wikipedia_id stringlengths 2 8 | wikipedia_title stringlengths 1 243 | url stringlengths 44 370 | contents stringlengths 53 2.22k | id int64 0 6.14M |
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1642843 | Continuous production | https://en.wikipedia.org/w/index.php?title=Continuous%20production | Continuous production
- Crystallizing
- Encapsulating
- Packing
The Continuous Processor has an unlimited material mixing capabilities but, it has proven its ability to mix:
- Plastics
- Adhesives
- Pigments
- Composites
- Candy
- Gum
- Paste
- Toners
- Peanut Butter
- Waste Products
# Sources and further reading.
- R H Perry, C H Chilton, D W Green (Ed), "Perry's Chemical Engineers' Handbook (7th Ed)", McGraw-Hill (1997),
- Major industries typically each have one or more trade magazines that constantly feature articles about plant operations, new equipment and processes and operating and maintenance tips. Trade magazines are one of the best ways to keep informed of state of the art developments. | 6,140,500 |
1642838 | Lucy Baxley | https://en.wikipedia.org/w/index.php?title=Lucy%20Baxley | Lucy Baxley
Lucy Baxley
Lucy Mae Bruner Baxley Smith (December 21, 1937 – October 14, 2016) was an American politician who served from 2003 to 2007 as the 28th Lieutenant Governor of Alabama and from 2009 until 2013 as President of the Alabama Public Service Commission. She was the first woman to hold the state's office of lieutenant governor. In 2006, she was the unsuccessful Democratic nominee for governor. In 2008, Lucy Baxley was elected President of the Alabama Public Service Commission, and was the only Democrat to win statewide that year. Until Democrat Doug Jones's victory over Republican Roy Moore in the 2017 U.S. Senate special election, Baxley was the most recent Democrat to hold statewide office | 6,140,501 |
1642838 | Lucy Baxley | https://en.wikipedia.org/w/index.php?title=Lucy%20Baxley | Lucy Baxley
in Alabama.
# Early life.
Baxley was born Lucy Mae Bruner in 1937 near rural Pansey, located near the larger city of Dothan in Houston County in southeastern Alabama. Baxley attended Auburn University at Montgomery but did not graduate.
# Political career.
In 1994, Baxley was elected Alabama State Treasurer, in which capacity she pursued office modernization, including the first personal computers for staffers. She worked for expansion of the Prepaid Affordable College Tuition Program. In 1998, Baxley was re-elected to that post. In 2002, Baxley defeated Bill Armistead in the election as elected lieutenant governor, having received more votes than either candidate for governor that year. | 6,140,502 |
1642838 | Lucy Baxley | https://en.wikipedia.org/w/index.php?title=Lucy%20Baxley | Lucy Baxley
She also served as a delegate to the 1996 Democratic National Convention, which met in Chicago to renominate the Clinton-Gore ticket, which lost in Alabama.
In 2005, Baxley announced plans to run for governor in 2006. Her main opponent in the primary was former Governor Don Siegelman. In large part because of Siegelman's indictment for bribery and racketeering, she was able to secure important endorsements from the Alabama Democratic Conference, the New South Coalition, and the Alabama State Employees Association. Despite running a relatively low-profile campaign, she coasted to a win in the primary election on June 6 with 60 percent of the vote. Baxley was an underdog in the general election, | 6,140,503 |
1642838 | Lucy Baxley | https://en.wikipedia.org/w/index.php?title=Lucy%20Baxley | Lucy Baxley
however, against incumbent Republican Bob Riley, trailing by as much as 30 points in some polls. Baxley proposed a raise in the minimum wage of $1 per hour, which generated some criticism from her opponents. She was heavily outspent in the campaign by Riley and pointed to Riley's receipt of large contributions from recipients of industrial development subsidies. Baxley lost to Riley, 58-42 percent.
Baxley's term as lieutenant governor ended in 2007, and she was succeeded by fellow Democrat and former Governor Jim Folsom, Jr., of Cullman. Making a political comeback in 2008, Baxley defeated Republican Twinkle A. Cavanaugh to become president of the Alabama Public Service Commission. She replaced | 6,140,504 |
1642838 | Lucy Baxley | https://en.wikipedia.org/w/index.php?title=Lucy%20Baxley | Lucy Baxley
the retiring Jim Sullivan. She was then defeated by Cavanaugh in 2012 during her bid for reelection.
In each of her campaigns for office, Baxley utilized media bearing the title of the iconic CBS situation comedy starring Lucille Ball, "I Love Lucy."
# Stroke and recovery.
Baxley was admitted to UAB hospital in Birmingham on November 23, 2006, Thanksgiving Day. She had become ill Wednesday evening, while visiting her family in Birmingham. Doctors kept her for tests and observations. A spokeswoman for UAB announced that Baxley had suffered a mild stroke, but was expected to fully recover. A statement was issued via her family that asked Alabamians to keep Baxley in their prayers. No further | 6,140,505 |
1642838 | Lucy Baxley | https://en.wikipedia.org/w/index.php?title=Lucy%20Baxley | Lucy Baxley
details of her condition were given at the time.
She was discharged from UAB on November 29 and then moved to Lakeshore Rehabilitation Center in Birmingham. She remained there until being released December 29. The cause of Baxley's stroke has not been determined. Following the advice of her neurologist, Baxley did not return to Montgomery to preside over the opening of the Senate, her last official duty as lieutenant governor. According to Senator Lowell Barron, a Democrat from Fyffe, "Lucy's situation is serious." It was difficult for her to move her left leg and "she was unable to move her left arm." Following her discharge, she underwent outpatient rehabilitation.
# Personal life and death.
Baxley | 6,140,506 |
1642838 | Lucy Baxley | https://en.wikipedia.org/w/index.php?title=Lucy%20Baxley | Lucy Baxley
first married at the age of eighteen; later, she married Bill Baxley, who from 1971 to 1979 was the state attorney general and later from 1983 to 1987 the lieutenant governor. Bill Baxley became involved with another woman in a widely publicized affair, and the couple divorced in 1987. From 1996 until her death in 2016, Baxley was married to Jim Smith.
A licensed real estate broker, Baxley opened a real estate practice in suburban Birmingham after leaving the office of lieutenant governor in 2007. She died at her home in Birmingham, Alabama on October 14, 2016.
# Electoral history.
2012 General Election: Alabama Public Service Commission
2008 General Election: Alabama Public Service Commission
2006 | 6,140,507 |
1642838 | Lucy Baxley | https://en.wikipedia.org/w/index.php?title=Lucy%20Baxley | Lucy Baxley
e died at her home in Birmingham, Alabama on October 14, 2016.
# Electoral history.
2012 General Election: Alabama Public Service Commission
2008 General Election: Alabama Public Service Commission
2006 General Election: Governor
2006 Democratic Primary: Governor
2002 General Election: Lieutenant Governor
1998 General Election: State Treasurer
1994 General Election: State Treasurer
1994 Democratic Primary: State Treasurer
* = Incumbent
Bold = Winner
"Note: All votes are official results from the Alabama Secretary of State website."
Alabama Secretary of State
# See also.
- List of female lieutenant governors in the United States
# External links.
- RE/MAX Alabama: Lucy Baxley | 6,140,508 |
1642882 | Mount Willing, Alabama | https://en.wikipedia.org/w/index.php?title=Mount%20Willing,%20Alabama | Mount Willing, Alabama
Mount Willing, Alabama
Mount Willing is located in Lowndes County, Alabama, United States. It is a small crossroads community and birthplace of Navy Admiral Thomas Hinman Moorer, who served as the Chief of Naval Operations from 1967 to 1970, and the Chairman of the Joint Chiefs of Staff from 1970 to 1974.
# Demographics.
Mount Willing appeared on the 1890 U.S. Census. It was the only time it appeared on the census rolls. | 6,140,509 |
1642887 | The Fallon Blood | https://en.wikipedia.org/w/index.php?title=The%20Fallon%20Blood | The Fallon Blood
The Fallon Blood
The Fallon Blood is a novel written by fantasy author James Oliver Rigney, Jr. (more commonly known as Robert Jordan) under the name Reagan O'Neal. It is typical of the genre historical romance. It is the first book in the Michael Fallon trilogy. The more common 1995 printing is a new reprint, released by Tor Books under the Forge imprint in order to capitalize on the success of "The Wheel of Time".
# Plot summary.
## The Fallon Blood.
In The Fallon Blood, escaping brutal English overlords, 1760s Irishman Michael Fallon becomes an indentured servant to Charleston, South Carolina merchant Thomas Carver, where his infatuation with Carver's sensual daughter Elizabeth causes | 6,140,510 |
1642887 | The Fallon Blood | https://en.wikipedia.org/w/index.php?title=The%20Fallon%20Blood | The Fallon Blood
life-changing complications.
