OpenLLM-France/wikimedia huggingface dataset:
# Representation on coordinate rings

In mathematics, a representation on coordinate rings is a representation of a group on coordinate rings of affine varieties.
Let X be an affine algebraic variety over an algebraically closed field k of characteristic zero with the action of a reductive algebraic group G. G then acts on the coordinate ring $k[X]$ of X as a left regular representation: $(g\cdot f)(x)=f(g^{-1}x)$. This is a representation of G on the coordinate ring of X.
The most basic case is when X is an affine space (that is, X is a finite-dimensional representation of G) and the coordinate ring is a polynomial ring. The most important case is when X is a symmetric variety; i.e., the quotient of G by a fixed-point subgroup of an involution.

## Isotypic decomposition

Let $k[X]_{(\lambda )}$ be the sum of all G-submodules of $k[X]$ that are isomorphic to the simple module $V^{\lambda }$; it is called the $\lambda$-isotypic component of $k[X]$. Then there is a direct sum decomposition:
    $k[X]=\bigoplus _{\lambda }k[X]_{(\lambda )}$
where the sum runs over all simple G-modules $V^{\lambda }$. The existence of the decomposition follows, for example, from the fact that the group algebra of G is semisimple since G is reductive.
X is called multiplicity-free (or spherical variety) if every irreducible representation of G appears at most one time in the coordinate ring; i.e., $\operatorname {dim} k[X]_{(\lambda )}\leq \operatorname {dim} V^{\lambda }$. For example, $G$ is multiplicity-free as $G\times G$-module. More precisely, given a closed subgroup H of G, define
    $\phi _{\lambda }:V^{{\lambda }*}\otimes (V^{\lambda })^{H}\to k[G/H]_{(\lambda )}$
by setting $\phi _{\lambda }(\alpha \otimes v)(gH)=\langle \alpha ,g\cdot v\rangle$ and then extending $\phi _{\lambda }$ by linearity. The functions in the image of $\phi _{\lambda }$ are usually called matrix coefficients. Then there is a direct sum decomposition of $G\times N$-modules (N the normalizer of H)
    $k[G/H]=\bigoplus _{\lambda }\phi _{\lambda }(V^{{\lambda }*}\otimes (V^{\lambda })^{H})$,
which is an algebraic version of the Peter–Weyl theorem (and in fact the analytic version is an immediate consequence.) Proof: let W be a simple $G\times N$-submodules of $k[G/H]_{(\lambda )}$. We can assume $V^{\lambda }=W$. Let $\delta _{1}$ be the linear functional of W such that $\delta _{1}(w)=w(1)$. Then $w(gH)=\phi _{\lambda }(\delta _{1}\otimes w)(gH)$. That is, the image of $\phi _{\lambda }$ contains $k[G/H]_{(\lambda )}$ and the opposite inclusion holds since $\phi _{\lambda }$ is equivariant.

## Examples

* Let $v_{\lambda }\in V^{\lambda }$ be a B-eigenvector and X the closure of the orbit $G\cdot v_{\lambda }$. It is an affine variety called the highest weight vector variety by Vinberg–Popov. It is multiplicity-free.
# 1966 Ohio State Buckeyes football team

The 1966 Ohio State Buckeyes football team represented the Ohio State University in the 1966 Big Ten Conference football season. The Buckeyes compiled a 4–5 record.

## Schedule

| Date | Time | Opponent | Site | Result | Attendance |
| September 24 | 1:30 p.m. | TCU* | Ohio StadiumColumbus, OH | W 14–7 | 75,375 |
| October 1 | 1:30 p.m. | Washington* | Ohio StadiumColumbus, OH | L 22–38 | 80,241 |
| October 8 | 1:30 p.m. | at Illinois | Memorial StadiumChampaign, IL (Illibuck Trophy) | L 9–10 | 51,069 |
| October 15 | 1:30 p.m. | No. 1 Michigan State | Ohio StadiumColumbus, OH | L 8–11 | 84,282 |
| October 22 | 1:30 p.m. | Wisconsin | Ohio StadiumColumbus, OH | W 24–13 | 84,265 |
| October 29 | 2:30 p.m. | at Minnesota | Memorial StadiumMinneapolis, MN | L 7–17 | 49,489 |
| November 5 | 1:30 p.m. | Indiana | Ohio StadiumColumbus, OH | W 7–0 | 80,834 |
| November 12 | 2:30 p.m. | at Iowa | Iowa StadiumIowa City, IA | W 14–10 | 44,677 |
| November 19 | 1:30 p.m. | Michigan | Ohio StadiumColumbus, OH (rivalry) | L 3–17 | 83,403 |
| *Non-conference gameRankings from AP Poll released prior to the gameAll times are in Eastern time |||||||

