欧氏空间中等角基的性质

等角基是正交基的推广,等角基具有和正交基相似的性质,因此研究等角基的性质能够为研究欧氏空间提供一种工具,加深对欧氏空间的了解．本文主要把n维欧氏空间中正交基的一些性质推广到等角基上,得到了五个关于等角基性质的定理．     

Hilbert 空间中的广义正交基

广义正交基是Hilbert 空间中正交基的一个自然推广. 本文首先给出一个广义正交基存在的较弱的充要条件; 然后研究广义正交基的性质, 特别地, 得到广义正交基版本的一些有关正交基的经典性质, 如广义正交基的Bessel 等式和不等式等. 作为广义正交基的一个应用, 本文给出广义Riesz 基的一些新刻画. 最后本文讨论广义框架的冗余问题.     

标准正交基的一种求法

在欧氏空间R~n,把R~n的一个基化为标准正交基通常是施行施密特方法,本文将利用矩阵的合同变换给出另一种方法。     

关于子基的连通性的注记

在粗糙集理论研究中,覆盖方法的应用越来越受重视,其中最重要的概念是最近引进的拓扑空间的子集关于子基的内部和闭包以及由它们导入的关于子基的开集、闭集.对由它们导入的拓扑空间关于子基的隔离子集、连通性作进一步研究,所得性质是一般拓扑空间中隔离子集和连通性相应结果的推广.     

Hermite 插值基函数正交展开求和

本文研究一类 Hermite 插值基函数在空间 E~p(D-),p>1上的不完备性,其闭包的特征性质以及在此空间中的双正交展开的求和问题.     

基与拟基的关系

我们研究了某些基与拟基的关系,证明了空间具有有限秩的基当且仅当它有有限秩的拟基,空间具有正交基当且仅当它有正交的拟基．     

关于子基的连通性

覆盖方法在粗糙集理论研究中的应用越来越受到重视,而其中最重要的两个概念是最近引入的拓扑空间的子集关于子基的内部和闭包.本文研究由它们导出的关于子基的连通性的概念,它比一般拓扑学中的连通性的概念弱,但具有许多类似的性质,这些性质事实上也是连通性相应结果的推广.     

准正交基与准正交变换

利用内积给出了准正交基,准正交变换与准对合变换的概念,研究了它们的性质及其之间的联系,获得了许多新的结果,推广了正交基,正交变换,对合变换的概念,性质以及张禾瑞,郝新,邹本强等先生的相关结果。     

关于子基的局部连通性

在粗燥集理论研究中,覆盖方法的应用越来越受到重视,其中拓扑空间的子集关于子基的内部和闭包两个概念尤为重要.在最近由它们导入的关于子基的连通性基础上,给出了关于子基的局部连通性概念,并研究它的性质,得到一般拓扑学中局部连通性的一种推广.     

拓扑空间关于子基的紧致性

覆盖方法的应用在粗糙集理论研究中越来越受到重视,其中拓扑空间的子集关于子基的内部和闭包两个概念尤为重要.在由它们导入的关于子基的开集,闭集的基础上,给出了拓扑空间关于子基的紧致性概念,并研究它的性质,得到一般拓扑空间中紧致性的一种推广.     

构造正交向量的一个新方法及其应用

利用向量的数量积及行列式的按行(列)展开定理,构造出一个n维向量,它能够与n-1个n维向量都正交.这种构造正交向量的方法简单明了.应用这种方法很容易证明克莱姆法则.对这种构造方法加以改进,给出了线性空间Rn中扩充一组正交基的新方法.     

Über Böschungslinien im dreidimensionalen elliptischen Raum

In accordance withH. R. Müller [3] we understand under a curve of constant slope in the elliptic 3-space an isogonal trajectory of the generators of an arbitrary Clifford cylinder. Using linegeometric methods in a special projective model, we study in particular those curves of constant slope, whose tangents form also a constant angle with a fixed plane. Thereby we meet with well-known classes of curves in the Euclidean space, such as spherical involutoids and tractrices of circles and loxodromes on a torus.     

