Two-Parametric Compound Binomial Approximations

We consider two-parametric compound binomial approximation of the generalized Poisson binomial distribution. We show that the accuracy of approximation essentially depends on the symmetry or shifting of distributions and construct asymptotic expansions. For the proofs, we combine the properties of norms with the results for convolutions of symmetric and shifted distributions. In the lattice case, we use the characteristic function method. In the case of almost binomial approximation, we apply Steins method.__________Published in Lietuvos Matematikos Rinkinys, Vol. 44, No. 4, pp. 443–466, October–December, 2004.     

非负Ricci曲率开流形的拓扑

我们证明了对于具有非负Rieei曲率,大体积增长且内半径下有界的完备n维Riemann流形,只要存在常数C>0使得 则它微分同胚于欧式空间Rn.我们还证明了在某些pinching条件下具有非负射线曲率的完备n维Riemarm流形微分同胚与Rn,改进了已知的结果.     

Nonnegatively Curved Metrics on S 2 × ℝ2

We classify the complete metrics of nonnegative sectional curvature on M ² × ², where M ² is any compact 2-manifold.     

B(A)CKLUND TRANSFORMATION ON SURFACES WITH CONSTANT MEAN CURVATURE IN R2'1

In this paper,the authors obtain the Backlund transformation on time-like surfaces with constant mean curvature in R2,1.Using this transformation,families of surfaces with constant mean curvature from known ones can be constructed.     

Hilbert polynomials and Arveson's curvature invariant

We define and study Hilbert polynomials for certain holomorphic Hilbert spaces. We obtain several estimates for these polynomials and their coefficients. Our estimates inspire us to investigate the connection between the leading coefficients of Hilbert polynomials for invariant subspaces of the symmetric Fock space and Arveson's curvature invariant for coinvariant subspaces. We are able to obtain some formulas relating the curvature invariant with other invariants. In particular, we prove that Arveson's version of the Gauss-Bonnet-Chern formula is true when the invariant subspaces are generated by any polynomials.     

曲面调和映照的广义Frenet公式及其应用

本文建立了从曲面到复Grassmamn流形调和映照的广义Frenet公式。作为应用，我们得到了调和映照为强共形的一个等价条件。我们也讨论了等距调和映照的曲率pinching性质。从而改进了有关伪全纯曲线的相应结果。     

有向全图的幂敛指数和周期

设G是有向图,T(G)表示G的有向全图.本文得到了它们的幂敛指数k(G)和k(T)之间的关系:对任何有向图G,周期p(T(G))=1;当G是本原图时,k(T)≤k(G)+1,文中给出了取得k(G)+1的两类图;当G是无圈图时,k(T)=2k(G)-1,当G是有向圈时,k(T)=2|V(G)|-1,当G是强连通时得到了k(T)的一些估计.     

R13中混合型曲面保主曲率等距变形

本文研究了Minkowski空间R₁³曲面的等距变形问题.建立了R₁³中曲面的共形、等距等概念.推广了O.Bonnet和S.S.Chern关于欧氏空间的结论.对R₁³出现的新情况——曲面的中曲率梯度类光作了一定探讨,得出的主要结果为:非平坦的、允许保主曲率等距变形的曲面一定不是W-曲面.     

常曲率空间中单形的中面公式及其应用

本文给出了n维常曲率空间中单形的中面面积公式，利用它我们还得到了一类几何不等式．     

Curvature Computations of 2-Manifolds in $\mathbb{R}^k$

In this paper, we provide simple and explicit formulas for computing Riemannian curvatures, mean curvature vectors, principal curvatures and principal directions for a 2-dimensional Riemannian manifold embedded in IR^k with k ≥ 3.