OpenLLM-France/wikimedia huggingface dataset:
# Galois extension

In mathematics, a Galois extension is an algebraic field extension E/F that is normal and separable; or equivalently, E/F is algebraic, and the field fixed by the automorphism group Aut(E/F) is precisely the base field F. The significance of being a Galois extension is that the extension has a Galois group and obeys the fundamental theorem of Galois theory.
A result of Emil Artin allows one to construct Galois extensions as follows: If E is a given field, and G is a finite group of automorphisms of E with fixed field F, then E/F is a Galois extension.
The property of an extension being Galois behaves well with respect to field composition and intersection.

## Characterization of Galois extensions

An important theorem of Emil Artin states that for a finite extension $E/F,$ each of the following statements is equivalent to the statement that $E/F$ is Galois:
* $E/F$ is a normal extension and a separable extension.
* $E$ is a splitting field of a separable polynomial with coefficients in $F.$
* $|\!\operatorname {Aut} (E/F)|=[E:F],$ that is, the number of automorphisms equals the degree of the extension.
Other equivalent statements are:
* Every irreducible polynomial in $F[x]$ with at least one root in $E$ splits over $E$ and is separable.
* $|\!\operatorname {Aut} (E/F)|\geq [E:F],$ that is, the number of automorphisms is at least the degree of the extension.
* $F$ is the fixed field of a subgroup of $\operatorname {Aut} (E).$
* $F$ is the fixed field of $\operatorname {Aut} (E/F).$
* There is a one-to-one correspondence between subfields of $E/F$ and subgroups of $\operatorname {Aut} (E/F).$
An infinite field extension $E/F$ is Galois if and only if $E$ is the union of finite Galois subextensions $E_{i}/F$ indexed by an (infinite) index set $I$, i.e. $E=\bigcup _{i\in I}E_{i}$ and the Galois group is an inverse limit $\operatorname {Aut} (E/F)=\varprojlim _{i\in I}{\operatorname {Aut} (E_{i}/F)}$ where the inverse system is ordered by field inclusion $E_{i}\subset E_{j}$.

## Examples

There are two basic ways to construct examples of Galois extensions.
* Take any field $E$, any finite subgroup of $\operatorname {Aut} (E)$, and let $F$ be the fixed field.
* Take any field $F$, any separable polynomial in $F[x]$, and let $E$ be its splitting field.
Adjoining to the rational number field the square root of 2 gives a Galois extension, while adjoining the cubic root of 2 gives a non-Galois extension. Both these extensions are separable, because they have characteristic zero. The first of them is the splitting field of $x^{2}-2$; the second has normal closure that includes the complex cubic roots of unity, and so is not a splitting field. In fact, it has no automorphism other than the identity, because it is contained in the real numbers and $x^{3}-2$ has just one real root. For more detailed examples, see the page on the fundamental theorem of Galois theory.
An algebraic closure ${\bar {K}}$ of an arbitrary field $K$ is Galois over $K$ if and only if $K$ is a perfect field.
# Khetasar

Khetasar is a village in the Osian Tehsil of Jodhpur District in the state of Rajasthan, India. It is part of the Jodhpur Division and is situated 57 kilometers north of the district headquarters Jodhpur. Khetasar is located 19 kilometers from Osian and 348 kilometers from the state capital Jaipur.

## Nearby Villages

* Khabra Khurd (8 km)
* Banakabas (10 km)
* Osian (10 km)
* Berdon Ka Bas (13 km)
* Tapu (13 km)
# Hope Whisper

The Hope Whisper was an electric car developed in Denmark in 1983. The sole model crashed at the unveiling when the car rolled away during the photoshoot and hit a barrier. It did not reach production.
The Whisper was a compact four-seater city car (two adults and two children), with a claimed range of 62 miles and a top speed of 50 mph. It has a glass fibre body and was 3,500 mm (136 in) long.
In 1985, a Whisper II was developed with Berlin University but funding for production was again not forthcoming.
# Flower (Tomiko Van song)

"Flower" is Tomiko Van's debut single under the Avex Trax label. The single was released on June 7, 2006 in two formats.

