Sentence examples for the inverse implications from inspiring English sources

where f ′ ( x ) is the first-order derivative of f ( x ) and f ( i ) ( x ) is the i th-order derivative of f ( x ), i ≥ 2. The definitions imply that the function tuple { f 0, f 1, …, f k − 1 } is an ECT-system on J, therefore it is a CT-system on J, and then a T-system on J; however, the inverse implications are all not true.

The inverse implication is evident.

The question is about the inverse implication.

The inverse implication, 2)⇒1), is checked similarly.

This completes the proof since the inverse implication is trivial.

For our further conclusions about the well-posedness, we formulate the inverse implication.

The following example proves that the inverse implication of Lemma 1.10 does not hold.

The following examples show that the inverse implication of Remark 2.5(1) does not hold.

To prove the inverse implication, we will need a simple lemma.

To conclude the inverse implication, a sufficient condition is that the ratio (m_{2}(x)/m_{1}(x)) is increasing in x (cf. [11]).

First, we will prove the inverse implication, that is, assuming that p from (47) is a solution of the mixed problem ({mathcal {P}}), we must prove that (delta {mathcal {F}}_{t}(p)=0).