His father died in the Battle Of Culloden. The threat of Irish Pickets forced Michael and his mother in both hiding and poverty. His mother sacrificed her own health to keep Michael fed for three years, when she died of malnutrition. Grogan "adopted" Michael and abused him in child labor. Michael ran away at the age of fifteen, vowing that none of his children would suffer the tragedy of poverty.
Sometime later Michael became a soldier, and was taught the sword by Timothy Cavanaugh. His time with the army was a full seven years, after which he managed to own land in Ireland. Michael's prospects seemed fruitful until the day he killed an Englishman colonel by accident. | 6,140,511 |
1642887 | The Fallon Blood | https://en.wikipedia.org/w/index.php?title=The%20Fallon%20Blood | The Fallon Blood
Since the punishment of killing an Englishman was death, Michael was left no choice but to flee Ireland to the American colonies, where he became an indentured servant to Thomas Carver. This was the "most fateful moment of his life." He fell instantly in love with Carver's daughter Elizabeth.
Elizabeth did not return Michael's feelings until he dueled with Justin Fourrier, scion of Fourrier family. Although Justin was of high blood, his sword skills paled next to Michael's, who won easily. This was the beginning of Justin's hatred for Michael, and in turn, Elizabeth's desire of Michael.
Elizabeth's desire was not love, however. She originally wanted a flirtation with the bound man to instill | 6,140,512 |
1642887 | The Fallon Blood | https://en.wikipedia.org/w/index.php?title=The%20Fallon%20Blood | The Fallon Blood
jealousy in Justin. It was her hope that the jealousy would make Justin a lover, instead of a distant man who cared only for her inheritance.
Elizabeth's plans culminated in a night of seduction, which hopefully would force Michael into marriage. However, Michael wanted to "set her up as a queen, not as a destitute." Michael's actions towards building their future left Elizabeth alone with child. Horrified of the shame of wedding with child, she manipulated Justin into raping her so that he would give her his hand in marriage.
Michael buried himself in working his plantation Tir Alanin to forget Elizabeth, and dabbled in aiding American resistance for the same purpose. He became good friends | 6,140,513 |
1642887 | The Fallon Blood | https://en.wikipedia.org/w/index.php?title=The%20Fallon%20Blood | The Fallon Blood
with Justin's brothers Louis and Henri, who then introduced him to their sister Gabrielle. Sometimes later Fourrier leaked news of Michael's slaying of the Englishman colonel and he was quite close of rotting away in prison. Saved by Gabrielle's plan, the two married.
The American Revolution separated Michael and Gabrielle for years, though the two mended the damage between them in raising their family. Twenty years pass, finding Michael with son James and daughter Catherine. On constant guard from Justin's assassinations, Michael met his son Robert Fallon (from Elizabeth). His presence tore a rift in the Fallon family, who more or less hate Robert for his status as a bastard. Gabrielle made | 6,140,514 |
1642887 | The Fallon Blood | https://en.wikipedia.org/w/index.php?title=The%20Fallon%20Blood | The Fallon Blood
the first step towards bridging that chasm when Fourrier assassins set the Fallon house on fire and subsequently killed both Gabrielle and James.
## The Fallon Pride.
In The Fallon Pride, Michael Fallon's son Robert Fallon survives years at sea fighting Barbary pirates and enduring the siege at Tripoli. He then returns to America with an Irish wife, Moira McConnell, and goes into business in Charleston where he raises a somewhat troublesome family.
In the eve of the Revolution, the Fourrier family is forced out of the colonies because their centuries-worth of power has no place in the new nation. It is then that Elizabeth accidentally reveals Robert's true heritage. With all of his hatred | 6,140,515 |
1642887 | The Fallon Blood | https://en.wikipedia.org/w/index.php?title=The%20Fallon%20Blood | The Fallon Blood
on the Fallon line, Justin spent years abusing Robert just to see the look on Elizabeth's face. "She fought for food, clothes, an education . . ." Years of spousal abuse had ground Elizabeth's will until she died. Her last words to Robert was the name of his real father.
Robert flees to the safety of the sea. During that time he has ventured to Charleston, though forcibly avoids his father, as he does not wish to be a burden to the Fallon family. His luck runs out when his name is casually offered to Michael, who then confronts him. The two try to make amends with Michael's family, though Gabrielle is livid and refuses to give Robert the benefit of the doubt. James takes this one step further, | 6,140,516 |
1642887 | The Fallon Blood | https://en.wikipedia.org/w/index.php?title=The%20Fallon%20Blood | The Fallon Blood
slugging Robert and warning him not to come back. A spoiled noble, James thinks him invincible due to his "noble" bloodline, and is thus astonished that he is beaten by a bastard.
At the end of the Fallon Blood, Robert kills Henry Tyree to save his father, and leads Michael from his grief over Gabrielle's death with a question of sizing a boat Robert wants to purchase. This attempt works, coaxing Michael out of his misery and allows Michael to move on with his life.
Sometime before the Fallon Pride, Robert develops incestuous feelings towards his half-sister Catherine. Like his father Robert buries himself in the arms of another woman, a French girl by the name of Louise de Chardonnay. Despite | 6,140,517 |
1642887 | The Fallon Blood | https://en.wikipedia.org/w/index.php?title=The%20Fallon%20Blood | The Fallon Blood
the stalker-like intents of powerful sea mogul Murad Reis, Robert takes Louise as a mistress, who eventually bears his first son James. Before they can marry, however, Robert falls victim to Murad's revenge and is shipped to North Africa. For three years Robert fights Tripoli forces under the command of a Colonel Eaten, only to find upon his return that his father is dead, and Louise marries a Thomas Martin.
Drunk on both grief and alcohol, Robert succumbs to his passion and sleeps with Catherine. The incest continues for years until finally a child named Edward is born. Edward's birth snaps Robert out of his passion for Catherine. He charges his niece Charollete to protect her new brother, | 6,140,518 |
1642887 | The Fallon Blood | https://en.wikipedia.org/w/index.php?title=The%20Fallon%20Blood | The Fallon Blood
and retreats back to the sea.
Years pass. Robert falls in love with Irish girl Moira McDonnel, and returns to America with her as his wife. Like his father before him, war looms on the horizon, drawing Robert away from his family. After the war Robert is content with the hope of both rebuilding his family's wealth and raising his family.
Robert has a minor role in the third volume, the Fallon Legacy. There are two pivotal moments that involve him. First he takes another French mistress named Lucille Gautier. This only exasperates the situation with his wife Moira, who is waging war with Robert over allowing his bastards into his household and the defense of his incestuous son Edward, who has | 6,140,519 |
1642887 | The Fallon Blood | https://en.wikipedia.org/w/index.php?title=The%20Fallon%20Blood | The Fallon Blood
grown up a spoiled noble much like his deceased half-uncle James. Robert breaks his defense for Edward when Edward arranges the kidnapping and rape of his half-sister Elizabeth by Lucien Fourrier's son Edouard.
Robert Fallon is a source of ironic circumstance. His life of survival and the dangers he has endured makes him a close parallel of his father, who possesses the same will and determination. James, on the other hand, grows up a nobleman with the blind faith of wealth through breeding. He lacks Michael's endurance, thus aligning James more towards his uncle Justin Fourrier than Michael Fallon.
## The Fallon Legacy.
In The Fallon Legacy, James Fallon, the last scion of the Fallon line, | 6,140,520 |
1642887 | The Fallon Blood | https://en.wikipedia.org/w/index.php?title=The%20Fallon%20Blood | The Fallon Blood
ael Fallon.
## The Fallon Legacy.
In The Fallon Legacy, James Fallon, the last scion of the Fallon line, strikes south and west, adventuring in New Orleans, Missouri, and finally Texas (then still part of Mexico). He loves and loses women, ranches and breeds horses, and becomes entangled in the schemes of shady men and women. Enemies made by Michael and Robert during their lifetimes converge upon James, who must find out if he has strength enough to stand against them.
# Characters in the Fallon trilogy.
- Michael Fallon – father to the family.
- Robert Fallon – Michael's illegitimate son through Elizabeth Carver.
- James Fallon – Robert's illegitimate son through Louise de Chardonnay. | 6,140,521 |
1642890 | Purley Oaks railway station | https://en.wikipedia.org/w/index.php?title=Purley%20Oaks%20railway%20station | Purley Oaks railway station
Purley Oaks railway station
Purley Oaks railway station is in the London Borough of Croydon in south London, on the Brighton Main Line measured from . All trains serving it are operated by Southern and it is in London Travelcard Zone 6. The station has four platforms: a disused side platform on the up fast line, an island platform with a disused face on the down fast line and an eastern face used by up trains, and a side platform on the eastern side used by down trains. The two platforms are only used during engineering works. There is also a pay-and-display car park at the station.
The ticket office (staffed for part of the day) is on the island platform with two self-service ticket machines | 6,140,522 |
1642890 | Purley Oaks railway station | https://en.wikipedia.org/w/index.php?title=Purley%20Oaks%20railway%20station | Purley Oaks railway station
in the subway beneath the station. There used to be a self-service PERTIS (permit to travel) ticket machine.
