Sentence examples for solutions in the cases from inspiring English sources

In order to select optimal solutions in the cases of single-objective and multi-objectives optimization problems, optimization includes two main approaches.

A comparison between the solutions in the cases of the gravitating and the non-gravitating medium with or without magnetic field is made.

A comparison is made between the solutions in the cases of the gravitating and the non-gravitating medium with or without magnetic field.

A comparison is made between the solutions in the cases of the self-gravitating and the non-gravitating medium for both the magnetic and non-magnetic cases.

In this subsection, we give sufficient conditions for the existence and stability of positive periodic solutions in the cases (h leq x^) and (h > x^), respectively.

A comparison between the solutions in the cases of the self-gravitating and the non-gravitating medium is made for both the magnetic and non-magnetic cases.

Proof We consider the existence of solutions in the case when f ( x ) ∈ L 1.

From Theorem 23 it follows that there are no solutions in the case (mu> 0).

For third order systems, an algorithm for the evaluation of common solutions in the case of existence is given.

We summarize here the results concerning stationary solutions in the case κ = 0. Theorem 2.1 (see [7], Th. 4.1).

This paper shows how to determine the asymptotic solutions in the case of degeneracy of order higher than two.