OpenLLM-France/wikimedia huggingface dataset:
# Carathéodory function

In mathematical analysis, a Carathéodory function (or Carathéodory integrand) is a multivariable function that allows us to solve the following problem effectively: A composition of two Lebesgue-measurable functions does not have to be Lebesgue-measurable as well. Nevertheless, a composition of a measurable function with a continuous function is indeed Lebesgue-measurable, but in many situations, continuity is a too restrictive assumption. Carathéodory functions are more general than continuous functions, but still allow a composition with Lebesgue-measurable function to be measurable. Carathéodory functions play a significant role in calculus of variation, and it is named after the Greek mathematician Constantin Carathéodory.

## Definition

$W:\Omega \times \mathbb {R} ^{N}\rightarrow \mathbb {R} \cup \left\{+\infty \right\}$, for $\Omega \subseteq \mathbb {R} ^{d}$ endowed with the Lebesgue measure, is a Carathéodory function if:
1. The mapping $x\mapsto W\left(x,\xi \right)$ is Lebesgue-measurable for every $\xi \in \mathbb {R} ^{N}$.
2. the mapping $\xi \mapsto W\left(x,\xi \right)$ is continuous for almost every $x\in \Omega$.
The main merit of Carathéodory function is the following: If $W:\Omega \times \mathbb {R} ^{N}\rightarrow \mathbb {R}$ is a Carathéodory function and $u:\Omega \rightarrow \mathbb {R} ^{N}$ is Lebesgue-measurable, then the composition $x\mapsto W\left(x,u\left(x\right)\right)$ is Lebesgue-measurable.

## Example

Many problems in the calculus of variation are formulated in the following way: find the minimizer of the functional ${\mathcal {F}}:W^{1,p}\left(\Omega ;\mathbb {R} ^{m}\right)\rightarrow \mathbb {R} \cup \left\{+\infty \right\}$ where $W^{1,p}\left(\Omega ;\mathbb {R} ^{m}\right)$ is the Sobolev space, the space consisting of all function $u:\Omega \rightarrow \mathbb {R} ^{m}$ that are weakly differentiable and that the function itself and all its first order derivative are in $L^{p}\left(\Omega ;\mathbb {R} ^{m}\right)$; and where ${\mathcal {F}}\left[u\right]=\int _{\Omega }W\left(x,u\left(x\right),\nabla u\left(x\right)\right)dx$ for some $W:\Omega \times \mathbb {R} ^{m}\times \mathbb {R} ^{d\times m}\rightarrow \mathbb {R}$, a Carathéodory function. The fact that $W$ is a Carathéodory function ensures us that ${\mathcal {F}}\left[u\right]=\int _{\Omega }W\left(x,u\left(x\right),\nabla u\left(x\right)\right)dx$ is well-defined.

## p-growth

If $W:\Omega \times \mathbb {R} ^{m}\times \mathbb {R} ^{d\times m}\rightarrow \mathbb {R}$ is Carathéodory and satisfies $\left|W\left(x,v,A\right)\right|\leq C\left(1+\left|v\right|^{p}+\left|A\right|^{p}\right)$ for some $C>0$ (this condition is called "p-growth"), then ${\mathcal {F}}:W^{1,p}\left(\Omega ;\mathbb {R} ^{m}\right)\rightarrow \mathbb {R}$ where ${\mathcal {F}}\left[u\right]=\int _{\Omega }W\left(x,u\left(x\right),\nabla u\left(x\right)\right)dx$ is finite, and continuous in the strong topology (i.e. in the norm) of $W^{1,p}\left(\Omega ;\mathbb {R} ^{m}\right)$.
# Babushka (game show)

Babushka is a British game show based on the babushka doll (also known as a matryoshka doll). It aired from 1 to 26 May 2017 on ITV daily at 5 pm as a temporary Spring replacement for The Chase. It was presented by Rylan Clark. On 29 November 2017, ITV announced the show had been cancelled after one series.

