Sentence examples for instead of the condition from inspiring English sources

Remark 19 Theorem 18 holds also if we replace one of the conditions below instead of the condition (41): (41) (41) (41) (41).

Kaluszka et al. [2] studied the Jensen inequality (1) for the generalized Sugeno integral by using the condition of monotonicity instead of the condition of convexity.

Instead of the condition (pgeq2), if we only assume that (p>1), then we also can obtain the uniqueness of the solutions in some cases.

Let us denote as the following set: Instead of the condition about existence of such that in the assertion 4, we can assume the following: Example 4.13.

Note that we can use (1-alpha_{n} < alpha_{n}), for n large enough, instead of the condition (1-alpha_{n} < alpha_{n}), for all (ngeq0).

In this paper, we use the following condition instead of the condition (F3) in Definition 1.3: (F3′) F is continuous on ( 0, ∞ ).

Since clinicians will not be blinded, it is possible that they will make additional efforts to improve treatment outcome when they receive feedback reports from the second and third feedback conditions instead of the first condition (control condition).

Instead of the conditions, and we consider the following conditions.

One can use similar conditions instead of the conditions which we will use in our results.

The influence of polishing bath composition and the operating conditions instead of the conditions of the process on the quality of the surface, evaluated by AFM and SEM methods, was established.

In [10], Xu used another control condition C5: lim n → ∞ ( α n + 1 − α n ) / α n + 1 = 0 instead of the conditions C3 or C4 and proved strong convergence of the sequence { x n } n ∈ N. In [11], Cho, Kang and Zhou pointed out that the control conditions C4 and C5 are not comparable, in general.