OpenLLM-France/wikimedia huggingface dataset:
# Symmetric function

In mathematics, a function of $n$ variables is symmetric if its value is the same no matter the order of its arguments. For example, a function $f\left(x_{1},x_{2}\right)$ of two arguments is a symmetric function if and only if $f\left(x_{1},x_{2}\right)=f\left(x_{2},x_{1}\right)$ for all $x_{1}$ and $x_{2}$ such that $\left(x_{1},x_{2}\right)$ and $\left(x_{2},x_{1}\right)$ are in the domain of $f.$ The most commonly encountered symmetric functions are polynomial functions, which are given by the symmetric polynomials.
A related notion is alternating polynomials, which change sign under an interchange of variables. Aside from polynomial functions, tensors that act as functions of several vectors can be symmetric, and in fact the space of symmetric $k$-tensors on a vector space $V$ is isomorphic to the space of homogeneous polynomials of degree $k$ on $V.$ Symmetric functions should not be confused with even and odd functions, which have a different sort of symmetry.

## Symmetrization

Given any function $f$ in $n$ variables with values in an abelian group, a symmetric function can be constructed by summing values of $f$ over all permutations of the arguments. Similarly, an anti-symmetric function can be constructed by summing over even permutations and subtracting the sum over odd permutations. These operations are of course not invertible, and could well result in a function that is identically zero for nontrivial functions $f.$ The only general case where $f$ can be recovered if both its symmetrization and antisymmetrization are known is when $n=2$ and the abelian group admits a division by 2 (inverse of doubling); then $f$ is equal to half the sum of its symmetrization and its antisymmetrization.

## Examples

* Consider the real function $f(x_{1},x_{2},x_{3})=(x-x_{1})(x-x_{2})(x-x_{3}).$ By definition, a symmetric function with $n$ variables has the property that $f(x_{1},x_{2},\ldots ,x_{n})=f(x_{2},x_{1},\ldots ,x_{n})=f(x_{3},x_{1},\ldots ,x_{n},x_{n-1}),\quad {\text{ etc.}}$ In general, the function remains the same for every permutation of its variables. This means that, in this case, $(x-x_{1})(x-x_{2})(x-x_{3})=(x-x_{2})(x-x_{1})(x-x_{3})=(x-x_{3})(x-x_{1})(x-x_{2})$ and so on, for all permutations of $x_{1},x_{2},x_{3}.$
* Consider the function $f(x,y)=x^{2}+y^{2}-r^{2}.$ If $x$ and $y$ are interchanged the function becomes $f(y,x)=y^{2}+x^{2}-r^{2},$ which yields exactly the same results as the original $f(x,y).$
* Consider now the function $f(x,y)=ax^{2}+by^{2}-r^{2}.$ If $x$ and $y$ are interchanged, the function becomes $f(y,x)=ay^{2}+bx^{2}-r^{2}.$ This function is not the same as the original if $a\neq b,$ which makes it non-symmetric.

## Applications
### U-statistics

In statistics, an $n$-sample statistic (a function in $n$ variables) that is obtained by bootstrapping symmetrization of a $k$-sample statistic, yielding a symmetric function in $n$ variables, is called a U-statistic. Examples include the sample mean and sample variance.
# Château du Sart

The Château du Sart is a château in the Sart-Babylone quarter of Villeneuve d'Ascq, the Nord department of France.

## History

The château was built in 1740. It was rarely occupied by its owners, the Seigneurs of Fourmestraux.
The park was transformed into an 18-hole golf course, and nowadays, the château has become the course club house.

## Collections

The château had the rich Van Der Cruisse de Waziers library, which was destroyed by the Germans during the First World War.
In the farmyard of the old farm, near the château, is a pigeon house which was designed following the model of Diderot et d’Alembert in their Encyclopédie.

