Sentence examples for by applying the variational from inspiring English sources

This statement is not entirely valid because perturbation is not variation such that it may be corrected by applying the variational principle to eq. (2), for example.

Conditions for resonance are obtained by applying the variational iteration method-II (VIM-II), which should be avoided in the cushioning packaging design.

By applying the variational principle to the dual variables, the wave propagation problem is transformed into a two-dimensional symplectic eigenvalue problem.

t ∈ [ 0, 2 π ], together with the Landesman-Lazer type condition, Jiang [9] obtained the existence of solutions of (1.1) by applying the variational methods and symplectic transformations.

For any w ∈ L p , we get that the following problem has a unique solution v ∈ W 0 1, p ∩ L ∞ by applying the variational method to { − div ( | ∇ v | p − 2 ∇ v ) = f n ( x ) ( | w | + 1 n ) α, x ∈ Ω, v = 0, x ∈ ∂ Ω. (2.2).

(31a - 31c 31a - 31c in totandenergy (30) because here thendouble-varintotall procenergywas considered; that is, the first optimization condition was considered as in eq. (29), and the resulting (optimum) density (30) was then employed in the quantum energy (17), which in turn was obecause by applying thereariathenal eq. (12) to the perceived phase transition in the Bohm eikonal wave-function (5).

By applying the weak variational approach, the necessary optimality conditions are provided and then an optimal state feedback controller is presented.

By introducing dual variables and applying the variational principle, the canonical equations of Hamiltonian system are constructed.

Applying the variational inference algorithm to StructHDP would improve its speed significantly.

By applying the Ekeland's variational principle in B ρ ( 0 ) ¯ [29], we obtain the result that there exists a ( PS ) c λ sequence { u n } ⊂ B ρ ( 0 ) ¯ of I.

In this section, by applying the definition of the variational solution of equation (1.6), we consider the existence of a pullback (mathscr {D}_{lambda_{1}}) attractor in (L^{p}) (p satisfying (1.4)).