OpenLLM-France/wikimedia huggingface dataset:
# Supporting hyperplane

In geometry, a supporting hyperplane of a set $S$ in Euclidean space $\mathbb {R} ^{n}$ is a hyperplane that has both of the following two properties:
* $S$ is entirely contained in one of the two closed half-spaces bounded by the hyperplane,
* $S$ has at least one boundary-point on the hyperplane.
Here, a closed half-space is the half-space that includes the points within the hyperplane.

## Supporting hyperplane theorem

This theorem states that if $S$ is a convex set in the topological vector space $X=\mathbb {R} ^{n},$ and $x_{0}$ is a point on the boundary of $S,$ then there exists a supporting hyperplane containing $x_{0}.$ If $x^{*}\in X^{*}\backslash \{0\}$ ($X^{*}$ is the dual space of $X$, $x^{*}$ is a nonzero linear functional) such that $x^{*}\left(x_{0}\right)\geq x^{*}(x)$ for all $x\in S$, then
    $H=\{x\in X:x^{*}(x)=x^{*}\left(x_{0}\right)\}$
defines a supporting hyperplane.
Conversely, if $S$ is a closed set with nonempty interior such that every point on the boundary has a supporting hyperplane, then $S$ is a convex set, and is the intersection of all its supporting closed half-spaces.
The hyperplane in the theorem may not be unique, as noticed in the second picture on the right. If the closed set $S$ is not convex, the statement of the theorem is not true at all points on the boundary of $S,$ as illustrated in the third picture on the right.
The supporting hyperplanes of convex sets are also called tac-planes or tac-hyperplanes.
The forward direction can be proved as a special case of the separating hyperplane theorem (see the page for the proof). For the converse direction,
Define $T$ to be the intersection of all its supporting closed half-spaces. Clearly $S\subset T$. Now let $y\not \in S$, show $y\not \in T$.
Let $x\in \mathrm {int} (S)$, and consider the line segment $[x,y]$. Let $t$ be the largest number such that $[x,t(y-x)+x]$ is contained in $S$. Then $t\in (0,1)$.
Let $b=t(y-x)+x$, then $b\in \partial S$. Draw a supporting hyperplane across $b$. Let it be represented as a nonzero linear functional $f:\mathbb {R} ^{n}\to \mathbb {R}$ such that $\forall a\in T,f(a)\geq f(b)$. Then since $x\in \mathrm {int} (S)$, we have $f(x)>f(b)$. Thus by ${\frac {f(y)-f(b)}{1-t}}={\frac {f(b)-f(x)}{t-0}}<0$, we have $f(y)<f(b)$, so $y\not \in T$.
# Who's on First? (album)

Who's on First? is a live 2000 vocal album by the songwriters Bob Dorough and Dave Frishberg. It was recorded at the Jazz Bakery in Los Angeles.
Dorough and Frishberg had been friends for several decades prior to this recording and had written the song "I'm Hip" together in 1965. The pair were persuaded to perform as a duo by the owner of the Jazz Bakery club, Ruth Price, and this live album was made of their collaboration. The opening song and title track, "Who's on First?" is about the problem of deciding which of the pair should perform first in the show.
The pair performed using two grand pianos that faced each other on the stage. Each performed four solo songs with the rest recorded in duet.

## Reception

Professional ratings :
| Review scores ||
| Source | Rating |
| Allmusic | |
Scott Yanow reviewed the album for Allmusic and wrote that Dorough and Frishberg " ... have a lot in common. Both are swinging pianists, likable vocalists that do not have conventional voices, and superb lyricists with very original wits" and that the album was "a fun CD that lives up to its potential".
Jim Santella reviewed the album for All About Jazz, writing of Dorough and Frishberg, "What individuals! As songwriters, both have come up with memorable keepers" and that the album was " ... an overview from both of these not-to-be-missed songsters, herald[ing] the work of two very different jazz singers. Both Dorough and Frishberg represent tongue-in-cheek hipster humor while maintaining excellent musical standards throughout".

