Sentence examples for using the hypothesis from inspiring English sources

Furthermore, using the hypothesis of conformity on Δ, these obtained quantities vanish.

But Y is closed, thus x ∈ Y and also by using the hypothesis x n ⪯ x.

Evidently, using the hypothesis (H8), it is straightforward to check that A, B, φ satisfy hypotheses (H1), (H3).

Using the hypothesis x = λ y, we can guarantee that ∥ x ∥ + ∥ y ∥ = ∥ x − y ∥, the rest is a repeat of each proof of the theorems mentioned above.

In each iteration i, an estimated value of the diversity function is computed using the hypothesis function formulated above (i.e. (f'(i))).

That the sum ∑ i = 1 t I ( w i ) is direct follows by again using the hypothesis that the w i are sinks.

In using the hypothesis-testing procedure to determine if the null hypothesis should be rejected, the person conducting the hypothesis test specifies the maximum allowable probability of making a type I error, called the level of significance for the test.

Using the hypotheses on and, (2.7), (3.11), and Gronwall's lemma, we obtain (3.27).

It is already seen that Γ has convex values, using the hypotheses that the multimap G has convex values.

This paper acts as continuation study using the hypotheses from the author's previous research on the same topic to validate the hypotheses.

If then all impulsive moments are in Multiplying both sides of (4.19) by and integrating on and using the hypotheses, we get (4.21).