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"improved very much" is correct and usable in written English.
You can use it to describe something that has experienced a great deal of improvement. For example, "Thanks to our hard work, the company's profits have improved very much this year."
Exact(15)
The tests showed that even with a term of instruction, their understanding hadn't improved very much.
After 12 weeks, 80percentt of children receiving the combined therapy had either shaken their anxiety or improved very much.
Netbooks are good value but they have not improved very much over the past couple of years, and you already have one.
But it's improved very much," he said.
Three hundred and eighty patients (81%) indicated their main problem had improved very much, moderately or slightly.
In addition, if we can successfully identify NLOS propagation or LOS propagation from related parameters, positioning accuracy would be improved very much.
Similar(44)
Though Konerko did not improve very much, finishing the season at.234, he liked the way he could drive the ball to center and right.
The analyst also found that the project would not create the numbers of ongoing jobs that Leiweke claimed, and that convention-center business was not likely to improve very much.
The proportion of patients rated as improved (somewhat improved, moderately improved, or very much improved) was calculated using the "intention-to-treat" approach in an "observed case" manner (i.e., no imputations were made for missing data).
It also suggested that responses in Patient Global Impression of Change of minimally improved, much improved, and very much improved would also constitute minimally important, moderately important, and substantial improvements.
In Silvennoinen et al. (2002), clear-felling was perceived to decrease scenic beauty "very much" when the effect of different cuttings were evaluated using a verbal scale ranging from "worsens very much" to "improves very much".
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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