Sentence examples for apply the stability from inspiring English sources

Next, we apply the stability results and we propose a new approach for stability robustness of variational difference equations.

To apply the stability analysis, the MRLW equation can be linearized by assuming that the quantity U in the non-linear term U2U x is locally constant.

This shows the assertion with ε ≔ β - S (F (x ′ ), y ) > 0. □ Lemma 4.2 allows us to apply the stability result Theorem 3.9, which shows that Assumption 4.1 implies the continuous dependence of the solutions of (4) on the data y and the regularization parameter β.

Frame design in the U.S. was only affected by stability effects when applying the stability requirements from AISC 360-10.

The Engesser critical load is derived by applying the stability procedures to the total potential energy associated with the linear shear formulation.

Applying the stability diagram to a TTR in irregular waves shows that the introduction of extra damping to an unstable system can suppress the instability.

Hence applying the stability conditions using Lemma 4.1 the results (i)–(iv) can be achieved.

Applying the stability conditions | λ 1 | < 1 and | λ 2 | < 1, we obtain the desired result.

Hence, applying the stability conditions using Lemma 1, one can obtain the results (i - v).

Hence, applying the stability conditions using Definition 2, one can obtain the results (i - iii).

Applying the stability condition on Gaussian messages with initial mean value, we get and, or equivalently, (19).