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There is an operator, called the Hamiltonian, that plays a special role in quantum theory because the dynamics of a system can be conveniently formulated by tracking its evolution.
Instead of heuristic selection schemes (such as many MI-based approaches), objective optimization methods have received more attention since they can be conveniently formulated as convex optimization problems with global optimal solutions.
Such a treatment converts the original contact problem concerning an inhomogeneous half space into a homogeneous half-space contact problem, for which governing equations with unknown contact load distribution can be conveniently formulated.
This type of problem can be conveniently formulated as an ILP.
The likelihood equations can be conveniently formulated using matrix algebra, allowing easy implementation on any software platform that supports matrix operations.
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The various sandwich theories are conveniently formulated by using the unified formulation by Carrera (CUF) that leads to governing equations which forms are formally the same for the different sandwich shell theories.
Tracking errors are conveniently formulated with vessel dynamics modeled in connected reference path coordinate systems and a coordinate transformation at switching coordinate systems.
All those regions and regimes are conveniently formulated and the flow key scales are analysed and described, which allows for a simplified and robust formulation.
The problem under consideration is not treated within the context of exact feedback linearization, where restrictive conditions arise, but is conveniently formulated in the context of singular partial differential equations (PDE) theory.
The resulting set of coupled non-linear convection-dispersion equations is posed as an initial-boundary value problem which is conveniently formulated for numerical solution using an extended method of lines approach.
The entire analysis can be conveniently programmed.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com