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https://en.wikipedia.org/wiki/1976%E2%80%9377%20Football%20League%20First%20Division | Statistics of Football League First Division in the 1976–77 season.
Overview
Liverpool retained their league championship trophy and won their first European Cup to confirm Bob Paisley as a successful replacement for Bill Shankly in his third season at the helm. Tottenham Hotspur and Stoke City's long spells in the First Division came to an end with relegation. Stoke sacked their manager Tony Waddington. On the last day of the season, Coventry City and Bristol City played out a controversial 2–2 draw, with play virtually stopping when it was heard that Sunderland had lost to Everton. Both clubs survived while Sunderland were relegated.
After Manchester United manager Tommy Docherty had admitted his affair with the wife of the club's physiotherapist, the club's directors decided that he had broken their moral code and he was sacked.
League standings
Stats
Record
Most wins: Liverpool (23)
Fewest losses: Manchester City (7)
Most goals scored: Aston Villa (76)
Fewest goals conceded: Liverpool (33)
Best goal difference ratio: Liverpool (+29)
Most draws: Derby County (19)
Fewest draws: Aston Villa (7)
Most losses: Tottenham Hotspur
Fewest wins: Derby County (9)
Fewest goals scored: Stoke City (28)
Most goals conceded: Tottenham Hotspur (72)
Worst goal difference ratio: Tottenham Hotspur (–24)
Results
Managerial changes
Team locations
References
RSSSF
Football League First Division seasons
Eng
1976–77 Football League
1976–77 in English football leagues
lt:Anglijos futbolo varžybos 1976–1977 m.
hu:1976–1977-es angol labdarúgó-bajnokság (első osztály)
ru:Футбольная лига Англии 1976-1977 |
https://en.wikipedia.org/wiki/Bethany%20Rose%20Marsh | Bethany Rose Marsh is a mathematician working in the areas of cluster algebras, representation theory of finite-dimensional algebras, homological algebra, tilting theory, quantum groups, algebraic groups, Lie algebras and Coxeter groups. Marsh currently works at the University of Leeds as a Professor of pure mathematics. She was a EPSRC Leadership Fellow from 2008 to 2014. In addition to her duties at the University of Leeds, Marsh was an editor of the Glasgow Mathematical Journal from 2008 to 2013 and served on the London Mathematical Society editorial board from 2014 to 2018.
Awards
In July 2009, Marsh was awarded the Whitehead Prize by the London Mathematical Society for her work on representation theory, and especially for her research on cluster categories and cluster algebras.
Publications
References
External links
Academics of the University of Leeds
Living people
Whitehead Prize winners
Alumni of the University of Oxford
Algebraists
20th-century British mathematicians
21st-century British mathematicians
British women mathematicians
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Nyoni%2C%20Tanzania | Nyoni is a ward in Mbinga District the Ruvuma Region of the Tanzanian Southern Highlands. It is located along the A19 road.
In 2016, the Tanzania National Bureau of Statistics report there were 11,885 people in the ward; this is up from a population of 10,918 in 2012.
References
Populated places in Iringa Region |
https://en.wikipedia.org/wiki/Syntette | The syntette combines the benefits of a universal curette and a Gracey curette in one. It is a dental instrument used by dentists and dental hygienists to remove calculus subgingivally on the mesial and distal surfaces on all teeth throughout the mouth.
The syntette is held parallel to the tooth and pushed under the gingiva, rotated slightly and moved upwards in a ‘pull’ stroke (vertical movement). Care must be taken not to get it stuck between the contact points of the teeth. The correct seating positions must be used, which position depends on where in the mouth you are working. Fulcrums (resting one finger on an adjacent tooth for stability) must always be used, preferably with the shank resting on the fulcrum finger.
The syntette has two elliptical cutting edges and a rounded toe. Double ended – one end for buccal/labial surfaces, the other for palatal/lingual surfaces.
The syntette was created by Leif Ericsson, Västervik Hospital, Västervik, Sweden in the 1980s. Leif Ericsson himself describes the inventing process and naming of the instrument as follows:
"Special finishing curettes Gracey 11/12 and 13/14 had been on the market since many years. Two popular instruments which, however, demanded switching instrument in the same interproximal space: Gracey 11/12 for mesial surfaces and Gracey 13/14 for distal surfaces. A simple thought – combine the instruments! A synthesis of two curettes – a Syntette."
The Syntette has been featured in several peer reviewed articles.
In addition to the original Syntette, a similar design was introduced under the brand names Scandette and Double Gracey.
References
Dental equipment |
https://en.wikipedia.org/wiki/Eduard%20Ritter%20von%20Weber | Eduard Ritter von Weber (May 12, 1870 in Munich – June 20, 1934 in Würzburg) was a German mathematician.
Von Weber attended the and afterward from 1888-1894 pursued studies in mathematics in Munich, Göttingen, and Paris. In 1893 he was awarded the Ph.D. from the University of Munich (his dissertation being titled Studien zur Theorie der infinitesimalen Transformationen, Gustav C. Bauer, advisor). Habilitation followed at the University of Munich in 1895, becoming full professor there in 1903. He moved to the University of Würzburg in 1907.
