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https://en.wikipedia.org/wiki/1929%E2%80%9330%20Swiss%20Serie%20A | Statistics of Swiss Super League in the 1929–30 season.
East
Table
Results
Central
Table
Results
West
Table
Results
Final
Table
Results
|colspan="3" style="background-color:#D0D0D0" align=center|11 May 1930
|-
|colspan="3" style="background-color:#D0D0D0" align=center|18 May 1930
|-
|colspan="3" style="background-color:#D0D0D0" align=center|25 May 1930
|-
|colspan="3" style="background-color:#D0D0D0" align=center|1 June 1930
|}
Servette Genf won the championship.
Sources
Switzerland 1929-30 at RSSSF
Swiss Serie A seasons
Swiss
Football |
https://en.wikipedia.org/wiki/1930%E2%80%9331%20Swiss%20Serie%20A | Statistics of Swiss Super League in the 1930–31 season.
West
Table
Results
Central
Table
Results
East
Table
Results
Final
Table
Results
|colspan="3" style="background-color:#D0D0D0" align=center|10 May 1931
|-
|colspan="3" style="background-color:#D0D0D0" align=center|17 May 1931
|-
|colspan="3" style="background-color:#D0D0D0" align=center|31 May 1931
|-
|colspan="3" style="background-color:#D0D0D0" align=center|7 June 1931
|-
|colspan="3" style="background-color:#D0D0D0" align=center|21 June 1931
|-
|colspan="3" style="background-color:#D0D0D0" align=center|28 June 1931
|}
Grasshopper Club Zürich won the championship.
Sources
Switzerland 1930-31 at RSSSF
Swiss Serie A seasons
Swiss
1930–31 in Swiss football |
https://en.wikipedia.org/wiki/1931%E2%80%9332%20Nationalliga | Statistics of Swiss Super League in the 1931–32 season.
Overview
It was contested by 18 teams, and Lausanne Sports won the championship.
Group 1
Table
Results
Group 2
Table
Results
Playoff
Table
Results
|colspan="3" style="background-color:#D0D0D0" align=center|29 May 1932
|-
|colspan="3" style="background-color:#D0D0D0" align=center|5 June 1932
|-
|colspan="3" style="background-color:#D0D0D0" align=center|12 June 1932
|-
|colspan="3" style="background-color:#D0D0D0" align=center|26 June 1932
|}
Championship play-off
|colspan="3" style="background-color:#D0D0D0" align=center|3 July 1932
|}
Sources
Switzerland 1931-32 at RSSSF
Nationalliga seasons
Swiss
1931–32 in Swiss football |
https://en.wikipedia.org/wiki/1932%E2%80%9333%20Nationalliga | Statistics of Swiss Super League in the 1932–33 season.
Overview
It was contested by 16 teams, and Servette FC Genève won the championship.
Group 1
Table
Results
Group 2
Table
Results
Playoff
Table
Results
|colspan="3" style="background-color:#D0D0D0" align=center|11 June 1933
|-
|colspan="3" style="background-color:#D0D0D0" align=center|18 June 1933
|-
|colspan="3" style="background-color:#D0D0D0" align=center|25 June 1933
Championship play-off
|colspan="3" style="background-color:#D0D0D0" align=center|2 July 1933
Sources
Switzerland 1932-33 at RSSSF
Nationalliga seasons
Swiss
Swiss Football, 1932-33 In |
https://en.wikipedia.org/wiki/1933%E2%80%9334%20Nationalliga | Statistics of Swiss Super League in the 1933–34 season.
Overview
It was contested by 16 teams, and Servette FC Genève won the championship.
League standings
Results
Sources
Switzerland 1933-34 at RSSSF
Nationalliga seasons
Swiss
1933–34 in Swiss football |
https://en.wikipedia.org/wiki/1934%E2%80%9335%20Nationalliga | Statistics of Swiss Super League in the 1934–35 season.
Overview
It was contested by 14 teams, and Lausanne Sports won the championship.
League standings
Results
Sources
Switzerland 1934-35 at RSSSF
Nationalliga seasons
Swiss
1934–35 in Swiss football |
https://en.wikipedia.org/wiki/1935%E2%80%9336%20Nationalliga | Statistics of Swiss Super League in the 1935–36 season.
Overview
It was contested by 14 teams, and Lausanne Sports won the championship.
League standings
Results
Sources
Switzerland 1935-36 at RSSSF
Nationalliga seasons
Swiss
1935–36 in Swiss football |
https://en.wikipedia.org/wiki/1936%E2%80%9337%20Nationalliga | Statistics of Swiss Super League in the 1936–37 season.
Overview
It was contested by 13 teams, and Grasshopper Club Zürich won the championship.
League standings
Results
Sources
Switzerland 1936-37 at RSSSF
Nationalliga seasons
Swiss
Football |
https://en.wikipedia.org/wiki/1937%E2%80%9338%20Nationalliga | Statistics of Swiss Super League in the 1937–38 season.
Overview
It was contested by 12 teams, and FC Lugano won the championship.
League standings
Results
Sources
Switzerland 1937-38 at RSSSF
Nationalliga seasons
Swiss
1937–38 in Swiss football |
https://en.wikipedia.org/wiki/1938%E2%80%9339%20Nationalliga | Statistics of Swiss Super League in the 1938–39 season.
Overview
It was contested by 12 teams, and Grasshopper Club Zürich won the championship.
League standings
Results
Sources
Switzerland 1938-39 at RSSSF
Nationalliga seasons
Swiss
Swiss Football, 1938-39 In |
https://en.wikipedia.org/wiki/1939%E2%80%9340%20Nationalliga | Statistics of Swiss Super League in the 1939–40 season.
Overview
It was contested by 12 teams, and Servette FC Genève won the championship.
League standings
Results
Sources
Switzerland 1939-40 at RSSSF
Nationalliga seasons
Swiss
Swiss Super League |
https://en.wikipedia.org/wiki/1940%E2%80%9341%20Nationalliga | Below are the statistics of Swiss Super League in the 1940–41 season.
Overview
It was contested by 12 teams, and FC Lugano won the championship.
League standings
Results
Sources
Switzerland 1940-41 at RSSSF
Swiss Football League seasons
Swiss
1940–41 in Swiss football |
https://en.wikipedia.org/wiki/1941%E2%80%9342%20Nationalliga | Statistics of Swiss Super League in the 1941–42 season.
Overview
The Nationalliga was contested by 14 teams and in this season it ended in a heat, because two teams ended the season equal on points. Thus a play-off was required, between the Grasshopper Club Zürich and FC Grenchen. The first game ended 0–0 in Bern, the second game ended 1–1 in Basel. The championship title awarded to GC on goal average. The 1st League was contested by 25 teams, these were divided into two groups. There were twelve teams contesting in group East and thirteen in group West. The winner of each group had to play a play-off for promotion to the Nationalliga. Basel finished their season as winners of group East and the play-offs were then against group West winners Bern, the away tie ending with a goalless draw and Basel won their home tie 3–1 to achieve Promotion.
Nationalliga standings
Results
League standings 1st League group East
League standings 1st League group West
Promotion play-off
Basel won 3–1 on aggregate
Sources
Rotblau: Jahrbuch Saison 2014/2015. Publisher: FC Basel Marketing AG.
Switzerland 1941–42 at RSSSF
Swiss Football League seasons
Swiss
Nationalliga |
https://en.wikipedia.org/wiki/1942%E2%80%9343%20Nationalliga | Statistics of Swiss Super League in the 1942–43 season.
Overview
It was contested by 14 teams, and Grasshopper Club Zürich won the championship.
League standings
Results
Sources
Switzerland 1942–43 at RSSSF
Swiss Football League seasons
Swiss
Nationalliga |
https://en.wikipedia.org/wiki/1943%E2%80%9344%20Nationalliga | Statistics of Swiss Super League in the 1943–44 season.
Overview
It was contested by 14 teams, and Lausanne Sports won the championship.
League standings
Results
Sources
Switzerland 1943–44 at RSSSF
Swiss Football League seasons
Swiss
Football |
https://en.wikipedia.org/wiki/1944%E2%80%9345%20Nationalliga%20A | Statistics of Swiss Super League in the 1944–45 season.
Overview
It was contested by 14 teams, and Grasshopper Club Zürich won the championship.
League standings
Results
Sources
Switzerland 1944–45 at RSSSF
Swiss Football League seasons
Swiss
Football |
https://en.wikipedia.org/wiki/1945%E2%80%9346%20Nationalliga%20A | Statistics of Swiss Super League in the 1945–46 season.
Overview
The Nationalliga A was contested by 14 teams this season and Servette FC Genève won the championship. La Chaux-de-Fonds and Zürich were relegated.
The Nationalliga B was contested by 14 teams. Basel won the league and were promoted together with Urania Genève Sport. SC Zug and SC Derendingen finished level on points at the bottom of the table. Zug won the play-off and saved themselves from relegation. Étoile-Sporting and Derendingen were relegated to the 1st League.
League standings Nationalliga A
Results
League standings Nationalliga B
Sources
Switzerland 1945–46 at RSSSF
Swiss Football League seasons
Swiss
Football |
https://en.wikipedia.org/wiki/1946%E2%80%9347%20Nationalliga%20A | Statistics of Swiss Super League in the 1946–47 season.
Overview
It was contested by 14 teams, and FC Biel-Bienne won the championship.
League standings
Results
Sources
Switzerland 1946–47 at RSSSF
Swiss Football League seasons
Swiss
Football |
https://en.wikipedia.org/wiki/1947%E2%80%9348%20Nationalliga%20A | Statistics of Swiss Super League in the 1947–48 season.
Overview
It was contested by 14 teams, and AC Bellinzona won the championship.
League standings
Results
Sources
Switzerland 1947–48 at RSSSF
Swiss Football League seasons
Swiss
Football |
https://en.wikipedia.org/wiki/1948%E2%80%9349%20Nationalliga%20A | Statistics of Swiss Super League in the 1948–49 season.
Overview
It was contested by 14 teams, and FC Lugano won the championship.
League standings
Results
Sources
Switzerland 1948–49 at RSSSF
Swiss Football League seasons
Swiss
Football |
https://en.wikipedia.org/wiki/1949%E2%80%9350%20Nationalliga%20A | Statistics of Swiss Super League in the 1949–50 season.
Overview
It was contested by 14 teams, and Servette FC Genève won the championship.
League standings
Results
Sources
Switzerland 1949–50 at RSSSF
Swiss Football League seasons
Swiss
Football |
https://en.wikipedia.org/wiki/1950%E2%80%9351%20Nationalliga%20A | Statistics of Swiss Super League in the 1950–51 season.
Overview
It was contested by 14 teams, and Lausanne Sports won the championship.
League standings
Results
Sources
Switzerland 1950–51 at RSSSF
Swiss Football League seasons
Swiss
1950–51 in Swiss football |
https://en.wikipedia.org/wiki/1951%E2%80%9352%20Nationalliga%20A | Statistics of Swiss Super League in the 1951–52 season.
Overview
It was contested by 14 teams, and Grasshopper Club Zürich won the championship.
