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A simple equation was derived from the solution properties to calculate the cooling curves corresponding to different growth parameters.
The non-stationary solution is derived from the solution in the case of a moving load with a deterministic amplitude.
The parameters, including advective velocity, and boundary conditions used for contaminant transport through the cap are derived from the solution of the first two equations.
The effects of the material inhomogeneities are described by perturbation functions derived from the solution of recursive cell problems.
The observer design is derived from the solution of linear matrix inequalities (LMIs), based on the solutions of algebraic constraints obtained from the unbiasedness conditions of estimation error.
The design approach of the UO is derived from the solution of the linear matrix inequality (LMI), based on the new dynamic observer formulation and the solution of the algebraic constraints obtained from the unbiased estimation error.
It is very interesting to show that the coupled Riccati equation is derived from the solution to the FBSDE, which has the similarity with the case of standard optimal control.
The standard nonlocal (DtN) boundary condition is derived from the solution of the exterior Dirichlet problem, and a discretized (DDtN) version is derived that applies at the nodes onB.
The effect of the microstructural heterogeneity is taken into account by means of periodic perturbation functions, which derive from the solution of nonhomogeneous recursive cell problems defined over the unit periodic cell.
The mass source-term distribution is derived from the solution of an inhomogeneous Helmholtz equation that contains a free parameter allowing to tune the spatial localization of the source.
The time evolution is considered to be magnetically quasi-static and magnetostatic forces are derived from the solution of (steady) Maxwell's equations, recomputed at each instant in time.
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