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where E system is the total energy of the optimized equilibrium configuration of the graphene and the adatom; E graphene is the total energy of the isolated graphene; E molecule is the total energy of the corresponding adsorption molecules in its ground state; n is the number of gas molecules in the system.
We implemented the GTR+I+Γ model of nucleotide substitution on the unpartitioned dataset, estimated proportion of invariable sites and gamma shape parameter using six substitution rate categories, and optimized equilibrium frequencies, branch lengths, and tree topology (using the nearest-neighbor interchange [NNI] and sub-tree pruning and regrafting [SPR]) on five random starting trees.
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The variational inequality approach to such problems begins with the seminal work of Smith [35] who proved that the user-optimized equilibrium can be expressed in terms of a variational inequality.
An optimized EPICS (Equilibrium Partitioning In Closed Systems) methodology was used to study equilibrium partitioning.
This process is repeated until the snake is optimized and equilibrium is achieved.
Table 1 shows the optimized values of equilibrium interatomic spacing in B1 and B2 phases.
This is due to the fact C ij are calculated at optimized values of equilibrium distances rather than at experimental values.
Three different situations are explored: the mutation-selection equilibrium (optimized population) in three different fitness landscapes, the dynamics during adaptation towards a goal structure (adapting population), and the behavior under periodic population bottlenecks (perturbed population).
The energies of activation and heats of adsorption were obtained from the optimized adsorption rates and equilibrium constants.
High-resolution T1-weighted MR images were obtained by an optimized 3D modified driven equilibrium Fourier transform (MDEFT) sequence at 3 and 9 months after stroke on the same 3T Siemens Magnetom Trio system (Erlangen, Germany) equipped with a 12-channel radio-frequency head coil (Deichmann et al. 2004; Ugurbil et al. 1993).
For the system-optimized flows, a user equilibrium traffic assignment problem with marginal costs can be solved at the lower level problem.
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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