A NEGATIVE ANSWER TO A CONJECTURE ON SELF-SIMILAR SETS WITH OPEN SET CONDITION

Zhou and Feng posed a conjecture on self-similar set in 2004. In this paper, a self-similar set is constructed which has a best covering but its natural covering is not a best one. Thus, we indeed give a negative answer to the conjecture.

AN ANSWER TO A CONJECTURE ON SELF-SIMILAR SETS

In this paper, we construct a self-similar set which has a best covering but it is not the natural covering, thus negate the conjecture on self-similar sets posed by Z. Zhou in 2004.

THE REGULARITY OF RANDOM GRAPH DIRECTED SELF-SIMILAR SETS

A set in Rd is called regular if its Hausdorff dimension coincides with its upper box counting dimension. It is proved that a random graph-directed self-similar set is regular a.e..

ON THE EXACT HAUSDORFF MEASURE OF A CLASS OF SELF-SIMILAR SETS SATISFYING OPEN SET CONDITION

In this paper, we provide a new effective method for computing the exact value of Hausdorff measures of a class of self-similar sets satisfying the open set condition （OSC）. As applications, we discuss a self-similar Cantor set satisfying OSC and give a simple method for computing its exact Hausdorff measure.

THE STRUCTURE AND APPROXIMATION OF A.S. SELF-SIMILAR SET

The structure of any a.s. self-similar set K(w) generated by a class of random elements {gn,wσ} taking values in the space of contractive operators is given and the approximation of K(w) by the fixed points {Pn,wσ} of {gn,ow} is obtained. It is useful to generate the fractal in computer.

The Structure and the Sufficent and Necessary Conditions for Generalized Statistically Self-Similar Sets

We constructed a class of generalized statistically self-similar set.S and give the necessary and sufficent conditions to ensure a random recursive set being a generalized statistically self-similar set. The statistically self-similar sets defined by Hutchinson,Falconer,Graf are the special cases of ours.

(S,T)-WEAK TRACTABILITY OF MULTIVARIATE LINEAR PROBLEMS IN THE AVERAGE CASE SETTING

The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear functionals. Generally, we obtained matching necessary and sufficient conditions for (s,t)-weak tractability in terms of the corresponding non-increasing sequence of eigenvalues. Specifically, we discussed (s, t)-weak tractability of linear tensor product problems and obtained necessary and sufficient conditions in terms of the corresponding one-dimensional problem. As an example of applications, we discussed also (s,t)-weak tractability of a multivariate approximation problem.

FRACTAL PROPERTIES OF STATISTICALLY SELF-SIMILAR SETS

In this paper, authors compute the Packing dimension of statistically selfsimilar sets and obtaine the dimension and dimension distribution of statistically self-similar measure.

THE EXACT MEASURES OF A CLASS OF SELF-SIMILAR SETS ON THE PLANE

Let S belong to R^2 be the attractor of the iterated function system {f1, f2, f3 } iterating on the unit equilateral triangle So. where fi（x） =λix ＋ bi, i = 1,2, 3, x =（x1, x2）, b1=（0, 0）, b3=（1-λ3 /2,√3/2 （1-λ3）） This paper determines the exact Hausdorff measure, centred covering measure and packing measure of S under some conditions relating to the contraction parameter.

A Local Property of Hausdorff Centered Measure of Self-Similar Sets

We analyze the local behavior of the Hausdorff centered measure for self- similar sets. If E is a self-similar set satisfying the open set condition, thenC^s（E∩B（x,r））≤（2r）^sfor all x ∈ E and r〉 0, where Cs denotes the s-dimensional Hausdorff centered measure. The above inequality is used to obtain the upper bound of the Hausdorff centered measure. As the applications of above inequality, We obtained the upper bound of the Hausdorff centered measure for some self-similar sets with Hausdorff dimension equal to 1, and prove that the upper bound reach the exact Hausdorff centered measure.

Hlder Estimate of Harmonic Functions on a Class of p.c.f. Self-Similar Sets

In this paper we establish sharp H/51der estimates of harmonic functions on a class of connected post critically finite （p.c.f.） self-similar sets, and show that functions in the domain of Laplacian enjoy the same property. Some weU-known examples, such as the Sierpinski gasket, the unit interval, the level 3 Sierpinski gasket, the hexagasket, the 3-dimensional Sierpinski gasket, and the Vicsek set are also considered.

Weakly Stable Sets of NTU Game

In this paper, the definition of weak dominance is proposed for a NTU game and two new solution concepts of NTU games are introduced: the refined core and weakly stable set. The relationship is explored among the core, the weakly stable set and the refined core.

