Sentence examples for using this equivalence we from inspiring English sources

Using this equivalence, we have first established criteria for the existence of solution of the proposed variational inequality problem.

Using this equivalence in this section, we construct a parallel iterative algorithm to approximate the solution of the problem (1.1) and study the convergence of the sequence generated by the algorithm.

We subsequently transformed the normalized expression levels to concentrations using this equivalence and took expression levels to be commensurate with protein levels following the validation described above.

We use this equivalence result in our paper.

In the next section we use this equivalence to prove the existence and uniqueness of solutions.

We use this equivalence to study the sensitivity analysis of the general nonconvex variational inequalities.

We use this equivalence to develop sensitivity analysis for the nonconvex variational inequalities without assuming the differentiability of the given data.

We will use this equivalence in the next section to standardize our sample.

We will use this equivalence during the derivation of the SIRT-FBP method in the "Methods" section.

As we changed the primary outcome measure to a time weighted measure by using the AUC, we could no longer use this equivalence margin.

We further propose a new learning algorithm that can effectively learn more accurate Bayesian networks using equivalence constraints, which we demonstrate empirically.