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Based on the Lagrange multiplier method, a discrete-time dynamical system is designed so that those constraints are automatically satisfied.
The procedure starts from the laws of thermo-dynamics, so that the first and second laws of thermo-dynamics are automatically satisfied.
A class of algebras is defined, with the property that every bounded set has compact closure, where the compatibility conditions are automatically satisfied.
Although there are many specialized configurator tools that aim to provide configuration support, they only assure that all dependencies from selected features are automatically satisfied.
Among all the proposed methods for solving free-surface seepage problems, the extended pressure (EP) method emerges as one of the easiest methods since the boundary conditions are simply imposed on the prescribed outer boundaries and those on the prior unknown free-surface are automatically satisfied.
When,,,, the conditions and are automatically satisfied.
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"[T]he requirement of inducement is automatically satisfied by the power connected with the public office.
With this approach, the continuity of the velocity field at the interface is automatically satisfied.
In other words, once observation limitations are respected, limitations on control will be automatically satisfied.
Hence the principle of the conservation of mass is automatically satisfied whenever we employ a closed system analysis.
Also the constraints can be automatically satisfied by constructing the proper set of all the possible configurations.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com