## Track listing

* "Who's on First" (Dave Frishberg) – 3:43
* "Lookin' Good" (Frishberg) – 3:04
* "Too Long in L.A." (Frishberg) – 4:22
* "You Are There" (Frishberg, Johnny Mandel) – 2:42
* Intro: The Underdog – 1:23
* "The Underdog" (Frishberg) – 3:45
* Intro: Where You At? – 0:27
* "Where You At?" (George Handy, Jack Segal) – 3:46
* "Health Food Nut" (Bob Dorough, Don Nelson) – 4:12
* "Devil May Care" (Dorough) – 3:28
* "Nothing Like You" (Dorough, Fran Landesman) – 4:57
* "Hong Kong Blues" (Hoagy Carmichael) – 3:20
* Intro: I'm Hip – 1:29
* "I'm Hip" (Dorough, Frishberg) – 3:59
* "At the Saturday Dance" (Dorough, Frishberg) – 5:00
* "Conjunction Junction" (Dorough) – 4:13
* "Rockin' in Rhythm" (Harry Carney, Duke Ellington, Irving Mills) – 2:53

## Personnel

* Bob Dorough and Dave Frishberg – piano, vocals
* Bob Blumenthal – liner notes
* Ruth Price – announcer
* Burton Yount – art direction, design
* Gordon H. Jee – creative director
* Kent Heckman – editing, mixing
* Kurt Lundvall – mastering
* Cynthia Levine – photography
* Mantis Evar – product manager
* Bill Goodwin – production
# William Chetwynd, 4th Viscount Chetwynd

William Chetwynd, 4th Viscount Chetwynd of Bearhaven (25 November 1721 – 12 November 1791) was a British Whig politician who sat in the House of Commons from 1747 to 1754.

## Early life

Chetwynd was born on 25 November 1721 and was baptised on 21 December 1721 at St Martin-in-the-Fields in London. He was the eldest of two sons and four daughters of William Chetwynd, 3rd Viscount Chetwynd and the former Honora Baker. His father was an MP and diplomat who served as British Resident Minister at Genoa and, later, Master of the Mint. His mother was the daughter of William Baker, Consul at Algiers in 1715.
His father was the youngest son of John Chetwynd and, thus, a younger brother of Walter Chetwynd, 1st Viscount Chetwynd and John Chetwynd, 2nd Viscount Chetwynd from whom he inherited the viscountcy.
He matriculated at Hertford College, Oxford on 2 December 1737.

## Career

He held the office of Whig Member of Parliament for Stockbridge between 1747 and 1754. He held the office of Equerry to the King between 1758 and 1760.
Upon his father's death on 3 April 1770, he succeeded as the 4th Viscount Chetwynd of Bearhaven as well as the 4th Baron Rathdowne, even though he had been disinherited by his father. His sister Mary Chetwynd married Rev. Hon. Richard Henry Roper (son of the 8th Baron Teynham).

## Personal life

On 28 October 1751, he married Susannah Cope, daughter of Sir Jonathan Cope, 1st Baronet, MP, and Mary Jenkinson (the third daughter of Sir Robert Jenkinson). Together, they were the parents of:
* Hon. Susannah Chetwynd (d. 1818), who married wealthy planter, Munbee Goulburn, of Amity Hall, Vere Parish, Jamaica, in 1782.
* Hon. William Chetwynd (1753–1779), a captain in the 46th Foot who died unmarried.
* Jonathan Chetwynd (b. c. 1756), who died in infancy.
* Hon. John Whitmore Chetwynd (1754–1788), a captain in the Royal Navy of HMS Expedition who died unmarried in Jamaica.
* Richard Chetwynd, 5th Viscount Chetwynd (1757–1821), who married Charlotte Cartwright, daughter of Thomas Cartwright and Mary Catherine Desaguliers (eldest daughter of Gen. Thomas Desaguliers), in 1791.
* Maj.-Gen. Granville Anson Chetwynd-Stapylton (1758–1834), the Paymaster and Inspector General of Marines who married Martha Stapylton, daughter of Henry Stapylton and Harriot Warton, in 1783.
* Hon. Anderlechtia Clarissa Chetwynd (1765–1855), who married, as his second wife, Lord Robert Seymour, son of Francis Seymour-Conway, 1st Marquess of Hertford and Lady Isabella Fitzroy (a daughter of Charles FitzRoy, 2nd Duke of Grafton, and thus descended in the illegitimate line from King Charles II), in 1806.
Lady Chetwynd died on 3 March 1790. Lord Chetwynd died at Donnybrook Green on 12 November 1791. He was buried at Christ Church, Dublin.

