OpenLLM-France/wikimedia huggingface dataset:
# Skorokhod's embedding theorem

In mathematics and probability theory, Skorokhod's embedding theorem is either or both of two theorems that allow one to regard any suitable collection of random variables as a Wiener process (Brownian motion) evaluated at a collection of stopping times. Both results are named for the Ukrainian mathematician A. V. Skorokhod.

## Skorokhod's first embedding theorem

Let X be a real-valued random variable with expected value 0 and finite variance; let W denote a canonical real-valued Wiener process. Then there is a stopping time (with respect to the natural filtration of W), τ, such that W$_τ$ has the same distribution as X,
    $\operatorname {E} [\tau ]=\operatorname {E} [X^{2}]$
and
    $\operatorname {E} [\tau ^{2}]\leq 4\operatorname {E} [X^{4}].$

## Skorokhod's second embedding theorem

Let X$_1$, X$_2$, ... be a sequence of independent and identically distributed random variables, each with expected value 0 and finite variance, and let
    $S_{n}=X_{1}+\cdots +X_{n}.$
Then there is a sequence of stopping times τ$_1$ ≤ τ$_2$ ≤ ... such that the $W_{\tau _{n}}$ have the same joint distributions as the partial sums S$_n$ and τ$_1$, τ$_2$ − τ$_1$, τ$_3$ − τ$_2$, ... are independent and identically distributed random variables satisfying
    $\operatorname {E} [\tau _{n}-\tau _{n-1}]=\operatorname {E} [X_{1}^{2}]$
and
    $\operatorname {E} [(\tau _{n}-\tau _{n-1})^{2}]\leq 4\operatorname {E} [X_{1}^{4}].$
# Skorokhod's representation theorem

In mathematics and statistics, Skorokhod's representation theorem is a result that shows that a weakly convergent sequence of probability measures whose limit measure is sufficiently well-behaved can be represented as the distribution/law of a pointwise convergent sequence of random variables defined on a common probability space. It is named for the Ukrainian mathematician A. V. Skorokhod.

## Statement

Let $(\mu _{n})_{n\in \mathbb {N} }$ be a sequence of probability measures on a metric space $S$ such that $\mu _{n}$ converges weakly to some probability measure $\mu _{\infty }$ on $S$ as $n\to \infty$. Suppose also that the support of $\mu _{\infty }$ is separable. Then there exist $S$-valued random variables $X_{n}$ defined on a common probability space $(\Omega ,{\mathcal {F}},\mathbf {P} )$ such that the law of $X_{n}$ is $\mu _{n}$ for all $n$ (including $n=\infty$) and such that $(X_{n})_{n\in \mathbb {N} }$ converges to $X_{\infty }$, $\mathbf {P}$-almost surely.
# Andrés González de Barcia

Andrés González de Barcia (died 4 November 1743) was a Spanish historian and one of the founders of the Royal Spanish Academy.

## Works

He published Ensayo cronologico para la historia general de la Florida (Madrid, 1723), and First Historians of the West Indies, issued in sections, and published collectively after his death (3 vols., folio, 1749). He also edited Herrera's Décadas (1725–30); de la Vega, La Florida (1723), Comentarios reales de los Incas (1723); and Torquemada; Gregorio García's Origen de los indios del Nuevo Mundo (1729); Antonio de Solís, Historia de la conquista de México (1732); Alonso de Ercilla, La Araucana (1733). Appearing posthumously are his Fernando de Colón, Historia del Almirante Colón (1749); Hernán Cortés, Cartas de relación (1749); Gonzalo Fernández de Oviedo y Valdés, Sumario de la natural historia de las Indias (1749); Alvar Núñez Cabeza de Vaca, Relación de la jornada que hizo a la Florida con el adelantado Pánfilo de Narvaez (1749); Francisco López de Gómara, Historia de las Indias y de la conquista de México (1749); and Francisco de Xérez, Verdadera relación de la conquista del Perú (1749).
# Tuspark

The Tuspark or Tsinghua University Science Park, Tuspark Holding Limited is a Chinese high-tech company which builds business parks. It has buildings in Zhongguancun of Beijing, in Kunshan, Suzhou, Jiangsu and in Nanjing. It has 30 branches all around China. About 400 companies and 25000 employees are working in Tuspark. The original branch is based just south-west next to the East Gate of the main campus of Tsinghua University in Wudaokou.
Tuspark, which is an abbreviation of the Tsinghua University Science Park, was set up in 1994, the first building, the TusPark Development Center was built in 1998.
The TusPark's founder and President is Mei Meng, the senior vice-president is Chen Hongbo, who is the vice-dean of the Tsinghua University. The Tuspark's CEO is Xu Jinghong.