Von Weber concerned himself particularly with partial differential equations, in particular the Pfaff problem, and wrote the article "Partial Differential Equations" in the Enzyklopädie der mathematischen Wissenschaften (Encyclopedia of the Mathematical Sciences).
Von Weber had versatile interests and spoke numerous languages, including Russian, Portuguese, Spanish, Norwegian, Persian, Arabic, Hebrew, and Irish.
References
Würzburger Mathematikgeschichte: Die Periode der Analytiker, University of Würzburg
External links
1870 births
1934 deaths
Bavarian nobility
19th-century German mathematicians
Mathematical analysts
Scientists from Munich
Ludwig Maximilian University of Munich alumni
Academic staff of the Ludwig Maximilian University of Munich
Academic staff of the University of Würzburg
20th-century German mathematicians |
https://en.wikipedia.org/wiki/Math-U-See | Math-U-See, developed by Steve Demme is a K–12 homeschool mathematics curriculum, emphasizing mastery of materials and encouraging instructors to let students learn at their own pace. Because of the tutor style model, Math-U-See is being adopted by special education departments Response to intervention programs. Math-U-See curricula includes Primer, Alpha, Beta, Gamma, Delta, & Epsilon as well as other books.
Notes
External links
Math-U-See website
Mathematics education reform
Homeschooling |
https://en.wikipedia.org/wiki/Jacobi%20method%20for%20complex%20Hermitian%20matrices | In mathematics, the Jacobi method for complex Hermitian matrices is a generalization of the Jacobi iteration method. The Jacobi iteration method is also explained in "Introduction to Linear Algebra" by .
Derivation
The complex unitary rotation matrices Rpq can be used for Jacobi iteration of complex Hermitian matrices in order to find a numerical estimation of their eigenvectors and eigenvalues simultaneously.
Similar to the Givens rotation matrices, Rpq are defined as:
Each rotation matrix, Rpq, will modify only the pth and qth rows or columns of a matrix M if it is applied from left or right, respectively:
A Hermitian matrix, H is defined by the conjugate transpose symmetry property:
By definition, the complex conjugate of a complex unitary rotation matrix, R is its inverse and also a complex unitary rotation matrix:
Hence, the complex equivalent Givens transformation of a Hermitian matrix H is also a Hermitian matrix similar to H:
The elements of T can be calculated by the relations above. The important elements for the Jacobi iteration are the following four:
Each Jacobi iteration with RJpq generates a transformed matrix, TJ, with TJp,q = 0. The rotation matrix RJp,q is defined as a product of two complex unitary rotation matrices.
where the phase terms, and are given by:
Finally, it is important to note that the product of two complex rotation matrices for given angles θ1 and θ2 cannot be transformed into a single complex unitary rotation matrix Rpq(θ). The product of two complex rotation matrices are given by:
References
.
Numerical linear algebra |
https://en.wikipedia.org/wiki/2001%E2%80%9302%20National%20Football%20League%20%28Bangladesh%29 | Statistics of 2001–02 National Football League (Bangladesh).
Overview
Mohammedan SC were crowned champions on 24 May 2002.
References
RSSSF
2
1
1 |
https://en.wikipedia.org/wiki/2003%20National%20Football%20League%20%28Bangladesh%29 | Statistics of 2003 National Football League (Bangladesh).
Overview
Muktijoddha Sangsad KC won the championship.
First stage
Group 1
Group 2
Playoff
Semifinals
Wanderers Club 0-1 Muktijoddha Sangsad KC
Mohammedan SC 1-0 Abahani Ltd
Final
Mohammedan SC 1-1 (pen 2–3) Muktijoddha Sangsad KC
Muktijoddha Sangsad KC won the championship.
References
RSSSF
3
1 |
https://en.wikipedia.org/wiki/2004%20National%20Football%20League%20%28Bangladesh%29 | Statistics of the 2004 National Football League (Bangladesh).
Overview
Brothers Union won the championship.
Playoff
Semifinals
Muktijoddha Sangsad KC 2-0 Mohammedan SC
Brothers Union 2-1 Abahani Ltd
Third place
Abahani Ltd 3-2 Mohammedan SC
Final
Muktijoddha Sangsad KC 0-0 (pen 2–4) Brothers Union
Brothers Union won the championship.
References
RSSSF
4
1 |
https://en.wikipedia.org/wiki/1985%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 1985 season.
Overview
April 25 Sports Club won the championship.
References
RSSSF
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/1986%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 1986 season.
Overview
4.25 Sports Club won the championship.
References
RSSSF
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/1987%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 1987 season.
Overview
4.25 Sports Club won the championship
References
RSSSF
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/1988%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 1988 season.
Overview
4.25 Sports Club won the championship.
References
RSSSF
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/1989%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 1989 season.
Overview
Chandongja Sports Club won the championship.
References
RSSSF
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/1990%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 1990 season.
Overview
4.25 Sports Club won the championship.
References
RSSSF
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/1991%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 1991 season.
Overview
Pyongyang Sports Club won the championship.
References
RSSSF
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/1992%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 1992 season.
Overview
April 25 SC won the championship.
References
RSSSF
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/1993%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 1993 season.
Overview
April 25 SC won the championship.
References
RSSSF
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/1994%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 1994 season.
Overview
April 25 SC won the championship.
