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https://en.wikipedia.org/wiki/1991%20Liberian%20Premier%20League | Statistics of Liberian Premier League in season 1991.
Overview
Liberia Petroleum Refining Company Oilers won the championship.
References
Liberia - List of final tables (RSSSF)
Football competitions in Liberia
Lea |
https://en.wikipedia.org/wiki/1992%20Liberian%20Premier%20League | Statistics of Liberian Premier League for the 1992 season.
Overview
It was contested by 16 teams, and Liberia Petroleum Refining Company Oilers won the championship.
Group stage
Group A
Group B
Group C
Group D
Final
References
Liberia - List of final tables (RSSSF)
Football competitions in Liberia
Lea |
https://en.wikipedia.org/wiki/1993%20Liberian%20Premier%20League | Statistics of Liberian Premier League for the 1993 season.
Overview
It was contested by 15 teams, and Mighty Barrolle won the championship.
League standings
References
Liberia - List of final tables (RSSSF)
Football competitions in Liberia
Lea |
https://en.wikipedia.org/wiki/1994%20Liberian%20Premier%20League | Statistics of Liberian Premier League in season 1994.
Overview
It was contested by 15 teams, and National Port Authority Anchors won the championship.
References
Liberia - List of final tables (RSSSF)
Football competitions in Liberia
Lea |
https://en.wikipedia.org/wiki/1995%20Liberian%20Premier%20League | Statistics of Liberian Premier League in season 1995.
Overview
Mighty Barrolle won the championship.
References
Liberia - List of final tables (RSSSF)
Football competitions in Liberia
Lea |
https://en.wikipedia.org/wiki/1996%20Liberian%20Premier%20League | Statistics of Liberian Premier League in season 1996.
Overview
Junior Professionals won the championship.
References
Liberia - List of final tables (RSSSF)
Football competitions in Liberia
Lea |
https://en.wikipedia.org/wiki/1997%20Liberian%20Premier%20League | Statistics of Liberian Premier League in season 1997.
Overview
Liberia Petroleum Refining Company Oilers won the championship.
References
Liberia - List of final tables (RSSSF)
Football competitions in Liberia
Lea |
https://en.wikipedia.org/wiki/1998%20Liberian%20Premier%20League | Statistics of Liberian Premier League in season 1998.
Overview
Invincible Eleven won the championship.
References
Liberia – List of final tables (RSSSF)
Football competitions in Liberia
Lea |
https://en.wikipedia.org/wiki/1999%20Liberian%20Premier%20League | Statistics of Liberian Premier League in season 1999.
Overview
It was contested by 9 teams, and Invincible Eleven won the championship.
References
Liberia – List of final tables (RSSSF)
Football competitions in Liberia
Lea |
https://en.wikipedia.org/wiki/2000%E2%80%9301%20Liberian%20Premier%20League | Statistics of Liberian Premier League for the 2000–01 season.
Overview
It was contested by 18 teams, and Mighty Barrolle won the championship.
Group stage
Group A
Group B
Final
Football competitions in Liberia
Lea
Lea |
https://en.wikipedia.org/wiki/2002%20Liberian%20Premier%20League | Statistics of Liberian Premier League for the 2002 season.
Overview
It was contested by 16 teams, and Liberia Petroleum Refining Company Oilers won the championship.
Group stage
Group A
Group B
Final
Top 4 clubs only
Football competitions in Liberia
Lea |
https://en.wikipedia.org/wiki/2003%20Liberian%20Premier%20League | Statistics of Liberian Premier League for the 2003 season.
Overview
It was contested by 8 teams, and it was not finished.
League standings
References
Liberia - List of final tables (RSSSF)
Football competitions in Liberia
Lea |
https://en.wikipedia.org/wiki/2004%20Liberian%20Premier%20League | Statistics of Liberian Premier League for the 2004 season.
Overview
It was contested by 7 teams, and Mighty Barrolle won the championship.
League standings
References
Liberia - List of final tables (RSSSF)
Football competitions in Liberia
Lea |
https://en.wikipedia.org/wiki/2005%20Liberian%20Premier%20League | Statistics of Liberian Premier League for the 2005 season.
Overview
It was contested by 8 teams, and Liberia Petroleum Refining Company Oilers won the championship.
League standings
References
Liberia - List of final tables (RSSSF)
Football competitions in Liberia
Lea |
https://en.wikipedia.org/wiki/2006%20Liberian%20Premier%20League | Statistics of Liberian Premier League for the 2006 season.
Overview
It was contested by 9 teams, and Mighty Barrolle won the championship.
League standings
References
Liberia - List of final tables (RSSSF)
Football competitions in Liberia
Lea |
https://en.wikipedia.org/wiki/2007%20Liberian%20Premier%20League | Statistics of Liberian Premier League in season 2007.
Overview
It was contested by 12 teams, and Invincible Eleven won the championship.
References
Liberia - List of final tables (RSSSF)
Football competitions in Liberia
Lea |
https://en.wikipedia.org/wiki/2008%20Liberian%20Premier%20League | Statistics of Liberian Premier League in season 2008.
Overview
It was contested by 16 teams, and Monrovia Black Star Football Club won the championship.
References
Liberia - List of final tables (RSSSF)
Football competitions in Liberia
Lea |
https://en.wikipedia.org/wiki/2009%20Liberian%20Premier%20League | Statistics of Liberian Premier League for the 2009 season.
League standings
References
Liberia - List of final tables (RSSSF)
Football competitions in Liberia
Liberian Premier League, 2009 |
https://en.wikipedia.org/wiki/1962%20Cameroonian%20Premier%20League | Statistics of the 1962 Cameroonian Premier League season.
Overview
Caïman Douala won the championship.
References
Cameroon - List of final tables (RSSSF)
1962 in Cameroonian football
Cam
Cam
Elite One seasons |
https://en.wikipedia.org/wiki/1963%20Cameroonian%20Premier%20League | Statistics of the 1963 Cameroonian Premier League season.
Overview
Oryx Douala won the championship.
References
Cameroon - List of final tables (RSSSF)
1963 in Cameroonian football
Cam
Cam
Elite One seasons |
https://en.wikipedia.org/wiki/1964%20Cameroonian%20Premier%20League | Statistics of the 1964 Cameroonian Premier League season.
Overview
Oryx Douala won the championship.
References
Cameroon - List of final tables (RSSSF)
1964 in Cameroonian football
Cam
Cam
Elite One seasons |
https://en.wikipedia.org/wiki/1965%20Cameroonian%20Premier%20League | Statistics of the 1965 Cameroonian Premier League season.
Overview
Oryx Douala won the championship.
