The results of this approximation are extended to the most general case using the Levi decomposition of Lie algebras.
Most popular approaches to approximation are extended Kalman Filter [20] [24] and sequential Monte Carlo methods [25] [29], [30] [32].
For estimating the effect of uncertain distribution parameter on the variance of failure probability function (FPF), the map from distribution parameters to FPF is built and the high efficient approximation form is extended to solve the parametric variance-based sensitivity index.
The first development is that the Saddlepoint Approximation (SAP -simulation iSAP -simulationonduct relisbility analysis accounting for thextendedependentodegradation proconductd fuzzy reliabilityanalysisnd we accounting give a method to select a proper saddlepoint.
In this paper, the fast spectral method [36], originally developed by Mouhot and Pareschi for the numerical approximation of the collision operator, is extended to deal with other collision kernels, such as those corresponding to the soft, Lennard Jones, and rigid attracting potentials.
A stacking sequence optimization method proposed previously by the authors which utilizes two-level approximations and a genetic algorithm is extended to solve the above problem, and an optimization framework is developed by interfacing the improved method with the finite element software MSC.Patran/Nastran.
Last, the analytical approximation for logΛ given in ref. 20) is extended to low temperatures by including a temperature-dependent function.
The method is extended into 3D, where the approximation of spherical surface is developed based on surface-intersecting facets.
The side-chain center of mass is determined by a two-rotamer approximation that depends on whether the local backbone configuration is extended or compact.
