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This case, which is recast as a logic AND relationship between the genes k 1 and k 2, can be enforced by the following set of constraints: (3) { w k 1. L B j ≤ v j ≤ w k 1. U B j w k 2. L B j ≤ v j ≤ w k 2. U B j Note that based on these equations, if at least one of w k 1 or w k 2 is zero, then the flux through reaction j is forced to zero.
A computer program based on these equations has been written in C++ programming language.
Based on these equations, the stability and dynamic response of the system are analysed.
Based on these equations, the dynamics near the bifurcation point is classified.
The free vibration problem formulated based on these equations is reduced to a transcendental equation.
A kinetic model based on these equations was proposed and the extent of leaching during the simultaneous dissolution with T. ferrooxidans was determined.
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Then a coupled equation is obtained based on these mKdV equations, which is solved for the reflected soliton under the use of solutions of mKdV equations corresponding to the incident and transmitted solitons.
Two types of flexure-based compliant proportion mechanisms based on the novel analytical model are designed and optimized based on these proposed equations.
Based on these observations, equations for the evolution of mobile and forest dislocation densities are posed, depicting boundary sources and dislocation dislocation interactions, respectively.
The net variation in the ratio nCl−/nF− thus computed based on these four equations by assuming uniform depletion of boron from the melt due to electrodeposition was compared with the experimental values obtained during many electrowinning runs.
Based on these conservation equations, some recent studies have been performed by Agarwal et al. [16,17], Bhadauria and Agarwal [18,19], Agarwal and Bhadauria [20], Rana and Agarwal [21], Agarwal [22].
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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