References
RSSSF
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/1995%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 1995 season.
Overview
April 25 Sports Club won the championship.
League standings
References
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/1996%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 1996 season.
Overview
Kigwancha Sports Club won the championship. Kigwanch'a and Rimyongsu Sports Club finished the season tied with 41 points in 22 matches played, but Kigwanch'a finished first on goal differential, having scored one goal more than Rimyŏngsu. April 25 finished third, with 40 points.
References
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/1997%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 1997 season.
Overview
Kigwancha Sports Club won the championship.
References
RSSSF
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/1998%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 1998 season.
Overview
Kigwancha Sports Club won the championship.
References
RSSSF
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/1999%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 1999 season.
Overview
Kigwancha Sports Club won the championship.
References
RSSSF
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/2000%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 2000 season.
Overview
Kigwancha Sports Club won the championship.
References
RSSSF
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/2001%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 2001 season.
Overview
Amrokgang Sports Club won the championship.
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/2002%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 2002 season.
Overview
April 25 won the championship, Rimyŏngsu finished second, and Amrokkang finished third. P'yŏngyang City, Wŏlmido, and the North Hwanghae Provincial College of Physical Education also took part in the competition.
The 2002 edition of the Mangyongdae Cup was won by April 25.
References
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/2003%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 2003 season.
Overview
4.25 Sports Club won the championship.
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/2004%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 2004 season.
Overview
Pyongyang City Sports Club won the championship.
References
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/2005%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 2005 season.
Overview
Pyongyang City Sports Club won the championship, their second in a row.
References
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/2006%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 2006 season.
Overview
Amrokkang won the championship; Kigwanch'a finished in third place, and Kyŏnggong'ŏp finished 6th. 4.25, Rimyŏngsu, P'yŏngyang City, and Wŏlmido also took part in the competition.
References
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/2007%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 2007 season. The 2007 edition of the Technical Innovation Contest was played with teams in two groups, with the first and second-place finishers in each group advancing to an elimination stage. In the semi-finals, P'yŏngyang City defeated Kigwanch'a 2–1, and Amrokkang defeated Kyŏnggong'ŏp. In the final, P'yŏngyang City defeated Amrokkang 2–0, and Kyŏnggong'ŏp defeated Kigwanch'a 3–1 in the third place match.
References
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/2008%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 2008 season.
Overview
Amrokkang won both the championship, and the 2008 edition of the Man'gyŏngdae Prize.
References
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/2009%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 2009 season.
Overview
P'yŏngyang City won the championship. Chadongch'a and Wŏlmido were relegated to the 2nd level.
Clubs
The football clubs in the season were as follows:
April 25 (Namp'o)
Amrokkang (P'yŏngyang)
Ch'ilbosan
Chadongch'a (Ch'ŏngjin)
Kigwanch'a (Sinŭiju)
P'yŏngyang City (P'yŏngyang)
Rimyŏngsu (Sariwŏn)
Sobaeksu (P'yŏngyang)
Wŏlmido (Kimch'aek)
Cup competitions
April 25 won the seventh edition of the Man'gyŏngdae Prize, whilst second division side Kyŏnggong'ŏp defeated Amrokkang 1-0 to win the Republican Championship.
References
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/2010%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 2010 season.
Highest Class Football League
From this season, The name of league changed to Highest Class Football League (Chosŏn'gŭl: 최상급축구련맹전; Hanja: 最上級蹴球聯盟戰).
Clubs
April 25
Amrokkang
Ponghwasan
Ch'ilbosan
Kyŏnggong'ŏp
Kigwanch'a
Man'gyŏngbong
P'yŏngyang City
Rimyŏngsu
Sobaeksu
Cup competitions
Man'gyŏngbong won the Republican Championship. Sobaeksu won the first known edition of the Poch'ŏnbo Torch Prize, with P'yŏngyang City being the runners-up, and Rimyŏngsu won the Man'gyŏngdae Prize.
References
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/1997%E2%80%9398%20Lebanese%20Premier%20League | Statistics of Lebanese Premier League for the 1997–98 season.
Overview
Al-Ansar won the championship.
League standings
References
RSSSF
Leb
1997–98 in Lebanese football
Lebanese Premier League seasons
1997–98 Lebanese Premier League |
https://en.wikipedia.org/wiki/1998%E2%80%9399%20Lebanese%20Premier%20League | Statistics of Lebanese Premier League for the 1998–99 season.
Overview
Al-Ansar won the championship.
League standings
References
RSSSF
Leb
1998–99 in Lebanese football
Lebanese Premier League seasons
1998–99 Lebanese Premier League |
https://en.wikipedia.org/wiki/1999%E2%80%932000%20Lebanese%20Premier%20League | Statistics of Lebanese Premier League for the 1999–2000 season.
Overview
Al-Nejmeh won the championship.
League standings
References
RSSSF
Lebanon
1999–2000 in Lebanese football
Lebanese Premier League seasons
1999–2000 Lebanese Premier League |
https://en.wikipedia.org/wiki/2000%E2%80%9301%20Lebanese%20Premier%20League | Statistics of Lebanese Premier League for the 2000–01 season.
