Sentence examples for mathematically establish from inspiring English sources

In this paper an analytical molecular mechanics model is proposed to mathematically establish a relationship between the structure and the elastic properties of β−graphyne.

Energetics of the deformation of these allotropes have been analyzed to mathematically establish a relationship between the sum of the second order nonlinear elastic constants and the area density.

As a result, the optimization of compliant mechanisms is mathematically established as a nonlinear programming problem, to which the method of moving asymptotes (MMA) belonging to the sequential convex programming can be applied.

In [12], the relationship between OPD and other spatial parameters was mathematically established.

Thus, the article mathematically establishes the general form of an option value for a capital project (Lintner 1965).

Besides, defining the distance measure of (mathcal{{M}} phi,p,mathcal{{F}})), we have also studied some of its mathematically established properties.

As the error bar of the cross-phase FLR frequency, we have used the half width of the cross-phase profile; this could be an overestimate, but there is no mathematically established procedure to estimate the confidence interval of the cross-phase FLR frequency.

Finally, we investigate the new model mathematically and establish the existence of the minimum to the new energy functional.

Moreover, we investigate the new model mathematically and establish the existence of the minimum to the new energy functional.

Spirited researchers endeavoring in assorted domains have been experimentally testing, mathematically modeling, establishing numerical approximations, and designing algorithms for analyzing various flow problems in different geometric and flow configurations [3 15].

However, although the algorithm is mathematically well established [ 12], it is rarely used in practice [ 13].