基于分数维的图像检索新方法

在研究两种分数维———微分计盒维数和多分形维数的基础上提出了分数维直方图的概念 ,并把它用于基于内容的图像检索 ,提出了一种新的纹理特征检索算法———二维分数维直方图相交法 对Brodatz标准纹理库和真实图像库检索的结果表明其方法具有良好的性能 。

Fractal dimension for porous metal materials of FeCrAl fiber

The FeCrA1 fiber was used to prepare porous metal materials with air-laid technology, and then followed by sintering at 1300 ℃ for a holding period of 2 h in the vacuum. In addition, a novel fractal soft, which was developed based on the fractal theory and the computer image processing technology, was explored to describe the pore structure of porous metal materials. Furthermore, the fractal dimension of pore structure was calculated by the soft and the effects of magnification and porosity on ffactal dimension were also discussed. The results show that the fractal dimension decreases with increase in the magnification, while it increases continuously with the porosity enhancing. The interrelationship between the fractal dimension and the magnification or porosity can be presented by the equation of D=α_0exp（-x/α_1）＋α_2和D=k_2-（k_1-k_2）/[1＋exp（（θ-k_0）/k_3）], respectively.

Investigation of Dynamic Behavior in 1D Non-uniform Granular System

We present a non-uniform granular system in one-dimensional case, whose granularity distribution has the fractal characteristic. The particles are subject to inelastic mutual collisions and obey Langevin equation between collisions. By Monte Carlo simulation we study the dynamic actions of the system. Far from the equilibrium, i.e., τ 〉〉 τe, the results of simulation indicate that the inhomogeneity of the system and the inelasticity of the particles have great influences on the dynamic properties of the system, and correspondingly the influence of the inhomogeneity is more significant.

Characterizations of PSD Fractal of Porous Medium

A volume-based method for measuring particle-size distribution (PSD) fractal dimensions of porous mediums was developed by employing laser size-analyzing technology. Compared with conventional approaches of using hydrometer or screen to determine PSD, this method can avoid calculation errors and measure smaller size-scale porous medium. In this paper the experimental porous mediums were brown soil, kaolin and sand soil. A micro-order of magnitude (10 -5 m) in particle-size interval could be shown in PSD results of brown soil and kaolin. The experiments indicated that brown soil had a nearly mono-fractal PSD character, while kaolin and sand soil showed multi-fractal PSD characters. By the adsorption isotherm experiments, the PSD fractal dimensions of the sand soil were also found to keep a linearly increasing relation with the linear adsorptive parameters of the soils in different intervals to adsorb benzene from aqueous solution.

A method for choice of optimum scale on land use monitoring in Tarim River Basin

Optimal scale is one of the important issues in ecology and geography.Based on land-use data of the Tarim River Basin in Xinjiang of China in the 1950s,regarding the area of land use types as the parameter in scale selecting,the histograms of the patches in area are charted.Then,by reinforcing the normalized scale variances(NSV) with 3 landscape indi-ces,the scale characteristics of land use in the Tarim River Basin can be summarized.(1) NSV in the Tarim River up to a maximum at scale of 1:50,000 which is considered appropriate for the Tarim River.(2) Diversity indices of saline land are consistent with NSV's.Diversity indices and NSV of sandy land showed that the appropriate scale is in the same scale domain.There is a significant difference between diversity indices and NSV of forestland and shrub-land.(3) Fractal dimension of sandy land and saline land showed a hierarchical structure at a scale of 1:10,000.Fractal dimension of forestland and shrubland are distributed under the same hierarchical structure in the region.

FINITE DIMENSIONAL BEHAVIOR FOR THE DISSIPATIVE GENERALIZED SYMMETRIC REGULARIZED LONG WAVE EQUATIONS

This paper deals with the asymptotic behaviour of solutions for thegeneralized symmetric regularized long wave equations with dissipation term. We first show theexistence of global weak attractors for the periodic initial value problem of this equations in H^2x H^1. And then by an energy equation and an idea of Ghidaglia and Guo, we conclude that the globalweak attractor is actually the global strong attractor for S(t) in H^2 (Ω) x H^1 (Ω). The finitedimensionality of the global attractor is also established.

Temperature Properties in Polydisperse Granular Mixtures

Numerical simulations are employed to consider the problem of determining the granular temperatures of the species of a homogeneous heated granular mixture with a power-law size distribution. The partial granular temperature ratios are studied as functions of the fractal dimension D, the restitution coefflcient e, the rescaled viscosity time, the average occupied area fraction φ, the total particle number N and the number fraction. Different species of particles in a power-law system typically do not have the same mean kinetic energy, namely the granular temperature. It is found that the extent of nonequipartition of kinetic energy is determined by the fractal dimension D, the restitution coemcient e and the rescaled viscosity time, while is insensitive to the total particle number N, the area fraction φ and the number fraction.

Self-similar fractals: An algorithmic point of view

This paper studies the self-similar fractals with overlaps from an algorithmic point of view.A decidable problem is a question such that there is an algorithm to answer"yes"or"no"to the question for every possible input.For a classical class of self-similar sets{E b.d}b,d where E b.d=Sn i=1(E b,d/d+b i)with b=(b1,...,b n)∈Qn and d∈N∩[n,∞),we prove that the following problems on the class are decidable:To test if the Hausdorff dimension of a given self-similar set is equal to its similarity dimension,and to test if a given self-similar set satisfies the open set condition(or the strong separation condition).In fact,based on graph algorithm,there are polynomial time algorithms for the above decidable problem.