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It is easy to check, from, that (4.7).
It is easy to check from (G_{i1}) that (liminf_{ttoinfty}x_{i}(t)=0) a.s.s
It is easy to check from w = ( w − P w ) + P w that Y = Ker ( P ) + Ker ( L ).
It is easy to check from ((x,y)= x,y -Q x,y -Q x,y)) that (Z= operatorname{Im}L+operatorname{Im}Q x
For γ = − 1 which corresponds to a vacuum-dominated epoch, it is easy to check from Equation 5 that the universe is inflating exponentially with time.
end{aligned} (4.12) Furthermore, it is easy to check from (2.10) that frac{N+beta-p}{alpha-beta+p}> frac{ p-1)[N+alpha-frac{ p-1}(N+beta-p)]}{alpha-beta+p}.
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Note it is easy to check that acts from into.
It is easy to check property (iii) from the definition of.
as is easy to check, we deduce from (12) that a h - ¯ + h + ¯ = g.
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However, it is easy to check that increasing τ from 0 to M − 1 M would decrease the value of the objective function g = (p1 + p2 + ⋯ + p M )2 in (3.8), which means the estimation performance deteriorates.
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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