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2024
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.
The main aim of this paper is to show that the first singular number of the generalized Cauchy–Dirichlet heat operator is minimized by a circular cylinder among all domains of the same measures with the circular cylinder in Euclidean space. This result gives us an analogue of the celebrated Rayleigh–Faber–Krahn inequality for the absolute value of the heat operator. Further, we obtain an analogue of the Hong–Krahn–Szegö inequality for the same operator.