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... | 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 offi... | 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 Treas... | 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... | 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 contributi... | 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 hosp... | 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, Ba... | 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 d... | 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 Gove... | 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 197... | 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... | 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... | 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.
Elizabet... | 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 ... | 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... | 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 Tripo... | 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 ... | 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 Gabriel... | 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 o... | 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 fa... | 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 h... | 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 schem... | 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 platfor... | 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 Bri... | 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, destr... | 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 coach... | 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-se... | 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 ... | 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 coac... | 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 ... | 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 w... | 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 th... | 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... | 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 appe... | 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 play... | 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-ath... | 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.
... | 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
- ... | 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 So... | 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 openin... | 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, ... | 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 ... | 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, incl... | 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... | 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 PS... | 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.... | 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 B... | 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 dat... | 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 ... | 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... | 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.
Le... | 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.
... | 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 sym... | 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-Riem... | 6,140,553 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
"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 ... | 6,140,554 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
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 symmet... | 6,140,555 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
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 ac... | 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 compac... | 6,140,557 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
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"... | 6,140,558 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
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 c... | 6,140,559 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
"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 i... | 6,140,560 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
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 iden... | 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 exa... | 6,140,562 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
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,... | 6,140,563 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
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... | 6,140,564 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
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 Grassm... | 6,140,565 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
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 spa... | 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 a... | 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 ... | 6,140,568 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
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 s... | 6,140,569 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
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 co... | 6,140,570 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
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 follo... | 6,140,571 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
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 norma... | 6,140,572 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
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... | 6,140,573 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
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... | 6,140,574 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
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 exceptiona... | 6,140,575 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
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. ... | 6,140,576 |
1642877 | Symmetric space | https://en.wikipedia.org/w/index.php?title=Symmetric%20space | Symmetric space
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 periodicit... | 6,140,577 |
1642922 | Dunglass | https://en.wikipedia.org/w/index.php?title=Dunglass | Dunglass
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... | 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 D... | 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 agai... | 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 e... | 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... | 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 aby... | 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... | 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 clu... | 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 program... | 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 "fille... | 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 qualif... | 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.... | 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 scho... | 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, ... | 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 re... | 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 univ... | 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 al... | 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 Busines... | 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 ... | 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 a... | 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 standar... | 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 ... | 6,140,599 |
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