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The phrase "shift up" is correct and usable in written English.
It is often used in the context of changing gears while driving a vehicle. Example: "As the car approached the steep hill, the driver shifted up to a higher gear in order to maintain speed."
Exact(60)
Just whack an axe in, shift up, kick a toe in, shift up, and so on.
The investigations also evidenced that the typical frequencies shift up while increasing Air Fuel ratio.
These band tails shift up to 2.32 and 1.44 eV when the interface is constructed.
In such circumstances, creditors could always shift up the yield curve.
Such innovations can shift up the entire curve shown in the graph above.
They will indeed raise costs, that is, shift up the aggregate supply curve.
Importantly, this figure is not set in stone and can shift up and down.
When the time comes to shift up a gear, our housebuilding industry is found wanting".
We also added chopsticks (and pipe-cleaners) so that the linkage didn't shift up, down, left or right too much.
These complexes displayed a unique feature that was a remarkably high Stokes shift up to about 240 nm.
When the grain boundaries concentrate in the tensile (compressive) stress zone, the steady-state stress lines shift up (down).
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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