Near-field imaging of locally perturbed periodic surfaces

This paper concerns the inverse scattering problem to reconstruct a locally perturbed periodic surface. Different from scattering problems with quasi-periodic incident fields and periodic surfaces, the scattered fields are no longer quasi-periodic. Thus the classical method for quasi-periodic scattering problems no longer works. In this paper, we apply a Floquet-Bloch transform based numerical method to reconstruct both the unknown periodic part and the unknown local perturbation from the near-field data. By transforming the original scattering problem into one defined in an infinite rectangle, the information of the surface is included in the coefficients. The numerical scheme contains two steps. The first step is to obtain an initial guess, i.e., the locations of both the periodic surfaces and the local perturbations, from a sampling method. The second step is to reconstruct the surface. As is proved in this paper, for some incident fields, the corresponding scattered fields carry little information of the perturbation. In this case, we use this scattered field to reconstruct the periodic surface. Then we could apply the data that carries more information of the perturbation to reconstruct the local perturbation. The Newton-CG method is applied to solve the associated optimization problems. Numerical examples are given at the end of this paper to show the efficiency of the numerical method

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

Bright lesion detection in retinal images

Master'sMASTER OF SCIENC