Temporary Official Final table
Revoked Final table
References
RSSSF
Lebanese Premier League seasons
Leb
2000–01 in Lebanese football
2000–01 Lebanese Premier League |
https://en.wikipedia.org/wiki/2001%E2%80%9302%20Lebanese%20Premier%20League | Statistics of Lebanese Premier League for the 2001–02 season.
Overview
Al-Nejmeh won the championship.
League standings
References
RSSSF
Lebanese Premier League seasons
Leb
2001–02 in Lebanese football
2001–02 Lebanese Premier League |
https://en.wikipedia.org/wiki/2002%E2%80%9303%20Lebanese%20Premier%20League | Statistics of Lebanese Premier League for the 2002–03 season.
Overview
Tripoli SC won the championship.
League standings
Playoff
References
RSSSF
Leb
2002–03 in Lebanese football
Lebanese Premier League seasons
2002–03 Lebanese Premier League |
https://en.wikipedia.org/wiki/2003%E2%80%9304%20Lebanese%20Premier%20League | Statistics of Lebanese Premier League for the 2003–04 season.
Overview
Al Nejmeh won the championship.
League standings
References
RSSSF
Leb
2003–04 in Lebanese football
Lebanese Premier League seasons
2003–04 Lebanese Premier League |
https://en.wikipedia.org/wiki/1973%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 1973 season.
Overview
Polícia de Segurança Pública won the championship.
References
RSSSF
Macau
Macau
Campeonato da 1ª Divisão do Futebol seasons
1973 in Macau |
https://en.wikipedia.org/wiki/1984%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 1984 season.
Overview
Wa Seng won the championship.
References
RSSSF
Macau
Macau
Campeonato da 1ª Divisão do Futebol seasons
football |
https://en.wikipedia.org/wiki/1986%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 1986 season.
Overview
Hap Kuan won the championship.
References
RSSSF
Macau
Macau
Campeonato da 1ª Divisão do Futebol seasons
football |
https://en.wikipedia.org/wiki/1987%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 1987 season.
Overview
Hap Kuan won the championship.
References
RSSSF
Macau
Macau
Campeonato da 1ª Divisão do Futebol seasons
football |
https://en.wikipedia.org/wiki/1988%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 1988 season.
Overview
Wa Seng won the championship.
References
RSSSF
Macau
Macau
Campeonato da 1ª Divisão do Futebol seasons
football |
https://en.wikipedia.org/wiki/1989%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 1989 season.
Overview
Hap Kuan won the championship.
References
RSSSF
Macau
Macau
Campeonato da 1ª Divisão do Futebol seasons
football |
https://en.wikipedia.org/wiki/1990%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 1990 season.
Overview
Hap Kuan won the championship.
References
RSSSF
Campeonato da 1ª Divisão do Futebol seasons
Macau
Macau
football |
https://en.wikipedia.org/wiki/1991%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 1991 season.
Overview
Sporting de Macau won the championship.
References
RSSSF
Campeonato da 1ª Divisão do Futebol seasons
Macau
Macau
football |
https://en.wikipedia.org/wiki/1992%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 1992 season.
Overview
Lam Pak won the championship.
References
RSSSF
Campeonato da 1ª Divisão do Futebol seasons
Macau
Macau
football |
https://en.wikipedia.org/wiki/1993%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 1993 season.
Overview
Leng Ngan won the championship.
References
RSSSF
Campeonato da 1ª Divisão do Futebol seasons
Macau
Macau
football |
https://en.wikipedia.org/wiki/1994%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 1994 season.
Overview
Lam Pak won the championship.
References
RSSSF
Campeonato da 1ª Divisão do Futebol seasons
Macau
Macau
football |
https://en.wikipedia.org/wiki/1995%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 1995 season.
Overview
Artilheiros won the championship.
References
RSSSF
Campeonato da 1ª Divisão do Futebol seasons
Macau
Macau
football |
https://en.wikipedia.org/wiki/1996%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 1996 season.
Overview
Artilheiros won the championship.
References
RSSSF
Campeonato da 1ª Divisão do Futebol seasons
Macau
Macau
football |
https://en.wikipedia.org/wiki/1997%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 1997 season.
Overview
Lam Pak won the championship.
References
RSSSF
Campeonato da 1ª Divisão do Futebol seasons
Macau
Macau
football |
https://en.wikipedia.org/wiki/1998%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 1998 season.
Overview
Lam Pak won the championship.
References
RSSSF
Campeonato da 1ª Divisão do Futebol seasons
Macau
Macau
football |
https://en.wikipedia.org/wiki/1999%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 1999 season.
Overview
Lam Pak won the championship.
References
RSSSF
Campeonato da 1ª Divisão do Futebol seasons
Macau
Macau
football |
https://en.wikipedia.org/wiki/2000%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 2000 season.
Overview
Polícia de Segurança Pública won the championship.
League standings
References
RSSSF
Campeonato da 1ª Divisão do Futebol seasons
Macau
Macau
1 |
https://en.wikipedia.org/wiki/2001%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 2001 season.
Overview
Lam Pak won the championship.
League standings
References
RSSSF
Campeonato da 1ª Divisão do Futebol seasons
Macau
Macau
1 |
https://en.wikipedia.org/wiki/2002%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 2002 season.
Overview
Monte Carlo won the championship.
