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Discover LudwigThe phrase "derived as with" is not standard in written English and may cause confusion.
It could be used in contexts where you are comparing derivation methods or processes, but it is not commonly used. Example: "The results were derived as with previous studies, indicating a consistent trend."
Exact(1)
The required quantization levels per dimension can be derived as, with, where represents the variance of the additive white Gaussian noise (AWGN) [7] and denotes the ceiling function (i.e., rounding to the smallest integer not less than the argument).
Similar(59)
Considering the limitation of probability conservative systems for the GPDEE, a novel concept of probability dissipation is introduced and a completely uncoupled partial differential equation is derived as well with respect to the evolutionary probability density function, which holds for any physical quantity of a probability dissipative system.
We review the evidence that archaea are derived, as well as their biggest differences with bacteria.
There is undoubtedly much fun to be had with those who, having freed themselves from the constraints of church and tradition, sought to define a new and fairer society, but the comedy in The Trouble With Tom derives as much from the ingenious involutions of its storytelling form.
We already get 20% of our electricity from nuclear, with France deriving as much as 80% from the clean, efficient and increasingly cost-effective source.
As multiple siRNAs from both strands of the precursor are programmed into RISC, siRNAs can potentially act both in cis and in trans by targeting the elements from which they derive as well as unrelated elements with substantial complementarity to their sequence.
The update rules for wi,n are derived as (49) with (46) and (17)–(19), where (49) coincides with (16) when ν→∞ and p=2.
The update rules for wi,n are derived as (34) with (32) and (17)–(19), where (34) coincides with (16) when β=p=2.
Obviously, the output of the NCFMV can be derived as follows with (17), (12), (13), and some simple manipulations: Y f = w NC H ( f ) X ( f ) = S ( f ) + w NC H ( f ) a ( ϕ i ) S i ( f ) + w NC H ( f ) N un ( f ) = S f + g ( ϕ i, f ) S i ( f ) + w NC H ( f ) N un ( f ) (18).
One was by comparing the least-squares means of TEE and activity energy expenditure (AEE, derived as TEE BMR) with body weight as the covariate, as most activities are presumed to be weight bearing.
The specific viscosity of polymer solution has been derived as 2.5(c/cI), with cI being the internal concentration associated with a polymer molecule.
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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