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The phrase "a complimentary basis" is correct and usable in written English
It can be used to describe a situation where something is provided free of charge or as a favor, often in a business or professional context. Example: "The services will be offered on a complimentary basis to all attendees of the conference."
Exact(6)
Facilities are impressive with a range of activities offered on a complimentary basis.
You can also search for prospective employees in our online resume books, which are available on a complimentary basis to prospective employers through Mailman CareerLink.
Desk copies are provided on a complimentary basis to professors who have already adopted a text for course use and placed an order with a university or local bookstore for the texts.
The 202-room Burj Al Arab in Dubai lends the logo-engraved devices on a complimentary basis, but anyone wishing to take one home can buy it for AED 37,490 alongside gold iPhones and Blackberrys in the hotel gift shop.
However, two months after the Super Bowl, Georgia told Clyde Gibson, then comptroller for the Rams, that the unaccounted-for tickets had been given out on a complimentary basis, the prosecutors said.
She had little or no knowledge about what was going on with those tickets". Cotchett added that in his own investigation into the scalping allegations in 1981, he found that some tickets had been given out on a complimentary basis and he was able to account for all but 167 tickets.
Similar(53)
Cross-contamination is very undesirable as it alters the original density values and introduces false anatomical or pathological information to the complimentary basis material density image.
Figure 6(a) contains a large amount of edge structures, such as ribs and vertebrae (arrows), suggesting a high likelihood of cross-contamination when the noise mask is used to denoise the complimentary basis material density image.
Taking advantage of this physical property, Kalender et al. has proposed to use a high-pass filtered version of the first basis material density image (e.g., water) to noise reduce the complimentary basis material density image (e.g., iodine) [ 12].
Send that man a complimentary Freeview box.
She'll receive a complimentary Festival ticket.
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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