Sentence examples for functional involving from inspiring English sources

In 1908, Ritz laid out his famous method for determining frequencies and mode shapes, choosing multiple admissible displacement functions, and minimizing a functional involving both potential and kinetic energies.

Our approach is based on the study of an extremal problem for a new functional involving the Paneitz operator.

A new Lyapunov Krasovskii functional involving more information on the state variables is established to derive a novel exponential stability criterion.

This method is deduced from a variational principle, which uses a modified hybrid functional involving the generalized displacements and generalized tractions on the boundary and the lateral deflection in the domain as independent variables.

Minimizing the M-S functional involves determining both a function and a contour across which smoothness is not.

However, these methods solving the M-S functional involve alternating optimization [21, 22] of the reconstruction function and the contour.

On the other hand, the load related to the calculation of the second derivative might be really large, especially when a cost functional involves a standard deviation.

These methods give somehow satisfactory answers for functionals involving u and (nabla u), but are not able to handle terms involving the Monge Ampère operator (det (D^2 u)).

However, B3LYP functional is not able to clearly distinguish energy changes related with non-bonding interactions which are better covered in density functionals involving dispersion term in their definition [39].

Fractional differential equations with both left and right fractional derivatives are also applicable to many fields, such as the extremal problems of fractional Euler-Lagrange equations [6, 7] and the optimal control theory for functionals involving fractional derivatives [8].

Following [ 8] it is straightforward to extend the analysis to time-dependent monotone-convex functionals involving an explicit time-dependency.