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Simplifications of the analytical solution are discussed using a random sampling method and it is shown that the thickness ratio between film and substrate can be neglected for thin films on rigid substrates.
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He discussed using a six-sided die to generate a random integer from 1 to 5, employing a modulo operation, and using a 16-bit source to randomly permute any list of up to 65,536 items.
A third instructional approach that participants discussed was using a random call to ask students to share their ideas with the whole class.
The effects of the constraint of causality on the performances of feedforward and feedback control of random disturbances are discussed using two simple examples; a minimum phase single-degree-of-freedom vibrating system and a non-minimum phase acoustical system.
Only 2 studies using mixed models explicitly accounted for the issue discussed in this paper: one by using a random intercept model with autoregressive error structure (Grindstaff et al. 2006) and one by using a random slope model (Sockman et al. 2008).
("I didn't want to $9.95 people," Steinberg said, using a random price as a verb).
Seroepidemiologic studies were conducted using a random sample of infants.
Random allocation was accomplished using a random number table.
Individuals or objects are then selected through a random process from this population (often using a random number generator).
A random number was drawn using a random number table.
Using a random number generator, outpatients were selected at random.
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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