OpenLLM-France/wikimedia huggingface dataset:
# Affine involution

In Euclidean geometry, of special interest are involutions which are linear or affine transformations over the Euclidean space ⁠$\mathbb {R} ^{n}.$⁠ Such involutions are easy to characterize and they can be described geometrically.

## Linear involutions

To give a linear involution is the same as giving an involutory matrix, a square matrix A such that ${\mathbf {A}}^{2}={\mathbf {I}}\quad \quad \quad \quad (1)$ where I is the identity matrix.
It is a quick check that a square matrix D whose elements are all zero off the main diagonal and ±1 on the diagonal, that is, a signature matrix of the form
${\mathbf {D}}={\begin{pmatrix}\pm 1&0&\cdots &0&0\\0&\pm 1&\cdots &0&0\\\vdots &\vdots &\ddots &\vdots &\vdots \\0&0&\cdots &\pm 1&0\\0&0&\cdots &0&\pm 1\end{pmatrix}}$
satisfies (1), i.e. is the matrix of a linear involution. It turns out that all the matrices satisfying (1) are of the form ${\mathbf {A}}={\mathbf {U}}^{-1}{\mathbf {DU}},$ where U is invertible and D is as above. That is to say, the matrix of any linear involution is of the form D up to a matrix similarity. Geometrically this means that any linear involution can be obtained by taking oblique reflections against any number from 0 through n hyperplanes going through the origin. (The term oblique reflection as used here includes ordinary reflections.)
One can easily verify that A represents a linear involution if and only if A has the form ${\mathbf {A}}=\pm (2{\mathbf {P}}-{\mathbf {I}})$ for a linear projection P.

## Affine involutions

If A represents a linear involution, then x→A(x−b)+b is an affine involution. One can check that any affine involution in fact has this form. Geometrically this means that any affine involution can be obtained by taking oblique reflections against any number from 0 through n hyperplanes going through a point b.
Affine involutions can be categorized by the dimension of the affine space of fixed points; this corresponds to the number of values 1 on the diagonal of the similar matrix D (see above), i.e., the dimension of the eigenspace for eigenvalue 1.
The affine involutions in 3D are:
* the identity
* the oblique reflection in respect to a plane
* the oblique reflection in respect to a line
* the reflection in respect to a point.

## Isometric involutions

In the case that the eigenspace for eigenvalue 1 is the orthogonal complement of that for eigenvalue −1, i.e., every eigenvector with eigenvalue 1 is orthogonal to every eigenvector with eigenvalue −1, such an affine involution is an isometry. The two extreme cases for which this always applies are the identity function and inversion in a point.
The other involutive isometries are inversion in a line (in 2D, 3D, and up; this is in 2D a reflection, and in 3D a rotation about the line by 180°), inversion in a plane (in 3D and up; in 3D this is a reflection in a plane), inversion in a 3D space (in 3D: the identity), etc.
# Cole County Historical Society Building

Cole County Historical Society Building, also known as the B. Gratz Brown House, is a historic building located at Jefferson City, Cole County, Missouri. It was built in 1871, and is a two-story, Victorian style, brick rowhouse. It is three bays wide and features segmental arched windows. It was renovated in 1948.$^{:2}$
It was listed on the National Register of Historic Places in 1969. It is located in the Missouri State Capitol Historic District.
# Andrea Legarreta

Andrea Legarreta Martínez (born 12 July 1971) is a Mexican actress and television host, she is best known as being one of the main hosts of the TV morning show Hoy.
She was married to the singer Erik Rubin, with whom she had two daughters.

## Filmography
### Films

| Year | Title | Role |
| 1989 | Ladrones de tumbas | Andrea |
| 1997 | Educación sexual en breves lecciones | Alejandra |
| 1999 | La segunda noche | Pharmacist |
| 2019 | Mamá se fue de viaje | Casandra |
| 2019 | Guadalupe Reyes | Herself |