References
Cameroon - List of final tables (RSSSF)
1965 in Cameroonian football
Cam
Cam
Elite One seasons |
https://en.wikipedia.org/wiki/1966%20Cameroonian%20Premier%20League | Statistics of the 1966 Cameroonian Premier League season.
Overview
Diamant Yaoundé won the championship.
References
Cameroon - List of final tables (RSSSF)
1966 in Cameroonian football
Cam
Cam
Elite One seasons |
https://en.wikipedia.org/wiki/1967%20Cameroonian%20Premier%20League | Statistics of the 1967 Cameroonian Premier League season.
Overview
Oryx Douala won the championship.
References
Cameroon - List of final tables (RSSSF)
1967 in Cameroonian football
Cam
Cam
Elite One seasons |
https://en.wikipedia.org/wiki/1968%20Cameroonian%20Premier%20League | Statistics of the 1968 Cameroonian Premier League season.
Overview
Caïman Douala won the championship.
References
Cameroon 1968 - List of final tables (RSSSF)
1968 in Cameroonian football
Cam
Cam
Elite One seasons |
https://en.wikipedia.org/wiki/1969%20Cameroonian%20Premier%20League | Statistics of the 1969 Cameroonian Premier League season.
Overview
Union Douala won the championship.
References
Cameroon - List of final tables (RSSSF)
1969 in Cameroonian football
Cam
Cam
Elite One seasons |
https://en.wikipedia.org/wiki/1970%20Cameroonian%20Premier%20League | Statistics of the 1970 Cameroonian Premier League season.
Overview
Canon Yaoundé won the championship.
References
Cameroon - List of final tables (RSSSF)
1970 in Cameroonian football
Cam
Cam
Elite One seasons |
https://en.wikipedia.org/wiki/1971%20Cameroonian%20Premier%20League | Statistics of the 1971 Cameroonian Premier League season.
Overview
Aigle Nkongsamba won the championship.
References
Cameroon - List of final tables (RSSSF)
1971 in Cameroonian football
Cam
Cam
Elite One seasons |
https://en.wikipedia.org/wiki/1972%20Cameroonian%20Premier%20League | Statistics of the 1972 Cameroonian Premier League season.
Overview
Léopards Douala won the championship.
References
Cameroon - List of final tables (RSSSF)
1972 in Cameroonian football
Cam
Cam
Elite One seasons |
https://en.wikipedia.org/wiki/1973%20Cameroonian%20Premier%20League | Statistics of the 1973 Cameroonian Premier League season.
Overview
Léopards Douala won the championship.
References
Cameroon - List of final tables (RSSSF)
1973 in Cameroonian football
Cam
Cam
Elite One seasons |
https://en.wikipedia.org/wiki/1974%20Cameroonian%20Premier%20League | Statistics of the 1974 Cameroonian Premier League season.
Overview
Canon Yaoundé won the championship.
References
Cameroon - List of final tables (RSSSF)
1974 in Cameroonian football
Cam
Cam
Elite One seasons |
https://en.wikipedia.org/wiki/1975%20Cameroonian%20Premier%20League | Statistics of the 1975 Cameroonian Premier League season.
Overview
Caïman Douala won the championship.
References
Cameroon - List of final tables (RSSSF)
1975 in Cameroonian football
Cam
Cam
Elite One seasons |
https://en.wikipedia.org/wiki/1976%20Cameroonian%20Premier%20League | Statistics of the 1976 Cameroonian Premier League season.
Overview
Union Douala won the championship.
References
Cameroon - List of final tables (RSSSF)
1976 in Cameroonian football
Cam
Cam
Elite One seasons |
https://en.wikipedia.org/wiki/1977%20Cameroonian%20Premier%20League | Statistics of the 1977 Cameroonian Premier League season.
Overview
Canon Yaoundé won the championship.
References
Cameroon - List of final tables (RSSSF)
1977 in Cameroonian football
Cam
Cam
Elite One seasons |
https://en.wikipedia.org/wiki/1978%20Cameroonian%20Premier%20League | Statistics of the 1978 Cameroonian Premier League season.
Overview
Union Douala won the championship.
References
Cameroon - List of final tables (RSSSF)
1978 in Cameroonian football
Cam
Cam
Elite One seasons |
https://en.wikipedia.org/wiki/1979%20Cameroonian%20Premier%20League | Statistics of the 1979 Cameroonian Premier League season.
Overview
Canon Yaoundé won the championship.
References
Cameroon - List of final tables (RSSSF)
1979 in Cameroonian football
Cam
Cam
Elite One seasons |
https://en.wikipedia.org/wiki/1980%20Cameroonian%20Premier%20League | Statistics of the 1980 Cameroonian Premier League season.
Overview
Canon Yaoundé won the championship.
References
Cameroon - List of final tables (RSSSF)
1980 in Cameroonian football
Cam
Cam
Elite One seasons |
https://en.wikipedia.org/wiki/1981%20Cameroonian%20Premier%20League | Statistics of the 1981 Cameroonian Premier League season.
Overview
Tonnerre Yaoundé won the championship.
References
Cameroon 1981 - List of final tables (RSSSF)
1981 in Cameroonian football
Cam
Cam
Elite One seasons |
https://en.wikipedia.org/wiki/1982%20Cameroonian%20Premier%20League | Statistics of the 1982 Cameroonian Premier League season.
Overview
Canon Yaoundé won the championship.
References
Cameroon - List of final tables (RSSSF)
1982 in Cameroonian football
Cam
Cam
Elite One seasons |
https://en.wikipedia.org/wiki/1984%20Cameroonian%20Premier%20League | Statistics of the 1984 Cameroonian Premier League season.
Overview
Tonnerre Yaoundé won the championship.
References
Cameroon 1984 - List of final tables (RSSSF)
1984 in Cameroonian football
Cam
Cam
Elite One seasons |
https://en.wikipedia.org/wiki/1985%20Cameroonian%20Premier%20League | Statistics of the 1985 Cameroonian Premier League season.
Overview
Canon Yaoundé won the championship.
References
Cameroon - List of final tables (RSSSF)
1985 in Cameroonian football
Cam
Cam
Elite One seasons |
https://en.wikipedia.org/wiki/1987%20Cameroonian%20Premier%20League | Statistics of the 1987 Cameroonian Premier League season.
Overview
It was contested by 16 teams, and Tonnerre Yaoundé won the championship.
References
Cameroon 1987 - List of final tables (RSSSF)
Cam
Cam
1
Elite One seasons |
https://en.wikipedia.org/wiki/1988%20Cameroonian%20Premier%20League | Statistics of the 1988 Cameroonian Premier League season.
