每个非奇异单左R-模均为GP-内射的环的正则性

In this paper, some new relations between GP-V′-rings and regular rings under certain special conditions have been found. It is proved that R is left self-injective regular with Soc(RR)≠0 if and only if R is a left GP-V′-ring containingan injective maximal left ideal and Soc(RR) 属于 Soc(RR). Moreover, for an MELTring R, it is shown that R is regular if and only if R is a left GP-injective left GP-V′-ring.     

The Perturbed Problem on the Boussinesq System of Rayleigh-Bénard Convection

In this paper,the infinite Prandtl number limit of Rayleigh-B′enard convection is studied.For well prepared initial data,the convergence of solutions in L∞(0,t;H2(G)) is rigorously justified by analysis of asymptotic expansions.     

Explicit Determination of Torsion Subgroups of Elliptic Curves Over Multi-Quadratic Fields

LotKbeanalgebraicnUmberfield,EanellipticcurveoverK.Thewell-knownMordelLWeiltheOemassertsthattheK-rationalpointsE(K)ofEisafinitelygeneratedabeliangroup(MordelgrouP):E(K)2E(K)torsxZ,whereE(K)torsisthetorsionsubgroup,ristherank(anonnegativeinteger),Zistheadditivegroupofrationalintegers.TheaboveisomorphismsometimesisaIsowrittellasequality:E(K)=E(K)torsxZ".TherearemanyliteraturesstudyingthetorsionsubgrouPE(K)tors'EspeciallyL.Merelrecenilyprovedthe"uniformb0undednessconjecture":F0ranyp…     

L 1-spaces of vector measures defined on δ-rings

Given a vector measure v defined on a -ring with values in a Banach space, we study the relation between the analytic properties of the measure v and the lattice properties of the space L¹(v) of real functions which are integrable with respect to v.Received: 22 April 2004; revised: 5 October 2004     

A geometric interpretation of the transition density of a symmetric Lévy process

We study for a class of symmetric Lévy processes with state space R n the transition density pt（x） in terms of two one-parameter families of metrics, （dt）t>0 and （δt）t>0. The first family of metrics describes the diagonal term pt（0）; it is induced by the characteristic exponent ψ of the Lévy process by dt（x, y） = ^1/2tψ（x-y）. The second and new family of metrics δt relates to ^1/2tψ through the formulawhere F denotes the Fourier transform. Thus we obtain the following "Gaussian" representation of the transition density: pt（x） = pt（0）e- δ2t （x,0） where pt（0） corresponds to a volume term related to tψ and where an "exponential" decay is governed by δ2t . This gives a complete and new geometric, intrinsic interpretation of pt（x）.     

Duality Theorems of Multiobjective Programming for a Class of Generalized Convex Functions

1.DefinitionsDefinition1.AfunctionalF(x)inthespaceVCE"issaidtobeasublinearfunctionalifforx,yeV,andor20,Inparticular,F(0)=0.Letop(x)beadifferentiablerealfunctiononasetCCEd.ForagivensublinearfunctionFandafunctionp:CxC-EIIp(x,u)/0(x/u),themoregeneralgeneralizedconvexfunctioncanbedefinedasthefollwing:Definition2.op(x)issaidtobe(F,p)--invarialltconvexfunctiononCifforxl,xZECDefinition3.op(x)issaidtobe(F,P)--invariantquasiconvexfunctiononCifforal,xZECthatis,Definition4.op(x)issaidtobe(F,…     