## Overview

"Flower" is former Do As Infinity lead singer Tomiko Van's debut single. Released in two versions, CD only and CD+DVD, there are two different covers for the single, though the covers have very little differences to them. The A-side song "Flower" was used as the TBS drama Oishii Proposal theme song, and a piano version of the song was used for the sound track of the drama. The B-side "Brave" was used as the ending theme song for PlayStation 2 game Sengoku Basara 2.
Unlike most of the songs on her debut album, "Flower" is an up-tempo pop song with a feeling of summer to it. The song features guitars, an instrument that was not as prominent in her debut album, and is reminiscent of songs that she would sing during her times in Do As Infinity.

## Track listing
### CD only format

* "Flower" (Maki Ogawa, Katsumi Ōnishi) - 4:14
* "Brave" (Tomiko Van, Katsumi Ōnishi) - 4:38
* "Flower" -Instrumental- - 4:14
* "Brave" -Instrumental- - 4:38

### CD and DVD
#### CD portion

* "Flower" (Maki Ogawa, Katsumi Ōnishi) - 4:14
* "Brave" (Tomiko Van, Katsumi Ōnishi) - 4:38
* "Flower" -Instrumental- - 4:14
* "Brave" -Instrumental- - 4:38

#### DVD portion

* "Flower" (Music Clip)

## TV performances

* June 2, 2006 - Music Fighter
* June 9, 2006 - Music Fighter

## Charts

Oricon Sales Chart (Japan)
| Release | Chart | Peak position | First week sales | Sales total |
| June 7, 2006 | Oricon Daily Singles Chart | 7 |
| June 7, 2006 | Oricon Weekly Singles Chart | 10 | 14,342 | 18,802+ |
* This 2000s Japanese single–related article is a stub. You can help Wikipedia by expanding it.
* v
* t
* e
# Hunts & Peterborough County Rugby Union

Hunts and Peterborough County Rugby Union is an amalgamation of Rugby Union teams from around Peterborough and Huntingdonshire.
It is a sub-county of the East Midlands Rugby Football Union and holds its own county cup each season.
Playing colours: Red, green, yellow & blue hoops.

## Member teams

* Deepings RUFC
* Huntingdon RFC
* Peterborough Lions RFC
* St Ives RFC
* St. Neots RUFC
* Thorney RUFC
* Westwood RUFC

## Representative teams

Hunts & Peterborough County Rugby Union has representative teams at U13, U14, U15 and U16 levels and these teams play matches against other counties in the East Midlands Rugby Union jurisdiction.

## County Cup draw

| Round One (by 1 Oct 2013) | Round One (by 1 Oct 2013) | Round One (by 1 Oct 2013) | Semifinals (by 1 Feb 2014) | Semifinals (by 1 Feb 2014) | Semifinals (by 1 Feb 2014) | Final (by 30 Apr 2014) | Final (by 30 Apr 2014) | Final (by 30 Apr 2014) |
| Thorney | Thorney | 18 | | | | | | |
| Deepings | Deepings | 05 | | | | | | |
| Deepings | Deepings | 05 | Thorney | Thorney | 20 | | | |
| | | | Peterborough RFC | Peterborough RFC | 15 | | | |
| St Neots | St Neots | 31 | Peterborough RFC | Peterborough RFC | 15 | | | |
| Peterborough RFC | Peterborough RFC | 10 | | | | | | |
| Peterborough RFC | Peterborough RFC | 10 | | | | Thorney | Thorney | 41 |
| | | | | | | Huntingdon | Huntingdon | 7 |
| TBA RUFC | TBA RUFC | | | | | | | | Huntingdon | Huntingdon | 7 |
| TBA RUFC | TBA RUFC | | | | | | | |
| TBA RUFC | TBA RUFC | | | | | | | |
| TBA RUFC | TBA RUFC | | | | | | | |

## Past Cup Champions

2012/13 season - St Ives RFC 12 April 2013 Deepings (21) V (24) St Ives
2011/12 season -
2010/11 season -
2009/10 season -
2008/09 season -
2007/08 season - Peterborough Lions 2 February 2008 Peterborough Lions (18) v (12) Deepings
# Bear Creek Township, Poweshiek County, Iowa

Bear Creek Township is a township in Poweshiek County, Iowa, United States.
# Toyooka (disambiguation)

