关于满足弱开集条件的自相似测度的局部维数的注记

对于自相似集合,已知开集条件与强开集条件是等价的,我们讨论了强开集条件的基些性质,并给出了自似测度局部维数研究的一个应用。     

自相似VBR业务环境下ABR流量控制算法的性能分析

近年的研究表明,无论是ＬＡＮ还是ＷＡＮ业务流,都表现出自相似业务特征。为准确评价ＡＢＲ流量控制算法在起初网络中的性能。本文用仿真方法研究了ＡＢＲ流量控制算法在自相似ＶＢＲ业务环境下的动态特性。其目的在于：为交换机设计另ＡＢＲ流量控制算法的选择提供理论依据;通过仿真来确定算法的优缺点,为进上步改进算法性能提供参考。     

Propagation of discontinuouswaves along a dry bed

The possibility of simulating the process of propagation of discontinuous waves along a dry bed on the basis of the equations of the first approximation of shallow water theory is studied. It is shown that the consistent losses of the free-stream total momentum and energy can be found from the mass conservation law within the framework of the shallow water equations. As an example, solutions of the problem of dam break with a dry bed in the lower pool and the problem of impingement of a discontinuous wave on a coastal shelf are constructed. These exact solutions are compared with the results of laboratory experiments.     

正交异性体反平面问题另一形式自相似解的推导

正交异性体的反平面运动方程有几种表达方式，而以自相似解表达方式尤为简单。由于在弹性动力学问题的计算中可以获得解析解，使得考虑的问题相应地简化，并具有一定的普遍性，因此对自相似形式的解的推导具有重要的意义。本文针对这一问题进行研究，利用复变函数论的方法导出另一形式自相似解的一般表达式。应用该法可以很容易地将所讨论的问题转化为Riemann—Hilbert问题，而后一问题可以用同通常的Muskhelishvili方法求解，并且可以相当简单地得到问题的闭合解。这些解在断裂动力学以及弹性动力学问题当中具有重要的应用价值。     

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

We analyze the local behavior of the Hausdorff centered measure for selfsimilar sets. If E is a self-similar set satisfying the open set condition, then Cs(E∩B(x,r)) ≤(2r)s for all x ∈ E and r 0, where Csdenotes 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.     

多分支自相似集的自仿嵌入

本文研究了一类多分支自相似集的自仿嵌入.利用压缩映射的不动点,在一定条件下,证明了若一个自相似集能自仿嵌入到另一个自相似集中,则它们对应的迭代函数系的压缩比满足某种代数性质.     

改进的基于时变FARIMA模型和小波变换的网络流量预测算法

网络的流量特性是反映网络实时状态的一个重要特征,对于网络流量的分析、预测一直是该领域的研究热点。传统的基于时间序列模型的方法在计算效率和多尺度分析能力方面存在一定的局限性。本文提出了一种改进的基于小波变换和时变FARIMA模型的流量预测方法,利用小波变换的多尺度分析特性将原有的流量数据进行分解,在使用时变FARIMA模型进行预测,可大大提高算法的执行效率和预测的准确性。最后,本文选取了Bellcore提供的真实的网络流量进行了仿真实验,验证了提出的预测方法的准确性和有效性。     

Singular problem for a third-order nonlinear ordinary differential equation arising in fluid dynamics

Results concerning singular Cauchy problems, smooth manifolds, and Lyapunov series are used to correctly state and analyze a singular “initial-boundary” problem for a third-order nonlinear ordinary differential equation defined on the entire real axis. This problem arises in viscous incompressible fluid dynamics and describes self-similar solutions to the boundary layer equation for the stream function with a zero pressure gradient (plane-parallel flow in a mixing layer). The analysis of the problem suggests a simple numerical method for its solution. Numerical results are presented.     

Cooling Process for Inelastic Boltzmann Equations for Hard Spheres, Part II: Self-Similar Solutions and Tail Behavior

We consider the spatially homogeneous Boltzmann equation for inelastic hard spheres, in the framework of so-called constant normal restitution coefficients. We prove the existence of self-similar solutions, and we give pointwise estimates on their tail. We also give general estimates on the tail and the regularity of generic solutions. In particular we prove Haff's law on the rate of decay of temperature, as well as the algebraic decay of singularities. The proofs are based on the regularity study of a rescaled problem, with the help of the regularity properties of the gain part of the Boltzmann collision integral, well-known in the elastic case, and which are extended here in the context of granular gases. Mathematics Subject Classification (2000): 76P05 Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05].