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This modification allows for a more marked separation of time-scales during the early dynamics, and thus describes a system more accurately approximated by a singular limit prediction (Fig. 14b).
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Consider the following nonlinear system with interval time-varying delay which could be approximated by a T-S singular model with r plant rules.
Consider a nonlinear singular system with time-varying delay that could be approximated by a time-delay T-S fuzzy singular model with r plant rules.
Thus, our analytic results are valid only for the initial growth of the trait variance where unimodal distribution (approximated by a normal distribution) becomes broader at the singular point.
The optimal control solution is usually singular but may be approximated by a bang bang solution.
The remaining complementary dynamic part is non-singular and can be approximated by a truncated modal series of fast accelerated convergence.
The analysis is based on a numerical solution of a complex singular integral equation with the unknown tractions at each circular boundary approximated by a truncated complex Fourier series.
This approach is used also in [12] when an impact oscillator is approximated by a one-parametric family of singularly perturbed differential equations, but as discussed in [12], the geometric singular perturbation theory does not apply.
It was one approximated by a Morgan Stanley analysis.
The optimal strategy was approximated by an iterative annealing process.
The largest r c singular values of X b can be approximated by the r c singular values of R A (t), i.e., the diagonal elements of D A (t) [46].
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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