Sentence examples for assumption conditions from inspiring English sources

Proof Let the assumption conditions in Theorem 3.2 hold.

Section 2 of this paper describes the scheduling issue and gives the model's assumption conditions.

It follows from the assumption conditions (E1), (E2), and Step 2 that (3.27).

The numerical results show that this technique is more competitive than the nonmonotone method of [47], but it requires strong assumption conditions for convergence analysis.  .

Additionally, the assumption conditions imposed on all C n ( n ≥ 2 ) are not weak at all since each one is in fact an intersection of countably many sets.

end{aligned} This, together with assumption conditions imposed on the sequence ({alpha_{i}}) and ({beta_{i}}), shows that (lim_{mathcal{K}_{i}ni krightarrowinfty}g (Vert Jx_{k}-Jw^{(i)}_{m_{k}}Vert )=0).

Thus, the assumption condition (8) is a special case of the assumption condition (7).

This is a contradiction to the assumption condition (1.7).

By assumption, condition (a) of Theorem 3.5 is satisfied.

By Lemma 3.3 and the assumption condition, it follows that (3.27).

It follows from the assumption condition (E1) and (3.42) that (3.50).