League standings
Results
Sources
Switzerland 1951–52 at RSSSF
Swiss Football League seasons
Swiss
1951–52 in Swiss football |
https://en.wikipedia.org/wiki/1952%E2%80%9353%20Nationalliga%20A | Statistics of Swiss Super League in the 1952–53 season.
Overview
It was contested by 14 teams, and FC Basel won the championship for the first time in the club's history.
League standings
Results
Sources
Switzerland 1952–53 at RSSSF
Swiss Football League seasons
Swiss
1952–53 in Swiss football |
https://en.wikipedia.org/wiki/1953%E2%80%9354%20Nationalliga%20A | Statistics of Swiss Super League in the 1953–54 season.
Overview
It was contested by 14 teams, and FC La Chaux-de-Fonds won the championship.
League standings
Results
Sources
Switzerland 1953–54 at RSSSF
Swiss Football League seasons
Swiss
1953–54 in Swiss football |
https://en.wikipedia.org/wiki/1954%E2%80%9355%20Nationalliga%20A | Statistics of Swiss Super League in the 1954–55 season.
Overview
It was contested by 14 teams, and FC La Chaux-de-Fonds won the championship.
League standings
Results
Sources
Switzerland 1954–55 at RSSSF
Swiss Football League seasons
Swiss
1954–55 in Swiss football |
https://en.wikipedia.org/wiki/1955%E2%80%9356%20Nationalliga%20A | Statistics of Swiss Super League in the 1955–56 season.
Overview
It was contested by 14 teams, and Grasshopper Club Zürich won the championship.
League standings
Results
Sources
Switzerland 1955–56 at RSSSF
Swiss Football League seasons
Swiss
1955–56 in Swiss football |
https://en.wikipedia.org/wiki/1956%E2%80%9357%20Nationalliga%20A | Statistics of Swiss Super League in the 1956–57 season.
Overview
It was contested by 14 teams, and BSC Young Boys won the championship. FC Zürich and FC Schaffhausen were both relegated down to the second division.
League standings
Results
References
Sources
Switzerland 1956–57 at RSSSF
Swiss Football League seasons
Swiss
1956–57 in Swiss football |
https://en.wikipedia.org/wiki/1957%E2%80%9358%20Nationalliga%20A | Statistics of Swiss Super League in the 1957–58 season.
Overview
It was contested by 14 teams, and BSC Young Boys won the championship.
League standings
Results
Sources
Switzerland 1957–58 at RSSSF
Swiss Football League seasons
Swiss
1957–58 in Swiss football |
https://en.wikipedia.org/wiki/1958%E2%80%9359%20Nationalliga%20A | Statistics of Swiss Super League in the 1958–59 season.
Overview
It was contested by 14 teams, and BSC Young Boys won the championship.
League standings
Results
Sources
Switzerland 1958–59 at RSSSF
Swiss Football League seasons
Swiss
1958–59 in Swiss football |
https://en.wikipedia.org/wiki/1959%E2%80%9360%20Nationalliga%20A | Statistics of Swiss Super League in the 1959–60 season.
Overview
It was contested by 14 teams, and BSC Young Boys won the championship.
League standings
Results
Sources
Switzerland 1959–60 at RSSSF
Swiss Football League seasons
Swiss
1959–60 in Swiss football |
https://en.wikipedia.org/wiki/1960%E2%80%9361%20Nationalliga%20A | Statistics of Swiss Super League in the 1960–61 season.
Overview
It was contested by 14 teams, and Servette FC Genève won the championship.
League standings
Results
Sources
Switzerland 1960–61 at RSSSF
Swiss Football League seasons
Swiss
1960–61 in Swiss football |
https://en.wikipedia.org/wiki/1961%E2%80%9362%20Nationalliga%20A | Statistics of Swiss Super League in the 1961–62 season.
Overview
It was contested by 14 teams, and Servette FC Genève won the championship.
League standings
Results
Sources
Switzerland 1961–62 at RSSSF
Swiss Football League seasons
Swiss
1961–62 in Swiss football |
https://en.wikipedia.org/wiki/1962%E2%80%9363%20Nationalliga%20A | Statistics of Swiss Super League in the 1962–63 season.
Overview
There were fourteen teams contesting in the 1962–63 Nationalliga A. These were the top 12 teams from the previous season 1961–62 and the two newly promoted teams Chiasso and Sion. The Championship was played in a double round-robin, the champions were to be qualified for 1963–64 European Cup and the bottom placed two teams in the table were to be relegated. FC Zürich won the championship.
League standings
Results
Topscorers
References
Summary at RSSSF
Sources
Switzerland 1962–63 at RSSSF
Swiss Football League seasons
Swiss
1962–63 in Swiss football |
https://en.wikipedia.org/wiki/1963%E2%80%9364%20Nationalliga%20A | Statistics of Swiss Super League in the 1963–64 season.
Overview
There were fourteen teams contesting in the 1963–64 Nationalliga A, these were the top 12 teams from the previous season 1962–63 and the two newly promoted teams Schaffhausen and Cantonal Neuchatel. The Championship was played in a double round-robin, the champions were to be qualified for 1964–65 European Cup and the bottom placed two teams in the table were to be relegated. The championship was won by La Chaux-de-Fonds. Swiss Cup winners were Lausanne-Sport. Relegated were Schaffhausen and Cantonal Neuchatel.
League standings
Results
References
Sources
Switzerland 1963–64 at RSSSF
Swiss Football League seasons
Swiss
1963–64 in Swiss football |
https://en.wikipedia.org/wiki/1964%E2%80%9365%20Nationalliga%20A | Statistics of Swiss Super League in the 1964–65 season.
Overview
Fourteen teams contested the 1964–65 Nationalliga A, these were the top 12 teams from the previous season 1963–64 and the two newly promoted teams Lugano and Bellinzona. Lausanne Sports won the championship with 36 points and thus qualified for the following year's 1965–66 European Cup. They were four points clear of Young Boys in second position. Bellinzona and Chiasso suffered relegation. Sion were Swiss Cup winners and qualified for 1965–66 European Cup Winners' Cup.
League standings
Results
References
Sources
Switzerland 1964–65 at RSSSF
Swiss Football League seasons
Swiss
1964–65 in Swiss football |
https://en.wikipedia.org/wiki/1965%E2%80%9366%20Nationalliga%20A | Statistics of Swiss Super League football (soccer) competition in the 1965–66 season.
Overview
Fourteen teams contested the 1965–66 Nationalliga A. These were the top 12 teams from the previous 1964–65 season and the two newly promoted teams Urania Genève Sport and Young Fellows Zürich. Zürich won the championship with 42 points and qualified for 1966–67 European Cup. They were seven points ahead of Servette in second place. Servette won the Swiss Cup and qualified for the 1966–67 Cup Winners' Cup.
League standings
Results
Top scorers
References
Sources
Switzerland 1965–66 at RSSSF
Swiss Football League seasons
Swiss
1965–66 in Swiss football |
https://en.wikipedia.org/wiki/1966%E2%80%9367%20Nationalliga%20A | Statistics of Swiss Super League football (soccer) competition in the 1966–67 season.
Overview
There were 14 teams contesting in the 1966–67 Nationalliga A and Basel finished the seasons as champions just one point clear of both FC Zürich in second position and FC Lugano who finished third. Basel won 16 of the 26 games, drawing eight, losing twice, and they scored 60 goals conceding just 20. FC Moutier finished in last position and were relegated. FC Winterthur and FC La Chaux-de-Fonds finished level on points and thus played a relegation play-out. La Chaux-de-Fonds won 3–1 and Winterthur were also relegated.
Basel also won the Swiss Cup. In the Cup final Basel's opponents were Lausanne-Sports. In the former Wankdorf Stadium on 15 May 1967, Helmut Hauser scored the decisive goal via penalty. The game went down in football history due to the sit-down strike that followed this goal. After 88 minutes of play, with the score at 1–1, referee Karl Göppel awarded Basel a controversial penalty. André Grobéty had pushed Hauser gently in the back and he let himself drop theatrically. Subsequent to the 2–1 for Basel the Lausanne players refused to resume the game and they sat down demonstratively on the pitch. The referee had to abandon the match. Basel were awarded the cup with a 3–0 forfait. Basel won the double for the first time in the club's history.
League standings
Results
References
Sources
Switzerland 1966–67 at RSSSF
Swiss Football League seasons
Swiss
1966–67 in Swiss football |
https://en.wikipedia.org/wiki/1967%E2%80%9368%20Nationalliga%20A | Statistics of Swiss Super League in the 1967–68 season.
Overview
There were 14 teams contesting in the 1967–68 Nationalliga A. These were the top 12 teams from the previous 1966–67 season and the two newly promoted teams Luzern and Bellinzona. The three teams Zürich, Grasshopper Club and Lugano all ended the season with 38 points. Thus all three then had to play a championship play-off round. Zürich won both games and became champions. Young Fellows Zürich and Grenchen suffered relegation.
League standings
Results
References
Sources
Switzerland 1967–68 at RSSSF
Swiss Football League seasons
Swiss
1967–68 in Swiss football |
https://en.wikipedia.org/wiki/1968%E2%80%9369%20Nationalliga%20A | Statistics of Swiss Super League in the 1968–69 season.
Overview
There were 14 teams contesting in the 1968–69 Nationalliga A. These were the top 12 teams from the previous 1967–68 season and the two newly promoted teams Winterthur and St. Gallen. Basel finished the league season as champions one point ahead of Lausanne Sports in second position, who Basel defeated 4–0 in the second last match of the season, and six points clear of FC Zürich who finished third. Basel won 13 of the 26 games, drawing ten, losing three times, they scored 48 goals conceding 28. St. Gallen won the Swiss Cup and were thus qualified for the 1969–70 Cup Winners' Cup.
League standings
Results
References
Sources
Switzerland 1968–69 at RSSSF
Swiss Football League seasons
Swiss
1968–69 in Swiss football |
https://en.wikipedia.org/wiki/1969%E2%80%9370%20Nationalliga%20A | Statistics of Swiss Super League in the 1969–70 season.
Overview
14 teams contested in the 1969–70 Nationalliga A. These were the top 12 teams from the previous 1968–69 season and the two newly promoted teams Wettingen and Fribourg. The championship was played in a double round robin, the last two teams at the end of the season to be relegated. Basel won the championship a point clear of Lausanne Sports who ended in second position and three points ahead of FC Zürich who finished third. Wettingen and St. Gallen suffered relegation.
League standings
Results
References
Sources
Switzerland 1969–70 at RSSSF
Swiss Football League seasons
Swiss
1969–70 in Swiss football |
https://en.wikipedia.org/wiki/1970%E2%80%9371%20Nationalliga%20A | Statistics of Swiss Super League in the 1970–71 season.
Overview
14 teams contested in the 1970–71 Nationalliga A. These were the top 12 teams from the previous 1969–70 season and the two newly promoted teams Sion and Luzern. The championship was played in a double round robin. The champions would qualify for the 1971–72 European Cup and the last two teams in the league table at the end of the season were to be relegated. FC Basel finished the regular season level on points with Grasshopper Club Zürich and so these two teams had to contest a play-off game on 8 June 1971 to decide the title winners. Grasshopper won the play-off 4–3 after extra time. Bellinzona finished last and the table and were relegated. Sion and Fribourg, level on points, were both second last and thus they had to have a play-off against relegation. Sion won 1–0, so Fribourg were relegated.
