We develop an inverse scattering scheme of recovering impenetrable anomalies buried in a two-layered medium. The recovery scheme works in a rather general setting and possesses several salient features. It makes use of a single far-field measurement in the half-space above the anomalies, and works independently of the physical properties of the anomalies. There might be anomalous components of multiscale sizes presented simultaneously. Moreover, the proposed scheme is of a totally direct nature without any inversion involved, and hence it is very fast and robust against measurement noise. Both theoretical foundation and numerical experiments are presented. This extends related results in the literature on recovering multiscale scatterers located in homogeneous space.

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The Chinese central government introduced the ‘Chinese Green Building Label’ in 2008, which makes China one of the few developing countries with an official rating system of buildings’ performance in sustainability. This paper investigates the existence and magnitude of the price premium associated with this official green label in the residential sector. Based on a unique data set of green-labelled, newly built housing projects and their non-labelled counterparts from around the country in 2013, an empirical analysis suggests that the labelled housing projects attract a price premium of 6.9% compared with their non-labelled counterparts. Further analysis suggests that this official green label is more effective as a reliable signal of buildings’ energy efficiency in the Chinese context compared with developers’ self-advertised ‘greenness’. These results provide preliminary evidence that with this official rating system, the investment in buildings’ energy-efficiency could be potentially profitable for housing developers in China, and such profitability may herald a rapid development of the green housing market in urban China.

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This paper is concerned with the intrinsic geometric structures of conductive transmission eigenfunctions. The geometric properties of interior transmission eigenfunctions were first studied in [9]. It is shown in two scenarios that the interior transmission eigenfunction must be locally vanishing near a corner of the domain with an interior angle less than π. We significantly extend and generalize those results in several aspects. First, we consider the conductive transmission eigenfunctions which include the interior transmission eigenfunctions as a special case. The geometric structures established for the conductive transmission eigenfunctions in this paper include the results in [9] as a special case. Second, the vanishing property of the conductive transmission eigenfunctions is established for any corner as long as its interior angle is not π. That means, as long as the corner singularity is not degenerate, the vanishing property holds. Third, the regularity requirements on the interior transmission eigenfunctions in [9] are significantly relaxed in the present study for the conductive transmission eigenfunctions. In order to establish the geometric properties for the conductive transmission eigenfunctions, we develop technically new methods and the corresponding analysis is much more complicated than that in [9]. Finally, as an interesting and practical application of the obtained geometric results, we establish a unique recovery result for the inverse problem associated with the transverse electromagnetic scattering by a single far-field measurement in simultaneously determining a polygonal conductive obstacle and its surface conductive parameter.