## Gallery

* Northern side
* Northern and eastern side
# Ivar Nørgaard

Ivar Nørgaard (26 July 1922 – 3 November 2011), also spelled Ivar Noergaard, was a Danish politician, former economics minister and member of the Social Democrats. Nørgaard led the negotiations for Denmark's ascension into the European Union in 1973.
Nørgaard served as the head of several ministries within Social Democratic governments during the 1960s and 1970s. He supported Denmark's membership into the European Economic Community, the predecessor of the European Union, and headed his country's successful negotiations. Nørgaard was an opponent of the euro and the eurozone.
Nørgaard died of a cerebral blood clot on 3 November 2011, at the age of 89. He was survived by his wife, children and grandchildren.
# Millard (surname)

Millard is a surname, and may refer to:
* Alan Millard (born 1937), British scholar of ancient Semitic languages
* Benjamin Franklin Millard (1850–1926), American politician in Wisconsin
* Bert Millard (1898–after 1925), British professional footballer
* Bryan Millard (born 1960), American football player
* Burton Millard (1828–1862), American politician in Wisconsin
* Charles E. F. Millard (born 1957), American politician from New York
* Charles Millard (1896–1978), Canadian trade union activist and politician
* Christopher Sclater Millard (1872-1927), Bibliographer
* Daryl Millard (born 1985), British rugby league player
* Don Millard (born 1955), American electrical engineer
* Ezra Millard (1833–1886), mayor of Omaha, Nebraska
* Guy Millard (1917–2013), British diplomat
* Helene Millard (1905–1974) American actress
* Henry Millard (c.1796–1844), Texan revolutionary
* Joseph Millard (1836–1922), U.S. Senator from Nebraska
* Keith Millard (born 1962), American football player
* Killick Millard (1870–1952), British euthanasia campaigner
* Len Millard (1919–1997), British football player
* Mike Millard (died 1990), 1970s and '80s U.S. bootleg recorder
* Muriel Millard (1922–2014), Canadian actress, dancer, painter, singer-songwriter
* Oscar Millard (1908–1990), British screenwriter
* Naomi A. H. Millard (1914-1997), South African biologist
* Pierre de Milard (1736–1778), also spelled Millard, French Navy officer, Burmese officer and governor
* Ralph Millard (1919–2011), American plastic surgeon
* Ross Millard (born 1982), British guitarist
* Russ Millard (born 1973), American basketball player
* Shane Millard (born 1975), British rugby league player
* Spencer G. Millard (1856–1895), American politician from California
* Stephen C. Millard (1841–1914), American politician from New York
* Thomas Franklin Fairfax Millard (1868–1942), American war correspondent
* Walter Samuel Millard (1864–1952), British entrepreneur and naturalist
* William Millard (disambiguation), several people
# Cesare Viazzi

Cesare Viazzi (1857 – 1943) was an Italian painter.

## Biography

Born in Alessandria, he was initially a student of the sculptor and architect Angelo Cavanna in Novi Ligure. He then became a pupil of Andrea Gastaldi, first in Rome then at the Accademia Albertina in Turin. In 1893, he was named professor of the Accademia Ligustica di Belle Arti in Genoa. Among his pupils was Pietro Gaudenzi.
In Genoa, he was known for his portraits, but also completed large fresco or decorative cycles, including for the Società promotrice di Belle Arti, Palazzo Raggio in via Balbi, Castello Raggio a Cornigliano, Villa Weil, and the Villa Bisio in Albaro. He painted sacred subjects for chapels in the Monumental Cemetery of Staglieno.
At the 1883 Exposition of Rome, he exhibited a canvas of Il Beccaio. In the 1884 Turin, exhibition, he displayed: La vanità nei campi; Fiori di biancospino; La Scrivia; Il giorno di San Bovo; Ore calde. In 1887, in Venice: Un pescatore sul lago; Idillio; Mar. In 1888, in Bologna: Autunno mesto; Fede; Fiori. Among other works Il Canto del mattino and Ritorno dai campi
The contemporary critic Ercole Arturo Marescotti described his paintings at the Promotrice di Genoa:
   The paintings of Viazzi portray the truth of the environment: what first impresses the observer: is the truth that most stubbornly look for in the abstruse, in the baroque, and almost despise them for failing to remain modest and simple: the truth of which you can overcome without studying the great and true mastery that is nature: ... Passionate lover of the truth, the atmosphere, but to arrive (there you have) sacrifice (the reality) for the effect, I would say almost to destroy the color found there, Viazzi well shows that what worries him most is not only vulgar effect ... and much less complacency before the intonation: his only care, his only study, is the tone, the totality of the painting. .. He cares very little to talk to the eye, but seeks, puts all his concerns, because his painting speaks to the heart.
He died in Predosa in 1943.
# Casa de São Bernardo

