Abstract This paper is concerned with the inverse problem of determining the shape of penetrable periodic scatterers from scattered field data. We propose a sampling method with a novel indicator function for solving this inverse problem. This indicator function is very simple to implement and robust against noise in the data. The resolution and stability analysis of the indicator function is analyzed. Our numerical study shows that the proposed sampling method is more stable than the factorization method and more efficient than the direct or orthogonality sampling method in reconstructing periodic scatterers.
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Electrochemical borylation of carboxylic acids
A simple electrochemically mediated method for the conversion of alkyl carboxylic acids to their borylated congeners is presented. This protocol features an undivided cell setup with inexpensive carbon-based electrodes and exhibits a broad substrate scope and scalability in both flow and batch reactors. The use of this method in challenging contexts is exemplified with a modular formal synthesis of jawsamycin, a natural product harboring five cyclopropane rings.
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- Award ID(s):
- 2002158
- PAR ID:
- 10322736
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 118
- Issue:
- 34
- ISSN:
- 0027-8424
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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