League standings
References
RSSSF
Campeonato da 1ª Divisão do Futebol seasons
Macau
Macau
1 |
https://en.wikipedia.org/wiki/2003%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 2003 season.
Overview
Monte Carlo won the championship.
References
RSSSF
Campeonato da 1ª Divisão do Futebol seasons
Macau
Macau
1 |
https://en.wikipedia.org/wiki/2004%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 2004 season.
Overview
Monte Carlo won the championship.
League standings
References
RSSSF
Campeonato da 1ª Divisão do Futebol seasons
Macau
Macau
1 |
https://en.wikipedia.org/wiki/2005%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 2005 season.
Overview
Polícia de Segurança Pública won the championship.
League standings
References
RSSSF
Campeonato da 1ª Divisão do Futebol seasons
Macau
Macau
1 |
https://en.wikipedia.org/wiki/2007%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 2007 season.
Overview
Lam Pak won the championship.
League standings
References
RSSSF
Campeonato da 1ª Divisão do Futebol seasons
Macau
Macau
1 |
https://en.wikipedia.org/wiki/2008%20Campeonato%20da%201%C2%AA%20Divis%C3%A3o%20do%20Futebol | Statistics of Campeonato da 1ª Divisão do Futebol in the 2008 season.
Overview
Monte Carlo won the championship.
League standings
References
RSSSF
Campeonato da 1ª Divisão do Futebol seasons
Macau
Macau
1 |
https://en.wikipedia.org/wiki/International%20Recommendations%20on%20Water%20Statistics | The International Recommendations for Water Statistics (IRWS) is a statistical intermediate output framework developed by the United Nations Statistics Division (UNSD) and approved by the United Nations Statistical Commission (UNSC) that was designed for guiding countries in the development of their water information systems to design and evaluate policies for better water management.
The IRWS are aligned with the United Nations Water Accounts (SEEA-Water), a statistical output framework.
The IRWS consolidates the experiences and practices of countries and international organisations in the field of water statistics, and were developed in collaboration and consultations with many country and international experts.
The IRWS is divided into two main parts followed by annexes. The first part contains the international recommendations with the main concepts, definitions, classifications of statistical units and data items. The second part provides guidance for implementation, covering data sources, data quality, data collection strategies and dissemination. The annexes provide reference information as well as indicators.
References
United Nations Economic and Social Council |
https://en.wikipedia.org/wiki/Fahad%20Al%20Hamad | Fahad Hazza Al Hamad Al Fahad (, born 1 December 1983) is a Kuwaiti former footballer who played as a forward.
Club career statistics
References
1983 births
Living people
Kuwaiti men's footballers
Footballers from Kuwait City
Men's association football forwards
Kuwait men's international footballers
Kazma SC players
Al-Nahda Club (Oman) players
Al-Salmiya SC players
Kuwait Premier League players
Oman Professional League players
Expatriate men's footballers in Oman
Kuwaiti expatriate men's footballers
Kuwaiti expatriate sportspeople in Oman |
https://en.wikipedia.org/wiki/Ian%20Ford | Ian Ford [ FRSE FRCP(Glas) FSCT ] is a professor of biostatistics and a director of the Robertson Centre for Biostatistics, and a former Dean of Faculty of Information and Mathematical Sciences, at the University of Glasgow.
Biography
Ford was born in Glasgow and educated at the former Hamilton Academy. He studied at the University of Glasgow, graduating with a BSc and in 1976, was awarded a PhD in Statistics. From 1976-77, he was visiting Lecturer to the University of Wisconsin-Madison and since then successively Lecturer, Senior Lecturer, Reader, Personal Professor and Professor at the University of Glasgow. He is the first holder of the Chair of Biostatistics at the University.
Ford has been the Director of the Robertson Centre for Biostatistics since 1991 and Director of the Glasgow Clinical Trials Unit. He is also a member of the editorial boards for the international journals, Statistical Methods for Medical Research; Journal of Evaluation in Clinical Practice and Public Library of Science Medicine. He has written numerous papers.
In 1999, Ford was elected Fellow of the Royal Society of Edinburgh. He is also a Fellow of both the International Statistical Institute and the Royal College of Physicians and Surgeons of Glasgow. A member of the Cholesterol Triallists Collaboration and the Fibrinogen Studies Collaboration, Ford is also a member of the American Statistical Association; Statisticians in the Pharmaceutical Industry; the Drug Information Association; the Royal Statistical Society; and the International Society for Clinical Biostatistics.
From 2000–04, Ford served as Dean of the Faculty of Information and Mathematical Sciences, University of Glasgow..
References
External links
Robertson Centre for Biostatistics, University of Glasgow
1951 births
20th-century British biologists
21st-century British biologists
20th-century British mathematicians
21st-century British mathematicians
Academics of the University of Glasgow
Alumni of the University of Glasgow
Biostatisticians
British statisticians
Fellows of the Royal College of Physicians and Surgeons of Glasgow
Fellows of the Royal Society of Edinburgh
Living people
People educated at Hamilton Academy
Scottish biologists
Scottish mathematicians |
https://en.wikipedia.org/wiki/Structuralism%20%28philosophy%20of%20mathematics%29 | Structuralism is a theory in the philosophy of mathematics that holds that mathematical theories describe structures of mathematical objects. Mathematical objects are exhaustively defined by their place in such structures. Consequently, structuralism maintains that mathematical objects do not possess any intrinsic properties but are defined by their external relations in a system. For instance, structuralism holds that the number 1 is exhaustively defined by being the successor of 0 in the structure of the theory of natural numbers. By generalization of this example, any natural number is defined by its respective place in that theory. Other examples of mathematical objects might include lines and planes in geometry, or elements and operations in abstract algebra.
