复射影空间和四元数射影空间中广义赤道的一个新特征

本文研究复射影空间ＣＰ＾ｎ和四元数射影空间ＱＰ＾ｎ中的紧致极小超曲面，对其上Ｊａｃｏｂｉ算子的最小特征值给出了一个最佳上界估计，由此给出了ＣＰ＾ｎ和ＱＰ＾ｎ中广义赤道的一个新的特征。     

关于类空W超曲面的一个存在性定理

利用超曲面的旋转对称性，将ＰＤＥ的求解转化为ＯＤＥ的求解，确定了Ｄｅ Ｓｉｔｔｅｒ空间中的一类旋转型的Ｗｅｉｎｇａｒｔｅｎ超曲面。即获得：给定Ｒ＾ｎ－１内开集（０，∞）＾ｎ－１上一个Ｃ＾１函数ｋｎ＝ｆ（ｋ１，…，ｋｎ－１）（ｎ≥２），一定存在Ｄｅ Ｓｉｔｔｅｒ空间Ｓ１＾ｎ＋１内的ｎ维类空旋转超曲面Ｍ，使得Ｍ的ｎ个主曲率ｋ１，…，ｋｎ恰有上述函数关系。     

极小超曲面上Laplace算子的谱

本文证明了单位球面Ｓ＾ｎ＋１中某些Ｃｌｉｆｆｏｒｄ超曲面，复射影空间和四元数射影空间中广ＹＱ ＬＩＦＦＯＲＤＦＨＶ ＭＡ ＤＭ Ｊ ＭＨ ＡＤＷ Ｈ Ｌａｐｌａｃｅ算子的谱唯一确定。     

具有平行平均曲率向量场的子流形

本文改进了Ｓ．Ｔ．Ｙａｕ（文［１］）中关于单位球面中具有平行平均曲率向量场的子流形的一个结果。然而从截面曲率这一角度出发，给出了空间形式Ｒ＾ｎ＋ｐ（ｃ）（ｎ＞１，ｐ＞１）中具有平行平均曲率向量场的可定向闭子流形Ｍ＾ｎ的有关结果和积分不等式。     

De Sitter空间中具有常均曲率的类空超曲面（Ⅱ）

设Ｍ＾ｎ是Ｄｅ Ｓｉｔｔｅｒ空间Ｓ１＾ｎ＋１中具有常数平均曲率且第二基本形式长度的平方为常数的完备类空超曲面，若Ｓ≤２（ｎ－１）＾１／２，则Ｍ＾ｎ是等参超曲面。     

某类有界拟凸域双全纯不变量的极限

Ｅ＝Ｅ（ｍ，ｎ，ｋ）＝｛（ｚ，ω）∈Ｃ＾ｎ＋ｍ：│ｚ│＾２＋│ω│＾２ｋ〈１，ｚ∈Ｃ＾ｎ，ω∈Ｃ＾ｍ，ｋ〉０｝是Ｃ＾ｍ＋ｍ中的一类有界拟凸域。该文证明了在δＥ的强拟凸点上，当ｍ〉１时，ｌｉｍ（ｚ，ω）→δＥＪＥ（（ｚ，ω））＝π＾ｎ＋ｍ（ｎ＋ｍ＋１）＾ｎ／（ｎ＋ｍ）！．ｍ＝１时，ｌｉｎ（ｚ，ω）→δＥＪＥ（ｚ，ω））＝π＾ｎ＋１（ｎ＝）＾ｎ＋１／（ｎ＋１）！，在δＥ的弱拟凸点上，上述极限不存在。     

拟常曲率空间中的2-调和子流形为极小子流形的条件

研究了拟常曲率空间中的2-调和子流形与极小子流形.首先得到了拟常曲率空间中具有平行平均曲率的2-调和子流形为极小子流形的一个较好的充分条件,然后得到了2-调和超曲面与极小超曲面在一定条件下是等价的结论.     

