We prove that
Massive gully land consolidation projects, launched in China’s Loess Plateau, aim to restore 2667
- NSF-PAR ID:
- 10197459
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- Scientific Reports
- Volume:
- 10
- Issue:
- 1
- ISSN:
- 2045-2322
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract The selection of low-radioactive construction materials is of utmost importance for the success of low-energy rare event search experiments. Besides radioactive contaminants in the bulk, the emanation of radioactive radon atoms from material surfaces attains increasing relevance in the effort to further reduce the background of such experiments. In this work, we present the
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Abstract In this article, we study the moduli of irregular surfaces of general type with at worst canonical singularities satisfying
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Abstract Let
be a positive map from the$$\phi $$ matrices$$n\times n$$ to the$$\mathcal {M}_n$$ matrices$$m\times m$$ . It is known that$$\mathcal {M}_m$$ is 2-positive if and only if for all$$\phi $$ and all strictly positive$$K\in \mathcal {M}_n$$ ,$$X\in \mathcal {M}_n$$ . This inequality is not generally true if$$\phi (K^*X^{-1}K) \geqslant \phi (K)^*\phi (X)^{-1}\phi (K)$$ is merely a Schwarz map. We show that the corresponding tracial inequality$$\phi $$ holds for a wider class of positive maps that is specified here. We also comment on the connections of this inequality with various monotonicity statements that have found wide use in mathematical physics, and apply it, and a close relative, to obtain some new, definitive results.$${{\,\textrm{Tr}\,}}[\phi (K^*X^{-1}K)] \geqslant {{\,\textrm{Tr}\,}}[\phi (K)^*\phi (X)^{-1}\phi (K)]$$