Geometry of the structure of linear complements

Two geometries can be considered in the structure of linear complements: an affine spine space and an affine space. An affine spine space arises from a space of pencils. In terms of this geometry an affine partial line space may be defined. It is extensible to the affine space. Automorphisms of the affine spine space are automorphisms of appropriate affine space.     

On the Borelness of the intersection operation

We study the intersection operation of closed linear subspaces in a separable Banach space. We show that if the ambient space is quasi-reflexive, then the intersection operation is Borel. On the other hand, if the space contains a closed subspace with a Schauder decomposition into infinitely many non-reflexive spaces, then the intersection operation is not Borel. As a corollary, for a closed subspace of a Banach space with an unconditional basis, the intersection operation of the closed linear subspaces is Borel if and only if the space is reflexive. We also consider the intersection operation of additive subgroups in an infinite-dimensional separable Banach space, and show that if this intersection operation is Borel then the space is hereditarily indecomposable.     

约束离散空间的试验设计方案研究

目前的试验设计大体在连续空间或者无约束的离散空间下进行研究,但实际工程中不少场景都需要在离散空间中挑选试验点来进行试验设计,通常的试验设计方法无法应用于约束的离散空间中.文章立足于实际工程背景,基于连续空间下的均匀试验设计,采用Gale-Shapley算法,给出了连续空间到离散空间的映射设计方案.最后,结合实例进行了Gale-Shapley算法与经验方法所得设计的对比验证研究,在约束的离散空间下,Gale-Shapley算法所得到的映射设计具有更好的均匀性,且计算效率满足工程实际需求.     

事件空间中二阶非Четаев型非完整系统的守恒律

研究事件空间中二阶非чeTaeB型非完整系统的守恒律。提出事件空间中的Jourdain原理，引入事件空间中的Jorudain生成元，给出无限小变换下的Jourdain原理的不变性条件。在一定条件下得到事件空间中系统的守恒律。并举例说明结果的应用。     

Banach空间的Lipschitz对偶及其应用

本文引进Banach空间E的一个全新对偶空间概念—Lipschitz对偶空间,并证明：任何Banach空间的Lipschitz对偶空间是某个包含E的Banach空间的线性对偶空间,以所引进的新对偶空间为框架,本文定义了非线性Lipschitz算子的Lipshitz对偶算子,证明：任何非线性Lipschitz算子的Lipschitz对偶算子是有界线性算子．所获结果为推广线性算子理论到非线性情形（特别,运用线性算子理论研究非线性算子的特性）开辟了一条新的途径．作为例证,我们应用所建立的理论证明了若干新的非线性一致Lipschitz映象遍历收敛性定理.     

The image of the coefficient space in the universal deformation space of a flat Galois representation of a p-adic field

The coefficient space is a kind of resolution of singularities of the universal flat deformation space for a given Galois representation of some local field. It parametrizes (in some sense) the finite flat models for the Galois representation. The aim of this note is to determine the image of the coefficient space in the universal deformation space.     

伪辛空间的生成及其表现形式

通过对辛空间的深入分析和研究,从空间中的度量与向量的迷向性问题入手并展开较为详细的讨论,定义"伪辛"的概念,阐述"辛"概念的演变、扩充与伪辛空间生成的事实,进而揭示伪辛空间的本质属性及其与辛空间的内在联系与区别.论述过程同时给出了伪辛空间关于辛空间的内蕴和外延表示式.     

Reconstruction of norm by geometry of minimal networks

An inverse problem to the Steiner minimal tree searching problem in a normed space is studied. Namely, let a normed space be given and let all Steiner minimal trees be known in this space. The problem is to describe all norms with the same Steiner minimal trees for all finite boundary sets as in the given space. The paper presents a review of known results on the problem and announces the uniqueness of the set of Steiner minimal trees for any two-dimensional space with a strongly convex and differentiable norm.     

一种基于欧拉的非接触式检测生理参数的加速方法

成像式光电容积描记技术(IPPG)是近几年发展起来的一种新的检测生理参数的技术.欧拉视频放大技术以一种空间多尺度的方法来研究像素随时间的变化,揭示了视频中微弱运动的变化,使得现代的医学技术更好地发展.在环境光照射下使用智能手机的摄像头采集人脸部视频,将原始视频信号进行欧拉放大提取心率和血氧饱和度.传统的欧拉放大技术基于YIQ色彩空间,所以要对采集到的视频做一个色彩空间转换,放大完后再由YIQ空间转换到RGB空间,这种方法计算量大,耗时多,不利于生理参数的实时检测.提出一种不对色彩空间进行转换,直接利用RGB空间对视频进行放大的方法.与传统方法相比,RGB色彩空间测量的准确性与YIQ色彩空间具有高度的一致性,同时处理速度提升了百分之三十以上.     

A characterization of reflexive spaces

We prove that a Banach space is reflexive if for every equivalent norm, the set of norm attaining functionals has non-empty norm-interior in the dual space. It is also proved that the set of norm attaining functionals on a Banach space that is not a Grothendieck space is not a w*-G _δ subset of the dual space.     

