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Jankovic will face qualifier Vera Dushevina , who beat Anastasia Rodionova 6-2 7-6 (9-7).
BBC: Ana Ivanovic beats Victoria Azarenka at Cincinnati Open
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But Serena Williams beat Vera Dushevina 6-7 7-6 7-6 to reach round three.
BBC: Defending champion Safina suffers shock Madrid exit
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Sharapova was deep in trouble at a set and 5-3 down before battling back for a 4-6 7-5 6-2 victory over compatriot Vera Dushevina.
CNN: Henin and Li Na crash out at Indian Wells
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Serena had made hard work of beating another Russian, Vera Dushevina, in a three-set opener on Monday, but appeared in command against world number 18 Petrova as she won the first set.
CNN: Serena loses but Venus rises after Madrid win
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Henin made her return to a grand slam after a 20-month retirement by beating compatriot Kirsten Flipkens 6-4 6-3, before Dementieva conceded just three games to see off Vera Dushevina 6-2 6-1.
CNN: Kirilenko shocks Sharapova in Melbourne
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Aga made her own slice of history in 2007, becoming the first Pole to win a WTA singles title when as an 18-year-old she beat Russia's Vera Dushevina in Stockholm's Nordic Light Open.
CNN: Net gain
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Home favourite Sam Stosur , the fifth seed, made short work of Vera Dushevina, beating the Russian 6-3 6-2 to secure a third-round match against the Czech Republic's 25th seed Petra Kvitova , who beat Russia's Anna Chakvetadze 6-3 6-4.
BBC: Australian Open: Seventh seed Jelena Jankovic falls