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Braking point, turning point, clipping point, all that pretty much goes out of the window – well, it would if there were any.
We considered HF propagation characteristics such as the minimum slant range, skip distance, elevation angle, true reflection height, slant range, and ground distance to the ionospheric reflection point (turning point).
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Stable and unstable conditions, bifurcations points, turning points and oscillatory behavior were determined.
The referencing saddle points (turning points) were pH 6.33 and As 359 μM for plant biomass and pH 5.87 and As 331 μM for P uptake based on the response surface plot.
To make examples where typical trajectories exhibit rotational chaos, one way is to suppose the map has negative Schwarzian derivative (a relatively mild condition which can be written as ( 1 / ( log | f ′ | ) ′ ) ′ > − 1 2 ) and to oblige the orbits of the critical points (turning points) of the map to land on unstable periodic orbits.
What might have been an early turning point was no turning point at all.
Black arrowhead points to the turning point of an axon.
Then came 1968: the high point and turning point of her life.
The program analyzes and calculates a characteristical point, the turning point of the S-shaped ascent of the profile.
Assign a high point, a low point and a turning point to each chapter.
Out of this turning point comes the opposite – a turning point for the better.
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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