League standings
Results
Championship play-off
Relegation play-off
References
Sources
Switzerland 1970–71 at RSSSF
Swiss Football League seasons
Swiss
1970–71 in Swiss football |
https://en.wikipedia.org/wiki/1971%E2%80%9372%20Nationalliga%20A | Statistics of Swiss Super League in the 1971–72 season.
Overview
14 teams contested in the 1971–72 Nationalliga A. These were the top 12 teams from the previous 1970–71 season and the two newly promoted teams St. Gallen and Grenchen. The championship was played in a double round robin. The champions would qualify for the 1972–73 European Cup and the last two teams in the table at the end of the season were to be relegated. Basel remained undefeated in the league during the first 24 rounds. Of their 26 league games Basel won 18, drawing seven, losing just once, scoring 66 goals conceding 28. Basel won the championship four points ahead of Zürich and five points ahead of the Grasshoppers. Zürich were Swiss Cup winners and qualified for 1972–73 Cup Winners' Cup. Grasshopper Club and Lausanne-Sport qualified for 1972–73 UEFA Cup. Luzern and Biel-Bienne suffered relegation.
League standings
Results
References
Sources
Switzerland 1971–72 at RSSSF
Swiss Football League seasons
Swiss
1971–72 in Swiss football |
https://en.wikipedia.org/wiki/1972%E2%80%9373%20Nationalliga%20A | Statistics of Swiss Super League in the 1972–73 season.
Overview
14 teams contested in the 1972–73 Nationalliga A. These were the top 12 teams from the previous 1971–72 season and the two newly promoted teams Chiasso and Fribourg. The championship was played in a double round robin. The champions would qualify for the 1973–74 European Cup, the second and third placed teams were to qualify for 1973–74 UEFA Cup and the last two teams in the table at the end of the season were to be relegated. Basel won the championship four points ahead of Grasshopper Club and six ahead of the Sion. Basel won 17 of their 26 league games, drew five and lost four. They scored a total of 57 goals conceding 30. Ottmar Hitzfeld (Basel) was joint leagues top goal scorer with Ove Grahn of Lausanne-Sports both with 18 league goals.
League standings
Results
References
Sources
Switzerland 1972–73 at RSSSF
Swiss Football League seasons
Swiss
1972–73 in Swiss football |
https://en.wikipedia.org/wiki/1973%E2%80%9374%20Nationalliga%20A | Statistics of Swiss Super League in the 1973–74 season.
Overview
The Nationalliga A season 1973–74 was contested under 14 teams. These were the top 12 teams from the previous 1972–73 season and the two newly promoted teams Xamax and Chênois. The championship was played in a double round robin. The champions would qualify for the 1974–75 European Cup, the second and third placed teams were to qualify for 1974–75 UEFA Cup and the last two teams in the table at the end of the season were to be relegated. Zürich won the championship 12 points ahead of Grasshopper Club, 13 ahead of the Servette and Winterthur. La Chaux-de-Fonds and Chiasso suffered relegation.
League standings
Results
Top goalscorers
References
Sources
Switzerland 1973–74 at RSSSF
Swiss Football League seasons
Swiss
1973–74 in Swiss football |
https://en.wikipedia.org/wiki/1974%E2%80%9375%20Nationalliga%20A | Statistics of Swiss Super League in the 1974–75 season.
Overview
The Nationalliga A season 1974–75 was contested under 14 teams. These were the top 12 teams from the previous 1973–74 season and the two newly promoted teams Luzern and Vevey-Sports. The championship was played in a double round robin. The champions would qualify for the 1975–76 European Cup, the second and third placed teams were to qualify for 1975–76 UEFA Cup and the last two teams in the table at the end of the season were to be relegated. Zürich won the championship six points ahead of both BSC Young Boys who were second and Grasshopper Club who were third. Luzern and Vevey-Sports suffered relegation.
League standings
Results
Top goalscorers
References
Sources
Switzerland 1974–75 at RSSSF
Swiss Football League seasons
Swiss
1974–75 in Swiss football |
https://en.wikipedia.org/wiki/1975%E2%80%9376%20Nationalliga%20A | Statistics of Swiss Super League in the 1975–76 season.
Overview
The Swiss Football Association was reforming the Swiss football league system this year, reducing the number of teams in the Nationalliga A from 14 to 12 and increasing the Nationalliga B teams from 14 to 16. Therefore, three teams were being relegated and only one promoted. These 14 teams were the top 12 teams from the previous 1974–75 season and the two newly promoted teams Biel-Bienne and La Chaux-de-Fonds. The champions would qualify for the 1975–76 European Cup. Reigning champions Zürich ran away with the title, they won the championship with 44 points, five points clear of second placed Servette and ten points clear of third placed Basel. The second and third placed teams were to have qualified for UEFA Cup, but because Zürich won the double the cup runners-up Servette advanced to the 1976–77 Cup Winners' Cup and the third and forth placed teams advanced tp the 1975–76 UEFA Cup. Lugano and the two newly promoted teams, Biel-Bienne and La Chaux-de-Fonds, suffered relegation.
League standings
Results
References
Sources
Switzerland 1975–76 at RSSSF
Swiss Football League seasons
Swiss
1975–76 in Swiss football |
https://en.wikipedia.org/wiki/1976%E2%80%9377%20Nationalliga%20A | Statistics of Swiss Super League in the 1976–77 season.
Overview
The Swiss Football Association had reformed the Swiss football league system that year, reducing the number of teams in the Nationalliga A from 14 to 12 and increasing the Nationalliga B teams from 14 to 16. The Nationalliga A season 1976–77 was contested by the first 11 teams from the 1975–76 season and the sole promoted team from Nationalliga B AC Bellinzona. The Nationalliga A was played in two stages. The qualification phase was played by all teams in a round robin and after completion was divided into two groups. The first six teams contended in the championship group (with half the obtained points as bonus) and the positions seventh to twelfth contended the relegation group (also with half the obtained points as bonus). Servette FC Genève and Basel finished the qualification phase in first and second position with 35 and 33 points from 22 games and so entered the championship group with a bonus of 18 and 17. At the end of the championship phase these two teams were level on 29 points. Therefore they had to compete a play-off match for champions. This play-off was held at the Wankdorf Stadium in Bern in front of 55,000 supporters. Basel won the match 2–1 and were awarded the championship.
The playout round ended with FC Winterthur and AC Bellinzona being relegated.
First stage
Table
Results
Second stage
Championship group
Table
Playoff match
Results
Playout group
Table
Results
Sources
Rotblau: Jahrbuch Saison 2015/2016. Publisher: FC Basel Marketing AG.
Switzerland 1976–77 at RSSSF
Swiss Football League seasons
Swiss
1976–77 in Swiss football |
https://en.wikipedia.org/wiki/1977%E2%80%9378%20Nationalliga%20A | Statistics of Swiss Super League in the 1977–78 season.
Overview
It was contested by 12 teams, and Grasshopper Club Zürich won the championship.
First stage
Table
Results
Second stage
Playoff
Table
Results
Playout
Table
Results
Sources
Switzerland 1977–78 at RSSSF
Swiss Football League seasons
Swiss
1977–78 in Swiss football |
https://en.wikipedia.org/wiki/1978%E2%80%9379%20Nationalliga%20A | Statistics of Swiss Super League in the 1978–79 season.
Overview
It was contested by 12 teams, and Servette FC Genève won the championship.
First stage
Table
Results
Second stage
Playoff
Table
Results
Playout
Table
Results
Sources
Switzerland 1978–79 at RSSSF
Swiss Football League seasons
Swiss
1978–79 in Swiss football |
https://en.wikipedia.org/wiki/1979%E2%80%9380%20Nationalliga%20A | Statistics of Swiss Super League in the 1979–80 season.
Overview
It was contested by 14 teams, and FC Basel won the championship.
First stage
Table
Results
Playoff
Table
Results
Sources
Switzerland 1979–80 at RSSSF
Swiss Football League seasons
Swiss
1979–80 in Swiss football |
https://en.wikipedia.org/wiki/1980%E2%80%9381%20Nationalliga%20A | Statistics of Swiss Super League in the 1980–81 season.
Overview
It was contested by 14 teams, and FC Zürich won the championship.
League standings
Results
Sources
Switzerland 1980–81 at RSSSF
Swiss Football League seasons
Swiss
1980–81 in Swiss football |
https://en.wikipedia.org/wiki/1982%E2%80%9383%20Nationalliga%20A | Statistics of Swiss Super League in the 1982–83 season.
Overview
It was contested by 16 teams, and Grasshopper Club Zürich won the championship.
The Swiss top level league was contested by sixteen teams, including 14 clubs from the previous season and the two sides promoted from the second level 1981–82 Nationalliga B, FC Winterthur and FC Wettingen. The league was contested in a double round robin format, with each club playing every other club twice, for a total of 30 rounds. Two points were awarded for wins and one point for draws.
League standings
Results
Sources
Switzerland 1982–83 at RSSSF
Swiss Football League seasons
Swiss
1982–83 in Swiss football |
https://en.wikipedia.org/wiki/1983%E2%80%9384%20Nationalliga%20A | Statistics of Swiss Super League in the 1983–84 season.
Overview
It was contested by 16 teams, and Grasshopper Club Zürich won the championship.
League standings
Championship play-off
Results
Sources
Switzerland 1983–84 at RSSSF
Swiss Football League seasons
Swiss
1983–84 in Swiss football |
https://en.wikipedia.org/wiki/1984%E2%80%9385%20Nationalliga%20A | Statistics of Swiss Super League in the 1984–85 season.
Overview
It was contested by 16 teams, and Servette FC Genève won the championship.
League standings
Results
Sources
Switzerland 1984–85 at RSSSF
Swiss Football League seasons
Swiss
1984–85 in Swiss football |
https://en.wikipedia.org/wiki/1985%E2%80%9386%20Nationalliga%20A | Statistics of Swiss National League A in the 1985–86 football season.
Overview
It was contested by 16 teams, and BSC Young Boys won the championship.
League standings
Results
References
Sources
Switzerland 1985–86 at RSSSF
Swiss Football League seasons
Swiss
1985–86 in Swiss football |
https://en.wikipedia.org/wiki/1986%E2%80%9387%20Nationalliga%20A | Statistics of Swiss National League A in the 1986–87 football season.
Overview
It was contested by 16 teams, and Neuchâtel Xamax won the championship.
League standings
Results
Sources
Switzerland 1986–87 at RSSSF
Swiss Football League seasons
Swiss
1986–87 in Swiss football |
https://en.wikipedia.org/wiki/1987%E2%80%9388%20Nationalliga%20A | Statistics of Swiss National League A in the 1987–88 football season.
Overview
It was contested by 12 teams, and Neuchâtel Xamax won the championship.
First stage
Table
Results
Second stage
Championship group
Table
Results
Promotion/relegation group
Group A
Table
Results
Group B
Table
Results
Sources
Switzerland 1987–88 at RSSSF
Swiss Football League seasons
Swiss
1987–88 in Swiss football |
https://en.wikipedia.org/wiki/1989%E2%80%9390%20Nationalliga%20A | Statistics of Swiss National League A in the 1989–90 football season.