Structuralism is an epistemologically realistic view in that it holds that mathematical statements have an objective truth value. However, its central claim only relates to what kind of entity a mathematical object is, not to what kind of existence mathematical objects or structures have (not, in other words, to their ontology). The kind of existence that mathematical objects have would be dependent on that of the structures in which they are embedded; different sub-varieties of structuralism make different ontological claims in this regard.
Structuralism in the philosophy of mathematics is particularly associated with Paul Benacerraf, Geoffrey Hellman, Michael Resnik, Stewart Shapiro and James Franklin.
Historical motivation
The historical motivation for the development of structuralism derives from a fundamental problem of ontology. Since Medieval times, philosophers have argued as to whether the ontology of mathematics contains abstract objects. In the philosophy of mathematics, an abstract object is traditionally defined as an entity that: (1) exists independent of the mind; (2) exists independent of the empirical world; and (3) has eternal, unchangeable properties. Traditional mathematical Platonism maintains that some set of mathematical elements—natural numbers, real numbers, functions, relations, systems—are such abstract objects. Contrarily, mathematical nominalism denies the existence of any such abstract objects in the ontology of mathematics.
In the late 19th and early 20th century, a number of anti-Platonist programs gained in popularity. These included intuitionism, formalism, and predicativism. By the mid-20th century, however, these anti-Platonist theories had a number of their own issues. This subsequently resulted in a resurgence of interest in Platonism. It was in this historic context that the motivations for structuralism developed. In 1965, Paul Benacerraf published a paradigm changing article entitled "What Numbers Could Not Be". Benacerraf concluded, on two principal arguments, that set-theoretic Platonism cannot succeed as a philosophical theory of mathematics.
Firstly, Benacerraf argued that Platonic approaches do not pass the ontological test. |
https://en.wikipedia.org/wiki/Friedrich-Wilhelm%20Kiel | Friedrich-Wilhelm Kiel (17 May 1934 – 4 April 2022) was a German politician and member of the FDP.
Kiel studied physics, mathematics, and sport at the Karlsruhe Institute of Technology and became a member of the FDP in 1964 whilst teaching at a gymnasium in Ettlingen, where he later became mayor (1966–1970). In 1970, Kiel became mayor of Pforzheim, until 1976, when he was elected to become mayor of Fellbach, a position he held until 2000.
From 1992 until 2001, Kiel was also a member of the Landtag of Baden-Württemberg. For his services to the state, minister-president Erwin Teufel awarded him the Order of Merit of Baden-Württemberg on 5 May 2001. Kiel was made an honorary citizen of Fellbach and the Hungarian city Pécs, whilst the University of Pécs appointed him an honorary senator of their educational establishment.
References
Biography of Friedrich-Wilhelm Kiel from the Landtag of Baden-Württemberg
Further reading
1934 births
2022 deaths
Politicians from Berlin
Karlsruhe Institute of Technology alumni
Free Democratic Party (Germany) politicians
Mayors of places in Baden-Württemberg
Members of the Landtag of Baden-Württemberg
Recipients of the Order of Merit of Baden-Württemberg |
https://en.wikipedia.org/wiki/1985%20Dhivehi%20League | Statistics of Dhivehi League in the 1985 season.
Overview
Victory SC won the championship.
References
RSSSF
Dhivehi League seasons
Maldives
Maldives
Dhivehi |
https://en.wikipedia.org/wiki/1986%20Dhivehi%20League | Statistics of Dhivehi League in the 1986 season.
Overview
Victory SC won the championship.
References
RSSSF
Dhivehi League seasons
Maldives
Maldives
Dhivehi |
https://en.wikipedia.org/wiki/1987%20Dhivehi%20League | Football statistics for the Dhivehi League for the 1987 season.
Overview
New Radiant SC won the championship.
References
RSSSF
Dhivehi League seasons
Maldives
Maldives
Dhivehi |
https://en.wikipedia.org/wiki/1988%20Dhivehi%20League | Statistics of Dhivehi League in the 1988 season.
Overview
Victory SC won the championship.
References
RSSSF
Dhivehi League seasons
Maldives
Maldives
Dhivehi |
https://en.wikipedia.org/wiki/1989%20Dhivehi%20League | Statistics of Dhivehi League in the 1989 season.
Overview
Club Lagoons won the championship.
References
RSSSF
Dhivehi League seasons
Maldives
Maldives
football |
https://en.wikipedia.org/wiki/1990%20Dhivehi%20League | Statistics of Dhivehi League in the 1990 season.
Overview
New Radiant SC won the championship.
References
RSSSF
Dhivehi League seasons
Maldives
Maldives
football |
https://en.wikipedia.org/wiki/1991%20Dhivehi%20League | Statistics of Dhivehi League in the 1991 season.
Overview
New Radiant SC won the championship.
