On a question of A. Kameyama concerning self-similar metrics

A. Kameyama introduced the concept of self-similar topological system and asked the following fundamental question: given a topological self-similar system (K,_{(fi)i∈{1,2,...,N}})$(K,{(f_i)}_{i\in \{1,2,...,N\}})$, does there exist a metric on K   comparable to the topology such that all the functions _fi$f_i$ are contractions? We modify Kameyama's question (which has a negative answer for an arbitrary topological self-similar system) by weakening the requirement that the functions in the topological self-similar system be contractions to requiring that they be φ  -contractions. More precisely we give an affirmative answer to the following question: given a topological self-similar system (K,_{(fi)i∈{1,2,...,N}})$(K,{(f_i)}_{i\in \{1,2,...,N\}})$ does there exist a metric δ on K   which is compatible with the original topology and a comparison function φ:[0,∞)→[0,∞)$\phi :[0,\infty )\to [0,\infty )$ such that all the functions _fi:(K,δ)→(K,δ)$f_i:(K,\delta )\to (K,\delta )$ are φ  -contractions? Consequently the iterated function system ((K,d),_{(fi)i∈{1,2,...,N}})$((K,d),{(f_i)}_{i\in \{1,2,...,N\}})$, where d is a metric on K compatible with the original topology on K, is φ-hyperbolic.     

Self-similar Solutions of the Navier–Stokes Equations on Weak Weighted Lorentz Spaces

In the present paper, we prove the existence of global solutions for the Navier–Stokes equations in Rnwhen the initial velocity belongs to the weighted weak Lorentz space Λn,∞(u) with a sufficiently small norm under certain restriction on the weight u. At the same time, self-similar solutions are induced if the initial velocity is, besides, a homogeneous function of degree-1. Also the uniqueness is discussed.     

Bounds of the Hausdorff Measure of Sierpinski carpet

By means of the idea of [2]（Jia Baoguo,J.Math.Anal.Appl.In press） and the self.similarity of Sierpinski carpet, we obtain the lower and upper bounds of the Hausdorff Measure of Sierpinski carpet, which can approach the Hausdorff Measure of Sierpinski carpet infinitely.     

Quantization dimension of random self-similar measures

In this paper, we study the quantization dimension of a random self-similar measure μ supported on the random self-similar set K(ω). We establish a relationship between the quantization dimension of μ and its distribution. At last we give a simple example to show that how to use the formula of the quantization dimension.     

基于分形点过程自相似流的队列性能分析

通过对交换机排队系统进行仿真,分析了以分形点过程( FPP )自相似业务流为输入的排队系统的性能.仿真结果显示,自相似业务流量模型下队列的性能与传统指数流量模型下的队列性能大不相同.文中所获得的仿真结果可用于网络流量模型、网络设计、网络拥塞控制和流量工程等.     

补偿光纤的参数对自相似脉冲压缩效应的影响

从非线性薛定谔（NLS）方程出发,用数值方法研究了在自相似脉冲压缩技术中反常色散补偿光纤的群速度色散参量(GVD参量)和非线性参量对脉冲压缩效应的影响。结果表明,补偿光纤的GVD参量对压缩因子和脉冲峰值功率的影响是周期性的,随着GVD参量数值的增大,脉冲能量按集中-分散-集中的规律周期性变化,且变化周期逐渐增大,一周期内的能量转移加剧;每次能量集中时,脉宽接近压缩极限。最佳光纤长度随着GVD参量数值的增加而下降,但不受非线性参量的影响。另一方面,非线性参量的增大会降低压缩因子,不利于脉冲压缩。通过优化选择补偿光纤参数,能够接近脉宽压缩极限,提高脉冲压缩质量。     

Hausdorff measure of uniform self-similar fractals

Let d ≥ 1 be an integer and E a self-similar fractal set, which is the attractor of a uniform contracting iterated function system (UIFS) on R ^d . Denote by D the Hausdorff dimension, by H ^D (E) the Hausdorff measure and by diam(E) the diameter of E. If the UIFS is parametrised by its contracting factor c, while the set ω of fixed points of the UIFS does not depend on c, we will show the existence of a positive constant depending only on ω, such that the Hausdorff dimension is smaller than one and H ^D (E) = diam(E) ^D if c is smaller than this constant. We apply our result to modified versions of various classical fractals. Moreover, we present a parametrised UIFS, where ω depends on c and show the inequatily H ^D (E) < diam(E) ^D , if c is small enough.     

自相似集的质量分布原理与Hausdorff测度及其应用

本文提出了满足开集条件的自相似集的质量分布原理.作为应用,得到了计算一类满足开集条件的自相似集的Hausdorff测度的准确值的方法,并举例说明了此方法对于计算一类满足开集条件的自相似集的Hausdorff测度的准确值是行之有效的.     

正实数维分形集的构造方法

给出了测量一类分形集维数的简单方法. 根据这种测量方法, 可以构造出任意实数维分形集,并且分形集可以不是自相似的.     

Overflow and loss probabilities in a finite ATM buffer fed by self-similar traffic

In [13], real-time measurements from LANs, variable-bit-rate video sources, ISDN control-channels, the World Wide Web and other communication systems have shown that traffic exhibits a behaviour of self-similar nature. In this paper, we give new lower bounds to buffer-overflow and cell-loss probabilities for an ATM queue system with a self-similar cell input traffic and finite buffer. The bounds are better than those obtained in [20], in an important region of parameters. As in [20], they decay hyperbolically with buffer size, when the latter goes to infinity. However, in some region, a factor which accompanies the decay is higher in this paper than in [20]. This revised version was published online in June 2006 with corrections to the Cover Date.