A particular class of symmetric spaces

Summary The metric of the general harmonic symmetric Riemannian 4-space expressed in tensor form is generalised to n dimensions, and it is verified that the space so obtained is symmetric, harmonic and complete, the underlying manifold being Euclidean. The metric of this space can be put in one of a number of simple canonical forms, by means of which the space can be classified. Under certain conditions the space is locally isometric to complex projective space or to a related space. To Enrico Bompiani on his scientific Jubilee I wish to aknowledge the hospitality of the University of Washington where this work was carried out as part of a research contract from the U. S. Office of Naval Research.     

On an EVI curve characterization of Hilbert spaces

It is shown that the existence of a large enough collection of EVI (evolution variational inequality) curves for a lower semi-continuous functional on a Banach space implies that the space is in fact a Hilbert space. The main result is exemplified by the p-Laplacian evolution in Banach space.     

关于概率度量空间的等距同构

概率度量空间理论中有两种等距同构,一种是一个概率度量空间等距同构于另一个概率度量空间.另一种是一个概率度量空间等距同于一个准度量族生成空间.该文建立了这两种等距同构之间的联系.     

The Embedding Theory of Native Spaces

In the theory of radial basis functions, mathematicians use linear combinations of the translates of the radial basis functions as interpolants. The set of these linear combinations is a normed vector space. This space can be completed and become a Hilbert space, called native space, which is of great importance in the last decade. The native space then contains some abstract elements which are not linear combinations of radial basis functions. The meaning of these abstract elements is not fully known. This paper presents some interpretations for the these elements. The native spaces are embedded into some well-known spaces. For example, the Sobolev-space is shown to be a native space. Since many differential equations have solutions in the Sobolev-space, we can therefore approximate the solutions by linear combinations of radial basis functions. Moreover, the famous question of the embedding of the native space into L²(Ω) is also solved by the author.     

An algebraic characterization of planar graphs

A cycle in a graph is a set of edges that covers each vertex an even number of times. A cocycle is a collection of edges that intersects each cycle in an even number of edges. A bicycle is a collection of edges that is both a cycle and a cocycle. The cycles, cocycles, and bicycles each form a vector space over the integers modulo two when addition is defined as symmetric difference of sets. In this paper we examine the relationship between the left-right paths in a planar graph and the cycle space, cocylce space, and bicycle space. We show that planar graphs are characterized by the existence of a diagonal—a double cover by tours that interacts with the cycle space, cocycle space, and bicycle space in a special manner. This generalizes a result of Rosenstiehl and Read that characterized those planar graphs with no nonempty bicycles. © 1995 John Wiley & Sons, Inc.     

Operators on the orthogonal complement of the Dirichlet space

In this paper we prove that a dual Hankel operator is zero if and only if its symbol is orthogonal to the Dirichlet space in the Sobolev space, and characterize the symbols for (semi-)commuting dual Toeplitz operators on the orthogonal complement of the Dirichlet space in Sobolev space.     

Gauss小波变换像空间的描述

在连续小波变换像空间是再生核Hilbert空间的基础上,针对经常用于边界检测并且使用效果非常好的Gauss小波,给出了其小波变换像空间的再生核具体表达式.并且当固定尺度因子和固定平移因子时,利用再生核空间理论,对Gauss小波变换像空间做了具体描述,分别给出了Gauss小波变换像空间中的等距恒等式和反演公式,这为进一步研究一般的小波变换像空间提供了理论基础.     

A-拓扑以及A-拓扑空间的相关性质

设E是一个A rch im edean R iesz空间,a∈E,Φ≠A E,则有如下的两个结论:1)由a生成的a-拓扑空间E是一个H ausdorff空间;2)若以下条件之一成立,则由A生成的A-拓扑空间E是一个H ausdorff空间:(a)子集{a:a∈A}有上界;(b)E具有强单位元;(c)若E=C(X),其中X是一个局部紧H ausdorff空间.     

Spaces of geodesics: products, coverings, connectedness

We continue our study of the space of geodesics of a manifold with linear connection. We obtain sufficient conditions for a product to have a space of geodesics which is a manifold. We investigate the relationship of the space of geodesics of a covering manifold to that of the base space. We obtain sufficient conditions for a space to be geodesically connected in terms of the topology of its space of geodesics.     

On farthest points of sets

For a convex closed bounded set in a Banach space, we study the existence and uniqueness problem for a point of this set that is the farthest point from a given point in space. In terms of the existence and uniqueness of the farthest point, as well as the Lipschitzian dependence of this point on a point in space, we obtain necessary and su.cient conditions for the strong convexity of a set in several infinite-dimensional spaces, in particular, in a Hilbert space. A set representable as the intersection of closed balls of a fixed radius is called a strongly convex set. We show that the condition “for each point in space that is sufficiently far from a set, there exists a unique farthest point of the set” is a criterion for the strong convexity of a set in a finite-dimensional normed space, where the norm ball is a strongly convex set and a generating set.