关于L′Hospital法则的一个注记

在微积分这门课程当中 ,常常碰到求 00 型、∞∞ 型的极限问题 ,解决这类问题的一种简单而有效的方法是 L′Hospital法则。过去 ,在不少有关的书籍中 [1,2 ,3] ,∞∞ 的 L′Hospital法则的表述是 :若 (1 )函数 f (x)和 g(x)在 (a,a δ)有定义 (δ>0 ) ,limx→ a 0 f (x) =∞ ,limx→ a 0 g(x) =∞(2 ) f(x)和 g(x)在 (a,a δ)都可导 ,g′(x)≠ 0 ,并且 limx→ a 0f′(x)g′(x) =A　 (包括 A=∞的情形 )则limx→ a 0f (x)g(x) =limx→ a 0f′(x)g′(x) =A　　最近 ,我们在 [4,5,6 ]中看到 ,去掉条件 (1 )中的 limx→ a 0 f (x) =∞…     

On Some Results of Critical Edge-chromatic Graphs

Allgraphsconsideredaresimpleandundirected.LetGbeagraphwithvertexsetV(G)andedgesetE(G).FOravertexuofG,thedegreeofuinGisdenotedbyd(u).NG(u)isthesetofthevenicesadjacellttouinG.WedenotethemaximumdegreeofGbyAandtheminimumdegreeby6respectively.WecallavertexvofGamajorvertexifd(v)=A,andaminorvertexifd(v)相似文献   

Convergence in Distribution of Optimal Solutions to Stochastic Optimization Problems

1.IntroductionDistributionproblemsareofgreatimportanceinstochasticoptimizationandstatis-tics.Usuallythiskindofproblemscanbedescribedinthefollowingform:wheref(x,w)isafuncti0ndefinedonR"xflandSisasubsetin'R".Because0fc0mplexityoftheproblems,ingeneral,onecangetonlytheirapproximatesolutions.Thefollowingtypeofapproximationis0ftenused:Letuscall(2)thefirsttype0fapproximation.DenotebyZ(w),A(w)theoptima1valueandoptimalsolutionsetofproblem(1)respectivelyandbyZk(w),Ak(w)thecorrespondingonesofproblem(…     

S-harmonic Function and RieszDecomposition Theorem of Superprocesses

RecentlyItheremanyprogressinthetheoryofsuperprocesses(seeLZ'4--gi).Inthispaper,wewillestablishtheRicszdecompositiontheoremofexcessivefunctionsofaclassofsuperprocesses,andgeneralizetheclassicalRicszdecompositiontheoremofHuntprocess.FortheconstructionofsupcrprocesscswecanseeL2,4,sj.ConsiderthefollowingrealfunctionPX,9(x,z)=a(x)z b(x)zZ J,(e":--I "z)n.(du),(1)Pcowheren.(du)isakernelfromR'lto(0,~)and'a(x),b(x)andA(x)~I(uZAu)n.(du)areJ0positiveboundedBorclfunctions.AssumingthatE~{Et,11.}is…     

作为T－空间T－伦型不变量的特异指数

对Ｔ-空间之间引进了Ｔ-映射，Ｔ-同胚，Ｔ-映射的Ｔ-同伦，Ｔ-空间的Ｔ-同伦等价等概念．对Ｔ-紧致连通Ｈａｕｓｄｏｒｆｆ空间应用Cｅｃｈ-ｓｍｉｔｈ特异上同调理论定义了特异指数的概念，并在此基础上证明了Ｔ-空间的特异指数是Ｔ-空间的Ｔ-伦型不变量，从而也证明了它是Ｔ-空间的Ｔ-同胚不变量．     

Closed embeddings of Hilbert spaces

Motivated by questions related to embeddings of homogeneous Sobolev spaces and to comparison of function spaces and operator ranges, we introduce the notion of closely embedded Hilbert spaces as an extension of that of continuous embedding of Hilbert spaces. We show that this notion is a special case of that of Hilbert spaces induced by unbounded positive selfadjoint operators that corresponds to kernel operators in the sense of L. Schwartz. Certain canonical representations and characterizations of uniqueness of closed embeddings are obtained. We exemplify these constructions by closed, but not continuous, embeddings of Hilbert spaces of holomorphic functions. An application to the closed embedding of a homogeneous Sobolev space on Rn in L₂(Rn), based on the singular integral operator associated to the Riesz potential, and a comparison to the case of the singular integral operator associated to the Bessel potential are also presented. As a second application we show that a closed embedding of two operator ranges corresponds to absolute continuity, in the sense of T. Ando, of the corresponding kernel operators.     

