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The method is based on a transformation of the dynamic water volume onto a fixed domain.
Second, the electrode movement inside the furnace is avoided by implementing time-dependent boundary conditions applied to a fixed domain.
The consistency of the two formulations is shown through an appropriate transformation of the governing equations to a fixed domain.
A level set method combining features of front tracking methods and fixed domain methods is presented to model microstructure evolution in the solidification of multi-component alloys.
By adding a certain penalty term to the Black-Scholes equation, the solution of this variational inequality is extended to a fixed domain.
By mapping a fixed domain onto the evolving domain at each time level, we generalize to evolving domains the ADI extrapolated Crank Nicolson orthogonal spline collocation technique developed in [8], [9] for fixed domains.
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Cresswell (1991) makes the interesting observation that world-relative quantification has limited expressive power relative to fixed-domain quantification.
A related problem is that on the fixed-domain interpretation, the sentence ∀y□∃x(x=y) is valid.
Because of the restrictiveness and implausibility of fixed-domain semantics, many modal logicians loosen Kripke's strictures and adopt free logics.
A more serious objection to fixed-domain quantification is that it strips the quantifier of a role which Quine recommended for it, namely to record robust ontological commitment.
The fixed-domain interpretation has advantages of simplicity and familiarity, but it does not provide a direct account of the semantics of certain quantifier expressions of natural language.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com