广义Moran集的重Fractal分解

设Ｋ为广义Ｍｏｒａｎ集．μ为支撑在Ｋ上的无穷乘积测度，本文研究结合μ的Ｋ的重ｆｒａｃｔａｌ分解，利用配齐降阶技巧与网测度技巧讨论了在此分解下维谱ｆ（α）的性质，并讨论了若干很重要的典型例子．     

广义重fractal分解及加权的f（α）曲线

设Ｋ为广义Ｍｏｒａｎ集，μ为定义在Ｋ上的无穷乘积测定，本文研究结合μ的Ｋ的重ｆｒａｃｔａｌ分解，其中维谱ｆ（ａ，ω）的性质，并讨论了若干很重要的典型例子。     

有限义性质下一类广义MORAN集的重分形分解

本文在一类广义Moran集上定义了一种弱分离条件－有限交性质,并证明了重分形分解在广泛的一类分形上仍然成立。本文部分的推广了Cawley和Manlain的结果。     

具有有限记忆的随机分形的重分形分解

Dryakhlov和Tempelman对具有有限记忆的随机分形集的Hausdorff维数进行了研究,本文对具有有限记忆的随机分形集K(ω)的重分形分解集Kα(ω)进行研究,得到了在一定条件下,这种随机分形集重分形分解集Kα(ω)的Hausdorff维数表达式.     

数学年刊第16卷B辑第2期目次和提要

数学年刊第１６卷Ｂ辑第２期目次和提要Ｒ２到Ｕ（Ｎ）的调和映射的显示结构谷超豪胡和生利用Ｄａｒｂｏｕｘ变换构造Ｒ２到Ｕ（Ｎ）调和映射，并且得到新的调和映射（包括Ｕｎｉｔｏｎ）的显示公式；广义Ｍｏｒａｎ分形的Ｈａｎｓｄｏｒｆｆ维数、测度和Ｆｏｕｒｉｅｒ极...     

R~d中齐次Moran集的Hausdorff维数

本文利用位势理论给出了Ｒｄ中齐次Ｍｏｒａｎ集的Ｈａｕｓｄｏｒｆｆ维数公式,从而回答了山中的问题．     

局部熵的高维重分形分析

对不变测度建立了高维形式的重分形分析,即考察与多维参数相关联的重分形分解.利用非紧集或非不变集的高维(q,μ)熵,给出了局部熵的高维重分形谱的一个关系式.     

一类随机递归集的重分形分解

本文讨论了一类广义的随机递归集的重分形性质,通过将其构造中的子集间的不重叠条件减弱到有限交性质,使得子集间允许适当重叠,同时保证递归集不为空集和其重分形维数计算仍具有明显的表达式.     

由表示系统生成的分形的维数

在这篇文章里,由Ｒｎ中点的表示系统所生成的自仿射集中,给出了自仿射集满足Ｍｏｒａｎ开集条件的一个新的判别方法和不满足开集条件的自相似集的Ｈａｕｓｄｏｒｆｆ维数的上界和下界,并根据两个实例估计出其上下界是相等的．     

多型随机递归集关于统计自相似测度的Multifractal分解

本文构造了一类多型随机递归集K,并利用Falconer的方法[1]获得了K的重分形分解集Kα(α>0)的Hausdorff维数和Packing维数.     

Quasisymmetric mappings on Moran sets

This paper studies the quasisymmetric mappings on Moran sets. We introduce a generalized form of weak quasisymmetry and prove that, on Moran set satisfying the small gap condition, a generalized weakly quasisymmetric mapping is quasisymmetric. We further give a criterion for the quasisymmetry of mappings between Moran sets with some regular structure.     

The HAUSDORFF DIMENSION AND MEASURE OF THE GENERALIZED MORAN FRACTALS AND FOURIER SERIES

ＴｈｅＨＡＵＳＤＯＲＦＦＤＩＭＥＮＳＩＯＮＡＮＤＭＥＡＳＵＲＥＯＦＴＨＥＧＥＮＥＲＡＬＩＺＥＤＭＯＲＡＮＦＲＡＣＴＡＬＳＡＮＤＦＯＵＲＩＥＲＳＥＲＩＥＳ￥ＲＥＮＦＵＴｈＯ；ＬＩＡＮＧＪＩＮＲＯＮＧＡｂｓｔｒａｃｔ：Ｔｈｉｓｐａｐｅｒｓｔｕｄｉｅｓｔｈ...     

