(with respect both to the mathematical tools used, and the need to take fully into account and interpret correctly all the mechanical effects) ...

or "... to take all the mechanical effects fully into account and interpret them correctly ..."

I guess you're worried about how to work in "полного учета", etc., and not only "both ... and"?

"from the standpoint of" instead of "with respect to" would be OK, but the latter sounds better, I think, in this long clause when there are two different requirements being listed.

As for the beginning of the sentence, I assume you'd write something like "Because of the factors just mentioned..."


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Note added at 3 hrs (2009-05-20 13:54:18 GMT)
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Reply to asker's note:

"both to" and "to both" are both legal, but here there are good reasons to prefer "both to". For one thing, it doesn't separate the preposition "to" from its complex end-object. But the more important reason to use that word order is that if you write "with respect to both the mathematical tools and...", it sounds as if there are two mathematical tools. I suppose that actually, with that word order, "to" should be repeated, like this:

(with respect both to the mathematical tools used, and TO the need to take fully into account and interpret correctly all the mechanical effects)