### Television

| Year | Title | Role |
| 1989 | Carousel | Aurelia |
| 1989 | Mi segunda madre | Denisse |
| 1989 | Simplemente María | Ivonne D'Angelle |
| 1990 | Alcanzar una estrella | Adriana |
| 1991 | Alcanzar una estrella II | Adriana |
| 1992 | Baila conmigo | Rebeca |
| 1993 | Valentina | Constanza "Connie" Basurto |
| 1996 | La sombra del otro | Marlena Gutiérrez |
| 1996 | Complices en familia | Host |
| 1997 | No tengo madre | Consuelito |
| 1998 | El noticiero con Guillermo Ortega Ruiz | Host |
| 1998 | Una luz en el camino | Ana |
| 1998-2000, 2003-present | Hoy | Host |
| 1999 | Derbez en cuando | Guest |
| 2000-2001 | Aquí entre dos | Host |
| 2002-2003 | ¡Vivan los niños! | Guadalupe "Lupita" Gómez |
| 2003 | Velo de novia | Reporter |
| 2004 | Amarte es mi pecado | TV host |
| 2007 | Sexo y otros secretos | Host of "Hoy, mañana y siempre" |
| 2008 | Mañana es para siempre | Reporter |
| 2009 | Me quiero enamorar | Host |
| 2011 | La fuerza del destino | Veronica Resendiz |
# (392741) 2012 SQ31

(392741) 2012 SQ$_{31}$, provisional designation 2012 SQ$_{31}$, is a sub-kilometer Florian asteroid from the inner regions of the asteroid belt, approximately 700 meters (2,300 feet) in diameter. It was originally considered a trans-Neptunian object and lost minor planet during 2004–2012. The date of the official discovery was later set to 27 December 2009, and credited to astronomers of the Spacewatch program conducted at the Kitt Peak National Observatory near Tucson, Arizona, in the United States.

## Orbit and classification

2012 SQ$_{31}$ a member of the Flora family (402), a giant asteroid family and the largest family of stony asteroids in the main-belt.$^{:23}$ It orbits the Sun in the inner asteroid belt at a distance of 1.9–2.6 AU once every 3 years and 5 months (1,242 days; semi-major axis of 2.26 AU). Its orbit has an eccentricity of 0.14 and an inclination of 4° with respect to the ecliptic. The body's observation arc begins with a precovery taken at Haleakala-AMOS, Hawaii, in December 2005, four years prior to its official discovery observation.

### Trans-Neptunian object

On 11 August 2004, the asteroid was already observed as 2004 PR$_{107}$ by astronomers at the Cerro Tololo Inter-American Observatory in Chile, but became a lost minor planet until 2012 due to a lack of follow-up observations. During this time, and with only two observations taken on the same day, it was thought to be a trans-Neptunian object with a semi-major axis of 46 AU. Michael Brown listed it as a likely a dwarf planet on his website with an estimated diameter of 555 kilometers based on an absolute magnitude of 4.6 and an assumed albedo of 0.09.
In 2009, the lost asteroid was observed again as 2009 YS$_{20}$, but was not identified at the time as being related to 2004 PR$_{107}$. In 2012, it was finally rediscovered under its principal designation, reclassified as a small main-belt asteroid, and numbered two years later (see below).

## Physical characteristics

2012 SQ$_{31}$ has been characterized as a member of the Flora family, which are stony S-type asteroids with albedo typically around 0.24, corresponding to that of the family's parent body, 8 Flora.$^{:23}$ Based on a generic magnitude-to-diameter conversion, 2012 SQ$_{31}$ measures 690 meters for an absolute magnitude of 18.0 and an assumed albedo of 0.24. As of 2018, no rotational lightcurve has been obtained from photometric observations. The asteroid's rotation period, poles and shape remain unknown.

## Numbering and naming

This minor planet was numbered by the Minor Planet Center on 15 April 2014 (M.P.C. 87941). As of 2018, it has not been named.
# Green-breasted bushshrike

The green-breasted bushshrike or gladiator bushshrike (Malaconotus gladiator) is a species of bird in the family Malaconotidae. It is found in the Cameroonian Highlands forests. With a total length of 25 to 28 cm (9.8 to 11.0 in) and a body mass of around 99 g (3.5 oz) this may be the largest of the Malaconotidae.
Its natural habitats are subtropical or tropical moist montane forests and subtropical or tropical high-altitude grassland. It is threatened by habitat loss.
# Estoy Aquí (album)

Estoy Aquí (I'm Here) is a studio album by Lalo Rodríguez released in 1996. It is the final studio album released by Rodríguez, as his album Con Todo Mi Corazon, originally set to be released in March 2013, was completed but never publicly released.
# 2013 Pekao Szczecin Open

The 2013 Pekao Szczecin Open was a professional tennis tournament played on clay courts. It was the 21st edition of the tournament which was part of the 2013 ATP Challenger Tour. It took place in Szczecin, Poland between 16 and 22 September 2013.