Some Results on the Upper Convex Densities of the Self-Similar Sets at the Contracting-Similarity Fixed Points

In this paper, some results on the upper convex densities of self-similar sets at the contracting-similarity fixed points are discussed. Firstly, a characterization of the upper convex densities of self-similar sets at the contracting-similarity fixed points is given. Next, under the strong separation open set condition, the existence of the best shape for the upper convex densities of self-similar sets at the contracting-similarity fixed points is proven. As consequences, an open problem and a conjecture, which were posed by Zhou and Xu, are answered.

The Oscillation Inequality of Harmonic Functions on Post Critically Finite Self-Similar Sets

In this paper we establish the oscillation inequality of harmonic functions and HOlder estimate of the functions in the domain of the Laplacian on connected post critically finite （p.c.f.） self-similar sets.

NOTE ON THE PAPER “ AN NEGATIVE ANSWER TO A CONJECTURE ON THE SELF-SIMILAR SETS SATISFYING THE OPEN SET CONDITION”

In this paper, we present a more simple and much shorter proof for the main result in the paper ＂ An negative answer to a conjecture on the self-similar sets satisfy- ing the open set condition＂, which was published in the journal Analysis in Theory and Applications in 2009.

Cantor Type Fixed Sets of Iterated Multifunction Systems Corresponding to Self-Similar Networks

We propose a new approach to the investigation of deterministic self-similar networks by using contractive iterated multifunction systems (briefly IMSs). Our paper focuses on the generalized version of two graph models introduced by Barabási, Ravasz and Vicsek ([1] [2]). We generalize the graph models using stars and cliques: both algorithm construct graph sequences such that the next iteration is always based on n replicas of the current iteration, where n is the size of the initial graph structure, being a star or a clique. We analyze these self-similar graph sequences using IMSs in function of the size of the initial star and clique, respectively. Our research uses the Cantor set for the description of the fixed set of these IMSs, which we interpret as the limit object of the analyzed self-similar networks.

THE EXISTENCE THEOREM OF THE CONE-WEAK SUBDIFFERENTIAL OF SET-VALUED MAPPING

In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 47H17,90C29.

基于SET-CNN的紧凑型地波雷达弱目标检测方法

紧凑型高频地波雷达发射功率较低且采用小孔径阵列,导致雷达回波中的弱目标增多,进而引起基于距离-多普勒谱的目标检测方法性能降低,目标探测能力减弱。为提高紧凑型地波雷达对弱目标的检测性能,本文提出一种基于同步提取变换-卷积神经网络(Synchroextracting Transform-Convolutional Neural Network,SET-CNN)的紧凑型地波雷达弱目标检测方法:首先在时频谱处理中,利用信噪比方法抑制信号中的海杂波,减少杂波时频脊线对目标检测的影响;然后基于SET时频谱构建时频脊线样本数据库,再通过卷积神经网络进行时频脊线分类,并基于分类结果的后处理完成船只目标检测。通过仿真和实测数据验证提出的目标检测方法,结果表明,本文提出的方法能够有效检测到弱目标,提高紧凑型地波雷达的目标检测性能。

关于一些特殊图类的弱控制多项式的研究

研究一些特殊图类的弱控制多项式.令图G=(V(G),E(G))是一个简单连通图,若对任意v∈V(G),存在u∈V(G),使得uv∈E(G)且d(u)≥d(v)成立,则称v弱控制u.设W(G)?V(G),如果对任意u∈V(G)W(G),存在v∈W(G),使得v弱控制u,则称W(G)为图G的一个弱控制集.含点数最少的弱控制集称为最小弱控制集,最小弱控制集中所包含点的个数称为图G的弱控制数,记为γwd(G).图G的弱控制多项式为WD(G,x)=nΣj=γwd(G)Wd(G,j)x印j,其中Wd(G,j)表示图G中阶为j的弱控制集的个数.

一类弱监督数据中多视角扰动的特征选择方法

弱标签消歧技术可以用来消除数据中的噪声标签.然而,经由弱标签消歧后的数据中依然可能存在冗余或不相关特征,因此带来了弱监督数据中的特征选择这一实际问题.在弱标签消歧后得到的数据的基础上,提出了一种基于多视角扰动的特征选择框架,其能够分别从样本和特征多个视角出发,构造不同的扰动数据,以便求解出多个不同的特征选择结果,从而为后续的学习任务提供基础性集成工具.此外,所提的多视角扰动特征选择框架适用于不同类型、不同约束下的搜索进程.在12组高维数据上,通过注入5种不同比例的标签噪声和使用3种不同类型的特征度量准则,实验结果表明,所提方法求得的特征选择结果能够从准确率和稳定性的层面极大地提升分类性能.