Casa de São Bernardo is a building in Cascais in the Lisbon District of Portugal that was owned by Bernardo Pinheiro Correia de Melo, First Count of Arnoso, who was private secretary to King Carlos. It is considered to be an example of the summer architecture found in Cascais and neighbouring Estoril from the 1870s onwards. The building was designed in 1890 but not completed until 1902.
The Casa de São Bernardo was called the "Minho house" as its design is reminiscent of the buildings found in Minho Province in the north of Portugal, where Correia de Melo was born, and was the first of the summer architecture buildings to be built in what was regarded as "Portuguese style". It was sometimes used for dinners of the Vencidos da Vida (Life's Vanquished), a group of intellectuals that included the novelists José Maria de Eça de Queirós and Ramalho Ortigão, as well as Correia de Melo. Eça de Queirós would often stay at the house. Although not considered a member, King Carlos would sometimes join them for dinner. The King, who was an enthusiastic watercolour artist, would occasionally paint at the house.
Casa de São Bernardo is now owned by the Cascais Marina.
# Hubert Pál Álgyay

Hubert Pál Álgyay (Szeged, 6 June 1894 – Budapest, 27 August 1945) was a Hungarian engineer and lecturer.
Álgyay finished his studies at the Budapest Technical University and became adjunct lecturer in bridge building in 1924. Also in that year he completed a doctoral thesis. In 1926 he began work for the Ministry of Transport and from 1934 was director of the bridge building department there. Later he became state secretary of transport. He designed the Petőfi Bridge in Budapest (1933–37) and also directed the widening of Margaret Bridge. He was president of the Capitol building council between 1935 and 1937. He taught at the Technical University from 1937, becoming head lecturer in bridge building. His technical writing was also significant.
# Ivar P. Enge

Ivar Paul Enge (12 September 1922 – 18 July 2013) was a Norwegian radiologist.
He hailed from Vågå and took the cand.med. degree in Copenhagen in 1953 and the dr.med. degree in 1977. He was stationed at hospitals like Sauda Hospital, Ullevål Hospital, the University of Virginia Hospital and Rikshospitalet. From 1978 to 1991 he was director of the x-ray department at Aker Hospital and professor of radiology at the University of Oslo Faculty of Medicine.
He was one of Norway's foremost radiologists, specializing in interventional radiology. He was decorated as a Knight, First Class of the Order of St. Olav in 1991. He resided in Lillehammer. He died in July 2013.
# Iowa District

The Iowa District was a region of north-central North America west of the Mississippi River claimed by the United States. From June 28, 1834, to July 4, 1838, it was part of the Michigan Territory and, later, the Wisconsin Territory. It included not only the area which became the state of Iowa, but parts of what would become Minnesota, North Dakota and South Dakota. In September 1834, at an extra session of the Sixth Legislative Assembly of Michigan, the Iowa District was divided into two counties. A border was drawn due west from the lower end of Rock Island in the Mississippi River. The territory north of this line (which started just south of the present-day Davenport) was named Dubuque County, and all area to the south of the line was named Des Moines County.
The Wisconsin Territory was trimmed back on July 4, 1838, and the entirety of the Iowa District became the new Iowa Territory.
# Kolad

Kolad is a village in Raigad district, Maharashtra State, India. It is 117 km from Mumbai on the National Highway no 66(Mumbai-Goa) its also connected to Pune via Kolad Pune- Kolad state highway. It lies on the banks of River Kundalika. The village post office Postal Index Number (PIN code) is 402304 & 402109.