## Singles main draw entrants
### Seeds

| Country | Player | Rank$^1$ | Seed |
| ESP | Albert Montañés | 53 | 1 |
| ESP | Pablo Andújar | 54 | 2 |
| FRA | Guillaume Rufin | 81 | 3 |
| BRA | Thomaz Bellucci | 116 | 4 |
| ARG | Diego Sebastián Schwartzman | 137 | 5 |
| GER | Dustin Brown | 146 | 6 |
| UKR | Oleksandr Nedovyesov | 152 | 7 |
| ESP | Pere Riba | 157 | 8 |
| RSA | Rik de Voest | 162 | 9 |
* $^1$ Rankings are as of September 9, 2013.

### Other entrants

The following players received wildcards into the singles main draw:
* Paweł Ciaś
* Piotr Gadomski
* Kamil Majchrzak
* Albert Montañés
The following players received entry from the qualifying draw:
* Mate Delić
* Jan Kuncik
* Grzegorz Panfil
* Michal Schmid

## Champions
### Singles

* Oleksandr Nedovyesov def. Pere Riba 6–2, 7–5

### Doubles

* Ken Skupski / Neal Skupski def. Andrea Arnaboldi / Alessandro Giannessi 6–4, 1–6, [10–7]
# Afrim

Afrim is an Albanian male given name.
Notable people with this name include:
* Afrim Bilali, Albanian basketball player
* Afrim Kuci, Kosovar football player
* Afrim Taku, Albanian football player
* Afrim Tole (born 1970), Albanian football player
* Afrim Tovërlani, Kosovar football player
# Command module

Command module may refer to:
* The Apollo command module, the crew cabin used in the Apollo program designed specifically to return through the atmosphere to a water landing
* The crew module of the Orion spacecraft, designed to function similarly to the Apollo command module
* An electronic control unit used to control a motor vehicle system or subsystem
# Coronary Drug Project

The Coronary Drug Project (CDP) was a large clinical trial which assessed several different treatments for coronary heart disease in men with previous myocardial infarction. The study was conducted from 1965 to 1985 at 53 clinical centers and randomized 8,341 men age 30 to 64 years to six different treatment groups: low-dose estrogen therapy (2.5 mg/day oral conjugated estrogens), high-dose estrogen therapy (5 mg/day oral conjugated estrogens), clofibrate (1.8 g/day), dextrothyroxine (6 mg/day), niacin (3 g/day), and placebo (lactose 3.8 mg/day).
The high-dose estrogen group was discontinued in 1970 due to increased non-fatal cardiovascular complications and an unfavorable trend in overall mortality, while the low-dose estrogen group was discontinued in 1970 due to lack of indication of benefit and also an unfavorable trend in overall mortality. Both dose levels of estrogen as well as clofibrate were also found to increase the incidence of gallbladder disease in the study. The dextrothyroxine group was discontinued in late 1971 due to increased cardiovascular mortality.
The Coronary Drug Project Aspirin Study was a substudy of the CDP which randomized men from the estrogen and dextrothyroxine groups of the trial which had been terminated early to either aspirin or placebo.
# An Elixir for Existence

Professional ratings :
| Review scores ||
| Source | Rating |
| Metal Storm | |
An Elixir for Existence is the second studio album by the Norwegian gothic metal band Sirenia, released in 2004. The album follows in the same vein as the previous At Sixes and Sevens, but includes a new female vocalist, Henriette Bordvik. From this album, Sirenia has been presented as a 4-piece band, with Morten Veland as the only permanent member.