## Format

There are 10 dolls: Angelina, Anastasia, Katya, Natalya, Nushka, Olya, Sonya, Svetlana, Tatiana and Viktoriya. The team of two must choose eight out of the ten dolls to open in turn. Two are completely empty, two contain £500, two contain £1,000, two more go to £2,000, one goes all the way to £5,000 and the top babushka contains £10,000. Before they may open each doll they are presented with a true or false question. Should they get this correct, they have the chance to open the doll in play, gambling whether to keep opening the successive smaller dolls inside—for example the £10,000 doll would contain smaller dolls worth £500, £1,000, £2,000, £5,000 and £10,000. Other dolls won't contain all of these. If they push their luck too far and reveal nothing inside the current doll they lose any money banked. They can, at any time, stop opening the doll, bank what is currently showing and proceed to the next question. If they answer their question incorrectly, the players will lose all their banked money.
To help, contestants have two lifelines and a third, conditional lifeline: Switch, Peek, and X-ray, respectively. Switch allows the contestants to swap their question and answer a different one. Peek allows them to look at one hidden level of a doll. The X-ray lifeline allows the team to view everything inside one doll, however this is only attained by having banked at least £5,000 by the end of their fourth doll. Lifelines can be used at any point, however only the X-ray can be used on the final doll. If any money is won at the end of the game, the team is offered the choice of taking their money or gambling it all for a chance to double their winnings by selecting the matryoshka doll containing a gold centre. There are two dolls on the table at this stage—one black and one white. The players go home empty-handed if they pick the empty doll, which is revealed on a screen before it is actually opened. The maximum prize money available is £44,000, obtained by fully opening all 8 dolls with money and the final "double" doll.
After a single game has finished, the dolls are randomised for the next two contestants to play in the next game.

## Reception

The show was received with a negative reception. Readers of UKGameshows voted it the worst new show in their Poll of 2017.
# Campodea monticola

Campodea monticola is a species of two-pronged bristletail in the family Campodeidae.

## Subspecies

These four subspecies belong to the species Campodea monticola:
* Campodea monticola helenae Bareth and Conde, 1958$^{icg}$
* Campodea monticola monticola Conde and Thomas, 1957$^{icg}$
* Campodea monticola obsoleta Conde and Thomas, 1957$^{icg}$
* Campodea monticola pilosa Conde and Thomas, 1957$^{icg}$
Data sources: i = ITIS, c = Catalogue of Life, g = GBIF, b = Bugguide.net
# Bitenas

Bitenas was a settlement and station (mutatio) of ancient Thrace, inhabited during Byzantine times.
Its site is located near İnecik in European Turkey.
# Catherine Meadows

Catherine Ann Meadows is an American cryptographer known for her development of tools for the formal verification and automated discovery of flaws in cryptographic protocols. She is a senior researcher in the Center for High Assurance Systems at the Naval Research Laboratory and the head of the laboratory's Formal Methods Section.

## Education and career

Meadows is a 1975 graduate of the University of Chicago. She completed a Ph.D. in mathematics at the University of Illinois at Urbana–Champaign in 1981. Her dissertation, Projections of Varieties, concerned algebraic geometry and was supervised by E. Graham Evans Jr. She was an assistant professor of mathematics at Texas A&M University from 1981 to 1985 before joining the Naval Research Laboratory.

## Recognition

A symposium was held in Meadows's honor in Fredericksburg, Virginia in May 2019, and a collection of essays from the symposium was published as a festschrift.
# Audrey Atterbury

Audrey Selma Atterbury (19 April 1921 – 8 April 1997) was a British puppeteer best known for her work on the 1950s pioneering BBC children's series Andy Pandy.

