高维铁磁链系统与p—调和映射

研究了与ｐ－Ｌａｐｌａｃｅ算子对映的铁磁甸系统的Ｌａｎｄａｕ－Ｌｉｆｓｈｉｔｚ方程，证明了该方程的从ｍ（ｍ≥３）维紧流形Ｍ（不带边界）映射到Ｒ＾３中的单位球面Ｓ＾２上的整体弱解的存性；建立了ｐ调和映射理论与该方程的联系。     

关于分次环的分次性质和非分次性质

本文证明了对有限群分次环Ｒ而言,下列条件等价：（１）Ｒ是左ｇｒ－自内射环（左ｇｒ－ＰＦ环,左ｇｒ－ＱＦ环,左ｇｒ－线性紧环）．（２）Ｒ是左自内射环（左ＰＦ环,左ＱＦ环,左线性紧环）．（３）Ｒ＃Ｇ^*是左自内射环（左ＰＦ环,左ＱＦ环,左线性紧环）．     

L-Fuzzy θ-良紧空间

引入θ－拓扑和θ－良紧的概念,并对其作了较深刻的研究,主要结果有：（１）θ－良紧是半正则性质和Ｌ好的推广;（２）θ－良紧是弱同胚不变性质;（３）满层θ－良紧空间与θ－良紧空间与θ－良紧空间的积空间是θ－良紧;（４）对于弱艉导空间（Ｌ＾Ｘ〈δ）,它是θ－良紧当且仅当它的底空间（Ｘ,「δ」是θ－紧。     

紧局部完全ω凸空间

本文引入紧完全ω凸空间（ＣωＲ）和紧局部完全ω凸空间（ＣＬωＲ）概念，得到如下结果：若Ｘ是ＣＬωＲ，则Ｘ有（Ｋ）性质；若Ｘ＾＊是ＣＬωＲ，则Ｘ＾＊有（＊＊）性质。     

关于Szasz—Kantorovich算子的强逆不等式

本文对Ｓｚａｓｚ－Ｋａｎｔｏｒｏｖｉｃｈ算子Ｓｎ＾＊（ｆ，ｘ）证明了，当１〈ｐ≤∝时存在某一正整数ｍ，使得ｗψ＾２（ｆ；１／√ｎ）ｐ≤Ｍ（‖Ｓｎ＾＊（ｆ，ｘ）－ｆ‖ｐ＋‖Ｓｍｍ＾＊（ｆ，ｘ）－ｆ‖ｐ），ψ（ｘ）＾２＝ｘ，Ｍ〉０，ｗψ＾（ｆ，ｔ）ｐ为Ｄｉｔｚａｉｎ和Ｔｏｔｉｋ光滑模〔２〕。     

Fell-拓扑的伪紧性（英文）

设X是拓扑空间，CL（X）表示X的所有非空闭子集的族，本文得到了下述结果：在CL（X）上的Fell-拓扑是伪肾的当且仅当X是feebly-紧或者非局部紧或者非σ－紧，由此得到了对于伪紧性不是闭遗传的两类新的拓扑空间。     

诱导的L—fuzzy拓扑空间的a—结构

本文研究Ｌ－ｆｕｚｚｙ拓扑空间的一类几乎开Ｌ－ｆｕｚｚｙ集的性质,在Ｌ－ｆｕｚｚｙ拓扑空间中引入了ａ－结构的概念,证明了由一般拓扑空间（Ｘ,Ｆ）诱导的Ｌ－ｆｕｚｚｙ拓扑空间（Ｌ＾Ｘ,ＷＬ（Ｔ））的ａ－结构必是Ｌ＾Ｘ上的Ｌ－ｆｕｚｚｙ拓扑,并且指出这个拓扑就是由一般拓扑空间（Ｘ,Ｔ）的ａ－结构诱导的,此外,本文还给出了与诱导的Ｌ－ｆｕｚｚｙ拓扑空间的ａ－结构相关的若干性质。     

Littlewood—Paley的gλ函数与面积函数在Lipα（R^n）上的有界性

本文证明，对于Ｌｉｐｓｃｈｉｔｚ空间Ｌｉｐａ（Ｒ＾ｎ）的函数ｆ，若相应Ｌｉｔｔｌｅｗｏｏｄ－Ｐａｌｅｙ的ｇλ函数ｇλ（ｆ）（ｘ）（或面积函数Ｓ（ｆ）（ｘ））在Ｒ＾ｎ中一点有限，则它必处处有限，并且作为Ｌｉｐａ（Ｒ＾ｎ）上的算子，ｇλ和Ｓ在一定意义下有界，这对一切ａ，０＜ａ＜１，和适当的λ成立。     

环的优越扩张与凝聚维数

设Ｓ和Ｒ是环．本文证明了若下述条件之一成立，则Ｓ和Ｒ具有相同的凝聚维数：（１）Ｓ是Ｒ的优越扩张；（２）Ｓ和ＭＭｏｒｉｔａ等价．作为上述结果的推论，我们证明了环Ｒ和下述环类具有相同的凝聚维数：（ｉ）Ｒ上的矩阵环Ｍｎ（Ｒ）；（ｉ）Ｒ和有限群Ｇ（要求｜Ｇ｜－１∈Ｒ）的斜群环；（ｉｉ）Ｓｍａｓｈ积Ｒ＃Ｇ＊（要求Ｇ是有限群且｜Ｇ｜－１∈Ｒ，Ｒ是Ｇ分次环）     

