Sentence examples for another expression for from inspiring English sources

You will get another expression for f up to a constant that depends on x.

Thus (3.2) gives another expression for the Donald relative entropy.

Thus (3.1) gives us another expression for the Donald relative entropy.

Chit-chat is another expression for small talk: conversation topics which aren't important but are part of everyday social communication, like talking about the weather.

On the other hand, recalling the power-series expansion of the function e x, we have another expression for the Estrada index of G as follows: E E ( G ) = ∑ k = 0 ∞ M k ( G ) k !

Another expression for the probability of detection over Nakagmai fading channels can easily be derived by rewriting the right-hand side of (21) as: Q u γ, λ ′ = 1 - ∑ n ≥ 0 exp - γ / 2 γ 2 n γ ∗ ( u + n, λ ′ / 2 ) n !

In addition, the non-linear ordinary differential equation is solved using the homotopy perturbation method (HPM) and one another expressions for the non-linear frequency parameters and non-linear to linear frequency ratio are obtained.

And this, they claim (again pace Williams), is because tropes are essentially of some object, because they are ways the objects are (for another expression of this view, see Heil 2003: 126f).

Previously: It Is AButlutely NOT ConfirmeDanny Boylege Galloway Will Be Running for London Mayor .

Corresponding to Theorem 2, another determinant expression for this zeta function (tilde {mathbf {Z}}_{G} u)) can be obtained.

While the poet may wish for another expression, the cliche was excusable in this case because the Liberty responded just as she predicted.