The Hausdorff Dimension and Hausdorff Measure of Full Parry Measure Subset of Finite Type

All the full Parry measure subsets of a given subshift of finite type determined by an irreducible 0-1 matrix have the same Hausdorrf dimension and Hausdorff measure which coincide with those of the set of finite type.

THE DIMENSION FOR RANDOM SUB-SELF-SIMILAR SET

In this article, the Hausdorff dimension and exact Hausdorff measure function of any random sub-self-similar set are obtained under some reasonable conditions. Several examples are given at the end.

On the Equality of Hausdorff Dimensions and Conformal Measures of Parabolic Maps

Let f, g be two parabolic maps of degree ≥ 2. HD(J) denotes the Hausdorff dimension of the Julia set J and m f and m g denote the t-conformal measure supported on the Julia set J(f) and J(g) respectively. In this paper we show that if J(f) and J(g) are locally connected and f and g topologically conjugate, then HD(J(f)) = HD(J(g)), mg = mfoh-1 .

On the Continuity of Julia Sets and Hausdorff Dimension of N CP and Parabolic Maps

Denote by HD（J（f）） the Hausdorff dimension of the Julia set J（f） of a rational function f. Our first result asserts that if f is an NCP map, and fn → f horocyclically,preserving sub-critical relations, then fn is an NCP map for all n ≥≥ 0 and J（fn） →J（f） in the Hausdorff topology. We also prove that if f is a parabolic map and fn is an NCP map for all n ≥≥ 0 such that fn→4 f horocyclically, then J（fn） → J（f） in the Hausdorff topology, and HD（J（fn）） →4 HD（J（f））.

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.

HAUSDORFF DIMENSION OF GENERALIZED STATISTICALLY SELF-AFFINE FRACTALS

The authors consider generalized statistically self-affine recursive fractals K with random numbers of subsets on each level. They obtain the Hausdorff dimensions of K without considering whether the subsets on each level are non-overlapping or not. They also give some examples to show that many important sets are the special cases of their models.

The Proof of the Sufficient and Necessary Conditions which Make the Hausdorff Measure of the Generalized Non-uniform Cantor Set'exist

The paper succeeds in the obtaining a class of generalized non-uniform Cantor set based on the iteration （1）： Si（x） = αix ＋ bi, x ∈ [0, 1], i = 1,2,…, m, where 0 〈 αi 〈 1, i = 1,2,…,m; bi ＋ αi 〉 0, i = 1,2,…,m- 1, b1 = 0 and αm ＋ bm = 1. Providing the sufficient and necessary conditions of its existence Hausdorff measure.

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 RANDOM SHIFT SET AND RANDOM SUB-SELF-SIMILAR SET

First of all the authors introduce the concepts of random sub-self-similar set and random shift set and then construct the random sub-self-similar set by a random shift set and a collection of statistical contraction operators.

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 Advances of the Research for Random Recursive Sets(Ⅰ)

We introduce the probability properties of random recursive sets systematically in this paper. The main contents include convergence, zero\|one law and support of distribution and self\|similarity.Hutchinson constructed a class of strictly self\|similar sets and got many important results on fractal properties.Graf investigated the fractal properties of a special statistically self\|similar set. We have investigated various self\|similar sets and their probability properties and fractal properties.\;

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.

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.

MEASURES AND THEIR DIMENSION SPECTRUMS FOR COOKIE-CUTTER SETS IN R^d

The characteristics of cookie-cutter sets in R^d are investigated. A Bowen's formula for the Hausdorff dimension of a cookie-cutter set in terms of the pressure function is derived. The existence of self-similar measures, conformal measures and Gibbs measures on cookie-cutter sets is proved. The dimension spectrum of each of these measures is analyzed. In addition, the locally uniformly a-dimensional condition and the fractal Plancherel Theorem for these measures are shown. Finally, the existence of order-two density for the Hausdorff measure of a cookie-cutter set is proved.

多宽带雷达协同目标微动周期估计方法

微动周期是区分弹头和仿形诱饵的重要特征.针对当前主要的雷达微动周期估计方法存在时间资源消耗大、对单雷达测量精度要求高、需要多宽带雷达同步观测等缺点,提出一种多宽带雷达协同目标微动周期估计方法.首先利用最小均方(LMS)算法进行目标真实尺寸估计;然后利用变尺度差频处理通过尺寸序列提取目标微动周期;最后通过仿真验证了本文方法的有效性,并探索了应用边界条件.该方法无需多宽带雷达同步观测,且在单雷达常规尺寸测量精度和时间资源消耗条件下即可准确估计目标微动周期.

The pointwise dimensions of Moran measures

In this paper,we get the formulas of upper(lower) pointwise dimensions of some Moran measures on Moran sets in Rd under the strong separation condition.We also obtain formulas for the dimension of the Moran measures.Our results extend the known results of some self-similar measures and Moran measures studied by Cawley and Mauldin.

The Dense Fractal Sets with the Hausdorff Dimension

In this paper, for any given s (0 ≤s≤1), we construct a Cantor-type set E, such that dimH Es- s and Es is dense in [0,1].

砂轮磨损自动补偿技术在硬质合金刀具产线中的应用

为保证硬质合金刀具加工精度以及减少停机时间,实现硬质合金刀具各尺寸参数的自动补偿至关重要。介绍了一种硬质合金刀具尺寸参数的自动补偿方法,通过对砂轮状态的在线检测与补偿来间接保证硬质合金刀具的尺寸参数,并阐述了砂轮在线检测技术、砂轮磨损自动补偿在实际生产中的应用。试验结果表明:砂轮磨损自动补偿技术具有较高的准确性,误差≤0.004mm,能有效补偿因砂轮磨损而造成的硬质合金刀具尺寸参数变化。

基于犹豫模糊集的水质评价方法

为了更全面反映水体综合状态,本文基于单因子评价水质等级的结果,计算指标与等级的相关系数,筛选出强相关的指标.采用专家打分构造犹豫模糊水质评价初始矩阵,建立基于犹豫模糊指数熵和线性插值悲观升维的加权犹豫模糊兰氏距离测度多属性评价方法.最后,结合浙江省部分水库水质数据进行实例分析.结果表明,所提出的基于犹豫模糊集距离测度的水质综合评价方法更为合理有效.

轮对几何参数及踏面缺陷光电检测方法

提出了一种基于光电检测技术的车辆轮对综合参数自动检测方法。运用精密激光位移传感、CCD及数字图像处理技术,实现了轮缘厚度、轮缘高度、车轮直径等尺寸参数的非接触自动检测;再结合精密运动控制,以及车轴和圆周方向的快速激光扫描,实现了踏面擦伤和剥离等缺陷参数的分类和识别。实验结果表明,基于上述测量方法的检测系统,其尺寸参数测量精度为0.2mm,擦伤深度测量精度为0.1mm,剥离长度测量精度为0.5mm,能满足车辆段修现场使用的要求。