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The applicability of the cusp catastrophe is demonstrated by applying the equations to the Mentougou coal mine.
By applying the equations of momentum and angular momentum conservation, for each infinitesimal dr sector of the blade, axial force and torque can be defined [Eqs. (27), (28)].
By applying the equations of designed rack profiles of hob cutters, the principle of coordinate transformation, the theory of differential geometry, and the theory of gearing, the mathematical models of the helical cutting tool can be derived.
By applying the equations, a plotting approach is proposed to determine the apparent initiator efficiency defined as f[(αtd+1)/2] and the constant of chain transfer to monomer, where f is the initiator efficiency and αtd denotes the fraction of the termination rate constants by disproportionation.
By applying the Equations 11 and 12, the mutation rate can be automatically adjusted according to user different purposes.
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The parameters (a) and (b) in Eq. 10 are calculated by applying the equation at the critical point.
The density of the hydrous basaltic glass was calculated by applying the equation of Ohlhorst et al. (2001).
Experimental values closely approached those calculated by applying the equation describing the diffusion of a vapour in equilibrium with the liquid through a capillary tube.
In simple terms, the generalized energy method modifies the Newmark method by applying the equation of motion to a general mid-point instead of to the end point.
To select the appropriate section for background subtraction operation, the changed and unchanged regions can be detected by applying the equation below [38]: D x ij k = x ij k ( t 2 ) - x ij k ( t 1 ).
The percentage match of extracted silhouette with the most matched silhouette is computed by applying the equation below: Percentage match = ∑ i = 0 total segments ( AR of extracted silhouette ) ∑ i = 0 total segments ( AR of stored silhouette ) × ( 1 k ) × 100.
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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