Sentence examples for minimal solutions from inspiring English sources

It is the class of semi-stable solutions, which includes local minimizers, minimal solutions, and extremal solutions.

We searched for the minimal solutions corresponding to different ammonium concentrations that minimized the squared distance Z from their original reference values (Fig. 5; see Methods for the details).

( S P − ⪯ )  ⪯-minimize F ( x ), subject to x ∈ X, where minimal solutions of ( S P − ⪯ ) are defined in the following way: Definition 4 (Minimal solutions of ( S P − ⪯ ) w.r.t. the preorder ⪯).

We will now show that these are minimal solutions.

Then problem (1) has maximal and minimal solutions in.

Theorem 6 (Second Perron-Kreuser bound for minimal solutions).

To obtain the maximal and minimal solutions, we use the same arguments in Theorem 3.1.

In this section, we consider the existence of maximal and minimal solutions for (1.2).

Assume that conditions (S1)–(S5) hold, then (4.2) has maximal and minimal solutions in.

The conditions for the existence of the maximal and minimal solutions to the system were established.

Next, we formulate a comparison statement for minimal solutions of two Riccati equations.