Sentence examples for firstly proved from inspiring English sources

Inequality (1.3) was firstly proved by Leray [9] in the lower-dimensional case.

This result was firstly proved independently by Brosamler [1] and Schatte [2] under a stronger moment condition.

In the case of the Heisenberg group, Garofalo and Lanconelli (cf. [1]) firstly proved the following Hardy inequality: (1.2).

The conventional linear model is firstly proved to fail to predict precisely the long-duration free decay responses of the SSSM system.

In the case when the space is normed and under the additional assumption that the cone is normal, these results were firstly proved in [10].

It is firstly proved by drilling tests that the tool shape always acts as a determining factor that significantly influences the drilling force and machining quality, for either the uncoated or diamond coated drills.

Firstly, prove (C) ⇒ (A).

Proof We firstly prove (4.1).

We firstly prove the first formula.

(2.6) It is convenient to firstly prove the following result.

We firstly prove that λ ( f − z ) = ρ ( f ).