A short walk away from Purley Oaks is Sanderstead railway station, also in Zone 6, with services to Victoria and East Grinstead.
# History.
The station was opened by the London Brighton and South Coast Railway on 5 November 1899 as part of the improvements to the main line and the opening of the Quarry Line.
Until 1983:
Platform 1 served up trains to London Victoria from Coulsdon North, calling at South and East Croydon and stations to Victoria);
Platform 2 down trains from Victoria to Purley and Coulsdon North;
Platform 3 up trains to London Bridge and Charing Cross from Caterham/Tattenham | 6,140,523 |
1642890 | Purley Oaks railway station | https://en.wikipedia.org/w/index.php?title=Purley%20Oaks%20railway%20station | Purley Oaks railway station
enham Corner, calling at South and East Croydon, New Cross Gate, London Bridge and Waterloo East;
Platform 4 down trains from Charing Cross to Purley, the front portion all stations to Caterham, the rear portion all stations to Tattenham Corner.
Platform 1 was gutted by fire in 1989, destroying Croydon Model Railway Society's clubrooms.
On Saturday 4th March 1989, it was affected by the Purley station rail crash.
# Services.
The typical off-peak train service per hour is:
- 4 to London Bridge via East Croydon of which 2 run non stop from East Croydon, at which the other two stop all stations to London Bridge
- 2 to Caterham and Tattenham Corner dividing at Purley
- 1 to Coulsdon Town | 6,140,524 |
1642868 | Doc Rivers | https://en.wikipedia.org/w/index.php?title=Doc%20Rivers | Doc Rivers
Doc Rivers
Glenn Anton "Doc" Rivers (born October 13, 1961) is an American basketball coach and former player who is the head coach for the Los Angeles Clippers of the National Basketball Association (NBA). As an NBA point guard, Rivers was known for his defense, a trait that has carried over into his coaching.
# Playing career.
Rivers was a McDonald's All-American for Proviso East High School in the Chicago metropolitan area. Rivers represented the United States with the national team in the 1982 FIBA World Championship, in which he led the team to the silver medal, despite missing the last shot in the final, which could have given the title to his team. After his third season at Marquette | 6,140,525 |
1642868 | Doc Rivers | https://en.wikipedia.org/w/index.php?title=Doc%20Rivers | Doc Rivers
University, Rivers was drafted in the second round (31st overall) of the 1983 NBA draft by the Atlanta Hawks. He graduated from Marquette while completing course work as an NBA player. He spent the next seven seasons as a starter in Atlanta, assisting star Dominique Wilkins as the team found great regular-season success. He averaged a double-double for the 1986–87 season with 12.8 points and 10.0 assists per game. Rivers later spent one year as a starter for the Los Angeles Clippers and two more for the New York Knicks, before finishing his career as a player for the San Antonio Spurs from 1994 to 1996.
# Coaching career.
## Orlando Magic (1999–2003).
Rivers began his coaching career with | 6,140,526 |
1642868 | Doc Rivers | https://en.wikipedia.org/w/index.php?title=Doc%20Rivers | Doc Rivers
the Orlando Magic in 1999, where he coached for more than four NBA seasons. Rivers won the Coach of the Year award in 2000 after his first year with the Magic. That season, he led the team that was picked to finish last in the league to a near playoff berth.
During the Magic's free agency spending spree in the summer of 2000, Doc Rivers had the opportunity to assemble the first "Big Three" team in the NBA, as the Magic were courting free agent Tim Duncan, who came close to signing with the Magic and teaming up with Grant Hill and Tracy McGrady. However, Tim Duncan re-signed with the San Antonio Spurs due to Rivers' strict policy of family members not being allowed to travel in the team's plane.
He | 6,140,527 |
1642868 | Doc Rivers | https://en.wikipedia.org/w/index.php?title=Doc%20Rivers | Doc Rivers
made the post-season in his next three years as coach, but was fired in 2003 after a 1–10 start to the season.
## Boston Celtics (2004–2013).
After spending a year working as a commentator for the "NBA on ABC" (calling the 2004 Finals with Al Michaels), he was hired by the Boston Celtics as their head coach in 2004. During his first years with the Celtics, he was criticized by many in the media for his coaching style, most vociferously by Bill Simmons, who in 2006 publicly called for Rivers to be fired in his columns.
As a result of the Celtics' 109–93 victory over the New York Knicks on January 21, 2008, Rivers, as the coach of the team with the best winning percentage in the Eastern Conference, | 6,140,528 |
1642868 | Doc Rivers | https://en.wikipedia.org/w/index.php?title=Doc%20Rivers | Doc Rivers
earned the honor to coach the East for the 2008 NBA All-Star Game in New Orleans. On June 17, 2008, Rivers won his first NBA Championship as a head coach after defeating the Los Angeles Lakers in six games. The Celtics needed an NBA record 26 post-season games to win it. Rivers played for the team that held the previous record for most games played in a single post-season: the 1994 New York Knicks played 25 post-season games.
Rivers led the Celtics to the 2010 NBA Finals where they once again faced the Los Angeles Lakers and lost the series in seven games.
After deliberating between staying on the job and leaving the job and returning to spend more time with his family in Orlando, Rivers finally | 6,140,529 |
1642868 | Doc Rivers | https://en.wikipedia.org/w/index.php?title=Doc%20Rivers | Doc Rivers
decided that he would honor the last year of his contract and return for the 2010–11 season.
On May 13, 2011, after months of rumors that he would retire, ESPN reported that the Celtics and Rivers agreed upon a 5-year contract extension worth $35 million.
On February 6, 2013, Rivers notched his 400th win with the Celtics in a 99–95 victory over the Toronto Raptors.
## Los Angeles Clippers (2013–present).
On June 25, 2013, the Los Angeles Clippers acquired Rivers from the Celtics for an unprotected 2015 NBA first round draft pick. He also became the senior vice president of basketball operations on the team. In his first season as their head coach, Rivers led the Clippers to a franchise-record | 6,140,530 |
1642868 | Doc Rivers | https://en.wikipedia.org/w/index.php?title=Doc%20Rivers | Doc Rivers
57 wins, garnering the 3rd seed in the Western conference. The 2014 NBA playoffs first round playoff series against the Golden State Warriors was marred when TMZ released an audiotape containing racially insensitive remarks made by the then-Clippers owner Donald Sterling. Though there was a possibility of the Clippers boycotting the series, they would play on, holding a silent protest by leaving their shooting jerseys at center court and obscuring the Clippers logo on their warm-up shirts. Rivers himself stated that he would not return to the Clippers if Sterling remained as owner the following season. NBA commissioner Adam Silver responded to the controversy by banning Sterling for life and | 6,140,531 |
1642868 | Doc Rivers | https://en.wikipedia.org/w/index.php?title=Doc%20Rivers | Doc Rivers
compelling him to sell the team. After the team was sold to Microsoft CEO Steve Ballmer for $2 billion on August 12, 2014, Rivers remained with the Clippers.
On June 16, 2014, the Clippers promoted Rivers to president of basketball operations in conjunction with his continuing head coaching duties. Although Dave Wohl was hired as general manager, Rivers had the final say in basketball matters. On August 27, 2014, he signed a new five-year contract with the Clippers.
On January 16, 2015, Rivers became the first NBA coach to coach his own son, Austin Rivers until June 26, 2018, when he was traded to the Washington Wizards for Marcin Gortat.
On August 4, 2017, Rivers gave up his post as president | 6,140,532 |
1642868 | Doc Rivers | https://en.wikipedia.org/w/index.php?title=Doc%20Rivers | Doc Rivers
of basketball operations. However, he continued to split responsibility for basketball matters with executive vice president of basketball operations Lawrence Frank. On May 23, 2018, Rivers and the Clippers agreed to a contract extension.
On May 31, 2019, Rivers made comments on Kawhi Leonard during an appearance on ESPN, stating that "He is the most like Jordan that we've seen". The Clippers were fined $50,000 due to Rivers' comments in violation of the league's anti-tampering rule.
# Personal life.
Rivers is the nephew of former NBA player Jim Brewer. He lives in Orlando, Florida, with his wife Kristen; they have four children. His oldest son Jeremiah played basketball at Georgetown University | 6,140,533 |
1642868 | Doc Rivers | https://en.wikipedia.org/w/index.php?title=Doc%20Rivers | Doc Rivers
and Indiana University, and has played in the NBA D-League for the Maine Red Claws. His daughter Callie played volleyball for the University of Florida and is engaged to NBA player Seth Curry, while his younger son Austin currently plays for the Houston Rockets. His youngest son, Spencer, is a guard who played for Winter Park High School and for UC Irvine.
Rivers is a cousin of former NBA guard Byron Irvin and former MLB outfielder Ken Singleton.
