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We group the first three values: 'fairly important' to 'essential' and calculate the proportion who think that race is important to get ahead in each country at each survey wave (1987, 1992, and 2009).
The first three values – freedom, fairness, and well-being – are derived from Beauchamp and Childress' 'Four Principles of Bioethics' (1977): autonomy (freedom), justice (fairness), beneficence, and nonmalfeasance (well-being).
The updated mean BMI was defined as the mean value that was updated each time a new BMI measurement was made (e.g., when the third measurement from baseline was performed, the updated mean BMI was the mean of the first three values).
Similar(57)
On the whole, catalytic rate constants k FBB and k BA were biased towards the 3rd and the 4th value class, respectively, while all five Michaelis-Menten constants were biased towards one or more of the first three value classes.
To facilitate and simplify the comparison, we dictated that parameters with a value in the first three value classes (i.e., < 10) are small-value parameters, while those in the 4th and 5th value class (i.e. ≧10) are large-value parameters.
d=3: 0 3 2 1 0 3 2 1 … this is beautiful labeling 3.4 when you take just the first four values.
For n=3, consider all of the possible arithmetic progressions mod 4 that contain 0. Let the common difference be d: d=0: 0 0 0 0 0 0 0 0 … which is an arithmetic progression, but not one that contains all residues mod 4 since gcd 0,4) > 1. d=1: 0 1 2 3 0 1 2 3 … this is beautiful labeling 3.1 when you take just the first four values.
Table 2 gives the first eight values of δ n.
A third calibrating injection was performed if the first two values differed by more than 10%.
We list the first ten values of ∑ ( a + b + c ) x = n a in Table 1.
First, zero values of mud/gravel fractions were replaced by the maximum rounding error (0.01%).
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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