## Companies

More than 200 companies are local ventures, like Viador, Achivo, Visionox, Hansky with a variety of science fields. For example, they have incubation Systems: Bio and Life Science, Software, IC Design, Digital TV, 3G Mobile Communication. In Beijing Microsoft, Sohu, Google Beijing, Sun Microsystems, msn.cn, Schlumberger, P&G, Toyota, NEC belong to the Tsinghua University Science Park. Google Beijing had 1200 square meters first, later the company extended it to 13888 square meters, 350 employees were working for the Google Beijing in 2007. In 2006 the total park had 690,000 square meters with 20 buildings there.

## Locations
### TusParks in China

| TusPark (Haian) Tuspark (Caofeidian) TusPark (Cixi) TusPark (Hebei) TusPark (Guanlin) TusPark (Shenyang) TusPark (Jiangxi) TusPark (Kunshan) TusPark (Nanjing) TusPark (Shaanxhi) or TusPark (Shanxi) | TusPark (Shanghai) or (Shanghai Multimedia Valley) TusPark (Shunyi) TusPark (Suizhong) TusPark (Huigu) TusPark (Hebei) TusPark (Weihai) TusPark (Zhuhai) TusPark (Yangzhou) TusPark (Yuquanhuigu) TusPark (Weihai) |

### TusParks in Hong Kong

Tuspark Hong Kong has three locations in Kwun Tong, Central and Causeway Bay.

### TusStar

TusStar Incubator is an innovation and entrepreneurship platform originated from TusPark which pioneers the incubator projects.

#### TusStar Malaysia

TusStar Malaysia is a joint venture between Tus Holdings and Brunsfield International.

### Other Science parks in China

There were 62 Science Parks based on 122 universities with 0.2 million employees in the PRC. The total investments of these science parks are 30 billion RMB.
# Olive Wyndham

Olive Frances Wyndham Meysenberg (June 16, 1886 – November 24, 1971) was an American actress on stage and in silent films.

## Early life

Meysenburg was born in Philadelphia, Pennsylvania, the daughter of E. A. von Meysenburg, a German diplomat, and Oral Josephine Wyndham. Her older sister Janet Beecher was also an actress. The sisters were related to Harriet Beecher Stowe on their mother's side.
Her father's work as a vice-consul for Germany led to her growing up in Chicago.

## Career

Wyndham's stage credits included roles in The Ruling Power (1904), She Stoops to Conquer (1905), Sir Anthony (1906), The Aero Club (1907), The Man From Home (1908), Blue Grass (1908), The Cottage in the Air (1909), The School for Scandal (1909), Sister Beatrice (1910), The Thunderbolt (1910), Nobody's Daughter (1911), The Only Son (1911), Chains (1912), Oliver Twist (1912), What Happened to Mary (1913), Countess Julia (1913), The Last Resort (1914), Children of Earth (1915), The Greatest Nation (1916), The Sweetmeat Game (1916), The Knife (1917), Nothing But Lies (1918), A Voice in the Dark (1919), The Green Goddess (1921), The Charlatan (1922), Thin Ice (1922), The Steam Roller (1924), Dinner at Eight (1932). In 1927, she was acting in Massachusetts, including in Cradle Snatchers with her sister Janet Beecher.
Wyndham appeared in two silent films, Your Girl and Mine, a 1914 suffrage film backed by the National American Woman Suffrage Association, and Fighting Bob (1915). Her striking fashion choices were a matter of press interest, as in the 1907 headline "Olive Wyndham's Hat Biggest in United States".

## Personal life

Olive Wyndham was engaged to marry lawyer Walter Kirkpatrick Brice in 1915, but the engagement was broken a few months later. She married mining engineer Andrew White Newberry in 1925. After they divorced, she married a second time to Lucien Hamilton Tyng in 1933. She was married a third time to the New Thought metaphysician and writer Harry Gaze (1878–1959) who died in a car accident en route to a speaking engagement at the Hollywood Church of Religious Science. She died in Santa Monica, California in 1971, aged 85 years.
# Slave collar

Slave collar may refer to:
* Collar used to identify and discipline slaves
* Collar (BDSM), collar used in bondage
# Two Tone Club

Two Tone Club is a French ska band from Montbéliard. They are mainly influenced by 2 Tone ska, but also reggae and rocksteady. Their track "Club 69" pays homage to the roots of the skinhead movement.