Rivers was given his nickname of "Doc" by then-Marquette assistant coach Rick Majerus. Rivers attended a summer basketball camp wearing a "Dr. J" T-shirt. Majerus immediately called him "Doc" and the players at camp followed suit. The name has stuck | 6,140,534 |
1642868 | Doc Rivers | https://en.wikipedia.org/w/index.php?title=Doc%20Rivers | Doc Rivers
ever since.
Rivers has attention deficit hyperactivity disorder according to a personality test he took when he was coaching the Celtics.
# Other work.
Rivers is also currently a member of the National Advisory Board for Positive Coaching Alliance, a national non-profit organization that helps student-athletes and their coaches. Rivers has appeared in several videos for this organization, all of which can be found on the group's YouTube channel.
# See also.
- List of National Basketball Association career steals leaders
- List of National Basketball Association players with most assists in a game
- List of National Basketball Association players with most steals in a game
# External | 6,140,535 |
1642868 | Doc Rivers | https://en.wikipedia.org/w/index.php?title=Doc%20Rivers | Doc Rivers
her work.
Rivers is also currently a member of the National Advisory Board for Positive Coaching Alliance, a national non-profit organization that helps student-athletes and their coaches. Rivers has appeared in several videos for this organization, all of which can be found on the group's YouTube channel.
# See also.
- List of National Basketball Association career steals leaders
- List of National Basketball Association players with most assists in a game
- List of National Basketball Association players with most steals in a game
# External links.
- Doc Rivers Coaching Info at NBA.com
- databaseBasketball.com: Doc Rivers (as coach)
- databaseBasketball.com: Doc Rivers (as player) | 6,140,536 |
1642909 | Peter Vogel | https://en.wikipedia.org/w/index.php?title=Peter%20Vogel | Peter Vogel
Peter Vogel
Peter Vogel may refer to:
- Peter Vogel (actor) (1937–1978), German actor, appeared in "Holocaust" miniseries
- Peter Vogel (cyclist) (born 1939), Swiss cyclist
- Peter Vogel (footballer) (born 1952), German footballer
- Peter Vogel (banker) (born 1954), Polish murderer and later banker
- Peter Vogel (computer designer) (born 1954), Australian computer designer of Fairlight CMI
- Peter Vogel (artist) (1937–2017), German sound artist
# See also.
- Peter Vogelzang (born 1945), Dutch businessman | 6,140,537 |
1642881 | South Croydon railway station | https://en.wikipedia.org/w/index.php?title=South%20Croydon%20railway%20station | South Croydon railway station
South Croydon railway station
South Croydon railway station is in the London Borough of Croydon in south London, in Travelcard Zone 5. It is on the Brighton Line at its junction with the Oxted Line, measured from .
The station is operated by Southern, and the station is served by both Southern and Thameslink services.
# History.
Originally South Croydon was a terminus next to the through lines of the Brighton Line but without any platforms on them, the end of a extension of the local lines from New Croydon, opened by the London Brighton and South Coast Railway on 1 September 1865. The aim was to provide more space for reversing local trains than could be afforded at busy New Croydon. The | 6,140,538 |
1642881 | South Croydon railway station | https://en.wikipedia.org/w/index.php?title=South%20Croydon%20railway%20station | South Croydon railway station
rapid growth of the town in this area may also have been a factor.
In 1894 the railway obtained authority to extend the local lines to Coulsdon, where they connected with the new Quarry line. The station was rebuilt as a through station with platform faces on all lines prior to the opening of the line in November 1899.
In 1947 a train crash about south of the station killed 32 people, the worst accident in the history of the Southern Railway.
On 1 August 2011, a landslide caused by a burst water main occurred approximately north of the station, blocking the railway for 24 hours.
# Platforms.
South Croydon has five platforms connected by a narrow subway.
The tracks through platforms 1 and | 6,140,539 |
1642881 | South Croydon railway station | https://en.wikipedia.org/w/index.php?title=South%20Croydon%20railway%20station | South Croydon railway station
2 are used by services that do not call, for example fast Southern services from London Victoria to Brighton, Thameslink services and Gatwick Express. Platform 3 is used by up trains to London Bridge and London Victoria. Platform 4 is used by services that do not call, heading southbound, except some peak time services in both directions.
Platform 5 is used by down trains to Caterham and other destinations.
Ticket gates became operational in April 2009.
# Services.
The typical off-peak service in trains per hour is:
- 2 to London Bridge calling at East Croydon only
- 2 to London Bridge via East Croydon and Forest Hill
- 2 to Caterham/Tattenham Corner
- 2 to Coulsdon Town - 2 to Caterham/Tattenham | 6,140,540 |
1642881 | South Croydon railway station | https://en.wikipedia.org/w/index.php?title=South%20Croydon%20railway%20station | South Croydon railway station
ndon Bridge and London Victoria. Platform 4 is used by services that do not call, heading southbound, except some peak time services in both directions.
Platform 5 is used by down trains to Caterham and other destinations.
Ticket gates became operational in April 2009.
# Services.
The typical off-peak service in trains per hour is:
- 2 to London Bridge calling at East Croydon only
- 2 to London Bridge via East Croydon and Forest Hill
- 2 to Caterham/Tattenham Corner
- 2 to Coulsdon Town - 2 to Caterham/Tattenham Corner in peak
At peak times services operate to other destinations, including , via , and .
# Connections.
London Buses route 64, 403, 412, 433 and 455 serve the station. | 6,140,541 |
1642895 | Maxillopoda | https://en.wikipedia.org/w/index.php?title=Maxillopoda | Maxillopoda
Maxillopoda
Maxillopoda is a diverse class of crustaceans including barnacles, copepods and a number of related animals. It does not appear to be a monophyletic group, and no single character unites all the members.
# Description.
With the exception of some barnacles, maxillopodans are mostly small, including the smallest known arthropod, "Stygotantulus stocki". They often have short bodies, with the abdomen reduced in size, and generally lacking any appendages. This may have arisen through paedomorphosis.
Apart from barnacles, which use their legs for filter feeding, most maxillopodans feed with their maxillae. They have a "bauplan" comprising 5 cephalic segments, 6 thoracic segments and | 6,140,542 |
1642895 | Maxillopoda | https://en.wikipedia.org/w/index.php?title=Maxillopoda | Maxillopoda
ding, most maxillopodans feed with their maxillae. They have a "bauplan" comprising 5 cephalic segments, 6 thoracic segments and 4 abdominal segments, followed by a telson.
# Fossil record.
The fossil record of the group extends back into the Cambrian, with fossils of both barnacles and tongue worms known from that period.
# Classification.
Six subclasses are generally recognised, although many works have further included the ostracods among the Maxillopoda. Of the six groups, only the Mystacocarida are entirely free-living; all the members of the Tantulocarida, Pentastomida, and Branchiura are parasitic, and many of the Copepoda and Thecostraca are parasites.
# See also.
- Skaracarida | 6,140,543 |
1642908 | Permanent staff instructor | https://en.wikipedia.org/w/index.php?title=Permanent%20staff%20instructor | Permanent staff instructor
Permanent staff instructor
A permanent staff instructor (PSI) is a warrant officer class 2 (WO2), or senior non-commissioned officer (sergeant, staff sergeant or colour sergeant), of the Regular British Army who has been selected to instruct Army Reserve soldiers. Each AR unit has several PSIs attached to it. A normal rifle company in a Regular Army battalion has a single WO2, serving in the role of company sergeant major (CSM). An Army Reserve rifle company normally has two WO2s. One is the CSM, normally a part-time member of the Army Reserve, and the other is the seconded PSI, the only full-time member of the company. The PSI is meant to provide the reserve company with the benefit of his | 6,140,544 |
1642908 | Permanent staff instructor | https://en.wikipedia.org/w/index.php?title=Permanent%20staff%20instructor | Permanent staff instructor
in a Regular Army battalion has a single WO2, serving in the role of company sergeant major (CSM). An Army Reserve rifle company normally has two WO2s. One is the CSM, normally a part-time member of the Army Reserve, and the other is the seconded PSI, the only full-time member of the company. The PSI is meant to provide the reserve company with the benefit of his professional experience, as well as to ensure that the training and operation of the company adheres to the Army's methods and standards. The PSI is typically responsible for much of the company's administration work, and usually takes a particular role in the training of junior NCOs (corporals and lance-corporals, and equivalent). | 6,140,545 |
1642904 | Madiwala | https://en.wikipedia.org/w/index.php?title=Madiwala | Madiwala
Madiwala
Madiwala is a locality in Bangalore, India. It is a bustling center of activity from grocery markets to IT to shopping mall. Being at the center of the IT corridor it is well known across Bangalore.
Madiwala is one of the city's bustling trade centres similar to Jalahalli at Peenya and DVG road at Basavanagudi and other similar places inhabited for the most part by middle class and upper middle class citizens. It is close to Koramangala, Bommanahalli, BTM Layout, HSR Layout, Arekere Mico Layout, Bannerghatta Road, Jayanagar and JP Nagar among other localities, each situated at
a distance of less than five kilometres from Madiwala. The City Railway Station at Majestic is eight kilometres | 6,140,546 |
1642904 | Madiwala | https://en.wikipedia.org/w/index.php?title=Madiwala | Madiwala
kilometres from Madiwala. The City Railway Station at Majestic is eight kilometres from Madiwala. St. John's Medical College Hospital, a renowned missionary hospital, is at Madiwala. The Madiwala Lake in BTM Layout is considered as one of the biggest lakes in Bangalore.