## Musical style

Like its predecessor album At Sixes and Sevens (2002), the musical style in An Elixir for Existence corresponds to the more classic Sirenia's gothic metal of their origins, with some elements of symphonic death-doom.
A large number of the songs are concerned with mental conditions, be it depression ("Voices Within"), drug use ("Euphoria") or thoughts of suicide ("The Fall Within"); of course, the meanings of all of these songs are subject to further conjecture.

## Track listing

All songs written by Morten Veland.

## Personnel

Credits for An Elixir for Existence adapted from liner notes.
Sirenia
* Morten Veland – harsh vocals (tracks 1–5, 7, 8), guitars, bass, keyboards, drum programming, mixing
* Henriette Bordvik – female vocals (tracks 1–8)
Additional personnel
* Kristian Gundersen – clean male vocals (tracks 3, 4, 7)
* Anne Verdot – violin (tracks 2–4, 6)
* Damien Surian, Mathieu Landry, Emmanuelle Zoldan, Sandrine Gouttebel, Emilie Lesbros – choir (tracks 1–5, 7–9)
Production
* Joachim Luetke – cover art, artwork
* Terje Refsnes – mixing, engineering
* Emile M.E. Ashley – photography
* Ulf Horbelt – mastering
* Wolfgang Voglhuber – photography
# Greg Scott (rugby league)

Greg Scott (born 21 June 1991) is a professional rugby league footballer who most recently played for the Swinton Lions in the Kingstone Press Championship. He plays on the wing.
Scott came through the Widnes Vikings Academy.
Scott has previously played for Swinton, Widnes and the Dewsbury Rams.
# Boisot

Boisot is a surname. Notable people with the surname include:
* Georges Boisot (1774-1853), Chancellor of the Swiss State
* Jean-Baptiste Boisot (1638–1694), French abbot, bibliophile and scholar
* Louis Boisot (1856–1933), American banker
* Max Boisot (1943–2011), British architect and management consultant
# Aled Williams

Aled Williams may refer to:
* Aled Williams (footballer)
* Aled Williams (rugby union)
# 2013 Patriot League men's basketball tournament

The 2013 Patriot League men's basketball tournament was held March 6, 9 and 13 at campus sites of the higher seed. The winner of the tournament, the BucknellBison received an automatic bid to the NCAA tournament.

## Bracket

| Quarterfinals March 6 | Quarterfinals March 6 | Quarterfinals March 6 | Semifinals March 9 | Semifinals March 9 | Semifinals March 9 | Championship March 13 CBS Sports Network | Championship March 13 CBS Sports Network | Championship March 13 CBS Sports Network |
| 1 | Bucknell | 58 | | | | | | |
| 8 | Navy | 42 | | | | | | |
| 8 | Navy | 42 | 1 | Bucknell | 78 | | | |
| | | | 4 | Army | 70 | | | |
| 4 | Army | 65 | 4 | Army | 70 | | | |
| 5 | American | 44 | | | | | | |
| 5 | American | 44 | | | | 1 | Bucknell | 64 |
| | | | | | | 2 | Lafayette | 56 |
| 2 | Lafayette | 77 | | | | | | | 2 | Lafayette | 56 |
| 7 | Holy Cross | 54 | | | | | | |
| 7 | Holy Cross | 54 | 2 | Lafayette | 82 | | | |
| | | | 3 | Lehigh | 69 | | | |
| 3 | Lehigh | 71 | 3 | Lehigh | 69 | | | |
| 6 | Colgate | 64 | | | | | | |
# Combined Court

The Combined Court was the legislature of British Guiana until 1928. In its final form, it consisted of a sitting of the Court of Policy together with the elected Financial Representatives.