## Weather

Kolad has a varied climate; spring (March to May) is hot and sultry, while the monsoon season (June to September) is accompanied by heavy rainfalls. Winters are during November and February and are characterized by a medium level of humidity and cool weather.

## Demographics

At the 2001 India census, Kolad had a population of 12,116.

## Geography

Nearby villages include dagadwadi, Gove, Pugaon, Pui, Pahur, Suttarwadi, Kudali, Ambewadi, Kamat, Jamgaon, Durtoli, Bhira, Ville, Tise, Bhuvan, Talavali and Yeral.
Nearby towns are Roha, Indapur, Mangaon and Nagothane.

## Transport

Kolad is located on NH 17, popularly known as the Mumbai - Goa highway. Kolad can also be accessed from the Mumbai Pune Expressway, via the Khopoli exit, and State Highway 60. The Maharashtra State Road Transport Corporation (MSRTC) operates regular bus services to Roha. Mangaon. Auto rickshaws also ply the route.

### Kolad Railway Station

Kolad railway station is the first station on the Konkan Railway line. Express and mail trains connect Kolad to Mumbai in approximately three hours. Kolad is the starting point for the roll-on/roll-off (RORO) service of the Konkan Railway, a road-rail synergy system, where loaded trucks are directly carried by railway wagons and delivered to their destination by rail. This service was introduced in January 1999.

## Infrastructure

Most of the infrastructure in Kolad is maintained by Gram Panchayat, which includes paving the roads, provision of water supply and other essential services like garbage disposal and beautification.
Electricity is provided by the state-run Maharashtra State Electricity Board (MSEB). Telecom services are managed by the state-run BSNL telecom and other private companies. Broadband is provided by BSNL. BSNL & TATA are the only service providers with a complete network.

## River rafting at Kolad

White water river rafting is a popular adventure water sport for people from Mumbai and Pune. The Kundalika River in Kolad is the best option for white water rafting in Maharashtra. The huge amount of water released from a local dam each morning creates good opportunities for rafting. The Maharashtra government promotes river rafting through its official tourism website.
# Casey Jones (disambiguation)

Casey Jones (1863–1900) was an American railroad engineer.
Casey Jones may also refer to:

## People

* Casey Jones (ice hockey) (born 1968), Canadian ice hockey coach
* Casey Jones (politician) (1915–2002), former member of the Ohio House of Representatives; also a professional basketball player in the NBL during the 1940s
* Casey Jones (catcher) (1918–1998), American Negro league baseball player
* Casey Jones (outfielder), American Negro league baseball player
* Casey Jones (musician) (1939–2017), solo blues artist and former drummer for guitarist Albert Collins
* Casey Veggies (born 1993), hip hop artist
* Casey Jones, former member of Blessed by a Broken Heart
* Casey Jones (1936–2022), stage name of British singer Brian Cassar
* Casey Jones, alternate identity for radio personality Al Anthony
* Casey Jones, television persona of Lunch With Casey show host Roger Awsumb
* Casey Jones, author of the American comic book All Fall Down

## Music

* "The Ballad of Casey Jones", a c. 1909 folk song about the railroad engineer
* "Casey Jones" (Grateful Dead song), a 1970 song by the Grateful Dead, also about the railroad engineer
* Casey Jones (band), a straight edge hardcore punk band from Florida

## Fiction

* Casey Jones (play), a 1938 play by Robert Ardrey
* Casey Jones (TV series), a 1957 television show starring Alan Hale Jr
* Casey Jones (Teenage Mutant Ninja Turtles), a character from the Teenage Mutant Ninja Turtles series
** Casey Jones (film), a 2011 fan film based on the Teenage Mutant Ninja Turtles character
# Breakish

