The coupled plastic-damage constitutive model is integrated with an implicit stress return algorithm for the plastic part, while the damage part can be integrated implicitly.
The resulting matrix has properties that allow the diagonal terms to be integrated implicitly and the off-diagonal terms to be integrated explicitly.
Lastdrager (2002) used a Rosenbrock method with approximate Jacobians for the same system so that effectively the field equations are integrated implicitly and the state equations explicitly, as with IMEX (IMplicit-EXplicit) methods (Hundsdorfer and Verwer, 2003).
The dynamics of Eq. 30 continue until the turning point of the Hill function, which occurs at A ≈ K A. Terming t K as the time when A = K A in this regime, Eq. 30 is integrated implicitly to yield (31) t (A ) = ∫ X A d A [ β X A n ] − 1 = [ β X (n − 1 ) ] − 1 [ X − n + 1 − A − n + 1 ], t K = [ B X (n − 1 ) ] − 1 [ X 1 − n − K A 1 − n ], A (t ) = [ X 1 − n − (n − 1 ) β X t ] 1 / (1 − n ).
This distinction seems to be implicitly present in the existing empirical studies on vicarious embarrassment; however, it has not yet been integrated into a conceptualization of situations eliciting vicarious embarrassment.
Implicitly Restarted Arnoldi Algorithm [9] is a widely-used eigenvalue-analytical method with some certain advantages in practical analysis of large-scale power systems and has been integrated into the Power System Department-Bonneville Power Administration (PSD-BPA) business program.
The nonlinear advection terms are time-integrated explicitly, the pressure/enthalpy terms are integrated semi-implicitly, and the Coriolis force and buoyancy terms are treated semi-analytically.
The momentum equations are integrated semi-implicitly by the approximate factorization technique.
When a representation of action is integrated, state constraints implicitly define indirect effects of actions and impose further preconditions on the performance of actions.
The social frame of the racial lens permeates the clinical decision making process, is integrated both explicitly and implicitly by provider and patient, and furthers several hypotheses related to the role of race in clinical decision making.