## Discography

* 2002 Number 1
* 2005 Turn Off (Big8Records/Grover)
* 2007 Now Is The Time
* 2018 Don't Look Back
# Herbert Trustram Eve

Sir Herbert Trustram Eve KBE (1865–1936) was a noted British expert in real property.

## Biography

Born on 4 June 1865, Herbert Trustram Eve was educated at Bedford School. In 1893, he married Fanny Jean Turing, who later became a Conservative Party politician.
In 1904, Eve was appointed as Agricultural Correspondent to the Board of Agriculture. During the First World War he was appointed as Chairman of the Forage Committee at the War Office, which oversaw the requisitioning of foodstuffs for the British Army. In 1920 he was elected as President of the Farmers Club (an office held by both his father and his grandfather). He was an expert in the valuation of real property, was President of the Rating Surveyors Association, and was retained as an expert witness in a number of high-profile compensation cases. He would often appear in court opposite his son, the barrister Malcolm Trustram Eve, 1st Baron Silsoe. He was a frequent contributor to The Times, and his articles included an article in April 1922 entitled "Reduce the Rates", and another in April 1926 on "the Rating Act". He was keenly interested in the preservation of London's "Green Belt".
Sir Herbert Trustram Eve was invested as a Knight Commander of the Order of the British Empire in 1918. He died in London on 11 November 1936, aged 71.
# Orchard Lake (Minnesota)

Orchard Lake is a lake in Lakeville, Dakota County, in the U.S. state of Minnesota.
Orchard Lake was named for the wild groves of crab apple and wild plum that grew near this lake.
# Optical link

An optical link is a telecommunications link that consists of a single end-to-end optical circuit. A cable of optical fibers, possibly concatenated into a dark fiber link, is the simplest form of an optical link.
Other forms of optical link can include single-"colour" links over a wavelength-division multiplexing infrastructure, and/or links that use optical amplifiers to compensate for attenuation over long distances.
Other forms of optical links include free-space optical telecommunication links.
In the rail transport sector, optical links are used in two forms depending on whether the feeding station is a main station or not. Thus main stations are called 'long halls', and all remaining stations are said to be 'short halls'.
# Tylopilus bulbosus

Tylopilus bulbosus is a bolete fungus of the genus Tylopilus. Described as new to science in 2001 by mycologists Roy Halling and Greg Mueller, it is found in Costa Rica, where it grows on the ground in montane forests dominated by the oak species Quercus copeyensis, Q. oocarpa, and Q. seemannii. The fungus produces fruit bodies with convex to flattened caps measuring 4.5–11 cm (1.8–4.3 in) in diameter. Its color is initially violet to purplish brown, and eventually fades to brown. The pore surface is initially pale pinkish purple to grayish red, and bruises brown where it has been handled. The white flesh stains pinkish brown where it has been exposed. Spores are more or less spindle shaped (subfusoid), smooth, and measure 10–14 by 4.2–5.6 μm; the fresh spore deposit is pinkish. Morphologically similar Tylopilus species include the eastern North American T. rubrobrunneus and the North and Central American T. williamsii.
# Tylopilus corneri

Tylopilus corneri is a bolete fungus in the family Boletaceae found in Costa Rica, where it grows under oak in montane forest. Described as new to science in 1991, it is named after English mycologist E.J.H. Corner.
# Hexaspora

Hexaspora is a monotypic genus of flowering plants belonging to the family Celastraceae. The only species is Hexaspora pubescens.
Its native range is Northeastern Australia.
# Slipstream (Sherbet album)

Slipstream is the third studio album by Sherbet released in September 1974 and it peaked at No. 3 in Australia and was certified gold.

## Personnel

* Lead vocals – Daryl Braithwaite
* Bass, vocals – Tony Mitchell
* Keyboards, vocals – Garth Porter
* Drums – Alan Sandow
* Guitar, vocals – Clive Shakespeare
* Co-producers – Richard Batchens, Sherbet
* Engineer – Richard Batchens
* Remastered by William Bowden

## Charts
### Weekly charts

| Chart (1974/75) | Peak position |
| Australia (Kent Music Report) | 3 |

### Year-end charts

| Chart (1974) | Peak position |
| Australia (Kent Music Report) | 19 |

## Certifications

| Region | Certification | Certified units/sales |
| Australia (ARIA) | Gold | 20,000$^^$ |
| $^^$ Shipments figures based on certification alone. |||

