关于度量及纲函数的Hausdorff测度的两个反例

本文研究了度量空间中Hausdorff测度与度量及纲函数的关系.利用拓扑学及Hausdorff测度论中一些性质,构造了两反例来说明存在不等价纲函数g,h和某一紧度量空间(ρ,X),使得Hρ,g与Hρ,h对此紧度量空间等价等问题.这些反例有助于从另一个角度理解文胜友、文志英[4]中主要结果.     

Sierpinski地毯上自相似测度以及Markov测度的加倍性质

众所周知,当自相似集满足强分离条件时,其上的自相似测度都是加倍的.本文进一步证明在强分离条件下,自相似集上的Markov测度都是加倍的.随后,本文讨论了Sierpinski地毯S上自相似测度及Markov测度的加倍性质.当S不满足强分离条件时,将S分为不同的类型,完全刻画了S上加倍的自相似测度及加倍的Markov测度.     

Ahlfors 正则空间上的开集分解与加倍测度

对于一致完全的加倍度量空间建立了 Whitney 分解定理. 作为应用, 借助于 Ahlfors 正则空间上的加倍测度描述了它的任意非空闭集的 Whitney 修正集上的加倍测度.     

加倍测度空间中的热核估计

该文讨论了在加倍测度度量空间中,热核估计的上界与下界的关系.若相应的狄氏型满足局部性条件,则可以由近对角下界估计推出上对角估计.和此前这类问题的研究工作相比,该文给出了更加一般性的结果.     

时空各向异性Gauss场的碰撞概率和维数

设X={X(t)∈R~d,t∈R~N}是一个零均值的时空各向异性的Gauss随机场,ρ和τ分别是在R~N和R~d上引进的两个各向异性的时空度量.在某些一般条件下,本文通过τ下的Hausdorff测度和容度,分别给出了X碰撞概率的上、下界.同时,在ρ、τ和Euclid度量下,本文分别得到了又的像集、图集、逆像集和水平集的Hausdorff维数和填充维数.这些结果包含和推广了现有的仅在时间上各向异性的一类Gauss随机场的相关结果.     

非齐度量测度空间上的Herz型Hardy空间

设(X, d,μ)是一个同时满足上双倍条件和几何双倍条件的非齐度量测度空间.本文首先引进了非齐度量测度空间上的Herz空间,并利用中心块得到了该空间的分解定理.然后,根据离散系数K_(B,S)~((ρ),p),引入了非齐度量测度空间上的原子Herz型Hardy空间与分子Herz型Hardy空间,并证明了原子Herz型Hardy空间和分子Herz型Hardy空间的等价性.最后作为应用,本文讨论了Calderón-Zygmund算子在这些空间上的有界性.     

Lp(Ω)空间上的Coherent风险度量

本文在Banach空间L^P(Ω)上定义Coherent风险度量ρ：L^P(Ω)→R，证明了ρ是下半连续的Coherent风险度量当且仅当存在Banach空间L^q(Ω)中的一个弱^*闭凸概率测度集Q使得ρ(X)=Z∈Q^sup E(-X/rZ)，其中1/p 1/q=1,推广了[3]中的部分结果。     

概率逻辑伪度量空间及其性质

论证有限多个公式的概率分布与生成它的原子公式集的概率分布之间的关系,然后把计量逻辑学与概率逻辑学相结合,提出了概率真度、概率逻辑伪度量空间(F(n),ρP);指出当取均匀概率分布时,概率真度就转化为计量逻辑学中的真度,同时两公式间的概率逻辑伪距离Pρ就转化为计量逻辑学中的伪距离ρ.从而在有限理论中建立了一种更具一般性的概率逻辑伪度量空间理论。     

关于模糊数序列收敛性问题的研究

讨论了模糊数序列在EW-型积分度量下的收敛性问题.首先给出了模糊数序列关于EW-型积分度量、水平EW-型度量以及水平EW-型测度收敛的概念;其次,讨论了模糊数序列关于EW-型积分度量、下方图度量以及水平度量收敛之间的关系,证明了在一定条件下模糊数序列关于EW-型积分度量、下方图度量以及水平度量收敛的等价性.     

自相似集上马尔科夫测度的加倍性质

该文讨论满足开集条件的自相似集上的马尔科夫测度,给出了马尔科夫测度具有加倍性质的一个充分必要条件.作为应用,刻画了几个具体的自相似集上具有加倍性质的马尔科夫测度.     

Gauges for the self‐similar sets

For a self‐similar set E with the open set condition we completely determine the class of its Hausdorff gauges and the class of its prepacking gauges. Moreover, its Hausdorff measures and its packing premeasures with respect to the corresponding gauges are estimated. Without the open set condition we prove that a doubling gauge function is a packing gauge of E if and only if it is a prepacking gauge of E. Also, we give some extensions and applications of these results. Here a gauge function is called a Hausdorff, a prepacking, and a packing gauge of a set, if with respect to the function the set has positive and finite Hausdorff measure, packing premeasure, and packing measure, respectively. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

一类自相似集重分形分支的量纲

本文首先定义具有量纲函数的重分形测度,然后证明当Euclid空间中的两个重分形测度具有等价的量纲函数时,它们也等价.进一步,对于直线上满足强分离条件(SSC)的自相似集,在某些加倍条件下,本文给出判断其重分形分支的量纲函数的充要条件.     

