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https://en.wikipedia.org/wiki/Eric%20H%C3%BCbsch | Eric Hübsch is a Grand Prix motorcycle racer from Germany.
Career statistics
By season
Races by year
(key)
References
External links
Profile on motogp.com
1990 births
German motorcycle racers
Living people
125cc World Championship riders |
https://en.wikipedia.org/wiki/Eduard%20L%C3%B3pez | Eduard López López is a Grand Prix motorcycle racer from Spain.
Career statistics
By season
Races by year
(key)
References
External links
Profile on motogp.com
Spanish motorcycle racers
Motorcycle racers from Catalonia
Living people
1992 births
125cc World Championship riders |
https://en.wikipedia.org/wiki/Roy%20Pouw | Roy Pouw (born 7 June 1992) is a Dutch motorcycle racer. He won the Dutch 125cc Championship in 2010.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
(key)
References
External links
Profile on MotoGP.com
1992 births
Living people
Dutch motorcycle racers
125cc World Championship riders
21st-century Dutch people |
https://en.wikipedia.org/wiki/Morgan%20Berchet | Morgan Berchet (born 2 March 1994) is a Grand Prix motorcycle racer from France. He races in the French Superbike Championship aboard a Yamaha YZF-R1.
Career statistics
2009- 9th, French 125cc Championship #163 Honda RS125R
2010- 5th, French 125cc Championship #163 Honda RS125R
2011-
2012- 4th, French 600 Trophy #63 Yamaha YZF-R6
2013- 1st, French 600 Trophy #63 Yamaha YZF-R6
2014- 6th, French Supersport Championship #63 Yamaha YZF-R6
2015- 8th, French Supersport Championship #63 Yamaha YZF-R6
2016- 8th, Endurance FIM World Cup #33 Kawasaki ZX-10R
2016- 16th, French Superbike Championship #33 Kawasaki ZX-10R
2017- 8th, French Superbike Championship #63 Kawasaki ZX-10R
2018- French Superbike Championship #63 Yamaha YZF-R1
By season
Races by year
References
External links
Profile on motogp.com
1994 births
Living people
French motorcycle racers
125cc World Championship riders |
https://en.wikipedia.org/wiki/Gr%C3%A9gory%20Di%20Carlo | Grégory Di Carlo is a Grand Prix motorcycle racer from France.
Career statistics
By season
Races by year
References
External links
Profile on motogp.com
1993 births
French motorcycle racers
Living people
125cc World Championship riders |
https://en.wikipedia.org/wiki/Pepijn%20Bijsterbosch | Pepijn Bijsterbosch (born 3 November 1989) is a Dutch motorcycle racer. He currently competes in the IDM Superbike Championship aboard a BMW S1000R.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
(key)
Supersport World Championship
Races by year
(key)
External links
Profile on MotoGP.com
Profile on WorldSBK.com
1989 births
Dutch motorcycle racers
Living people
125cc World Championship riders
Supersport World Championship riders
21st-century Dutch people |
https://en.wikipedia.org/wiki/Toby%20Markham | Toby Markham is a Grand Prix motorcycle racer from the United Kingdom.
Career statistics
By season
Races by year
External links
Profile on motogp.com
1988 births
Living people
British motorcycle racers
English motorcycle racers
250cc World Championship riders |
https://en.wikipedia.org/wiki/Stevie%20Bonsey | Stevie Bonsey (born January 18, 1990) is an American motorcycle racer.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
(key) (Races in bold indicate pole position, races in italics indicate fastest lap)
References
Profile on MotoGP.com
1990 births
Living people
American motorcycle racers
125cc World Championship riders
250cc World Championship riders |
https://en.wikipedia.org/wiki/Aitor%20Rodr%C3%ADguez | Aitor Rodríguez Fernández is a Grand Prix motorcycle racer from Spain.
Career statistics
By season
Races by year
References
External links
Profile on motogp.com
1984 births
Living people
Spanish motorcycle racers
250cc World Championship riders |
https://en.wikipedia.org/wiki/Iv%C3%A1n%20Maestro | Iván Maestro Martínez (born 17 December 1988) is a Spanish motorcycle racer. His brother, Borja Maestro, is also a motorcycle racer.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
References
External links
Profile on MotoGP.com
Living people
1988 births
Spanish motorcycle racers
125cc World Championship riders
250cc World Championship riders |
https://en.wikipedia.org/wiki/Daniel%20Arcas | Daniel Arcas Aznar is a Grand Prix motorcycle racer from Spain.
Career statistics
By season
Races by year
(key)
References
External links
Profile on motogp.com
1990 births
Living people
Spanish motorcycle racers
Motorcycle racers from Catalonia
250cc World Championship riders
Sportspeople from Barcelona |
https://en.wikipedia.org/wiki/Joakim%20Stensm%C3%B6 | Joakim Stensmo is a Grand Prix motorcycle racer from Sweden.
Career statistics
By season
Races by year
References
Swedish motorcycle racers
Living people
250cc World Championship riders
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Barrett%20Long | Barrett Long is a Grand Prix motorcycle racer from United States. He races in the MotoAmerica Superstock 1000 Championship aboard a Ducati Panigale.
Career statistics
By season
Races by year
(key)
References
External links
Profile on motogp.com
1984 births
Living people
American motorcycle racers
250cc World Championship riders
AMA Superbike Championship riders |
https://en.wikipedia.org/wiki/Adam%20Roberts%20%28motorcyclist%29 | Adam Roberts (born December 28, 1984) is a Canadian Grand Prix motorcycle racer
Career statistics
By season
Races by year
References
External links
Profile on motogp.com
Canadian motorcycle racers
Living people
250cc World Championship riders
1984 births |
https://en.wikipedia.org/wiki/Christopher%20Moretti | Christopher Moretti (born November 8, 1986 in Cesena) is an Italian Grand Prix motorcycle racer.
Career statistics
By season
Races by year
References
External links
Profile on motogp.com
Living people
1986 births
Italian motorcycle racers
250cc World Championship riders
Sportspeople from Cesena
Supersport World Championship riders |
https://en.wikipedia.org/wiki/Bogdan%20Stefanovi%C4%87 | Bogdan Stefanović (born 9 July 1977 in Stara Pazova) is a retired Serbian-Slovak football goalkeeper.
Career statistics
2004/2005 - Tatran Prešov - II.League: 29 Matches
2005/2006 - Tatran Prešov - II.League: 13 Matches
2006/2007 - Tatran Prešov - II.League: 03 Matches
2006/2007 - FK Ekranas - A Lyga: 33 Matches
2007/2008 - FK Ekranas - A Lyga: 08 Matches, UEFA-Cup Qualifikation: 1 Match
2008/2009 - FK Ekranas - UI Cup: 03 Matches
2009/2010 - MFK Košice - Corgoň liga: 08 Matches
References
External links
MFK Košice profile
1977 births
Living people
Serbian men's footballers
Men's association football goalkeepers
MŠK Rimavská Sobota players
1. FC Tatran Prešov players
FC VSS Košice players
FK Ekranas players
ŠK Futura Humenné players
Slovak First Football League players
People from Stara Pazova
Footballers from Srem District
Slovaks of Vojvodina
Slovak men's footballers
Serbia and Montenegro men's footballers
Serbia and Montenegro expatriate men's footballers
Slovak expatriate men's footballers
Serbia and Montenegro expatriate sportspeople in the Czech Republic
Serbian expatriate men's footballers
Expatriate men's footballers in the Czech Republic
Serbian expatriate sportspeople in Lithuania
Slovak expatriate sportspeople in Lithuania
Expatriate men's footballers in Lithuania
Association football goalkeeping coaches |
https://en.wikipedia.org/wiki/Martin%20Glossop | Martin Glossop (born 18 July 1989 in Bristol) is a Grand Prix motorcycle racer from the United Kingdom.
Career statistics
By season
Races by year
(key) (Races in bold indicate pole position)
References
External links
Profile on motogp.com
British motorcycle racers
English motorcycle racers
Living people
1989 births |
https://en.wikipedia.org/wiki/Luk%C3%A1%C5%A1%20%C5%A0embera | Lukáš Šembera is a Grand Prix motorcycle racer from Czech Republic.