## Release history

| Country | Date | Label | Format | Catalog |
| Australia | September 1974 | Festival | LP, Cassette | L35275 |
| Australia | 1999 | Festival | CD | D20025 |
# Oostbuurt

Oostbuurt is a hamlet in the Dutch province of South Holland. It is a part of the municipality of Westland, and lies about 6 km north of Maassluis.
The statistical area "Oostbuurt", which also can include the surrounding countryside, has a population of around 150.
# Oostdijk, South Holland

Oostdijk is a hamlet in the Dutch province of South Holland. It is a part of the municipality of Goeree-Overflakkee, and lies about 13 km west of Hellevoetsluis.
It was first mentioned in 1515 as "gelegen in Westvoirne bijder Goederee inder banne vanden oestdijck", and means "eastern dike". It is named after the eponymous polder.
Oostdijk is not a statistical entity, It is considered part of Goedereede. It consists of about 100 houses.
# Skyfall (novel)

Skyfall is a 2003 novel by Catherine Asaro which tells the story of how Roca met her husband Eldrinson, Bard of Dalvador, ruler of a province on Skyfall.

## Overview

The novel won Third Place Sapphire Award for Best Science Fiction Romance Novel of 2004 from the Science Fiction Romance Newsletter. It was also the first science fiction novel from a science fiction publisher to be nominated for the RITA Award.
Skyfall also refers to the name of the planet where the story takes place - the name given to the planet by the Allieds. In the local language, the planet is called Lyshriol.

## Plot summary

It is a turbulent time for the Skolian Empire. Kurj is trying to lead his people into war with the Traders, a more massive empire. He uses his powerful connections to control his mother who is attempting to sway the Assembly otherwise. The book begins with Roca, in hiding, trying to get to the Assembly meeting. During her voyage, she ends up stranded on a planet known as Skyfall. There, on a planet once part of the Ruby Empire but now antiquated in its technology, she meets Eldrinson Valdoria, and due to extreme weather and lack of incoming ships, she is stranded there for approximately one year. During that time she falls in love with Eldrinson and becomes pregnant.
The novel also periodically shifts to describe the perspective of Kurj, a Primary (top ranking) Jagernaut (most feared warriors of the Skolian Empire) and grandson of the ruling couple of Skolian Empire, Pharaoh Lahaylia and Imperator Jarac. Kurj is obsessed with stopping the slave-driven empire of the Traders. But when his mother escapes his clutches, he fears the worst, and spends much of the novel obsessing over finding her instead. We also learn of some of the horrors from his past, giving meaning to his stoic nature.
Back on the planet of Skyfall, Roca and her new husband come under siege by a rival who claims the title that Eldrinson possesses. At the point of his final breach into the castle, Kurj arrives with his much superior technology, and ceases hostilities. Roca gives birth to her child which she names Eldrin.
The remainder of the novel revolves around the forced separation of Eldrinson from Roca and his child.
# Hiawatha and Minnehaha

Hiawatha and Minnehaha is a sculpture by Jacob Fjelde that has stood in Minnehaha Park in Minneapolis since the early twentieth century. Now a popular fixture of the park, its placement there was originally controversial.
In 1855, Henry Wadsworth Longfellow published a book-length poem entitled The Song of Hiawatha. Longfellow never visited Minnesota, but he set his poem among the Ojibwe and Dakota of the region. The poem's story line was based on traditional Haudenosaunee (Iroquois) tales, as recorded, sometimes incorrectly, by Henry Rowe Schoolcraft. The Song of Hiawatha was widely read and had significant cultural influence in the United States through the rest of the nineteenth century and into the twentieth century.
Accomplished Norwegian sculptor Jacob Fjelde immigrated to Minnesota in 1887, following family members to the area. He established a studio in Minneapolis and began receiving public and private commissions. One commission was to create a sculpture for the Minnesota Building at the 1893 World's Columbian Exposition in Chicago. Fjelde chose to create Hiawatha and Minnehaha, a plaster sculpture illustrating a particular section of Longfellow's poem, The Song of Hiawatha. This work was installed at the entrance of the Minnesota Building for the duration of the 1893 Exposition. Then, it was put on display in the Minneapolis Public Library.
Fjelde's expenses for Hiawatha and Minnehaha were paid for by small donations collected from Minnesota schoolchildren. Mrs. L.P. (Lizzie) Hunt, a founding member of the Mankato Art History Club and later an official art critic for the state, organized the fund-raising drive.
Beginning in 1902, an informal public campaign was launched to cast Fjelde's original plaster Hiawatha and Minnehaha sculpture in bronze and place it in Minneapolis's Minnehaha Park, near the falls mentioned in Longfellow's poem. Critics of the move said that the piece was "flawed," specifically that the features of Hiawatha and Minnehaha were not Indian enough. Fjelde had struggled to find American Indian people to model the faces after, and he relied on photographs to guide his work. The sculptor died in 1896, so significant changes to the sculpture were no longer possible by 1902.
The debate continued until 1912, when the sculpture finally was cast, then installed and unveiled in a public ceremony at Minnehaha Park on October 5. Charles M. Loring, the first president of the Board of Park Commissioners for the Minneapolis Park System, gave a dedicatory speech. Local schoolchildren sang and recited parts of Longfellow's poem as part of the program.
Fjelde's Hiawatha and Minnehaha soon became a visitor attraction in the park, and postcards depicting it were widely available. As of 2021, the sculpture remains in its location along Minnehaha Creek and is one of Fjelde's best-known works.
# Omiodes odontosticta

