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In this figure, the author selected a part of the explanation marked by underline.
Define a map (sigma : mathbb {Z}^{n} longrightarrow mathbb {Z}) by (underline {i} mapsto sum underline {i}).
Let (f(x)) be a fuzzy valued-function on ([a,infty[) which is represented by ((underline {f} x,r),overline{f} x,r))).
For an integer d, we denote by (underline {v}/d) the vector (left (frac {v_{1}}{d},ldots,frac {v_{n}}{d}right)).
Replacing R k by (underline {R}{{_{k}^{mathrm {Z}}}}) and (underline {R}{{_{k}^{mathrm {M}}}}), we can obtain the lower bounds of the SE and EE for the shared-antenna FD massive MU-MIMO system with imperfect estimation.
Along the same lines the sequence ({v_{n}= overline{w}_{n}, overline{z}_{n})}) is monotonically decreasing and bounded below by ((underline {w}^{(0)}, underline{z}^{(0)})), thus it is convergent to its greatest lower bound say ((w^, z^)).
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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