Breakish may refer to:
* Lower Breakish, Isle of Skye, Scotland
* Upper Breakish, Isle of Skye, Scotland
# Miyamae

Miyamae (written: 宮前) is a Japanese surname. Notable people with the surname include:
* Ami Miyamae (宮前 杏実, born 1997), member of the Japanese idol girl group SKE48
* Maki Miyamae (宮前 真樹, born 1973), Japanese pop singer
* Shinzan Miyamae Roshi (宮前 心山, born 1935), Japanese Zen Buddhist rōshi
# Iowa District West of the Lutheran Church – Missouri Synod

The Iowa District West is one of the 35 districts of the Lutheran Church – Missouri Synod (LCMS), and covers the western half of the state of Iowa including the state capital, Des Moines; the rest of the state forms the Iowa District East. The Iowa District West includes approximately 175 congregations and missions, subdivided into 19 circuits, as well as 45 preschools and 8 elementary schools. Baptized membership in district congregations is approximately 59,000.
The Iowa District West was formed in 1936 when the Iowa District (created in 1879) was divided in half. District offices are located in Fort Dodge, Iowa. Delegates from each congregation meet in convention every three years to elect the district president, vice presidents, circuit counselors, a board of directors, and other officers.

## Presidents

* Rev. Adolph Schwidder, 1936–1945
* Rev. Herbert W. Berner, 1945–1946
* Rev. John Theodore Martin Hoemann, 1946–1948
* Rev. Gustav W. Lobeck, 1948–1966
* Rev. A. Ellis Nieting, 1966–1985
* Rev. Richard G. Kapfer, 1985–2000
* Rev. Paul G. Sieveking, 2000–2015
* Rev. Dr. Steven Turner, 2015–Present
# Kolach

Kolach is the Slavonic term for a number of traditional baked products, such as:
* Kolach (bread), a circular bread, most often made as a sweet dish
* Slavski kolač, a Serbian variant of the kolach, made for the celebration of Slava
* Kolach (cake), a Czech and Slovak sweet pastry different from the above
* Klobasnek, a savory bread known as kolache in Texas
# Chapel Allerton Hospital

Chapel Allerton Hospital is located in the area of Chapel Allerton, Leeds, West Yorkshire, England and is operated by the Leeds Teaching Hospitals NHS Trust. The main entrance is on Chapeltown Road, with vehicle exits onto Harehills Lane and Newton Road.

## History

The hospital was founded in 1927, to care for injured soldiers from the First World War under the then Ministry of Pensions, replacing a military hospital at Beckett Park. It was opened on 16 May 1927 by Princess Mary. She had been welcomed by the Leeds Lord Mayor Hugh Lupton, whose niece, Anne Lupton, had been appointed a MBE in 1920 for her work on the Leeds War Pensions Committee, advising injured soldiers. The hospital was built in the grounds of Gledhow Grove mansion, and the mansion itself was also used. Gledhow Grove had been the home of both Albert Kitson, Lord Airedale and his first cousin - Frederick James Kitson, Leeds Lord Mayor in 1908 and 1910. Lord and Lady Airedale had owned the nearby Gledhow Hall Estate.
In 1953 the hospital was transferred to the Ministry of Health and developed as a general hospital. In 1975 the Newton Green Wing was opened in purpose-built buildings on the opposite, south, side of Harehills Lane. It was named after the Newton Green Hall estate, acquired in 1936, upon which the new hospital buildings were built. New accommodation for the whole hospital was added on this site 1992-1994, and opened by the Duchess of Kent. The old hospital buildings were demolished, the Grade II listed mansion has been left derelict with new housing built in the grounds.

## Chapel

The chapel is located on the third floor of the north wing.