# History.
The history of Madiwala dates back to many thousands of years ago. It is one of the oldest locality in Bangalore,Seems to be central part of Bangalore, based on archaeological documents and the temple of Someshwara contains inscriptions that refer to the Chola kings having presided over the construction of the Temple of Someshwara in Madiwala.
# Languages.
Widely spoken languages are Kannada, Hindi and English. | 6,140,547 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
Symmetric space
In differential geometry, representation theory and harmonic analysis, a symmetric space is a pseudo-Riemannian manifold whose group of symmetries contains an inversion symmetry about every point. This can be studied with the tools of Riemannian geometry, leading to consequences in the theory of holonomy; or algebraically through Lie theory, which allowed Cartan to give a complete classification.
In geometric terms, a complete, simply connected Riemannian manifold is a symmetric space if and only if its curvature tensor is invariant under parallel transport. More generally, a Riemannian manifold ("M", "g") is said to be symmetric if and only if, for each point "p" of "M", there | 6,140,548 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
exists an isometry of "M" fixing "p" and acting on the tangent space formula_1 as minus the identity. Every symmetric space is complete, and has a finite cover which is a simply connected symmetric space; thus these two characterizations coincide up to finite covers. Both descriptions can also naturally be extended to the setting of pseudo-Riemannian manifolds.
From the point of view of Lie theory, a symmetric space is the quotient "G"/"H" of a connected Lie group "G" by a Lie subgroup "H" which is (a connected component of) the invariant group of an involution of "G." This definition includes more that the Riemannian definition, and reduces to it when "H" is compact.
Riemannian symmetric | 6,140,549 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
spaces arise in a wide variety of situations in both mathematics and physics. Their central role in the theory of holonomy was discovered by Marcel Berger. They are important objects of study in representation theory and harmonic analysis as well as in differential geometry.
# Geometric definition.
Let "M" be a connected Riemannian manifold and "p" a point of "M". A diffeomorphism "f" of a neighborhood of "p" is said to be a geodesic symmetry if it fixes the point "p" and reverses geodesics through that point, i.e. if "γ" is a geodesic with formula_2 then formula_3 It follows that the derivative of the map "f" at "p" is minus the identity map on the tangent space of "p". On a general Riemannian | 6,140,550 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
manifold, "f" need not be isometric, nor can it be extended, in general, from a neighbourhood of "p" to all of "M".
"M" is said to be locally Riemannian symmetric if its geodesic symmetries are in fact isometric. This is equivalent to the vanishing of the covariant derivative of the curvature tensor.
A locally symmetric space is said to be a (globally) symmetric space if, in addition, its geodesic symmetries are defined on all of "M".
## Basic properties.
The Cartan–Ambrose–Hicks theorem implies that "M" is locally Riemannian symmetric if and only if its curvature tensor is covariantly constant, and furthermore that every simply connected, complete locally Riemannian symmetric space is actually | 6,140,551 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
Riemannian symmetric.
Every Riemannian symmetric space "M" is complete and Riemannian homogeneous (meaning that the isometry group of "M" acts transitively on "M"). In fact, already the identity component of the isometry group acts transitively on "M" (because "M" is connected).
Locally Riemannian symmetric spaces that are not Riemannian symmetric may be constructed as quotients of Riemannian symmetric spaces by discrete groups of isometries with no fixed points, and as open subsets of (locally) Riemannian symmetric spaces.
## Examples.
Basic examples of Riemannian symmetric spaces are Euclidean space, spheres, projective spaces, and hyperbolic spaces, each with their standard Riemannian | 6,140,552 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
metrics. More examples are provided by compact, semi-simple Lie groups equipped with a bi-invariant Riemannian metric.
Every compact Riemann surface of genus greater than 1 (with its usual metric of constant curvature −1) is a locally symmetric space but not a symmetric space.
An example of a non-Riemannian symmetric space is anti-de Sitter space.
# Algebraic definition.
Let "G" be a connected Lie group. Then a symmetric space for "G" is a homogeneous space "G"/"H" where the stabilizer "H" of a typical point is an open subgroup of the fixed point set of an involution "σ" in Aut("G"). Thus "σ" is an automorphism of "G" with "σ" = id and "H" is an open subgroup of the invariant set
Because | 6,140,553 |
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"H" is open, it is a union of components of "G" (including, of course, the identity component).
As an automorphism of "G", "σ" fixes the identity element, and hence, by differentiating at the identity, it induces an automorphism of the Lie algebra formula_5 of "G", also denoted by "σ", whose square is the identity. It follows that the eigenvalues of "σ" are ±1. The +1 eigenspace is the Lie algebra formula_6 of "H" (since this is the Lie algebra of "G"), and the −1 eigenspace will be denoted formula_7. Since "σ" is an automorphism of formula_5, this gives a direct sum decomposition
with
The first condition is automatic for any homogeneous space: it just says the infinitesimal stabilizer formula_6 | 6,140,554 |
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is a Lie subalgebra of formula_5. The second condition means that formula_7 is an formula_6-invariant complement to formula_6 in formula_5. Thus any symmetric space is a reductive homogeneous space, but there are many reductive homogeneous spaces which are not symmetric spaces. The key feature of symmetric spaces is the third condition that formula_7 brackets into formula_6.
Conversely, given any Lie algebra formula_19 with a direct sum decomposition satisfying these three conditions, the linear map "σ", equal to the identity on formula_6 and minus the identity on formula_7, is an involutive automorphism.
# Riemannian symmetric spaces satisfy the Lie-theoretic characterization.
If "M" is | 6,140,555 |
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a Riemannian symmetric space, the identity component "G" of the isometry group of "M" is a Lie group acting transitively on "M" (that is, "M" is Riemannian homogeneous). Therefore, if we fix some point "p" of "M", "M" is diffeomorphic to the quotient "G/K", where "K" denotes the isotropy group of the action of "G" on "M" at "p". By differentiating the action at "p" we obtain an isometric action of "K" on T"M". This action is faithful (e.g., by a theorem of Kostant, any isometry in the identity component is determined by its 1-jet at any point) and so "K" is a subgroup of the orthogonal group of T"M", hence compact. Moreover, if we denote by "s": M → M the geodesic symmetry of "M" at "p", the | 6,140,556 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
map
is an involutive Lie group automorphism such that the isotropy group "K" is contained between the fixed point group of "σ" and its identity component (hence an open subgroup).
To summarize, "M" is a symmetric space "G"/"K" with a compact isotropy group "K". Conversely, symmetric spaces with compact isotropy group are Riemannian symmetric spaces, although not necessarily in a unique way. To obtain a Riemannian symmetric space structure we need to fix a "K"-invariant inner product on the tangent space to "G"/"K" at the identity coset "eK": such an inner product always exists by averaging, since "K" is compact, and by acting with "G", we obtain a "G"-invariant Riemannian metric "g" on "G"/"K".
To | 6,140,557 |
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show that "G"/"K" is Riemannian symmetric, consider any point "p" = "hK" (a coset of "K", where "h" ∈ "G") and define
where "σ" is the involution of "G" fixing "K". Then one can check that "s" is an isometry with (clearly) "s"("p") = "p" and (by differentiating) d"s" equal to minus the identity on T"M". Thus "s" is a geodesic symmetry and, since "p" was arbitrary, "M" is a Riemannian symmetric space.
If one starts with a Riemannian symmetric space "M", and then performs these two constructions in sequence, then the Riemannian symmetric space yielded is isometric to the original one. This shows that the "algebraic data" ("G","K","σ","g") completely describe the structure of "M".
# Classification | 6,140,558 |
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of Riemannian symmetric spaces.
The algebraic description of Riemannian symmetric spaces enabled Élie Cartan to obtain a complete classification of them in 1926.
For a given Riemannian symmetric space "M" let ("G","K","σ","g") be the algebraic data associated to it. To classify the possible isometry classes of "M", first note that the universal cover of a Riemannian symmetric space is again Riemannian symmetric, and the covering map is described by dividing the connected isometry group "G" of the covering by a subgroup of its center. Therefore, we may suppose without loss of generality that "M" is simply connected. (This implies "K" is connected by the long exact sequence of a fibration, because | 6,140,559 |
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"G" is connected by assumption.)
## Classification scheme.
A simply connected Riemannian symmetric space is said to be irreducible if it is not the product of two or more Riemannian symmetric spaces. It can then be shown that any simply connected Riemannian symmetric space is a Riemannian product of irreducible ones. Therefore, we may further restrict ourselves to classifying the irreducible, simply connected Riemannian symmetric spaces.