样条函数空间的维数级数和基函数

本文考虑多元样条函数维数级数和基函数的计算．文［２］，［３］中，讨论了通过ｄ－１维面上的光滑连接条件，用Ｇｒ?ｂｎｅｒ基方法计算多元样条函数的维数级数和基函数．事实上，样条函数的结构可由ｄ－２维面上协调方程决定．本文通过构造合冲序列及Ｇｒ?ｂｎｅｒ基的性质，推导协调矩阵与维数级数的关系，给出了由协调矩阵的核空间计算样条函数基函数的方法．     

The finite-dimensional decomposition property in non-Archimedean Banach spaces

A non-Archimedean Banach space has the orthogonal finite-dimensional decomposition property（OFDDP） if it is the orthogonal direct sum of a sequence of finite-dimensional subspaces.This property has an influence in the non-Archimedean Grothendieck＇s approximation theory,where an open problem is the following： Let E be a non-Archimedean Banach space of countable type with the OFDDP and let D be a closed subspace of E.Does D have the OFDDP？ In this paper we give a negative answer to this question; we construct a Banach space of countable type with the OFDDP having a one-codimensional subspace without the OFDDP.Next we prove that,however,for certain classes of Banach spaces of countable type,the OFDDP is preserved by taking finite-codimensional subspaces.     

Wavelet decomposition of the space of discrete periodic splines

An orthogonal basis for the spaceS _r ^m of discrete periodic splines is constructed. The wavelet decomposition of the spaceS _r ^m form=2 ^t is obtained using this basis. We derive recurrence formulas for the transformation from the decomposition with respect to the orthogonal basis to the wavelet decomposition, as well as recurrence formulas for the inverse transformation. Translated fromMatematicheskie Zametki, Vol. 67, No. 5, pp. 712–720, May, 2000.     

Special bases for solutions of a generalized Maxwell system in 3‐dimensional space

The aim of this paper is to study complete polynomial systems in the kernel space of conformally invariant differential operators in higher spin theory. We investigate the kernel space of a generalized Maxwell operator in 3‐dimensional space. With the already known decomposition of its homogeneous kernel space into 2 subspaces, we investigate first projections from the homogeneous kernel space to each subspace. Then, we provide complete polynomial systems depending on the given inner product for each subspace in the decomposition. More specifically, the complete polynomial system for the homogenous kernel space is an orthogonal system wrt a given Fischer inner product. In the case of the standard inner product in L² on the unit ball, the provided complete polynomial system for the homogeneous kernel space is a partially orthogonal system. Further, if the degree of homogeneity for the respective subspaces in the decomposed kernel spaces approaches infinity, then the angle between the 2 subspaces approaches π/2.     

CLASSIFICATION OF FINITE GROUPS GENERATED BY REFLECTIONS AND ROTATIONS

We classify finite groups generated by orthogonal transformations in a finite-dimensional Euclidean space whose fixed point subspace has codimension one or two. These groups naturally arise in the study of the quotient of a Euclidean space by a finite orthogonal group and hence in the theory of orbifolds.     

Dense computability structures

We examine computability structures on a metric space and the relationships between maximal, separable and dense computability structures. We prove that in a computable metric space which has the effective covering property and compact closed balls for a given computable sequence which is a metric basis there exists a unique maximal computability structure which contains that sequence. Furthermore, we prove that each maximal computability structure on a convex subspace of Euclidean space is dense. We also examine subspaces of Euclidean space on which each dense maximal computability structure is separable and prove that spheres, boundaries of simplices and conics are such spaces.     

闭极大线性子空间正交补的唯一性

研究赋范线性空间中闭极大线性子空间的正交可补性.利用空间的对偶映射给出固定闭极大线性子空间至多存在一个正交补的充分必要条件,从而给出每个闭极大线性子空间至多存在一个正交补的几何刻画.