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Parenthetical adverbials are adverbs or adverbial phrases that provide additional information or commentary within a sentence. They are often set off by commas, dashes, or parentheses, and can be removed without affecting the grammatical structure of the sentence. Here are some examples:

 1 However, the project was completed on time.

 Here, "however" is a parenthetical adverbial that adds contrast to the sentence.

 2 The meeting, unfortunately, was canceled.

 "Unfortunately" provides a comment on the situation.

 3 She decided to go to the party—surprisingly—despite her busy schedule.

 "Surprisingly" adds a note of unexpectedness.

 4 The results, in my opinion, were quite impressive.

 "In my opinion" offers a personal perspective.

 5 He was, without a doubt, the best candidate for the job.

 "Without a doubt" emphasizes certainty.

 6 The weather, as expected, turned out to be perfect for the picnic.

 "As expected" provides a contextual comment.

 In each case, the parenthetical adverbial can be removed, and the sentence would still be grammatically complete, though the additional nuance or commentary would be lost.