Sentence examples for dependence of the initial from inspiring English sources

Finally, we prove the uniqueness and continuous dependence of the initial data of the solutions.

The different polymer foils showed a different angular dependence of the initial electrolyte uptake.

The angular dependence of the initial thermal residual stress state and the final deformed state have also been obtained.

For comparison, Fig. 5 also illustrates the temperature dependence of the initial heat release rates in the AN thermal decomposition studied previously [20].

More detailed study about the orientation dependence of the transition length is needed to further understand the orientation dependence of the initial growth of the electrodeposited nanowires.

Figure 9 shows the dependence of the initial detection performance on average moving distance of a mobile node in order to achieve a desired performance.

Stability and invariance results are also studied, together with the property of continuous dependence on the initial conditions.

Recently, Fan et al. [8, 9] obtained the existence, the uniqueness and the Lipschitz continuous dependence on the initial data of global weak solutions of compressible MHD when the initial data lie in the Lebesgue spaces.

The rate of ATP degradation showed a non-linear dependence on the initial concentration of unlabelled ATP, suggesting saturable ATP-consuming reactions.

It has been found that thermal oxidation products differ in dependence on the initial composition of the surface after the use of a pulsed-periodic laser treatment.

Also, a sensitive dependence on the initial conditions of two trajectories for y-coordinate of the model (3) is plotted in Figure 6(b).