## Coaching staff

* Woody Hayes – Head coach – 16th year

## Game summaries
### TCU

| | 1 | 2 | 3 | 4 | Total |
| TCU | 0 | 0 | 7 | 0 | 7 |
| • Ohio St | 7 | 0 | 0 | 7 | 14 |

### Washington

| | 1 | 2 | 3 | 4 | Total |
| • Washington | 7 | 14 | 7 | 10 | 38 |
| Ohio State | 0 | 7 | 8 | 7 | 22 |

### Illinois

| | 1 | 2 | 3 | 4 | Total |
| Ohio State | 3 | 3 | 3 | 0 | 9 |
| • Illinois | 0 | 3 | 0 | 7 | 10 |

### Michigan State

| | 1 | 2 | 3 | 4 | Total |
| • Michigan State | 0 | 0 | 3 | 8 | 11 |
| Ohio State | 2 | 0 | 0 | 6 | 8 |

### Wisconsin

| | 1 | 2 | 3 | 4 | Total |
| Wisconsin | 0 | 6 | 7 | 0 | 13 |
| • Ohio St | 7 | 0 | 3 | 14 | 24 |

### Minnesota

| | 1 | 2 | 3 | 4 | Total |
| Ohio State | 0 | 0 | 0 | 7 | 7 |
| • Minnesota | 0 | 7 | 7 | 3 | 17 |

### Indiana

| | 1 | 2 | 3 | 4 | Total |
| Indiana | 0 | 0 | 0 | 0 | 0 |
| • Ohio St | 0 | 0 | 7 | 0 | 7 |

### Iowa

| | 1 | 2 | 3 | 4 | Total |
| • Ohio St | 0 | 7 | 0 | 7 | 14 |
| Iowa | 0 | 3 | 0 | 7 | 10 |

### Michigan

| | 1 | 2 | 3 | 4 | Total |
| • Michigan | 3 | 7 | 7 | 0 | 17 |
| Ohio St | 0 | 3 | 0 | 0 | 3 |

## 1967 NFL draftees

| Player | Round | Pick | Position | NFL club |
| Mike Current | 3 | 58 | Tackle | Denver Broncos |
| Bo Rein | 7 | 179 | Flanker | Baltimore Colts |
| Ron Sepic | 12 | 300 | End | Washington Redskins |
# Greenlawn Cemetery (Salem, Massachusetts)

Greenlawn Cemetery is a historic cemetery at 57 Orne Street in Salem, Massachusetts. The cemetery was founded in 1807, but received a major redesign in the 1880s to bring it into the then-popular rural cemetery style, with winding lanes and landscaping. The 100-acre (40 ha) is notable for its large number of specimen plants, which is second in the state to the Arnold Arboretum in Boston. It has more than 6000 burials, and is still in active use.
The cemetery was listed on the National Register of Historic Places in 2015.
It is the burial place of Medal of Honor recipient John Phillip Riley (1877–1950). Reverend Jacob Stroyer (1848–1908) is buried there too. Medal of Honor recipient Thomas E. Atkinson (1824–1868 †) has a cenotaph in his honor.
# The Qualified Adventurer

The Qualified Adventurer is a 1925 British silent adventure film directed by Sinclair Hill and starring Matheson Lang, Genevieve Townsend, and Fred Raynham. It was based on the 1922 novel The Qualified Adventurer by Selwyn Jepson.

