Gasquet, a semifinalist in Miami last month, beat Croatian ninth seed Marin Cilic 7-5 6-4.
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Last year's semifinalist Jie Zheng of China loves the surface and could figure again.
The U.S. team is without the Williams sisters Serena and Venus as well as Australian Open semifinalist Sloane Stephens.
American 16th seed John Isner survived another marathon match as he defeated 2006 semifinalist David Nalbandian 4-6 6-3 2-6 7-6 (7-5) 10-8.
He reached the final at Indian Wells before losing to Nadal's conqueror Ivan Ljubicic, and was also a semifinalist in Miami in 2008.
The Australian Open semifinalist beat compatriot Tommy Robredo 6-3 6-2 on Saturday, while Stanislas Wawrinka beat yet another Spaniard in Nicolas Almagro, winning 6-3 7-5.
Gonzalez's best prior performance at the U.S. Open was as a quarterfinalist in 2002, and he was a semifinalist at the French Open this year.
The Dane, now ranked 10th and a winner of the tournament in 2011, progressed with a 6-0 6-1 drubbing of China's former Wimbledon semifinalist Zheng Jie.
Spain's Ferrer will be hoping to reach the final of this event for the first time in his career, having been a semifinalist in 2005 and 2006.
Jankovic, seeded 18th, is a three-time semifinalist at Roland Garros.
And when she learned that she was a semifinalist for the Intel Science Talent Search, when she found this out her family was living in a homeless shelter.
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Henin was tested to the limit by last year's surprise U.S. Open semifinalist Wickmayer before going through 7-6 1-6 6-3 but her two Russian rivals were not so fortunate.
Nadal will be top seed at the Barcelona Open starting next week, with the draw also including Sweden's Soderling, Verdasco, Jo-Wilfried Tsonga of France and Monte Carlo semifinalist David Ferrer.
No. 13 Jankovic, a semifinalist in 2008, won 6-2 6-0 against 42nd-ranked American Christina McHale, who had reached the third round of the Australian Open for the first time in her career.
Last year's U.S. Open finalist Wozniacki defeated China's Zheng Jie, a semifinalist at the Australian Open in January, 6-4 4-6 6-1 in a match lasting more than two hours later on Wednesday.
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Tim Henman, a four-time Wimbledon semifinalist and one of the few players of his generation to embrace the serve-and-volley game, thinks Federer has been forced to adapt his style at the London venue.
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Russian seventh seed Vera Zvonareva battled past Romanian world No. 61 Alexandra Dulgheru, as last year's semifinalist won 7-6 (7-4) 6-7 (5-7) 6-3 to set up a clash with 51st-ranked Czech Lucie Hradecka.
Third seed Novak Djokovic, the in-form Nikolay Davydenko, 2008 finalist Jo-Wilfried Tsonga and last year's semifinalist Fernando Verdasco all progressed as the reputation for surprises at the season-opening grand slam continued to be undermined.
Now, Insert Coin semifinalist Radiator Labs is working to bring a solution to market that'll make your living space a lot more tolerable, and as an added bonus, it'll save energy at the same time.
The 20-year-old U.S. Open semifinalist is ranked 16th in the world but had to come through the qualifying draw following her title in New Zealand as her ban for an anti-doping sanction was suspended too late for her inclusion in the main field.
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