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In our computational experiments we use the mean value.
Then, we use the mean value of 's to provide a simplified approximate analysis based on the fixed-length random arc placement over the circle [12].
end{aligned} (9)In this research, we use the mean value of the distribution as the predicted value of the GPR.
We use the mean value of a single operator to measure the distance between the final state and the ideal ground state.
Notice that when is small, can be approximated as follows: (A11)In addition to the cdf of the arc length, we use the mean value of for our approximate analysis.
(8) To establish (8), we use the mean value theorem for integrals once again, this time with one of the 'functions' involved being actually a distribution written in terms of the Dirac delta.
Similar(44)
Hence, we either use the mean values from similar existing equipment or mean reliability estimates provided by equipment manufacturers.
Same as Fig. 5 but we use the mean values between silicate and graphite for fgrow and fdisr.
As "observed" statistics, we use the mean values obtained after 10,000 resamplings from the original dataset (Table 2).
By using the mean value theorem for vector-valued functions [12], the above equation can be rewritten as (25).
For all analyses, we used the mean value for each trait for each species.
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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