关于高维蝴蝶定理

利用距离几何方法将古典的蝴蝶定理推广到n维欧氏空间一般二次超曲面情形,同时也得到高维蝴蝶定理的逆定理.     

Lorentz-Minkowski空间中给定主曲率函数的旋转超曲面

给出(n,1)型orentz-Minkowski空间中给定主曲率函数的旋转类空超曲面的位置向量场,通过计算超曲面的主曲率,证明了这类超曲面的存在性.     

Monotonicity of zeros of Laguerre polynomials

Denote by x_nk(α), k=1,…,n, the zeros of the Laguerre polynomial . We establish monotonicity with respect to the parameter α of certain functions involving x_nk(α). As a consequence we obtain sharp upper bounds for the largest zero of .     

Hopf hypersurfaces of small Hopf principal curvature in $${\mathbb{C}{\rm H}^2}$$

Using the methods of moving frames and exterior differential systems, we show that there exist Hopf hypersurfaces in complex hyperbolic space with any specified value of the Hopf principal curvature α less than or equal to the corresponding value for the horosphere. We give a construction for all such hypersurfaces in terms of Weierstrass-type data, and also obtain a classification of pseudo-Einstein hypersurfaces in .      

Weak-type inequalities for higher order Riesz-Laguerre transforms

In this paper we study the weak-type (1,1) boundedness of the higher order Riesz-Laguerre transforms associated with the Laguerre polynomials. In particular, we obtain the boundedness for the Riesz-Laguerre transforms of order 2 and we find also the sharp polynomial weight ω that makes the Riesz-Laguerre transforms of order greater than two continuous from into L1,∞(dμα), being μα the Laguerre measure.     

C~3中一类拟凸超曲面的局部全纯自同构

给出了C~3中一类拟凸超曲面定义在原点邻域内的实解析无穷小CR自同构,并得到了这类超曲面在原点处稳定群的单位连通分支.     

On Möbius form and Möbius isoparametric hypersurfaces

An umbilic-free hypersurface in the unit sphere is called MSbius isoparametric if it satisfies two conditions, namely, it has vanishing MSbius form and has constant MSbius principal curvatures. In this paper, under the condition of having constant MSbius principal curvatures, we show that the hypersurface is of vanishing MSbius form if and only if its MSbius form is parallel with respect to the Levi-Civita connection of its MSbius metric. Moreover, typical examples are constructed to show that the condition of having constant MSbius principal curvatures and that of having vanishing MSbius form are independent of each other.     

曲率相关的爆轰波在非结构四边形网格上的数值方法

假设爆轰波阵面的法向速度是曲率的线性函数,在非结构四边形网格上采用水平集方法模拟爆轰波阵面的运动过程.水平集方程的曲率无关项采用正格式离散,曲率项采用伽辽金等参有限元方法空间离散,时间离散采用半隐格式.在笛卡儿网格和随机网格上,含曲率的水平集方程的离散格式为强一阶精度,重新初始化方程的离散格式精度为近似一阶精度.曲率收缩的不光滑界面和多个爆轰波阵面相互作用的算例说明格式可有效地模拟爆轰波与曲率相关的运动.     

精确简洁解析的原子组态相互作用波函数的计算

使用广义Laguerre类型轨道,在组态相互作用框架内,发展并完善了一套精确、简洁、解析的原子(离子)波函数从头计算的Fortran程序,计算原子中电子的结构.通过对指定能态能量求其最小值实现对波函数节点位置和空间范围的优化,从而求出最优波函数.作为例子,计算了⁵G态下的Ti的能量最小值和优化波函数.