All preferences are stored on your device.
2020
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.
Let (M,τ) be a semi-finite von Neumann algebra, L0(M) be the set of all τ-measurable operators, μt(x) be the generalized singular number of x∈L0(M) and f:[0,∞)→[0,∞) be a concave function. We proved that if x1,x2,…,xn are normal operators in L0(M), then μ(f(|∑k=1nxk|)) is submajorized by μ(f(∑k=1n|xk|)). As an application, we obtained that if x is a matrix of normal operators xij in L0(M), then μ(f(|x|)) is submajorized by μ(∑i,j=1nf(|xij|)).