Overview
Tonnerre Yaoundé won the championship.
References
Cameroon - List of final tables (RSSSF)
Cam
Cam
1
Elite One seasons |
https://en.wikipedia.org/wiki/1992%20Cameroonian%20Premier%20League | Statistics of the 1992 Cameroonian Premier League season.
Overview
Racing Bafoussam won the championship.
References
Cameroon 1992 - List of final tables (RSSSF)
Cam
Cam
1
Elite One seasons |
https://en.wikipedia.org/wiki/Algebraic%20Petri%20net | An algebraic Petri net (APN) is an evolution of the well known Petri net in which elements of user defined data types (called algebraic abstract data types (AADT)) replace black tokens. This formalism can be compared to coloured Petri nets (CPN) in many aspects. However, in the APN case, the semantics of the data types is given by an axiomatization enabling proofs and computations on it.
Algebraic Petri nets were invented by Jacques Vautherin in 1985 in his PhD thesis and later improved by Wolfang Reisig.
The formalism has two aspects :
The control part which is handled by a Petri net.
The data part which is handled by one or many AADTs.
AADT can be themselves split in two parts:
The signature (Sort and Ops in the example below) which gives the valid constants and operations of the term algebra.
The axiomatization (Axioms in the example below) which gives the semantics of the operations described in the signature part.
The following picture describes an algebraic Petri net model of the "dining philosophers problem". There are two AADT in this model, one for the forks algebra, one for the philosophers algebra. Please note that the philosophers AADT uses the fork AADT. Since all philosophers can take their left fork without taking their right fork, executing this model can result in a deadlock.
The control part is composed of :
Places contain multiset (bags) of tokens. Those tokens are elements of a term algebra built upon the signature of the AADT (in the example, terms that represent either a philosopher or a fork). Each place contains one and only one multiset of terms, the place is typed by its multiset.
Arcs can be labeled with multisets of either closed or free terms. Again terms are built from the AADT signature.
Transitions are events that can be fired whenever there are enough resources (namely enough tokens in the input places to satisfy all the input arcs) and the guard (firing conditions) of the transition holds. Then the produced tokens are put in the target places of the output arcs. Usually term rewriting is used for the operational semantics in order to check if conditions hold and to compute output terms.
In the example below only transition goEat is firable at the beginning. One goEat has been fired, takeL and takeR are also enabled and thus can also be fired.
Algebraic Petri nets are the basic formalism of more advanced ones such as CO-OPN.
References
Further reading
External links
An Introduction to the Algebraic Specification of Abstract Data Types
Specification languages
Petri nets |
https://en.wikipedia.org/wiki/2009%E2%80%9310%20Scottish%20Football%20League | Statistics of the Scottish Football League in season 2009–10.
Scottish First Division
Playoffs
Scottish Second Division
Play-Offs
Scottish Third Division
See also
2009–10 in Scottish football
References
Scottish Football League seasons |
https://en.wikipedia.org/wiki/Virgil%20Dr%C4%83ghia | Virgil Andrei Drăghia (born 31 July 1990) is a Romanian professional footballer who plays as a goalkeeper for Liga I club Rapid București.
Career statistics
Honours
Rapid București
Liga II: 2015–16
Liga III: 2018–19
References
External links
1990 births
Living people
Footballers from Bucharest
Romanian men's footballers
Men's association football goalkeepers
Romania men's under-21 international footballers
Liga I players
Liga II players
FC Rapid București players
CS Concordia Chiajna players
ASC Daco-Getica București players
FC Voluntari players |
https://en.wikipedia.org/wiki/1973%E2%80%9374%20UAE%20Football%20League | Statistics of UAE Football League for the 1973–74 season.
Overview
The season was played as a trial season with two stages. First round being divided into three regional groups and final being played between the three winners. Al-Orouba won the championship after defeating Al Ahli and Oman.
First round
Group 1
Al Najah
Al Nasr (Dubai)
Al Orouba (winners)
Al Shaab
Shoala Al Ajmani
Zamalek
Group 2
Al Ahli (Dubai) (winners)
Al Hilal (Ajman)
Al Khaleej
Al Nasr (Ajman)
Al Shabab
Group 3
Al Ahly (Fujairah)
Al Hisn
Al Rams
Kalba
Oman (winners)
Ras Al Khaimah
Final
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
1973–74 in Emirati football
Emir |
https://en.wikipedia.org/wiki/1974%E2%80%9375%20UAE%20Football%20League | Statistics of UAE Football League for the 1974–75 season.
Overview
It was contested by 6 teams, and Al Ahli won the championship.
League standings
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
1
Emir |
https://en.wikipedia.org/wiki/1975%E2%80%9376%20UAE%20Football%20League | Statistics of UAE Football League in season 1975–76.
Overview
Al-Ahli Football Club - Dubai won the championship.
Ali Nawaz Baloch of Pakistan emerged as top scorer with 13 goals.
League standings
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
1
Emir |
https://en.wikipedia.org/wiki/1976%E2%80%9377%20UAE%20Football%20League | Statistics of UAE Football League in season 1976/77.
Overview
Al Ain FC won the championship.
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
1
Emir |
https://en.wikipedia.org/wiki/1977%E2%80%9378%20UAE%20Football%20League | Statistics of UAE Football League in season 1977/78.
Overview
Al-Nasr Sports Club won the championship.
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
1
Emir |
https://en.wikipedia.org/wiki/1978%E2%80%9379%20UAE%20Football%20League | Statistics of UAE Football League in season 1978/79.
Overview
Al-Nasr Sports Club won the championship.
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
1
Emir |
https://en.wikipedia.org/wiki/1979%E2%80%9380%20UAE%20Football%20League | Statistics of UAE Football League in season 1979/80.
Overview
Al-Ahli Football Club - Dubai won the championship.
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
1
Emir |
https://en.wikipedia.org/wiki/1980%E2%80%9381%20UAE%20Football%20League | Statistics of UAE Football League in season 1980/81.
Overview
Al Ain FC won the championship.
League standings
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1980–81 in Emirati football |
https://en.wikipedia.org/wiki/1981%E2%80%9382%20UAE%20Football%20League | Statistics of UAE Football League in season 1981/82.
Overview
Al Wasl FC won the championship. They were captained by Danish international Peter Engelsen, 17.
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1981–82 in Emirati football |
https://en.wikipedia.org/wiki/1982%E2%80%9383%20UAE%20Football%20League | Statistics of UAE Football League in season 1982/83.
Overview
Al Wasl FC won the championship.