Career statistics
Red Bull MotoGP Rookies Cup
Races by year
(key) (Races in bold indicate pole position, races in italics indicate fastest lap)
Grand Prix motorcycle racing
By season
Races by year
References
External links
Profile on motogp.com
1992 births
Living people
Czech motorcycle racers
Sportspeople from Brno
125cc World Championship riders |
https://en.wikipedia.org/wiki/Yuuichi%20Yanagisawa | is a Japanese motorcycle racer.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
(key)
References
External links
Profile on MotoGP.com
1984 births
Living people
Japanese motorcycle racers
125cc World Championship riders |
https://en.wikipedia.org/wiki/Hiroomi%20Iwata | is a Japanese motorcycle racer. Within the All Japan Road Race Championship, he has competed in the GP125 class, where he was champion in 2007, and in the J-GP3 class.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
(key)
References
External links
1983 births
Living people
Japanese motorcycle racers
125cc World Championship riders |
https://en.wikipedia.org/wiki/Satoru%20Kamada | is a Japanese motorcycle racer.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
(key)
References
External links
Profile on MotoGP.com
Japanese motorcycle racers
Living people
1984 births
125cc World Championship riders |
https://en.wikipedia.org/wiki/Yuki%20Oogane | is a Japanese motorcycle racer. He has competed in the GP125 and J-GP3 classes of the All Japan Road Race Championship.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
(key)
References
External links
Profile on MotoGP.com
Japanese motorcycle racers
Living people
1992 births
125cc World Championship riders |
https://en.wikipedia.org/wiki/Borja%20Maestro | Borja Maestro Martínez (born 4 September 1991) is a Spanish motorcycle racer. His brother, Iván Maestro, is also a motorcycle racer.
Career statistics
Grand Prix motorcycle racer
By season
Races by year
References
External links
Profile on MotoGP.com
1991 births
Living people
Spanish motorcycle racers
125cc World Championship riders |
https://en.wikipedia.org/wiki/Jordi%20Dalmau | Jordi Dalmau Nieves (born 21 May 1989) is a Grand Prix motorcycle racer from Spain.
Career statistics
By season
Races by year
References
External links
Profile on motogp.com
Living people
Spanish motorcycle racers
Motorcycle racers from Catalonia
1989 births
125cc World Championship riders
Sportspeople from Barcelona |
https://en.wikipedia.org/wiki/Steven%20Le%20Coquen | Steven Le Coquen is a Grand Prix motorcycle racer from France. He competes in the Endurance World Cup aboard a Yamaha YZF-R1.
Career statistics
By season
Races by year
References
External links
Profile on motogp.com
1991 births
Living people
French motorcycle racers
125cc World Championship riders |
https://en.wikipedia.org/wiki/Gennaro%20Sabatino | Gennaro Sabatino (born 1 January 1993) is an Italian motorcycle racer. He currently races in the CIV Supersport 600 Championship aboard a Kawasaki ZX-6R.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
External links
Profile on MotoGP.com
Profile on WorldSBK.com
Italian motorcycle racers
Living people
1993 births
Sportspeople from the Province of Naples
125cc World Championship riders |
https://en.wikipedia.org/wiki/Gabriele%20Ferro | Gabriele Ferro is a Grand Prix motorcycle racer from Italy.
Career statistics
By season
Grand Prix motorcycle racing
Races by year
(key)
References
External links
Profile on motogp.com
1988 births
Living people
Italian motorcycle racers
250cc World Championship riders
125cc World Championship riders
Sportspeople from Biella |
https://en.wikipedia.org/wiki/Paul%20Jordan%20%28motorcyclist%29 | Paul Jordan is a Grand Prix motorcycle racer from Northern Ireland. He now competes in International Road Races aboard a Yamaha R6 and a Suzuki 1000 Superbike.
Career statistics
By season
Races by year
References
External links
Profile on motogp.com
Motorcycle racers from Northern Ireland
Living people
1991 births
125cc World Championship riders
Motorsport people from Belfast |
https://en.wikipedia.org/wiki/Miles%20Thornton | Miles Thornton (born April 2, 1994) is a Grand Prix motorcycle racer from United States. He races in the AMA Pro Supersport Championship for CTR Racing aboard a Yamaha YZF-R6.
Career statistics
By season
Races by year
References
Miles Thornton profile at AMA Pro Road Racing
Miles Thornton profile at MotoGP.com
American motorcycle racers
Living people
1994 births
125cc World Championship riders |
https://en.wikipedia.org/wiki/Brad%20Gross%20%28motorcyclist%29 | Brad Gross (born 29 October 1990) is a Grand Prix motorcycle racer from Australia.
Career statistics
By season
Races by year
References
External links
Profile on motogp.com
Australian motorcycle racers
Living people
1990 births
125cc World Championship riders |
https://en.wikipedia.org/wiki/Andrew%20Lawson%20%28motorcyclist%29 | Andrew Lawson (born 2 March 1993) is a Grand Prix motorcycle racer from Australia.
Career statistics
By season
Races by year
References
External links
Profile on motogp.com
Australian motorcycle racers
Living people
1993 births
125cc World Championship riders |
https://en.wikipedia.org/wiki/Elly%20Ilias | Elly Ilias is a Grand Prix motorcycle racer from Malaysia. He competes in the Malaysian Cub Prix CP130 Championship.
Career statistics
By season
Races by year
References
External links
Profile on motogp.com
Malaysian motorcycle racers
Living people
1984 births
125cc World Championship riders
People from Perlis |
https://en.wikipedia.org/wiki/Toni%20Wirsing | Toni Wirsing is a Grand Prix motorcycle racer from Germany.
Career statistics
By season
Races by year
References
External links
Profile on motogp.com
1990 births
Living people
German motorcycle racers
125cc World Championship riders
250cc World Championship riders
Sportspeople from Chemnitz |
https://en.wikipedia.org/wiki/Frederik%20Watz | Frederik Watz is a Grand Prix motorcycle racer from Sweden.
Career statistics
By season
Races by year
(key)
References
External links
Profile on motogp.com
1976 births
Living people
Swedish motorcycle racers
250cc World Championship riders
Sportspeople from Linköping |
https://en.wikipedia.org/wiki/Alen%20Gy%C5%91rfi | Alen Győrfi is a Grand Prix motorcycle racer from Hungary. In 2018 he will race in the Alpe-Adria Superstock 600 Championship aboard a Yamaha YZF-R6.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
(key) (Races in bold indicate pole position, races in italics indicate fastest lap)
References
External links
Profile on motogp.com
1989 births
Living people
Hungarian motorcycle racers
125cc World Championship riders
250cc World Championship riders
FIM Superstock 1000 Cup riders
Supersport World Championship riders |
https://en.wikipedia.org/wiki/Takumi%20Endoh | is a Japanese motorcycle racer.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
(key)
References
External links
Profile on MotoGP.com
Japanese motorcycle racers
Living people
1984 births
250cc World Championship riders |
https://en.wikipedia.org/wiki/Enrique%20Jerez | Enrique Jerez Rodríguez is a Grand Prix motorcycle racer from Spain.
Career statistics
By season
Races by year
(key)
References
External links
Profile on motogp.com
1986 births
Living people
Spanish motorcycle racers
125cc World Championship riders |
https://en.wikipedia.org/wiki/Robin%20L%C3%A4sser | Robin Lässer (born 12 January 1991) is a Grand Prix motorcycle racer from Germany.
Career statistics
By season
Races by year
References
External links
Profile on motogp.com
1991 births
Living people
German motorcycle racers
125cc World Championship riders |
https://en.wikipedia.org/wiki/Hugo%20van%20den%20Berg | Hugo van den Berg is a Grand Prix motorcycle racer from the Netherlands.
Career statistics
By season
Races by year
References
External links
Profile on motogp.com
1990 births
Living people
Dutch motorcycle racers
125cc World Championship riders
21st-century Dutch people |
https://en.wikipedia.org/wiki/Roberto%20Lacalendola | Roberto Lacalendola is a Grand Prix motorcycle racer from Italy.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
References
External links
Profile on motogp.com
motoblog.it article
1988 births
Living people
Italian motorcycle racers
125cc World Championship riders
FIM Superstock 1000 Cup riders
Sportspeople from Turin |
https://en.wikipedia.org/wiki/Pere%20Tutusaus | Pere Tutusaus Vila is a Grand Prix motorcycle racer from Spain.
Career statistics
By season
Races by year
References
External links
Profile on motogp.com
1990 births
Living people
Spanish motorcycle racers
Motorcycle racers from Catalonia
125cc World Championship riders
FIM Superstock 1000 Cup riders |
https://en.wikipedia.org/wiki/Luke%20Hinton | Luke Hinton is a Grand Prix motorcycle racer from Great Britain.
