This paper puts forward the concept of fractal company is in the process of online shopping. According to the characteristics of the network shopping, the paper establishes the mathematical model of fractal clustering, and uses the fractal dimension to describe and depict Fractal Company. Online shopping is actually the management of the entire supply chain. Based on similar structure of fracta...

this note introduces a new general conjecture correlating the dimensionality dt of an infinitelattice with n nodes to the asymptotic value of its wiener index w(n). in the limit of large nthe general asymptotic behavior w(n)≈ns is proposed, where the exponent s and dt are relatedby the conjectured formula s=2+1/dt allowing a new definition of dimensionality dw=(s-2)-1.being related to the topol...

This paper deals with the stabilization of Takagi-Sugeno models (T-S) using state feedback controllers. New sufficient stability conditions are given for both continuous and discrete T-S models. The stability conditions, formulated in term of bilinear matrix inequalities (BMIs), are based on a piecewise quadratic Lyapunov function and the use of the so-called S-procedure. A method of linearisat...

On the basis of the analysis of random pulse signal, the mathematical model of the two-parameter random signal is established. Based on which, it is found that the random signal has a non-integer dimension fractal characteristics, and the fractal dimension is the ratio of the count distribution and the number of discrete degree ln σ . Besides, the mass distribution of the particle group is also...

In-line holographic microscopy images of micrometer-scale fractal aggregates can be interpreted with an effective-sphere model to obtain each aggregate's size and the population-averaged fractal dimension. We demonstrate this technique experimentally using model fractal clusters of polystyrene nanoparticles and fractal protein aggregates composed of bovine serum albumin and bovine pancreas insu...

We introduce a model for prediction the behavior of electrodes which modified withcarbon nanotubes in a polymer medium. These kinds of polymer composites aredeveloped in recent years, and experimental data for its percolation threshold isavailable. We construct a model based on percolation theory and fractal dimensionsand using experimental percolation threshold for calculating the moments of c...

BACKGROUND AND AIMS Fractal analysis allows calculation of fractal dimension, fractal abundance and lacunarity. Fractal analysis of plant roots has revealed correlations of fractal dimension with age, topology or genotypic variation, while fractal abundance has been associated with root length. Lacunarity is associated with heterogeneity of distribution, and has yet to be utilized in analysis o...

Colloidal particles that interact through strong, short-range, secondary attractions in liquids form irreversible "slippery" bonds that are not shear-rigid. Through event-driven simulations of slippery attractive spheres, we show that space-filling fractal clusters still emerge from the process of "slippery" diffusion-limited aggregation (DLA). Although slippery and classic DLA clusters have th...

DNS and laboratory experiments show that the spatial distribution of straining stagnation points in homogeneous isotropic 3D turbulence has a fractal structure with dimension D(s)=2. In kinematic simulations the exponent gamma in Richardson's law and the fractal dimension D(s) are related by gamma=6/D(s). The Richardson constant is found to be an increasing function of the number density of str...

In this paper, the optical properties of one dimensional fractal structures are investigated. We consider six typical fractal photonic structures: the symmetric dual cantor-like fractal structure, the asymmetric dual cantor-like fractal structure, the single cantor-like fractal structure, the symmetric dual golden-section fractal structure, the asymmetric dual golden-section fractal structure a...