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So why does the constant-force approximation work so well?
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One can see the Column-Sampling approximation works better and more approximately up to the ED reconstructed performance.
In general, the authors should either not consider the exact solution of the approximate linear system or specify the parameter domain in which the linear approximation works.
It is found that the LPW approximation works well only for mode propagation parallel or nearly parallel to the direction of flow.
This plot is a bit busy, but the main gist is this: the fraunhofer approximation works fine, even significantly off axis, in the sense that the shift is will approximated by the linear phase.
Since this project deals with waypoints that are no more than a couple kilometers apart, and there are very few, if any, people running near the poles, the equirectangular projection approximation works well.
The basis for his statistical mathematics came from a long tradition of work on the method of least squares approximation, worked out early in the 19th century in order to estimate quantities from repeated astronomical and geodetic measures using probability theory.
The approximation works in a restricted, but large, class of plasmas, those in which scattering of the α's and bending of their trajectories by magnetic fields can be neglected.
This approximation works for our system.
A new approximation working set is presented.
The approximation works perfectly and matches the simulation result well.
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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