Career statistics
By season
Races by year
References
External links
Profile on motogp.com
British motorcycle racers
Living people
1990 births
125cc World Championship riders |
https://en.wikipedia.org/wiki/Juli%C3%A1n%20Miralles | Julián Miralles is a former Grand Prix motorcycle racer from Spain. His son, Julián Miralles Rodríguez, is also a motorcycle racer.
Career statistics
By season
References
External links
Profile on motogp.com
1965 births
Living people
Spanish motorcycle racers
125cc World Championship riders
500cc World Championship riders
80cc World Championship riders |
https://en.wikipedia.org/wiki/Cristian%20Trabal%C3%B3n | Cristian Trabalón Laso is a Grand Prix motorcycle racer from Spain.
Career statistics
Red Bull MotoGP Rookies Cup
Races by year
(key) (Races in bold indicate pole position, races in italics indicate fastest lap)
Grand Prix motorcycle racing
By season
Races by year
(key)
References
External links
Profile on motogp.com
1992 births
Living people
Spanish motorcycle racers
125cc World Championship riders |
https://en.wikipedia.org/wiki/Rhys%20Moller | Rhys Moller (born 12 January 1989) is an Australian motorcycle racer. He has been a competitor in his home Grand Prix in the 125cc World Championship as a wild card rider.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
References
External links
Profile on MotoGP.com
1989 births
Living people
Australian motorcycle racers
125cc World Championship riders
Sportspeople from Ballarat |
https://en.wikipedia.org/wiki/Iori%20Namihira | is a Japanese motorcycle racer.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
(key)
References
External links
Profile on MotoGP.com
1983 births
Living people
Japanese motorcycle racers
125cc World Championship riders |
https://en.wikipedia.org/wiki/Sebastian%20Kreuziger | Sebastian Kreuziger is a Grand Prix motorcycle racer from Germany.
Career statistics
By season
Races by year
(key)
References
External links
Profile on motogp.com
German motorcycle racers
Living people
1991 births
125cc World Championship riders |
https://en.wikipedia.org/wiki/Lee%20Costello | Lee Costello is a Grand Prix motorcycle racer from Great Britain.
Career statistics
2013- 19th, British Superbike Championship #39 Kawasaki ZX-10R
2012- 5th, British National Superstock 1000 Championship #39 Kawasaki ZX-10R
2011- 20th, British National Superstock 1000 Championship #39 Honda CBR1000RR
2010- 29th, British National Superstock 1000 Championship #39 Honda CBR1000RR
2009- NC, British National Superstock 1000 Championship #14 Honda CBR1000RR
2008- 12th, British 125cc Championship #14 Honda RS125R
2007- 8th, British 125cc Championship #87 Honda RS125R
2006- 25th, British 125cc Championship #12 Honda RS125R
By season
Races by year
(key)
References
External links
Profile on motogp.com
Living people
1986 births
English motorcycle racers
125cc World Championship riders
FIM Superstock 1000 Cup riders |
https://en.wikipedia.org/wiki/Tobias%20Siegert | Tobias Siegert is a Grand Prix motorcycle racer from Germany.
Career statistics
By season
Races by year
(key)
References
External links
Profile on motogp.com
1991 births
Living people
German motorcycle racers
125cc World Championship riders
Sportspeople from Nuremberg |
https://en.wikipedia.org/wiki/Gioele%20Pellino | Gioele Pellino is a Grand Prix motorcycle racer from Italy.
Career statistics
By season
Races by year
(key) (Races in bold indicate pole position, races in italics indicate fastest lap)
CIV 125cc Championship
Races by year
(key) (Races in bold indicate pole position; races in italics indicate fastest lap)
References
External links
Profile on motogp.com
1983 births
Living people
Italian motorcycle racers
125cc World Championship riders
People from Foligno
Sportspeople from the Province of Perugia |
https://en.wikipedia.org/wiki/Daniel%20S%C3%A1ez%20%28motorcyclist%2C%20born%201985%29 | Daniel Sáez Tomás (born 10 June 1985) is a Spanish motorcycle racer.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
References
External links
Profile on MotoGP.com
1985 births
Living people
Spanish motorcycle racers
125cc World Championship riders |
https://en.wikipedia.org/wiki/Mapping%20cone | Mapping cone may refer to one of the following two different but related concepts in mathematics:
Mapping cone (topology)
Mapping cone (homological algebra) |
https://en.wikipedia.org/wiki/Seijin%20Oikawa | is a Grand Prix motorcycle racer from Japan.
Career statistics
By season
Races by year
References
External links
Profile on motogp.com
Japanese motorcycle racers
Living people
1970 births
250cc World Championship riders |
https://en.wikipedia.org/wiki/Wang%20Zhu%20%28motorcyclist%29 | Wang Zhu (; born August 13, 1987) is a Chinese Grand Prix motorcycle racer.
Career statistics
By season
Races by year
(key)
References
External links
Profile on motogp.com
Chinese motorcycle racers
Living people
1987 births
250cc World Championship riders
Sportspeople from Xi'an |
https://en.wikipedia.org/wiki/Thomas%20Walther | Thomas Walther was a Grand Prix motorcycle racer from Germany.
Career statistics
By season
Races by year
(key)
References
External links
Profile on motogp.com
German motorcycle racers
Living people
1977 births
250cc World Championship riders |
https://en.wikipedia.org/wiki/Yuki%20Hamamoto | is a Japanese motorcycle racer. He has competed in the GP125, GP250 and ST600 classes of the All Japan Road Race Championship.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
(key)
References
External links
1985 births
Living people
Japanese motorcycle racers
125cc World Championship riders
250cc World Championship riders |
https://en.wikipedia.org/wiki/Omar%20Menghi | Omar Menghi (born 18 October 1975) is an Italian motorcycle racer. His brother, Fabio Menghi, is also a motorcycle racer.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
(key)
References
External links
Profile on MotoGP.com
1975 births
Living people
Italian motorcycle racers
250cc World Championship riders
Sportspeople from Rimini |
https://en.wikipedia.org/wiki/Georg%20Fr%C3%B6hlich | Georg Fröhlich (born 17 March 1988) is a German motorcycle racer who has competed in the 125cc World Championship. He won the IDM 125 Championship in 2007.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
(key)
References
External links
Profile on MotoGP.com
1988 births
Living people
German motorcycle racers
125cc World Championship riders
People from Rochlitz
Sportspeople from Saxony |
https://en.wikipedia.org/wiki/Stefano%20Musco | Stefano Musco is a Grand Prix motorcycle racer from Italy.
Career statistics
By season
Races by year
(key)
References
External links
Profile on motogp.com
Italian motorcycle racers
Living people
1989 births
125cc World Championship riders
People from Spoleto
Sportspeople from the Province of Perugia |
https://en.wikipedia.org/wiki/Nikolett%20Kov%C3%A1cs | Nikolett Kovács is a Hungarian Grand Prix motorcycle racer.
Career statistics
By season
Races by year
References
External links
Profile on motogp.com
Living people
1982 births
Hungarian sportswomen
Hungarian motorcycle racers
125cc World Championship riders
Supersport World Championship riders
Female motorcycle racers
Sportspeople from Budapest |
https://en.wikipedia.org/wiki/Julien%20Cartron | Julien Cartron is a Grand Prix motorcycle racer from France.
Career statistics
By season
Races by year
References
External links
Profile on motogp.com
French motorcycle racers
Living people
1989 births
125cc World Championship riders |
https://en.wikipedia.org/wiki/Federico%20Biaggi | Federico Mandatori, also known as Federico Biaggi, is a Grand Prix motorcycle racer from Italy. He is Max Biaggi's nephew.
Career statistics
By season
Races by year
References
External links
Profile on motogp.com
Profile on worldsbk.com
1987 births
Living people
Italian motorcycle racers
125cc World Championship riders
FIM Superstock 1000 Cup riders
Sportspeople from Rome |
https://en.wikipedia.org/wiki/Philipp%20Eitzinger | Philipp Eitzinger is a Grand Prix motorcycle racer from Austria.
Career statistics
By season
Races by year
References
1990 births
Living people
Austrian motorcycle racers
125cc World Championship riders |
https://en.wikipedia.org/wiki/Robbie%20Stewart | Robbie Stewart is a Grand Prix motorcycle racer from Great Britain.
Career statistics
By season
Races by year
References
External links
Profile on motogp.com
Scottish motorcycle racers
Living people
Sportspeople from Perth, Scotland
1991 births
125cc World Championship riders |
https://en.wikipedia.org/wiki/Romain%20Maitre | Romain Maitre is a Grand Prix motorcycle racer from France. He competes in the Endurance FIM World Cup aboard a Kawasaki ZX-10R.
Career statistics
By season
Races by year
References
External links
Profile on motogp.com
1988 births
Living people
French motorcycle racers
125cc World Championship riders
FIM Superstock 1000 Cup riders |
https://en.wikipedia.org/wiki/Nikki%20Coates | Nikki Coates is a Grand Prix motorcycle racer from Great Britain. , he competes in the FIM CEV Moto2 European Championship for Team Stratos aboard an .
Career statistics
2004- Irish 125cc Championship #65 Honda RS125R
2005- 32nd, British 125cc Championship #29 Honda RS125R
2006- 18th, British 125cc Championship #65 Honda RS125R
2007- 5th, British 125cc Championship #65 Honda RS125R
2008- 17th, British National Superstock 600 Championship #65 Honda CBR600RR
2009- 10th, British National Superstock 600 Championship #65 Yamaha YZF-R6
2010- 11th, British National Superstock 600 Championship #65 Yamaha YZF-R6
2011- 34th, CEV Moto2 Championship #65 AJR EVO 2011
2012- 15th, British Supersport Championship #65 Yamaha YZF-R6
2013- 26th, British Supersport Championship #85 Kawasaki ZX-6R
2014- NC, British National Superstock 1000 Championship #65 Kawasaki ZX-10R
2015- 27th, CEV Moto2 European Championship #65
FIM Moto2 European Championship
Races by year
(key) (Races in bold indicate pole position) (Races in italics indicate fastest lap)
Grand Prix motorcycle racing
By season
Races by year
References
External links
Profile on motogp.com
British motorcycle racers
Living people
1989 births
Sportspeople from Belfast |
https://en.wikipedia.org/wiki/Simone%20Sancioni | Simone Sancioni (born 8 November 1988) is an Italian motorcycle racer.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
References
External links
Living people
1988 births
Italian motorcycle racers
125cc World Championship riders
Sportspeople from Cesena |
https://en.wikipedia.org/wiki/Joshua%20Sommer | Joshua Sommer is a Grand Prix motorcycle racer from Germany.
Career statistics
By season
Races by year
(key)
References
External links
Profile on motogp.com
German motorcycle racers
Living people
1989 births
250cc World Championship riders |
https://en.wikipedia.org/wiki/%C3%81lvaro%20Molina%20%28motorcyclist%29 | Álvaro Molina is a Grand Prix motorcycle racer from Spain.
Career statistics
By season
Races by year
(key) (Races in bold indicate pole position, races in italics indicate fastest lap)
References
External links
Profile on motogp.com
1976 births
Spanish motorcycle racers
125cc World Championship riders
250cc World Championship riders
Living people |
https://en.wikipedia.org/wiki/Technical%20failure | A technical failure is an (unwanted) error of technology based systems.
Causality
Causalities include fatigue and attenuation distortions.
See also
Absolute probability judgement
Accident-proneness
Human reliability
Human–machine system
Latent human error
Order and disorder (physics)
Sociotechnical system
Why–because analysis
Security engineering
Error
Reliability engineering
Articles containing video clips |
https://en.wikipedia.org/wiki/Hilda%20Phoebe%20Hudson | Hilda Phoebe Hudson (11 June 1881 Cambridge – 26 November 1965 London) was an English mathematician who worked on algebraic geometry, in particular on Cremona transformations. Hudson was interested in the link between mathematics and her religious beliefs.
Life and work
In 1900 Hudson gained a scholarship and entered Newnham College at the University of Cambridge, graduating in 1903, coming 7th equal among the First Class students. After a year of further study at the University of Berlin, she returned to Newnham in 1905, first as lecturer in mathematics and later as Associate Research Fellow. Trinity College Dublin awarded her an ad eundam MA, and later a DSc, in 1906 and 1913, respectively.
She was an Invited Speaker of the International Congress of Mathematicians (ICM) in 1912 at Cambridge UK. Although Laura Pisati had been invited to the 1908 ICM, she died just before the start of the conference, so Hudson became the first female invited speaker at an ICM.
She spent the academic year 1912–1913 at Bryn Mawr in the US, and the years 1913–1917 back in England, this time as lecturer at West Ham Technical Institute. She joined an Air Ministry subdivision undertaking aeronautical engineering research in 1917, where she applied pioneering work on the application of mathematical modelling to aircraft design. She was appointed OBE in 1919. As a distinguished mathematician she was one of the few women of her time to serve on the council of the London Mathematical Society.
Most of Hudson's pure mathematical research was concerned with surfaces and plane curves, her special interest being in Cremona transformations. Her 1916 monograph Ruler and Compasses was well-received as "a welcome addition to the literature on the boundary between elementary and advanced mathematics". Her 454-page 1927 treatise Cremona transformations in plane and space is considered by John Semple to be her magnum opus.
Epidemiology
Hudson published work with Ronald Ross on epidemiology and the measurement of disease spread. "The classical susceptible-infectious-recovered (SIR) model, originated from the seminal papers of Ross and Ross and Hudson in 1916-1917 and the fundamental contributions of Kermack and McKendrick in 1927-1932, describes the transmission of infectious diseases between susceptible and infective individuals and provides the basic framework for almost all later epidemic models."
Books
Ruler and Compasses, first published as a monograph (Longman's Modern Mathematical Series, 1916) and then included in the compendium Squaring the circle and other monographs (Chelsea n.d.)
Cremona Transformations in Plane and Space, Cambridge University Press, 1927.
References
External links
A list of her papers can be found at Biographies of Women Mathematicians: Hilda Phoebe Hudson
1881 births
1965 deaths
English mathematicians
People from Cambridge
Women mathematicians
English women non-fiction writers
English non-fiction writers
20th-century English women writers
2 |
https://en.wikipedia.org/wiki/Quadratic%20transformation | In mathematics, a quadratic transformation may be
A quadratic transformation in the Cremona group
Kummer's quadratic transformation of the hypergeometric function |
https://en.wikipedia.org/wiki/Tangential%20polygon | In Euclidean geometry, a tangential polygon, also known as a circumscribed polygon, is a convex polygon that contains an inscribed circle (also called an incircle). This is a circle that is tangent to each of the polygon's sides. The dual polygon of a tangential polygon is a cyclic polygon, which has a circumscribed circle passing through each of its vertices.
All triangles are tangential, as are all regular polygons with any number of sides. A well-studied group of tangential polygons are the tangential quadrilaterals, which include the rhombi and kites.
Characterizations
A convex polygon has an incircle if and only if all of its internal angle bisectors are concurrent. This common point is the incenter (the center of the incircle).
There exists a tangential polygon of n sequential sides a1, ..., an if and only if the system of equations
has a solution (x1, ..., xn) in positive reals. If such a solution exists, then x1, ..., xn are the tangent lengths of the polygon (the lengths from the vertices to the points where the incircle is tangent to the sides).
Uniqueness and non-uniqueness
If the number of sides n is odd, then for any given set of sidelengths satisfying the existence criterion above there is only one tangential polygon. But if n is even there are an infinitude of them. For example, in the quadrilateral case where all sides are equal we can have a rhombus with any value of the acute angles, and all rhombi are tangential to an incircle.
Inradius
If the n sides of a tangential polygon are a1, ..., an, the inradius (radius of the incircle) is
where K is the area of the polygon and s is the semiperimeter. (Since all triangles are tangential, this formula applies to all triangles.)
Other properties
For a tangential polygon with an odd number of sides, all sides are equal if and only if all angles are equal (so the polygon is regular). A tangential polygon with an even number of sides has all sides equal if and only if the alternate angles are equal (that is, angles A, C, E, ... are equal, and angles B, D, F, ... are equal).
In a tangential polygon with an even number of sides, the sum of the odd numbered sides' lengths is equal to the sum of the even numbered sides' lengths.
A tangential polygon has a larger area than any other polygon with the same perimeter and the same interior angles in the same sequence.
The centroid of any tangential polygon, the centroid of its boundary points, and the center of the inscribed circle are collinear, with the polygon's centroid between the others and twice as far from the incenter as from the boundary's centroid.
Tangential triangle
While all triangles are tangential to some circle, a triangle is called the tangential triangle of a reference triangle if the tangencies of the tangential triangle with the circle are also the vertices of the reference triangle.
Tangential quadrilateral
Tangential hexagon
In a tangential hexagon ABCDEF, the main diagonals AD, BE, and CF are concurrent accord |
https://en.wikipedia.org/wiki/Fabricio%20Perren | Fabricio Perren is a Grand Prix motorcycle racer from Argentina.
Career statistics
By season
Races by year
(key)
References
External links
Profile on motogp.com
1988 births
Living people
Argentine motorcycle racers
125cc World Championship riders
250cc World Championship riders |
https://en.wikipedia.org/wiki/D%C3%A1niel%20Nagy%20%28footballer%2C%20born%201991%29 | Dániel Nagy (born 15 March 1991) is a Hungarian football midfielder.
Club statistics
Hamburger SV
He was signed from Hungarian Újpest FC in 2007,
In 2008, he signed a professional contract with Hamburger SV. He played mainly for the reserves, in the fourth division.
In a friendly match, he made his debut in the first team and scored a goal in the summer of 2011. In 2012, Hamburg and Nagy have been cancelled his contract with mutual consent.
VfL Osnabrück
In the summer of 2012, Nagy signed for Osnasbrück in the third division. In his first season, he made 3 goals and 6 assist.
On 2 August 2013, he made his debut in the DFB-Pokal against second division-side Erzgebirge Aue, at an eventual 3–0 home win, where he scored two goals.
Club statistics
Updated to games played as of 15 May 2021.
References
1991 births
Living people
Footballers from Budapest
Hungarian men's footballers
Hungary men's youth international footballers
Hungary men's international footballers
Men's association football midfielders
Hamburger SV II players
Hamburger SV players
VfL Osnabrück players
Ferencvárosi TC footballers
Würzburger Kickers players
Újpest FC players
Mezőkövesdi SE footballers
3. Liga players
Nemzeti Bajnokság I players
2. Bundesliga players
Hungarian expatriate men's footballers
Expatriate men's footballers in Germany
Hungarian expatriate sportspeople in Germany |
https://en.wikipedia.org/wiki/Saint%20Petersburg%20Lyceum%2030 | Saint Petersburg Lyceum 30 (), is a public high school in Saint Petersburg, Russia that specializes in mathematics and physics. The school opened in 1897 became a specialized city school in 1965.
History
The history of the school began October 6, 1897, with its establishment on Vasilyevsky Island, becoming the first 12-grade primary school in Saint Petersburg. The namesake of the school is Catherine II (Catherine the Great).
The establishment of the institution was a significant event in the history of St. Petersburg, as the school was a first step by the local government to address and solve a number of problems that existed within the primary education system at the time.
The initiative of building the school was led by Mikhail Stasyulevich, a historian, publisher, and chairman of the Commission on Public Education. Stasyulevich sought to create an institution where both young men and women would coexist and learn together. As a result of this, however, Stasyulevich encountered many opponents, and constantly fought against those who sought to defend the old type of primary school. The most serious objection was an indication of the "great danger of schools having several classes as the source of infectious diseases." Despite these setbacks, the project had still gained majority support by City Council, and the school was erected. The Emperor Nikolay II was familiar with the project and approved it himself. The school was then opened on October 6, 1897, and was blessed by the home church 33 days later on November 9, 1896.
In 1965, the school became specialized in mathematics. In 1976, the school was united with School 38 and moved to a building at Shevchenko street, 23/2. Following the merger and move, the school's namesake was changed to Physico-Mathematical School. In 1990, the school was again renamed to Physico-Mathematical Gymnasium, but in 2002 it was finally renamed to Physico-Mathematical Lyceum. In 2005, the school was given back its historical building at the Sredniy prospect, and from that moment on the school has had two buildings: the first at Shevchenko street, where classes 5 to 7 are held, and the second near the Vasileostrovskaya metro station, where 8 - 11 classes are situated.
Famous alumni
Lev Y. Lurie, TV presenter
Andrei Borisenko, cosmonaut
Andrey Krasko, actor
Alexander Lazarev, Soviet theater and film actor
Vladimir Churov, chairman of the Central Election Commission of Russia
Maria Chudnovsky, mathematics professor at Princeton
Marina Neyolova, actress
Pavel Belov, scientist
Dmitry Dmitriyenko, Governor of Murmansk
See also
Saint Petersburg Lyceum 239
References
External links
Official web site of Lyceum 30
Information about the Lyceum at city portal
A website dedicated to a history of the school
Schools in Saint Petersburg
Educational institutions established in 1897
1897 establishments in the Russian Empire
Lyceums in Russia |
https://en.wikipedia.org/wiki/Michele%20Danese | Michele Danese (born 11 September 1982) is an Italian motorcycle racer.
Career statistics
CIV 125cc Championship
Races by year
(key) (Races in bold indicate pole position; races in italics indicate fastest lap)
Grand Prix motorcycle racing
By season
Races by year
(key) (Races in bold indicate pole position)
References
External links
Profile on MotoGP.com
1982 births
Living people
Sportspeople from the Province of Vicenza
Italian motorcycle racers
125cc World Championship riders
250cc World Championship riders |
https://en.wikipedia.org/wiki/Lorenzo%20Baroni | Lorenzo Baroni (born 23 February 1990) is an Italian motorcycle racer.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
(key)
External links
Profile on MotoGP.com
Profile on WorldSBK.com
1990 births
Living people
People from Lugo, Emilia-Romagna
Italian motorcycle racers
125cc World Championship riders
FIM Superstock 1000 Cup riders
Sportspeople from the Province of Ravenna |
https://en.wikipedia.org/wiki/Michele%20Conti%20%28motorcyclist%29 | Michele Giovanni Conti (born 3 July 1983) is an Italian motorcycle racer. He was the European 125cc champion in 2005.
Career statistics
CIV 125cc Championship
Races by year
(key) (Races in bold indicate pole position; races in italics indicate fastest lap)
Grand Prix motorcycle racing
By season
Races by year
(key)
Supersport World Championship
Races by year
(key)
References
External links
Profile on MotoGP.com
Profile on WorldSBK.com
1983 births
Living people
Italian motorcycle racers
125cc World Championship riders
Supersport World Championship riders
Sportspeople from Lecco |
https://en.wikipedia.org/wiki/Daniele%20Rossi | Daniele Rossi (born 24 April 1987) is an Italian motorcycle racer.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
(key)
External links
Profile on MotoGP.com
Profile on WorldSBK.com
1987 births
Living people
People from Seriate
Italian motorcycle racers
125cc World Championship riders
Sportspeople from the Province of Bergamo |
https://en.wikipedia.org/wiki/Alessandro%20Brannetti | Alessandro Brannetti (born 9 June 1980) is an Italian motorcycle racer.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
(key) (Races in bold indicate pole position, races in italics indicate fastest lap)
Supersport World Championship
Races by year
(key)
External links
Profile on MotoGP.com
Profile on WorldSBK.com
1980 births
Living people
People from Fermo
Italian motorcycle racers
125cc World Championship riders
250cc World Championship riders
Supersport World Championship riders
FIM Superstock 1000 Cup riders
Sportspeople from the Province of Fermo |
https://en.wikipedia.org/wiki/Nico%20Vivarelli | Nico Vivarelli is a Grand Prix motorcycle racer from Italy.
Career statistics
By season
Races by year
(key)
References
External links
Profile on motogp.com
Italian motorcycle racers
1986 births
Living people
125cc World Championship riders
FIM Superstock 1000 Cup riders
People from Grosseto
Sportspeople from the Province of Grosseto |
https://en.wikipedia.org/wiki/2012%20BK%20H%C3%A4cken%20season | In 2012 BK Häcken finished second in the Allsvenskan championship and were eliminated from the Svenska Cupen at the group stage.
2012 season squad
Statistics prior to season start only
Transfers
In
Out
Appearances and goals
As of 25 May 2012
|}
Matches
Pre-season/friendlies
Allsvenskan
Svenska cupen
Competitions
Allsvenskan
Standings
Results summary
Results by round
Season statistics
Superettan
= Number of bookings
8px= Number of sending offs after a second yellow card
= Number of sending offs by a direct red card
References
Footnotes
References
External links
BK Häcken homepage
SvFF homepage
BK Häcken seasons
Hacken |
https://en.wikipedia.org/wiki/Lichnerowicz%20conjecture | In mathematics, the Lichnerowicz conjecture is a generalization of a conjecture introduced by . Lichnerowicz's original conjecture was that locally harmonic 4-manifolds are locally symmetric, and was proved by . The Lichnerowicz conjecture usually refers to the generalization that locally harmonic manifolds are flat or rank-1 locally symmetric. It has been proven true for compact manifolds with fundamental groups that are finite groups but counterexamples exist in seven or more dimensions in the non-compact case
References
Riemannian geometry |
https://en.wikipedia.org/wiki/List%20of%20Indian%20settlements%20in%20Quebec | This is the list of communities in Quebec that have the legal status of Indian settlements (établissement amérindien, code=SE) as defined by Statistics Canada.
Note these are not the same as Indian reserves (réserve indien, code=IRI), nor does it include Cree villages (code=VC), Naskapi villages (code=VK), or Northern villages (Inuit, code=VN), which have a separate legal status.
Indian settlements
Note: Oujé-Bougoumou is a village and is inhabited by Cree, but does not have the legal status of "Cree village" as defined by legislation.
See also
Indigenous peoples in Quebec
List of Indian reserves in Quebec
List of northern villages and Inuit reserved lands in Quebec
List of Cree and Naskapi territories in Quebec
References
Indian settlements |
https://en.wikipedia.org/wiki/2012%20Dhivehi%20League%20Round%201 | In Round 1, all eight teams play against each other. A total of 28 matches will be played in this round.
League table
Matches
Round 1 statistics
Scorers
Assists
Hat-tricks
4 Player scored 4 goals
Clean sheets
Clean sheets by Club:
New Radiant SC (5)
Vyansa (3)
Victory SC (2)
Club Valencia (2)
Club Eagles (2)
VB Addu FC (1)
Club All Youth Linkage (0)
Clean sheets by goalkeepers:
Imran Mohamed (New Radiant SC) (4)
Alexander Osei Domfeh (Vyansa) (3)
Lavent Vanli (Victory SC) (2)
Ibrahim Ifrah Areef (Club Valencia) (2)
Mohamed Yamaan (Club Eagles) (2)
Abdulla Fayaz (New Radiant SC) (2)
Mohamed Imran (Maziya S&RC) (1)
Mohamed Shinan (VB Addu FC) (1)
Athif Ahmed (Maziya S&RC) (0)
Hussain Habeeb (VB Addu FC) (0)
Ibrahim Siyad (Club All Youth Linkage) (0)
Abdulla Ziyazan (VB Addu FC) (0)
References
1 |
https://en.wikipedia.org/wiki/Topological%20rigidity | In the mathematical field of topology, a manifold M is called topologically rigid if every manifold homotopically equivalent to M is also homeomorphic to M.
Motivation
A central problem in topology is determining when two spaces are the same i.e. homeomorphic or diffeomorphic. Constructing a morphism explicitly is almost always impractical. If we put further condition on one or both spaces (manifolds) we can exploit this additional structure in order to show that the desired morphism must exist.
Rigidity theorem is about when a fairly weak equivalence between two manifolds (usually a homotopy equivalence) implies the existence of stronger equivalence homeomorphism, diffeomorphism or isometry.
Definition.
A closed topological manifold M is called topological rigid if any homotopy equivalence f : N → M with some manifold N as source and M as target is homotopic to a homeomorphism.
Examples
Example 1.
If closed 2-manifolds M and N are homotopically equivalent then they are homeomorphic. Moreover, any homotopy equivalence of closed surfaces deforms to a homeomorphism.
Example 2.
If a closed manifold Mn (n ≠ 3) is homotopy-equivalent to Sn then Mn is homeomorphic to Sn.
Rigidity theorem in geometry
Definition.
A diffeomorphism of flat-Riemannian manifolds is said to be affine iff it carries geodesics to geodesic.
Theorem (Bieberbach)
If f : M → N is a homotopy equivalence between flat closed connected Riemannian manifolds then f is homotopic to an affine homeomorphism.
Mostow's rigidity theorem
Theorem: Let M and N be compact, locally symmetric Riemannian manifolds with everywhere non-positive curvature having no closed one or two dimensional geodesic subspace which are direct factor locally. If f : M → N is a homotopy equivalence then f is homotopic to an isometry.
Theorem (Mostow's theorem for hyperbolic n-manifolds, n ≥ 3): If M and N are complete hyperbolic n-manifolds, n ≥ 3 with finite volume and f : M → N is a homotopy equivalence then f is homotopic to an isometry.
These results are named after George Mostow.
Algebraic form
Let Γ and Δ be discrete subgroups of the isometry group of hyperbolic n-space H, where n ≥ 3, whose quotients H/Γ and H/Δ have finite volume. If Γ and Δ are isomorphic as discrete groups then they are conjugate.
Remarks
(1) In the 2-dimensional case any manifold of genus at least two has a hyperbolic structure. Mostow's rigidity theorem does not apply in this case. In fact, there are many hyperbolic structures on any such manifold; each such structure corresponds to a point in Teichmuller space.
(2) On the other hand, if M and N are 2-manifolds of finite volume then it is easy to show that they are homeomorphic exactly when their fundamental groups are the same.
Application
The group of isometries of a finite-volume hyperbolic n-manifold M (for n ≥ 3) is finitely generated and isomorphic to π1(M).
References
Topology
Maps of manifolds
Homotopy theory |
https://en.wikipedia.org/wiki/Ho%20Chi%20Fung | Ho Chi Fung (; born September 17, 1976) is a Chinese Grand Prix motorcycle racer. He won the 2013 FIM eRoad Racing World Cup.
Career statistics
By season
Races by year
(key)
References
External links
Profile on motogp.com
Living people
1976 births
Chinese motorcycle racers
250cc World Championship riders |
https://en.wikipedia.org/wiki/Su%20Rongzai | Su Rongzai (; born November 29, 1975) is a Chinese Grand Prix motorcycle racer.
Career statistics
By season
Races by year
(key)
References
External links
Profile on motogp.com
1975 births
Living people
Chinese motorcycle racers
250cc World Championship riders
Sportspeople from Guangzhou |
https://en.wikipedia.org/wiki/Li%20Zhengpeng | Li Zhengpeng (; born December 1, 1988) is a Chinese Grand Prix motorcycle racer.
Career statistics
By season
Races by year
(key)
References
External links
Profile on motogp.com
1988 births
Living people
Chinese motorcycle racers
250cc World Championship riders
Sportspeople from Xi'an |
https://en.wikipedia.org/wiki/List%20of%20Hertha%20BSC%20records%20and%20statistics | This article has details on Hertha BSC Berlin statistics.
Recent seasons
Coaches since 1963
Honours
League
German Champions: 2
Winners: 1930, 1931
Runners-up: 1926, 1927, 1928, 1929, 1975
2. Bundesliga Champions: 3
1990, 2011, 2013
Cup
DFB-Ligapokal: 2
Winners: 2001, 2002
Runners-up: 2000
DFB-Pokal: 0
Runners-up: 1977, 1979, 19931
Regional
Oberliga Berlin Champions:
1925, 1926, 1927, 1928, 1929, 1930, 1931, 1933
Gauliga Berlin-Brandenburg Champions:
1935, 1937, 1944
Brandenburg football champions:
1906, 1915, 1917, 1918, 1925–31, 1933
Berliner Landespokal (Tiers 3-7):
Winners: 1920, 1924, 1928, 1929, 1943, 1958, 1959, 1966, 1967, 19761, 1987, 19921, 20041
Note 1: Reserve Team
Youth
German Under 19 Championship
Champions: 2018
Runners-up: 2022
German Under 17 championship
Champions: 2000, 2003, 2005
Runners-up: 1991
Under 19 Bundesliga North/Northeast
Champions: 2005, 2006
Under 17 Bundesliga North/Northeast
Champions: 2008
External links
Hertha BSC Berlin on fussballdaten.de (German)
(German)
German football club statistics |
https://en.wikipedia.org/wiki/Gray%27s%20conjecture | In mathematics, Gray's conjecture is a conjecture made by Brayton Gray in 1984 about maps between loop spaces of spheres. It was later proved by John Harper.
References
Algebraic topology
Conjectures that have been proved |
https://en.wikipedia.org/wiki/List%20of%201.%20FC%20K%C3%B6ln%20records%20and%20statistics | This article has details on 1. FC Köln statistics.
Recent seasons
By season
By competition
In European football
By season
Key
Pld = Matches played
W = Matches won
D = Matches drawn
L = Matches lost
GF = Goals for
GA = Goals against
GD = Goal difference
Grp = Group stage
GS2 = Second group stage
R1 = First round
R2 = Second round
R3 = Third round
R4 = Fourth round
R16 = Round of 16
QF = Quarter-final
SF = Semi-final
Key to colours and symbols:
By competition
Honours
German Champions
Winners: 1961–62, 1963–64, 1977–78
Runners-up: 1959–60, 1962–63, 1964–65, 1972–73, 1981–82, 1988–89, 1989–90
2. Bundesliga
Winners: 1999–2000, 2004–05, 2013–14, 2018–19
Runners-up: 2002–03
DFB-Pokal
Winners: 1967–68, 1976–77, 1977–78, 1982–83
Runners-up: 1953–54, 1969–70, 1970–71, 1972–73, 1979–80, 1990–91
UEFA Europa League / UEFA Cup
Runners-up: 1985–86
Regional
Oberliga West
Winners: 1953–54, 1959–60, 1960–61, 1961–62, 1962–63
Runners-up: 1952–53, 1957–58, 1958–59
Doubles
1977–78: League and DFB-Pokal
Reserve team
German amateur champions: 1981
Youth
German Under 19 championship
Champions: 1970–71
Runners-up: 1973–74, 1982–83, 1991–92
Under 19 Bundesliga Division West
Champions: 2007–08
Runners-up: 2003–04, 2009–10, 2013–14, 2014–15
Under 19 Juniors DFB-Pokal
Champions: 2012–13
Runners-up: 1990–91, 1993–94
German Under 17 championship
Champions: 1989–90, 2010–11, 2018–19
Under 17 Bundesliga Division West
Champions: 2010–11, 2011–12
Runners-up: 2008–09, 2018–19
Club records
Record wins
Home
13–0 against Union Luxembourg, 5 October 1965 (Inter-Cities Fairs Cup)
9–1 against Viking FK, 7 November 1972 (UEFA Cup)
8–0 against Tottenham Hotspur, 22 July 1995 (Intertoto Cup)
8–0 against Schalke 04, 8 November 1969 (League)
8–0 against Eintracht Braunschweig, 8 September 1979 (League)
8–1 against Dynamo Dresden, 10 November 2018 (League)
7–0 against Schalke 04, 9 September 1967 (League)
7–0 against Eintracht Frankfurt, 29 October 1983 (League)
7–1 against Tennis Borussia Berlin, 31 May 1975 (League)
7–1 against Werder Bremen, 21 January 2023 (League)
Away
9–1 against BFC Dynamo, 19 August 2018 (Cup)
6–0 against SC Tasmania 1900 Berlin, 30 October 1965 (League)
6–0 against VSG Altglienicke, 12 September 2020 (Cup)
5–0 against FC St. Pauli, 29 April 1978 (League)
5–0 against Werder Bremen, 24 May 1980 (League)
5–0 against Hertha BSC, 22 February 2020 (League)
4–0 against Barcelona, 5 November 1980 (UEFA Cup)
Record defeats
Home
1–6 against Borussia Dortmund, 23 August 1994 (League)
1–6 against VfB Stuttgart, 1 June 1991 (League)
1–6 against Borussia Dortmund, 25 March 2012 (League)
1–3 against Inter Milan, 20 March 1985 (UEFA Cup) (heaviest home defeat in European football)
Away
1–8 against Dundee, 5 September 1962 (European Cup) (heaviest away defeat in European football)
0–7 against Bayern Munich, 15 May 1971 (League)
0–6 against VfL Wolfsburg, 21 October 2000 (League)
0–6 against 1899 Hoffenheim, 31 March 20 |
https://en.wikipedia.org/wiki/Ward%27s%20conjecture | In mathematics, Ward's conjecture is the conjecture made by that "many (and perhaps all?) of the ordinary and partial differential equations that are regarded as being integrable or solvable may be obtained from the self-dual gauge field equations (or its generalizations) by reduction".
Examples
explain how a variety of completely integrable equations such as the Korteweg-de Vries equation (KdV) equation, the Kadomtsev–Petviashvili equation (KP) equation, the nonlinear Schrödinger equation, the sine-Gordon equation, the Ernst equation and the Painlevé equations all arise as reductions or other simplifications of the self-dual Yang-Mills equations:
where is the curvature of a connection on an oriented 4-dimensional pseudo-Riemannian manifold, and is the Hodge star operator.
They also obtain the equations of an integrable system known as the Euler–Arnold–Manakov top, a generalization of the Euler top, and they state that the Kowalevsaya top is also a reduction of the self-dual Yang-Mills equations.
Penrose-Ward transform
Via the Penrose-Ward transform these solutions give the holomorphic vector bundles often seen in the context of algebraic integrable systems.
References
http://www.ucl.ac.uk/~ucahrha/Publications/sdym-03.pdf
Integrable systems |
https://en.wikipedia.org/wiki/Yang%E2%80%93Mills%20equations | In physics and mathematics, and especially differential geometry and gauge theory, the Yang–Mills equations are a system of partial differential equations for a connection on a vector bundle or principal bundle. They arise in physics as the Euler–Lagrange equations of the Yang–Mills action functional. They have also found significant use in mathematics.
Solutions of the equations are called Yang–Mills connections or instantons. The moduli space of instantons was used by Simon Donaldson to prove Donaldson's theorem.
Motivation
Physics
In their foundational paper on the topic of gauge theories, Robert Mills and Chen-Ning Yang developed (essentially independent of the mathematical literature) the theory of principal bundles and connections in order to explain the concept of gauge symmetry and gauge invariance as it applies to physical theories. The gauge theories Yang and Mills discovered, now called Yang–Mills theories, generalised the classical work of James Maxwell on Maxwell's equations, which had been phrased in the language of a gauge theory by Wolfgang Pauli and others. The novelty of the work of Yang and Mills was to define gauge theories for an arbitrary choice of Lie group , called the structure group (or in physics the gauge group, see Gauge group (mathematics) for more details). This group could be non-Abelian as opposed to the case corresponding to electromagnetism, and the right framework to discuss such objects is the theory of principal bundles.
The essential points of the work of Yang and Mills are as follows. One assumes that the fundamental description of a physical model is through the use of fields, and derives that under a local gauge transformation (change of local trivialisation of principal bundle), these physical fields must transform in precisely the way that a connection (in physics, a gauge field) on a principal bundle transforms. The gauge field strength is the curvature of the connection, and the energy of the gauge field is given (up to a constant) by the Yang–Mills action functional
The principle of least action dictates that the correct equations of motion for this physical theory should be given by the Euler–Lagrange equations of this functional, which are the Yang–Mills equations derived below:
Mathematics
In addition to the physical origins of the theory, the Yang–Mills equations are of important geometric interest. There is in general no natural choice of connection on a vector bundle or principal bundle. In the special case where this bundle is the tangent bundle to a Riemannian manifold, there is such a natural choice, the Levi-Civita connection, but in general there is an infinite-dimensional space of possible choices. A Yang–Mills connection gives some kind of natural choice of a connection for a general fibre bundle, as we now describe.
A connection is defined by its local forms for a trivialising open cover for the bundle . The first attempt at choosing a canonical connection might be to dema |
https://en.wikipedia.org/wiki/Constant-mean-curvature%20surface | In differential geometry, constant-mean-curvature (CMC) surfaces are surfaces with constant mean curvature. This includes minimal surfaces as a subset, but typically they are treated as special case.
Note that these surfaces are generally different from constant Gaussian curvature surfaces, with the important exception of the sphere.
History
In 1841 Delaunay proved that the only surfaces of revolution with constant mean curvature were the surfaces obtained by rotating the roulettes of the conics. These are the plane, cylinder, sphere, the catenoid, the unduloid and nodoid.
In 1853 J. H. Jellet showed that if is a compact star-shaped surface in with constant mean curvature, then it is the standard sphere. Subsequently, A. D. Alexandrov proved that a compact embedded surface in with constant mean curvature must be a sphere. Based on this H. Hopf conjectured in 1956 that any immersed compact orientable constant mean curvature hypersurface in must be a standard embedded sphere. This conjecture was disproven in 1982 by Wu-Yi Hsiang using a counterexample in . In 1984 Henry C. Wente constructed the Wente torus, an immersion into of a torus with constant mean curvature.
Up until this point it had seemed that CMC surfaces were rare; new techniques produced a plethora of examples. In particular gluing methods appear to allow combining CMC surfaces fairly arbitrarily. Delaunay surfaces can also be combined with immersed "bubbles", retaining their CMC properties.
Meeks showed that there are no embedded CMC surfaces with just one end in . Korevaar, Kusner and Solomon proved that a complete embedded CMC surface will have ends asymptotic to unduloids. Each end carries a "force" along the asymptotic axis of the unduloid (where n is the circumference of the necks), the sum of which must be balanced for the surface to exist. Current work involves classification of families of embedded CMC surfaces in terms of their moduli spaces. In particular, for coplanar k-unduloids of genus 0 satisfy for odd k, and for even k. At most k − 2 ends can be cylindrical.
Generation methods
Representation formula
Like for minimal surfaces, there exist a close link to harmonic functions. An oriented surface in has constant mean curvature if and only if its Gauss map is a harmonic map. Kenmotsu’s representation formula is the counterpart to the Weierstrass–Enneper parameterization of minimal surfaces:
Let be an open simply connected subset of and be an arbitrary non-zero real constant. Suppose is a harmonic function into the Riemann sphere. If then defined by
with
for is a regular surface having as Gauss map and mean curvature .
For and this produces the sphere. and gives a cylinder where .
Conjugate cousin method
Lawson showed in 1970 that each CMC surface in has an isometric "cousin" minimal surface in . This allows constructions starting from geodesic polygons in , which are spanned by a minimal patch that can be extended into a complete surface |
https://en.wikipedia.org/wiki/Regularized%20meshless%20method | In numerical mathematics, the regularized meshless method (RMM), also known as the singular meshless method or desingularized meshless method, is a meshless boundary collocation method designed to solve certain partial differential equations whose fundamental solution is explicitly known. The RMM is a strong-form collocation method with merits being meshless, integration-free, easy-to-implement, and high stability. Until now this method has been successfully applied to some typical problems, such as potential, acoustics, water wave, and inverse problems of bounded and unbounded domains.
Description
The RMM employs the double layer potentials from the potential theory as its basis/kernel functions. Like the method of fundamental solutions (MFS), the numerical solution is approximated by a linear combination of double layer kernel functions with respect to different source points. Unlike the MFS, the collocation and source points of the RMM, however, are coincident and placed on the physical boundary without the need of a fictitious boundary in the MFS. Thus, the RMM overcomes the major bottleneck in the MFS applications to the real world problems.
Upon the coincidence of the collocation and source points, the double layer kernel functions will present various orders of singularity. Thus, a subtracting and adding-back regularizing technique is introduced and, hence, removes or cancels such singularities.
History and recent development
These days the finite element method (FEM), finite difference method (FDM), finite volume method (FVM), and boundary element method (BEM) are dominant numerical techniques in numerical modelings of many fields of engineering and sciences. Mesh generation is tedious and even very challenging problems in their solution of high-dimensional moving or complex-shaped boundary problems and is computationally costly and often mathematically troublesome.
The BEM has long been claimed to alleviate such drawbacks thanks to the boundary-only discretizations and its semi-analytical nature. Despite these merits, the BEM, however, involves quite sophisticated mathematics and some tricky singular integrals. Moreover, surface meshing in a three-dimensional domain remains to be a nontrivial task. Over the past decades, considerable efforts have been devoted to alleviating or eliminating these difficulties, leading to the development of meshless/meshfree boundary collocation methods which require neither domain nor boundary meshing. Among these methods, the MFS is the most popular with the merit of easy programming, mathematical simplicity, high accuracy, and fast convergence.
In the MFS, a fictitious boundary outside the problem domain is required in order to avoid the singularity of the fundamental solution. However, determining the optimal location of the fictitious boundary is a nontrivial task to be studied. Dramatic efforts have ever since been made to remove this long perplexing issue. Recent advances include, for exampl |
https://en.wikipedia.org/wiki/Albrecht%20Pfister%20%28mathematician%29 | Albrecht Pfister (born July 30, 1934) is a German mathematician specializing in algebra and in particular quadratic forms.
Pfister received his doctoral degree in 1961 at the Ludwig Maximilian University of Munich. The title of his doctoral thesis was Über das Koeffizientenproblem der beschränkten Funktionen von zwei Veränderlichen ("On the coefficient problem of the bounded functions of two variables"). His thesis advisors were Martin Kneser and Karl Stein. In 1966 he received his habilitation at the Georg August University of Göttingen. From 1970 until his retirement he was professor at the Johannes Gutenberg University of Mainz.
In the theory of quadratic forms over fields, the Pfister forms that he introduced in 1965 bear his name.
In 1970, he was an invited speaker on the topic Sums of squares in real function fields at the International Congress of Mathematicians in Nice.
Writings
Quadratic forms with applications to algebraic geometry and topology. In: London Mathematical Society Lecture Notes. Cambridge University Press 1995.
Quadratische Formen. In: Fischer, Hirzebruch et al. (eds.): 100 Jahre Mathematik 1890–1990. Vieweg 1990.
External links
1934 births
Scientists from Munich
20th-century German mathematicians
Living people |
https://en.wikipedia.org/wiki/Carlitz%20exponential | In mathematics, the Carlitz exponential is a characteristic p analogue to the usual exponential function studied in real and complex analysis. It is used in the definition of the Carlitz module – an example of a Drinfeld module.
Definition
We work over the polynomial ring Fq[T] of one variable over a finite field Fq with q elements. The completion C∞ of an algebraic closure of the field Fq((T−1)) of formal Laurent series in T−1 will be useful. It is a complete and algebraically closed field.
First we need analogues to the factorials, which appear in the definition of the usual exponential function. For i > 0 we define
and D0 := 1. Note that the usual factorial is inappropriate here, since n! vanishes in Fq[T] unless n is smaller than the characteristic of Fq[T].
Using this we define the Carlitz exponential eC:C∞ → C∞ by the convergent sum
Relation to the Carlitz module
The Carlitz exponential satisfies the functional equation
where we may view as the power of map or as an element of the ring of noncommutative polynomials. By the universal property of polynomial rings in one variable this extends to a ring homomorphism ψ:Fq[T]→C∞{τ}, defining a Drinfeld Fq[T]-module over C∞{τ}. It is called the Carlitz module.
References
Algebraic number theory
Finite fields |
https://en.wikipedia.org/wiki/Thierry%20Goudon | Thierry Goudon (born January 1969 in Aix-en-Provence, France) is a French mathematician. He works in applied mathematics, with interest in the study of Partial Differential Equations motivated from physics. He has made contributions on kinetic theory, which corresponds to a description of matter in terms of statistical physics. The Boltzmann equation for gas dynamics is a typical example of this activity. The kinetic framework also arises in many other fields: neutron transport, radiative transfer, and biology. He is interested in asymptotic analysis, including the study of hydrodynamic regimes and homogenization theory, establishing relationships between microscopic and macroscopic descriptions. He also works on fluid mechanics, both as regards the analysis of the equations and also the design of numerical methods for computing the solutions. Currently he holds a Senior INRIA Researcher (Directeur de recherche) position at Sophia Antipolis; he is the head of the team COFFEE devoted to Complex Flows For Energy and Environment.
Biography
Thierry Goudon completed his undergraduate studies in Aix-en-Provence and in Bordeaux, where he attended the Matmeca program. He obtained the PhD degree under supervision of Kamal Hamdache in 1997 at University Bordeaux 1. He joined the University of Nice as Assistant Professor (Maitre de conferences). He obtain the Habilitation to conduct research in 2001 and he became Full Professor at the University of Lille in 2003. Since 2008, he has held the pots of a Senior INRIA Researcher, in Lille until 2011, then in Sophia Antipolis. In 2008, he was awarded the Robert Dautray prize, jointly with Jean-Francois Clouet from the French Atomic Commission: this exceptional prize, funded by the French Society of Applied and Industrial Mathematics in the honor of R. Dautray's 80th birthday, honours remarkable works on radiative transfer theory and its applications.
References
External links
Thierry Goudon's professional website
Movie: Avis de recherche
1969 births
Living people
French mathematicians |
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