Overview
It was contested by 12 teams, and Grasshopper Club Zürich won the championship.
First stage
Table
Results
Second stage
Championship group
Table
Results
Promotion/relegation group
Group A
Table
Results
Group B
Table
Results
See also
1989 Klötzli incident
Sources
Switzerland 1989–90 at RSSSF
Swiss Football League seasons
Swiss
1989–90 in Swiss football |
https://en.wikipedia.org/wiki/1990%E2%80%9391%20Nationalliga%20A | Statistics of Swiss National League A in the 1990–91 football season.
Overview
It was contested by 12 teams, and Grasshopper Club Zürich won the championship.
First stage
Table
Results
Second stage
Championship group
Table
Results
Promotion/relegation group
Group A
Table
Results
Group B
Table
Results
Sources
Switzerland 1990–91 at RSSSF
Swiss Football League seasons
Swiss
1990–91 in Swiss football |
https://en.wikipedia.org/wiki/1991%E2%80%9392%20Nationalliga%20A | Statistics of the Swiss National League A in the 1991–92 football season.
Overview
It was contested by 12 teams, and FC Sion won the championship.
First stage
Table
Results
Second stage
Championship group
Table
Results
Promotion/relegation group
Group A
Table
Results
Group B
Table
Results
Sources
Switzerland 1991–92 at RSSSF
Swiss Football League seasons
Swiss
1991–92 in Swiss football |
https://en.wikipedia.org/wiki/1992%E2%80%9393%20Nationalliga%20A | Statistics of Swiss National League A in the 1992–93 football season.
Overview
It was contested by 12 teams, and FC Aarau won the championship.
First stage
Table
Results
Second stage
Championship group
Table
Results
Promotion/relegation group
Group A
Table
Results
Group B
Table
Results
Sources
Switzerland 1992–93 at RSSSF
Swiss Football League seasons
Swiss
1992–93 in Swiss football |
https://en.wikipedia.org/wiki/1993%E2%80%9394%20Nationalliga%20A | Statistics of the Swiss National League A in the 1993–94 football season.
Overview
It was contested by 12 teams, and Servette FC won the championship.
First stage
Table
Results
Second stage
Championship group
Table
Results
Promotion/relegation group
Table
Results
Sources
Switzerland 1993–94 at RSSSF
Swiss Football League seasons
Swiss
1993–94 in Swiss football |
https://en.wikipedia.org/wiki/1994%E2%80%9395%20Nationalliga%20A | Statistics of the Swiss National League A in the 1994–95 football season.
Overview
It was contested by 12 teams, and Grasshopper Club Zürich won the championship.
First stage
Table
Results
Second stage
Championship group
Table
Results
Promotion/relegation group
Table
Results
Sources
Switzerland 1994–95 at RSSSF
Switzerland - List of Champions rsssf.com
Swiss Football League seasons
Swiss
1994–95 in Swiss football |
https://en.wikipedia.org/wiki/1995%E2%80%9396%20Nationalliga%20A | Statistics of Swiss National League A in the 1995–96 football season.
Overview
It was contested by 12 teams, and Grasshopper Club Zürich won the championship.
First stage
Table
Results
Second stage
Championship group
Table
Results
Promotion/relegation group
Table
Results
Sources
Switzerland 1995–96 at RSSSF
Swiss Football League seasons
Swiss
1995–96 in Swiss football |
https://en.wikipedia.org/wiki/1996%E2%80%9397%20Nationalliga%20A | Statistics of Swiss National League A in the 1996–97 football season.
Overview
It was contested by 12 teams, and FC Sion won the championship.
First stage
Table
Results
Second stage
Championship group
Table
Results
Promotion/relegation group
Table
Results
Sources
Switzerland 1996–97 at RSSSF
Swiss Football League seasons
Swiss
1996–97 in Swiss football |
https://en.wikipedia.org/wiki/1997%E2%80%9398%20Nationalliga%20A | Statistics of the Swiss National League A in the 1997–98 football season.
Overview
It was contested by 12 teams with each team playing each other twice in the first stage before being separated into a championship group and a relegation group; Grasshoppers won the championship.
First stage
Table
Results
Second stage
Championship group
Table
Results
Promotion/relegation group
Table
Results
Sources
Switzerland 1997–98 at RSSSF
Swiss Football League seasons
Swiss
1997–98 in Swiss football |
https://en.wikipedia.org/wiki/1999%E2%80%932000%20Nationalliga%20A | Statistics of National League A in the 1999–2000 football season.
Nationalliga A
The Qualification Round to the League season 2001–02 was contested by twelve teams. The first eight teams of the First Stage (or Qualification) were then to compete in the Championship Playoff Round. The teams in ninth to twelfth position completed with the top four teams of the Nationalliga B in a Nationalliga A/B Playoff round. At the end of the season FC St. Gallen won the championship.
First stage
Table
Results
Champion Playoffs
The first eight teams of the regular season (or Qualification) competed in the Championship Playoff Round. They took half of the points (rounded up to complete units) gained in the Qualification as Bonus with them.
Table
Results
Nationalliga A/B Playoffs
The teams in ninth to twelfth position in the Nationalliga A completed with the top four teams of the Nationalliga B in a Nationalliga A/B Playoff round.
Table
Results
Sources
RSSSF
Swiss Football League seasons
Swiss
1999–2000 in Swiss football |
https://en.wikipedia.org/wiki/2001%E2%80%9302%20Nationalliga%20A | Statistics of National League A in the 2001–02 football season.
Nationalliga A
The Qualification Round to the League season 2001–02 was contested by twelve teams. The first eight teams of the regular season (or Qualification) were then to compete in the Championship Playoff Round. The teams in ninth to twelfth position completed with the top four teams of the Nationalliga B in a Nationalliga A/B Playoff round. At the end of the season FC Basel won the championship.
Regular season
Table
Results
Champion playoffs
The first eight teams of the regular season (or Qualification) competed in the Championship Playoff Round. They took half of the points (rounded up to complete units) gained in the Qualification as Bonus with them.
Table
Results
Nationalliga A/B Playoffs
Table
Results
Sources
RSSSF
Swiss Football League seasons
Swiss
1 |
https://en.wikipedia.org/wiki/2002%E2%80%9303%20Nationalliga%20A | Statistics of Nationalliga A (, ) in the 2002–03 football season.
Nationalliga A
Overview
The Qualification Round to the League season 2002–03 was contested by twelve teams. The first eight teams of the regular season (or Qualification) were then to compete in the Championship Playoff Round. The teams in ninth to twelfth position competed with the top four teams of the Nationalliga B in a Nationalliga A/B Playoff round. At the end of the season Grasshopper Club Zürich won the championship.
Regular season
Table
Results
Champion Playoffs
The first eight teams of the regular season (or Qualification) competed in the Championship Playoff Round. They took half of the points (rounded up to complete units) gained in the Qualification as Bonus with them.
Table
Results
Nationalliga A/B Playoffs
Table
Results
Sources
RSSSF
Swiss Football League seasons
Swiss
1 |
https://en.wikipedia.org/wiki/James%27s%20theorem | In mathematics, particularly functional analysis, James' theorem, named for Robert C. James, states that a Banach space is reflexive if and only if every continuous linear functional's norm on attains its supremum on the closed unit ball in
A stronger version of the theorem states that a weakly closed subset of a Banach space is weakly compact if and only if the dual norm each continuous linear functional on attains a maximum on
The hypothesis of completeness in the theorem cannot be dropped.
Statements
The space considered can be a real or complex Banach space. Its continuous dual space is denoted by The topological dual of ℝ-Banach space deduced from by any restriction scalar will be denoted (It is of interest only if is a complex space because if is a -space then )
A Banach space being reflexive if and only if its closed unit ball is weakly compact one deduces from this, since the norm of a continuous linear form is the upper bound of its modulus on this ball:
History
Historically, these sentences were proved in reverse order. In 1957, James had proved the reflexivity criterion for separable Banach spaces and 1964 for general Banach spaces. Since the reflexivity is equivalent to the weak compactness of the unit sphere, Victor L. Klee reformulated this as a compactness criterion for the unit sphere in 1962 and assumes that this criterion characterizes any weakly compact quantities. This was then actually proved by James in 1964.
See also
Notes
References
.
.
.
.
Theorems in functional analysis |
https://en.wikipedia.org/wiki/Pure%20type%20system |
In the branches of mathematical logic known as proof theory and type theory, a pure type system (PTS), previously known as a generalized type system (GTS), is a form of typed lambda calculus that allows an arbitrary number of sorts and dependencies between any of these. The framework can be seen as a generalisation of Barendregt's lambda cube, in the sense that all corners of the cube can be represented as instances of a PTS with just two sorts. In fact, Barendregt (1991) framed his cube in this setting. Pure type systems may obscure the distinction between types and terms and collapse the type hierarchy, as is the case with the calculus of constructions, but this is not generally the case, e.g. the simply typed lambda calculus allows only terms to depend on terms.
Pure type systems were independently introduced by Stefano Berardi (1988) and Jan Terlouw (1989). Barendregt discussed them at length in his subsequent papers. In his PhD thesis, Berardi defined a cube of constructive logics akin to the lambda cube (these specifications are non-dependent). A modification of this cube was later called the L-cube by Geuvers, who in his PhD thesis extended the Curry–Howard correspondence to this setting. Based on these ideas, Barthe and others defined classical pure type systems (CPTS) by adding a double negation operator.
Similarly, in 1998, Tijn Borghuis introduced modal pure type systems (MPTS). Roorda has discussed the application of pure type systems to functional programming; and Roorda and Jeuring have proposed a programming language based on pure type systems.
The systems from the lambda cube are all known to be strongly normalizing. Pure type systems in general need not be, for example System U from Girard's paradox is not. (Roughly speaking, Girard found pure systems in which one can express the sentence "the types form a type".) Furthermore, all known examples of pure type systems that are not strongly normalizing are not even (weakly) normalizing: they contain expressions that do not have normal forms, just like the untyped lambda calculus. It is a major open problem in the field whether this is always the case, i.e. whether a (weakly) normalizing PTS always has the strong normalization property. This is known as the Barendregt–Geuvers–Klop conjecture (named after Henk Barendregt, Herman Geuvers, and Jan Willem Klop).
Definition
A pure type system is defined by a triple where is the set of sorts, is the set of axioms, and is the set of rules. Typing in pure type systems is determined by the following rules, where is any sort:
Implementations
The following programming languages have pure type systems:
SAGE
Yarrow
Henk 2000
See also
System U – an example of an inconsistent PTS
λμ-calculus uses a different approach to control than CPTS
Notes
References
Further reading
External links
Proof theory
Type theory
Lambda calculus |
https://en.wikipedia.org/wiki/Run%20and%20Hide | Run and Hide may refer to:
"Run & Hide" (The Automatic song), a 2010 song by The Automatic
"Run & Hide" (Gracia Baur song), a 2005 song by Gracia Baur
"Run and Hide", a song by Algebra from Purpose
"Run and Hide", a song by Anna Chalon
"Run and Hide", a song by Blackfoot from Strikes
"Run and Hide", a song by Jay Electronica
"Run and Hide", a song by The Uniques
"Run and Hide", a song by Sabrina Carpenter from Evolution
"Run and Hide (The Gun Song)", a song by Status Quo from Bula Quo!