DOUBLING MEASURES ON GENERALIZED CANTOR SETS

We study the doubling property of binomial measures on generalized ternary Cantor subsets of [0, 1]. We find some new phenomena. There are three different cases. In the first case, we obtain an equivalent condition for the measure to be doubling. In the other cases, we show that the condition is not necessary. Then facts and partial results are discussed.     

Generalized M-Matrices

Let ρ?Rⁿ be a proper cone. From the theory of M-matrices (see e.g. [1]) it is known that if there exist α > 0 and a matrix B: ρ→ρ such that A = B?αI, then the following conditions are equivalent: (i) ? A is ρ-monotone,(ii) A is ρ-seminegative, (iii) Re[Spectrum(A)]<0. In this paper we show that while the condition (e) e^tAρ?ρ ?t≥0 is more general than the structural assumption A = B?αI, conditions (i)-(iii) are nevertheless all equivalent to (iv) {x∈ρ: Ax∈ρ}={0} when (e) holds.     

Fuzzy蕴涵代数的素MP-滤子空间(英文)

In this paper,the topological space(PF_MP（X）,T) based on prime MP-filters of a lattice FI-algebra X is constructed firstly and we proved that it is a compact T₀-space if X with condition（P）.Secondly,we restricted T to the set of all maximal MP-filters MF_MP（X） of X and concluded that(PF_MP（X）,T |_PFMP（X） )is a compact T₂ space if X with conditions（P） and（S）.     

单峰扩张映射的捏制序列

设Ｐ及ＡＣ均是准素序列并满足ｍｉｎ｛Ｐ，ＡＣ｝ＲＬＲ∞，ρ（Ｐ）及ρ（ＡＣ）分别是Ｐ及ＡＣ的特征值．设ｆ∈Ｃ０（Ｉ，Ｉ）是个单峰扩张映射并具有扩张常数λ，ｍ是个非负整数．本文证明了若λ（ρ（Ｐ））１／２ｍ，则ｆ的捏制序列Ｋ（ｆ）（ＲＣ）ｍＰ；若λ＞（ρ（ＡＣ））１／２ｍ，则对任极大序列Ｅ，Ｋ（ｆ）＞（ＲＣ）ｍＡＣＥ．（ρ（Ｐ））１／２ｍ及（ρ（ＡＣ））１／２ｍ均是下述意义下的最佳值，即若其中任一个被较小的值代替，则相应的结论便不成立．     

Packing in regular graphs

A set S of vertices in a graph G is a packing if the vertices in S are pairwise at distance at least 3 apart in G. The packing number of G, denoted by ρ(G), is the maximum cardinality of a packing in G. Favaron [Discrete Math. 158 (1996), 287–293] showed that if G is a connected cubic graph of order n different from the Petersen graph, then ρ(G) ≥ n/8. In this paper, we generalize Favaron’s result. We show that for k ≥ 3, if G is a connected k-regular graph of order n that is not a diameter-2 Moore graph, then ρ(G) ≥ n/(k² ? 1).     

Third power associative composition algebras

Classical composition algebras, with a unit element, are well-known and can be obtained by means of the Cayley-Dickson doubling process. If the condition on the existence of unit element is dropped, many new algebras arise. However, it is shown in this paper that if such a weak condition as the associativity of third powers of any element is imposed, only the known flexible composition algebras appear. Partially supported by the DGICYT (PS 90-0129) and by the DGA (PCB-6/91) Supported by a grant from the ‘Plan de Formación del Personal Investigador’ (DGICYT, Spain) This article was processed by the authors using the Springer-Verlag TEX P Jour1g macro package 1991.     

UPPER BOUNDS ON THE LOWER OPEN PACKING NUMBER OF A TREE

Abstract

Let G be a graph and let v be a vertex of G. The open neigbourhood N(v) of v is the set of all vertices adjacent with v in G. An open packing of G is a set of vertices whose open neighbourhoods are pairwise disjoint. The lower open packing number of G, denoted ρ^° _L(G), is the minimum cardinality of a maximal open packing of G while the (upper) open packing number of G, denoted ρ^°(G), is the maximum cardinality among all open packings of G. It is known (see [7]) that if G is a connected graph of order n ≥3, then ρ^°(G) ≤ 2n/3 and this bound is sharp (even for trees). As a consequence of this result, we know that ρ^° _L(G) ≤ 2n/3. In this paper, we improve this bound when G is a tree. We show that if G is a tree of order n with radius 3, then ρ^° _L(G) ≤ n/2 + 2 √n-1, and this bound is sharp, while if G is a tree of order n with radius at least 4, then ρ^° _L(G) is bounded above by 2n/3—O√n).     

Some characterizations of upper doubling conditions on metric measure spaces

We provide several equivalent characterizations for the upper doubling condition introduced in the framework of T. Hytönen for non‐homogeneous metric measure spaces. We also introduce the “smooth strong upper doubling” condition and provide equivalent characterizations, which is related to the development of Littlewood–Paley theory on this non‐homogeneous setting.