## Biography

Born in London in 1921 as Audrey Holman, during World War II she worked for an average adjusters firm in London. She married Rowley Atterbury in 1943, and had one child, Paul Atterbury, who went on to become an antiques expert and a regular on the BBC's Antiques Roadshow. In about 1949 Rowley Atterbury founded the Westerham Press, and Audrey worked with her husband in the printing business.
During a train journey in 1950, Audrey met Freda Lingstrom, the newly appointed head of BBC Children's Television. After striking up a conversation and establishing common interests, Lingstrom persuaded Atterbury to become a puppeteer on a new television series, to be called Andy Pandy (1950–52). It is claimed that Lingstrom based the appearance of Andy Pandy on the young Paul Atterbury. Audrey Atterbury trained under John Wright, later the founder of the Little Angel Theatre in Islington, North London.
Atterbury continued to work as a puppeteer in such series as Flower Pot Men (1952–54), and The Woodentops (1955–58). In around 1956, after separating from her husband, Audrey Atterbury went to live in Highgate in London, near to her fellow BBC puppeteer, Molly Gibson, who was a close friend. The two worked together on Rubovian Legends and other Gordon Murray puppet plays. Atterbury also worked for the Little Angel Theatre, by then one of Britain’s leading puppet theatres. Atterbury worked on the puppet series The Telegoons (1963–64), which was based on Spike Milligan's radio show The Goon Show.
In the 1960s, television puppets started to be replaced by animation, which led Atterbury to leave the BBC to take up a career in antiques, specialising in pottery and porcelain. She became a part-time antiques dealer, at the same time building up a large personal collection of ceramics. Later, Atterbury worked for a number of antique dealers and in 1987 she joined Christie's, becoming the longest serving and most respected member of the team of lady saleroom assistants. She was Secretary of the Morley College Ceramic Circle for about 18 years.

### Death

After her divorce, Atterbury did not remarry and lived in South London from about 1962 until she died in 1997 aged 75. On her death her collection of ceramics, including rare examples by Royal Doulton and Moorcroft, was sold at auction by Christie's.
# Carathéodory–Jacobi–Lie theorem

The Carathéodory–Jacobi–Lie theorem is a theorem in symplectic geometry which generalizes Darboux's theorem.

## Statement

Let M be a 2n-dimensional symplectic manifold with symplectic form ω. For p ∈ M and r ≤ n, let f$_1$, f$_2$, ..., f$_r$ be smooth functions defined on an open neighborhood V of p whose differentials are linearly independent at each point, or equivalently
    $df_{1}(p)\wedge \ldots \wedge df_{r}(p)\neq 0,$
where {f$_i$, f$_j$} = 0. (In other words, they are pairwise in involution.) Here {–,–} is the Poisson bracket. Then there are functions f$_{r+1}$, ..., f$_n$, g$_1$, g$_2$, ..., g$_n$ defined on an open neighborhood U ⊂ V of p such that (f$_i$, g$_i$) is a symplectic chart of M, i.e., ω is expressed on U as
    $\omega =\sum _{i=1}^{n}df_{i}\wedge dg_{i}.$

## Applications

As a direct application we have the following. Given a Hamiltonian system as $(M,\omega ,H)$ where M is a symplectic manifold with symplectic form $\omega$ and H is the Hamiltonian function, around every point where $dH\neq 0$ there is a symplectic chart such that one of its coordinates is H.
# Deliktaş, Bitlis

Deliktaş is a village in the Bitlis District of Bitlis Province in Turkey. Its population is 104 (2021).
# Fiji at the 2012 Summer Paralympics

Fiji participated in the 2012 Summer Paralympics in London, United Kingdom, from August 29 to September 9.
Two Fijians qualified for track and field events: Iliesa Delana and Lusiana Rogoimuri. Following Rogoimuri's withdrawal due to an accident prior to the Games, however, Delana was Fiji's sole athlete in London. He was also Fiji's flag-bearer during the Games' opening ceremony.
Delana won the gold in the men's high jump F42, giving Fiji its first ever Paralympic or Olympic medal. It was only the second ever Paralympic medal (and the first gold) won by an athlete from a Pacific Island nation, following Francis Kompaon's silver in sprinting for Papua New Guinea in 2008.

