Computing Equilibria of Semi-algebraic Economies Using Triangular Decomposition and Real Solution Classification

In this paper, we are concerned with the problem of determining the existence of multiple equilibria in economic models. We propose a general and complete approach for identifying multiplicities of equilibria in semi-algebraic economies, which may be expressed as semi-algebraic systems. The approach is based on triangular decomposition and real solution classification, two powerful tools of algebraic computation. Its effectiveness is illustrated by two examples of application.Comment: 24 pages, 5 figure

A method of calculating bandstructure in real-space with application to all-electron and full potential

We introduce a practical and efficient approach for calculating the all-electron full potential bandstructure in real space, employing a finite element basis. As an alternative to the k-space method, the method involves the self-consistent solution of the Kohn-Sham equation within a larger finite system that encloses the unit-cell. It is based on the fact that the net potential of the unit-cell converges at a certain radius point. Bandstructure results are then obtained by performing non-self-consistent calculations in the Brillouin zone. Numerous numerical experiments demonstrate that the obtained valence and conduction bands are in excellent agreement with the pseudopotential k-space method. Moreover, we successfully observe the band bending of core electrons

The influence of cultural exchange on international trade: an empirical test of Confucius Institutes based on China and the ‘Belt and Road’ areas

With the implementation of the Belt and Road initiative, the development of trade governance between China and countries along the line has expanded. Firstly, this paper analyzes the impact of cultural exchanges through Confucius Institutes on regional trade cooperation from three dimensions: improving cultural identity, reducing trade costs and sharing information. Secondly, we utilise data trade data from the 64 countries along the line from 2004 to 2015 to examine the effects of Confucius Institutes in regional trade cooperation with China. Overall, we found that Confucius Institutes have significantly promoted the trade growth of China and those countries. Compared to exports, Confucius Institutes promote greater growth imports to the Belt and Road countries from China. Compared to countries in the Road, Confucius Institutes better promoted trade growth between China and countries in the Belt. This empirical conclusion stands under various robustness tests. Forth, after the 12th five-yearplan, the promoting effects of the Confucius Institute has been strengthening. Fifth, the smaller the cultural distance, the stronger the promoting effects of the Confucius Institute on the trade in BRI countries. However, the effect of language similarity is not significant. This study indicates that the Chinese government should pay more attention to the economic effects of cultural factors, such as the Confucius Institute, in policy design