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Both conditions seem to be different in nature because one of them refers to the mapping and the other one is assumed on the ambient space.
When a one-sided Lipschitz condition of the following type: (1.20). is assumed on function for some and all, it is possible to deduce the existence of extremal solutions in the sector of the considered problem.
Reaction equilibrium is assumed on each reactive stage, and vapour liquid equilibrium is assumed on all stages.
The infinite-frequency limit is assumed on the free surface.
In the first scheme, no knowledge is assumed on the bounds of unknown system parameters.
A semi-elliptical crack is assumed on the y-z plane in a semi-infinite body.
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That is assuming on ad per session.
No restrictions are assumed on the shape and trajectories of obstacles.
No restrictions were assumed on both the concrete microstructure and inhomogeneity of stress fields in the inclusions.
Prior distributions are assumed on the model parameters which are then incorporated into the DA-optimal design criterion by integrating it over the prior distribution.
Beams are assumed on all grid lines.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com