League standings
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1982–83 in Emirati football |
https://en.wikipedia.org/wiki/1983%E2%80%9384%20UAE%20Football%20League | Statistics of UAE Football League for the 1983–84 season.
Overview
It was contested by 10 teams, and Al Ain FC won the championship.
League standings
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1983–84 in Emirati football |
https://en.wikipedia.org/wiki/1984%E2%80%9385%20UAE%20Football%20League | Statistics of UAE Football League in season 1984/85.
Overview
Al Wasl FC won the championship.
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1984–85 in Emirati football |
https://en.wikipedia.org/wiki/1985%E2%80%9386%20UAE%20Football%20League | Statistics of UAE Football League in season 1985/86.
Overview
It was contested by 10 teams, and Al-Nasr Sports Club won the championship.
League standings
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1985–86 in Emirati football |
https://en.wikipedia.org/wiki/1986%E2%80%9387%20UAE%20Football%20League | Statistics of UAE Football League in season 1986/87.
Overview
Sharjah FC won the championship.
League standings
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1986–87 in Emirati football |
https://en.wikipedia.org/wiki/1988%E2%80%9389%20UAE%20Football%20League | Statistics of UAE Football League for the 1988–89 season.
Overview
It was contested by 12 teams, and Sharjah FC won the championship.
League standings
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1988–89 in Emirati football |
https://en.wikipedia.org/wiki/1989%E2%80%9390%20UAE%20Football%20League | Statistics of the UAE Football League for the 1989–90 season.
Overview
It was contested by 14 teams, and Al-Shabab (United Arab Emirates) won the championship.
League standings
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1989–90 in Emirati football |
https://en.wikipedia.org/wiki/1991%E2%80%9392%20UAE%20Football%20League | Statistics of the UAE Football League for the 1991–92 season.
Overview
It was contested by 16 teams, and Al Wasl FC won the championship.
League standings
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1991–92 in Emirati football |
https://en.wikipedia.org/wiki/1992%E2%80%9393%20UAE%20Football%20League | Statistics of the UAE Football League for the 1992–93 season.
Overview
It was contested by 12 teams, and Al Ain FC won the championship.
League standings
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1992–93 in Emirati football |
https://en.wikipedia.org/wiki/1993%E2%80%9394%20UAE%20Football%20League | Statistics of UAE Football League for the 1993–94 season.
Overview
It was contested by 10 teams, and Sharjah FC won the championship.
League standings
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1993–94 in Emirati football |
https://en.wikipedia.org/wiki/1994%E2%80%9395%20UAE%20Football%20League | Statistics of UAE Football League for the 1994–95 season.
Overview
It was contested by 10 teams, and Al-Shabab (United Arab Emirates) won the championship.
League standings
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1994–95 in Emirati football |
https://en.wikipedia.org/wiki/1995%E2%80%9396%20UAE%20Football%20League | Statistics of UAE Football League for the 1995–96 season.
Overview
It was contested by 10 teams, and Sharjah won the championship.
First stage
Playoff
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1995–96 in Emirati football |
https://en.wikipedia.org/wiki/1996%E2%80%9397%20UAE%20Football%20League | Statistics of the UAE Football League for the 1996–97 UAE Football League.
Overview
It was contested by 10 teams, and Al Wasl FC won the championship.
First stage
Playoff
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1996–97 in Emirati football |
https://en.wikipedia.org/wiki/1997%E2%80%9398%20UAE%20Football%20League | Statistics of UAE Football League for the 1997–98 season.
Overview
It was contested by 10 teams, and Al Ain FC won the championship.
First stage
Playoff
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1997–98 in Emirati football |
https://en.wikipedia.org/wiki/1998%E2%80%9399%20UAE%20Football%20League | Statistics of UAE Football League for the 1998–99 season.
Overview
It was contested by 12 teams, and Al-Wahda FC (Abu Dhabi) won the championship.
League standings
References
United Arab Emirates – List of final tables (RSSSF)
UAE Pro League seasons
United
1998–99 in Emirati football |
https://en.wikipedia.org/wiki/1999%E2%80%932000%20UAE%20Football%20League | Statistics of UAE Football League for the 1999–2000 season.
Overview
It was contested by 12 teams, and Al Ain FC won the championship.
League standings
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1999–2000 in Emirati football |
https://en.wikipedia.org/wiki/2000%E2%80%9301%20UAE%20Football%20League | Statistics of UAE Football League for the 2000–01 season.
Overview
It was contested by 12 teams, and Al-Wahda FC (Abu Dhabi) won the championship.
League standings
Goalscorers
22 goals
Mohammed Salem Al-Enazi (Al-Wahda S.C.C.)
14 goals
Farhad Majidi (Al Wasl SC)
Baba Adamo (Al-Shabab)
Rachid Benmahmoud (Al-Ahli)
13 goals
Joël Tiéhi (Al Jazira Club)
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1 |
https://en.wikipedia.org/wiki/2001%E2%80%9302%20UAE%20Football%20League | Statistics of UAE Football League for the 2001–02 season.
Overview
It was contested by 12 teams, and Al Ain FC won the championship.
League standings
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1 |
https://en.wikipedia.org/wiki/2002%E2%80%9303%20UAE%20Football%20League | Statistics of UAE Football League for the 2002–03 season.
Overview
It was contested by 12 teams, and Al Ain FC won the championship.
League standings
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1 |
https://en.wikipedia.org/wiki/2003%E2%80%9304%20UAE%20Football%20League | Statistics of UAE Football League for the 2003–04 season.
Overview
It was contested by 12 teams, and Al Ain FC won the championship.
Group stage
Group A
Group B
Playoff
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1 |
https://en.wikipedia.org/wiki/2004%E2%80%9305%20UAE%20Football%20League | Statistics of UAE Football League for the 2004–05 season.
Overview
It was contested by 14 teams, and Al-Wahda FC (Abu Dhabi) won the championship.
League standings
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1 |
https://en.wikipedia.org/wiki/2005%E2%80%9306%20UAE%20Football%20League | Statistics of UAE Football League for the 2005–06 season.
Overview
It was contested by 12 teams, and Al-Ahli Football Club - Dubai won the championship.
League standings
Championship Playoff
NB: Ahli played under protest following accusations of bribery against Wahda in their final match at Sharjah (where they were down 3-1 at half-time before winning 3-6; they allegedly bought 5 Sharjah players for 120,000 Euro).
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1 |
https://en.wikipedia.org/wiki/2006%E2%80%9307%20UAE%20Football%20League | Statistics of UAE Football League for the 2006–07 season.
Overview
It was contested by 12 teams, and Al Wasl FC won the championship.