The next step is to show that any irreducible, simply connected Riemannian symmetric space "M" is of one of the following three types:
1. Euclidean type: "M" has vanishing curvature, and is therefore isometric to a Euclidean space.
2. Compact type: "M" | 6,140,560 |
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has nonnegative (but not identically zero) sectional curvature.
3. Non-compact type: "M" has nonpositive (but not identically zero) sectional curvature.
A more refined invariant is the rank, which is the maximum dimension of a subspace of the tangent space (to any point) on which the curvature is identically zero. The rank is always at least one, with equality if the sectional curvature is positive or negative. If the curvature is positive, the space is of compact type, and if negative, it is of noncompact type. The spaces of Euclidean type have rank equal to their dimension and are isometric to a Euclidean space of that dimension. Therefore, it remains to classify the irreducible, simply | 6,140,561 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
connected Riemannian symmetric spaces of compact and non-compact type. In both cases there are two classes.
A. "G" is a (real) simple Lie group;
B. "G" is either the product of a compact simple Lie group with itself (compact type), or a complexification of such a Lie group (non-compact type).
The examples in class B are completely described by the classification of simple Lie groups. For compact type, "M" is a compact simply connected simple Lie group, "G" is "M"×"M" and "K" is the diagonal subgroup. For non-compact type, "G" is a simply connected complex simple Lie group and "K" is its maximal compact subgroup. In both cases, the rank is the rank of "G".
The compact simply connected Lie | 6,140,562 |
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groups are the universal covers of the classical Lie groups formula_24, formula_25, formula_26 and the five exceptional Lie groups "E", "E", "E", "F", "G".
The examples of class A are completely described by the classification of noncompact simply connected real simple Lie groups. For non-compact type, "G" is such a group and "K" is its maximal compact subgroup. Each such example has a corresponding example of compact type, by considering a maximal compact subgroup of the complexification of "G" which contains "K". More directly, the examples of compact type are classified by involutive automorphisms of compact simply connected simple Lie groups "G" (up to conjugation). Such involutions extend | 6,140,563 |
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to involutions of the complexification of "G", and these in turn classify non-compact real forms of "G".
In both class A and class B there is thus a correspondence between symmetric spaces of compact type and non-compact type. This is known as duality for Riemannian symmetric spaces.
## Classification result.
Specializing to the Riemannian symmetric spaces of class A and compact type, Cartan found that there are the following seven infinite series and twelve exceptional Riemannian symmetric spaces "G"/"K". They are here given in terms of "G" and "K", together with a geometric interpretation, if readily available. The labelling of these spaces is the one given by Cartan.
## As Grassmannians.
A | 6,140,564 |
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more modern classification uniformly classifies the Riemannian symmetric spaces, both compact and non-compact, via a Freudenthal magic square construction. The irreducible compact Riemannian symmetric spaces are, up to finite covers, either a compact simple Lie group, a Grassmannian, a Lagrangian Grassmannian, or a double Lagrangian Grassmannian of subspaces of formula_27 for normed division algebras A and B. A similar construction produces the irreducible non-compact Riemannian symmetric spaces.
# General symmetric spaces.
An important class of symmetric spaces generalizing the Riemannian symmetric spaces are pseudo-Riemannian symmetric spaces, in which the Riemannian metric is replaced by | 6,140,565 |
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a pseudo-Riemannian metric (nondegenerate instead of positive definite on each tangent space). In particular, Lorentzian symmetric spaces, i.e., "n" dimensional pseudo-Riemannian symmetric spaces of signature ("n" − 1,1), are important in general relativity, the most notable examples being Minkowski space, De Sitter space and anti-de Sitter space (with zero, positive and negative curvature respectively). De Sitter space of dimension "n" may be identified with the 1-sheeted hyperboloid in a Minkowski space of dimension "n" + 1.
Symmetric and locally symmetric spaces in general can be regarded as affine symmetric spaces. If "M" = "G"/"H" is a symmetric space, then Nomizu showed that there is | 6,140,566 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
a "G"-invariant torsion-free affine connection (i.e. an affine connection whose torsion tensor vanishes) on "M" whose curvature is parallel. Conversely a manifold with such a connection is locally symmetric (i.e., its universal cover is a symmetric space). Such manifolds can also be described as those affine manifolds whose geodesic symmetries are all globally defined affine diffeomorphisms, generalizing the Riemannian and pseudo-Riemannian case.
## Classification results.
The classification of Riemannian symmetric spaces does not extend readily to the general case for the simple reason that there is no general splitting of a symmetric space into a product of irreducibles. Here a symmetric | 6,140,567 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
space "G"/"H" with Lie algebra
is said to be irreducible if formula_7 is an irreducible representation of formula_6. Since formula_6 is not semisimple (or even reductive) in general, it can have indecomposable representations which are not irreducible.
However, the irreducible symmetric spaces can be classified. As shown by Katsumi Nomizu, there is a dichotomy: an irreducible symmetric space "G"/"H" is either flat (i.e., an affine space) or formula_5 is semisimple. This is the analogue of the Riemannian dichotomy between Euclidean spaces and those of compact or noncompact type, and it motivated M. Berger to classify semisimple symmetric spaces (i.e., those with formula_5 semisimple) and determine | 6,140,568 |
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which of these are irreducible. The latter question is more subtle than in the Riemannian case: even if formula_5 is simple, "G"/"H" might not be irreducible.
As in the Riemannian case there are semisimple symmetric spaces with "G" = "H" × "H". Any semisimple symmetric space is a product of symmetric spaces of this form with symmetric spaces such that formula_5 is simple. It remains to describe the latter case. For this, one needs to classify involutions "σ" of a (real) simple Lie algebra formula_5. If formula_37 is not simple, then formula_5 is a complex simple Lie algebra, and the corresponding symmetric spaces have the form "G"/"H", where "H" is a real form of "G": these are the analogues | 6,140,569 |
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of the Riemannian symmetric spaces "G"/"K" with "G" a complex simple Lie group, and "K" a maximal compact subgroup.
Thus we may assume formula_37 is simple. The real subalgebra formula_5 may be viewed as the fixed point set of a complex antilinear involution "τ" of formula_37, while "σ" extends to a complex antilinear involution of formula_37 commuting with "τ" and hence also a complex linear involution "σ"∘"τ".
The classification therefore reduces to the classification of commuting pairs of antilinear involutions of a complex Lie algebra. The composite "σ"∘"τ" determines a complex symmetric space, while "τ" determines a real form. From this it is easy to construct tables of symmetric spaces | 6,140,570 |
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for any given formula_37, and furthermore, there is an obvious duality given by exchanging "σ" and "τ". This extends the compact/non-compact duality from the Riemannian case, where either "σ" or "τ" is a Cartan involution, i.e., its fixed point set is a maximal compact subalgebra.
## Tables.
The following table indexes the real symmetric spaces by complex symmetric spaces and real forms, for each classical and exceptional complex simple Lie group.
For exceptional simple Lie groups, the Riemannian case is included explicitly below, by allowing "σ" to be the identity involution (indicated by a dash). In the above tables this is implicitly covered by the case "kl"=0.
# Weakly symmetric Riemannian | 6,140,571 |
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spaces.
In the 1950s Atle Selberg extended Cartan's definition of symmetric space to that of weakly symmetric Riemannian space, or in current terminology weakly symmetric space. These are defined as Riemannian manifolds "M" with a transitive connected Lie group of isometries "G" and an isometry σ normalising "G" such that given "x", "y" in "M" there is an isometry "s" in "G" such that "sx" = σ"y" and "sy" = σ"x". (Selberg's assumption that σ should be an element of "G" was later shown to be unnecessary by Ernest Vinberg.) Selberg proved that weakly symmetric spaces give rise to Gelfand pairs, so that in particular the unitary representation of "G" on "L"("M") is multiplicity free.
Selberg's | 6,140,572 |
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definition can also be phrased equivalently in terms of a generalization of geodesic symmetry. It is required that for every point "x" in "M" and tangent vector "X" at "x", there is an isometry "s" of "M", depending on "x" and "X", such that
- "s" fixes "x";
- the derivative of "s" at "x" sends "X" to –"X".
When "s" is independent of "X", "M" is a symmetric space.
An account of weakly symmetric spaces and their classification by Akhiezer and Vinberg, based on the classification of periodic automorphisms of complex semisimple Lie algebras, is given in .
# Applications and special cases.
## Symmetric spaces and holonomy.
If the identity component of the holonomy group of a Riemannian manifold | 6,140,573 |
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at a point acts irreducibly on the tangent space, then either the manifold is a locally Riemannian symmetric space, or it is in one of 7 families.
## Hermitian symmetric spaces.
A Riemannian symmetric space which is additionally equipped with a parallel complex structure compatible with the Riemannian metric is called a Hermitian symmetric space. Some examples are complex vector spaces and complex projective spaces, both with their usual Riemannian metric, and the complex unit balls with suitable metrics so that they become complete and Riemannian symmetric.
