We prove a relationship between the Cleaning problem and the Balanced Vertex– Ordering problem, namely that the minimum total imbalance of a graph equals twice the brush number of a graph. This equality has consequences for both problems. On one hand, it allows us to prove the NP-completeness of the Cleaning problem, which was conjectured by Messinger et al. [7]. On the other hand, it also enab...

Linear depolarization ratios in clean air ranges were measured with POLIS-6 at 355 and 532 nm. The mean deviation from the theoretical values, including the rotational Raman lines within the filter bandwidths, amounts to 0.0005 at 355 nm and to 0.0012 at 532 nm. The mean uncertainty of the measured linear depolarization ratio of clean air is about 0.0005 at 355 nm and about 0.0006 at 532 nm.

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I begin with the proposition that eating is an agricultural act. Eating ends the annual drama of the food economy that begins with planting and birth. Most eaters, however, are no longer aware that this is true. They think of food as an agricultural product, perhaps, but they do not think of themselves as participants in agriculture. They think of themselves as “consumers.” If they think beyond...