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In the frequency domain, this relation can be written as (2).
This relation can be written as the following equation: i m a g e ( i, j ) = L P ( i, j ) + H P ( i, j ), (4).
For the hardness H, the following relation can be written, σH / Hmean = δσE / Emean with 1.2 ≤ δ ≤ 2 according to the material, the presence and the nature of the substrate.
Considering Eq. (33), the following relation can be written for D min: D_{hbox{min} } = (EI_{0} ),t_{hbox{min} } (37 where t min is a design constraint which could be dependent on some practical requirements.
If we denote the signal created by multiplying elementwise {x[n]} and { e - j 2 π k ^ n N } by { x ^ [ n ] }, the previous relation can be written in the form of X ( ω k ) = ∑ n = 0 N - 1 x ^ [ n ] e - j 2 π k n N, (33).
The dispersion relation can be written down as follows: {K}^2kern1em =left({varepsilon}_{left|right|}left(nu right)left 1-{varepsilon}_{perp}left 1-{varepsilont)right)/left(left(1-{varepsilon}_{perp}left(nu right){varightlon}_{left|right|}left(nu right)right)right), (3)where ε z = ε ||, ε x = ε ⊥.
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The resulting flux force relations can be written entirely in terms of conventional transport coefficients: transference numbers, electrical conductivity, diffusion coefficients of electroneutral electrolytes and intra-diffusion coefficients.
At a distance z from the mid-plane, the strain displacement relations can be written as follows: ε xx = ∂ u ∂ x − z ∂ θ ∂ x, γ xz = − θ + ∂ w ∂ x.
These relations can be written in the form begin{aligned} x phi _j x)=alpha _j phi _{j+1}(x) +beta _j phi _j x) + gamma _jphi _{j-1}(x), quad quad j=0,1,2,ldots, end{aligned} (2.1 where the (alpha _j, beta _j, gamma _j) are real, (alpha _jne 0), (phi _{-1}(x equiv 0), (phi _0 x equiv 1).
These relations can be written symbolically as: :1 mg = 0.001 g :1 km = 1000 m In the early days, multipliers that were positive powers of ten were given Greek-derived prefixes such as kilo- and mega-, and those that were negative powers of ten were given Latin-derived prefixes such as centi- and milli-.
Relation (3.1) can be written as (3.5).
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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