## History

The Combined Court was established by the Dutch authorities at a time when the colonies of Berbice, Demerara and Essequibo were under the control of the Netherlands. It originally consisted of a joint sitting of the Court of Policy and the College of Kiezers. However, Lieutenant Governor of Demerara Hugh Lyle Carmichael abolished the College of Kiezers in 1812, giving its duties to the Financial Representatives.
The Court of Policy was part-appointed and part-elected by the re-established College of Kiezers, whilst the Financial Representatives were elected by the public, although using a severely limited franchise. Its responsibilities included raising and spending public revenue, and from 1855 onwards, setting the salaries of civil servants.
Following the 1891 constitutional reforms, the Combined Court consisted had 22 members, six of which were the Financial Representatives now elected by the public in the single member constituencies of Demerara, Essequebo North Western, Essequebo South Eastern, Berbice, Georgetown and New Amsterdam, and the remainder were the 16-member Court of Policy, half of which was elected. The Court of Policy included the Governor, seven government officials (the Attorney General, the Government Secretary, the Immigration Agent General and the Receiver General, together with three other appointees). The eight elected members were elected from seven constituencies by the public;
Demerara East, Demerara West, Essequebo North Western, Essequebo South Eastern, Berbice, City of Georgetown (2 members) and New Amsterdam. The franchise was severely limited. By the 1926 elections only 4.2% of the population were eligible to vote, up from 1.08% in 1921.
Elections were held under this system in 1892, 1897, 1901, 1906, 1911, 1916, 1921 and 1926. The Combined Court was abolished in 1928 when a new constitution replaced it with the Legislative Council.
# 2005–06 NBL All-Star Game

The 2005/06 NBL All-Star Game was held at the Sydney Entertainment Centre in Sydney, New South Wales on 27 December 2005. The attendance for this All-Star game was 4783 spectators.
The Aussie All-Stars defeated the World All-Stars 151–116. Veteran Darryl McDonald from the Melbourne Tigers won the All-Star MVP award, registering 19 points, 10 assists, 5 rebounds and 6 steals. Game high scorers included Chris Anstey (22), Glen Saville (20) and McDonald for the Aussie All-Stars, and Cortez Groves (19), Mike Helms (16) and Dusty Rychart (14) for the World All-Stars.
While named in the World All-Stars squad, Rolan Roberts did not play in the All-Star game due to suffering a season-ending shoulder injury during the Dunk Competition.

## Line-up
### Aussies

Head Coach: Brian Goorjian (Sydney Kings)
| Name | Club |
| Chris Anstey | Melbourne Tigers |
| Mark Bradtke | Brisbane Bullets |
| C. J. Bruton | Sydney Kings |
| Martin Cattalini | Cairns Taipans |
| Brett Maher | Adelaide 36ers |
| Sam Mackinnon | Brisbane Bullets |
| Darryl McDonald | Melbourne Tigers |
| Scott McGregor | West Sydney Razorbacks |
| Glen Saville | Wollongong Hawks |
| Jason Smith | Sydney Kings |

### World

Head Coach: Phil Smyth (Adelaide 36ers)
| Name | Club |
| Larry Abney | Townsville Crocodiles |
| Adam Ballinger | Wollongong Hawks |
| Bobby Brannen | Brisbane Bullets |
| Willie Farley | Adelaide 36ers |
| Cortez Groves | Wollongong Hawks |
| Mike Helms | Hunter Pirates |
| Shawn Redhage | Perth Wildcats |
| Rolan Roberts | Sydney Kings |
| Dusty Rychart | Adelaide 36ers |
| Dave Thomas | Melbourne Tigers |
| Liu Wei – Invitational | Shanghai Sharks |

## Dunk Competition

The Dunk Competition was won by Everard Bartlett of the New Zealand Breakers.
Other competitors in the Dunk Competition included:
* Larry Abney (Townsville Crocodiles)
* Deba George (Cairns Taipans)
* Cortez Groves (Wollongong Hawks)
* Rolan Roberts (Sydney Kings)
* Liam Rush (Perth Wildcats)
* Pero Vasiljevic (West Sydney Razorbacks)
# Greg Scott

Greg or Gregory Scott may refer to:
* Gregory Scott (1879–?), British film actor
* Gregory K. Scott (c. 1949–2021), Colorado Supreme Court justice
* Greg Scott (American football) (born 1979), former American football defensive end
* Greg Scott (ice hockey) (born 1988), Canadian ice hockey right winger
* Greg Scott (politician), member of the Pennsylvania House of Representatives (2023 – present)
* Greg Scott (rugby league) (born 1991), rugby league player
* Greg Scott (violinist), English violinist
* Malcom Gregory Scott, (born 1962) American writer, activist, and AIDS survivor
# Boggart Hole Brook