## Medallists

| Medal | Name | Sport | Event | Date |
| Gold | Iliesa Delana | Athletics | Men's High Jump F42 | 3 September |

## Athletics

Iliesa Delana, a left leg amputee, qualified to compete in the men's high jump, F42 category (for lower limb amputees). Delana was the opening ceremonies flag bearer for Fiji. He had emerged as the "world number two" in his sport and category during qualifiers, giving his country hopes for its first ever Paralympic medal. He won gold, with a jump of 1.74 metres, an Oceania regional record. Girisha Hosanagara Nagarajegowda of India and Lukasz Mamczarz of Poland also cleared 1.74 metres, but while Delana cleared both 1.71m and 1.74m on his first attempt, Nagarajegowda took two attempts on 1.71, while Mamczarz only cleared 1.74 on his third attempt.
Lusiana Rogoimuri qualified (B standard) to compete in the women's 100m and 200m, T36 category; she has cerebral palsy. On 1 August, however, less than a month before the Games, she was "rushed to hospital" in a "critical condition" after a car accident. She was discharged from the hospital on 21 August, but ordered to rest, and had to withdraw from the Games.

### Men’s field events

| Athlete | Event | Height | Rank |
| Iliesa Delana | High Jump F42 | 1.74 OC | |
# Atheist's Cornea

Professional ratings :
| Review scores ||
| Source | Rating |
| Drowned In Sound | (4/10) |
| Pitchfork Media | (6.0/10) |
| Punknews.org | |
| AllMusic | |
| Consequence of Sound | B+ |
Atheist's Cornea is the sixth album from Japanese post-hardcore band Envy. Atheist's Cornea is Envy's shortest full-length release since 1998's From Here to Eternity and continues along the artistic path set by their preceding record Recitation. It is the last Envy release to feature founding guitarist Masahiro Tobita and founding drummer Dairoku Seki.

## Personnel

* Dairoku Seki - drums
* Tetsuya Fukagawa - sequencer, vocals
* Nobukata Kawai - guitar
* Masahiro Tobita - guitar
* Manabu Nakagawa - bass guitar
# Barr Smith

Barr Smith may refer to:

## People

* Robert Barr Smith (1824–1915), Australian businessman and philanthropist
* Tom Elder Barr Smith (1863–1941), South Australian pastoralist and philanthropist
* Sir Tom Elder Barr Smith (1904–1968), South Australian pastoralist and businessman

## Other

* Barr Smith Library of the University of Adelaide
* Mount Barr Smith, Antarctica, named in 1912 by Douglas Mawson after Robert Barr Smith
# Flow to market

In United States agriculture, flow to market is a quantity provision in a fruit or vegetable marketing order that does not change the total quantity that can be marketed during a season, but rather controls the rate or time period that quantities can be shipped to markets by means of shipping holidays and prorates.
# Admiral Barry

Admiral Barry may refer to:
* Claud Barry (1891–1951), British Royal Navy admiral
* Henry Deacon Barry (1849–1908), British Royal Navy vice admiral
# Audrey Bastien

Audrey Bastien (born 10 December 1991) is a French actress. She appeared in more than twenty films since 2010.

## Selected filmography

| Year | Title | Role |
| 2010 | Lights Out | Clara |
| 2011 | 18 Years Old and Rising | Delphine |
| 2013 | Puppylove | Julia |
| 2014 | 2 Autumns, 3 Winters | Katia |
| 2015 | The Great Game | |
# Forehand & Wadsworth

Forehand & Wadsworth (later known as Forehand Arms) was an American firearms manufacturing company based in Worcester, Massachusetts. It was formed in 1871 by Sullivan Forehand and Henry C. Wadsworth after the death of their father-in-law, Ethan Allen of Ethan Allen & Company, and was acquired in 1902 by Hopkins & Allen, a firearms company based in Connecticut.

## History

In 1871, Sullivan Forehand and Henry C. Wadsworth founded Forehand & Wadsworth from the remnants of Ethan Allen & Company after the death of their father-in-law, Ethan Allen. Wadsworth sold his share of the company to Forehand in 1890 in order to retire, and the company was rebranded as Forehand Arms.
From 1871-1890, the firm was known as Forehand and Wadsworth. In 1890, Henry Wadsworth retired, and the company name was changed to Forehand Arms Company. It operated under the name Forehand Arms Company until the death of Sullivan Forehand in 1898. In 1902, the company was acquired by Hopkins and Allen.$^{:479}$
The company manufactured a variety of black powder and cartridge revolvers, including several versions of the British Bull Dog revolver. Other offerings included derringers,$^{:381}$ rifles,$^{:560}$ and shotguns.$^{:604}$
Forehand's sons ran the business for several years following the death of their father, then sold it in 1902 to Hopkins & Allen, who had been making Forehand Arms' revolvers under contract.

