Sentence examples for for both problem from inspiring English sources

Mathematical models are constructed for both problem specifications.

Computational results for both problem variations are presented.

Closed-form or compact solutions are provided for both problem formulations.

Based on the values of DB and Dunn, Figs. 7, 8, 9, 10 similarly illustrate that the optimal number of clusters (k) is 2 for both problem contexts.

We further investigated the use of a general local search heuristic, thus offering numerical results for both problem specific as well as generic black-box heuristic solution methods.

The following results give a characterization of the optimal controls for both problem at level ε and homogenized problem (2.24) (see [11], Chapter 4).

Thus, Theorem 5 gives a condition for the existence of solutions for both these problems.

Mr. Obama's budget is a step in the right direction for both problems.

Computational results for both problems are presented.

This equality has consequences for both problems.

Gap functions have also been proposed for both problems.