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Several simple but plausible simplificatons are made to render the solution analytically tractable.
The order of the complexity may render the solution impractical.
However, the penalty that is paid to improve the system performance in both cases is an increased complexity burden, which may render the solution impractical.
Luckily, the resulting max-min optimization problem, we show, conforms to a set of sufficient conditions that render the solution manageable, even for an arbitrarily large number of bands.
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During the computations, one must make appropriate choices not only on the type of the solution functions but also on the parameters which occurred during the computations, such as some integral constants, to render the solutions physically meaningful and have correct asymptotic forms.
The method renders the solution and its gradient uniformly second-order accurate in the entire computed domain.
The complete coupling renders the solution appreciably more complex in structure and behavior than solutions for unicomponent or partially coupled models.
When such a mixture is dissolved, the large content of ammonium ion renders the solution slightly acidic, thus preventing oxidation of iron (II) [36] as well as the hydrolysis of aluminium and other hydrated cations.
We provide sufficient conditions under which the associated max-min problem is equivalent to a supporting plane problem, which renders the solution for an arbitrary number of bands tractable.
A hard penalty is one that generally renders the solution uncompetitive for use by the optimisation engine to help make new candidate solutions.
This was achieved by defining the regulating penalty function, which renders the solutions unique, as a global ℓ1-norm of local ℓ2-norms.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com