A Hierarchical Allometric Scaling Analysis of Chinese Cities: 1991-2014

The law of allometric scaling based on Zipf distributions can be employed to research hierarchies of cities in a geographical region. However, the allometric patterns are easily influenced by random disturbance from the noises in observational data. In theory, both the allometric growth law and Zipf's law are related to the hierarchical scaling laws associated with fractal structure. In this paper, the scaling laws of hierarchies with cascade structure are used to study Chinese cities, and the method of R/S analysis is applied to analyzing the change trend of the allometric scaling exponents. The results show that the hierarchical scaling relations of Chinese cities became clearer and clearer from 1991 to 2014 year; the global allometric scaling exponent values fluctuated around 0.85, and the local scaling exponent approached to 0.85. The Hurst exponent of the allometric parameter change is greater than 0.5, indicating persistence and a long-term memory of urban evolution. The main conclusions can be reached as follows: the allometric scaling law of cities represents an evolutionary order rather than an invariable rule, which emerges from self-organized process of urbanization, and the ideas from allometry and fractals can be combined to optimize spatial and hierarchical structure of urban systems in future city planning.Comment: 28 pages, 10 figures, 5 table

Perturbations of Functional Inequalities for L\'evy Type Dirichlet Forms

Perturbations of super Poincar\'e and weak Poincar\'e inequalities for L\'evy type Dirichlet forms are studied. When the range of jumps is finite our results are natural extensions to the corresponding ones derived earlier for diffusion processes; and we show that the study for the situation with infinite range of jumps is essentially different. Some examples are presented to illustrate the optimality of our results

3-(3,5-Dimethyl-1H-pyrazol-1-yl)propanamide

In the crystal of the title compound, C8H13N3O, mol­ecules are linked by inter­molecular N—H⋯N and N—H⋯O hydrogen bonds into a three-dimensional network. Additional stabilization is provided by weak inter­molecular C—H⋯O hydrogen bonds

Treatment of juxtafoveal central serous chorioretinopathy by compound anisodine injection

AIM: To investigate the efficiency and security of compound anisodine injection in the treatment of juxtafoveal central serous chorioretinopathy(CSC). <p>METHODS: Sixty patients(60 eyes)who were diagnosed of juxtafoveal CSC were assigned randomly into 2 groups: 32 cases(32 eyes, therapeutic group)were injected subcutaneously compound anisodine injection for 2mL q.d around superficial temporal arteries in the affected eyes; 28 cases(28 eyes, control group)received only traditional oral medication. Both groups received therapy for 2 to 4 courses of treatment. The main observations were the best corrected visual acuity(BCVA), subjective symptom, visual field, average light sensitivity and optical coherent topography(OCT).<p>RESULTS: There was no significant difference between the therapeutic group and the control group before treatment(<i>P</i>>0.05), but all the outcome measures at 1, 3mo in the treatment group were significantly improved as compared with control group(<i>P</i><0.05). After 6mo, there were no significant difference between the two groups in all measures(<i>P</i>>0.05). No severe adverse reaction was noted except mild ones such as temporary dry mouth, dizziness and palpitation in a few cases.<p>CONCLUSION: Compound anisodine injection has remarkable effects in the treatment of juxtafoveal CSC. It can shorten the course, improved the visual function and decreased the recurrence rate of CSC