Sentence examples similar to it originally proved from inspiring English sources

It was originally proved in [17].

The characterization for the first fragment was originally proved by Cohen, Perrin, and Pin using sophisticated semigroup-theoretic techniques.

Here we prove a Hardy-type inequality in the upper half-space which generalize an inequality originally proved by Maz'ya (Sobolev Spaces, Springer, Berlin, 1985, p. 99).

Like computers, 3-D printers originally proved their worth in the business sector, cost a fortune and were bulkier than a Kelvinator.

For a version of the inequalities originally proved by Arveson for positive operators in von Neumann algebras with a tracial state, we give a different proof.

The result in Lemma 2 was originally proved in [4].

This lemma was originally proved by Jia et al. [2].

Square, the payment processor, originally proved itself a boon to small businesses, remote retailers, and freelancers.

Levinson [2] originally proved the inequality for functions (f: (0,2c) tomathbb{R}) such that (f"' geq0).

The result in Theorem 4 was originally proved in [30], albeit by a different method.

Note that the proof of Lemma 9 holds the following result originally proved in [6], Remark 10.