An irreducible symmetric space "G"/"K" is Hermitian if and only if "K" contains a central circle. A quarter turn by this circle acts | 6,140,574 |
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as multiplication by "i" on the tangent space at the identity coset. Thus the Hermitian symmetric spaces are easily read off of the classification. In both the compact and the non-compact cases it turns out that there are four infinite series, namely AIII, BDI with "p=2", DIII and CI, and two exceptional spaces, namely EIII and EVII. The non-compact Hermitian symmetric spaces can be realized as bounded symmetric domains in complex vector spaces.
## Quaternion-Kähler symmetric spaces.
A Riemannian symmetric space which is additionally equipped with a parallel subbundle of End(T"M") isomorphic to the imaginary quaternions at each point, and compatible with the Riemannian metric, is called quaternion-Kähler | 6,140,575 |
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symmetric space.
An irreducible symmetric space "G"/"K" is quaternion-Kähler if and only if isotropy representation of "K" contains an Sp(1) summand acting like the unit quaternions on a quaternionic vector space. Thus the quaternion-Kähler symmetric spaces are easily read off from the classification. In both the compact and the non-compact cases it turns out that there is exactly one for each complex simple Lie group, namely AI with "p" = 2 or "q" = 2 (these are isomorphic), BDI with "p" = 4 or "q" = 4, CII with "p" = 1 or "q" = 1, EII, EVI, EIX, FI and G.
## Bott periodicity theorem.
In the Bott periodicity theorem, the loop spaces of the stable orthogonal group can be interpreted as reductive | 6,140,576 |
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e compact and the non-compact cases it turns out that there is exactly one for each complex simple Lie group, namely AI with "p" = 2 or "q" = 2 (these are isomorphic), BDI with "p" = 4 or "q" = 4, CII with "p" = 1 or "q" = 1, EII, EVI, EIX, FI and G.
## Bott periodicity theorem.
In the Bott periodicity theorem, the loop spaces of the stable orthogonal group can be interpreted as reductive symmetric spaces.
# See also.
- Orthogonal symmetric Lie algebra
- Relative root system
- Satake diagram
# References.
- Contains a compact introduction and lots of tables.
- The standard book on Riemannian symmetric spaces.
- Chapter XI contains a good introduction to Riemannian symmetric spaces. | 6,140,577 |
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Dunglass
Dunglass is a hamlet in East Lothian, Scotland, lying east of the Lammermuir Hills on the North Sea coast, within the parish of Oldhamstocks. It has a 15th-century collegiate church, now in the care of Historic Scotland. Dunglass is the birthplace of Sir James Hall, an 18th-century Scottish geologist and geophysicist. The name "Dunglass" comes from the Brittonic for "grey-green hill".
# Geography.
Dunglass is a small settlement located about 1 km (0.5 mi) north-west of Cockburnspath and 11 km (7 mi) south-east of Dunbar. The whole of Dunglass lies in an area of 2.47 km². It lies to the east of the Lammermuir Hills on the North Sea coast at the point where the old Great North Road | 6,140,578 |
1642922 | Dunglass | https://en.wikipedia.org/w/index.php?title=Dunglass | Dunglass
and modern A1 as well as the London-Edinburgh railway cross the gorge of the Dunglass Burn. The burn forms the boundary between the shires of East Lothian and Berwick. Other settlements nearby include Cove, Pease Bay, and Pease Dean.
# Dunglass Castle and estate.
Dunglass Castle was built by the Pepdies of Dunglass in the 14th century. On the marriage of Nicola Pepdie to Sir Thomas Home, the castle and lands passed to the Home family. It remained in their possession until their forfeiture in 1516, when it passed to Archibald Douglas, Earl of Angus, but it was later besieged and destroyed by the English under the command of Earl Henry of Northumberland in the winter of 1532, and again under | 6,140,579 |
1642922 | Dunglass | https://en.wikipedia.org/w/index.php?title=Dunglass | Dunglass
Duke Edward of Somerset in 1547, when held by Sir George Douglas.
The castle was rebuilt, in an enlarged and improved form, and gave accommodation in 1603 to King James VI, and all his retinue, when on his journey to London to take up the English throne. It was improved by Mary, Countess of Home, but was again destroyed on 30 August 1640 when held by a party of Covenanters under Thomas, Earl of Haddington. An English page, according to Scotstarvet, vexed by a taunt against his countrymen, thrust a red-hot iron into a powder barrel, and himself was killed, with the Earl, his half-brother, Richard, and many others. A pamphlet with a verse account of the explosion and a list of casualties was | 6,140,580 |
1642922 | Dunglass | https://en.wikipedia.org/w/index.php?title=Dunglass | Dunglass
published by the author and poet William Lithgow. He named thirty nine dead including five women, and John White, an English plasterer working for Lady Home.
The Hall family occupied Dunglass for 232 years from 1687. Francis James Usher bought the Estate from Sir John Richard Hall, 9th Bart in 1919, and the estate remains in the Usher family. The Earl of Home continues to hold the title "Lord of Dunglass", despite the fact his family have not held Dunglass for several centuries.
# Sir James Hall.
In the Spring of 1788, the geologist Sir James Hall together with John Playfair and James Hutton set off from Dunglass Burn in a boat heading east along the coast looking for evidence to support | 6,140,581 |
1642922 | Dunglass | https://en.wikipedia.org/w/index.php?title=Dunglass | Dunglass
Hutton's theory that rock formations were laid down in an unending cycle over immense periods of time. They found examples of Hutton's Unconformity at several places, particularly an outcrop at Siccar Point sketched by Sir James Hall. As Playfair later recalled, "The mind seemed to grow giddy by looking so far back into the abyss of time".
# See also.
- List of places in East Lothian
- List of places in the Scottish Borders
# External links.
- SCRAN: Collegiate Church of Dunglass - Sedilia with details, windows, door
- SCRAN: Coloured print of Dunglass House
- CANMORE (RCAHMS): Dunglass Collegiate Church
- RCAHMS: Dunglass, New Bridge
- RCAHMS: Dunglass Railway Viaduct
- Dunglass @ | 6,140,582 |
1642922 | Dunglass | https://en.wikipedia.org/w/index.php?title=Dunglass | Dunglass
at rock formations were laid down in an unending cycle over immense periods of time. They found examples of Hutton's Unconformity at several places, particularly an outcrop at Siccar Point sketched by Sir James Hall. As Playfair later recalled, "The mind seemed to grow giddy by looking so far back into the abyss of time".
# See also.
- List of places in East Lothian
- List of places in the Scottish Borders
# External links.
- SCRAN: Collegiate Church of Dunglass - Sedilia with details, windows, door
- SCRAN: Coloured print of Dunglass House
- CANMORE (RCAHMS): Dunglass Collegiate Church
- RCAHMS: Dunglass, New Bridge
- RCAHMS: Dunglass Railway Viaduct
- Dunglass @ the UKPG Database | 6,140,583 |
1642924 | Lutheran Gymnasium Tisovec | https://en.wikipedia.org/w/index.php?title=Lutheran%20Gymnasium%20Tisovec | Lutheran Gymnasium Tisovec
Lutheran Gymnasium Tisovec
Lutheran Gymnasium Tisovec () is an elite boarding school in Slovakia founded in 1992. The school is partly bilingual (Slovak/English), which is made possible thanks to the number of American Lutheran missionaries who teach at the school.
# History.
The school is based on a long tradition of Lutheran education in the town. Church affiliated education was impossible during the communist era of Czechoslovakia. After the Velvet Revolution in 1989, Slovak Evangelical Lutheran Church started to work on the restoration of the Lutheran high school which used to be in Tisovec before World War II.
Currently, more than 300 students attend the school. The entrance exams are | 6,140,584 |
1642924 | Lutheran Gymnasium Tisovec | https://en.wikipedia.org/w/index.php?title=Lutheran%20Gymnasium%20Tisovec | Lutheran Gymnasium Tisovec
held every year in the spring. The school offers general education, aiming to prepare students for the entrance to a university. Over 90% of EGT's graduates continue their studies on a university level. Extracurricular activities include school choir, musical ensemble, bible study, debate club, student-run mock company, and computer programming. A Model United Nations Security Council session is organized at the school every year in April.
# Successes.
The school's debate club won the Slovak Debate League in 2005, 2006 and 2007. In 2008, EGT debaters came in second in Slovakia. EGT student company was named the best student company in Slovakia in 2006 and 2008. The school choir has also earned | 6,140,585 |
1642924 | Lutheran Gymnasium Tisovec | https://en.wikipedia.org/w/index.php?title=Lutheran%20Gymnasium%20Tisovec | Lutheran Gymnasium Tisovec
general education, aiming to prepare students for the entrance to a university. Over 90% of EGT's graduates continue their studies on a university level. Extracurricular activities include school choir, musical ensemble, bible study, debate club, student-run mock company, and computer programming. A Model United Nations Security Council session is organized at the school every year in April.
