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1) General subject: bear sway over (на кого-л.), bias (обыкн. плохое), bring to bear influence, govern pass, have a bearing, have influence with (на кого-л.), hold sway over (на кого-л.), influence, operate, stroke, stroke-oar, work on, bring influence to bear, exert influence on (на кого-л.), have an impact on (на кого-л.), touch on (на что-л.), touch upon (на что-л.)

2) Engineering: act, act on, impact

3) Mathematics: have an effect on

4) Religion: have impact, make a difference

5) Accounting: bias (напр. на результат исследований)

6) Australian slang: twist round (one's) little finger

7) Diplomatic term: have influence on (на кого-л.), impact (на общественное мнение)

8) Business: reach

9) Drilling: affect, management implication

10) Aviation medicine: exert

11) Makarov: exert an influence, govern, have an effect on (...), take effect, work (on), create effect, exercise influence, exert influence, exert influence (на)