Sentence examples for this definition coincides from inspiring English sources

In special case when α is a whole number, this definition coincides with the above definition.

This definition coincides with the notion of a nondecreasing function in the case and represents the usual total order in.

Now, the fact that if this definition coincides or not with some other ones as these given in [8, 10 12] seems to be an interesting problem.

This definition coincides with the notion of a nondecreasing function in the case where X = ℝ and ≤ represents the usual total order in ℝ. Remark 2.2.

Further, this definition coincides with the classical definitions of RL and of Caputo fractional derivatives on polynomials (up to constant multiple)".

This definition coincides with the conventional diversity definition in the high SNR regime [32]. 2 Other selection of Θ, e.g., optimal index set, can be employed, but are beyond the scope of this paper.

If Φ = I d the identity function, then the above definition coincides with that of stabilizability, and in this case, we simply say M is ( m 1, m 2 ) -stabilizable.

If (alpha=min N), then the above definition coincides with the classical mth derivative (y^{(m)}(x)).

If f, g, h are bivariate symmetric means, the above definition coincides with that introduced in [8].

In the following, we prove that our definition coincides with Definition 4.1 in [1] for s > 0, 1 ≤ p ≤ ∞ and 1 ≤ q ≤ ∞.

In the case where (f(x)=|x|), our definition coincides with the classical definition of a contractive mapping used in the literature [9].