### Legal matters

The company was involved with a patent infringement lawsuit on behalf of one of their employees, John C. Howe, against the United States government. Howe had patented an ammunition cartridge in 1864, and the US government infringed upon this design in 1868 with the "Cup Anvil Cartridge" until the expiration of Howe's patent in 1881. Howe asked Forehand to bring a lawsuit against the government, and eight years later the company won the suit on behalf of Howe with a judgement of $66,000. The lawsuit was not paid until after Howe's death and a few weeks before the death of Forehand in 1898.

## In popular culture

A Forehand & Wadsworth British Bull Dog revolver was used in the 1993 movie, Tombstone, by Joanna Pacula while portraying Big Nose Kate.

## Gallery

* Forehand & Wadsworth British Bull Dog revolver chambered for .44 Bull Dog
* Forehand & Wadsworth advertisement from March 1872 as it appeared in the Quad-City Times of Davenport, Iowa
* Forehand Arms 5-shot revolver chambered for .32 S&W
* Forehand Arms advertisement from February 1899 as it appeared in The Belle Plaine News of Belle Plaine, Kansas
# Fikret Orman

Fikret Orman (born 4 November 1967) is a Turkish businessman and sports executive.

## Career

Orman graduated from Işık Lisesi [tr], before going on to study at Yıldız Technical University, and later at the University of Florida in the United States. He has a degree in civil engineering. Orman has been involved in the construction and tourism sectors.
On March 25, 2012, Orman became the 33rd president of Beşiktaş J.K., receiving 4,025 of the 4,545 votes cast in the extraordinary congress held after previous president Yıldırım Demirören resigned to be appointed at Turkish Football Federation. He was re-elected at the next ordinary congress in 2013, and once again in May 2016. His latest term ended in May 2019.
On 24 September 2019, Orman announced his resignation from Beşiktaş J.K. During his 7.5 years of tenure, commercial debts of club raised from TRY580 million up to TRY2.6 billion. During same period, there were total of 77 transfers made in and out, including Pepe, Mario Gómez, Demba Ba, Anderson Talisca, Jose Sosa, Gary Medel, Alvaro Negredo and Domagoj Vida.
# Bishop of Ribe

The Bishop of Ribe, in Denmark, may refer to a bishop of either:
* the former Roman Catholic diocese of Ribe, dissolved in 1536: see Ancient Diocese of Ribe; or
* the present Lutheran Diocese of Ribe
# Daniel Bernard

Daniel Bernard may refer to:
* Daniel Bernard (academic) (died 1588), English clergyman and scholar
* Daniel Bernard (businessman) (born 1946), French businessman
* Daniel Bernard (politician) (born 1959), Canadian serving as Member of the National Assembly
* Daniel Bernard (war criminal) [nl] (1914–1962), Dutch war criminal, see Operation Silbertanne
* Daniel Bernard (diplomat) (1941–2004), French Ambassador to the United Kingdom
* Daniel Bernard Roumain (born 1970),American classically trained composer, performer, violinist and band-leader
* Daniel Bernard (footballer) (1949–2020), French footballer
# Basketball at the 1997 West Asian Games

Basketball was one of the disciplines which was held at the 1997 West Asian Games in Tehran, Iran. Because of some last minute withdrawals, only two teams were left for the competition, Iran and Turkmenistan. Two other Iranian teams were added to the competition but they didn't receive medals. Only gold and silver medals were awarded. Iran beat Turkmenistan in the final to win the gold medal.

