关于Henstock积分的Harnack扩张的一个注记

本文定义了（ＲＬ）条件，利用（ＲＬ）条件给出了等式成立的充分必要条件．     

强忠实右S－系

本文引入了相对平坦左Ｓ－系的概念，用来给出了强忠实右Ｓ－系的特征刻划。     

G(F4′)条件与加强形式的停止定理

首次提出了Ｇ（Ｆ４′）条件，给出了Ｇ（Ｆ４′）条件的两个等价关系，得到了加强形式的停止定理和强鞅的一个等价关系．     

可数状态MDP的平均模型

本文考虑可数状态空间任意行动空间MDP的平均模型，分析了四个平均报酬准则，在通常的遍历性条件下，用鞅论的方法证明了其最优报酬值的一致性和最优策略的存在性，从而较好地解决了Feinberg和Park[1]再次提及的Open问题．通过导入相应于Feinberg和Park[1]的非循环条件，用概率分析的方法证明了一致最优（f，B）-生成策略的存在性，推广了Feinberg和Park（1994）的主要结果。     

关于（F,ρ）—不变凸性函数多目标规划的最优性条件

本文给出了一类更一般的广义凸性函数的定义：（Ｆ，ρ）——不变凸性函数，并讨论了其最优性条件。     

Ekeland变分原理的一个注记

给出了一般形式的Ekeland变分原理,并根据新得到的结论讨论了泛函强制性条件与一般性弱PS条件之间的关系.     

BCI-代数的Fuzzy广义结合理想

引入了BCI-代数的fuzzy广义结合理想的概念，给出了它的一种刻画，讨论了fuzzy广义结合理想与其它fuzzy理想的关系，并利用fuzzy广义结合理想得到了拟结合BCI-代数成为结合BCI-代数的几个特征。     

（S↑-）模糊积分意义下的可积函数空间的若干性质

给出(S↑-)模糊积分的定义，讨论其基本性质。当模糊测度μ满足(T)条件(见命题3.3)时，可以得到，(S↑-)模糊积分的p次(S↑-)模糊可积函数空间Lp(p≥1)是实数域R上的线性空间，且当μ次可加时，Lp(p≥1)在相应的距离ρp(定义4．3)下，(Lp，ρp)构成一完备的距离空间。     

关于非单调算子的变分问题

该文应用有限维逼近的方法讨论了一类非单调算子的变分不等方程，并在所谓的（Ｆ）条件下将锐角原理推广到变分问题之中，从而得到了很一般的解的存在性．     

基于矩阵分裂的广义逆A_（T，S）~（2）的表示及其应用

本文首先给出基于矩阵分裂的广义逆Ａ_（Ｔ，Ｓ）~（２）的表示，并将其应用于某些线性方程组迭代格式。本文的结果是一般性的，推广了文［３，４］中的结论。     

Beurling Zeta Functions, Generalised Primes, and Fractal Membranes

We study generalised prime systems , with tending to infinity) and the associated Beurling zeta function . Under appropriate assumptions, we establish various analytic properties of , including its analytic continuation, and we characterise the existence of a suitable generalised functional equation. In particular, we examine the relationship between a counterpart of the Prime Number Theorem (with error term) and the properties of the analytic continuation of . Further we study ‘well-behaved’ g-prime systems, namely, systems for which both the prime and integer counting function are asymptotically well-behaved. Finally, we show that there exists a natural correspondence between generalised prime systems and suitable orders on . Some of the above results are relevant to the second author’s theory of ‘fractal membranes’, whose spectral partition functions are given by Beurling-type zeta functions, as well as to joint work of that author and R. Nest on zeta functions attached to quasicrystals.The work of M. L. Lapidus was partially supported by the U. S. National Science Foundation under grant DMS-0070497.     

（Inco） Projective Modules of Relatively Hereditary Torsion Theroy

In the paper, we define(inco) project modules of relatively hereditary torsion theory Υ by intersection complement of module and study their properties; secondly, we define the(inco) Υ-semisimple ring by(inco) Υ-projective module and study their properties. When Υ is a trivial torsion theory on R-rood, we prove that R is a semisimple ring if and only if R is a(inco) semisimple ring and satisfies(inco) condition.     