Boggart Hole Brook is a river in Blackley, Manchester, England, which a tributary of the River Irk. It rises in Boggart Hole Clough, near the main lake, and has a length of just over a mile (1.6 km).
53°31′12″N 2°12′41″W﻿ / ﻿53.52000°N 2.21139°W﻿ / 53.52000; -2.21139
* This Greater Manchester location article is a stub. You can help Wikipedia by expanding it.
* v
* t
* e
* This article related to a river in England is a stub. You can help Wikipedia by expanding it.
* v
* t
* e
# Alejandra Ribera

Alejandra Ribera is a Canadian pop and jazz singer-songwriter, who performs material in English, French and Spanish.
Of mixed Argentine and Scottish descent, Ribera was born and raised in Toronto, Ontario, and has been professionally based in Montreal, Quebec. She released her debut album, Navigator/Navigateher, in 2009, and followed up with La Boca in 2014. NPR's Alt.Latino referred to La Boca and her voice as Alt.Latino's favorite of 2014.
In 2014, Ribera's song "I Want" won the SOCAN Songwriting Prize, an annual competition that honours the best song written and released by 'emerging' songwriters over the past year, as voted by the public.
Her third album, This Island, was released in 2017.
# Bivolje

Bivolje is a republic in the city of Kruševac, Serbia. According to the 2011 census, it has a population of 275. Bivolje Is one of favelas in Krusevac, with Big crime reputation.
# Agios Thomas Diaporion

Agios Thomas (Saint Thomas / Άγιος Θωμάς ) is an island in the Saronic Gulf, located north of the gulf and northwest of Aegina, part of the Saronic Islands. It belongs to the municipality of Aegina.
The island can be reached by 45-minute ferry ride from Athens and a 20-minute ride from Corinth. In 2015, it was bought by Warren Buffett and Alessandro Proto for 15 million euros.
# Carl Engel von der Rabenau

Carl Engel von der Rabenau (1817-1870), a German painter, was born at Londorf, and died at Rödelheim, today part of Frankfurt am Main.
The Darmstadt Gallery has a View of the Studio of the Sculptor Scholl [de], by him. Another painting Family Portrait of Councillor Debus from 1840 was added to the museum's collection, donated by the Museumsverein of Darmstadt in 2011.
# Bolivaridia

Bolivaridia is a genus of proturans in the family Acerentomidae.

## Species

* Bolivaridia boneti Tuxen, 1976
* Bolivaridia imadatei Prabhoo, 1975
* Bolivaridia perissochaeta Bonet, 1942
* Bolivaridia somalicum Yin & Dallai, 1985
# Eudonia philetaera

Eudonia philetaera is a moth in the family Crambidae. It was named by Edward Meyrick in 1884. Meyrick gave a description of the adult moth in 1885. It is endemic to New Zealand.
The wingspan is about 19 mm. The forewings are white, mixed with light grey and with some fine scattered black scales. There is a suffused blackish spot on the costa at the base. The first line is white and blackish-margined and the second line is whitish, margined with dark anteriorly. The hindwings are very pale whitish-grey. The lunule, postmedian line and hindmargin are slightly darker. Adults have been recorded on wing in January.
# Ain't Had No Lovin'

"Ain't Had No Lovin'" is a single by American country music artist Connie Smith. Released in May 1966, the song reached #2 on the Billboard Hot Country Singles chart. The single was later issued onto Smith's second album of the year, Born to Sing.

## Chart performance

| Chart (1966) | Peak position |
| U.S. Billboard Hot Country Singles | 2 |
# Agios Vasileios

Agios Vasileios (Greek for Saint Basil) may refer to the following places:

## In Greece

* Agios Vasileios, Rethymno, a municipality near Rethymno, Crete
* Agios Vasileios, Archanes-Asterousia, a village in the municipality Archanes-Asterousia, Heraklion regional unit, Crete
* Agios Vasileios, Viannos, a village in the municipality Viannos, Heraklion regional unit, Crete
* Agios Vasileios, Achaea, a village near Patras
* Agios Vasileios, Corinthia, a village near Corinth
* Agios Vasileios, Laconia, site of a Mycenaean palace
* Agios Vasileios, a village in the municipality East Mani
* Agios Vasileios, Mount Athos, a hermitage in Mount Athos
# Collin River (Chile)

The Collin River is a river of Chile.