League standings
Top goalscorers
Source: goalzz.com
19 goals
Anderson Barbosa (Al Wasl)
17 goals
Gregory du Frencie (Dubai Club)
Ali Samereh (Al-Shaab)
15 goals
Saeed Al Kass (Sharjah)
14 goals
Nenad Jestrović (Al-Nasr)
13 goals
Reza Enayati (Emirates Club)
12 goals
Rasoul Khatibi (Sharja, Emirates Club)
11 goals
Javad Kazemian (Al-Shaab)
Faisal Khalil (Al-Ahli)
10 goals
Prince Tagoe (Al-Shabab)
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1 |
https://en.wikipedia.org/wiki/2007%E2%80%9308%20UAE%20Football%20League | Statistics of UAE Football League for the 2007–08 season.
Overview
It was contested by 12 teams, and Al-Shabab (United Arab Emirates) won the championship.
League standings
Top goalscorers
Source: goalzz.com
16 goals
Faisal Khalil (Al-Ahli)
Anderson Barbosa (Sharjah)
15 goals
Mehrzad Madanchi (Al-Shaab)
14 goals
André Dias (Al Wasl)
Rasoul Khatibi (Emirates Club)
12 goals
Reza Enayati (Emirates Club)
12 goals
Antonin Koutouan (Al-Jazira)
Ali Samereh (Al-Shaab)
11 goals
Ousman Jallow (Al Ain)
10 goals
Clederson (Al-Ahli)
Renato Abreu (Al-Nasr)
References
United Arab Emirates - List of final tables (RSSSF)
UAE Pro League seasons
United
1 |
https://en.wikipedia.org/wiki/NUTS%20statistical%20regions%20of%20Romania | In the NUTS (Nomenclature of Territorial Units for Statistics) codes of Romania (RO), the three levels are:
NUTS codes
RO1 Macroregion one (Macroregiunea Unu)
RO11 Nord-Vest
RO111 Bihor County
RO112 Bistrița-Năsăud County
RO113 Cluj County
RO114 Maramureș County
RO115 Satu Mare County
RO116 Sălaj County
RO12 Centru
RO121 Alba County
RO122 Brașov County
RO123 Covasna County
RO124 Harghita County
RO125 Mureș County
RO126 Sibiu County
RO2 Macroregion two (Macroregiunea doi)
RO21 Nord-Est
RO211 Bacău County
RO212 Botoșani County
RO213 Iași County
RO214 Neamț County
RO215 Suceava County
RO216 Vaslui County
RO22 Sud-Est
RO221 Brăila County
RO222 Buzău County
RO223 Constanța County
RO224 Galați County
RO225 Tulcea County
RO226 Vrancea County
RO3 Macroregion three (Macroregiunea trei)
RO31 Sud-Muntenia
RO311 Argeș County
RO312 Călărași County
RO313 Dâmbovița County
RO314 Giurgiu County
RO315 Ialomița County
RO316 Prahova County
RO317 Teleorman County
RO32 București-Ilfov
RO321 București
RO322 Ilfov County
RO4 Macroregion four (Macroregiunea patru)
RO41 Sud-Vest Oltenia
RO411 Dolj County
RO412 Gorj County
RO413 Mehedinți County
RO414 Olt County
RO415 Vâlcea County
RO42 Vest
RO421 Arad County
RO422 Caraș-Severin County
RO423 Hunedoara County
RO424 Timiș County
In the 2003 version, the codes were as follows:
RO0 Romania
RO01 Nord-Est
RO011 Bacău County
RO012 Botoșani County
RO013 Iași County
RO014 Neamț County
RO015 Suceava County
RO016 Vaslui County
RO02 Sud-Est
RO021 Brăila County
RO022 Buzău County
RO023 Constanța County
RO024 Galați County
RO025 Tulcea County
RO026 Vrancea County
RO03 Sud-Muntenia
RO031 Argeș County
RO032 Călărași County
RO033 Dâmbovița County
RO034 Giurgiu County
RO035 Ialomița County
RO036 Prahova County
RO037 Teleorman County
RO04 Sud-Vest Oltenia
RO041 Dolj County
RO042 Gorj County
RO043 Mehedinți County
RO044 Olt County
RO045 Vâlcea County
RO05 Vest
RO051 Arad County
RO052 Caraș-Severin County
RO053 Hunedoara County
RO054 Timiș County
RO06 Nord-Vest
RO061 Bihor County
RO062 Bistrița-Năsăud County
RO063 Cluj County
RO064 Maramureș County
RO065 Satu Mare County
RO066 Sălaj County
RO07 Centru
RO071 Alba County
RO072 Brașov County
RO073 Covasna County
RO074 Harghita County
RO075 Mureș County
RO076 Sibiu County
RO08 București-Ilfov
RO081 București
RO082 Ilfov County
Local administrative units
Below the NUTS levels, the two LAU (Local Administrative Units) levels are:
The LAU codes of Romania can be downloaded here: ''
See also
List of Romanian regions by Human Development Index
Subdivisions of Romania
ISO 3166-2 codes of Romania
FIPS region codes of Romania
Sources
Hierarchical list of the Nomenclature of territorial units for statistics - NUTS and the Statistical regions of Europe
Overview map of EU Countries - NUTS level 1
ROMÂNIA - NUTS level 2
ROMÂNIA - NUTS level 3
Correspondence between the NUTS levels and the national administrative units
List of current NUTS codes
Download current NUTS codes (ODS format)
Cou |
https://en.wikipedia.org/wiki/Sergei%20Berdnikov | Sergei Pavlovich Berdnikov (; born January 5, 1971, in Bratsk, USSR), is a Russian former ice hockey player. He played for Avangard Omsk from 1989–1994 and 1996-1998.
Career statistics
References
External links
1971 births
Avangard Omsk players
Charlotte Checkers (1993–2010) players
HC Lada Togliatti players
Metallurg Novokuznetsk players
HC MVD players
Severstal Cherepovets players
HC Sibir Novosibirsk players
Living people
Lokomotiv Yaroslavl players
Providence Bruins players
Russian ice hockey coaches
Russian ice hockey left wingers
Soviet ice hockey left wingers
Portland Rage players
Sacramento River Rats players
People from Angarsk
Sportspeople from Irkutsk Oblast |
https://en.wikipedia.org/wiki/Perspectivity | In geometry and in its applications to drawing, a perspectivity is the formation of an image in a picture plane of a scene viewed from a fixed point.