Run and Hide (novel), by Pankaj Mishra |
https://en.wikipedia.org/wiki/Ergodic%20Ramsey%20theory | Ergodic Ramsey theory is a branch of mathematics where problems motivated by additive combinatorics are proven using ergodic theory.
History
Ergodic Ramsey theory arose shortly after Endre Szemerédi's proof that a set of positive upper density contains arbitrarily long arithmetic progressions, when Hillel Furstenberg gave a new proof of this theorem using ergodic theory. It has since produced combinatorial results, some of which have yet to be obtained by other means, and has also given a deeper understanding of the structure of measure-preserving dynamical systems.
Szemerédi's theorem
Szemerédi's theorem is a result in arithmetic combinatorics, concerning arithmetic progressions in subsets of the integers. In 1936, Erdős and Turán conjectured that every set of integers A with positive natural density contains a k term arithmetic progression for every k. This conjecture, which became Szemerédi's theorem, generalizes the statement of van der Waerden's theorem. Hillel Furstenberg proved the theorem using ergodic principles in 1977.
See also
IP set
Piecewise syndetic set
Ramsey theory
Syndetic set
Thick set
References
Ergodic Methods in Additive Combinatorics
Vitaly Bergelson (1996) Ergodic Ramsey Theory -an update
Sources
Ergodic theory
Ramsey theory |
https://en.wikipedia.org/wiki/Markov%20information%20source | In mathematics, a Markov information source, or simply, a Markov source, is an information source whose underlying dynamics are given by a stationary finite Markov chain.
Formal definition
An information source is a sequence of random variables ranging over a finite alphabet , having a stationary distribution.
A Markov information source is then a (stationary) Markov chain , together with a function
that maps states in the Markov chain to letters in the alphabet .
A unifilar Markov source is a Markov source for which the values are distinct whenever each of the states are reachable, in one step, from a common prior state. Unifilar sources are notable in that many of their properties are far more easily analyzed, as compared to the general case.
Applications
Markov sources are commonly used in communication theory, as a model of a transmitter. Markov sources also occur in natural language processing, where they are used to represent hidden meaning in a text. Given the output of a Markov source, whose underlying Markov chain is unknown, the task of solving for the underlying chain is undertaken by the techniques of hidden Markov models, such as the Viterbi algorithm.
See also
Entropy rate
References
Robert B. Ash, Information Theory, (1965) Dover Publications.
Markov processes
Statistical natural language processing |
https://en.wikipedia.org/wiki/Information%20source | Information source may refer to:
Information source (mathematics), a kind of sequence of random variables
Source text, a text (sometimes oral) from which information or ideas are derived
Guide to information sources, a kind of "metabibliography". Ideally it is not just a listing of bibliographies, reference works and other source texts, but more like a textbook introducing users to the information sources in a given field (in general).
, a grapheme used to indicate the existence of an information board or to highlight other information in a manual |
https://en.wikipedia.org/wiki/Orthogonal%20array | In mathematics, an orthogonal array (more specifically, a fixed-level orthogonal array) is a "table" (array) whose entries come from a fixed finite set of symbols (for example, {1,2,...,v}), arranged in such a way that there is an integer t so that for every selection of t columns of the table, all ordered t-tuples of the symbols, formed by taking the entries in each row restricted to these columns, appear the same number of times. The number t is called the strength of the orthogonal array. Here are two examples:
The example at left is that of an orthogonal array with symbol set {1,2} and strength 2. Notice that the four ordered pairs (2-tuples) formed by the rows restricted to the first and third columns, namely (1,1), (2,1), (1,2) and (2,2), are all the possible ordered pairs of the two element set and each appears exactly once. The second and third columns would give, (1,1), (2,1), (2,2) and (1,2); again, all possible ordered pairs each appearing once. The same statement would hold had the first and second columns been used. This is thus an orthogonal array of strength two.
In the example on the right, the rows restricted to the first three columns contain the 8 possible ordered triples consisting of 0's and 1's, each appearing once. The same holds for any other choice of three columns. Thus this is an orthogonal array of strength 3.
A mixed-level orthogonal array is one in which each column may have a different number of symbols. An example is given below.
Orthogonal arrays generalize, in a tabular form, the idea of mutually orthogonal Latin squares. These arrays have many connections to other combinatorial designs and have applications in the statistical design of experiments, coding theory, cryptography and various types of software testing.
Definition
For t ≤ k, an orthogonal array of type (N, k, v, t) – an OA(N, k, v, t) for short – is an N × k array whose entries are chosen from a set X with v points (a v-set) such that in every subset of t columns of the array, every t-tuple of points of X is repeated the same number of times. The number of repeats is usually denoted λ.
In many applications these parameters are given the following names:
N is the number of experimental runs,
k is the number of factors,
v is the number of levels,
t is the strength, and
λ is the index.
The definition of strength leads to the parameter relation
N = λvt.
An orthogonal array is simple if it does not contain any repeated rows. (Subarrays of t columns may have repeated rows, as in the OA(18, 7, 3, 2) example pictured in this section.)
An orthogonal array is linear if X is a finite field Fq of order q (q a prime power) and the rows of the array form a subspace of the vector space (Fq)k. The right-hand example in the introduction is linear over the field F2. Every linear orthogonal array is simple.
In a mixed-level orthogonal array, the symbols in the columns may be chosen from different sets having different numbers of points, as in the |
https://en.wikipedia.org/wiki/2007%E2%80%9308%20South%20China%20AA%20season | The 2007–08 season is South China's 2nd year after giving up the all-Chinese policy. This article shows statistics of the club's players in the season, and also lists all matches that the club have and will play in the season.
Events
On the 24 July 2007, South China were beaten 3-1 by Liverpool in the Barclays Asia Trophy 2007. Liverpool goals were scored by John Arne Riise, Xabi Alonso and Daniel Agger. South China's goal was scored by Li Haiqiang who found the net by curving the ball from 46 yards into the top left corner.
On the 27 July 2007, Fulham beat South China 4-1 in the 3rd place play-off. South China pull one back after 56 minutes when Li Haiqiang’s quickly taken free-kick was volleyed home in impressive fashion by Flavio Barros.
On November 27, 2008, Hong Kong Red Cross officially entered a charity partnership with the club and its logo will be printed on SCAA team jerseys, extending and spreading humanity everywhere the team goes. The charity partnership is a pioneer between a sports association and a humanitarian organization in Hong Kong.
On March 9, 2008, an All-Star team primarily consisting of SCAA players (credited as Hong Kong Union) hosted a friendly versus Los Angeles Galaxy in the MLS side's last match in their preseason tour of Asia. The Hong Kong side won the penalty shootout 5-4 after drawing 2-2 in regulation.
Players
Squad stats
Players in/out
In
Wong Chin Hung (黃展鴻) from Rangers
Yip Chi Ho (葉志豪) from Rangers
Flavio Barros (巴路士) from Vila Nova Futebol Clube (loan)
Sidrailson (沙域臣) from Santa Cruz (Brazilian Pernambuco Football Championship Série A1) (loan)
Juninho Petrolina (S·祖利亞) from Central (Brazilian Campeonato Pernambucano Série A1 / Campeonato Brasileiro Série C)
Fan Weijun (樊偉軍) from Rangers
Du Ping (杜蘋) from Shaanxi Baorong (Chinese Super League) (loan)
Cris (基斯) from Metropolitano (Brazilian Campeonato Catarinense) (loan)
Itaparica (伊達) from Paysandu (loan)
Maxwell (麥士維) from Riffa Club (Bahraini Premier League)
Nuno (盧諾) from Moreirense FC (Portuguese Second Division Serie A)
Chung Ho Yin (鍾皓賢) from Eastern (return from loan)
Tales Schütz (T·史高斯) from Leixões (Portuguese Liga)
Out
Edemar Picoli (比高) to Eastern
Cris (基斯) to Metropolitano (return from loan)
Yaw Anane (友友) to Citizen (return from loan)
Cleiton (基頓) to Santa Cruz (return from loan)
Mihailo Jovanović (袓雲奴域) (released)
Wong Chun Yue (黃鎮宇) (released)
Au Wai Lun (歐偉倫) (retired)
Tales Schütz (T·史高斯) to Grêmio Inhumense (Brazilian Campeonato Goiano) (return from loan)
Chung Ho Yin (鍾皓賢) to Eastern (loan)
Juninho Petrolina (S·祖利亞) to ABC (Brazilian Campeonato Potiguar / Campeonato Brasileiro Série C)
Liang Zicheng (梁子成) to Rangers (loan)
Flavio Barros (巴路士) to Vila Nova (return from loan)
Du Ping (杜蘋) (released)
Nuno (盧諾) to Rangers
Club
Coaching staff
Kit
Other information
Competitions
Hong Kong First Division League
Results by round
Matches
Hong Kong First Division
Senior Shield
League Cup
AFC Cup
FA |
https://en.wikipedia.org/wiki/Grothendieck%20space | In mathematics, a Grothendieck space, named after Alexander Grothendieck, is a Banach space in which every sequence in its continuous dual space that converges in the weak-* topology (also known as the topology of pointwise convergence) will also converge when is endowed with which is the weak topology induced on by its bidual. Said differently, a Grothendieck space is a Banach space for which a sequence in its dual space converges weak-* if and only if it converges weakly.
Characterizations
Let be a Banach space. Then the following conditions are equivalent:
is a Grothendieck space,
for every separable Banach space every bounded linear operator from to is weakly compact, that is, the image of a bounded subset of is a weakly compact subset of
for every weakly compactly generated Banach space every bounded linear operator from to is weakly compact.
every weak*-continuous function on the dual is weakly Riemann integrable.
Examples
Every reflexive Banach space is a Grothendieck space. Conversely, it is a consequence of the Eberlein–Šmulian theorem that a separable Grothendieck space must be reflexive, since the identity from is weakly compact in this case.
Grothendieck spaces which are not reflexive include the space of all continuous functions on a Stonean compact space and the space for a positive measure (a Stonean compact space is a Hausdorff compact space in which the closure of every open set is open).
Jean Bourgain proved that the space of bounded holomorphic functions on the disk is a Grothendieck space.
See also
References
J. Diestel, Geometry of Banach spaces, Selected Topics, Springer, 1975.
J. Diestel, J. J. Uhl: Vector measures. Providence, R.I.: American Mathematical Society, 1977. .
Nisar A. Lone, on weak Riemann integrability of weak* - continuous functions. Mediterranean journal of Mathematics, 2017.
Banach spaces |
https://en.wikipedia.org/wiki/Steve%20Olson | Steve Olson is an American writer who specializes in science, mathematics, and public policy. He is the author of several nonfiction trade books: Mapping Human History: Genes, Race, and Our Common Origins, which was nominated for the National Book Award in 2002; Count Down: Six Kids Vie for Glory at the World’s Toughest Math Competition in 2004; Anarchy Evolution: Faith, Science, and Bad Religion in a World Without God in 2010; Eruption: The Untold Story of Mt. St. Helens in 2016.
