Spherical Tiling by 12 Congruent Pentagons

The tilings of the 2-dimensional sphere by congruent triangles have been extensively studied, and the edge-to-edge tilings have been completely classified. However, not much is known about the tilings by other congruent polygons. In this paper, we classify the simplest case, which is the edge-to-edge tilings of the 2-dimensional sphere by 12 congruent pentagons. We find one major class allowing two independent continuous parameters and four classes of isolated examples. The classification is done by first separately classifying the combinatorial, edge length, and angle aspects, and then combining the respective classifications together.Comment: 53 pages, 40 figures, spherical geometr

China’s new exchange rate regime, optimal basket currency and currency diversification

We build an optimising framework to analyse a class of economies that adopt an ECU-type basket currency while in transition to increased flexibility of the exchange rate regime. Instead of conventional basket pegging, such an economy uses an ECU-type currency index as a benchmark for monitoring and assessing exchange rate movements. This provides an anchoring device for the nations exchange rate regime and allows the home currencys exchange rate to fluctuate. Under the assumption that the central bank is chiefly interested in maintaining stability, the optimal structure of the basket currency is based on its contribution to minimizing the volatility of the countrys external account. A currency invariance index is applied to capture the effect of the countrys exit from exclusive linkage with the US dollar. The approach is illustrated by Chinese exchange rate policy. We find it advisable and viable for China to form a basket currency with a diversified portfolio of currencies. While the portfolios weighting scheme could favour the dollar, euro and Japanese yen, we show that the composition of the basket is open to a wide range of possibilities. Moreover, contrary to general fears, there is considerable potential for China to engage in currency diversification, which will not necessarily affect the dollars position.basket currency; currency diversification; China

Monotonicity Results for Arithmetic Means of Concave and Convex Functions

By majorization approaches, some known results on monotonicity of the arithmetic means of convex and concave functions are proved and generalized once again

A Multi-Country NOEM Analysis of China with Cross-Country Heterogeneity

This thesis develops a multi-country model for China based on the New Open Economy Macroeconomics to study China's interactions with the United States, the Euro Area and the rest of the world. The model is estimated to identify heterogeneous structural characteristics of these economies using the Bayesian approach. Then the estimated model is simulated to find the international transmission of productivity improvements originated in each area. In particular, the model is applied to the modelling of heterogeneous external asset and liability positions and to analysis of the influences of international investment on the spillover effects of the shocks. Our model provides a comprehensive framework with heterogeneous structural features for open economy analysis between multiple countries, while the scale of the model is moderate and the identification is robust. In addition, our work broadens the family of general equilibrium models designed for the Chinese economy. Our estimation finds large heterogeneity of structural parameter values and policy functions between these economies. China and the US have more distorted consumption patterns than other areas, and the production of the Euro Area is more vulnerable to shocks. The monetary policy of China can be described by both interest rate and money quantity rules with different targets, while other economies generally follow interest rate rules. Simulations show that productivity improvements from the US and the EA have larger spillover effects than the improvements originated in China. The US can promote trade surplus by stimulating growth. For China, productivity increase cannot easily build up her international investment position further, due to the adjustment costs induced by her large net position. The valuation effects are significant under large gross positions. Such effects are caused by interest rate differentials more than by exchange rate movements