Sentence examples for equivalence solution from inspiring English sources

The approach of the paper Based on the partition (1) in the Proposition 2 (which divides the solution set into disjoint equivalence solution sub-classes), we first mine only once the lattice ({mathcal L}{mathcal C}{mathcal G}) containing closed itemsets and their generators from ({mathcal T}).

In summary, in this article, we first establish the relation S K and S K, loc D for the GVEP under suitable conditions, and then establish the equivalence between solution set of the GVEP and solution set of the DGVEP.

Moreover, the equivalence of solutions and weak solutions for the above-mentioned equations are showed.

Moreover, the equivalence of solutions and weak solutions for the above-mentioned equations are presented.

In the following we would like to point out the equivalence of solutions and weak solutions for the generalized Navier-Stokes equations; this point is similar to the case of the Stokes equations.

This equivalence of solution criteria lays the basis for proving Proposition 8 (about uniqueness of distributional solutions) and Proposition 9 (about its continuous dependence of data) by the same arguments as for (L^p({{mathbb R}^{N}}))-valued solutions in Sect.

By virtue of C-pseudomonotonity of F, the equivalence between solution set of the GVEP and that of the DGVEP can be established.

Furthermore, the equivalences of solutions and weak solutions for the aforementioned equations are justified.

In particular, we would like to point out the equivalences of solutions and weak solutions for the above-mentioned equations, which has not been clearly stated by the previous works in [28].

One can obtain a formulation of equivalence between solutions of first-order random fuzzy differential equations and random fuzzy integral equations (see [29, 30]).

One can obtain a formulation of equivalence between solutions of second-order random fuzzy differential equations and random fuzzy integral equations.