有限秩算子的表示(Ⅰ)

定义了子空间格代数的(弱闭双边)模,对有限维Hilbert空间的强自反子空间格代数的模及原子Boolean格代数的模中的有限秩算子进行了讨论,得到有限秩算子一定可以表示为秩1算子的和.     

子空间非相似性度量(WWF-SSD)的三角不等式

2005年,W ang,W ang和Feng在国际期刊Pattern R ecogn ition上提出了用来刻画子空间非相似性的度量(WW F-SSD),而且利用这个度量设计人脸识别算法,取得了很好的效果.但是该文章中没能证明WW F-SSD满足一个距离必须具有的三角不等式性质.本文给出了WW F-SSD的一个矩阵形式等价定义.基于这个定义不但可以使利用M atL ab实现的算法更有效率,而且可以很直观的证明WW F-SSD不依赖于子空间标准正交基的选择这一性质.进一步,我们在这个定义的基础上,利用矩阵的有关性质证明了WW F-SSD的三角不等式,从而最终证明了WW F-SSD是距离.     

格蕴涵代数中滤子的逻辑性质(英文)

讨论了当格蕴涵代数L是完全分配格时蕴涵运算的一些性质 ,在格蕴涵代数L上引入了集合的蕴涵传递性概念 ,证明了格蕴涵代数的滤子满足蕴涵传递性和替换定理 ,即格蕴涵代数的滤子满足命题逻辑的三段论推理规则和替换定理     

单形中的两个几何不等式(英文)

给出了n维欧氏空间中关于单形的n-1维体积与单形内部任意一点到所对界面的距离的两个不等式.     

剩余格上的(λ,μ)直觉模糊滤子北大核心

在剩余格上引入λ,μ直觉模糊滤子的概念,讨论了它与剩余格上滤子之间的关系,研究了λ,μ直觉模糊滤子在剩余格同态下的像与原像的相关性质.     

强并半格中的C-滤子及其应用

首先,在并半格中引入了上覆盖关系的概念以及由上覆盖关系确定的强并半格中的上覆盖概念,在强并半格中讨论了它们的基本性质;其次,通过上覆盖概念在强并半格中引入了C-滤子概念,证明了强并半格中的C-滤子是通常滤子,但强并半格中的通常滤子并非C-滤子;最后,研究了强并半格同态和余Frame同态之间的关系,证明了余Frame S与相应的C_S-滤子型余Frame之间的同构定理.     

数量经济中的统计分析与预测方法(Ⅱ)

§2经济波动的频率域分析 周期分析是经济波动研究的一个重要方面.经济波动可有历经世纪的长期波动、十年几十年的中期波动和几年过程的短期波动,但往往这种划分是经验的和粗糙的.国民经济系统是一个有机的整体,众多统计指标之间的错综复杂关系相互推动,彼此制约,因此有必要考察它们之间是否存在着一种协同现象,有较为同节奏的同期性波动.我们.希望确定各类经济变量的隐含周期分量,寻找各种经济波动频率谱的共同部分,这是用观察和经验所无法得到的.共同频率或隐含同期找出后,它们适应倍数即可理解为不同.类型经济波动的频率或周期.此外,还应…     

格蕴涵代数的关联理想与模糊关联理想(英文)

本文提出了格蕴涵代数的关联理想和模糊关联理想的概念 ,讨论了它们的性质 ,指出了关联理想与理想、关联理想与关联滤子、关联理想与模糊关联理想、模糊关联理想与模糊关联滤子、模糊关联理想与模糊理想之间的关系     

AUTOMORPHISM GROUP OF FINITELY GENERATED FREE ALGEBRAS FV(Lκ)(n)

本文研究了自同构群AutLκ和AutFV(LK)(n)的结构问题.利用了正交模格及其自同构群的直积分解方法,获得了正交模格Lκ和自由代数FV(LK)(n)的自同构群的直积分解式.     

不同分布(φ)混合序列的最大值不等式及其应用

利用矩不等式和截尾的方法,讨论了不同分布的φ混合序列的最大值不等式.作为应用,获得了混合序列的一阶矩及p（p〉1）阶矩分别存在有限的充分条件,这是一个与独立同分布情形一致的结果.     

关于在∧-∨复合之下格矩阵的收敛性

本文研究了在复合∧-∨下格矩阵幂序列的收敛性，利用格中∧与∨运算的特性，获得了格矩阵幂序列的一些性质，证明了在∧-∨复合下．任一个几乎非自反格矩阵的幂序列是递减与收敛的．     

自由正交模格FMOk(n)的自同构群

文章先利用自同构映射保有限并的性质研究了一般正交模格的次直积的自同构群与自同构群的次直积的关系,再用块置换的方法研究了MOk的自同构群的生成元集,由此得到自由正交模格FMOk(n)的自同构群的直积分解式,从而完全解决了FMOk(n)的自同构群的结构问题.     