### Descendants

Through his daughter Susannah, he was a grandfather of Henry Goulburn, Chancellor of the Exchequer, and Frederick Goulburn, Colonial Secretary of New South Wales, among others.
Through his son Granville, he was a grandfather of Granville William Chetwynd Stapylton, a pioneer explorer and surveyor in Australia.
# William L. Pollard

Dr. William L. Pollard was the President of Medgar Evers College of The City University of New York from 2009 to 2013 and the former President of the University of the District of Columbia. As President of Medgar Evers College, he succeeded Dr. Edison O. Jackson (1989–2009), Dr. Leo A. Corbie (acting, 1987–1989), Dr. Jay Carrington Chunn, 2nd (1984–1987), Dr. Dennis Paul (Interim Administrator, 1982–1984), and Dr. Richard Trent (1970–1982).
Dr. Pollard began his tenure at Syracuse University in 1989, serving as dean of the Syracuse University School of Social Work for ten years, where he led the School in its development of a student-centered program. Following this, he became the founding dean of the School of Human Services and Health Professions until he left for the University of the District of Columbia in 2002. Prior to this, he served as Dean and founder of the Grambling State University School of Social Work from 1984 to 1989. In 1976, Dr. Pollard joined the University of Pittsburgh, where he was named the coordinator of the Community Organization Skills Set at the University. In 1972, Dr. Pollard was the Social Welfare department head at Livingstone College.
Dr. Pollard received his Ph.D. in policy and planning from the University of Chicago School of Social Administration in 1976, where the members of his dissertation committee included the late John Hope Franklin, the brilliant historian and educator who, in 1956, became the first African-American department chair at a major college when he was named chairman of Brooklyn College’s history department. Dr. Pollard earned his M.S.W. from the University of North Carolina School of Social Work, and a B.A. from Shaw University.
# Richie Cole (footballer)

Richard Cole (born 15 July 1983) is a former Australian rules footballer for the Collingwood and Essendon Football Clubs in the Australian Football League.
Cole was a half-back flanker and was drafted by Collingwood at pick 11 of the 2001 national draft. 2004 was the best season in his AFL career, in which he played every game and finished sixth in Collingwood's best and fairest. He played a total of 56 games for the Magpies.
Essendon acquired Cole via trade at the end of the 2005 season. He made a total of 7 AFL appearances for the Bombers and was delisted at the end of the 2007 season. He is now a part of the Buffaloes football club (NT)
# Tatsumi, Tokyo

Tatsumi (辰巳) is an area of Koto, Tokyo, Japan. It is surrounded by water on all sides, but is joined by bridges to Shiomi to the north, Shin-Kiba and Yumenoshima to the east, and Shinonome to the west. The west side is largely residential, the east largely consists of parks. It is built on reclaimed land.

## Etymology

The name "Tatsumi" means "South East", and is taken from the area's direction from the Tokyo Imperial Palace.

## History

The swimming events for the 2020 Summer Olympics will be held in Tatsumi at the Tokyo Tatsumi International Swimming Center.

## Transportation

* Tatsumi Station (Yurakucho Line)

## Organizations

* Japanese Red Cross Tatsumi Building
* WOWOW Broadcasting Center

## Public facilities

* Tokyo Tatsumi International Swimming Center
* Tatsumi Seaside Park
* Tatsumi No Mori Green Park

## Schools

Koto Ward Board of Education operates public elementary and junior high schools.
Tatsumi Elementary School (辰巳小学校) and Number Two Tatsumi Elementary School (第二辰巳小学校) are zoned public elementary schools for different parts of Tatsumi. All of Tatsumi is zoned to Tatsumi Junior High School (辰巳中学校).
Schools in Tatsumi:
* Tatsumi Elementary School
* Number Two Tatsumi Elementary School
* Tatsumi Junior High School

## Residences

* Tatsumi 1-chome Apartments
# Richard Harden

Richard Harden may refer to:
* Richard Harden (cricketer) (born 1965), English cricketer
* Richard Harden (politician) (1916–2000), Northern Irish politician
* Rich Harden (born 1981), Canadian baseball pitcher
# The Young Animals

The Young Animals, also known as Born Wild, is a 1968 drama film directed by Maury Dexter. It was the second in a four-picture deal he did with AIP and was filmed at Tucson, Arizona.

## Plot

WASP Bruce (David Macklin) and his gang beat up Mexican American Paco (Zooey Hall) and rape his girlfriend, Raquel (Joanna Frank). Super cool Latino Tony (Tom Nardini) comes to town and hits it off with the blonde Janet (Patty McCormack), who Bruce thinks is his girl. Bruce and his pals chase Tony down, but let him go with a warning to stay away from Janet. Tony decides to organize the Mexican-American students at school, and when principal Wilson (Arthur Petersen) refuses to even listen to their complaints, organizes a walk out by the Mexican-American students. The students picket the school and even brawl with Bruce's gang. After Raquel tells Janet that she was raped, some of the white students walk out in solidarity. Then Paco and a group of students who favor a more radical approach, attack Din-din (Keith Taylor), a member of Bruce's group and his girlfriend. Bruce and his followers get their revenge, killing Paco and Raquel in a staged road "accident". Bruce and his pals try to kill Tony and Janet, but in the end Bruce is arrested. Principal Wilson finally agrees to talk with the students and the walk out ends.