He also has written for many magazines, including the Atlantic Monthly, the Smithsonian, Science, Scientific American, Wired, the Yale Alumni Magazine, the Washingtonian, Slate, and Paste. His articles have been reprinted in Best American Science and Nature Writing 2003 and 2007.
Research on ancestry
Mapping Human History contained a conjecture about human ancestry that was disputed when the book was published. The book claimed that the most recent common ancestor of everyone living on the earth today must have lived just 2,000 to 3,000 years ago, a number that geneticists thought much too small. However, a more formal version of the conjecture was proven by the author, working with coauthors Douglas Rohde and Joseph Chang, in a September 30, 2004, article in Nature. They modeled the human population as a set of randomly mating subpopulations that are connected by occasional migrants. If the size of the population is n, then the time to the most recent common ancestor is a small multiple of the base-2 logarithm of n, even if the levels of migration among the populations are very low. Using a model of the world's landmasses and populations with moderate levels of migration, the authors calculated that the most recent common ancestor could have lived as recently as AD 55.
These results lead to some highly counterintuitive conclusions. In the generations before that of the most recent common ancestor, more and more people are common ancestors of everyone living on Earth today. At a time 2,000 to 3,000 years before the appearance of the most recent common ancestor, everyone in the world is either an ancestor of everyone living today or an ancestor of no one living today. Thus, everyone living today has exactly the same set of ancestors who lived 5,000 to 6,000 years ago, even though those ancestors are represented in very different proportions on a person's family tree.
In an article published in the Los Angeles Times on the day the movie The Da Vinci Code was released, Olson pointed to several other consequences of the analysis in the Nature paper.
Personal information
Olson is married to Lynn Olson, a long-time education journalist who is currently a senior program officer with the Bill and Melinda Gates Foundation. They have two children, Sarah and Eric.
References
External links
American science writers
Living people
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Rational%20dependence | In mathematics, a collection of real numbers is rationally independent if none of them can be written as a linear combination of the other numbers in the collection with rational coefficients. A collection of numbers which is not rationally independent is called rationally dependent. For instance we have the following example.
Because if we let , then .
Formal definition
The real numbers ω1, ω2, ... , ωn are said to be rationally dependent if there exist integers k1, k2, ... , kn, not all of which are zero, such that
If such integers do not exist, then the vectors are said to be rationally independent. This condition can be reformulated as follows: ω1, ω2, ... , ωn are rationally independent if the only n-tuple of integers k1, k2, ... , kn such that
is the trivial solution in which every ki is zero.
The real numbers form a vector space over the rational numbers, and this is equivalent to the usual definition of linear independence in this vector space.
See also
Baker's theorem
Dehn invariant
Gelfond–Schneider theorem
Hamel basis
Hodge conjecture
Lindemann–Weierstrass theorem
Linear flow on the torus
Schanuel's conjecture
Bibliography
Dynamical systems |
https://en.wikipedia.org/wiki/Linear%20flow%20on%20the%20torus | In mathematics, especially in the area of mathematical analysis known as dynamical systems theory, a linear flow on the torus is a flow on the n-dimensional torus
which is represented by the following differential equations with respect to the standard angular coordinates
The solution of these equations can explicitly be expressed as
If we represent the torus as we see that a starting point is moved by the flow in the direction at constant speed and when it reaches the border of the unitary -cube it jumps to the opposite face of the cube.
For a linear flow on the torus either all orbits are periodic or all orbits are dense on a subset of the -torus which is a -torus. When the components of are rationally independent all the orbits are dense on the whole space. This can be easily seen in the two dimensional case: if the two components of are rationally independent then the Poincaré section of the flow on an edge of the unit square is an irrational rotation on a circle and therefore its orbits are dense on the circle, as a consequence the orbits of the flow must be dense on the torus.
Irrational winding of a torus
In topology, an irrational winding of a torus is a continuous injection of a line into a two-dimensional torus that is used to set up several counterexamples. A related notion is the Kronecker foliation of a torus, a foliation formed by the set of all translates of a given irrational winding.
Definition
One way of constructing a torus is as the quotient space of a two-dimensional real vector space by the additive subgroup of integer vectors, with the corresponding projection Each point in the torus has as its preimage one of the translates of the square lattice in and factors through a map that takes any point in the plane to a point in the unit square given by the fractional parts of the original point's Cartesian coordinates. Now consider a line in given by the equation If the slope of the line is rational, then it can be represented by a fraction and a corresponding lattice point of It can be shown that then the projection of this line is a simple closed curve on a torus. If, however, is irrational, then it will not cross any lattice points except 0, which means that its projection on the torus will not be a closed curve, and the restriction of on this line is injective. Moreover, it can be shown that the image of this restricted projection as a subspace, called the irrational winding of a torus, is dense in the torus.
Applications
Irrational windings of a torus may be used to set up counter-examples related to monomorphisms. An irrational winding is an immersed submanifold but not a regular submanifold of the torus, which shows that the image of a manifold under a continuous injection to another manifold is not necessarily a (regular) submanifold. Irrational windings are also examples of the fact that the topology of the submanifold does not have to coincide with the subspace topology of the submanifold.
S |
https://en.wikipedia.org/wiki/Jos%C3%A9%20Luis%20Garc%C3%ADa%20%28footballer%29 | José Luis García (; born 18 April 1985) is an Argentinian footballer who plays as a midfielder for Almirante Brown.
External links
José Luis García – Argentine Primera statistics at Fútbol XXI
1985 births
Living people
Sportspeople from La Matanza Partido
Argentine men's footballers
Argentine expatriate men's footballers
San Lorenzo de Almagro footballers
Club Olimpo footballers
Club Almirante Brown footballers
Rosario Central footballers
Liga I players
FC Politehnica Timișoara players
FC Gloria Buzău players
Atlético Morelia players
Sportivo Luqueño players
Club Universidad de Chile footballers
Expatriate men's footballers in Chile
Argentine expatriate sportspeople in Chile
Expatriate men's footballers in Mexico
Argentine expatriate sportspeople in Mexico
Expatriate men's footballers in Paraguay
Argentine expatriate sportspeople in Paraguay
Expatriate men's footballers in Costa Rica
Argentine expatriate sportspeople in Costa Rica
Expatriate men's footballers in Romania
Argentine expatriate sportspeople in Romania
Men's association football midfielders
Footballers from Buenos Aires Province |
https://en.wikipedia.org/wiki/BMW%20GINA | The GINA Light Visionary Model is a fabric-skinned shape-shifting sports car concept built by BMW. GINA stands for "Geometry and functions In 'N' Adaptions". It was designed by a team led by BMW's head of design, Chris Bangle, who says GINA allowed his team to "challenge existing principles and conventional processes." Other designers include Anders Warming.
Construction began in 2001, with the finished car being presented in 2008.
Fabric body
BMW claims the elastic, water resistant, translucent man-made fabric skin—polyurethane-coated Spandex—is resilient and durable. It resists high or low temperatures, does not swell or shrink, and the movement does not slacken or damage the fabric. The body changes its shape according to exterior conditions and speeds, and it also allows the driver to change its shape at will. The fabric is stretched over a frame with moving parts; shapes are formed beneath the skin by an aluminium wire structure, though at points where flexibility is needed (ducts, door openings, spoiler), flexible carbon struts are used.
The shape of the frame is controlled by many electric and hydraulic actuators; for example, the headlights are revealed when small motors pull the fabric open from slits in an eyelid-like fashion, and access to the engine can be gained through a slit that opens down the middle of the bonnet. As the fabric is translucent, the taillights simply shine through it.
GINA has just four "panels"—the bonnet, the two side panels and the trunk. Its skin appears seamless, but it can "grow" out its rear spoiler for stability at high speed. Its doors open in a butterfly style and are each covered by a fabric piece reaching all the way from the nose of the car to their trailing edge which, when closed, leaves a perfectly smooth surface.
Interior
When the car is parked, the car's steering wheel and instruments sit in an "idle" position on the centre console to allow the driver easy entry. The steering wheel and instruments assume their correct positions when the driver presses the start button and the headrest rises from the seat once the driver is seated, making it easier to get in and out of the car.
Jokes around the name
The unusual name for the concept vehicle has amused some commentators. A few have compared the opening on the bonnet/hood to a vagina. Carscoops did so after receiving an image of the vehicle from Top Gear Magazine, commenting: "Mystery Solved: Why BMW Calls it 'Gina...". Jalopnik also picked up on the name but refused to clarify, joking that they were a "family show".
References
External links
BMW GINA Light Visionary Model: Premiere
BMW GINA Light Visionary Model: Design
BMW GINA Light Visionary Model trailer
Wired - BMW Builds a Shape-Shifting Car Out of Cloth (with many pictures)
Pictures of GINA
BMW Visionen: GINA Light
GINA Light im BMW Museum
GINA |
https://en.wikipedia.org/wiki/Tetrahedron%20packing | In geometry, tetrahedron packing is the problem of arranging identical regular tetrahedra throughout three-dimensional space so as to fill the maximum possible fraction of space.
Currently, the best lower bound achieved on the optimal packing fraction of regular tetrahedra is 85.63%. Tetrahedra do not tile space, and an upper bound below 100% (namely, 1 − (2.6...)·10−25) has been reported.
Historical results
Aristotle claimed that tetrahedra could fill space completely.
In 2006, Conway and Torquato showed that a packing fraction about 72% can be obtained by constructing a non-Bravais lattice packing of tetrahedra (with multiple particles with generally different orientations per repeating unit), and thus they showed that the best tetrahedron packing cannot be a lattice packing (with one particle per repeating unit such that each particle has a common orientation). These packing constructions almost doubled the optimal Bravais-lattice-packing fraction 36.73% obtained by Hoylman. In 2007 and 2010, Chaikin and coworkers experimentally showed that tetrahedron-like dice can randomly pack in a finite container up to a packing fraction between 75% and 76%. In 2008, Chen was the first to propose a packing of hard, regular tetrahedra that packed more densely than spheres, demonstrating numerically a packing fraction of 77.86%. A further improvement was made in 2009 by Torquato and Jiao, who compressed Chen's structure using a computer algorithm to a packing fraction of 78.2021%.
In mid-2009 Haji-Akbari et al. showed, using MC simulations of initially random systems that at packing densities >50% an equilibrium fluid of hard tetrahedra spontaneously transforms to a dodecagonal quasicrystal, which can be compressed to 83.24%. They also reported a glassy, disordered packing at densities exceeding 78%. For a periodic approximant to a quasicrystal with an 82-tetrahedron unit cell, they obtained a packing density as high as 85.03%.
In late 2009, a new, much simpler family of packings with a packing fraction of 85.47% was discovered by Kallus, Elser, and Gravel. These packings were also the basis of a slightly improved packing obtained by Torquato and Jiao at the end of 2009 with a packing fraction of 85.55%, and by Chen, Engel, and Glotzer in early 2010 with a packing fraction of 85.63%. The Chen, Engel and Glotzer result currently stands as the densest known packing of hard, regular tetrahedra. Surprisingly, the square-triangle tiling packs denser than this double lattice of triangular bipyramids when tetrahedra are slightly rounded (the Minkowski sum of a tetrahedron and a sphere), making the 82-tetrahedron crystal the largest unit cell for a densest packing of identical particles to date.
