高维常平均曲率超曲面的数量曲率的空隙

本文证明了当高维球面中闭常平均曲率超曲面Ｍ＾ｎ的平均曲率│Ｈ│＜Ｃ（ｎ）时，若Ｍ的数量曲率Ｒ为常数，则Ｒ不属于［ａ（ｎ，Ｈ），ａ（ｎ，Ｈ）＋ｎ／４），其中ａ（ｎ，Ｈ）＝ｎ（ｎ－９／４）＋ｎ＾２（ｎ－２）／２（ｎ－１）Ｈ＾２－ｎ（ｎ－２）／２（ｎ－１）√ｎ＾２Ｈ＾４＋４（ｎ－１）Ｈ＾２。     

A generalization of the classical sphere theorem

In this paper, we prove a sphere theorem for Riemannian manifolds with partially positive curvature which generalizes the classical sphere theorem.

     

On an inequality of Oprea for Lagrangian submanifolds

We show that a Lagrangian submanifold of a complex space form attaining equality in the inequality obtained by Oprea in [8], must be totally geodesic.      

On the Essential Spectrum of the Laplacian and Vague Convergence of the Curvature at Infinity

We shall prove that under some volume growth condition, the essential spectrum of the Laplacian contains the interval [(n ? 1)² K/4, ∞) if an n-dimensional Rieman-nian manifold has an end and the average of the part of the Ricci curvature on the end which lies below a nonpositive constant (n ? 1)K converges to zero at infinity.     

Dimension and local structures of attracting manifolds of smooth dynamical systems

We give a numerical algorithm to compute the dimension and local structures of attracting sets or invariant manifolds of smooth dynamical systems. This algorithm is based on local adaptive Galerkin bases and is tested for several examples. The important degrees of freedom that are preferentially selected, from the geometrical point of view, are found.     

关于曲线ρ=r＋αa＋b∫s0^s βds的曲率和挠率的计算

已知曲线Γ：r=r（s）的基本向量α、β、γ且曲率和挠率分别为κ、τ，本文研究了由α、β和γ所作出的曲线Γ：ρ=r＋αa＋b∫s0^s βds的曲率κ和挠率τ的计算问题。     

Rational Homotopy Theory and Nonnegative Curvature

in this note, we answer positively a question by Belegradek and Kapovitch about the relation between rational homotopy theory and a problem in Riemannian geometry which asks that total spaces of which vector bundles over compact non-negative curved manifolds admit （complete） metrics with non-negative curvature.     

ASSESSMENT OF LOCAL INFLUENCE ONCOX'S PROPORTIONAL HAZARDS MODEL

1.IntroductionTheproportionalhazardsregressionmodelisasemiparametricmodel.Theloglikelihoodforthismodelisasumoverrisksets.Theperturbationofoneobservationedictsseveraloftheserisksets.Thus,theassessmentofcaseinfluenceismorecomplexforthismodelthanlinearandgeneralizedlinearmodels.TheglobalialluenceofindividualcaseonregressionparameterestimatesforCox'smodelhasbeenanalysedbyCainandLange[4],ReidandCrepeaull4],etal.TheideaofdtherentiationinsteadofdeletionisprominentinthelocalinduenceapproachofCook[…     

欧氏空间中紧致超曲面的欧氏直径的一点注记

本文对欧氏空间中分别具有给定截面曲率和Ｒｉｃｃｉ曲率的紧致超曲面的欧氏直径做了估计     

Assessment of local influence on Cox’s proportional hazards model

The second order approach of local influence (see [15]) is developed and applied to Cox’s proportional hazards model, and compared with Cook's local influence approach (see [6] and [13]) which was used in this model. To study local influence, we perturb not only all cases simultaneously, but also cases individually to obtain “direction curvature” in directionl and “curvature” for single case. Some examples are used to illustrate these methods. This work is supported by the Youth Science Foundation of Peking University and a research grant from State Educational Committee     

Surface billiards and nonvanishing Lyapunov exponents

We study in this paper the billiards on surfaces with mix-valued Gaussian curvature and the condition which gives nonvanishing Lyapunov exponents of the system. We introduce a criterion upon which a small perturbation of the surface will also produce a system with positive Lyapunov exponents. Some examples of such surfaces are given in this article.     

关于曲线ρ=r+αα+b integral from n=s_0 to s βds的曲率和挠率的计算

已知曲线Γ:r=r(s)的基本向量α、β、γ且曲率和挠率分别为κ、τ,本文研究了由α、β和r所作出的曲线Γ:ρ=r+aα+b integral from n=s_0 to s βds的曲率κ-和挠率τ-的计算问题。     

曲率变化率最小约束下的五次Hermite插值曲线

本文提出了在曲率变化率最小约束条件下的五次Hermite插值曲线算法,与传统的Hermite插值曲线算法相比,利用该算法获得的插值曲线具有更均匀的曲率分布,曲线更光顺,质量更好。     

一种负高斯曲率的双三次Bézier曲面

负高斯曲率的曲面在建筑业、造船业及航空工业中都有广泛的应用。该文提出一种负高斯曲率双三次Ｂｅｚｉｅｒ曲面的构造方法，简单直观，几何意义明显。     

保持高斯映射的仿射形变

给定Ｒｉｅｍａｎｎ流形到欧氏空间的仿射浸入ｆ：　Ｍｎ→ＲＮ　　，我们建立存在另一个与ｆ有相同高斯映射的仿射浸入ｆ：Ｍｎ→ＲＮ　　的条件，进一步利用这个条件，解答了仿射浸入的高斯映射将其确定到何种程度的问题．     

Curvature variation minimizing cubic Hermite interpolants

In this paper, planar parametric Hermite cubic interpolants with small curvature variation are studied. By minimization of an appropriate approximate functional, it is shown that a unique solution of the interpolation problem exists, and has a nice geometric interpretation. The best solution of such a problem is a quadratic geometric interpolant. The optimal approximation order 4 of the solution is confirmed. The approach is combined with strain energy minimization in order to obtain G¹ cubic interpolatory spline.     

Some generalizations of Ahlfors Lemma

One of the most influential versions of the classical Schwarz–Pick Lemma is probably that of Ahlfors. Pulling back a conformal semimetric on a Riemann surface under any holomorphic map from the open unit disk equipped with a Poincaré metric, the curvature of which is assumed to bound from above the curvature of the Riemann surface, he successfully showed that a conformal semimetric to be compared with the Poincaré metric is obtained. In the present paper, we give a comparison theorem between two conformal semimetrics of variable curvature in the same spirit. Our main theorem is a local one by its nature, but global results can be derived therefrom.     

Semi-symmetric Lorentzian metrics and three-dimensional curvature homogeneity of order one

We completely classify three-dimensional semi-symmetric Lorentzian manifolds which are curvature homogeneous up to order one. Curvature restrictions for semi-symmetry turn out to be the same ones which ensure the existence on these manifolds of a degenerate parallel null line field (Chaichi et al., J. Phys. A, Math. Gen. 38, 841–850, 2005). Supported by funds of MURST, GNSAGA and University of Salento.     

A Comparison Theorem for an Elliptic Operator

In this note, using ₂ (Bakry–Emery curvature operator) and the classical maximum principle, we establish a comparison estimate for a general elliptic operator on a manifold, without using Jacobi field theory.     

类拟的Euler公式

经典的欧拉公式描述了两曲面交线的曲率和曲面的法曲率以及曲面夹角之间的关系。本文给出了R3中曲面的法曲率的欧拉公式的简单证明。并得到一个关于曲面交线曲率及曲面测地曲率的类似的欧拉公式。