Sentence examples for 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.

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

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

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).