## Cast

* Tom Nardini as Tony
* Patty McCormack as Janet
* Joanna Frank as Raquel
* David Macklin as Bruce
* Zooey Hall as Paco
* Arthur Petersen as Principal Wilson
* Keith Taylor as Din-din
According to IMDB, Cher appeared in this film as an uncredited extra.
# The Electric Boogaloos

The Electric Boogaloos are a street dance crew responsible for the spread of popping and electric boogaloo. The name "Boogaloo" came from a song called "Do a Boogaloo" by James Brown, which was also adapted as a Boogaloo street dance done from Oakland, CA. They were founded by Boogaloo Sam in Fresno, California in 1977. Their original name was the Electronic Boogaloo Lockers but "Lockers" was dropped the following year.
On January 25, 2012, The Electric Boogaloos were honored with a Lifetime Achievement Award at the 13th anniversary show of The Carnival: Choreographer's Ball, for their role in popularizing dance styles such as popping and electric boogie, presented by choreographer and dancer Toni Basil.

## Members

Boogaloo Sam, also known as Sam Solomon grew up in Fresno, California. He was inspired to innovate a new dance style after learning from the Bay City Boogaloos and meeting Tick'n Will and Darnell McDowell - the Ace Tre Lockers - they danced a form of Boogaloo from Oakland. Sam also watched dancers locking on the television. He innovated popping and the EB Boogaloo dance style from Fresno. Popin’ Pete, Boogaloo Sam's little brother, practiced his dance moves by watching Soul Train and doing the robot. Poppin' Pete was taught how to pop styles by his older brother Boogaloo Sam. He watched his brother pop styles and wanted to learn too. The original members of the first group from long beach California were: Boogaloo Sam, Popin Pete, Robot Dane, Puppet Boozer, Creeping Sidney and Scarecrow Scalley. "Skeeter Rabbit of the EBs"who took his dance name from an early original Locker and Robot dancer James @ "Skeeter Rabbit" Higgins, Stephan grew up in Los Angeles, and originally was followed in his name sakes tradition as a locker until his cousins, Boogaloo Sam and Popin’ Pete introduced him to popping. Suga Pop was determined to become part of the Electric Boogaloos after he saw them perform on Soul Train. Later, he moved to Los Angeles where he met Popin’ Pete and Skeeter Rabbit and joined the Electric Boogaloos in 1979. He is currently a music producer. Mr. Wiggles is the most recent addition to the Electric Boogaloos, growing up from South Bronx, New York he is also a member of the Rock Steady Crew.
# Robert Baldock (disambiguation)

Robert Baldock (died 1327) was the Lord Privy Seal and Lord Chancellor of England.
Robert Baldock may also refer to:
* Robert Baldock (judge) (1624/5–1691), English judge
* Bob Baldock (1937–2022), American citizen who participated in Cuban Revolution
# Pitavia

Pitavia is a genus of plants in the family Rutaceae. It contains the following species (but this list may be incomplete):
# Where I Belong (Tanya Chua song)

Where I Belong is an EP released in 2001 by Singaporean singer and songwriter, Tanya Chua. It was officially commissioned as the theme song to the 2001 National Day celebrations in Singapore.
The song is easily recognized by many for its rock tune and smooth melody. In Singapore, the song became an immediate hit after its release, reaching number one status by mid-July 2001. It is the first and only EP to be released in NDP history.
Twelve years later at NDP 2013, this song was sung by the combined schools choir, acknowledging the arrival of former prime ministers, Mr Lee Kuan Yew and ESM Goh Chok Tong. A rendition performed by the Singapore Symphony Orchestra and Singapore Symphony Youth Choir was released in August 2021 to celebrate the twentieth anniversary of the song's release.

## Background

Originally part of the Sing Singapore project, the song was written and composed by Tanya. It was later recorded in Atomic Studios in early 2001 and mixed in the same studio by Mo Lee.
In July 2001, the song was officially released at a press conference. A few days after its release, it reached Platinum status and later a number one hit in Singapore. On the actual parade day in 2001, it was performed by Tanya herself. The song is known to be the only National Day theme piece to use cover art.

