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The shortest time T s of a hypha to grow in a longitudinal direction from a tracheid into an adjacent one, indicated in Figure 7a by the dotted line connecting the points 1 and 3 (by the super indices of T) may be given by T S 1 − 3 = l S 2 ⋅ μ 12 + l S 2 ⋅ μ 23 + τ, (2).
The same pattern was observed when stratified by weight status, with the exception of light and vigorous intensity activities in the overweight/obese group, where no statistical differences were found across instruments.> -wrap-foot> a,b.cDifferent super indices represent statistically significant differences between methods (p < 0.05).
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Moreover, we drop the super-indices (a) or (b) when interchangeably referring to the game G ( a ) or G ( b ).
where the super-index ∗ represents complex conjugation.
Again, super-index (d) is omitted to simplify the notation.
The super-index ( (m) ) denotes the any variable associated with the medium ( varOmega_{m} ).
These indexes were subsequently integrated into a single super-index: an effectiveness index for the protected area.
The super-index w and b refer to the well (In x Ga1−xN) and barrier (GaN) materials.
where γ ̂ th is the threshold that defines the SR condition in the cross-link (note that the super-index (c) has been omitted to simplify the notation).
Hence, the MIMO SNR is SNR ( H ) = tr H C s H H tr C n = tr H H H n T n R N 0, where tr denotes the trace operator and the super-index H represents conjugate transposition.
The j th element of a vector x is denoted as x j, element (i,k) of a matrix A is denoted as Ai,k, a super-index in parenthesis (j) denotes a node within a range of distances, a sub-index within square brackets such as [i] denotes an element of a set.
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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