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As mentioned, the bias vector b t) is assumed as constant, so we can express that b(t + 1) = b t).
And it's the depth of where we can pull that out, you know, how we can express that beauty.
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We can express opinions that show either what fine, upstanding people we are, or what liberal, tolerant people we are, accordingly.
Let L be the first-order language whose signature is that of R. Because of the expressive strength of L, we can write down any number of theorems of calculus as sentences of L. Because of the expressive weakness of L, there is no way that we can express in L that R has no infinitesimals.
The question of cosmetics now appears to have been resolved and we can express ourselves satisfied with that agreement.
To know that "trying" is easier today compared to the past is a luxury for which we can express gratitude, and that humankind should be proud to have accomplished.
In particular, it is unclear how we can express the fact that Q lacks a truth value.
Here we can express our feelings and know that someone cares about us".
Similarly, we can express the set of SUs that can choose channel 3 as Ψ ( 3 ) a = Ψ 3 a ∖ ( ( ∪ i = 1 2 S i n i ) ∩ Ψ 3 a ) and consider all possible ways that n3 SUs in the set Ψ ( 3 ) a can choose channel 3, and so on.
That is, we can express the true amplitude α as alphaapproxalpha_{0} + u/sqrt{n},quad u inmathbb{C}, (3) where the parameter u follows the Gaussian distribution G u) = frac{1}{pimu^{2}} e^{-u^{2}/mu^{2}}.
For a particular way that the specific set of n1 SUs S 1 n 1 choose channel 1 (there are C N 1 n 1 such ways), we can express the set of remaining SUs that can choose channel 2 as Ψ ( 2 ) a = Ψ 2 a ∖ ( S 1 n 1 ∩ Ψ 2 a ).
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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