Graphics
The science of graphical perspective uses perspectivities to make realistic images in proper proportion. According to Kirsti Andersen, the first author to describe perspectivity was Leon Alberti in his De Pictura (1435). In English, Brook Taylor presented his Linear Perspective in 1715, where he explained "Perspective is the Art of drawing on a Plane the Appearances of any Figures, by the Rules of Geometry". In a second book, New Principles of Linear Perspective (1719), Taylor wrote
When Lines drawn according to a certain Law from the several Parts of any Figure, cut a Plane, and by that Cutting or Intersection describe a figure on that Plane, that Figure so described is called the Projection of the other Figure. The Lines producing that Projection, taken all together, are called the System of Rays. And when those Rays all pass thro’ one and same Point, they are called the Cone of Rays. And when that Point is consider’d as the Eye of a Spectator, that System of Rays is called the Optic Cone
Projective geometry
In projective geometry the points of a line are called a projective range, and the set of lines in a plane on a point is called a pencil.
Given two lines and in a projective plane and a point P of that plane on neither line, the bijective mapping between the points of the range of and the range of determined by the lines of the pencil on P is called a perspectivity (or more precisely, a central perspectivity with center P). A special symbol has been used to show that points X and Y are related by a perspectivity; In this notation, to show that the center of perspectivity is P, write
The existence of a perspectivity means that corresponding points are in perspective. The dual concept, axial perspectivity, is the correspondence between the lines of two pencils determined by a projective range.
Projectivity
The composition of two perspectivities is, in general, not a perspectivity. A perspectivity or a composition of two or more perspectivities is called a projectivity (projective transformation, projective collineation and homography are synonyms).
There are several results concerning projectivities and perspectivities which hold in any pappian projective plane:
Theorem: Any projectivity between two distinct projective ranges can be written as the composition of no more than two perspectivities.
Theorem: Any projectivity from a projective range to itself can be written as the composition of three perspectivities.
Theorem: A projectivity between two distinct projective ranges which fixes a point is a perspectivity.
Higher-dimensional perspectivities
The bijective correspondence between points on two lines in a plane determined by a point of that plane not on either line has higher-dimensional analogues which will also be called perspectivities.
Let Sm and Tm be two di |
https://en.wikipedia.org/wiki/Aleksandar%20Markoski | Aleksandar Markoski (Serbian Cyrillic: Александар Маркоски; born 17 September 1975) is a Serbian former football player.
Career statistics
References
External links
Living people
1975 births
Footballers from Zrenjanin
Serbian men's footballers
FK Bežanija players
FK Hajduk Kula players
FK Banat Zrenjanin players
FK Proleter Zrenjanin players
Serbian SuperLiga players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Elementary%20definition | In mathematical logic, an elementary definition is a definition that can be made using only finitary first-order logic, and in particular without reference to set theory or using extensions such as plural quantification. Elementary definitions are of particular interest because they admit a complete proof apparatus while still being expressive enough to support most everyday mathematics (via the addition of elementarily-expressible axioms such as Zermelo–Fraenkel set theory (ZFC)).
Saying that a definition is elementary is a weaker condition than saying it is algebraic.
Related
Elementary sentence
Elementary theory
References
Mac Lane and Moerdijk, Sheaves in Geometry and Logic: A First Introduction to Topos Theory, page 4.
Mathematical logic |
https://en.wikipedia.org/wiki/Algebraic%20definition | In mathematical logic, an algebraic definition is one that can be given using only equations between terms with free variables. Inequalities and quantifiers are specifically disallowed.
Saying that a definition is algebraic is a stronger condition than saying it is elementary.
Related
Algebraic sentence
Algebraic theory
Algebraic expression
Algebraic equation
References
Mathematical logic |
https://en.wikipedia.org/wiki/Multiple-scale%20analysis | In mathematics and physics, multiple-scale analysis (also called the method of multiple scales) comprises techniques used to construct uniformly valid approximations to the solutions of perturbation problems, both for small as well as large values of the independent variables. This is done by introducing fast-scale and slow-scale variables for an independent variable, and subsequently treating these variables, fast and slow, as if they are independent. In the solution process of the perturbation problem thereafter, the resulting additional freedom – introduced by the new independent variables – is used to remove (unwanted) secular terms. The latter puts constraints on the approximate solution, which are called solvability conditions.
Mathematics research from about the 1980s proposes that coordinate transforms and invariant manifolds provide a sounder support for multiscale modelling (for example, see center manifold and slow manifold).
Example: undamped Duffing equation
Differential equation and energy conservation
As an example for the method of multiple-scale analysis, consider the undamped and unforced Duffing equation:
which is a second-order ordinary differential equation describing a nonlinear oscillator. A solution y(t) is sought for small values of the (positive) nonlinearity parameter 0 < ε ≪ 1. The undamped Duffing equation is known to be a Hamiltonian system:
with q = y(t) and p = dy/dt. Consequently, the Hamiltonian H(p, q) is a conserved quantity, a constant, equal to H = ½ + ¼ ε for the given initial conditions. This implies that both y and dy/dt have to be bounded:
Straightforward perturbation-series solution
A regular perturbation-series approach to the problem proceeds by writing and substituting this into the undamped Duffing equation. Matching powers of gives the system of equations
Solving these subject to the initial conditions yields
Note that the last term between the square braces is secular: it grows without bound for large |t|. In particular, for this term is O(1) and has the same order of magnitude as the leading-order term. Because the terms have become disordered, the series is no longer an asymptotic expansion of the solution.
Method of multiple scales
To construct a solution that is valid beyond , the method of multiple-scale analysis is used. Introduce the slow scale t1:
and assume the solution y(t) is a perturbation-series solution dependent both on t and t1, treated as:
So:
using dt1/dt = ε. Similarly:
Then the zeroth- and first-order problems of the multiple-scales perturbation series for the Duffing equation become:
Solution
The zeroth-order problem has the general solution:
with A(t1) a complex-valued amplitude to the zeroth-order solution Y0(t, t1) and i2 = −1. Now, in the first-order problem the forcing in the right hand side of the differential equation is
where c.c. denotes the complex conjugate of the preceding terms. The occurrence of secular terms can be prevented by imposing on th |
https://en.wikipedia.org/wiki/2009%20Urawa%20Red%20Diamonds%20season | 2009 Urawa Red Diamonds season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
Urawa Red Diamonds
Urawa Red Diamonds seasons |
https://en.wikipedia.org/wiki/Cover%20%28algebra%29 | In abstract algebra, a cover is one instance of some mathematical structure mapping onto another instance, such as a group (trivially) covering a subgroup. This should not be confused with the concept of a cover in topology.
