n维二次曲面的切超平面

利用特征根研究n维二次曲面的切超平面问题,给出平面为n维二次曲面的切超平面的充要条件.     

凸域上拟双曲测地线直径的Gehring-Hayman 恒等式

利用型函数和最大项m（σ）的几何意义研究全平面上Dirichlet级数的增长性,得到了Dirichlet级数增长性与系数、指数之间关系的四个结论,推广了以往研究增长性的相关结果.     

Minimal universal covers inE n

It is shown that any plane set of constant unit width contains a semi-circle of radius 1/2, and using this a minimal univeral plane cover is explicitly constructed. It is also shown that in an n-dimensional space with n>2 there are minimal universal covers of arbitrary large diameter. This paper was written while the author was a National Science Foundation Visiting Senior Fellow at the University of Washington, Seattle, Washington, U.S.A.     

Iteration of Analytic Normal Functions of Matrices

In this paper, the author proves that the classical theorem of Wolff in the theory of complex functions may be extended to the class of operator-valued functions f, where f is an analytic function from the open unit disc \Delta in the complex plane into a family of commutative normal operators on a certain n-dimensional complex Hilbert space, and ||f(z)||<1 holds for every z in \Delta.     

Thin sets and common transversals

An m-transversal of a family of convex sets in Euclidean n-dimensional space Rⁿ is an m-dimensional flat which intersects each member of the family. This paper establishes some results dealing with (n–1)-transversals in Rⁿ. The results are related to a theorem of Hadwiger on 1-transversals in the plane.     

广义重心坐标与凸多胞形的性质

提出n维欧氏空间中广义重心坐标的概念,建立了广义重心坐标下两点间的距离公式,并利用于研究凸多胞形的若干性质,将欧氏平面上凸多边形的一些定值与极值性质推广到n维空间.     

关于高维单形的两个性质

应用度量几何理论与解析方法,研究了n维欧氏空间En中n维单形的性质,将三角形内心与中线两个性质推广到n维单形,获得n维单形内心与中位面的两个性质.     

Arbitrary-norm separating plane

A plane separating two point sets in n-dimensional real space is constructed such that it minimizes the sum of arbitrary-norm distances of misclassified points to the plane. In contrast to previous approaches that used surrogates for distance-minimization, the present work is based on a precise norm-dependent explicit closed form for the projection of a point on a plane. This projection is used to formulate the separating-plane problem as a minimization of a convex function on a unit sphere in a norm dual to that of the arbitrary norm used. For the 1-norm, the problem can be solved in polynomial time by solving 2n linear programs or by solving a bilinear program. For a general p-norm, the minimization problem can be transformed via an exact penalty formulation to minimizing the sum ofa convex function and a bilinear function on a convex set. For the one and infinity norms, a finite successive linearization algorithm can be used for solving the exact penalty formulation.     

Dirichlet空间上的超循环复合算子

设Bn是复平面C中的单位圆盘(n=1)或复空间Cn中的单位球.众所周知,在Hardy空间上存在丰富的符号在Aut(Bn)中的超循环复合算子.然而,在复平面中单位圆盘上的Dirichlet空间中, 任何复合算子都不能是超循环的.本文则证明,当n>1时,Bn上的Dirichlet空间中确有超循环复合算子.     

On automorphisms of n-dimensional Laguerre space

We examine some properties of two types of inversions in the isotropical model of n-dimensional Laguerre space. Moreover we establish an isomorphism between the isotropical and the cylinder models of the n-dimensional Laguerre space. We prove also that every automorphism of the n-dimensional Laguerre space is a composition of a pseudodilatation and some involutive maps.     