# Successes.
The school's debate club won the Slovak Debate League in 2005, 2006 and 2007. In 2008, EGT debaters came in second in Slovakia. EGT student company was named the best student company in Slovakia in 2006 and 2008. The school choir has also earned several distinctions on the national level. | 6,140,586 |
1642927 | Empty triangle | https://en.wikipedia.org/w/index.php?title=Empty%20triangle | Empty triangle
Empty triangle
In the game of Go, the empty triangle is the most fundamental example of the concept of bad shape.
Three stones of one color form an empty triangle when they are placed in a triangle arrangement that fits in a 2×2 square, and when one intersection is left empty. If the triangle is "filled" by a stone of the opponent's at the fourth point of the 2×2, the shape is neutral – not necessarily good or bad.
The deficiencies of the empty triangle are twofold. Three stones in a straight line have eight liberties, while in an empty triangle they have only seven. This can mean the difference between success and failure in a life-and-death struggle. Also the formation lacks efficiency. | 6,140,587 |
1642927 | Empty triangle | https://en.wikipedia.org/w/index.php?title=Empty%20triangle | Empty triangle
In the case cited, the diagonally adjacent stones are tactically connected without the third stone, since the opponent can't prevent them from connecting unless he is ignored for a turn.
However even though the empty triangle is a prime example of bad shape, creating one could make sense, or even qualify as brilliant, in certain situations. An example of this is the third "ghost move" in the famous blood-vomiting game. The move was played by Hon'inbō Jōwa as white against Akaboshi Intetsu. The move allowed Jowa to launch a splitting attack that would ultimately lead to his victory.
"The Empty Triangle" is also the name of a popular series of comic panels about the game of Go that features | 6,140,588 |
1642927 | Empty triangle | https://en.wikipedia.org/w/index.php?title=Empty%20triangle | Empty triangle
sense, or even qualify as brilliant, in certain situations. An example of this is the third "ghost move" in the famous blood-vomiting game. The move was played by Hon'inbō Jōwa as white against Akaboshi Intetsu. The move allowed Jowa to launch a splitting attack that would ultimately lead to his victory.
"The Empty Triangle" is also the name of a popular series of comic panels about the game of Go that features personalities from the KGS Go Server.
# See also.
- International Go Federation
# External links.
- "Empty triangle" from Sensei's Library
- "The empty triangle is bad" from Sensei's Library
- "Full triangle" from Sensei's Library
- "Good Empty Triangle" from Sensei's Library | 6,140,589 |
1642893 | Dean (education) | https://en.wikipedia.org/w/index.php?title=Dean%20(education) | Dean (education)
Dean (education)
Dean is a title employed in academic administrations such as colleges or universities for a person with significant authority over a specific academic unit, over a specific area of concern, or both. Deans are common in private preparatory schools, and occasionally found in middle schools and high schools as well.
# Origin.
A "dean" (Latin "decanus") was originally the head of a group of ten soldiers or monks. Eventually an ecclesiastical dean became the head of a group of canons or other religious groups.
When the universities grew out of the cathedral and monastery schools, the title of dean was used for officials with various administrative duties.
# Use.
## Bulgaria.
In | 6,140,590 |
1642893 | Dean (education) | https://en.wikipedia.org/w/index.php?title=Dean%20(education) | Dean (education)
Bulgarian universities, a dean is the head of a faculty, which may include several academic departments. Every faculty unit of university or academy. The Dean can appoint his deputies: a vice dean of university work and vice dean of science activity.
## Canada.
In a Canadian university or a college, a dean is typically the head of a faculty, which may include several academic departments. Typical positions include Dean of Arts, Dean of Engineering, Dean of Science and Dean of Business. Many universities also have a Dean of Graduate Studies, responsible for work at the postgraduate level in all parts of the university.
The job description for deans at the University of Waterloo is probably | 6,140,591 |
1642893 | Dean (education) | https://en.wikipedia.org/w/index.php?title=Dean%20(education) | Dean (education)
typical, and reads in part, "The dean of a faculty is primarily a university officer, serving in that capacity on the senate, appropriate major committees and on other university bodies. As university officer, the dean has the dual role of making independent judgments on total university matters and representing the particular faculty's policies and points of view. The dean should oversee the particular faculty's relations with other faculties to ensure that they are harmonious and serve the total university's objectives. The dean will report directly to the vice president, academic and provost."
There may be associate deans responsible to the dean for particular administrative functions. McGill | 6,140,592 |
1642893 | Dean (education) | https://en.wikipedia.org/w/index.php?title=Dean%20(education) | Dean (education)
University also uses the title of pro-dean to refer to the ad-hoc officer responsible for administering a PhD thesis defence. They serve as the direct representative of the Dean of Graduate and Postdoctoral Studies and are responsible for the defence being handled in strict correspondence with the university regulations.
Some universities also have a dean of students, responsible for aspects of welfare and discipline and serving as an advocate for students within the institution.
## United Kingdom and Ireland.
In some universities in the United Kingdom the term "dean" is used for the head of a faculty, a collection of related academic departments. Examples include "Dean of the Faculty of | 6,140,593 |
1642893 | Dean (education) | https://en.wikipedia.org/w/index.php?title=Dean%20(education) | Dean (education)
Arts and Humanities". Similar usage is found in Australia and New Zealand.
In collegiate universities such as Oxford and Cambridge, each college may have a dean who is responsible for discipline. An interview with the dean as a result of misbehaviour is referred to as a being "deaned". The dean may also, or instead, be responsible for the running of the college chapel. At Queens' College, Cambridge and Jesus College, Cambridge, for example, the posts of "Dean of College" and "Dean of Chapel" are separate; likewise at Trinity College, Dublin, the posts of Senior and Junior Deans (charged with the discipline of Junior and Senior members respectively) are distinct from the Deans of Residence (who | 6,140,594 |
1642893 | Dean (education) | https://en.wikipedia.org/w/index.php?title=Dean%20(education) | Dean (education)
organise worship in the college chapel).
The University of Durham also has a Dean of Colleges, who is chosen from the various college principals and masters and takes a parallel role to the faculty deans in university-wide debate. There are also Deans of Durham Law School and Durham University Business School.
Each of the colleges of the University of Lancaster has a Dean in charge of student discipline.
## United States.
### Higher education.
The term and position of dean is prevalent in American higher education. Although usage differs from one institution to another, the title is used in two principle ways:
- A dean is usually the head of a significant collection of departments within | 6,140,595 |
1642893 | Dean (education) | https://en.wikipedia.org/w/index.php?title=Dean%20(education) | Dean (education)
a university (e.g., "dean of the downtown campus", "dean of the college of arts and sciences", "dean of the school of medicine"), with responsibilities for approving faculty hiring, setting academic policies, overseeing the budget, fundraising, and other administrative duties. Such a dean is usually a tenured professor from one of the departments but gives up most teaching and research activities upon assuming the deanship.
- Other senior administrative positions in higher education may also carry the title of dean (or a lesser title such as associate dean or assistant dean). For example, many colleges and universities have a position known as "dean of students", who is in charge of student | 6,140,596 |
1642893 | Dean (education) | https://en.wikipedia.org/w/index.php?title=Dean%20(education) | Dean (education)
affairs, and a "dean of the faculty", who serves as the faculty's voice in the school's day-to-day administration.
#### Professional schools.
Almost every American law school, medical school, divinity school, or other professional school is part of a university, and so refers to its highest-ranking administrator as a dean. Most have several assistant or associate deans as well (such as an associate dean of academics or an associate dean of students), as well as a select few vice deans.
The American Bar Association regulations on the operation of law schools, which must be followed for such an institution to receive and maintain ABA accreditation, define the role of the law school dean. These | 6,140,597 |
1642893 | Dean (education) | https://en.wikipedia.org/w/index.php?title=Dean%20(education) | Dean (education)
regulations specify that "A law school shall have a full-time dean, selected by the governing board or its designee, to whom the dean shall be responsible." Thus, a law school dean may not simply be a professor selected by fellow professors, nor even by the president of the university.
Similar standards exist with respect to medical school deans. Specifically, the Liaison Committee on Medical Education (LCME), which accredits medical schools, thereby making them eligible for federal grants and state licensure, sets forth the operative conditions. LCME regulations require that the "chief official of the medical school, who usually holds the title 'dean,' must have ready access to the university | 6,140,598 |
1642893 | Dean (education) | https://en.wikipedia.org/w/index.php?title=Dean%20(education) | Dean (education)
president or other university official charged with final responsibility for the school, and to other university officials as are necessary to fulfill the responsibilities of the dean's office." The LCME further require that the dean "must be qualified by education and experience to provide leadership in medical education, scholarly activity, and care of patients" and that "[t]he dean and a committee of the faculty should determine medical school policies."
### Secondary education.
The term or office of dean is much less common in American secondary education.
Although most high schools are led by a principal or headmaster, a few (particularly private preparatory schools) refer to their chief | 6,140,599 |
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