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Sixth seed Pliskova, 18, came back from 4-1 down in the tie-break to seal victory in one hour 20 minutes.
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But Sharapova's nerve soon returned as she took an early lead in the tie-break which she never relinquished to seal a win over the Czech who beat her in last year's Wimbledon final.
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Agassi showed his class to break Henman again, and in the tie-break the Briton spurned four match points before the American held his nerve to seal the match.
BBC: Henman upbeat after Agassi escapes
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And although the 26-year-old Lopez did claw one break back, the mercurial Safin held his nerve to seal the match.
BBC: Safin books meeting with Federer
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But Safin did not have to stretch himself much to seal the set, Lopez making a string of unforced errors to lose the tie-break 7-1 and fall 2-1 behind in sets.
BBC: Safin books meeting with Federer
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After dominating the first set, two stunning winners - a backhand down the line and crosscourt forehand winner - saw the two-time semi-finalist, whose only Grand Slam title came at the 2005 US Open, break to love to seal it and she opened the second with a confident hold.
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The Englishman trailed 3-0 before a break of 137 gave him a foothold, but from 5-4 down he needed breaks of 80 and 75 to seal the victory.
BBC: CHOOSE A SPORT
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In return for its half-hearted blockade around Abkhazia, which tried to break away from Georgia in 1993, Russia is demanding that Georgia seal its own border with Chechnya.
ECONOMIST: On the Chechen road, to Georgia