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For convenience of notation, let denote the.
This is an argument from convenience of notation, and does not bear on logical coherence.
For convenience of notation, we define these following normalized flux amplitudes.
For convenience of notation, denote x ( t ; φ ) by x ( t ).
To begin with, for convenience of notation, we state the classical symmetric mountain pass theorem as follows.
For the convenience of notation, write (r_{ab}=w(a -w(b)) a -w(r_{bc}=w(b)-w(c)).
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Applying this generic definition to the canonical distribution from Eq. (8a), one gets fluctuation-dissipation theorem [ 2] (11) where, for convenience of the notation, the subscript V has been dropped.
Next, for the sake of convenience, in notation let us agree to write (k=N) when (n=2N) and (k=N-1) when (n=2N-1).
end{aligned} For convenience of representation, the following notation is introduced: begin{aligned}& e_{i}=operatorname{col} {underbrace{0_{n},ldots,0_{n}}_{i-1},I_{n}, underbrace{0_{n},ldots,0_{n}}_{9-i} }, & xi^{T} (t )=bigl[ textstylebegin{array}c@{quad}c} zeta^{T} (t )&chi_{d}^{T} (t ) end{array}displaystyle bigr].
All crystallographic indexes used in this paper are expressed in the rhombohedral notation for convenience of discussion (see Additional file 1 for conversion between the rhombohedral notation and the hexagonal notation).
For convenience, we will make an abuse of notation in the proof and denote X t k = X t ∧ τ U k k.
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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