关于超曲面上测度的Fourier交换的零点

设Ｓ是Ｅｕｃｌｉｄ空间Ｒ＾ｎ（ｎ≥２）中一个紧闭光滑超曲面，它关于原点中心对称，其Ｇａｕｓｓ曲率处处非零，设ｄμ是Ｓ上一个光滑正测度，ｄμ是其Ｆｏｕｒｉｅｒ变换，本文证明，ｄμ的零点集是一个紧集与可列多个微分同胚于单位球面的超曲面之无交并。     

单位球面中极小子流形的曲率拼挤

本文证明了单位球面中极小子流形的一些拼挤定理,特别注意到单位球面中的极小超曲面、给出了截曲率的拼挤常数,我们也改进了由Ｎ．Ｅｊｉｒｉ得到的Ｒｉｃｃｉ曲率拼挤常数。     

关于有限序列的Z—L复杂度

讨论了有限序列Ｚ－Ｌ复杂度，得到了Ｎ＾ｎ３和Ｅ／Ｎ＾ｎ３的公式。     

MATLAB曲面绘制中的挖补方法

在MATLAB绘图中,将函数数据的某一部分换成内置变量NaN(或Inf),或者将函数数据中的NaN换成适当的实数,可分别实现绘图中的挖、补方法.并且给出一些具体的应用实例.     

G~1 Continuity Conditions of B-spline Surfaces

According to the B-spline theory and Boehm algorithm, this paper presents several necessary and sufficient G1 continuity conditions between two adjacent B-spline surfaces. In order to meet the need of application, a kind of sufficient conditions of G1 continuity are developed, and a kind of sufficient conditions of G1 continuity among N(N > 2) patch B-spline surfaces meeting at a common corner are given at the end.     

双三次B样条插值曲面

本文研究三次B样条插值曲面。对于给定的拓扑网格点阵Pi,j。导出了其插值三次B样条曲面的控制顶点,每四个顶点Pi,j,Pi l,j,Pi,j 1,Pi 1,j 1由九个三次B样条曲面片构成,整个曲面是C^2连续的,最后,给出了一个数值实例。     

关于凸曲面的几个定义的关系

本文讨论了凸曲面的几种定义及其关系，发现有的定义是局部凸的定义，有的是整体凸的定义，有的则对于局部凸和整体凸都适合，最后给出了各种定义之间互推的证明，对于局部凸和整体凸定义之间不能推证的，则说明了原因．     

在某些正则区域上的多元B形式曲面

本文首先通过在多面体区域上抬高维数的技巧给出了多元Ｂ形式中曲面的一般性定义．由此我们构造了平行四边形域上、正六边形域上和正八边形成上Ｂ形式的同次曲面格式，并给出了其基函数的递推公式和求导公式．同时我们也给出了正六边形域上插值角点的Ｂ形式同次曲面的表示式．     

Implicit Surface Fitting Using Directional Constraints

A commonly used technique for fitting curves and surfaces to measured data is that known as orthogonal distance regression, where the sum of squares of orthogonal distances from the data points to the surface is minimized. An alternative has recently been proposed for curves and surfaces which are parametrically defined, which minimizes the sum of squares in given directions which depend on the measuring process. In addition to taking account of that process, it is claimed that this technique has the advantage of complying with traditional fixed-regressor assumptions, enabling standard inference theory to apply. Here we consider extending this idea to curves and surfaces where the only assumption made is that there is an implicit formulation. Numerical results are given to illustrate the algorithmic performance.This revised version was published online in October 2005 with corrections to the Cover Date.     

Least-Squares Fitting of Algebraic Spline Surfaces

We present an algorithm for fitting implicitly defined algebraic spline surfaces to given scattered data. By simultaneously approximating points and associated normal vectors, we obtain a method which is computationally simple, as the result is obtained by solving a system of linear equations. In addition, the result is geometrically invariant, as no artificial normalization is introduced. The potential applications of the algorithm include the reconstruction of free-form surfaces in reverse engineering. The paper also addresses the generation of exact error bounds, directly from the coefficients of the implicit representation.     

Construction of Surfaces with Parallelism Conditions

In this paper we define the notion of pseudo-parallel parameterized surfaces, extending that of offset surfaces. Then we consider the problem of fitting a set of scattered points with a surface pseudo-parallel to a given reference surface. We propose a method of solution based on a modified version of the classical smoothing D ^m -splines over a bounded domain. The convergence of the method is established and some numerical examples are given.     

参数曲面保凸的一个定理

本文讨论了参数曲面的凸性，给出了参数曲面为凸的充要条件．并给出了具体的应用实例．     

Ruled surfaces with constant terms in the relative Theorema Egregium

Two complete classifications are given: (a) relative surfaces with isoparametric relative shape operator and projectively flat relative induced connection and (b) relative Tchebychev surfaces with constant terms in the relative Theorema Egregium. Both classifications share the occurrence of certain classes of ruled surfaces satisfying these strong conditions with respect to a relative geometry.