Toyooka is a city in Hyōgo Prefecture, Japan.
Toyooka may also refer to:
* Toyooka, Nagano, a village in Shimoina District, Nagano Prefecture, Japan
* Toyooka, Shizuoka, a former village in Iwata District, Shizuoka Prefecture, Japan
* Toyooka Domain, a feudal domain of Japan
* Toyooka Station (disambiguation), multiple railway stations in Japan

## People with the surname

* Hiroshi Toyooka (豊岡 弘, born 1969), Japanese cyclist
# Gamocarpha

Gamocarpha is a genus of flowering plants in the family Calyceraceae, native to the Andes of Chile and Argentina. It includes the former genus Nastanthus.

## Species

Currently accepted species include:
* Gamocarpha alpina (Poepp. ex Less.) H.V.Hansen
* Gamocarpha australis (Decne.) S.Denham & Pozner
* Gamocarpha caespitosa (Phil.) S.Denham & Pozner
* Gamocarpha chubutensis (Speg.) S.Denham & Pozner
* Gamocarpha compacta (Phil.) S.Denham & Pozner
* Gamocarpha falklandica (D.M.Moore) S.Denham & Pozner
* Gamocarpha graminea (Phil.) S.Denham & Pozner
* Gamocarpha macrocephala S.Denham & Pozner
* Gamocarpha multicaulis (Phil.) S.Denham & Pozner
* Gamocarpha raffaellii (Speg.) S.Denham & Pozner
* Gamocarpha scapigera (J.Rémy) S.Denham & Pozner
* Gamocarpha selliana Reiche
* Gamocarpha ventosa (Meyen) S.Denham & Pozner
# Winsted Township, McLeod County, Minnesota

Winsted Township is a township in McLeod County, Minnesota, United States. The population was 936 at the 2020 census.
The township was named after Winsted, Connecticut.

## Geography

Winsted Township is in the northeast corner of McLeod County, bordered to the north by Wright County and to the east by Carver County. The city of Winsted, a separate municipality, is surrounded by the northeast part of the township.
According to the U.S. Census Bureau, Winsted Township has a total area of 34.0 square miles (88 km$^2$), of which 33.0 square miles (85 km$^2$) are land and 1.1 square miles (2.8 km$^2$), or 3.10%, are water. Winsted Lake and South Lake are in the northeast part of the township.

## Demographics

As of the census of 2000, there were 987 people, 330 households, and 287 families residing in the township. The population density was 29.5 inhabitants per square mile (11.4/km$^2$). There were 342 housing units at an average density of 10.2/sq mi (3.9/km$^2$). The racial makeup of the township was 98.68% White, 0.10% Asian, 0.81% from other races, and 0.41% from two or more races. Hispanic or Latino of any race were 1.52% of the population.
There were 330 households, out of which 38.5% had children under the age of 18 living with them, 77.0% were married couples living together, 4.8% had a female householder with no husband present, and 13.0% were non-families. 9.7% of all households were made up of individuals, and 5.8% had someone living alone who was 65 years of age or older. The average household size was 2.99 and the average family size was 3.21.
In the township the population was spread out, with 29.2% under the age of 18, 7.0% from 18 to 24, 30.3% from 25 to 44, 23.0% from 45 to 64, and 10.5% who were 65 years of age or older. The median age was 36 years. For every 100 females, there were 106.1 males. For every 100 females age 18 and over, there were 109.3 males.
The median income for a household in the township was $52,778, and the median income for a family was $56,563. Males had a median income of $32,316 versus $25,000 for females. The per capita income for the township was $19,060. About 5.9% of families and 6.7% of the population were below the poverty line, including 8.7% of those under age 18 and 5.6% of those age 65 or over.
# Josef Ackermann (disambiguation)

Josef Ackermann (born 1948) is a Swiss banker and former chief executive officer of Deutsche Bank.
Josef Ackermann may also refer to:
* Josef Ackermann (journalist) (1896–1959), German journalist
* Josef Ackermann (politician) (1905–1997), German politician and a representative of the Reichstag for the Nazi Party (NSDAP)
# Setting Sun (horse)

Setting Sun (foaled 1952) was a Tennessee Walking Horse stallion who competed in his breed's World Grand Championship three times. On his first attempt, in 1956, he placed third; he won the Reserve World Grand Championship in 1957 and the World Grand Championship in 1958. He was trained by Sam Paschal. After his wins, Setting Sun made nationwide television appearances. He died in 1976 and is buried near Newport, Tennessee.