## Cast

* Matheson Lang as Peter Duff
* Genevieve Townsend as Jimmy Fellowes
* Fred Raynham as Northcote
* Kiyoshi Takase as Yen San
* Cameron Carr as Weames
* Nelson Ramsey as McNab
* Moore Marriott as Bosun
* Wyndham Guise as Captain Fellowes
* Dave O'Toole as Evans
# Majdan Sobolewski

Majdan Sobolewski (Polish pronunciation:) is a village in the administrative district of Gmina Firlej, within Lubartów County, Lublin Voivodeship, in eastern Poland. It lies approximately 6 km (4 mi) south-west of Firlej, 14 km (9 mi) north-west of Lubartów, and 34 km (21 mi) north of the regional capital Lublin.
# Anti-submarine missile

An anti-submarine missile is a standoff anti-submarine weapon, often a specialized variant of anti-ship missile. Anti-submarine missiles usually include a jet or rocket engine and a warhead aimed directly at a submarine. In these missiles, a torpedo or a depth charge is used as a warhead. The anti-submarine missile can be either a cruise missile or a ballistic missile.

## History

Depth charges were the earliest weapons designed for use by ships against submerged submarines. These explosives were initially dropped as the ship moved over the presumed location of a submarine. Before World War II, shipboard sonar was unable to maintain contact with a submarine at close range.
Various mortar-type projectors, including Hedgehog and Squid, were devised during World War II to allow a ship to maintain sonar contact while lobbing explosive charges toward the submarine.
During the Cold War, missiles were developed to provide greater range with reduced recoil. Some missiles and rockets, such as Red Shark carry homing torpedoes to provide terminal guidance for the warhead. The advantage of an anti-submarine missile is the attack stand-off range.

## Examples

* Australia
** Ikara
* France
** Malafon
* India
** SMART
* Italy
** MILAS
* Japan
** Type 07 vertical-launch anti-submarine rocket
* People's Republic of China
** CJ-1 Torpedo
** CY Series
* South Korea
** K745A1 Red Shark
* Soviet Union/Russian Federation
** 85RU
** RPK-2 Vyuga
** 86R
** 88R
** RPK-1 Vikhr
** RPK-9 Medvedka
** Metel Anti-Ship Complex
** 3M-54 Kalibr
* United Kingdom/Australia
** Ikara
* United States
** RUM-139 VL-ASROC
** RUR-5 ASROC
** UUM-44 SUBROC
# Wong Yeung-tat

Wong Yeung-tat (Chinese: 黃洋達; born 29 May 1979) is a Hong Kong social activist and the founder and former leader of radical populist group Civic Passion.

## Biography

Wong was born in Hong Kong and graduated from Hong Kong Baptist University. He joined Television Broadcasts Limited (TVB) and became a screenwriter. He later quit TVB and started his career as a novelist in 2004.
Wong became active in politics in 2010 when he began to host online radio shows for Hong Kong Reporter, an internet radio station affiliated with the democratic party People Power. He quickly rose as the protege of democrat legislator Raymond Wong Yuk-man.
In February 2012, Wong helped found activist group, Civic Passion. The group grew out of dissent with the course that the moderates in the pro-democracy camp had taken. In October 2012, Civic Passion launched Passion Times, a free-of-charge hard-copy newspaper distributed in MTR stations. In November 2012, Passion Times started a radio station, which went on to play an important role in attracting further supporters for Civic Passion, and other cultural products including comics and novels.
Wong ran for the Legislative Council in the 2012 LegCo election as a People Power candidate. Before he ran for the election, he took the initiative to waive bail and serve his sentence for his conviction of gate-crashing a public forum at the Hong Kong Science Museum protesting against a government proposal of the Legislative Council (Amendment) Bill 2012 in September 2011, as he would not have been eligible for candidacy if his prison term had still been pending. After he served his three-week sentence, he ran for the election but failed in Kowloon East by 2,900 votes.
On 11 December 2014, Wong was arrested at his home on suspicion of multiple counts of unauthorized assembly, according to his wife Chan Sau-wai. Wong had been active at the protest site in Mong Kok during the 2014 Hong Kong Protests. The Civic Passion group had made the Mong Kok base their stronghold as the protests began to be showing signs of internal dissent, advocating for escalation, with Wong comparing mainland immigration to a "colonization of Hong Kong".
In September 2016, Wong resigned as the leader of Civic Passion, saying that he did so out of taking responsibility for the failure of the election alliance that Civic Passion had formed with the Proletariat Political Institute and Hong Kong Resurgence Order for the 2016 Legislative Council election. At that election, Wong's mentor Raymond Wong Yuk-man had narrowly lost to Youngspiration's Yau Wai-ching, an outcome about which the latter expressed her disappointment. Wong continued to run Passion Times independently.

