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We first introduce and study the notion of multi-weighted blow-ups, which is later used to systematically construct an explicit yet efficient algorithm for functorial logarithmic resolution in characteristic zero, in the sense of Hironaka. Specifically, for a singular, reduced closed subscheme $$X$$ of a smooth scheme $$Y$$ over a field of characteristic zero, we resolve the singularities of $$X$$ by taking proper transforms $$X_i \subset Y_i$$ along a sequence of multi-weighted blow-ups $$Y_N \to Y_{N-1} \to \dotsb \to Y_0 = Y$$ which satisfies the following properties: (i) the $$Y_i$$ are smooth Artin stacks with simple normal crossing exceptional loci; (ii) at each step we always blow up the worst singular locus of $$X_i$$, and witness on $$X_{i+1}$$ an immediate improvement in singularities; (iii) and finally, the singular locus of $$X$$ is transformed into a simple normal crossing divisor on $$X_N$$. Comment: Final published version 

ABSTRACT The radiance of sky brightness differs principally with wavelength passband. Atmospheric scattering of sunlight causes the radiation in the near-infrared band. The Antarctic is a singular area of the planet, marked by an unparalleled climate and geographical conditions, including the coldest temperatures and driest climate on Earth, which leads it to be the best candidate site for observing in infrared bands. At present, there are still no measurements of night-sky brightness at DOME A. We have developed the Near-Infrared Sky Brightness Monitor (NISBM) in the J, H, and Ks bands for measurements at DOME A. The instruments were installed at DOME A in 2019 and early results of NIR sky brightness from 2019 January–April have been obtained. The variation of sky background brightness with solar elevation and scanning angle is analysed. The zenith sky flux intensity for the early night at DOME A in the J band is in the 600–1100 μJy arcsec−2 range, that in the H band is between 1100 and 2600 μJy arcsec−2, and that in the Ks band is in the range ∼200–900 μJy arcsec−2. This result shows that the sky brightness in J and H bands is close to that of Ali in China and Mauna Kea in the USA. The sky brightness in the Ks band is much better than that in Ali, China and Mauna Kea, USA. This shows that, from our early results, DOME A is a good site for astronomical observation in the Ks band.