Sums of moran sets

We find conditions on the dissection of Moran set so that the group it generates under addition has positive Lebesgue measure.     

SUMS OF MORAN SETS

We find conditions on the dissection of moran set so that the group it generates under addition has positive Lebesgue masure.     

Multi Input Dynamical Modeling of Heat Flow With Uncertain Diffusivity Parameter

This paper focuses on the multi-input dynamical modeling of one-dimensional heat conduction process with uncertainty on thermal diffusivity parameter. Singular value decomposition is used to extract the most significant modes. The results of the spatiotemporal decomposition have been used in cooperation with Galerkin projection to obtain the set of ordinary differential equations, the solution of which synthesizes the temporal variables. The spatial properties have been generalized through a series of test cases and a low order model has been obtained. Since the value of the thermal diffusivity parameter is not known perfectly, the obtained model contains uncertainty. The paper describes how the uncertainty is modeled and how the boundary conditions are separated from the remaining terms of the dynamical equations. The results have been compared with those obtained through analytic solution.     

Components of generalized Kato resolvent set and single-valued extension property

In this paper, we use the constancy of certain subspace valued mappings on the components of the generalized Kato resolvent set and the equivalences of the single-valued extension property at a point 0 for operators which admit a generalized Kato decomposition to obtain a classification of the components of the generalized Kato resolvent set of operators. We also give some applications of these results.     

On the convergence of cross decomposition

Cross decomposition is a recent method for mixed integer programming problems, exploiting simultaneously both the primal and the dual structure of the problem, thus combining the advantages of Dantzig—Wolfe decomposition and Benders decomposition. Finite convergence of the algorithm equipped with some simple convergence tests has been proved. Stronger convergence tests have been proposed, but not shown to yield finite convergence.In this paper cross decomposition is generalized and applied to linear programming problems, mixed integer programming problems and nonlinear programming problems (with and without linear parts). Using the stronger convergence tests finite exact convergence is shown in the first cases. Unbounded cases are discussed and also included in the convergence tests. The behaviour of the algorithm when parts of the constraint matrix are zero is also discussed. The cross decomposition procedure is generalized (by using generalized Benders decomposition) in order to enable the solution of nonlinear programming problems.     

Pointwise dimensions of general Moran measures with open set condition

Recently Lou and Wu obtained the formulas of pointwise dimensions of some Moran measures on Moran sets in Rd under the strong separation condition.In this paper,we prove that the result is still true under the open set condition.Due to the lack of the strong separation condition,our approach is essentially different from that used by Lou and Wu.We also obtain the formulas of the Hausdorff and packing dimensions of the Moran measures and discuss some interesting examples.     

The isolated invariant sets of a flow

Some definitions such as m-chain recurrent set, weakly gradient flow and generalized Morse decomposition for a flow defined on a topological space are introduced in this paper. Some conclusions, include the chain recurrent set contain the m-chain recurrent set; the m-chain recurrent set contain the non-wandering set, are proved. In some flows the non-wandering set is proper subset of the m-chain recurrent set; in the meantime the m-chain recurrent set is proper subset of the chain recurrent set. Moreover some criterions for the existence of trajectories joining singular points and a necessary and sufficient condition of the weakly gradient flow are also given here. At last the generalized Morse decomposition of the invariant set are discussed in the paper.     

Covers of generalized quadrangles, 2. Kantor-Knuth covers and embedded ovoids

In this paper, which is a sequel to [12], we proceed with our study of covers and decomposition laws for geometries related to generalized quadrangles. In particular, we obtain a higher decomposition law for all Kantor-Knuth generalized quadrangles which generalizes one of the main results in [12]. In a second part of the paper, we study the set of all Kantor-Knuth ovoids (with given parameter) in a fixed finite parabolic quadrangle, and relate this set to embeddings of parabolic quadrangles into Kantor-Knuth quadrangles. This point of view gives rise to an answer of a question posed in [11].