## Filmography

Assistant Director:
* Gimme Gimme
* Love au Zen
Story:
* 72 Tenants of Prosperity
* I Love Hong Kong
* The Fortune Buddies
* I Love Hong Kong 2012
Actor:
* Forever and Ever ... Patient
Writer:
* Killer 2
* Unplugging Nightmare
* Turning Point
* 72 Tenants of Prosperity
* I Love Hong Kong
* The Fortune Buddies
# Brew-Hatcher

The Brew-Hatcher or B & H was an American automobile introduced in January 1904 at the Chicago Automobile Show and manufactured from 1904 until 1905.
Around 1903 William A. Hatcher, one of the founders of and engineers for the Ohio Automobile Company (which later became known as the Packard Motor Car Company) and Francis O. Brew started a component supply company. They launched their first automobile, built from many of their company's components, in January 1904.
1904 Model: A five-passenger, 16 hp tourer, it hailed from Cleveland, Ohio. 16 hp horizontally-opposed twin engine and rear-entrance tonneau body.
Specifications:
* Weighs 1,000 lbs, everything on.
* Bevel Gear Drive - Sliding Gear.
* Three speeds forward and reverse.
* Direct drive on high speed.
* Wheel base, 83 1/2" inches.
* Two sets Brakes, double acting.
* Heavy cylinder Double Tube, 30x3 1/2 inch Tires.
* Foot Control.
* Irreversible Steering Wheel."
Price: $1,750
1905 Model: The same model was offered, but on a longer wheelbase, which allowed for a side-entrance tonneau, and there was also an 18/24 hp 4-cylinder tourer.
Car manufacture ended in Fall 1905 when Brew retired to join the Internal Revenue Service.
# Oak Hill, Maine

Oak Hill is a census-designated place (CDP) in the town of Scarborough in Cumberland County, Maine, United States. Prior to the 2020 census, the CDP was known as Scarborough. The population was 4,403 at the 2010 census. It is part of the Portland–South Portland–Biddeford, Maine Metropolitan Statistical Area.

## Geography

Oak Hill is located at 43°35′33″N 70°20′01″W﻿ / ﻿43.59258°N 70.333608°W﻿ / 43.59258; -70.333608 (43.59258, -70.333608).
According to the United States Census Bureau, the CDP has a total area of 5.0 square miles (12.9 km$^2$), of which 0.012 square miles (0.03 km$^2$), or 0.27%, is water.

## Demographics

As of the census of 2000, there were 3,867 people, 1,615 households, and 1,046 families residing in the CDP. The population density was 777.1 inhabitants per square mile (300.0/km$^2$). There were 1,697 housing units at an average density of 341.0 per square mile (131.7/km$^2$). The racial makeup of the CDP was 96.15% White, 0.47% Black or African American, 0.26% Native American, 1.99% Asian, 0.31% from other races, and 0.83% from two or more races. Hispanic or Latino of any race were 0.80% of the population.
There were 1,615 households, out of which 29.4% had children under the age of 18 living with them, 54.4% were married couples living together, 8.1% had a female householder with no husband present, and 35.2% were non-families. 27.1% of all households were made up of individuals, and 11.1% had someone living alone who was 65 years of age or older. The average household size was 2.35 and the average family size was 2.90.
In the CDP, the population was spread out, with 22.3% under the age of 18, 5.8% from 18 to 24, 31.9% from 25 to 44, 22.2% from 45 to 64, and 17.7% who were 65 years of age or older. The median age was 39 years. For every 100 females, there were 88.0 males. For every 100 females age 18 and over, there were 83.9 males.
The median income for a household in the CDP was $46,705, and the median income for a family was $60,037. Males had a median income of $37,891 versus $27,407 for females. The per capita income for the CDP was $24,013. About 5.2% of families and 7.7% of the population were below the poverty line, including 6.4% of those under age 18 and 3.0% of those age 65 or over.
# Greenlevel