## Life

Setting Sun was a chestnut stallion sired by the notable breeding stallion Midnight Sun, and out of the mare Alice Carver. He was foaled in 1952 and bred by W. H. Webb of Carthage, Tennessee. He was owned by the industrialist M. M. Bullard of Newport, Tennessee, and trained by Sam Paschal of Murfreesboro, Tennessee. Paschal showed Setting Sun at the Tennessee Walking Horse National Celebration for the first time in 1956. They placed third in the World Grand Championship. The following year Setting Sun was the Reserve World Grand Champion, and in 1958 he finally won the World Grand Championship. After his World Grand Championship, Setting Sun made nationwide television appearances in the United States. He had 159 wins in 160 shows, and was estimated to be one of the most widely known Tennessee Walkers of the time. Setting Sun retired from showing in the mid-1960s. His last public appearance was at a horse show in Birmingham, Alabama. Following retirement from the show ring, he was used for breeding. He died of a kidney disease in September 1976 and was buried in a formal funeral on Bullard's farm. TV personality Stan Brock read the eulogy at the ceremony.
# Tanquecitos South Acres II, Texas

Tanquecitos South Acres II is a census-designated place (CDP) in Webb County, Texas, United States. This was a new CDP formed from parts of the Laredo Ranchettes CDP prior to the 2010 census with a population of 50.
It is one of several colonias in the county.

## Geography

Tanquecitos South Acres II is located at 27°29′13″N 99°23′17″W﻿ / ﻿27.48694°N 99.38806°W﻿ / 27.48694; -99.38806 (27.486961, -99.388178). The CDP has a total area of 0.1 square miles (0.26 km$^2$), all land.

## Demographics

Tanquecitos South Acres II first appeared as a census designated place in the 2010 U.S. Census, one of nine CDPS (La Coma, Laredo Ranchettes West, Los Altos, Ranchitos East, San Carlos I, San Carlos II, Tanquecitos South Acres, Tanquecitos South Acres II, and Pueblo Nuevo) carved out from parts of Laredo Ranchettes CDP.

### 2020 census

Tanquecitos South Acres II CDP, Texas – Racial and ethnic composition Note: the US Census treats Hispanic/Latino as an ethnic category. This table excludes Latinos from the racial categories and assigns them to a separate category. Hispanics/Latinos may be of any race. :
| Race / Ethnicity (NH = Non-Hispanic) | Pop 2010 | Pop 2020 | % 2010 | % 2020 |
| White alone (NH) | 0 | 1 | 0.00% | 1.67% |
| Black or African American alone (NH) | 0 | 0 | 0.00% | 0.00% |
| Native American or Alaska Native alone (NH) | 0 | 0 | 0.00% | 0.00% |
| Asian alone (NH) | 0 | 0 | 0.00% | 0.00% |
| Pacific Islander alone (NH) | 0 | 0 | 0.00% | 0.00% |
| Some Other Race alone (NH) | 0 | 0 | 0.00% | 0.00% |
| Mixed Race or Multi-Racial (NH) | 0 | 0 | 0.00% | 0.00% |
| Hispanic or Latino (any race) | 50 | 59 | 100.00% | 98.33% |
| Total | 50 | 60 | 100.00% | 100.00% |

## Education

Residents are in the United Independent School District. Zoned schools include: Freedom Elementary School, Raul Perales Middle School, and United South High School.
The designated community college for Webb County is Laredo Community College.
# John Whitbeck

John Carroll Leon Whitbeck Jr. is an American attorney and Republican Party official from Loudoun County, Virginia. Whitbeck was the chairman of the Republican Party of Virginia from 2015 to 2018.

## Early life

Whitbeck is originally from California. He attended Occidental College where he played football as a center and earned a degree in politics. He obtained his J.D. degree from the George Mason University School of Law.

