Sentence examples for will use the formulation from inspiring English sources

Here we will use the formulation in Equation 3 as can be verified by inspecting the coding of method L in [ 25].

We will use the above formulation for a pair of distributions F x) and G x), where G x) is a submodel or the baseline distribution of F x).

Therefore, we will use the second formulation in the following for our calculations.

Thus we will use the more general formulation given by Eq. (31).

In this paper we will use the path integral formulation of the background field method of QCD to predict the correct definition of the non-perturbative matrix element of the (chi _{text{cJ}}) production from color singlet (c{bar{c}}) pair in non-equilibrium QCD which is gauge invariant and is consistent with the factorization of infrared divergences at all orders in coupling constant.

We will use this formulation in what follows.

We will use this formulation when (Omega) is a strip.

We use Table 2 to summarize most of the notation we will use in the formulation.

In addition, in Section 5, we will use these formulations to provide precise convex formulations for three important special cases of the optimal power allocation problem.

You can't use the formulation, "But O…" without seeming a little too invested in your glorious history.

We will use a variational formulation of the inference problem [ 34].