德摩根拓扑代数上的紧性与q—收敛性

在文（１），（２），（３）的基础上，我们首先在德摩根拓扑代数上用有限覆盖性质定义了紧性，并引入ω－元，ω－ｄ－ｑ－聚点等概念，并着重讨论了紧性与ｑ－收敛性之间的关系。     

A simple proof of Sanov’s theorem*

A simple self-contained proof of Sanov's theorem in τ-topology is given, well suited for a first course on large deviations. *This work was supported by the Hungarian National Foundation for Scientific Research under Grant T046376     

Limit theorems of continuous-time random walks with tails

We study the functional limits of continuous-time random walks (CTRWs) with tails under certain conditions. We find that the scaled CTRWs with tails converge weakly to an α-stable Lévy process in D([0, 1]) with M ₁-topology but the corresponding scaled CTRWs converge weakly to the same limit in D([0, 1]) with J ₁-topology.     

函数芽的有限R_r~*(S;n)-决定性

光滑映射芽的有限决定性是奇点理论中一个重要专题 .对函数芽的有限决定性问题 ,主要是在右等价群及其一些子群作用下来讨论的 .本文在 [1]和 [4 ]的基础上讨论函数芽在右等价群的正规子群 R*n (S;n)作用下的有限决定性 ,并组出函数芽有限 R*r (S;n) -决定的一个充分必要条件 .     

On the topology induced by the adjoint of a semigroup of operators

The adjoint of aC ₀-semigroup on a Banach spaceX induces a locally convex σ(X,X ^ℴ)-topology inX, which is weaker than the weak topology ofX. In this paper we study the relation between these two topologies. Among other things a class of subsets ofX is given on which they coincide. As an application, an Eberlein-Shmulyan type theorem is proved for the σ(X,X ^ℴ)-topology and it is shown that the uniform limit of σ(X,X ^ℴ)-compact operators is σ(X,X ^ℴ)-compact. Finally our results are applied to the problem when the Favard class of a semigroup equals the domain of the infinitesimal generator.     

Shorted算子的几何结构

使用算子分块矩阵的技巧,研究了shorted算子,揭示了任意一个正算子和它的shorted算子之间的几何结构关系.此外,对由一个自伴算子A和一个闭子空间S组成的元素对(A,S)的兼容性(compatibility)进行了研究.特别地,当A是正算子时得出了集合∏(A,S)={Q∈∏:R(Q)=S⊥,AQ=Q*A}非空的充要条件;并且对集合∏(A,S)进行了详细的刻化,这里∏和S⊥分别表示一个复Hilbert空间上的所有幂等算子构成的集合和子空间S的正交补空间.     

Some Notes on Large Deviations of Markov Processes

In this paper we shall characterize the large deviation principles (abbreviated to LDP) of Donsker-Varadhan of a Markov process both for the weak convergence topology and for the τ-topology, by means of a hyper-exponential recurrence property. A Lyapunov criterion for this type of recurrence property is presented. These results are applied to countable Markov chains, unidimensional diffusions, elliptic or hypoelliptic diffusions on Rienmannian manifolds. Several counter-examples are equally presented. Received July 20, 1998, Accepted March 25, 1999     

关于随机最远点

首先给出在随机赋范模中子集的随机最远点的概念．进一步,利用随机一致凸性和经典一致凸性之间的联系证明了下面的结果：令（E,｜｜·｜｜）为完备的随机一致凸的随机赋范模,S为E中几乎处处有界并在（ε, λ）一拓扑下的闭子集,则具有S中随机最远点的集合稠于E．     

Every Banach Space is Reflexive

The title above is wrong, because the strong dual of a Banach space is too strong to assert that the natural correspondence between a space and its bidual is an isomorphism. However, for many applications it suffices to replace the norm on the first dual by the weak*-structure in order to solve the non-reflexiveness problem [1]. But in this way, only the original vector space is recovered by taking the second dual. In this work we introduce a suitable numerical structure on vector spaces such that Banach balls, or more precisely totally convex modules, arise naturally in duality, namely as a category of Eilenberg–Moore algebras. This numerical structure naturally overlies the weak*-topology on the algebraic dual, so the entire Banach space can be reconstructed as a second dual. Moreover, the isomorphism between the original space and its bidual is the unit of an adjunction between the two-dualisation functors. Notice that the weak*-topology is normable only if it lives on a finite dimensional space; in that case the original space is trivial as well, hence reflexive. So the overlying numerical structure should be something more general than a norm or a seminorm and thus approach theory [2, 3] enters the picture.     

On unitary transposable matrices of order three

Mathematical Notes - A matrix A ∈ M n (?) is said to be unitarily transposable if A T = Q*AQ for a certain unitary matrix Q. Every 2 × 2 matrix is unitarily transposable; however,...     

关于分次本质右理想

设 Ｒ是 Ｇ－分次,本文讨论了环 Ｒ的相关环 Ｒ,Ｒ＃ Ｇ^*, Ｒｅ, Ｑ（Ｒ）, Ｒ^G, Ｒ*Ｇ及 Ｒ的正规化扩张Ｓ的非奇异性,右一致性,右基座之间的关系．当Ｒ_Ｒ是ＹＪ－内射模时,证明了Ｊ（Ｒ）＝Ｚ（Ｒ）。