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The sum of the squares of three and three.
The index number is the sum of the squares of the market shares of the companies in an industry.
In contrast, the sum of the squares of the averaged quantities never exceeds 1 (see the blue curves).
The data show the sum of the squares of the measured conditional visibilities and predictabilities together with the average quantities.
The square root of the sum of the squares (i.e., sum in quadrature) of the residuals is minimized.
In both figures, we see that the sum of the squares of the conditional measurements exceeds 1 (see the red curves).
To calculate the fluxes, we fixed the growth rate to 0.1 g/gDW per day and minimised the sum of the squares of all fluxes in the system.
The sum of the squares of and is always bounded below by 1 and above by 2. This result is in apparent violation of the duality principle.
The Frobenius norms of the two similarity matrices correspond to the sum of the squares of the connection weights in the two projections.
Combining the two results, each obtained with different postselections, gives rise to a sum of the squares of the visibility and predictability that is greater than 1.
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Fitting is done by minimizing the sum-of-the-squares of the difference between the two, to obtain the best-fit values of D and β.
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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