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The arrows denote the corresponding curves for given system parameters.
The first simulation experiments have been applied to decide on the number of steps to simulate for given system size.
While for given system parameters convergence of the detection process may be successful for flat channels, it might fail for frequency selective channels.
(a) Impact of ω ϕ and (b) impact of outage thresholds μ th S. The arrows denote the corresponding curves for given system parameters.
An interesting feature of this method is finding the analytical solution for given system, if the exact solution be polynomials of degree n or less than n.
Thus, for given system composition and structure, this numerical methodology is in essence a model built on sound physics principles with prior validity, without resorting to ad hoc empirical treatment.
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The positivity of entropy unveils the spatial chaos for given systems and pattern formation for zero entropy.
Equations for particular density and the moment equations for given systems are derived and used in the investigation of solvability of initial problems and stability.
When treating a time-dependent Hamiltonian system dynamically, one usually employs classical solutions of the equation of motion for a given system (or for a system similar to a given system) [6, 7].
Simple empirical equations for the initial sizing design stage are provided for the entire state for a given system.
Lin and Yang (2010) also proposed a methodology for estimating the location and number of docking stations needed for a given system.
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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