References
RSSSF
Dhivehi League seasons
Maldives
Maldives
football |
https://en.wikipedia.org/wiki/1992%20Dhivehi%20League | Statistics of Dhivehi League in the 1992 season.
Overview
Victory SC won the championship.
References
RSSSF
Dhivehi League seasons
Maldives
Maldives
football |
https://en.wikipedia.org/wiki/1993%20Dhivehi%20League | Statistics of Dhivehi League in the 1993 season.
Overview
Club Valencia won the championship.
References
RSSSF
Dhivehi League seasons
Maldives
Maldives
football |
https://en.wikipedia.org/wiki/1994%20Dhivehi%20League | Statistics of Dhivehi League in the 1994 season.
Overview
Club Valencia won the championship.
References
RSSSF
Dhivehi League seasons
Maldives
Maldives
football |
https://en.wikipedia.org/wiki/1995%20Dhivehi%20League | Statistics of Dhivehi League in the 1995 season.
Overview
New Radiant SC won the championship.
References
RSSSF
Dhivehi League seasons
Maldives
Maldives
football |
https://en.wikipedia.org/wiki/1996%20Dhivehi%20League | Statistics of Dhivehi League in the 1996 season.
Overview
Club Lagoons won the championship.
References
RSSSF
Dhivehi League seasons
Maldives
Maldives
football |
https://en.wikipedia.org/wiki/1997%20Dhivehi%20League | Statistics of Dhivehi League in the 1997 season.
Overview
New Radiant SC won the championship.
References
RSSSF
Dhivehi League seasons
Maldives
Maldives
football |
https://en.wikipedia.org/wiki/1998%20Dhivehi%20League | Statistics of Dhivehi League in the 1998 season.
Overview
Club Valencia won the championship.
References
RSSSF
Dhivehi League seasons
Maldives
Maldives
football |
https://en.wikipedia.org/wiki/2000%20Dhivehi%20League | Statistics of Dhivehi League in the 2000 season.
Overview
Victory Sports Club won both the Dhivehi League and the Maldives National Championship.
References
RSSSF
Dhivehi League seasons
Maldives
Maldives
1 |
https://en.wikipedia.org/wiki/2001%20Dhivehi%20League | Statistics of Dhivehi League in the 2001 season.
Overview
Club Valencia won the Dhivehi League. Victory Sports Club won the Maldives National Championship.
References
RSSSF
Dhivehi League seasons
Maldives
Maldives
1 |
https://en.wikipedia.org/wiki/2002%20Dhivehi%20League | Statistics of Dhivehi League in the 2002 season.
Overview
Club Valencia won the Dhivehi League. Victory Sports Club won the Maldives National Championship.
References
RSSSF
Dhivehi League seasons
Maldives
Maldives
1 |
https://en.wikipedia.org/wiki/2003%20Dhivehi%20League | Statistics of Dhivehi League in the 2003 season.
Overview
Club Valencia won the Dhivehi League. Victory Sports Club won the Maldives National Championship.
References
RSSSF
Dhivehi League seasons
Maldives
Maldives
1 |
https://en.wikipedia.org/wiki/2005%20Dhivehi%20League | Statistics of Dhivehi League in the 2005 season.
Overview
Hurriyya SC won the Dhivehi League. Victory Sports Club won the Maldives National Championship.
References
RSSSF
Dhivehi League seasons
Maldives
Maldives
1 |
https://en.wikipedia.org/wiki/2006%20Dhivehi%20League | Statistics of Dhivehi League in the 2006 season.
Overview
New Radiant won the Dhivehi League. Victory Sports Club won the Maldives National Championship.
References
RSSSF
Dhivehi League seasons
Maldives
Maldives
1 |
https://en.wikipedia.org/wiki/2007%20Dhivehi%20League | Statistics of Dhivehi League in the 2007 season.
Overview
Victory Sports Club won the Dhivehi League. New Radiant SC won the Maldives National Championship.
Promotion/relegation playoff Zone 9 for 2008 Dhivehi League
Final standings
References
RSSSF
Dhivehi League seasons
Maldives
Maldives
1 |
https://en.wikipedia.org/wiki/2008%20Dhivehi%20League | Statistics football matches of Dhivehi League in the 2008 season.
Overview
Club Valencia won both the Dhivehi League and the Maldives National Championship.
Clubs
Club Valencia
Kalhaidhoo ZJ
Maziya S&RC
New Radiant SC
Thinadhoo ZC
VB Sports
Victory Sports Club
Vyansa
Final standings
Promotion/relegation playoff for 2009 Dhivehi League
References
RSSSF
Dhivehi League seasons
Maldives
Maldives
1 |
https://en.wikipedia.org/wiki/2010%20Dhivehi%20League | Statistics of Dhivehi League in the 2010 season.
Clubs
All Youth Linkage FC
Club Valencia
Maaziya SRC
New Radiant SC
Thoddoo FC (name changed from Kalhaidhoo ZJ)
VB Sports
Victory Sports Club
Vyansa
League table
2011 Dhivehi League promotion/relegation play-off
External links
Maldives 2010, RSSSF.com
Dhivehi League seasons
Maldives
Maldives
1 |
https://en.wikipedia.org/wiki/2008%20Mongolian%20Premier%20League | Statistics of the Mongolia Premier League for the 2008 season.
