From Sequential to Parallel Growth of Cities： Theory and Evidence from Canada

This paper examines city growth patterns and the corresponding city size distribution evolution over long periods of time using a simple New Economic Geography(NEG) model and urban population data from Canada. The main findings are twofold. First, there is a transition from sequential to parallel growth of cities over long periods of time: city growth shows a sequential mode in the stage of rapid urbanization, i.e., the cities with the best development conditions will take the lead in growth, after which the cities with higher ranks will become the fastest-growing cities; in the late stage of urbanization, city growth converges according to Gibrat′s law, and exhibits a parallel growth pattern. Second, city size distribution is found to have persistent structural characteristics: the city system is self-organized into multiple discrete size groups; city growth shows club convergence characteristics, and the cities with similar development conditions eventually converge to a similar size. The results will not only enhance our understanding of urbanization process, but will also provide a timely and clear policy reference for promoting the healthy urbanization of developing countries.

Some Properties of Infinite Direct Sums

In this paper, we study the sequential convergence in E-direct sums E（X） where X is an Ω-ofamily of Banach spaces and discuss the lifting of the Kadec-Klee property from X to E（X）.

Modeling and Dynamic Analysis for the Foundation of a Blade-Rotor System

In order to achieve the model-based fault monitoring and diagnosis,an accurate model for the rotor system is necessary to locate and quantify faults.Since the dynamic characteristics of a blade-rotor system is influenced by foundation flexibility,the modeling and dynamic analyses on the foundation were sequentially investigated.Firstly,the effect of element size on the model convergence was investigated using the forward difference quotient as the slope of the frequency difference,which found that the model converged when the element size refined to 4mm.Secondly,a modal analysis and a harmonic response analysis were performed to obtain the dynamic characteristics of the foundation structure.Finally,an optimization to the foundation utilizing an additional stiffener was conducted to reduce the foundation response and make the critical speed far away from the working frequency band of 20—50Hz.

Sequential city growth： Theory and evidence from the US

City growth patterns are attracting more attention in urban geography studies. This paper examines how cities develop and grow in the upper tail of size distribution in a large-scale economy based on a theoretical model under new economic geography framework and the empirical evidence from the US. The results show that cities grow in a sequential pattern. Cities with the best economic conditions are the first to grow fastest until they reach a critical size, then their growth rates slow down and the smaller cities farther down in the urban hierarchy become the fastest-growing ones in sequence. This paper also reveals three related features of urban system. First, the city size distribution evolves from low-level balanced to primate and finally high-level balanced pattern in an inverted U-shaped path. Second, there exist persistent discontinuities, or gaps, between city size classes. Third, city size in the upper tail exhibits conditional convergence characteristics. This paper could not only contribute to enhancing the understanding of urbanization process and city size distribution dynamics, but also be widely used in making effective policies and scientific urban planning.

Synthesis of the tetracyclic core of chlorospermines

Chlorospermines A and B are biologically interesting acridone natural products and recently isolated from Glycosmis chlorosperma.We report here a convergent approach to construct the tetracyclic core of the natural products.The two fragments are assembled together through Sonogashira coupling,and a cis-triene intermediate was prepared by using hydrosilylation/desilylation.A 6p-electrocyclization/aromatization sequence served as the key step of the synthesis,which formed the tetrasubstituted arene motif in one pot.