3,874 research outputs found
On a generalized Calabi-Yau equation
Dealing with the generalized Calabi-Yau equation proposed by Gromov on closed
almost-K\"ahler manifolds, we extend to arbitrary dimension a non-existence
result proved in complex dimension 2.Comment: 22 page
Locating Multiple Multi-scale Electromagnetic Scatterers by A Single Far-field Measurement
Two inverse scattering schemes were recently developed in
\cite{LiLiuShangSun} for locating multiple electromagnetic (EM) scatterers,
respectively, of small size and regular size compared to the detecting EM
wavelength. Both schemes make use of a single far-field measurement. The scheme
of locating regular-size scatterers requires the {\it a priori} knowledge of
the possible shapes, orientations and sizes of the underlying scatterer
components. In this paper, we extend that imaging scheme to a much more
practical setting by relaxing the requirement on the orientations and sizes. We
also develop an imaging scheme of locating multiple multi-scale EM scatterers,
which may include at the same time, both components of regular size and small
size. For the second scheme, a novel local re-sampling technique is developed.
Furthermore, more robust and accurate reconstruction can be achieved for the
second scheme if an additional far-field measurement is used. Rigorous
mathematical justifications are provided and numerical results are presented to
demonstrate the effectiveness and the promising features of the proposed
imaging schemes.Comment: Any comments are welcom
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