1. This does not make sense to me, can you try phrasing this differently? Are you trying to say "I like working with computers"? "Indulgence" can sometimes have a negative connotation in English, as it can imply "enjoying too much" or "enjoying too greedily". This is also the only one that is not a complete sentence, if this is a concern for you. 2. "Staff" is already plural, so just say "staff." Otherwise, yes, this makes sense. 3. This means perfect sense to me! 4. This makes sense, although if you want to sound more natural, I would say "Exploiting supercomputers is the best technique for resolving academic and industrial problems."

1. Indulgence in working with computers It is not a complete sentence, but as a phrase it sounds correct to me. 2. The efficiency of the staffs deteriorates without using computers. *The efficiency of the staff deteriorates without the use of computers. 3.It is not plausible theoretically. It is not theoretically plausible. (I don't know if this is an error or if it just sounds better to me this way. Putting the adverb at the end makes it sound as if it is an afterthought. In such a case there should be a comma after "plausible". Then it would make sense to me, but would not be good written English. We might speak this way if our ideas were not completely formed yet, for example in a casual conversation, not a lecture. 4. Exploitation of supercomputers is the best technique for resolution of academic and industrial problems. ..... to resolve academic and industrial problems. I don't understand your usage of "exploitation".

1) The word indulgence should not be used in this sentence. Indulgence is when I eat an entire pizza and then feel a little sick afterwards. Or if I spend a lot of money on a gift for myself. As you can see, this word would not work with "working with computers." 2) The sentence would be much better if it started as "the staff's efficiency deteriorates...". And "without using computers" is a little awkward. Maybe better would be, "without the use of computers.' 3) This sentence should be written, "it's not theoretically plausible." Even if you rearrange those words as suggested, I don't like the sentence. In my opinion, plausibility already has an element of the theoretical. As such, to me, it has a hint of redundancy. I may not be good at explaining why I think things are not well-written but I can often tell when my past English teachers would not like a sentence. 4) Technically, this sentence is fine but I don't like the word exploitation being used here. Since when do we exploit supercomputers??? How about "the use of supercomputers...".

The second sentence is missing the possessive, and it would be better written as "The staff's efficiency deteriorates without computer's." 3 would be better written as "It's not theoretically plausible." OR "It is not theoretically plausible." The other two seem fine to me.