## Track listing

All tracks are written by Tanya Chua

## Music video

The video was officially sponsored by government bodies which include the National Arts Council, Ministry of Information, Communications and the Arts and the Sing Singapore project. It was directed by Roslan Ismail, who is affiliated with Gravity Films.
# William Clark (Australian politician)

William McGregor Clark (April 1844 - 29 January 1900) was an Australian politician and newspaper proprietor. He was a member of the Victorian Legislative Assembly from 1879 to 1894, representing the electorate of Footscray. He was a part-owner of the Williamstown Advertiser and co-founder of Footscray newspaper The Independent.
# William Kelley (baseball)

William Kelley (May 1875 – death date unknown), nicknamed "King", was an American Negro league outfielder in 1900.
A native of Pennsylvania, Kelley played for the Cuban Giants in 1900. In his two recorded games, he went hitless with a walk in nine plate appearances.
# Rigoberto Torres

Rigoberto Torres (born 1960) is a sculptor who was born in Aguadilla, Puerto Rico and worked in New York City, before moving to Florida where he currently lives and works. Torres began working in a factory where religious figures were cast, producing religious statuary. He also considers himself to be a community based artist.

## Sculptures

Torres is known in part for the sculptures in plaster and fiberglass that he created of his neighbors in the Bronx, together with his partner John Ahearn. Between the years 1981 and 1985, they collaborated on four murals. These were We Are Family, Life on Dawson Street, Double Dutch, and Back to School. The mural Double Dutch (1981/2010), for example, was acquired by the Pérez Art Museum Miami, city in which Torres lives. The sculptures, like much of Torres' work, were displayed in public attached to buildings, free standing and in street events as an element of performance art. On many occasions, Torres would prompt Ahearn to move their studio to the sidewalk along Walton Avenue so that neighborhood children could watch and also volunteer as subjects.
Torres' sculptures show an instinctive drive to create tableaux from single figures and are included in the field of humanistic naturalism because they accurately portray people. He met frequent collaborator Ahearn in 1980, when Torres was working in a factory casting religious statues. They worked together on the Bronx sculptures, sometimes known as the South Bronx Hall of Fame, creating monuments to ordinary people as a response to the practice of enshrining famous, heroic figures in public places.

## Public Art
### The Bronx

Rigoberto and John have sculpture installed on the exterior walls of buildings throughout The Bronx.
* "Double Dutch," 1981-2 is located on Kelly Street and Intervale Ave.
* "Life on Dawson St.," 1981-82 on Longwood Ave and Dawson St.
* "We Are Family" is on Southern Blvd. facing 156th St.
* There are also other casts installed outside The POINT Community Development Corporation at 940 Garrison Ave.

## Biography

Torres was born in Aguadilla, Puerto Rico, in 1960. At age four, he moved to New York, first in upper Manhattan and then to the Bronx.
In 1990 he returned to Puerto Rico where he produced twenty-two works over the course of a year, including Ruth Fernandez in 1991.
# Tatsuma Ejiri

Tatsuma Ejiri (江尻立真, Ejiri Tatsuma) is a Japanese manga artist from Kyoto Prefecture. After graduating from Kanazawa University he worked as a manga assistant for, among others, Eiichiro Oda and Jin Kobayashi.
His first professionally published work was CHILDS published in the 1999 winter edition of Akamaru Jump. In 2006 his sports manga P2! -let's Play Pingpong!- was serialized in Weekly Shonen Jump.
His latest work is Infini-T Force, which celebrates Tatsunoko Productions’ 55th anniversary and has been licensed in English by Udon Entertainment.

## Works

* CHILDS (1999, Shueisha)
* Oasis Dancer (2000, Shueisha)
* World 4U (2003-2006, Shueisha) - string of one-shots published between 2003 and 2014. Serialized in 'Jump Plus' (2014 - 2015)
* P2! -let's Play Pingpong!- (2006 – 2007 Shueisha)
* Papa no Iu Koto o Kikinasai! - Sorairo no Hibiki (2011-ongoing, Shueisha) (illustrator)
* Ojarumaru (2012-2014, Shueisha) -adaptation of the anime based on the original work of Rin Inumaru.
* Infini-T Force: Arc to the Future (Infini-T Force 未来の描線, Infini-T Force - Mirai no Byōsen) (2015–present), Shogakukan (illustrator).
* Mobile Suits Gundam Red Giant 03rd MS Team (2023–ongoing, Kadokawa Shoten).