫＳＺＨＥＮＧＫＥ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃ...     

RECOGNIZING ESSENTIALLY DISCONNECTED BENZENOIDS WITH FIXED DOUBLE BONDS

ＲＥＣＯＧＮＩＺＩＮＧＥＳＳＥＮＴＩＡＬＬＹＤＩＳＣＯＮＮＥＣＴＥＤＢＥＮＺＥＮＯＩＤＳＷＩＴＨＦＩＸＥＤＤＯＵＢＬＥＢＯＮＤＳ￥ＬＩＮＫＥＲＯＮＧ；Ｓ．Ｊ．ＣＹＶＩＮ；Ｂ．Ｎ．ＣＹＶＩＮ；ＣＨＥＮＲＯＮＧＳＩ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａ...     

A NOTE ON THE STRONG CONSISTENCY OF ESTEMATES IN PARTIALLY LINEAR MODELS

ＡＮＯＴＥＯＮＴＨＥＳＴＲＯＮＧＣＯＮＳＩＳＴＥＮＣＹＯＦＥＳＴＥＭＡＴＥＳＩＮ　ＰＡＲＴＩＡＬＬＹ　ＬＩＮＥＡＲ　ＭＯＤＥＬＳＺｈｕＬｉｘｉｎｇ；（朱力行）ＡｎＨｏｎｇｚｈｉ（安鸿志）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，Ｃ...     

带有热传导的波动方程组的无条件稳定二阶收敛的差分格式

带有热传导的波动方程组的无条件稳定二阶收敛的差分格式孙志忠（东南大学数学力学系）ＡＮＵＮＣＯＮＤＩＴＩＯＮＡＬＬＹＳＴＡＢＬＥＡＮＤＳＥＣＯＮＤ－ＯＲＤＥＲＣＯＮＶＥＲＧＥＮＴＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＦＯＲＴＨＥＳＹＳＴＥＭＯＦＷＡＶＥＥＱＵ...     

UNIQUENESS AND ITERATIVE METHOD OF POSITIVE RADIALLY SYMMETRIC SOLUTIONS FOR SINGULAR ELLIPTIC EQUATIONS

ＵＮＩＱＵＥＮＥＳＳＡＮＤＩＴＥＲＡＴＩＶＥＭＥＴＨＯＤＯＦＰＯＳＩＴＩＶＥＲＡＤＩＡＬＬＹＳＹＭＭＥＴＲＩＣＳＯＬＵＴＩＯＮＳＦＯＲＳＩＮＧＵＬＡＲＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳ￥ＺｈａｏＺｅｎｇｑｉｎ（赵增勤）（ＱｕｆｕＮｏｒｍａｌＵｎｉｖｅ...     

Euler族算法的一般收敛性

Ｅｕｌｅｒ族算法的一般收敛性傅晓阳（中国银行浙江省分行电脑部，杭州３１０００６）周幼英（杭州大学数学系，杭州３１００２８）ＧＥＮＥＲＡＬＬＹＣＯＮＶＥＲＧＥＮＣＥＯＦＡＦＡＭＩＬＹＯＦＥＵＬＥＲ＇ＳＡＬＧＯＲＯＴＨＭＳ￥ＦＵＸＩＡＯＹＡＮＧ（Ｃｏｍｐ...     

关于球面的紧子流形

本文讨论单位球面的紧致子流形的Pinching问题.改进了S.T.Yan与莫小欢有关球面中具有平行平均曲率的紧致子流形的Pinching常数及S.S.Chern等与沈一兵有关紧致极小子流形的Pinching常数.对截曲率的情形,本文还改进了沈一兵有关截曲率的Pinching常数.     

关于单位球面的子流形的一个Pinching定理

设Ｍ是单位球面的一个浸入子流形，ＵＭ＝∪ＵＭｘ是Ｍ的单位切丛.本文研究函数ｆ（ｘ）＝ｍａｘ－Ｂ（ｕ，ｕ）－Ｂ（ｖ，ｖ）２。其中Ｂ是Ｍ的第二基本形式．当Ｍ具平行平均曲率时，我们给出关于第二基本形式的一个Ｐｉｎｃｈｉｎｇ定理．对Ｍ是极小的情形，我们有相同的讨论．     

Lower bounds for eigenvalues of the Dirac-Witten operator

We get optimal lower bounds for the eigenvalues of the Dirac-Witten operator of compact(with or without boundary) spacelike hypersurfaces of Lorentian manifold satisfying certain conditions,just in terms of the mean curvature and the scalar curvature and the spinor energy-momentum tensor. In the limiting case,the spacelike hypersurface is either maximal and Einstein manifold with positive scalar curvature or Ricci-flat manifold with nonzero constant mean curvature.     

