We show that analytic expressions for the frequency of second-order nonlinear oscillations can be obtained from dual variational principles.
S can be obtained from Equation (1) using the variational Bayesian learning (Lappalainen and Honkela, 2000) and the FastICA algorithm (Hyvarinen and Oja, 2000).
Note that the new estimate is a continuous function of ν t and the standard variational iterative scheme can be obtained from Equation 9 by setting ν t to −1.
The SPN equations are derived by an asymptotic analysis, while the boundary conditions are obtained from a variational analysis.
The governing equations of the problem are obtained from a variational principle in which a hybrid modified functional is employed.
The various equations at the surfaces and triple contact lines of a deformable body are obtained from a variational condition, by applying Green's formula in the whole space and on the Riemannian surfaces.
Probabilities of differential expression were obtained from a variational Bayesian analysis of variance (ANOVA) model which was implemented along the lines of (Posekany et al., 2011).
This dispersion equation is obtained from the 3D variational formulation governing elastodynamics.
Recursive updates are obtained from a restricted variational Bayesian perspective, using a dual filtering formulation where parameters are allowed to evolve in time.
The weak solution of problem (4.1) is obtained from the following variational problem: Find (u_{infty}in V) such that mu a u_{infty},w +bigllangle f u_{infty}),wbigrrangle =langle f_{1infty },wrangle (4.2) for all (win V), where (a(cdot,cdot)) is the symmetric bilinear form on (Vtimes V) defined by (2.6).