De Branges spaces and Fock spaces

Abstract

Relations between two classes of Hilbert spaces of entire functions, de Branges spaces and Fock-type spaces with nonradial weights, are studied. It is shown that any de Branges space can be realized as a Fock-type space with equivalent area norm, and several constructions of a representing weight are suggested. For some special classes of weights (e.g. weights depending on the imaginary part only) the corresponding de Branges spaces are explicitly described.     

On spaces of fractal functions

In this paper we Ointroduce linear-spaces consisting of continuous functions whose graphs are the attactors of a special class of iterated function systems. We show that such spaces are finite dimensional and give the bases of these spaces in an implicit way. Given such a space, we discuss how to obtain a set of knots for which the Lagrange interpolation problem by the space is uniquely solvable.     

Harmonic forms and cohomology of singular stratified spaces

We construct a potential theory for differential forms on compact stratified spaces, and we show that the space of harmonic forms of degree k is isomorphic to the singular cohomology of degree k. This theory applies to any triangulable topological space.     

Singular symmetric functionals and stabilizing subspaces of Marcinkiewicz spaces

We consider Marcinkiewicz spaces of functions measurable on a semiaxis that admit a wide set of singular symmetric Dixmier functionals. For elements of these spaces we study the measurability property introduced by A. Connes. We establish that this property is closely connected with the Tauberian property (which is more strong) but is not reduced to it. We specify the maximal subspace of the Marcinkiewicz space such that for its elements both properties are equivalent. We prove that this subspace is not reducible to other known subspaces of the Marcinkiewicz space and that it plays an important role in the theory of Dixmier functionals.     

Equilibrium maps between metric spaces

We show the existence of harmonic mappings with values in possibly singular and not necessarily locally compact complete metric length spaces of nonpositive curvature in the sense of Alexandrov. As a technical tool, we show that any bounded sequence in such a space has a subsequence whose mean values converge. We also give a general definition of harmonic maps between metric spaces based on mean value properties and-convergence.     

Orbifold fibrations of Eschenburg spaces

Most of the few known examples of compact Riemannian manifolds with positive sectional curvature are the total space of a Riemannian submersion. In this article we show that this is true for all known examples, if we enlarge the category to orbifold fibrations. For this purpose we study all almost free isometric circle actions on positively curved Eschenburg spaces, which give rise to principle orbifold bundle structures, and we examine in detail their geometric properties. In particular, we obtain a new family of 6-dimensional orbifolds with positive sectional curvature whose singular locus consists of just two points.      

Singular homology groups of fuzzy topological spaces

Let L be a completely distributive lattice with order reversing involution, and (X, τ) an L-fuzzy topological space. The purpose of this paper is to introduce the fundamental concept of fuzzy algebraic topology-the singular homology groups of the L-fuzzy topological space, in such a way that they take the (usual) cubical singular homology groups of a topological space as a special case. Also, we shall prove that they are L-fuzzy homeomorphic invariants.     

On projectively flat Finsler spaces

First we present a short overview of the long history of projectively flat Finsler spaces. We give a simple and quite elementary proof of the already known condition for the projective flatness, and we give a criterion for the projective flatness of a special Lagrange space (Theorem 1). After this we obtain a second-order PDE system, whose solvability is necessary and sufficient for a Finsler space to be projectively flat (Theorem 2). We also derive a condition in order that an infinitesimal transformation takes geodesics of a Finsler space into geodesics. This yields a Killing type vector field (Theorem 3). In the last section we present a characterization of the Finsler spaces which are projectively flat in a parameter-preserving manner (Theorem 4), and we show that these spaces over ${\mathbb {R}}^{n}$ are exactly the Minkowski spaces (Theorems 5 and 6).