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Exact(17)
The two values are then substituted into the second equation of (1.81).
Substituting into the second equation of (3.26), we obtain (3.30).
Substituting (2.15) into the second equation of (2.12), we have (2.16).
Substituting it into the second equation of (4.39) yields the existence of interior equilibria as follows.
Substituting (2.8) into the second equation of system (1.3), it follows that (2.9).
(6) and (7) into the second equation of (5), we obtain A I 2 + B I + C = 0, (8).
Similar(43)
In the arteries the volume increases due to fluid flowing in from the arch and decreases as it flows out of the arteries into the veins, leading to the second equation.
The second equation takes into account diabetes duration when predicting the risk of an initial CHD event and we thus referred to it as the duration UKPDS risk equation.
This fact is usually represented in the form of an equation that simply relocates brackets in an obvious way: We see that relocating the brackets in accord with this format, the left-hand term of the second equation is transformed into the left-hand term of the third equation, and the same for the right-hand terms.
substituting the second equation of (3.15) into (3.29), we have (3.30).
The system formed by the n equations satisfies a suitable Hörmander condition: the second equation feels the noise plugged into the first equation, the third equation feels the noise transmitted from the first to the second equation and so on … , so that the noise propagates one way through the system.
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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