重分形Hausdorff测度的有限测度子集

设μ为 Ｒ^d上 Ｂｏｒｅｌ概率测度,ｑ,ｔ∈Ｒ,记 Ｈ_μ^q,t为 Ｏｌｓｅｎ定义的重分形 Ｈａｕｓｄｏｒｆｆ测度,证明了当μ为测度时,Ｈ_μ^q,t的有限测度子集存在．     

On the Isaacs Problem Concerning Finite p-Solvable Linear Groups

In this work a finite $\Pi$ -separable complex irreducible linear group G is studied. The conditions for its $S_\Pi$ -subgroup to be normal in G and Abelian are determined. The results provide a solution to the well-known Isaacs problem in some particular cases.     

A Topological View of Ramsey Families of Finite Subsets of Positive Integers

If is an initially hereditary family of finite subsets of positive integers (i.e., if and G is initial segment of F then ) and M an infinite subset of positive integers then we define an ordinal index . We prove that if is a family of finite subsets of positive integers such that for every the characteristic function χ_F is isolated point of the subspace

Packing Measure Analysis of Harmonic Measure

We show that, for any Jordan domain J in R², harmonic measureis supported by a Borel set of packing dimension 1. We alsoobtain incomplete analogs to the results of Makarov, which connectthe almost everywhere behavior of the derivative near the boundaryfor the conformal mapping function from the unit disk J withthe Hausdorff measure properties of sets supporting the harmonicmeasure.     

Construction of Subsets of Finite Positive Hausdorff Measure on the Hyperspace (𝔉(X), ρH)

Subsets of finite positive Hausdorff measure will be constructed for all Hausdorff functions h_α(t)=t^α, α>0 a real number.     

Some Relations Between Packing Premeasure and Packing Measure

Let K be a compact subset of Rⁿ, 0 s n. Let , P^s denote s-dimensional packing premeasure andmeasure, respectively. We discuss in this paper the relationbetween and P^s. We prove:if , then ; and if , then for any > 0, there exists a compact subset F of K such that and P^s(F) P^s(K) – .1991 Mathematics Subject Classification 28A80, 28A78.     

基于有界度抛物复形的解析函数边值问题

该文讨论使用Circle Packing 方法来考虑解析函数边值问题. 寻求满足给定边界条件的解析函数, 是许多理论和实际问题中应用极为广泛的重要问题. 该文使用有界度的Circle Packing来构造给定区域上满足一定边界条件的解析函数, 为此首先讨论了 Circle Packing 映射与经典多项式之间的关系, 并在此基础上证明离散序列对解析函数的收敛性. 这个结果扩展了Carter和Rodin以及Dubejko早期使用正则6-packing取得的结果.     

Some Measure-Theoretic Properties of Packing Measure

Periodica Mathematica Hungarica -     

广义谢尔宾斯基海绵的Packing测度

讨论了三维欧氏空间上的一类自仿射集──广义谢尔宾斯基(Sierpinski)海绵的填充测度(Packing Measure),对φ(t)=t^θ,φ(t)=t^θ/|logt|及更一般的情况,证明了填充测度P_ψ[K(T,D)]为无穷或有限的条件,     

MPQ-trees for the Orthogonal Packing Problem

Given a set of rectangular items of different sizes and a rectangular container, the aim of the bi-dimensional Orthogonal Packing Problem (OPP-2 for short) is to decide whether there exists a non-overlapping packing of the items in this container. The rotation of items is not allowed. In this paper we present a new exact algorithm for solving OPP-2, based upon the characterization of solutions using interval graphs proposed by Fekete and Schepers. The algorithm uses MPQ-trees, which were introduced by Korte and M?hring to recognize interval graphs.     

Kronecker Constants for Finite Subsets of Integers

A set of integers S is called ε-Kronecker if every function on S of modulus one can be approximated uniformly to within ε by a character. The least such ε is called the ε-Kronecker constant.     

Packing Measure and Dimension of Random Fractals

We consider random fractals generated by random recursive constructions. We prove that the box-counting and packing dimensions of these random fractals, K, equals , their almost sure Hausdorff dimension. We show that some almost deterministic conditions known to ensure that the Hausdorff measure satisfies also imply that the packing measure satisfies 0< . When these conditions are not satisfied, it is known . Correspondingly, we show that in this case , provided a random strong open set condition is satisfied. We also find gauge functions (t) so that the -packing measure is finite.     

The Two-Dimensional Finite Bin Packing Problem. Part II: New lower and upper bounds

This paper is the second of a two part series and describes new lower and upper bounds for a more general version of the Two-Dimensional Finite Bin Packing Problem (2BP) than the one considered in Part I (see Boschetti and Mingozzi 2002). With each item is associated an input parameter specifying if it has a fixed orientation or it can be rotated by . This problem contains as special cases the oriented and non-oriented 2BP. The new lower bound is based on the one described in Part I for the oriented 2BP. The computational results on the test problems derived from the literature show the effectiveness of the new proposed lower and upper bounds.     

半正定两相驱动问题的多步有限体积方法及其理论分析

考虑多维半正定两相驱动方程的初边值问题,在非结构网格上构造多步的迎风有限体积格式,利用微分方程先验估计理论证明了格式的离散模形式的误差估计为D(△t~2 h),其中△t和h分别表示时空步长．数值算例进一步验证了格式的有效性．     

The Finite Subsets of Z2 Having the Extension Property

The paper considers finite subsets Z^d which possess the extensionproperty, namely that every collection {c_k}_k– of complexnumbers which is positive definite with respect to is the restrictionof the Fourier coefficients of some positive measure on T^d.All finite subsets of Z² which possess the extension propertyare described.     

求解等圆Packing问题的完全拟物算法

沿着拟物的思路进一步研究了具有NP难度的等圆Packing问题.提出了两个拟物策略,第一个是拟物下降算法,第二是让诸圆饼在某种物理定律下做剧烈运动.结合这两个策略,提出了一个统一的拟物算法.当使用N(N=1,2,3,…,100)等圆最紧布局的国际记录对此算法进行检验时,发现对于N=66,67,70,71,77,89这6个算例,本算法找到了比当前国际纪录更优的布局.     

二阶测度链上Sturm-Liouville型边值问题的多个正解存在性

本文讨论一类二阶测度链上Sturm-Liouville型边值问题X~△△ f(t,x(σ(t))=0,t∈[t_1,t_2],αx(t_1)—βx~△(t_1)=0,γx(σ(t_2)) δx~△(σ(t_2))=0,其中f_1,t_2](?),(?)是测度链．在适当的条件下,通过运用Leggett-Williams不动点定理,得到了三个正解的存在性．