Sentence examples for using the variational identity from inspiring English sources

Furthermore, the Hamiltonian structure of the integrable hierarchy is produced by using the variational identity again.

In this paper, using the variational characteristic of the virial identity and a new estimate of the kinetic energy, we obtain a new sufficient condition for the existence of blow-up solutions.

Using the variational principle, the governing equations of the magnetoelectroelastic plate are derived.

The oscillating frequencies in vertical and horizontal directions are obtained approximately using the variational iteration method.

In this study, delay differential equations are investigated using the variational iteration method.

We obtained these results by using the variational reduction method.

He has made contributions on the well-posedness and asymptotic properties (such as large deviation principle, ergodicity and random attractor) of a general class of stochastic partial differential equations using the variational approach.

To carry out this calculation, we first located current plateaus using the Variational Baysean Gaussian Mixture Model, VBGMM.

S can be obtained from Equation (1) using the variational Bayesian learning (Lappalainen and Honkela, 2000) and the FastICA algorithm (Hyvarinen and Oja, 2000).

In the case where lattice equations including the positive and negative lattices by using the semi-direct sums of Lie algebras have been present [12, 13], their mathematical structures such as Hamiltonian structures usually investigated by the variational identity [14].

The corresponding Hamiltonian structure of the equation hierarchy is derived from the variational identity.