This is the 5308th most frequent Russian word.
опубликованные
"Published."
In this sentence, "опубликованные" refers to books that have been published, functioning as an adjective describing the noun "книги" (books).
Опубликованные книги получили положительные отзывы.
The published books received positive reviews.
Here, "опубликованные" is again used adjectivally, describing "письма" (letters) that have been published.
Газета напечатала все опубликованные письма.
The newspaper printed all the published letters.
In this sentence, "опубликованными" is used in the instrumental case, modifying "данными" (data) to indicate that the confirmation was done by means of the published data.