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The phrase "a fast resolution of" is correct and usable in written English.
It can be used when discussing the quick solving or settling of an issue or problem.
Example: "We are looking for a fast resolution of the technical difficulties we are currently facing."
Alternatives: "a quick solution to" or "an expedited resolution of".
Exact(4)
However, along with the demands to protect modest gains in women's rights since the fall of the Taliban, there is also some pressure for a fast resolution of the current standoff, because Afghanistan is in desperate need of a new criminal prosecution code.
Responding to Arthur Andersen's argument that its survival depends on a fast resolution of the criminal indictment filed against it, a federal judge ruled today that a trial would begin in just 47 days on a charge that the firm obstructed justice in the Enron investigation.
The admittedly optimistic forecast by McKinsey — the firm has a less rosy version as well — presumes a fast resolution of regulatory challenges and widespread acceptance by consumers.
Although there are no studies comparing gradual and abrupt interruption, the widespread opinion of specialists considers drug withdrawal to be more effective when done abruptly because this is believed to achieve a fast resolution of the drug-induced pain-coping behavior [21, 40, 43, 49, 54].
Similar(56)
The new body would also ensure a faster resolution of complaints, easier access and better support for those complaining, and an ability to deal with organisational as well as individual policing failings.
Japanese bankers are digging in to oppose vociferously efforts by Japan's new chief financial regulator, Heizo Takenaka, to force a faster resolution of the country's bad-loan crisis.
Nebulization was associated with a faster resolution of signs of infection and weaning, as well as reduced use of systemic antibiotics.
Delivery of IL-4 treated cells in the cerebrospinal fluid of mice led to a faster resolution of EAE [ 25].
Moreover, the combination of conventional and biological DMARDs may provide a faster resolution of the inflammatory process and may increase the response rate [ 4].
In the setting where antibiotics are often prescribed, a wait and see approach and earlier consideration of the possibility of asthma would lead to a faster resolution of symptoms and the establishment of a correct diagnosis.
Our experience is that the parallel usage of nonsteroidal anti-inflammatory drugs right from the beginning does reduce symptoms of inflammation and contributes to a faster resolution of arthritis, even though no prospective long-term data are available.
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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