## Career

Whitbeck is the managing partner of the law firm WhitbeckBennett, a family law practice based in Leesburg, Virginia. He was an adjunct professor at George Mason Law School and also previously served as a substitute judge in District Court for five years. Whitbeck unsuccessfully ran for a seat in the Virginia House of Delegates in 2011 elections.
In 2013, he was the chairman of the Republican committee for the 10th congressional district when he was nominated by his party to run in the 2014 State Senate special elections for the 33rd district. He lost the election to Jennifer Wexton. In January 2015, he was elected chairman of the Republican Party of Virginia to succeed Pat Mullins.
Following the primary elections for the 2018 Senate election in Virginia, Whitbeck announced his resignation from the chairmanship of the Republican Party of Virginia.
In January 2019, Whitbeck announced that he would seek the office of Loudoun County Chair. Whitbeck lost the election for Loudoun Chair in November to Phyllis Randall.

## Electoral history

2011 Virginia House of Delegates, 10th District Republican Primary :
| Party | Party | Candidate | Votes | % |
| | Republican | Randy Minchew | 1,193 | 40.50 |
| | Republican | John Whitbeck | 1,106 | 37.54 |
| | Republican | Cara Michelle Townsend | 647 | 21.96 |
| Total votes | Total votes | Total votes | 2,946 | 100.00 |
2014 Virginia Senate, 33rd District Special Election :
| Party | Party | Candidate | Votes | % |
| | Democratic | Jennifer Wexton | 11,431 | 52.71 |
| | Republican | John Whitbeck | 8,133 | 37.51 |
| | Independent | Joe T. May | 2,117 | 09.76 |
| | Write-in | Write-in | 4 | 00.02 |
| Total votes | Total votes | Total votes | 21,685 | 100.00 |
2019 Loudoun County Board of Supervisors, Chair At-Large General Election :
| Party | Party | Candidate | Votes | % |
| | Democratic | Phyllis Randall (Incumbent) | 63,230 | 56.68 |
| | Republican | John Whitbeck | 43,673 | 39.14 |
| | Independent | Robert Joseph Ohneiser | 4,494 | 04.03 |
| | Write-in | Write-in | 172 | 00.15 |
| Total votes | Total votes | Total votes | 111,569 | 100.00 |
# HD 97048

HD 97048 or CU Chamaeleontis is a Herbig Ae/Be star 603 ly away in the constellation Chamaeleon. It is a variable star embedded in a dust cloud containing a stellar nursery, and is itself surrounded by a dust disk.
HD 97048 is a young star still contracting towards the main sequence. Its brightness varies between magnitudes 8.38 and 8.48 and it is classified as an Orion variable. It was given the variable star designation CU Chamaeleontis in 1981. Its spectrum is also variable. The spectral class is usually given as A0 or B9, sometimes with a giant luminosity class, sometimes main sequence. The spectrum shows strong variable emission lines indicative of a shell surrounding the star.
HD 97048 is a member of the Chamaeleon T1 stellar association and is still embedded within the dark molecular cloud that it is forming from. It illuminates a small reflection nebula against the dark cloud.

## Planetary system

This star has a substantial dust disk having a central cavity with a 40−46 AU radius The disk has a carbon monoxide gas velocity kink and intensity gap at 130 AUs, which is suspected to be caused by a superjovian planet. In 2019, HCO$^+$ ion and Hydrogen cyanide emission was detected from the disk, suggesting a large amount of gas is orbiting beyond 200 AU radius.
In the system a kink in the velocity of carbon monoxide gas (CO 3–2) as well as a gap in the dust emission of the disk are seen as evidence for a jovian protoplanet. The protoplanet is located at 130 au from the star and has a mass of about 2.5 Jupiter masses. It is one of the lowest mass protoplanets discovered as of 2023.
The HD 97048 planetary system :
| Companion (in order from star) | Mass | Semimajor axis (AU) | Orbital period ([]s) | Eccentricity | Inclination | Radius |
| protoplanetary disk | 40–850 AU | 40–850 AU | 40–850 AU | 40–850 AU | 40° | — |
| b | 2.5±0.5 M$_J$ | 130 | — | — | 40° | — |
# Hildisvíni

