The phrase "appreciated importance" is correct and usable in written English.
It can be used when discussing the significance or value of something that is recognized or acknowledged.
Example: "The appreciated importance of teamwork in achieving our goals cannot be overstated."
Alternatives: "recognized significance" or "valued importance".
Recently, however, the status of biology has increased substantially, largely because of its success in studying genes and their expression and because of the widely appreciated importance of life sciences for the welfare of humanity and to safeguard our living space on Earth", and this line of reasoning continues throughout.
We will emphasize the newly appreciated importance of neurotransmitter signalling in WM, particularly glutamate and ATP signalling, to understanding both normal and abnormal brain functions.
Although recent studies have highlighted the long appreciated importance of SF in joint function [ 10, 11], identification of the protein constituents of SF and elucidation of their function remain areas of active investigation.
Both appreciated the importance of communications data in relation to the fight against crime and terrorism.
"I've always appreciated the importance of classical music being available on a community level," she said.
Marc La Vorgna, a spokesman for Mr. Bloomberg, said that the mayor appreciated the importance of Mr. Liu's job.
He also appreciated the importance of explaining precisely how they are related.
Like Hilbert, Weyl appreciated the importance of a close relationship between mathematics and physics.
He appreciated the importance of explaining precisely what each of these terms means.
While the role of biochemical signals has long been appreciated, the importance of biophysical signals has only recently been investigated.
Philosophers only recently appreciated the importance of this work (C. Parsons 1965, Smiley 1981, Wright 1983, and Boolos 1987, 1990 , 1995.
