Extraction formulae in Inverse problems

1. 将封闭方法应用于背景多层材料中未知夹杂物和裂纹信息的提取；未知多边形声硬障碍和分段线性裂缝。给出了从Dirichlet-to-Neumann图或远场图中提取信息的一些公式。我们对以往探针法的应用进行了反思，明确了探针法的两面性。对封闭法在EIT和薛定谔方程Cauchy问题中的应用进行了分析和数值试验。

1. We applied the enclosure method to the problem of extracting information about unknown inclusions and cracks embedded in a background multilayered material ; unknown polygonal sound-hard obstacles and piecewise linear cracks. Some extraction formulae of the information from the Dirichlet-to-Neumann map or the far field pattern were given.2. We reconsidered the previous applications of the probe method and clarified that the probe method has two sides.3. We did analysis and numerical testing of the applications of the enclosure method to EIT and Cauchy problem for the Schroedinger equation.