Hildisvíni (Old Norse:, “battle swine”) is Freyja's boar In Norse mythology.
The story of Hildisvíni appears in Hyndluljóð, an Old Norse poem found in Flateyjarbok but often considered a part of the Poetic Edda. In the poem, Freyja is searching for the ancestry of her protégé, Óttar. Freyja rides on her boar Hildisvíni, who is in fact Óttar in disguise. They meet Hyndla who is a seeress. Freyja succeeds in forcing Hyndla to tell Óttar about his ancestors.
Snorri Sturluson also records that among boar-names for helmets was Hildisvín, the helmet of Áli. This helmet was among the things that were taken by the Swedish king Adils after his victory at the Battle on the Ice of Lake Vänern.
# Propaganda in the United Kingdom

Propaganda in the United Kingdom can refer to:
* British propaganda during World War I
* British propaganda during World War II
** Nazi propaganda and the United Kingdom
# Homecoming (Bill Evans album)

Homecoming is a live album by jazz pianist Bill Evans with Marc Johnson and Joe LaBarbera recorded at Southeastern Louisiana University in 1979 but not released until 1999 on the Milestone label.

## Reception

The Allmusic review by Rick Anderson awarded the album 4 stars and states "This disc is a valuable historical document, but it's also a genuine pleasure to listen to". The All About Jazz review by Douglas Payne stated "Homecoming is a rich, instructive insight into the genius of this already over-recorded piano wonder — for hardcore devotees and the mildly interested alike... Homecoming is worth coming home to".
Professional ratings :
| Review scores ||
| Source | Rating |
| Allmusic | |
| The Penguin Guide to Jazz Recordings | |

## Track listing

    All compositions by Bill Evans except as indicated
* "Re: Person I Knew" - 4:03
* "Midnight Mood" (Ben Raleigh, Joe Zawinul) - 6:22
* "Laurie" - 7:46
* "Theme from M*A*S*H (Suicide Is Painless)" (Mike Altman, Johnny Mandel) - 4:11
* "Turn Out the Stars" - 4:52
* "Very Early" - 5:11
* "But Beautiful" (Johnny Burke, Jimmy Van Heusen) - 4:12
* "I Loves You, Porgy" (George Gershwin, Ira Gershwin, DuBose Heyward) - 5:40
* "Up with the Lark" (Jerome Kern, Leo Robin) - 5:38
* "Minha (All Mine)" (Francis Hime) - 3:41
* "I Do It for Your Love" (Paul Simon) - 5:52
* "Some Day My Prince Will Come" (Frank Churchill, Larry Morey) - 6:25
* Interview with Bill Evans by Rod Starns - 6:00
   * Recorded at the Southeastern Louisiana University in Hammond, Louisiana on November 6, 1979.

## Personnel

* Bill Evans - piano
* Marc Johnson - bass
* Joe LaBarbera - drums
# Wadi al-Qarn

Wadi al-Qarn could refer to the following:
* Wadi al-Qarn (Nahal Kziv) — A perennial stream in northern Israel
* Wadi al-Qarn – Burqush Important Bird Area, a bird area in southwestern Syria
# Francisco da Silva

Francisco da Silva is the name of:
* Francisco da Silva (politician) (1957–2010), president of the National Assembly of São Tomé and Príncipe
* Francisco da Silva (fencer) (born 1945), Portuguese Olympic fencer
* Francisco da Silva (painter) (1910–1985) Brazilian painter
# Bedwellty Greyhound Track

Bedwellty Greyhound Track was a greyhound racing track in the hamlet of Bedwellty, near Aberbargoed, South Wales. It was sometimes called Bedwellty Park.
The track was situated north of the Bedwellty Road and east of Aberbargoed. The track was larger than the hamlet of Bedwellty itself and sat at a high altitude in Gwent not far from the Brecon Beacons. The track was behind the Church Inn.
Racing began in 1929 on Monday and Friday evenings, the track was independent (unaffiliated to a governing body) and race distances were over 300, 510 and 700 yards with the circuit being described as suiting early paced well balanced dogs. There was car parking for 150 vehicles and on course bookmakers.
In 1995, Noel Watkins bought the track but leased it to bookmakers Alan Davies and Trevor Jones in 1998.
In 2007, after 78 years of racing the stadium closed.