Relationship to other packing problems
Because the earliest lower bound known for packings of tetrahedra was less than that of spheres, it was suggested that the regular tetrahedra might be a counterexample to Ulam's conjecture that the optimal density for packin |
https://en.wikipedia.org/wiki/Bareiss%20algorithm | In mathematics, the Bareiss algorithm, named after Erwin Bareiss, is an algorithm to calculate the determinant or the echelon form of a matrix with integer entries using only integer arithmetic; any divisions that are performed are guaranteed to be exact (there is no remainder). The method can also be used to compute the determinant of matrices with (approximated) real entries, avoiding the introduction of any round-off errors beyond those already present in the input.
History
The general Bareiss algorithm is distinct from the Bareiss algorithm for Toeplitz matrices.
In some Spanish-speaking countries, this algorithm is also known as Bareiss-Montante, because of René Mario Montante Pardo, a professor of the Universidad Autónoma de Nuevo León, Mexico, who popularized the method among his students.
Overview
Determinant definition has only multiplication, addition and subtraction operations. Obviously the determinant is integer if all matrix entries are integer. However actual computation of the determinant using the definition or Leibniz formula is impractical, as it requires O(n!) operations.
Gaussian elimination has O(n3) complexity, but introduces division, which results in round-off errors when implemented using floating point numbers.
Round-off errors can be avoided if all the numbers are kept as integer fractions instead of floating point. But then the size of each element grows in size exponentially with the number of rows.
Bareiss brings up a question of performing an integer-preserving elimination while keeping the magnitudes of the intermediate coefficients reasonably small. Two algorithms are suggested:
Division-free algorithm — performs matrix reduction to triangular form without any division operation.
Fraction-free algorithm — uses division to keep the intermediate entries smaller, but due to the Sylvester's Identity the transformation is still integer-preserving (the division has zero remainder).
For completeness Bareiss also suggests fraction-producing multiplication-free elimination methods.
The algorithm
The program structure of this algorithm is a simple triple-loop, as in the standard Gaussian elimination. However in this case the matrix is modified so that each entry contains the leading principal minor []. Algorithm correctness is easily shown by induction on .
Input: — an -square matrixassuming its leading principal minors [] are all non-zero.
Let M0,0 1 (Note: M0,0 is a special variable)
For from 1 to −1:
For from +1 to :
For from +1 to :
Set
Output: The matrix is modified in-place,each entry contains the leading minor [],entry contains the determinant of the original .
If the assumption about principal minors turns out to be false, e.g. if −1,−1 = 0 and some ,−1 ≠ 0 ( = ,...,) then we can exchange the −1-th row with the -th row and change the sign of the final answer.
Analysis
During execution of the Bareiss algorithm, every integer that is computed is the determinant of a submatrix of the input |
https://en.wikipedia.org/wiki/Perfect%20map | In mathematics, especially topology, a perfect map is a particular kind of continuous function between topological spaces. Perfect maps are weaker than homeomorphisms, but strong enough to preserve some topological properties such as local compactness that are not always preserved by continuous maps.
Formal definition
Let and be topological spaces and let be a map from to that is continuous, closed, surjective and such that each fiber is compact relative to for each in . Then is known as a perfect map.
Examples and properties
If is a perfect map and is compact, then is compact.
If is a perfect map and is regular, then is regular. (If is merely continuous, then even if is regular, need not be regular. An example of this is if is a regular space and is an infinite set in the indiscrete topology.)
If is a perfect map and if is locally compact, then is locally compact.
If is a perfect map and if is second countable, then is second countable.
Every injective perfect map is a homeomorphism. This follows from the fact that a bijective closed map has a continuous inverse.
If is a perfect map and if is connected, then need not be connected. For example, the constant map from a compact disconnected space to a singleton space is a perfect map.
A perfect map need not be open. Indeed, consider the map given by if and if . This map is closed, continuous (by the pasting lemma), and surjective and therefore is a perfect map (the other condition is trivially satisfied). However, p is not open, for the image of under p is which is not open relative to (the range of p). Note that this map is a quotient map and the quotient operation is 'gluing' two intervals together.
Notice how, to preserve properties such as local connectedness, second countability, local compactness etc. ... the map must be not only continuous but also open. A perfect map need not be open (see previous example), but these properties are still preserved under perfect maps.
Every homeomorphism is a perfect map. This follows from the fact that a bijective open map is closed and that since a homeomorphism is injective, the inverse of each element of the range must be finite in the domain (in fact, the inverse must have precisely one element).
Every perfect map is a quotient map. This follows from the fact that a closed, continuous surjective map is always a quotient map.
Let G be a compact topological group which acts continuously on X. Then the quotient map from X to X/G is a perfect map.
Perfect maps are proper. The converse is true, provided the topology of Y is Hausdorff and compactly generated.
See also
References
Theory of continuous functions |
https://en.wikipedia.org/wiki/Jit%2C%20Qalqilya | Jit () is a Palestinian town in the northern West Bank, located 10 kilometers (6.2 mi) west of Nablus. According to the Palestinian Central Bureau of Statistics, the village had a population of 2,405 inhabitants in 2017.
Location
Jit is located (horizontally) north-east of Qalqilya. It is bordered by Sarra and Beit Iba to the east, Fara'ata and Immatain to the south, Kafr Qaddum to the west, and Qusin to the north.
History
No Byzantine remains have been found here, leading scholars to suggest that the early Muslim inhabitants came there as a result of migration, and not conversion. However, in 2011 two reliefs of menorahs dating from the Byzantine period, probably of Samaritan origin, were discovered in Jit.
Diya al-Din (1173-1245) refers to the presence of Muslims in Jit during his lifetime, and that followers of Ibn Qudamah lived here.
Ottoman era
In 1517, the village was included in the Ottoman empire with the rest of Palestine, and in the 1596 tax-records it appeared as Jit Jammal, located in the Nahiya of Jabal Qubal of the Liwa of Nablus. The population was 50 households, all Muslim. They paid a fixed tax rate of 33.3% on agricultural products, such as wheat, barley, summer crops, olive trees, goats and beehives, a press for olive oil or grape syrup, in addition to occasional revenues and a fixed tax for people of Nablus area; a total of 20,000 akçe.
A map from Napoleon's invasion of 1799 by Pierre Jacotin named it Qarihagi, (Quryet Jitt) as a village by the road from Jaffa to Nablus.
In 1838, Kuryet Jit was noted as a village located in the District of Jurat 'Amra, south of Nablus.
In 1870, Victor Guérin noted between seven hundred and fifty and eight hundred people in the village. Also, "here Guérin observed among the houses a certain number of cut stones of apparent
antiquity. Many of the houses are in a ruinous condition, others are completely destroyed. On the north-west side of the hill he found a great well, into which one descends by fifteen steps, now fallen to pieces. It gives a supply of water which never fails. The place is probably the old Gitta mentioned by Justin Martyr and Eusebius as the birthplace of Simon the Magician."
In 1870/1871 (1288 AH), an Ottoman census listed the village in the nahiya (sub-district) of Jamma'in al-Thani, subordinate to Nablus.
In 1882, the PEF's Survey of Western Palestine (SWP) described Kuryet Jit as: "A well-built stone village with a high house in it, standing on a knoll by the main road, surrounded with olives; it has a well to the west; the inhabitants are remarkable for their courtesy, this part of the country and all the district west of it being little visited by tourists."
British Mandate era
In the 1922 census of Palestine conducted by the British Mandate authorities, Qariyet Jit had a population of 285 Muslims, increasing in the 1931 census to 289 Muslims, in 70 houses.
In the 1945 statistics the population of Jit was 440 (all Muslim), while the total land area was 6,4 |
https://en.wikipedia.org/wiki/Uniform%2010-polytope | In ten-dimensional geometry, a 10-polytope is a 10-dimensional polytope whose boundary consists of 9-polytope facets, exactly two such facets meeting at each 8-polytope ridge.
A uniform 10-polytope is one which is vertex-transitive, and constructed from uniform facets.
Regular 10-polytopes
Regular 10-polytopes can be represented by the Schläfli symbol {p,q,r,s,t,u,v,w,x}, with x {p,q,r,s,t,u,v,w} 9-polytope facets around each peak.
There are exactly three such convex regular 10-polytopes:
{3,3,3,3,3,3,3,3,3} - 10-simplex
{4,3,3,3,3,3,3,3,3} - 10-cube
{3,3,3,3,3,3,3,3,4} - 10-orthoplex
There are no nonconvex regular 10-polytopes.
Euler characteristic
The topology of any given 10-polytope is defined by its Betti numbers and torsion coefficients.
The value of the Euler characteristic used to characterise polyhedra does not generalize usefully to higher dimensions, and is zero for all 10-polytopes, whatever their underlying topology. This inadequacy of the Euler characteristic to reliably distinguish between different topologies in higher dimensions led to the discovery of the more sophisticated Betti numbers.
Similarly, the notion of orientability of a polyhedron is insufficient to characterise the surface twistings of toroidal polytopes, and this led to the use of torsion coefficients.
Uniform 10-polytopes by fundamental Coxeter groups
Uniform 10-polytopes with reflective symmetry can be generated by these three Coxeter groups, represented by permutations of rings of the Coxeter-Dynkin diagrams:
Selected regular and uniform 10-polytopes from each family include:
Simplex family: A10 [39] -
527 uniform 10-polytopes as permutations of rings in the group diagram, including one regular:
{39} - 10-simplex -
Hypercube/orthoplex family: B10 [4,38] -
1023 uniform 10-polytopes as permutations of rings in the group diagram, including two regular ones:
{4,38} - 10-cube or dekeract -
{38,4} - 10-orthoplex or decacross -
h{4,38} - 10-demicube .
Demihypercube D10 family: [37,1,1] -
767 uniform 10-polytopes as permutations of rings in the group diagram, including:
17,1 - 10-demicube or demidekeract -
71,1 - 10-orthoplex -
The A10 family
The A10 family has symmetry of order 39,916,800 (11 factorial).
There are 512+16-1=527 forms based on all permutations of the Coxeter-Dynkin diagrams with one or more rings. 31 are shown below: all one and two ringed forms, and the final omnitruncated form. Bowers-style acronym names are given in parentheses for cross-referencing.
The B10 family
There are 1023 forms based on all permutations of the Coxeter-Dynkin diagrams with one or more rings.
Twelve cases are shown below: ten single-ring (rectified) forms, and two truncations. Bowers-style acronym names are given in parentheses for cross-referencing.
The D10 family
The D10 family has symmetry of order 1,857,945,600 (10 factorial × 29).
This family has 3×256−1=767 Wythoffian uniform polytopes, generated by marking one or more nodes |
https://en.wikipedia.org/wiki/Dyadics | In mathematics, specifically multilinear algebra, a dyadic or dyadic tensor is a second order tensor, written in a notation that fits in with vector algebra.
