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The phrase "increases with increased" is grammatically correct and can be used in written English.
It is typically used to show a correlation between two things, where an increase in one thing leads to an increase in another thing. Example: "The demand for this product increases with increased advertising efforts." This sentence means that the more the product is advertised, the higher the demand for it becomes.
Exact(59)
"BBC staff have had three years in a row of below-inflation pay increases, with increased workload, and we don't think that's sustainable," he said.
The rate of an enzymatic reaction increases with increased substrate concentration, reaching maximum velocity when all active sites of the enzyme molecules are engaged.
Catalytic activity increases with increased Lewis acid sites.
Therefore, the viscosity of hydrogel unlike gelation time increases with increased AAm/AA mole ratio.
Moreover, the Raptor code processing overhead increases with increased source block size.
The average diameter of the wires increases with increased Co ions concentration.
Similarly, we show that permeability increases with increased porosity and reduced acoustic velocity.
It is seen that the THD increases with increased DC-link voltage.
The degree of adsorption increases with increased temperature, indicating that the adsorption is endothermic [32].
And the temperature-current characteristic indicated a tendency toward linear increases with increased current.
A critical assumption is that the true detectability increases with increased defect size.
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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