A HIERARCHY OF INTEGRABLE LATTICE SOLITON EQUMIONS AND ITS INTEGRABLE SYMPLECTIC MAP

1TheLatticeSolitonHierarchyDenoteEf(n)-f(n 1),nEZ,andwritef(n)=f,f(n k)=E*f.Considerthediscrete3x3matrixspectralproblem:whereajb,carethreepotentials,Aisaconstantspectralparameter.Theadjointrepresentationequationof(1)iswhereeachentryVj=Kj(B(A),C(A),D(A))0fthe3x3matrixVisaLaurentexpansionofA:Then(2)isequivaentt0'therecursi0nrelations:,Theaboverecursionequationscanbesolvedsuccessivelyt0deducethefollowingresults:Wedefine{Dj}bythefollowingrelation:From(3)we0btainKGj-1=JGj,Gj=(Aj,Bj,Cj…     

二维双重定向渗流及其临界概率函数

本文研究二维双重定向渗流模型，我们给出模型临界概率函数的一些基本性质，包括严格单调性、对称性和连续性，另外，我们指出，该临界概率函数的严格凹性是Grimmett相关猜想的充分条件。     

THE HAUSDORFF MEASURE OF SIERPINSKI CARPETS BASING ON REGULAR PENTAGON

In this paper,we address the problem of exact computation of the Hausdorff measure of a class of Sierpinski carpets E the self-similar sets generating in a unit regular pentagon on the plane.Under some conditions,we show the natural covering is the best one,and the Hausdorff measures of those sets are euqal to | E | s,where s=dim H E.     

ON THE EMBEDDING OF TOP IN THE CATEGORY OF STRATIFIED L-TOPOLOGICAL SPACES

§1. Introduction and PreliminariesLet L be a complete lattice. An L-topology on a set X is a subset τ of LX closed withrespect to ?nite meets and arbitrary joins. (X,τ) is called an L-topological space. The L-topology τ is called strati?ed if it contains all the constant maps from X to L, and in this case(X,τ) is called a strati?ed L-topological space. A continuous map between two L-topologicalspaces (X,τX) and (Y,τY ) is a function f : X ?→ Y such that f←(λ) = λ ? f ∈ τX…     

ISOLATED POINTS OF THE APPROXIMATE POINT SPECTRUM OF CERTAIN LATTICE HOMOMORPHISMS ON Co (X)

Abstract

Suppose X is a locally compact Hausdorff space and C (X) the apace of all continuous complex valued functions on X which vanish at infinity. Let T be a (complex) linear lattice homomorphism on C_o (X) whose adjoint is also a lattice homomorphism. It is sham that every non-zero isolated point of the approximate point spectrum of T lies in the point spectrum of T. An example is given to show that the exclusion of zero is necessary, even when X is compact. The same techniques are then used to show that if also the spectrum of T is finite then T can be written, in a natural manner, as a direct sum of two such lattice homomorphisms; one being an n'th root of an invertible multiplication operator and the other quasi-nilpotent.     

ON THE SPECTRAL PROPERTIES OF M-MATRICES AND ITS APPLICATIONS

1.IntroductionAndPreliminariesThespectralpropertiesofM-matricesplayanimportantroleinnonnegativemainstheory,andhavebeenappliedtostudythenumericalsolutionoflinearsystems.Recentlylmanyarticleshavediscussedwiththistopics(see[l--5]).ThepurposeofthispaperistoestablishthespectralinequalitiesofsingularM-matrices.ByapplyingthesepropertiesweanswerpartiallyanopenproblemandsolveanopenproblemposedbySchneiderin[4,5],somerecelltresultI2'4'6]onsplittingsofanM-matrixarealsoimproved.Allnotationsanddefinitio…     

关于代数体函数的展布关系及其应用

关于代数体函数的展布关系及其应用杨连中（山东大学数学系，济南２５０１００）国家青年自然科学基金资助课题．１９９１年５月１５日收到，１９９２年２月２１日收到修改稿．一、引言设ｆ（ｚ）于开平面亚纯，下级为有穷正数．若复数ａ是ｆ（ｚ）的一个亏值，则下述展布...     

ON THE MINIMUM INTRINSIC 1-VOLUME OF VORONOI CELLS IN LATTICE UNIT SPHERE PACKINGS

A typical 3-dimensional (in short '3D') Voronoi cell of a 3Dlattice has six families of parallel edges. We call any six representants of these six families the generating edges of the Voronoi cell. The sum s of lengths of generating edges of a Voronoi-cell of a lattice unit sphere packing in the 3-dimensional Euclidean space is a special case of intrinsic 1-volumes of 3Dzonotopes with inradius 1 which are investigated accurately in [B]. However, the minimum of this value is unknown even in this special case. As the regular rhombic dodecahedron shows optimal properties in many similar problems, it was reasonable to conjecture that it also has the minimal s value. In this note we present a construction of a lattice unit ball packing whose Voronoi cell possesses an intrinsic 1-volume strictly less than the one of the proper regular rhombic dodecahedron, hence providing a smaller upper bound for s than it was conjectured. A further issue of the note is a formula for edge-lengths of Voronoi cells of lattice unit ball packings that can be used efficiently in similar calculations. This revised version was published online in August 2006 with corrections to the Cover Date.