Existence of solutions for elliptic equations without superquadraticity condition

By weakening or dropping the superquadraticity condition (SQC), the existence of positive solutions for a class of elliptic equations is established. In particular, we deal with the asymptotical linearities as well as the superlinear nonlinearities.     

Zur Kennzeichnung Fanoscher Affin-Metrischer Geometrien

Let V be a vector space over the commutative field K such that char K 2 2 dim V , and let Q:V K be a quadratic form of rank 2. The pair (A(V,K),_Q), consisting of the affine space A(V,K) and the congruence relation _Q, defined by (a,b)_Q (c,d) Q(a–b) = Q(c–d) (a,b),(c,d) V×V, is called an affine-metric fano-space of rank 2. In this paper, such spaces are characterized by three simple geometrical properties.     

Characterization of Amalgamated Free Blocks of a Graph von Neumann Algebra

We identify two noncommutative structures naturally associated with countable directed graphs. They are formulated in the language of operators on Hilbert spaces. If G is a countable directed graphs with its vertex set V(G) and its edge set E(G), then we associate partial isometries to the edges in E(G) and projections to the vertices in V(G). We construct a corresponding von Neumann algebra as a groupoid crossed product algebra of an arbitrary fixed von Neumann algebra M and the graph groupoid induced by G, via a graph-representation (or a groupoid action) α. Graph groupoids are well-determined (categorial) groupoids. The graph groupoid of G has its binary operation, called admissibility. This has concrete local parts , for all e ∈ E(G). We characterize of , induced by the local parts of , for all e ∈ E(G). We then characterize all amalgamated free blocks of . They are chracterized by well-known von Neumann algebras: the classical group crossed product algebras , and certain subalgebras (M) of operator-valued matricial algebra . This shows that graph von Neumann algebras identify the key properties of graph groupoids. Received: December 20, 2006. Revised: March 07, 2007. Accepted: March 13, 2007.     

用条件(Pw)刻画的幺半群

本文引入了条件（P_w）,讨论了条件（P_w）与条件（P）、条件（P_E）之间的关系,刻画了幺半群上S-系的平坦性.     

Minimal imperfect graphs: A simple approach

We provide a very short proof of the following theorem of Lovász, and of its consequences:A graph is perfect if and only if in every induced subgraph the number of vertices does not exceed the product of the stability and clique numbers of the subgraph.This proof is conceptually new: it does not use the replication operation, or any kind of polyhedral argument; the arguments resemble more the well-known ways of deducing structural properties of minimal imperfect graphs. However, the known proofs of these structural properties use Lovász's result, whereas the present work leads to a proof of Lovász's result itself, and actually to a slight sharpening.The author gratefully acknowledges financial support from Ministère de la Recherche et de la Technologie (the French Ministry of Research and Technology, MRT) which sponsored his three month visit to Laboratory ARTEMIS of Grenoble University which motivated him to do this work.     

一类拟线性椭圆方程组非平凡解的存在性

首先证明了一个抽象的紧性定理,然后借此定理证明了对应于一类拟线性椭圆方程组的泛函在比Boccardo和De．Figueiredo(2002)的条件更弱的条件(文中记为弱类(AR)条件)下满足(C)条件,并利用山路引理证明了这类拟线性椭圆方程组非平凡解的存在性,最后举出两个例子验证了文中所给条件(即弱类(AR)条件)的确比Boccardo和De．Figueiredo(2002)的条件弱．     

The strong open set condition in the random case

To describe some fractal properties of a self-similar set or measure, such as the Hausdorff dimension and the multifractal spectrum, it is useful that it satisfy the strong open set condition, which means there is an open set satisfying the open set condition and, additionally, a part of the self-similar set must meet the open set. It is known that in the non-random case the strong open set condition and the open set condition are equivalent. This paper treats the random case. If the open set condition is assumed, we show that there is a random open set satisfying the strong open set condition. Further, we give an application to multifractal analysis of the random self-similar fractal.

     

On products of experiments

Summary An experiment in the sense of Blackwell is a finite parameterized set of probability distributions on a sample space. The product of a parameterized set of experiments is the experiment which describes the process in which independent elements from all of the sample spaces in the set are observed. In the paper, methods are developed for computing the properties of a product of experiments from the properties of the components. In particular, asymptotic properties (as N ) of the experiment describing N independent observations from a single sample space are investigated.Research partially supported by National Science Foundation Grant (GP-5227).