Omiodes odontosticta is a species of moth in the family Crambidae. It was first described by George Hampson in 1898 and is found Australia in Northern Territory and Queensland.
The wingspan is about 30 mm.
# Omiodes mostella

Omiodes mostella is a moth in the family Crambidae. It was described by Harrison Gray Dyar Jr. in 1912. It is found in Veracruz, Mexico.
# Tytocha

Tytocha is a genus of moths in the family Lasiocampidae. The genus was first described by William Schaus in 1924.

## Species

* Tytocha crassilinea Dognin, 1923
* Tytocha lineata Dognin, 1923
# Anhrefn Records

Recordiau Anhrefn (Welsh for Anhrefn Records) was a record label established in 1983 by Rhys Mwyn.
Based in the small mid-Wales village of Llanfair Caereinion, before Rhys and his brother Sion Sebon moved to Bangor, North Wales, the record label was initially an outlet for their own band Yr Anhrefn but soon went on to release records by other Welsh groups, providing early exposure for such influential names as Datblygu, Fflaps and Llwybr Llaethog.
Its second release came in the form of a compilation album called Cam o'r Tywyllwch which rose to prominence on its release in 1985 when John Peel played tracks off it on his BBC Radio One show. The album spawned Machlud (who featured a very young Gruff Rhys who would later form Super Furry Animals) and Y Cyrff (two of whom would later form Catatonia).
Although only releasing a handful of records between 1983 and its dissolution in 1990, the label provided a subversive alternative to the ultra-conservative Welsh music scene of the time. Its independent and outward looking approach contrasted drastically with the establishment's isolated entrenchment and brought Welsh language music to corners of the World that had no previous knowledge of its existence, providing a foundation for the Welsh 'Cool Cymru' music boom of the mid '90s, led by Super Furry Animals, Catatonia and Gorky's Zygotic Mynci. The label's legacy has continued to be lauded 25 years since 'Cool Cymru'.
In 2007 Rhys Mwyn reactivated the label from his PR office at The Galeri in Caernarfon, and began releasing left-field artists such as Beastellabeast and Patrick Jones.
# Oreini

Oreini may refer to:
* Oreini, Ilia, or Mostenitsa, a village in southern Greece
* Oreini, Serres, a community in northern Greece
# Oosthuizen (surname)

Oosthuizen is a South African surname, especially common among Afrikaners. Notable people with the name include:
* Abrie Oosthuizen (fl. 1994–2013), South African politician
* Andries Oosthuizen (born c. 1954), South African golfer
* Caylib Oosthuizen (born 1989), South African rugby union player for the Tel Aviv Heat
* Coenie Oosthuizen (born 1989), South African rugby union player for Sale Sharks
* D. C. S. Oosthuizen (1926–1969; also known as Daantjie Oosthuizen), South African philosopher
* Etienne Oosthuizen (born 1992), South African rugby union player
* Etienne Oosthuizen (born 1994), South African rugby union player
* John Robert Oosthuizen (born 1987), South African javelin thrower
* Louis Oosthuizen (born 1982), South African professional golfer
* Ockie Oosthuizen (1955–2019), South African rugby union player
* Sarel Oosthuizen (1862–1900), Orange Free State Anglo-Boer War general
* Theo Oosthuizen (born 1964), South African rugby union player and coach
* Thomas Oosthuizen (born 1989), South African professional boxer
Also: