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https://en.wikipedia.org/wiki/1960%E2%80%9361%20French%20Division%202 | Statistics of Division 2 in the 1960–61 season.
Overview
It was contested by 19 teams, and Montpellier won the championship.
League standings
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1961%E2%80%9362%20French%20Division%202 | Statistics of Division 2 in the 1961–62 season.
Overview
It was contested by 19 teams, and Grenoble won the championship.
League standings
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1962%E2%80%9363%20French%20Division%202 | Statistics of Division 2 in the 1962–63 season.
Overview
It was contested by 19 teams, and Saint-Étienne won the championship.
League standings
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1963%E2%80%9364%20French%20Division%202 | Statistics of Division 2 in the 1963–64 season.
Overview
It was contested by 18 teams, and Lille won the championship, after Le Havre was disqualified.
League standings
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1964%E2%80%9365%20French%20Division%202 | Statistics of Division 2 in the 1964–65 season.
Overview
It was contested by 16 teams, and OGC Nice won the championship.
League standings
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1965%E2%80%9366%20French%20Division%202 | Statistics of Division 2 in the 1965–66 season.
Overview
It was contested by 19 teams, and Stade Reims won the championship.
League standings
References
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1966%E2%80%9367%20French%20Division%202 | Statistics of Division 2 in the 1966–67 season.
Overview
It was contested by 18 teams, and Ajaccio won the championship.
League standings
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1967%E2%80%9368%20French%20Division%202 | Statistics of Division 2 for the 1967–68 season.
Overview
It was contested by 19 teams, and Bastia won the championship.
League standings
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1968%E2%80%9369%20French%20Division%202 | Statistics of Division 2 in the 1968–69 season.
Overview
It was contested by 21 teams, and Angers won the championship.
League standings
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1969%E2%80%9370%20French%20Division%202 | Statistics of Division 2 in the 1969/1970 season.
Overview
It was contested by 16 teams, and Nice won the championship.
League standings
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1971%E2%80%9372%20French%20Division%202 | Statistics of Division 2 in the 1971–72 season.
Overview
It was contested by 48 teams, and CS Sedan Ardennes, Valenciennes and RC Strasbourg won the championship.
League tables
Group A
Group B
Group C
Championship play-offs
|}
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1972%E2%80%9373%20French%20Division%202 | Statistics of Division 2 in the 1972–73 season.
Overview
It was contested by 36 teams, and Lens and AS Troyes won the championship.
League tables
Group A
Group B
Championship play-offs
|}
Promotion play-offs
|}
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1974%E2%80%9375%20French%20Division%202 | Statistics of Division 2 in the 1974–75 season.
Overview
It was contested by 35 teams, and Valenciennes and Nancy won the championship.
League tables
Group A
Group B
Championship play-offs
|}
Promotion play-offs
|}
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1975%E2%80%9376%20French%20Division%202 | Statistics of Division 2 in the 1975–76 season.
Overview
It was contested by 36 teams, and Stade Rennais and Angers won the championship.
League tables
Group A
Group B
Championship play-offs
|}
Promotion play-offs
|}
Top scorers
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1976%E2%80%9377%20French%20Division%202 | Statistics of Division 2 in the 1976/1977 season.
Overview
It was contested by 36 teams, and AS Monaco and RC Strasbourg won the championship.
League tables
Group A
Group B
Championship play-offs
|}
Promotion play-offs
|}
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1977%E2%80%9378%20French%20Division%202 | Statistics of Division 2 in the 1977/1978 season.
Overview
It was contested by 36 teams, and Angers and Lille won the championship.
League tables
Group A
Group B
Championship play-offs
|}
Promotion play-offs
|}
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1978%E2%80%9379%20French%20Division%202 | Statistics of Division 2 in the 1978/1979 season.
Overview
It was contested by 36 teams, and Gueugnon and Stade Brest won the championship.
League tables
Group A
Group B
Championship play-offs
|}
Promotion play-offs
|}
Lens was qualified to the play-off against 19th placed team of Division 1, Paris FC.
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1979%E2%80%9380%20French%20Division%202 | Statistics of Division 2 in the 1979/1980 season.
Overview
It was contested by 36 teams, and Tours and Auxerre won the championship.
League tables
Group A
Group B
Championship play-offs
|}
Promotion play-offs
|}
Avignon was qualified to the play-off against 18th placed team of Division 1, Lyon.
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1980%E2%80%9381%20French%20Division%202 | Statistics of Division 2 in the 1980/1981 season.
Overview
It was contested by 36 teams, and Montpellier and Stade Brest won the championship.
League tables
Group A
Group B
Championship play-offs
|}
Promotion play-offs
|}
Toulouse was qualified to the play-off against 18th placed team of Division 1, Tours.
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1981%E2%80%9382%20French%20Division%202 | Statistics of Division 2 in the 1981/1982 season.
Overview
It was contested by 36 teams, and Toulouse and Rouen won the championship.
League tables
Group A
Group B
Championship play-offs
|}
Promotion play-offs
|}
Mulhouse was qualified to the play-off against 18th placed team of Division 1, Valenciennes.
Top goalscorers
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1982%E2%80%9383%20French%20Division%202 | Statistics of Division 2 in the 1982/1983 season.
Overview
It was contested by 36 teams, and Stade Rennais and Toulon won the championship.
League tables
Group A
Group B
Championship play-offs
|}
Promotion play-offs
|}
Nîmes was qualified to the play-off against 18th placed team of Division 1, Tours.
Top goalscorers
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1983%E2%80%9384%20French%20Division%202 | Statistics of Division 2 in the 1983/1984 season.
Overview
It was contested by 37 teams, and Olympique Marseille and Tours won the championship.
League tables
Group A
Group B
Championship play-offs
|}
Promotion play-offs
Top goalscorers
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1984%E2%80%9385%20French%20Division%202 | Statistics of Division 2 in the 1984/1985 season.
Overview
It was contested by 36 teams, and Le Havre and Nice won the championship.
League tables
Group A
Group B
Championship play-offs
|}
Promotion play-offs
Top goalscorers
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1985%E2%80%9386%20French%20Division%202 | Statistics of Division 2 in the 1985–86 season.
Overview
It was contested by 36 teams, and Saint-Étienne and Paris won the championship.
League tables
Group A
Group B
Championship play-offs
|}
Promotion play-offs
Top goalscorers
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1986%E2%80%9387%20French%20Division%202 | Statistics of Division 2 in the 1986–87 season.
Overview
It was contested by 36 teams, and Chamois Niort and Montpellier won the championship.
League tables
Group A
Group B
Championship play-offs
|}
Promotion play-offs
Top goalscorers
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1987%E2%80%9388%20French%20Division%202 | Statistics of Division 2 in the 1987–88 season.
Overview
It was contested by 36 teams, and Sochaux-Montbéliard and RC Strasbourg won the championship.
League tables
Group A
Group B
Championship play-offs
|}
Promotion play-offs
Top goalscorers
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1988%E2%80%9389%20French%20Division%202 | Statistics of Division 2 in the 1988/1989 season.
Overview
It was contested by 36 teams, and Mulhouse and Olympique Lyonnais won the championship.
League tables
Group A
Group B
Championship play-offs
|}
Promotion play-offs
Top goalscorers
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1989%E2%80%9390%20French%20Division%202 | Statistics of Division 2 in the 1989/1990 season.
Overview
It was contested by 36 teams, and Nancy and Stade Rennais won the championship.
League tables
Group A
Group B
Championship play-offs
|}
Promotion play-offs
Top goalscorers
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1990%E2%80%9391%20French%20Division%202 | Statistics of Division 2 in the 1990–91 season.
Overview
It was contested by 36 teams, and Nîmes Olympique and Le Havre won the championship.
League tables
Group A
Group B
Championship play-offs
|}
Promotion play-offs
Top goalscorers
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/1991%E2%80%9392%20French%20Division%202 | Statistics of Division 2 in the 1991/1992 season.
Overview
It was contested by 36 teams, and Valenciennes and Girondins Bordeaux won the championship.
League tables
Group A
Group B
Championship play-offs
|}
Promotion play-offs
Top goalscorers
References
France - List of final tables (RSSSF)
Ligue 2 seasons
French
2 |
https://en.wikipedia.org/wiki/2008%E2%80%9309%20FC%20O%C8%9Belul%20Gala%C8%9Bi%20season |
Match results
Friendlies
Liga I
League table
Results by round
Results summary
Matches
Cupa României
Players
Squad statistics
Transfers
In
Out
Club
Coaching staff
References
ASC Oțelul Galați seasons
Otelul Galati |
https://en.wikipedia.org/wiki/1992%20Japan%20Football%20League | Statistics of Japan Football League in the 1992 season.
First Division
Second Division
Seino Unyu and Osaka Gas had been promoted automatically after winning the Regional Playoffs.
References
1996
2
Japan
Japan |
https://en.wikipedia.org/wiki/1993%20Japan%20Football%20League | Statistics of Japan Football League in the 1993 season.
Division 1
Overview
It was contested by 10 teams, and Fujita won the championship.
League Standings
Division 2
Overview
It was contested by 10 teams, and Honda won the championship.
League standings
References
1996
2
Japan
Japan |
https://en.wikipedia.org/wiki/1994%20Japan%20Football%20League | Statistics of Japan Football League in the 1994 season.
Overview
It was contested by 16 teams, and Cerezo Osaka won the championship. Along with Kashiwa Reysol they were promoted to the J.League.
NEC Yamagata, the future Montedio Yamagata, were promoted to the JFL before the season, having won the Regional Promotion Series.
League standings
References
1996
2
Japan
Japan |
https://en.wikipedia.org/wiki/1995%20Japan%20Football%20League | Statistics of Japan Football League in the 1995 season.
Overview
It was contested by 16 teams, and Fukuoka Blux won the championship. They were promoted to the J.League along with Kyoto Purple Sanga.
Newly promoted before the season were Brummell Sendai (the future Vegalta Sendai), and Fukushima FC, which despite its name was based in Kōriyama.
League table
References
1996
2
Japan
Japan |
https://en.wikipedia.org/wiki/1996%20Japan%20Football%20League | Statistics of Japan Football League in the 1996 season.
Overview
It was contested by 16 teams, and Honda won the championship. However, citing continuing corporate ownership, they were refused promotion by the J.League, who took in the runner-up, Vissel Kobe, instead.
Newly promoted before the season were Nippon Denso, later known as FC Kariya, and Oita Trinity, later known as Oita Trinita.
League standings
Updated to match(es) played in November 1996. Source:
Rules for classification: 1) points; 2) goal difference; 3) number of goals scored.
Notes:
Teams in Bold are the J.League associate members
After the season Tosu Futures & Cosmo Oil Yokkaichi folded
References
1996
2
Japan
Japan |
https://en.wikipedia.org/wiki/1997%20Japan%20Football%20League | Statistics of Japan Football League in the 1997 season.
Overview
It was contested by 16 teams, and Consadole Sapporo won the championship.
As a result of Cosmo Oil Yokkaichi's closure the previous year, Jatco F.C. and Mito HollyHock were promoted before the season.
League standings
Promotion and Relegation
Because Fukushima FC and Seino Transportation were disbanded, no relegation has occurred. At the end of the season, the winner and runner-up of Regional League promotion series, Sony Sendai and Albirex Niigata were promoted automatically.
1996
2
Japan
Japan |
https://en.wikipedia.org/wiki/1998%20Japan%20Football%20League | Statistics of Japan Football League in the 1998 season.
Overview
The 1998 season was the seventh and the last of the former Japan Football League. It was contested by 16 teams, and Tokyo Gas won the championship. After the season, nine teams together with J. League Promotion and Relegation series' losers Consadole Sapporo formed the second division of J.League. Other seven clubs together with Regional Leagues promotion series winners Yokogawa Electric and newly created Yokohama FC have formed the new Japan Football League.
Table
Results
Promotion and relegation
Kawasaki Frontale were awarded a spot in the first round of J.League Promotion and Relegation Series where they have played against Avispa Fukuoka.
Avispa proceeded to the next round and Frontale entered the second division.
Successor seasons
1999 J.League Division 2
1999 Japan Football League
1996
2
Japan
Japan |
https://en.wikipedia.org/wiki/1966%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues in the 1966 season.
Champions list
League standings
Tōkai
Kansai
References
External links
1966
Japanese Regional Leagues
2 |
https://en.wikipedia.org/wiki/1967%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1967 season.
Champions list
League standings
Kanto
Tokai
Kansai
1967
Japanese Regional Leagues
2 |
https://en.wikipedia.org/wiki/1968%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1968 season.
Champions list
League standings
Kanto
Tokai
Kansai
1968
Japanese Regional Leagues
2 |
https://en.wikipedia.org/wiki/1969%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues in the 1969 season.
Champions list
League standings
Kanto
Tokai
Kansai
1969
Japanese Regional Leagues
2 |
https://en.wikipedia.org/wiki/1970%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1970 season.
Champions list
League standings
Kanto
Tokai
Kansai
1970
Jap
Jap
3 |
https://en.wikipedia.org/wiki/1971%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues in the 1971 season.
Champions list
By winning the All Japan Senior Football Championship and then defeating Nagoya Bank in a promotion/relegation Series, Towa ED was promoted to the Japan Soccer League; it and the remaining JSL clubs constituted the new JSL First Division, while Toyota, Kyoto and eight other clubs were chosen for the new JSL Second Division.
League standings
Kanto
Tokai
Kansai
1971
Jap
Jap
2 |
https://en.wikipedia.org/wiki/1972%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1972 season.
Champions list
League standings
Kanto
Tokai
Kansai
1972
Jap
Jap
3 |
https://en.wikipedia.org/wiki/1973%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1973 season.
Champions list
League standings
Kanto
Tokai
Kansai
Chūgoku
Kyushu
1973
Jap
Jap
3 |
https://en.wikipedia.org/wiki/1974%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1974 season.
Champions list
League standings
Kanto
Tokai
Kansai
Chūgoku
Kyushu
1974
Jap
Jap
3 |
https://en.wikipedia.org/wiki/1975%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1975 season.
Champions list
League standings
Kanto
Hokushinetsu
Tokai
Kansai
Chūgoku
Kyushu
1975
Jap
Jap
3 |
https://en.wikipedia.org/wiki/1976%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues in the 1976 season.
Champions list
League standings
Kanto
Hokushinetsu
Tokai
Kansai
Chūgoku
Kyushu
1976
Japanese Regional Leagues
3
Japanese Regional Leagues |
https://en.wikipedia.org/wiki/1977%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1977 season.
Champions list
League standings
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chūgoku
Shikoku
Kyushu
1977
Jap
Jap
3 |
https://en.wikipedia.org/wiki/1978%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1978 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chūgoku
Shikoku
Kyushu
1978
Jap
Jap
3 |
https://en.wikipedia.org/wiki/1979%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1979 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chūgoku
Shikoku
Kyushu
1979
Jap
Jap
3 |
https://en.wikipedia.org/wiki/1980%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1980 season.
Champions list
League standings
Hokkaido
Tohoku
Kantō
Hokushinetsu
Tōkai
Kansai
Chūgoku
Shikoku
Kyushu
1980
Jap
Jap
3 |
https://en.wikipedia.org/wiki/1981%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1981 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chūgoku
Shikoku
Kyushu
1981
Jap
Jap
3 |
https://en.wikipedia.org/wiki/1982%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1982 season.
Champions list
League standings
Hokkaido
Hakodate FC 1976 changed name to Blackpecker Hakodate.
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chūgoku
Shikoku
Kyushu
References
1982
Jap
Jap
3 |
https://en.wikipedia.org/wiki/1983%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1983 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chūgoku
Shikoku
Kyushu
1983
Jap
Jap
3 |
https://en.wikipedia.org/wiki/1984%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1984 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chūgoku
Shikoku
Kyushu
1984
Jap
Jap
3 |
https://en.wikipedia.org/wiki/1985%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1985 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chūgoku
Shikoku
Kyushu
1985
Jap
Jap
3 |
https://en.wikipedia.org/wiki/1986%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1986 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chūgoku
Shikoku
Kyushu
1986
Jap
Jap
3 |
https://en.wikipedia.org/wiki/1987%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1987 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chūgoku
Shikoku
Kyushu
1987
Jap
Jap
3 |
https://en.wikipedia.org/wiki/1988%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1988 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chugoku
Shikoku
Kyushu
1988
Jap
Jap
3 |
https://en.wikipedia.org/wiki/1989%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1989 football season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chugoku
Shikoku
Kyushu
1989
Jap
Jap
3 |
https://en.wikipedia.org/wiki/1990%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1990 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chugoku
Shikoku
Kyushu
Japanese Regional Leagues seasons
Jap
Jap
3 |
https://en.wikipedia.org/wiki/1991%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1991 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chugoku
Shikoku
Kyushu
Japanese Regional Leagues seasons
Jap
Jap
3 |
https://en.wikipedia.org/wiki/1992%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1992 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chugoku
Shikoku
Kyushu
Japanese Regional Leagues seasons
3 |
https://en.wikipedia.org/wiki/1993%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1993 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chugoku
Shikoku
Kyushu
Japanese Regional Leagues seasons
3 |
https://en.wikipedia.org/wiki/1994%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1994 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chugoku
Shikoku
Kyushu
Japanese Regional Leagues seasons
3 |
https://en.wikipedia.org/wiki/1995%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1995 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chugoku
Shikoku
Kyushu
Japanese Regional Leagues seasons
3 |
https://en.wikipedia.org/wiki/1996%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1996 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chugoku
Shikoku
Kyushu
Japanese Regional Leagues seasons
3 |
https://en.wikipedia.org/wiki/1997%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1997 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chugoku
Shikoku
Kyushu
Japanese Regional Leagues seasons
3 |
https://en.wikipedia.org/wiki/1998%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1998 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chugoku
Shikoku
Kyushu
Japanese Regional Leagues seasons
3 |
https://en.wikipedia.org/wiki/1999%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 1999 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chugoku
Shikoku
Kyushu
Japanese Regional Leagues seasons
4 |
https://en.wikipedia.org/wiki/2000%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 2000 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chugoku
Shikoku
Kyushu
2000
4 |
https://en.wikipedia.org/wiki/2001%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 2001 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chugoku
Shikoku
Kyushu
4
Japanese Regional Leagues seasons |
https://en.wikipedia.org/wiki/2002%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 2002 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chugoku
Shikoku
Kyushu
4
2002 |
https://en.wikipedia.org/wiki/2003%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 2003 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chugoku
Shikoku
Kyushu
2003
4 |
https://en.wikipedia.org/wiki/2004%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 2004 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chugoku
Shikoku
Kyushu
4
2004 |
https://en.wikipedia.org/wiki/2005%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 2005 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chugoku
Shikoku
Kyushu
2005
4 |
https://en.wikipedia.org/wiki/2006%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 2006 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chugoku
Shikoku
Kyushu
2006
4 |
https://en.wikipedia.org/wiki/2007%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 2007 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chugoku
After 14 matches the league is split into two playoffs (top and bottom) of three games to decide the league champion and promotion candidates. This would normally also decide relegation candidates, though this did not happen this year due to league expansion. Owing to this, teams can have more points but still remain in a lower league position than others.
Shikoku
Kyushu
References
2007
4 |
https://en.wikipedia.org/wiki/2008%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 2008 season.
Champions list
League standings
Hokkaido
Tohoku
Kanto
Hokushinetsu
Tokai
Kansai
Chugoku
Shikoku
Kyushu
Regional promotion series
2008
4 |
https://en.wikipedia.org/wiki/2009%20Japanese%20Regional%20Leagues | Statistics of Japanese Regional Leagues for the 2009 season.
Champions list
As of October 25, 2009
Club names in bold indicates clubs advance to the Regional League promotion series held in late November. Club names in italic indicates winners and runners-up of All Japan Senior Football Championship which advance to the Regional League promotion series as well.
Source:33rd Regional Football League Tournament
Hokkaido
2009 was the 32nd season of Hokkaido League. The season started on May 10 and ended on September 13.
It was contested by six teams and Sapporo University GP won the tournament.
After the season, Barefoot Hokkaido and Toyota Motor Hokkaido were relegated to the Block Leagues. They were replaced by Blackpecker Hakodate and Maruseizu FC
League table
Results
Tohoku
Division 1
2009 was the 33rd season of Tohoku League. The season started on April 12 and ended on October 11.
It was contested by eight teams and Grulla Morioka won the championship for the third consecutive year.
After the season, Sendai Nakada were relegated to the second division (south group) and Cobaltore Onagawa took their place.
League table
Results
Division 2
2009 was the 13th season of Tohoku League Division 2. North and South groups were won by Fuji Club 2003 and Cobaltore Onagawa respectively, and in post-season playoff series the latter earned promotion to Division 1.
North league table
North league results
South league table
South league results
Tohoku Promotion and Relegation Series
In order to decide the direct exchange between two divisions, two D2 winners played against each other in two-legged series. Cobaltore Onagawa defeated Fuji Club 2003 and received direct promotion to Division 1, replacing the bottom-placed Sendai Nakada, while Fuji Club 2003 were scheduled to face Shiogama Wiese in another two-legged series. By overall result, Shiogama Wiese have saved their Division 1 position.
The bottom-placed teams in both groups of Division 2 were directly relegated to the prefectural leagues, though in the north FC Shiwa have escaped relegation because of post-season disbandment of Grulla Istria. Their spots were filled by Omiya FC and Scheinen Fukushima, respectively. Second to last finishers, ReinMeer Aomori and Soma SC were scheduled to play against Hokuto Bank S.C. and Sakata Migaku Club, respectively, and both won their challenges, thus remaining in the Regional League for another year.
Kanto
Division 1
2009 was the 43rd season of Kanto League. The season started on April 4 and ended on September 6.
It was contested by eight teams and YSCC Yokohama won the championship for the second time in their history after two-year pause.
After the season, Hitachi Tochigi Uva were promoted to Japan Football League. Because of that, only Honda Luminozo Sayama were relegated to the second division, and both its winner and runner-up, Vertfee Takahara Nasu and Tonan Maebashi were promoted automatically.
League table
Results
Division 2
2009 wa |
https://en.wikipedia.org/wiki/Biology%20Battle | Biology Battle is a multidirectional shooter for the Xbox 360 and Microsoft Windows. It is a dual-stick shooter with elements similar to Robotron: 2084, Smash TV, and Geometry Wars.
Development
According to an interview with Novaleaf Game Studios, the game cost US$100,000 to make, higher than other XBLIG games.
The game was written using C# and XNA.
Reception
Biology Battle received mixed reviews upon release. On Metacritic, the Xbox 360 version of the game holds a score of 69/100 based on 13 reviews, indicating "mixed or average reviews". On GameRankings, the Xbox 360 version of the game holds a score of 71.25% based on 12 reviews.
References
External links
Official Biology Battle website
Biology Battle at Xbox.com
2008 video games
Microsoft games
Multidirectional shooters
Video games developed in Thailand
Windows games
Xbox 360 games
Xbox 360 Live Indie games
Multiplayer and single-player video games |
https://en.wikipedia.org/wiki/Compatible%20system%20of%20%E2%84%93-adic%20representations | In number theory, a compatible system of ℓ-adic representations is an abstraction of certain important families of ℓ-adic Galois representations, indexed by prime numbers ℓ, that have compatibility properties for almost all ℓ.
Examples
Prototypical examples include the cyclotomic character and the Tate module of an abelian variety.
Variations
A slightly more restrictive notion is that of a strictly compatible system of ℓ-adic representations which offers more control on the compatibility properties. More recently, some authors have started requiring more compatibility related to p-adic Hodge theory.
Importance
Compatible systems of ℓ-adic representations are a fundamental concept in contemporary algebraic number theory.
Notes
References
Algebraic number theory |
https://en.wikipedia.org/wiki/Peru%20national%20football%20team%20records%20and%20statistics | This is a list of statistical records of the Peru national football team.
Player records
Players in bold are still active with Peru.
Most appearances
Most goals
Competition records
FIFA World Cup
Copa América
Head-to-head results
As of 19 November 2022 after the match against .
References
Peru national football team
National association football team records and statistics |
https://en.wikipedia.org/wiki/Fence%20%28mathematics%29 | In mathematics, a fence, also called a zigzag poset, is a partially ordered set (poset) in which the order relations form a path with alternating orientations:
or
A fence may be finite, or it may be formed by an infinite alternating sequence extending in both directions. The incidence posets of path graphs form examples of fences.
A linear extension of a fence is called an alternating permutation; André's problem of counting the number of different linear extensions has been studied since the 19th century. The solutions to this counting problem, the so-called Euler zigzag numbers or up/down numbers, are:
.
The number of antichains in a fence is a Fibonacci number; the distributive lattice with this many elements, generated from a fence via Birkhoff's representation theorem, has as its graph the Fibonacci cube.
A partially ordered set is series-parallel if and only if it does not have four elements forming a fence.
Several authors have also investigated the number of order-preserving maps from fences to themselves, or to fences of other sizes.
An up-down poset is a generalization of a zigzag poset in which there are downward orientations for every upward one and total elements. For instance, has the elements and relations
In this notation, a fence is a partially ordered set of the form .
Equivalent conditions
The following conditions are equivalent for a poset :
is a disjoint union of zigzag posets.
If in , either or .
, i.e. it is never the case that and , so that is vacuously transitive.
has dimension at most one (defined analogously to the Krull dimension of a commutative ring).
Every element of is either maximal or minimal.
The slice category is cartesian closed.
The prime ideals of a commutative ring , ordered by inclusion, satisfy the equivalent conditions above if and only if has Krull dimension at most one.
Notes
References
.
.
.
.
.
.
.
.
.
.
.
Exercise 3.23a, page 157.
.
External links
Order theory
Enumerative combinatorics |
https://en.wikipedia.org/wiki/Thomas%20Hood%20%28mathematician%29 | Thomas Hood (1556–1620) was an English mathematician and physician, the first lecturer in mathematics appointed in England, a few years before the founding of Gresham College. He publicized the Copernican theory, and discussed the nova SN 1572. (Tycho's Nova). He also innovated in the design of mathematical and astronomical instruments.
Life
He entered Trinity College, Cambridge in 1573, and graduated B.A. in 1578; he was elected to a fellowship in the same year, and graduated M.A. in 1581. His Cambridge licence to practice as a physician was from 1585. He was approached to lecture in mathematics in 1582, by the merchant Thomas Smythe. The lectures in fact began in 1588.
He lectured from 1588 to 1592. The applications in view were military (intended for Captains of train bands, in other words for militia commanders at the time of the Spanish Armada), and subsequently aimed at naval needs and navigation. The first lectures were in the Staples Inn Chapel, but the regular venue became Smythe's London house, Leadenhall in Gracechurch Street. Other supporters of the lectures were Sir John Wolstenholme and John Lumley, 1st Baron Lumley; Hood was a subscriber in 1589 to the Virginia Company, with which his merchant backers were associated. Hood's original publications were probably derived from notes of the talks. He collaborated with the engraver Augustine Ryther on both celestial and terrestrial charts.
In later life he lived in Abchurch Lane, London, practiced as a physician, and sold copies of his hemisphere charts.
Works
A Copie of the Speache ... (1588)
The Use of the Celestial Globe in Plano, set forth in two hemispheres (1590)
The Use of Jacobs Staffe
Making and Use of the Sector
Elementes of Geometrie (1590), translated from the Latin of Petrus Ramus, Geometriae Septem Et Viginti
A translation of the arithmetic of Christian Wursteisen (1596)
Work on surveying (1598).
See also
Backstaff
Sector (instrument)
Notes
Further reading
Francis R. Johnson, Thomas Hood's inaugural address as Mathematical Lecturer of the City of London (1588), Journal of the History of Ideas, 3: 94-106, (1942)
External links
Felice Stoppa in Atlas Coelestis:Thomas Hood, The Use of the Celestial Globe in Plano, set forth in two Hemispheres.., Imprinted for Thobie Cooke at London, 1590
Stephen Johnston, The astrological instruments of Thomas Hood
Nicolàs de Hilster, 1590 Master Hood's cross-staff (reconstruction)
17th-century English astronomers
16th-century English mathematicians
17th-century English mathematicians
1556 births
1620 deaths
16th-century English medical doctors
17th-century English medical doctors
People of the Elizabethan era
Alumni of Trinity College, Cambridge
Fellows of Trinity College, Cambridge
16th-century English astronomers |
https://en.wikipedia.org/wiki/Multiplicatively%20closed%20set | In abstract algebra, a multiplicatively closed set (or multiplicative set) is a subset S of a ring R such that the following two conditions hold:
,
for all .
In other words, S is closed under taking finite products, including the empty product 1.
Equivalently, a multiplicative set is a submonoid of the multiplicative monoid of a ring.
Multiplicative sets are important especially in commutative algebra, where they are used to build localizations of commutative rings.
A subset S of a ring R is called saturated if it is closed under taking divisors: i.e., whenever a product xy is in S, the elements x and y are in S too.
Examples
Examples of multiplicative sets include:
the set-theoretic complement of a prime ideal in a commutative ring;
the set , where x is an element of a ring;
the set of units of a ring;
the set of non-zero-divisors in a ring;
for an ideal I.
the Jordan–Pólya numbers, the multiplicative closure of the factorials
Properties
An ideal P of a commutative ring R is prime if and only if its complement is multiplicatively closed.
A subset S is both saturated and multiplicatively closed if and only if S is the complement of a union of prime ideals. In particular, the complement of a prime ideal is both saturated and multiplicatively closed.
The intersection of a family of multiplicative sets is a multiplicative set.
The intersection of a family of saturated sets is saturated.
See also
Localization of a ring
Right denominator set
Notes
References
M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra, Addison-Wesley, 1969.
David Eisenbud, Commutative algebra with a view toward algebraic geometry, Springer, 1995.
Serge Lang, Algebra 3rd ed., Springer, 2002.
Commutative algebra |
https://en.wikipedia.org/wiki/Definitions%20of%20mathematics | Mathematics has no generally accepted definition. Different schools of thought, particularly in philosophy, have put forth radically different definitions. All proposed definitions are controversial in their own ways.
Early definitions
Pythagoras stated "All is number. Number rules the universe", paraphrased by Plato, from which Platonism historically was the main mathematics school of thought and is still large. His student Aristotle defined mathematics as "the science of quantity", and this definition prevailed until the 18th century. In his classification of the sciences, he further distinguished between arithmetic, which studies discrete quantities, and geometry that studies continuous quantities. However, Aristotle also noted a focus on quantity alone may not distinguish mathematics from sciences like physics; in his view, abstraction and studying quantity as a property "separable in thought" from real instances set mathematics apart. Peripatetic/Aristotelian Realism influenced most modern Realism.
Auguste Comte's definition tried to explain the role of mathematics in coordinating phenomena in all other fields:
The science of indirect measurement. Auguste Comte 1851
The "indirectness" in Comte's definition refers to determining quantities that cannot be measured directly, such as the distance to planets or the size of atoms, by means of their relations to quantities that can be measured directly.
Greater abstraction and competing philosophical schools
In the 19th century, as mathematics branched out into abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and measurement, mathematicians and philosophers began to propose a variety of new definitions.
Three leading types of definition of mathematics today are called logicist, intuitionist, and formalist, each reflecting a different philosophy of mathematics. However, each has its own flaws, none have achieved mainstream consensus, and all three appear irreconcilable.
Logicism
With mathematicians pursuing greater rigor and more abstract foundations, some proposed defining mathematics purely in terms of deduction and logic:
Mathematics is the science that draws necessary conclusions. Benjamin Peirce 1870
All Mathematics is Symbolic Logic. Bertrand Russell 1903
Peirce did not think that mathematics is the same as logic, since he thought mathematics makes only hypothetical assertions, not categorical ones. Russell's definition, on the other hand, expresses the logicist view without reservation.
Intuitionism
Rather than characterize mathematics by deductive logic, intuitionism views mathematics as primarily about the construction of ideas in the mind:
The only possible foundation of mathematics must be sought in this construction under the obligation carefully to watch which constructions intuition allows and which not. L. E. J. Brouwer 1907
... intuitionist mathematics is nothing more nor less than an investigation of the u |
https://en.wikipedia.org/wiki/2009%20Puerto%20Rico%20Islanders%20season | The 2009 season is the Puerto Rico Islanders 6th season in the USL First Division. This article shows player statistics and all matches (official and friendly) that the club have and will play during the 2009 season. It also includes matched played in 2009 for the CONCACAF Champions League 2008–09 and CONCACAF Champions League 2009–10.
Club
Management
Kit
Squad
First team
As of July 4, 2009
2009 transfers
In
Out
Competitions
Overall
USL 1
Results summary
Results by match day (regular season)
* Positions are tabulated at the end of each week.
CONCACAF Champions League 2008–2009
Championship round (bracket)
Matches
Friendlies
* A round of penalty kicks was played after the match, this was already agreed upon by both sides regardless of the match's outcome, Austin won this 3-0.
USL-1 regular season
All kickoff times are in EST. Names in brackets are players who were awarded the assist for the goal.
CONCACAF Champions League 2008-09
CFU Club Championship 2009
CONCACAF Champions League 2009-2010
Squad statistics
Competitive matches only. Numbers in brackets indicate appearances as a substitute under the Appearance column and number of assists under the Goal column.
Updated to games played June 20, 2009.
Players
Goalkeepers
Disciplinary record
Only players with at least one card included.
Updated to games played May 15, 2009.
References
2009
Puerto Rico Islanders
Puerto Rico Islanders
Islanders |
https://en.wikipedia.org/wiki/Analytic%20polyhedron | In mathematics, especially several complex variables, an analytic polyhedron is a subset of the complex space of the form
where is a bounded connected open subset of , are holomorphic on and is assumed to be relatively compact in . If above are polynomials, then the set is called a polynomial polyhedron. Every analytic polyhedron is a domain of holomorphy and it is thus pseudo-convex.
The boundary of an analytic polyhedron is contained in the union of the set of hypersurfaces
An analytic polyhedron is a Weil polyhedron, or Weil domain if the intersection of any of the above hypersurfaces has dimension no greater than .
See also
Behnke–Stein theorem
Bergman–Weil formula
Oka–Weil theorem
Notes
References
.
(also available as ).
.
.
.
.
. Notes from a course held by Francesco Severi at the Istituto Nazionale di Alta Matematica (which at present bears his name), containing appendices of Enzo Martinelli, Giovanni Battista Rizza and Mario Benedicty. An English translation of the title reads as:-"Lectures on analytic functions of several complex variables – Lectured in 1956–57 at the Istituto Nazionale di Alta Matematica in Rome".
Several complex variables |
https://en.wikipedia.org/wiki/William%20Benjamin%20Smith | William Benjamin Smith (October 26, 1850 – August 6, 1934) was a professor of mathematics at Tulane University, best known as a proponent of the Christ myth theory.
Biography
In a series of books, beginning with Ecce Deus: The Pre-Christian Jesus, published in 1894, and ending with The Birth of the Gospel, published posthumously in 1954, Smith argued that the earliest Christian sources, particularly the Pauline epistles, stress Christ's divinity at the expense of any human personality, and that this would have been implausible, if there had been a human Jesus. Smith therefore argued that Christianity's origins lay in a pre-Christian Jesus cult—that is, a Jewish sect had worshipped a divine being Jesus in the centuries before the human Jesus was supposedly born. Evidence for this cult was found in Hippolytus' mention of the Naassenes and Epiphanius' report of a Nasarene sect that existed before Christ, as well as passages in Acts. The seemingly historical details in the New Testament were built by the early Christian community around narratives of the pre-Christian Jesus.
Smith also argued against the historical value of non-Christian writers regarding Jesus, particularly Josephus and Tacitus.
Infamously, Smith was also a white supremacy advocate whose book The Color Line: A Brief on Behalf of the Unborn (1905) argued for the racial inferiority of Negroes. He unsuccessfully challenged the studies of races by American anthropologist Franz Boas.
Translator
Upon his death in 1934, Smith left a partial translation of Homer's Iliad. This work was completed by his old Tulane colleague Walter Miller and when published in 1944 was the first English translation in the original dactylic hexameter.
Publications
Books
Elementary Co-Ordinate Geometry for Collegiate Use and Private Study (Boston: Ginn & Company, 1886)
James Sidney Rollins: Memoir (New York: De Vinne Press, 1891)
Introductory Modern Geometry of Point, Ray, and Circle (New York: Macmillan & Co, 1893)
Color Line: A Brief on Behalf of the Unborn (New York: McClure, Phillips & Company, 1905)
Der Vorchristliche Jesus (Giessen: Töpelmann, 1906) [with an introduction by Paul Wilhelm Schmiedel]
The Silence of Josephus & Tacitus (Chicago: Open Court Publishing Company, 1910)
Ecce Deus: Studies of Primitive Christianity (Open Court Publishing Company, 1913)
The Birth of the Gospel: A Study of the Origin and Purport of the Primitive Allegory of the Jesus (1957) [edited by Addison Gulick]
Papers
Smith, William Benjamin. (1903). The Pauline Manuscripts F and G. A Text-Critical Study. The American Journal of Theology 7 (3): 452-485.
Smith, William Benjamin. (1911). The Pre-Christian Jesus. The American Journal of Theology 15 (2): 259-265.
Smith, William Benjamin. (1914). Latest Lights and Shadows on the Jesus Question. The Monist 24 (4): 618-634.
Smith, William Benjamin. (1919). What Remaineth? The Monist 29 (1): 1-31.
See also
Christ myth theory
Footnotes
References
External links
1 |
https://en.wikipedia.org/wiki/Behnke%E2%80%93Stein%20theorem | In mathematics, especially several complex variables, the Behnke–Stein theorem states that a union of an increasing sequence (i.e., ) of domains of holomorphy is again a domain of holomorphy. It was proved by Heinrich Behnke and Karl Stein in 1938.
This is related to the fact that an increasing union of pseudoconvex domains is pseudoconvex and so it can be proven using that fact and the solution of the Levi problem. Though historically this theorem was in fact used to solve the Levi problem, and the theorem itself was proved using the Oka–Weil theorem. This theorem again holds for Stein manifolds, but it is not known if it holds for Stein space.
References
Several complex variables
Theorems in complex analysis |
https://en.wikipedia.org/wiki/Hourya%20Benis%20Sinaceur | Hourya Sinaceur is a Moroccan philosopher. She is an expert in the theory and history of mathematics.
Biography
Hourya Benis was born in 1940 in Casablanca in Morocco. Sinaceur worked for Paris-Sorbonne University and the French National Centre for Scientific Research which is also in Paris, and the URS in Rabat. She has also served as a member of the National French Committee of History and Philosophy of Science (Comité National Francais d'Histoire et de Philosophie des Sciences.
Books
She is the author of the book Corps et Modèles (1991), translated into English as Field and Models: From Sturm to Tarski and Robinson (Birkhauser, 2003). and of Functions and Generality of Logic: Reflections on Dedekind's and Frege's logicisms (Springer, 2015).
References
External links
Sinaceur, H., 2001. "Alfred Tarski: Semantic shift, heuristic shift in metamathematics", Synthese 126: 49–65.
"Alfred Tarski Life and Logic", Review by Sinaceur
Presentation (in French) and bibliography of recent work on IHPST (retrieved on Feb. 22, 2009)
Academic staff of the University of Paris
Moroccan writers
Moroccan philosophers
Moroccan academics
Living people
People from Casablanca
Year of birth missing (living people)
Moroccan women philosophers
Women mathematicians
Philosophers of science
Moroccan women writers
Academic staff of Paris-Sorbonne University |
https://en.wikipedia.org/wiki/Ant%C3%ADmano | Antímano is a district of Caracas, Venezuela. It is part of Libertador municipality. According to a 2007 estimate of the National Institute of Statistics of Venezuela, it had a population of 150,971 people in 2007.
The name Antímano derives from a combination of the words Atamanona and Amatima, the names of two indigenous groups which lived in the area before the Spanish Conquest. Antímano was established in 1621 as an agricultural village, and remained rural until the first part of the twentieth century. Towards the end of the nineteenth century the Venezuelan President Antonio Guzmán Blanco built a country house in Antímano, calling it "La Pequeña Versalles" (Little Versailles). From the mid-1940s Antímano began to develop as an industrial zone, with the first factories producing Polar beer and Pepsi. The steel company Sidetur was founded here in 1948.
The house of Guzman Blanco fell into disuse for over 30 years (despite being declared a National Monument) and was eventually restored in 2004, the building being turned into a Sociocultural Complex, and its grounds converted into a sports facility with baseball, football and basketball fields.
Since it is a large neighborhood, it is possible to get there on a number of Caracas Metro stations on Line 2 (the green one) including Antímano, Carapita, and Mamera.
References
Parishes of Capital District (Venezuela) |
https://en.wikipedia.org/wiki/FEE%20method | In mathematics, the FEE method, or fast E-function evaluation method, is the method of fast summation of series of a special form. It was constructed in 1990 by Ekaterina Karatsuba and is so-named because it makes fast computations of the Siegel -functions possible, in particular of .
A class of functions, which are "similar to the exponential function," was given the name "E-functions" by Carl Ludwig Siegel. Among these functions are such special functions as the hypergeometric function, cylinder, spherical functions and so on.
Using the FEE, it is possible to prove the following theorem:
Theorem: Let be an elementary transcendental function, that is the exponential function, or a
trigonometric function, or an elementary algebraic function, or their superposition, or their inverse, or a superposition of the inverses. Then
Here is the complexity of computation (bit) of the function with accuracy up to digits, is the complexity of multiplication of two -digit integers.
The algorithms based on the method FEE include the algorithms for fast calculation of any elementary transcendental function for any value of the argument, the classical constants e, the Euler constant the Catalan and the Apéry constants, such higher transcendental functions as the Euler gamma function and its derivatives, the hypergeometric, spherical, cylinder (including the Bessel) functions and some other functions for
algebraic values of the argument and parameters, the Riemann zeta function for integer values of the argument and the Hurwitz zeta function for integer argument and algebraic values of the parameter, and also such special integrals as the integral of probability, the Fresnel integrals, the integral exponential function, the trigonometric integrals, and some other integrals for algebraic values of the argument with the complexity bound which is close to the optimal one, namely
At present, only the FEE makes it possible to calculate fast the values of the functions from the class of higher transcendental functions, certain special integrals of mathematical physics and such classical constants as Euler's, Catalan's and Apéry's constants. An additional advantage of the method FEE is the possibility of parallelizing the algorithms based on the FEE.
FEE computation of classical constants
For fast evaluation of the
constant one can use the Euler formula
and apply the FEE to sum the Taylor series for
with the remainder terms which satisfy the bounds
and for
To calculate by the
FEE it is possible to use also other approximations In all cases the complexity is
To compute the Euler constant gamma with accuracy up to
digits, it is necessary to sum by the FEE two series. Namely, for
The complexity is
To evaluate fast the constant
it is possible to apply the
FEE to other approximations.
FEE computation of certain power series
By the FEE the two following series are calculated fast:
under the assumption that are
integers,
and are constant |
https://en.wikipedia.org/wiki/Verbal%20subgroup | In mathematics, in the area of abstract algebra known as group theory, a verbal subgroup is a subgroup of a group that is generated by all elements that can be formed by substituting group elements for variables in a given set of words.
For example, given the word xy, the corresponding verbal subgroup is generated by the set of all products of two elements in the group, substituting any element for x and any element for y, and hence would be the group itself. On the other hand, the verbal subgroup for the set of words is generated by the set of squares and their conjugates. Verbal subgroups are the only fully characteristic subgroups of a free group and therefore represent the generic example of fully characteristic subgroups, .
Another example is the verbal subgroup for , which is the derived subgroup.
References
Infinite group theory
Subgroup properties |
https://en.wikipedia.org/wiki/Katate%20Masatsuka | is a Japanese part-time author. He is an author of unique three-volume high-school Math textbooks (in Japanese) titled
Seishun High-School Mathematics and a technical book on
Computational fluid dynamics (CFD) titled I do like CFD, VOL.1. He is also a singer and songwriter with over 100 songs written so far
(2003–2009). Other creations such as Kanji-humanoids can be found at his official website.
He also runs a Japanese school at his home to establish a new style oversea Japanese education.
He was born in Sakai, Osaka, Japan, in 1971. He graduated from Tokai University in 1994 and entered the graduate school of the University of Tokyo. He then moved to the University of Michigan to study Computational Fluid Dynamics. During his graduate study in Michigan, he also worked at Koby International Academy in Novi as a part-time instructor in Math and Science. He obtained his Ph.D. in 2001 and stayed in Michigan as a post-doctoral researcher until 2007 when he moved to Virginia. Based on his 10 years of experience in teaching high-school Math, he wrote three-volume Math textbooks. Also, he wrote a book on Computational fluid dynamics, I do like CFD, VOL.1, in which he explains fundamental concepts and formulas in CFD by explaining how he likes them. The second edition of I do like CFD, VOL.1 was released on October 1, 2013, in both hard copy and PDF versions. The PDF version is sponsored by Software Cradle and it is available for free. The second volume of the series has not yet been completed. His interest lies exclusively in creating something new and unique. He has also published a lot of articles in computational physics.
Education
Ph.D. in Aerospace Engineering and Scientific Computing, 2001 University of Michigan
M.S., in Applied Mathematics, 1999 University of Michigan
M.S.E. in Aerospace Engineering, 1996 University of Michigan
B.E. in Aerospace Engineering, 1994 Tokai University
References
Japanese writers
Living people
People from Sakai, Osaka
1971 births
University of Michigan alumni
Tokai University alumni |
https://en.wikipedia.org/wiki/Young%E2%80%93Fibonacci%20lattice | In mathematics, the Young–Fibonacci graph and Young–Fibonacci lattice, named after Alfred Young and Leonardo Fibonacci, are two closely related structures involving sequences of the digits 1 and 2. Any digit sequence of this type can be assigned a rank, the sum of its digits: for instance, the rank of 11212 is 1 + 1 + 2 + 1 + 2 = 7. As was already known in ancient India, the number of sequences with a given rank is a Fibonacci number. The Young–Fibonacci lattice is an infinite modular lattice having these digit sequences as its elements, compatible with this rank structure. The Young–Fibonacci graph is the graph of this lattice, and has a vertex for each digit sequence. As the graph of a modular lattice, it is a modular graph.
The Young–Fibonacci graph and the Young–Fibonacci lattice were both initially studied in two papers by and . They are named after the closely related Young's lattice and after the Fibonacci number of their elements at any given rank.
Digit sequences with a given rank
A digit sequence with rank may be formed either by adding the digit 2 to a sequence with rank , or by adding the digit 1 to a sequence with rank . If is the function that maps to the number of different digit sequences of that rank, therefore, satisfies the recurrence relation defining the Fibonacci numbers, but with slightly different initial conditions: (there is one rank-0 string, the empty string, and one rank-1 string, consisting of the single digit 1). These initial conditions cause the sequence of values of to be shifted by one position from the Fibonacci numbers: .
In the ancient Indian study of prosody, the Fibonacci numbers were used to count the number of different sequences of short and long syllables with a given total length; if the digit 1 corresponds to a short syllable, and the digit 2 corresponds to a long syllable, the rank of a digit sequence measures the total length of the corresponding sequence of syllables. See the Fibonacci number article for details.
Graphs of digit sequences
The Young–Fibonacci graph is an infinite graph, with a vertex for each string of the digits "1" and "2" (including the empty string). The neighbors of a string s are the strings formed from s by one of the following operations:
Insert a "1" into s, prior to the leftmost "1" (or anywhere in s if it does not already contain a "1").
Change the leftmost "1" of s into a "2".
Remove the leftmost "1" from s.
Change a "2" that does not have a "1" to the left of it into a "1".
It is straightforward to verify that each operation can be inverted: operations 1 and 3 are inverse to each other, as are operations 2 and 4. Therefore, the resulting graph may be considered to be undirected. However, it is usually considered to be a directed acyclic graph in which each edge connects from a vertex of lower rank to a vertex of higher rank.
As both and observe, this graph has the following properties:
It is connected: any nonempty string may have its rank reduced by some |
https://en.wikipedia.org/wiki/Frink%20ideal | In mathematics, a Frink ideal, introduced by Orrin Frink, is a certain kind of subset of a partially ordered set.
Basic definitions
LU(A) is the set of all common lower bounds of the set of all common upper bounds of the subset A of a partially ordered set.
A subset I of a partially ordered set (P, ≤) is a Frink ideal, if the following condition holds:
For every finite subset S of I, we have LU(S) I.
A subset I of a partially ordered set (P, ≤) is a normal ideal or a cut if LU(I) I.
Remarks
Every Frink ideal I is a lower set.
A subset I of a lattice (P, ≤) is a Frink ideal if and only if it is a lower set that is closed under finite joins (suprema).
Every normal ideal is a Frink ideal.
Related notions
pseudoideal
Doyle pseudoideal
References
Order theory |
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