Greenlevel is a historic mansion in Collierville, Tennessee. It was built in 1833 for Judge John Overton, and it was home to a state senator and the mayor of Collierville. It is listed on the National Register of Historic Places.

## History

The house was built in 1830 for Judge John Overton, a banker and politician who owned slaves. From 1833 to 1844, it belonged to his daughter Ann and her husband, Robert Campbell Brinkley, who helped build the Memphis and Charleston Railroad.
In 1850, The house was acquired by Dr. Virginius Leake, a physician and developer, in 1850. During the American Civil War of 1861–1865, Leake turned the house into a hospital for the Confederate States Army. After the war, he served in the Tennessee Senate. His son, E.K. Leake, served as the mayor of Collierville.

## Architectural significance

The house was redesigned by Ace Edwards in the Greek Revival architectural style in the 1850s. It has been listed on the National Register of Historic Places since March 6, 1987.
# Shadow of Egypt

Shadow of Egypt is a 1924 British silent adventure film directed by Sidney Morgan and starring Carlyle Blackwell, Alma Taylor and Milton Rosmer. A European adventurer tries to steal from an ancient Egyptian tomb, only to become afflicted by a mysterious curse.
The film was shot on location around Cairo in Egypt.
The Shadow of Egypt is based on Norma Lorimer's 1923 novel of the same name.

## Cast

* Carlyle Blackwell as Sheik Hanan
* Alma Taylor as Lilian Westcott
* Milton Rosmer as Harold Westcott
* Joan Morgan as Princess Moonface
* Arthur Walcott as Abdallah
* Charles Levey as Yusef
* John F. Hamilton as Apollo
# Majdan Trzebieski

Majdan Trzebieski (Polish pronunciation:) is a village in the administrative district of Gmina Opole Lubelskie, within Opole Lubelskie County, Lublin Voivodeship, in eastern Poland.
# Griffith House (Aberdeen, Maryland)

Griffith House, or Wright House, is a historic home located at Aberdeen, Harford County, Maryland, United States. It dates to the 18th century and is a 1+1⁄2-story, frame house measuring approximately 18+1⁄2 by 38 feet. The house is reflective of the type of dwelling of a moderately successful 18th-century farmer or planter.
Griffith House was listed on the National Register of Historic Places in 1978.
# Uzma Kardar

Uzma Kardar (Urdu: عظمیٰ کاردار; born 8 April 1956) is a Pakistani politician who has been a Member of the Provincial Assembly of the Punjab since 2024.

## Early life and education

Kardar was born on 8 April 1956 in Lahore, Pakistan.
She did graduation from Kinnaird College for Women in 1980 and has a degree of Bachelor of Arts.

## Political career

Kardar was elected to the Provincial Assembly of the Punjab as a candidate of Pakistan Tehreek-e-Insaf (PTI) on a reserved seat for women in 2018 Pakistani general election.
In July 2020, she was expelled from PTI for violation of party discipline and was ordered to resign from the Punjab Assembly. In May 2022, she was de-notified by the ECP as a member of the assembly due to her vote in favor of Pakistan Muslim League (N) (PML-N) candidate, Hamza Shahbaz, in the chief minister election held on 16 April 2022.
In the 2024 Pakistani general election, she secured a seat in the Provincial Assembly of the Punjab through a reserved quota for women as a candidate of PML-N.
# Galium × pomeranicum

Galium × pomeranicum is a species of plants in the family Rubiaceae, named for the region historically called Pomerania, now divided between Germany and Poland. The plant is apparently of hybrid origin, a cross between G. album × G. verum, though established in the wild. It is widespread across most of Europe and sparingly naturalized in a few locations in North America (New York, Massachusetts, Connecticut and New Brunswick).
# Smashing Through (1929 film)

Smashing Through is a 1929 British silent adventure film directed by W. P. Kellino and starring John Stuart, Eve Gray and Hayford Hobbs. It was made at Lime Grove Studios in Shepherd's Bush.