A characterization of ovoidal quadrics by plane sections

In [11], J. TITS characterized ovoidal quadrics of n-dimensional projective spaces (n N, n 3) by considering sections of planes passing through a fixed point of an ovoid. We want to show that a corresponding result is true if the set of planes under consideration is restricted to n-2 bundles of planes and one further plane, where this further plane may not be omitted. Moreover, our considerations will include the cases of infinite dimension.Dedicated to Professor Helmut Karzel on the occasion of his 60th birthday     

k-Plane Clustering

A finite new algorithm is proposed for clustering m given points in n-dimensional real space into k clusters by generating k planes that constitute a local solution to the nonconvex problem of minimizing the sum of squares of the 2-norm distances between each point and a nearest plane. The key to the algorithm lies in a formulation that generates a plane in n-dimensional space that minimizes the sum of the squares of the 2-norm distances to each of m₁ given points in the space. The plane is generated by an eigenvector corresponding to a smallest eigenvalue of an n × n simple matrix derived from the m₁ points. The algorithm was tested on the publicly available Wisconsin Breast Prognosis Cancer database to generate well separated patient survival curves. In contrast, the k-mean algorithm did not generate such well-separated survival curves.     

度量方程应用于Krause定理的推广

本文用距离几何的方法证明了主要定理,对曲率为Ｋ的ｎ维常曲率空间,其内任意ｎ＋１个ｎ－１维球Ｓｉ（ｉ＝１,２,…,ｎ＋１）,它们中的任一个都与其它球不变,则与Ｓｉ交角为βｉ（ｉ＝１,２,…,ｎ＋１）的ｎ－１维一般有２＾ｎ＋１个,当ｎ为偶数时,它们的测地线曲率之交错和为零;当ｎ为奇数时,此结论不成立,该定理包括非欧情形,而当ｎ＝２,βｉ＝１（ｉ＝１,２,…,ｎ＋１）时,就是ｉｉｌｋｅｒＪＢ在「１」中所     

多元FFT与FST的直接方法

一、多元变换矩阵与矩阵的张量积 矩阵的张量积(Kronecker乘积)是导出多元直接变换的主要工具,因此,这里首先列出张量积的定义及其简单性质. 定义.设A_n,B_m分别是n×n,m×m方阵,则A_n与B_m的张量积是一个(n·m)×(n·m)方阵:A_nB_m=[A_nb_(ij)],其中B_m=[b_(ij)].并记A~(k)=?.     

n维特殊伸缩矩阵的构造与n维广义插值细分函数向量

本文构造了一种特殊的n维特殊伸缩矩阵,且定义了n维正交广义插值多小波.基于这种特殊的伸缩矩阵,讨论n维正交广义插值多小波的构造算法. 并且最后给出了算例.     

关于无穷维算子的有限维最佳逼近

A method of approaching to the infinite-dimensional linear operators by the finite-dimensional operators is discussed. It is shown that,for every infinite-dimensional operator A and every natural number n,there exists an n-dimensional optimal approximation to A. The norm error is found and the necessary and sufficient condition for such n-dimensional optimal approximations to be unique is obtained.     

欧氏空间E~n中Euler不等式的加强推广(英文)

The relation between the circum-radius and the in-radius of an n-dimensional simplex in E~n is studied.Two new generalizations of Euler inequality for the n-dimensional simplex are established.Besides,we obtain some stronger generalizations of Euler inequality for the n-dimensional simplex than previously known results.     

Kubota公式的注记

本文研究了n维欧式空间中En中r-维平面的密度与(n-1)维球的体积元之间的关系.利用了复合叠加等的方法,得到了n维欧式空间En的凸体和任意n-r维投影空间Ln-r之间均值积分的关系,推广了Kubota公式得到的结果     

关于单形一个对偶式的商榷与两个新的对偶式

讨论了n维欧氏空间E^n中n维单形不等式的对偶式．利用距离几何理论与解析方法，建立了n维单形两个不等式的对偶式，指出了最近所建立的单形Finsler-Hadwiger不等式的A维对偶式是错误的．     

高维情形的Routh定理

本文研究了n维欧氏空间En中n维单形的体积有关问题.利用距离几何的理论与解析方法,建立了n维情形的Routh定理,作为其特例建立了n维情形的Ceva定理.