Strongly Regular Decompositions of the Complete Graph

We study several questions about amorphic association schemes and other strongly regular decompositions of the complete graph. We investigate how two commuting edge-disjoint strongly regular graphs interact. We show that any decomposition of the complete graph into three strongly regular graphs must be an amorphic association scheme. Likewise we show that any decomposition of the complete graph into strongly regular graphs of (negative) Latin square type is an amorphic association scheme. We study strongly regular decompositions of the complete graph consisting of four graphs, and find a primitive counterexample to A.V. Ivanov's conjecture which states that any association scheme consisting of strongly regular graphs only must be amorphic.     

Strong Martingales: Their Decompositions and Quadratic Variation

Set-indexed strong martingales and a form of predictability for set-indexed processes are defined. Under a natural integrability condition, we show that any set-indexed strong submartingale can be decomposed in the Doob–Meyer sense. A form of predictable quadratic variation for square-integrable set-indexed strong martingales is defined and sufficient conditions for its existence are given. Under a conditional independence assumption, these reduce to a simple moment condition and, if the strong martingale has continuous sample paths, the resulting quadratic variation can be approximated in the L ₂-sense by sums of conditional expectations of squared increments.     

The Strong Continuity of Convex Functions

A convex function defined on an open convex set of a finite-dimensional space is known to be continuous at every point of this set. In fact, a convex function has a strengthened continuity property. The notion of strong continuity is introduced in this study to show that a convex function has this property. The proof is based on only the definition of convexity and Jensen’s inequality. The definition of strong continuity involves a constant (the constant of strong continuity). An unimprovable value of this constant is given in the case of convex functions. The constant of strong continuity depends, in particular, on the form of a norm introduced in the space of arguments of a convex function. The polyhedral norm is of particular interest. It is straightforward to calculate the constant of strong continuity when it is used. This requires a finite number of values of the convex function.     

Strong Wedderburn Decompositions of Banach Algebras Containing Analytic Semigroups

We prove that if a Banach algebra contains an analytic semigroupwhich satisfies a certain growth condition then neither it norany homomorphic image of it may have a Strong Wedderburn Decomposition,in particular it must be weakly amenable.     

Modulus of Strong Proximinality and Continuity of Metric Projection

In this paper we initiate a quantitative study of strong proximinality. We define a quantity ϵ(x, t) which we call as modulus of strong proximinality and show that the metric projection onto a strongly proximinal subspace Y of a Banach space X is continuous at x if and only if ϵ(x, t) is continuous at x whenever t > 0. The best possible estimate of ϵ(x, t) characterizes spaces with 1 \frac121 \frac{1}{2} ball property. Estimates of ϵ(x, t) are obtained for subspaces of uniformly convex spaces and of strongly proximinal subspaces of finite codimension in C(K).     

推点与二部竞赛图的强连通性

设D是一个有向图,S是V(D)的子集．在D中推S,是指颠倒D中所有的只有一个端点在S中的弧的方向． Klostermeyer提出了对于任给的一个有向图D,能否通过推点使之成为强连通的有向图的问题．他证明了上述判定问题是NP-完备的．而我们论证了对于任意的二部竞赛图D,如果V(D)的二划分是(X,Y),并满足3≤|X|≤|Y|≤2|X|-1-1, 则可以通过推点使D成为强连通的有向图,而且,|Y|的上界2|X|-1-1是最好可能的．     

Strong local homogeneity and coset spaces

We prove that for every homogeneous and strongly locally homogeneous separable metrizable space there is a metrizable compactification of such that, among other things, for all there is a homeomorphism such that . This implies that is a coset space of some separable metrizable topological group .

     

强奇异积分算子的多线性交换子的Sharp极大函数估计和连续性

本文对由强奇异积分算子和加权Lipschitz函数生成的多线性交换子证明了其sharp极大函数估计,作为应用,得到了该多线性交换子的连续性.     

关于p-叶星形性和强星形性的充分条件 (英)

本文利用微分从属的方法得到了单位圆盘内p-叶星形函数和强星形函数的某些充分条件．     

交C-连续偏序集

利用偏序集上的半拓扑结构,引入了交C-连续偏序集概念,探讨了交C-连续偏序集的性质、刻画及与C-连续偏序集、拟C-连续偏序集等之间的关系.主要结果有:(1)交C-连续的格一定是分配格;(2)有界完备偏序集(简记为bc-poset)L是交C-连续的当且仅当对任意x∈L及非空Scott闭集S,当∨S存在时有x∧∨S=∨{x∧s:s∈S};(3)完备格是完备Heyting代数当且仅当它是交连续且交C-连续的;(4)有界完备偏序集是C-连续的当且仅当它是交C-连续且拟C-连续的;(5)获得了反例说明分配的完备格可以不是交C-连续格,交C-连续格也可以不是交连续格.     

On Strong Reality of Finite Simple Groups

In this paper we shall consider the following problem. Which finite simple groups have the property: any element is inverted by an involution?     

无限族非扩张映象及非扩张半群的强收敛定理

目的是研究Banach空间中无限族非扩张映象和非扩张半群的强收敛问题.为此提出一个改进的迭代序列,在适当条件下,某些强收敛定理被证明.结果改进和推广了一些人的最新结果.     

算子强不可约的充要条件

本文证明了Cowen-Douglas 算子是强不可约的充要条件,是它的换位代数模去其Jacobson 根同构于$H^{\infty}(D)$中的一个闭子代数,这里$D$表示开单位圆盘, $H^{\infty}(D)$表示$D$上的有界解析函数的全体.     

一类非自相似集的强正则性

给出了由压缩函数族Si(x)=xM+im,(M>m>1,i=0,1,2,…,m-1)通过限制某个Si出现的方式而产生的压缩不变集Eu,v.根据一个相关序列集个数的特征及连分数性质,证明了集Eu,v的盒维数与Hausdorff维数相等.     

Strong compactness and a partition property

We show that if holds for every , then is strongly compact.

     

Continuity of Weak Solutions for Quasilinear Parabolic Equations with Strong Degeneracy

The aim of this paper is to study the continuity of weak solutions for quasilinear degenerate parabolic equations of the form U_t-Δφ(u)=O, whereφ■C~1(R~1)is a strictly monotone increasing function.Clearly,the above equation has strong degeneracy,i.e.,the set of zero points ofφ′(·)is permitted to have zero measure. This is an answer to an open problem in[13,p.288].     

Strong clique trees,neighborhood trees,and strongly chordal graphs

Maximal complete subgraphs and clique trees are basic to both the theory and applications of chordal graphs. A simple notion of strong clique tree extends this structure to strongly chordal graphs. Replacing maximal complete subgraphs with open or closed vertex neighborhoods discloses new relationships between chordal and strongly chordal graphs and the previously studied families of chordal bipartite graphs, clique graphs of chordal graphs (dually chordal graphs), and incidence graphs of biacyclic hypergraphs. © 2000 John Wiley & Sons, Inc. J. Graph Theory 33: 151–160, 2000