Sentence examples for use the hypothesis from inspiring English sources

Now, we use the hypothesis that and are weakly compatible to deduce that is a common fixed point of and.

In order to obtain and we use the hypothesis (iv) as well as (2.33)–(3.16) and (2.34)–(3.17), respectively.

In this paper, we use the hypothesis that is an array of positive real numbers satisfying (1.5) and continue to study the problem of finding the sufficient condition for the strong law of large numbers (1.2).

Several prediction programs use the hypothesis that low free energy is required for the formation of stable RNA-RNA duplex [ 33– 37, 37, 40, 43, 47].

Although all approaches already mentioned use the hypothesis of Gaussian additive noise for mathematical convenience, in practice, remote sensing imagery noise shows non-Gaussian characteristics [84].

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

end{aligned} Here we used the hypothesis ((frac{S'(R)}{S R)} )'=o(1)).

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).

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

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.