Sure I can.
Make it easy by taking out the unnecessary parts of the sentence. You need to look at the subject and verb of the sentence.
1. Ongoing research by several scientists (suggest) that regular periods of meditation reduce blood pressure and are likely to contribute to other improvements in health.
First, take out the prepositional phrases. They are just in the way and they confuse you. By is a preposition. By several scientists is a prepositional phrase. Once you take it out, you get
Ongoing research (suggest) that regular periods of meditation reduce blood pressure and are likely to contribute to other improvements in health.
Find the subject of the sentence. Research is the subject of this sentence. Because research is singular, the verb (in this case it is suggest) needs the be plural. You have to put the prepositional phrase back in the rewrite the sentence, of course. The sentence should be
Ongoing research by several scientists suggests that regular periods of meditation reduce blood pressure and are likely to contribute to other improvements in health.
Here is a list of prepositions to help you. http://www.englishclub.com/grammar/prepo…
Sorry I'm not sure about the second one.
Good luck! (:
2. Five years in the writing, her new book is both a response to her critic's mistrust (with) her earlier findings and an elaboration of her original thesis.
You need to change the verb. Maybe you could replace "with" with from or because.
because parentheses is used to give extra information, the words in the brackets aren't extra information, they are part of the sentence.
1. The subject is research, not scientists,. so you need a plural verb. (suggests)
2. I would change with to of, since you used of in the second part of the sentence... (?)