## Cast

* John Stuart as Richard Bristol
* Eve Gray as Kitty Masters
* Hayford Hobbs as James Masters, her brother
* Julie Suedo as Miss Duprez
* Sandy McKenzie as Mr. Sergius
* Alf Goddard as Alf, a mechanic
* Mike Johnson as His mate
* Gladys Hamer as Ethyl
* Charles Ashton as Westlake
* Harold Saxon-Snell as Driver
# Malinówka, Łęczna County

Malinówka is a village in the administrative district of Gmina Cyców, within Łęczna County, Lublin Voivodeship, in eastern Poland. It lies approximately 7 km (4 mi) south-west of Cyców, 14 km (9 mi) east of Łęczna, and 36 km (22 mi) east of the regional capital Lublin.
# Devaki (2019 film)

Devaki is a 2019 Indian Kannada-language crime thriller film written and directed by H. Lohith and produced by Akshay C.S. and Ravish R.C. The film was produced under RCS Banner. It stars Priyanka Upendra and Kishore along with Aishwarya Upendra. The supporting cast includes Bollywood actor Sanjeev Jaiswal known for his role in the film – The Attacks of 26/11 . The score is by Nobin Paul, and the cinematography is by H.C. Venu. The film was edited by Ravichandran. The film marks the first appearance of Aishwarya Upendra, opposite her mother.
The film was announced soon after the success of Upendra and Lohith's movie Mummy. This is their second collaboration. The London Economic newspaper cited this movie as one of the examples of Indian thriller movies of 2019 which have the potential to gain global attention due to the absence of songs – which it considered as a staple in Indian movies irrespective of the genre.

## Cast

* Priyanka Upendra as Devaki
* Kishore as Inspector
* Aishwarya Upendra as Devaki's Daughter
* Sanjeev Jaiswal as a kidnapper

## Soundtrack

The film's score was composed by Nobin Paul.

## Production

The film was first titled Howrah Bridge. Following the success of actor-director duo in Mummy, Lohith announced his next project with Upendra. Later, her daughter was cast to play a pivotal role. Kishore was signed to the project to play the antagonist. Three-fourths of the film was shot in Kolkata, with some portions shot in Bengaluru and Mysuru.

## Release

The official first look and teaser of the film was released on 13 March 2019. The theatrical trailer debuted on 27 June 2019. The film was released on 5 July 2019.

## Home media

The film was made available to stream on OTT platform Amazon Prime on 21 February 2020.

## Critical reception

The Times of India paper rated the movie 4/5 and wrote that, "Devaki is not the usual outing that one would go to. It can leave one teary-eyed, especially towards the end of the film. If you're looking for an experience that brings in something new, then this is for you." The New Indian Express paper rated the film 4/5 and wrote "In his second outing after Mummy – Save Me, director Lohith has again displayed a shade of the mark of a genius. It is not just perfection that comes to the fore in Devaki, but the opening of new frontiers, inviting the audience to the kingdom of ingenuity. There is not a scintilla of mediocrity in his execution, which is enhanced by Kolkata’s vibrant yet moody aura. A suspense thriller, Devaki is a film about love and loss, told with a lot of sensitivity. A must watch." The Bangalore Mirror said, "Technically, this is one of the better films you have seen." Aravind Shwetha of The News Minute gave three stars out of five and said, "Devaki manages to keep us invested all through. But for its slow pace, this is a film that deserves a watch." Vivek M V of The Deccan Herald gave three and a half out of five stars and noted, "Devaki, after Bell Bottom, is another thriller that deserves a watch in the theatres."