COMPLETE HYPERSURFACES WITH CONSTANT MEAN CURVATURE AND FINITE INDEX IN HYPERBOLIC SPACES

In this article, we prove that any complete finite index hypersurface in the hyperbolic space H4(-1)(H5(-1)) with constant mean curvature H satisfying H2 > 6634 (H2 > 114785 respectively) must be compact. Specially, we verify that any complete and stable hypersurface in the hyperbolic space H4(-1) (resp. H5(-1)) with constant mean curvature H satisfying H2 > 6643 (resp. H2 > 114785 ) must be compact. It shows that there is no manifold satisfying the conditions of some theorems in [7, 9].     

具有负数量曲率的紧致黎曼流形的Killing向量场

本文研究了具有负数量曲率的紧致黎曼流形上的Killing向量场.利用Bochner方法,得到在此类流形上非平凡的Killing向量场的存在的必要条件.这个结果拓广了文献[6]中的定理1.     

有关法曲率的若干性质

以[2]中经典微分几何问题为切入点,运用复数与三角工具广泛深入地探讨了“过曲面上一点有n条切线,若相邻两条切线的交角为2nπ,曲面法线与切线所定平面截得曲线的曲率半径为ρ1,ρ2,ρ3,…,ρn时,∑ni=11ρim,∑ni=1ρi,∏ni=1ρi的结果”,得到了法曲率与相关的三个有趣定理.     

单位球面的三维紧致极小子流形

本文得到高维球面上三维紧致极小子流形的若干刚性定理．在一个整体拚挤条件下，数量曲率的拚挤常数被改进了，也对李奇曲率的拚挤问题进行了讨论．     

The Huber theorem for non-compact conformally flat manifolds

It was proved in 1957 by Huber that any complete surface with integrable Gauss curvature is conformally equivalent to a compact surface with a finite number of points removed. Counterexamples show that the curvature assumption must necessarily be strengthened in order to get an analogous conclusion in higher dimensions. We show in this paper that any non compact Riemannian manifold with finite -norm of the Ricci curvature satisfies Huber-type conclusions if either it is a conformal domain with volume growth controlled from above in a compact Riemannian manifold or if it is conformally flat of dimension 4 and a natural Sobolev inequality together with a mild scalar curvature decay assumption hold. We also get partial results in other dimensions. Received: April 14, 2000; revised version: March 20, 2001     

A Theorem on Infinitesimal I-isometry of Surfaces Immersed in a Space with Constant Curvature

1.IntroductionTheproblemsofinfinitesimalrigidityandisometricdeformationhavebeenextensivelyin-vestigatedforsurfacesinthreedimensionalEuclideanspaceE'.See,forexample,A.SvecL1]'E.Kann[2j,ZhouJiazu[3Jandthepapers[4j,[5J,[6JbyYangWenmao3also,KobayashiandNomizu[7].ThefirstauthorandZhangGaoyonggeneralizedthetheoryofinfinitesimali-sometriesofsurfacesinE3tothehypersurfacesimmersedinaspaceofconstantcurvature[8j.K.Tenenblat[9]andR.A.GoldsteinandP.J.Ryan[1o]studiedtheinfinitesimalI-isometryfors…     

复射影空间中具有平行平均曲率向量的全实叶的Pinching定理

本文研究了复射影空间中具有平行平均曲率向量的黎曼叶状结构(F).利用Nalcagawa 和Takagi的计算散度的方法,得到了复射影窄问中具有平行平均曲率向量的黎曼叶状结构(F)上向量场的散度,证明了其上的一个整体Pinching定理,从而将复射影空间中任何具有极小法平面场的调和叶的仵质推广到复射影窄间中具有平行平均曲率向量的黎曼叶状结构(F)上.