There are numerous ways to multiply two Euclidean vectors. The dot product takes in two vectors and returns a scalar, while the cross product returns a pseudovector. Both of these have various significant geometric interpretations and are widely used in mathematics, physics, and engineering. The dyadic product takes in two vectors and returns a second order tensor called a dyadic in this context. A dyadic can be used to contain physical or geometric information, although in general there is no direct way of geometrically interpreting it.
The dyadic product is distributive over vector addition, and associative with scalar multiplication. Therefore, the dyadic product is linear in both of its operands. In general, two dyadics can be added to get another dyadic, and multiplied by numbers to scale the dyadic. However, the product is not commutative; changing the order of the vectors results in a different dyadic.
The formalism of dyadic algebra is an extension of vector algebra to include the dyadic product of vectors. The dyadic product is also associative with the dot and cross products with other vectors, which allows the dot, cross, and dyadic products to be combined to obtain other scalars, vectors, or dyadics.
It also has some aspects of matrix algebra, as the numerical components of vectors can be arranged into row and column vectors, and those of second order tensors in square matrices. Also, the dot, cross, and dyadic products can all be expressed in matrix form. Dyadic expressions may closely resemble the matrix equivalents.
The dot product of a dyadic with a vector gives another vector, and taking the dot product of this result gives a scalar derived from the dyadic. The effect that a given dyadic has on other vectors can provide indirect physical or geometric interpretations.
Dyadic notation was first established by Josiah Willard Gibbs in 1884. The notation and terminology are relatively obsolete today. Its uses in physics include continuum mechanics and electromagnetism.
In this article, upper-case bold variables denote dyadics (including dyads) whereas lower-case bold variables denote vectors. An alternative notation uses respectively double and single over- or underbars.
Definitions and terminology
Dyadic, outer, and tensor products
A dyad is a tensor of order two and rank one, and is the dyadic product of two vectors (complex vectors in general), whereas a dyadic is a general tensor of order two (which may be full rank or not).
There are several equivalent terms and notations for this product:
the dyadic product of two vectors and is denoted by (juxtaposed; no symbols, multiplication signs, crosses, dots, etc.)
the outer product of two column vectors and is denoted and defined as or , where means transpose,
the tensor product of two vectors and is denoted |
https://en.wikipedia.org/wiki/Al-Midya | al-Midya () is a Palestinian village in the Ramallah and al-Bireh Governorate in the western West Bank, located west of Ramallah. According to the Palestinian Central Bureau of Statistics, the village had a population of over 1,533 inhabitants in 2017.
Location
Al Midya is located (horizontally) west of Ramallah. It is bordered by Ni'lin to the east and north, the Green Line (the Armistice Line 1949) to the west, and Saffa to the south.
History
The ancient village site is located in Ras al-Midya, S-E of the village, where pottery from the Iron Age and later periods has been found. Additional findings include the ruins of structures, watering holes, coins from the Hellenistic and Roman periods, and an underground hiding complex where five coins, including two from the Bar Kokhba revolt, were discovered. Based on the archeological data, as well as the site's location, Raviv suggests that it was a Jewish settlement during the early Roman period.
The ancient village of Modiʿin / Modiʿuth, described in the Madaba Map as , Mōdeeim, and once the dwelling place of the Hasmoneans, is thought to have been preserved in its Arabicised form al-Midya., and which village originally occupied the site (now Khirbet er-Râs) directly to its south-east. In the Madaba Map, the site is marked by two towers having a single entranceway, and reads in Greek uncials: "Modiʿim, today Modʿitha, whence came the Maccabees."
Al-Midya was apparently mentioned by Ishtori Haparchi during the Mamluk era.
Ottoman era
Al-Midya was incorporated into the Ottoman Empire in 1517 with all of Palestine, and in the 1596 tax−records it appeared under the name of Midya as-Sarqiyya as being in the Nahiya of Ramla, part of Gaza Sanjak. It had a population of 25 Muslim households and paid a fixed tax rate of 25% on wheat, barley, summer crops or olives or fruit trees, and a press for olives or grapes; a total of 6,500 akçe.
In 1870, Victor Guérin visited, and thought that ruins found there were the graves of the Maccabees. However, Clermont-Ganneau made extensive excavations later, and he found Christian crosses in the oldest part of the largest structure. He concluded the ruins were from the 5th century or later, that is, from the Byzantine era.
An official Ottoman village list of about 1870 showed that el-medje had a total of 42 houses and a population of 159, though the population count included men only. It also noted that it was located half an hour east of Jimzu.
In 1882, PEF's Survey of Western Palestine described Midieh as being a village of a "good size", with houses either built of adobe or stone. To the north was a small olive grove, to the south a tank. The most "peculiar feature" they found was named er Ras. It was a high conical knoll, with a maqam on top, and rock-cut tombs on the side.
British Mandate era
In the 1922 census of Palestine conducted by the British Mandate authorities, Midya had an all Muslim population of 245, increasing in the 1931 census to 286, |
https://en.wikipedia.org/wiki/Time-hopping | Time-hopping (TH) is a communications signal technique which can be used to achieve anti-jamming (AJ) or low probability of intercept (LPI). It can also refer to pulse-position modulation, which in its simplest form employs 2k discrete pulses (referring to the unique positions of the pulse within the transmission window) to transmit k bit(s) per pulse.
Details
To achieve LPI, the transmission time is changed randomly by varying the period and duty cycle of the pulse (carrier) using a pseudo-random sequence. The transmitted signal will then have intermittent start and stop times. Although often used to form hybrid spread-spectrum (SS) systems, TH is strictly speaking a non-SS technique. Spreading of the spectrum is caused by other factors associated with TH, such as using pulses with low duty cycle having a wide frequency response. An example of hybrid SS is TH-FHSS or hybrid TDMA (time division multiple access).
See also
Spread spectrum
Frequency-hopping spread spectrum
Direct-sequence spread spectrum
Ultra-wideband
References
External links
"Time hopping and frequency hopping in ultrawideband systems"
Channel access methods
Wireless locating |
https://en.wikipedia.org/wiki/List%20of%20men%27s%20footballers%20with%2050%20or%20more%20international%20goals | In total, 77 male footballers to date have scored at least 50 goals with their national team at senior level, according to FIFA documents, RSSSF and IFFHS statistics. Since October 2021, the International Olympic Committee (IOC) has also been publishing an according list, but only of the top 10. Cristiano Ronaldo of Portugal holds the all-time record with 127 international goals.
Brazil and Hungary hold the record of having the most players to have scored 50 or more international goals with four each. England, Iraq, Japan, Kuwait, Malaysia and Thailand each have three players who have achieved the feat. The Asian Football Confederation (AFC) has the highest number of footballers who scored at least 50 international goals, with 30 players. Egypt is the only African team with more than one player who has scored at least 50 international goals, after Mohamed Salah achieved the feat on 24 March 2023.
Bader Al-Mutawa of Kuwait has played the most matches so far to score 50 international goals. He scored his 50th goal during his 155th international appearance, in a hat-trick against Myanmar on 3 September 2015, in a 2018 FIFA World Cup qualification match.
History
The first player to score 50 international goals was Imre Schlosser of Hungary. He achieved the feat when he scored a brace (two goals) in a 6–2 victory against Austria on 3 June 1917. In total, he scored 59 international goals in 68 matches, playing his last match on 10 April 1927. He remained the highest international goalscorer for 26 years, until his fellow countryman Ferenc Puskás broke the record in 1953. Puskás was the third player, after Poul Nielsen of Denmark, to achieve 50 goals in his international career. Nielsen achieved this feat on his 36th cap against Sweden in the 1924–28 Nordic Football Championship on 14 June 1925 and scored 52 goals in just 38 matches in his international career. Puskás netted his 50th goal on 24 July 1952, when he scored a brace in the semi-final match against Turkey at the 1952 Summer Olympics. However, Vivian Woodward scored 75 goals in 53 matches considered official internationals by the opposing sides, which would make him the first footballer to score 50 or more international goals, ahead of Imre Schlosser, and was the fastest to achieve the feat, scoring his 50th goal in his 32nd official international match, with a four-goal haul against Hungary on 31 May 1909.
Puskás overall scored 84 goals in his international career, and remained the highest international goalscorer for 24 years following his 84th goal in 1956 against Austria, until Mokhtar Dahari of Malaysia broke the record in the Merdeka Tournament after scoring his 85th goal on 27 October 1980 against Kuwait and he went on to score 89 goals for his country in 142 international appearances. In 2004, Ali Daei of Iran broke the record after scoring his 90th goal against Lebanon.
Daei also became the first player to score over 100 goals in international football, ending his career with 1 |
https://en.wikipedia.org/wiki/2008%20Universitario%20de%20Deportes%20season | This article shows statistics of the club's players in the season, and also lists all matches that the club played in the 2008 season.
Players
Summer and winter transfers correspond to Southern Hemisphere seasons.
Squad information
The following table shows only appearances and goals made this season.
In/out
In
Out
Goalscorers
Matches
Competitive
Copa Sudamericana
Torneo Descentralizado
Torneo Apertura
Torneo Clausura
Friendly
2008
Universitario De Deportes |
https://en.wikipedia.org/wiki/1943%E2%80%9344%20Primeira%20Divis%C3%A3o | Statistics of Primeira Liga in the 1943–44 season.
Overview
It was contested by 10 teams, and Sporting Clube de Portugal won the championship.
League standings
Results
References
Primeira Liga seasons
1943–44 in Portuguese football
Portugal |
https://en.wikipedia.org/wiki/1945%E2%80%9346%20Primeira%20Divis%C3%A3o | Statistics of Portuguese Liga in the 1945–46 season.
Overview
It was contested by 12 teams, and C.F. Os Belenenses won the championship, the first time that the competition had been won by a team outside the Portuguese "Big Three" (Os Três Grandes) of Benfica, Porto and Sporting.
League standings
Results
References
Primeira Liga seasons
1945–46 in Portuguese football
Portugal |
https://en.wikipedia.org/wiki/1946%E2%80%9347%20Primeira%20Divis%C3%A3o | Statistics of Portuguese Liga in the 1946–47 season.
Overview
It was contested by 14 teams, and Sporting Clube de Portugal won the championship.
League standings
Results
Footnotes
Primeira Liga seasons
1946–47 in Portuguese football
Portugal |
https://en.wikipedia.org/wiki/1947%E2%80%9348%20Primeira%20Divis%C3%A3o | Statistics of Portuguese Liga in the 1947–48 season.
Overview
It was contested by 14 teams, and Sporting Clube de Portugal won the championship.
League standings
Results
References
Primeira Liga seasons
1947–48 in Portuguese football
Portugal |
https://en.wikipedia.org/wiki/1948%E2%80%9349%20Primeira%20Divis%C3%A3o | Statistics of Portuguese Liga in the 1948–49 season.
Overview
It was contested by 14 teams, and Sporting Clube de Portugal won the championship.
League standings
Results
References
Primeira Liga seasons
1948–49 in Portuguese football
Portugal |
https://en.wikipedia.org/wiki/1950%E2%80%9351%20Primeira%20Divis%C3%A3o | Statistics of Portuguese Liga in the 1950–51 season.
Overview
It was contested by 14 teams, and Sporting Clube de Portugal won the championship.
League standings
Results
References
Primeira Liga seasons
Primeira Divisão
Portugal |
Subsets and Splits
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