Overview
Erchim won the championship.
League standings
Playoff
Semifinals
Khoromkhon 2-2 (pen 4-3) Khasiin Khulguud
Erchim 5-1 Selenge Press
Third Place
Khasiin Khulguud 3-3 (pen 5-4) Selenge Press
Final
Erchim 3-1 Khoromkhon
References
RSSSF
Mongolia Premier League seasons
Mongolia
Mongolia
football |
https://en.wikipedia.org/wiki/2009%E2%80%9310%20Myanmar%20National%20League | Statistics of Myanmar National League in the 2009–10 season.
Overview
Yadanarbon FC won the championship.
League standings
Season statistics
Top scorers
As of 17 Jan, 2010.
References
RSSSF
Myanmar National League seasons
1
1
Myanmar |
https://en.wikipedia.org/wiki/3-transposition%20group | In mathematical group theory, a 3-transposition group is a group generated by a conjugacy class of involutions, called the 3-transpositions, such that the product of any two involutions from the conjugacy class has order at most 3.
They were first studied by who discovered the three Fischer groups as examples of 3-transposition groups.
History
first studied 3-transposition groups in the special case when the product of any two distinct 3-transpositions has order 3. He showed that a finite group with this property is solvable, and has a (nilpotent) 3-group of index 2. used these groups to construct examples of non-abelian CH-quasigroups and to describe the structure of commutative Moufang loops of exponent 3.
Fischer's theorem
Suppose that G is a group that is generated by a conjugacy class D of 3-transpositions and such that the 2 and 3 cores O2(G) and O3(G) are both contained in the center Z(G) of G. Then proved that up to isomorphism G/Z(G) is one of the following groups and D is the image of the given conjugacy class:
G/Z(G) is the trivial group.
G/Z(G) is a symmetric group Sn for n≥5, and D is the class of transpositions. (If n=6 there is a second class of 3-transpositions).
G/Z(G) is a symplectic group Sp2n(2) with n≥3 over the field of order 2, and D is the class of transvections. (When n=2 there is a second class of transpositions.)
G/Z(G) is a projective special unitary group PSUn(2) with n≥5, and D is the class of transvections
G/Z(G) is an orthogonal group Oμ2n(2) with μ=±1 and n≥4, and D is the class of transvections
G/Z(G) is an index 2 subgroup POnμ,+(3) of the projective orthogonal group POnμ(3) (with μ=±1 and n≥5) generated by the class D of reflections of norm +1 vectors.
G/Z(G) is one of the three Fischer groups Fi22, Fi23, Fi24.
G/Z(G) is one of two groups of the form Ω8+(2).S3 and PΩ8+(3).S3, where Ω stands for the derived subgroup of the orthogonal group and S3 is the group of diagram automorphisms for the D4 Dynkin diagram.
The missing cases with n small above either do not satisfy the condition about 2 and 3 cores or have exceptional isomorphisms to other groups on the list.
Important examples
The group Sn has order n! and for n>1 has a subgroup An of index 2 that is simple if n>4.
The symmetric group Sn is a 3-transposition group for all n>1. The 3-transpositions are the elements that exchange two points, and leaving each of the remaining points fixed. These elements are the transpositions (in the usual sense) of Sn. (For n=6 there is a second class of 3-transpositions, namely the class of the elements of S6 which are products of 3 disjoint transpositions.)
The symplectic group Sp2n(2) has order
It is a 3-transposition group for all n≥1. It is simple if n>2, while for n=1 it is S3, and for n=2 it is S6 with a simple subgroup of index 2, namely A6. The 3-transpositions are of the form x↦x+(x,v)v for non-zero v.
The special unitary group SUn(2) has order
The projective special unitary group PSUn(2) is the q |
https://en.wikipedia.org/wiki/A8%20polytope | {{DISPLAYTITLE:A8 polytope}}
In 8-dimensional geometry, there are 135 uniform polytopes with A8 symmetry. There is one self-dual regular form, the 8-simplex with 9 vertices.
Each can be visualized as symmetric orthographic projections in Coxeter planes of the A8 Coxeter group, and other subgroups.
Graphs
Symmetric orthographic projections of these 135 polytopes can be made in the A8, A7, A6, A5, A4, A3, A2 Coxeter planes. Ak has [k+1] symmetry.
These 135 polytopes are each shown in these 7 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position.
References
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966
External links
Notes
8-polytopes |
https://en.wikipedia.org/wiki/B8%20polytope | {{DISPLAYTITLE:B8 polytope}}
In 8-dimensional geometry, there are 256 uniform polytopes with B8 symmetry. There are two regular forms, the 8-orthoplex and 8-cube, with 16 and 256 vertices respectively. The 8-demicube is added with half the symmetry.
They can be visualized as symmetric orthographic projections in Coxeter planes of the B8 Coxeter group, and other subgroups.
Graphs
Symmetric orthographic projections of these 256 polytopes can be made in the B8, B7, B6, B5, B4, B3, B2, A7, A5, A3, Coxeter planes. Ak has [k+1] symmetry, and Bk has [2k] symmetry.
These 256 polytopes are each shown in these 10 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position.
References
Notes
8-polytopes |
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