## Results

| Semifinals | Semifinals | Final | Final |
| 21 November | 21 November |
| Iran | 85 |
| Iran | 85 | 22 November | 22 November |
| Iran U18 | 60 | 22 November | 22 November |
| Iran U18 | 60 | Iran | 64 |
| 21 November | 21 November | | Iran | 64 |
| 21 November | 21 November | Turkmenistan | 56 |
| Turkmenistan | 79 | Turkmenistan | 56 |
| Fath Tehran | 63 | | |
| Fath Tehran | 63 | Third place | Third place |
| | | 22 November | 22 November |
| | | Iran U18 | 56 |
| | | Fath Tehran | 75 |

### Semifinals

* 21 November
| Iran | 85–60 | Iran U18 |
* Azadi Basketball Hall, Tehran
* 21 November
| Turkmenistan | 79–63 | Fath Tehran |
* Azadi Basketball Hall, Tehran

### Third place

* 22 November
| Iran U18 | 56–75 | Fath Tehran |
* Azadi Basketball Hall, Tehran

### Final

* 22 November
| Iran | 64–56 | Turkmenistan |
* Azadi Basketball Hall, Tehran
# Food Blue 2

Food Blue 2 may refer to:
* Indigo carmine, a food colorant also known as FD&C Blue 2
* Brilliant blue FCF, a food colorant also known as CI Food Blue 2, more commonly known as FD&C Blue 1
# Catherine Arlove

Catherine Arlove (born 5 February 1971 in Malvern, Victoria) is an Australian judoka who has also represented Australia in wrestling and competed at a national level in cycling. Arlove has won ten Gold medals at the Australian National Judo Championships.
She competed in judo at the 2000, 2004 and 2008 Olympics with her best result being a fourth placing in the 63 kg class at the Athens Games. She also competed in the third season of Gladiators, coming runner-up to Marissa Huettner.
# Attorney General Archibald

Attorney General Archibald may refer to:
* Frank C. Archibald (Vermont politician) (1857–1935), Attorney General of Vermont
* Joseph Archibald (1934–2014), Attorney General of the British Virgin Islands
* Samuel George William Archibald (1776–1846), Acting Attorney General for Nova Scotia
# Carlo Berlingeri

Carlo Berlingeri (1643–1719) was a Roman Catholic prelate who served as Archbishop of Santa Severina (1679–1719).

## Biography

Carlo Berlingeri was born in Cotrone, Italy in 1643 and ordained a priest on 9 December 1668. On 27 November 1679, he was appointed during the papacy of Pope Innocent XI as Archbishop of Santa Severina. On 30 November 1679, he was consecrated bishop by Alessandro Crescenzi, Bishop of Recanati e Loreto, with Prospero Bottini, Titular Archbishop of Myra, and Pier Antonio Capobianco, Bishop Emeritus of Lacedonia, serving as co-consecrators. He served as Archbishop of Santa Severina until his death on 5 January 1719.
# Bican Efendi Vekilharç

Bican Efendi Vekilharç is a 1921 Turkish film directed by Şadi Karagözoğlu. It stars Karagözoğlu, Bayan Şadi, Galip Arcan, Behzat Butak, Nurettin Şefkati, Şehper Karagözoğlu, and Behzat Haki. The 22 minute comedy film is one of Turkey's earliest comedy films. Bican Efendi, who served as a steward in a mansion is the centre of the story in the movie.
# World junior heavyweight championship

World junior heavyweight championship may refer to:
* World Junior Heavyweight Championship (AJPW)
* World Junior Heavyweight Championship (National Wrestling Association)
* CZW World Junior Heavyweight Championship
* Independent Junior Heavyweight Championship
* IWA World Junior Heavyweight Championship
* NWA World Junior Heavyweight Championship
* NWA World Junior Heavyweight Championship (Zero1)
* UWA World Junior Heavyweight Championship
* WWC World Junior Heavyweight Championship
# Cana Chapetón

Cana Chapetón is a town in the Monte Cristi province of the Dominican Republic.

## Sources

* World Gazeteer: Dominican Republic – World-Gazetteer.com
* This Dominican Republic location article is a stub. You can help Wikipedia by expanding it.
* v
* t
* e