When some object X is said to cover another object Y, the cover is given by some surjective and structure-preserving map . The precise meaning of "structure-preserving" depends on the kind of mathematical structure of which X and Y are instances. In order to be interesting, the cover is usually endowed with additional properties, which are highly dependent on the context.
Examples
A classic result in semigroup theory due to D. B. McAlister states that every inverse semigroup has an E-unitary cover; besides being surjective, the homomorphism in this case is also idempotent separating, meaning that in its kernel an idempotent and non-idempotent never belong to the same equivalence class.; something slightly stronger has actually be shown for inverse semigroups: every inverse semigroup admits an F-inverse cover. McAlister's covering theorem generalizes to orthodox semigroups: every orthodox semigroup has a unitary cover.
Examples from other areas of algebra include the Frattini cover of a profinite group and the universal cover of a Lie group.
Modules
If F is some family of modules over some ring R, then an F-cover of a module M is a homomorphism X→M with the following properties:
X is in the family F
X→M is surjective
Any surjective map from a module in the family F to M factors through X
Any endomorphism of X commuting with the map to M is an automorphism.
In general an F-cover of M need not exist, but if it does exist then it is unique up to (non-unique) isomorphism.
Examples include:
Projective covers (always exist over perfect rings)
flat covers (always exist)
torsion-free covers (always exist over integral domains)
injective covers
See also
Embedding
Notes
References
Abstract algebra |
https://en.wikipedia.org/wiki/Canoe%20Creek%20Indian%20Reserve%20No.%201 | Canoe Creek Indian Reserve No. 1, referred to by Statistics Canada as Canoe Creek 1, is an Indian reserve of the Canoe Creek Band/Dog Creek Indian Band of the Secwepemc people, located five miles northeast of the confluence of Canoe Creek with the Fraser River in British Columbia, Canada, in that province's Cariboo district. The reserve is 37.2 ha. in size.
See also
List of Indian Reserves in British Columbia
Canoe Creek (disambiguation)
References
Indian reserves in British Columbia
Secwepemc
Geography of the Cariboo |
https://en.wikipedia.org/wiki/Infrastructure%20%28number%20theory%29 | In mathematics, an infrastructure is a group-like structure appearing in global fields.
Historic development
In 1972, D. Shanks first discovered the infrastructure of a real quadratic number field and applied his baby-step giant-step algorithm to compute the regulator of such a field in binary operations (for every ), where is the discriminant of the quadratic field; previous methods required binary operations. Ten years later, H. W. Lenstra published a mathematical framework describing the infrastructure of a real quadratic number field in terms of "circular groups". It was also described by R. Schoof and H. C. Williams, and later extended by H. C. Williams, G. W. Dueck and B. K. Schmid to certain cubic number fields of unit rank one and by J. Buchmann and H. C. Williams to all number fields of unit rank one. In his habilitation thesis, J. Buchmann presented a baby-step giant-step algorithm to compute the regulator of a number field of arbitrary unit rank. The first description of infrastructures in number fields of arbitrary unit rank was given by R. Schoof using Arakelov divisors in 2008.
The infrastructure was also described for other global fields, namely for algebraic function fields over finite fields. This was done first by A. Stein and H. G. Zimmer in the case of real hyperelliptic function fields. It was extended to certain cubic function fields of unit rank one by R. Scheidler and A. Stein. In 1999, S. Paulus and H.-G. Rück related the infrastructure of a real quadratic function field to the divisor class group. This connection can be generalized to arbitrary function fields and, combining with R. Schoof's results, to all global fields.
One-dimensional case
Abstract definition
A one-dimensional (abstract) infrastructure consists of a real number , a finite set together with an injective map . The map is often called the distance map.
By interpreting as a circle of circumference and by identifying with , one can see a one-dimensional infrastructure as a circle with a finite set of points on it.
Baby steps
A baby step is a unary operation on a one-dimensional infrastructure . Visualizing the infrastructure as a circle, a baby step assigns each point of the next one. Formally, one can define this by assigning to the real number ; then, one can define .
Giant steps and reduction maps
Observing that is naturally an abelian group, one can consider the sum for . In general, this is not an element of . But instead, one can take an element of which lies nearby. To formalize this concept, assume that there is a map ; then, one can define to obtain a binary operation , called the giant step operation. Note that this operation is in general not associative.
The main difficulty is how to choose the map . Assuming that one wants to have the condition , a range of possibilities remain. One possible choice is given as follows: for , define ; then one can define . This choice, seeming somewhat arbitrary, appears in a n |
https://en.wikipedia.org/wiki/Differential%20algebraic%20geometry | Differential algebraic geometry is an area of differential algebra that adapts concepts and methods from algebraic geometry and applies them to systems of differential equations, especially algebraic differential equations.
Another way of generalizing ideas from algebraic geometry is diffiety theory.
References
Differential algebraic geometry (three parts in one pdf), part of the Kolchin Seminar in Differential Algebra
, Henri Gillet (2000), Differential algebra - A Scheme Theory Approach, Differential algebra and related topics: proceedings of the International Workshop, Newark Campus of Rutgers, The State University of New Jersey, 2-3 November 2000, Editors Li Guo, William F. Keigher, World Scientific,
Differential algebra |
https://en.wikipedia.org/wiki/Algebraic%20differential%20geometry | Algebraic differential geometry may refer to:
Differential algebraic geometry
Differential geometry of algebraic manifolds
Manifolds equipped with a derivation |
https://en.wikipedia.org/wiki/Prosolvable%20group | In mathematics, more precisely in algebra, a prosolvable group (less common: prosoluble group) is a group that is isomorphic to the inverse limit of an inverse system of solvable groups. Equivalently, a group is called prosolvable, if, viewed as a topological group, every open neighborhood of the identity contains a normal subgroup whose corresponding quotient group is a solvable group.
Examples
Let p be a prime, and denote the field of p-adic numbers, as usual, by . Then the Galois group , where denotes the algebraic closure of , is prosolvable. This follows from the fact that, for any finite Galois extension of , the Galois group can be written as semidirect product , with cyclic of order for some , cyclic of order dividing , and of -power order. Therefore, is solvable.
See also
Galois theory
References
Mathematical structures
Algebra
Number theory
Topology
Properties of groups
Topological groups |
https://en.wikipedia.org/wiki/Daniela%20Hantuchov%C3%A1%20career%20statistics | This is a list of the main career statistics of professional Slovak tennis player Daniela Hantuchová.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup and Olympic Games are included in win–loss records.
Singles
Doubles
Mixed doubles
Grand Slam finals
Doubles: 3 (3 runner-ups)
Mixed doubles: 5 (4 titles, 1 runner-up)
By winning the 2005 US Open title, Hantuchová completed the mixed doubles Career Grand Slam. She became only the fifth female player in history to achieve this.
