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2019
It is built from checkable properties of the record itself: whether the article has a DOI, how many independent sources confirmed its data, whether the required fields are filled in, and how recent the latest confirmation is. Disagreement between sources and a missing identifier lower it. A value of 80 or above means the record was published without further checking; 60 to 79 means it is published at reduced confidence, with a manual check advisable. A record verified by an editor by hand is never pushed below 90 by a recalculation. This scores our data about the article, not the article itself.
On a set $\Omega \subset \mathbb {R}^d$ that is formed from a finite collection of manifolds that adjoin each other in a special way (i.e., on a stratified set) an exact analog of the Sobolev inequality is proved, in which the exponents are expressed via the characteristics of the intrinsic geometric structure of $\Omega$. The result is applied in order to prove the solvability of the Dirichlet problem for the $p$-Laplacian.