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"The image of Sicily in the movies is valid up to a point," he says.
Suppose that the lemma is valid up to n.
This simple assumption is valid up to strain rates of some hundreds per second.
Darcy's law is valid up to Reynolds number less than about 10; i.e., laminar flow.
The model is valid up to 300 Hz and includes a submodel of the wheel and the air cavity.
However, the Langmuir equation is valid up to a concentration limit, which is a characteristic of each phenolic compound[53, 57, 172].
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Bridgman formulae were reported to be valid up to the peak load.
Hence, the present design of steel reinforced concrete was valid up to the initial modulus of elasticity.
Then, singular perturbation solutions to the governing eigenvalue problem are derived that are valid up to and including order ϵ for any given non-zero hub radius.
The analytical expression parameters and pressure corrections used for barite and celestine in Pitzer.dat are valid up to >200 °C, and 1000 bar (Monnin 1999; Blount 1977; Appelo et al. 2014).
This work intends to increase the efficiency of the performance evaluation of systems by providing real-time guarantees on delays and backlogs that are valid up to a certain level of confidence, as opposed to the hard guarantees commonly derived by formal methods.
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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