Other significant finals
WTA Premier Mandatory & 5 finals
Singles: 3 (2 titles, 1 runner-up)
Doubles: 7 (2 titles, 5 runner-ups)
WTA career finals
Singles: 16 (7 titles, 9 runner-ups)
Doubles: 21 (9 titles, 12 runner-ups)
ITF titles
Singles: 3 titles
Doubles: 1 title
Fed Cup results
Singles
Doubles
WTA Tour career earnings
Hantuchová earned more than 10 million dollars during her career.
Record against other players
Record against top 10 players
Hantuchová's record against players who have been ranked in the top 10. Active players are in boldface.
No. 1 wins
Top 10 wins
Notes
References
Tennis career statistics |
https://en.wikipedia.org/wiki/Georgy%20Gabulov | Georgy Borisovich Gabulov (, ; born 4 September 1988) is a Russian former footballer. He played as an attacking midfielder.
Club career
Career statistics
Notes
Personal life
He is a younger brother of Vladimir Gabulov.
Honours
Lokomotiv
2007: Russian Cup
Rostov
2013–14: Russian Cup
External links
1988 births
People from Mozdoksky District
Living people
Russian men's footballers
Russia men's under-21 international footballers
Russia men's B international footballers
Men's association football midfielders
FC Lokomotiv Moscow players
FC Spartak Vladikavkaz players
FC Anzhi Makhachkala players
FC Rostov players
PFC Krylia Sovetov Samara players
FC SKA-Khabarovsk players
FC Metalurgi Rustavi players
Russian expatriate men's footballers
Expatriate men's footballers in Georgia (country)
Russian Premier League players
Ossetian people
Ossetian footballers
FC Orenburg players
Sportspeople from North Ossetia–Alania |
https://en.wikipedia.org/wiki/Robert%20Morgan%20%28poet%29 | Robert Morgan (born 1944) is an American poet, short story writer, and novelist.
Life
He studied at North Carolina State University as an engineering and mathematics major, transferred to the University of North Carolina at Chapel Hill as an English major, graduating in 1965, and completed an MFA degree at the University of North Carolina Greensboro in 1968.
He has taught at Cornell University since 1971, and was appointed Professor of English in 1984.
Awards
Academy Award in Literature by the American Academy of Arts and Letters
2008 Thomas Wolfe Prize
2012 SIBA Book Award (nonfiction) for Lions of the West
2013 William "Singing Billy" Walker Award for Lifetime Achievement in Southern Letters
Bibliography
Poetry
Collections
Zirconia Poems. Northwood Narrows, New Hampshire: Lillabulero Press, 1969.
Red Owl. New York: Norton, 1972.
Trunk & Thicket. Fort Collins, Colorado: L’Epervier Press, 1978.
Groundwork. Frankfort, Kentucky: Gnomon Press, 1979.
Bronze Age. Emory, Virginia: Iron Mountain Press, 1981.
At the Edge of the Orchard Country. Middletown, Connecticut: Wesleyan University Press, 1987.
Green River: New and Selected Poems. Hanover, New Hampshire: University Press of New England, 1991.
Wild Peavines: New Poems. Frankfort, Kentucky: Gnomon Press, 1996.
List of poems
"OPTION", The Atlantic, October 1997
"Wind From a Waterfall", The Atlantic, September 1999
"Girdling", The Atlantic, December 1997
"Holy Cussing", Southern Poetry Review, Vol. 43, No. 1, 2004
Short fiction
Collections
The Mountains Won’t Remember Us and Other Stories. Atlanta, Georgia: Peachtree Publishers, 1992.
Stories
Novels
Non-fiction
Good Measure: Essays, Interviews and Notes on Poetry. Baton Rouge: Louisiana State University Press, 1993.
Boone: A Biography, Algonquin Books of Chapel Hill, 2007,
Lions of the West - Heroes and Villains of the Westward Expansion, Shannon Ravenel Books, 2011,
References
External links
"Author's website"
"Nostalgia May Not Be the Right Word," an Interview with Robert Morgan, Southern Spaces, December 11, 2013.
1944 births
Living people
20th-century American biographers
20th-century American essayists
20th-century American male writers
20th-century American novelists
20th-century American poets
20th-century American short story writers
21st-century American essayists
21st-century American male writers
21st-century American novelists
21st-century American poets
21st-century American short story writers
American male essayists
American male novelists
American male poets
American male short story writers
The Atlantic (magazine) people
Cornell University faculty
North Carolina State University people
Novelists from New York (state)
University of North Carolina at Chapel Hill alumni
University of North Carolina at Greensboro alumni
American male biographers |
https://en.wikipedia.org/wiki/Law%20of%20total%20covariance | In probability theory, the law of total covariance, covariance decomposition formula, or conditional covariance formula states that if X, Y, and Z are random variables on the same probability space, and the covariance of X and Y is finite, then
The nomenclature in this article's title parallels the phrase law of total variance. Some writers on probability call this the "conditional covariance formula" or use other names.
Note: The conditional expected values E( X | Z ) and E( Y | Z ) are random variables whose values depend on the value of Z. Note that the conditional expected value of X given the event Z = z is a function of z. If we write E( X | Z = z) = g(z) then the random variable E( X | Z ) is g(Z). Similar comments apply to the conditional covariance.
Proof
The law of total covariance can be proved using the law of total expectation: First,
from a simple standard identity on covariances. Then we apply the law of total expectation by conditioning on the random variable Z:
Now we rewrite the term inside the first expectation using the definition of covariance:
Since expectation of a sum is the sum of expectations, we can regroup the terms:
Finally, we recognize the final two terms as the covariance of the conditional expectations E[X | Z] and E[Y | Z]:
See also
Law of total variance, a special case corresponding to X = Y.
Law of total cumulance, of this the law of total covariance is a special case.
Notes and references
Algebra of random variables
Covariance and correlation
Articles containing proofs
Theory of probability distributions
Theorems in statistics
Statistical laws |
https://en.wikipedia.org/wiki/1963%E2%80%9364%20Q-League | Statistics of Qatar Stars League for the 1963–64 season.
Overview
Al-Maref won the championship.
References
Qatar - List of final tables (RSSSF)
Qatar Stars League seasons
Qatar
football |
https://en.wikipedia.org/wiki/1964%E2%80%9365%20Qatar%20Stars%20League | Statistics of Qatar Stars League for the 1964–65 season.
Overview
Al-Maref won the championship.
References
Qatar - List of final tables (RSSSF)
Qatar Stars League seasons
Qatar
football |
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