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Simple: those extra numbers are a specification, and if there's one thing certain groups of men (it's always men) love above all other things, it's a specification on a list.
Aristotle goes on by adding a specification on his doctrine of the four causes: the form and the end often coincide, and they are formally the same as that which produces the change (Phys. 198 a 23 26).
The coefficients in the polynomial function are defined in such a way that the total energy difference between the quantization function and the polynomial function is minimized subject to a specification on the upper bound of the absolute difference.
In particular, the transmission power gain is minimised subject to a specification on the ratio of the signal gain to the noise gain as well as to the relaxed zero forcing condition.
A specification on the meta-data part such as journal titles can be expressed as additional fields to the subject-verb-object tuple.
Similar(55)
The stack was designed using a top-down approach, based on a specification of an APU system that is installed on board of vehicles.
It is agnostic to the execution environment of the real-time system and relies on a specification of the tasks.
The proposed characterisation is parametric on a specification of the underlying behaviour model introduced as a strong monad.
Although BSDEs (64) and (69) have the same shape, the features of their solutions heavily depend on a specification of the processes X k and βk,l.
The proposed solution is based on a specification of a common data model to represent engineering knowledge and a service-oriented tool integration with the Engineering Service Bus.
In robotics, such knowledge can for instance be used in the design of a robot's sensorimotor mechanisms based on a specification of the desired cognitive capabilities.
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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