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Mathematical formulas have been derived for each considered ray contribution in terms of the building dimensions and the distances between the building, mobile and transmitter.
Finally, analytical expressions of the optimum thrust-vector angle have been derived for each performance, in complement to the expressions already provided by former studies on this subject.
The load data of all the test customers have been collected and the typical load patterns of customer classes have been derived for each service district.
The effective scale-height of the electron density for two altitude ranges, 145 165 km and 165 185 km have been derived for each of the profiles studied.
Expressions for occurrence probabilities of the categories have been derived in Section 4. Interference type based on MAC protocol and the throughput achieved by each link has been derived for each category in Section 5. Section 6 concludes the paper.
The dislocation density has been calculated at each strain and by assuming that the shear stress is proportional to the square root of the dislocation density the shear stress strain relationship has been derived for each of the three groups of grains showing different deformation microstructures.
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Real fundamental solutions are derived for each eigenvalue distribution.
Commonly human mobility measures, including detected home and activity centers, are derived for each user trajectory.
Moreover, compact models are derived for each point, further reducing the computation cost.
From the autocorrelation parameter ρ, catchment average correlation lengths were derived for each compound.
Based on experiments a set of plant models was derived for each patient.
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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