Sentence examples similar to a solution was established from inspiring English sources

A new result on the existence of a solution is established by using fixed point theorems.

Theorems on the existence and uniqueness of a solution are established under some sufficient conditions on nonlinear terms.

In Theorem 3, unimprovable bounds of the difference between the maximum and the minimum of a solution are established.

Even if it were possible to find the solvability conditions for the mentioned overdetermined problems, since the real data usually have some errors in practice, and thus fall out of the data class for which the existence of a solution is established, it appears that these conditions would not always be satisfactory in applications.

To determine the volumetric ratio of coarse aggregate per unit weight, a mathematical solution was established under two boundary conditions: the absolute volume and the dry density of concrete.

Antunes and Peeters (2000) studied education network planning model with changing general facilities capacity and then in the next year a new solution was established.

However, an approximate solution was established that could be used instead of the rigorous model to predict the energy reuse factor at a given production density.

As expected resultantly, a novel 3D surface topography modeling solution was established, which aims to predict and modify the finished KDP (potassium dihydrogen phosphate or KH2PO4) crystal surfaces.

Some existence results for a nontrivial solution are established by the mountain pass theorem and a variant version of the mountain pass theorem in the general case 2 < p < N. Similar results are also established by combining the mountain pass theorem and a variant version of the mountain pass theorem with the Moser-Trudinger inequality in the case of p = N.

And then combining the high efficient state dependent parameter (SDP) method for the calculation of the conditional moments of the model output, a SDP solution is established to solve two moment-independent importance measures.

More precisely, the existence of a global solution is established via the standard comparison principle.