## Broadcasting

The hospital operates a 24/7 radio station, Radio Allerton, which has broadcast to both staff and patients since 1978.
* Map Sign for Chapel Allerton Hospital
* Entrance
* Wards
# Lisa Moore

Lisa Moore may refer to:
* Lisa Moore (musician) (born 1960), Australian classical musician
* Lisa Moore (writer) (born 1964), Canadian writer
* Lisa L. Moore, American academic
* Lisa Bronwyn Moore, Canadian actress
* Lisa Jean Moore (born 1967), professor of sociology and gender studies
* Lisa Schulte Moore, American landscape ecologist
* Lisa Moore (figure skater), American pairs figure skater, see 2006 United States Figure Skating Championships
* Lisa Moore, a character in the American comic strip Funky Winkerbean
# C14H17N3O

The molecular formula C$_{14}$H$_{17}$N$_3$O (molar mass: 243.30 g/mol, exact mass: 243.1372 u) may refer to:
* Frovatriptan
* YM-348
# Choondiko

Choondiko City is the administrative headquarters of Nara Tehsil within the Khairpur District of Sindh province, Pakistan. Located approximately 56 kilometers from the city of Khairpur, Choondiko serves as a vital center for the surrounding rural communities.

## History and Significance

While the exact date of Choondiko's establishment remains unclear, historical records suggest its existence predates the British Raj in the region. The city likely developed as a trading post and agricultural hub due to its strategic location along the Nara Canal. Following the creation of Nara Tehsil in the 20th century, Choondiko was designated as its administrative headquarters, solidifying its importance in the regional governance structure.
# City Fun

City Fun was a magazine/fanzine documenting the music scene in Manchester, England, between 1977 and 1984 and sold up to 2000 copies per issue via gigs, music stores, and selected news agents across Manchester, Liverpool, Sheffield and Leeds. The magazine was started by Andy Waide (Zero), Neil Hargreaves, Martin Heywood (X) and 'JC'. On the day it was decided to write & publish the first issue Andy Waide adopted the name Andy Zero and Martin Heywood became Martin X. The first edition was dedicated to The Distractions, and City Fun went on to document and inform the music scene in Manchester in the late 1970s and early 1980s. No one else at the time was writing about what was happening as it happened, and when others did write about Manchester music and culture it was from the outside not the inside. City Fun invited its readers to contribute articles and reviews and to tell people what was going on, or what they felt about life at the time.
City Fun went through various stages of evolution, Series 1 was anarchic and inclusive trying to include the submissions from all contributors. Series 2 was more structured and selective, Neil, Martin and JC left the 'day to day' operations and a new editorial team of Andy Zero, Cath Carroll, Liz Naylor and Bob Dickenson became the core editors. Andy Zero left in 1982 and publication/editorship was continued by Liz, Cath and latterly (vol 3 which lasted 4 issues), Nigel Chatfield. During the beginning of Volume 2, City Fun operated from an office in Lower Broughton in the building where The Fall had rehearsal rooms. Later this was produced from Liz Naylor and Cath Carroll's flat in Hulme.
Many people contributed articles including Ray Lowry (every edition of series 1 and 2), Tony Wilson, Mark E Smith, Claude Bessey, Steve Morrissey and many others.
City Fun periodically promoted benefit concerts to top up the funds needed for publication, The Distractions, Joy Division, and The Fall all performed. "Stuff The Superstars" all day festival (which include The Distractions, The Fall, Joy Division, The Hamsters, the Frantic Elevators among the dozen bands) attracted about 2000 people and a later benefit "Dr Fun's Carnival Chance" at Manchester Polytechnic (also with The Fall) featured John Peel as DJ.
The film No City Fun, by Charles Salem, was based on a City Fun article by Liz Naylor. This was used as a basis for the film Factory Flick with music by Joy Division. This super 8 film was referenced in the Joy Division film of 2010.
An online exhibition of scanned articles from City Fun was curated by Abigail Ward, Dave Haslam and David Wilkinson and appears on the Manchester District Music Archive website. The permanent exhibition includes an introduction from Haslam.