Sentence examples for solution explicitly from inspiring English sources

Then we define the optimal guarantee as the solution of the contributor's optimization program and find the solution explicitly.

Given that the resulting nonlinear complex-valued equations do not provide the solution explicitly, a numerical technique must be used.

The scheme employs Ianniruberto Marrucci model as a constitutive equation to express the viscoelastic behavior of the solution explicitly.

The transient solution explicitly relates temperature profile to the input power, size and the thermal properties of the element, and the heat transfer properties of the substrate.

Interactions between the helium atom and the GBs atoms are rather localized for all eight GBs studied here, and the helium solution explicitly relates to the local environment of the interstitial site.

Thus, the resulting analytical solution explicitly offers all remaining mp−n degrees of freedom beyond eigenvalue assignment which can be used for additional design goals such as response shaping, minimizing the norm of the feedback matrix, and robust control, respectively.

His work showed, at least in theory, that it is possible to determine all the solutions explicitly for a large class of equations.

These solutions explicitly illustrate how the reduction of front displacement speed for increasing ℓ can be interpreted in terms of leading points dynamics in some cases.

However, note that a few solutions explicitly addressing these issues can be found in literature [4, 37, 38].

It is worth mentioning that in many important problems, the closed convex set Kalso depends upon the solutions explicitly or implicitly.

In the linear forcing regime, we compute the solutions explicitly and analyze the asymptotic behavior, through which we verify that satisfying fluctuation-dissipation indeed leads to the correct physical behavior.