NaP zeolite was synthesized via ultrasonic-assisted hydrothermal synthesis. The methods for Cu or Fe doping were screened while exploring element distributions in liquid and solid phases. Oxidation process of methylene blue (MB) and methyl violet-6B (MV-6B) by doped NaP zeolites was surveyed....

Zipf’s law can be used to describe the rank-size distribution of cities in a region. It has seldom been employed to research urban internal structure. In this paper, we demonstrate that the space-filling process within a city follows Zipf’s law and can be characterized with the rank-size...

Central place systems have been demonstrated to possess self-similarity in both the theoretical and empirical perspectives. A central place model can be treated as a monofractal with a single scaling process. However, a real system of human settlements is a complex network with multi-scaling...

Replacements resulting from competition are ubiquitous phenomena in both nature and society. The evolution of a self-organized system is always a physical process substituting one type of components for another type of components. A logistic model of replacement dynamics has been proposed in...

<i>Urban form takes on properties similar to random growing fractals and can be described in terms of fractal geometry. However, a model of simple fractals is not effectual enough to characterize</i> <i>both the global and local features of urban patterns. In this paper</i> multifractal measurements are...

The rank-size regularity known as Zipf’s law is one of the scaling laws and is frequently observed in the natural living world and social institutions. Many scientists have tried to derive the rank-size scaling relation through entropy-maximizing methods, but they have not been entirely...

The empirical studies of city-size distribution show that Zipf’s law and the hierarchical scaling law are linked in many ways. The rank-size scaling and hierarchical scaling seem to be two different sides of the same coin, but their relationship has never been revealed by strict mathematical...

Using fractal theory and urban land-use maps for 1949, 1959, 1980, and 1996, this study is devoted to analyzing the evolutionary features of urban form and land-use structure in Hangzhou, China. We find that self-similarity exists in both the built-up area and the municipal area, and fractal...