Sentence examples for limits of the solution from inspiring English sources

Since the assumptions of Theorem 1 ii), hold, we can expect to get four random limits of the solution.

Now we are under assumptions of Theorem 1(i)(c), so we can expect to get two nonrandom limits of the solution.

While this may not be readily apparent from a cursory comparison of Figures 3A and 3C, connecting the extreme upper-left and upper-right points on each subfigure shows that the limits of the solution space (in terms of biomass yield on photons and oxygen competition at the rubisco enzyme) are quite comparable, although the nested approach identifies fewer suboptimal solutions.

They also lack a proper comparison with other solutions, whereas we compared our algorithms against planners with the specific goal of assessing the limits of the solutions.

Berezansky [8] considers the asymptotic convergence of solutions in discrete and difference equations with delay and gives strong sufficient conditions of the asymptotic convergence of all solutions without computing the limits of the solutions as n → ∞.

The limits of the solutions of the present theory for the special case of thin films on substrates with only mismatch strains are shown to converge to prior analytical results.

In this section, we use the limits of the solutions to VEPs, each of which has a unique solution, to provide an interesting representation of the solution set of each VEP in M, which in forms is very similar with the Clarke subdifferentials of the local Lipschitz functions.

It is enough that the upstream limit of the solution is available.

This example shows the significance of the middle sum in (1.3), since only this term contributes to the limit of the solution of (1.1) in this case.

In addition, it is not difficult to find that (mathit{RP}(U_{l},U_{r})) is the limit of the solution of the initial value problem.

Furthermore, we observe that as (varepsilonrightarrow0), the limit of the solution of (1.3) and (3.1) is the corresponding Riemann solution of (1.3) and (1.4).